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-rw-r--r--Makefile14
-rw-r--r--include/math.h796
-rw-r--r--libm/Makefile75
-rw-r--r--libm/README42
-rw-r--r--libm/double/Makefile115
-rw-r--r--libm/double/README.txt5845
-rw-r--r--libm/double/acosh.c167
-rw-r--r--libm/double/airy.c965
-rw-r--r--libm/double/arcdot.c110
-rw-r--r--libm/double/asin.c324
-rw-r--r--libm/double/asinh.c165
-rw-r--r--libm/double/atan.c393
-rw-r--r--libm/double/atanh.c156
-rw-r--r--libm/double/bdtr.c263
-rw-r--r--libm/double/bernum.c74
-rw-r--r--libm/double/beta.c201
-rw-r--r--libm/double/btdtr.c64
-rw-r--r--libm/double/cbrt.c142
-rw-r--r--libm/double/chbevl.c82
-rw-r--r--libm/double/chdtr.c200
-rw-r--r--libm/double/cheby.c149
-rw-r--r--libm/double/clog.c1043
-rw-r--r--libm/double/cmplx.c461
-rw-r--r--libm/double/coil.c63
-rw-r--r--libm/double/const.c252
-rw-r--r--libm/double/cosh.c83
-rw-r--r--libm/double/cpmul.c104
-rw-r--r--libm/double/dawsn.c392
-rw-r--r--libm/double/dcalc.c1512
-rw-r--r--libm/double/dcalc.h77
-rw-r--r--libm/double/dtestvec.c543
-rw-r--r--libm/double/ei.c1062
-rw-r--r--libm/double/eigens.c181
-rw-r--r--libm/double/ellie.c148
-rw-r--r--libm/double/ellik.c148
-rw-r--r--libm/double/ellpe.c195
-rw-r--r--libm/double/ellpj.c171
-rw-r--r--libm/double/ellpk.c234
-rw-r--r--libm/double/eltst.c37
-rw-r--r--libm/double/euclid.c251
-rw-r--r--libm/double/exp.c203
-rw-r--r--libm/double/exp10.c223
-rw-r--r--libm/double/exp2.c183
-rw-r--r--libm/double/expn.c208
-rw-r--r--libm/double/fabs.c56
-rw-r--r--libm/double/fac.c263
-rw-r--r--libm/double/fdtr.c237
-rw-r--r--libm/double/fftr.c237
-rw-r--r--libm/double/floor.c453
-rw-r--r--libm/double/fltest.c272
-rw-r--r--libm/double/fltest2.c18
-rw-r--r--libm/double/fltest3.c259
-rw-r--r--libm/double/fresnl.c515
-rw-r--r--libm/double/gamma.c685
-rw-r--r--libm/double/gdtr.c130
-rw-r--r--libm/double/gels.c232
-rw-r--r--libm/double/hyp2f1.c460
-rw-r--r--libm/double/hyperg.c386
-rw-r--r--libm/double/i0.c397
-rw-r--r--libm/double/i1.c402
-rw-r--r--libm/double/igam.c210
-rw-r--r--libm/double/igami.c187
-rw-r--r--libm/double/incbet.c409
-rw-r--r--libm/double/incbi.c313
-rw-r--r--libm/double/isnan.c237
-rw-r--r--libm/double/iv.c116
-rw-r--r--libm/double/j0.c543
-rw-r--r--libm/double/j1.c515
-rw-r--r--libm/double/jn.c133
-rw-r--r--libm/double/jv.c884
-rw-r--r--libm/double/k0.c333
-rw-r--r--libm/double/k1.c335
-rw-r--r--libm/double/kn.c255
-rw-r--r--libm/double/kolmogorov.c243
-rw-r--r--libm/double/levnsn.c82
-rw-r--r--libm/double/log.c341
-rw-r--r--libm/double/log10.c250
-rw-r--r--libm/double/log2.c348
-rw-r--r--libm/double/lrand.c86
-rw-r--r--libm/double/lsqrt.c85
-rw-r--r--libm/double/ltstd.c469
-rw-r--r--libm/double/minv.c61
-rw-r--r--libm/double/mod2pi.c122
-rw-r--r--libm/double/monot.c308
-rw-r--r--libm/double/mtherr.c102
-rw-r--r--libm/double/mtransp.c61
-rw-r--r--libm/double/mtst.c464
-rw-r--r--libm/double/nbdtr.c222
-rw-r--r--libm/double/ndtr.c481
-rw-r--r--libm/double/ndtri.c417
-rw-r--r--libm/double/paranoia.c2156
-rw-r--r--libm/double/pdtr.c184
-rw-r--r--libm/double/planck.c223
-rw-r--r--libm/double/polevl.c97
-rw-r--r--libm/double/polmisc.c309
-rw-r--r--libm/double/polrt.c227
-rw-r--r--libm/double/polylog.c467
-rw-r--r--libm/double/polyn.c471
-rw-r--r--libm/double/polyr.c533
-rw-r--r--libm/double/pow.c756
-rw-r--r--libm/double/powi.c186
-rw-r--r--libm/double/psi.c201
-rw-r--r--libm/double/revers.c156
-rw-r--r--libm/double/rgamma.c209
-rw-r--r--libm/double/round.c70
-rw-r--r--libm/double/setprec.c10
-rw-r--r--libm/double/shichi.c599
-rw-r--r--libm/double/sici.c675
-rw-r--r--libm/double/simpsn.c81
-rw-r--r--libm/double/simq.c180
-rw-r--r--libm/double/sin.c387
-rw-r--r--libm/double/sincos.c364
-rw-r--r--libm/double/sindg.c308
-rw-r--r--libm/double/sinh.c148
-rw-r--r--libm/double/spence.c205
-rw-r--r--libm/double/sqrt.c178
-rw-r--r--libm/double/stdtr.c225
-rw-r--r--libm/double/struve.c312
-rw-r--r--libm/double/tan.c304
-rw-r--r--libm/double/tandg.c267
-rw-r--r--libm/double/tanh.c141
-rw-r--r--libm/double/time-it.c38
-rw-r--r--libm/double/unity.c138
-rw-r--r--libm/double/yn.c114
-rw-r--r--libm/double/zeta.c189
-rw-r--r--libm/double/zetac.c599
-rw-r--r--libm/float/Makefile62
-rw-r--r--libm/float/README.txt4721
-rw-r--r--libm/float/acoshf.c97
-rw-r--r--libm/float/airyf.c377
-rw-r--r--libm/float/asinf.c186
-rw-r--r--libm/float/asinhf.c88
-rw-r--r--libm/float/atanf.c190
-rw-r--r--libm/float/atanhf.c92
-rw-r--r--libm/float/bdtrf.c247
-rw-r--r--libm/float/betaf.c122
-rw-r--r--libm/float/cbrtf.c119
-rw-r--r--libm/float/chbevlf.c86
-rw-r--r--libm/float/chdtrf.c210
-rw-r--r--libm/float/clogf.c669
-rw-r--r--libm/float/cmplxf.c407
-rw-r--r--libm/float/constf.c20
-rw-r--r--libm/float/coshf.c67
-rw-r--r--libm/float/dawsnf.c168
-rw-r--r--libm/float/ellief.c115
-rw-r--r--libm/float/ellikf.c113
-rw-r--r--libm/float/ellpef.c105
-rw-r--r--libm/float/ellpjf.c161
-rw-r--r--libm/float/ellpkf.c128
-rw-r--r--libm/float/exp10f.c115
-rw-r--r--libm/float/exp2f.c116
-rw-r--r--libm/float/expf.c122
-rw-r--r--libm/float/expnf.c207
-rw-r--r--libm/float/facf.c106
-rw-r--r--libm/float/fdtrf.c214
-rw-r--r--libm/float/floorf.c526
-rw-r--r--libm/float/fresnlf.c173
-rw-r--r--libm/float/gammaf.c423
-rw-r--r--libm/float/gdtrf.c144
-rw-r--r--libm/float/hyp2f1f.c442
-rw-r--r--libm/float/hypergf.c384
-rw-r--r--libm/float/i0f.c160
-rw-r--r--libm/float/i1f.c177
-rw-r--r--libm/float/igamf.c223
-rw-r--r--libm/float/igamif.c112
-rw-r--r--libm/float/incbetf.c424
-rw-r--r--libm/float/incbif.c197
-rw-r--r--libm/float/ivf.c114
-rw-r--r--libm/float/j0f.c228
-rw-r--r--libm/float/j0tst.c43
-rw-r--r--libm/float/j1f.c211
-rw-r--r--libm/float/jnf.c124
-rw-r--r--libm/float/jvf.c848
-rw-r--r--libm/float/k0f.c175
-rw-r--r--libm/float/k1f.c174
-rw-r--r--libm/float/knf.c252
-rw-r--r--libm/float/log10f.c129
-rw-r--r--libm/float/log2f.c129
-rw-r--r--libm/float/logf.c128
-rw-r--r--libm/float/mtherr.c99
-rw-r--r--libm/float/nantst.c54
-rw-r--r--libm/float/nbdtrf.c141
-rw-r--r--libm/float/ndtrf.c281
-rw-r--r--libm/float/ndtrif.c186
-rw-r--r--libm/float/pdtrf.c188
-rw-r--r--libm/float/polevlf.c99
-rw-r--r--libm/float/polynf.c520
-rw-r--r--libm/float/powf.c338
-rw-r--r--libm/float/powif.c156
-rw-r--r--libm/float/powtst.c41
-rw-r--r--libm/float/psif.c153
-rw-r--r--libm/float/rgammaf.c130
-rw-r--r--libm/float/setprec.c10
-rw-r--r--libm/float/shichif.c212
-rw-r--r--libm/float/sicif.c279
-rw-r--r--libm/float/sindgf.c232
-rw-r--r--libm/float/sinf.c283
-rw-r--r--libm/float/sinhf.c87
-rw-r--r--libm/float/spencef.c135
-rw-r--r--libm/float/sqrtf.c140
-rw-r--r--libm/float/stdtrf.c154
-rw-r--r--libm/float/struvef.c315
-rw-r--r--libm/float/tandgf.c206
-rw-r--r--libm/float/tanf.c192
-rw-r--r--libm/float/tanhf.c88
-rw-r--r--libm/float/ynf.c120
-rw-r--r--libm/float/zetacf.c266
-rw-r--r--libm/float/zetaf.c175
-rw-r--r--libm/ldouble/Makefile123
-rw-r--r--libm/ldouble/README.txt3502
-rw-r--r--libm/ldouble/acoshl.c167
-rw-r--r--libm/ldouble/arcdotl.c108
-rw-r--r--libm/ldouble/asinhl.c156
-rw-r--r--libm/ldouble/asinl.c249
-rw-r--r--libm/ldouble/atanhl.c163
-rw-r--r--libm/ldouble/atanl.c376
-rw-r--r--libm/ldouble/bdtrl.c260
-rw-r--r--libm/ldouble/btdtrl.c68
-rw-r--r--libm/ldouble/cbrtl.c143
-rw-r--r--libm/ldouble/chdtrl.c200
-rw-r--r--libm/ldouble/clogl.c720
-rw-r--r--libm/ldouble/cmplxl.c461
-rw-r--r--libm/ldouble/coshl.c89
-rw-r--r--libm/ldouble/econst.c96
-rw-r--r--libm/ldouble/ehead.h45
-rw-r--r--libm/ldouble/elliel.c146
-rw-r--r--libm/ldouble/ellikl.c148
-rw-r--r--libm/ldouble/ellpel.c173
-rw-r--r--libm/ldouble/ellpjl.c164
-rw-r--r--libm/ldouble/ellpkl.c203
-rw-r--r--libm/ldouble/exp10l.c192
-rw-r--r--libm/ldouble/exp2l.c166
-rw-r--r--libm/ldouble/expl.c183
-rw-r--r--libm/ldouble/fdtrl.c237
-rw-r--r--libm/ldouble/floorl.c432
-rw-r--r--libm/ldouble/flrtstl.c104
-rw-r--r--libm/ldouble/fltestl.c265
-rw-r--r--libm/ldouble/gammal.c764
-rw-r--r--libm/ldouble/gdtrl.c130
-rw-r--r--libm/ldouble/gelsl.c240
-rw-r--r--libm/ldouble/ieee.c4182
-rw-r--r--libm/ldouble/igamil.c193
-rw-r--r--libm/ldouble/igaml.c220
-rw-r--r--libm/ldouble/incbetl.c406
-rw-r--r--libm/ldouble/incbil.c305
-rw-r--r--libm/ldouble/isnanl.c186
-rw-r--r--libm/ldouble/j0l.c541
-rw-r--r--libm/ldouble/j1l.c551
-rw-r--r--libm/ldouble/jnl.c130
-rw-r--r--libm/ldouble/lcalc.c1484
-rw-r--r--libm/ldouble/lcalc.h79
-rw-r--r--libm/ldouble/ldrand.c175
-rw-r--r--libm/ldouble/log10l.c319
-rw-r--r--libm/ldouble/log2l.c302
-rw-r--r--libm/ldouble/logl.c292
-rw-r--r--libm/ldouble/lparanoi.c2348
-rw-r--r--libm/ldouble/monotl.c307
-rw-r--r--libm/ldouble/mtherr.c102
-rw-r--r--libm/ldouble/mtstl.c521
-rw-r--r--libm/ldouble/nantst.c61
-rw-r--r--libm/ldouble/nbdtrl.c197
-rw-r--r--libm/ldouble/ndtril.c416
-rw-r--r--libm/ldouble/ndtrl.c473
-rw-r--r--libm/ldouble/pdtrl.c184
-rw-r--r--libm/ldouble/polevll.c182
-rw-r--r--libm/ldouble/powil.c164
-rw-r--r--libm/ldouble/powl.c739
-rw-r--r--libm/ldouble/sinhl.c150
-rw-r--r--libm/ldouble/sinl.c342
-rw-r--r--libm/ldouble/sqrtl.c172
-rw-r--r--libm/ldouble/stdtrl.c225
-rw-r--r--libm/ldouble/tanhl.c129
-rw-r--r--libm/ldouble/tanl.c279
-rw-r--r--libm/ldouble/testvect.c497
-rw-r--r--libm/ldouble/unityl.c128
-rw-r--r--libm/ldouble/wronkl.c67
-rw-r--r--libm/ldouble/ynl.c113
277 files changed, 91551 insertions, 170 deletions
diff --git a/Makefile b/Makefile
index 5ccc78a42..7368b4410 100644
--- a/Makefile
+++ b/Makefile
@@ -29,7 +29,7 @@
TOPDIR=./
include Rules.mak
-DIRS = extra misc pwd_grp stdio string termios inet signal stdlib sysdeps unistd crypt libutil
+DIRS = extra misc pwd_grp stdio string termios inet signal stdlib sysdeps unistd crypt libutil libm
ifeq ($(strip $(HAS_MMU)),true)
DO_SHARED=shared
@@ -60,6 +60,7 @@ shared: $(LIBNAME)
ln -sf $(SHARED_MAJORNAME) libc.so
@$(MAKE) -C crypt shared
@$(MAKE) -C libutil shared
+ @$(MAKE) -C libm shared
@$(MAKE) -C ld.so-1
done: $(LIBNAME) $(DO_SHARED)
@@ -116,6 +117,7 @@ install: install_runtime install_dev install_ldso
install_runtime:
@$(MAKE) -C crypt install
@$(MAKE) -C libutil install
+ @$(MAKE) -C libm install
ifneq ($(DO_SHARED),)
install -d $(INSTALL_DIR)/lib
rm -rf $(INSTALL_DIR)/lib/$(SHARED_FULLNAME)
@@ -180,6 +182,16 @@ uClibc_config.h: Config
else \
echo "#undef __UCLIBC_HAS_FLOATS__" >> uClibc_config.h ; \
fi
+ @if [ "$(HAS_DOUBLE)" = "true" ] ; then \
+ echo "#define __UCLIBC_HAS_DOUBLE__ 1" >> uClibc_config.h ; \
+ else \
+ echo "#undef __UCLIBC_HAS_DOUBLE__" >> uClibc_config.h ; \
+ fi
+ @if [ "$(HAS_LONG_DOUBLE)" = "true" ] ; then \
+ echo "#define __UCLIBC_HAS_LONG_DOUBLE__ 1" >> uClibc_config.h ; \
+ else \
+ echo "#undef __UCLIBC_HAS_LONG_DOUBLE__" >> uClibc_config.h ; \
+ fi
@if [ "$(HAS_LONG_LONG)" = "true" ] ; then \
echo "#define __UCLIBC_HAS_LONG_LONG__ 1" >> uClibc_config.h ; \
else \
diff --git a/include/math.h b/include/math.h
index ab74e5ee8..853d71368 100644
--- a/include/math.h
+++ b/include/math.h
@@ -1,176 +1,634 @@
-#ifndef _MATH_H
-#define _MATH_H
-/*
- * This file was automatically generated by version 1.7 of cextract.
- * Manual editing not recommended.
+/* mconf.h
+ * <math.h>
+ * ISO/IEC 9899:1999 -- Programming Languages C: 7.12 Mathematics
+ * Derived from the Cephes Math Library Release 2.3
+ * Copyright 1984, 1987, 1989, 1995 by Stephen L. Moshier
*
- * Created: Fri Feb 23 20:31:13 1996
*
- * Modified (anyway) for PalmOS Feb 22, 1997, D.Jeff Dionne
+ * DESCRIPTION:
+ *
+ * The file also includes a conditional assembly definition
+ * for the type of computer arithmetic (IEEE, DEC, Motorola
+ * IEEE, or UNKnown).
+ *
+ * For Digital Equipment PDP-11 and VAX computers, certain
+ * IBM systems, and others that use numbers with a 56-bit
+ * significand, the symbol DEC should be defined. In this
+ * mode, most floating point constants are given as arrays
+ * of octal integers to eliminate decimal to binary conversion
+ * errors that might be introduced by the compiler.
+ *
+ * For little-endian computers, such as IBM PC, that follow the
+ * IEEE Standard for Binary Floating Point Arithmetic (ANSI/IEEE
+ * Std 754-1985), the symbol IBMPC should be defined. These
+ * numbers have 53-bit significands. In this mode, constants
+ * are provided as arrays of hexadecimal 16 bit integers.
+ *
+ * Big-endian IEEE format is denoted MIEEE. On some RISC
+ * systems such as Sun SPARC, double precision constants
+ * must be stored on 8-byte address boundaries. Since integer
+ * arrays may be aligned differently, the MIEEE configuration
+ * may fail on such machines.
+ *
+ * To accommodate other types of computer arithmetic, all
+ * constants are also provided in a normal decimal radix
+ * which one can hope are correctly converted to a suitable
+ * format by the available C language compiler. To invoke
+ * this mode, define the symbol UNK.
+ *
+ * An important difference among these modes is a predefined
+ * set of machine arithmetic constants for each. The numbers
+ * MACHEP (the machine roundoff error), MAXNUM (largest number
+ * represented), and several other parameters are preset by
+ * the configuration symbol. Check the file const.c to
+ * ensure that these values are correct for your computer.
+ *
+ * Configurations NANS, INFINITIES, MINUSZERO, and DENORMAL
+ * may fail on many systems. Verify that they are supposed
+ * to work on your computer.
+ */
+
+
+#ifndef _MATH_H
+#define _MATH_H 1
+
+#include <features.h>
+
+#ifndef __UCLIBC_HAS_FLOATS__
+ #define float int
+#endif
+#ifndef __UCLIBC_HAS_DOUBLE__
+ #define double int
+#endif
+#ifndef __UCLIBC_HAS_LONG_DOUBLE__
+ #define long
+ #ifndef double
+ # define double int
+ #endif
+#endif
+
+/* Type of computer arithmetic */
+
+/* PDP-11, Pro350, VAX:
+ */
+/* #define DEC 1 */
+
+/* Intel IEEE, low order words come first:
+ */
+/* #define IBMPC 1 */
+
+/* Motorola IEEE, high order words come first
+ * (Sun 680x0 workstation):
+ */
+/* #define MIEEE 1 */
+
+/* UNKnown arithmetic, invokes coefficients given in
+ * normal decimal format. Beware of range boundary
+ * problems (MACHEP, MAXLOG, etc. in const.c) and
+ * roundoff problems in pow.c:
+ * (Sun SPARCstation)
+ */
+#define UNK 1
+
+
+/* Define if the `long double' type works. */
+#define HAVE_LONG_DOUBLE 1
+
+/* Define as the return type of signal handlers (int or void). */
+#define RETSIGTYPE void
+
+/* Define if you have the ANSI C header files. */
+#define STDC_HEADERS 1
+
+/* Define if your processor stores words with the most significant
+ byte first (like Motorola and SPARC, unlike Intel and VAX). */
+/* #undef WORDS_BIGENDIAN */
+
+/* Define if floating point words are bigendian. */
+/* #undef FLOAT_WORDS_BIGENDIAN */
+
+/* The number of bytes in a int. */
+#define SIZEOF_INT 4
+
+/* Define if you have the <string.h> header file. */
+#define HAVE_STRING_H 1
+
+
+/* Define this `volatile' if your compiler thinks
+ * that floating point arithmetic obeys the associative
+ * and distributive laws. It will defeat some optimizations
+ * (but probably not enough of them).
+ *
+ * #define VOLATILE volatile
+ */
+#define VOLATILE
+
+/* For 12-byte long doubles on an i386, pad a 16-bit short 0
+ * to the end of real constants initialized by integer arrays.
+ *
+ * #define XPD 0,
+ *
+ * Otherwise, the type is 10 bytes long and XPD should be
+ * defined blank (e.g., Microsoft C).
+ *
+ * #define XPD
*/
+#define XPD 0,
+
+/* Define to support tiny denormal numbers, else undefine. */
+#define DENORMAL 1
+
+/* Define to ask for infinity support, else undefine. */
+#define INFINITIES 1
+
+/* Define to ask for support of numbers that are Not-a-Number,
+ else undefine. This may automatically define INFINITIES in some files. */
+#define NANS 1
+
+/* Define to distinguish between -0.0 and +0.0. */
+#define MINUSZERO 1
+
+/* Define 1 for ANSI C atan2() function
+ and ANSI prototypes for float arguments.
+ See atan.c and clog.c. */
+#define ANSIC 1
+#define ANSIPROT 1
+
+
+/* Constant definitions for math error conditions */
+
+#define DOMAIN 1 /* argument domain error */
+#define SING 2 /* argument singularity */
+#define OVERFLOW 3 /* overflow range error */
+#define UNDERFLOW 4 /* underflow range error */
+#define TLOSS 5 /* total loss of precision */
+#define PLOSS 6 /* partial loss of precision */
+
+#define EDOM 33
+#define ERANGE 34
+
+/* Complex numeral. */
+typedef struct
+ {
+ double r;
+ double i;
+ } cmplx;
+
+typedef struct
+ {
+ float r;
+ float i;
+ } cmplxf;
+
+#ifdef HAVE_LONG_DOUBLE
+/* Long double complex numeral. */
+typedef struct
+ {
+ long double r;
+ long double i;
+ } cmplxl;
+#endif
+
+
+
+/* Variable for error reporting. See mtherr.c. */
+extern int mtherr();
+extern int merror;
+
+
+/* If you define UNK, then be sure to set BIGENDIAN properly. */
+#include <endian.h>
+#if __BYTE_ORDER == __BIG_ENDIAN
+# define BIGENDIAN 1
+#else /* __BYTE_ORDER == __LITTLE_ENDIAN */
+# define BIGENDIAN 0
+#endif
+
+
+#define __USE_ISOC9X
+/* Get general and ISO C 9X specific information. */
+#include <bits/mathdef.h>
+#undef INFINITY
+#undef DECIMAL_DIG
+#undef FP_ILOGB0
+#undef FP_ILOGBNAN
+
+/* Get the architecture specific values describing the floating-point
+ evaluation. The following symbols will get defined:
+
+ float_t floating-point type at least as wide as `float' used
+ to evaluate `float' expressions
+ double_t floating-point type at least as wide as `double' used
+ to evaluate `double' expressions
+
+ FLT_EVAL_METHOD
+ Defined to
+ 0 if `float_t' is `float' and `double_t' is `double'
+ 1 if `float_t' and `double_t' are `double'
+ 2 if `float_t' and `double_t' are `long double'
+ else `float_t' and `double_t' are unspecified
+
+ INFINITY representation of the infinity value of type `float'
+
+ FP_FAST_FMA
+ FP_FAST_FMAF
+ FP_FAST_FMAL
+ If defined it indicates that the `fma' function
+ generally executes about as fast as a multiply and an add.
+ This macro is defined only iff the `fma' function is
+ implemented directly with a hardware multiply-add instructions.
+
+ FP_ILOGB0 Expands to a value returned by `ilogb (0.0)'.
+ FP_ILOGBNAN Expands to a value returned by `ilogb (NAN)'.
+
+ DECIMAL_DIG Number of decimal digits supported by conversion between
+ decimal and all internal floating-point formats.
+
+*/
+
+/* All floating-point numbers can be put in one of these categories. */
+enum
+ {
+ FP_NAN,
+# define FP_NAN FP_NAN
+ FP_INFINITE,
+# define FP_INFINITE FP_INFINITE
+ FP_ZERO,
+# define FP_ZERO FP_ZERO
+ FP_SUBNORMAL,
+# define FP_SUBNORMAL FP_SUBNORMAL
+ FP_NORMAL
+# define FP_NORMAL FP_NORMAL
+ };
+
+/* Return number of classification appropriate for X. */
+# ifdef __NO_LONG_DOUBLE_MATH
+# define fpclassify(x) \
+ (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
+# else
+# define fpclassify(x) \
+ (sizeof (x) == sizeof (float) ? \
+ __fpclassifyf (x) \
+ : sizeof (x) == sizeof (double) ? \
+ __fpclassify (x) : __fpclassifyl (x))
+# endif
+
+/* Return nonzero value if sign of X is negative. */
+int signbit(double x);
+int signbitl(long double x);
+
+/* Return nonzero value if X is not +-Inf or NaN. */
+int isfinite(double x);
+int isfinitel(long double x);
+
+/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN. */
+# define isnormal(x) (fpclassify (x) == FP_NORMAL)
+
+/* Return nonzero value if X is a NaN */
+int isnan(double x);
+int isnanl(long double x);
+
+/* Return nonzero value is X is positive or negative infinity. */
+# ifdef __NO_LONG_DOUBLE_MATH
+# define isinf(x) \
+ (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
+# else
+# define isinf(x) \
+ (sizeof (x) == sizeof (float) ? \
+ __isinff (x) \
+ : sizeof (x) == sizeof (double) ? \
+ __isinf (x) : __isinfl (x))
+# endif
+
-typedef struct {
- double r;
- double i;
-}cmplxf;
/* Some useful constants. */
-#define M_E 2.7182818284590452354 /* e */
-#define M_LOG2E 1.4426950408889634074 /* log_2 e */
-#define M_LOG10E 0.43429448190325182765 /* log_10 e */
-#define M_LN2 0.69314718055994530942 /* log_e 2 */
-#define M_LN10 2.30258509299404568402 /* log_e 10 */
-#define M_PI 3.14159265358979323846 /* pi */
-#define M_PI_2 1.57079632679489661923 /* pi/2 */
-#define M_PI_4 0.78539816339744830962 /* pi/4 */
-#define M_1_PI 0.31830988618379067154 /* 1/pi */
-#define M_2_PI 0.63661977236758134308 /* 2/pi */
-#define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
-#define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
-#define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
-
-
-extern double acos ( double x );
-extern double acosh ( double xx );
-extern int airy ( double xx, double *ai, double *aip, double *bi, double *bip );
-extern double asin ( double xx );
-extern double asinh ( double xx );
-extern double atan2 ( double y, double x );
-extern double atan ( double xx );
-extern double atanh ( double xx );
-extern double bdtrc ( int k, int n, double pp );
-extern double bdtr ( int k, int n, double pp );
-extern double bdtri ( int k, int n, double yy );
-extern double beta ( double aa, double bb );
-extern double cabs ( cmplxf *z );
-extern void cacos ( cmplxf *z, cmplxf *w );
-extern void cadd ( cmplxf *a, cmplxf *b, cmplxf *c );
-extern void casin ( cmplxf *z, cmplxf *w );
-extern void catan ( cmplxf *z, cmplxf *w );
-extern double cbrt ( double xx );
-extern void cchsh ( double xx, double *c, double *s );
-extern void ccos ( cmplxf *z, cmplxf *w );
-extern void ccot ( cmplxf *z, cmplxf *w );
-extern void cdiv ( cmplxf *a, cmplxf *b, cmplxf *c );
-extern double ceil ( double x );
-extern void cexp ( cmplxf *z, cmplxf *w );
-extern double chbevl ( double x, double *array, int n );
-extern double chdtrc ( double dff, double xx );
-extern double chdtr ( double dff, double xx );
-extern double chdtri ( double dff, double yy );
-#if 0
-extern void clog ( cmplxf *z, cmplxf *w );
+#if defined __USE_BSD || defined __USE_XOPEN
+# define M_E 2.7182818284590452354 /* e */
+# define M_LOG2E 1.4426950408889634074 /* log_2 e */
+# define M_LOG10E 0.43429448190325182765 /* log_10 e */
+# define M_LN2 0.69314718055994530942 /* log_e 2 */
+# define M_LN10 2.30258509299404568402 /* log_e 10 */
+# define M_PI 3.14159265358979323846 /* pi */
+# define M_PI_2 1.57079632679489661923 /* pi/2 */
+# define M_PI_4 0.78539816339744830962 /* pi/4 */
+# define M_1_PI 0.31830988618379067154 /* 1/pi */
+# define M_2_PI 0.63661977236758134308 /* 2/pi */
+# define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
+# define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
+# define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
+#endif
+#ifdef __USE_GNU
+# define M_El M_E
+# define M_LOG2El M_LOG2E
+# define M_LOG10El M_LOG10E
+# define M_LN2l M_LN2
+# define M_LN10l M_LN10
+# define M_PIl M_PI
+# define M_PI_2l M_PI_2
+# define M_PI_4l M_PI_4
+# define M_1_PIl M_1_PI
+# define M_2_PIl M_2_PI
+# define M_2_SQRTPIl M_2_SQRTPI
+# define M_SQRT2l M_SQRT2
+# define M_SQRT1_2l M_SQRT1_2
+#endif
+
+
+
+
+/* 7.12.4 Trigonometric functions */
+extern double acos(double x);
+extern float acosf(float x);
+extern long double acosl(long double x);
+
+extern double asin(double x);
+extern float asinf(float x);
+extern long double asinl(long double x);
+
+extern double atan(double x);
+extern float atanf(float x);
+extern long double atanl(long double x);
+
+double atan2(double y, double x);
+float atan2f(float y, float x);
+long double atan2l(long double y, long double x);
+
+double cos(double x);
+float cosf(float x);
+long double cosl(long double x);
+
+double sin(double x);
+float sinf(float x);
+long double sinl(long double x);
+
+double tan(double x);
+float tanf(float x);
+long double tanl(long double x);
+
+
+/* 7.12.5 Hyperbolic functions */
+double acosh(double x);
+float acoshf(float x);
+long double acoshl(long double x);
+
+double asinh(double x);
+float asinhf(float x);
+long double asinhl(long double x);
+
+double atanh(double x);
+float atanhf(float x);
+long double atanhl(long double x);
+
+double cosh(double x);
+float coshf(float x);
+long double coshl(long double x);
+
+double sinh(double x);
+float sinhf(float x);
+long double sinhl(long double x);
+
+double tanh(double x);
+float tanhf(float x);
+long double tanhl(long double x);
+
+
+/* 7.12.6 Exponential and logarithmic functions */
+double exp(double x);
+float expf(float x);
+long double expl(long double x);
+
+double exp2(double x);
+float exp2f(float x);
+long double exp2l(long double x);
+
+double expm1(double x);
+float expm1f(float x);
+long double expm1l(long double x);
+
+double frexp(double value, int *exp);
+float frexpf(float value, int *exp);
+long double frexpl(long double value, int *exp);
+
+int ilogb(double x);
+int ilogbf(float x);
+int ilogbl(long double x);
+
+double ldexp(double x, int exp);
+float ldexpf(float x, int exp);
+long double ldexpl(long double x, int exp);
+
+double log(double x);
+float logf(float x);
+long double logl(long double x);
+
+double log10(double x);
+float log10f(float x);
+long double log10l(long double x);
+
+double log1p(double x);
+float log1pf(float x);
+long double log1pl(long double x);
+
+double log2(double x);
+float log2f(float x);
+long double log2l(long double x);
+
+double logb(double x);
+float logbf(float x);
+long double logbl(long double x);
+
+double modf(double value, double *iptr);
+float modff(float value, float *iptr);
+long double modfl(long double value, long double *iptr);
+
+double scalbn(double x, int n);
+float scalbnf(float x, int n);
+long double scalbnl(long double x, int n);
+double scalbln(double x, long int n);
+float scalblnf(float x, long int n);
+long double scalblnl(long double x, long int n);
+
+/* 7.12.7 Power and absolute-value functions */
+double fabs(double x);
+float fabsf(float x);
+long double fabsl(long double x);
+
+double hypot(double x, double y);
+float hypotf(float x, float y);
+long double hypotl(long double x, long double y);
+
+double pow(double x, double y);
+float powf(float x, float y);
+long double powl(long double x, long double y);
+
+double sqrt(double x);
+float sqrtf(float x);
+long double sqrtl(long double x);
+
+/* 7.12.8 Error and gamma functions */
+double erf(double x);
+float erff(float x);
+long double erfl(long double x);
+
+double erfc(double x);
+float erfcf(float x);
+long double erfcl(long double x);
+
+double lgamma(double x);
+float lgammaf(float x);
+long double lgammal(long double x);
+
+double tgamma(double x);
+float tgammaf(float x);
+long double tgammal(long double x);
+
+/* 7.12.9 Nearest integer functions */
+double ceil(double x);
+float ceilf(float x);
+long double ceill(long double x);
+
+double floor(double x);
+float floorf(float x);
+long double floorl(long double x);
+
+double nearbyint(double x);
+float nearbyintf(float x);
+long double nearbyintl(long double x);
+
+double rint(double x);
+float rintf(float x);
+long double rintl(long double x);
+
+long int lrint(double x);
+long int lrintf(float x);
+long int lrintl(long double x);
+long long int llrint(double x);
+long long int llrintf(float x);
+long long int llrintl(long double x);
+
+double round(double x);
+float roundf(float x);
+long double roundl(long double x);
+
+long int lround(double x);
+long int lroundf(float x);
+long int lroundl(long double x);
+long long int llround(double x);
+long long int llroundf(float x);
+long long int llroundl(long double x);
+
+double trunc(double x);
+float truncf(float x);
+long double truncl(long double x);
+
+/* 7.12.10 Remainder functions */
+double fmod(double x, double y);
+float fmodf(float x, float y);
+long double fmodl(long double x, long double y);
+
+double remainder(double x, double y);
+float remainderf(float x, float y);
+long double remainderl(long double x, long double y);
+
+double remquo(double x, double y, int *quo);
+float remquof(float x, float y, int *quo);
+long double remquol(long double x, long double y, int *quo);
+
+/* 7.12.11 Manipulation functions */
+double copysign(double x, double y);
+float copysignf(float x, float y);
+long double copysignl(long double x, long double y);
+
+double nan(const char *tagp);
+float nanf(const char *tagp);
+long double nanl(const char *tagp);
+
+double nextafter(double x, double y);
+float nextafterf(float x, float y);
+long double nextafterl(long double x, long double y);
+
+double nexttoward(double x, long double y);
+float nexttowardf(float x, long double y);
+long double nexttowardl(long double x, long double y);
+
+/* 7.12.12 Maximum, minimum, and positive difference functions */
+double fdim(double x, double y);
+float fdimf(float x, float y);
+long double fdiml(long double x, long double y);
+
+double fmax(double x, double y);
+float fmaxf(float x, float y);
+long double fmaxl(long double x, long double y);
+
+double fmin(double x, double y);
+float fminf(float x, float y);
+long double fminl(long double x, long double y);
+
+/* 7.12.13 Floating multiply-add */
+double fma(double x, double y, double z);
+float fmaf(float x, float y, float z);
+long double fmal(long double x, long double y, long double z);
+
+/* 7.12.14 Comparison macros */
+# ifndef isgreater
+# define isgreater(x, y) \
+ (__extension__ \
+ ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
+ !isunordered (__x, __y) && __x > __y; }))
+# endif
+
+/* Return nonzero value if X is greater than or equal to Y. */
+# ifndef isgreaterequal
+# define isgreaterequal(x, y) \
+ (__extension__ \
+ ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
+ !isunordered (__x, __y) && __x >= __y; }))
+# endif
+
+/* Return nonzero value if X is less than Y. */
+# ifndef isless
+# define isless(x, y) \
+ (__extension__ \
+ ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
+ !isunordered (__x, __y) && __x < __y; }))
+# endif
+
+/* Return nonzero value if X is less than or equal to Y. */
+# ifndef islessequal
+# define islessequal(x, y) \
+ (__extension__ \
+ ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
+ !isunordered (__x, __y) && __x <= __y; }))
+# endif
+
+/* Return nonzero value if either X is less than Y or Y is less than X. */
+# ifndef islessgreater
+# define islessgreater(x, y) \
+ (__extension__ \
+ ({ __typeof__(x) __x = (x); __typeof__(y) __y = (y); \
+ !isunordered (__x, __y) && (__x < __y || __y < __x); }))
+# endif
+
+/* Return nonzero value if arguments are unordered. */
+# ifndef isunordered
+# define isunordered(u, v) \
+ (__extension__ \
+ ({ __typeof__(u) __u = (u); __typeof__(v) __v = (v); \
+ fpclassify (__u) == FP_NAN || fpclassify (__v) == FP_NAN; }))
+# endif
+
+
+#ifndef __UCLIBC_HAS_FLOATS__
+ #undef float
#endif
-extern void cmov ( short *a, short *b );
-extern void cmul ( cmplxf *a, cmplxf *b, cmplxf *c );
-extern void cneg ( cmplxf *a );
-extern double cosdg ( double xx );
-extern double cos ( double xx );
-extern double cosh ( double xx );
-extern double cotdg ( double x );
-extern double cot ( double x );
-extern void csin ( cmplxf *z, cmplxf *w );
-extern void csqrt ( cmplxf *z, cmplxf *w );
-extern void csub ( cmplxf *a, cmplxf *b, cmplxf *c );
-extern void ctan ( cmplxf *z, cmplxf *w );
-extern double ctans ( cmplxf *z );
-extern double dawsn ( double xxx );
-extern int dprec ( void );
-extern double ellie ( double phia, double ma );
-extern double ellik ( double phia, double ma );
-extern double ellpe ( double xx );
-extern int ellpj ( double uu, double mm, double *sn, double *cn, double *dn, double *ph );
-extern double ellpk ( double xx );
-extern double erfc ( double aa );
-extern double erf ( double xx );
-extern double exp10 ( double xx );
-extern double exp2 ( double xx );
-extern double exp ( double xx );
-extern double expn ( int n, double xx );
-extern double fac ( int i );
-extern double fdtrc ( int ia, int ib, double xx );
-extern double fdtr ( int ia, int ib, int xx );
-extern double fdtri ( int ia, int ib, double yy );
-extern double floor ( double x );
-extern void fresnl ( double xxa, double *ssa, double *cca );
-extern double frexp ( double x, int *pw2 );
-extern double gamma ( double xx );
-extern double gdtrc ( double aa, double bb, double xx );
-extern double gdtr ( double aa, double bb, double xx );
-extern double hyp2f0 ( double aa, double bb, double xx, int type, double *err );
-extern double hyp2f1 ( double aa, double bb, double cc, double xx );
-extern double hyperg ( double aa, double bb, double xx );
-extern double i0e ( double x );
-extern double i0 ( double x );
-extern double i1e ( double xx );
-extern double i1 ( double xx );
-extern double igamc ( double aa, double xx );
-extern double igam ( double aa, double xx );
-extern double igami ( double aa, double yy0 );
-extern double incbet ( double aaa, double bbb, double xxx );
-extern double incbi ( double aaa, double bbb, double yyy0 );
-extern double incbps ( double aa, double bb, double xx );
-extern double iv ( double v, double x );
-extern double j0 ( double xx );
-extern double j1 ( double xx );
-extern double jn ( int n, double xx );
-extern double jv ( double nn, double xx );
-extern double k0e ( double xx );
-extern double k0 ( double xx );
-extern double k1e ( double xx );
-extern double k1 ( double xx );
-extern double kn ( int nnn, double xx );
-extern double ldexp ( double x, int pw2 );
-extern int ldprec ( void );
-extern double lgam ( double xx );
-extern double log10 ( double xx );
-extern double log2 ( double xx );
-extern double log ( double xx );
-/* extern int mtherr ( char *name, int code ); */
-extern double nbdtrc ( int k, int n, double pp );
-extern double nbdtr ( int k, int n, double pp );
-extern double ndtr ( double aa );
-extern double ndtri ( double yy0 );
-extern double onef2 ( double aa, double bb, double cc, double xx, double *err );
-extern double p1evl ( double xx, double *coef, int N );
-extern double pdtrc ( int k, double mm );
-extern double pdtr ( int k, double mm );
-extern double pdtri ( int k, double yy );
-extern void poladd ( double a[], int na, double b[], int nb, double c[] );
-extern void polclr ( double *a, int n );
-extern int poldiv ( double a[], int na, double b[], int nb, double c[] );
-extern double poleva ( double *a, int na, double xx );
-extern double polevl ( double xx, double *coef, int N );
-extern void polini ( int maxdeg );
-extern void polmov ( double *a, int na, double *b );
-extern void polmul ( double a[], int na, double b[], int nb, double c[] );
-extern void polprt ( double *a, int na, int d );
-extern void polsbt ( double a[], int na, double b[], int nb, double c[] );
-extern void polsub ( double a[], int na, double b[], int nb, double c[] );
-extern double pow ( double x, double y );
-extern double powi ( double x, int nn );
-extern double psi ( double xx );
-extern double redupi ( double xx );
-extern double rgamma ( double xx );
-extern int shichi ( double xx, double *si, double *ci );
-extern int sici ( double xx, double *si, double *ci );
-extern double sindg ( double xx );
-extern double sin ( double xx );
-extern double sinh ( double xx );
-extern double spence ( double xx );
-extern int sprec ( void );
-extern double sqrt ( double xx );
-extern double stdtr ( int k, double tt );
-extern double struve ( double vv, double xx );
-extern double tandg ( double x );
-extern double tan ( double x );
-extern double tanh ( double xx );
-extern double threef0 ( double aa, double bb, double cc, double xx, double *err );
-extern double y0 ( double xx );
-extern double y1 ( double xx );
-extern double yn ( int nn, double xx );
-extern double yv ( double vv, double xx );
-extern double zetac ( double xx );
-extern double zeta ( double xx, double qq );
-
-#endif /* _MATH_H */
+#ifndef __UCLIBC_HAS_DOUBLE__
+ #undef double
+#endif
+#ifndef __UCLIBC_HAS_LONG_DOUBLE__
+ #undef long
+ #undef double
+#endif
+
+
+#endif /* math.h */
diff --git a/libm/Makefile b/libm/Makefile
new file mode 100644
index 000000000..c151d7cbd
--- /dev/null
+++ b/libm/Makefile
@@ -0,0 +1,75 @@
+# Makefile for uClibc's math library
+#
+# Copyright (C) 2001 by Lineo, inc.
+#
+# This program is free software; you can redistribute it and/or modify it under
+# the terms of the GNU Library General Public License as published by the Free
+# Software Foundation; either version 2 of the License, or (at your option) any
+# later version.
+#
+# This program is distributed in the hope that it will be useful, but WITHOUT
+# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+# FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more
+# details.
+#
+# You should have received a copy of the GNU Library General Public License
+# along with this program; if not, write to the Free Software Foundation, Inc.,
+# 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+#
+# Derived in part from the Linux-8086 C library, the GNU C Library, and several
+# other sundry sources. Files within this library are copyright by their
+# respective copyright holders.
+
+TOPDIR=../
+include $(TOPDIR)Rules.mak
+
+LIBM=libm.a
+LIBM_SHARED=libm.so
+TARGET_CC= $(TOPDIR)extra/gcc-uClibc/$(TARGET_ARCH)-uclibc-gcc
+
+DIRS=
+ifeq ($(strip $(HAS_FLOATS)),true)
+ DIRS+=float
+endif
+ifeq ($(strip $(HAS_DOUBLE)),true)
+ DIRS+=double
+endif
+ifeq ($(strip $(HAS_LONG_DOUBLE)),true)
+ DIRS+=ldouble
+endif
+ALL_SUBDIRS = $(shell find * -type d -prune -name [a-z]\*)
+
+all: $(LIBM)
+
+$(LIBM): subdirs
+
+tags:
+ ctags -R
+
+shared: $(LIBM)
+ $(TARGET_CC) $(LDFLAGS) -shared -o $(LIBM_SHARED).$(MAJOR_VERSION) \
+ -Wl,-soname,$(LIBM_SHARED).$(MAJOR_VERSION) -Wl,--whole-archive $(LIBM) $(TOPDIR)$(SHARED_FULLNAME)
+
+install: all
+ install -d $(INSTALL_DIR)/lib
+ install -m 644 $(LIBM) $(INSTALL_DIR)/lib/
+ @if [ -f $(LIBM_SHARED).$(MAJOR_VERSION) ] ; then \
+ install -m 644 $(LIBM_SHARED).$(MAJOR_VERSION) $(INSTALL_DIR)/lib/; \
+ (cd $(INSTALL_DIR)/lib/;ln -sf $(LIBM_SHARED).$(MAJOR_VERSION) $(LIBM_SHARED)); \
+ fi;
+
+subdirs: $(patsubst %, _dir_%, $(DIRS))
+subdirs_clean: $(patsubst %, _dirclean_%, $(ALL_SUBDIRS))
+
+$(patsubst %, _dir_%, $(DIRS)) : dummy
+ $(MAKE) -C $(patsubst _dir_%, %, $@)
+
+$(patsubst %, _dirclean_%, $(ALL_SUBDIRS)) : dummy
+ $(MAKE) -C $(patsubst _dirclean_%, %, $@) clean
+
+clean: subdirs_clean
+ rm -f *.[oa] *~ core $(LIBM_SHARED)* $(LIBM)
+
+.PHONY: dummy
+
+
diff --git a/libm/README b/libm/README
new file mode 100644
index 000000000..023e46846
--- /dev/null
+++ b/libm/README
@@ -0,0 +1,42 @@
+The actual routines included in this math library are derived almost
+exclusively from the Cephes Mathematical Library, which "is copyrighted by the
+author [and] may be used freely but ... comes with no support or guarantee"
+
+It has been ported to fit into uClibc and generally behave
+by Erik Andersen <andersen@lineo.com>, <andersee@debian.org>
+ 5 May, 2001
+
+--------------------------------------------------
+
+ Some software in this archive may be from the book _Methods and
+Programs for Mathematical Functions_ (Prentice-Hall, 1989) or
+from the Cephes Mathematical Library, a commercial product. In
+either event, it is copyrighted by the author. What you see here
+may be used freely but it comes with no support or guarantee.
+
+ The two known misprints in the book are repaired here in the
+source listings for the gamma function and the incomplete beta
+integral.
+
+
+ Stephen L. Moshier
+ moshier@world.std.com
+
+--------------------------------------------------
+
+19 November 1992
+
+ZIP archive constructed and index compiled.
+
+To reconstruct the original directory structure, use the -d switch:
+
+ C:\CEPHES>pkunzip -d cephes
+
+This archive includes all the programs in the /netlib/cephes directory
+on research.att.com as of 17 Nov 92. The file "index" will tell you in
+what directory and file each function can be found. If there is
+something else mentioned in cephes.doc that you need, you can check
+research.att.com to see whether it has been added. Failing that, you
+can contact Stephen Moshier.
+
+ Jim Van Zandt <jrv@mbunix.mitre.org>
diff --git a/libm/double/Makefile b/libm/double/Makefile
new file mode 100644
index 000000000..be3c5878a
--- /dev/null
+++ b/libm/double/Makefile
@@ -0,0 +1,115 @@
+# Makefile for uClibc's math library
+#
+# Copyright (C) 2001 by Lineo, inc.
+#
+# This program is free software; you can redistribute it and/or modify it under
+# the terms of the GNU Library General Public License as published by the Free
+# Software Foundation; either version 2 of the License, or (at your option) any
+# later version.
+#
+# This program is distributed in the hope that it will be useful, but WITHOUT
+# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+# FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more
+# details.
+#
+# You should have received a copy of the GNU Library General Public License
+# along with this program; if not, write to the Free Software Foundation, Inc.,
+# 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+#
+# Derived in part from the Linux-8086 C library, the GNU C Library, and several
+# other sundry sources. Files within this library are copyright by their
+# respective copyright holders.
+
+TOPDIR=../../
+include $(TOPDIR)Rules.mak
+
+LIBM=../libm.a
+TARGET_CC= $(TOPDIR)/extra/gcc-uClibc/$(TARGET_ARCH)-uclibc-gcc
+
+CSRC=acosh.c airy.c asin.c asinh.c atan.c atanh.c bdtr.c beta.c \
+ btdtr.c cbrt.c chbevl.c chdtr.c clog.c cmplx.c const.c \
+ cosh.c dawsn.c ei.c ellie.c ellik.c ellpe.c ellpj.c ellpk.c \
+ exp.c exp10.c exp2.c expn.c fabs.c fac.c fdtr.c \
+ fresnl.c gamma.c gdtr.c hyp2f1.c hyperg.c i0.c i1.c igami.c incbet.c \
+ incbi.c igam.c isnan.c iv.c j0.c j1.c jn.c jv.c k0.c k1.c kn.c kolmogorov.c \
+ log.c log2.c log10.c lrand.c nbdtr.c ndtr.c ndtri.c pdtr.c planck.c \
+ polevl.c polmisc.c polylog.c polyn.c pow.c powi.c psi.c rgamma.c round.c \
+ shichi.c sici.c sin.c sindg.c sinh.c spence.c stdtr.c struve.c \
+ tan.c tandg.c tanh.c unity.c yn.c zeta.c zetac.c \
+ sqrt.c floor.c setprec.c mtherr.c
+
+COBJS=$(patsubst %.c,%.o, $(CSRC))
+
+
+OBJS=$(COBJS)
+
+all: $(OBJS) $(LIBM)
+
+$(LIBM): ar-target
+
+ar-target: $(OBJS)
+ $(AR) $(ARFLAGS) $(LIBM) $(OBJS)
+
+$(COBJS): %.o : %.c
+ $(TARGET_CC) $(CFLAGS) -c $< -o $@
+ $(STRIPTOOL) -x -R .note -R .comment $*.o
+
+$(OBJ): Makefile
+
+clean:
+ rm -f *.[oa] *~ core
+
+
+
+#-----------------------------------------
+
+#all: libmd.a mtst dtestvec monot dcalc paranoia
+
+time-it: time-it.o
+ $(CC) -o time-it time-it.o
+
+time-it.o: time-it.c
+ $(CC) -O2 -c time-it.c
+
+dcalc: dcalc.o libmd.a
+ $(CC) -o dcalc dcalc.o libmd.a
+
+mtst: mtst.o libmd.a
+ $(CC) -v -o mtst mtst.o libmd.a
+
+mtst.o: mtst.c
+ $(CC) -O2 -Wall -c mtst.c
+
+dtestvec: dtestvec.o libmd.a
+ $(CC) -o dtestvec dtestvec.o libmd.a
+
+dtestvec.o: dtestvec.c
+ $(CC) -g -c dtestvec.c
+
+monot: monot.o libmd.a
+ $(CC) -o monot monot.o libmd.a
+
+monot.o: monot.c
+ $(CC) -g -c monot.c
+
+paranoia: paranoia.o setprec.o libmd.a
+ $(CC) -o paranoia paranoia.o setprec.o libmd.a
+
+paranoia.o: paranoia.c
+ $(CC) $(CFLAGS) -Wno-implicit -c paranoia.c
+
+libmd.a: $(OBJS) $(INCS)
+ $(AR) rv libmd.a $(OBJS)
+
+#clean:
+# rm -f *.o
+# rm -f mtst
+# rm -f paranoia
+# rm -f dcalc
+# rm -f dtestvec
+# rm -f monot
+# rm -f libmd.a
+# rm -f time-it
+# rm -f dtestvec
+
+
diff --git a/libm/double/README.txt b/libm/double/README.txt
new file mode 100644
index 000000000..f2cb6c3dc
--- /dev/null
+++ b/libm/double/README.txt
@@ -0,0 +1,5845 @@
+/* acosh.c
+ *
+ * Inverse hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, acosh();
+ *
+ * y = acosh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic cosine of argument.
+ *
+ * If 1 <= x < 1.5, a rational approximation
+ *
+ * sqrt(z) * P(z)/Q(z)
+ *
+ * where z = x-1, is used. Otherwise,
+ *
+ * acosh(x) = log( x + sqrt( (x-1)(x+1) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 1,3 30000 4.2e-17 1.1e-17
+ * IEEE 1,3 30000 4.6e-16 8.7e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * acosh domain |x| < 1 NAN
+ *
+ */
+
+/* airy.c
+ *
+ * Airy function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, ai, aip, bi, bip;
+ * int airy();
+ *
+ * airy( x, _&ai, _&aip, _&bi, _&bip );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Solution of the differential equation
+ *
+ * y"(x) = xy.
+ *
+ * The function returns the two independent solutions Ai, Bi
+ * and their first derivatives Ai'(x), Bi'(x).
+ *
+ * Evaluation is by power series summation for small x,
+ * by rational minimax approximations for large x.
+ *
+ *
+ *
+ * ACCURACY:
+ * Error criterion is absolute when function <= 1, relative
+ * when function > 1, except * denotes relative error criterion.
+ * For large negative x, the absolute error increases as x^1.5.
+ * For large positive x, the relative error increases as x^1.5.
+ *
+ * Arithmetic domain function # trials peak rms
+ * IEEE -10, 0 Ai 10000 1.6e-15 2.7e-16
+ * IEEE 0, 10 Ai 10000 2.3e-14* 1.8e-15*
+ * IEEE -10, 0 Ai' 10000 4.6e-15 7.6e-16
+ * IEEE 0, 10 Ai' 10000 1.8e-14* 1.5e-15*
+ * IEEE -10, 10 Bi 30000 4.2e-15 5.3e-16
+ * IEEE -10, 10 Bi' 30000 4.9e-15 7.3e-16
+ * DEC -10, 0 Ai 5000 1.7e-16 2.8e-17
+ * DEC 0, 10 Ai 5000 2.1e-15* 1.7e-16*
+ * DEC -10, 0 Ai' 5000 4.7e-16 7.8e-17
+ * DEC 0, 10 Ai' 12000 1.8e-15* 1.5e-16*
+ * DEC -10, 10 Bi 10000 5.5e-16 6.8e-17
+ * DEC -10, 10 Bi' 7000 5.3e-16 8.7e-17
+ *
+ */
+
+/* asin.c
+ *
+ * Inverse circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, asin();
+ *
+ * y = asin( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
+ *
+ * A rational function of the form x + x**3 P(x**2)/Q(x**2)
+ * is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is
+ * transformed by the identity
+ *
+ * asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -1, 1 40000 2.6e-17 7.1e-18
+ * IEEE -1, 1 10^6 1.9e-16 5.4e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * asin domain |x| > 1 NAN
+ *
+ */
+ /* acos()
+ *
+ * Inverse circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, acos();
+ *
+ * y = acos( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between 0 and pi whose cosine
+ * is x.
+ *
+ * Analytically, acos(x) = pi/2 - asin(x). However if |x| is
+ * near 1, there is cancellation error in subtracting asin(x)
+ * from pi/2. Hence if x < -0.5,
+ *
+ * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
+ *
+ * or if x > +0.5,
+ *
+ * acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -1, 1 50000 3.3e-17 8.2e-18
+ * IEEE -1, 1 10^6 2.2e-16 6.5e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * asin domain |x| > 1 NAN
+ */
+
+/* asinh.c
+ *
+ * Inverse hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, asinh();
+ *
+ * y = asinh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic sine of argument.
+ *
+ * If |x| < 0.5, the function is approximated by a rational
+ * form x + x**3 P(x)/Q(x). Otherwise,
+ *
+ * asinh(x) = log( x + sqrt(1 + x*x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -3,3 75000 4.6e-17 1.1e-17
+ * IEEE -1,1 30000 3.7e-16 7.8e-17
+ * IEEE 1,3 30000 2.5e-16 6.7e-17
+ *
+ */
+
+/* atan.c
+ *
+ * Inverse circular tangent
+ * (arctangent)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, atan();
+ *
+ * y = atan( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose tangent
+ * is x.
+ *
+ * Range reduction is from three intervals into the interval
+ * from zero to 0.66. The approximant uses a rational
+ * function of degree 4/5 of the form x + x**3 P(x)/Q(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10, 10 50000 2.4e-17 8.3e-18
+ * IEEE -10, 10 10^6 1.8e-16 5.0e-17
+ *
+ */
+ /* atan2()
+ *
+ * Quadrant correct inverse circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, z, atan2();
+ *
+ * z = atan2( y, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle whose tangent is y/x.
+ * Define compile time symbol ANSIC = 1 for ANSI standard,
+ * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
+ * 0 to 2PI, args (x,y).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10, 10 10^6 2.5e-16 6.9e-17
+ * See atan.c.
+ *
+ */
+
+/* atanh.c
+ *
+ * Inverse hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, atanh();
+ *
+ * y = atanh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic tangent of argument in the range
+ * MINLOG to MAXLOG.
+ *
+ * If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is
+ * employed. Otherwise,
+ * atanh(x) = 0.5 * log( (1+x)/(1-x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -1,1 50000 2.4e-17 6.4e-18
+ * IEEE -1,1 30000 1.9e-16 5.2e-17
+ *
+ */
+
+/* bdtr.c
+ *
+ * Binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtr();
+ *
+ * y = bdtr( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the Binomial
+ * probability density:
+ *
+ * k
+ * -- ( n ) j n-j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p), with p between 0 and 1.
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * For p between 0.001 and 1:
+ * IEEE 0,100 100000 4.3e-15 2.6e-16
+ * See also incbet.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtr domain k < 0 0.0
+ * n < k
+ * x < 0, x > 1
+ */
+ /* bdtrc()
+ *
+ * Complemented binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtrc();
+ *
+ * y = bdtrc( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 through n of the Binomial
+ * probability density:
+ *
+ * n
+ * -- ( n ) j n-j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p).
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * For p between 0.001 and 1:
+ * IEEE 0,100 100000 6.7e-15 8.2e-16
+ * For p between 0 and .001:
+ * IEEE 0,100 100000 1.5e-13 2.7e-15
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtrc domain x<0, x>1, n<k 0.0
+ */
+ /* bdtri()
+ *
+ * Inverse binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtri();
+ *
+ * p = bdtr( k, n, y );
+ *
+ * DESCRIPTION:
+ *
+ * Finds the event probability p such that the sum of the
+ * terms 0 through k of the Binomial probability density
+ * is equal to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relation
+ *
+ * 1 - p = incbi( n-k, k+1, y ).
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p).
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * For p between 0.001 and 1:
+ * IEEE 0,100 100000 2.3e-14 6.4e-16
+ * IEEE 0,10000 100000 6.6e-12 1.2e-13
+ * For p between 10^-6 and 0.001:
+ * IEEE 0,100 100000 2.0e-12 1.3e-14
+ * IEEE 0,10000 100000 1.5e-12 3.2e-14
+ * See also incbi.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtri domain k < 0, n <= k 0.0
+ * x < 0, x > 1
+ */
+
+/* beta.c
+ *
+ * Beta function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, y, beta();
+ *
+ * y = beta( a, b );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * - -
+ * | (a) | (b)
+ * beta( a, b ) = -----------.
+ * -
+ * | (a+b)
+ *
+ * For large arguments the logarithm of the function is
+ * evaluated using lgam(), then exponentiated.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 1700 7.7e-15 1.5e-15
+ * IEEE 0,30 30000 8.1e-14 1.1e-14
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * beta overflow log(beta) > MAXLOG 0.0
+ * a or b <0 integer 0.0
+ *
+ */
+
+/* btdtr.c
+ *
+ * Beta distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, btdtr();
+ *
+ * y = btdtr( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the beta density
+ * function:
+ *
+ *
+ * x
+ * - -
+ * | (a+b) | | a-1 b-1
+ * P(x) = ---------- | t (1-t) dt
+ * - - | |
+ * | (a) | (b) -
+ * 0
+ *
+ *
+ * This function is identical to the incomplete beta
+ * integral function incbet(a, b, x).
+ *
+ * The complemented function is
+ *
+ * 1 - P(1-x) = incbet( b, a, x );
+ *
+ *
+ * ACCURACY:
+ *
+ * See incbet.c.
+ *
+ */
+
+/* cbrt.c
+ *
+ * Cube root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cbrt();
+ *
+ * y = cbrt( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the cube root of the argument, which may be negative.
+ *
+ * Range reduction involves determining the power of 2 of
+ * the argument. A polynomial of degree 2 applied to the
+ * mantissa, and multiplication by the cube root of 1, 2, or 4
+ * approximates the root to within about 0.1%. Then Newton's
+ * iteration is used three times to converge to an accurate
+ * result.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,10 200000 1.8e-17 6.2e-18
+ * IEEE 0,1e308 30000 1.5e-16 5.0e-17
+ *
+ */
+
+/* chbevl.c
+ *
+ * Evaluate Chebyshev series
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * double x, y, coef[N], chebevl();
+ *
+ * y = chbevl( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the series
+ *
+ * N-1
+ * - '
+ * y = > coef[i] T (x/2)
+ * - i
+ * i=0
+ *
+ * of Chebyshev polynomials Ti at argument x/2.
+ *
+ * Coefficients are stored in reverse order, i.e. the zero
+ * order term is last in the array. Note N is the number of
+ * coefficients, not the order.
+ *
+ * If coefficients are for the interval a to b, x must
+ * have been transformed to x -> 2(2x - b - a)/(b-a) before
+ * entering the routine. This maps x from (a, b) to (-1, 1),
+ * over which the Chebyshev polynomials are defined.
+ *
+ * If the coefficients are for the inverted interval, in
+ * which (a, b) is mapped to (1/b, 1/a), the transformation
+ * required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
+ * this becomes x -> 4a/x - 1.
+ *
+ *
+ *
+ * SPEED:
+ *
+ * Taking advantage of the recurrence properties of the
+ * Chebyshev polynomials, the routine requires one more
+ * addition per loop than evaluating a nested polynomial of
+ * the same degree.
+ *
+ */
+
+/* chdtr.c
+ *
+ * Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double df, x, y, chdtr();
+ *
+ * y = chdtr( df, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the left hand tail (from 0 to x)
+ * of the Chi square probability density function with
+ * v degrees of freedom.
+ *
+ *
+ * inf.
+ * -
+ * 1 | | v/2-1 -t/2
+ * P( x | v ) = ----------- | t e dt
+ * v/2 - | |
+ * 2 | (v/2) -
+ * x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ * y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtr domain x < 0 or v < 1 0.0
+ */
+ /* chdtrc()
+ *
+ * Complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, chdtrc();
+ *
+ * y = chdtrc( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the right hand tail (from x to
+ * infinity) of the Chi square probability density function
+ * with v degrees of freedom:
+ *
+ *
+ * inf.
+ * -
+ * 1 | | v/2-1 -t/2
+ * P( x | v ) = ----------- | t e dt
+ * v/2 - | |
+ * 2 | (v/2) -
+ * x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ * y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtrc domain x < 0 or v < 1 0.0
+ */
+ /* chdtri()
+ *
+ * Inverse of complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double df, x, y, chdtri();
+ *
+ * x = chdtri( df, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Chi-square argument x such that the integral
+ * from x to infinity of the Chi-square density is equal
+ * to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ * x/2 = igami( df/2, y );
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igami.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtri domain y < 0 or y > 1 0.0
+ * v < 1
+ *
+ */
+
+/* clog.c
+ *
+ * Complex natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void clog();
+ * cmplx z, w;
+ *
+ * clog( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns complex logarithm to the base e (2.718...) of
+ * the complex argument x.
+ *
+ * If z = x + iy, r = sqrt( x**2 + y**2 ),
+ * then
+ * w = log(r) + i arctan(y/x).
+ *
+ * The arctangent ranges from -PI to +PI.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 7000 8.5e-17 1.9e-17
+ * IEEE -10,+10 30000 5.0e-15 1.1e-16
+ *
+ * Larger relative error can be observed for z near 1 +i0.
+ * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
+ * absolute error 1.0e-16.
+ */
+
+/* cexp()
+ *
+ * Complex exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cexp();
+ * cmplx z, w;
+ *
+ * cexp( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the exponential of the complex argument z
+ * into the complex result w.
+ *
+ * If
+ * z = x + iy,
+ * r = exp(x),
+ *
+ * then
+ *
+ * w = r cos y + i r sin y.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 8700 3.7e-17 1.1e-17
+ * IEEE -10,+10 30000 3.0e-16 8.7e-17
+ *
+ */
+ /* csin()
+ *
+ * Complex circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csin();
+ * cmplx z, w;
+ *
+ * csin( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * w = sin x cosh y + i cos x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 8400 5.3e-17 1.3e-17
+ * IEEE -10,+10 30000 3.8e-16 1.0e-16
+ * Also tested by csin(casin(z)) = z.
+ *
+ */
+ /* ccos()
+ *
+ * Complex circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccos();
+ * cmplx z, w;
+ *
+ * ccos( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * w = cos x cosh y - i sin x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 8400 4.5e-17 1.3e-17
+ * IEEE -10,+10 30000 3.8e-16 1.0e-16
+ */
+ /* ctan()
+ *
+ * Complex circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ctan();
+ * cmplx z, w;
+ *
+ * ctan( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * sin 2x + i sinh 2y
+ * w = --------------------.
+ * cos 2x + cosh 2y
+ *
+ * On the real axis the denominator is zero at odd multiples
+ * of PI/2. The denominator is evaluated by its Taylor
+ * series near these points.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 5200 7.1e-17 1.6e-17
+ * IEEE -10,+10 30000 7.2e-16 1.2e-16
+ * Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
+ */
+ /* ccot()
+ *
+ * Complex circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccot();
+ * cmplx z, w;
+ *
+ * ccot( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * sin 2x - i sinh 2y
+ * w = --------------------.
+ * cosh 2y - cos 2x
+ *
+ * On the real axis, the denominator has zeros at even
+ * multiples of PI/2. Near these points it is evaluated
+ * by a Taylor series.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 3000 6.5e-17 1.6e-17
+ * IEEE -10,+10 30000 9.2e-16 1.2e-16
+ * Also tested by ctan * ccot = 1 + i0.
+ */
+ /* casin()
+ *
+ * Complex circular arc sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void casin();
+ * cmplx z, w;
+ *
+ * casin( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Inverse complex sine:
+ *
+ * 2
+ * w = -i clog( iz + csqrt( 1 - z ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 10100 2.1e-15 3.4e-16
+ * IEEE -10,+10 30000 2.2e-14 2.7e-15
+ * Larger relative error can be observed for z near zero.
+ * Also tested by csin(casin(z)) = z.
+ */
+
+ /* cacos()
+ *
+ * Complex circular arc cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cacos();
+ * cmplx z, w;
+ *
+ * cacos( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * w = arccos z = PI/2 - arcsin z.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 5200 1.6e-15 2.8e-16
+ * IEEE -10,+10 30000 1.8e-14 2.2e-15
+ */
+ /* catan()
+ *
+ * Complex circular arc tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void catan();
+ * cmplx z, w;
+ *
+ * catan( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ * 1 ( 2x )
+ * Re w = - arctan(-----------) + k PI
+ * 2 ( 2 2)
+ * (1 - x - y )
+ *
+ * ( 2 2)
+ * 1 (x + (y+1) )
+ * Im w = - log(------------)
+ * 4 ( 2 2)
+ * (x + (y-1) )
+ *
+ * Where k is an arbitrary integer.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 5900 1.3e-16 7.8e-18
+ * IEEE -10,+10 30000 2.3e-15 8.5e-17
+ * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
+ * had peak relative error 1.5e-16, rms relative error
+ * 2.9e-17. See also clog().
+ */
+
+/* cmplx.c
+ *
+ * Complex number arithmetic
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct {
+ * double r; real part
+ * double i; imaginary part
+ * }cmplx;
+ *
+ * cmplx *a, *b, *c;
+ *
+ * cadd( a, b, c ); c = b + a
+ * csub( a, b, c ); c = b - a
+ * cmul( a, b, c ); c = b * a
+ * cdiv( a, b, c ); c = b / a
+ * cneg( c ); c = -c
+ * cmov( b, c ); c = b
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Addition:
+ * c.r = b.r + a.r
+ * c.i = b.i + a.i
+ *
+ * Subtraction:
+ * c.r = b.r - a.r
+ * c.i = b.i - a.i
+ *
+ * Multiplication:
+ * c.r = b.r * a.r - b.i * a.i
+ * c.i = b.r * a.i + b.i * a.r
+ *
+ * Division:
+ * d = a.r * a.r + a.i * a.i
+ * c.r = (b.r * a.r + b.i * a.i)/d
+ * c.i = (b.i * a.r - b.r * a.i)/d
+ * ACCURACY:
+ *
+ * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
+ * error 3.1e-17, rms 1.2e-17. The test (y/z) * (z/y) = 1 had
+ * peak relative error 8.3e-17, rms 2.1e-17.
+ *
+ * Tests in the rectangle {-10,+10}:
+ * Relative error:
+ * arithmetic function # trials peak rms
+ * DEC cadd 10000 1.4e-17 3.4e-18
+ * IEEE cadd 100000 1.1e-16 2.7e-17
+ * DEC csub 10000 1.4e-17 4.5e-18
+ * IEEE csub 100000 1.1e-16 3.4e-17
+ * DEC cmul 3000 2.3e-17 8.7e-18
+ * IEEE cmul 100000 2.1e-16 6.9e-17
+ * DEC cdiv 18000 4.9e-17 1.3e-17
+ * IEEE cdiv 100000 3.7e-16 1.1e-16
+ */
+
+/* cabs()
+ *
+ * Complex absolute value
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double cabs();
+ * cmplx z;
+ * double a;
+ *
+ * a = cabs( &z );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy
+ *
+ * then
+ *
+ * a = sqrt( x**2 + y**2 ).
+ *
+ * Overflow and underflow are avoided by testing the magnitudes
+ * of x and y before squaring. If either is outside half of
+ * the floating point full scale range, both are rescaled.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -30,+30 30000 3.2e-17 9.2e-18
+ * IEEE -10,+10 100000 2.7e-16 6.9e-17
+ */
+ /* csqrt()
+ *
+ * Complex square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csqrt();
+ * cmplx z, w;
+ *
+ * csqrt( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy, r = |z|, then
+ *
+ * 1/2
+ * Im w = [ (r - x)/2 ] ,
+ *
+ * Re w = y / 2 Im w.
+ *
+ *
+ * Note that -w is also a square root of z. The root chosen
+ * is always in the upper half plane.
+ *
+ * Because of the potential for cancellation error in r - x,
+ * the result is sharpened by doing a Heron iteration
+ * (see sqrt.c) in complex arithmetic.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 25000 3.2e-17 9.6e-18
+ * IEEE -10,+10 100000 3.2e-16 7.7e-17
+ *
+ * 2
+ * Also tested by csqrt( z ) = z, and tested by arguments
+ * close to the real axis.
+ */
+
+/* const.c
+ *
+ * Globally declared constants
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * extern double nameofconstant;
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This file contains a number of mathematical constants and
+ * also some needed size parameters of the computer arithmetic.
+ * The values are supplied as arrays of hexadecimal integers
+ * for IEEE arithmetic; arrays of octal constants for DEC
+ * arithmetic; and in a normal decimal scientific notation for
+ * other machines. The particular notation used is determined
+ * by a symbol (DEC, IBMPC, or UNK) defined in the include file
+ * math.h.
+ *
+ * The default size parameters are as follows.
+ *
+ * For DEC and UNK modes:
+ * MACHEP = 1.38777878078144567553E-17 2**-56
+ * MAXLOG = 8.8029691931113054295988E1 log(2**127)
+ * MINLOG = -8.872283911167299960540E1 log(2**-128)
+ * MAXNUM = 1.701411834604692317316873e38 2**127
+ *
+ * For IEEE arithmetic (IBMPC):
+ * MACHEP = 1.11022302462515654042E-16 2**-53
+ * MAXLOG = 7.09782712893383996843E2 log(2**1024)
+ * MINLOG = -7.08396418532264106224E2 log(2**-1022)
+ * MAXNUM = 1.7976931348623158E308 2**1024
+ *
+ * The global symbols for mathematical constants are
+ * PI = 3.14159265358979323846 pi
+ * PIO2 = 1.57079632679489661923 pi/2
+ * PIO4 = 7.85398163397448309616E-1 pi/4
+ * SQRT2 = 1.41421356237309504880 sqrt(2)
+ * SQRTH = 7.07106781186547524401E-1 sqrt(2)/2
+ * LOG2E = 1.4426950408889634073599 1/log(2)
+ * SQ2OPI = 7.9788456080286535587989E-1 sqrt( 2/pi )
+ * LOGE2 = 6.93147180559945309417E-1 log(2)
+ * LOGSQ2 = 3.46573590279972654709E-1 log(2)/2
+ * THPIO4 = 2.35619449019234492885 3*pi/4
+ * TWOOPI = 6.36619772367581343075535E-1 2/pi
+ *
+ * These lists are subject to change.
+ */
+
+/* cosh.c
+ *
+ * Hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cosh();
+ *
+ * y = cosh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic cosine of argument in the range MINLOG to
+ * MAXLOG.
+ *
+ * cosh(x) = ( exp(x) + exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC +- 88 50000 4.0e-17 7.7e-18
+ * IEEE +-MAXLOG 30000 2.6e-16 5.7e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * cosh overflow |x| > MAXLOG MAXNUM
+ *
+ *
+ */
+
+/* cpmul.c
+ *
+ * Multiply two polynomials with complex coefficients
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct
+ * {
+ * double r;
+ * double i;
+ * }cmplx;
+ *
+ * cmplx a[], b[], c[];
+ * int da, db, dc;
+ *
+ * cpmul( a, da, b, db, c, &dc );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The two argument polynomials are multiplied together, and
+ * their product is placed in c.
+ *
+ * Each polynomial is represented by its coefficients stored
+ * as an array of complex number structures (see the typedef).
+ * The degree of a is da, which must be passed to the routine
+ * as an argument; similarly the degree db of b is an argument.
+ * Array a has da + 1 elements and array b has db + 1 elements.
+ * Array c must have storage allocated for at least da + db + 1
+ * elements. The value da + db is returned in dc; this is
+ * the degree of the product polynomial.
+ *
+ * Polynomial coefficients are stored in ascending order; i.e.,
+ * a(x) = a[0]*x**0 + a[1]*x**1 + ... + a[da]*x**da.
+ *
+ *
+ * If desired, c may be the same as either a or b, in which
+ * case the input argument array is replaced by the product
+ * array (but only up to terms of degree da + db).
+ *
+ */
+
+/* dawsn.c
+ *
+ * Dawson's Integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, dawsn();
+ *
+ * y = dawsn( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ * x
+ * -
+ * 2 | | 2
+ * dawsn(x) = exp( -x ) | exp( t ) dt
+ * | |
+ * -
+ * 0
+ *
+ * Three different rational approximations are employed, for
+ * the intervals 0 to 3.25; 3.25 to 6.25; and 6.25 up.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,10 10000 6.9e-16 1.0e-16
+ * DEC 0,10 6000 7.4e-17 1.4e-17
+ *
+ *
+ */
+
+/* drand.c
+ *
+ * Pseudorandom number generator
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double y, drand();
+ *
+ * drand( &y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Yields a random number 1.0 <= y < 2.0.
+ *
+ * The three-generator congruential algorithm by Brian
+ * Wichmann and David Hill (BYTE magazine, March, 1987,
+ * pp 127-8) is used. The period, given by them, is
+ * 6953607871644.
+ *
+ * Versions invoked by the different arithmetic compile
+ * time options DEC, IBMPC, and MIEEE, produce
+ * approximately the same sequences, differing only in the
+ * least significant bits of the numbers. The UNK option
+ * implements the algorithm as recommended in the BYTE
+ * article. It may be used on all computers. However,
+ * the low order bits of a double precision number may
+ * not be adequately random, and may vary due to arithmetic
+ * implementation details on different computers.
+ *
+ * The other compile options generate an additional random
+ * integer that overwrites the low order bits of the double
+ * precision number. This reduces the period by a factor of
+ * two but tends to overcome the problems mentioned.
+ *
+ */
+
+/* eigens.c
+ *
+ * Eigenvalues and eigenvectors of a real symmetric matrix
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double A[n*(n+1)/2], EV[n*n], E[n];
+ * void eigens( A, EV, E, n );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The algorithm is due to J. vonNeumann.
+ *
+ * A[] is a symmetric matrix stored in lower triangular form.
+ * That is, A[ row, column ] = A[ (row*row+row)/2 + column ]
+ * or equivalently with row and column interchanged. The
+ * indices row and column run from 0 through n-1.
+ *
+ * EV[] is the output matrix of eigenvectors stored columnwise.
+ * That is, the elements of each eigenvector appear in sequential
+ * memory order. The jth element of the ith eigenvector is
+ * EV[ n*i+j ] = EV[i][j].
+ *
+ * E[] is the output matrix of eigenvalues. The ith element
+ * of E corresponds to the ith eigenvector (the ith row of EV).
+ *
+ * On output, the matrix A will have been diagonalized and its
+ * orginal contents are destroyed.
+ *
+ * ACCURACY:
+ *
+ * The error is controlled by an internal parameter called RANGE
+ * which is set to 1e-10. After diagonalization, the
+ * off-diagonal elements of A will have been reduced by
+ * this factor.
+ *
+ * ERROR MESSAGES:
+ *
+ * None.
+ *
+ */
+
+/* ellie.c
+ *
+ * Incomplete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double phi, m, y, ellie();
+ *
+ * y = ellie( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ * phi
+ * -
+ * | |
+ * | 2
+ * E(phi_\m) = | sqrt( 1 - m sin t ) dt
+ * |
+ * | |
+ * -
+ * 0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random arguments with phi in [-10, 10] and m in
+ * [0, 1].
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,2 2000 1.9e-16 3.4e-17
+ * IEEE -10,10 150000 3.3e-15 1.4e-16
+ *
+ *
+ */
+
+/* ellik.c
+ *
+ * Incomplete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double phi, m, y, ellik();
+ *
+ * y = ellik( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ * phi
+ * -
+ * | |
+ * | dt
+ * F(phi_\m) = | ------------------
+ * | 2
+ * | | sqrt( 1 - m sin t )
+ * -
+ * 0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with m in [0, 1] and phi as indicated.
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,10 200000 7.4e-16 1.0e-16
+ *
+ *
+ */
+
+/* ellpe.c
+ *
+ * Complete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double m1, y, ellpe();
+ *
+ * y = ellpe( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ * pi/2
+ * -
+ * | | 2
+ * E(m) = | sqrt( 1 - m sin t ) dt
+ * | |
+ * -
+ * 0
+ *
+ * Where m = 1 - m1, using the approximation
+ *
+ * P(x) - x log x Q(x).
+ *
+ * Though there are no singularities, the argument m1 is used
+ * rather than m for compatibility with ellpk().
+ *
+ * E(1) = 1; E(0) = pi/2.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 1 13000 3.1e-17 9.4e-18
+ * IEEE 0, 1 10000 2.1e-16 7.3e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ellpe domain x<0, x>1 0.0
+ *
+ */
+
+/* ellpj.c
+ *
+ * Jacobian Elliptic Functions
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double u, m, sn, cn, dn, phi;
+ * int ellpj();
+ *
+ * ellpj( u, m, _&sn, _&cn, _&dn, _&phi );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
+ * and dn(u|m) of parameter m between 0 and 1, and real
+ * argument u.
+ *
+ * These functions are periodic, with quarter-period on the
+ * real axis equal to the complete elliptic integral
+ * ellpk(1.0-m).
+ *
+ * Relation to incomplete elliptic integral:
+ * If u = ellik(phi,m), then sn(u|m) = sin(phi),
+ * and cn(u|m) = cos(phi). Phi is called the amplitude of u.
+ *
+ * Computation is by means of the arithmetic-geometric mean
+ * algorithm, except when m is within 1e-9 of 0 or 1. In the
+ * latter case with m close to 1, the approximation applies
+ * only for phi < pi/2.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with u between 0 and 10, m between
+ * 0 and 1.
+ *
+ * Absolute error (* = relative error):
+ * arithmetic function # trials peak rms
+ * DEC sn 1800 4.5e-16 8.7e-17
+ * IEEE phi 10000 9.2e-16* 1.4e-16*
+ * IEEE sn 50000 4.1e-15 4.6e-16
+ * IEEE cn 40000 3.6e-15 4.4e-16
+ * IEEE dn 10000 1.3e-12 1.8e-14
+ *
+ * Peak error observed in consistency check using addition
+ * theorem for sn(u+v) was 4e-16 (absolute). Also tested by
+ * the above relation to the incomplete elliptic integral.
+ * Accuracy deteriorates when u is large.
+ *
+ */
+
+/* ellpk.c
+ *
+ * Complete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double m1, y, ellpk();
+ *
+ * y = ellpk( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ * pi/2
+ * -
+ * | |
+ * | dt
+ * K(m) = | ------------------
+ * | 2
+ * | | sqrt( 1 - m sin t )
+ * -
+ * 0
+ *
+ * where m = 1 - m1, using the approximation
+ *
+ * P(x) - log x Q(x).
+ *
+ * The argument m1 is used rather than m so that the logarithmic
+ * singularity at m = 1 will be shifted to the origin; this
+ * preserves maximum accuracy.
+ *
+ * K(0) = pi/2.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,1 16000 3.5e-17 1.1e-17
+ * IEEE 0,1 30000 2.5e-16 6.8e-17
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ellpk domain x<0, x>1 0.0
+ *
+ */
+
+/* euclid.c
+ *
+ * Rational arithmetic routines
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ *
+ * typedef struct
+ * {
+ * double n; numerator
+ * double d; denominator
+ * }fract;
+ *
+ * radd( a, b, c ) c = b + a
+ * rsub( a, b, c ) c = b - a
+ * rmul( a, b, c ) c = b * a
+ * rdiv( a, b, c ) c = b / a
+ * euclid( &n, &d ) Reduce n/d to lowest terms,
+ * return greatest common divisor.
+ *
+ * Arguments of the routines are pointers to the structures.
+ * The double precision numbers are assumed, without checking,
+ * to be integer valued. Overflow conditions are reported.
+ */
+
+/* exp.c
+ *
+ * Exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, exp();
+ *
+ * y = exp( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns e (2.71828...) raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *
+ * x k f
+ * e = 2 e.
+ *
+ * A Pade' form 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ * of degree 2/3 is used to approximate exp(f) in the basic
+ * interval [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC +- 88 50000 2.8e-17 7.0e-18
+ * IEEE +- 708 40000 2.0e-16 5.6e-17
+ *
+ *
+ * Error amplification in the exponential function can be
+ * a serious matter. The error propagation involves
+ * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
+ * which shows that a 1 lsb error in representing X produces
+ * a relative error of X times 1 lsb in the function.
+ * While the routine gives an accurate result for arguments
+ * that are exactly represented by a double precision
+ * computer number, the result contains amplified roundoff
+ * error for large arguments not exactly represented.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp underflow x < MINLOG 0.0
+ * exp overflow x > MAXLOG INFINITY
+ *
+ */
+
+/* exp10.c
+ *
+ * Base 10 exponential function
+ * (Common antilogarithm)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, exp10();
+ *
+ * y = exp10( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 10 raised to the x power.
+ *
+ * Range reduction is accomplished by expressing the argument
+ * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
+ * The Pade' form
+ *
+ * 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ *
+ * is used to approximate 10**f.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -307,+307 30000 2.2e-16 5.5e-17
+ * Test result from an earlier version (2.1):
+ * DEC -38,+38 70000 3.1e-17 7.0e-18
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp10 underflow x < -MAXL10 0.0
+ * exp10 overflow x > MAXL10 MAXNUM
+ *
+ * DEC arithmetic: MAXL10 = 38.230809449325611792.
+ * IEEE arithmetic: MAXL10 = 308.2547155599167.
+ *
+ */
+
+/* exp2.c
+ *
+ * Base 2 exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, exp2();
+ *
+ * y = exp2( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 2 raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ * x k f
+ * 2 = 2 2.
+ *
+ * A Pade' form
+ *
+ * 1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
+ *
+ * approximates 2**x in the basic range [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1022,+1024 30000 1.8e-16 5.4e-17
+ *
+ *
+ * See exp.c for comments on error amplification.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp underflow x < -MAXL2 0.0
+ * exp overflow x > MAXL2 MAXNUM
+ *
+ * For DEC arithmetic, MAXL2 = 127.
+ * For IEEE arithmetic, MAXL2 = 1024.
+ */
+
+/* expn.c
+ *
+ * Exponential integral En
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double x, y, expn();
+ *
+ * y = expn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the exponential integral
+ *
+ * inf.
+ * -
+ * | | -xt
+ * | e
+ * E (x) = | ---- dt.
+ * n | n
+ * | | t
+ * -
+ * 1
+ *
+ *
+ * Both n and x must be nonnegative.
+ *
+ * The routine employs either a power series, a continued
+ * fraction, or an asymptotic formula depending on the
+ * relative values of n and x.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 5000 2.0e-16 4.6e-17
+ * IEEE 0, 30 10000 1.7e-15 3.6e-16
+ *
+ */
+
+/* fabs.c
+ *
+ * Absolute value
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y;
+ *
+ * y = fabs( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the absolute value of the argument.
+ *
+ */
+
+/* fac.c
+ *
+ * Factorial function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double y, fac();
+ * int i;
+ *
+ * y = fac( i );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns factorial of i = 1 * 2 * 3 * ... * i.
+ * fac(0) = 1.0.
+ *
+ * Due to machine arithmetic bounds the largest value of
+ * i accepted is 33 in DEC arithmetic or 170 in IEEE
+ * arithmetic. Greater values, or negative ones,
+ * produce an error message and return MAXNUM.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * For i < 34 the values are simply tabulated, and have
+ * full machine accuracy. If i > 55, fac(i) = gamma(i+1);
+ * see gamma.c.
+ *
+ * Relative error:
+ * arithmetic domain peak
+ * IEEE 0, 170 1.4e-15
+ * DEC 0, 33 1.4e-17
+ *
+ */
+
+/* fdtr.c
+ *
+ * F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * double x, y, fdtr();
+ *
+ * y = fdtr( df1, df2, x );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density). This is the density
+ * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
+ * variables having Chi square distributions with df1
+ * and df2 degrees of freedom, respectively.
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ * P(x) = incbet( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
+ *
+ *
+ * The arguments a and b are greater than zero, and x is
+ * nonnegative.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,x).
+ *
+ * x a,b Relative error:
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0,1 0,100 100000 9.8e-15 1.7e-15
+ * IEEE 1,5 0,100 100000 6.5e-15 3.5e-16
+ * IEEE 0,1 1,10000 100000 2.2e-11 3.3e-12
+ * IEEE 1,5 1,10000 100000 1.1e-11 1.7e-13
+ * See also incbet.c.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtr domain a<0, b<0, x<0 0.0
+ *
+ */
+ /* fdtrc()
+ *
+ * Complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * double x, y, fdtrc();
+ *
+ * y = fdtrc( df1, df2, x );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from x to infinity under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density).
+ *
+ *
+ * inf.
+ * -
+ * 1 | | a-1 b-1
+ * 1-P(x) = ------ | t (1-t) dt
+ * B(a,b) | |
+ * -
+ * x
+ *
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,x) in the indicated intervals.
+ * x a,b Relative error:
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0,1 1,100 100000 3.7e-14 5.9e-16
+ * IEEE 1,5 1,100 100000 8.0e-15 1.6e-15
+ * IEEE 0,1 1,10000 100000 1.8e-11 3.5e-13
+ * IEEE 1,5 1,10000 100000 2.0e-11 3.0e-12
+ * See also incbet.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrc domain a<0, b<0, x<0 0.0
+ *
+ */
+ /* fdtri()
+ *
+ * Inverse of complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * double x, p, fdtri();
+ *
+ * x = fdtri( df1, df2, p );
+ *
+ * DESCRIPTION:
+ *
+ * Finds the F density argument x such that the integral
+ * from x to infinity of the F density is equal to the
+ * given probability p.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relations
+ *
+ * z = incbi( df2/2, df1/2, p )
+ * x = df2 (1-z) / (df1 z).
+ *
+ * Note: the following relations hold for the inverse of
+ * the uncomplemented F distribution:
+ *
+ * z = incbi( df1/2, df2/2, p )
+ * x = df2 z / (df1 (1-z)).
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p).
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * For p between .001 and 1:
+ * IEEE 1,100 100000 8.3e-15 4.7e-16
+ * IEEE 1,10000 100000 2.1e-11 1.4e-13
+ * For p between 10^-6 and 10^-3:
+ * IEEE 1,100 50000 1.3e-12 8.4e-15
+ * IEEE 1,10000 50000 3.0e-12 4.8e-14
+ * See also fdtrc.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtri domain p <= 0 or p > 1 0.0
+ * v < 1
+ *
+ */
+
+/* fftr.c
+ *
+ * FFT of Real Valued Sequence
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x[], sine[];
+ * int m;
+ *
+ * fftr( x, m, sine );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the (complex valued) discrete Fourier transform of
+ * the real valued sequence x[]. The input sequence x[] contains
+ * n = 2**m samples. The program fills array sine[k] with
+ * n/4 + 1 values of sin( 2 PI k / n ).
+ *
+ * Data format for complex valued output is real part followed
+ * by imaginary part. The output is developed in the input
+ * array x[].
+ *
+ * The algorithm takes advantage of the fact that the FFT of an
+ * n point real sequence can be obtained from an n/2 point
+ * complex FFT.
+ *
+ * A radix 2 FFT algorithm is used.
+ *
+ * Execution time on an LSI-11/23 with floating point chip
+ * is 1.0 sec for n = 256.
+ *
+ *
+ *
+ * REFERENCE:
+ *
+ * E. Oran Brigham, The Fast Fourier Transform;
+ * Prentice-Hall, Inc., 1974
+ *
+ */
+
+/* ceil()
+ * floor()
+ * frexp()
+ * ldexp()
+ * signbit()
+ * isnan()
+ * isfinite()
+ *
+ * Floating point numeric utilities
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double ceil(), floor(), frexp(), ldexp();
+ * int signbit(), isnan(), isfinite();
+ * double x, y;
+ * int expnt, n;
+ *
+ * y = floor(x);
+ * y = ceil(x);
+ * y = frexp( x, &expnt );
+ * y = ldexp( x, n );
+ * n = signbit(x);
+ * n = isnan(x);
+ * n = isfinite(x);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * All four routines return a double precision floating point
+ * result.
+ *
+ * floor() returns the largest integer less than or equal to x.
+ * It truncates toward minus infinity.
+ *
+ * ceil() returns the smallest integer greater than or equal
+ * to x. It truncates toward plus infinity.
+ *
+ * frexp() extracts the exponent from x. It returns an integer
+ * power of two to expnt and the significand between 0.5 and 1
+ * to y. Thus x = y * 2**expn.
+ *
+ * ldexp() multiplies x by 2**n.
+ *
+ * signbit(x) returns 1 if the sign bit of x is 1, else 0.
+ *
+ * These functions are part of the standard C run time library
+ * for many but not all C compilers. The ones supplied are
+ * written in C for either DEC or IEEE arithmetic. They should
+ * be used only if your compiler library does not already have
+ * them.
+ *
+ * The IEEE versions assume that denormal numbers are implemented
+ * in the arithmetic. Some modifications will be required if
+ * the arithmetic has abrupt rather than gradual underflow.
+ */
+
+/* fresnl.c
+ *
+ * Fresnel integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, S, C;
+ * void fresnl();
+ *
+ * fresnl( x, _&S, _&C );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the Fresnel integrals
+ *
+ * x
+ * -
+ * | |
+ * C(x) = | cos(pi/2 t**2) dt,
+ * | |
+ * -
+ * 0
+ *
+ * x
+ * -
+ * | |
+ * S(x) = | sin(pi/2 t**2) dt.
+ * | |
+ * -
+ * 0
+ *
+ *
+ * The integrals are evaluated by a power series for x < 1.
+ * For x >= 1 auxiliary functions f(x) and g(x) are employed
+ * such that
+ *
+ * C(x) = 0.5 + f(x) sin( pi/2 x**2 ) - g(x) cos( pi/2 x**2 )
+ * S(x) = 0.5 - f(x) cos( pi/2 x**2 ) - g(x) sin( pi/2 x**2 )
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error.
+ *
+ * Arithmetic function domain # trials peak rms
+ * IEEE S(x) 0, 10 10000 2.0e-15 3.2e-16
+ * IEEE C(x) 0, 10 10000 1.8e-15 3.3e-16
+ * DEC S(x) 0, 10 6000 2.2e-16 3.9e-17
+ * DEC C(x) 0, 10 5000 2.3e-16 3.9e-17
+ */
+
+/* gamma.c
+ *
+ * Gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, gamma();
+ * extern int sgngam;
+ *
+ * y = gamma( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns gamma function of the argument. The result is
+ * correctly signed, and the sign (+1 or -1) is also
+ * returned in a global (extern) variable named sgngam.
+ * This variable is also filled in by the logarithmic gamma
+ * function lgam().
+ *
+ * Arguments |x| <= 34 are reduced by recurrence and the function
+ * approximated by a rational function of degree 6/7 in the
+ * interval (2,3). Large arguments are handled by Stirling's
+ * formula. Large negative arguments are made positive using
+ * a reflection formula.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -34, 34 10000 1.3e-16 2.5e-17
+ * IEEE -170,-33 20000 2.3e-15 3.3e-16
+ * IEEE -33, 33 20000 9.4e-16 2.2e-16
+ * IEEE 33, 171.6 20000 2.3e-15 3.2e-16
+ *
+ * Error for arguments outside the test range will be larger
+ * owing to error amplification by the exponential function.
+ *
+ */
+/* lgam()
+ *
+ * Natural logarithm of gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, lgam();
+ * extern int sgngam;
+ *
+ * y = lgam( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of the absolute
+ * value of the gamma function of the argument.
+ * The sign (+1 or -1) of the gamma function is returned in a
+ * global (extern) variable named sgngam.
+ *
+ * For arguments greater than 13, the logarithm of the gamma
+ * function is approximated by the logarithmic version of
+ * Stirling's formula using a polynomial approximation of
+ * degree 4. Arguments between -33 and +33 are reduced by
+ * recurrence to the interval [2,3] of a rational approximation.
+ * The cosecant reflection formula is employed for arguments
+ * less than -33.
+ *
+ * Arguments greater than MAXLGM return MAXNUM and an error
+ * message. MAXLGM = 2.035093e36 for DEC
+ * arithmetic or 2.556348e305 for IEEE arithmetic.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * arithmetic domain # trials peak rms
+ * DEC 0, 3 7000 5.2e-17 1.3e-17
+ * DEC 2.718, 2.035e36 5000 3.9e-17 9.9e-18
+ * IEEE 0, 3 28000 5.4e-16 1.1e-16
+ * IEEE 2.718, 2.556e305 40000 3.5e-16 8.3e-17
+ * The error criterion was relative when the function magnitude
+ * was greater than one but absolute when it was less than one.
+ *
+ * The following test used the relative error criterion, though
+ * at certain points the relative error could be much higher than
+ * indicated.
+ * IEEE -200, -4 10000 4.8e-16 1.3e-16
+ *
+ */
+
+/* gdtr.c
+ *
+ * Gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, gdtr();
+ *
+ * y = gdtr( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from zero to x of the gamma probability
+ * density function:
+ *
+ *
+ * x
+ * b -
+ * a | | b-1 -at
+ * y = ----- | t e dt
+ * - | |
+ * | (b) -
+ * 0
+ *
+ * The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igam( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * gdtr domain x < 0 0.0
+ *
+ */
+ /* gdtrc.c
+ *
+ * Complemented gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, gdtrc();
+ *
+ * y = gdtrc( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from x to infinity of the gamma
+ * probability density function:
+ *
+ *
+ * inf.
+ * b -
+ * a | | b-1 -at
+ * y = ----- | t e dt
+ * - | |
+ * | (b) -
+ * x
+ *
+ * The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igamc( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * gdtrc domain x < 0 0.0
+ *
+ */
+
+/*
+C
+C ..................................................................
+C
+C SUBROUTINE GELS
+C
+C PURPOSE
+C TO SOLVE A SYSTEM OF SIMULTANEOUS LINEAR EQUATIONS WITH
+C SYMMETRIC COEFFICIENT MATRIX UPPER TRIANGULAR PART OF WHICH
+C IS ASSUMED TO BE STORED COLUMNWISE.
+C
+C USAGE
+C CALL GELS(R,A,M,N,EPS,IER,AUX)
+C
+C DESCRIPTION OF PARAMETERS
+C R - M BY N RIGHT HAND SIDE MATRIX. (DESTROYED)
+C ON RETURN R CONTAINS THE SOLUTION OF THE EQUATIONS.
+C A - UPPER TRIANGULAR PART OF THE SYMMETRIC
+C M BY M COEFFICIENT MATRIX. (DESTROYED)
+C M - THE NUMBER OF EQUATIONS IN THE SYSTEM.
+C N - THE NUMBER OF RIGHT HAND SIDE VECTORS.
+C EPS - AN INPUT CONSTANT WHICH IS USED AS RELATIVE
+C TOLERANCE FOR TEST ON LOSS OF SIGNIFICANCE.
+C IER - RESULTING ERROR PARAMETER CODED AS FOLLOWS
+C IER=0 - NO ERROR,
+C IER=-1 - NO RESULT BECAUSE OF M LESS THAN 1 OR
+C PIVOT ELEMENT AT ANY ELIMINATION STEP
+C EQUAL TO 0,
+C IER=K - WARNING DUE TO POSSIBLE LOSS OF SIGNIFI-
+C CANCE INDICATED AT ELIMINATION STEP K+1,
+C WHERE PIVOT ELEMENT WAS LESS THAN OR
+C EQUAL TO THE INTERNAL TOLERANCE EPS TIMES
+C ABSOLUTELY GREATEST MAIN DIAGONAL
+C ELEMENT OF MATRIX A.
+C AUX - AN AUXILIARY STORAGE ARRAY WITH DIMENSION M-1.
+C
+C REMARKS
+C UPPER TRIANGULAR PART OF MATRIX A IS ASSUMED TO BE STORED
+C COLUMNWISE IN M*(M+1)/2 SUCCESSIVE STORAGE LOCATIONS, RIGHT
+C HAND SIDE MATRIX R COLUMNWISE IN N*M SUCCESSIVE STORAGE
+C LOCATIONS. ON RETURN SOLUTION MATRIX R IS STORED COLUMNWISE
+C TOO.
+C THE PROCEDURE GIVES RESULTS IF THE NUMBER OF EQUATIONS M IS
+C GREATER THAN 0 AND PIVOT ELEMENTS AT ALL ELIMINATION STEPS
+C ARE DIFFERENT FROM 0. HOWEVER WARNING IER=K - IF GIVEN -
+C INDICATES POSSIBLE LOSS OF SIGNIFICANCE. IN CASE OF A WELL
+C SCALED MATRIX A AND APPROPRIATE TOLERANCE EPS, IER=K MAY BE
+C INTERPRETED THAT MATRIX A HAS THE RANK K. NO WARNING IS
+C GIVEN IN CASE M=1.
+C ERROR PARAMETER IER=-1 DOES NOT NECESSARILY MEAN THAT
+C MATRIX A IS SINGULAR, AS ONLY MAIN DIAGONAL ELEMENTS
+C ARE USED AS PIVOT ELEMENTS. POSSIBLY SUBROUTINE GELG (WHICH
+C WORKS WITH TOTAL PIVOTING) WOULD BE ABLE TO FIND A SOLUTION.
+C
+C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
+C NONE
+C
+C METHOD
+C SOLUTION IS DONE BY MEANS OF GAUSS-ELIMINATION WITH
+C PIVOTING IN MAIN DIAGONAL, IN ORDER TO PRESERVE
+C SYMMETRY IN REMAINING COEFFICIENT MATRICES.
+C
+C ..................................................................
+C
+*/
+
+/* hyp2f1.c
+ *
+ * Gauss hypergeometric function F
+ * 2 1
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, c, x, y, hyp2f1();
+ *
+ * y = hyp2f1( a, b, c, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * hyp2f1( a, b, c, x ) = F ( a, b; c; x )
+ * 2 1
+ *
+ * inf.
+ * - a(a+1)...(a+k) b(b+1)...(b+k) k+1
+ * = 1 + > ----------------------------- x .
+ * - c(c+1)...(c+k) (k+1)!
+ * k = 0
+ *
+ * Cases addressed are
+ * Tests and escapes for negative integer a, b, or c
+ * Linear transformation if c - a or c - b negative integer
+ * Special case c = a or c = b
+ * Linear transformation for x near +1
+ * Transformation for x < -0.5
+ * Psi function expansion if x > 0.5 and c - a - b integer
+ * Conditionally, a recurrence on c to make c-a-b > 0
+ *
+ * |x| > 1 is rejected.
+ *
+ * The parameters a, b, c are considered to be integer
+ * valued if they are within 1.0e-14 of the nearest integer
+ * (1.0e-13 for IEEE arithmetic).
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error (-1 < x < 1):
+ * arithmetic domain # trials peak rms
+ * IEEE -1,7 230000 1.2e-11 5.2e-14
+ *
+ * Several special cases also tested with a, b, c in
+ * the range -7 to 7.
+ *
+ * ERROR MESSAGES:
+ *
+ * A "partial loss of precision" message is printed if
+ * the internally estimated relative error exceeds 1^-12.
+ * A "singularity" message is printed on overflow or
+ * in cases not addressed (such as x < -1).
+ */
+
+/* hyperg.c
+ *
+ * Confluent hypergeometric function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, hyperg();
+ *
+ * y = hyperg( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the confluent hypergeometric function
+ *
+ * 1 2
+ * a x a(a+1) x
+ * F ( a,b;x ) = 1 + ---- + --------- + ...
+ * 1 1 b 1! b(b+1) 2!
+ *
+ * Many higher transcendental functions are special cases of
+ * this power series.
+ *
+ * As is evident from the formula, b must not be a negative
+ * integer or zero unless a is an integer with 0 >= a > b.
+ *
+ * The routine attempts both a direct summation of the series
+ * and an asymptotic expansion. In each case error due to
+ * roundoff, cancellation, and nonconvergence is estimated.
+ * The result with smaller estimated error is returned.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a, b, x), all three variables
+ * ranging from 0 to 30.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 2000 1.2e-15 1.3e-16
+ * IEEE 0,30 30000 1.8e-14 1.1e-15
+ *
+ * Larger errors can be observed when b is near a negative
+ * integer or zero. Certain combinations of arguments yield
+ * serious cancellation error in the power series summation
+ * and also are not in the region of near convergence of the
+ * asymptotic series. An error message is printed if the
+ * self-estimated relative error is greater than 1.0e-12.
+ *
+ */
+
+/* i0.c
+ *
+ * Modified Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i0();
+ *
+ * y = i0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order zero of the
+ * argument.
+ *
+ * The function is defined as i0(x) = j0( ix ).
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 6000 8.2e-17 1.9e-17
+ * IEEE 0,30 30000 5.8e-16 1.4e-16
+ *
+ */
+ /* i0e.c
+ *
+ * Modified Bessel function of order zero,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i0e();
+ *
+ * y = i0e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order zero of the argument.
+ *
+ * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 30000 5.4e-16 1.2e-16
+ * See i0().
+ *
+ */
+
+/* i1.c
+ *
+ * Modified Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i1();
+ *
+ * y = i1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order one of the
+ * argument.
+ *
+ * The function is defined as i1(x) = -i j1( ix ).
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 3400 1.2e-16 2.3e-17
+ * IEEE 0, 30 30000 1.9e-15 2.1e-16
+ *
+ *
+ */
+ /* i1e.c
+ *
+ * Modified Bessel function of order one,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i1e();
+ *
+ * y = i1e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order one of the argument.
+ *
+ * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 2.0e-15 2.0e-16
+ * See i1().
+ *
+ */
+
+/* igam.c
+ *
+ * Incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, y, igam();
+ *
+ * y = igam( a, x );
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ * x
+ * -
+ * 1 | | -t a-1
+ * igam(a,x) = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * 0
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 200000 3.6e-14 2.9e-15
+ * IEEE 0,100 300000 9.9e-14 1.5e-14
+ */
+ /* igamc()
+ *
+ * Complemented incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, y, igamc();
+ *
+ * y = igamc( a, x );
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ *
+ * igamc(a,x) = 1 - igam(a,x)
+ *
+ * inf.
+ * -
+ * 1 | | -t a-1
+ * = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * x
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ * ACCURACY:
+ *
+ * Tested at random a, x.
+ * a x Relative error:
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0.5,100 0,100 200000 1.9e-14 1.7e-15
+ * IEEE 0.01,0.5 0,100 200000 1.4e-13 1.6e-15
+ */
+
+/* igami()
+ *
+ * Inverse of complemented imcomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, p, igami();
+ *
+ * x = igami( a, p );
+ *
+ * DESCRIPTION:
+ *
+ * Given p, the function finds x such that
+ *
+ * igamc( a, x ) = p.
+ *
+ * Starting with the approximate value
+ *
+ * 3
+ * x = a t
+ *
+ * where
+ *
+ * t = 1 - d - ndtri(p) sqrt(d)
+ *
+ * and
+ *
+ * d = 1/9a,
+ *
+ * the routine performs up to 10 Newton iterations to find the
+ * root of igamc(a,x) - p = 0.
+ *
+ * ACCURACY:
+ *
+ * Tested at random a, p in the intervals indicated.
+ *
+ * a p Relative error:
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0.5,100 0,0.5 100000 1.0e-14 1.7e-15
+ * IEEE 0.01,0.5 0,0.5 100000 9.0e-14 3.4e-15
+ * IEEE 0.5,10000 0,0.5 20000 2.3e-13 3.8e-14
+ */
+
+/* incbet.c
+ *
+ * Incomplete beta integral
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, incbet();
+ *
+ * y = incbet( a, b, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns incomplete beta integral of the arguments, evaluated
+ * from zero to x. The function is defined as
+ *
+ * x
+ * - -
+ * | (a+b) | | a-1 b-1
+ * ----------- | t (1-t) dt.
+ * - - | |
+ * | (a) | (b) -
+ * 0
+ *
+ * The domain of definition is 0 <= x <= 1. In this
+ * implementation a and b are restricted to positive values.
+ * The integral from x to 1 may be obtained by the symmetry
+ * relation
+ *
+ * 1 - incbet( a, b, x ) = incbet( b, a, 1-x ).
+ *
+ * The integral is evaluated by a continued fraction expansion
+ * or, when b*x is small, by a power series.
+ *
+ * ACCURACY:
+ *
+ * Tested at uniformly distributed random points (a,b,x) with a and b
+ * in "domain" and x between 0 and 1.
+ * Relative error
+ * arithmetic domain # trials peak rms
+ * IEEE 0,5 10000 6.9e-15 4.5e-16
+ * IEEE 0,85 250000 2.2e-13 1.7e-14
+ * IEEE 0,1000 30000 5.3e-12 6.3e-13
+ * IEEE 0,10000 250000 9.3e-11 7.1e-12
+ * IEEE 0,100000 10000 8.7e-10 4.8e-11
+ * Outputs smaller than the IEEE gradual underflow threshold
+ * were excluded from these statistics.
+ *
+ * ERROR MESSAGES:
+ * message condition value returned
+ * incbet domain x<0, x>1 0.0
+ * incbet underflow 0.0
+ */
+
+/* incbi()
+ *
+ * Inverse of imcomplete beta integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, incbi();
+ *
+ * x = incbi( a, b, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given y, the function finds x such that
+ *
+ * incbet( a, b, x ) = y .
+ *
+ * The routine performs interval halving or Newton iterations to find the
+ * root of incbet(a,b,x) - y = 0.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * x a,b
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0,1 .5,10000 50000 5.8e-12 1.3e-13
+ * IEEE 0,1 .25,100 100000 1.8e-13 3.9e-15
+ * IEEE 0,1 0,5 50000 1.1e-12 5.5e-15
+ * VAX 0,1 .5,100 25000 3.5e-14 1.1e-15
+ * With a and b constrained to half-integer or integer values:
+ * IEEE 0,1 .5,10000 50000 5.8e-12 1.1e-13
+ * IEEE 0,1 .5,100 100000 1.7e-14 7.9e-16
+ * With a = .5, b constrained to half-integer or integer values:
+ * IEEE 0,1 .5,10000 10000 8.3e-11 1.0e-11
+ */
+
+/* iv.c
+ *
+ * Modified Bessel function of noninteger order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, iv();
+ *
+ * y = iv( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order v of the
+ * argument. If x is negative, v must be integer valued.
+ *
+ * The function is defined as Iv(x) = Jv( ix ). It is
+ * here computed in terms of the confluent hypergeometric
+ * function, according to the formula
+ *
+ * v -x
+ * Iv(x) = (x/2) e hyperg( v+0.5, 2v+1, 2x ) / gamma(v+1)
+ *
+ * If v is a negative integer, then v is replaced by -v.
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (v, x), with v between 0 and
+ * 30, x between 0 and 28.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 2000 3.1e-15 5.4e-16
+ * IEEE 0,30 10000 1.7e-14 2.7e-15
+ *
+ * Accuracy is diminished if v is near a negative integer.
+ *
+ * See also hyperg.c.
+ *
+ */
+
+/* j0.c
+ *
+ * Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, j0();
+ *
+ * y = j0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order zero of the argument.
+ *
+ * The domain is divided into the intervals [0, 5] and
+ * (5, infinity). In the first interval the following rational
+ * approximation is used:
+ *
+ *
+ * 2 2
+ * (w - r ) (w - r ) P (w) / Q (w)
+ * 1 2 3 8
+ *
+ * 2
+ * where w = x and the two r's are zeros of the function.
+ *
+ * In the second interval, the Hankel asymptotic expansion
+ * is employed with two rational functions of degree 6/6
+ * and 7/7.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 10000 4.4e-17 6.3e-18
+ * IEEE 0, 30 60000 4.2e-16 1.1e-16
+ *
+ */
+ /* y0.c
+ *
+ * Bessel function of the second kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y0();
+ *
+ * y = y0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind, of order
+ * zero, of the argument.
+ *
+ * The domain is divided into the intervals [0, 5] and
+ * (5, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute
+ * y0(x) = R(x) + 2 * log(x) * j0(x) / PI.
+ * Thus a call to j0() is required.
+ *
+ * In the second interval, the Hankel asymptotic expansion
+ * is employed with two rational functions of degree 6/6
+ * and 7/7.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error, when y0(x) < 1; else relative error:
+ *
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 9400 7.0e-17 7.9e-18
+ * IEEE 0, 30 30000 1.3e-15 1.6e-16
+ *
+ */
+
+/* j1.c
+ *
+ * Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, j1();
+ *
+ * y = j1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order one of the argument.
+ *
+ * The domain is divided into the intervals [0, 8] and
+ * (8, infinity). In the first interval a 24 term Chebyshev
+ * expansion is used. In the second, the asymptotic
+ * trigonometric representation is employed using two
+ * rational functions of degree 5/5.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 10000 4.0e-17 1.1e-17
+ * IEEE 0, 30 30000 2.6e-16 1.1e-16
+ *
+ *
+ */
+ /* y1.c
+ *
+ * Bessel function of second kind of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y1();
+ *
+ * y = y1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind of order one
+ * of the argument.
+ *
+ * The domain is divided into the intervals [0, 8] and
+ * (8, infinity). In the first interval a 25 term Chebyshev
+ * expansion is used, and a call to j1() is required.
+ * In the second, the asymptotic trigonometric representation
+ * is employed using two rational functions of degree 5/5.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 10000 8.6e-17 1.3e-17
+ * IEEE 0, 30 30000 1.0e-15 1.3e-16
+ *
+ * (error criterion relative when |y1| > 1).
+ *
+ */
+
+/* jn.c
+ *
+ * Bessel function of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double x, y, jn();
+ *
+ * y = jn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The ratio of jn(x) to j0(x) is computed by backward
+ * recurrence. First the ratio jn/jn-1 is found by a
+ * continued fraction expansion. Then the recurrence
+ * relating successive orders is applied until j0 or j1 is
+ * reached.
+ *
+ * If n = 0 or 1 the routine for j0 or j1 is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic range # trials peak rms
+ * DEC 0, 30 5500 6.9e-17 9.3e-18
+ * IEEE 0, 30 5000 4.4e-16 7.9e-17
+ *
+ *
+ * Not suitable for large n or x. Use jv() instead.
+ *
+ */
+
+/* jv.c
+ *
+ * Bessel function of noninteger order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, jv();
+ *
+ * y = jv( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order v of the argument,
+ * where v is real. Negative x is allowed if v is an integer.
+ *
+ * Several expansions are included: the ascending power
+ * series, the Hankel expansion, and two transitional
+ * expansions for large v. If v is not too large, it
+ * is reduced by recurrence to a region of best accuracy.
+ * The transitional expansions give 12D accuracy for v > 500.
+ *
+ *
+ *
+ * ACCURACY:
+ * Results for integer v are indicated by *, where x and v
+ * both vary from -125 to +125. Otherwise,
+ * x ranges from 0 to 125, v ranges as indicated by "domain."
+ * Error criterion is absolute, except relative when |jv()| > 1.
+ *
+ * arithmetic v domain x domain # trials peak rms
+ * IEEE 0,125 0,125 100000 4.6e-15 2.2e-16
+ * IEEE -125,0 0,125 40000 5.4e-11 3.7e-13
+ * IEEE 0,500 0,500 20000 4.4e-15 4.0e-16
+ * Integer v:
+ * IEEE -125,125 -125,125 50000 3.5e-15* 1.9e-16*
+ *
+ */
+
+/* k0.c
+ *
+ * Modified Bessel function, third kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k0();
+ *
+ * y = k0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of the third kind
+ * of order zero of the argument.
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at 2000 random points between 0 and 8. Peak absolute
+ * error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 3100 1.3e-16 2.1e-17
+ * IEEE 0, 30 30000 1.2e-15 1.6e-16
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * K0 domain x <= 0 MAXNUM
+ *
+ */
+ /* k0e()
+ *
+ * Modified Bessel function, third kind, order zero,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k0e();
+ *
+ * y = k0e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order zero of the argument.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 1.4e-15 1.4e-16
+ * See k0().
+ *
+ */
+
+/* k1.c
+ *
+ * Modified Bessel function, third kind, order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k1();
+ *
+ * y = k1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the modified Bessel function of the third kind
+ * of order one of the argument.
+ *
+ * The range is partitioned into the two intervals [0,2] and
+ * (2, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 3300 8.9e-17 2.2e-17
+ * IEEE 0, 30 30000 1.2e-15 1.6e-16
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * k1 domain x <= 0 MAXNUM
+ *
+ */
+ /* k1e.c
+ *
+ * Modified Bessel function, third kind, order one,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k1e();
+ *
+ * y = k1e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order one of the argument:
+ *
+ * k1e(x) = exp(x) * k1(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 7.8e-16 1.2e-16
+ * See k1().
+ *
+ */
+
+/* kn.c
+ *
+ * Modified Bessel function, third kind, integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, kn();
+ * int n;
+ *
+ * y = kn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of the third kind
+ * of order n of the argument.
+ *
+ * The range is partitioned into the two intervals [0,9.55] and
+ * (9.55, infinity). An ascending power series is used in the
+ * low range, and an asymptotic expansion in the high range.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 3000 1.3e-9 5.8e-11
+ * IEEE 0,30 90000 1.8e-8 3.0e-10
+ *
+ * Error is high only near the crossover point x = 9.55
+ * between the two expansions used.
+ */
+
+
+/* Re Kolmogorov statistics, here is Birnbaum and Tingey's formula for the
+ distribution of D+, the maximum of all positive deviations between a
+ theoretical distribution function P(x) and an empirical one Sn(x)
+ from n samples.
+
+ +
+ D = sup [ P(x) - Sn(x) ]
+ n -inf < x < inf
+
+
+ [n(1-e)]
+ + - v-1 n-v
+ Pr{D > e} = > C e (e + v/n) (1 - e - v/n)
+ n - n v
+ v=0
+ [n(1-e)] is the largest integer not exceeding n(1-e).
+ nCv is the number of combinations of n things taken v at a time.
+
+ Exact Smirnov statistic, for one-sided test:
+double
+smirnov (n, e)
+ int n;
+ double e;
+
+ Kolmogorov's limiting distribution of two-sided test, returns
+ probability that sqrt(n) * max deviation > y,
+ or that max deviation > y/sqrt(n).
+ The approximation is useful for the tail of the distribution
+ when n is large.
+double
+kolmogorov (y)
+ double y;
+
+
+ Functional inverse of Smirnov distribution
+ finds e such that smirnov(n,e) = p.
+double
+smirnovi (n, p)
+ int n;
+ double p;
+
+ Functional inverse of Kolmogorov statistic for two-sided test.
+ Finds y such that kolmogorov(y) = p.
+ If e = smirnovi (n,p), then kolmogi(2 * p) / sqrt(n) should
+ be close to e.
+double
+kolmogi (p)
+ double p;
+ */
+
+/* Levnsn.c */
+/* Levinson-Durbin LPC
+ *
+ * | R0 R1 R2 ... RN-1 | | A1 | | -R1 |
+ * | R1 R0 R1 ... RN-2 | | A2 | | -R2 |
+ * | R2 R1 R0 ... RN-3 | | A3 | = | -R3 |
+ * | ... | | ...| | ... |
+ * | RN-1 RN-2... R0 | | AN | | -RN |
+ *
+ * Ref: John Makhoul, "Linear Prediction, A Tutorial Review"
+ * Proc. IEEE Vol. 63, PP 561-580 April, 1975.
+ *
+ * R is the input autocorrelation function. R0 is the zero lag
+ * term. A is the output array of predictor coefficients. Note
+ * that a filter impulse response has a coefficient of 1.0 preceding
+ * A1. E is an array of mean square error for each prediction order
+ * 1 to N. REFL is an output array of the reflection coefficients.
+ */
+
+/* log.c
+ *
+ * Natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, log();
+ *
+ * y = log( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the logarithm
+ * of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting z = 2(x-1)/x+1),
+ *
+ * log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 150000 1.44e-16 5.06e-17
+ * IEEE +-MAXNUM 30000 1.20e-16 4.78e-17
+ * DEC 0, 10 170000 1.8e-17 6.3e-18
+ *
+ * In the tests over the interval [+-MAXNUM], the logarithms
+ * of the random arguments were uniformly distributed over
+ * [0, MAXLOG].
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity: x = 0; returns -INFINITY
+ * log domain: x < 0; returns NAN
+ */
+
+/* log10.c
+ *
+ * Common logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, log10();
+ *
+ * y = log10( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns logarithm to the base 10 of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. The logarithm of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 30000 1.5e-16 5.0e-17
+ * IEEE 0, MAXNUM 30000 1.4e-16 4.8e-17
+ * DEC 1, MAXNUM 50000 2.5e-17 6.0e-18
+ *
+ * In the tests over the interval [1, MAXNUM], the logarithms
+ * of the random arguments were uniformly distributed over
+ * [0, MAXLOG].
+ *
+ * ERROR MESSAGES:
+ *
+ * log10 singularity: x = 0; returns -INFINITY
+ * log10 domain: x < 0; returns NAN
+ */
+
+/* log2.c
+ *
+ * Base 2 logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, log2();
+ *
+ * y = log2( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base 2 logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the base e
+ * logarithm of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting z = 2(x-1)/x+1),
+ *
+ * log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 30000 2.0e-16 5.5e-17
+ * IEEE exp(+-700) 40000 1.3e-16 4.6e-17
+ *
+ * In the tests over the interval [exp(+-700)], the logarithms
+ * of the random arguments were uniformly distributed.
+ *
+ * ERROR MESSAGES:
+ *
+ * log2 singularity: x = 0; returns -INFINITY
+ * log2 domain: x < 0; returns NAN
+ */
+
+/* lrand.c
+ *
+ * Pseudorandom number generator
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long y, drand();
+ *
+ * drand( &y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Yields a long integer random number.
+ *
+ * The three-generator congruential algorithm by Brian
+ * Wichmann and David Hill (BYTE magazine, March, 1987,
+ * pp 127-8) is used. The period, given by them, is
+ * 6953607871644.
+ *
+ *
+ */
+
+/* lsqrt.c
+ *
+ * Integer square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long x, y;
+ * long lsqrt();
+ *
+ * y = lsqrt( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns a long integer square root of the long integer
+ * argument. The computation is by binary long division.
+ *
+ * The largest possible result is lsqrt(2,147,483,647)
+ * = 46341.
+ *
+ * If x < 0, the square root of |x| is returned, and an
+ * error message is printed.
+ *
+ *
+ * ACCURACY:
+ *
+ * An extra, roundoff, bit is computed; hence the result
+ * is the nearest integer to the actual square root.
+ * NOTE: only DEC arithmetic is currently supported.
+ *
+ */
+
+/* minv.c
+ *
+ * Matrix inversion
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n, errcod;
+ * double A[n*n], X[n*n];
+ * double B[n];
+ * int IPS[n];
+ * int minv();
+ *
+ * errcod = minv( A, X, n, B, IPS );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the inverse of the n by n matrix A. The result goes
+ * to X. B and IPS are scratch pad arrays of length n.
+ * The contents of matrix A are destroyed.
+ *
+ * The routine returns nonzero on error; error messages are printed
+ * by subroutine simq().
+ *
+ */
+
+/* mmmpy.c
+ *
+ * Matrix multiply
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int r, c;
+ * double A[r*c], B[c*r], Y[r*r];
+ *
+ * mmmpy( r, c, A, B, Y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Y = A B
+ * c-1
+ * --
+ * Y[i][j] = > A[i][k] B[k][j]
+ * --
+ * k=0
+ *
+ * Multiplies an r (rows) by c (columns) matrix A on the left
+ * by a c (rows) by r (columns) matrix B on the right
+ * to produce an r by r matrix Y.
+ *
+ *
+ */
+
+/* mtherr.c
+ *
+ * Library common error handling routine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * char *fctnam;
+ * int code;
+ * int mtherr();
+ *
+ * mtherr( fctnam, code );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This routine may be called to report one of the following
+ * error conditions (in the include file math.h).
+ *
+ * Mnemonic Value Significance
+ *
+ * DOMAIN 1 argument domain error
+ * SING 2 function singularity
+ * OVERFLOW 3 overflow range error
+ * UNDERFLOW 4 underflow range error
+ * TLOSS 5 total loss of precision
+ * PLOSS 6 partial loss of precision
+ * EDOM 33 Unix domain error code
+ * ERANGE 34 Unix range error code
+ *
+ * The default version of the file prints the function name,
+ * passed to it by the pointer fctnam, followed by the
+ * error condition. The display is directed to the standard
+ * output device. The routine then returns to the calling
+ * program. Users may wish to modify the program to abort by
+ * calling exit() under severe error conditions such as domain
+ * errors.
+ *
+ * Since all error conditions pass control to this function,
+ * the display may be easily changed, eliminated, or directed
+ * to an error logging device.
+ *
+ * SEE ALSO:
+ *
+ * math.h
+ *
+ */
+
+/* mtransp.c
+ *
+ * Matrix transpose
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double A[n*n], T[n*n];
+ *
+ * mtransp( n, A, T );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * T[r][c] = A[c][r]
+ *
+ *
+ * Transposes the n by n square matrix A and puts the result in T.
+ * The output, T, may occupy the same storage as A.
+ *
+ *
+ *
+ */
+
+/* mvmpy.c
+ *
+ * Matrix times vector
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int r, c;
+ * double A[r*c], V[c], Y[r];
+ *
+ * mvmpy( r, c, A, V, Y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * c-1
+ * --
+ * Y[j] = > A[j][k] V[k] , j = 1, ..., r
+ * --
+ * k=0
+ *
+ * Multiplies the r (rows) by c (columns) matrix A on the left
+ * by column vector V of dimension c on the right
+ * to produce a (column) vector Y output of dimension r.
+ *
+ *
+ *
+ *
+ */
+
+/* nbdtr.c
+ *
+ * Negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtr();
+ *
+ * y = nbdtr( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the negative
+ * binomial distribution:
+ *
+ * k
+ * -- ( n+j-1 ) n j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=0
+ *
+ * In a sequence of Bernoulli trials, this is the probability
+ * that k or fewer failures precede the nth success.
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p), with p between 0 and 1.
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 100000 1.7e-13 8.8e-15
+ * See also incbet.c.
+ *
+ */
+ /* nbdtrc.c
+ *
+ * Complemented negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtrc();
+ *
+ * y = nbdtrc( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the negative
+ * binomial distribution:
+ *
+ * inf
+ * -- ( n+j-1 ) n j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=k+1
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p), with p between 0 and 1.
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 100000 1.7e-13 8.8e-15
+ * See also incbet.c.
+ */
+
+/* nbdtrc
+ *
+ * Complemented negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtrc();
+ *
+ * y = nbdtrc( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the negative
+ * binomial distribution:
+ *
+ * inf
+ * -- ( n+j-1 ) n j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=k+1
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * See incbet.c.
+ */
+ /* nbdtri
+ *
+ * Functional inverse of negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtri();
+ *
+ * p = nbdtri( k, n, y );
+ *
+ * DESCRIPTION:
+ *
+ * Finds the argument p such that nbdtr(k,n,p) is equal to y.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,y), with y between 0 and 1.
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 100000 1.5e-14 8.5e-16
+ * See also incbi.c.
+ */
+
+/* ndtr.c
+ *
+ * Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, ndtr();
+ *
+ * y = ndtr( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the Gaussian probability density
+ * function, integrated from minus infinity to x:
+ *
+ * x
+ * -
+ * 1 | | 2
+ * ndtr(x) = --------- | exp( - t /2 ) dt
+ * sqrt(2pi) | |
+ * -
+ * -inf.
+ *
+ * = ( 1 + erf(z) ) / 2
+ * = erfc(z) / 2
+ *
+ * where z = x/sqrt(2). Computation is via the functions
+ * erf and erfc.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -13,0 8000 2.1e-15 4.8e-16
+ * IEEE -13,0 30000 3.4e-14 6.7e-15
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * erfc underflow x > 37.519379347 0.0
+ *
+ */
+ /* erf.c
+ *
+ * Error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, erf();
+ *
+ * y = erf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The integral is
+ *
+ * x
+ * -
+ * 2 | | 2
+ * erf(x) = -------- | exp( - t ) dt.
+ * sqrt(pi) | |
+ * -
+ * 0
+ *
+ * The magnitude of x is limited to 9.231948545 for DEC
+ * arithmetic; 1 or -1 is returned outside this range.
+ *
+ * For 0 <= |x| < 1, erf(x) = x * P4(x**2)/Q5(x**2); otherwise
+ * erf(x) = 1 - erfc(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,1 14000 4.7e-17 1.5e-17
+ * IEEE 0,1 30000 3.7e-16 1.0e-16
+ *
+ */
+ /* erfc.c
+ *
+ * Complementary error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, erfc();
+ *
+ * y = erfc( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * 1 - erf(x) =
+ *
+ * inf.
+ * -
+ * 2 | | 2
+ * erfc(x) = -------- | exp( - t ) dt
+ * sqrt(pi) | |
+ * -
+ * x
+ *
+ *
+ * For small x, erfc(x) = 1 - erf(x); otherwise rational
+ * approximations are computed.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 9.2319 12000 5.1e-16 1.2e-16
+ * IEEE 0,26.6417 30000 5.7e-14 1.5e-14
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * erfc underflow x > 9.231948545 (DEC) 0.0
+ *
+ *
+ */
+
+/* ndtri.c
+ *
+ * Inverse of Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, ndtri();
+ *
+ * x = ndtri( y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the argument, x, for which the area under the
+ * Gaussian probability density function (integrated from
+ * minus infinity to x) is equal to y.
+ *
+ *
+ * For small arguments 0 < y < exp(-2), the program computes
+ * z = sqrt( -2.0 * log(y) ); then the approximation is
+ * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).
+ * There are two rational functions P/Q, one for 0 < y < exp(-32)
+ * and the other for y up to exp(-2). For larger arguments,
+ * w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0.125, 1 5500 9.5e-17 2.1e-17
+ * DEC 6e-39, 0.135 3500 5.7e-17 1.3e-17
+ * IEEE 0.125, 1 20000 7.2e-16 1.3e-16
+ * IEEE 3e-308, 0.135 50000 4.6e-16 9.8e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ndtri domain x <= 0 -MAXNUM
+ * ndtri domain x >= 1 MAXNUM
+ *
+ */
+
+/* pdtr.c
+ *
+ * Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * double m, y, pdtr();
+ *
+ * y = pdtr( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the first k terms of the Poisson
+ * distribution:
+ *
+ * k j
+ * -- -m m
+ * > e --
+ * -- j!
+ * j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the relation
+ *
+ * y = pdtr( k, m ) = igamc( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ */
+ /* pdtrc()
+ *
+ * Complemented poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * double m, y, pdtrc();
+ *
+ * y = pdtrc( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the Poisson
+ * distribution:
+ *
+ * inf. j
+ * -- -m m
+ * > e --
+ * -- j!
+ * j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the formula
+ *
+ * y = pdtrc( k, m ) = igam( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam.c.
+ *
+ */
+ /* pdtri()
+ *
+ * Inverse Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * double m, y, pdtr();
+ *
+ * m = pdtri( k, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Poisson variable x such that the integral
+ * from 0 to x of the Poisson density is equal to the
+ * given probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ * m = igami( k+1, y ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igami.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * pdtri domain y < 0 or y >= 1 0.0
+ * k < 0
+ *
+ */
+
+/* polevl.c
+ * p1evl.c
+ *
+ * Evaluate polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * double x, y, coef[N+1], polevl[];
+ *
+ * y = polevl( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates polynomial of degree N:
+ *
+ * 2 N
+ * y = C + C x + C x +...+ C x
+ * 0 1 2 N
+ *
+ * Coefficients are stored in reverse order:
+ *
+ * coef[0] = C , ..., coef[N] = C .
+ * N 0
+ *
+ * The function p1evl() assumes that coef[N] = 1.0 and is
+ * omitted from the array. Its calling arguments are
+ * otherwise the same as polevl().
+ *
+ *
+ * SPEED:
+ *
+ * In the interest of speed, there are no checks for out
+ * of bounds arithmetic. This routine is used by most of
+ * the functions in the library. Depending on available
+ * equipment features, the user may wish to rewrite the
+ * program in microcode or assembly language.
+ *
+ */
+
+/* polmisc.c
+ * Square root, sine, cosine, and arctangent of polynomial.
+ * See polyn.c for data structures and discussion.
+ */
+
+/* polrt.c
+ *
+ * Find roots of a polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct
+ * {
+ * double r;
+ * double i;
+ * }cmplx;
+ *
+ * double xcof[], cof[];
+ * int m;
+ * cmplx root[];
+ *
+ * polrt( xcof, cof, m, root )
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Iterative determination of the roots of a polynomial of
+ * degree m whose coefficient vector is xcof[]. The
+ * coefficients are arranged in ascending order; i.e., the
+ * coefficient of x**m is xcof[m].
+ *
+ * The array cof[] is working storage the same size as xcof[].
+ * root[] is the output array containing the complex roots.
+ *
+ *
+ * ACCURACY:
+ *
+ * Termination depends on evaluation of the polynomial at
+ * the trial values of the roots. The values of multiple roots
+ * or of roots that are nearly equal may have poor relative
+ * accuracy after the first root in the neighborhood has been
+ * found.
+ *
+ */
+
+/* polyn.c
+ * polyr.c
+ * Arithmetic operations on polynomials
+ *
+ * In the following descriptions a, b, c are polynomials of degree
+ * na, nb, nc respectively. The degree of a polynomial cannot
+ * exceed a run-time value MAXPOL. An operation that attempts
+ * to use or generate a polynomial of higher degree may produce a
+ * result that suffers truncation at degree MAXPOL. The value of
+ * MAXPOL is set by calling the function
+ *
+ * polini( maxpol );
+ *
+ * where maxpol is the desired maximum degree. This must be
+ * done prior to calling any of the other functions in this module.
+ * Memory for internal temporary polynomial storage is allocated
+ * by polini().
+ *
+ * Each polynomial is represented by an array containing its
+ * coefficients, together with a separately declared integer equal
+ * to the degree of the polynomial. The coefficients appear in
+ * ascending order; that is,
+ *
+ * 2 na
+ * a(x) = a[0] + a[1] * x + a[2] * x + ... + a[na] * x .
+ *
+ *
+ *
+ * sum = poleva( a, na, x ); Evaluate polynomial a(t) at t = x.
+ * polprt( a, na, D ); Print the coefficients of a to D digits.
+ * polclr( a, na ); Set a identically equal to zero, up to a[na].
+ * polmov( a, na, b ); Set b = a.
+ * poladd( a, na, b, nb, c ); c = b + a, nc = max(na,nb)
+ * polsub( a, na, b, nb, c ); c = b - a, nc = max(na,nb)
+ * polmul( a, na, b, nb, c ); c = b * a, nc = na+nb
+ *
+ *
+ * Division:
+ *
+ * i = poldiv( a, na, b, nb, c ); c = b / a, nc = MAXPOL
+ *
+ * returns i = the degree of the first nonzero coefficient of a.
+ * The computed quotient c must be divided by x^i. An error message
+ * is printed if a is identically zero.
+ *
+ *
+ * Change of variables:
+ * If a and b are polynomials, and t = a(x), then
+ * c(t) = b(a(x))
+ * is a polynomial found by substituting a(x) for t. The
+ * subroutine call for this is
+ *
+ * polsbt( a, na, b, nb, c );
+ *
+ *
+ * Notes:
+ * poldiv() is an integer routine; poleva() is double.
+ * Any of the arguments a, b, c may refer to the same array.
+ *
+ */
+
+/* pow.c
+ *
+ * Power function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, z, pow();
+ *
+ * z = pow( x, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes x raised to the yth power. Analytically,
+ *
+ * x**y = exp( y log(x) ).
+ *
+ * Following Cody and Waite, this program uses a lookup table
+ * of 2**-i/16 and pseudo extended precision arithmetic to
+ * obtain an extra three bits of accuracy in both the logarithm
+ * and the exponential.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -26,26 30000 4.2e-16 7.7e-17
+ * DEC -26,26 60000 4.8e-17 9.1e-18
+ * 1/26 < x < 26, with log(x) uniformly distributed.
+ * -26 < y < 26, y uniformly distributed.
+ * IEEE 0,8700 30000 1.5e-14 2.1e-15
+ * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * pow overflow x**y > MAXNUM INFINITY
+ * pow underflow x**y < 1/MAXNUM 0.0
+ * pow domain x<0 and y noninteger 0.0
+ *
+ */
+
+/* powi.c
+ *
+ * Real raised to integer power
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, powi();
+ * int n;
+ *
+ * y = powi( x, n );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns argument x raised to the nth power.
+ * The routine efficiently decomposes n as a sum of powers of
+ * two. The desired power is a product of two-to-the-kth
+ * powers of x. Thus to compute the 32767 power of x requires
+ * 28 multiplications instead of 32767 multiplications.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error:
+ * arithmetic x domain n domain # trials peak rms
+ * DEC .04,26 -26,26 100000 2.7e-16 4.3e-17
+ * IEEE .04,26 -26,26 50000 2.0e-15 3.8e-16
+ * IEEE 1,2 -1022,1023 50000 8.6e-14 1.6e-14
+ *
+ * Returns MAXNUM on overflow, zero on underflow.
+ *
+ */
+
+/* psi.c
+ *
+ * Psi (digamma) function
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, psi();
+ *
+ * y = psi( x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * d -
+ * psi(x) = -- ln | (x)
+ * dx
+ *
+ * is the logarithmic derivative of the gamma function.
+ * For integer x,
+ * n-1
+ * -
+ * psi(n) = -EUL + > 1/k.
+ * -
+ * k=1
+ *
+ * This formula is used for 0 < n <= 10. If x is negative, it
+ * is transformed to a positive argument by the reflection
+ * formula psi(1-x) = psi(x) + pi cot(pi x).
+ * For general positive x, the argument is made greater than 10
+ * using the recurrence psi(x+1) = psi(x) + 1/x.
+ * Then the following asymptotic expansion is applied:
+ *
+ * inf. B
+ * - 2k
+ * psi(x) = log(x) - 1/2x - > -------
+ * - 2k
+ * k=1 2k x
+ *
+ * where the B2k are Bernoulli numbers.
+ *
+ * ACCURACY:
+ * Relative error (except absolute when |psi| < 1):
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 2500 1.7e-16 2.0e-17
+ * IEEE 0,30 30000 1.3e-15 1.4e-16
+ * IEEE -30,0 40000 1.5e-15 2.2e-16
+ *
+ * ERROR MESSAGES:
+ * message condition value returned
+ * psi singularity x integer <=0 MAXNUM
+ */
+
+/* revers.c
+ *
+ * Reversion of power series
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * extern int MAXPOL;
+ * int n;
+ * double x[n+1], y[n+1];
+ *
+ * polini(n);
+ * revers( y, x, n );
+ *
+ * Note, polini() initializes the polynomial arithmetic subroutines;
+ * see polyn.c.
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *
+ * inf
+ * - i
+ * y(x) = > a x
+ * - i
+ * i=1
+ *
+ * then
+ *
+ * inf
+ * - j
+ * x(y) = > A y ,
+ * - j
+ * j=1
+ *
+ * where
+ * 1
+ * A = ---
+ * 1 a
+ * 1
+ *
+ * etc. The coefficients of x(y) are found by expanding
+ *
+ * inf inf
+ * - - i
+ * x(y) = > A > a x
+ * - j - i
+ * j=1 i=1
+ *
+ * and setting each coefficient of x , higher than the first,
+ * to zero.
+ *
+ *
+ *
+ * RESTRICTIONS:
+ *
+ * y[0] must be zero, and y[1] must be nonzero.
+ *
+ */
+
+/* rgamma.c
+ *
+ * Reciprocal gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, rgamma();
+ *
+ * y = rgamma( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns one divided by the gamma function of the argument.
+ *
+ * The function is approximated by a Chebyshev expansion in
+ * the interval [0,1]. Range reduction is by recurrence
+ * for arguments between -34.034 and +34.84425627277176174.
+ * 1/MAXNUM is returned for positive arguments outside this
+ * range. For arguments less than -34.034 the cosecant
+ * reflection formula is applied; lograrithms are employed
+ * to avoid unnecessary overflow.
+ *
+ * The reciprocal gamma function has no singularities,
+ * but overflow and underflow may occur for large arguments.
+ * These conditions return either MAXNUM or 1/MAXNUM with
+ * appropriate sign.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -30,+30 4000 1.2e-16 1.8e-17
+ * IEEE -30,+30 30000 1.1e-15 2.0e-16
+ * For arguments less than -34.034 the peak error is on the
+ * order of 5e-15 (DEC), excepting overflow or underflow.
+ */
+
+/* round.c
+ *
+ * Round double to nearest or even integer valued double
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, round();
+ *
+ * y = round(x);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the nearest integer to x as a double precision
+ * floating point result. If x ends in 0.5 exactly, the
+ * nearest even integer is chosen.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * If x is greater than 1/(2*MACHEP), its closest machine
+ * representation is already an integer, so rounding does
+ * not change it.
+ */
+
+/* shichi.c
+ *
+ * Hyperbolic sine and cosine integrals
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, Chi, Shi, shichi();
+ *
+ * shichi( x, &Chi, &Shi );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integrals
+ *
+ * x
+ * -
+ * | | cosh t - 1
+ * Chi(x) = eul + ln x + | ----------- dt,
+ * | | t
+ * -
+ * 0
+ *
+ * x
+ * -
+ * | | sinh t
+ * Shi(x) = | ------ dt
+ * | | t
+ * -
+ * 0
+ *
+ * where eul = 0.57721566490153286061 is Euler's constant.
+ * The integrals are evaluated by power series for x < 8
+ * and by Chebyshev expansions for x between 8 and 88.
+ * For large x, both functions approach exp(x)/2x.
+ * Arguments greater than 88 in magnitude return MAXNUM.
+ *
+ *
+ * ACCURACY:
+ *
+ * Test interval 0 to 88.
+ * Relative error:
+ * arithmetic function # trials peak rms
+ * DEC Shi 3000 9.1e-17
+ * IEEE Shi 30000 6.9e-16 1.6e-16
+ * Absolute error, except relative when |Chi| > 1:
+ * DEC Chi 2500 9.3e-17
+ * IEEE Chi 30000 8.4e-16 1.4e-16
+ */
+
+/* sici.c
+ *
+ * Sine and cosine integrals
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, Ci, Si, sici();
+ *
+ * sici( x, &Si, &Ci );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the integrals
+ *
+ * x
+ * -
+ * | cos t - 1
+ * Ci(x) = eul + ln x + | --------- dt,
+ * | t
+ * -
+ * 0
+ * x
+ * -
+ * | sin t
+ * Si(x) = | ----- dt
+ * | t
+ * -
+ * 0
+ *
+ * where eul = 0.57721566490153286061 is Euler's constant.
+ * The integrals are approximated by rational functions.
+ * For x > 8 auxiliary functions f(x) and g(x) are employed
+ * such that
+ *
+ * Ci(x) = f(x) sin(x) - g(x) cos(x)
+ * Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)
+ *
+ *
+ * ACCURACY:
+ * Test interval = [0,50].
+ * Absolute error, except relative when > 1:
+ * arithmetic function # trials peak rms
+ * IEEE Si 30000 4.4e-16 7.3e-17
+ * IEEE Ci 30000 6.9e-16 5.1e-17
+ * DEC Si 5000 4.4e-17 9.0e-18
+ * DEC Ci 5300 7.9e-17 5.2e-18
+ */
+
+/* simpsn.c */
+ * Numerical integration of function tabulated
+ * at equally spaced arguments
+ */
+
+/* simq.c
+ *
+ * Solution of simultaneous linear equations AX = B
+ * by Gaussian elimination with partial pivoting
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double A[n*n], B[n], X[n];
+ * int n, flag;
+ * int IPS[];
+ * int simq();
+ *
+ * ercode = simq( A, B, X, n, flag, IPS );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * B, X, IPS are vectors of length n.
+ * A is an n x n matrix (i.e., a vector of length n*n),
+ * stored row-wise: that is, A(i,j) = A[ij],
+ * where ij = i*n + j, which is the transpose of the normal
+ * column-wise storage.
+ *
+ * The contents of matrix A are destroyed.
+ *
+ * Set flag=0 to solve.
+ * Set flag=-1 to do a new back substitution for different B vector
+ * using the same A matrix previously reduced when flag=0.
+ *
+ * The routine returns nonzero on error; messages are printed.
+ *
+ *
+ * ACCURACY:
+ *
+ * Depends on the conditioning (range of eigenvalues) of matrix A.
+ *
+ *
+ * REFERENCE:
+ *
+ * Computer Solution of Linear Algebraic Systems,
+ * by George E. Forsythe and Cleve B. Moler; Prentice-Hall, 1967.
+ *
+ */
+
+/* sin.c
+ *
+ * Circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, sin();
+ *
+ * y = sin( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of pi/4. The reduction
+ * error is nearly eliminated by contriving an extended precision
+ * modular arithmetic.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the sine is approximated by
+ * x + x**3 P(x**2).
+ * Between pi/4 and pi/2 the cosine is represented as
+ * 1 - x**2 Q(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 10 150000 3.0e-17 7.8e-18
+ * IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sin total loss x > 1.073741824e9 0.0
+ *
+ * Partial loss of accuracy begins to occur at x = 2**30
+ * = 1.074e9. The loss is not gradual, but jumps suddenly to
+ * about 1 part in 10e7. Results may be meaningless for
+ * x > 2**49 = 5.6e14. The routine as implemented flags a
+ * TLOSS error for x > 2**30 and returns 0.0.
+ */
+ /* cos.c
+ *
+ * Circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cos();
+ *
+ * y = cos( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of pi/4. The reduction
+ * error is nearly eliminated by contriving an extended precision
+ * modular arithmetic.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the cosine is approximated by
+ * 1 - x**2 Q(x**2).
+ * Between pi/4 and pi/2 the sine is represented as
+ * x + x**3 P(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
+ * DEC 0,+1.07e9 17000 3.0e-17 7.2e-18
+ */
+
+/* sincos.c
+ *
+ * Circular sine and cosine of argument in degrees
+ * Table lookup and interpolation algorithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, sine, cosine, flg, sincos();
+ *
+ * sincos( x, &sine, &cosine, flg );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns both the sine and the cosine of the argument x.
+ * Several different compile time options and minimax
+ * approximations are supplied to permit tailoring the
+ * tradeoff between computation speed and accuracy.
+ *
+ * Since range reduction is time consuming, the reduction
+ * of x modulo 360 degrees is also made optional.
+ *
+ * sin(i) is internally tabulated for 0 <= i <= 90 degrees.
+ * Approximation polynomials, ranging from linear interpolation
+ * to cubics in (x-i)**2, compute the sine and cosine
+ * of the residual x-i which is between -0.5 and +0.5 degree.
+ * In the case of the high accuracy options, the residual
+ * and the tabulated values are combined using the trigonometry
+ * formulas for sin(A+B) and cos(A+B).
+ *
+ * Compile time options are supplied for 5, 11, or 17 decimal
+ * relative accuracy (ACC5, ACC11, ACC17 respectively).
+ * A subroutine flag argument "flg" chooses betwen this
+ * accuracy and table lookup only (peak absolute error
+ * = 0.0087).
+ *
+ * If the argument flg = 1, then the tabulated value is
+ * returned for the nearest whole number of degrees. The
+ * approximation polynomials are not computed. At
+ * x = 0.5 deg, the absolute error is then sin(0.5) = 0.0087.
+ *
+ * An intermediate speed and precision can be obtained using
+ * the compile time option LINTERP and flg = 1. This yields
+ * a linear interpolation using a slope estimated from the sine
+ * or cosine at the nearest integer argument. The peak absolute
+ * error with this option is 3.8e-5. Relative error at small
+ * angles is about 1e-5.
+ *
+ * If flg = 0, then the approximation polynomials are computed
+ * and applied.
+ *
+ *
+ *
+ * SPEED:
+ *
+ * Relative speed comparisons follow for 6MHz IBM AT clone
+ * and Microsoft C version 4.0. These figures include
+ * software overhead of do loop and function calls.
+ * Since system hardware and software vary widely, the
+ * numbers should be taken as representative only.
+ *
+ * flg=0 flg=0 flg=1 flg=1
+ * ACC11 ACC5 LINTERP Lookup only
+ * In-line 8087 (/FPi)
+ * sin(), cos() 1.0 1.0 1.0 1.0
+ *
+ * In-line 8087 (/FPi)
+ * sincos() 1.1 1.4 1.9 3.0
+ *
+ * Software (/FPa)
+ * sin(), cos() 0.19 0.19 0.19 0.19
+ *
+ * Software (/FPa)
+ * sincos() 0.39 0.50 0.73 1.7
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * The accurate approximations are designed with a relative error
+ * criterion. The absolute error is greatest at x = 0.5 degree.
+ * It decreases from a local maximum at i+0.5 degrees to full
+ * machine precision at each integer i degrees. With the
+ * ACC5 option, the relative error of 6.3e-6 is equivalent to
+ * an absolute angular error of 0.01 arc second in the argument
+ * at x = i+0.5 degrees. For small angles < 0.5 deg, the ACC5
+ * accuracy is 6.3e-6 (.00063%) of reading; i.e., the absolute
+ * error decreases in proportion to the argument. This is true
+ * for both the sine and cosine approximations, since the latter
+ * is for the function 1 - cos(x).
+ *
+ * If absolute error is of most concern, use the compile time
+ * option ABSERR to obtain an absolute error of 2.7e-8 for ACC5
+ * precision. This is about half the absolute error of the
+ * relative precision option. In this case the relative error
+ * for small angles will increase to 9.5e-6 -- a reasonable
+ * tradeoff.
+ */
+
+/* sindg.c
+ *
+ * Circular sine of angle in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, sindg();
+ *
+ * y = sindg( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of 45 degrees.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the sine is approximated by
+ * x + x**3 P(x**2).
+ * Between pi/4 and pi/2 the cosine is represented as
+ * 1 - x**2 P(x**2).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC +-1000 3100 3.3e-17 9.0e-18
+ * IEEE +-1000 30000 2.3e-16 5.6e-17
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sindg total loss x > 8.0e14 (DEC) 0.0
+ * x > 1.0e14 (IEEE)
+ *
+ */
+ /* cosdg.c
+ *
+ * Circular cosine of angle in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cosdg();
+ *
+ * y = cosdg( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of 45 degrees.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the cosine is approximated by
+ * 1 - x**2 P(x**2).
+ * Between pi/4 and pi/2 the sine is represented as
+ * x + x**3 P(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC +-1000 3400 3.5e-17 9.1e-18
+ * IEEE +-1000 30000 2.1e-16 5.7e-17
+ * See also sin().
+ *
+ */
+
+/* sinh.c
+ *
+ * Hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, sinh();
+ *
+ * y = sinh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic sine of argument in the range MINLOG to
+ * MAXLOG.
+ *
+ * The range is partitioned into two segments. If |x| <= 1, a
+ * rational function of the form x + x**3 P(x)/Q(x) is employed.
+ * Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC +- 88 50000 4.0e-17 7.7e-18
+ * IEEE +-MAXLOG 30000 2.6e-16 5.7e-17
+ *
+ */
+
+/* spence.c
+ *
+ * Dilogarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, spence();
+ *
+ * y = spence( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the integral
+ *
+ * x
+ * -
+ * | | log t
+ * spence(x) = - | ----- dt
+ * | | t - 1
+ * -
+ * 1
+ *
+ * for x >= 0. A rational approximation gives the integral in
+ * the interval (0.5, 1.5). Transformation formulas for 1/x
+ * and 1-x are employed outside the basic expansion range.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,4 30000 3.9e-15 5.4e-16
+ * DEC 0,4 3000 2.5e-16 4.5e-17
+ *
+ *
+ */
+
+/* sqrt.c
+ *
+ * Square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, sqrt();
+ *
+ * y = sqrt( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the square root of x.
+ *
+ * Range reduction involves isolating the power of two of the
+ * argument and using a polynomial approximation to obtain
+ * a rough value for the square root. Then Heron's iteration
+ * is used three times to converge to an accurate value.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 10 60000 2.1e-17 7.9e-18
+ * IEEE 0,1.7e308 30000 1.7e-16 6.3e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sqrt domain x < 0 0.0
+ *
+ */
+
+/* stdtr.c
+ *
+ * Student's t distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double t, stdtr();
+ * short k;
+ *
+ * y = stdtr( k, t );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the integral from minus infinity to t of the Student
+ * t distribution with integer k > 0 degrees of freedom:
+ *
+ * t
+ * -
+ * | |
+ * - | 2 -(k+1)/2
+ * | ( (k+1)/2 ) | ( x )
+ * ---------------------- | ( 1 + --- ) dx
+ * - | ( k )
+ * sqrt( k pi ) | ( k/2 ) |
+ * | |
+ * -
+ * -inf.
+ *
+ * Relation to incomplete beta integral:
+ *
+ * 1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
+ * where
+ * z = k/(k + t**2).
+ *
+ * For t < -2, this is the method of computation. For higher t,
+ * a direct method is derived from integration by parts.
+ * Since the function is symmetric about t=0, the area under the
+ * right tail of the density is found by calling the function
+ * with -t instead of t.
+ *
+ * ACCURACY:
+ *
+ * Tested at random 1 <= k <= 25. The "domain" refers to t.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -100,-2 50000 5.9e-15 1.4e-15
+ * IEEE -2,100 500000 2.7e-15 4.9e-17
+ */
+
+/* stdtri.c
+ *
+ * Functional inverse of Student's t distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double p, t, stdtri();
+ * int k;
+ *
+ * t = stdtri( k, p );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given probability p, finds the argument t such that stdtr(k,t)
+ * is equal to p.
+ *
+ * ACCURACY:
+ *
+ * Tested at random 1 <= k <= 100. The "domain" refers to p:
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE .001,.999 25000 5.7e-15 8.0e-16
+ * IEEE 10^-6,.001 25000 2.0e-12 2.9e-14
+ */
+
+/* struve.c
+ *
+ * Struve function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, struve();
+ *
+ * y = struve( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the Struve function Hv(x) of order v, argument x.
+ * Negative x is rejected unless v is an integer.
+ *
+ * This module also contains the hypergeometric functions 1F2
+ * and 3F0 and a routine for the Bessel function Yv(x) with
+ * noninteger v.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Not accurately characterized, but spot checked against tables.
+ *
+ */
+
+/* tan.c
+ *
+ * Circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, tan();
+ *
+ * y = tan( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular tangent of the radian argument x.
+ *
+ * Range reduction is modulo pi/4. A rational function
+ * x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC +-1.07e9 44000 4.1e-17 1.0e-17
+ * IEEE +-1.07e9 30000 2.9e-16 8.1e-17
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * tan total loss x > 1.073741824e9 0.0
+ *
+ */
+ /* cot.c
+ *
+ * Circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cot();
+ *
+ * y = cot( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular cotangent of the radian argument x.
+ *
+ * Range reduction is modulo pi/4. A rational function
+ * x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-1.07e9 30000 2.9e-16 8.2e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * cot total loss x > 1.073741824e9 0.0
+ * cot singularity x = 0 INFINITY
+ *
+ */
+
+/* tandg.c
+ *
+ * Circular tangent of argument in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, tandg();
+ *
+ * y = tandg( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular tangent of the argument x in degrees.
+ *
+ * Range reduction is modulo pi/4. A rational function
+ * x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,10 8000 3.4e-17 1.2e-17
+ * IEEE 0,10 30000 3.2e-16 8.4e-17
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * tandg total loss x > 8.0e14 (DEC) 0.0
+ * x > 1.0e14 (IEEE)
+ * tandg singularity x = 180 k + 90 MAXNUM
+ */
+ /* cotdg.c
+ *
+ * Circular cotangent of argument in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cotdg();
+ *
+ * y = cotdg( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular cotangent of the argument x in degrees.
+ *
+ * Range reduction is modulo pi/4. A rational function
+ * x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * cotdg total loss x > 8.0e14 (DEC) 0.0
+ * x > 1.0e14 (IEEE)
+ * cotdg singularity x = 180 k MAXNUM
+ */
+
+/* tanh.c
+ *
+ * Hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, tanh();
+ *
+ * y = tanh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic tangent of argument in the range MINLOG to
+ * MAXLOG.
+ *
+ * A rational function is used for |x| < 0.625. The form
+ * x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
+ * Otherwise,
+ * tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -2,2 50000 3.3e-17 6.4e-18
+ * IEEE -2,2 30000 2.5e-16 5.8e-17
+ *
+ */
+
+/* unity.c
+ *
+ * Relative error approximations for function arguments near
+ * unity.
+ *
+ * log1p(x) = log(1+x)
+ * expm1(x) = exp(x) - 1
+ * cosm1(x) = cos(x) - 1
+ *
+ */
+
+/* yn.c
+ *
+ * Bessel function of second kind of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, yn();
+ * int n;
+ *
+ * y = yn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The function is evaluated by forward recurrence on
+ * n, starting with values computed by the routines
+ * y0() and y1().
+ *
+ * If n = 0 or 1 the routine for y0 or y1 is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Absolute error, except relative
+ * when y > 1:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 2200 2.9e-16 5.3e-17
+ * IEEE 0, 30 30000 3.4e-15 4.3e-16
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * yn singularity x = 0 MAXNUM
+ * yn overflow MAXNUM
+ *
+ * Spot checked against tables for x, n between 0 and 100.
+ *
+ */
+
+/* zeta.c
+ *
+ * Riemann zeta function of two arguments
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, q, y, zeta();
+ *
+ * y = zeta( x, q );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *
+ * inf.
+ * - -x
+ * zeta(x,q) = > (k+q)
+ * -
+ * k=0
+ *
+ * where x > 1 and q is not a negative integer or zero.
+ * The Euler-Maclaurin summation formula is used to obtain
+ * the expansion
+ *
+ * n
+ * - -x
+ * zeta(x,q) = > (k+q)
+ * -
+ * k=1
+ *
+ * 1-x inf. B x(x+1)...(x+2j)
+ * (n+q) 1 - 2j
+ * + --------- - ------- + > --------------------
+ * x-1 x - x+2j+1
+ * 2(n+q) j=1 (2j)! (n+q)
+ *
+ * where the B2j are Bernoulli numbers. Note that (see zetac.c)
+ * zeta(x,1) = zetac(x) + 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ *
+ * REFERENCE:
+ *
+ * Gradshteyn, I. S., and I. M. Ryzhik, Tables of Integrals,
+ * Series, and Products, p. 1073; Academic Press, 1980.
+ *
+ */
+
+ /* zetac.c
+ *
+ * Riemann zeta function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, zetac();
+ *
+ * y = zetac( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *
+ * inf.
+ * - -x
+ * zetac(x) = > k , x > 1,
+ * -
+ * k=2
+ *
+ * is related to the Riemann zeta function by
+ *
+ * Riemann zeta(x) = zetac(x) + 1.
+ *
+ * Extension of the function definition for x < 1 is implemented.
+ * Zero is returned for x > log2(MAXNUM).
+ *
+ * An overflow error may occur for large negative x, due to the
+ * gamma function in the reflection formula.
+ *
+ * ACCURACY:
+ *
+ * Tabulated values have full machine accuracy.
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 1,50 10000 9.8e-16 1.3e-16
+ * DEC 1,50 2000 1.1e-16 1.9e-17
+ *
+ *
+ */
diff --git a/libm/double/acosh.c b/libm/double/acosh.c
new file mode 100644
index 000000000..49d9a40e2
--- /dev/null
+++ b/libm/double/acosh.c
@@ -0,0 +1,167 @@
+/* acosh.c
+ *
+ * Inverse hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, acosh();
+ *
+ * y = acosh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic cosine of argument.
+ *
+ * If 1 <= x < 1.5, a rational approximation
+ *
+ * sqrt(z) * P(z)/Q(z)
+ *
+ * where z = x-1, is used. Otherwise,
+ *
+ * acosh(x) = log( x + sqrt( (x-1)(x+1) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 1,3 30000 4.2e-17 1.1e-17
+ * IEEE 1,3 30000 4.6e-16 8.7e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * acosh domain |x| < 1 NAN
+ *
+ */
+
+/* acosh.c */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+/* acosh(z) = sqrt(x) * R(x), z = x + 1, interval 0 < x < 0.5 */
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+ 1.18801130533544501356E2,
+ 3.94726656571334401102E3,
+ 3.43989375926195455866E4,
+ 1.08102874834699867335E5,
+ 1.10855947270161294369E5
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 1.86145380837903397292E2,
+ 4.15352677227719831579E3,
+ 2.97683430363289370382E4,
+ 8.29725251988426222434E4,
+ 7.83869920495893927727E4
+};
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0041755,0115055,0144002,0146444,
+0043166,0132103,0155150,0150302,
+0044006,0057360,0003021,0162753,
+0044323,0021557,0175225,0056253,
+0044330,0101771,0040046,0006636
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0042072,0022467,0126670,0041232,
+0043201,0146066,0152142,0034015,
+0043750,0110257,0121165,0026100,
+0044242,0007103,0034667,0033173,
+0044231,0014576,0175573,0017472
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x59a4,0xb900,0xb345,0x405d,
+0x1a18,0x7b4d,0xd688,0x40ae,
+0x3cbd,0x00c2,0xcbde,0x40e0,
+0xab95,0xff52,0x646d,0x40fa,
+0xc1b4,0x2804,0x107f,0x40fb
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x0853,0xf5b7,0x44a6,0x4067,
+0x4702,0xda8c,0x3986,0x40b0,
+0xa588,0xf44e,0x1215,0x40dd,
+0xe6cf,0x6736,0x41c8,0x40f4,
+0x63e7,0xdf6f,0x232f,0x40f3
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x405d,0xb345,0xb900,0x59a4,
+0x40ae,0xd688,0x7b4d,0x1a18,
+0x40e0,0xcbde,0x00c2,0x3cbd,
+0x40fa,0x646d,0xff52,0xab95,
+0x40fb,0x107f,0x2804,0xc1b4
+};
+static unsigned short Q[] = {
+0x4067,0x44a6,0xf5b7,0x0853,
+0x40b0,0x3986,0xda8c,0x4702,
+0x40dd,0x1215,0xf44e,0xa588,
+0x40f4,0x41c8,0x6736,0xe6cf,
+0x40f3,0x232f,0xdf6f,0x63e7,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double log ( double );
+extern double sqrt ( double );
+#else
+double log(), sqrt(), polevl(), p1evl();
+#endif
+extern double LOGE2, INFINITY, NAN;
+
+double acosh(x)
+double x;
+{
+double a, z;
+
+if( x < 1.0 )
+ {
+ mtherr( "acosh", DOMAIN );
+ return(NAN);
+ }
+
+if( x > 1.0e8 )
+ {
+#ifdef INFINITIES
+ if( x == INFINITY )
+ return( INFINITY );
+#endif
+ return( log(x) + LOGE2 );
+ }
+
+z = x - 1.0;
+
+if( z < 0.5 )
+ {
+ a = sqrt(z) * (polevl(z, P, 4) / p1evl(z, Q, 5) );
+ return( a );
+ }
+
+a = sqrt( z*(x+1.0) );
+return( log(x + a) );
+}
diff --git a/libm/double/airy.c b/libm/double/airy.c
new file mode 100644
index 000000000..91e29088a
--- /dev/null
+++ b/libm/double/airy.c
@@ -0,0 +1,965 @@
+/* airy.c
+ *
+ * Airy function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, ai, aip, bi, bip;
+ * int airy();
+ *
+ * airy( x, _&ai, _&aip, _&bi, _&bip );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Solution of the differential equation
+ *
+ * y"(x) = xy.
+ *
+ * The function returns the two independent solutions Ai, Bi
+ * and their first derivatives Ai'(x), Bi'(x).
+ *
+ * Evaluation is by power series summation for small x,
+ * by rational minimax approximations for large x.
+ *
+ *
+ *
+ * ACCURACY:
+ * Error criterion is absolute when function <= 1, relative
+ * when function > 1, except * denotes relative error criterion.
+ * For large negative x, the absolute error increases as x^1.5.
+ * For large positive x, the relative error increases as x^1.5.
+ *
+ * Arithmetic domain function # trials peak rms
+ * IEEE -10, 0 Ai 10000 1.6e-15 2.7e-16
+ * IEEE 0, 10 Ai 10000 2.3e-14* 1.8e-15*
+ * IEEE -10, 0 Ai' 10000 4.6e-15 7.6e-16
+ * IEEE 0, 10 Ai' 10000 1.8e-14* 1.5e-15*
+ * IEEE -10, 10 Bi 30000 4.2e-15 5.3e-16
+ * IEEE -10, 10 Bi' 30000 4.9e-15 7.3e-16
+ * DEC -10, 0 Ai 5000 1.7e-16 2.8e-17
+ * DEC 0, 10 Ai 5000 2.1e-15* 1.7e-16*
+ * DEC -10, 0 Ai' 5000 4.7e-16 7.8e-17
+ * DEC 0, 10 Ai' 12000 1.8e-15* 1.5e-16*
+ * DEC -10, 10 Bi 10000 5.5e-16 6.8e-17
+ * DEC -10, 10 Bi' 7000 5.3e-16 8.7e-17
+ *
+ */
+ /* airy.c */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+static double c1 = 0.35502805388781723926;
+static double c2 = 0.258819403792806798405;
+static double sqrt3 = 1.732050807568877293527;
+static double sqpii = 5.64189583547756286948E-1;
+extern double PI;
+
+extern double MAXNUM, MACHEP;
+#ifdef UNK
+#define MAXAIRY 25.77
+#endif
+#ifdef DEC
+#define MAXAIRY 25.77
+#endif
+#ifdef IBMPC
+#define MAXAIRY 103.892
+#endif
+#ifdef MIEEE
+#define MAXAIRY 103.892
+#endif
+
+
+#ifdef UNK
+static double AN[8] = {
+ 3.46538101525629032477E-1,
+ 1.20075952739645805542E1,
+ 7.62796053615234516538E1,
+ 1.68089224934630576269E2,
+ 1.59756391350164413639E2,
+ 7.05360906840444183113E1,
+ 1.40264691163389668864E1,
+ 9.99999999999999995305E-1,
+};
+static double AD[8] = {
+ 5.67594532638770212846E-1,
+ 1.47562562584847203173E1,
+ 8.45138970141474626562E1,
+ 1.77318088145400459522E2,
+ 1.64234692871529701831E2,
+ 7.14778400825575695274E1,
+ 1.40959135607834029598E1,
+ 1.00000000000000000470E0,
+};
+#endif
+#ifdef DEC
+static unsigned short AN[32] = {
+0037661,0066561,0024675,0131301,
+0041100,0017434,0034324,0101466,
+0041630,0107450,0067427,0007430,
+0042050,0013327,0071000,0034737,
+0042037,0140642,0156417,0167366,
+0041615,0011172,0075147,0051165,
+0041140,0066152,0160520,0075146,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short AD[32] = {
+0040021,0046740,0011422,0064606,
+0041154,0014640,0024631,0062450,
+0041651,0003435,0101152,0106401,
+0042061,0050556,0034605,0136602,
+0042044,0036024,0152377,0151414,
+0041616,0172247,0072216,0115374,
+0041141,0104334,0124154,0166007,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short AN[32] = {
+0xb658,0x2537,0x2dae,0x3fd6,
+0x9067,0x871a,0x03e3,0x4028,
+0xe1e3,0x0de2,0x11e5,0x4053,
+0x073c,0xee40,0x02da,0x4065,
+0xfddf,0x5ba1,0xf834,0x4063,
+0xea4f,0x4f4c,0xa24f,0x4051,
+0x0f4d,0x5c2a,0x0d8d,0x402c,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short AD[32] = {
+0x4d31,0x0262,0x29bc,0x3fe2,
+0x2ca5,0x0533,0x8334,0x402d,
+0x51a0,0xb04d,0x20e3,0x4055,
+0xb7b0,0xc730,0x2a2d,0x4066,
+0xfa61,0x9a9f,0x8782,0x4064,
+0xd35f,0xee91,0xde94,0x4051,
+0x9d81,0x950d,0x311b,0x402c,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short AN[32] = {
+0x3fd6,0x2dae,0x2537,0xb658,
+0x4028,0x03e3,0x871a,0x9067,
+0x4053,0x11e5,0x0de2,0xe1e3,
+0x4065,0x02da,0xee40,0x073c,
+0x4063,0xf834,0x5ba1,0xfddf,
+0x4051,0xa24f,0x4f4c,0xea4f,
+0x402c,0x0d8d,0x5c2a,0x0f4d,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short AD[32] = {
+0x3fe2,0x29bc,0x0262,0x4d31,
+0x402d,0x8334,0x0533,0x2ca5,
+0x4055,0x20e3,0xb04d,0x51a0,
+0x4066,0x2a2d,0xc730,0xb7b0,
+0x4064,0x8782,0x9a9f,0xfa61,
+0x4051,0xde94,0xee91,0xd35f,
+0x402c,0x311b,0x950d,0x9d81,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+
+#ifdef UNK
+static double APN[8] = {
+ 6.13759184814035759225E-1,
+ 1.47454670787755323881E1,
+ 8.20584123476060982430E1,
+ 1.71184781360976385540E2,
+ 1.59317847137141783523E2,
+ 6.99778599330103016170E1,
+ 1.39470856980481566958E1,
+ 1.00000000000000000550E0,
+};
+static double APD[8] = {
+ 3.34203677749736953049E-1,
+ 1.11810297306158156705E1,
+ 7.11727352147859965283E1,
+ 1.58778084372838313640E2,
+ 1.53206427475809220834E2,
+ 6.86752304592780337944E1,
+ 1.38498634758259442477E1,
+ 9.99999999999999994502E-1,
+};
+#endif
+#ifdef DEC
+static unsigned short APN[32] = {
+0040035,0017522,0065145,0054755,
+0041153,0166556,0161471,0057174,
+0041644,0016750,0034445,0046462,
+0042053,0027515,0152316,0046717,
+0042037,0050536,0067023,0023264,
+0041613,0172252,0007240,0131055,
+0041137,0023503,0052472,0002305,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short APD[32] = {
+0037653,0016276,0112106,0126625,
+0041062,0162577,0067111,0111761,
+0041616,0054160,0140004,0137455,
+0042036,0143460,0104626,0157206,
+0042031,0032330,0067131,0114260,
+0041611,0054667,0147207,0134564,
+0041135,0114412,0070653,0146015,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short APN[32] = {
+0xab3e,0x4d4c,0xa3ea,0x3fe3,
+0x2bcf,0xdc67,0x7dad,0x402d,
+0xa9a6,0x0724,0x83bd,0x4054,
+0xc9ba,0xba99,0x65e9,0x4065,
+0x64d7,0xcdc2,0xea2b,0x4063,
+0x1646,0x41d4,0x7e95,0x4051,
+0x4099,0x6aa7,0xe4e8,0x402b,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short APD[32] = {
+0xd5b3,0xd288,0x6397,0x3fd5,
+0x327e,0xedc9,0x5caf,0x4026,
+0x97e6,0x1800,0xcb0e,0x4051,
+0xdbd1,0x1132,0xd8e6,0x4063,
+0x3316,0x0dcb,0x269b,0x4063,
+0xf72f,0xf9d0,0x2b36,0x4051,
+0x7982,0x4e35,0xb321,0x402b,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short APN[32] = {
+0x3fe3,0xa3ea,0x4d4c,0xab3e,
+0x402d,0x7dad,0xdc67,0x2bcf,
+0x4054,0x83bd,0x0724,0xa9a6,
+0x4065,0x65e9,0xba99,0xc9ba,
+0x4063,0xea2b,0xcdc2,0x64d7,
+0x4051,0x7e95,0x41d4,0x1646,
+0x402b,0xe4e8,0x6aa7,0x4099,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short APD[32] = {
+0x3fd5,0x6397,0xd288,0xd5b3,
+0x4026,0x5caf,0xedc9,0x327e,
+0x4051,0xcb0e,0x1800,0x97e6,
+0x4063,0xd8e6,0x1132,0xdbd1,
+0x4063,0x269b,0x0dcb,0x3316,
+0x4051,0x2b36,0xf9d0,0xf72f,
+0x402b,0xb321,0x4e35,0x7982,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+
+#ifdef UNK
+static double BN16[5] = {
+-2.53240795869364152689E-1,
+ 5.75285167332467384228E-1,
+-3.29907036873225371650E-1,
+ 6.44404068948199951727E-2,
+-3.82519546641336734394E-3,
+};
+static double BD16[5] = {
+/* 1.00000000000000000000E0,*/
+-7.15685095054035237902E0,
+ 1.06039580715664694291E1,
+-5.23246636471251500874E0,
+ 9.57395864378383833152E-1,
+-5.50828147163549611107E-2,
+};
+#endif
+#ifdef DEC
+static unsigned short BN16[20] = {
+0137601,0124307,0010213,0035210,
+0040023,0042743,0101621,0016031,
+0137650,0164623,0036056,0074511,
+0037203,0174525,0000473,0142474,
+0136172,0130041,0066726,0064324,
+};
+static unsigned short BD16[20] = {
+/*0040200,0000000,0000000,0000000,*/
+0140745,0002354,0044335,0055276,
+0041051,0124717,0170130,0104013,
+0140647,0070135,0046473,0103501,
+0040165,0013745,0033324,0127766,
+0137141,0117204,0076164,0033107,
+};
+#endif
+#ifdef IBMPC
+static unsigned short BN16[20] = {
+0x6751,0xe211,0x3518,0xbfd0,
+0x2383,0x7072,0x68bc,0x3fe2,
+0xcf29,0x6785,0x1d32,0xbfd5,
+0x78a8,0xa027,0x7f2a,0x3fb0,
+0xcd1b,0x2dba,0x5604,0xbf6f,
+};
+static unsigned short BD16[20] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xab58,0x891b,0xa09d,0xc01c,
+0x1101,0xfe0b,0x3539,0x4025,
+0x70e8,0xa9a7,0xee0b,0xc014,
+0x95ff,0xa6da,0xa2fc,0x3fee,
+0x86c9,0x8f8e,0x33d0,0xbfac,
+};
+#endif
+#ifdef MIEEE
+static unsigned short BN16[20] = {
+0xbfd0,0x3518,0xe211,0x6751,
+0x3fe2,0x68bc,0x7072,0x2383,
+0xbfd5,0x1d32,0x6785,0xcf29,
+0x3fb0,0x7f2a,0xa027,0x78a8,
+0xbf6f,0x5604,0x2dba,0xcd1b,
+};
+static unsigned short BD16[20] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0xc01c,0xa09d,0x891b,0xab58,
+0x4025,0x3539,0xfe0b,0x1101,
+0xc014,0xee0b,0xa9a7,0x70e8,
+0x3fee,0xa2fc,0xa6da,0x95ff,
+0xbfac,0x33d0,0x8f8e,0x86c9,
+};
+#endif
+
+#ifdef UNK
+static double BPPN[5] = {
+ 4.65461162774651610328E-1,
+-1.08992173800493920734E0,
+ 6.38800117371827987759E-1,
+-1.26844349553102907034E-1,
+ 7.62487844342109852105E-3,
+};
+static double BPPD[5] = {
+/* 1.00000000000000000000E0,*/
+-8.70622787633159124240E0,
+ 1.38993162704553213172E1,
+-7.14116144616431159572E0,
+ 1.34008595960680518666E0,
+-7.84273211323341930448E-2,
+};
+#endif
+#ifdef DEC
+static unsigned short BPPN[20] = {
+0037756,0050354,0167531,0135731,
+0140213,0101216,0032767,0020375,
+0040043,0104147,0106312,0177632,
+0137401,0161574,0032015,0043714,
+0036371,0155035,0143165,0142262,
+};
+static unsigned short BPPD[20] = {
+/*0040200,0000000,0000000,0000000,*/
+0141013,0046265,0115005,0161053,
+0041136,0061631,0072445,0156131,
+0140744,0102145,0001127,0065304,
+0040253,0103757,0146453,0102513,
+0137240,0117200,0155402,0113500,
+};
+#endif
+#ifdef IBMPC
+static unsigned short BPPN[20] = {
+0x377b,0x9deb,0xca1d,0x3fdd,
+0xe420,0xc6be,0x7051,0xbff1,
+0x5ff3,0xf199,0x710c,0x3fe4,
+0xa8fa,0x8681,0x3c6f,0xbfc0,
+0xb896,0xb8ce,0x3b43,0x3f7f,
+};
+static unsigned short BPPD[20] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xbc45,0xb340,0x6996,0xc021,
+0xbb8b,0x2ea4,0xcc73,0x402b,
+0xed59,0xa04a,0x908c,0xc01c,
+0x70a9,0xf9a5,0x70fd,0x3ff5,
+0x52e8,0x1b60,0x13d0,0xbfb4,
+};
+#endif
+#ifdef MIEEE
+static unsigned short BPPN[20] = {
+0x3fdd,0xca1d,0x9deb,0x377b,
+0xbff1,0x7051,0xc6be,0xe420,
+0x3fe4,0x710c,0xf199,0x5ff3,
+0xbfc0,0x3c6f,0x8681,0xa8fa,
+0x3f7f,0x3b43,0xb8ce,0xb896,
+};
+static unsigned short BPPD[20] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0xc021,0x6996,0xb340,0xbc45,
+0x402b,0xcc73,0x2ea4,0xbb8b,
+0xc01c,0x908c,0xa04a,0xed59,
+0x3ff5,0x70fd,0xf9a5,0x70a9,
+0xbfb4,0x13d0,0x1b60,0x52e8,
+};
+#endif
+
+#ifdef UNK
+static double AFN[9] = {
+-1.31696323418331795333E-1,
+-6.26456544431912369773E-1,
+-6.93158036036933542233E-1,
+-2.79779981545119124951E-1,
+-4.91900132609500318020E-2,
+-4.06265923594885404393E-3,
+-1.59276496239262096340E-4,
+-2.77649108155232920844E-6,
+-1.67787698489114633780E-8,
+};
+static double AFD[9] = {
+/* 1.00000000000000000000E0,*/
+ 1.33560420706553243746E1,
+ 3.26825032795224613948E1,
+ 2.67367040941499554804E1,
+ 9.18707402907259625840E0,
+ 1.47529146771666414581E0,
+ 1.15687173795188044134E-1,
+ 4.40291641615211203805E-3,
+ 7.54720348287414296618E-5,
+ 4.51850092970580378464E-7,
+};
+#endif
+#ifdef DEC
+static unsigned short AFN[36] = {
+0137406,0155546,0124127,0033732,
+0140040,0057564,0141263,0041222,
+0140061,0071316,0013674,0175754,
+0137617,0037522,0056637,0120130,
+0137111,0075567,0121755,0166122,
+0136205,0020016,0043317,0002201,
+0135047,0001565,0075130,0002334,
+0133472,0051700,0165021,0131551,
+0131620,0020347,0132165,0013215,
+};
+static unsigned short AFD[36] = {
+/*0040200,0000000,0000000,0000000,*/
+0041125,0131131,0025627,0067623,
+0041402,0135342,0021703,0154315,
+0041325,0162305,0016671,0120175,
+0041022,0177101,0053114,0141632,
+0040274,0153131,0147364,0114306,
+0037354,0166545,0120042,0150530,
+0036220,0043127,0000727,0130273,
+0034636,0043275,0075667,0034733,
+0032762,0112715,0146250,0142474,
+};
+#endif
+#ifdef IBMPC
+static unsigned short AFN[36] = {
+0xe6fb,0xd50a,0xdb6c,0xbfc0,
+0x6852,0x9856,0x0bee,0xbfe4,
+0x9f7d,0xc2f7,0x2e59,0xbfe6,
+0xf40b,0x4bb3,0xe7ea,0xbfd1,
+0xbd8a,0xf47d,0x2f6e,0xbfa9,
+0xe090,0xc8d9,0xa401,0xbf70,
+0x009c,0xaf4b,0xe06e,0xbf24,
+0x366d,0x1d42,0x4a78,0xbec7,
+0xa2d2,0xf68e,0x041c,0xbe52,
+};
+static unsigned short AFD[36] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xedf2,0x2572,0xb64b,0x402a,
+0x7b1a,0x4478,0x575c,0x4040,
+0x3410,0xa3b7,0xbc98,0x403a,
+0x9873,0x2ac9,0x5fc8,0x4022,
+0x9319,0x39de,0x9acb,0x3ff7,
+0x5a2b,0xb404,0x9dac,0x3fbd,
+0xf617,0xe03a,0x08ca,0x3f72,
+0xe73b,0xaf76,0xc8d7,0x3f13,
+0x18a7,0xb995,0x52b9,0x3e9e,
+};
+#endif
+#ifdef MIEEE
+static unsigned short AFN[36] = {
+0xbfc0,0xdb6c,0xd50a,0xe6fb,
+0xbfe4,0x0bee,0x9856,0x6852,
+0xbfe6,0x2e59,0xc2f7,0x9f7d,
+0xbfd1,0xe7ea,0x4bb3,0xf40b,
+0xbfa9,0x2f6e,0xf47d,0xbd8a,
+0xbf70,0xa401,0xc8d9,0xe090,
+0xbf24,0xe06e,0xaf4b,0x009c,
+0xbec7,0x4a78,0x1d42,0x366d,
+0xbe52,0x041c,0xf68e,0xa2d2,
+};
+static unsigned short AFD[36] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x402a,0xb64b,0x2572,0xedf2,
+0x4040,0x575c,0x4478,0x7b1a,
+0x403a,0xbc98,0xa3b7,0x3410,
+0x4022,0x5fc8,0x2ac9,0x9873,
+0x3ff7,0x9acb,0x39de,0x9319,
+0x3fbd,0x9dac,0xb404,0x5a2b,
+0x3f72,0x08ca,0xe03a,0xf617,
+0x3f13,0xc8d7,0xaf76,0xe73b,
+0x3e9e,0x52b9,0xb995,0x18a7,
+};
+#endif
+
+#ifdef UNK
+static double AGN[11] = {
+ 1.97339932091685679179E-2,
+ 3.91103029615688277255E-1,
+ 1.06579897599595591108E0,
+ 9.39169229816650230044E-1,
+ 3.51465656105547619242E-1,
+ 6.33888919628925490927E-2,
+ 5.85804113048388458567E-3,
+ 2.82851600836737019778E-4,
+ 6.98793669997260967291E-6,
+ 8.11789239554389293311E-8,
+ 3.41551784765923618484E-10,
+};
+static double AGD[10] = {
+/* 1.00000000000000000000E0,*/
+ 9.30892908077441974853E0,
+ 1.98352928718312140417E1,
+ 1.55646628932864612953E1,
+ 5.47686069422975497931E0,
+ 9.54293611618961883998E-1,
+ 8.64580826352392193095E-2,
+ 4.12656523824222607191E-3,
+ 1.01259085116509135510E-4,
+ 1.17166733214413521882E-6,
+ 4.91834570062930015649E-9,
+};
+#endif
+#ifdef DEC
+static unsigned short AGN[44] = {
+0036641,0124456,0167175,0157354,
+0037710,0037250,0001441,0136671,
+0040210,0066031,0150401,0123532,
+0040160,0066545,0003570,0153133,
+0037663,0171516,0072507,0170345,
+0037201,0151011,0007510,0045702,
+0036277,0172317,0104572,0101030,
+0035224,0045663,0000160,0136422,
+0033752,0074753,0047702,0135160,
+0032256,0052225,0156550,0107103,
+0030273,0142443,0166277,0071720,
+};
+static unsigned short AGD[40] = {
+/*0040200,0000000,0000000,0000000,*/
+0041024,0170537,0117253,0055003,
+0041236,0127256,0003570,0143240,
+0041171,0004333,0172476,0160645,
+0040657,0041161,0055716,0157161,
+0040164,0046226,0006257,0063431,
+0037261,0010357,0065445,0047563,
+0036207,0034043,0057434,0116732,
+0034724,0055416,0130035,0026377,
+0033235,0041056,0154071,0023502,
+0031250,0177071,0167254,0047242,
+};
+#endif
+#ifdef IBMPC
+static unsigned short AGN[44] = {
+0xbbde,0xddcf,0x3525,0x3f94,
+0x37b7,0x0064,0x07d5,0x3fd9,
+0x34eb,0x3a20,0x0d83,0x3ff1,
+0x1acb,0xa0ef,0x0dac,0x3fee,
+0xfe1d,0xcea8,0x7e69,0x3fd6,
+0x0978,0x21e9,0x3a41,0x3fb0,
+0x5043,0xf12f,0xfe99,0x3f77,
+0x17a2,0x600e,0x8976,0x3f32,
+0x574e,0x69f8,0x4f3d,0x3edd,
+0x11c8,0xbbad,0xca92,0x3e75,
+0xee7a,0x7d97,0x78a4,0x3df7,
+};
+static unsigned short AGD[40] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x6b40,0xf3d5,0x9e2b,0x4022,
+0x18d4,0xc0ef,0xd5d5,0x4033,
+0xdc35,0x7ea7,0x211b,0x402f,
+0xdbce,0x2b79,0xe84e,0x4015,
+0xece3,0xc195,0x8992,0x3fee,
+0xa9ee,0xed64,0x221d,0x3fb6,
+0x93bb,0x6be3,0xe704,0x3f70,
+0xa5a0,0xd603,0x8b61,0x3f1a,
+0x24e8,0xdb07,0xa845,0x3eb3,
+0x89d4,0x3dd5,0x1fc7,0x3e35,
+};
+#endif
+#ifdef MIEEE
+static unsigned short AGN[44] = {
+0x3f94,0x3525,0xddcf,0xbbde,
+0x3fd9,0x07d5,0x0064,0x37b7,
+0x3ff1,0x0d83,0x3a20,0x34eb,
+0x3fee,0x0dac,0xa0ef,0x1acb,
+0x3fd6,0x7e69,0xcea8,0xfe1d,
+0x3fb0,0x3a41,0x21e9,0x0978,
+0x3f77,0xfe99,0xf12f,0x5043,
+0x3f32,0x8976,0x600e,0x17a2,
+0x3edd,0x4f3d,0x69f8,0x574e,
+0x3e75,0xca92,0xbbad,0x11c8,
+0x3df7,0x78a4,0x7d97,0xee7a,
+};
+static unsigned short AGD[40] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4022,0x9e2b,0xf3d5,0x6b40,
+0x4033,0xd5d5,0xc0ef,0x18d4,
+0x402f,0x211b,0x7ea7,0xdc35,
+0x4015,0xe84e,0x2b79,0xdbce,
+0x3fee,0x8992,0xc195,0xece3,
+0x3fb6,0x221d,0xed64,0xa9ee,
+0x3f70,0xe704,0x6be3,0x93bb,
+0x3f1a,0x8b61,0xd603,0xa5a0,
+0x3eb3,0xa845,0xdb07,0x24e8,
+0x3e35,0x1fc7,0x3dd5,0x89d4,
+};
+#endif
+
+#ifdef UNK
+static double APFN[9] = {
+ 1.85365624022535566142E-1,
+ 8.86712188052584095637E-1,
+ 9.87391981747398547272E-1,
+ 4.01241082318003734092E-1,
+ 7.10304926289631174579E-2,
+ 5.90618657995661810071E-3,
+ 2.33051409401776799569E-4,
+ 4.08718778289035454598E-6,
+ 2.48379932900442457853E-8,
+};
+static double APFD[9] = {
+/* 1.00000000000000000000E0,*/
+ 1.47345854687502542552E1,
+ 3.75423933435489594466E1,
+ 3.14657751203046424330E1,
+ 1.09969125207298778536E1,
+ 1.78885054766999417817E0,
+ 1.41733275753662636873E-1,
+ 5.44066067017226003627E-3,
+ 9.39421290654511171663E-5,
+ 5.65978713036027009243E-7,
+};
+#endif
+#ifdef DEC
+static unsigned short APFN[36] = {
+0037475,0150174,0071752,0166651,
+0040142,0177621,0164246,0101757,
+0040174,0142670,0106760,0006573,
+0037715,0067570,0116274,0022404,
+0037221,0074157,0053341,0117207,
+0036301,0104257,0015075,0004777,
+0035164,0057502,0164034,0001313,
+0033611,0022254,0176000,0112565,
+0031725,0055523,0025153,0166057,
+};
+static unsigned short APFD[36] = {
+/*0040200,0000000,0000000,0000000,*/
+0041153,0140334,0130506,0061402,
+0041426,0025551,0024440,0070611,
+0041373,0134750,0047147,0176702,
+0041057,0171532,0105430,0017674,
+0040344,0174416,0001726,0047754,
+0037421,0021207,0020167,0136264,
+0036262,0043621,0151321,0124324,
+0034705,0001313,0163733,0016407,
+0033027,0166702,0150440,0170561,
+};
+#endif
+#ifdef IBMPC
+static unsigned short APFN[36] = {
+0x5db5,0x8e7d,0xba0f,0x3fc7,
+0xd07e,0x3d14,0x5ff2,0x3fec,
+0x01af,0x11be,0x98b7,0x3fef,
+0x84a1,0x1397,0xadef,0x3fd9,
+0x33d1,0xeadc,0x2f0d,0x3fb2,
+0xa140,0xe347,0x3115,0x3f78,
+0x8059,0x5d03,0x8be8,0x3f2e,
+0x12af,0x9f80,0x2495,0x3ed1,
+0x7d86,0x654d,0xab6a,0x3e5a,
+};
+static unsigned short APFD[36] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xcc60,0x9628,0x781b,0x402d,
+0x0e31,0x2524,0xc56d,0x4042,
+0xffb8,0x09cc,0x773d,0x403f,
+0x03f7,0x5163,0xfe6b,0x4025,
+0xc9fd,0xc07a,0x9f21,0x3ffc,
+0xf796,0xe40e,0x2450,0x3fc2,
+0x351a,0x3a5a,0x48f2,0x3f76,
+0x63a1,0x7cfb,0xa059,0x3f18,
+0x1e2e,0x5a24,0xfdb8,0x3ea2,
+};
+#endif
+#ifdef MIEEE
+static unsigned short APFN[36] = {
+0x3fc7,0xba0f,0x8e7d,0x5db5,
+0x3fec,0x5ff2,0x3d14,0xd07e,
+0x3fef,0x98b7,0x11be,0x01af,
+0x3fd9,0xadef,0x1397,0x84a1,
+0x3fb2,0x2f0d,0xeadc,0x33d1,
+0x3f78,0x3115,0xe347,0xa140,
+0x3f2e,0x8be8,0x5d03,0x8059,
+0x3ed1,0x2495,0x9f80,0x12af,
+0x3e5a,0xab6a,0x654d,0x7d86,
+};
+static unsigned short APFD[36] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x402d,0x781b,0x9628,0xcc60,
+0x4042,0xc56d,0x2524,0x0e31,
+0x403f,0x773d,0x09cc,0xffb8,
+0x4025,0xfe6b,0x5163,0x03f7,
+0x3ffc,0x9f21,0xc07a,0xc9fd,
+0x3fc2,0x2450,0xe40e,0xf796,
+0x3f76,0x48f2,0x3a5a,0x351a,
+0x3f18,0xa059,0x7cfb,0x63a1,
+0x3ea2,0xfdb8,0x5a24,0x1e2e,
+};
+#endif
+
+#ifdef UNK
+static double APGN[11] = {
+-3.55615429033082288335E-2,
+-6.37311518129435504426E-1,
+-1.70856738884312371053E0,
+-1.50221872117316635393E0,
+-5.63606665822102676611E-1,
+-1.02101031120216891789E-1,
+-9.48396695961445269093E-3,
+-4.60325307486780994357E-4,
+-1.14300836484517375919E-5,
+-1.33415518685547420648E-7,
+-5.63803833958893494476E-10,
+};
+static double APGD[11] = {
+/* 1.00000000000000000000E0,*/
+ 9.85865801696130355144E0,
+ 2.16401867356585941885E1,
+ 1.73130776389749389525E1,
+ 6.17872175280828766327E0,
+ 1.08848694396321495475E0,
+ 9.95005543440888479402E-2,
+ 4.78468199683886610842E-3,
+ 1.18159633322838625562E-4,
+ 1.37480673554219441465E-6,
+ 5.79912514929147598821E-9,
+};
+#endif
+#ifdef DEC
+static unsigned short APGN[44] = {
+0137021,0124372,0176075,0075331,
+0140043,0023330,0177672,0161655,
+0140332,0131126,0010413,0171112,
+0140300,0044263,0175560,0054070,
+0140020,0044206,0142603,0073324,
+0137321,0015130,0066144,0144033,
+0136433,0061243,0175542,0103373,
+0135361,0053721,0020441,0053203,
+0134077,0141725,0160277,0130612,
+0132417,0040372,0100363,0060200,
+0130432,0175052,0171064,0034147,
+};
+static unsigned short APGD[40] = {
+/*0040200,0000000,0000000,0000000,*/
+0041035,0136420,0030124,0140220,
+0041255,0017432,0034447,0162256,
+0041212,0100456,0154544,0006321,
+0040705,0134026,0127154,0123414,
+0040213,0051612,0044470,0172607,
+0037313,0143362,0053273,0157051,
+0036234,0144322,0054536,0007264,
+0034767,0146170,0054265,0170342,
+0033270,0102777,0167362,0073631,
+0031307,0040644,0167103,0021763,
+};
+#endif
+#ifdef IBMPC
+static unsigned short APGN[44] = {
+0xaf5b,0x5f87,0x351f,0xbfa2,
+0x5c76,0x1ff7,0x64db,0xbfe4,
+0x7e49,0xc221,0x564a,0xbffb,
+0x0b07,0x7f6e,0x0916,0xbff8,
+0x6edb,0xd8b0,0x0910,0xbfe2,
+0x9903,0x0d8c,0x234b,0xbfba,
+0x50df,0x7f6c,0x6c54,0xbf83,
+0x2ad0,0x2424,0x2afa,0xbf3e,
+0xf631,0xbc17,0xf87a,0xbee7,
+0x6c10,0x501e,0xe81f,0xbe81,
+0x870d,0x5e46,0x5f45,0xbe03,
+};
+static unsigned short APGD[40] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x9812,0x060a,0xb7a2,0x4023,
+0xfc96,0x4724,0xa3e3,0x4035,
+0x819a,0xdb2c,0x5025,0x4031,
+0x94e2,0xd5cd,0xb702,0x4018,
+0x1eb1,0x4927,0x6a71,0x3ff1,
+0x7bc5,0x4ad7,0x78de,0x3fb9,
+0xc1d7,0x4b2b,0x991a,0x3f73,
+0xbe1c,0x0b16,0xf98f,0x3f1e,
+0x4ef3,0xfdde,0x10bf,0x3eb7,
+0x647e,0x9dc8,0xe834,0x3e38,
+};
+#endif
+#ifdef MIEEE
+static unsigned short APGN[44] = {
+0xbfa2,0x351f,0x5f87,0xaf5b,
+0xbfe4,0x64db,0x1ff7,0x5c76,
+0xbffb,0x564a,0xc221,0x7e49,
+0xbff8,0x0916,0x7f6e,0x0b07,
+0xbfe2,0x0910,0xd8b0,0x6edb,
+0xbfba,0x234b,0x0d8c,0x9903,
+0xbf83,0x6c54,0x7f6c,0x50df,
+0xbf3e,0x2afa,0x2424,0x2ad0,
+0xbee7,0xf87a,0xbc17,0xf631,
+0xbe81,0xe81f,0x501e,0x6c10,
+0xbe03,0x5f45,0x5e46,0x870d,
+};
+static unsigned short APGD[40] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4023,0xb7a2,0x060a,0x9812,
+0x4035,0xa3e3,0x4724,0xfc96,
+0x4031,0x5025,0xdb2c,0x819a,
+0x4018,0xb702,0xd5cd,0x94e2,
+0x3ff1,0x6a71,0x4927,0x1eb1,
+0x3fb9,0x78de,0x4ad7,0x7bc5,
+0x3f73,0x991a,0x4b2b,0xc1d7,
+0x3f1e,0xf98f,0x0b16,0xbe1c,
+0x3eb7,0x10bf,0xfdde,0x4ef3,
+0x3e38,0xe834,0x9dc8,0x647e,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double exp ( double );
+extern double sqrt ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double sin ( double );
+extern double cos ( double );
+#else
+double fabs(), exp(), sqrt();
+double polevl(), p1evl(), sin(), cos();
+#endif
+
+int airy( x, ai, aip, bi, bip )
+double x, *ai, *aip, *bi, *bip;
+{
+double z, zz, t, f, g, uf, ug, k, zeta, theta;
+int domflg;
+
+domflg = 0;
+if( x > MAXAIRY )
+ {
+ *ai = 0;
+ *aip = 0;
+ *bi = MAXNUM;
+ *bip = MAXNUM;
+ return(-1);
+ }
+
+if( x < -2.09 )
+ {
+ domflg = 15;
+ t = sqrt(-x);
+ zeta = -2.0 * x * t / 3.0;
+ t = sqrt(t);
+ k = sqpii / t;
+ z = 1.0/zeta;
+ zz = z * z;
+ uf = 1.0 + zz * polevl( zz, AFN, 8 ) / p1evl( zz, AFD, 9 );
+ ug = z * polevl( zz, AGN, 10 ) / p1evl( zz, AGD, 10 );
+ theta = zeta + 0.25 * PI;
+ f = sin( theta );
+ g = cos( theta );
+ *ai = k * (f * uf - g * ug);
+ *bi = k * (g * uf + f * ug);
+ uf = 1.0 + zz * polevl( zz, APFN, 8 ) / p1evl( zz, APFD, 9 );
+ ug = z * polevl( zz, APGN, 10 ) / p1evl( zz, APGD, 10 );
+ k = sqpii * t;
+ *aip = -k * (g * uf + f * ug);
+ *bip = k * (f * uf - g * ug);
+ return(0);
+ }
+
+if( x >= 2.09 ) /* cbrt(9) */
+ {
+ domflg = 5;
+ t = sqrt(x);
+ zeta = 2.0 * x * t / 3.0;
+ g = exp( zeta );
+ t = sqrt(t);
+ k = 2.0 * t * g;
+ z = 1.0/zeta;
+ f = polevl( z, AN, 7 ) / polevl( z, AD, 7 );
+ *ai = sqpii * f / k;
+ k = -0.5 * sqpii * t / g;
+ f = polevl( z, APN, 7 ) / polevl( z, APD, 7 );
+ *aip = f * k;
+
+ if( x > 8.3203353 ) /* zeta > 16 */
+ {
+ f = z * polevl( z, BN16, 4 ) / p1evl( z, BD16, 5 );
+ k = sqpii * g;
+ *bi = k * (1.0 + f) / t;
+ f = z * polevl( z, BPPN, 4 ) / p1evl( z, BPPD, 5 );
+ *bip = k * t * (1.0 + f);
+ return(0);
+ }
+ }
+
+f = 1.0;
+g = x;
+t = 1.0;
+uf = 1.0;
+ug = x;
+k = 1.0;
+z = x * x * x;
+while( t > MACHEP )
+ {
+ uf *= z;
+ k += 1.0;
+ uf /=k;
+ ug *= z;
+ k += 1.0;
+ ug /=k;
+ uf /=k;
+ f += uf;
+ k += 1.0;
+ ug /=k;
+ g += ug;
+ t = fabs(uf/f);
+ }
+uf = c1 * f;
+ug = c2 * g;
+if( (domflg & 1) == 0 )
+ *ai = uf - ug;
+if( (domflg & 2) == 0 )
+ *bi = sqrt3 * (uf + ug);
+
+/* the deriviative of ai */
+k = 4.0;
+uf = x * x/2.0;
+ug = z/3.0;
+f = uf;
+g = 1.0 + ug;
+uf /= 3.0;
+t = 1.0;
+
+while( t > MACHEP )
+ {
+ uf *= z;
+ ug /=k;
+ k += 1.0;
+ ug *= z;
+ uf /=k;
+ f += uf;
+ k += 1.0;
+ ug /=k;
+ uf /=k;
+ g += ug;
+ k += 1.0;
+ t = fabs(ug/g);
+ }
+
+uf = c1 * f;
+ug = c2 * g;
+if( (domflg & 4) == 0 )
+ *aip = uf - ug;
+if( (domflg & 8) == 0 )
+ *bip = sqrt3 * (uf + ug);
+return(0);
+}
diff --git a/libm/double/arcdot.c b/libm/double/arcdot.c
new file mode 100644
index 000000000..44c057229
--- /dev/null
+++ b/libm/double/arcdot.c
@@ -0,0 +1,110 @@
+/* arcdot.c
+ *
+ * Angle between two vectors
+ *
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double p[3], q[3], arcdot();
+ *
+ * y = arcdot( p, q );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * For two vectors p, q, the angle A between them is given by
+ *
+ * p.q / (|p| |q|) = cos A .
+ *
+ * where "." represents inner product, "|x|" the length of vector x.
+ * If the angle is small, an expression in sin A is preferred.
+ * Set r = q - p. Then
+ *
+ * p.q = p.p + p.r ,
+ *
+ * |p|^2 = p.p ,
+ *
+ * |q|^2 = p.p + 2 p.r + r.r ,
+ *
+ * p.p^2 + 2 p.p p.r + p.r^2
+ * cos^2 A = ----------------------------
+ * p.p (p.p + 2 p.r + r.r)
+ *
+ * p.p + 2 p.r + p.r^2 / p.p
+ * = --------------------------- ,
+ * p.p + 2 p.r + r.r
+ *
+ * sin^2 A = 1 - cos^2 A
+ *
+ * r.r - p.r^2 / p.p
+ * = --------------------
+ * p.p + 2 p.r + r.r
+ *
+ * = (r.r - p.r^2 / p.p) / q.q .
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1, 1 10^6 1.7e-16 4.2e-17
+ *
+ */
+
+/*
+Cephes Math Library Release 2.3: November, 1995
+Copyright 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double sqrt ( double );
+extern double acos ( double );
+extern double asin ( double );
+extern double atan ( double );
+#else
+double sqrt(), acos(), asin(), atan();
+#endif
+extern double PI;
+
+double arcdot(p,q)
+double p[], q[];
+{
+double pp, pr, qq, rr, rt, pt, qt, pq;
+int i;
+
+pq = 0.0;
+qq = 0.0;
+pp = 0.0;
+pr = 0.0;
+rr = 0.0;
+for (i=0; i<3; i++)
+ {
+ pt = p[i];
+ qt = q[i];
+ pq += pt * qt;
+ qq += qt * qt;
+ pp += pt * pt;
+ rt = qt - pt;
+ pr += pt * rt;
+ rr += rt * rt;
+ }
+if (rr == 0.0 || pp == 0.0 || qq == 0.0)
+ return 0.0;
+rt = (rr - (pr * pr) / pp) / qq;
+if (rt <= 0.75)
+ {
+ rt = sqrt(rt);
+ qt = asin(rt);
+ if (pq < 0.0)
+ qt = PI - qt;
+ }
+else
+ {
+ pt = pq / sqrt(pp*qq);
+ qt = acos(pt);
+ }
+return qt;
+}
diff --git a/libm/double/asin.c b/libm/double/asin.c
new file mode 100644
index 000000000..1f83eccc8
--- /dev/null
+++ b/libm/double/asin.c
@@ -0,0 +1,324 @@
+/* asin.c
+ *
+ * Inverse circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, asin();
+ *
+ * y = asin( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
+ *
+ * A rational function of the form x + x**3 P(x**2)/Q(x**2)
+ * is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is
+ * transformed by the identity
+ *
+ * asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -1, 1 40000 2.6e-17 7.1e-18
+ * IEEE -1, 1 10^6 1.9e-16 5.4e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * asin domain |x| > 1 NAN
+ *
+ */
+ /* acos()
+ *
+ * Inverse circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, acos();
+ *
+ * y = acos( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between 0 and pi whose cosine
+ * is x.
+ *
+ * Analytically, acos(x) = pi/2 - asin(x). However if |x| is
+ * near 1, there is cancellation error in subtracting asin(x)
+ * from pi/2. Hence if x < -0.5,
+ *
+ * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
+ *
+ * or if x > +0.5,
+ *
+ * acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -1, 1 50000 3.3e-17 8.2e-18
+ * IEEE -1, 1 10^6 2.2e-16 6.5e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * asin domain |x| > 1 NAN
+ */
+
+/* asin.c */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* arcsin(x) = x + x^3 P(x^2)/Q(x^2)
+ 0 <= x <= 0.625
+ Peak relative error = 1.2e-18 */
+#if UNK
+static double P[6] = {
+ 4.253011369004428248960E-3,
+-6.019598008014123785661E-1,
+ 5.444622390564711410273E0,
+-1.626247967210700244449E1,
+ 1.956261983317594739197E1,
+-8.198089802484824371615E0,
+};
+static double Q[5] = {
+/* 1.000000000000000000000E0, */
+-1.474091372988853791896E1,
+ 7.049610280856842141659E1,
+-1.471791292232726029859E2,
+ 1.395105614657485689735E2,
+-4.918853881490881290097E1,
+};
+#endif
+#if DEC
+static short P[24] = {
+0036213,0056330,0057244,0053234,
+0140032,0015011,0114762,0160255,
+0040656,0035130,0136121,0067313,
+0141202,0014616,0170474,0101731,
+0041234,0100076,0151674,0111310,
+0141003,0025540,0033165,0077246,
+};
+static short Q[20] = {
+/* 0040200,0000000,0000000,0000000, */
+0141153,0155310,0055360,0072530,
+0041614,0177001,0027764,0101237,
+0142023,0026733,0064653,0133266,
+0042013,0101264,0023775,0176351,
+0141504,0140420,0050660,0036543,
+};
+#endif
+#if IBMPC
+static short P[24] = {
+0x8ad3,0x0bd4,0x6b9b,0x3f71,
+0x5c16,0x333e,0x4341,0xbfe3,
+0x2dd9,0x178a,0xc74b,0x4015,
+0x907b,0xde27,0x4331,0xc030,
+0x9259,0xda77,0x9007,0x4033,
+0xafd5,0x06ce,0x656c,0xc020,
+};
+static short Q[20] = {
+/* 0x0000,0x0000,0x0000,0x3ff0, */
+0x0eab,0x0b5e,0x7b59,0xc02d,
+0x9054,0x25fe,0x9fc0,0x4051,
+0x76d7,0x6d35,0x65bb,0xc062,
+0xbf9d,0x84ff,0x7056,0x4061,
+0x07ac,0x0a36,0x9822,0xc048,
+};
+#endif
+#if MIEEE
+static short P[24] = {
+0x3f71,0x6b9b,0x0bd4,0x8ad3,
+0xbfe3,0x4341,0x333e,0x5c16,
+0x4015,0xc74b,0x178a,0x2dd9,
+0xc030,0x4331,0xde27,0x907b,
+0x4033,0x9007,0xda77,0x9259,
+0xc020,0x656c,0x06ce,0xafd5,
+};
+static short Q[20] = {
+/* 0x3ff0,0x0000,0x0000,0x0000, */
+0xc02d,0x7b59,0x0b5e,0x0eab,
+0x4051,0x9fc0,0x25fe,0x9054,
+0xc062,0x65bb,0x6d35,0x76d7,
+0x4061,0x7056,0x84ff,0xbf9d,
+0xc048,0x9822,0x0a36,0x07ac,
+};
+#endif
+
+/* arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x))
+ 0 <= x <= 0.5
+ Peak relative error = 4.2e-18 */
+#if UNK
+static double R[5] = {
+ 2.967721961301243206100E-3,
+-5.634242780008963776856E-1,
+ 6.968710824104713396794E0,
+-2.556901049652824852289E1,
+ 2.853665548261061424989E1,
+};
+static double S[4] = {
+/* 1.000000000000000000000E0, */
+-2.194779531642920639778E1,
+ 1.470656354026814941758E2,
+-3.838770957603691357202E2,
+ 3.424398657913078477438E2,
+};
+#endif
+#if DEC
+static short R[20] = {
+0036102,0077034,0142164,0174103,
+0140020,0036222,0147711,0044173,
+0040736,0177655,0153631,0171523,
+0141314,0106525,0060015,0055474,
+0041344,0045422,0003630,0040344,
+};
+static short S[16] = {
+/* 0040200,0000000,0000000,0000000, */
+0141257,0112425,0132772,0166136,
+0042023,0010315,0075523,0175020,
+0142277,0170104,0126203,0017563,
+0042253,0034115,0102662,0022757,
+};
+#endif
+#if IBMPC
+static short R[20] = {
+0x9f08,0x988e,0x4fc3,0x3f68,
+0x290f,0x59f9,0x0792,0xbfe2,
+0x3e6a,0xbaf3,0xdff5,0x401b,
+0xab68,0xac01,0x91aa,0xc039,
+0x081d,0x40f3,0x8962,0x403c,
+};
+static short S[16] = {
+/* 0x0000,0x0000,0x0000,0x3ff0, */
+0x5d8c,0xb6bf,0xf2a2,0xc035,
+0x7f42,0xaf6a,0x6219,0x4062,
+0x63ee,0x9590,0xfe08,0xc077,
+0x44be,0xb0b6,0x6709,0x4075,
+};
+#endif
+#if MIEEE
+static short R[20] = {
+0x3f68,0x4fc3,0x988e,0x9f08,
+0xbfe2,0x0792,0x59f9,0x290f,
+0x401b,0xdff5,0xbaf3,0x3e6a,
+0xc039,0x91aa,0xac01,0xab68,
+0x403c,0x8962,0x40f3,0x081d,
+};
+static short S[16] = {
+/* 0x3ff0,0x0000,0x0000,0x0000, */
+0xc035,0xf2a2,0xb6bf,0x5d8c,
+0x4062,0x6219,0xaf6a,0x7f42,
+0xc077,0xfe08,0x9590,0x63ee,
+0x4075,0x6709,0xb0b6,0x44be,
+};
+#endif
+
+/* pi/2 = PIO2 + MOREBITS. */
+#ifdef DEC
+#define MOREBITS 5.721188726109831840122E-18
+#else
+#define MOREBITS 6.123233995736765886130E-17
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double sqrt ( double );
+double asin ( double );
+#else
+double sqrt(), polevl(), p1evl();
+double asin();
+#endif
+extern double PIO2, PIO4, NAN;
+
+double asin(x)
+double x;
+{
+double a, p, z, zz;
+short sign;
+
+if( x > 0 )
+ {
+ sign = 1;
+ a = x;
+ }
+else
+ {
+ sign = -1;
+ a = -x;
+ }
+
+if( a > 1.0 )
+ {
+ mtherr( "asin", DOMAIN );
+ return( NAN );
+ }
+
+if( a > 0.625 )
+ {
+ /* arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x)) */
+ zz = 1.0 - a;
+ p = zz * polevl( zz, R, 4)/p1evl( zz, S, 4);
+ zz = sqrt(zz+zz);
+ z = PIO4 - zz;
+ zz = zz * p - MOREBITS;
+ z = z - zz;
+ z = z + PIO4;
+ }
+else
+ {
+ if( a < 1.0e-8 )
+ {
+ return(x);
+ }
+ zz = a * a;
+ z = zz * polevl( zz, P, 5)/p1evl( zz, Q, 5);
+ z = a * z + a;
+ }
+if( sign < 0 )
+ z = -z;
+return(z);
+}
+
+
+
+double acos(x)
+double x;
+{
+double z;
+
+if( (x < -1.0) || (x > 1.0) )
+ {
+ mtherr( "acos", DOMAIN );
+ return( NAN );
+ }
+if( x > 0.5 )
+ {
+ return( 2.0 * asin( sqrt(0.5 - 0.5*x) ) );
+ }
+z = PIO4 - asin(x);
+z = z + MOREBITS;
+z = z + PIO4;
+return( z );
+}
diff --git a/libm/double/asinh.c b/libm/double/asinh.c
new file mode 100644
index 000000000..57966d264
--- /dev/null
+++ b/libm/double/asinh.c
@@ -0,0 +1,165 @@
+/* asinh.c
+ *
+ * Inverse hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, asinh();
+ *
+ * y = asinh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic sine of argument.
+ *
+ * If |x| < 0.5, the function is approximated by a rational
+ * form x + x**3 P(x)/Q(x). Otherwise,
+ *
+ * asinh(x) = log( x + sqrt(1 + x*x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -3,3 75000 4.6e-17 1.1e-17
+ * IEEE -1,1 30000 3.7e-16 7.8e-17
+ * IEEE 1,3 30000 2.5e-16 6.7e-17
+ *
+ */
+
+/* asinh.c */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+-4.33231683752342103572E-3,
+-5.91750212056387121207E-1,
+-4.37390226194356683570E0,
+-9.09030533308377316566E0,
+-5.56682227230859640450E0
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 1.28757002067426453537E1,
+ 4.86042483805291788324E1,
+ 6.95722521337257608734E1,
+ 3.34009336338516356383E1
+};
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0136215,0173033,0110410,0105475,
+0140027,0076361,0020056,0164520,
+0140613,0173401,0160136,0053142,
+0141021,0070744,0000503,0176261,
+0140662,0021550,0073106,0133351
+};
+static unsigned short Q[] = {
+/* 0040200,0000000,0000000,0000000,*/
+0041116,0001336,0034120,0173054,
+0041502,0065300,0013144,0021231,
+0041613,0022376,0035516,0153063,
+0041405,0115216,0054265,0004557
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x1168,0x7221,0xbec3,0xbf71,
+0xdd2a,0x2405,0xef9e,0xbfe2,
+0xcacc,0x3c0b,0x7ee0,0xc011,
+0x7f96,0x8028,0x2e3c,0xc022,
+0xd6dd,0x0ec8,0x446d,0xc016
+};
+static unsigned short Q[] = {
+/* 0x0000,0x0000,0x0000,0x3ff0,*/
+0x1ec5,0xc70a,0xc05b,0x4029,
+0x8453,0x02cc,0x4d58,0x4048,
+0xdac6,0xc769,0x649f,0x4051,
+0xa12e,0xcb16,0xb351,0x4040
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0xbf71,0xbec3,0x7221,0x1168,
+0xbfe2,0xef9e,0x2405,0xdd2a,
+0xc011,0x7ee0,0x3c0b,0xcacc,
+0xc022,0x2e3c,0x8028,0x7f96,
+0xc016,0x446d,0x0ec8,0xd6dd
+};
+static unsigned short Q[] = {
+0x4029,0xc05b,0xc70a,0x1ec5,
+0x4048,0x4d58,0x02cc,0x8453,
+0x4051,0x649f,0xc769,0xdac6,
+0x4040,0xb351,0xcb16,0xa12e
+};
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double sqrt ( double );
+extern double log ( double );
+#else
+double log(), sqrt(), polevl(), p1evl();
+#endif
+extern double LOGE2, INFINITY;
+
+double asinh(xx)
+double xx;
+{
+double a, z, x;
+int sign;
+
+#ifdef MINUSZERO
+if( xx == 0.0 )
+ return(xx);
+#endif
+if( xx < 0.0 )
+ {
+ sign = -1;
+ x = -xx;
+ }
+else
+ {
+ sign = 1;
+ x = xx;
+ }
+
+if( x > 1.0e8 )
+ {
+#ifdef INFINITIES
+ if( x == INFINITY )
+ return(xx);
+#endif
+ return( sign * (log(x) + LOGE2) );
+ }
+
+z = x * x;
+if( x < 0.5 )
+ {
+ a = ( polevl(z, P, 4)/p1evl(z, Q, 4) ) * z;
+ a = a * x + x;
+ if( sign < 0 )
+ a = -a;
+ return(a);
+ }
+
+a = sqrt( z + 1.0 );
+return( sign * log(x + a) );
+}
diff --git a/libm/double/atan.c b/libm/double/atan.c
new file mode 100644
index 000000000..f2d50768d
--- /dev/null
+++ b/libm/double/atan.c
@@ -0,0 +1,393 @@
+/* atan.c
+ *
+ * Inverse circular tangent
+ * (arctangent)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, atan();
+ *
+ * y = atan( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose tangent
+ * is x.
+ *
+ * Range reduction is from three intervals into the interval
+ * from zero to 0.66. The approximant uses a rational
+ * function of degree 4/5 of the form x + x**3 P(x)/Q(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10, 10 50000 2.4e-17 8.3e-18
+ * IEEE -10, 10 10^6 1.8e-16 5.0e-17
+ *
+ */
+ /* atan2()
+ *
+ * Quadrant correct inverse circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, z, atan2();
+ *
+ * z = atan2( y, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle whose tangent is y/x.
+ * Define compile time symbol ANSIC = 1 for ANSI standard,
+ * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
+ * 0 to 2PI, args (x,y).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10, 10 10^6 2.5e-16 6.9e-17
+ * See atan.c.
+ *
+ */
+
+/* atan.c */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+/* arctan(x) = x + x^3 P(x^2)/Q(x^2)
+ 0 <= x <= 0.66
+ Peak relative error = 2.6e-18 */
+#ifdef UNK
+static double P[5] = {
+-8.750608600031904122785E-1,
+-1.615753718733365076637E1,
+-7.500855792314704667340E1,
+-1.228866684490136173410E2,
+-6.485021904942025371773E1,
+};
+static double Q[5] = {
+/* 1.000000000000000000000E0, */
+ 2.485846490142306297962E1,
+ 1.650270098316988542046E2,
+ 4.328810604912902668951E2,
+ 4.853903996359136964868E2,
+ 1.945506571482613964425E2,
+};
+
+/* tan( 3*pi/8 ) */
+static double T3P8 = 2.41421356237309504880;
+#endif
+
+#ifdef DEC
+static short P[20] = {
+0140140,0001775,0007671,0026242,
+0141201,0041242,0155534,0001715,
+0141626,0002141,0132100,0011625,
+0141765,0142771,0064055,0150453,
+0141601,0131517,0164507,0062164,
+};
+static short Q[20] = {
+/* 0040200,0000000,0000000,0000000, */
+0041306,0157042,0154243,0000742,
+0042045,0003352,0016707,0150452,
+0042330,0070306,0113425,0170730,
+0042362,0130770,0116602,0047520,
+0042102,0106367,0156753,0013541,
+};
+
+/* tan( 3*pi/8 ) = 2.41421356237309504880 */
+static unsigned short T3P8A[] = {040432,0101171,0114774,0167462,};
+#define T3P8 *(double *)T3P8A
+#endif
+
+#ifdef IBMPC
+static short P[20] = {
+0x2594,0xa1f7,0x007f,0xbfec,
+0x807a,0x5b6b,0x2854,0xc030,
+0x0273,0x3688,0xc08c,0xc052,
+0xba25,0x2d05,0xb8bf,0xc05e,
+0xec8e,0xfd28,0x3669,0xc050,
+};
+static short Q[20] = {
+/* 0x0000,0x0000,0x0000,0x3ff0, */
+0x603c,0x5b14,0xdbc4,0x4038,
+0xfa25,0x43b8,0xa0dd,0x4064,
+0xbe3b,0xd2e2,0x0e18,0x407b,
+0x49ea,0x13b0,0x563f,0x407e,
+0x62ec,0xfbbd,0x519e,0x4068,
+};
+
+/* tan( 3*pi/8 ) = 2.41421356237309504880 */
+static unsigned short T3P8A[] = {0x9de6,0x333f,0x504f,0x4003};
+#define T3P8 *(double *)T3P8A
+#endif
+
+#ifdef MIEEE
+static short P[20] = {
+0xbfec,0x007f,0xa1f7,0x2594,
+0xc030,0x2854,0x5b6b,0x807a,
+0xc052,0xc08c,0x3688,0x0273,
+0xc05e,0xb8bf,0x2d05,0xba25,
+0xc050,0x3669,0xfd28,0xec8e,
+};
+static short Q[20] = {
+/* 0x3ff0,0x0000,0x0000,0x0000, */
+0x4038,0xdbc4,0x5b14,0x603c,
+0x4064,0xa0dd,0x43b8,0xfa25,
+0x407b,0x0e18,0xd2e2,0xbe3b,
+0x407e,0x563f,0x13b0,0x49ea,
+0x4068,0x519e,0xfbbd,0x62ec,
+};
+
+/* tan( 3*pi/8 ) = 2.41421356237309504880 */
+static unsigned short T3P8A[] = {
+0x4003,0x504f,0x333f,0x9de6
+};
+#define T3P8 *(double *)T3P8A
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double atan ( double );
+extern double fabs ( double );
+extern int signbit ( double );
+extern int isnan ( double );
+#else
+double polevl(), p1evl(), atan(), fabs();
+//int signbit(), isnan();
+#endif
+extern double PI, PIO2, PIO4, INFINITY, NEGZERO, MAXNUM;
+
+/* pi/2 = PIO2 + MOREBITS. */
+#ifdef DEC
+#define MOREBITS 5.721188726109831840122E-18
+#else
+#define MOREBITS 6.123233995736765886130E-17
+#endif
+
+
+double atan(x)
+double x;
+{
+double y, z;
+short sign, flag;
+
+#ifdef MINUSZERO
+if( x == 0.0 )
+ return(x);
+#endif
+#ifdef INFINITIES
+if(x == INFINITY)
+ return(PIO2);
+if(x == -INFINITY)
+ return(-PIO2);
+#endif
+/* make argument positive and save the sign */
+sign = 1;
+if( x < 0.0 )
+ {
+ sign = -1;
+ x = -x;
+ }
+/* range reduction */
+flag = 0;
+if( x > T3P8 )
+ {
+ y = PIO2;
+ flag = 1;
+ x = -( 1.0/x );
+ }
+else if( x <= 0.66 )
+ {
+ y = 0.0;
+ }
+else
+ {
+ y = PIO4;
+ flag = 2;
+ x = (x-1.0)/(x+1.0);
+ }
+z = x * x;
+z = z * polevl( z, P, 4 ) / p1evl( z, Q, 5 );
+z = x * z + x;
+if( flag == 2 )
+ z += 0.5 * MOREBITS;
+else if( flag == 1 )
+ z += MOREBITS;
+y = y + z;
+if( sign < 0 )
+ y = -y;
+return(y);
+}
+
+/* atan2 */
+
+#ifdef ANSIC
+double atan2( y, x )
+#else
+double atan2( x, y )
+#endif
+double x, y;
+{
+double z, w;
+short code;
+
+code = 0;
+
+#ifdef NANS
+if( isnan(x) )
+ return(x);
+if( isnan(y) )
+ return(y);
+#endif
+#ifdef MINUSZERO
+if( y == 0.0 )
+ {
+ if( signbit(y) )
+ {
+ if( x > 0.0 )
+ z = y;
+ else if( x < 0.0 )
+ z = -PI;
+ else
+ {
+ if( signbit(x) )
+ z = -PI;
+ else
+ z = y;
+ }
+ }
+ else /* y is +0 */
+ {
+ if( x == 0.0 )
+ {
+ if( signbit(x) )
+ z = PI;
+ else
+ z = 0.0;
+ }
+ else if( x > 0.0 )
+ z = 0.0;
+ else
+ z = PI;
+ }
+ return z;
+ }
+if( x == 0.0 )
+ {
+ if( y > 0.0 )
+ z = PIO2;
+ else
+ z = -PIO2;
+ return z;
+ }
+#endif /* MINUSZERO */
+#ifdef INFINITIES
+if( x == INFINITY )
+ {
+ if( y == INFINITY )
+ z = 0.25 * PI;
+ else if( y == -INFINITY )
+ z = -0.25 * PI;
+ else if( y < 0.0 )
+ z = NEGZERO;
+ else
+ z = 0.0;
+ return z;
+ }
+if( x == -INFINITY )
+ {
+ if( y == INFINITY )
+ z = 0.75 * PI;
+ else if( y <= -INFINITY )
+ z = -0.75 * PI;
+ else if( y >= 0.0 )
+ z = PI;
+ else
+ z = -PI;
+ return z;
+ }
+if( y == INFINITY )
+ return( PIO2 );
+if( y == -INFINITY )
+ return( -PIO2 );
+#endif
+
+if( x < 0.0 )
+ code = 2;
+if( y < 0.0 )
+ code |= 1;
+
+#ifdef INFINITIES
+if( x == 0.0 )
+#else
+if( fabs(x) <= (fabs(y) / MAXNUM) )
+#endif
+ {
+ if( code & 1 )
+ {
+#if ANSIC
+ return( -PIO2 );
+#else
+ return( 3.0*PIO2 );
+#endif
+ }
+ if( y == 0.0 )
+ return( 0.0 );
+ return( PIO2 );
+ }
+
+if( y == 0.0 )
+ {
+ if( code & 2 )
+ return( PI );
+ return( 0.0 );
+ }
+
+
+switch( code )
+ {
+#if ANSIC
+ default:
+ case 0:
+ case 1: w = 0.0; break;
+ case 2: w = PI; break;
+ case 3: w = -PI; break;
+#else
+ default:
+ case 0: w = 0.0; break;
+ case 1: w = 2.0 * PI; break;
+ case 2:
+ case 3: w = PI; break;
+#endif
+ }
+
+z = w + atan( y/x );
+#ifdef MINUSZERO
+if( z == 0.0 && y < 0 )
+ z = NEGZERO;
+#endif
+return( z );
+}
diff --git a/libm/double/atanh.c b/libm/double/atanh.c
new file mode 100644
index 000000000..7bb742d3d
--- /dev/null
+++ b/libm/double/atanh.c
@@ -0,0 +1,156 @@
+/* atanh.c
+ *
+ * Inverse hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, atanh();
+ *
+ * y = atanh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic tangent of argument in the range
+ * MINLOG to MAXLOG.
+ *
+ * If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is
+ * employed. Otherwise,
+ * atanh(x) = 0.5 * log( (1+x)/(1-x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -1,1 50000 2.4e-17 6.4e-18
+ * IEEE -1,1 30000 1.9e-16 5.2e-17
+ *
+ */
+
+/* atanh.c */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright (C) 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+-8.54074331929669305196E-1,
+ 1.20426861384072379242E1,
+-4.61252884198732692637E1,
+ 6.54566728676544377376E1,
+-3.09092539379866942570E1
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+-1.95638849376911654834E1,
+ 1.08938092147140262656E2,
+-2.49839401325893582852E2,
+ 2.52006675691344555838E2,
+-9.27277618139601130017E1
+};
+#endif
+#ifdef DEC
+static unsigned short P[] = {
+0140132,0122235,0105775,0130300,
+0041100,0127327,0124407,0034722,
+0141470,0100113,0115607,0130535,
+0041602,0164721,0003257,0013673,
+0141367,0043046,0166673,0045750
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0141234,0101326,0015460,0134564,
+0041731,0160115,0116451,0032045,
+0142171,0153343,0000532,0167226,
+0042174,0000665,0077604,0000310,
+0141671,0072235,0031114,0074377
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0xb618,0xb17f,0x5493,0xbfeb,
+0xe73a,0xf520,0x15da,0x4028,
+0xf62c,0x7370,0x1009,0xc047,
+0xe2f7,0x20d5,0x5d3a,0x4050,
+0x697d,0xddb7,0xe8c4,0xc03e
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x172f,0xc366,0x905a,0xc033,
+0x2685,0xb3a5,0x3c09,0x405b,
+0x5dd3,0x602b,0x3adc,0xc06f,
+0x8019,0xaff0,0x8036,0x406f,
+0x8f20,0xa649,0x2e93,0xc057
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0xbfeb,0x5493,0xb17f,0xb618,
+0x4028,0x15da,0xf520,0xe73a,
+0xc047,0x1009,0x7370,0xf62c,
+0x4050,0x5d3a,0x20d5,0xe2f7,
+0xc03e,0xe8c4,0xddb7,0x697d
+};
+static unsigned short Q[] = {
+0xc033,0x905a,0xc366,0x172f,
+0x405b,0x3c09,0xb3a5,0x2685,
+0xc06f,0x3adc,0x602b,0x5dd3,
+0x406f,0x8036,0xaff0,0x8019,
+0xc057,0x2e93,0xa649,0x8f20
+};
+#endif
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double log ( double x );
+extern double polevl ( double x, void *P, int N );
+extern double p1evl ( double x, void *P, int N );
+#else
+double fabs(), log(), polevl(), p1evl();
+#endif
+extern double INFINITY, NAN;
+
+double atanh(x)
+double x;
+{
+double s, z;
+
+#ifdef MINUSZERO
+if( x == 0.0 )
+ return(x);
+#endif
+z = fabs(x);
+if( z >= 1.0 )
+ {
+ if( x == 1.0 )
+ return( INFINITY );
+ if( x == -1.0 )
+ return( -INFINITY );
+ mtherr( "atanh", DOMAIN );
+ return( NAN );
+ }
+
+if( z < 1.0e-7 )
+ return(x);
+
+if( z < 0.5 )
+ {
+ z = x * x;
+ s = x + x * z * (polevl(z, P, 4) / p1evl(z, Q, 5));
+ return(s);
+ }
+
+return( 0.5 * log((1.0+x)/(1.0-x)) );
+}
diff --git a/libm/double/bdtr.c b/libm/double/bdtr.c
new file mode 100644
index 000000000..a268c7a10
--- /dev/null
+++ b/libm/double/bdtr.c
@@ -0,0 +1,263 @@
+/* bdtr.c
+ *
+ * Binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtr();
+ *
+ * y = bdtr( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the Binomial
+ * probability density:
+ *
+ * k
+ * -- ( n ) j n-j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p), with p between 0 and 1.
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * For p between 0.001 and 1:
+ * IEEE 0,100 100000 4.3e-15 2.6e-16
+ * See also incbet.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtr domain k < 0 0.0
+ * n < k
+ * x < 0, x > 1
+ */
+ /* bdtrc()
+ *
+ * Complemented binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtrc();
+ *
+ * y = bdtrc( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 through n of the Binomial
+ * probability density:
+ *
+ * n
+ * -- ( n ) j n-j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p).
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * For p between 0.001 and 1:
+ * IEEE 0,100 100000 6.7e-15 8.2e-16
+ * For p between 0 and .001:
+ * IEEE 0,100 100000 1.5e-13 2.7e-15
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtrc domain x<0, x>1, n<k 0.0
+ */
+ /* bdtri()
+ *
+ * Inverse binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, bdtri();
+ *
+ * p = bdtr( k, n, y );
+ *
+ * DESCRIPTION:
+ *
+ * Finds the event probability p such that the sum of the
+ * terms 0 through k of the Binomial probability density
+ * is equal to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relation
+ *
+ * 1 - p = incbi( n-k, k+1, y ).
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p).
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * For p between 0.001 and 1:
+ * IEEE 0,100 100000 2.3e-14 6.4e-16
+ * IEEE 0,10000 100000 6.6e-12 1.2e-13
+ * For p between 10^-6 and 0.001:
+ * IEEE 0,100 100000 2.0e-12 1.3e-14
+ * IEEE 0,10000 100000 1.5e-12 3.2e-14
+ * See also incbi.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtri domain k < 0, n <= k 0.0
+ * x < 0, x > 1
+ */
+
+/* bdtr() */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double incbet ( double, double, double );
+extern double incbi ( double, double, double );
+extern double pow ( double, double );
+extern double log1p ( double );
+extern double expm1 ( double );
+#else
+double incbet(), incbi(), pow(), log1p(), expm1();
+#endif
+
+double bdtrc( k, n, p )
+int k, n;
+double p;
+{
+double dk, dn;
+
+if( (p < 0.0) || (p > 1.0) )
+ goto domerr;
+if( k < 0 )
+ return( 1.0 );
+
+if( n < k )
+ {
+domerr:
+ mtherr( "bdtrc", DOMAIN );
+ return( 0.0 );
+ }
+
+if( k == n )
+ return( 0.0 );
+dn = n - k;
+if( k == 0 )
+ {
+ if( p < .01 )
+ dk = -expm1( dn * log1p(-p) );
+ else
+ dk = 1.0 - pow( 1.0-p, dn );
+ }
+else
+ {
+ dk = k + 1;
+ dk = incbet( dk, dn, p );
+ }
+return( dk );
+}
+
+
+
+double bdtr( k, n, p )
+int k, n;
+double p;
+{
+double dk, dn;
+
+if( (p < 0.0) || (p > 1.0) )
+ goto domerr;
+if( (k < 0) || (n < k) )
+ {
+domerr:
+ mtherr( "bdtr", DOMAIN );
+ return( 0.0 );
+ }
+
+if( k == n )
+ return( 1.0 );
+
+dn = n - k;
+if( k == 0 )
+ {
+ dk = pow( 1.0-p, dn );
+ }
+else
+ {
+ dk = k + 1;
+ dk = incbet( dn, dk, 1.0 - p );
+ }
+return( dk );
+}
+
+
+double bdtri( k, n, y )
+int k, n;
+double y;
+{
+double dk, dn, p;
+
+if( (y < 0.0) || (y > 1.0) )
+ goto domerr;
+if( (k < 0) || (n <= k) )
+ {
+domerr:
+ mtherr( "bdtri", DOMAIN );
+ return( 0.0 );
+ }
+
+dn = n - k;
+if( k == 0 )
+ {
+ if( y > 0.8 )
+ p = -expm1( log1p(y-1.0) / dn );
+ else
+ p = 1.0 - pow( y, 1.0/dn );
+ }
+else
+ {
+ dk = k + 1;
+ p = incbet( dn, dk, 0.5 );
+ if( p > 0.5 )
+ p = incbi( dk, dn, 1.0-y );
+ else
+ p = 1.0 - incbi( dn, dk, y );
+ }
+return( p );
+}
diff --git a/libm/double/bernum.c b/libm/double/bernum.c
new file mode 100644
index 000000000..e401ff5df
--- /dev/null
+++ b/libm/double/bernum.c
@@ -0,0 +1,74 @@
+/* This program computes the Bernoulli numbers.
+ * See radd.c for rational arithmetic.
+ */
+
+typedef struct{
+ double n;
+ double d;
+ }fract;
+
+#define PD 44
+fract x[PD+1] = {0.0};
+fract p[PD+1] = {0.0};
+#include <math.h>
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double log10 ( double );
+#else
+double fabs(), log10();
+#endif
+extern double MACHEP;
+
+main()
+{
+int nx, np, nu;
+int i, j, k, n, sign;
+fract r, s, t;
+
+
+for(i=0; i<=PD; i++ )
+ {
+ x[i].n = 0.0;
+ x[i].d = 1.0;
+ p[i].n = 0.0;
+ p[i].d = 1.0;
+ }
+p[0].n = 1.0;
+p[0].d = 1.0;
+p[1].n = 1.0;
+p[1].d = 1.0;
+np = 1;
+x[0].n = 1.0;
+x[0].d = 1.0;
+
+for( n=1; n<PD-2; n++ )
+{
+
+/* Create line of Pascal's triangle */
+/* multiply p = u * p */
+for( k=0; k<=np; k++ )
+ {
+ radd( &p[np-k+1], &p[np-k], &p[np-k+1] );
+ }
+np += 1;
+
+/* B0 + nC1 B1 + ... + nCn-1 Bn-1 = 0 */
+s.n = 0.0;
+s.d = 1.0;
+
+for( i=0; i<n; i++ )
+ {
+ rmul( &p[i], &x[i], &t );
+ radd( &s, &t, &s );
+ }
+
+
+rdiv( &p[n], &s, &x[n] ); /* x[n] = -s/p[n] */
+x[n].n = -x[n].n;
+nx += 1;
+printf( "%2d %.15e / %.15e\n", n, x[n].n, x[n].d );
+}
+
+
+}
+
diff --git a/libm/double/beta.c b/libm/double/beta.c
new file mode 100644
index 000000000..410760f32
--- /dev/null
+++ b/libm/double/beta.c
@@ -0,0 +1,201 @@
+/* beta.c
+ *
+ * Beta function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, y, beta();
+ *
+ * y = beta( a, b );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * - -
+ * | (a) | (b)
+ * beta( a, b ) = -----------.
+ * -
+ * | (a+b)
+ *
+ * For large arguments the logarithm of the function is
+ * evaluated using lgam(), then exponentiated.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 1700 7.7e-15 1.5e-15
+ * IEEE 0,30 30000 8.1e-14 1.1e-14
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * beta overflow log(beta) > MAXLOG 0.0
+ * a or b <0 integer 0.0
+ *
+ */
+
+/* beta.c */
+
+
+/*
+Cephes Math Library Release 2.0: April, 1987
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+#ifdef UNK
+#define MAXGAM 34.84425627277176174
+#endif
+#ifdef DEC
+#define MAXGAM 34.84425627277176174
+#endif
+#ifdef IBMPC
+#define MAXGAM 171.624376956302725
+#endif
+#ifdef MIEEE
+#define MAXGAM 171.624376956302725
+#endif
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double gamma ( double );
+extern double lgam ( double );
+extern double exp ( double );
+extern double log ( double );
+extern double floor ( double );
+#else
+double fabs(), gamma(), lgam(), exp(), log(), floor();
+#endif
+extern double MAXLOG, MAXNUM;
+extern int sgngam;
+
+double beta( a, b )
+double a, b;
+{
+double y;
+int sign;
+
+sign = 1;
+
+if( a <= 0.0 )
+ {
+ if( a == floor(a) )
+ goto over;
+ }
+if( b <= 0.0 )
+ {
+ if( b == floor(b) )
+ goto over;
+ }
+
+
+y = a + b;
+if( fabs(y) > MAXGAM )
+ {
+ y = lgam(y);
+ sign *= sgngam; /* keep track of the sign */
+ y = lgam(b) - y;
+ sign *= sgngam;
+ y = lgam(a) + y;
+ sign *= sgngam;
+ if( y > MAXLOG )
+ {
+over:
+ mtherr( "beta", OVERFLOW );
+ return( sign * MAXNUM );
+ }
+ return( sign * exp(y) );
+ }
+
+y = gamma(y);
+if( y == 0.0 )
+ goto over;
+
+if( a > b )
+ {
+ y = gamma(a)/y;
+ y *= gamma(b);
+ }
+else
+ {
+ y = gamma(b)/y;
+ y *= gamma(a);
+ }
+
+return(y);
+}
+
+
+
+/* Natural log of |beta|. Return the sign of beta in sgngam. */
+
+double lbeta( a, b )
+double a, b;
+{
+double y;
+int sign;
+
+sign = 1;
+
+if( a <= 0.0 )
+ {
+ if( a == floor(a) )
+ goto over;
+ }
+if( b <= 0.0 )
+ {
+ if( b == floor(b) )
+ goto over;
+ }
+
+
+y = a + b;
+if( fabs(y) > MAXGAM )
+ {
+ y = lgam(y);
+ sign *= sgngam; /* keep track of the sign */
+ y = lgam(b) - y;
+ sign *= sgngam;
+ y = lgam(a) + y;
+ sign *= sgngam;
+ sgngam = sign;
+ return( y );
+ }
+
+y = gamma(y);
+if( y == 0.0 )
+ {
+over:
+ mtherr( "lbeta", OVERFLOW );
+ return( sign * MAXNUM );
+ }
+
+if( a > b )
+ {
+ y = gamma(a)/y;
+ y *= gamma(b);
+ }
+else
+ {
+ y = gamma(b)/y;
+ y *= gamma(a);
+ }
+
+if( y < 0 )
+ {
+ sgngam = -1;
+ y = -y;
+ }
+else
+ sgngam = 1;
+
+return( log(y) );
+}
diff --git a/libm/double/btdtr.c b/libm/double/btdtr.c
new file mode 100644
index 000000000..633ba7591
--- /dev/null
+++ b/libm/double/btdtr.c
@@ -0,0 +1,64 @@
+
+/* btdtr.c
+ *
+ * Beta distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, btdtr();
+ *
+ * y = btdtr( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the beta density
+ * function:
+ *
+ *
+ * x
+ * - -
+ * | (a+b) | | a-1 b-1
+ * P(x) = ---------- | t (1-t) dt
+ * - - | |
+ * | (a) | (b) -
+ * 0
+ *
+ *
+ * This function is identical to the incomplete beta
+ * integral function incbet(a, b, x).
+ *
+ * The complemented function is
+ *
+ * 1 - P(1-x) = incbet( b, a, x );
+ *
+ *
+ * ACCURACY:
+ *
+ * See incbet.c.
+ *
+ */
+
+/* btdtr() */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+#include <math.h>
+#ifdef ANSIPROT
+extern double incbet ( double, double, double );
+#else
+double incbet();
+#endif
+
+double btdtr( a, b, x )
+double a, b, x;
+{
+
+return( incbet( a, b, x ) );
+}
diff --git a/libm/double/cbrt.c b/libm/double/cbrt.c
new file mode 100644
index 000000000..026207275
--- /dev/null
+++ b/libm/double/cbrt.c
@@ -0,0 +1,142 @@
+/* cbrt.c
+ *
+ * Cube root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cbrt();
+ *
+ * y = cbrt( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the cube root of the argument, which may be negative.
+ *
+ * Range reduction involves determining the power of 2 of
+ * the argument. A polynomial of degree 2 applied to the
+ * mantissa, and multiplication by the cube root of 1, 2, or 4
+ * approximates the root to within about 0.1%. Then Newton's
+ * iteration is used three times to converge to an accurate
+ * result.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,10 200000 1.8e-17 6.2e-18
+ * IEEE 0,1e308 30000 1.5e-16 5.0e-17
+ *
+ */
+ /* cbrt.c */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1991, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+static double CBRT2 = 1.2599210498948731647672;
+static double CBRT4 = 1.5874010519681994747517;
+static double CBRT2I = 0.79370052598409973737585;
+static double CBRT4I = 0.62996052494743658238361;
+
+#ifdef ANSIPROT
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double frexp(), ldexp();
+int isnan(), isfinite();
+#endif
+
+double cbrt(x)
+double x;
+{
+int e, rem, sign;
+double z;
+
+#ifdef NANS
+if( isnan(x) )
+ return x;
+#endif
+#ifdef INFINITIES
+if( !isfinite(x) )
+ return x;
+#endif
+if( x == 0 )
+ return( x );
+if( x > 0 )
+ sign = 1;
+else
+ {
+ sign = -1;
+ x = -x;
+ }
+
+z = x;
+/* extract power of 2, leaving
+ * mantissa between 0.5 and 1
+ */
+x = frexp( x, &e );
+
+/* Approximate cube root of number between .5 and 1,
+ * peak relative error = 9.2e-6
+ */
+x = (((-1.3466110473359520655053e-1 * x
+ + 5.4664601366395524503440e-1) * x
+ - 9.5438224771509446525043e-1) * x
+ + 1.1399983354717293273738e0 ) * x
+ + 4.0238979564544752126924e-1;
+
+/* exponent divided by 3 */
+if( e >= 0 )
+ {
+ rem = e;
+ e /= 3;
+ rem -= 3*e;
+ if( rem == 1 )
+ x *= CBRT2;
+ else if( rem == 2 )
+ x *= CBRT4;
+ }
+
+
+/* argument less than 1 */
+
+else
+ {
+ e = -e;
+ rem = e;
+ e /= 3;
+ rem -= 3*e;
+ if( rem == 1 )
+ x *= CBRT2I;
+ else if( rem == 2 )
+ x *= CBRT4I;
+ e = -e;
+ }
+
+/* multiply by power of 2 */
+x = ldexp( x, e );
+
+/* Newton iteration */
+x -= ( x - (z/(x*x)) )*0.33333333333333333333;
+#ifdef DEC
+x -= ( x - (z/(x*x)) )/3.0;
+#else
+x -= ( x - (z/(x*x)) )*0.33333333333333333333;
+#endif
+
+if( sign < 0 )
+ x = -x;
+return(x);
+}
diff --git a/libm/double/chbevl.c b/libm/double/chbevl.c
new file mode 100644
index 000000000..539388164
--- /dev/null
+++ b/libm/double/chbevl.c
@@ -0,0 +1,82 @@
+/* chbevl.c
+ *
+ * Evaluate Chebyshev series
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * double x, y, coef[N], chebevl();
+ *
+ * y = chbevl( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the series
+ *
+ * N-1
+ * - '
+ * y = > coef[i] T (x/2)
+ * - i
+ * i=0
+ *
+ * of Chebyshev polynomials Ti at argument x/2.
+ *
+ * Coefficients are stored in reverse order, i.e. the zero
+ * order term is last in the array. Note N is the number of
+ * coefficients, not the order.
+ *
+ * If coefficients are for the interval a to b, x must
+ * have been transformed to x -> 2(2x - b - a)/(b-a) before
+ * entering the routine. This maps x from (a, b) to (-1, 1),
+ * over which the Chebyshev polynomials are defined.
+ *
+ * If the coefficients are for the inverted interval, in
+ * which (a, b) is mapped to (1/b, 1/a), the transformation
+ * required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
+ * this becomes x -> 4a/x - 1.
+ *
+ *
+ *
+ * SPEED:
+ *
+ * Taking advantage of the recurrence properties of the
+ * Chebyshev polynomials, the routine requires one more
+ * addition per loop than evaluating a nested polynomial of
+ * the same degree.
+ *
+ */
+ /* chbevl.c */
+
+/*
+Cephes Math Library Release 2.0: April, 1987
+Copyright 1985, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+double chbevl( x, array, n )
+double x;
+double array[];
+int n;
+{
+double b0, b1, b2, *p;
+int i;
+
+p = array;
+b0 = *p++;
+b1 = 0.0;
+i = n - 1;
+
+do
+ {
+ b2 = b1;
+ b1 = b0;
+ b0 = x * b1 - b2 + *p++;
+ }
+while( --i );
+
+return( 0.5*(b0-b2) );
+}
diff --git a/libm/double/chdtr.c b/libm/double/chdtr.c
new file mode 100644
index 000000000..a29da7535
--- /dev/null
+++ b/libm/double/chdtr.c
@@ -0,0 +1,200 @@
+/* chdtr.c
+ *
+ * Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double df, x, y, chdtr();
+ *
+ * y = chdtr( df, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the left hand tail (from 0 to x)
+ * of the Chi square probability density function with
+ * v degrees of freedom.
+ *
+ *
+ * inf.
+ * -
+ * 1 | | v/2-1 -t/2
+ * P( x | v ) = ----------- | t e dt
+ * v/2 - | |
+ * 2 | (v/2) -
+ * x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ * y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtr domain x < 0 or v < 1 0.0
+ */
+ /* chdtrc()
+ *
+ * Complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, chdtrc();
+ *
+ * y = chdtrc( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the right hand tail (from x to
+ * infinity) of the Chi square probability density function
+ * with v degrees of freedom:
+ *
+ *
+ * inf.
+ * -
+ * 1 | | v/2-1 -t/2
+ * P( x | v ) = ----------- | t e dt
+ * v/2 - | |
+ * 2 | (v/2) -
+ * x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ * y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtrc domain x < 0 or v < 1 0.0
+ */
+ /* chdtri()
+ *
+ * Inverse of complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double df, x, y, chdtri();
+ *
+ * x = chdtri( df, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Chi-square argument x such that the integral
+ * from x to infinity of the Chi-square density is equal
+ * to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ * x/2 = igami( df/2, y );
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igami.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtri domain y < 0 or y > 1 0.0
+ * v < 1
+ *
+ */
+
+/* chdtr() */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double igamc ( double, double );
+extern double igam ( double, double );
+extern double igami ( double, double );
+#else
+double igamc(), igam(), igami();
+#endif
+
+double chdtrc(df,x)
+double df, x;
+{
+
+if( (x < 0.0) || (df < 1.0) )
+ {
+ mtherr( "chdtrc", DOMAIN );
+ return(0.0);
+ }
+return( igamc( df/2.0, x/2.0 ) );
+}
+
+
+
+double chdtr(df,x)
+double df, x;
+{
+
+if( (x < 0.0) || (df < 1.0) )
+ {
+ mtherr( "chdtr", DOMAIN );
+ return(0.0);
+ }
+return( igam( df/2.0, x/2.0 ) );
+}
+
+
+
+double chdtri( df, y )
+double df, y;
+{
+double x;
+
+if( (y < 0.0) || (y > 1.0) || (df < 1.0) )
+ {
+ mtherr( "chdtri", DOMAIN );
+ return(0.0);
+ }
+
+x = igami( 0.5 * df, y );
+return( 2.0 * x );
+}
diff --git a/libm/double/cheby.c b/libm/double/cheby.c
new file mode 100644
index 000000000..8da9b350e
--- /dev/null
+++ b/libm/double/cheby.c
@@ -0,0 +1,149 @@
+/* cheby.c
+ *
+ * Program to calculate coefficients of the Chebyshev polynomial
+ * expansion of a given input function. The algorithm computes
+ * the discrete Fourier cosine transform of the function evaluated
+ * at unevenly spaced points. Library routine chbevl.c uses the
+ * coefficients to calculate an approximate value of the original
+ * function.
+ * -- S. L. Moshier
+ */
+
+extern double PI; /* 3.14159... */
+extern double PIO2;
+double cosi[33] = {0.0,}; /* cosine array for Fourier transform */
+double func[65] = {0.0,}; /* values of the function */
+double cos(), log(), exp(), sqrt();
+
+main()
+{
+double c, r, s, t, x, y, z, temp;
+double low, high, dtemp;
+long n;
+int i, ii, j, n2, k, rr, invflg;
+short *p;
+char st[40];
+
+low = 0.0; /* low end of approximation interval */
+high = 1.0; /* high end */
+invflg = 0; /* set to 1 if inverted interval, else zero */
+/* Note: inverted interval goes from 1/high to 1/low */
+z = 0.0;
+n = 64; /* will find 64 coefficients */
+ /* but use only those greater than roundoff error */
+n2 = n/2;
+t = n;
+t = PI/t;
+
+/* calculate array of cosines */
+puts("calculating cosines");
+s = 1.0;
+cosi[0] = 1.0;
+i = 1;
+while( i < 32 )
+ {
+ y = cos( s * t );
+ cosi[i] = y;
+ s += 1.0;
+ ++i;
+ }
+cosi[32] = 0.0;
+
+/* cheby.c 2 */
+
+/* calculate function at special values of the argument */
+puts("calculating function values");
+x = low;
+y = high;
+if( invflg && (low != 0.0) )
+ { /* inverted interval */
+ temp = 1.0/x;
+ x = 1.0/y;
+ y = temp;
+ }
+r = (x + y)/2.0;
+printf( "center %.15E ", r);
+s = (y - x)/2.0;
+printf( "width %.15E\n", s);
+i = 0;
+while( i < 65 )
+ {
+ if( i < n2 )
+ c = cosi[i];
+ else
+ c = -cosi[64-i];
+ temp = r + s * c;
+/* if inverted interval, compute function(1/x) */
+ if( invflg && (temp != 0.0) )
+ temp = 1.0/temp;
+
+ printf( "%.15E ", temp );
+
+/* insert call to function routine here: */
+/**********************************/
+
+ if( temp == 0.0 )
+ y = 1.0;
+ else
+ y = exp( temp * log(2.0) );
+
+/**********************************/
+ func[i] = y;
+ printf( "%.15E\n", y );
+ ++i;
+ }
+
+/* cheby.c 3 */
+
+puts( "calculating Chebyshev coefficients");
+rr = 0;
+while( rr < 65 )
+ {
+ z = func[0]/2.0;
+ j = 1;
+ while( j < 65 )
+ {
+ k = (rr * j)/n2;
+ i = rr * j - n2 * k;
+ k &= 3;
+ if( k == 0 )
+ c = cosi[i];
+ if( k == 1 )
+ {
+ i = 32-i;
+ c = -cosi[i];
+ if( i == 32 )
+ c = -c;
+ }
+ if( k == 2 )
+ {
+ c = -cosi[i];
+ }
+ if( k == 3 )
+ {
+ i = 32-i;
+ c = cosi[i];
+ }
+ if( i != 32)
+ {
+ temp = func[j];
+ temp = c * temp;
+ z += temp;
+ }
+ ++j;
+ }
+
+ if( i != 32 )
+ {
+ temp /= 2.0;
+ z = z - temp;
+ }
+ z *= 2.0;
+ temp = n;
+ z /= temp;
+ dtemp = z;
+ ++rr;
+ sprintf( st, "/* %.16E */", dtemp );
+ puts( st );
+ }
+}
diff --git a/libm/double/clog.c b/libm/double/clog.c
new file mode 100644
index 000000000..70a318a50
--- /dev/null
+++ b/libm/double/clog.c
@@ -0,0 +1,1043 @@
+/* clog.c
+ *
+ * Complex natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void clog();
+ * cmplx z, w;
+ *
+ * clog( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns complex logarithm to the base e (2.718...) of
+ * the complex argument x.
+ *
+ * If z = x + iy, r = sqrt( x**2 + y**2 ),
+ * then
+ * w = log(r) + i arctan(y/x).
+ *
+ * The arctangent ranges from -PI to +PI.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 7000 8.5e-17 1.9e-17
+ * IEEE -10,+10 30000 5.0e-15 1.1e-16
+ *
+ * Larger relative error can be observed for z near 1 +i0.
+ * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
+ * absolute error 1.0e-16.
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+#include <math.h>
+#ifdef ANSIPROT
+static void cchsh ( double x, double *c, double *s );
+static double redupi ( double x );
+static double ctans ( cmplx *z );
+/* These are supposed to be in some standard place. */
+double fabs (double);
+double sqrt (double);
+double pow (double, double);
+double log (double);
+double exp (double);
+double atan2 (double, double);
+double cosh (double);
+double sinh (double);
+double asin (double);
+double sin (double);
+double cos (double);
+double cabs (cmplx *);
+void cadd ( cmplx *, cmplx *, cmplx * );
+void cmul ( cmplx *, cmplx *, cmplx * );
+void csqrt ( cmplx *, cmplx * );
+static void cchsh ( double, double *, double * );
+static double redupi ( double );
+static double ctans ( cmplx * );
+void clog ( cmplx *, cmplx * );
+void casin ( cmplx *, cmplx * );
+void cacos ( cmplx *, cmplx * );
+void catan ( cmplx *, cmplx * );
+#else
+static void cchsh();
+static double redupi();
+static double ctans();
+double cabs(), fabs(), sqrt(), pow();
+double log(), exp(), atan2(), cosh(), sinh();
+double asin(), sin(), cos();
+void cadd(), cmul(), csqrt();
+void clog(), casin(), cacos(), catan();
+#endif
+
+
+extern double MAXNUM, MACHEP, PI, PIO2;
+
+void clog( z, w )
+register cmplx *z, *w;
+{
+double p, rr;
+
+/*rr = sqrt( z->r * z->r + z->i * z->i );*/
+rr = cabs(z);
+p = log(rr);
+#if ANSIC
+rr = atan2( z->i, z->r );
+#else
+rr = atan2( z->r, z->i );
+if( rr > PI )
+ rr -= PI + PI;
+#endif
+w->i = rr;
+w->r = p;
+}
+ /* cexp()
+ *
+ * Complex exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cexp();
+ * cmplx z, w;
+ *
+ * cexp( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the exponential of the complex argument z
+ * into the complex result w.
+ *
+ * If
+ * z = x + iy,
+ * r = exp(x),
+ *
+ * then
+ *
+ * w = r cos y + i r sin y.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 8700 3.7e-17 1.1e-17
+ * IEEE -10,+10 30000 3.0e-16 8.7e-17
+ *
+ */
+
+void cexp( z, w )
+register cmplx *z, *w;
+{
+double r;
+
+r = exp( z->r );
+w->r = r * cos( z->i );
+w->i = r * sin( z->i );
+}
+ /* csin()
+ *
+ * Complex circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csin();
+ * cmplx z, w;
+ *
+ * csin( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * w = sin x cosh y + i cos x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 8400 5.3e-17 1.3e-17
+ * IEEE -10,+10 30000 3.8e-16 1.0e-16
+ * Also tested by csin(casin(z)) = z.
+ *
+ */
+
+void csin( z, w )
+register cmplx *z, *w;
+{
+double ch, sh;
+
+cchsh( z->i, &ch, &sh );
+w->r = sin( z->r ) * ch;
+w->i = cos( z->r ) * sh;
+}
+
+
+
+/* calculate cosh and sinh */
+
+static void cchsh( x, c, s )
+double x, *c, *s;
+{
+double e, ei;
+
+if( fabs(x) <= 0.5 )
+ {
+ *c = cosh(x);
+ *s = sinh(x);
+ }
+else
+ {
+ e = exp(x);
+ ei = 0.5/e;
+ e = 0.5 * e;
+ *s = e - ei;
+ *c = e + ei;
+ }
+}
+
+ /* ccos()
+ *
+ * Complex circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccos();
+ * cmplx z, w;
+ *
+ * ccos( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * w = cos x cosh y - i sin x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 8400 4.5e-17 1.3e-17
+ * IEEE -10,+10 30000 3.8e-16 1.0e-16
+ */
+
+void ccos( z, w )
+register cmplx *z, *w;
+{
+double ch, sh;
+
+cchsh( z->i, &ch, &sh );
+w->r = cos( z->r ) * ch;
+w->i = -sin( z->r ) * sh;
+}
+ /* ctan()
+ *
+ * Complex circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ctan();
+ * cmplx z, w;
+ *
+ * ctan( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * sin 2x + i sinh 2y
+ * w = --------------------.
+ * cos 2x + cosh 2y
+ *
+ * On the real axis the denominator is zero at odd multiples
+ * of PI/2. The denominator is evaluated by its Taylor
+ * series near these points.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 5200 7.1e-17 1.6e-17
+ * IEEE -10,+10 30000 7.2e-16 1.2e-16
+ * Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
+ */
+
+void ctan( z, w )
+register cmplx *z, *w;
+{
+double d;
+
+d = cos( 2.0 * z->r ) + cosh( 2.0 * z->i );
+
+if( fabs(d) < 0.25 )
+ d = ctans(z);
+
+if( d == 0.0 )
+ {
+ mtherr( "ctan", OVERFLOW );
+ w->r = MAXNUM;
+ w->i = MAXNUM;
+ return;
+ }
+
+w->r = sin( 2.0 * z->r ) / d;
+w->i = sinh( 2.0 * z->i ) / d;
+}
+ /* ccot()
+ *
+ * Complex circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccot();
+ * cmplx z, w;
+ *
+ * ccot( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * sin 2x - i sinh 2y
+ * w = --------------------.
+ * cosh 2y - cos 2x
+ *
+ * On the real axis, the denominator has zeros at even
+ * multiples of PI/2. Near these points it is evaluated
+ * by a Taylor series.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 3000 6.5e-17 1.6e-17
+ * IEEE -10,+10 30000 9.2e-16 1.2e-16
+ * Also tested by ctan * ccot = 1 + i0.
+ */
+
+void ccot( z, w )
+register cmplx *z, *w;
+{
+double d;
+
+d = cosh(2.0 * z->i) - cos(2.0 * z->r);
+
+if( fabs(d) < 0.25 )
+ d = ctans(z);
+
+if( d == 0.0 )
+ {
+ mtherr( "ccot", OVERFLOW );
+ w->r = MAXNUM;
+ w->i = MAXNUM;
+ return;
+ }
+
+w->r = sin( 2.0 * z->r ) / d;
+w->i = -sinh( 2.0 * z->i ) / d;
+}
+
+/* Program to subtract nearest integer multiple of PI */
+/* extended precision value of PI: */
+#ifdef UNK
+static double DP1 = 3.14159265160560607910E0;
+static double DP2 = 1.98418714791870343106E-9;
+static double DP3 = 1.14423774522196636802E-17;
+#endif
+
+#ifdef DEC
+static unsigned short P1[] = {0040511,0007732,0120000,0000000,};
+static unsigned short P2[] = {0031010,0055060,0100000,0000000,};
+static unsigned short P3[] = {0022123,0011431,0105056,0001560,};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+#ifdef IBMPC
+static unsigned short P1[] = {0x0000,0x5400,0x21fb,0x4009};
+static unsigned short P2[] = {0x0000,0x1000,0x0b46,0x3e21};
+static unsigned short P3[] = {0xc06e,0x3145,0x6263,0x3c6a};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+#ifdef MIEEE
+static unsigned short P1[] = {
+0x4009,0x21fb,0x5400,0x0000
+};
+static unsigned short P2[] = {
+0x3e21,0x0b46,0x1000,0x0000
+};
+static unsigned short P3[] = {
+0x3c6a,0x6263,0x3145,0xc06e
+};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+static double redupi(x)
+double x;
+{
+double t;
+long i;
+
+t = x/PI;
+if( t >= 0.0 )
+ t += 0.5;
+else
+ t -= 0.5;
+
+i = t; /* the multiple */
+t = i;
+t = ((x - t * DP1) - t * DP2) - t * DP3;
+return(t);
+}
+
+/* Taylor series expansion for cosh(2y) - cos(2x) */
+
+static double ctans(z)
+cmplx *z;
+{
+double f, x, x2, y, y2, rn, t;
+double d;
+
+x = fabs( 2.0 * z->r );
+y = fabs( 2.0 * z->i );
+
+x = redupi(x);
+
+x = x * x;
+y = y * y;
+x2 = 1.0;
+y2 = 1.0;
+f = 1.0;
+rn = 0.0;
+d = 0.0;
+do
+ {
+ rn += 1.0;
+ f *= rn;
+ rn += 1.0;
+ f *= rn;
+ x2 *= x;
+ y2 *= y;
+ t = y2 + x2;
+ t /= f;
+ d += t;
+
+ rn += 1.0;
+ f *= rn;
+ rn += 1.0;
+ f *= rn;
+ x2 *= x;
+ y2 *= y;
+ t = y2 - x2;
+ t /= f;
+ d += t;
+ }
+while( fabs(t/d) > MACHEP );
+return(d);
+}
+ /* casin()
+ *
+ * Complex circular arc sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void casin();
+ * cmplx z, w;
+ *
+ * casin( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Inverse complex sine:
+ *
+ * 2
+ * w = -i clog( iz + csqrt( 1 - z ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 10100 2.1e-15 3.4e-16
+ * IEEE -10,+10 30000 2.2e-14 2.7e-15
+ * Larger relative error can be observed for z near zero.
+ * Also tested by csin(casin(z)) = z.
+ */
+
+void casin( z, w )
+cmplx *z, *w;
+{
+static cmplx ca, ct, zz, z2;
+double x, y;
+
+x = z->r;
+y = z->i;
+
+if( y == 0.0 )
+ {
+ if( fabs(x) > 1.0 )
+ {
+ w->r = PIO2;
+ w->i = 0.0;
+ mtherr( "casin", DOMAIN );
+ }
+ else
+ {
+ w->r = asin(x);
+ w->i = 0.0;
+ }
+ return;
+ }
+
+/* Power series expansion */
+/*
+b = cabs(z);
+if( b < 0.125 )
+{
+z2.r = (x - y) * (x + y);
+z2.i = 2.0 * x * y;
+
+cn = 1.0;
+n = 1.0;
+ca.r = x;
+ca.i = y;
+sum.r = x;
+sum.i = y;
+do
+ {
+ ct.r = z2.r * ca.r - z2.i * ca.i;
+ ct.i = z2.r * ca.i + z2.i * ca.r;
+ ca.r = ct.r;
+ ca.i = ct.i;
+
+ cn *= n;
+ n += 1.0;
+ cn /= n;
+ n += 1.0;
+ b = cn/n;
+
+ ct.r *= b;
+ ct.i *= b;
+ sum.r += ct.r;
+ sum.i += ct.i;
+ b = fabs(ct.r) + fabs(ct.i);
+ }
+while( b > MACHEP );
+w->r = sum.r;
+w->i = sum.i;
+return;
+}
+*/
+
+
+ca.r = x;
+ca.i = y;
+
+ct.r = -ca.i; /* iz */
+ct.i = ca.r;
+
+ /* sqrt( 1 - z*z) */
+/* cmul( &ca, &ca, &zz ) */
+zz.r = (ca.r - ca.i) * (ca.r + ca.i); /*x * x - y * y */
+zz.i = 2.0 * ca.r * ca.i;
+
+zz.r = 1.0 - zz.r;
+zz.i = -zz.i;
+csqrt( &zz, &z2 );
+
+cadd( &z2, &ct, &zz );
+clog( &zz, &zz );
+w->r = zz.i; /* mult by 1/i = -i */
+w->i = -zz.r;
+return;
+}
+ /* cacos()
+ *
+ * Complex circular arc cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cacos();
+ * cmplx z, w;
+ *
+ * cacos( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * w = arccos z = PI/2 - arcsin z.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 5200 1.6e-15 2.8e-16
+ * IEEE -10,+10 30000 1.8e-14 2.2e-15
+ */
+
+void cacos( z, w )
+cmplx *z, *w;
+{
+
+casin( z, w );
+w->r = PIO2 - w->r;
+w->i = -w->i;
+}
+ /* catan()
+ *
+ * Complex circular arc tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void catan();
+ * cmplx z, w;
+ *
+ * catan( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ * 1 ( 2x )
+ * Re w = - arctan(-----------) + k PI
+ * 2 ( 2 2)
+ * (1 - x - y )
+ *
+ * ( 2 2)
+ * 1 (x + (y+1) )
+ * Im w = - log(------------)
+ * 4 ( 2 2)
+ * (x + (y-1) )
+ *
+ * Where k is an arbitrary integer.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 5900 1.3e-16 7.8e-18
+ * IEEE -10,+10 30000 2.3e-15 8.5e-17
+ * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
+ * had peak relative error 1.5e-16, rms relative error
+ * 2.9e-17. See also clog().
+ */
+
+void catan( z, w )
+cmplx *z, *w;
+{
+double a, t, x, x2, y;
+
+x = z->r;
+y = z->i;
+
+if( (x == 0.0) && (y > 1.0) )
+ goto ovrf;
+
+x2 = x * x;
+a = 1.0 - x2 - (y * y);
+if( a == 0.0 )
+ goto ovrf;
+
+#if ANSIC
+t = atan2( 2.0 * x, a )/2.0;
+#else
+t = atan2( a, 2.0 * x )/2.0;
+#endif
+w->r = redupi( t );
+
+t = y - 1.0;
+a = x2 + (t * t);
+if( a == 0.0 )
+ goto ovrf;
+
+t = y + 1.0;
+a = (x2 + (t * t))/a;
+w->i = log(a)/4.0;
+return;
+
+ovrf:
+mtherr( "catan", OVERFLOW );
+w->r = MAXNUM;
+w->i = MAXNUM;
+}
+
+
+/* csinh
+ *
+ * Complex hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csinh();
+ * cmplx z, w;
+ *
+ * csinh( &z, &w );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * csinh z = (cexp(z) - cexp(-z))/2
+ * = sinh x * cos y + i cosh x * sin y .
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 3.1e-16 8.2e-17
+ *
+ */
+
+void
+csinh (z, w)
+ cmplx *z, *w;
+{
+ double x, y;
+
+ x = z->r;
+ y = z->i;
+ w->r = sinh (x) * cos (y);
+ w->i = cosh (x) * sin (y);
+}
+
+
+/* casinh
+ *
+ * Complex inverse hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void casinh();
+ * cmplx z, w;
+ *
+ * casinh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * casinh z = -i casin iz .
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.8e-14 2.6e-15
+ *
+ */
+
+void
+casinh (z, w)
+ cmplx *z, *w;
+{
+ cmplx u;
+
+ u.r = 0.0;
+ u.i = 1.0;
+ cmul( z, &u, &u );
+ casin( &u, w );
+ u.r = 0.0;
+ u.i = -1.0;
+ cmul( &u, w, w );
+}
+
+/* ccosh
+ *
+ * Complex hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccosh();
+ * cmplx z, w;
+ *
+ * ccosh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * ccosh(z) = cosh x cos y + i sinh x sin y .
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 2.9e-16 8.1e-17
+ *
+ */
+
+void
+ccosh (z, w)
+ cmplx *z, *w;
+{
+ double x, y;
+
+ x = z->r;
+ y = z->i;
+ w->r = cosh (x) * cos (y);
+ w->i = sinh (x) * sin (y);
+}
+
+
+/* cacosh
+ *
+ * Complex inverse hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cacosh();
+ * cmplx z, w;
+ *
+ * cacosh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * acosh z = i acos z .
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.6e-14 2.1e-15
+ *
+ */
+
+void
+cacosh (z, w)
+ cmplx *z, *w;
+{
+ cmplx u;
+
+ cacos( z, w );
+ u.r = 0.0;
+ u.i = 1.0;
+ cmul( &u, w, w );
+}
+
+
+/* ctanh
+ *
+ * Complex hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ctanh();
+ * cmplx z, w;
+ *
+ * ctanh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * tanh z = (sinh 2x + i sin 2y) / (cosh 2x + cos 2y) .
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.7e-14 2.4e-16
+ *
+ */
+
+/* 5.253E-02,1.550E+00 1.643E+01,6.553E+00 1.729E-14 21355 */
+
+void
+ctanh (z, w)
+ cmplx *z, *w;
+{
+ double x, y, d;
+
+ x = z->r;
+ y = z->i;
+ d = cosh (2.0 * x) + cos (2.0 * y);
+ w->r = sinh (2.0 * x) / d;
+ w->i = sin (2.0 * y) / d;
+ return;
+}
+
+
+/* catanh
+ *
+ * Complex inverse hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void catanh();
+ * cmplx z, w;
+ *
+ * catanh (&z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Inverse tanh, equal to -i catan (iz);
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 2.3e-16 6.2e-17
+ *
+ */
+
+void
+catanh (z, w)
+ cmplx *z, *w;
+{
+ cmplx u;
+
+ u.r = 0.0;
+ u.i = 1.0;
+ cmul (z, &u, &u); /* i z */
+ catan (&u, w);
+ u.r = 0.0;
+ u.i = -1.0;
+ cmul (&u, w, w); /* -i catan iz */
+ return;
+}
+
+
+/* cpow
+ *
+ * Complex power function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cpow();
+ * cmplx a, z, w;
+ *
+ * cpow (&a, &z, &w);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Raises complex A to the complex Zth power.
+ * Definition is per AMS55 # 4.2.8,
+ * analytically equivalent to cpow(a,z) = cexp(z clog(a)).
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 9.4e-15 1.5e-15
+ *
+ */
+
+
+void
+cpow (a, z, w)
+ cmplx *a, *z, *w;
+{
+ double x, y, r, theta, absa, arga;
+
+ x = z->r;
+ y = z->i;
+ absa = cabs (a);
+ if (absa == 0.0)
+ {
+ w->r = 0.0;
+ w->i = 0.0;
+ return;
+ }
+ arga = atan2 (a->i, a->r);
+ r = pow (absa, x);
+ theta = x * arga;
+ if (y != 0.0)
+ {
+ r = r * exp (-y * arga);
+ theta = theta + y * log (absa);
+ }
+ w->r = r * cos (theta);
+ w->i = r * sin (theta);
+ return;
+}
diff --git a/libm/double/cmplx.c b/libm/double/cmplx.c
new file mode 100644
index 000000000..dcd972bea
--- /dev/null
+++ b/libm/double/cmplx.c
@@ -0,0 +1,461 @@
+/* cmplx.c
+ *
+ * Complex number arithmetic
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct {
+ * double r; real part
+ * double i; imaginary part
+ * }cmplx;
+ *
+ * cmplx *a, *b, *c;
+ *
+ * cadd( a, b, c ); c = b + a
+ * csub( a, b, c ); c = b - a
+ * cmul( a, b, c ); c = b * a
+ * cdiv( a, b, c ); c = b / a
+ * cneg( c ); c = -c
+ * cmov( b, c ); c = b
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Addition:
+ * c.r = b.r + a.r
+ * c.i = b.i + a.i
+ *
+ * Subtraction:
+ * c.r = b.r - a.r
+ * c.i = b.i - a.i
+ *
+ * Multiplication:
+ * c.r = b.r * a.r - b.i * a.i
+ * c.i = b.r * a.i + b.i * a.r
+ *
+ * Division:
+ * d = a.r * a.r + a.i * a.i
+ * c.r = (b.r * a.r + b.i * a.i)/d
+ * c.i = (b.i * a.r - b.r * a.i)/d
+ * ACCURACY:
+ *
+ * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
+ * error 3.1e-17, rms 1.2e-17. The test (y/z) * (z/y) = 1 had
+ * peak relative error 8.3e-17, rms 2.1e-17.
+ *
+ * Tests in the rectangle {-10,+10}:
+ * Relative error:
+ * arithmetic function # trials peak rms
+ * DEC cadd 10000 1.4e-17 3.4e-18
+ * IEEE cadd 100000 1.1e-16 2.7e-17
+ * DEC csub 10000 1.4e-17 4.5e-18
+ * IEEE csub 100000 1.1e-16 3.4e-17
+ * DEC cmul 3000 2.3e-17 8.7e-18
+ * IEEE cmul 100000 2.1e-16 6.9e-17
+ * DEC cdiv 18000 4.9e-17 1.3e-17
+ * IEEE cdiv 100000 3.7e-16 1.1e-16
+ */
+ /* cmplx.c
+ * complex number arithmetic
+ */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double cabs ( cmplx * );
+extern double sqrt ( double );
+extern double atan2 ( double, double );
+extern double cos ( double );
+extern double sin ( double );
+extern double sqrt ( double );
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+int isnan ( double );
+void cdiv ( cmplx *, cmplx *, cmplx * );
+void cadd ( cmplx *, cmplx *, cmplx * );
+#else
+double fabs(), cabs(), sqrt(), atan2(), cos(), sin();
+double sqrt(), frexp(), ldexp();
+int isnan();
+void cdiv(), cadd();
+#endif
+
+extern double MAXNUM, MACHEP, PI, PIO2, INFINITY, NAN;
+/*
+typedef struct
+ {
+ double r;
+ double i;
+ }cmplx;
+*/
+cmplx czero = {0.0, 0.0};
+extern cmplx czero;
+cmplx cone = {1.0, 0.0};
+extern cmplx cone;
+
+/* c = b + a */
+
+void cadd( a, b, c )
+register cmplx *a, *b;
+cmplx *c;
+{
+
+c->r = b->r + a->r;
+c->i = b->i + a->i;
+}
+
+
+/* c = b - a */
+
+void csub( a, b, c )
+register cmplx *a, *b;
+cmplx *c;
+{
+
+c->r = b->r - a->r;
+c->i = b->i - a->i;
+}
+
+/* c = b * a */
+
+void cmul( a, b, c )
+register cmplx *a, *b;
+cmplx *c;
+{
+double y;
+
+y = b->r * a->r - b->i * a->i;
+c->i = b->r * a->i + b->i * a->r;
+c->r = y;
+}
+
+
+
+/* c = b / a */
+
+void cdiv( a, b, c )
+register cmplx *a, *b;
+cmplx *c;
+{
+double y, p, q, w;
+
+
+y = a->r * a->r + a->i * a->i;
+p = b->r * a->r + b->i * a->i;
+q = b->i * a->r - b->r * a->i;
+
+if( y < 1.0 )
+ {
+ w = MAXNUM * y;
+ if( (fabs(p) > w) || (fabs(q) > w) || (y == 0.0) )
+ {
+ c->r = MAXNUM;
+ c->i = MAXNUM;
+ mtherr( "cdiv", OVERFLOW );
+ return;
+ }
+ }
+c->r = p/y;
+c->i = q/y;
+}
+
+
+/* b = a
+ Caution, a `short' is assumed to be 16 bits wide. */
+
+void cmov( a, b )
+void *a, *b;
+{
+register short *pa, *pb;
+int i;
+
+pa = (short *) a;
+pb = (short *) b;
+i = 8;
+do
+ *pb++ = *pa++;
+while( --i );
+}
+
+
+void cneg( a )
+register cmplx *a;
+{
+
+a->r = -a->r;
+a->i = -a->i;
+}
+
+/* cabs()
+ *
+ * Complex absolute value
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double cabs();
+ * cmplx z;
+ * double a;
+ *
+ * a = cabs( &z );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy
+ *
+ * then
+ *
+ * a = sqrt( x**2 + y**2 ).
+ *
+ * Overflow and underflow are avoided by testing the magnitudes
+ * of x and y before squaring. If either is outside half of
+ * the floating point full scale range, both are rescaled.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -30,+30 30000 3.2e-17 9.2e-18
+ * IEEE -10,+10 100000 2.7e-16 6.9e-17
+ */
+
+
+/*
+Cephes Math Library Release 2.1: January, 1989
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+/*
+typedef struct
+ {
+ double r;
+ double i;
+ }cmplx;
+*/
+
+#ifdef UNK
+#define PREC 27
+#define MAXEXP 1024
+#define MINEXP -1077
+#endif
+#ifdef DEC
+#define PREC 29
+#define MAXEXP 128
+#define MINEXP -128
+#endif
+#ifdef IBMPC
+#define PREC 27
+#define MAXEXP 1024
+#define MINEXP -1077
+#endif
+#ifdef MIEEE
+#define PREC 27
+#define MAXEXP 1024
+#define MINEXP -1077
+#endif
+
+
+double cabs( z )
+register cmplx *z;
+{
+double x, y, b, re, im;
+int ex, ey, e;
+
+#ifdef INFINITIES
+/* Note, cabs(INFINITY,NAN) = INFINITY. */
+if( z->r == INFINITY || z->i == INFINITY
+ || z->r == -INFINITY || z->i == -INFINITY )
+ return( INFINITY );
+#endif
+
+#ifdef NANS
+if( isnan(z->r) )
+ return(z->r);
+if( isnan(z->i) )
+ return(z->i);
+#endif
+
+re = fabs( z->r );
+im = fabs( z->i );
+
+if( re == 0.0 )
+ return( im );
+if( im == 0.0 )
+ return( re );
+
+/* Get the exponents of the numbers */
+x = frexp( re, &ex );
+y = frexp( im, &ey );
+
+/* Check if one number is tiny compared to the other */
+e = ex - ey;
+if( e > PREC )
+ return( re );
+if( e < -PREC )
+ return( im );
+
+/* Find approximate exponent e of the geometric mean. */
+e = (ex + ey) >> 1;
+
+/* Rescale so mean is about 1 */
+x = ldexp( re, -e );
+y = ldexp( im, -e );
+
+/* Hypotenuse of the right triangle */
+b = sqrt( x * x + y * y );
+
+/* Compute the exponent of the answer. */
+y = frexp( b, &ey );
+ey = e + ey;
+
+/* Check it for overflow and underflow. */
+if( ey > MAXEXP )
+ {
+ mtherr( "cabs", OVERFLOW );
+ return( INFINITY );
+ }
+if( ey < MINEXP )
+ return(0.0);
+
+/* Undo the scaling */
+b = ldexp( b, e );
+return( b );
+}
+ /* csqrt()
+ *
+ * Complex square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csqrt();
+ * cmplx z, w;
+ *
+ * csqrt( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy, r = |z|, then
+ *
+ * 1/2
+ * Im w = [ (r - x)/2 ] ,
+ *
+ * Re w = y / 2 Im w.
+ *
+ *
+ * Note that -w is also a square root of z. The root chosen
+ * is always in the upper half plane.
+ *
+ * Because of the potential for cancellation error in r - x,
+ * the result is sharpened by doing a Heron iteration
+ * (see sqrt.c) in complex arithmetic.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 25000 3.2e-17 9.6e-18
+ * IEEE -10,+10 100000 3.2e-16 7.7e-17
+ *
+ * 2
+ * Also tested by csqrt( z ) = z, and tested by arguments
+ * close to the real axis.
+ */
+
+
+void csqrt( z, w )
+cmplx *z, *w;
+{
+cmplx q, s;
+double x, y, r, t;
+
+x = z->r;
+y = z->i;
+
+if( y == 0.0 )
+ {
+ if( x < 0.0 )
+ {
+ w->r = 0.0;
+ w->i = sqrt(-x);
+ return;
+ }
+ else
+ {
+ w->r = sqrt(x);
+ w->i = 0.0;
+ return;
+ }
+ }
+
+
+if( x == 0.0 )
+ {
+ r = fabs(y);
+ r = sqrt(0.5*r);
+ if( y > 0 )
+ w->r = r;
+ else
+ w->r = -r;
+ w->i = r;
+ return;
+ }
+
+/* Approximate sqrt(x^2+y^2) - x = y^2/2x - y^4/24x^3 + ... .
+ * The relative error in the first term is approximately y^2/12x^2 .
+ */
+if( (fabs(y) < 2.e-4 * fabs(x))
+ && (x > 0) )
+ {
+ t = 0.25*y*(y/x);
+ }
+else
+ {
+ r = cabs(z);
+ t = 0.5*(r - x);
+ }
+
+r = sqrt(t);
+q.i = r;
+q.r = y/(2.0*r);
+/* Heron iteration in complex arithmetic */
+cdiv( &q, z, &s );
+cadd( &q, &s, w );
+w->r *= 0.5;
+w->i *= 0.5;
+}
+
+
+double hypot( x, y )
+double x, y;
+{
+cmplx z;
+
+z.r = x;
+z.i = y;
+return( cabs(&z) );
+}
diff --git a/libm/double/coil.c b/libm/double/coil.c
new file mode 100644
index 000000000..f7156497c
--- /dev/null
+++ b/libm/double/coil.c
@@ -0,0 +1,63 @@
+/* Program to calculate the inductance of a coil
+ *
+ * Reference: E. Jahnke and F. Emde, _Tables of Functions_,
+ * 4th edition, Dover, 1945, pp 86-89.
+ */
+
+double sin(), cos(), atan(), ellpe(), ellpk();
+
+double d;
+double l;
+double N;
+
+/* double PI = 3.14159265358979323846; */
+extern double PI;
+
+main()
+{
+double a, f, tana, sina, K, E, m, L, t;
+
+printf( "Self inductance of circular solenoidal coil\n" );
+
+loop:
+getnum( "diameter in centimeters", &d );
+if( d < 0.0 )
+ exit(0); /* escape gracefully */
+getnum( "length in centimeters", &l );
+if( d < 0.0 )
+ exit(0);
+getnum( "total number of turns", &N );
+if( d < 0.0 )
+ exit(0);
+tana = d/l; /* form factor */
+a = atan( tana );
+sina = sin(a); /* modulus of the elliptic functions (k) */
+m = cos(a); /* subroutine argument = 1 - k^2 */
+m = m * m;
+K = ellpk(m);
+E = ellpe(m);
+tana = tana * tana; /* square of tan(a) */
+
+f = ((K + (tana - 1.0) * E)/sina - tana)/3.0;
+L = 4.e-9 * PI * N * N * d * f;
+printf( "L = %.4e Henries\n", L );
+goto loop;
+}
+
+
+/* Get value entered on keyboard
+ */
+getnum( str, pd )
+char *str;
+double *pd;
+{
+char s[40];
+
+printf( "%s (%.10e) ? ", str, *pd );
+gets(s);
+if( s[0] != '\0' )
+ {
+ sscanf( s, "%lf", pd );
+ printf( "%.10e\n", *pd );
+ }
+}
diff --git a/libm/double/const.c b/libm/double/const.c
new file mode 100644
index 000000000..de4451497
--- /dev/null
+++ b/libm/double/const.c
@@ -0,0 +1,252 @@
+/* const.c
+ *
+ * Globally declared constants
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * extern double nameofconstant;
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This file contains a number of mathematical constants and
+ * also some needed size parameters of the computer arithmetic.
+ * The values are supplied as arrays of hexadecimal integers
+ * for IEEE arithmetic; arrays of octal constants for DEC
+ * arithmetic; and in a normal decimal scientific notation for
+ * other machines. The particular notation used is determined
+ * by a symbol (DEC, IBMPC, or UNK) defined in the include file
+ * math.h.
+ *
+ * The default size parameters are as follows.
+ *
+ * For DEC and UNK modes:
+ * MACHEP = 1.38777878078144567553E-17 2**-56
+ * MAXLOG = 8.8029691931113054295988E1 log(2**127)
+ * MINLOG = -8.872283911167299960540E1 log(2**-128)
+ * MAXNUM = 1.701411834604692317316873e38 2**127
+ *
+ * For IEEE arithmetic (IBMPC):
+ * MACHEP = 1.11022302462515654042E-16 2**-53
+ * MAXLOG = 7.09782712893383996843E2 log(2**1024)
+ * MINLOG = -7.08396418532264106224E2 log(2**-1022)
+ * MAXNUM = 1.7976931348623158E308 2**1024
+ *
+ * The global symbols for mathematical constants are
+ * PI = 3.14159265358979323846 pi
+ * PIO2 = 1.57079632679489661923 pi/2
+ * PIO4 = 7.85398163397448309616E-1 pi/4
+ * SQRT2 = 1.41421356237309504880 sqrt(2)
+ * SQRTH = 7.07106781186547524401E-1 sqrt(2)/2
+ * LOG2E = 1.4426950408889634073599 1/log(2)
+ * SQ2OPI = 7.9788456080286535587989E-1 sqrt( 2/pi )
+ * LOGE2 = 6.93147180559945309417E-1 log(2)
+ * LOGSQ2 = 3.46573590279972654709E-1 log(2)/2
+ * THPIO4 = 2.35619449019234492885 3*pi/4
+ * TWOOPI = 6.36619772367581343075535E-1 2/pi
+ *
+ * These lists are subject to change.
+ */
+
+/* const.c */
+
+/*
+Cephes Math Library Release 2.3: March, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+#if 1
+double MACHEP = 1.11022302462515654042E-16; /* 2**-53 */
+#else
+double MACHEP = 1.38777878078144567553E-17; /* 2**-56 */
+#endif
+double UFLOWTHRESH = 2.22507385850720138309E-308; /* 2**-1022 */
+#ifdef DENORMAL
+double MAXLOG = 7.09782712893383996732E2; /* log(MAXNUM) */
+/* double MINLOG = -7.44440071921381262314E2; */ /* log(2**-1074) */
+double MINLOG = -7.451332191019412076235E2; /* log(2**-1075) */
+#else
+double MAXLOG = 7.08396418532264106224E2; /* log 2**1022 */
+double MINLOG = -7.08396418532264106224E2; /* log 2**-1022 */
+#endif
+double MAXNUM = 1.79769313486231570815E308; /* 2**1024*(1-MACHEP) */
+double PI = 3.14159265358979323846; /* pi */
+double PIO2 = 1.57079632679489661923; /* pi/2 */
+double PIO4 = 7.85398163397448309616E-1; /* pi/4 */
+double SQRT2 = 1.41421356237309504880; /* sqrt(2) */
+double SQRTH = 7.07106781186547524401E-1; /* sqrt(2)/2 */
+double LOG2E = 1.4426950408889634073599; /* 1/log(2) */
+double SQ2OPI = 7.9788456080286535587989E-1; /* sqrt( 2/pi ) */
+double LOGE2 = 6.93147180559945309417E-1; /* log(2) */
+double LOGSQ2 = 3.46573590279972654709E-1; /* log(2)/2 */
+double THPIO4 = 2.35619449019234492885; /* 3*pi/4 */
+double TWOOPI = 6.36619772367581343075535E-1; /* 2/pi */
+#ifdef INFINITIES
+double INFINITY = 1.0/0.0; /* 99e999; */
+#else
+double INFINITY = 1.79769313486231570815E308; /* 2**1024*(1-MACHEP) */
+#endif
+#ifdef NANS
+double NAN = 1.0/0.0 - 1.0/0.0;
+#else
+double NAN = 0.0;
+#endif
+#ifdef MINUSZERO
+double NEGZERO = -0.0;
+#else
+double NEGZERO = 0.0;
+#endif
+#endif
+
+#ifdef IBMPC
+ /* 2**-53 = 1.11022302462515654042E-16 */
+unsigned short MACHEP[4] = {0x0000,0x0000,0x0000,0x3ca0};
+unsigned short UFLOWTHRESH[4] = {0x0000,0x0000,0x0000,0x0010};
+#ifdef DENORMAL
+ /* log(MAXNUM) = 7.09782712893383996732224E2 */
+unsigned short MAXLOG[4] = {0x39ef,0xfefa,0x2e42,0x4086};
+ /* log(2**-1074) = - -7.44440071921381262314E2 */
+/*unsigned short MINLOG[4] = {0x71c3,0x446d,0x4385,0xc087};*/
+unsigned short MINLOG[4] = {0x3052,0xd52d,0x4910,0xc087};
+#else
+ /* log(2**1022) = 7.08396418532264106224E2 */
+unsigned short MAXLOG[4] = {0xbcd2,0xdd7a,0x232b,0x4086};
+ /* log(2**-1022) = - 7.08396418532264106224E2 */
+unsigned short MINLOG[4] = {0xbcd2,0xdd7a,0x232b,0xc086};
+#endif
+ /* 2**1024*(1-MACHEP) = 1.7976931348623158E308 */
+unsigned short MAXNUM[4] = {0xffff,0xffff,0xffff,0x7fef};
+unsigned short PI[4] = {0x2d18,0x5444,0x21fb,0x4009};
+unsigned short PIO2[4] = {0x2d18,0x5444,0x21fb,0x3ff9};
+unsigned short PIO4[4] = {0x2d18,0x5444,0x21fb,0x3fe9};
+unsigned short SQRT2[4] = {0x3bcd,0x667f,0xa09e,0x3ff6};
+unsigned short SQRTH[4] = {0x3bcd,0x667f,0xa09e,0x3fe6};
+unsigned short LOG2E[4] = {0x82fe,0x652b,0x1547,0x3ff7};
+unsigned short SQ2OPI[4] = {0x3651,0x33d4,0x8845,0x3fe9};
+unsigned short LOGE2[4] = {0x39ef,0xfefa,0x2e42,0x3fe6};
+unsigned short LOGSQ2[4] = {0x39ef,0xfefa,0x2e42,0x3fd6};
+unsigned short THPIO4[4] = {0x21d2,0x7f33,0xd97c,0x4002};
+unsigned short TWOOPI[4] = {0xc883,0x6dc9,0x5f30,0x3fe4};
+#ifdef INFINITIES
+unsigned short INFINITY[4] = {0x0000,0x0000,0x0000,0x7ff0};
+#else
+unsigned short INFINITY[4] = {0xffff,0xffff,0xffff,0x7fef};
+#endif
+#ifdef NANS
+unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x7ffc};
+#else
+unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000};
+#endif
+#ifdef MINUSZERO
+unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x8000};
+#else
+unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000};
+#endif
+#endif
+
+#ifdef MIEEE
+ /* 2**-53 = 1.11022302462515654042E-16 */
+unsigned short MACHEP[4] = {0x3ca0,0x0000,0x0000,0x0000};
+unsigned short UFLOWTHRESH[4] = {0x0010,0x0000,0x0000,0x0000};
+#ifdef DENORMAL
+ /* log(2**1024) = 7.09782712893383996843E2 */
+unsigned short MAXLOG[4] = {0x4086,0x2e42,0xfefa,0x39ef};
+ /* log(2**-1074) = - -7.44440071921381262314E2 */
+/* unsigned short MINLOG[4] = {0xc087,0x4385,0x446d,0x71c3}; */
+unsigned short MINLOG[4] = {0xc087,0x4910,0xd52d,0x3052};
+#else
+ /* log(2**1022) = 7.08396418532264106224E2 */
+unsigned short MAXLOG[4] = {0x4086,0x232b,0xdd7a,0xbcd2};
+ /* log(2**-1022) = - 7.08396418532264106224E2 */
+unsigned short MINLOG[4] = {0xc086,0x232b,0xdd7a,0xbcd2};
+#endif
+ /* 2**1024*(1-MACHEP) = 1.7976931348623158E308 */
+unsigned short MAXNUM[4] = {0x7fef,0xffff,0xffff,0xffff};
+unsigned short PI[4] = {0x4009,0x21fb,0x5444,0x2d18};
+unsigned short PIO2[4] = {0x3ff9,0x21fb,0x5444,0x2d18};
+unsigned short PIO4[4] = {0x3fe9,0x21fb,0x5444,0x2d18};
+unsigned short SQRT2[4] = {0x3ff6,0xa09e,0x667f,0x3bcd};
+unsigned short SQRTH[4] = {0x3fe6,0xa09e,0x667f,0x3bcd};
+unsigned short LOG2E[4] = {0x3ff7,0x1547,0x652b,0x82fe};
+unsigned short SQ2OPI[4] = {0x3fe9,0x8845,0x33d4,0x3651};
+unsigned short LOGE2[4] = {0x3fe6,0x2e42,0xfefa,0x39ef};
+unsigned short LOGSQ2[4] = {0x3fd6,0x2e42,0xfefa,0x39ef};
+unsigned short THPIO4[4] = {0x4002,0xd97c,0x7f33,0x21d2};
+unsigned short TWOOPI[4] = {0x3fe4,0x5f30,0x6dc9,0xc883};
+#ifdef INFINITIES
+unsigned short INFINITY[4] = {0x7ff0,0x0000,0x0000,0x0000};
+#else
+unsigned short INFINITY[4] = {0x7fef,0xffff,0xffff,0xffff};
+#endif
+#ifdef NANS
+unsigned short NAN[4] = {0x7ff8,0x0000,0x0000,0x0000};
+#else
+unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000};
+#endif
+#ifdef MINUSZERO
+unsigned short NEGZERO[4] = {0x8000,0x0000,0x0000,0x0000};
+#else
+unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000};
+#endif
+#endif
+
+#ifdef DEC
+ /* 2**-56 = 1.38777878078144567553E-17 */
+unsigned short MACHEP[4] = {0022200,0000000,0000000,0000000};
+unsigned short UFLOWTHRESH[4] = {0x0080,0x0000,0x0000,0x0000};
+ /* log 2**127 = 88.029691931113054295988 */
+unsigned short MAXLOG[4] = {041660,007463,0143742,025733,};
+ /* log 2**-128 = -88.72283911167299960540 */
+unsigned short MINLOG[4] = {0141661,071027,0173721,0147572,};
+ /* 2**127 = 1.701411834604692317316873e38 */
+unsigned short MAXNUM[4] = {077777,0177777,0177777,0177777,};
+unsigned short PI[4] = {040511,007732,0121041,064302,};
+unsigned short PIO2[4] = {040311,007732,0121041,064302,};
+unsigned short PIO4[4] = {040111,007732,0121041,064302,};
+unsigned short SQRT2[4] = {040265,002363,031771,0157145,};
+unsigned short SQRTH[4] = {040065,002363,031771,0157144,};
+unsigned short LOG2E[4] = {040270,0125073,024534,013761,};
+unsigned short SQ2OPI[4] = {040114,041051,0117241,0131204,};
+unsigned short LOGE2[4] = {040061,071027,0173721,0147572,};
+unsigned short LOGSQ2[4] = {037661,071027,0173721,0147572,};
+unsigned short THPIO4[4] = {040426,0145743,0174631,007222,};
+unsigned short TWOOPI[4] = {040042,0174603,067116,042025,};
+/* Approximate infinity by MAXNUM. */
+unsigned short INFINITY[4] = {077777,0177777,0177777,0177777,};
+unsigned short NAN[4] = {0000000,0000000,0000000,0000000};
+#ifdef MINUSZERO
+unsigned short NEGZERO[4] = {0000000,0000000,0000000,0100000};
+#else
+unsigned short NEGZERO[4] = {0000000,0000000,0000000,0000000};
+#endif
+#endif
+
+#ifndef UNK
+extern unsigned short MACHEP[];
+extern unsigned short UFLOWTHRESH[];
+extern unsigned short MAXLOG[];
+extern unsigned short UNDLOG[];
+extern unsigned short MINLOG[];
+extern unsigned short MAXNUM[];
+extern unsigned short PI[];
+extern unsigned short PIO2[];
+extern unsigned short PIO4[];
+extern unsigned short SQRT2[];
+extern unsigned short SQRTH[];
+extern unsigned short LOG2E[];
+extern unsigned short SQ2OPI[];
+extern unsigned short LOGE2[];
+extern unsigned short LOGSQ2[];
+extern unsigned short THPIO4[];
+extern unsigned short TWOOPI[];
+extern unsigned short INFINITY[];
+extern unsigned short NAN[];
+extern unsigned short NEGZERO[];
+#endif
diff --git a/libm/double/cosh.c b/libm/double/cosh.c
new file mode 100644
index 000000000..77a70da3e
--- /dev/null
+++ b/libm/double/cosh.c
@@ -0,0 +1,83 @@
+/* cosh.c
+ *
+ * Hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cosh();
+ *
+ * y = cosh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic cosine of argument in the range MINLOG to
+ * MAXLOG.
+ *
+ * cosh(x) = ( exp(x) + exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC +- 88 50000 4.0e-17 7.7e-18
+ * IEEE +-MAXLOG 30000 2.6e-16 5.7e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * cosh overflow |x| > MAXLOG MAXNUM
+ *
+ *
+ */
+
+/* cosh.c */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1985, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double exp ( double );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double exp();
+int isnan(), isfinite();
+#endif
+extern double MAXLOG, INFINITY, LOGE2;
+
+double cosh(x)
+double x;
+{
+double y;
+
+#ifdef NANS
+if( isnan(x) )
+ return(x);
+#endif
+if( x < 0 )
+ x = -x;
+if( x > (MAXLOG + LOGE2) )
+ {
+ mtherr( "cosh", OVERFLOW );
+ return( INFINITY );
+ }
+if( x >= (MAXLOG - LOGE2) )
+ {
+ y = exp(0.5 * x);
+ y = (0.5 * y) * y;
+ return(y);
+ }
+y = exp(x);
+y = 0.5 * (y + 1.0 / y);
+return( y );
+}
diff --git a/libm/double/cpmul.c b/libm/double/cpmul.c
new file mode 100644
index 000000000..3880ac5a1
--- /dev/null
+++ b/libm/double/cpmul.c
@@ -0,0 +1,104 @@
+/* cpmul.c
+ *
+ * Multiply two polynomials with complex coefficients
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct
+ * {
+ * double r;
+ * double i;
+ * }cmplx;
+ *
+ * cmplx a[], b[], c[];
+ * int da, db, dc;
+ *
+ * cpmul( a, da, b, db, c, &dc );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The two argument polynomials are multiplied together, and
+ * their product is placed in c.
+ *
+ * Each polynomial is represented by its coefficients stored
+ * as an array of complex number structures (see the typedef).
+ * The degree of a is da, which must be passed to the routine
+ * as an argument; similarly the degree db of b is an argument.
+ * Array a has da + 1 elements and array b has db + 1 elements.
+ * Array c must have storage allocated for at least da + db + 1
+ * elements. The value da + db is returned in dc; this is
+ * the degree of the product polynomial.
+ *
+ * Polynomial coefficients are stored in ascending order; i.e.,
+ * a(x) = a[0]*x**0 + a[1]*x**1 + ... + a[da]*x**da.
+ *
+ *
+ * If desired, c may be the same as either a or b, in which
+ * case the input argument array is replaced by the product
+ * array (but only up to terms of degree da + db).
+ *
+ */
+
+/* cpmul */
+
+typedef struct
+ {
+ double r;
+ double i;
+ }cmplx;
+
+int cpmul( a, da, b, db, c, dc )
+cmplx *a, *b, *c;
+int da, db;
+int *dc;
+{
+int i, j, k;
+cmplx y;
+register cmplx *pa, *pb, *pc;
+
+if( da > db ) /* Know which polynomial has higher degree */
+ {
+ i = da; /* Swapping is OK because args are on the stack */
+ da = db;
+ db = i;
+ pa = a;
+ a = b;
+ b = pa;
+ }
+
+k = da + db;
+*dc = k; /* Output the degree of the product */
+pc = &c[db+1];
+for( i=db+1; i<=k; i++ ) /* Clear high order terms of output */
+ {
+ pc->r = 0;
+ pc->i = 0;
+ pc++;
+ }
+/* To permit replacement of input, work backward from highest degree */
+pb = &b[db];
+for( j=0; j<=db; j++ )
+ {
+ pa = &a[da];
+ pc = &c[k-j];
+ for( i=0; i<da; i++ )
+ {
+ y.r = pa->r * pb->r - pa->i * pb->i; /* cmpx multiply */
+ y.i = pa->r * pb->i + pa->i * pb->r;
+ pc->r += y.r; /* accumulate partial product */
+ pc->i += y.i;
+ pa--;
+ pc--;
+ }
+ y.r = pa->r * pb->r - pa->i * pb->i; /* replace last term, */
+ y.i = pa->r * pb->i + pa->i * pb->r; /* ...do not accumulate */
+ pc->r = y.r;
+ pc->i = y.i;
+ pb--;
+ }
+ return 0;
+}
diff --git a/libm/double/dawsn.c b/libm/double/dawsn.c
new file mode 100644
index 000000000..4f8d27a0c
--- /dev/null
+++ b/libm/double/dawsn.c
@@ -0,0 +1,392 @@
+/* dawsn.c
+ *
+ * Dawson's Integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, dawsn();
+ *
+ * y = dawsn( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ * x
+ * -
+ * 2 | | 2
+ * dawsn(x) = exp( -x ) | exp( t ) dt
+ * | |
+ * -
+ * 0
+ *
+ * Three different rational approximations are employed, for
+ * the intervals 0 to 3.25; 3.25 to 6.25; and 6.25 up.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,10 10000 6.9e-16 1.0e-16
+ * DEC 0,10 6000 7.4e-17 1.4e-17
+ *
+ *
+ */
+
+/* dawsn.c */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+/* Dawson's integral, interval 0 to 3.25 */
+#ifdef UNK
+static double AN[10] = {
+ 1.13681498971755972054E-11,
+ 8.49262267667473811108E-10,
+ 1.94434204175553054283E-8,
+ 9.53151741254484363489E-7,
+ 3.07828309874913200438E-6,
+ 3.52513368520288738649E-4,
+-8.50149846724410912031E-4,
+ 4.22618223005546594270E-2,
+-9.17480371773452345351E-2,
+ 9.99999999999999994612E-1,
+};
+static double AD[11] = {
+ 2.40372073066762605484E-11,
+ 1.48864681368493396752E-9,
+ 5.21265281010541664570E-8,
+ 1.27258478273186970203E-6,
+ 2.32490249820789513991E-5,
+ 3.25524741826057911661E-4,
+ 3.48805814657162590916E-3,
+ 2.79448531198828973716E-2,
+ 1.58874241960120565368E-1,
+ 5.74918629489320327824E-1,
+ 1.00000000000000000539E0,
+};
+#endif
+#ifdef DEC
+static unsigned short AN[40] = {
+0027107,0176630,0075752,0107612,
+0030551,0070604,0166707,0127727,
+0031647,0002210,0117120,0056376,
+0033177,0156026,0141275,0140627,
+0033516,0112200,0037035,0165515,
+0035270,0150613,0016423,0105634,
+0135536,0156227,0023515,0044413,
+0037055,0015273,0105147,0064025,
+0137273,0163145,0014460,0166465,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short AD[44] = {
+0027323,0067372,0115566,0131320,
+0030714,0114432,0074206,0006637,
+0032137,0160671,0044203,0026344,
+0033252,0146656,0020247,0100231,
+0034303,0003346,0123260,0022433,
+0035252,0125460,0173041,0155415,
+0036144,0113747,0125203,0124617,
+0036744,0166232,0143671,0133670,
+0037442,0127755,0162625,0000100,
+0040023,0026736,0003604,0106265,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short AN[40] = {
+0x51f1,0x0f7d,0xffb3,0x3da8,
+0xf5fb,0x9db8,0x2e30,0x3e0d,
+0x0ba0,0x13ca,0xe091,0x3e54,
+0xb833,0xd857,0xfb82,0x3eaf,
+0xbd6a,0x07c3,0xd290,0x3ec9,
+0x7174,0x63a2,0x1a31,0x3f37,
+0xa921,0xe4e9,0xdb92,0xbf4b,
+0xed03,0x714c,0xa357,0x3fa5,
+0x1da7,0xa326,0x7ccc,0xbfb7,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short AD[44] = {
+0xd65a,0x536e,0x6ddf,0x3dba,
+0xc1b4,0x4f10,0x9323,0x3e19,
+0x659c,0x2910,0xfc37,0x3e6b,
+0xf013,0xc414,0x59b5,0x3eb5,
+0x04a3,0xd4d6,0x60dc,0x3ef8,
+0x3b62,0x1ec4,0x5566,0x3f35,
+0x7532,0xf550,0x92fc,0x3f6c,
+0x36f7,0x58f7,0x9d93,0x3f9c,
+0xa008,0xbcb2,0x55fd,0x3fc4,
+0x9197,0xc0f0,0x65bb,0x3fe2,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short AN[40] = {
+0x3da8,0xffb3,0x0f7d,0x51f1,
+0x3e0d,0x2e30,0x9db8,0xf5fb,
+0x3e54,0xe091,0x13ca,0x0ba0,
+0x3eaf,0xfb82,0xd857,0xb833,
+0x3ec9,0xd290,0x07c3,0xbd6a,
+0x3f37,0x1a31,0x63a2,0x7174,
+0xbf4b,0xdb92,0xe4e9,0xa921,
+0x3fa5,0xa357,0x714c,0xed03,
+0xbfb7,0x7ccc,0xa326,0x1da7,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short AD[44] = {
+0x3dba,0x6ddf,0x536e,0xd65a,
+0x3e19,0x9323,0x4f10,0xc1b4,
+0x3e6b,0xfc37,0x2910,0x659c,
+0x3eb5,0x59b5,0xc414,0xf013,
+0x3ef8,0x60dc,0xd4d6,0x04a3,
+0x3f35,0x5566,0x1ec4,0x3b62,
+0x3f6c,0x92fc,0xf550,0x7532,
+0x3f9c,0x9d93,0x58f7,0x36f7,
+0x3fc4,0x55fd,0xbcb2,0xa008,
+0x3fe2,0x65bb,0xc0f0,0x9197,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+
+/* interval 3.25 to 6.25 */
+#ifdef UNK
+static double BN[11] = {
+ 5.08955156417900903354E-1,
+-2.44754418142697847934E-1,
+ 9.41512335303534411857E-2,
+-2.18711255142039025206E-2,
+ 3.66207612329569181322E-3,
+-4.23209114460388756528E-4,
+ 3.59641304793896631888E-5,
+-2.14640351719968974225E-6,
+ 9.10010780076391431042E-8,
+-2.40274520828250956942E-9,
+ 3.59233385440928410398E-11,
+};
+static double BD[10] = {
+/* 1.00000000000000000000E0,*/
+-6.31839869873368190192E-1,
+ 2.36706788228248691528E-1,
+-5.31806367003223277662E-2,
+ 8.48041718586295374409E-3,
+-9.47996768486665330168E-4,
+ 7.81025592944552338085E-5,
+-4.55875153252442634831E-6,
+ 1.89100358111421846170E-7,
+-4.91324691331920606875E-9,
+ 7.18466403235734541950E-11,
+};
+#endif
+#ifdef DEC
+static unsigned short BN[44] = {
+0040002,0045342,0113762,0004360,
+0137572,0120346,0172745,0144046,
+0037300,0151134,0123440,0117047,
+0136663,0025423,0014755,0046026,
+0036157,0177561,0027535,0046744,
+0135335,0161052,0071243,0146535,
+0034426,0154060,0164506,0135625,
+0133420,0005356,0100017,0151334,
+0032303,0066137,0024013,0046212,
+0131045,0016612,0066270,0047574,
+0027435,0177025,0060625,0116363,
+};
+static unsigned short BD[40] = {
+/*0040200,0000000,0000000,0000000,*/
+0140041,0140101,0174552,0037073,
+0037562,0061503,0124271,0160756,
+0137131,0151760,0073210,0110534,
+0036412,0170562,0117017,0155377,
+0135570,0101374,0074056,0037276,
+0034643,0145376,0001516,0060636,
+0133630,0173540,0121344,0155231,
+0032513,0005602,0134516,0007144,
+0131250,0150540,0075747,0105341,
+0027635,0177020,0012465,0125402,
+};
+#endif
+#ifdef IBMPC
+static unsigned short BN[44] = {
+0x411e,0x52fe,0x495c,0x3fe0,
+0xb905,0xdebc,0x541c,0xbfcf,
+0x13c5,0x94e4,0x1a4b,0x3fb8,
+0xa983,0x633d,0x6562,0xbf96,
+0xa9bd,0x25eb,0xffee,0x3f6d,
+0x79ac,0x4e54,0xbc45,0xbf3b,
+0xd773,0x1d28,0xdb06,0x3f02,
+0xfa5b,0xd001,0x015d,0xbec2,
+0x6991,0xe501,0x6d8b,0x3e78,
+0x09f0,0x4d97,0xa3b1,0xbe24,
+0xb39e,0xac32,0xbfc2,0x3dc3,
+};
+static unsigned short BD[40] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x47c7,0x3f2d,0x3808,0xbfe4,
+0x3c3e,0x7517,0x4c68,0x3fce,
+0x122b,0x0ed1,0x3a7e,0xbfab,
+0xfb60,0x53c1,0x5e2e,0x3f81,
+0xc7d8,0x8f05,0x105f,0xbf4f,
+0xcc34,0xc069,0x795f,0x3f14,
+0x9b53,0x145c,0x1eec,0xbed3,
+0xc1cd,0x5729,0x6170,0x3e89,
+0xf15c,0x0f7c,0x1a2c,0xbe35,
+0xb560,0x02a6,0xbfc2,0x3dd3,
+};
+#endif
+#ifdef MIEEE
+static unsigned short BN[44] = {
+0x3fe0,0x495c,0x52fe,0x411e,
+0xbfcf,0x541c,0xdebc,0xb905,
+0x3fb8,0x1a4b,0x94e4,0x13c5,
+0xbf96,0x6562,0x633d,0xa983,
+0x3f6d,0xffee,0x25eb,0xa9bd,
+0xbf3b,0xbc45,0x4e54,0x79ac,
+0x3f02,0xdb06,0x1d28,0xd773,
+0xbec2,0x015d,0xd001,0xfa5b,
+0x3e78,0x6d8b,0xe501,0x6991,
+0xbe24,0xa3b1,0x4d97,0x09f0,
+0x3dc3,0xbfc2,0xac32,0xb39e,
+};
+static unsigned short BD[40] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0xbfe4,0x3808,0x3f2d,0x47c7,
+0x3fce,0x4c68,0x7517,0x3c3e,
+0xbfab,0x3a7e,0x0ed1,0x122b,
+0x3f81,0x5e2e,0x53c1,0xfb60,
+0xbf4f,0x105f,0x8f05,0xc7d8,
+0x3f14,0x795f,0xc069,0xcc34,
+0xbed3,0x1eec,0x145c,0x9b53,
+0x3e89,0x6170,0x5729,0xc1cd,
+0xbe35,0x1a2c,0x0f7c,0xf15c,
+0x3dd3,0xbfc2,0x02a6,0xb560,
+};
+#endif
+
+/* 6.25 to infinity */
+#ifdef UNK
+static double CN[5] = {
+-5.90592860534773254987E-1,
+ 6.29235242724368800674E-1,
+-1.72858975380388136411E-1,
+ 1.64837047825189632310E-2,
+-4.86827613020462700845E-4,
+};
+static double CD[5] = {
+/* 1.00000000000000000000E0,*/
+-2.69820057197544900361E0,
+ 1.73270799045947845857E0,
+-3.93708582281939493482E-1,
+ 3.44278924041233391079E-2,
+-9.73655226040941223894E-4,
+};
+#endif
+#ifdef DEC
+static unsigned short CN[20] = {
+0140027,0030427,0176477,0074402,
+0040041,0012617,0112375,0162657,
+0137461,0000761,0074120,0135160,
+0036607,0004325,0117246,0115525,
+0135377,0036345,0064750,0047732,
+};
+static unsigned short CD[20] = {
+/*0040200,0000000,0000000,0000000,*/
+0140454,0127521,0071653,0133415,
+0040335,0144540,0016105,0045241,
+0137711,0112053,0155034,0062237,
+0037015,0002102,0177442,0074546,
+0135577,0036345,0064750,0052152,
+};
+#endif
+#ifdef IBMPC
+static unsigned short CN[20] = {
+0xef20,0xffa7,0xe622,0xbfe2,
+0xbcb6,0xf29f,0x22b1,0x3fe4,
+0x174e,0x2f0a,0x203e,0xbfc6,
+0xd36b,0xb3d4,0xe11a,0x3f90,
+0x09fb,0xad3d,0xe79c,0xbf3f,
+};
+static unsigned short CD[20] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x76e2,0x2e75,0x95ea,0xc005,
+0xa954,0x0388,0xb92c,0x3ffb,
+0x8c94,0x7b43,0x3285,0xbfd9,
+0x4f2d,0x5fe4,0xa088,0x3fa1,
+0x0a8d,0xad3d,0xe79c,0xbf4f,
+};
+#endif
+#ifdef MIEEE
+static unsigned short CN[20] = {
+0xbfe2,0xe622,0xffa7,0xef20,
+0x3fe4,0x22b1,0xf29f,0xbcb6,
+0xbfc6,0x203e,0x2f0a,0x174e,
+0x3f90,0xe11a,0xb3d4,0xd36b,
+0xbf3f,0xe79c,0xad3d,0x09fb,
+};
+static unsigned short CD[20] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0xc005,0x95ea,0x2e75,0x76e2,
+0x3ffb,0xb92c,0x0388,0xa954,
+0xbfd9,0x3285,0x7b43,0x8c94,
+0x3fa1,0xa088,0x5fe4,0x4f2d,
+0xbf4f,0xe79c,0xad3d,0x0a8d,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double chbevl ( double, void *, int );
+extern double sqrt ( double );
+extern double fabs ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+#else
+double chbevl(), sqrt(), fabs(), polevl(), p1evl();
+#endif
+extern double PI, MACHEP;
+
+double dawsn( xx )
+double xx;
+{
+double x, y;
+int sign;
+
+
+sign = 1;
+if( xx < 0.0 )
+ {
+ sign = -1;
+ xx = -xx;
+ }
+
+if( xx < 3.25 )
+{
+x = xx*xx;
+y = xx * polevl( x, AN, 9 )/polevl( x, AD, 10 );
+return( sign * y );
+}
+
+
+x = 1.0/(xx*xx);
+
+if( xx < 6.25 )
+ {
+ y = 1.0/xx + x * polevl( x, BN, 10) / (p1evl( x, BD, 10) * xx);
+ return( sign * 0.5 * y );
+ }
+
+
+if( xx > 1.0e9 )
+ return( (sign * 0.5)/xx );
+
+/* 6.25 to infinity */
+y = 1.0/xx + x * polevl( x, CN, 4) / (p1evl( x, CD, 5) * xx);
+return( sign * 0.5 * y );
+}
diff --git a/libm/double/dcalc.c b/libm/double/dcalc.c
new file mode 100644
index 000000000..b740edae2
--- /dev/null
+++ b/libm/double/dcalc.c
@@ -0,0 +1,1512 @@
+/* calc.c */
+/* Keyboard command interpreter */
+/* by Stephen L. Moshier */
+
+
+/* length of command line: */
+#define LINLEN 128
+
+#define XON 0x11
+#define XOFF 0x13
+
+#define SALONE 1
+#define DECPDP 0
+#define INTLOGIN 0
+#define INTHELP 1
+#ifndef TRUE
+#define TRUE 1
+#endif
+
+/* Initialize squirrel printf: */
+#define INIPRINTF 0
+
+#if DECPDP
+#define TRUE 1
+#endif
+
+#include <stdio.h>
+#include <string.h>
+
+static char idterp[] = {
+"\n\nSteve Moshier's command interpreter V1.3\n"};
+#define ISLOWER(c) ((c >= 'a') && (c <= 'z'))
+#define ISUPPER(c) ((c >= 'A') && (c <= 'Z'))
+#define ISALPHA(c) (ISLOWER(c) || ISUPPER(c))
+#define ISDIGIT(c) ((c >= '0') && (c <= '9'))
+#define ISATF(c) (((c >= 'a')&&(c <= 'f')) || ((c >= 'A')&&(c <= 'F')))
+#define ISXDIGIT(c) (ISDIGIT(c) || ISATF(c))
+#define ISOCTAL(c) ((c >= '0') && (c < '8'))
+#define ISALNUM(c) (ISALPHA(c) || (ISDIGIT(c))
+FILE *fopen();
+
+#include "dcalc.h"
+/* #include "ehead.h" */
+#include <math.h>
+/* int strlen(), strcmp(); */
+int system();
+
+/* space for working precision numbers */
+static double vs[22];
+
+/* the symbol table of temporary variables: */
+
+#define NTEMP 4
+struct varent temp[NTEMP] = {
+{"T", OPR | TEMP, &vs[14]},
+{"T", OPR | TEMP, &vs[15]},
+{"T", OPR | TEMP, &vs[16]},
+{"\0", OPR | TEMP, &vs[17]}
+};
+
+/* the symbol table of operators */
+/* EOL is interpreted on null, newline, or ; */
+struct symbol oprtbl[] = {
+{"BOL", OPR | BOL, 0},
+{"EOL", OPR | EOL, 0},
+{"-", OPR | UMINUS, 8},
+/*"~", OPR | COMP, 8,*/
+{",", OPR | EOE, 1},
+{"=", OPR | EQU, 2},
+/*"|", OPR | LOR, 3,*/
+/*"^", OPR | LXOR, 4,*/
+/*"&", OPR | LAND, 5,*/
+{"+", OPR | PLUS, 6},
+{"-", OPR | MINUS, 6},
+{"*", OPR | MULT, 7},
+{"/", OPR | DIV, 7},
+/*"%", OPR | MOD, 7,*/
+{"(", OPR | LPAREN, 11},
+{")", OPR | RPAREN, 11},
+{"\0", ILLEG, 0}
+};
+
+#define NOPR 8
+
+/* the symbol table of indirect variables: */
+extern double PI;
+struct varent indtbl[] = {
+{"t", VAR | IND, &vs[21]},
+{"u", VAR | IND, &vs[20]},
+{"v", VAR | IND, &vs[19]},
+{"w", VAR | IND, &vs[18]},
+{"x", VAR | IND, &vs[10]},
+{"y", VAR | IND, &vs[11]},
+{"z", VAR | IND, &vs[12]},
+{"pi", VAR | IND, &PI},
+{"\0", ILLEG, 0}
+};
+
+/* the symbol table of constants: */
+
+#define NCONST 10
+struct varent contbl[NCONST] = {
+{"C",CONST,&vs[0]},
+{"C",CONST,&vs[1]},
+{"C",CONST,&vs[2]},
+{"C",CONST,&vs[3]},
+{"C",CONST,&vs[4]},
+{"C",CONST,&vs[5]},
+{"C",CONST,&vs[6]},
+{"C",CONST,&vs[7]},
+{"C",CONST,&vs[8]},
+{"\0",CONST,&vs[9]}
+};
+
+/* the symbol table of string variables: */
+
+static char strngs[160] = {0};
+
+#define NSTRNG 5
+struct strent strtbl[NSTRNG] = {
+{0, VAR | STRING, 0},
+{0, VAR | STRING, 0},
+{0, VAR | STRING, 0},
+{0, VAR | STRING, 0},
+{"\0",ILLEG,0},
+};
+
+
+/* Help messages */
+#if INTHELP
+static char *intmsg[] = {
+"?",
+"Unkown symbol",
+"Expression ends in illegal operator",
+"Precede ( by operator",
+")( is illegal",
+"Unmatched )",
+"Missing )",
+"Illegal left hand side",
+"Missing symbol",
+"Must assign to a variable",
+"Divide by zero",
+"Missing symbol",
+"Missing operator",
+"Precede quantity by operator",
+"Quantity preceded by )",
+"Function syntax",
+"Too many function args",
+"No more temps",
+"Arg list"
+};
+#endif
+
+#ifdef ANSIPROT
+double floor ( double );
+int dprec ( void );
+#else
+double floor();
+int dprec();
+#endif
+/* the symbol table of functions: */
+#if SALONE
+#ifdef ANSIPROT
+extern double floor ( double );
+extern double log ( double );
+extern double pow ( double, double );
+extern double sqrt ( double );
+extern double tanh ( double );
+extern double exp ( double );
+extern double fabs ( double );
+extern double hypot ( double, double );
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+extern double incbet ( double, double, double );
+extern double incbi ( double, double, double );
+extern double sin ( double );
+extern double cos ( double );
+extern double atan ( double );
+extern double atan2 ( double, double );
+extern double gamma ( double );
+extern double lgam ( double );
+double zfrexp ( double );
+double zldexp ( double, double );
+double makenan ( double );
+double makeinfinity ( double );
+double hex ( double );
+double hexinput ( double, double );
+double cmdh ( void );
+double cmdhlp ( void );
+double init ( void );
+double cmddm ( void );
+double cmdtm ( void );
+double cmdem ( double );
+double take ( char * );
+double mxit ( void );
+double bits ( double );
+double csys ( char * );
+double cmddig ( double );
+double prhlst ( void * );
+double abmac ( void );
+double ifrac ( double );
+double xcmpl ( double, double );
+void exit ( int );
+#else
+void exit();
+double hex(), hexinput(), cmdh(), cmdhlp(), init();
+double cmddm(), cmdtm(), cmdem();
+double take(), mxit(), bits(), csys();
+double cmddig(), prhlst(), abmac();
+double ifrac(), xcmpl();
+double floor(), log(), pow(), sqrt(), tanh(), exp(), fabs(), hypot();
+double frexp(), zfrexp(), ldexp(), zldexp(), makenan(), makeinfinity();
+double incbet(), incbi(), sin(), cos(), atan(), atan2(), gamma(), lgam();
+#define GLIBC2 0
+#if GLIBC2
+double lgamma();
+#endif
+#endif /* not ANSIPROT */
+struct funent funtbl[] = {
+{"h", OPR | FUNC, cmdh},
+{"help", OPR | FUNC, cmdhlp},
+{"hex", OPR | FUNC, hex},
+{"hexinput", OPR | FUNC, hexinput},
+/*"view", OPR | FUNC, view,*/
+{"exp", OPR | FUNC, exp},
+{"floor", OPR | FUNC, floor},
+{"log", OPR | FUNC, log},
+{"pow", OPR | FUNC, pow},
+{"sqrt", OPR | FUNC, sqrt},
+{"tanh", OPR | FUNC, tanh},
+{"sin", OPR | FUNC, sin},
+{"cos", OPR | FUNC, cos},
+{"atan", OPR | FUNC, atan},
+{"atantwo", OPR | FUNC, atan2},
+{"tanh", OPR | FUNC, tanh},
+{"gamma", OPR | FUNC, gamma},
+#if GLIBC2
+{"lgamma", OPR | FUNC, lgamma},
+#else
+{"lgam", OPR | FUNC, lgam},
+#endif
+{"incbet", OPR | FUNC, incbet},
+{"incbi", OPR | FUNC, incbi},
+{"fabs", OPR | FUNC, fabs},
+{"hypot", OPR | FUNC, hypot},
+{"ldexp", OPR | FUNC, zldexp},
+{"frexp", OPR | FUNC, zfrexp},
+{"nan", OPR | FUNC, makenan},
+{"infinity", OPR | FUNC, makeinfinity},
+{"ifrac", OPR | FUNC, ifrac},
+{"cmp", OPR | FUNC, xcmpl},
+{"bits", OPR | FUNC, bits},
+{"digits", OPR | FUNC, cmddig},
+{"dm", OPR | FUNC, cmddm},
+{"tm", OPR | FUNC, cmdtm},
+{"em", OPR | FUNC, cmdem},
+{"take", OPR | FUNC | COMMAN, take},
+{"system", OPR | FUNC | COMMAN, csys},
+{"exit", OPR | FUNC, mxit},
+/*
+"remain", OPR | FUNC, eremain,
+*/
+{"\0", OPR | FUNC, 0}
+};
+
+/* the symbol table of key words */
+struct funent keytbl[] = {
+{"\0", ILLEG, 0}
+};
+#endif
+
+void zgets();
+
+/* Number of decimals to display */
+#define DEFDIS 70
+static int ndigits = DEFDIS;
+
+/* Menu stack */
+struct funent *menstk[5] = {&funtbl[0], NULL, NULL, NULL, NULL};
+int menptr = 0;
+
+/* Take file stack */
+FILE *takstk[10] = {0};
+int takptr = -1;
+
+/* size of the expression scan list: */
+#define NSCAN 20
+
+/* previous token, saved for syntax checking: */
+struct symbol *lastok = 0;
+
+/* variables used by parser: */
+static char str[128] = {0};
+int uposs = 0; /* possible unary operator */
+static double qnc;
+char lc[40] = { '\n' }; /* ASCII string of token symbol */
+static char line[LINLEN] = { '\n','\0' }; /* input command line */
+static char maclin[LINLEN] = { '\n','\0' }; /* macro command */
+char *interl = line; /* pointer into line */
+extern char *interl;
+static int maccnt = 0; /* number of times to execute macro command */
+static int comptr = 0; /* comma stack pointer */
+static double comstk[5]; /* comma argument stack */
+static int narptr = 0; /* pointer to number of args */
+static int narstk[5] = {0}; /* stack of number of function args */
+
+/* main() */
+
+/* Entire program starts here */
+
+int main()
+{
+
+/* the scan table: */
+
+/* array of pointers to symbols which have been parsed: */
+struct symbol *ascsym[NSCAN];
+
+/* current place in ascsym: */
+register struct symbol **as;
+
+/* array of attributes of operators parsed: */
+int ascopr[NSCAN];
+
+/* current place in ascopr: */
+register int *ao;
+
+#if LARGEMEM
+/* array of precedence levels of operators: */
+long asclev[NSCAN];
+/* current place in asclev: */
+long *al;
+long symval; /* value of symbol just parsed */
+#else
+int asclev[NSCAN];
+int *al;
+int symval;
+#endif
+
+double acc; /* the accumulator, for arithmetic */
+int accflg; /* flags accumulator in use */
+double val; /* value to be combined into accumulator */
+register struct symbol *psym; /* pointer to symbol just parsed */
+struct varent *pvar; /* pointer to an indirect variable symbol */
+struct funent *pfun; /* pointer to a function symbol */
+struct strent *pstr; /* pointer to a string symbol */
+int att; /* attributes of symbol just parsed */
+int i; /* counter */
+int offset; /* parenthesis level */
+int lhsflg; /* kluge to detect illegal assignments */
+struct symbol *parser(); /* parser returns pointer to symbol */
+int errcod; /* for syntax error printout */
+
+
+/* Perform general initialization */
+
+init();
+
+menstk[0] = &funtbl[0];
+menptr = 0;
+cmdhlp(); /* print out list of symbols */
+
+
+/* Return here to get next command line to execute */
+getcmd:
+
+/* initialize registers and mutable symbols */
+
+accflg = 0; /* Accumulator not in use */
+acc = 0.0; /* Clear the accumulator */
+offset = 0; /* Parenthesis level zero */
+comptr = 0; /* Start of comma stack */
+narptr = -1; /* Start of function arg counter stack */
+
+psym = (struct symbol *)&contbl[0];
+for( i=0; i<NCONST; i++ )
+ {
+ psym->attrib = CONST; /* clearing the busy bit */
+ ++psym;
+ }
+psym = (struct symbol *)&temp[0];
+for( i=0; i<NTEMP; i++ )
+ {
+ psym->attrib = VAR | TEMP; /* clearing the busy bit */
+ ++psym;
+ }
+
+pstr = &strtbl[0];
+for( i=0; i<NSTRNG; i++ )
+ {
+ pstr->spel = &strngs[ 40*i ];
+ pstr->attrib = STRING | VAR;
+ pstr->string = &strngs[ 40*i ];
+ ++pstr;
+ }
+
+/* List of scanned symbols is empty: */
+as = &ascsym[0];
+*as = 0;
+--as;
+/* First item in scan list is Beginning of Line operator */
+ao = &ascopr[0];
+*ao = oprtbl[0].attrib & 0xf; /* BOL */
+/* value of first item: */
+al = &asclev[0];
+*al = oprtbl[0].sym;
+
+lhsflg = 0; /* illegal left hand side flag */
+psym = &oprtbl[0]; /* pointer to current token */
+
+/* get next token from input string */
+
+gettok:
+lastok = psym; /* last token = current token */
+psym = parser(); /* get a new current token */
+/*printf( "%s attrib %7o value %7o\n", psym->spel, psym->attrib & 0xffff,
+ psym->sym );*/
+
+/* Examine attributes of the symbol returned by the parser */
+att = psym->attrib;
+if( att == ILLEG )
+ {
+ errcod = 1;
+ goto synerr;
+ }
+
+/* Push functions onto scan list without analyzing further */
+if( att & FUNC )
+ {
+ /* A command is a function whose argument is
+ * a pointer to the rest of the input line.
+ * A second argument is also passed: the address
+ * of the last token parsed.
+ */
+ if( att & COMMAN )
+ {
+ pfun = (struct funent *)psym;
+ ( *(pfun->fun))( interl, lastok );
+ abmac(); /* scrub the input line */
+ goto getcmd; /* and ask for more input */
+ }
+ ++narptr; /* offset to number of args */
+ narstk[narptr] = 0;
+ i = lastok->attrib & 0xffff; /* attrib=short, i=int */
+ if( ((i & OPR) == 0)
+ || (i == (OPR | RPAREN))
+ || (i == (OPR | FUNC)) )
+ {
+ errcod = 15;
+ goto synerr;
+ }
+
+ ++lhsflg;
+ ++as;
+ *as = psym;
+ ++ao;
+ *ao = FUNC;
+ ++al;
+ *al = offset + UMINUS;
+ goto gettok;
+ }
+
+/* deal with operators */
+if( att & OPR )
+ {
+ att &= 0xf;
+ /* expression cannot end with an operator other than
+ * (, ), BOL, or a function
+ */
+ if( (att == RPAREN) || (att == EOL) || (att == EOE))
+ {
+ i = lastok->attrib & 0xffff; /* attrib=short, i=int */
+ if( (i & OPR)
+ && (i != (OPR | RPAREN))
+ && (i != (OPR | LPAREN))
+ && (i != (OPR | FUNC))
+ && (i != (OPR | BOL)) )
+ {
+ errcod = 2;
+ goto synerr;
+ }
+ }
+ ++lhsflg; /* any operator but ( and = is not a legal lhs */
+
+/* operator processing, continued */
+
+ switch( att )
+ {
+ case EOE:
+ lhsflg = 0;
+ break;
+ case LPAREN:
+ /* ( must be preceded by an operator of some sort. */
+ if( ((lastok->attrib & OPR) == 0) )
+ {
+ errcod = 3;
+ goto synerr;
+ }
+ /* also, a preceding ) is illegal */
+ if( (unsigned short )lastok->attrib == (OPR|RPAREN))
+ {
+ errcod = 4;
+ goto synerr;
+ }
+ /* Begin looking for illegal left hand sides: */
+ lhsflg = 0;
+ offset += RPAREN; /* new parenthesis level */
+ goto gettok;
+ case RPAREN:
+ offset -= RPAREN; /* parenthesis level */
+ if( offset < 0 )
+ {
+ errcod = 5; /* parenthesis error */
+ goto synerr;
+ }
+ goto gettok;
+ case EOL:
+ if( offset != 0 )
+ {
+ errcod = 6; /* parenthesis error */
+ goto synerr;
+ }
+ break;
+ case EQU:
+ if( --lhsflg ) /* was incremented before switch{} */
+ {
+ errcod = 7;
+ goto synerr;
+ }
+ case UMINUS:
+ case COMP:
+ goto pshopr; /* evaluate right to left */
+ default: ;
+ }
+
+
+/* evaluate expression whenever precedence is not increasing */
+
+symval = psym->sym + offset;
+
+while( symval <= *al )
+ {
+ /* if just starting, must fill accumulator with last
+ * thing on the line
+ */
+ if( (accflg == 0) && (as >= ascsym) && (((*as)->attrib & FUNC) == 0 ))
+ {
+ pvar = (struct varent *)*as;
+/*
+ if( pvar->attrib & STRING )
+ strcpy( (char *)&acc, (char *)pvar->value );
+ else
+*/
+ acc = *pvar->value;
+ --as;
+ accflg = 1;
+ }
+
+/* handle beginning of line type cases, where the symbol
+ * list ascsym[] may be empty.
+ */
+ switch( *ao )
+ {
+ case BOL:
+ printf( "%.16e\n", acc );
+#if 0
+#if NE == 6
+ e64toasc( &acc, str, 100 );
+#else
+ e113toasc( &acc, str, 100 );
+#endif
+#endif
+ printf( "%s\n", str );
+ goto getcmd; /* all finished */
+ case UMINUS:
+ acc = -acc;
+ goto nochg;
+/*
+ case COMP:
+ acc = ~acc;
+ goto nochg;
+*/
+ default: ;
+ }
+/* Now it is illegal for symbol list to be empty,
+ * because we are going to need a symbol below.
+ */
+ if( as < &ascsym[0] )
+ {
+ errcod = 8;
+ goto synerr;
+ }
+/* get attributes and value of current symbol */
+ att = (*as)->attrib;
+ pvar = (struct varent *)*as;
+ if( att & FUNC )
+ val = 0.0;
+ else
+ {
+/*
+ if( att & STRING )
+ strcpy( (char *)&val, (char *)pvar->value );
+ else
+*/
+ val = *pvar->value;
+ }
+
+/* Expression evaluation, continued. */
+
+ switch( *ao )
+ {
+ case FUNC:
+ pfun = (struct funent *)*as;
+ /* Call the function with appropriate number of args */
+ i = narstk[ narptr ];
+ --narptr;
+ switch(i)
+ {
+ case 0:
+ acc = ( *(pfun->fun) )(acc);
+ break;
+ case 1:
+ acc = ( *(pfun->fun) )(acc, comstk[comptr-1]);
+ break;
+ case 2:
+ acc = ( *(pfun->fun) )(acc, comstk[comptr-2],
+ comstk[comptr-1]);
+ break;
+ case 3:
+ acc = ( *(pfun->fun) )(acc, comstk[comptr-3],
+ comstk[comptr-2], comstk[comptr-1]);
+ break;
+ default:
+ errcod = 16;
+ goto synerr;
+ }
+ comptr -= i;
+ accflg = 1; /* in case at end of line */
+ break;
+ case EQU:
+ if( ( att & TEMP) || ((att & VAR) == 0) || (att & STRING) )
+ {
+ errcod = 9;
+ goto synerr; /* can only assign to a variable */
+ }
+ pvar = (struct varent *)*as;
+ *pvar->value = acc;
+ break;
+ case PLUS:
+ acc = acc + val; break;
+ case MINUS:
+ acc = val - acc; break;
+ case MULT:
+ acc = acc * val; break;
+ case DIV:
+ if( acc == 0.0 )
+ {
+/*
+divzer:
+*/
+ errcod = 10;
+ goto synerr;
+ }
+ acc = val / acc; break;
+/*
+ case MOD:
+ if( acc == 0 )
+ goto divzer;
+ acc = val % acc; break;
+ case LOR:
+ acc |= val; break;
+ case LXOR:
+ acc ^= val; break;
+ case LAND:
+ acc &= val; break;
+*/
+ case EOE:
+ if( narptr < 0 )
+ {
+ errcod = 18;
+ goto synerr;
+ }
+ narstk[narptr] += 1;
+ comstk[comptr++] = acc;
+/* printf( "\ncomptr: %d narptr: %d %d\n", comptr, narptr, acc );*/
+ acc = val;
+ break;
+ }
+
+
+/* expression evaluation, continued */
+
+/* Pop evaluated tokens from scan list: */
+ /* make temporary variable not busy */
+ if( att & TEMP )
+ (*as)->attrib &= ~BUSY;
+ if( as < &ascsym[0] ) /* can this happen? */
+ {
+ errcod = 11;
+ goto synerr;
+ }
+ --as;
+nochg:
+ --ao;
+ --al;
+ if( ao < &ascopr[0] ) /* can this happen? */
+ {
+ errcod = 12;
+ goto synerr;
+ }
+/* If precedence level will now increase, then */
+/* save accumulator in a temporary location */
+ if( symval > *al )
+ {
+ /* find a free temp location */
+ pvar = &temp[0];
+ for( i=0; i<NTEMP; i++ )
+ {
+ if( (pvar->attrib & BUSY) == 0)
+ goto temfnd;
+ ++pvar;
+ }
+ errcod = 17;
+ printf( "no more temps\n" );
+ pvar = &temp[0];
+ goto synerr;
+
+ temfnd:
+ pvar->attrib |= BUSY;
+ *pvar->value = acc;
+ /*printf( "temp %d\n", acc );*/
+ accflg = 0;
+ ++as; /* push the temp onto the scan list */
+ *as = (struct symbol *)pvar;
+ }
+ } /* End of evaluation loop */
+
+
+/* Push operator onto scan list when precedence increases */
+
+pshopr:
+ ++ao;
+ *ao = psym->attrib & 0xf;
+ ++al;
+ *al = psym->sym + offset;
+ goto gettok;
+ } /* end of OPR processing */
+
+
+/* Token was not an operator. Push symbol onto scan list. */
+if( (lastok->attrib & OPR) == 0 )
+ {
+ errcod = 13;
+ goto synerr; /* quantities must be preceded by an operator */
+ }
+if( (unsigned short )lastok->attrib == (OPR | RPAREN) ) /* ...but not by ) */
+ {
+ errcod = 14;
+ goto synerr;
+ }
+++as;
+*as = psym;
+goto gettok;
+
+synerr:
+
+#if INTHELP
+printf( "%s ", intmsg[errcod] );
+#endif
+printf( " error %d\n", errcod );
+abmac(); /* flush the command line */
+goto getcmd;
+} /* end of program */
+
+/* parser() */
+
+/* Get token from input string and identify it. */
+
+
+static char number[128];
+
+struct symbol *parser( )
+{
+register struct symbol *psym;
+register char *pline;
+struct varent *pvar;
+struct strent *pstr;
+char *cp, *plc, *pn;
+long lnc;
+int i;
+double tem;
+
+/* reference for old Whitesmiths compiler: */
+/*
+ *extern FILE *stdout;
+ */
+
+pline = interl; /* get current location in command string */
+
+
+/* If at beginning of string, must ask for more input */
+if( pline == line )
+ {
+
+ if( maccnt > 0 )
+ {
+ --maccnt;
+ cp = maclin;
+ plc = pline;
+ while( (*plc++ = *cp++) != 0 )
+ ;
+ goto mstart;
+ }
+ if( takptr < 0 )
+ { /* no take file active: prompt keyboard input */
+ printf("* ");
+ }
+/* Various ways of typing in a command line. */
+
+/*
+ * Old Whitesmiths call to print "*" immediately
+ * use RT11 .GTLIN to get command string
+ * from command file or terminal
+ */
+
+/*
+ * fflush(stdout);
+ * gtlin(line);
+ */
+
+
+ zgets( line, TRUE ); /* keyboard input for other systems: */
+
+
+mstart:
+ uposs = 1; /* unary operators possible at start of line */
+ }
+
+ignore:
+/* Skip over spaces */
+while( *pline == ' ' )
+ ++pline;
+
+/* unary minus after operator */
+if( uposs && (*pline == '-') )
+ {
+ psym = &oprtbl[2]; /* UMINUS */
+ ++pline;
+ goto pdon3;
+ }
+ /* COMP */
+/*
+if( uposs && (*pline == '~') )
+ {
+ psym = &oprtbl[3];
+ ++pline;
+ goto pdon3;
+ }
+*/
+if( uposs && (*pline == '+') ) /* ignore leading plus sign */
+ {
+ ++pline;
+ goto ignore;
+ }
+
+/* end of null terminated input */
+if( (*pline == '\n') || (*pline == '\0') || (*pline == '\r') )
+ {
+ pline = line;
+ goto endlin;
+ }
+if( *pline == ';' )
+ {
+ ++pline;
+endlin:
+ psym = &oprtbl[1]; /* EOL */
+ goto pdon2;
+ }
+
+
+/* parser() */
+
+
+/* Test for numeric input */
+if( (ISDIGIT(*pline)) || (*pline == '.') )
+ {
+ lnc = 0; /* initialize numeric input to zero */
+ qnc = 0.0;
+ if( *pline == '0' )
+ { /* leading "0" may mean octal or hex radix */
+ ++pline;
+ if( *pline == '.' )
+ goto decimal; /* 0.ddd */
+ /* leading "0x" means hexadecimal radix */
+ if( (*pline == 'x') || (*pline == 'X') )
+ {
+ ++pline;
+ while( ISXDIGIT(*pline) )
+ {
+ i = *pline++ & 0xff;
+ if( i >= 'a' )
+ i -= 047;
+ if( i >= 'A' )
+ i -= 07;
+ i -= 060;
+ lnc = (lnc << 4) + i;
+ qnc = lnc;
+ }
+ goto numdon;
+ }
+ else
+ {
+ while( ISOCTAL( *pline ) )
+ {
+ i = ((*pline++) & 0xff) - 060;
+ lnc = (lnc << 3) + i;
+ qnc = lnc;
+ }
+ goto numdon;
+ }
+ }
+ else
+ {
+ /* no leading "0" means decimal radix */
+/******/
+decimal:
+ pn = number;
+ while( (ISDIGIT(*pline)) || (*pline == '.') )
+ *pn++ = *pline++;
+/* get possible exponent field */
+ if( (*pline == 'e') || (*pline == 'E') )
+ *pn++ = *pline++;
+ else
+ goto numcvt;
+ if( (*pline == '-') || (*pline == '+') )
+ *pn++ = *pline++;
+ while( ISDIGIT(*pline) )
+ *pn++ = *pline++;
+numcvt:
+ *pn++ = ' ';
+ *pn++ = 0;
+#if 0
+#if NE == 6
+ asctoe64( number, &qnc );
+#else
+ asctoe113( number, &qnc );
+#endif
+#endif
+ sscanf( number, "%le", &qnc );
+ }
+/* output the number */
+numdon:
+ /* search the symbol table of constants */
+ pvar = &contbl[0];
+ for( i=0; i<NCONST; i++ )
+ {
+ if( (pvar->attrib & BUSY) == 0 )
+ goto confnd;
+ tem = *pvar->value;
+ if( tem == qnc )
+ {
+ psym = (struct symbol *)pvar;
+ goto pdon2;
+ }
+ ++pvar;
+ }
+ printf( "no room for constant\n" );
+ psym = (struct symbol *)&contbl[0];
+ goto pdon2;
+
+confnd:
+ pvar->spel= contbl[0].spel;
+ pvar->attrib = CONST | BUSY;
+ *pvar->value = qnc;
+ psym = (struct symbol *)pvar;
+ goto pdon2;
+ }
+
+/* check for operators */
+psym = &oprtbl[3];
+for( i=0; i<NOPR; i++ )
+ {
+ if( *pline == *(psym->spel) )
+ goto pdon1;
+ ++psym;
+ }
+
+/* if quoted, it is a string variable */
+if( *pline == '"' )
+ {
+ /* find an empty slot for the string */
+ pstr = strtbl; /* string table */
+ for( i=0; i<NSTRNG-1; i++ )
+ {
+ if( (pstr->attrib & BUSY) == 0 )
+ goto fndstr;
+ ++pstr;
+ }
+ printf( "No room for string\n" );
+ pstr->attrib |= ILLEG;
+ psym = (struct symbol *)pstr;
+ goto pdon0;
+
+fndstr:
+ pstr->attrib |= BUSY;
+ plc = pstr->string;
+ ++pline;
+ for( i=0; i<39; i++ )
+ {
+ *plc++ = *pline;
+ if( (*pline == '\n') || (*pline == '\0') || (*pline == '\r') )
+ {
+illstr:
+ pstr = &strtbl[NSTRNG-1];
+ pstr->attrib |= ILLEG;
+ printf( "Missing string terminator\n" );
+ psym = (struct symbol *)pstr;
+ goto pdon0;
+ }
+ if( *pline++ == '"' )
+ goto finstr;
+ }
+
+ goto illstr; /* no terminator found */
+
+finstr:
+ --plc;
+ *plc = '\0';
+ psym = (struct symbol *)pstr;
+ goto pdon2;
+ }
+/* If none of the above, search function and symbol tables: */
+
+/* copy character string to array lc[] */
+plc = &lc[0];
+while( ISALPHA(*pline) )
+ {
+ /* convert to lower case characters */
+ if( ISUPPER( *pline ) )
+ *pline += 040;
+ *plc++ = *pline++;
+ }
+*plc = 0; /* Null terminate the output string */
+
+/* parser() */
+
+psym = (struct symbol *)menstk[menptr]; /* function table */
+plc = &lc[0];
+cp = psym->spel;
+do
+ {
+ if( strcmp( plc, cp ) == 0 )
+ goto pdon3; /* following unary minus is possible */
+ ++psym;
+ cp = psym->spel;
+ }
+while( *cp != '\0' );
+
+psym = (struct symbol *)&indtbl[0]; /* indirect symbol table */
+plc = &lc[0];
+cp = psym->spel;
+do
+ {
+ if( strcmp( plc, cp ) == 0 )
+ goto pdon2;
+ ++psym;
+ cp = psym->spel;
+ }
+while( *cp != '\0' );
+
+pdon0:
+pline = line; /* scrub line if illegal symbol */
+goto pdon2;
+
+pdon1:
+++pline;
+if( (psym->attrib & 0xf) == RPAREN )
+pdon2: uposs = 0;
+else
+pdon3: uposs = 1;
+
+interl = pline;
+return( psym );
+} /* end of parser */
+
+/* exit from current menu */
+
+double cmdex()
+{
+
+if( menptr == 0 )
+ {
+ printf( "Main menu is active.\n" );
+ }
+else
+ --menptr;
+
+cmdh();
+return(0.0);
+}
+
+
+/* gets() */
+
+void zgets( gline, echo )
+char *gline;
+int echo;
+{
+register char *pline;
+register int i;
+
+
+scrub:
+pline = gline;
+getsl:
+ if( (pline - gline) >= LINLEN )
+ {
+ printf( "\nLine too long\n *" );
+ goto scrub;
+ }
+ if( takptr < 0 )
+ { /* get character from keyboard */
+/*
+if DECPDP
+ gtlin( gline );
+ return(0);
+else
+*/
+ *pline = getchar();
+/*endif*/
+ }
+ else
+ { /* get a character from take file */
+ i = fgetc( takstk[takptr] );
+ if( i == -1 )
+ { /* end of take file */
+ if( takptr >= 0 )
+ { /* close file and bump take stack */
+ fclose( takstk[takptr] );
+ takptr -= 1;
+ }
+ if( takptr < 0 ) /* no more take files: */
+ printf( "*" ); /* prompt keyboard input */
+ goto scrub; /* start a new input line */
+ }
+ *pline = i;
+ }
+
+ *pline &= 0x7f;
+ /* xon or xoff characters need filtering out. */
+ if ( *pline == XON || *pline == XOFF )
+ goto getsl;
+
+ /* control U or control C */
+ if( (*pline == 025) || (*pline == 03) )
+ {
+ printf( "\n" );
+ goto scrub;
+ }
+
+ /* Backspace or rubout */
+ if( (*pline == 010) || (*pline == 0177) )
+ {
+ pline -= 1;
+ if( pline >= gline )
+ {
+ if ( echo )
+ printf( "\010\040\010" );
+ goto getsl;
+ }
+ else
+ goto scrub;
+ }
+ if ( echo )
+ printf( "%c", *pline );
+ if( (*pline != '\n') && (*pline != '\r') )
+ {
+ ++pline;
+ goto getsl;
+ }
+ *pline = 0;
+ if ( echo )
+ printf( "%c", '\n' ); /* \r already echoed */
+}
+
+
+/* help function */
+double cmdhlp()
+{
+
+printf( "%s", idterp );
+printf( "\nFunctions:\n" );
+prhlst( &funtbl[0] );
+printf( "\nVariables:\n" );
+prhlst( &indtbl[0] );
+printf( "\nOperators:\n" );
+prhlst( &oprtbl[2] );
+printf("\n");
+return(0.0);
+}
+
+
+double cmdh()
+{
+
+prhlst( menstk[menptr] );
+printf( "\n" );
+return(0.0);
+}
+
+/* print keyword spellings */
+
+double prhlst(vps)
+void *vps;
+{
+register int j, k;
+int m;
+register struct symbol *ps = vps;
+
+j = 0;
+while( *(ps->spel) != '\0' )
+ {
+ k = strlen( ps->spel ) - 1;
+/* size of a tab field is 2**3 chars */
+ m = ((k >> 3) + 1) << 3;
+ j += m;
+ if( j > 72 )
+ {
+ printf( "\n" );
+ j = m;
+ }
+ printf( "%s\t", ps->spel );
+ ++ps;
+ }
+return(0.0);
+}
+
+
+#if SALONE
+double init()
+{
+/* Set coprocessor to double precision. */
+dprec();
+return 0.0;
+}
+#endif
+
+
+/* macro commands */
+
+/* define macro */
+double cmddm()
+{
+
+zgets( maclin, TRUE );
+return(0.0);
+}
+
+/* type (i.e., display) macro */
+double cmdtm()
+{
+
+printf( "%s\n", maclin );
+return 0.0;
+}
+
+/* execute macro # times */
+double cmdem( arg )
+double arg;
+{
+double f;
+long n;
+
+f = floor(arg);
+n = f;
+if( n <= 0 )
+ n = 1;
+maccnt = n;
+return(0.0);
+}
+
+
+/* open a take file */
+
+double take( fname )
+char *fname;
+{
+FILE *f;
+
+while( *fname == ' ' )
+ fname += 1;
+f = fopen( fname, "r" );
+
+if( f == 0 )
+ {
+ printf( "Can't open take file %s\n", fname );
+ takptr = -1; /* terminate all take file input */
+ return 0.0;
+ }
+takptr += 1;
+takstk[ takptr ] = f;
+printf( "Running %s\n", fname );
+return(0.0);
+}
+
+
+/* abort macro execution */
+double abmac()
+{
+
+maccnt = 0;
+interl = line;
+return(0.0);
+}
+
+
+/* display integer part in hex, octal, and decimal
+ */
+double hex(qx)
+double qx;
+{
+double f;
+long z;
+
+f = floor(qx);
+z = f;
+printf( "0%lo 0x%lx %ld.\n", z, z, z );
+return(qx);
+}
+
+#define NASC 16
+
+double bits( x )
+double x;
+{
+union
+ {
+ double d;
+ short i[4];
+ } du;
+union
+ {
+ float f;
+ short i[2];
+ } df;
+int i;
+
+du.d = x;
+printf( "double: " );
+for( i=0; i<4; i++ )
+ printf( "0x%04x,", du.i[i] & 0xffff );
+printf( "\n" );
+
+df.f = (float) x;
+printf( "float: " );
+for( i=0; i<2; i++ )
+ printf( "0x%04x,", df.i[i] & 0xffff );
+printf( "\n" );
+return(x);
+}
+
+
+/* Exit to monitor. */
+double mxit()
+{
+
+exit(0);
+return(0.0);
+}
+
+
+double cmddig( x )
+double x;
+{
+double f;
+long lx;
+
+f = floor(x);
+lx = f;
+ndigits = lx;
+if( ndigits <= 0 )
+ ndigits = DEFDIS;
+return(f);
+}
+
+
+double csys(x)
+char *x;
+{
+
+system( x+1 );
+cmdh();
+return(0.0);
+}
+
+
+double ifrac(x)
+double x;
+{
+unsigned long lx;
+long double y, z;
+
+z = floor(x);
+lx = z;
+y = x - z;
+printf( " int = %lx\n", lx );
+return(y);
+}
+
+double xcmpl(x,y)
+double x,y;
+{
+double ans;
+
+ans = -2.0;
+if( x == y )
+ {
+ printf( "x == y " );
+ ans = 0.0;
+ }
+if( x < y )
+ {
+ printf( "x < y" );
+ ans = -1.0;
+ }
+if( x > y )
+ {
+ printf( "x > y" );
+ ans = 1.0;
+ }
+return( ans );
+}
+
+extern double INFINITY, NAN;
+
+double makenan(x)
+double x;
+{
+return(NAN);
+}
+
+double makeinfinity(x)
+double x;
+{
+return(INFINITY);
+}
+
+double zfrexp(x)
+double x;
+{
+double y;
+int e;
+y = frexp(x, &e);
+printf("exponent = %d, significand = ", e );
+return(y);
+}
+
+double zldexp(x,e)
+double x, e;
+{
+double y;
+int i;
+
+i = e;
+y = ldexp(x,i);
+return(y);
+}
+
+double hexinput(a, b)
+double a,b;
+{
+union
+ {
+ double d;
+ unsigned short i[4];
+ } u;
+unsigned long l;
+
+#ifdef IBMPC
+l = a;
+u.i[3] = l >> 16;
+u.i[2] = l;
+l = b;
+u.i[1] = l >> 16;
+u.i[0] = l;
+#endif
+#ifdef DEC
+l = a;
+u.i[3] = l >> 16;
+u.i[2] = l;
+l = b;
+u.i[1] = l >> 16;
+u.i[0] = l;
+#endif
+#ifdef MIEEE
+l = a;
+u.i[0] = l >> 16;
+u.i[1] = l;
+l = b;
+u.i[2] = l >> 16;
+u.i[3] = l;
+#endif
+#ifdef UNK
+l = a;
+u.i[0] = l >> 16;
+u.i[1] = l;
+l = b;
+u.i[2] = l >> 16;
+u.i[3] = l;
+#endif
+return(u.d);
+}
diff --git a/libm/double/dcalc.h b/libm/double/dcalc.h
new file mode 100644
index 000000000..0ec2a46da
--- /dev/null
+++ b/libm/double/dcalc.h
@@ -0,0 +1,77 @@
+/* calc.h
+ * include file for calc.c
+ */
+
+/* 32 bit memory addresses: */
+#define LARGEMEM 1
+
+/* data structure of symbol table */
+struct symbol
+ {
+ char *spel;
+ short attrib;
+#if LARGEMEM
+ long sym;
+#else
+ short sym;
+#endif
+ };
+
+struct funent
+ {
+ char *spel;
+ short attrib;
+ double (*fun )();
+ };
+
+struct varent
+ {
+ char *spel;
+ short attrib;
+ double *value;
+ };
+
+struct strent
+ {
+ char *spel;
+ short attrib;
+ char *string;
+ };
+
+
+/* general symbol attributes: */
+#define OPR 0x8000
+#define VAR 0x4000
+#define CONST 0x2000
+#define FUNC 0x1000
+#define ILLEG 0x800
+#define BUSY 0x400
+#define TEMP 0x200
+#define STRING 0x100
+#define COMMAN 0x80
+#define IND 0x1
+
+/* attributes of operators (ordered by precedence): */
+#define BOL 1
+#define EOL 2
+/* end of expression (comma): */
+#define EOE 3
+#define EQU 4
+#define PLUS 5
+#define MINUS 6
+#define MULT 7
+#define DIV 8
+#define UMINUS 9
+#define LPAREN 10
+#define RPAREN 11
+#define COMP 12
+#define MOD 13
+#define LAND 14
+#define LOR 15
+#define LXOR 16
+
+
+extern struct funent funtbl[];
+/*extern struct symbol symtbl[];*/
+extern struct varent indtbl[];
+
diff --git a/libm/double/dtestvec.c b/libm/double/dtestvec.c
new file mode 100644
index 000000000..ea494029b
--- /dev/null
+++ b/libm/double/dtestvec.c
@@ -0,0 +1,543 @@
+
+/* Test vectors for math functions.
+ See C9X section F.9. */
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1998, 2000 by Stephen L. Moshier
+*/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+int isfinite (double);
+
+/* C9X spells lgam lgamma. */
+#define GLIBC2 0
+
+extern double PI;
+static double MPI, PIO2, MPIO2, PIO4, MPIO4, THPIO4, MTHPIO4;
+
+#if 0
+#define PI 3.141592653589793238463E0
+#define PIO2 1.570796326794896619231E0
+#define PIO4 7.853981633974483096157E-1
+#define THPIO4 2.35619449019234492884698
+#define SQRT2 1.414213562373095048802E0
+#define SQRTH 7.071067811865475244008E-1
+#define INF (1.0/0.0)
+#define MINF (-1.0/0.0)
+#endif
+
+extern double MACHEP, SQRTH, SQRT2;
+extern double NAN, INFINITY, NEGZERO;
+static double INF, MINF;
+static double ZERO, MZERO, HALF, MHALF, ONE, MONE, TWO, MTWO, THREE, MTHREE;
+/* #define NAN (1.0/0.0 - 1.0/0.0) */
+
+/* Functions of one variable. */
+double log (double);
+double exp ( double);
+double atan (double);
+double sin (double);
+double cos (double);
+double tan (double);
+double acos (double);
+double asin (double);
+double acosh (double);
+double asinh (double);
+double atanh (double);
+double sinh (double);
+double cosh (double);
+double tanh (double);
+double exp2 (double);
+double expm1 (double);
+double log10 (double);
+double log1p (double);
+double log2 (double);
+double fabs (double);
+double erf (double);
+double erfc (double);
+double gamma (double);
+double floor (double);
+double ceil (double);
+double cbrt (double);
+#if GLIBC2
+double lgamma (double);
+#else
+double lgam (double);
+#endif
+
+struct oneargument
+ {
+ char *name; /* Name of the function. */
+ double (*func) (double);
+ double *arg1;
+ double *answer;
+ int thresh; /* Error report threshold. */
+ };
+
+struct oneargument test1[] =
+{
+ {"atan", atan, &ONE, &PIO4, 0},
+ {"sin", sin, &PIO2, &ONE, 0},
+#if 0
+ {"cos", cos, &PIO4, &SQRTH, 0},
+ {"sin", sin, 32767., 1.8750655394138942394239E-1, 0},
+ {"cos", cos, 32767., 9.8226335176928229845654E-1, 0},
+ {"tan", tan, 32767., 1.9089234430221485740826E-1, 0},
+ {"sin", sin, 8388607., 9.9234509376961249835628E-1, 0},
+ {"cos", cos, 8388607., -1.2349580912475928183718E-1, 0},
+ {"tan", tan, 8388607., -8.0354556223613614748329E0, 0},
+ /*
+ {"sin", sin, 2147483647., -7.2491655514455639054829E-1, 0},
+ {"cos", cos, 2147483647., -6.8883669187794383467976E-1, 0},
+ {"tan", tan, 2147483647., 1.0523779637351339136698E0, 0},
+ */
+ {"cos", cos, &PIO2, 6.1232339957367574e-17, 1},
+ {"sin", sin, &PIO4, &SQRTH, 1},
+#endif
+ {"acos", acos, &NAN, &NAN, 0},
+ {"acos", acos, &ONE, &ZERO, 0},
+ {"acos", acos, &TWO, &NAN, 0},
+ {"acos", acos, &MTWO, &NAN, 0},
+ {"asin", asin, &NAN, &NAN, 0},
+ {"asin", asin, &ZERO, &ZERO, 0},
+ {"asin", asin, &MZERO, &MZERO, 0},
+ {"asin", asin, &TWO, &NAN, 0},
+ {"asin", asin, &MTWO, &NAN, 0},
+ {"atan", atan, &NAN, &NAN, 0},
+ {"atan", atan, &ZERO, &ZERO, 0},
+ {"atan", atan, &MZERO, &MZERO, 0},
+ {"atan", atan, &INF, &PIO2, 0},
+ {"atan", atan, &MINF, &MPIO2, 0},
+ {"cos", cos, &NAN, &NAN, 0},
+ {"cos", cos, &ZERO, &ONE, 0},
+ {"cos", cos, &MZERO, &ONE, 0},
+ {"cos", cos, &INF, &NAN, 0},
+ {"cos", cos, &MINF, &NAN, 0},
+ {"sin", sin, &NAN, &NAN, 0},
+ {"sin", sin, &MZERO, &MZERO, 0},
+ {"sin", sin, &ZERO, &ZERO, 0},
+ {"sin", sin, &INF, &NAN, 0},
+ {"sin", sin, &MINF, &NAN, 0},
+ {"tan", tan, &NAN, &NAN, 0},
+ {"tan", tan, &ZERO, &ZERO, 0},
+ {"tan", tan, &MZERO, &MZERO, 0},
+ {"tan", tan, &INF, &NAN, 0},
+ {"tan", tan, &MINF, &NAN, 0},
+ {"acosh", acosh, &NAN, &NAN, 0},
+ {"acosh", acosh, &ONE, &ZERO, 0},
+ {"acosh", acosh, &INF, &INF, 0},
+ {"acosh", acosh, &HALF, &NAN, 0},
+ {"acosh", acosh, &MONE, &NAN, 0},
+ {"asinh", asinh, &NAN, &NAN, 0},
+ {"asinh", asinh, &ZERO, &ZERO, 0},
+ {"asinh", asinh, &MZERO, &MZERO, 0},
+ {"asinh", asinh, &INF, &INF, 0},
+ {"asinh", asinh, &MINF, &MINF, 0},
+ {"atanh", atanh, &NAN, &NAN, 0},
+ {"atanh", atanh, &ZERO, &ZERO, 0},
+ {"atanh", atanh, &MZERO, &MZERO, 0},
+ {"atanh", atanh, &ONE, &INF, 0},
+ {"atanh", atanh, &MONE, &MINF, 0},
+ {"atanh", atanh, &TWO, &NAN, 0},
+ {"atanh", atanh, &MTWO, &NAN, 0},
+ {"cosh", cosh, &NAN, &NAN, 0},
+ {"cosh", cosh, &ZERO, &ONE, 0},
+ {"cosh", cosh, &MZERO, &ONE, 0},
+ {"cosh", cosh, &INF, &INF, 0},
+ {"cosh", cosh, &MINF, &INF, 0},
+ {"sinh", sinh, &NAN, &NAN, 0},
+ {"sinh", sinh, &ZERO, &ZERO, 0},
+ {"sinh", sinh, &MZERO, &MZERO, 0},
+ {"sinh", sinh, &INF, &INF, 0},
+ {"sinh", sinh, &MINF, &MINF, 0},
+ {"tanh", tanh, &NAN, &NAN, 0},
+ {"tanh", tanh, &ZERO, &ZERO, 0},
+ {"tanh", tanh, &MZERO, &MZERO, 0},
+ {"tanh", tanh, &INF, &ONE, 0},
+ {"tanh", tanh, &MINF, &MONE, 0},
+ {"exp", exp, &NAN, &NAN, 0},
+ {"exp", exp, &ZERO, &ONE, 0},
+ {"exp", exp, &MZERO, &ONE, 0},
+ {"exp", exp, &INF, &INF, 0},
+ {"exp", exp, &MINF, &ZERO, 0},
+#if !GLIBC2
+ {"exp2", exp2, &NAN, &NAN, 0},
+ {"exp2", exp2, &ZERO, &ONE, 0},
+ {"exp2", exp2, &MZERO, &ONE, 0},
+ {"exp2", exp2, &INF, &INF, 0},
+ {"exp2", exp2, &MINF, &ZERO, 0},
+#endif
+ {"expm1", expm1, &NAN, &NAN, 0},
+ {"expm1", expm1, &ZERO, &ZERO, 0},
+ {"expm1", expm1, &MZERO, &MZERO, 0},
+ {"expm1", expm1, &INF, &INF, 0},
+ {"expm1", expm1, &MINF, &MONE, 0},
+ {"log", log, &NAN, &NAN, 0},
+ {"log", log, &ZERO, &MINF, 0},
+ {"log", log, &MZERO, &MINF, 0},
+ {"log", log, &ONE, &ZERO, 0},
+ {"log", log, &MONE, &NAN, 0},
+ {"log", log, &INF, &INF, 0},
+ {"log10", log10, &NAN, &NAN, 0},
+ {"log10", log10, &ZERO, &MINF, 0},
+ {"log10", log10, &MZERO, &MINF, 0},
+ {"log10", log10, &ONE, &ZERO, 0},
+ {"log10", log10, &MONE, &NAN, 0},
+ {"log10", log10, &INF, &INF, 0},
+ {"log1p", log1p, &NAN, &NAN, 0},
+ {"log1p", log1p, &ZERO, &ZERO, 0},
+ {"log1p", log1p, &MZERO, &MZERO, 0},
+ {"log1p", log1p, &MONE, &MINF, 0},
+ {"log1p", log1p, &MTWO, &NAN, 0},
+ {"log1p", log1p, &INF, &INF, 0},
+#if !GLIBC2
+ {"log2", log2, &NAN, &NAN, 0},
+ {"log2", log2, &ZERO, &MINF, 0},
+ {"log2", log2, &MZERO, &MINF, 0},
+ {"log2", log2, &MONE, &NAN, 0},
+ {"log2", log2, &INF, &INF, 0},
+#endif
+ /* {"fabs", fabs, NAN, NAN, 0}, */
+ {"fabs", fabs, &ONE, &ONE, 0},
+ {"fabs", fabs, &MONE, &ONE, 0},
+ {"fabs", fabs, &ZERO, &ZERO, 0},
+ {"fabs", fabs, &MZERO, &ZERO, 0},
+ {"fabs", fabs, &INF, &INF, 0},
+ {"fabs", fabs, &MINF, &INF, 0},
+ {"cbrt", cbrt, &NAN, &NAN, 0},
+ {"cbrt", cbrt, &ZERO, &ZERO, 0},
+ {"cbrt", cbrt, &MZERO, &MZERO, 0},
+ {"cbrt", cbrt, &INF, &INF, 0},
+ {"cbrt", cbrt, &MINF, &MINF, 0},
+ {"erf", erf, &NAN, &NAN, 0},
+ {"erf", erf, &ZERO, &ZERO, 0},
+ {"erf", erf, &MZERO, &MZERO, 0},
+ {"erf", erf, &INF, &ONE, 0},
+ {"erf", erf, &MINF, &MONE, 0},
+ {"erfc", erfc, &NAN, &NAN, 0},
+ {"erfc", erfc, &INF, &ZERO, 0},
+ {"erfc", erfc, &MINF, &TWO, 0},
+ {"gamma", gamma, &NAN, &NAN, 0},
+ {"gamma", gamma, &INF, &INF, 0},
+ {"gamma", gamma, &MONE, &NAN, 0},
+ {"gamma", gamma, &ZERO, &NAN, 0},
+ {"gamma", gamma, &MINF, &NAN, 0},
+#if GLIBC2
+ {"lgamma", lgamma, &NAN, &NAN, 0},
+ {"lgamma", lgamma, &INF, &INF, 0},
+ {"lgamma", lgamma, &MONE, &INF, 0},
+ {"lgamma", lgamma, &ZERO, &INF, 0},
+ {"lgamma", lgamma, &MINF, &INF, 0},
+#else
+ {"lgam", lgam, &NAN, &NAN, 0},
+ {"lgam", lgam, &INF, &INF, 0},
+ {"lgam", lgam, &MONE, &INF, 0},
+ {"lgam", lgam, &ZERO, &INF, 0},
+ {"lgam", lgam, &MINF, &INF, 0},
+#endif
+ {"ceil", ceil, &NAN, &NAN, 0},
+ {"ceil", ceil, &ZERO, &ZERO, 0},
+ {"ceil", ceil, &MZERO, &MZERO, 0},
+ {"ceil", ceil, &INF, &INF, 0},
+ {"ceil", ceil, &MINF, &MINF, 0},
+ {"floor", floor, &NAN, &NAN, 0},
+ {"floor", floor, &ZERO, &ZERO, 0},
+ {"floor", floor, &MZERO, &MZERO, 0},
+ {"floor", floor, &INF, &INF, 0},
+ {"floor", floor, &MINF, &MINF, 0},
+ {"null", NULL, &ZERO, &ZERO, 0},
+};
+
+/* Functions of two variables. */
+double atan2 (double, double);
+double pow (double, double);
+
+struct twoarguments
+ {
+ char *name; /* Name of the function. */
+ double (*func) (double, double);
+ double *arg1;
+ double *arg2;
+ double *answer;
+ int thresh;
+ };
+
+struct twoarguments test2[] =
+{
+ {"atan2", atan2, &ZERO, &ONE, &ZERO, 0},
+ {"atan2", atan2, &MZERO, &ONE, &MZERO, 0},
+ {"atan2", atan2, &ZERO, &ZERO, &ZERO, 0},
+ {"atan2", atan2, &MZERO, &ZERO, &MZERO, 0},
+ {"atan2", atan2, &ZERO, &MONE, &PI, 0},
+ {"atan2", atan2, &MZERO, &MONE, &MPI, 0},
+ {"atan2", atan2, &ZERO, &MZERO, &PI, 0},
+ {"atan2", atan2, &MZERO, &MZERO, &MPI, 0},
+ {"atan2", atan2, &ONE, &ZERO, &PIO2, 0},
+ {"atan2", atan2, &ONE, &MZERO, &PIO2, 0},
+ {"atan2", atan2, &MONE, &ZERO, &MPIO2, 0},
+ {"atan2", atan2, &MONE, &MZERO, &MPIO2, 0},
+ {"atan2", atan2, &ONE, &INF, &ZERO, 0},
+ {"atan2", atan2, &MONE, &INF, &MZERO, 0},
+ {"atan2", atan2, &INF, &ONE, &PIO2, 0},
+ {"atan2", atan2, &INF, &MONE, &PIO2, 0},
+ {"atan2", atan2, &MINF, &ONE, &MPIO2, 0},
+ {"atan2", atan2, &MINF, &MONE, &MPIO2, 0},
+ {"atan2", atan2, &ONE, &MINF, &PI, 0},
+ {"atan2", atan2, &MONE, &MINF, &MPI, 0},
+ {"atan2", atan2, &INF, &INF, &PIO4, 0},
+ {"atan2", atan2, &MINF, &INF, &MPIO4, 0},
+ {"atan2", atan2, &INF, &MINF, &THPIO4, 0},
+ {"atan2", atan2, &MINF, &MINF, &MTHPIO4, 0},
+ {"atan2", atan2, &ONE, &ONE, &PIO4, 0},
+ {"atan2", atan2, &NAN, &ONE, &NAN, 0},
+ {"atan2", atan2, &ONE, &NAN, &NAN, 0},
+ {"atan2", atan2, &NAN, &NAN, &NAN, 0},
+ {"pow", pow, &ONE, &ZERO, &ONE, 0},
+ {"pow", pow, &ONE, &MZERO, &ONE, 0},
+ {"pow", pow, &MONE, &ZERO, &ONE, 0},
+ {"pow", pow, &MONE, &MZERO, &ONE, 0},
+ {"pow", pow, &INF, &ZERO, &ONE, 0},
+ {"pow", pow, &INF, &MZERO, &ONE, 0},
+ {"pow", pow, &NAN, &ZERO, &ONE, 0},
+ {"pow", pow, &NAN, &MZERO, &ONE, 0},
+ {"pow", pow, &TWO, &INF, &INF, 0},
+ {"pow", pow, &MTWO, &INF, &INF, 0},
+ {"pow", pow, &HALF, &INF, &ZERO, 0},
+ {"pow", pow, &MHALF, &INF, &ZERO, 0},
+ {"pow", pow, &TWO, &MINF, &ZERO, 0},
+ {"pow", pow, &MTWO, &MINF, &ZERO, 0},
+ {"pow", pow, &HALF, &MINF, &INF, 0},
+ {"pow", pow, &MHALF, &MINF, &INF, 0},
+ {"pow", pow, &INF, &HALF, &INF, 0},
+ {"pow", pow, &INF, &TWO, &INF, 0},
+ {"pow", pow, &INF, &MHALF, &ZERO, 0},
+ {"pow", pow, &INF, &MTWO, &ZERO, 0},
+ {"pow", pow, &MINF, &THREE, &MINF, 0},
+ {"pow", pow, &MINF, &TWO, &INF, 0},
+ {"pow", pow, &MINF, &MTHREE, &MZERO, 0},
+ {"pow", pow, &MINF, &MTWO, &ZERO, 0},
+ {"pow", pow, &NAN, &ONE, &NAN, 0},
+ {"pow", pow, &ONE, &NAN, &NAN, 0},
+ {"pow", pow, &NAN, &NAN, &NAN, 0},
+ {"pow", pow, &ONE, &INF, &NAN, 0},
+ {"pow", pow, &MONE, &INF, &NAN, 0},
+ {"pow", pow, &ONE, &MINF, &NAN, 0},
+ {"pow", pow, &MONE, &MINF, &NAN, 0},
+ {"pow", pow, &MTWO, &HALF, &NAN, 0},
+ {"pow", pow, &ZERO, &MTHREE, &INF, 0},
+ {"pow", pow, &MZERO, &MTHREE, &MINF, 0},
+ {"pow", pow, &ZERO, &MHALF, &INF, 0},
+ {"pow", pow, &MZERO, &MHALF, &INF, 0},
+ {"pow", pow, &ZERO, &THREE, &ZERO, 0},
+ {"pow", pow, &MZERO, &THREE, &MZERO, 0},
+ {"pow", pow, &ZERO, &HALF, &ZERO, 0},
+ {"pow", pow, &MZERO, &HALF, &ZERO, 0},
+ {"null", NULL, &ZERO, &ZERO, &ZERO, 0},
+};
+
+/* Integer functions of one variable. */
+
+int isnan (double);
+int signbit (double);
+
+struct intans
+ {
+ char *name; /* Name of the function. */
+ int (*func) (double);
+ double *arg1;
+ int ianswer;
+ };
+
+struct intans test3[] =
+{
+ {"isfinite", isfinite, &ZERO, 1},
+ {"isfinite", isfinite, &INF, 0},
+ {"isfinite", isfinite, &MINF, 0},
+ {"isnan", isnan, &NAN, 1},
+ {"isnan", isnan, &INF, 0},
+ {"isnan", isnan, &ZERO, 0},
+ {"isnan", isnan, &MZERO, 0},
+ {"signbit", signbit, &MZERO, 1},
+ {"signbit", signbit, &MONE, 1},
+ {"signbit", signbit, &ZERO, 0},
+ {"signbit", signbit, &ONE, 0},
+ {"signbit", signbit, &MINF, 1},
+ {"signbit", signbit, &INF, 0},
+ {"null", NULL, &ZERO, 0},
+};
+
+static volatile double x1;
+static volatile double x2;
+static volatile double y;
+static volatile double answer;
+
+void
+pvec(x)
+double x;
+{
+ union
+ {
+ double d;
+ unsigned short s[4];
+ } u;
+ int i;
+
+ u.d = x;
+ for (i = 0; i < 4; i++)
+ printf ("0x%04x ", u.s[i]);
+ printf ("\n");
+}
+
+
+int
+main ()
+{
+ int i, nerrors, k, ianswer, ntests;
+ double (*fun1) (double);
+ double (*fun2) (double, double);
+ int (*fun3) (double);
+ double e;
+ union
+ {
+ double d;
+ char c[8];
+ } u, v;
+
+ ZERO = 0.0;
+ MZERO = NEGZERO;
+ HALF = 0.5;
+ MHALF = -HALF;
+ ONE = 1.0;
+ MONE = -ONE;
+ TWO = 2.0;
+ MTWO = -TWO;
+ THREE = 3.0;
+ MTHREE = -THREE;
+ INF = INFINITY;
+ MINF = -INFINITY;
+ MPI = -PI;
+ PIO2 = 0.5 * PI;
+ MPIO2 = -PIO2;
+ PIO4 = 0.5 * PIO2;
+ MPIO4 = -PIO4;
+ THPIO4 = 3.0 * PIO4;
+ MTHPIO4 = -THPIO4;
+
+ nerrors = 0;
+ ntests = 0;
+ i = 0;
+ for (;;)
+ {
+ fun1 = test1[i].func;
+ if (fun1 == NULL)
+ break;
+ x1 = *(test1[i].arg1);
+ y = (*(fun1)) (x1);
+ answer = *(test1[i].answer);
+ if (test1[i].thresh == 0)
+ {
+ v.d = answer;
+ u.d = y;
+ if (memcmp(u.c, v.c, 8) != 0)
+ {
+ if( isnan(v.d) && isnan(u.d) )
+ goto nxttest1;
+ goto wrongone;
+ }
+ else
+ goto nxttest1;
+ }
+ if (y != answer)
+ {
+ e = y - answer;
+ if (answer != 0.0)
+ e = e / answer;
+ if (e < 0)
+ e = -e;
+ if (e > test1[i].thresh * MACHEP)
+ {
+wrongone:
+ printf ("%s (%.16e) = %.16e\n should be %.16e\n",
+ test1[i].name, x1, y, answer);
+ nerrors += 1;
+ }
+ }
+nxttest1:
+ ntests += 1;
+ i += 1;
+ }
+
+ i = 0;
+ for (;;)
+ {
+ fun2 = test2[i].func;
+ if (fun2 == NULL)
+ break;
+ x1 = *(test2[i].arg1);
+ x2 = *(test2[i].arg2);
+ y = (*(fun2)) (x1, x2);
+ answer = *(test2[i].answer);
+ if (test2[i].thresh == 0)
+ {
+ v.d = answer;
+ u.d = y;
+ if (memcmp(u.c, v.c, 8) != 0)
+ {
+ if( isnan(v.d) && isnan(u.d) )
+ goto nxttest2;
+#if 0
+ if( isnan(v.d) )
+ pvec(v.d);
+ if( isnan(u.d) )
+ pvec(u.d);
+#endif
+ goto wrongtwo;
+ }
+ else
+ goto nxttest2;
+ }
+ if (y != answer)
+ {
+ e = y - answer;
+ if (answer != 0.0)
+ e = e / answer;
+ if (e < 0)
+ e = -e;
+ if (e > test2[i].thresh * MACHEP)
+ {
+wrongtwo:
+ printf ("%s (%.16e, %.16e) = %.16e\n should be %.16e\n",
+ test2[i].name, x1, x2, y, answer);
+ nerrors += 1;
+ }
+ }
+nxttest2:
+ ntests += 1;
+ i += 1;
+ }
+
+
+ i = 0;
+ for (;;)
+ {
+ fun3 = test3[i].func;
+ if (fun3 == NULL)
+ break;
+ x1 = *(test3[i].arg1);
+ k = (*(fun3)) (x1);
+ ianswer = test3[i].ianswer;
+ if (k != ianswer)
+ {
+ printf ("%s (%.16e) = %d\n should be. %d\n",
+ test3[i].name, x1, k, ianswer);
+ nerrors += 1;
+ }
+ ntests += 1;
+ i += 1;
+ }
+
+ printf ("testvect: %d errors in %d tests\n", nerrors, ntests);
+ exit (0);
+}
diff --git a/libm/double/ei.c b/libm/double/ei.c
new file mode 100644
index 000000000..4994fa99c
--- /dev/null
+++ b/libm/double/ei.c
@@ -0,0 +1,1062 @@
+/* ei.c
+ *
+ * Exponential integral
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, ei();
+ *
+ * y = ei( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * x
+ * - t
+ * | | e
+ * Ei(x) = -|- --- dt .
+ * | | t
+ * -
+ * -inf
+ *
+ * Not defined for x <= 0.
+ * See also expn.c.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 50000 8.6e-16 1.3e-16
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: May, 1999
+Copyright 1999 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double log ( double );
+extern double exp ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+#else
+extern double log(), exp(), polevl(), p1evl();
+#endif
+
+#define EUL 5.772156649015328606065e-1
+
+/* 0 < x <= 2
+ Ei(x) - EUL - ln(x) = x A(x)/B(x)
+ Theoretical peak relative error 9.73e-18 */
+#if UNK
+static double A[6] = {
+-5.350447357812542947283E0,
+ 2.185049168816613393830E2,
+-4.176572384826693777058E3,
+ 5.541176756393557601232E4,
+-3.313381331178144034309E5,
+ 1.592627163384945414220E6,
+};
+static double B[6] = {
+ /* 1.000000000000000000000E0, */
+-5.250547959112862969197E1,
+ 1.259616186786790571525E3,
+-1.756549581973534652631E4,
+ 1.493062117002725991967E5,
+-7.294949239640527645655E5,
+ 1.592627163384945429726E6,
+};
+#endif
+#if DEC
+static short A[24] = {
+0140653,0033335,0060230,0144217,
+0042132,0100502,0035625,0167413,
+0143202,0102224,0037176,0175403,
+0044130,0071704,0077421,0170343,
+0144641,0144504,0041200,0045154,
+0045302,0064631,0047234,0142052,
+};
+static short B[24] = {
+ /* 0040200,0000000,0000000,0000000, */
+0141522,0002634,0070442,0142614,
+0042635,0071667,0146532,0027705,
+0143611,0035375,0156025,0114015,
+0044421,0147215,0106177,0046330,
+0145062,0014556,0144216,0103725,
+0045302,0064631,0047234,0142052,
+};
+#endif
+#if IBMPC
+static short A[24] = {
+0x1912,0xac13,0x66db,0xc015,
+0xbde1,0x4772,0x5028,0x406b,
+0xdf60,0x87cf,0x5092,0xc0b0,
+0x3e1c,0x8fe2,0x0e78,0x40eb,
+0x094e,0x8850,0x3928,0xc114,
+0x9885,0x29d3,0x4d33,0x4138,
+};
+static short B[24] = {
+ /* 0x0000,0x0000,0x0000,0x3ff0, */
+0x58b1,0x8e24,0x40b3,0xc04a,
+0x45f9,0xf9ab,0xae76,0x4093,
+0xb302,0xbb82,0x275f,0xc0d1,
+0xe99b,0xb18f,0x39d1,0x4102,
+0xd0fb,0xd911,0x432d,0xc126,
+0x9885,0x29d3,0x4d33,0x4138,
+};
+#endif
+#if MIEEE
+static short A[24] = {
+0xc015,0x66db,0xac13,0x1912,
+0x406b,0x5028,0x4772,0xbde1,
+0xc0b0,0x5092,0x87cf,0xdf60,
+0x40eb,0x0e78,0x8fe2,0x3e1c,
+0xc114,0x3928,0x8850,0x094e,
+0x4138,0x4d33,0x29d3,0x9885,
+};
+static short B[24] = {
+ /* 0x3ff0,0x0000,0x0000,0x0000, */
+0xc04a,0x40b3,0x8e24,0x58b1,
+0x4093,0xae76,0xf9ab,0x45f9,
+0xc0d1,0x275f,0xbb82,0xb302,
+0x4102,0x39d1,0xb18f,0xe99b,
+0xc126,0x432d,0xd911,0xd0fb,
+0x4138,0x4d33,0x29d3,0x9885,
+};
+#endif
+
+#if 0
+/* 0 < x <= 4
+ Ei(x) - EUL - ln(x) = x A(x)/B(x)
+ Theoretical peak relative error 4.75e-17 */
+#if UNK
+static double A[7] = {
+-6.831869820732773831942E0,
+ 2.920190530726774500309E2,
+-1.195883839286649567993E4,
+ 1.761045255472548975666E5,
+-2.623034438354006526979E6,
+ 1.472430336917880803157E7,
+-8.205359388213261174960E7,
+};
+static double B[7] = {
+ /* 1.000000000000000000000E0, */
+-7.731946237840033971071E1,
+ 2.751808700543578450827E3,
+-5.829268609072186897994E4,
+ 7.916610857961870631379E5,
+-6.873926904825733094076E6,
+ 3.523770183971164032710E7,
+-8.205359388213260785363E7,
+};
+#endif
+#if DEC
+static short A[28] = {
+0140732,0117255,0072522,0071743,
+0042222,0001160,0052302,0002334,
+0143472,0155532,0101650,0155462,
+0044453,0175041,0121220,0172022,
+0145440,0014351,0140337,0157550,
+0046140,0126317,0057202,0100233,
+0146634,0100473,0036072,0067054,
+};
+static short B[28] = {
+ /* 0040200,0000000,0000000,0000000, */
+0141632,0121620,0111247,0010115,
+0043053,0176360,0067773,0027324,
+0144143,0132257,0121644,0036204,
+0045101,0043321,0057553,0151231,
+0145721,0143215,0147505,0050610,
+0046406,0065721,0072675,0152744,
+0146634,0100473,0036072,0067052,
+};
+#endif
+#if IBMPC
+static short A[28] = {
+0x4e7c,0xaeaa,0x53d5,0xc01b,
+0x409b,0x0a98,0x404e,0x4072,
+0x1b66,0x5075,0x5b6b,0xc0c7,
+0x1e82,0x3452,0x7f44,0x4105,
+0xfbed,0x381b,0x031d,0xc144,
+0x5013,0xebd0,0x1599,0x416c,
+0x4dc5,0x6787,0x9027,0xc193,
+};
+static short B[28] = {
+ /* 0x0000,0x0000,0x0000,0x3ff0, */
+0xe20a,0x1254,0x5472,0xc053,
+0x65db,0x0dff,0x7f9e,0x40a5,
+0x8791,0xf474,0x7695,0xc0ec,
+0x7a53,0x2bed,0x28da,0x4128,
+0xaa31,0xb9e8,0x38d1,0xc15a,
+0xbabd,0x2eb7,0xcd7a,0x4180,
+0x4dc5,0x6787,0x9027,0xc193,
+};
+#endif
+#if MIEEE
+static short A[28] = {
+0xc01b,0x53d5,0xaeaa,0x4e7c,
+0x4072,0x404e,0x0a98,0x409b,
+0xc0c7,0x5b6b,0x5075,0x1b66,
+0x4105,0x7f44,0x3452,0x1e82,
+0xc144,0x031d,0x381b,0xfbed,
+0x416c,0x1599,0xebd0,0x5013,
+0xc193,0x9027,0x6787,0x4dc5,
+};
+static short B[28] = {
+ /* 0x3ff0,0x0000,0x0000,0x0000, */
+0xc053,0x5472,0x1254,0xe20a,
+0x40a5,0x7f9e,0x0dff,0x65db,
+0xc0ec,0x7695,0xf474,0x8791,
+0x4128,0x28da,0x2bed,0x7a53,
+0xc15a,0x38d1,0xb9e8,0xaa31,
+0x4180,0xcd7a,0x2eb7,0xbabd,
+0xc193,0x9027,0x6787,0x4dc5,
+};
+#endif
+#endif /* 0 */
+
+#if 0
+/* 0 < x <= 8
+ Ei(x) - EUL - ln(x) = x A(x)/B(x)
+ Theoretical peak relative error 2.14e-17 */
+
+#if UNK
+static double A[9] = {
+-1.111230942210860450145E1,
+ 3.688203982071386319616E2,
+-4.924786153494029574350E4,
+ 1.050677503345557903241E6,
+-3.626713709916703688968E7,
+ 4.353499908839918635414E8,
+-6.454613717232006895409E9,
+ 3.408243056457762907071E10,
+-1.995466674647028468613E11,
+};
+static double B[9] = {
+ /* 1.000000000000000000000E0, */
+-1.356757648138514017969E2,
+ 8.562181317107341736606E3,
+-3.298257180413775117555E5,
+ 8.543534058481435917210E6,
+-1.542380618535140055068E8,
+ 1.939251779195993632028E9,
+-1.636096210465615015435E10,
+ 8.396909743075306970605E10,
+-1.995466674647028425886E11,
+};
+#endif
+#if DEC
+static short A[36] = {
+0141061,0146004,0173357,0151553,
+0042270,0064402,0147366,0126701,
+0144100,0057734,0106615,0144356,
+0045200,0040654,0003332,0004456,
+0146412,0054440,0043130,0140263,
+0047317,0113517,0033422,0065123,
+0150300,0056313,0065235,0131147,
+0050775,0167423,0146222,0075760,
+0151471,0153642,0003442,0147667,
+};
+static short B[36] = {
+ /* 0040200,0000000,0000000,0000000, */
+0142007,0126376,0166077,0043600,
+0043405,0144271,0125461,0014364,
+0144641,0006066,0175061,0164463,
+0046002,0056456,0007370,0121657,
+0147023,0013706,0156647,0177115,
+0047747,0026504,0103144,0054507,
+0150563,0146036,0007051,0177135,
+0051234,0063625,0173266,0003111,
+0151471,0153642,0003442,0147666,
+};
+#endif
+#if IBMPC
+static short A[36] = {
+0xfa6d,0x9edd,0x3980,0xc026,
+0xd5b8,0x59de,0x0d20,0x4077,
+0xb91e,0x91b1,0x0bfb,0xc0e8,
+0x4126,0x80db,0x0835,0x4130,
+0x1816,0x08cb,0x4b24,0xc181,
+0x4d4a,0xe6e2,0xf2e9,0x41b9,
+0xb64d,0x6d53,0x0b99,0xc1f8,
+0x4f7e,0x7992,0xbde2,0x421f,
+0x59f7,0x40e4,0x3af4,0xc247,
+};
+static short B[36] = {
+ /* 0x0000,0x0000,0x0000,0x3ff0, */
+0xe8f0,0xdd87,0xf59f,0xc060,
+0x231e,0x3566,0xb917,0x40c0,
+0x3d26,0xdf46,0x2186,0xc114,
+0x1476,0xc1df,0x4ba5,0x4160,
+0xffca,0xdbb4,0x62f8,0xc1a2,
+0x8b29,0x90cc,0xe5a8,0x41dc,
+0x3fcc,0xc1c5,0x7983,0xc20e,
+0xc0c9,0xbed6,0x8cf2,0x4233,
+0x59f7,0x40e4,0x3af4,0xc247,
+};
+#endif
+#if MIEEE
+static short A[36] = {
+0xc026,0x3980,0x9edd,0xfa6d,
+0x4077,0x0d20,0x59de,0xd5b8,
+0xc0e8,0x0bfb,0x91b1,0xb91e,
+0x4130,0x0835,0x80db,0x4126,
+0xc181,0x4b24,0x08cb,0x1816,
+0x41b9,0xf2e9,0xe6e2,0x4d4a,
+0xc1f8,0x0b99,0x6d53,0xb64d,
+0x421f,0xbde2,0x7992,0x4f7e,
+0xc247,0x3af4,0x40e4,0x59f7,
+};
+static short B[36] = {
+ /* 0x3ff0,0x0000,0x0000,0x0000, */
+0xc060,0xf59f,0xdd87,0xe8f0,
+0x40c0,0xb917,0x3566,0x231e,
+0xc114,0x2186,0xdf46,0x3d26,
+0x4160,0x4ba5,0xc1df,0x1476,
+0xc1a2,0x62f8,0xdbb4,0xffca,
+0x41dc,0xe5a8,0x90cc,0x8b29,
+0xc20e,0x7983,0xc1c5,0x3fcc,
+0x4233,0x8cf2,0xbed6,0xc0c9,
+0xc247,0x3af4,0x40e4,0x59f7,
+};
+#endif
+#endif /* 0 */
+
+/* 8 <= x <= 20
+ x exp(-x) Ei(x) - 1 = 1/x R(1/x)
+ Theoretical peak absolute error = 1.07e-17 */
+#if UNK
+static double A2[10] = {
+-2.106934601691916512584E0,
+ 1.732733869664688041885E0,
+-2.423619178935841904839E-1,
+ 2.322724180937565842585E-2,
+ 2.372880440493179832059E-4,
+-8.343219561192552752335E-5,
+ 1.363408795605250394881E-5,
+-3.655412321999253963714E-7,
+ 1.464941733975961318456E-8,
+ 6.176407863710360207074E-10,
+};
+static double B2[9] = {
+ /* 1.000000000000000000000E0, */
+-2.298062239901678075778E-1,
+ 1.105077041474037862347E-1,
+-1.566542966630792353556E-2,
+ 2.761106850817352773874E-3,
+-2.089148012284048449115E-4,
+ 1.708528938807675304186E-5,
+-4.459311796356686423199E-7,
+ 1.394634930353847498145E-8,
+ 6.150865933977338354138E-10,
+};
+#endif
+#if DEC
+static short A2[40] = {
+0140406,0154004,0035104,0173336,
+0040335,0145071,0031560,0150165,
+0137570,0026670,0176230,0055040,
+0036676,0043416,0077122,0054476,
+0035170,0150206,0034407,0175571,
+0134656,0174121,0123231,0021751,
+0034144,0136766,0036746,0121115,
+0132704,0037632,0135077,0107300,
+0031573,0126321,0117076,0004314,
+0030451,0143233,0041352,0172464,
+};
+static short B2[36] = {
+ /* 0040200,0000000,0000000,0000000, */
+0137553,0051122,0120721,0170437,
+0037342,0050734,0175047,0032132,
+0136600,0052311,0101406,0147050,
+0036064,0171657,0120001,0071165,
+0135133,0010043,0151244,0066340,
+0034217,0051141,0026115,0043305,
+0132757,0064120,0106341,0051217,
+0031557,0114261,0060663,0135017,
+0030451,0011337,0001344,0175542,
+};
+#endif
+#if IBMPC
+static short A2[40] = {
+0x9edc,0x8748,0xdb00,0xc000,
+0x1a0f,0x266e,0xb947,0x3ffb,
+0x0b44,0x1f93,0x05b7,0xbfcf,
+0x4b28,0xcfca,0xc8e1,0x3f97,
+0xff6f,0xc720,0x1a10,0x3f2f,
+0x247d,0x34d3,0xdf0a,0xbf15,
+0xd44a,0xc7bc,0x97be,0x3eec,
+0xf1d8,0x5747,0x87f3,0xbe98,
+0xc119,0x33c7,0x759a,0x3e4f,
+0x5ea6,0x685d,0x38d3,0x3e05,
+};
+static short B2[36] = {
+ /* 0x0000,0x0000,0x0000,0x3ff0, */
+0x3e24,0x543a,0x6a4a,0xbfcd,
+0xe68b,0x9f44,0x4a3b,0x3fbc,
+0xd9c5,0x3060,0x0a99,0xbf90,
+0x2e4f,0xf400,0x9e75,0x3f66,
+0x8d9c,0x7a54,0x6204,0xbf2b,
+0xa8d9,0x2589,0xea4c,0x3ef1,
+0x2a52,0x119c,0xed0a,0xbe9d,
+0x7742,0x2c36,0xf316,0x3e4d,
+0x9f6c,0xe05c,0x225b,0x3e05,
+};
+#endif
+#if MIEEE
+static short A2[40] = {
+0xc000,0xdb00,0x8748,0x9edc,
+0x3ffb,0xb947,0x266e,0x1a0f,
+0xbfcf,0x05b7,0x1f93,0x0b44,
+0x3f97,0xc8e1,0xcfca,0x4b28,
+0x3f2f,0x1a10,0xc720,0xff6f,
+0xbf15,0xdf0a,0x34d3,0x247d,
+0x3eec,0x97be,0xc7bc,0xd44a,
+0xbe98,0x87f3,0x5747,0xf1d8,
+0x3e4f,0x759a,0x33c7,0xc119,
+0x3e05,0x38d3,0x685d,0x5ea6,
+};
+static short B2[36] = {
+ /* 0x3ff0,0x0000,0x0000,0x0000, */
+0xbfcd,0x6a4a,0x543a,0x3e24,
+0x3fbc,0x4a3b,0x9f44,0xe68b,
+0xbf90,0x0a99,0x3060,0xd9c5,
+0x3f66,0x9e75,0xf400,0x2e4f,
+0xbf2b,0x6204,0x7a54,0x8d9c,
+0x3ef1,0xea4c,0x2589,0xa8d9,
+0xbe9d,0xed0a,0x119c,0x2a52,
+0x3e4d,0xf316,0x2c36,0x7742,
+0x3e05,0x225b,0xe05c,0x9f6c,
+};
+#endif
+
+/* x > 20
+ x exp(-x) Ei(x) - 1 = 1/x A3(1/x)/B3(1/x)
+ Theoretical absolute error = 6.15e-17 */
+#if UNK
+static double A3[9] = {
+-7.657847078286127362028E-1,
+ 6.886192415566705051750E-1,
+-2.132598113545206124553E-1,
+ 3.346107552384193813594E-2,
+-3.076541477344756050249E-3,
+ 1.747119316454907477380E-4,
+-6.103711682274170530369E-6,
+ 1.218032765428652199087E-7,
+-1.086076102793290233007E-9,
+};
+static double B3[9] = {
+ /* 1.000000000000000000000E0, */
+-1.888802868662308731041E0,
+ 1.066691687211408896850E0,
+-2.751915982306380647738E-1,
+ 3.930852688233823569726E-2,
+-3.414684558602365085394E-3,
+ 1.866844370703555398195E-4,
+-6.345146083130515357861E-6,
+ 1.239754287483206878024E-7,
+-1.086076102793126632978E-9,
+};
+#endif
+#if DEC
+static short A3[36] = {
+0140104,0005167,0071746,0115510,
+0040060,0044531,0140741,0154556,
+0137532,0060307,0126506,0071123,
+0037011,0007173,0010405,0127224,
+0136111,0117715,0003654,0175577,
+0035067,0031340,0102657,0147714,
+0133714,0147173,0167473,0136640,
+0032402,0144407,0115547,0060114,
+0130625,0042347,0156431,0113425,
+};
+static short B3[36] = {
+ /* 0040200,0000000,0000000,0000000, */
+0140361,0142112,0155277,0067714,
+0040210,0104532,0065676,0074326,
+0137614,0162751,0142421,0131033,
+0037041,0000772,0053236,0002632,
+0136137,0144346,0100536,0153136,
+0035103,0140270,0152211,0166215,
+0133724,0164143,0145763,0021153,
+0032405,0017033,0035333,0025736,
+0130625,0042347,0156431,0077134,
+};
+#endif
+#if IBMPC
+static short A3[36] = {
+0xd369,0xee7c,0x814e,0xbfe8,
+0x3b2e,0x383c,0x092b,0x3fe6,
+0xce4a,0xf5a8,0x4c18,0xbfcb,
+0xb5d2,0x6220,0x21cf,0x3fa1,
+0x9f70,0xa0f5,0x33f9,0xbf69,
+0xf9f9,0x10b5,0xe65c,0x3f26,
+0x77b4,0x7de7,0x99cf,0xbed9,
+0xec09,0xf36c,0x5920,0x3e80,
+0x32e3,0xfba3,0xa89c,0xbe12,
+};
+static short B3[36] = {
+ /* 0x0000,0x0000,0x0000,0x3ff0, */
+0xedf9,0x5b57,0x3889,0xbffe,
+0xcf1b,0x4d77,0x112b,0x3ff1,
+0x3643,0x38a2,0x9cbd,0xbfd1,
+0xc0b3,0x4ad3,0x203f,0x3fa4,
+0xdacc,0xd02b,0xf91c,0xbf6b,
+0x3d92,0x1a91,0x7817,0x3f28,
+0x644d,0x797e,0x9d0c,0xbeda,
+0x657c,0x675b,0xa3c3,0x3e80,
+0x2fcb,0xfba3,0xa89c,0xbe12,
+};
+#endif
+#if MIEEE
+static short A3[36] = {
+0xbfe8,0x814e,0xee7c,0xd369,
+0x3fe6,0x092b,0x383c,0x3b2e,
+0xbfcb,0x4c18,0xf5a8,0xce4a,
+0x3fa1,0x21cf,0x6220,0xb5d2,
+0xbf69,0x33f9,0xa0f5,0x9f70,
+0x3f26,0xe65c,0x10b5,0xf9f9,
+0xbed9,0x99cf,0x7de7,0x77b4,
+0x3e80,0x5920,0xf36c,0xec09,
+0xbe12,0xa89c,0xfba3,0x32e3,
+};
+static short B3[36] = {
+/* 0x3ff0,0x0000,0x0000,0x0000, */
+0xbffe,0x3889,0x5b57,0xedf9,
+0x3ff1,0x112b,0x4d77,0xcf1b,
+0xbfd1,0x9cbd,0x38a2,0x3643,
+0x3fa4,0x203f,0x4ad3,0xc0b3,
+0xbf6b,0xf91c,0xd02b,0xdacc,
+0x3f28,0x7817,0x1a91,0x3d92,
+0xbeda,0x9d0c,0x797e,0x644d,
+0x3e80,0xa3c3,0x675b,0x657c,
+0xbe12,0xa89c,0xfba3,0x2fcb,
+};
+#endif
+
+/* 16 <= x <= 32
+ x exp(-x) Ei(x) - 1 = 1/x A4(1/x) / B4(1/x)
+ Theoretical absolute error = 1.22e-17 */
+#if UNK
+static double A4[8] = {
+-2.458119367674020323359E-1,
+-1.483382253322077687183E-1,
+ 7.248291795735551591813E-2,
+-1.348315687380940523823E-2,
+ 1.342775069788636972294E-3,
+-7.942465637159712264564E-5,
+ 2.644179518984235952241E-6,
+-4.239473659313765177195E-8,
+};
+static double B4[8] = {
+ /* 1.000000000000000000000E0, */
+-1.044225908443871106315E-1,
+-2.676453128101402655055E-1,
+ 9.695000254621984627876E-2,
+-1.601745692712991078208E-2,
+ 1.496414899205908021882E-3,
+-8.462452563778485013756E-5,
+ 2.728938403476726394024E-6,
+-4.239462431819542051337E-8,
+};
+#endif
+#if DEC
+static short A4[32] = {
+0137573,0133037,0152607,0113356,
+0137427,0162771,0145061,0126345,
+0037224,0070754,0110451,0174104,
+0136534,0164165,0072170,0063753,
+0035660,0000016,0002560,0147751,
+0134646,0110311,0123316,0047432,
+0033461,0071250,0101031,0075202,
+0132066,0012601,0077305,0170177,
+};
+static short B4[32] = {
+ /* 0040200,0000000,0000000,0000000, */
+0137325,0155602,0162437,0030710,
+0137611,0004316,0071344,0176361,
+0037306,0106671,0011103,0155053,
+0136603,0033412,0132530,0175171,
+0035704,0021532,0015516,0166130,
+0134661,0074162,0036741,0073466,
+0033467,0021316,0003100,0171325,
+0132066,0012541,0162202,0150160,
+};
+#endif
+#if IBMPC
+static short A4[] = {
+0xf2de,0xfab0,0x76c3,0xbfcf,
+0x359d,0x3946,0xfcbf,0xbfc2,
+0x3f09,0x9225,0x8e3d,0x3fb2,
+0x0cfd,0xae8f,0x9d0e,0xbf8b,
+0x19fd,0xc0ae,0x0001,0x3f56,
+0xc9e3,0x34d9,0xd219,0xbf14,
+0x2f50,0x1043,0x2e55,0x3ec6,
+0xbe10,0x2fd8,0xc2b0,0xbe66,
+};
+static short B4[] = {
+ /* 0x0000,0x0000,0x0000,0x3ff0, */
+0xe639,0x5ca3,0xbb70,0xbfba,
+0x9f9e,0xce5c,0x2119,0xbfd1,
+0x7b45,0x2248,0xd1b7,0x3fb8,
+0x1f4f,0x56ab,0x66e1,0xbf90,
+0xdd8b,0x4369,0x846b,0x3f58,
+0x2ee7,0x47bc,0x2f0e,0xbf16,
+0x1e5b,0xc0c8,0xe459,0x3ec6,
+0x5a0e,0x3c90,0xc2ac,0xbe66,
+};
+#endif
+#if MIEEE
+static short A4[32] = {
+0xbfcf,0x76c3,0xfab0,0xf2de,
+0xbfc2,0xfcbf,0x3946,0x359d,
+0x3fb2,0x8e3d,0x9225,0x3f09,
+0xbf8b,0x9d0e,0xae8f,0x0cfd,
+0x3f56,0x0001,0xc0ae,0x19fd,
+0xbf14,0xd219,0x34d9,0xc9e3,
+0x3ec6,0x2e55,0x1043,0x2f50,
+0xbe66,0xc2b0,0x2fd8,0xbe10,
+};
+static short B4[32] = {
+ /* 0x3ff0,0x0000,0x0000,0x0000, */
+0xbfba,0xbb70,0x5ca3,0xe639,
+0xbfd1,0x2119,0xce5c,0x9f9e,
+0x3fb8,0xd1b7,0x2248,0x7b45,
+0xbf90,0x66e1,0x56ab,0x1f4f,
+0x3f58,0x846b,0x4369,0xdd8b,
+0xbf16,0x2f0e,0x47bc,0x2ee7,
+0x3ec6,0xe459,0xc0c8,0x1e5b,
+0xbe66,0xc2ac,0x3c90,0x5a0e,
+};
+#endif
+
+
+#if 0
+/* 20 <= x <= 40
+ x exp(-x) Ei(x) - 1 = 1/x A4(1/x) / B4(1/x)
+ Theoretical absolute error = 1.78e-17 */
+#if UNK
+static double A4[8] = {
+ 2.067245813525780707978E-1,
+-5.153749551345223645670E-1,
+ 1.928289589546695033096E-1,
+-3.124468842857260044075E-2,
+ 2.740283734277352539912E-3,
+-1.377775664366875175601E-4,
+ 3.803788980664744242323E-6,
+-4.611038277393688031154E-8,
+};
+static double B4[8] = {
+ /* 1.000000000000000000000E0, */
+-8.544436025219516861531E-1,
+ 2.507436807692907385181E-1,
+-3.647688090228423114064E-2,
+ 3.008576950332041388892E-3,
+-1.452926405348421286334E-4,
+ 3.896007735260115431965E-6,
+-4.611037642697098234083E-8,
+};
+#endif
+#if DEC
+static short A4[32] = {
+0037523,0127633,0150301,0022031,
+0140003,0167634,0170572,0170420,
+0037505,0072364,0060672,0063220,
+0136777,0172334,0057456,0102640,
+0036063,0113125,0002476,0047251,
+0135020,0074142,0042600,0043630,
+0033577,0042230,0155372,0136105,
+0132106,0005346,0165333,0114541,
+};
+static short B4[28] = {
+ /* 0040200,0000000,0000000,0000000, */
+0140132,0136320,0160433,0131535,
+0037600,0060571,0144452,0060214,
+0137025,0064310,0024220,0176472,
+0036105,0025613,0115762,0166605,
+0135030,0054662,0035454,0061763,
+0033602,0135163,0116430,0000066,
+0132106,0005345,0020602,0137133,
+};
+#endif
+#if IBMPC
+static short A4[32] = {
+0x2483,0x7a18,0x75f3,0x3fca,
+0x5e22,0x9e2f,0x7df3,0xbfe0,
+0x4cd2,0x8c37,0xae9e,0x3fc8,
+0xd0b4,0x8be5,0xfe9b,0xbf9f,
+0xc9d5,0xa0a7,0x72ca,0x3f66,
+0x08f3,0x48b0,0x0f0c,0xbf22,
+0x5789,0x1b5f,0xe893,0x3ecf,
+0x732c,0xdd5b,0xc15c,0xbe68,
+};
+static short B4[28] = {
+ /* 0x0000,0x0000,0x0000,0x3ff0, */
+0x766c,0x1c23,0x579a,0xbfeb,
+0x4c11,0x3925,0x0c2f,0x3fd0,
+0x1fa7,0x0512,0xad19,0xbfa2,
+0x5db1,0x737e,0xa571,0x3f68,
+0x8c7e,0x4765,0x0b36,0xbf23,
+0x0007,0x73a3,0x574e,0x3ed0,
+0x57cb,0xa430,0xc15c,0xbe68,
+};
+#endif
+#if MIEEE
+static short A4[32] = {
+0x3fca,0x75f3,0x7a18,0x2483,
+0xbfe0,0x7df3,0x9e2f,0x5e22,
+0x3fc8,0xae9e,0x8c37,0x4cd2,
+0xbf9f,0xfe9b,0x8be5,0xd0b4,
+0x3f66,0x72ca,0xa0a7,0xc9d5,
+0xbf22,0x0f0c,0x48b0,0x08f3,
+0x3ecf,0xe893,0x1b5f,0x5789,
+0xbe68,0xc15c,0xdd5b,0x732c,
+};
+static short B4[28] = {
+ /* 0x3ff0,0x0000,0x0000,0x0000, */
+0xbfeb,0x579a,0x1c23,0x766c,
+0x3fd0,0x0c2f,0x3925,0x4c11,
+0xbfa2,0xad19,0x0512,0x1fa7,
+0x3f68,0xa571,0x737e,0x5db1,
+0xbf23,0x0b36,0x4765,0x8c7e,
+0x3ed0,0x574e,0x73a3,0x0007,
+0xbe68,0xc15c,0xa430,0x57cb,
+};
+#endif
+#endif /* 0 */
+
+/* 4 <= x <= 8
+ x exp(-x) Ei(x) - 1 = 1/x A5(1/x) / B5(1/x)
+ Theoretical absolute error = 2.20e-17 */
+#if UNK
+static double A5[8] = {
+-1.373215375871208729803E0,
+-7.084559133740838761406E-1,
+ 1.580806855547941010501E0,
+-2.601500427425622944234E-1,
+ 2.994674694113713763365E-2,
+-1.038086040188744005513E-3,
+ 4.371064420753005429514E-5,
+ 2.141783679522602903795E-6,
+};
+static double B5[8] = {
+ /* 1.000000000000000000000E0, */
+ 8.585231423622028380768E-1,
+ 4.483285822873995129957E-1,
+ 7.687932158124475434091E-2,
+ 2.449868241021887685904E-2,
+ 8.832165941927796567926E-4,
+ 4.590952299511353531215E-4,
+-4.729848351866523044863E-6,
+ 2.665195537390710170105E-6,
+};
+#endif
+#if DEC
+static short A5[32] = {
+0140257,0142605,0076335,0113632,
+0140065,0056535,0161231,0074311,
+0040312,0053741,0004357,0076405,
+0137605,0031142,0165503,0136705,
+0036765,0051341,0053573,0007602,
+0135610,0010143,0027643,0110522,
+0034467,0052762,0062024,0120161,
+0033417,0135620,0036500,0062647,
+};
+static short B[32] = {
+ /* 0040200,0000000,0000000,0000000, */
+0040133,0144054,0031516,0004100,
+0037745,0105522,0166622,0123146,
+0037235,0071347,0157560,0157464,
+0036710,0130565,0173747,0041670,
+0035547,0103651,0106243,0101240,
+0035360,0131267,0176263,0140257,
+0133636,0132426,0102537,0102531,
+0033462,0155665,0167503,0176350,
+};
+#endif
+#if IBMPC
+static short A5[32] = {
+0xb2f3,0xaf9b,0xf8b0,0xbff5,
+0x2f19,0xbc53,0xabab,0xbfe6,
+0xefa1,0x211d,0x4afc,0x3ff9,
+0x77b9,0x5d68,0xa64c,0xbfd0,
+0x61f0,0x2aef,0xaa5c,0x3f9e,
+0x722a,0x65f4,0x020c,0xbf51,
+0x940e,0x4c82,0xeabe,0x3f06,
+0x0cb5,0x07a8,0xf772,0x3ec1,
+};
+static short B5[32] = {
+ /* 0x0000,0x0000,0x0000,0x3ff0, */
+0xc108,0x8669,0x7905,0x3feb,
+0x54cd,0x5db2,0xb16a,0x3fdc,
+0x1be7,0xfbee,0xae5c,0x3fb3,
+0xe877,0xbefc,0x162e,0x3f99,
+0x7054,0x3194,0xf0f5,0x3f4c,
+0x7816,0xff96,0x1656,0x3f3e,
+0xf0ab,0xd0ab,0xd6a2,0xbed3,
+0x7f9d,0xbde8,0x5b76,0x3ec6,
+};
+#endif
+#if MIEEE
+static short A5[32] = {
+0xbff5,0xf8b0,0xaf9b,0xb2f3,
+0xbfe6,0xabab,0xbc53,0x2f19,
+0x3ff9,0x4afc,0x211d,0xefa1,
+0xbfd0,0xa64c,0x5d68,0x77b9,
+0x3f9e,0xaa5c,0x2aef,0x61f0,
+0xbf51,0x020c,0x65f4,0x722a,
+0x3f06,0xeabe,0x4c82,0x940e,
+0x3ec1,0xf772,0x07a8,0x0cb5,
+};
+static short B5[32] = {
+ /* 0x3ff0,0x0000,0x0000,0x0000, */
+0x3feb,0x7905,0x8669,0xc108,
+0x3fdc,0xb16a,0x5db2,0x54cd,
+0x3fb3,0xae5c,0xfbee,0x1be7,
+0x3f99,0x162e,0xbefc,0xe877,
+0x3f4c,0xf0f5,0x3194,0x7054,
+0x3f3e,0x1656,0xff96,0x7816,
+0xbed3,0xd6a2,0xd0ab,0xf0ab,
+0x3ec6,0x5b76,0xbde8,0x7f9d,
+};
+#endif
+/* 2 <= x <= 4
+ x exp(-x) Ei(x) - 1 = 1/x A6(1/x) / B6(1/x)
+ Theoretical absolute error = 4.89e-17 */
+#if UNK
+static double A6[8] = {
+ 1.981808503259689673238E-2,
+-1.271645625984917501326E0,
+-2.088160335681228318920E0,
+ 2.755544509187936721172E0,
+-4.409507048701600257171E-1,
+ 4.665623805935891391017E-2,
+-1.545042679673485262580E-3,
+ 7.059980605299617478514E-5,
+};
+static double B6[7] = {
+ /* 1.000000000000000000000E0, */
+ 1.476498670914921440652E0,
+ 5.629177174822436244827E-1,
+ 1.699017897879307263248E-1,
+ 2.291647179034212017463E-2,
+ 4.450150439728752875043E-3,
+ 1.727439612206521482874E-4,
+ 3.953167195549672482304E-5,
+};
+#endif
+#if DEC
+static short A6[32] = {
+0036642,0054611,0061263,0000140,
+0140242,0142510,0125732,0072035,
+0140405,0122153,0037643,0104527,
+0040460,0055327,0055550,0116240,
+0137741,0142112,0070441,0103510,
+0037077,0015234,0104750,0146765,
+0135712,0101407,0107554,0020253,
+0034624,0007373,0072621,0063735,
+};
+static short B6[28] = {
+ /* 0040200,0000000,0000000,0000000, */
+0040274,0176750,0110025,0061006,
+0040020,0015540,0021354,0155050,
+0037455,0175274,0015257,0021112,
+0036673,0135523,0016042,0117203,
+0036221,0151221,0046352,0144174,
+0035065,0021232,0117727,0152432,
+0034445,0147317,0037300,0067123,
+};
+#endif
+#if IBMPC
+static short A6[32] = {
+0x600c,0x2c56,0x4b31,0x3f94,
+0x4e84,0x157b,0x58a9,0xbff4,
+0x712b,0x67f4,0xb48d,0xc000,
+0x1394,0xeb6d,0x0b5a,0x4006,
+0x30e9,0x4e24,0x3889,0xbfdc,
+0x19bf,0x913d,0xe353,0x3fa7,
+0x8415,0xf1ed,0x5060,0xbf59,
+0x2cfc,0x6eb2,0x81df,0x3f12,
+};
+static short B6[28] = {
+ /* 0x0000,0x0000,0x0000,0x3ff0, */
+0xac41,0x1202,0x9fbd,0x3ff7,
+0x9b45,0x045d,0x036c,0x3fe2,
+0xe449,0x8355,0xbf57,0x3fc5,
+0x53d0,0x6384,0x776a,0x3f97,
+0x590f,0x299d,0x3a52,0x3f72,
+0xfaa3,0x53fa,0xa453,0x3f26,
+0x0dca,0xe7d8,0xb9d9,0x3f04,
+};
+#endif
+#if MIEEE
+static short A6[32] = {
+0x3f94,0x4b31,0x2c56,0x600c,
+0xbff4,0x58a9,0x157b,0x4e84,
+0xc000,0xb48d,0x67f4,0x712b,
+0x4006,0x0b5a,0xeb6d,0x1394,
+0xbfdc,0x3889,0x4e24,0x30e9,
+0x3fa7,0xe353,0x913d,0x19bf,
+0xbf59,0x5060,0xf1ed,0x8415,
+0x3f12,0x81df,0x6eb2,0x2cfc,
+};
+static short B6[28] = {
+ /* 0x3ff0,0x0000,0x0000,0x0000, */
+0x3ff7,0x9fbd,0x1202,0xac41,
+0x3fe2,0x036c,0x045d,0x9b45,
+0x3fc5,0xbf57,0x8355,0xe449,
+0x3f97,0x776a,0x6384,0x53d0,
+0x3f72,0x3a52,0x299d,0x590f,
+0x3f26,0xa453,0x53fa,0xfaa3,
+0x3f04,0xb9d9,0xe7d8,0x0dca,
+};
+#endif
+/* 32 <= x <= 64
+ x exp(-x) Ei(x) - 1 = 1/x A7(1/x) / B7(1/x)
+ Theoretical absolute error = 7.71e-18 */
+#if UNK
+static double A7[6] = {
+ 1.212561118105456670844E-1,
+-5.823133179043894485122E-1,
+ 2.348887314557016779211E-1,
+-3.040034318113248237280E-2,
+ 1.510082146865190661777E-3,
+-2.523137095499571377122E-5,
+};
+static double B7[5] = {
+ /* 1.000000000000000000000E0, */
+-1.002252150365854016662E0,
+ 2.928709694872224144953E-1,
+-3.337004338674007801307E-2,
+ 1.560544881127388842819E-3,
+-2.523137093603234562648E-5,
+};
+#endif
+#if DEC
+static short A7[24] = {
+0037370,0052437,0152524,0150125,
+0140025,0011174,0050154,0131330,
+0037560,0103253,0167464,0062245,
+0136771,0005043,0174001,0023345,
+0035705,0166762,0157300,0016451,
+0134323,0123764,0157767,0134477,
+};
+static short B7[20] = {
+ /* 0040200,0000000,0000000,0000000, */
+0140200,0044714,0064025,0060324,
+0037625,0171457,0003712,0073131,
+0137010,0127406,0150061,0141746,
+0035714,0105462,0072356,0103712,
+0134323,0123764,0156514,0077414,
+};
+#endif
+#if IBMPC
+static short A7[24] = {
+0x9a0b,0xfaaa,0x0aa3,0x3fbf,
+0x965b,0x8a0d,0xa24f,0xbfe2,
+0x8c95,0x7de6,0x10d5,0x3fce,
+0x24dd,0x7f00,0x2144,0xbf9f,
+0x03a5,0x5bd8,0xbdbe,0x3f58,
+0xf728,0x9bfe,0x74fe,0xbefa,
+};
+static short B7[20] = {
+ /* 0x0000,0x0000,0x0000,0x3ff0, */
+0xac1a,0x8d02,0x0939,0xbff0,
+0x4ecb,0xe0f9,0xbe65,0x3fd2,
+0x387d,0xda06,0x15e0,0xbfa1,
+0xd0f9,0x4e9d,0x9166,0x3f59,
+0x8fe2,0x9ba9,0x74fe,0xbefa,
+};
+#endif
+#if MIEEE
+static short A7[24] = {
+0x3fbf,0x0aa3,0xfaaa,0x9a0b,
+0xbfe2,0xa24f,0x8a0d,0x965b,
+0x3fce,0x10d5,0x7de6,0x8c95,
+0xbf9f,0x2144,0x7f00,0x24dd,
+0x3f58,0xbdbe,0x5bd8,0x03a5,
+0xbefa,0x74fe,0x9bfe,0xf728,
+};
+static short B7[20] = {
+ /* 0x3ff0,0x0000,0x0000,0x0000, */
+0xbff0,0x0939,0x8d02,0xac1a,
+0x3fd2,0xbe65,0xe0f9,0x4ecb,
+0xbfa1,0x15e0,0xda06,0x387d,
+0x3f59,0x9166,0x4e9d,0xd0f9,
+0xbefa,0x74fe,0x9ba9,0x8fe2,
+};
+#endif
+
+double ei (x)
+double x;
+{
+ double f, w;
+
+ if (x <= 0.0)
+ {
+ mtherr("ei", DOMAIN);
+ return 0.0;
+ }
+ else if (x < 2.0)
+ {
+ /* Power series.
+ inf n
+ - x
+ Ei(x) = EUL + ln x + > ----
+ - n n!
+ n=1
+ */
+ f = polevl(x,A,5) / p1evl(x,B,6);
+ /* f = polevl(x,A,6) / p1evl(x,B,7); */
+ /* f = polevl(x,A,8) / p1evl(x,B,9); */
+ return (EUL + log(x) + x * f);
+ }
+ else if (x < 4.0)
+ {
+ /* Asymptotic expansion.
+ 1 2 6
+ x exp(-x) Ei(x) = 1 + --- + --- + ---- + ...
+ x 2 3
+ x x
+ */
+ w = 1.0/x;
+ f = polevl(w,A6,7) / p1evl(w,B6,7);
+ return (exp(x) * w * (1.0 + w * f));
+ }
+ else if (x < 8.0)
+ {
+ w = 1.0/x;
+ f = polevl(w,A5,7) / p1evl(w,B5,8);
+ return (exp(x) * w * (1.0 + w * f));
+ }
+ else if (x < 16.0)
+ {
+ w = 1.0/x;
+ f = polevl(w,A2,9) / p1evl(w,B2,9);
+ return (exp(x) * w * (1.0 + w * f));
+ }
+ else if (x < 32.0)
+ {
+ w = 1.0/x;
+ f = polevl(w,A4,7) / p1evl(w,B4,8);
+ return (exp(x) * w * (1.0 + w * f));
+ }
+ else if (x < 64.0)
+ {
+ w = 1.0/x;
+ f = polevl(w,A7,5) / p1evl(w,B7,5);
+ return (exp(x) * w * (1.0 + w * f));
+ }
+ else
+ {
+ w = 1.0/x;
+ f = polevl(w,A3,8) / p1evl(w,B3,9);
+ return (exp(x) * w * (1.0 + w * f));
+ }
+}
diff --git a/libm/double/eigens.c b/libm/double/eigens.c
new file mode 100644
index 000000000..4035e76a1
--- /dev/null
+++ b/libm/double/eigens.c
@@ -0,0 +1,181 @@
+/* eigens.c
+ *
+ * Eigenvalues and eigenvectors of a real symmetric matrix
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double A[n*(n+1)/2], EV[n*n], E[n];
+ * void eigens( A, EV, E, n );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The algorithm is due to J. vonNeumann.
+ *
+ * A[] is a symmetric matrix stored in lower triangular form.
+ * That is, A[ row, column ] = A[ (row*row+row)/2 + column ]
+ * or equivalently with row and column interchanged. The
+ * indices row and column run from 0 through n-1.
+ *
+ * EV[] is the output matrix of eigenvectors stored columnwise.
+ * That is, the elements of each eigenvector appear in sequential
+ * memory order. The jth element of the ith eigenvector is
+ * EV[ n*i+j ] = EV[i][j].
+ *
+ * E[] is the output matrix of eigenvalues. The ith element
+ * of E corresponds to the ith eigenvector (the ith row of EV).
+ *
+ * On output, the matrix A will have been diagonalized and its
+ * orginal contents are destroyed.
+ *
+ * ACCURACY:
+ *
+ * The error is controlled by an internal parameter called RANGE
+ * which is set to 1e-10. After diagonalization, the
+ * off-diagonal elements of A will have been reduced by
+ * this factor.
+ *
+ * ERROR MESSAGES:
+ *
+ * None.
+ *
+ */
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double sqrt ( double );
+extern double fabs ( double );
+#else
+double sqrt(), fabs();
+#endif
+
+void eigens( A, RR, E, N )
+double A[], RR[], E[];
+int N;
+{
+int IND, L, LL, LM, M, MM, MQ, I, J, IA, LQ;
+int IQ, IM, IL, NLI, NMI;
+double ANORM, ANORMX, AIA, THR, ALM, ALL, AMM, X, Y;
+double SINX, SINX2, COSX, COSX2, SINCS, AIL, AIM;
+double RLI, RMI;
+static double RANGE = 1.0e-10; /*3.0517578e-5;*/
+
+
+/* Initialize identity matrix in RR[] */
+for( J=0; J<N*N; J++ )
+ RR[J] = 0.0;
+MM = 0;
+for( J=0; J<N; J++ )
+ {
+ RR[MM + J] = 1.0;
+ MM += N;
+ }
+
+ANORM=0.0;
+for( I=0; I<N; I++ )
+ {
+ for( J=0; J<N; J++ )
+ {
+ if( I != J )
+ {
+ IA = I + (J*J+J)/2;
+ AIA = A[IA];
+ ANORM += AIA * AIA;
+ }
+ }
+ }
+if( ANORM <= 0.0 )
+ goto done;
+ANORM = sqrt( ANORM + ANORM );
+ANORMX = ANORM * RANGE / N;
+THR = ANORM;
+
+while( THR > ANORMX )
+{
+THR=THR/N;
+
+do
+{ /* while IND != 0 */
+IND = 0;
+
+for( L=0; L<N-1; L++ )
+ {
+
+for( M=L+1; M<N; M++ )
+ {
+ MQ=(M*M+M)/2;
+ LM=L+MQ;
+ ALM=A[LM];
+ if( fabs(ALM) < THR )
+ continue;
+
+ IND=1;
+ LQ=(L*L+L)/2;
+ LL=L+LQ;
+ MM=M+MQ;
+ ALL=A[LL];
+ AMM=A[MM];
+ X=(ALL-AMM)/2.0;
+ Y=-ALM/sqrt(ALM*ALM+X*X);
+ if(X < 0.0)
+ Y=-Y;
+ SINX = Y / sqrt( 2.0 * (1.0 + sqrt( 1.0-Y*Y)) );
+ SINX2=SINX*SINX;
+ COSX=sqrt(1.0-SINX2);
+ COSX2=COSX*COSX;
+ SINCS=SINX*COSX;
+
+/* ROTATE L AND M COLUMNS */
+for( I=0; I<N; I++ )
+ {
+ IQ=(I*I+I)/2;
+ if( (I != M) && (I != L) )
+ {
+ if(I > M)
+ IM=M+IQ;
+ else
+ IM=I+MQ;
+ if(I >= L)
+ IL=L+IQ;
+ else
+ IL=I+LQ;
+ AIL=A[IL];
+ AIM=A[IM];
+ X=AIL*COSX-AIM*SINX;
+ A[IM]=AIL*SINX+AIM*COSX;
+ A[IL]=X;
+ }
+ NLI = N*L + I;
+ NMI = N*M + I;
+ RLI = RR[ NLI ];
+ RMI = RR[ NMI ];
+ RR[NLI]=RLI*COSX-RMI*SINX;
+ RR[NMI]=RLI*SINX+RMI*COSX;
+ }
+
+ X=2.0*ALM*SINCS;
+ A[LL]=ALL*COSX2+AMM*SINX2-X;
+ A[MM]=ALL*SINX2+AMM*COSX2+X;
+ A[LM]=(ALL-AMM)*SINCS+ALM*(COSX2-SINX2);
+ } /* for M=L+1 to N-1 */
+ } /* for L=0 to N-2 */
+
+ }
+while( IND != 0 );
+
+} /* while THR > ANORMX */
+
+done: ;
+
+/* Extract eigenvalues from the reduced matrix */
+L=0;
+for( J=1; J<=N; J++ )
+ {
+ L=L+J;
+ E[J-1]=A[L-1];
+ }
+}
diff --git a/libm/double/ellie.c b/libm/double/ellie.c
new file mode 100644
index 000000000..4f3379aa6
--- /dev/null
+++ b/libm/double/ellie.c
@@ -0,0 +1,148 @@
+/* ellie.c
+ *
+ * Incomplete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double phi, m, y, ellie();
+ *
+ * y = ellie( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ * phi
+ * -
+ * | |
+ * | 2
+ * E(phi_\m) = | sqrt( 1 - m sin t ) dt
+ * |
+ * | |
+ * -
+ * 0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random arguments with phi in [-10, 10] and m in
+ * [0, 1].
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,2 2000 1.9e-16 3.4e-17
+ * IEEE -10,10 150000 3.3e-15 1.4e-16
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1993, 2000 by Stephen L. Moshier
+*/
+
+/* Incomplete elliptic integral of second kind */
+#include <math.h>
+extern double PI, PIO2, MACHEP;
+#ifdef ANSIPROT
+extern double sqrt ( double );
+extern double fabs ( double );
+extern double log ( double );
+extern double sin ( double x );
+extern double tan ( double x );
+extern double atan ( double );
+extern double floor ( double );
+extern double ellpe ( double );
+extern double ellpk ( double );
+double ellie ( double, double );
+#else
+double sqrt(), fabs(), log(), sin(), tan(), atan(), floor();
+double ellpe(), ellpk(), ellie();
+#endif
+
+double ellie( phi, m )
+double phi, m;
+{
+double a, b, c, e, temp;
+double lphi, t, E;
+int d, mod, npio2, sign;
+
+if( m == 0.0 )
+ return( phi );
+lphi = phi;
+npio2 = floor( lphi/PIO2 );
+if( npio2 & 1 )
+ npio2 += 1;
+lphi = lphi - npio2 * PIO2;
+if( lphi < 0.0 )
+ {
+ lphi = -lphi;
+ sign = -1;
+ }
+else
+ {
+ sign = 1;
+ }
+a = 1.0 - m;
+E = ellpe( a );
+if( a == 0.0 )
+ {
+ temp = sin( lphi );
+ goto done;
+ }
+t = tan( lphi );
+b = sqrt(a);
+/* Thanks to Brian Fitzgerald <fitzgb@mml0.meche.rpi.edu>
+ for pointing out an instability near odd multiples of pi/2. */
+if( fabs(t) > 10.0 )
+ {
+ /* Transform the amplitude */
+ e = 1.0/(b*t);
+ /* ... but avoid multiple recursions. */
+ if( fabs(e) < 10.0 )
+ {
+ e = atan(e);
+ temp = E + m * sin( lphi ) * sin( e ) - ellie( e, m );
+ goto done;
+ }
+ }
+c = sqrt(m);
+a = 1.0;
+d = 1;
+e = 0.0;
+mod = 0;
+
+while( fabs(c/a) > MACHEP )
+ {
+ temp = b/a;
+ lphi = lphi + atan(t*temp) + mod * PI;
+ mod = (lphi + PIO2)/PI;
+ t = t * ( 1.0 + temp )/( 1.0 - temp * t * t );
+ c = ( a - b )/2.0;
+ temp = sqrt( a * b );
+ a = ( a + b )/2.0;
+ b = temp;
+ d += d;
+ e += c * sin(lphi);
+ }
+
+temp = E / ellpk( 1.0 - m );
+temp *= (atan(t) + mod * PI)/(d * a);
+temp += e;
+
+done:
+
+if( sign < 0 )
+ temp = -temp;
+temp += npio2 * E;
+return( temp );
+}
diff --git a/libm/double/ellik.c b/libm/double/ellik.c
new file mode 100644
index 000000000..1c9053676
--- /dev/null
+++ b/libm/double/ellik.c
@@ -0,0 +1,148 @@
+/* ellik.c
+ *
+ * Incomplete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double phi, m, y, ellik();
+ *
+ * y = ellik( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ * phi
+ * -
+ * | |
+ * | dt
+ * F(phi_\m) = | ------------------
+ * | 2
+ * | | sqrt( 1 - m sin t )
+ * -
+ * 0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with m in [0, 1] and phi as indicated.
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,10 200000 7.4e-16 1.0e-16
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+/* Incomplete elliptic integral of first kind */
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double sqrt ( double );
+extern double fabs ( double );
+extern double log ( double );
+extern double tan ( double );
+extern double atan ( double );
+extern double floor ( double );
+extern double ellpk ( double );
+double ellik ( double, double );
+#else
+double sqrt(), fabs(), log(), tan(), atan(), floor(), ellpk();
+double ellik();
+#endif
+extern double PI, PIO2, MACHEP, MAXNUM;
+
+double ellik( phi, m )
+double phi, m;
+{
+double a, b, c, e, temp, t, K;
+int d, mod, sign, npio2;
+
+if( m == 0.0 )
+ return( phi );
+a = 1.0 - m;
+if( a == 0.0 )
+ {
+ if( fabs(phi) >= PIO2 )
+ {
+ mtherr( "ellik", SING );
+ return( MAXNUM );
+ }
+ return( log( tan( (PIO2 + phi)/2.0 ) ) );
+ }
+npio2 = floor( phi/PIO2 );
+if( npio2 & 1 )
+ npio2 += 1;
+if( npio2 )
+ {
+ K = ellpk( a );
+ phi = phi - npio2 * PIO2;
+ }
+else
+ K = 0.0;
+if( phi < 0.0 )
+ {
+ phi = -phi;
+ sign = -1;
+ }
+else
+ sign = 0;
+b = sqrt(a);
+t = tan( phi );
+if( fabs(t) > 10.0 )
+ {
+ /* Transform the amplitude */
+ e = 1.0/(b*t);
+ /* ... but avoid multiple recursions. */
+ if( fabs(e) < 10.0 )
+ {
+ e = atan(e);
+ if( npio2 == 0 )
+ K = ellpk( a );
+ temp = K - ellik( e, m );
+ goto done;
+ }
+ }
+a = 1.0;
+c = sqrt(m);
+d = 1;
+mod = 0;
+
+while( fabs(c/a) > MACHEP )
+ {
+ temp = b/a;
+ phi = phi + atan(t*temp) + mod * PI;
+ mod = (phi + PIO2)/PI;
+ t = t * ( 1.0 + temp )/( 1.0 - temp * t * t );
+ c = ( a - b )/2.0;
+ temp = sqrt( a * b );
+ a = ( a + b )/2.0;
+ b = temp;
+ d += d;
+ }
+
+temp = (atan(t) + mod * PI)/(d * a);
+
+done:
+if( sign < 0 )
+ temp = -temp;
+temp += npio2 * K;
+return( temp );
+}
diff --git a/libm/double/ellpe.c b/libm/double/ellpe.c
new file mode 100644
index 000000000..9b2438e0e
--- /dev/null
+++ b/libm/double/ellpe.c
@@ -0,0 +1,195 @@
+/* ellpe.c
+ *
+ * Complete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double m1, y, ellpe();
+ *
+ * y = ellpe( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ * pi/2
+ * -
+ * | | 2
+ * E(m) = | sqrt( 1 - m sin t ) dt
+ * | |
+ * -
+ * 0
+ *
+ * Where m = 1 - m1, using the approximation
+ *
+ * P(x) - x log x Q(x).
+ *
+ * Though there are no singularities, the argument m1 is used
+ * rather than m for compatibility with ellpk().
+ *
+ * E(1) = 1; E(0) = pi/2.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 1 13000 3.1e-17 9.4e-18
+ * IEEE 0, 1 10000 2.1e-16 7.3e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ellpe domain x<0, x>1 0.0
+ *
+ */
+
+/* ellpe.c */
+
+/* Elliptic integral of second kind */
+
+/*
+Cephes Math Library, Release 2.8: June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+ 1.53552577301013293365E-4,
+ 2.50888492163602060990E-3,
+ 8.68786816565889628429E-3,
+ 1.07350949056076193403E-2,
+ 7.77395492516787092951E-3,
+ 7.58395289413514708519E-3,
+ 1.15688436810574127319E-2,
+ 2.18317996015557253103E-2,
+ 5.68051945617860553470E-2,
+ 4.43147180560990850618E-1,
+ 1.00000000000000000299E0
+};
+static double Q[] = {
+ 3.27954898576485872656E-5,
+ 1.00962792679356715133E-3,
+ 6.50609489976927491433E-3,
+ 1.68862163993311317300E-2,
+ 2.61769742454493659583E-2,
+ 3.34833904888224918614E-2,
+ 4.27180926518931511717E-2,
+ 5.85936634471101055642E-2,
+ 9.37499997197644278445E-2,
+ 2.49999999999888314361E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0035041,0001364,0141572,0117555,
+0036044,0066032,0130027,0033404,
+0036416,0053617,0064456,0102632,
+0036457,0161100,0061177,0122612,
+0036376,0136251,0012403,0124162,
+0036370,0101316,0151715,0131613,
+0036475,0105477,0050317,0133272,
+0036662,0154232,0024645,0171552,
+0037150,0126220,0047054,0030064,
+0037742,0162057,0167645,0165612,
+0040200,0000000,0000000,0000000
+};
+static unsigned short Q[] = {
+0034411,0106743,0115771,0055462,
+0035604,0052575,0155171,0045540,
+0036325,0030424,0064332,0167756,
+0036612,0052366,0063006,0115175,
+0036726,0070430,0004533,0124654,
+0037011,0022741,0030675,0030711,
+0037056,0174452,0127062,0132122,
+0037157,0177750,0142041,0072523,
+0037277,0177777,0173137,0002627,
+0037577,0177777,0177777,0101101
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x53ee,0x986f,0x205e,0x3f24,
+0xe6e0,0x5602,0x8d83,0x3f64,
+0xd0b3,0xed25,0xcaf1,0x3f81,
+0xf4b1,0x0c4f,0xfc48,0x3f85,
+0x750e,0x22a0,0xd795,0x3f7f,
+0xb671,0xda79,0x1059,0x3f7f,
+0xf6d7,0xea19,0xb167,0x3f87,
+0xbe6d,0x4534,0x5b13,0x3f96,
+0x8607,0x09c5,0x1592,0x3fad,
+0xbd71,0xfdf4,0x5c85,0x3fdc,
+0x0000,0x0000,0x0000,0x3ff0
+};
+static unsigned short Q[] = {
+0x2b66,0x737f,0x31bc,0x3f01,
+0x296c,0xbb4f,0x8aaf,0x3f50,
+0x5dfe,0x8d1b,0xa622,0x3f7a,
+0xd350,0xccc0,0x4a9e,0x3f91,
+0x7535,0x012b,0xce23,0x3f9a,
+0xa639,0x2637,0x24bc,0x3fa1,
+0x568a,0x55c6,0xdf25,0x3fa5,
+0x2eaa,0x1884,0xfffd,0x3fad,
+0xe0b3,0xfecb,0xffff,0x3fb7,
+0xf048,0xffff,0xffff,0x3fcf
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f24,0x205e,0x986f,0x53ee,
+0x3f64,0x8d83,0x5602,0xe6e0,
+0x3f81,0xcaf1,0xed25,0xd0b3,
+0x3f85,0xfc48,0x0c4f,0xf4b1,
+0x3f7f,0xd795,0x22a0,0x750e,
+0x3f7f,0x1059,0xda79,0xb671,
+0x3f87,0xb167,0xea19,0xf6d7,
+0x3f96,0x5b13,0x4534,0xbe6d,
+0x3fad,0x1592,0x09c5,0x8607,
+0x3fdc,0x5c85,0xfdf4,0xbd71,
+0x3ff0,0x0000,0x0000,0x0000
+};
+static unsigned short Q[] = {
+0x3f01,0x31bc,0x737f,0x2b66,
+0x3f50,0x8aaf,0xbb4f,0x296c,
+0x3f7a,0xa622,0x8d1b,0x5dfe,
+0x3f91,0x4a9e,0xccc0,0xd350,
+0x3f9a,0xce23,0x012b,0x7535,
+0x3fa1,0x24bc,0x2637,0xa639,
+0x3fa5,0xdf25,0x55c6,0x568a,
+0x3fad,0xfffd,0x1884,0x2eaa,
+0x3fb7,0xffff,0xfecb,0xe0b3,
+0x3fcf,0xffff,0xffff,0xf048
+};
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double log ( double );
+#else
+double polevl(), log();
+#endif
+
+double ellpe(x)
+double x;
+{
+
+if( (x <= 0.0) || (x > 1.0) )
+ {
+ if( x == 0.0 )
+ return( 1.0 );
+ mtherr( "ellpe", DOMAIN );
+ return( 0.0 );
+ }
+return( polevl(x,P,10) - log(x) * (x * polevl(x,Q,9)) );
+}
diff --git a/libm/double/ellpj.c b/libm/double/ellpj.c
new file mode 100644
index 000000000..327fc56e8
--- /dev/null
+++ b/libm/double/ellpj.c
@@ -0,0 +1,171 @@
+/* ellpj.c
+ *
+ * Jacobian Elliptic Functions
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double u, m, sn, cn, dn, phi;
+ * int ellpj();
+ *
+ * ellpj( u, m, _&sn, _&cn, _&dn, _&phi );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
+ * and dn(u|m) of parameter m between 0 and 1, and real
+ * argument u.
+ *
+ * These functions are periodic, with quarter-period on the
+ * real axis equal to the complete elliptic integral
+ * ellpk(1.0-m).
+ *
+ * Relation to incomplete elliptic integral:
+ * If u = ellik(phi,m), then sn(u|m) = sin(phi),
+ * and cn(u|m) = cos(phi). Phi is called the amplitude of u.
+ *
+ * Computation is by means of the arithmetic-geometric mean
+ * algorithm, except when m is within 1e-9 of 0 or 1. In the
+ * latter case with m close to 1, the approximation applies
+ * only for phi < pi/2.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with u between 0 and 10, m between
+ * 0 and 1.
+ *
+ * Absolute error (* = relative error):
+ * arithmetic function # trials peak rms
+ * DEC sn 1800 4.5e-16 8.7e-17
+ * IEEE phi 10000 9.2e-16* 1.4e-16*
+ * IEEE sn 50000 4.1e-15 4.6e-16
+ * IEEE cn 40000 3.6e-15 4.4e-16
+ * IEEE dn 10000 1.3e-12 1.8e-14
+ *
+ * Peak error observed in consistency check using addition
+ * theorem for sn(u+v) was 4e-16 (absolute). Also tested by
+ * the above relation to the incomplete elliptic integral.
+ * Accuracy deteriorates when u is large.
+ *
+ */
+
+/* ellpj.c */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double sqrt ( double );
+extern double fabs ( double );
+extern double sin ( double );
+extern double cos ( double );
+extern double asin ( double );
+extern double tanh ( double );
+extern double sinh ( double );
+extern double cosh ( double );
+extern double atan ( double );
+extern double exp ( double );
+#else
+double sqrt(), fabs(), sin(), cos(), asin(), tanh();
+double sinh(), cosh(), atan(), exp();
+#endif
+extern double PIO2, MACHEP;
+
+int ellpj( u, m, sn, cn, dn, ph )
+double u, m;
+double *sn, *cn, *dn, *ph;
+{
+double ai, b, phi, t, twon;
+double a[9], c[9];
+int i;
+
+
+/* Check for special cases */
+
+if( m < 0.0 || m > 1.0 )
+ {
+ mtherr( "ellpj", DOMAIN );
+ *sn = 0.0;
+ *cn = 0.0;
+ *ph = 0.0;
+ *dn = 0.0;
+ return(-1);
+ }
+if( m < 1.0e-9 )
+ {
+ t = sin(u);
+ b = cos(u);
+ ai = 0.25 * m * (u - t*b);
+ *sn = t - ai*b;
+ *cn = b + ai*t;
+ *ph = u - ai;
+ *dn = 1.0 - 0.5*m*t*t;
+ return(0);
+ }
+
+if( m >= 0.9999999999 )
+ {
+ ai = 0.25 * (1.0-m);
+ b = cosh(u);
+ t = tanh(u);
+ phi = 1.0/b;
+ twon = b * sinh(u);
+ *sn = t + ai * (twon - u)/(b*b);
+ *ph = 2.0*atan(exp(u)) - PIO2 + ai*(twon - u)/b;
+ ai *= t * phi;
+ *cn = phi - ai * (twon - u);
+ *dn = phi + ai * (twon + u);
+ return(0);
+ }
+
+
+/* A. G. M. scale */
+a[0] = 1.0;
+b = sqrt(1.0 - m);
+c[0] = sqrt(m);
+twon = 1.0;
+i = 0;
+
+while( fabs(c[i]/a[i]) > MACHEP )
+ {
+ if( i > 7 )
+ {
+ mtherr( "ellpj", OVERFLOW );
+ goto done;
+ }
+ ai = a[i];
+ ++i;
+ c[i] = ( ai - b )/2.0;
+ t = sqrt( ai * b );
+ a[i] = ( ai + b )/2.0;
+ b = t;
+ twon *= 2.0;
+ }
+
+done:
+
+/* backward recurrence */
+phi = twon * a[i] * u;
+do
+ {
+ t = c[i] * sin(phi) / a[i];
+ b = phi;
+ phi = (asin(t) + phi)/2.0;
+ }
+while( --i );
+
+*sn = sin(phi);
+t = cos(phi);
+*cn = t;
+*dn = t/cos(phi-b);
+*ph = phi;
+return(0);
+}
diff --git a/libm/double/ellpk.c b/libm/double/ellpk.c
new file mode 100644
index 000000000..8b36690e2
--- /dev/null
+++ b/libm/double/ellpk.c
@@ -0,0 +1,234 @@
+/* ellpk.c
+ *
+ * Complete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double m1, y, ellpk();
+ *
+ * y = ellpk( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ * pi/2
+ * -
+ * | |
+ * | dt
+ * K(m) = | ------------------
+ * | 2
+ * | | sqrt( 1 - m sin t )
+ * -
+ * 0
+ *
+ * where m = 1 - m1, using the approximation
+ *
+ * P(x) - log x Q(x).
+ *
+ * The argument m1 is used rather than m so that the logarithmic
+ * singularity at m = 1 will be shifted to the origin; this
+ * preserves maximum accuracy.
+ *
+ * K(0) = pi/2.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,1 16000 3.5e-17 1.1e-17
+ * IEEE 0,1 30000 2.5e-16 6.8e-17
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ellpk domain x<0, x>1 0.0
+ *
+ */
+
+/* ellpk.c */
+
+
+/*
+Cephes Math Library, Release 2.8: June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef DEC
+static unsigned short P[] =
+{
+0035020,0127576,0040430,0051544,
+0036025,0070136,0042703,0153716,
+0036402,0122614,0062555,0077777,
+0036441,0102130,0072334,0025172,
+0036341,0043320,0117242,0172076,
+0036312,0146456,0077242,0154141,
+0036420,0003467,0013727,0035407,
+0036564,0137263,0110651,0020237,
+0036775,0001330,0144056,0020305,
+0037305,0144137,0157521,0141734,
+0040261,0071027,0173721,0147572
+};
+static unsigned short Q[] =
+{
+0034366,0130371,0103453,0077633,
+0035557,0122745,0173515,0113016,
+0036302,0124470,0167304,0074473,
+0036575,0132403,0117226,0117576,
+0036703,0156271,0047124,0147733,
+0036766,0137465,0002053,0157312,
+0037031,0014423,0154274,0176515,
+0037107,0177747,0143216,0016145,
+0037217,0177777,0172621,0074000,
+0037377,0177777,0177776,0156435,
+0040000,0000000,0000000,0000000
+};
+static unsigned short ac1[] = {0040261,0071027,0173721,0147572};
+#define C1 (*(double *)ac1)
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] =
+{
+0x0a6d,0xc823,0x15ef,0x3f22,
+0x7afa,0xc8b8,0xae0b,0x3f62,
+0xb000,0x8cad,0x54b1,0x3f80,
+0x854f,0x0e9b,0x308b,0x3f84,
+0x5e88,0x13d4,0x28da,0x3f7c,
+0x5b0c,0xcfd4,0x59a5,0x3f79,
+0xe761,0xe2fa,0x00e6,0x3f82,
+0x2414,0x7235,0x97d6,0x3f8e,
+0xc419,0x1905,0xa05b,0x3f9f,
+0x387c,0xfbea,0xb90b,0x3fb8,
+0x39ef,0xfefa,0x2e42,0x3ff6
+};
+static unsigned short Q[] =
+{
+0x6ff3,0x30e5,0xd61f,0x3efe,
+0xb2c2,0xbee9,0xf4bc,0x3f4d,
+0x8f27,0x1dd8,0x5527,0x3f78,
+0xd3f0,0x73d2,0xb6a0,0x3f8f,
+0x99fb,0x29ca,0x7b97,0x3f98,
+0x7bd9,0xa085,0xd7e6,0x3f9e,
+0x9faa,0x7b17,0x2322,0x3fa3,
+0xc38d,0xf8d1,0xfffc,0x3fa8,
+0x2f00,0xfeb2,0xffff,0x3fb1,
+0xdba4,0xffff,0xffff,0x3fbf,
+0x0000,0x0000,0x0000,0x3fe0
+};
+static unsigned short ac1[] = {0x39ef,0xfefa,0x2e42,0x3ff6};
+#define C1 (*(double *)ac1)
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] =
+{
+0x3f22,0x15ef,0xc823,0x0a6d,
+0x3f62,0xae0b,0xc8b8,0x7afa,
+0x3f80,0x54b1,0x8cad,0xb000,
+0x3f84,0x308b,0x0e9b,0x854f,
+0x3f7c,0x28da,0x13d4,0x5e88,
+0x3f79,0x59a5,0xcfd4,0x5b0c,
+0x3f82,0x00e6,0xe2fa,0xe761,
+0x3f8e,0x97d6,0x7235,0x2414,
+0x3f9f,0xa05b,0x1905,0xc419,
+0x3fb8,0xb90b,0xfbea,0x387c,
+0x3ff6,0x2e42,0xfefa,0x39ef
+};
+static unsigned short Q[] =
+{
+0x3efe,0xd61f,0x30e5,0x6ff3,
+0x3f4d,0xf4bc,0xbee9,0xb2c2,
+0x3f78,0x5527,0x1dd8,0x8f27,
+0x3f8f,0xb6a0,0x73d2,0xd3f0,
+0x3f98,0x7b97,0x29ca,0x99fb,
+0x3f9e,0xd7e6,0xa085,0x7bd9,
+0x3fa3,0x2322,0x7b17,0x9faa,
+0x3fa8,0xfffc,0xf8d1,0xc38d,
+0x3fb1,0xffff,0xfeb2,0x2f00,
+0x3fbf,0xffff,0xffff,0xdba4,
+0x3fe0,0x0000,0x0000,0x0000
+};
+static unsigned short ac1[] = {
+0x3ff6,0x2e42,0xfefa,0x39ef
+};
+#define C1 (*(double *)ac1)
+#endif
+
+#ifdef UNK
+static double P[] =
+{
+ 1.37982864606273237150E-4,
+ 2.28025724005875567385E-3,
+ 7.97404013220415179367E-3,
+ 9.85821379021226008714E-3,
+ 6.87489687449949877925E-3,
+ 6.18901033637687613229E-3,
+ 8.79078273952743772254E-3,
+ 1.49380448916805252718E-2,
+ 3.08851465246711995998E-2,
+ 9.65735902811690126535E-2,
+ 1.38629436111989062502E0
+};
+
+static double Q[] =
+{
+ 2.94078955048598507511E-5,
+ 9.14184723865917226571E-4,
+ 5.94058303753167793257E-3,
+ 1.54850516649762399335E-2,
+ 2.39089602715924892727E-2,
+ 3.01204715227604046988E-2,
+ 3.73774314173823228969E-2,
+ 4.88280347570998239232E-2,
+ 7.03124996963957469739E-2,
+ 1.24999999999870820058E-1,
+ 4.99999999999999999821E-1
+};
+static double C1 = 1.3862943611198906188E0; /* log(4) */
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double log ( double );
+#else
+double polevl(), p1evl(), log();
+#endif
+extern double MACHEP, MAXNUM;
+
+double ellpk(x)
+double x;
+{
+
+if( (x < 0.0) || (x > 1.0) )
+ {
+ mtherr( "ellpk", DOMAIN );
+ return( 0.0 );
+ }
+
+if( x > MACHEP )
+ {
+ return( polevl(x,P,10) - log(x) * polevl(x,Q,10) );
+ }
+else
+ {
+ if( x == 0.0 )
+ {
+ mtherr( "ellpk", SING );
+ return( MAXNUM );
+ }
+ else
+ {
+ return( C1 - 0.5 * log(x) );
+ }
+ }
+}
diff --git a/libm/double/eltst.c b/libm/double/eltst.c
new file mode 100644
index 000000000..cef249eaf
--- /dev/null
+++ b/libm/double/eltst.c
@@ -0,0 +1,37 @@
+extern double MACHEP, PIO2, PI;
+double ellie(), ellpe(), floor(), fabs();
+double ellie2();
+
+main()
+{
+double y, m, phi, e, E, phipi, y1;
+int i, j, npi;
+
+/* dprec(); */
+m = 0.9;
+E = ellpe(0.1);
+for( j=-10; j<=10; j++ )
+ {
+ printf( "%d * PIO2\n", j );
+ for( i=-2; i<=2; i++ )
+ {
+ phi = PIO2 * j + 50 * MACHEP * i;
+ npi = floor(phi/PIO2);
+ if( npi & 1 )
+ npi += 1;
+ phipi = phi - npi * PIO2;
+ npi = floor(phi/PIO2);
+ if( npi & 1 )
+ npi += 1;
+ phipi = phi - npi * PIO2;
+ printf( "phi %.9e npi %d ", phi, npi );
+ y1 = E * npi + ellie(phipi,m);
+ y = ellie2( phi, m );
+ printf( "y %.9e ", y );
+ e = fabs(y - y1);
+ if( y1 != 0.0 )
+ e /= y1;
+ printf( "e %.4e\n", e );
+ }
+ }
+}
diff --git a/libm/double/euclid.c b/libm/double/euclid.c
new file mode 100644
index 000000000..3a899a6d2
--- /dev/null
+++ b/libm/double/euclid.c
@@ -0,0 +1,251 @@
+/* euclid.c
+ *
+ * Rational arithmetic routines
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ *
+ * typedef struct
+ * {
+ * double n; numerator
+ * double d; denominator
+ * }fract;
+ *
+ * radd( a, b, c ) c = b + a
+ * rsub( a, b, c ) c = b - a
+ * rmul( a, b, c ) c = b * a
+ * rdiv( a, b, c ) c = b / a
+ * euclid( &n, &d ) Reduce n/d to lowest terms,
+ * return greatest common divisor.
+ *
+ * Arguments of the routines are pointers to the structures.
+ * The double precision numbers are assumed, without checking,
+ * to be integer valued. Overflow conditions are reported.
+ */
+
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double floor ( double );
+double euclid( double *, double * );
+#else
+double fabs(), floor(), euclid();
+#endif
+
+extern double MACHEP;
+#define BIG (1.0/MACHEP)
+
+typedef struct
+ {
+ double n; /* numerator */
+ double d; /* denominator */
+ }fract;
+
+/* Add fractions. */
+
+void radd( f1, f2, f3 )
+fract *f1, *f2, *f3;
+{
+double gcd, d1, d2, gcn, n1, n2;
+
+n1 = f1->n;
+d1 = f1->d;
+n2 = f2->n;
+d2 = f2->d;
+if( n1 == 0.0 )
+ {
+ f3->n = n2;
+ f3->d = d2;
+ return;
+ }
+if( n2 == 0.0 )
+ {
+ f3->n = n1;
+ f3->d = d1;
+ return;
+ }
+
+gcd = euclid( &d1, &d2 ); /* common divisors of denominators */
+gcn = euclid( &n1, &n2 ); /* common divisors of numerators */
+/* Note, factoring the numerators
+ * makes overflow slightly less likely.
+ */
+f3->n = ( n1 * d2 + n2 * d1) * gcn;
+f3->d = d1 * d2 * gcd;
+euclid( &f3->n, &f3->d );
+}
+
+
+/* Subtract fractions. */
+
+void rsub( f1, f2, f3 )
+fract *f1, *f2, *f3;
+{
+double gcd, d1, d2, gcn, n1, n2;
+
+n1 = f1->n;
+d1 = f1->d;
+n2 = f2->n;
+d2 = f2->d;
+if( n1 == 0.0 )
+ {
+ f3->n = n2;
+ f3->d = d2;
+ return;
+ }
+if( n2 == 0.0 )
+ {
+ f3->n = -n1;
+ f3->d = d1;
+ return;
+ }
+
+gcd = euclid( &d1, &d2 );
+gcn = euclid( &n1, &n2 );
+f3->n = (n2 * d1 - n1 * d2) * gcn;
+f3->d = d1 * d2 * gcd;
+euclid( &f3->n, &f3->d );
+}
+
+
+
+
+/* Multiply fractions. */
+
+void rmul( ff1, ff2, ff3 )
+fract *ff1, *ff2, *ff3;
+{
+double d1, d2, n1, n2;
+
+n1 = ff1->n;
+d1 = ff1->d;
+n2 = ff2->n;
+d2 = ff2->d;
+
+if( (n1 == 0.0) || (n2 == 0.0) )
+ {
+ ff3->n = 0.0;
+ ff3->d = 1.0;
+ return;
+ }
+euclid( &n1, &d2 ); /* cross cancel common divisors */
+euclid( &n2, &d1 );
+ff3->n = n1 * n2;
+ff3->d = d1 * d2;
+/* Report overflow. */
+if( (fabs(ff3->n) >= BIG) || (fabs(ff3->d) >= BIG) )
+ {
+ mtherr( "rmul", OVERFLOW );
+ return;
+ }
+/* euclid( &ff3->n, &ff3->d );*/
+}
+
+
+
+/* Divide fractions. */
+
+void rdiv( ff1, ff2, ff3 )
+fract *ff1, *ff2, *ff3;
+{
+double d1, d2, n1, n2;
+
+n1 = ff1->d; /* Invert ff1, then multiply */
+d1 = ff1->n;
+if( d1 < 0.0 )
+ { /* keep denominator positive */
+ n1 = -n1;
+ d1 = -d1;
+ }
+n2 = ff2->n;
+d2 = ff2->d;
+if( (n1 == 0.0) || (n2 == 0.0) )
+ {
+ ff3->n = 0.0;
+ ff3->d = 1.0;
+ return;
+ }
+
+euclid( &n1, &d2 ); /* cross cancel any common divisors */
+euclid( &n2, &d1 );
+ff3->n = n1 * n2;
+ff3->d = d1 * d2;
+/* Report overflow. */
+if( (fabs(ff3->n) >= BIG) || (fabs(ff3->d) >= BIG) )
+ {
+ mtherr( "rdiv", OVERFLOW );
+ return;
+ }
+/* euclid( &ff3->n, &ff3->d );*/
+}
+
+
+
+
+
+/* Euclidean algorithm
+ * reduces fraction to lowest terms,
+ * returns greatest common divisor.
+ */
+
+
+double euclid( num, den )
+double *num, *den;
+{
+double n, d, q, r;
+
+n = *num; /* Numerator. */
+d = *den; /* Denominator. */
+
+/* Make numbers positive, locally. */
+if( n < 0.0 )
+ n = -n;
+if( d < 0.0 )
+ d = -d;
+
+/* Abort if numbers are too big for integer arithmetic. */
+if( (n >= BIG) || (d >= BIG) )
+ {
+ mtherr( "euclid", OVERFLOW );
+ return(1.0);
+ }
+
+/* Divide by zero, gcd = 1. */
+if(d == 0.0)
+ return( 1.0 );
+
+/* Zero. Return 0/1, gcd = denominator. */
+if(n == 0.0)
+ {
+/*
+ if( *den < 0.0 )
+ *den = -1.0;
+ else
+ *den = 1.0;
+*/
+ *den = 1.0;
+ return( d );
+ }
+
+while( d > 0.5 )
+ {
+/* Find integer part of n divided by d. */
+ q = floor( n/d );
+/* Find remainder after dividing n by d. */
+ r = n - d * q;
+/* The next fraction is d/r. */
+ n = d;
+ d = r;
+ }
+
+if( n < 0.0 )
+ mtherr( "euclid", UNDERFLOW );
+
+*num /= n;
+*den /= n;
+return( n );
+}
+
diff --git a/libm/double/exp.c b/libm/double/exp.c
new file mode 100644
index 000000000..6d0a8a872
--- /dev/null
+++ b/libm/double/exp.c
@@ -0,0 +1,203 @@
+/* exp.c
+ *
+ * Exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, exp();
+ *
+ * y = exp( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns e (2.71828...) raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *
+ * x k f
+ * e = 2 e.
+ *
+ * A Pade' form 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ * of degree 2/3 is used to approximate exp(f) in the basic
+ * interval [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC +- 88 50000 2.8e-17 7.0e-18
+ * IEEE +- 708 40000 2.0e-16 5.6e-17
+ *
+ *
+ * Error amplification in the exponential function can be
+ * a serious matter. The error propagation involves
+ * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
+ * which shows that a 1 lsb error in representing X produces
+ * a relative error of X times 1 lsb in the function.
+ * While the routine gives an accurate result for arguments
+ * that are exactly represented by a double precision
+ * computer number, the result contains amplified roundoff
+ * error for large arguments not exactly represented.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp underflow x < MINLOG 0.0
+ * exp overflow x > MAXLOG INFINITY
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+/* Exponential function */
+
+#include <math.h>
+
+#ifdef UNK
+
+static double P[] = {
+ 1.26177193074810590878E-4,
+ 3.02994407707441961300E-2,
+ 9.99999999999999999910E-1,
+};
+static double Q[] = {
+ 3.00198505138664455042E-6,
+ 2.52448340349684104192E-3,
+ 2.27265548208155028766E-1,
+ 2.00000000000000000009E0,
+};
+static double C1 = 6.93145751953125E-1;
+static double C2 = 1.42860682030941723212E-6;
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0035004,0047156,0127442,0057502,
+0036770,0033210,0063121,0061764,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short Q[] = {
+0033511,0072665,0160662,0176377,
+0036045,0070715,0124105,0132777,
+0037550,0134114,0142077,0001637,
+0040400,0000000,0000000,0000000,
+};
+static unsigned short sc1[] = {0040061,0071000,0000000,0000000};
+#define C1 (*(double *)sc1)
+static unsigned short sc2[] = {0033277,0137216,0075715,0057117};
+#define C2 (*(double *)sc2)
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x4be8,0xd5e4,0x89cd,0x3f20,
+0x2c7e,0x0cca,0x06d1,0x3f9f,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short Q[] = {
+0x5fa0,0xbc36,0x2eb6,0x3ec9,
+0xb6c0,0xb508,0xae39,0x3f64,
+0xe074,0x9887,0x1709,0x3fcd,
+0x0000,0x0000,0x0000,0x4000,
+};
+static unsigned short sc1[] = {0x0000,0x0000,0x2e40,0x3fe6};
+#define C1 (*(double *)sc1)
+static unsigned short sc2[] = {0xabca,0xcf79,0xf7d1,0x3eb7};
+#define C2 (*(double *)sc2)
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f20,0x89cd,0xd5e4,0x4be8,
+0x3f9f,0x06d1,0x0cca,0x2c7e,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short Q[] = {
+0x3ec9,0x2eb6,0xbc36,0x5fa0,
+0x3f64,0xae39,0xb508,0xb6c0,
+0x3fcd,0x1709,0x9887,0xe074,
+0x4000,0x0000,0x0000,0x0000,
+};
+static unsigned short sc1[] = {0x3fe6,0x2e40,0x0000,0x0000};
+#define C1 (*(double *)sc1)
+static unsigned short sc2[] = {0x3eb7,0xf7d1,0xcf79,0xabca};
+#define C2 (*(double *)sc2)
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double floor ( double );
+extern double ldexp ( double, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double polevl(), p1evl(), floor(), ldexp();
+int isnan(), isfinite();
+#endif
+extern double LOGE2, LOG2E, MAXLOG, MINLOG, MAXNUM;
+#ifdef INFINITIES
+extern double INFINITY;
+#endif
+
+double exp(x)
+double x;
+{
+double px, xx;
+int n;
+
+#ifdef NANS
+if( isnan(x) )
+ return(x);
+#endif
+if( x > MAXLOG)
+ {
+#ifdef INFINITIES
+ return( INFINITY );
+#else
+ mtherr( "exp", OVERFLOW );
+ return( MAXNUM );
+#endif
+ }
+
+if( x < MINLOG )
+ {
+#ifndef INFINITIES
+ mtherr( "exp", UNDERFLOW );
+#endif
+ return(0.0);
+ }
+
+/* Express e**x = e**g 2**n
+ * = e**g e**( n loge(2) )
+ * = e**( g + n loge(2) )
+ */
+px = floor( LOG2E * x + 0.5 ); /* floor() truncates toward -infinity. */
+n = px;
+x -= px * C1;
+x -= px * C2;
+
+/* rational approximation for exponential
+ * of the fractional part:
+ * e**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ */
+xx = x * x;
+px = x * polevl( xx, P, 2 );
+x = px/( polevl( xx, Q, 3 ) - px );
+x = 1.0 + 2.0 * x;
+
+/* multiply by power of 2 */
+x = ldexp( x, n );
+return(x);
+}
diff --git a/libm/double/exp10.c b/libm/double/exp10.c
new file mode 100644
index 000000000..dd0e5a48f
--- /dev/null
+++ b/libm/double/exp10.c
@@ -0,0 +1,223 @@
+/* exp10.c
+ *
+ * Base 10 exponential function
+ * (Common antilogarithm)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, exp10();
+ *
+ * y = exp10( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 10 raised to the x power.
+ *
+ * Range reduction is accomplished by expressing the argument
+ * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
+ * The Pade' form
+ *
+ * 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ *
+ * is used to approximate 10**f.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -307,+307 30000 2.2e-16 5.5e-17
+ * Test result from an earlier version (2.1):
+ * DEC -38,+38 70000 3.1e-17 7.0e-18
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp10 underflow x < -MAXL10 0.0
+ * exp10 overflow x > MAXL10 MAXNUM
+ *
+ * DEC arithmetic: MAXL10 = 38.230809449325611792.
+ * IEEE arithmetic: MAXL10 = 308.2547155599167.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1991, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+ 4.09962519798587023075E-2,
+ 1.17452732554344059015E1,
+ 4.06717289936872725516E2,
+ 2.39423741207388267439E3,
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 8.50936160849306532625E1,
+ 1.27209271178345121210E3,
+ 2.07960819286001865907E3,
+};
+/* static double LOG102 = 3.01029995663981195214e-1; */
+static double LOG210 = 3.32192809488736234787e0;
+static double LG102A = 3.01025390625000000000E-1;
+static double LG102B = 4.60503898119521373889E-6;
+/* static double MAXL10 = 38.230809449325611792; */
+static double MAXL10 = 308.2547155599167;
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0037047,0165657,0114061,0067234,
+0041073,0166243,0123052,0144643,
+0042313,0055720,0024032,0047443,
+0043025,0121714,0070232,0050007,
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041652,0027756,0071216,0050075,
+0042637,0001367,0077263,0136017,
+0043001,0174673,0024157,0133416,
+};
+/*
+static unsigned short L102[] = {0037632,0020232,0102373,0147770};
+#define LOG102 *(double *)L102
+*/
+static unsigned short L210[] = {0040524,0115170,0045715,0015613};
+#define LOG210 *(double *)L210
+static unsigned short L102A[] = {0037632,0020000,0000000,0000000,};
+#define LG102A *(double *)L102A
+static unsigned short L102B[] = {0033632,0102373,0147767,0114220,};
+#define LG102B *(double *)L102B
+static unsigned short MXL[] = {0041430,0166131,0047761,0154130,};
+#define MAXL10 ( *(double *)MXL )
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x2dd4,0xf306,0xfd75,0x3fa4,
+0x5934,0x74c5,0x7d94,0x4027,
+0x49e4,0x0503,0x6b7a,0x4079,
+0x4a01,0x8e13,0xb479,0x40a2,
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xca08,0xce51,0x45fd,0x4055,
+0x7782,0xefd6,0xe05e,0x4093,
+0xf6e2,0x650d,0x3f37,0x40a0,
+};
+/*
+static unsigned short L102[] = {0x79ff,0x509f,0x4413,0x3fd3};
+#define LOG102 *(double *)L102
+*/
+static unsigned short L210[] = {0xa371,0x0979,0x934f,0x400a};
+#define LOG210 *(double *)L210
+static unsigned short L102A[] = {0x0000,0x0000,0x4400,0x3fd3,};
+#define LG102A *(double *)L102A
+static unsigned short L102B[] = {0xf312,0x79fe,0x509f,0x3ed3,};
+#define LG102B *(double *)L102B
+static double MAXL10 = 308.2547155599167;
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3fa4,0xfd75,0xf306,0x2dd4,
+0x4027,0x7d94,0x74c5,0x5934,
+0x4079,0x6b7a,0x0503,0x49e4,
+0x40a2,0xb479,0x8e13,0x4a01,
+};
+static unsigned short Q[] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4055,0x45fd,0xce51,0xca08,
+0x4093,0xe05e,0xefd6,0x7782,
+0x40a0,0x3f37,0x650d,0xf6e2,
+};
+/*
+static unsigned short L102[] = {0x3fd3,0x4413,0x509f,0x79ff};
+#define LOG102 *(double *)L102
+*/
+static unsigned short L210[] = {0x400a,0x934f,0x0979,0xa371};
+#define LOG210 *(double *)L210
+static unsigned short L102A[] = {0x3fd3,0x4400,0x0000,0x0000,};
+#define LG102A *(double *)L102A
+static unsigned short L102B[] = {0x3ed3,0x509f,0x79fe,0xf312,};
+#define LG102B *(double *)L102B
+static double MAXL10 = 308.2547155599167;
+#endif
+
+#ifdef ANSIPROT
+extern double floor ( double );
+extern double ldexp ( double, int );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double floor(), ldexp(), polevl(), p1evl();
+int isnan(), isfinite();
+#endif
+extern double MAXNUM;
+#ifdef INFINITIES
+extern double INFINITY;
+#endif
+
+double exp10(x)
+double x;
+{
+double px, xx;
+short n;
+
+#ifdef NANS
+if( isnan(x) )
+ return(x);
+#endif
+if( x > MAXL10 )
+ {
+#ifdef INFINITIES
+ return( INFINITY );
+#else
+ mtherr( "exp10", OVERFLOW );
+ return( MAXNUM );
+#endif
+ }
+
+if( x < -MAXL10 ) /* Would like to use MINLOG but can't */
+ {
+#ifndef INFINITIES
+ mtherr( "exp10", UNDERFLOW );
+#endif
+ return(0.0);
+ }
+
+/* Express 10**x = 10**g 2**n
+ * = 10**g 10**( n log10(2) )
+ * = 10**( g + n log10(2) )
+ */
+px = floor( LOG210 * x + 0.5 );
+n = px;
+x -= px * LG102A;
+x -= px * LG102B;
+
+/* rational approximation for exponential
+ * of the fractional part:
+ * 10**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ */
+xx = x * x;
+px = x * polevl( xx, P, 3 );
+x = px/( p1evl( xx, Q, 3 ) - px );
+x = 1.0 + ldexp( x, 1 );
+
+/* multiply by power of 2 */
+x = ldexp( x, n );
+
+return(x);
+}
diff --git a/libm/double/exp2.c b/libm/double/exp2.c
new file mode 100644
index 000000000..be5bdfd0c
--- /dev/null
+++ b/libm/double/exp2.c
@@ -0,0 +1,183 @@
+/* exp2.c
+ *
+ * Base 2 exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, exp2();
+ *
+ * y = exp2( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 2 raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ * x k f
+ * 2 = 2 2.
+ *
+ * A Pade' form
+ *
+ * 1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
+ *
+ * approximates 2**x in the basic range [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1022,+1024 30000 1.8e-16 5.4e-17
+ *
+ *
+ * See exp.c for comments on error amplification.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp underflow x < -MAXL2 0.0
+ * exp overflow x > MAXL2 MAXNUM
+ *
+ * For DEC arithmetic, MAXL2 = 127.
+ * For IEEE arithmetic, MAXL2 = 1024.
+ */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+ 2.30933477057345225087E-2,
+ 2.02020656693165307700E1,
+ 1.51390680115615096133E3,
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 2.33184211722314911771E2,
+ 4.36821166879210612817E3,
+};
+#define MAXL2 1024.0
+#define MINL2 -1024.0
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0036675,0027102,0122327,0053227,
+0041241,0116724,0115412,0157355,
+0042675,0036404,0101733,0132226,
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0042151,0027450,0077732,0160744,
+0043210,0100661,0077550,0056560,
+};
+#define MAXL2 127.0
+#define MINL2 -127.0
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0xead3,0x549a,0xa5c8,0x3f97,
+0x5bde,0x9361,0x33ba,0x4034,
+0x7693,0x907b,0xa7a0,0x4097,
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x5c3c,0x0ffb,0x25e5,0x406d,
+0x0bae,0x2fed,0x1036,0x40b1,
+};
+#define MAXL2 1024.0
+#define MINL2 -1022.0
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f97,0xa5c8,0x549a,0xead3,
+0x4034,0x33ba,0x9361,0x5bde,
+0x4097,0xa7a0,0x907b,0x7693,
+};
+static unsigned short Q[] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x406d,0x25e5,0x0ffb,0x5c3c,
+0x40b1,0x1036,0x2fed,0x0bae,
+};
+#define MAXL2 1024.0
+#define MINL2 -1022.0
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double floor ( double );
+extern double ldexp ( double, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double polevl(), p1evl(), floor(), ldexp();
+int isnan(), isfinite();
+#endif
+#ifdef INFINITIES
+extern double INFINITY;
+#endif
+extern double MAXNUM;
+
+double exp2(x)
+double x;
+{
+double px, xx;
+short n;
+
+#ifdef NANS
+if( isnan(x) )
+ return(x);
+#endif
+if( x > MAXL2)
+ {
+#ifdef INFINITIES
+ return( INFINITY );
+#else
+ mtherr( "exp2", OVERFLOW );
+ return( MAXNUM );
+#endif
+ }
+
+if( x < MINL2 )
+ {
+#ifndef INFINITIES
+ mtherr( "exp2", UNDERFLOW );
+#endif
+ return(0.0);
+ }
+
+xx = x; /* save x */
+/* separate into integer and fractional parts */
+px = floor(x+0.5);
+n = px;
+x = x - px;
+
+/* rational approximation
+ * exp2(x) = 1 + 2xP(xx)/(Q(xx) - P(xx))
+ * where xx = x**2
+ */
+xx = x * x;
+px = x * polevl( xx, P, 2 );
+x = px / ( p1evl( xx, Q, 2 ) - px );
+x = 1.0 + ldexp( x, 1 );
+
+/* scale by power of 2 */
+x = ldexp( x, n );
+return(x);
+}
diff --git a/libm/double/expn.c b/libm/double/expn.c
new file mode 100644
index 000000000..89b6b139e
--- /dev/null
+++ b/libm/double/expn.c
@@ -0,0 +1,208 @@
+/* expn.c
+ *
+ * Exponential integral En
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double x, y, expn();
+ *
+ * y = expn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the exponential integral
+ *
+ * inf.
+ * -
+ * | | -xt
+ * | e
+ * E (x) = | ---- dt.
+ * n | n
+ * | | t
+ * -
+ * 1
+ *
+ *
+ * Both n and x must be nonnegative.
+ *
+ * The routine employs either a power series, a continued
+ * fraction, or an asymptotic formula depending on the
+ * relative values of n and x.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 5000 2.0e-16 4.6e-17
+ * IEEE 0, 30 10000 1.7e-15 3.6e-16
+ *
+ */
+
+/* expn.c */
+
+/* Cephes Math Library Release 2.8: June, 2000
+ Copyright 1985, 2000 by Stephen L. Moshier */
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double pow ( double, double );
+extern double gamma ( double );
+extern double log ( double );
+extern double exp ( double );
+extern double fabs ( double );
+#else
+double pow(), gamma(), log(), exp(), fabs();
+#endif
+#define EUL 0.57721566490153286060
+#define BIG 1.44115188075855872E+17
+extern double MAXNUM, MACHEP, MAXLOG;
+
+double expn( n, x )
+int n;
+double x;
+{
+double ans, r, t, yk, xk;
+double pk, pkm1, pkm2, qk, qkm1, qkm2;
+double psi, z;
+int i, k;
+static double big = BIG;
+
+if( n < 0 )
+ goto domerr;
+
+if( x < 0 )
+ {
+domerr: mtherr( "expn", DOMAIN );
+ return( MAXNUM );
+ }
+
+if( x > MAXLOG )
+ return( 0.0 );
+
+if( x == 0.0 )
+ {
+ if( n < 2 )
+ {
+ mtherr( "expn", SING );
+ return( MAXNUM );
+ }
+ else
+ return( 1.0/(n-1.0) );
+ }
+
+if( n == 0 )
+ return( exp(-x)/x );
+
+/* expn.c */
+/* Expansion for large n */
+
+if( n > 5000 )
+ {
+ xk = x + n;
+ yk = 1.0 / (xk * xk);
+ t = n;
+ ans = yk * t * (6.0 * x * x - 8.0 * t * x + t * t);
+ ans = yk * (ans + t * (t - 2.0 * x));
+ ans = yk * (ans + t);
+ ans = (ans + 1.0) * exp( -x ) / xk;
+ goto done;
+ }
+
+if( x > 1.0 )
+ goto cfrac;
+
+/* expn.c */
+
+/* Power series expansion */
+
+psi = -EUL - log(x);
+for( i=1; i<n; i++ )
+ psi = psi + 1.0/i;
+
+z = -x;
+xk = 0.0;
+yk = 1.0;
+pk = 1.0 - n;
+if( n == 1 )
+ ans = 0.0;
+else
+ ans = 1.0/pk;
+do
+ {
+ xk += 1.0;
+ yk *= z/xk;
+ pk += 1.0;
+ if( pk != 0.0 )
+ {
+ ans += yk/pk;
+ }
+ if( ans != 0.0 )
+ t = fabs(yk/ans);
+ else
+ t = 1.0;
+ }
+while( t > MACHEP );
+k = xk;
+t = n;
+r = n - 1;
+ans = (pow(z, r) * psi / gamma(t)) - ans;
+goto done;
+
+/* expn.c */
+/* continued fraction */
+cfrac:
+k = 1;
+pkm2 = 1.0;
+qkm2 = x;
+pkm1 = 1.0;
+qkm1 = x + n;
+ans = pkm1/qkm1;
+
+do
+ {
+ k += 1;
+ if( k & 1 )
+ {
+ yk = 1.0;
+ xk = n + (k-1)/2;
+ }
+ else
+ {
+ yk = x;
+ xk = k/2;
+ }
+ pk = pkm1 * yk + pkm2 * xk;
+ qk = qkm1 * yk + qkm2 * xk;
+ if( qk != 0 )
+ {
+ r = pk/qk;
+ t = fabs( (ans - r)/r );
+ ans = r;
+ }
+ else
+ t = 1.0;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+if( fabs(pk) > big )
+ {
+ pkm2 /= big;
+ pkm1 /= big;
+ qkm2 /= big;
+ qkm1 /= big;
+ }
+ }
+while( t > MACHEP );
+
+ans *= exp( -x );
+
+done:
+return( ans );
+}
+
diff --git a/libm/double/fabs.c b/libm/double/fabs.c
new file mode 100644
index 000000000..0c4531a6c
--- /dev/null
+++ b/libm/double/fabs.c
@@ -0,0 +1,56 @@
+/* fabs.c
+ *
+ * Absolute value
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y;
+ *
+ * y = fabs( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the absolute value of the argument.
+ *
+ */
+
+
+#include <math.h>
+/* Avoid using UNK if possible. */
+#ifdef UNK
+#if BIGENDIAN
+#define MIEEE 1
+#else
+#define IBMPC 1
+#endif
+#endif
+
+double fabs(x)
+double x;
+{
+union
+ {
+ double d;
+ short i[4];
+ } u;
+
+u.d = x;
+#ifdef IBMPC
+ u.i[3] &= 0x7fff;
+#endif
+#ifdef MIEEE
+ u.i[0] &= 0x7fff;
+#endif
+#ifdef DEC
+ u.i[3] &= 0x7fff;
+#endif
+#ifdef UNK
+if( u.d < 0 )
+ u.d = -u.d;
+#endif
+return( u.d );
+}
diff --git a/libm/double/fac.c b/libm/double/fac.c
new file mode 100644
index 000000000..a5748ac74
--- /dev/null
+++ b/libm/double/fac.c
@@ -0,0 +1,263 @@
+/* fac.c
+ *
+ * Factorial function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double y, fac();
+ * int i;
+ *
+ * y = fac( i );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns factorial of i = 1 * 2 * 3 * ... * i.
+ * fac(0) = 1.0.
+ *
+ * Due to machine arithmetic bounds the largest value of
+ * i accepted is 33 in DEC arithmetic or 170 in IEEE
+ * arithmetic. Greater values, or negative ones,
+ * produce an error message and return MAXNUM.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * For i < 34 the values are simply tabulated, and have
+ * full machine accuracy. If i > 55, fac(i) = gamma(i+1);
+ * see gamma.c.
+ *
+ * Relative error:
+ * arithmetic domain peak
+ * IEEE 0, 170 1.4e-15
+ * DEC 0, 33 1.4e-17
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Factorials of integers from 0 through 33 */
+#ifdef UNK
+static double factbl[] = {
+ 1.00000000000000000000E0,
+ 1.00000000000000000000E0,
+ 2.00000000000000000000E0,
+ 6.00000000000000000000E0,
+ 2.40000000000000000000E1,
+ 1.20000000000000000000E2,
+ 7.20000000000000000000E2,
+ 5.04000000000000000000E3,
+ 4.03200000000000000000E4,
+ 3.62880000000000000000E5,
+ 3.62880000000000000000E6,
+ 3.99168000000000000000E7,
+ 4.79001600000000000000E8,
+ 6.22702080000000000000E9,
+ 8.71782912000000000000E10,
+ 1.30767436800000000000E12,
+ 2.09227898880000000000E13,
+ 3.55687428096000000000E14,
+ 6.40237370572800000000E15,
+ 1.21645100408832000000E17,
+ 2.43290200817664000000E18,
+ 5.10909421717094400000E19,
+ 1.12400072777760768000E21,
+ 2.58520167388849766400E22,
+ 6.20448401733239439360E23,
+ 1.55112100433309859840E25,
+ 4.03291461126605635584E26,
+ 1.0888869450418352160768E28,
+ 3.04888344611713860501504E29,
+ 8.841761993739701954543616E30,
+ 2.6525285981219105863630848E32,
+ 8.22283865417792281772556288E33,
+ 2.6313083693369353016721801216E35,
+ 8.68331761881188649551819440128E36
+};
+#define MAXFAC 33
+#endif
+
+#ifdef DEC
+static unsigned short factbl[] = {
+0040200,0000000,0000000,0000000,
+0040200,0000000,0000000,0000000,
+0040400,0000000,0000000,0000000,
+0040700,0000000,0000000,0000000,
+0041300,0000000,0000000,0000000,
+0041760,0000000,0000000,0000000,
+0042464,0000000,0000000,0000000,
+0043235,0100000,0000000,0000000,
+0044035,0100000,0000000,0000000,
+0044661,0030000,0000000,0000000,
+0045535,0076000,0000000,0000000,
+0046430,0042500,0000000,0000000,
+0047344,0063740,0000000,0000000,
+0050271,0112146,0000000,0000000,
+0051242,0060731,0040000,0000000,
+0052230,0035673,0126000,0000000,
+0053230,0035673,0126000,0000000,
+0054241,0137567,0063300,0000000,
+0055265,0173546,0051630,0000000,
+0056330,0012711,0101504,0100000,
+0057407,0006635,0171012,0150000,
+0060461,0040737,0046656,0030400,
+0061563,0135223,0005317,0101540,
+0062657,0027031,0127705,0023155,
+0064003,0061223,0041723,0156322,
+0065115,0045006,0014773,0004410,
+0066246,0146044,0172433,0173526,
+0067414,0136077,0027317,0114261,
+0070566,0044556,0110753,0045465,
+0071737,0031214,0032075,0036050,
+0073121,0037543,0070371,0064146,
+0074312,0132550,0052561,0116443,
+0075512,0132550,0052561,0116443,
+0076721,0005423,0114035,0025014
+};
+#define MAXFAC 33
+#endif
+
+#ifdef IBMPC
+static unsigned short factbl[] = {
+0x0000,0x0000,0x0000,0x3ff0,
+0x0000,0x0000,0x0000,0x3ff0,
+0x0000,0x0000,0x0000,0x4000,
+0x0000,0x0000,0x0000,0x4018,
+0x0000,0x0000,0x0000,0x4038,
+0x0000,0x0000,0x0000,0x405e,
+0x0000,0x0000,0x8000,0x4086,
+0x0000,0x0000,0xb000,0x40b3,
+0x0000,0x0000,0xb000,0x40e3,
+0x0000,0x0000,0x2600,0x4116,
+0x0000,0x0000,0xaf80,0x414b,
+0x0000,0x0000,0x08a8,0x4183,
+0x0000,0x0000,0x8cfc,0x41bc,
+0x0000,0xc000,0x328c,0x41f7,
+0x0000,0x2800,0x4c3b,0x4234,
+0x0000,0x7580,0x0777,0x4273,
+0x0000,0x7580,0x0777,0x42b3,
+0x0000,0xecd8,0x37ee,0x42f4,
+0x0000,0xca73,0xbeec,0x4336,
+0x9000,0x3068,0x02b9,0x437b,
+0x5a00,0xbe41,0xe1b3,0x43c0,
+0xc620,0xe9b5,0x283b,0x4406,
+0xf06c,0x6159,0x7752,0x444e,
+0xa4ce,0x35f8,0xe5c3,0x4495,
+0x7b9a,0x687a,0x6c52,0x44e0,
+0x6121,0xc33f,0xa940,0x4529,
+0x7eeb,0x9ea3,0xd984,0x4574,
+0xf316,0xe5d9,0x9787,0x45c1,
+0x6967,0xd23d,0xc92d,0x460e,
+0xa785,0x8687,0xe651,0x465b,
+0x2d0d,0x6e1f,0x27ec,0x46aa,
+0x33a4,0x0aae,0x56ad,0x46f9,
+0x33a4,0x0aae,0x56ad,0x4749,
+0xa541,0x7303,0x2162,0x479a
+};
+#define MAXFAC 170
+#endif
+
+#ifdef MIEEE
+static unsigned short factbl[] = {
+0x3ff0,0x0000,0x0000,0x0000,
+0x3ff0,0x0000,0x0000,0x0000,
+0x4000,0x0000,0x0000,0x0000,
+0x4018,0x0000,0x0000,0x0000,
+0x4038,0x0000,0x0000,0x0000,
+0x405e,0x0000,0x0000,0x0000,
+0x4086,0x8000,0x0000,0x0000,
+0x40b3,0xb000,0x0000,0x0000,
+0x40e3,0xb000,0x0000,0x0000,
+0x4116,0x2600,0x0000,0x0000,
+0x414b,0xaf80,0x0000,0x0000,
+0x4183,0x08a8,0x0000,0x0000,
+0x41bc,0x8cfc,0x0000,0x0000,
+0x41f7,0x328c,0xc000,0x0000,
+0x4234,0x4c3b,0x2800,0x0000,
+0x4273,0x0777,0x7580,0x0000,
+0x42b3,0x0777,0x7580,0x0000,
+0x42f4,0x37ee,0xecd8,0x0000,
+0x4336,0xbeec,0xca73,0x0000,
+0x437b,0x02b9,0x3068,0x9000,
+0x43c0,0xe1b3,0xbe41,0x5a00,
+0x4406,0x283b,0xe9b5,0xc620,
+0x444e,0x7752,0x6159,0xf06c,
+0x4495,0xe5c3,0x35f8,0xa4ce,
+0x44e0,0x6c52,0x687a,0x7b9a,
+0x4529,0xa940,0xc33f,0x6121,
+0x4574,0xd984,0x9ea3,0x7eeb,
+0x45c1,0x9787,0xe5d9,0xf316,
+0x460e,0xc92d,0xd23d,0x6967,
+0x465b,0xe651,0x8687,0xa785,
+0x46aa,0x27ec,0x6e1f,0x2d0d,
+0x46f9,0x56ad,0x0aae,0x33a4,
+0x4749,0x56ad,0x0aae,0x33a4,
+0x479a,0x2162,0x7303,0xa541
+};
+#define MAXFAC 170
+#endif
+
+#ifdef ANSIPROT
+double gamma ( double );
+#else
+double gamma();
+#endif
+extern double MAXNUM;
+
+double fac(i)
+int i;
+{
+double x, f, n;
+int j;
+
+if( i < 0 )
+ {
+ mtherr( "fac", SING );
+ return( MAXNUM );
+ }
+
+if( i > MAXFAC )
+ {
+ mtherr( "fac", OVERFLOW );
+ return( MAXNUM );
+ }
+
+/* Get answer from table for small i. */
+if( i < 34 )
+ {
+#ifdef UNK
+ return( factbl[i] );
+#else
+ return( *(double *)(&factbl[4*i]) );
+#endif
+ }
+/* Use gamma function for large i. */
+if( i > 55 )
+ {
+ x = i + 1;
+ return( gamma(x) );
+ }
+/* Compute directly for intermediate i. */
+n = 34.0;
+f = 34.0;
+for( j=35; j<=i; j++ )
+ {
+ n += 1.0;
+ f *= n;
+ }
+#ifdef UNK
+ f *= factbl[33];
+#else
+ f *= *(double *)(&factbl[4*33]);
+#endif
+return( f );
+}
diff --git a/libm/double/fdtr.c b/libm/double/fdtr.c
new file mode 100644
index 000000000..469b7bedf
--- /dev/null
+++ b/libm/double/fdtr.c
@@ -0,0 +1,237 @@
+/* fdtr.c
+ *
+ * F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * double x, y, fdtr();
+ *
+ * y = fdtr( df1, df2, x );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density). This is the density
+ * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
+ * variables having Chi square distributions with df1
+ * and df2 degrees of freedom, respectively.
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ * P(x) = incbet( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
+ *
+ *
+ * The arguments a and b are greater than zero, and x is
+ * nonnegative.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,x).
+ *
+ * x a,b Relative error:
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0,1 0,100 100000 9.8e-15 1.7e-15
+ * IEEE 1,5 0,100 100000 6.5e-15 3.5e-16
+ * IEEE 0,1 1,10000 100000 2.2e-11 3.3e-12
+ * IEEE 1,5 1,10000 100000 1.1e-11 1.7e-13
+ * See also incbet.c.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtr domain a<0, b<0, x<0 0.0
+ *
+ */
+ /* fdtrc()
+ *
+ * Complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * double x, y, fdtrc();
+ *
+ * y = fdtrc( df1, df2, x );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from x to infinity under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density).
+ *
+ *
+ * inf.
+ * -
+ * 1 | | a-1 b-1
+ * 1-P(x) = ------ | t (1-t) dt
+ * B(a,b) | |
+ * -
+ * x
+ *
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,x) in the indicated intervals.
+ * x a,b Relative error:
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0,1 1,100 100000 3.7e-14 5.9e-16
+ * IEEE 1,5 1,100 100000 8.0e-15 1.6e-15
+ * IEEE 0,1 1,10000 100000 1.8e-11 3.5e-13
+ * IEEE 1,5 1,10000 100000 2.0e-11 3.0e-12
+ * See also incbet.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrc domain a<0, b<0, x<0 0.0
+ *
+ */
+ /* fdtri()
+ *
+ * Inverse of complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * double x, p, fdtri();
+ *
+ * x = fdtri( df1, df2, p );
+ *
+ * DESCRIPTION:
+ *
+ * Finds the F density argument x such that the integral
+ * from x to infinity of the F density is equal to the
+ * given probability p.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relations
+ *
+ * z = incbi( df2/2, df1/2, p )
+ * x = df2 (1-z) / (df1 z).
+ *
+ * Note: the following relations hold for the inverse of
+ * the uncomplemented F distribution:
+ *
+ * z = incbi( df1/2, df2/2, p )
+ * x = df2 z / (df1 (1-z)).
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p).
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * For p between .001 and 1:
+ * IEEE 1,100 100000 8.3e-15 4.7e-16
+ * IEEE 1,10000 100000 2.1e-11 1.4e-13
+ * For p between 10^-6 and 10^-3:
+ * IEEE 1,100 50000 1.3e-12 8.4e-15
+ * IEEE 1,10000 50000 3.0e-12 4.8e-14
+ * See also fdtrc.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtri domain p <= 0 or p > 1 0.0
+ * v < 1
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double incbet ( double, double, double );
+extern double incbi ( double, double, double );
+#else
+double incbet(), incbi();
+#endif
+
+double fdtrc( ia, ib, x )
+int ia, ib;
+double x;
+{
+double a, b, w;
+
+if( (ia < 1) || (ib < 1) || (x < 0.0) )
+ {
+ mtherr( "fdtrc", DOMAIN );
+ return( 0.0 );
+ }
+a = ia;
+b = ib;
+w = b / (b + a * x);
+return( incbet( 0.5*b, 0.5*a, w ) );
+}
+
+
+
+double fdtr( ia, ib, x )
+int ia, ib;
+double x;
+{
+double a, b, w;
+
+if( (ia < 1) || (ib < 1) || (x < 0.0) )
+ {
+ mtherr( "fdtr", DOMAIN );
+ return( 0.0 );
+ }
+a = ia;
+b = ib;
+w = a * x;
+w = w / (b + w);
+return( incbet(0.5*a, 0.5*b, w) );
+}
+
+
+double fdtri( ia, ib, y )
+int ia, ib;
+double y;
+{
+double a, b, w, x;
+
+if( (ia < 1) || (ib < 1) || (y <= 0.0) || (y > 1.0) )
+ {
+ mtherr( "fdtri", DOMAIN );
+ return( 0.0 );
+ }
+a = ia;
+b = ib;
+/* Compute probability for x = 0.5. */
+w = incbet( 0.5*b, 0.5*a, 0.5 );
+/* If that is greater than y, then the solution w < .5.
+ Otherwise, solve at 1-y to remove cancellation in (b - b*w). */
+if( w > y || y < 0.001)
+ {
+ w = incbi( 0.5*b, 0.5*a, y );
+ x = (b - b*w)/(a*w);
+ }
+else
+ {
+ w = incbi( 0.5*a, 0.5*b, 1.0-y );
+ x = b*w/(a*(1.0-w));
+ }
+return(x);
+}
diff --git a/libm/double/fftr.c b/libm/double/fftr.c
new file mode 100644
index 000000000..d4ce23463
--- /dev/null
+++ b/libm/double/fftr.c
@@ -0,0 +1,237 @@
+/* fftr.c
+ *
+ * FFT of Real Valued Sequence
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x[], sine[];
+ * int m;
+ *
+ * fftr( x, m, sine );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the (complex valued) discrete Fourier transform of
+ * the real valued sequence x[]. The input sequence x[] contains
+ * n = 2**m samples. The program fills array sine[k] with
+ * n/4 + 1 values of sin( 2 PI k / n ).
+ *
+ * Data format for complex valued output is real part followed
+ * by imaginary part. The output is developed in the input
+ * array x[].
+ *
+ * The algorithm takes advantage of the fact that the FFT of an
+ * n point real sequence can be obtained from an n/2 point
+ * complex FFT.
+ *
+ * A radix 2 FFT algorithm is used.
+ *
+ * Execution time on an LSI-11/23 with floating point chip
+ * is 1.0 sec for n = 256.
+ *
+ *
+ *
+ * REFERENCE:
+ *
+ * E. Oran Brigham, The Fast Fourier Transform;
+ * Prentice-Hall, Inc., 1974
+ *
+ */
+
+
+#include <math.h>
+
+static short n0 = 0;
+static short n4 = 0;
+static short msav = 0;
+
+extern double PI;
+
+#ifdef ANSIPROT
+extern double sin ( double );
+static int bitrv(int, int);
+#else
+double sin();
+static int bitrv();
+#endif
+
+fftr( x, m0, sine )
+double x[];
+int m0;
+double sine[];
+{
+int th, nd, pth, nj, dth, m;
+int n, n2, j, k, l, r;
+double xr, xi, tr, ti, co, si;
+double a, b, c, d, bc, cs, bs, cc;
+double *p, *q;
+
+/* Array x assumed filled with real-valued data */
+/* m0 = log2(n0) */
+/* n0 is the number of real data samples */
+
+if( m0 != msav )
+ {
+ msav = m0;
+
+ /* Find n0 = 2**m0 */
+ n0 = 1;
+ for( j=0; j<m0; j++ )
+ n0 <<= 1;
+
+ n4 = n0 >> 2;
+
+ /* Calculate array of sines */
+ xr = 2.0 * PI / n0;
+ for( j=0; j<=n4; j++ )
+ sine[j] = sin( j * xr );
+ }
+
+n = n0 >> 1; /* doing half length transform */
+m = m0 - 1;
+
+
+/* fftr.c */
+
+/* Complex Fourier Transform of n Complex Data Points */
+
+/* First, bit reverse the input data */
+
+for( k=0; k<n; k++ )
+ {
+ j = bitrv( k, m );
+ if( j > k )
+ { /* executed approx. n/2 times */
+ p = &x[2*k];
+ tr = *p++;
+ ti = *p;
+ q = &x[2*j+1];
+ *p = *q;
+ *(--p) = *(--q);
+ *q++ = tr;
+ *q = ti;
+ }
+ }
+
+/* fftr.c */
+/* Radix 2 Complex FFT */
+n2 = n/2;
+nj = 1;
+pth = 1;
+dth = 0;
+th = 0;
+
+for( l=0; l<m; l++ )
+ { /* executed log2(n) times, total */
+ j = 0;
+ do
+ { /* executed n-1 times, total */
+ r = th << 1;
+ si = sine[r];
+ co = sine[ n4 - r ];
+ if( j >= pth )
+ {
+ th -= dth;
+ co = -co;
+ }
+ else
+ th += dth;
+
+ nd = j;
+
+ do
+ { /* executed n/2 log2(n) times, total */
+ r = (nd << 1) + (nj << 1);
+ p = &x[ r ];
+ xr = *p++;
+ xi = *p;
+ tr = xr * co + xi * si;
+ ti = xi * co - xr * si;
+ r = nd << 1;
+ q = &x[ r ];
+ xr = *q++;
+ xi = *q;
+ *p = xi - ti;
+ *(--p) = xr - tr;
+ *q = xi + ti;
+ *(--q) = xr + tr;
+ nd += nj << 1;
+ }
+ while( nd < n );
+ }
+ while( ++j < nj );
+
+ n2 >>= 1;
+ dth = n2;
+ pth = nj;
+ nj <<= 1;
+ }
+
+/* fftr.c */
+
+/* Special trick algorithm */
+/* converts to spectrum of real series */
+
+/* Highest frequency term; add space to input array if wanted */
+/*
+x[2*n] = x[0] - x[1];
+x[2*n+1] = 0.0;
+*/
+
+/* Zero frequency term */
+x[0] = x[0] + x[1];
+x[1] = 0.0;
+n2 = n/2;
+
+for( j=1; j<=n2; j++ )
+ { /* executed n/2 times */
+ si = sine[j];
+ co = sine[ n4 - j ];
+ p = &x[ 2*j ];
+ xr = *p++;
+ xi = *p;
+ q = &x[ 2*(n-j) ];
+ tr = *q++;
+ ti = *q;
+ a = xr + tr;
+ b = xi + ti;
+ c = xr - tr;
+ d = xi - ti;
+ bc = b * co;
+ cs = c * si;
+ bs = b * si;
+ cc = c * co;
+ *p = ( d - bs - cc )/2.0;
+ *(--p) = ( a + bc - cs )/2.0;
+ *q = -( d + bs + cc )/2.0;
+ *(--q) = ( a - bc + cs )/2.0;
+ }
+
+return(0);
+}
+
+/* fftr.c */
+
+/* Bit reverser */
+
+int bitrv( j, m )
+int j, m;
+{
+register int j1, ans;
+short k;
+
+ans = 0;
+j1 = j;
+
+for( k=0; k<m; k++ )
+ {
+ ans = (ans << 1) + (j1 & 1);
+ j1 >>= 1;
+ }
+
+return( ans );
+}
diff --git a/libm/double/floor.c b/libm/double/floor.c
new file mode 100644
index 000000000..dcc1a10f1
--- /dev/null
+++ b/libm/double/floor.c
@@ -0,0 +1,453 @@
+/* ceil()
+ * floor()
+ * frexp()
+ * ldexp()
+ * signbit()
+ * isnan()
+ * isfinite()
+ *
+ * Floating point numeric utilities
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double ceil(), floor(), frexp(), ldexp();
+ * int signbit(), isnan(), isfinite();
+ * double x, y;
+ * int expnt, n;
+ *
+ * y = floor(x);
+ * y = ceil(x);
+ * y = frexp( x, &expnt );
+ * y = ldexp( x, n );
+ * n = signbit(x);
+ * n = isnan(x);
+ * n = isfinite(x);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * All four routines return a double precision floating point
+ * result.
+ *
+ * floor() returns the largest integer less than or equal to x.
+ * It truncates toward minus infinity.
+ *
+ * ceil() returns the smallest integer greater than or equal
+ * to x. It truncates toward plus infinity.
+ *
+ * frexp() extracts the exponent from x. It returns an integer
+ * power of two to expnt and the significand between 0.5 and 1
+ * to y. Thus x = y * 2**expn.
+ *
+ * ldexp() multiplies x by 2**n.
+ *
+ * signbit(x) returns 1 if the sign bit of x is 1, else 0.
+ *
+ * These functions are part of the standard C run time library
+ * for many but not all C compilers. The ones supplied are
+ * written in C for either DEC or IEEE arithmetic. They should
+ * be used only if your compiler library does not already have
+ * them.
+ *
+ * The IEEE versions assume that denormal numbers are implemented
+ * in the arithmetic. Some modifications will be required if
+ * the arithmetic has abrupt rather than gradual underflow.
+ */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef UNK
+/* ceil(), floor(), frexp(), ldexp() may need to be rewritten. */
+#undef UNK
+#if BIGENDIAN
+#define MIEEE 1
+#else
+#define IBMPC 1
+#endif
+#endif
+
+#ifdef DEC
+#define EXPMSK 0x807f
+#define MEXP 255
+#define NBITS 56
+#endif
+
+#ifdef IBMPC
+#define EXPMSK 0x800f
+#define MEXP 0x7ff
+#define NBITS 53
+#endif
+
+#ifdef MIEEE
+#define EXPMSK 0x800f
+#define MEXP 0x7ff
+#define NBITS 53
+#endif
+
+extern double MAXNUM, NEGZERO;
+#ifdef ANSIPROT
+double floor ( double );
+int isnan ( double );
+int isfinite ( double );
+double ldexp ( double, int );
+#else
+double floor();
+int isnan(), isfinite();
+double ldexp();
+#endif
+
+double ceil(x)
+double x;
+{
+double y;
+
+#ifdef UNK
+mtherr( "ceil", DOMAIN );
+return(0.0);
+#endif
+#ifdef NANS
+if( isnan(x) )
+ return( x );
+#endif
+#ifdef INFINITIES
+if(!isfinite(x))
+ return(x);
+#endif
+
+y = floor(x);
+if( y < x )
+ y += 1.0;
+#ifdef MINUSZERO
+if( y == 0.0 && x < 0.0 )
+ return( NEGZERO );
+#endif
+return(y);
+}
+
+
+
+
+/* Bit clearing masks: */
+
+static unsigned short bmask[] = {
+0xffff,
+0xfffe,
+0xfffc,
+0xfff8,
+0xfff0,
+0xffe0,
+0xffc0,
+0xff80,
+0xff00,
+0xfe00,
+0xfc00,
+0xf800,
+0xf000,
+0xe000,
+0xc000,
+0x8000,
+0x0000,
+};
+
+
+
+
+
+double floor(x)
+double x;
+{
+union
+ {
+ double y;
+ unsigned short sh[4];
+ } u;
+unsigned short *p;
+int e;
+
+#ifdef UNK
+mtherr( "floor", DOMAIN );
+return(0.0);
+#endif
+#ifdef NANS
+if( isnan(x) )
+ return( x );
+#endif
+#ifdef INFINITIES
+if(!isfinite(x))
+ return(x);
+#endif
+#ifdef MINUSZERO
+if(x == 0.0L)
+ return(x);
+#endif
+u.y = x;
+/* find the exponent (power of 2) */
+#ifdef DEC
+p = (unsigned short *)&u.sh[0];
+e = (( *p >> 7) & 0377) - 0201;
+p += 3;
+#endif
+
+#ifdef IBMPC
+p = (unsigned short *)&u.sh[3];
+e = (( *p >> 4) & 0x7ff) - 0x3ff;
+p -= 3;
+#endif
+
+#ifdef MIEEE
+p = (unsigned short *)&u.sh[0];
+e = (( *p >> 4) & 0x7ff) - 0x3ff;
+p += 3;
+#endif
+
+if( e < 0 )
+ {
+ if( u.y < 0.0 )
+ return( -1.0 );
+ else
+ return( 0.0 );
+ }
+
+e = (NBITS -1) - e;
+/* clean out 16 bits at a time */
+while( e >= 16 )
+ {
+#ifdef IBMPC
+ *p++ = 0;
+#endif
+
+#ifdef DEC
+ *p-- = 0;
+#endif
+
+#ifdef MIEEE
+ *p-- = 0;
+#endif
+ e -= 16;
+ }
+
+/* clear the remaining bits */
+if( e > 0 )
+ *p &= bmask[e];
+
+if( (x < 0) && (u.y != x) )
+ u.y -= 1.0;
+
+return(u.y);
+}
+
+
+
+
+double frexp( x, pw2 )
+double x;
+int *pw2;
+{
+union
+ {
+ double y;
+ unsigned short sh[4];
+ } u;
+int i;
+#ifdef DENORMAL
+int k;
+#endif
+short *q;
+
+u.y = x;
+
+#ifdef UNK
+mtherr( "frexp", DOMAIN );
+return(0.0);
+#endif
+
+#ifdef IBMPC
+q = (short *)&u.sh[3];
+#endif
+
+#ifdef DEC
+q = (short *)&u.sh[0];
+#endif
+
+#ifdef MIEEE
+q = (short *)&u.sh[0];
+#endif
+
+/* find the exponent (power of 2) */
+#ifdef DEC
+i = ( *q >> 7) & 0377;
+if( i == 0 )
+ {
+ *pw2 = 0;
+ return(0.0);
+ }
+i -= 0200;
+*pw2 = i;
+*q &= 0x807f; /* strip all exponent bits */
+*q |= 040000; /* mantissa between 0.5 and 1 */
+return(u.y);
+#endif
+
+#ifdef IBMPC
+i = ( *q >> 4) & 0x7ff;
+if( i != 0 )
+ goto ieeedon;
+#endif
+
+#ifdef MIEEE
+i = *q >> 4;
+i &= 0x7ff;
+if( i != 0 )
+ goto ieeedon;
+#ifdef DENORMAL
+
+#else
+*pw2 = 0;
+return(0.0);
+#endif
+
+#endif
+
+
+#ifndef DEC
+/* Number is denormal or zero */
+#ifdef DENORMAL
+if( u.y == 0.0 )
+ {
+ *pw2 = 0;
+ return( 0.0 );
+ }
+
+
+/* Handle denormal number. */
+do
+ {
+ u.y *= 2.0;
+ i -= 1;
+ k = ( *q >> 4) & 0x7ff;
+ }
+while( k == 0 );
+i = i + k;
+#endif /* DENORMAL */
+
+ieeedon:
+
+i -= 0x3fe;
+*pw2 = i;
+*q &= 0x800f;
+*q |= 0x3fe0;
+return( u.y );
+#endif
+}
+
+
+
+
+
+
+
+double ldexp( x, pw2 )
+double x;
+int pw2;
+{
+union
+ {
+ double y;
+ unsigned short sh[4];
+ } u;
+short *q;
+int e;
+
+#ifdef UNK
+mtherr( "ldexp", DOMAIN );
+return(0.0);
+#endif
+
+u.y = x;
+#ifdef DEC
+q = (short *)&u.sh[0];
+e = ( *q >> 7) & 0377;
+if( e == 0 )
+ return(0.0);
+#else
+
+#ifdef IBMPC
+q = (short *)&u.sh[3];
+#endif
+#ifdef MIEEE
+q = (short *)&u.sh[0];
+#endif
+while( (e = (*q & 0x7ff0) >> 4) == 0 )
+ {
+ if( u.y == 0.0 )
+ {
+ return( 0.0 );
+ }
+/* Input is denormal. */
+ if( pw2 > 0 )
+ {
+ u.y *= 2.0;
+ pw2 -= 1;
+ }
+ if( pw2 < 0 )
+ {
+ if( pw2 < -53 )
+ return(0.0);
+ u.y /= 2.0;
+ pw2 += 1;
+ }
+ if( pw2 == 0 )
+ return(u.y);
+ }
+#endif /* not DEC */
+
+e += pw2;
+
+/* Handle overflow */
+#ifdef DEC
+if( e > MEXP )
+ return( MAXNUM );
+#else
+if( e >= MEXP )
+ return( 2.0*MAXNUM );
+#endif
+
+/* Handle denormalized results */
+if( e < 1 )
+ {
+#ifdef DENORMAL
+ if( e < -53 )
+ return(0.0);
+ *q &= 0x800f;
+ *q |= 0x10;
+ /* For denormals, significant bits may be lost even
+ when dividing by 2. Construct 2^-(1-e) so the result
+ is obtained with only one multiplication. */
+ u.y *= ldexp(1.0, e-1);
+ return(u.y);
+#else
+ return(0.0);
+#endif
+ }
+else
+ {
+#ifdef DEC
+ *q &= 0x807f; /* strip all exponent bits */
+ *q |= (e & 0xff) << 7;
+#else
+ *q &= 0x800f;
+ *q |= (e & 0x7ff) << 4;
+#endif
+ return(u.y);
+ }
+}
diff --git a/libm/double/fltest.c b/libm/double/fltest.c
new file mode 100644
index 000000000..f2e3d8665
--- /dev/null
+++ b/libm/double/fltest.c
@@ -0,0 +1,272 @@
+/* fltest.c
+ * Test program for floor(), frexp(), ldexp()
+ */
+
+/*
+Cephes Math Library Release 2.1: December, 1988
+Copyright 1984, 1987, 1988 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+
+#include <math.h>
+extern double MACHEP;
+#define UTH -1023
+
+main()
+{
+double x, y, y0, z, f, x00, y00;
+int i, j, k, e, e0;
+int errfr, errld, errfl, underexp, err, errth, e00;
+double frexp(), ldexp(), floor();
+
+
+/*
+if( 1 )
+ goto flrtst;
+*/
+
+printf( "Testing frexp() and ldexp().\n" );
+errfr = 0;
+errld = 0;
+underexp = 0;
+f = 1.0;
+x00 = 2.0;
+y00 = 0.5;
+e00 = 2;
+
+for( j=0; j<20; j++ )
+{
+if( j == 10 )
+ {
+ f = 1.0;
+ x00 = 2.0;
+ e00 = 1;
+/* Find 2**(2**10) / 2 */
+#ifdef DEC
+ for( i=0; i<5; i++ )
+#else
+ for( i=0; i<9; i++ )
+#endif
+ {
+ x00 *= x00;
+ e00 += e00;
+ }
+ y00 = x00/2.0;
+ x00 = x00 * y00;
+ e00 += e00;
+ y00 = 0.5;
+ }
+x = x00 * f;
+y0 = y00 * f;
+e0 = e00;
+for( i=0; i<2200; i++ )
+ {
+ x /= 2.0;
+ e0 -= 1;
+ if( x == 0.0 )
+ {
+ if( f == 1.0 )
+ underexp = e0;
+ y0 = 0.0;
+ e0 = 0;
+ }
+ y = frexp( x, &e );
+ if( (e0 < -1023) && (e != e0) )
+ {
+ if( e == (e0 - 1) )
+ {
+ e += 1;
+ y /= 2.0;
+ }
+ if( e == (e0 + 1) )
+ {
+ e -= 1;
+ y *= 2.0;
+ }
+ }
+ err = y - y0;
+ if( y0 != 0.0 )
+ err /= y0;
+ if( err < 0.0 )
+ err = -err;
+ if( e0 > -1023 )
+ errth = 0.0;
+ else
+ {/* Denormal numbers may have rounding errors */
+ if( e0 == -1023 )
+ {
+ errth = 2.0 * MACHEP;
+ }
+ else
+ {
+ errth *= 2.0;
+ }
+ }
+
+ if( (x != 0.0) && ((err > errth) || (e != e0)) )
+ {
+ printf( "Test %d: ", j+1 );
+ printf( " frexp( %.15e) =?= %.15e * 2**%d;", x, y, e );
+ printf( " should be %.15e * 2**%d\n", y0, e0 );
+ errfr += 1;
+ }
+ y = ldexp( x, 1-e0 );
+ err = y - 1.0;
+ if( err < 0.0 )
+ err = -err;
+ if( (err > errth) && ((x == 0.0) && (y != 0.0)) )
+ {
+ printf( "Test %d: ", j+1 );
+ printf( "ldexp( %.15e, %d ) =?= %.15e;", x, 1-e0, y );
+ if( x != 0.0 )
+ printf( " should be %.15e\n", f );
+ else
+ printf( " should be %.15e\n", 0.0 );
+ errld += 1;
+ }
+ if( x == 0.0 )
+ {
+ break;
+ }
+ }
+f = f * 1.08005973889;
+}
+
+
+x = 2.22507385850720138309e-308;
+for (i = 0; i < 52; i++)
+ {
+ y = ldexp (x, -i);
+ z = ldexp (y, i);
+ if (x != z)
+ {
+ printf ("x %.16e, i %d, y %.16e, z %.16e\n", x, i, y, z);
+ errld += 1;
+ }
+ }
+
+
+if( (errld == 0) && (errfr == 0) )
+ {
+ printf( "No errors found.\n" );
+ }
+
+flrtst:
+
+printf( "Testing floor().\n" );
+errfl = 0;
+
+f = 1.0/MACHEP;
+x00 = 1.0;
+for( j=0; j<57; j++ )
+{
+x = x00 - 1.0;
+for( i=0; i<128; i++ )
+ {
+ y = floor(x);
+ if( y != x )
+ {
+ flierr( x, y, j );
+ errfl += 1;
+ }
+/* Warning! the if() statement is compiler dependent,
+ * since x-0.49 may be held in extra precision accumulator
+ * so would never compare equal to x! The subroutine call
+ * y = floor() forces z to be stored as a double and reloaded
+ * for the if() statement.
+ */
+ z = x - 0.49;
+ y = floor(z);
+ if( z == x )
+ break;
+ if( y != (x - 1.0) )
+ {
+ flierr( z, y, j );
+ errfl += 1;
+ }
+
+ z = x + 0.49;
+ y = floor(z);
+ if( z != x )
+ {
+ if( y != x )
+ {
+ flierr( z, y, j );
+ errfl += 1;
+ }
+ }
+ x = -x;
+ y = floor(x);
+ if( z != x )
+ {
+ if( y != x )
+ {
+ flierr( x, y, j );
+ errfl += 1;
+ }
+ }
+ z = x + 0.49;
+ y = floor(z);
+ if( z != x )
+ {
+ if( y != x )
+ {
+ flierr( z, y, j );
+ errfl += 1;
+ }
+ }
+ z = x - 0.49;
+ y = floor(z);
+ if( z != x )
+ {
+ if( y != (x - 1.0) )
+ {
+ flierr( z, y, j );
+ errfl += 1;
+ }
+ }
+ x = -x;
+ x += 1.0;
+ }
+x00 = x00 + x00;
+}
+y = floor(0.0);
+if( y != 0.0 )
+ {
+ flierr( 0.0, y, 57 );
+ errfl += 1;
+ }
+y = floor(-0.0);
+if( y != 0.0 )
+ {
+ flierr( -0.0, y, 58 );
+ errfl += 1;
+ }
+y = floor(-1.0);
+if( y != -1.0 )
+ {
+ flierr( -1.0, y, 59 );
+ errfl += 1;
+ }
+y = floor(-0.1);
+if( y != -1.0 )
+ {
+ flierr( -0.1, y, 60 );
+ errfl += 1;
+ }
+
+if( errfl == 0 )
+ printf( "No errors found in floor().\n" );
+
+}
+
+
+flierr( x, y, k )
+double x, y;
+int k;
+{
+printf( "Test %d: ", k+1 );
+printf( "floor(%.15e) =?= %.15e\n", x, y );
+}
diff --git a/libm/double/fltest2.c b/libm/double/fltest2.c
new file mode 100644
index 000000000..405b81b6a
--- /dev/null
+++ b/libm/double/fltest2.c
@@ -0,0 +1,18 @@
+int drand();
+double exp(), frexp(), ldexp();
+volatile double x, y, z;
+
+main()
+{
+int i, e;
+
+for( i=0; i<100000; i++ )
+ {
+ drand(&x);
+ x = exp( 10.0*(x - 1.5) );
+ y = frexp( x, &e );
+ z = ldexp( y, e );
+ if( z != x )
+ abort();
+ }
+}
diff --git a/libm/double/fltest3.c b/libm/double/fltest3.c
new file mode 100644
index 000000000..f3025777e
--- /dev/null
+++ b/libm/double/fltest3.c
@@ -0,0 +1,259 @@
+/* fltest.c
+ * Test program for floor(), frexp(), ldexp()
+ */
+
+/*
+Cephes Math Library Release 2.1: December, 1988
+Copyright 1984, 1987, 1988 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+
+#include <math.h>
+/*extern double MACHEP;*/
+#define MACHEP 2.3e-16
+#define UTH -1023
+
+main()
+{
+double x, y, y0, z, f, x00, y00;
+int i, j, k, e, e0;
+int errfr, errld, errfl, underexp, err, errth, e00;
+double frexp(), ldexp(), floor();
+
+
+/*
+if( 1 )
+ goto flrtst;
+*/
+
+printf( "Testing frexp() and ldexp().\n" );
+errfr = 0;
+errld = 0;
+underexp = 0;
+f = 1.0;
+x00 = 2.0;
+y00 = 0.5;
+e00 = 2;
+
+for( j=0; j<20; j++ )
+{
+if( j == 10 )
+ {
+ f = 1.0;
+ x00 = 2.0;
+ e00 = 1;
+/* Find 2**(2**10) / 2 */
+#ifdef DEC
+ for( i=0; i<5; i++ )
+#else
+ for( i=0; i<9; i++ )
+#endif
+ {
+ x00 *= x00;
+ e00 += e00;
+ }
+ y00 = x00/2.0;
+ x00 = x00 * y00;
+ e00 += e00;
+ y00 = 0.5;
+ }
+x = x00 * f;
+y0 = y00 * f;
+e0 = e00;
+for( i=0; i<2200; i++ )
+ {
+ x /= 2.0;
+ e0 -= 1;
+ if( x == 0.0 )
+ {
+ if( f == 1.0 )
+ underexp = e0;
+ y0 = 0.0;
+ e0 = 0;
+ }
+ y = frexp( x, &e );
+ if( (e0 < -1023) && (e != e0) )
+ {
+ if( e == (e0 - 1) )
+ {
+ e += 1;
+ y /= 2.0;
+ }
+ if( e == (e0 + 1) )
+ {
+ e -= 1;
+ y *= 2.0;
+ }
+ }
+ err = y - y0;
+ if( y0 != 0.0 )
+ err /= y0;
+ if( err < 0.0 )
+ err = -err;
+ if( e0 > -1023 )
+ errth = 0.0;
+ else
+ {/* Denormal numbers may have rounding errors */
+ if( e0 == -1023 )
+ {
+ errth = 2.0 * MACHEP;
+ }
+ else
+ {
+ errth *= 2.0;
+ }
+ }
+
+ if( (x != 0.0) && ((err > errth) || (e != e0)) )
+ {
+ printf( "Test %d: ", j+1 );
+ printf( " frexp( %.15e) =?= %.15e * 2**%d;", x, y, e );
+ printf( " should be %.15e * 2**%d\n", y0, e0 );
+ errfr += 1;
+ }
+ y = ldexp( x, 1-e0 );
+ err = y - 1.0;
+ if( err < 0.0 )
+ err = -err;
+ if( (err > errth) && ((x == 0.0) && (y != 0.0)) )
+ {
+ printf( "Test %d: ", j+1 );
+ printf( "ldexp( %.15e, %d ) =?= %.15e;", x, 1-e0, y );
+ if( x != 0.0 )
+ printf( " should be %.15e\n", f );
+ else
+ printf( " should be %.15e\n", 0.0 );
+ errld += 1;
+ }
+ if( x == 0.0 )
+ {
+ break;
+ }
+ }
+f = f * 1.08005973889;
+}
+
+if( (errld == 0) && (errfr == 0) )
+ {
+ printf( "No errors found.\n" );
+ }
+
+flrtst:
+
+printf( "Testing floor().\n" );
+errfl = 0;
+
+f = 1.0/MACHEP;
+x00 = 1.0;
+for( j=0; j<57; j++ )
+{
+x = x00 - 1.0;
+for( i=0; i<128; i++ )
+ {
+ y = floor(x);
+ if( y != x )
+ {
+ flierr( x, y, j );
+ errfl += 1;
+ }
+/* Warning! the if() statement is compiler dependent,
+ * since x-0.49 may be held in extra precision accumulator
+ * so would never compare equal to x! The subroutine call
+ * y = floor() forces z to be stored as a double and reloaded
+ * for the if() statement.
+ */
+ z = x - 0.49;
+ y = floor(z);
+ if( z == x )
+ break;
+ if( y != (x - 1.0) )
+ {
+ flierr( z, y, j );
+ errfl += 1;
+ }
+
+ z = x + 0.49;
+ y = floor(z);
+ if( z != x )
+ {
+ if( y != x )
+ {
+ flierr( z, y, j );
+ errfl += 1;
+ }
+ }
+ x = -x;
+ y = floor(x);
+ if( z != x )
+ {
+ if( y != x )
+ {
+ flierr( x, y, j );
+ errfl += 1;
+ }
+ }
+ z = x + 0.49;
+ y = floor(z);
+ if( z != x )
+ {
+ if( y != x )
+ {
+ flierr( z, y, j );
+ errfl += 1;
+ }
+ }
+ z = x - 0.49;
+ y = floor(z);
+ if( z != x )
+ {
+ if( y != (x - 1.0) )
+ {
+ flierr( z, y, j );
+ errfl += 1;
+ }
+ }
+ x = -x;
+ x += 1.0;
+ }
+x00 = x00 + x00;
+}
+y = floor(0.0);
+if( y != 0.0 )
+ {
+ flierr( 0.0, y, 57 );
+ errfl += 1;
+ }
+y = floor(-0.0);
+if( y != 0.0 )
+ {
+ flierr( -0.0, y, 58 );
+ errfl += 1;
+ }
+y = floor(-1.0);
+if( y != -1.0 )
+ {
+ flierr( -1.0, y, 59 );
+ errfl += 1;
+ }
+y = floor(-0.1);
+if( y != -1.0 )
+ {
+ flierr( -0.1, y, 60 );
+ errfl += 1;
+ }
+
+if( errfl == 0 )
+ printf( "No errors found in floor().\n" );
+
+}
+
+
+flierr( x, y, k )
+double x, y;
+int k;
+{
+printf( "Test %d: ", k+1 );
+printf( "floor(%.15e) =?= %.15e\n", x, y );
+}
diff --git a/libm/double/fresnl.c b/libm/double/fresnl.c
new file mode 100644
index 000000000..0872d107a
--- /dev/null
+++ b/libm/double/fresnl.c
@@ -0,0 +1,515 @@
+/* fresnl.c
+ *
+ * Fresnel integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, S, C;
+ * void fresnl();
+ *
+ * fresnl( x, _&S, _&C );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the Fresnel integrals
+ *
+ * x
+ * -
+ * | |
+ * C(x) = | cos(pi/2 t**2) dt,
+ * | |
+ * -
+ * 0
+ *
+ * x
+ * -
+ * | |
+ * S(x) = | sin(pi/2 t**2) dt.
+ * | |
+ * -
+ * 0
+ *
+ *
+ * The integrals are evaluated by a power series for x < 1.
+ * For x >= 1 auxiliary functions f(x) and g(x) are employed
+ * such that
+ *
+ * C(x) = 0.5 + f(x) sin( pi/2 x**2 ) - g(x) cos( pi/2 x**2 )
+ * S(x) = 0.5 - f(x) cos( pi/2 x**2 ) - g(x) sin( pi/2 x**2 )
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error.
+ *
+ * Arithmetic function domain # trials peak rms
+ * IEEE S(x) 0, 10 10000 2.0e-15 3.2e-16
+ * IEEE C(x) 0, 10 10000 1.8e-15 3.3e-16
+ * DEC S(x) 0, 10 6000 2.2e-16 3.9e-17
+ * DEC C(x) 0, 10 5000 2.3e-16 3.9e-17
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* S(x) for small x */
+#ifdef UNK
+static double sn[6] = {
+-2.99181919401019853726E3,
+ 7.08840045257738576863E5,
+-6.29741486205862506537E7,
+ 2.54890880573376359104E9,
+-4.42979518059697779103E10,
+ 3.18016297876567817986E11,
+};
+static double sd[6] = {
+/* 1.00000000000000000000E0,*/
+ 2.81376268889994315696E2,
+ 4.55847810806532581675E4,
+ 5.17343888770096400730E6,
+ 4.19320245898111231129E8,
+ 2.24411795645340920940E10,
+ 6.07366389490084639049E11,
+};
+#endif
+#ifdef DEC
+static unsigned short sn[24] = {
+0143072,0176433,0065455,0127034,
+0045055,0007200,0134540,0026661,
+0146560,0035061,0023667,0127545,
+0050027,0166503,0002673,0153756,
+0151045,0002721,0121737,0102066,
+0051624,0013177,0033451,0021271,
+};
+static unsigned short sd[24] = {
+/*0040200,0000000,0000000,0000000,*/
+0042214,0130051,0112070,0101617,
+0044062,0010307,0172346,0152510,
+0045635,0160575,0143200,0136642,
+0047307,0171215,0127457,0052361,
+0050647,0031447,0032621,0013510,
+0052015,0064733,0117362,0012653,
+};
+#endif
+#ifdef IBMPC
+static unsigned short sn[24] = {
+0xb5c3,0x6d65,0x5fa3,0xc0a7,
+0x05b6,0x172c,0xa1d0,0x4125,
+0xf5ed,0x24f6,0x0746,0xc18e,
+0x7afe,0x60b7,0xfda8,0x41e2,
+0xf087,0x347b,0xa0ba,0xc224,
+0x2457,0xe6e5,0x82cf,0x4252,
+};
+static unsigned short sd[24] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x1072,0x3287,0x9605,0x4071,
+0xdaa9,0xfe9c,0x4218,0x40e6,
+0x17b4,0xb8d0,0xbc2f,0x4153,
+0xea9e,0xb5e5,0xfe51,0x41b8,
+0x22e9,0xe6b2,0xe664,0x4214,
+0x42b5,0x73de,0xad3b,0x4261,
+};
+#endif
+#ifdef MIEEE
+static unsigned short sn[24] = {
+0xc0a7,0x5fa3,0x6d65,0xb5c3,
+0x4125,0xa1d0,0x172c,0x05b6,
+0xc18e,0x0746,0x24f6,0xf5ed,
+0x41e2,0xfda8,0x60b7,0x7afe,
+0xc224,0xa0ba,0x347b,0xf087,
+0x4252,0x82cf,0xe6e5,0x2457,
+};
+static unsigned short sd[24] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4071,0x9605,0x3287,0x1072,
+0x40e6,0x4218,0xfe9c,0xdaa9,
+0x4153,0xbc2f,0xb8d0,0x17b4,
+0x41b8,0xfe51,0xb5e5,0xea9e,
+0x4214,0xe664,0xe6b2,0x22e9,
+0x4261,0xad3b,0x73de,0x42b5,
+};
+#endif
+
+/* C(x) for small x */
+#ifdef UNK
+static double cn[6] = {
+-4.98843114573573548651E-8,
+ 9.50428062829859605134E-6,
+-6.45191435683965050962E-4,
+ 1.88843319396703850064E-2,
+-2.05525900955013891793E-1,
+ 9.99999999999999998822E-1,
+};
+static double cd[7] = {
+ 3.99982968972495980367E-12,
+ 9.15439215774657478799E-10,
+ 1.25001862479598821474E-7,
+ 1.22262789024179030997E-5,
+ 8.68029542941784300606E-4,
+ 4.12142090722199792936E-2,
+ 1.00000000000000000118E0,
+};
+#endif
+#ifdef DEC
+static unsigned short cn[24] = {
+0132126,0040141,0063733,0013231,
+0034037,0072223,0010200,0075637,
+0135451,0021020,0073264,0036057,
+0036632,0131520,0101316,0060233,
+0137522,0072541,0136124,0132202,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short cd[28] = {
+0026614,0135503,0051776,0032631,
+0030573,0121116,0154033,0126712,
+0032406,0034100,0012442,0106212,
+0034115,0017567,0150520,0164623,
+0035543,0106171,0177336,0146351,
+0037050,0150073,0000607,0171635,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short cn[24] = {
+0x62d3,0x2cfb,0xc80c,0xbe6a,
+0x0f74,0x6210,0xee92,0x3ee3,
+0x8786,0x0ed6,0x2442,0xbf45,
+0xcc13,0x1059,0x566a,0x3f93,
+0x9690,0x378a,0x4eac,0xbfca,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short cd[28] = {
+0xc6b3,0x6a7f,0x9768,0x3d91,
+0x75b9,0xdb03,0x7449,0x3e0f,
+0x5191,0x02a4,0xc708,0x3e80,
+0x1d32,0xfa2a,0xa3ee,0x3ee9,
+0xd99d,0x3fdb,0x718f,0x3f4c,
+0xfe74,0x6030,0x1a07,0x3fa5,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short cn[24] = {
+0xbe6a,0xc80c,0x2cfb,0x62d3,
+0x3ee3,0xee92,0x6210,0x0f74,
+0xbf45,0x2442,0x0ed6,0x8786,
+0x3f93,0x566a,0x1059,0xcc13,
+0xbfca,0x4eac,0x378a,0x9690,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short cd[28] = {
+0x3d91,0x9768,0x6a7f,0xc6b3,
+0x3e0f,0x7449,0xdb03,0x75b9,
+0x3e80,0xc708,0x02a4,0x5191,
+0x3ee9,0xa3ee,0xfa2a,0x1d32,
+0x3f4c,0x718f,0x3fdb,0xd99d,
+0x3fa5,0x1a07,0x6030,0xfe74,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+
+/* Auxiliary function f(x) */
+#ifdef UNK
+static double fn[10] = {
+ 4.21543555043677546506E-1,
+ 1.43407919780758885261E-1,
+ 1.15220955073585758835E-2,
+ 3.45017939782574027900E-4,
+ 4.63613749287867322088E-6,
+ 3.05568983790257605827E-8,
+ 1.02304514164907233465E-10,
+ 1.72010743268161828879E-13,
+ 1.34283276233062758925E-16,
+ 3.76329711269987889006E-20,
+};
+static double fd[10] = {
+/* 1.00000000000000000000E0,*/
+ 7.51586398353378947175E-1,
+ 1.16888925859191382142E-1,
+ 6.44051526508858611005E-3,
+ 1.55934409164153020873E-4,
+ 1.84627567348930545870E-6,
+ 1.12699224763999035261E-8,
+ 3.60140029589371370404E-11,
+ 5.88754533621578410010E-14,
+ 4.52001434074129701496E-17,
+ 1.25443237090011264384E-20,
+};
+#endif
+#ifdef DEC
+static unsigned short fn[40] = {
+0037727,0152216,0106601,0016214,
+0037422,0154606,0112710,0071355,
+0036474,0143453,0154253,0166545,
+0035264,0161606,0022250,0073743,
+0033633,0110036,0024653,0136246,
+0032003,0036652,0041164,0036413,
+0027740,0174122,0046305,0036726,
+0025501,0125270,0121317,0167667,
+0023032,0150555,0076175,0047443,
+0020061,0133570,0070130,0027657,
+};
+static unsigned short fd[40] = {
+/*0040200,0000000,0000000,0000000,*/
+0040100,0063767,0054413,0151452,
+0037357,0061566,0007243,0065754,
+0036323,0005365,0033552,0133625,
+0035043,0101123,0000275,0165402,
+0033367,0146614,0110623,0023647,
+0031501,0116644,0125222,0144263,
+0027436,0062051,0117235,0001411,
+0025204,0111543,0056370,0036201,
+0022520,0071351,0015227,0122144,
+0017554,0172240,0112713,0005006,
+};
+#endif
+#ifdef IBMPC
+static unsigned short fn[40] = {
+0x2391,0xd1b0,0xfa91,0x3fda,
+0x0e5e,0xd2b9,0x5b30,0x3fc2,
+0x7dad,0x7b15,0x98e5,0x3f87,
+0x0efc,0xc495,0x9c70,0x3f36,
+0x7795,0xc535,0x7203,0x3ed3,
+0x87a1,0x484e,0x67b5,0x3e60,
+0xa7bb,0x4998,0x1f0a,0x3ddc,
+0xfdf7,0x1459,0x3557,0x3d48,
+0xa9e4,0xaf8f,0x5a2d,0x3ca3,
+0x05f6,0x0e0b,0x36ef,0x3be6,
+};
+static unsigned short fd[40] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x7a65,0xeb21,0x0cfe,0x3fe8,
+0x6d7d,0xc1d4,0xec6e,0x3fbd,
+0x56f3,0xa6ed,0x615e,0x3f7a,
+0xbd60,0x6017,0x704a,0x3f24,
+0x64f5,0x9232,0xf9b1,0x3ebe,
+0x5916,0x9552,0x33b4,0x3e48,
+0xa061,0x33d3,0xcc85,0x3dc3,
+0x0790,0x6b9f,0x926c,0x3d30,
+0xf48d,0x2352,0x0e5d,0x3c8a,
+0x6141,0x12b9,0x9e94,0x3bcd,
+};
+#endif
+#ifdef MIEEE
+static unsigned short fn[40] = {
+0x3fda,0xfa91,0xd1b0,0x2391,
+0x3fc2,0x5b30,0xd2b9,0x0e5e,
+0x3f87,0x98e5,0x7b15,0x7dad,
+0x3f36,0x9c70,0xc495,0x0efc,
+0x3ed3,0x7203,0xc535,0x7795,
+0x3e60,0x67b5,0x484e,0x87a1,
+0x3ddc,0x1f0a,0x4998,0xa7bb,
+0x3d48,0x3557,0x1459,0xfdf7,
+0x3ca3,0x5a2d,0xaf8f,0xa9e4,
+0x3be6,0x36ef,0x0e0b,0x05f6,
+};
+static unsigned short fd[40] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x3fe8,0x0cfe,0xeb21,0x7a65,
+0x3fbd,0xec6e,0xc1d4,0x6d7d,
+0x3f7a,0x615e,0xa6ed,0x56f3,
+0x3f24,0x704a,0x6017,0xbd60,
+0x3ebe,0xf9b1,0x9232,0x64f5,
+0x3e48,0x33b4,0x9552,0x5916,
+0x3dc3,0xcc85,0x33d3,0xa061,
+0x3d30,0x926c,0x6b9f,0x0790,
+0x3c8a,0x0e5d,0x2352,0xf48d,
+0x3bcd,0x9e94,0x12b9,0x6141,
+};
+#endif
+
+
+/* Auxiliary function g(x) */
+#ifdef UNK
+static double gn[11] = {
+ 5.04442073643383265887E-1,
+ 1.97102833525523411709E-1,
+ 1.87648584092575249293E-2,
+ 6.84079380915393090172E-4,
+ 1.15138826111884280931E-5,
+ 9.82852443688422223854E-8,
+ 4.45344415861750144738E-10,
+ 1.08268041139020870318E-12,
+ 1.37555460633261799868E-15,
+ 8.36354435630677421531E-19,
+ 1.86958710162783235106E-22,
+};
+static double gd[11] = {
+/* 1.00000000000000000000E0,*/
+ 1.47495759925128324529E0,
+ 3.37748989120019970451E-1,
+ 2.53603741420338795122E-2,
+ 8.14679107184306179049E-4,
+ 1.27545075667729118702E-5,
+ 1.04314589657571990585E-7,
+ 4.60680728146520428211E-10,
+ 1.10273215066240270757E-12,
+ 1.38796531259578871258E-15,
+ 8.39158816283118707363E-19,
+ 1.86958710162783236342E-22,
+};
+#endif
+#ifdef DEC
+static unsigned short gn[44] = {
+0040001,0021435,0120406,0053123,
+0037511,0152523,0037703,0122011,
+0036631,0134302,0122721,0110235,
+0035463,0051712,0043215,0114732,
+0034101,0025677,0147725,0057630,
+0032323,0010342,0067523,0002206,
+0030364,0152247,0110007,0054107,
+0026230,0057654,0035464,0047124,
+0023706,0036401,0167705,0045440,
+0021166,0154447,0105632,0142461,
+0016142,0002353,0011175,0170530,
+};
+static unsigned short gd[44] = {
+/*0040200,0000000,0000000,0000000,*/
+0040274,0145551,0016742,0127005,
+0037654,0166557,0076416,0015165,
+0036717,0140217,0030675,0050111,
+0035525,0110060,0076405,0070502,
+0034125,0176061,0060120,0031730,
+0032340,0001615,0054343,0120501,
+0030375,0041414,0070747,0107060,
+0026233,0031034,0160757,0074526,
+0023710,0003341,0137100,0144664,
+0021167,0126414,0023774,0015435,
+0016142,0002353,0011175,0170530,
+};
+#endif
+#ifdef IBMPC
+static unsigned short gn[44] = {
+0xcaca,0xb420,0x2463,0x3fe0,
+0x7481,0x67f8,0x3aaa,0x3fc9,
+0x3214,0x54ba,0x3718,0x3f93,
+0xb33b,0x48d1,0x6a79,0x3f46,
+0xabf3,0xf9fa,0x2577,0x3ee8,
+0x6091,0x4dea,0x621c,0x3e7a,
+0xeb09,0xf200,0x9a94,0x3dfe,
+0x89cb,0x8766,0x0bf5,0x3d73,
+0xa964,0x3df8,0xc7a0,0x3cd8,
+0x58a6,0xf173,0xdb24,0x3c2e,
+0xbe2b,0x624f,0x409d,0x3b6c,
+};
+static unsigned short gd[44] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x55c1,0x23bc,0x996d,0x3ff7,
+0xc34f,0xefa1,0x9dad,0x3fd5,
+0xaa09,0xe637,0xf811,0x3f99,
+0xae28,0x0fa0,0xb206,0x3f4a,
+0x067b,0x2c0a,0xbf86,0x3eea,
+0x7428,0xab1c,0x0071,0x3e7c,
+0xf1c6,0x8e3c,0xa861,0x3dff,
+0xef2b,0x9c3d,0x6643,0x3d73,
+0x1936,0x37c8,0x00dc,0x3cd9,
+0x8364,0x84ff,0xf5a1,0x3c2e,
+0xbe2b,0x624f,0x409d,0x3b6c,
+};
+#endif
+#ifdef MIEEE
+static unsigned short gn[44] = {
+0x3fe0,0x2463,0xb420,0xcaca,
+0x3fc9,0x3aaa,0x67f8,0x7481,
+0x3f93,0x3718,0x54ba,0x3214,
+0x3f46,0x6a79,0x48d1,0xb33b,
+0x3ee8,0x2577,0xf9fa,0xabf3,
+0x3e7a,0x621c,0x4dea,0x6091,
+0x3dfe,0x9a94,0xf200,0xeb09,
+0x3d73,0x0bf5,0x8766,0x89cb,
+0x3cd8,0xc7a0,0x3df8,0xa964,
+0x3c2e,0xdb24,0xf173,0x58a6,
+0x3b6c,0x409d,0x624f,0xbe2b,
+};
+static unsigned short gd[44] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x3ff7,0x996d,0x23bc,0x55c1,
+0x3fd5,0x9dad,0xefa1,0xc34f,
+0x3f99,0xf811,0xe637,0xaa09,
+0x3f4a,0xb206,0x0fa0,0xae28,
+0x3eea,0xbf86,0x2c0a,0x067b,
+0x3e7c,0x0071,0xab1c,0x7428,
+0x3dff,0xa861,0x8e3c,0xf1c6,
+0x3d73,0x6643,0x9c3d,0xef2b,
+0x3cd9,0x00dc,0x37c8,0x1936,
+0x3c2e,0xf5a1,0x84ff,0x8364,
+0x3b6c,0x409d,0x624f,0xbe2b,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double cos ( double );
+extern double sin ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+#else
+double fabs(), cos(), sin(), polevl(), p1evl();
+#endif
+extern double PI, PIO2, MACHEP;
+
+int fresnl( xxa, ssa, cca )
+double xxa, *ssa, *cca;
+{
+double f, g, cc, ss, c, s, t, u;
+double x, x2;
+
+x = fabs(xxa);
+x2 = x * x;
+if( x2 < 2.5625 )
+ {
+ t = x2 * x2;
+ ss = x * x2 * polevl( t, sn, 5)/p1evl( t, sd, 6 );
+ cc = x * polevl( t, cn, 5)/polevl(t, cd, 6 );
+ goto done;
+ }
+
+
+
+
+
+
+if( x > 36974.0 )
+ {
+ cc = 0.5;
+ ss = 0.5;
+ goto done;
+ }
+
+
+/* Asymptotic power series auxiliary functions
+ * for large argument
+ */
+ x2 = x * x;
+ t = PI * x2;
+ u = 1.0/(t * t);
+ t = 1.0/t;
+ f = 1.0 - u * polevl( u, fn, 9)/p1evl(u, fd, 10);
+ g = t * polevl( u, gn, 10)/p1evl(u, gd, 11);
+
+ t = PIO2 * x2;
+ c = cos(t);
+ s = sin(t);
+ t = PI * x;
+ cc = 0.5 + (f * s - g * c)/t;
+ ss = 0.5 - (f * c + g * s)/t;
+
+done:
+if( xxa < 0.0 )
+ {
+ cc = -cc;
+ ss = -ss;
+ }
+
+*cca = cc;
+*ssa = ss;
+return(0);
+}
diff --git a/libm/double/gamma.c b/libm/double/gamma.c
new file mode 100644
index 000000000..341b4e915
--- /dev/null
+++ b/libm/double/gamma.c
@@ -0,0 +1,685 @@
+/* gamma.c
+ *
+ * Gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, gamma();
+ * extern int sgngam;
+ *
+ * y = gamma( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns gamma function of the argument. The result is
+ * correctly signed, and the sign (+1 or -1) is also
+ * returned in a global (extern) variable named sgngam.
+ * This variable is also filled in by the logarithmic gamma
+ * function lgam().
+ *
+ * Arguments |x| <= 34 are reduced by recurrence and the function
+ * approximated by a rational function of degree 6/7 in the
+ * interval (2,3). Large arguments are handled by Stirling's
+ * formula. Large negative arguments are made positive using
+ * a reflection formula.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -34, 34 10000 1.3e-16 2.5e-17
+ * IEEE -170,-33 20000 2.3e-15 3.3e-16
+ * IEEE -33, 33 20000 9.4e-16 2.2e-16
+ * IEEE 33, 171.6 20000 2.3e-15 3.2e-16
+ *
+ * Error for arguments outside the test range will be larger
+ * owing to error amplification by the exponential function.
+ *
+ */
+/* lgam()
+ *
+ * Natural logarithm of gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, lgam();
+ * extern int sgngam;
+ *
+ * y = lgam( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of the absolute
+ * value of the gamma function of the argument.
+ * The sign (+1 or -1) of the gamma function is returned in a
+ * global (extern) variable named sgngam.
+ *
+ * For arguments greater than 13, the logarithm of the gamma
+ * function is approximated by the logarithmic version of
+ * Stirling's formula using a polynomial approximation of
+ * degree 4. Arguments between -33 and +33 are reduced by
+ * recurrence to the interval [2,3] of a rational approximation.
+ * The cosecant reflection formula is employed for arguments
+ * less than -33.
+ *
+ * Arguments greater than MAXLGM return MAXNUM and an error
+ * message. MAXLGM = 2.035093e36 for DEC
+ * arithmetic or 2.556348e305 for IEEE arithmetic.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * arithmetic domain # trials peak rms
+ * DEC 0, 3 7000 5.2e-17 1.3e-17
+ * DEC 2.718, 2.035e36 5000 3.9e-17 9.9e-18
+ * IEEE 0, 3 28000 5.4e-16 1.1e-16
+ * IEEE 2.718, 2.556e305 40000 3.5e-16 8.3e-17
+ * The error criterion was relative when the function magnitude
+ * was greater than one but absolute when it was less than one.
+ *
+ * The following test used the relative error criterion, though
+ * at certain points the relative error could be much higher than
+ * indicated.
+ * IEEE -200, -4 10000 4.8e-16 1.3e-16
+ *
+ */
+
+/* gamma.c */
+/* gamma function */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+ 1.60119522476751861407E-4,
+ 1.19135147006586384913E-3,
+ 1.04213797561761569935E-2,
+ 4.76367800457137231464E-2,
+ 2.07448227648435975150E-1,
+ 4.94214826801497100753E-1,
+ 9.99999999999999996796E-1
+};
+static double Q[] = {
+-2.31581873324120129819E-5,
+ 5.39605580493303397842E-4,
+-4.45641913851797240494E-3,
+ 1.18139785222060435552E-2,
+ 3.58236398605498653373E-2,
+-2.34591795718243348568E-1,
+ 7.14304917030273074085E-2,
+ 1.00000000000000000320E0
+};
+#define MAXGAM 171.624376956302725
+static double LOGPI = 1.14472988584940017414;
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0035047,0162701,0146301,0005234,
+0035634,0023437,0032065,0176530,
+0036452,0137157,0047330,0122574,
+0037103,0017310,0143041,0017232,
+0037524,0066516,0162563,0164605,
+0037775,0004671,0146237,0014222,
+0040200,0000000,0000000,0000000
+};
+static unsigned short Q[] = {
+0134302,0041724,0020006,0116565,
+0035415,0072121,0044251,0025634,
+0136222,0003447,0035205,0121114,
+0036501,0107552,0154335,0104271,
+0037022,0135717,0014776,0171471,
+0137560,0034324,0165024,0037021,
+0037222,0045046,0047151,0161213,
+0040200,0000000,0000000,0000000
+};
+#define MAXGAM 34.84425627277176174
+static unsigned short LPI[4] = {
+0040222,0103202,0043475,0006750,
+};
+#define LOGPI *(double *)LPI
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x2153,0x3998,0xfcb8,0x3f24,
+0xbfab,0xe686,0x84e3,0x3f53,
+0x14b0,0xe9db,0x57cd,0x3f85,
+0x23d3,0x18c4,0x63d9,0x3fa8,
+0x7d31,0xdcae,0x8da9,0x3fca,
+0xe312,0x3993,0xa137,0x3fdf,
+0x0000,0x0000,0x0000,0x3ff0
+};
+static unsigned short Q[] = {
+0xd3af,0x8400,0x487a,0xbef8,
+0x2573,0x2915,0xae8a,0x3f41,
+0xb44a,0xe750,0x40e4,0xbf72,
+0xb117,0x5b1b,0x31ed,0x3f88,
+0xde67,0xe33f,0x5779,0x3fa2,
+0x87c2,0x9d42,0x071a,0xbfce,
+0x3c51,0xc9cd,0x4944,0x3fb2,
+0x0000,0x0000,0x0000,0x3ff0
+};
+#define MAXGAM 171.624376956302725
+static unsigned short LPI[4] = {
+0xa1bd,0x48e7,0x50d0,0x3ff2,
+};
+#define LOGPI *(double *)LPI
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f24,0xfcb8,0x3998,0x2153,
+0x3f53,0x84e3,0xe686,0xbfab,
+0x3f85,0x57cd,0xe9db,0x14b0,
+0x3fa8,0x63d9,0x18c4,0x23d3,
+0x3fca,0x8da9,0xdcae,0x7d31,
+0x3fdf,0xa137,0x3993,0xe312,
+0x3ff0,0x0000,0x0000,0x0000
+};
+static unsigned short Q[] = {
+0xbef8,0x487a,0x8400,0xd3af,
+0x3f41,0xae8a,0x2915,0x2573,
+0xbf72,0x40e4,0xe750,0xb44a,
+0x3f88,0x31ed,0x5b1b,0xb117,
+0x3fa2,0x5779,0xe33f,0xde67,
+0xbfce,0x071a,0x9d42,0x87c2,
+0x3fb2,0x4944,0xc9cd,0x3c51,
+0x3ff0,0x0000,0x0000,0x0000
+};
+#define MAXGAM 171.624376956302725
+static unsigned short LPI[4] = {
+0x3ff2,0x50d0,0x48e7,0xa1bd,
+};
+#define LOGPI *(double *)LPI
+#endif
+
+/* Stirling's formula for the gamma function */
+#if UNK
+static double STIR[5] = {
+ 7.87311395793093628397E-4,
+-2.29549961613378126380E-4,
+-2.68132617805781232825E-3,
+ 3.47222221605458667310E-3,
+ 8.33333333333482257126E-2,
+};
+#define MAXSTIR 143.01608
+static double SQTPI = 2.50662827463100050242E0;
+#endif
+#if DEC
+static unsigned short STIR[20] = {
+0035516,0061622,0144553,0112224,
+0135160,0131531,0037460,0165740,
+0136057,0134460,0037242,0077270,
+0036143,0107070,0156306,0027751,
+0037252,0125252,0125252,0146064,
+};
+#define MAXSTIR 26.77
+static unsigned short SQT[4] = {
+0040440,0066230,0177661,0034055,
+};
+#define SQTPI *(double *)SQT
+#endif
+#if IBMPC
+static unsigned short STIR[20] = {
+0x7293,0x592d,0xcc72,0x3f49,
+0x1d7c,0x27e6,0x166b,0xbf2e,
+0x4fd7,0x07d4,0xf726,0xbf65,
+0xc5fd,0x1b98,0x71c7,0x3f6c,
+0x5986,0x5555,0x5555,0x3fb5,
+};
+#define MAXSTIR 143.01608
+static unsigned short SQT[4] = {
+0x2706,0x1ff6,0x0d93,0x4004,
+};
+#define SQTPI *(double *)SQT
+#endif
+#if MIEEE
+static unsigned short STIR[20] = {
+0x3f49,0xcc72,0x592d,0x7293,
+0xbf2e,0x166b,0x27e6,0x1d7c,
+0xbf65,0xf726,0x07d4,0x4fd7,
+0x3f6c,0x71c7,0x1b98,0xc5fd,
+0x3fb5,0x5555,0x5555,0x5986,
+};
+#define MAXSTIR 143.01608
+static unsigned short SQT[4] = {
+0x4004,0x0d93,0x1ff6,0x2706,
+};
+#define SQTPI *(double *)SQT
+#endif
+
+int sgngam = 0;
+extern int sgngam;
+extern double MAXLOG, MAXNUM, PI;
+#ifdef ANSIPROT
+extern double pow ( double, double );
+extern double log ( double );
+extern double exp ( double );
+extern double sin ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double floor ( double );
+extern double fabs ( double );
+extern int isnan ( double );
+extern int isfinite ( double );
+static double stirf ( double );
+double lgam ( double );
+#else
+double pow(), log(), exp(), sin(), polevl(), p1evl(), floor(), fabs();
+int isnan(), isfinite();
+static double stirf();
+double lgam();
+#endif
+#ifdef INFINITIES
+extern double INFINITY;
+#endif
+#ifdef NANS
+extern double NAN;
+#endif
+
+/* Gamma function computed by Stirling's formula.
+ * The polynomial STIR is valid for 33 <= x <= 172.
+ */
+static double stirf(x)
+double x;
+{
+double y, w, v;
+
+w = 1.0/x;
+w = 1.0 + w * polevl( w, STIR, 4 );
+y = exp(x);
+if( x > MAXSTIR )
+ { /* Avoid overflow in pow() */
+ v = pow( x, 0.5 * x - 0.25 );
+ y = v * (v / y);
+ }
+else
+ {
+ y = pow( x, x - 0.5 ) / y;
+ }
+y = SQTPI * y * w;
+return( y );
+}
+
+
+
+double gamma(x)
+double x;
+{
+double p, q, z;
+int i;
+
+sgngam = 1;
+#ifdef NANS
+if( isnan(x) )
+ return(x);
+#endif
+#ifdef INFINITIES
+#ifdef NANS
+if( x == INFINITY )
+ return(x);
+if( x == -INFINITY )
+ return(NAN);
+#else
+if( !isfinite(x) )
+ return(x);
+#endif
+#endif
+q = fabs(x);
+
+if( q > 33.0 )
+ {
+ if( x < 0.0 )
+ {
+ p = floor(q);
+ if( p == q )
+ {
+#ifdef NANS
+gamnan:
+ mtherr( "gamma", DOMAIN );
+ return (NAN);
+#else
+ goto goverf;
+#endif
+ }
+ i = p;
+ if( (i & 1) == 0 )
+ sgngam = -1;
+ z = q - p;
+ if( z > 0.5 )
+ {
+ p += 1.0;
+ z = q - p;
+ }
+ z = q * sin( PI * z );
+ if( z == 0.0 )
+ {
+#ifdef INFINITIES
+ return( sgngam * INFINITY);
+#else
+goverf:
+ mtherr( "gamma", OVERFLOW );
+ return( sgngam * MAXNUM);
+#endif
+ }
+ z = fabs(z);
+ z = PI/(z * stirf(q) );
+ }
+ else
+ {
+ z = stirf(x);
+ }
+ return( sgngam * z );
+ }
+
+z = 1.0;
+while( x >= 3.0 )
+ {
+ x -= 1.0;
+ z *= x;
+ }
+
+while( x < 0.0 )
+ {
+ if( x > -1.E-9 )
+ goto small;
+ z /= x;
+ x += 1.0;
+ }
+
+while( x < 2.0 )
+ {
+ if( x < 1.e-9 )
+ goto small;
+ z /= x;
+ x += 1.0;
+ }
+
+if( x == 2.0 )
+ return(z);
+
+x -= 2.0;
+p = polevl( x, P, 6 );
+q = polevl( x, Q, 7 );
+return( z * p / q );
+
+small:
+if( x == 0.0 )
+ {
+#ifdef INFINITIES
+#ifdef NANS
+ goto gamnan;
+#else
+ return( INFINITY );
+#endif
+#else
+ mtherr( "gamma", SING );
+ return( MAXNUM );
+#endif
+ }
+else
+ return( z/((1.0 + 0.5772156649015329 * x) * x) );
+}
+
+
+
+/* A[]: Stirling's formula expansion of log gamma
+ * B[], C[]: log gamma function between 2 and 3
+ */
+#ifdef UNK
+static double A[] = {
+ 8.11614167470508450300E-4,
+-5.95061904284301438324E-4,
+ 7.93650340457716943945E-4,
+-2.77777777730099687205E-3,
+ 8.33333333333331927722E-2
+};
+static double B[] = {
+-1.37825152569120859100E3,
+-3.88016315134637840924E4,
+-3.31612992738871184744E5,
+-1.16237097492762307383E6,
+-1.72173700820839662146E6,
+-8.53555664245765465627E5
+};
+static double C[] = {
+/* 1.00000000000000000000E0, */
+-3.51815701436523470549E2,
+-1.70642106651881159223E4,
+-2.20528590553854454839E5,
+-1.13933444367982507207E6,
+-2.53252307177582951285E6,
+-2.01889141433532773231E6
+};
+/* log( sqrt( 2*pi ) ) */
+static double LS2PI = 0.91893853320467274178;
+#define MAXLGM 2.556348e305
+#endif
+
+#ifdef DEC
+static unsigned short A[] = {
+0035524,0141201,0034633,0031405,
+0135433,0176755,0126007,0045030,
+0035520,0006371,0003342,0172730,
+0136066,0005540,0132605,0026407,
+0037252,0125252,0125252,0125132
+};
+static unsigned short B[] = {
+0142654,0044014,0077633,0035410,
+0144027,0110641,0125335,0144760,
+0144641,0165637,0142204,0047447,
+0145215,0162027,0146246,0155211,
+0145322,0026110,0010317,0110130,
+0145120,0061472,0120300,0025363
+};
+static unsigned short C[] = {
+/*0040200,0000000,0000000,0000000*/
+0142257,0164150,0163630,0112622,
+0143605,0050153,0156116,0135272,
+0144527,0056045,0145642,0062332,
+0145213,0012063,0106250,0001025,
+0145432,0111254,0044577,0115142,
+0145366,0071133,0050217,0005122
+};
+/* log( sqrt( 2*pi ) ) */
+static unsigned short LS2P[] = {040153,037616,041445,0172645,};
+#define LS2PI *(double *)LS2P
+#define MAXLGM 2.035093e36
+#endif
+
+#ifdef IBMPC
+static unsigned short A[] = {
+0x6661,0x2733,0x9850,0x3f4a,
+0xe943,0xb580,0x7fbd,0xbf43,
+0x5ebb,0x20dc,0x019f,0x3f4a,
+0xa5a1,0x16b0,0xc16c,0xbf66,
+0x554b,0x5555,0x5555,0x3fb5
+};
+static unsigned short B[] = {
+0x6761,0x8ff3,0x8901,0xc095,
+0xb93e,0x355b,0xf234,0xc0e2,
+0x89e5,0xf890,0x3d73,0xc114,
+0xdb51,0xf994,0xbc82,0xc131,
+0xf20b,0x0219,0x4589,0xc13a,
+0x055e,0x5418,0x0c67,0xc12a
+};
+static unsigned short C[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x12b2,0x1cf3,0xfd0d,0xc075,
+0xd757,0x7b89,0xaa0d,0xc0d0,
+0x4c9b,0xb974,0xeb84,0xc10a,
+0x0043,0x7195,0x6286,0xc131,
+0xf34c,0x892f,0x5255,0xc143,
+0xe14a,0x6a11,0xce4b,0xc13e
+};
+/* log( sqrt( 2*pi ) ) */
+static unsigned short LS2P[] = {
+0xbeb5,0xc864,0x67f1,0x3fed
+};
+#define LS2PI *(double *)LS2P
+#define MAXLGM 2.556348e305
+#endif
+
+#ifdef MIEEE
+static unsigned short A[] = {
+0x3f4a,0x9850,0x2733,0x6661,
+0xbf43,0x7fbd,0xb580,0xe943,
+0x3f4a,0x019f,0x20dc,0x5ebb,
+0xbf66,0xc16c,0x16b0,0xa5a1,
+0x3fb5,0x5555,0x5555,0x554b
+};
+static unsigned short B[] = {
+0xc095,0x8901,0x8ff3,0x6761,
+0xc0e2,0xf234,0x355b,0xb93e,
+0xc114,0x3d73,0xf890,0x89e5,
+0xc131,0xbc82,0xf994,0xdb51,
+0xc13a,0x4589,0x0219,0xf20b,
+0xc12a,0x0c67,0x5418,0x055e
+};
+static unsigned short C[] = {
+0xc075,0xfd0d,0x1cf3,0x12b2,
+0xc0d0,0xaa0d,0x7b89,0xd757,
+0xc10a,0xeb84,0xb974,0x4c9b,
+0xc131,0x6286,0x7195,0x0043,
+0xc143,0x5255,0x892f,0xf34c,
+0xc13e,0xce4b,0x6a11,0xe14a
+};
+/* log( sqrt( 2*pi ) ) */
+static unsigned short LS2P[] = {
+0x3fed,0x67f1,0xc864,0xbeb5
+};
+#define LS2PI *(double *)LS2P
+#define MAXLGM 2.556348e305
+#endif
+
+
+/* Logarithm of gamma function */
+
+
+double lgam(x)
+double x;
+{
+double p, q, u, w, z;
+int i;
+
+sgngam = 1;
+#ifdef NANS
+if( isnan(x) )
+ return(x);
+#endif
+
+#ifdef INFINITIES
+if( !isfinite(x) )
+ return(INFINITY);
+#endif
+
+if( x < -34.0 )
+ {
+ q = -x;
+ w = lgam(q); /* note this modifies sgngam! */
+ p = floor(q);
+ if( p == q )
+ {
+lgsing:
+#ifdef INFINITIES
+ mtherr( "lgam", SING );
+ return (INFINITY);
+#else
+ goto loverf;
+#endif
+ }
+ i = p;
+ if( (i & 1) == 0 )
+ sgngam = -1;
+ else
+ sgngam = 1;
+ z = q - p;
+ if( z > 0.5 )
+ {
+ p += 1.0;
+ z = p - q;
+ }
+ z = q * sin( PI * z );
+ if( z == 0.0 )
+ goto lgsing;
+/* z = log(PI) - log( z ) - w;*/
+ z = LOGPI - log( z ) - w;
+ return( z );
+ }
+
+if( x < 13.0 )
+ {
+ z = 1.0;
+ p = 0.0;
+ u = x;
+ while( u >= 3.0 )
+ {
+ p -= 1.0;
+ u = x + p;
+ z *= u;
+ }
+ while( u < 2.0 )
+ {
+ if( u == 0.0 )
+ goto lgsing;
+ z /= u;
+ p += 1.0;
+ u = x + p;
+ }
+ if( z < 0.0 )
+ {
+ sgngam = -1;
+ z = -z;
+ }
+ else
+ sgngam = 1;
+ if( u == 2.0 )
+ return( log(z) );
+ p -= 2.0;
+ x = x + p;
+ p = x * polevl( x, B, 5 ) / p1evl( x, C, 6);
+ return( log(z) + p );
+ }
+
+if( x > MAXLGM )
+ {
+#ifdef INFINITIES
+ return( sgngam * INFINITY );
+#else
+loverf:
+ mtherr( "lgam", OVERFLOW );
+ return( sgngam * MAXNUM );
+#endif
+ }
+
+q = ( x - 0.5 ) * log(x) - x + LS2PI;
+if( x > 1.0e8 )
+ return( q );
+
+p = 1.0/(x*x);
+if( x >= 1000.0 )
+ q += (( 7.9365079365079365079365e-4 * p
+ - 2.7777777777777777777778e-3) *p
+ + 0.0833333333333333333333) / x;
+else
+ q += polevl( p, A, 4 ) / x;
+return( q );
+}
diff --git a/libm/double/gdtr.c b/libm/double/gdtr.c
new file mode 100644
index 000000000..6b27d9abb
--- /dev/null
+++ b/libm/double/gdtr.c
@@ -0,0 +1,130 @@
+/* gdtr.c
+ *
+ * Gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, gdtr();
+ *
+ * y = gdtr( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from zero to x of the gamma probability
+ * density function:
+ *
+ *
+ * x
+ * b -
+ * a | | b-1 -at
+ * y = ----- | t e dt
+ * - | |
+ * | (b) -
+ * 0
+ *
+ * The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igam( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * gdtr domain x < 0 0.0
+ *
+ */
+ /* gdtrc.c
+ *
+ * Complemented gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, gdtrc();
+ *
+ * y = gdtrc( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from x to infinity of the gamma
+ * probability density function:
+ *
+ *
+ * inf.
+ * b -
+ * a | | b-1 -at
+ * y = ----- | t e dt
+ * - | |
+ * | (b) -
+ * x
+ *
+ * The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igamc( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * gdtrc domain x < 0 0.0
+ *
+ */
+
+/* gdtr() */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double igam ( double, double );
+extern double igamc ( double, double );
+#else
+double igam(), igamc();
+#endif
+
+double gdtr( a, b, x )
+double a, b, x;
+{
+
+if( x < 0.0 )
+ {
+ mtherr( "gdtr", DOMAIN );
+ return( 0.0 );
+ }
+return( igam( b, a * x ) );
+}
+
+
+
+double gdtrc( a, b, x )
+double a, b, x;
+{
+
+if( x < 0.0 )
+ {
+ mtherr( "gdtrc", DOMAIN );
+ return( 0.0 );
+ }
+return( igamc( b, a * x ) );
+}
diff --git a/libm/double/gels.c b/libm/double/gels.c
new file mode 100644
index 000000000..4d548d050
--- /dev/null
+++ b/libm/double/gels.c
@@ -0,0 +1,232 @@
+/*
+C
+C ..................................................................
+C
+C SUBROUTINE GELS
+C
+C PURPOSE
+C TO SOLVE A SYSTEM OF SIMULTANEOUS LINEAR EQUATIONS WITH
+C SYMMETRIC COEFFICIENT MATRIX UPPER TRIANGULAR PART OF WHICH
+C IS ASSUMED TO BE STORED COLUMNWISE.
+C
+C USAGE
+C CALL GELS(R,A,M,N,EPS,IER,AUX)
+C
+C DESCRIPTION OF PARAMETERS
+C R - M BY N RIGHT HAND SIDE MATRIX. (DESTROYED)
+C ON RETURN R CONTAINS THE SOLUTION OF THE EQUATIONS.
+C A - UPPER TRIANGULAR PART OF THE SYMMETRIC
+C M BY M COEFFICIENT MATRIX. (DESTROYED)
+C M - THE NUMBER OF EQUATIONS IN THE SYSTEM.
+C N - THE NUMBER OF RIGHT HAND SIDE VECTORS.
+C EPS - AN INPUT CONSTANT WHICH IS USED AS RELATIVE
+C TOLERANCE FOR TEST ON LOSS OF SIGNIFICANCE.
+C IER - RESULTING ERROR PARAMETER CODED AS FOLLOWS
+C IER=0 - NO ERROR,
+C IER=-1 - NO RESULT BECAUSE OF M LESS THAN 1 OR
+C PIVOT ELEMENT AT ANY ELIMINATION STEP
+C EQUAL TO 0,
+C IER=K - WARNING DUE TO POSSIBLE LOSS OF SIGNIFI-
+C CANCE INDICATED AT ELIMINATION STEP K+1,
+C WHERE PIVOT ELEMENT WAS LESS THAN OR
+C EQUAL TO THE INTERNAL TOLERANCE EPS TIMES
+C ABSOLUTELY GREATEST MAIN DIAGONAL
+C ELEMENT OF MATRIX A.
+C AUX - AN AUXILIARY STORAGE ARRAY WITH DIMENSION M-1.
+C
+C REMARKS
+C UPPER TRIANGULAR PART OF MATRIX A IS ASSUMED TO BE STORED
+C COLUMNWISE IN M*(M+1)/2 SUCCESSIVE STORAGE LOCATIONS, RIGHT
+C HAND SIDE MATRIX R COLUMNWISE IN N*M SUCCESSIVE STORAGE
+C LOCATIONS. ON RETURN SOLUTION MATRIX R IS STORED COLUMNWISE
+C TOO.
+C THE PROCEDURE GIVES RESULTS IF THE NUMBER OF EQUATIONS M IS
+C GREATER THAN 0 AND PIVOT ELEMENTS AT ALL ELIMINATION STEPS
+C ARE DIFFERENT FROM 0. HOWEVER WARNING IER=K - IF GIVEN -
+C INDICATES POSSIBLE LOSS OF SIGNIFICANCE. IN CASE OF A WELL
+C SCALED MATRIX A AND APPROPRIATE TOLERANCE EPS, IER=K MAY BE
+C INTERPRETED THAT MATRIX A HAS THE RANK K. NO WARNING IS
+C GIVEN IN CASE M=1.
+C ERROR PARAMETER IER=-1 DOES NOT NECESSARILY MEAN THAT
+C MATRIX A IS SINGULAR, AS ONLY MAIN DIAGONAL ELEMENTS
+C ARE USED AS PIVOT ELEMENTS. POSSIBLY SUBROUTINE GELG (WHICH
+C WORKS WITH TOTAL PIVOTING) WOULD BE ABLE TO FIND A SOLUTION.
+C
+C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
+C NONE
+C
+C METHOD
+C SOLUTION IS DONE BY MEANS OF GAUSS-ELIMINATION WITH
+C PIVOTING IN MAIN DIAGONAL, IN ORDER TO PRESERVE
+C SYMMETRY IN REMAINING COEFFICIENT MATRICES.
+C
+C ..................................................................
+C
+*/
+#include <math.h>
+#ifdef ANSIPROT
+extern double fabs ( double );
+#else
+double fabs();
+#endif
+
+gels( A, R, M, EPS, AUX )
+double A[],R[];
+int M;
+double EPS;
+double AUX[];
+{
+int I, J, K, L, IER;
+int II, LL, LLD, LR, LT, LST, LLST, LEND;
+double tb, piv, tol, pivi;
+
+if( M <= 0 )
+ {
+fatal:
+ IER = -1;
+ goto done;
+ }
+/* SEARCH FOR GREATEST MAIN DIAGONAL ELEMENT */
+
+/* Diagonal elements are at A(i,i) = 1, 3, 6, 10, ...
+ * A(i,j) = A( i(i-1)/2 + j )
+ */
+IER = 0;
+piv = 0.0;
+L = 0;
+for( K=1; K<=M; K++ )
+ {
+ L += K;
+ tb = fabs( A[L-1] );
+ if( tb > piv )
+ {
+ piv = tb;
+ I = L;
+ J = K;
+ }
+ }
+tol = EPS * piv;
+
+/*
+C MAIN DIAGONAL ELEMENT A(I)=A(J,J) IS FIRST PIVOT ELEMENT.
+C PIV CONTAINS THE ABSOLUTE VALUE OF A(I).
+*/
+
+/* START ELIMINATION LOOP */
+LST = 0;
+LEND = M - 1;
+for( K=1; K<=M; K++ )
+ {
+/* TEST ON USEFULNESS OF SYMMETRIC ALGORITHM */
+ if( piv <= 0.0 )
+ goto fatal;
+ if( IER == 0 )
+ {
+ if( piv <= tol )
+ {
+ IER = K - 1;
+ }
+ }
+ LT = J - K;
+ LST += K;
+
+/* PIVOT ROW REDUCTION AND ROW INTERCHANGE IN RIGHT HAND SIDE R */
+ pivi = 1.0 / A[I-1];
+ L = K;
+ LL = L + LT;
+ tb = pivi * R[LL-1];
+ R[LL-1] = R[L-1];
+ R[L-1] = tb;
+/* IS ELIMINATION TERMINATED */
+ if( K >= M )
+ break;
+/*
+C ROW AND COLUMN INTERCHANGE AND PIVOT ROW REDUCTION IN MATRIX A.
+C ELEMENTS OF PIVOT COLUMN ARE SAVED IN AUXILIARY VECTOR AUX.
+*/
+ LR = LST + (LT*(K+J-1))/2;
+ LL = LR;
+ L=LST;
+ for( II=K; II<=LEND; II++ )
+ {
+ L += II;
+ LL += 1;
+ if( L == LR )
+ {
+ A[LL-1] = A[LST-1];
+ tb = A[L-1];
+ goto lab13;
+ }
+ if( L > LR )
+ LL = L + LT;
+
+ tb = A[LL-1];
+ A[LL-1] = A[L-1];
+lab13:
+ AUX[II-1] = tb;
+ A[L-1] = pivi * tb;
+ }
+/* SAVE COLUMN INTERCHANGE INFORMATION */
+ A[LST-1] = LT;
+/* ELEMENT REDUCTION AND SEARCH FOR NEXT PIVOT */
+ piv = 0.0;
+ LLST = LST;
+ LT = 0;
+ for( II=K; II<=LEND; II++ )
+ {
+ pivi = -AUX[II-1];
+ LL = LLST;
+ LT += 1;
+ for( LLD=II; LLD<=LEND; LLD++ )
+ {
+ LL += LLD;
+ L = LL + LT;
+ A[L-1] += pivi * A[LL-1];
+ }
+ LLST += II;
+ LR = LLST + LT;
+ tb =fabs( A[LR-1] );
+ if( tb > piv )
+ {
+ piv = tb;
+ I = LR;
+ J = II + 1;
+ }
+ LR = K;
+ LL = LR + LT;
+ R[LL-1] += pivi * R[LR-1];
+ }
+ }
+/* END OF ELIMINATION LOOP */
+
+/* BACK SUBSTITUTION AND BACK INTERCHANGE */
+
+if( LEND <= 0 )
+ {
+ if( LEND < 0 )
+ goto fatal;
+ goto done;
+ }
+II = M;
+for( I=2; I<=M; I++ )
+ {
+ LST -= II;
+ II -= 1;
+ L = A[LST-1] + 0.5;
+ J = II;
+ tb = R[J-1];
+ LL = J;
+ K = LST;
+ for( LT=II; LT<=LEND; LT++ )
+ {
+ LL += 1;
+ K += LT;
+ tb -= A[K-1] * R[LL-1];
+ }
+ K = J + L;
+ R[J-1] = R[K-1];
+ R[K-1] = tb;
+ }
+done:
+return( IER );
+}
diff --git a/libm/double/hyp2f1.c b/libm/double/hyp2f1.c
new file mode 100644
index 000000000..f2e93106c
--- /dev/null
+++ b/libm/double/hyp2f1.c
@@ -0,0 +1,460 @@
+/* hyp2f1.c
+ *
+ * Gauss hypergeometric function F
+ * 2 1
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, c, x, y, hyp2f1();
+ *
+ * y = hyp2f1( a, b, c, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * hyp2f1( a, b, c, x ) = F ( a, b; c; x )
+ * 2 1
+ *
+ * inf.
+ * - a(a+1)...(a+k) b(b+1)...(b+k) k+1
+ * = 1 + > ----------------------------- x .
+ * - c(c+1)...(c+k) (k+1)!
+ * k = 0
+ *
+ * Cases addressed are
+ * Tests and escapes for negative integer a, b, or c
+ * Linear transformation if c - a or c - b negative integer
+ * Special case c = a or c = b
+ * Linear transformation for x near +1
+ * Transformation for x < -0.5
+ * Psi function expansion if x > 0.5 and c - a - b integer
+ * Conditionally, a recurrence on c to make c-a-b > 0
+ *
+ * |x| > 1 is rejected.
+ *
+ * The parameters a, b, c are considered to be integer
+ * valued if they are within 1.0e-14 of the nearest integer
+ * (1.0e-13 for IEEE arithmetic).
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error (-1 < x < 1):
+ * arithmetic domain # trials peak rms
+ * IEEE -1,7 230000 1.2e-11 5.2e-14
+ *
+ * Several special cases also tested with a, b, c in
+ * the range -7 to 7.
+ *
+ * ERROR MESSAGES:
+ *
+ * A "partial loss of precision" message is printed if
+ * the internally estimated relative error exceeds 1^-12.
+ * A "singularity" message is printed on overflow or
+ * in cases not addressed (such as x < -1).
+ */
+
+/* hyp2f1 */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef DEC
+#define EPS 1.0e-14
+#define EPS2 1.0e-11
+#endif
+
+#ifdef IBMPC
+#define EPS 1.0e-13
+#define EPS2 1.0e-10
+#endif
+
+#ifdef MIEEE
+#define EPS 1.0e-13
+#define EPS2 1.0e-10
+#endif
+
+#ifdef UNK
+#define EPS 1.0e-13
+#define EPS2 1.0e-10
+#endif
+
+#define ETHRESH 1.0e-12
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double pow ( double, double );
+extern double round ( double );
+extern double gamma ( double );
+extern double log ( double );
+extern double exp ( double );
+extern double psi ( double );
+static double hyt2f1(double, double, double, double, double *);
+static double hys2f1(double, double, double, double, double *);
+double hyp2f1(double, double, double, double);
+#else
+double fabs(), pow(), round(), gamma(), log(), exp(), psi();
+static double hyt2f1();
+static double hys2f1();
+double hyp2f1();
+#endif
+extern double MAXNUM, MACHEP;
+
+double hyp2f1( a, b, c, x )
+double a, b, c, x;
+{
+double d, d1, d2, e;
+double p, q, r, s, y, ax;
+double ia, ib, ic, id, err;
+int flag, i, aid;
+
+err = 0.0;
+ax = fabs(x);
+s = 1.0 - x;
+flag = 0;
+ia = round(a); /* nearest integer to a */
+ib = round(b);
+
+if( a <= 0 )
+ {
+ if( fabs(a-ia) < EPS ) /* a is a negative integer */
+ flag |= 1;
+ }
+
+if( b <= 0 )
+ {
+ if( fabs(b-ib) < EPS ) /* b is a negative integer */
+ flag |= 2;
+ }
+
+if( ax < 1.0 )
+ {
+ if( fabs(b-c) < EPS ) /* b = c */
+ {
+ y = pow( s, -a ); /* s to the -a power */
+ goto hypdon;
+ }
+ if( fabs(a-c) < EPS ) /* a = c */
+ {
+ y = pow( s, -b ); /* s to the -b power */
+ goto hypdon;
+ }
+ }
+
+
+
+if( c <= 0.0 )
+ {
+ ic = round(c); /* nearest integer to c */
+ if( fabs(c-ic) < EPS ) /* c is a negative integer */
+ {
+ /* check if termination before explosion */
+ if( (flag & 1) && (ia > ic) )
+ goto hypok;
+ if( (flag & 2) && (ib > ic) )
+ goto hypok;
+ goto hypdiv;
+ }
+ }
+
+if( flag ) /* function is a polynomial */
+ goto hypok;
+
+if( ax > 1.0 ) /* series diverges */
+ goto hypdiv;
+
+p = c - a;
+ia = round(p); /* nearest integer to c-a */
+if( (ia <= 0.0) && (fabs(p-ia) < EPS) ) /* negative int c - a */
+ flag |= 4;
+
+r = c - b;
+ib = round(r); /* nearest integer to c-b */
+if( (ib <= 0.0) && (fabs(r-ib) < EPS) ) /* negative int c - b */
+ flag |= 8;
+
+d = c - a - b;
+id = round(d); /* nearest integer to d */
+q = fabs(d-id);
+
+/* Thanks to Christian Burger <BURGER@DMRHRZ11.HRZ.Uni-Marburg.DE>
+ * for reporting a bug here. */
+if( fabs(ax-1.0) < EPS ) /* |x| == 1.0 */
+ {
+ if( x > 0.0 )
+ {
+ if( flag & 12 ) /* negative int c-a or c-b */
+ {
+ if( d >= 0.0 )
+ goto hypf;
+ else
+ goto hypdiv;
+ }
+ if( d <= 0.0 )
+ goto hypdiv;
+ y = gamma(c)*gamma(d)/(gamma(p)*gamma(r));
+ goto hypdon;
+ }
+
+ if( d <= -1.0 )
+ goto hypdiv;
+
+ }
+
+/* Conditionally make d > 0 by recurrence on c
+ * AMS55 #15.2.27
+ */
+if( d < 0.0 )
+ {
+/* Try the power series first */
+ y = hyt2f1( a, b, c, x, &err );
+ if( err < ETHRESH )
+ goto hypdon;
+/* Apply the recurrence if power series fails */
+ err = 0.0;
+ aid = 2 - id;
+ e = c + aid;
+ d2 = hyp2f1(a,b,e,x);
+ d1 = hyp2f1(a,b,e+1.0,x);
+ q = a + b + 1.0;
+ for( i=0; i<aid; i++ )
+ {
+ r = e - 1.0;
+ y = (e*(r-(2.0*e-q)*x)*d2 + (e-a)*(e-b)*x*d1)/(e*r*s);
+ e = r;
+ d1 = d2;
+ d2 = y;
+ }
+ goto hypdon;
+ }
+
+
+if( flag & 12 )
+ goto hypf; /* negative integer c-a or c-b */
+
+hypok:
+y = hyt2f1( a, b, c, x, &err );
+
+
+hypdon:
+if( err > ETHRESH )
+ {
+ mtherr( "hyp2f1", PLOSS );
+/* printf( "Estimated err = %.2e\n", err ); */
+ }
+return(y);
+
+/* The transformation for c-a or c-b negative integer
+ * AMS55 #15.3.3
+ */
+hypf:
+y = pow( s, d ) * hys2f1( c-a, c-b, c, x, &err );
+goto hypdon;
+
+/* The alarm exit */
+hypdiv:
+mtherr( "hyp2f1", OVERFLOW );
+return( MAXNUM );
+}
+
+
+
+
+
+
+/* Apply transformations for |x| near 1
+ * then call the power series
+ */
+static double hyt2f1( a, b, c, x, loss )
+double a, b, c, x;
+double *loss;
+{
+double p, q, r, s, t, y, d, err, err1;
+double ax, id, d1, d2, e, y1;
+int i, aid;
+
+err = 0.0;
+s = 1.0 - x;
+if( x < -0.5 )
+ {
+ if( b > a )
+ y = pow( s, -a ) * hys2f1( a, c-b, c, -x/s, &err );
+
+ else
+ y = pow( s, -b ) * hys2f1( c-a, b, c, -x/s, &err );
+
+ goto done;
+ }
+
+d = c - a - b;
+id = round(d); /* nearest integer to d */
+
+if( x > 0.9 )
+{
+if( fabs(d-id) > EPS ) /* test for integer c-a-b */
+ {
+/* Try the power series first */
+ y = hys2f1( a, b, c, x, &err );
+ if( err < ETHRESH )
+ goto done;
+/* If power series fails, then apply AMS55 #15.3.6 */
+ q = hys2f1( a, b, 1.0-d, s, &err );
+ q *= gamma(d) /(gamma(c-a) * gamma(c-b));
+ r = pow(s,d) * hys2f1( c-a, c-b, d+1.0, s, &err1 );
+ r *= gamma(-d)/(gamma(a) * gamma(b));
+ y = q + r;
+
+ q = fabs(q); /* estimate cancellation error */
+ r = fabs(r);
+ if( q > r )
+ r = q;
+ err += err1 + (MACHEP*r)/y;
+
+ y *= gamma(c);
+ goto done;
+ }
+else
+ {
+/* Psi function expansion, AMS55 #15.3.10, #15.3.11, #15.3.12 */
+ if( id >= 0.0 )
+ {
+ e = d;
+ d1 = d;
+ d2 = 0.0;
+ aid = id;
+ }
+ else
+ {
+ e = -d;
+ d1 = 0.0;
+ d2 = d;
+ aid = -id;
+ }
+
+ ax = log(s);
+
+ /* sum for t = 0 */
+ y = psi(1.0) + psi(1.0+e) - psi(a+d1) - psi(b+d1) - ax;
+ y /= gamma(e+1.0);
+
+ p = (a+d1) * (b+d1) * s / gamma(e+2.0); /* Poch for t=1 */
+ t = 1.0;
+ do
+ {
+ r = psi(1.0+t) + psi(1.0+t+e) - psi(a+t+d1)
+ - psi(b+t+d1) - ax;
+ q = p * r;
+ y += q;
+ p *= s * (a+t+d1) / (t+1.0);
+ p *= (b+t+d1) / (t+1.0+e);
+ t += 1.0;
+ }
+ while( fabs(q/y) > EPS );
+
+
+ if( id == 0.0 )
+ {
+ y *= gamma(c)/(gamma(a)*gamma(b));
+ goto psidon;
+ }
+
+ y1 = 1.0;
+
+ if( aid == 1 )
+ goto nosum;
+
+ t = 0.0;
+ p = 1.0;
+ for( i=1; i<aid; i++ )
+ {
+ r = 1.0-e+t;
+ p *= s * (a+t+d2) * (b+t+d2) / r;
+ t += 1.0;
+ p /= t;
+ y1 += p;
+ }
+nosum:
+ p = gamma(c);
+ y1 *= gamma(e) * p / (gamma(a+d1) * gamma(b+d1));
+
+ y *= p / (gamma(a+d2) * gamma(b+d2));
+ if( (aid & 1) != 0 )
+ y = -y;
+
+ q = pow( s, id ); /* s to the id power */
+ if( id > 0.0 )
+ y *= q;
+ else
+ y1 *= q;
+
+ y += y1;
+psidon:
+ goto done;
+ }
+
+}
+
+/* Use defining power series if no special cases */
+y = hys2f1( a, b, c, x, &err );
+
+done:
+*loss = err;
+return(y);
+}
+
+
+
+
+
+/* Defining power series expansion of Gauss hypergeometric function */
+
+static double hys2f1( a, b, c, x, loss )
+double a, b, c, x;
+double *loss; /* estimates loss of significance */
+{
+double f, g, h, k, m, s, u, umax;
+int i;
+
+i = 0;
+umax = 0.0;
+f = a;
+g = b;
+h = c;
+s = 1.0;
+u = 1.0;
+k = 0.0;
+do
+ {
+ if( fabs(h) < EPS )
+ {
+ *loss = 1.0;
+ return( MAXNUM );
+ }
+ m = k + 1.0;
+ u = u * ((f+k) * (g+k) * x / ((h+k) * m));
+ s += u;
+ k = fabs(u); /* remember largest term summed */
+ if( k > umax )
+ umax = k;
+ k = m;
+ if( ++i > 10000 ) /* should never happen */
+ {
+ *loss = 1.0;
+ return(s);
+ }
+ }
+while( fabs(u/s) > MACHEP );
+
+/* return estimated relative error */
+*loss = (MACHEP*umax)/fabs(s) + (MACHEP*i);
+
+return(s);
+}
diff --git a/libm/double/hyperg.c b/libm/double/hyperg.c
new file mode 100644
index 000000000..36a3f9781
--- /dev/null
+++ b/libm/double/hyperg.c
@@ -0,0 +1,386 @@
+/* hyperg.c
+ *
+ * Confluent hypergeometric function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, hyperg();
+ *
+ * y = hyperg( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the confluent hypergeometric function
+ *
+ * 1 2
+ * a x a(a+1) x
+ * F ( a,b;x ) = 1 + ---- + --------- + ...
+ * 1 1 b 1! b(b+1) 2!
+ *
+ * Many higher transcendental functions are special cases of
+ * this power series.
+ *
+ * As is evident from the formula, b must not be a negative
+ * integer or zero unless a is an integer with 0 >= a > b.
+ *
+ * The routine attempts both a direct summation of the series
+ * and an asymptotic expansion. In each case error due to
+ * roundoff, cancellation, and nonconvergence is estimated.
+ * The result with smaller estimated error is returned.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a, b, x), all three variables
+ * ranging from 0 to 30.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 2000 1.2e-15 1.3e-16
+ qtst1:
+ 21800 max = 1.4200E-14 rms = 1.0841E-15 ave = -5.3640E-17
+ ltstd:
+ 25500 max = 1.2759e-14 rms = 3.7155e-16 ave = 1.5384e-18
+ * IEEE 0,30 30000 1.8e-14 1.1e-15
+ *
+ * Larger errors can be observed when b is near a negative
+ * integer or zero. Certain combinations of arguments yield
+ * serious cancellation error in the power series summation
+ * and also are not in the region of near convergence of the
+ * asymptotic series. An error message is printed if the
+ * self-estimated relative error is greater than 1.0e-12.
+ *
+ */
+
+/* hyperg.c */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef ANSIPROT
+extern double exp ( double );
+extern double log ( double );
+extern double gamma ( double );
+extern double lgam ( double );
+extern double fabs ( double );
+double hyp2f0 ( double, double, double, int, double * );
+static double hy1f1p(double, double, double, double *);
+static double hy1f1a(double, double, double, double *);
+double hyperg (double, double, double);
+#else
+double exp(), log(), gamma(), lgam(), fabs(), hyp2f0();
+static double hy1f1p();
+static double hy1f1a();
+double hyperg();
+#endif
+extern double MAXNUM, MACHEP;
+
+double hyperg( a, b, x)
+double a, b, x;
+{
+double asum, psum, acanc, pcanc, temp;
+
+/* See if a Kummer transformation will help */
+temp = b - a;
+if( fabs(temp) < 0.001 * fabs(a) )
+ return( exp(x) * hyperg( temp, b, -x ) );
+
+
+psum = hy1f1p( a, b, x, &pcanc );
+if( pcanc < 1.0e-15 )
+ goto done;
+
+
+/* try asymptotic series */
+
+asum = hy1f1a( a, b, x, &acanc );
+
+
+/* Pick the result with less estimated error */
+
+if( acanc < pcanc )
+ {
+ pcanc = acanc;
+ psum = asum;
+ }
+
+done:
+if( pcanc > 1.0e-12 )
+ mtherr( "hyperg", PLOSS );
+
+return( psum );
+}
+
+
+
+
+/* Power series summation for confluent hypergeometric function */
+
+
+static double hy1f1p( a, b, x, err )
+double a, b, x;
+double *err;
+{
+double n, a0, sum, t, u, temp;
+double an, bn, maxt, pcanc;
+
+
+/* set up for power series summation */
+an = a;
+bn = b;
+a0 = 1.0;
+sum = 1.0;
+n = 1.0;
+t = 1.0;
+maxt = 0.0;
+
+
+while( t > MACHEP )
+ {
+ if( bn == 0 ) /* check bn first since if both */
+ {
+ mtherr( "hyperg", SING );
+ return( MAXNUM ); /* an and bn are zero it is */
+ }
+ if( an == 0 ) /* a singularity */
+ return( sum );
+ if( n > 200 )
+ goto pdone;
+ u = x * ( an / (bn * n) );
+
+ /* check for blowup */
+ temp = fabs(u);
+ if( (temp > 1.0 ) && (maxt > (MAXNUM/temp)) )
+ {
+ pcanc = 1.0; /* estimate 100% error */
+ goto blowup;
+ }
+
+ a0 *= u;
+ sum += a0;
+ t = fabs(a0);
+ if( t > maxt )
+ maxt = t;
+/*
+ if( (maxt/fabs(sum)) > 1.0e17 )
+ {
+ pcanc = 1.0;
+ goto blowup;
+ }
+*/
+ an += 1.0;
+ bn += 1.0;
+ n += 1.0;
+ }
+
+pdone:
+
+/* estimate error due to roundoff and cancellation */
+if( sum != 0.0 )
+ maxt /= fabs(sum);
+maxt *= MACHEP; /* this way avoids multiply overflow */
+pcanc = fabs( MACHEP * n + maxt );
+
+blowup:
+
+*err = pcanc;
+
+return( sum );
+}
+
+
+/* hy1f1a() */
+/* asymptotic formula for hypergeometric function:
+ *
+ * ( -a
+ * -- ( |z|
+ * | (b) ( -------- 2f0( a, 1+a-b, -1/x )
+ * ( --
+ * ( | (b-a)
+ *
+ *
+ * x a-b )
+ * e |x| )
+ * + -------- 2f0( b-a, 1-a, 1/x ) )
+ * -- )
+ * | (a) )
+ */
+
+static double hy1f1a( a, b, x, err )
+double a, b, x;
+double *err;
+{
+double h1, h2, t, u, temp, acanc, asum, err1, err2;
+
+if( x == 0 )
+ {
+ acanc = 1.0;
+ asum = MAXNUM;
+ goto adone;
+ }
+temp = log( fabs(x) );
+t = x + temp * (a-b);
+u = -temp * a;
+
+if( b > 0 )
+ {
+ temp = lgam(b);
+ t += temp;
+ u += temp;
+ }
+
+h1 = hyp2f0( a, a-b+1, -1.0/x, 1, &err1 );
+
+temp = exp(u) / gamma(b-a);
+h1 *= temp;
+err1 *= temp;
+
+h2 = hyp2f0( b-a, 1.0-a, 1.0/x, 2, &err2 );
+
+if( a < 0 )
+ temp = exp(t) / gamma(a);
+else
+ temp = exp( t - lgam(a) );
+
+h2 *= temp;
+err2 *= temp;
+
+if( x < 0.0 )
+ asum = h1;
+else
+ asum = h2;
+
+acanc = fabs(err1) + fabs(err2);
+
+
+if( b < 0 )
+ {
+ temp = gamma(b);
+ asum *= temp;
+ acanc *= fabs(temp);
+ }
+
+
+if( asum != 0.0 )
+ acanc /= fabs(asum);
+
+acanc *= 30.0; /* fudge factor, since error of asymptotic formula
+ * often seems this much larger than advertised */
+
+adone:
+
+
+*err = acanc;
+return( asum );
+}
+
+/* hyp2f0() */
+
+double hyp2f0( a, b, x, type, err )
+double a, b, x;
+int type; /* determines what converging factor to use */
+double *err;
+{
+double a0, alast, t, tlast, maxt;
+double n, an, bn, u, sum, temp;
+
+an = a;
+bn = b;
+a0 = 1.0e0;
+alast = 1.0e0;
+sum = 0.0;
+n = 1.0e0;
+t = 1.0e0;
+tlast = 1.0e9;
+maxt = 0.0;
+
+do
+ {
+ if( an == 0 )
+ goto pdone;
+ if( bn == 0 )
+ goto pdone;
+
+ u = an * (bn * x / n);
+
+ /* check for blowup */
+ temp = fabs(u);
+ if( (temp > 1.0 ) && (maxt > (MAXNUM/temp)) )
+ goto error;
+
+ a0 *= u;
+ t = fabs(a0);
+
+ /* terminating condition for asymptotic series */
+ if( t > tlast )
+ goto ndone;
+
+ tlast = t;
+ sum += alast; /* the sum is one term behind */
+ alast = a0;
+
+ if( n > 200 )
+ goto ndone;
+
+ an += 1.0e0;
+ bn += 1.0e0;
+ n += 1.0e0;
+ if( t > maxt )
+ maxt = t;
+ }
+while( t > MACHEP );
+
+
+pdone: /* series converged! */
+
+/* estimate error due to roundoff and cancellation */
+*err = fabs( MACHEP * (n + maxt) );
+
+alast = a0;
+goto done;
+
+ndone: /* series did not converge */
+
+/* The following "Converging factors" are supposed to improve accuracy,
+ * but do not actually seem to accomplish very much. */
+
+n -= 1.0;
+x = 1.0/x;
+
+switch( type ) /* "type" given as subroutine argument */
+{
+case 1:
+ alast *= ( 0.5 + (0.125 + 0.25*b - 0.5*a + 0.25*x - 0.25*n)/x );
+ break;
+
+case 2:
+ alast *= 2.0/3.0 - b + 2.0*a + x - n;
+ break;
+
+default:
+ ;
+}
+
+/* estimate error due to roundoff, cancellation, and nonconvergence */
+*err = MACHEP * (n + maxt) + fabs ( a0 );
+
+
+done:
+sum += alast;
+return( sum );
+
+/* series blew up: */
+error:
+*err = MAXNUM;
+mtherr( "hyperg", TLOSS );
+return( sum );
+}
diff --git a/libm/double/i0.c b/libm/double/i0.c
new file mode 100644
index 000000000..a4844ab7e
--- /dev/null
+++ b/libm/double/i0.c
@@ -0,0 +1,397 @@
+/* i0.c
+ *
+ * Modified Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i0();
+ *
+ * y = i0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order zero of the
+ * argument.
+ *
+ * The function is defined as i0(x) = j0( ix ).
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 6000 8.2e-17 1.9e-17
+ * IEEE 0,30 30000 5.8e-16 1.4e-16
+ *
+ */
+ /* i0e.c
+ *
+ * Modified Bessel function of order zero,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i0e();
+ *
+ * y = i0e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order zero of the argument.
+ *
+ * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 30000 5.4e-16 1.2e-16
+ * See i0().
+ *
+ */
+
+/* i0.c */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for exp(-x) I0(x)
+ * in the interval [0,8].
+ *
+ * lim(x->0){ exp(-x) I0(x) } = 1.
+ */
+
+#ifdef UNK
+static double A[] =
+{
+-4.41534164647933937950E-18,
+ 3.33079451882223809783E-17,
+-2.43127984654795469359E-16,
+ 1.71539128555513303061E-15,
+-1.16853328779934516808E-14,
+ 7.67618549860493561688E-14,
+-4.85644678311192946090E-13,
+ 2.95505266312963983461E-12,
+-1.72682629144155570723E-11,
+ 9.67580903537323691224E-11,
+-5.18979560163526290666E-10,
+ 2.65982372468238665035E-9,
+-1.30002500998624804212E-8,
+ 6.04699502254191894932E-8,
+-2.67079385394061173391E-7,
+ 1.11738753912010371815E-6,
+-4.41673835845875056359E-6,
+ 1.64484480707288970893E-5,
+-5.75419501008210370398E-5,
+ 1.88502885095841655729E-4,
+-5.76375574538582365885E-4,
+ 1.63947561694133579842E-3,
+-4.32430999505057594430E-3,
+ 1.05464603945949983183E-2,
+-2.37374148058994688156E-2,
+ 4.93052842396707084878E-2,
+-9.49010970480476444210E-2,
+ 1.71620901522208775349E-1,
+-3.04682672343198398683E-1,
+ 6.76795274409476084995E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short A[] = {
+0121642,0162671,0004646,0103567,
+0022431,0115424,0135755,0026104,
+0123214,0023533,0110365,0156635,
+0023767,0033304,0117662,0172716,
+0124522,0100426,0012277,0157531,
+0025254,0155062,0054461,0030465,
+0126010,0131143,0013560,0153604,
+0026517,0170577,0006336,0114437,
+0127227,0162253,0152243,0052734,
+0027724,0142766,0061641,0160200,
+0130416,0123760,0116564,0125262,
+0031066,0144035,0021246,0054641,
+0131537,0053664,0060131,0102530,
+0032201,0155664,0165153,0020652,
+0132617,0061434,0074423,0176145,
+0033225,0174444,0136147,0122542,
+0133624,0031576,0056453,0020470,
+0034211,0175305,0172321,0041314,
+0134561,0054462,0147040,0165315,
+0035105,0124333,0120203,0162532,
+0135427,0013750,0174257,0055221,
+0035726,0161654,0050220,0100162,
+0136215,0131361,0000325,0041110,
+0036454,0145417,0117357,0017352,
+0136702,0072367,0104415,0133574,
+0037111,0172126,0072505,0014544,
+0137302,0055601,0120550,0033523,
+0037457,0136543,0136544,0043002,
+0137633,0177536,0001276,0066150,
+0040055,0041164,0100655,0010521
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short A[] = {
+0xd0ef,0x2134,0x5cb7,0xbc54,
+0xa589,0x977d,0x3362,0x3c83,
+0xbbb4,0x721e,0x84eb,0xbcb1,
+0x5eba,0x93f6,0xe6d8,0x3cde,
+0xfbeb,0xc297,0x5022,0xbd0a,
+0x2627,0x4b26,0x9b46,0x3d35,
+0x1af0,0x62ee,0x164c,0xbd61,
+0xd324,0xe19b,0xfe2f,0x3d89,
+0x6abc,0x7a94,0xfc95,0xbdb2,
+0x3c10,0xcc74,0x98be,0x3dda,
+0x9556,0x13ae,0xd4fe,0xbe01,
+0xcb34,0xa454,0xd903,0x3e26,
+0x30ab,0x8c0b,0xeaf6,0xbe4b,
+0x6435,0x9d4d,0x3b76,0x3e70,
+0x7f8d,0x8f22,0xec63,0xbe91,
+0xf4ac,0x978c,0xbf24,0x3eb2,
+0x6427,0xcba5,0x866f,0xbed2,
+0x2859,0xbe9a,0x3f58,0x3ef1,
+0x1d5a,0x59c4,0x2b26,0xbf0e,
+0x7cab,0x7410,0xb51b,0x3f28,
+0xeb52,0x1f15,0xe2fd,0xbf42,
+0x100e,0x8a12,0xdc75,0x3f5a,
+0xa849,0x201a,0xb65e,0xbf71,
+0xe3dd,0xf3dd,0x9961,0x3f85,
+0xb6f0,0xf121,0x4e9e,0xbf98,
+0xa32d,0xcea8,0x3e8a,0x3fa9,
+0x06ea,0x342d,0x4b70,0xbfb8,
+0x88c0,0x77ac,0xf7ac,0x3fc5,
+0xcd8d,0xc057,0x7feb,0xbfd3,
+0xa22a,0x9035,0xa84e,0x3fe5,
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short A[] = {
+0xbc54,0x5cb7,0x2134,0xd0ef,
+0x3c83,0x3362,0x977d,0xa589,
+0xbcb1,0x84eb,0x721e,0xbbb4,
+0x3cde,0xe6d8,0x93f6,0x5eba,
+0xbd0a,0x5022,0xc297,0xfbeb,
+0x3d35,0x9b46,0x4b26,0x2627,
+0xbd61,0x164c,0x62ee,0x1af0,
+0x3d89,0xfe2f,0xe19b,0xd324,
+0xbdb2,0xfc95,0x7a94,0x6abc,
+0x3dda,0x98be,0xcc74,0x3c10,
+0xbe01,0xd4fe,0x13ae,0x9556,
+0x3e26,0xd903,0xa454,0xcb34,
+0xbe4b,0xeaf6,0x8c0b,0x30ab,
+0x3e70,0x3b76,0x9d4d,0x6435,
+0xbe91,0xec63,0x8f22,0x7f8d,
+0x3eb2,0xbf24,0x978c,0xf4ac,
+0xbed2,0x866f,0xcba5,0x6427,
+0x3ef1,0x3f58,0xbe9a,0x2859,
+0xbf0e,0x2b26,0x59c4,0x1d5a,
+0x3f28,0xb51b,0x7410,0x7cab,
+0xbf42,0xe2fd,0x1f15,0xeb52,
+0x3f5a,0xdc75,0x8a12,0x100e,
+0xbf71,0xb65e,0x201a,0xa849,
+0x3f85,0x9961,0xf3dd,0xe3dd,
+0xbf98,0x4e9e,0xf121,0xb6f0,
+0x3fa9,0x3e8a,0xcea8,0xa32d,
+0xbfb8,0x4b70,0x342d,0x06ea,
+0x3fc5,0xf7ac,0x77ac,0x88c0,
+0xbfd3,0x7feb,0xc057,0xcd8d,
+0x3fe5,0xa84e,0x9035,0xa22a
+};
+#endif
+
+
+/* Chebyshev coefficients for exp(-x) sqrt(x) I0(x)
+ * in the inverted interval [8,infinity].
+ *
+ * lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).
+ */
+
+#ifdef UNK
+static double B[] =
+{
+-7.23318048787475395456E-18,
+-4.83050448594418207126E-18,
+ 4.46562142029675999901E-17,
+ 3.46122286769746109310E-17,
+-2.82762398051658348494E-16,
+-3.42548561967721913462E-16,
+ 1.77256013305652638360E-15,
+ 3.81168066935262242075E-15,
+-9.55484669882830764870E-15,
+-4.15056934728722208663E-14,
+ 1.54008621752140982691E-14,
+ 3.85277838274214270114E-13,
+ 7.18012445138366623367E-13,
+-1.79417853150680611778E-12,
+-1.32158118404477131188E-11,
+-3.14991652796324136454E-11,
+ 1.18891471078464383424E-11,
+ 4.94060238822496958910E-10,
+ 3.39623202570838634515E-9,
+ 2.26666899049817806459E-8,
+ 2.04891858946906374183E-7,
+ 2.89137052083475648297E-6,
+ 6.88975834691682398426E-5,
+ 3.36911647825569408990E-3,
+ 8.04490411014108831608E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short B[] = {
+0122005,0066672,0123124,0054311,
+0121662,0033323,0030214,0104602,
+0022515,0170300,0113314,0020413,
+0022437,0117350,0035402,0007146,
+0123243,0000135,0057220,0177435,
+0123305,0073476,0144106,0170702,
+0023777,0071755,0017527,0154373,
+0024211,0052214,0102247,0033270,
+0124454,0017763,0171453,0012322,
+0125072,0166316,0075505,0154616,
+0024612,0133770,0065376,0025045,
+0025730,0162143,0056036,0001632,
+0026112,0015077,0150464,0063542,
+0126374,0101030,0014274,0065457,
+0127150,0077271,0125763,0157617,
+0127412,0104350,0040713,0120445,
+0027121,0023765,0057500,0001165,
+0030407,0147146,0003643,0075644,
+0031151,0061445,0044422,0156065,
+0031702,0132224,0003266,0125551,
+0032534,0000076,0147153,0005555,
+0033502,0004536,0004016,0026055,
+0034620,0076433,0142314,0171215,
+0036134,0146145,0013454,0101104,
+0040115,0171425,0062500,0047133
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short B[] = {
+0x8b19,0x54ca,0xadb7,0xbc60,
+0x9130,0x6611,0x46da,0xbc56,
+0x8421,0x12d9,0xbe18,0x3c89,
+0x41cd,0x0760,0xf3dd,0x3c83,
+0x1fe4,0xabd2,0x600b,0xbcb4,
+0xde38,0xd908,0xaee7,0xbcb8,
+0xfb1f,0xa3ea,0xee7d,0x3cdf,
+0xe6d7,0x9094,0x2a91,0x3cf1,
+0x629a,0x7e65,0x83fe,0xbd05,
+0xbb32,0xcf68,0x5d99,0xbd27,
+0xc545,0x0d5f,0x56ff,0x3d11,
+0xc073,0x6b83,0x1c8c,0x3d5b,
+0x8cec,0xfa26,0x4347,0x3d69,
+0x8d66,0x0317,0x9043,0xbd7f,
+0x7bf2,0x357e,0x0fd7,0xbdad,
+0x7425,0x0839,0x511d,0xbdc1,
+0x004f,0xabe8,0x24fe,0x3daa,
+0x6f75,0xc0f4,0xf9cc,0x3e00,
+0x5b87,0xa922,0x2c64,0x3e2d,
+0xd56d,0x80d6,0x5692,0x3e58,
+0x616e,0xd9cd,0x8007,0x3e8b,
+0xc586,0xc101,0x412b,0x3ec8,
+0x9e52,0x7899,0x0fa3,0x3f12,
+0x9049,0xa2e5,0x998c,0x3f6b,
+0x09cb,0xaca8,0xbe62,0x3fe9
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short B[] = {
+0xbc60,0xadb7,0x54ca,0x8b19,
+0xbc56,0x46da,0x6611,0x9130,
+0x3c89,0xbe18,0x12d9,0x8421,
+0x3c83,0xf3dd,0x0760,0x41cd,
+0xbcb4,0x600b,0xabd2,0x1fe4,
+0xbcb8,0xaee7,0xd908,0xde38,
+0x3cdf,0xee7d,0xa3ea,0xfb1f,
+0x3cf1,0x2a91,0x9094,0xe6d7,
+0xbd05,0x83fe,0x7e65,0x629a,
+0xbd27,0x5d99,0xcf68,0xbb32,
+0x3d11,0x56ff,0x0d5f,0xc545,
+0x3d5b,0x1c8c,0x6b83,0xc073,
+0x3d69,0x4347,0xfa26,0x8cec,
+0xbd7f,0x9043,0x0317,0x8d66,
+0xbdad,0x0fd7,0x357e,0x7bf2,
+0xbdc1,0x511d,0x0839,0x7425,
+0x3daa,0x24fe,0xabe8,0x004f,
+0x3e00,0xf9cc,0xc0f4,0x6f75,
+0x3e2d,0x2c64,0xa922,0x5b87,
+0x3e58,0x5692,0x80d6,0xd56d,
+0x3e8b,0x8007,0xd9cd,0x616e,
+0x3ec8,0x412b,0xc101,0xc586,
+0x3f12,0x0fa3,0x7899,0x9e52,
+0x3f6b,0x998c,0xa2e5,0x9049,
+0x3fe9,0xbe62,0xaca8,0x09cb
+};
+#endif
+
+#ifdef ANSIPROT
+extern double chbevl ( double, void *, int );
+extern double exp ( double );
+extern double sqrt ( double );
+#else
+double chbevl(), exp(), sqrt();
+#endif
+
+double i0(x)
+double x;
+{
+double y;
+
+if( x < 0 )
+ x = -x;
+if( x <= 8.0 )
+ {
+ y = (x/2.0) - 2.0;
+ return( exp(x) * chbevl( y, A, 30 ) );
+ }
+
+return( exp(x) * chbevl( 32.0/x - 2.0, B, 25 ) / sqrt(x) );
+
+}
+
+
+
+
+double i0e( x )
+double x;
+{
+double y;
+
+if( x < 0 )
+ x = -x;
+if( x <= 8.0 )
+ {
+ y = (x/2.0) - 2.0;
+ return( chbevl( y, A, 30 ) );
+ }
+
+return( chbevl( 32.0/x - 2.0, B, 25 ) / sqrt(x) );
+
+}
diff --git a/libm/double/i1.c b/libm/double/i1.c
new file mode 100644
index 000000000..dfde216dc
--- /dev/null
+++ b/libm/double/i1.c
@@ -0,0 +1,402 @@
+/* i1.c
+ *
+ * Modified Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i1();
+ *
+ * y = i1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order one of the
+ * argument.
+ *
+ * The function is defined as i1(x) = -i j1( ix ).
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 3400 1.2e-16 2.3e-17
+ * IEEE 0, 30 30000 1.9e-15 2.1e-16
+ *
+ *
+ */
+ /* i1e.c
+ *
+ * Modified Bessel function of order one,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, i1e();
+ *
+ * y = i1e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order one of the argument.
+ *
+ * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 2.0e-15 2.0e-16
+ * See i1().
+ *
+ */
+
+/* i1.c 2 */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1985, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for exp(-x) I1(x) / x
+ * in the interval [0,8].
+ *
+ * lim(x->0){ exp(-x) I1(x) / x } = 1/2.
+ */
+
+#ifdef UNK
+static double A[] =
+{
+ 2.77791411276104639959E-18,
+-2.11142121435816608115E-17,
+ 1.55363195773620046921E-16,
+-1.10559694773538630805E-15,
+ 7.60068429473540693410E-15,
+-5.04218550472791168711E-14,
+ 3.22379336594557470981E-13,
+-1.98397439776494371520E-12,
+ 1.17361862988909016308E-11,
+-6.66348972350202774223E-11,
+ 3.62559028155211703701E-10,
+-1.88724975172282928790E-9,
+ 9.38153738649577178388E-9,
+-4.44505912879632808065E-8,
+ 2.00329475355213526229E-7,
+-8.56872026469545474066E-7,
+ 3.47025130813767847674E-6,
+-1.32731636560394358279E-5,
+ 4.78156510755005422638E-5,
+-1.61760815825896745588E-4,
+ 5.12285956168575772895E-4,
+-1.51357245063125314899E-3,
+ 4.15642294431288815669E-3,
+-1.05640848946261981558E-2,
+ 2.47264490306265168283E-2,
+-5.29459812080949914269E-2,
+ 1.02643658689847095384E-1,
+-1.76416518357834055153E-1,
+ 2.52587186443633654823E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short A[] = {
+0021514,0174520,0060742,0000241,
+0122302,0137206,0016120,0025663,
+0023063,0017437,0026235,0176536,
+0123637,0052523,0170150,0125632,
+0024410,0165770,0030251,0044134,
+0125143,0012160,0162170,0054727,
+0025665,0075702,0035716,0145247,
+0126413,0116032,0176670,0015462,
+0027116,0073425,0110351,0105242,
+0127622,0104034,0137530,0037364,
+0030307,0050645,0120776,0175535,
+0131001,0130331,0043523,0037455,
+0031441,0026160,0010712,0100174,
+0132076,0164761,0022706,0017500,
+0032527,0015045,0115076,0104076,
+0133146,0001714,0015434,0144520,
+0033550,0161166,0124215,0077050,
+0134136,0127715,0143365,0157170,
+0034510,0106652,0013070,0064130,
+0135051,0117126,0117264,0123761,
+0035406,0045355,0133066,0175751,
+0135706,0061420,0054746,0122440,
+0036210,0031232,0047235,0006640,
+0136455,0012373,0144235,0011523,
+0036712,0107437,0036731,0015111,
+0137130,0156742,0115744,0172743,
+0037322,0033326,0124667,0124740,
+0137464,0123210,0021510,0144556,
+0037601,0051433,0111123,0177721
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short A[] = {
+0x4014,0x0c3c,0x9f2a,0x3c49,
+0x0576,0xc38a,0x57d0,0xbc78,
+0xbfac,0xe593,0x63e3,0x3ca6,
+0x1573,0x7e0d,0xeaaa,0xbcd3,
+0x290c,0x0615,0x1d7f,0x3d01,
+0x0b3b,0x1c8f,0x628e,0xbd2c,
+0xd955,0x4779,0xaf78,0x3d56,
+0x0366,0x5fb7,0x7383,0xbd81,
+0x3154,0xb21d,0xcee2,0x3da9,
+0x07de,0x97eb,0x5103,0xbdd2,
+0xdf6c,0xb43f,0xea34,0x3df8,
+0x67e6,0x28ea,0x361b,0xbe20,
+0x5010,0x0239,0x258e,0x3e44,
+0xc3e8,0x24b8,0xdd3e,0xbe67,
+0xd108,0xb347,0xe344,0x3e8a,
+0x992a,0x8363,0xc079,0xbeac,
+0xafc5,0xd511,0x1c4e,0x3ecd,
+0xbbcf,0xb8de,0xd5f9,0xbeeb,
+0x0d0b,0x42c7,0x11b5,0x3f09,
+0x94fe,0xd3d6,0x33ca,0xbf25,
+0xdf7d,0xb6c6,0xc95d,0x3f40,
+0xd4a4,0x0b3c,0xcc62,0xbf58,
+0xa1b4,0x49d3,0x0653,0x3f71,
+0xa26a,0x7913,0xa29f,0xbf85,
+0x2349,0xe7bb,0x51e3,0x3f99,
+0x9ebc,0x537c,0x1bbc,0xbfab,
+0xf53c,0xd536,0x46da,0x3fba,
+0x192e,0x0469,0x94d1,0xbfc6,
+0x7ffa,0x724a,0x2a63,0x3fd0
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short A[] = {
+0x3c49,0x9f2a,0x0c3c,0x4014,
+0xbc78,0x57d0,0xc38a,0x0576,
+0x3ca6,0x63e3,0xe593,0xbfac,
+0xbcd3,0xeaaa,0x7e0d,0x1573,
+0x3d01,0x1d7f,0x0615,0x290c,
+0xbd2c,0x628e,0x1c8f,0x0b3b,
+0x3d56,0xaf78,0x4779,0xd955,
+0xbd81,0x7383,0x5fb7,0x0366,
+0x3da9,0xcee2,0xb21d,0x3154,
+0xbdd2,0x5103,0x97eb,0x07de,
+0x3df8,0xea34,0xb43f,0xdf6c,
+0xbe20,0x361b,0x28ea,0x67e6,
+0x3e44,0x258e,0x0239,0x5010,
+0xbe67,0xdd3e,0x24b8,0xc3e8,
+0x3e8a,0xe344,0xb347,0xd108,
+0xbeac,0xc079,0x8363,0x992a,
+0x3ecd,0x1c4e,0xd511,0xafc5,
+0xbeeb,0xd5f9,0xb8de,0xbbcf,
+0x3f09,0x11b5,0x42c7,0x0d0b,
+0xbf25,0x33ca,0xd3d6,0x94fe,
+0x3f40,0xc95d,0xb6c6,0xdf7d,
+0xbf58,0xcc62,0x0b3c,0xd4a4,
+0x3f71,0x0653,0x49d3,0xa1b4,
+0xbf85,0xa29f,0x7913,0xa26a,
+0x3f99,0x51e3,0xe7bb,0x2349,
+0xbfab,0x1bbc,0x537c,0x9ebc,
+0x3fba,0x46da,0xd536,0xf53c,
+0xbfc6,0x94d1,0x0469,0x192e,
+0x3fd0,0x2a63,0x724a,0x7ffa
+};
+#endif
+
+/* i1.c */
+
+/* Chebyshev coefficients for exp(-x) sqrt(x) I1(x)
+ * in the inverted interval [8,infinity].
+ *
+ * lim(x->inf){ exp(-x) sqrt(x) I1(x) } = 1/sqrt(2pi).
+ */
+
+#ifdef UNK
+static double B[] =
+{
+ 7.51729631084210481353E-18,
+ 4.41434832307170791151E-18,
+-4.65030536848935832153E-17,
+-3.20952592199342395980E-17,
+ 2.96262899764595013876E-16,
+ 3.30820231092092828324E-16,
+-1.88035477551078244854E-15,
+-3.81440307243700780478E-15,
+ 1.04202769841288027642E-14,
+ 4.27244001671195135429E-14,
+-2.10154184277266431302E-14,
+-4.08355111109219731823E-13,
+-7.19855177624590851209E-13,
+ 2.03562854414708950722E-12,
+ 1.41258074366137813316E-11,
+ 3.25260358301548823856E-11,
+-1.89749581235054123450E-11,
+-5.58974346219658380687E-10,
+-3.83538038596423702205E-9,
+-2.63146884688951950684E-8,
+-2.51223623787020892529E-7,
+-3.88256480887769039346E-6,
+-1.10588938762623716291E-4,
+-9.76109749136146840777E-3,
+ 7.78576235018280120474E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short B[] = {
+0022012,0125555,0115227,0043456,
+0021642,0156127,0052075,0145203,
+0122526,0072435,0111231,0011664,
+0122424,0001544,0161671,0114403,
+0023252,0144257,0163532,0142121,
+0023276,0132162,0174045,0013204,
+0124007,0077154,0057046,0110517,
+0124211,0066650,0116127,0157073,
+0024473,0133413,0130551,0107504,
+0025100,0064741,0032631,0040364,
+0124675,0045101,0071551,0012400,
+0125745,0161054,0071637,0011247,
+0126112,0117410,0035525,0122231,
+0026417,0037237,0131034,0176427,
+0027170,0100373,0024742,0025725,
+0027417,0006417,0105303,0141446,
+0127246,0163716,0121202,0060137,
+0130431,0123122,0120436,0166000,
+0131203,0144134,0153251,0124500,
+0131742,0005234,0122732,0033006,
+0132606,0157751,0072362,0121031,
+0133602,0043372,0047120,0015626,
+0134747,0165774,0001125,0046462,
+0136437,0166402,0117746,0155137,
+0040107,0050305,0125330,0124241
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short B[] = {
+0xe8e6,0xb352,0x556d,0x3c61,
+0xb950,0xea87,0x5b8a,0x3c54,
+0x2277,0xb253,0xcea3,0xbc8a,
+0x3320,0x9c77,0x806c,0xbc82,
+0x588a,0xfceb,0x5915,0x3cb5,
+0xa2d1,0x5f04,0xd68e,0x3cb7,
+0xd22a,0x8bc4,0xefcd,0xbce0,
+0xfbc7,0x138a,0x2db5,0xbcf1,
+0x31e8,0x762d,0x76e1,0x3d07,
+0x281e,0x26b3,0x0d3c,0x3d28,
+0x22a0,0x2e6d,0xa948,0xbd17,
+0xe255,0x8e73,0xbc45,0xbd5c,
+0xb493,0x076a,0x53e1,0xbd69,
+0x9fa3,0xf643,0xe7d3,0x3d81,
+0x457b,0x653c,0x101f,0x3daf,
+0x7865,0xf158,0xe1a1,0x3dc1,
+0x4c0c,0xd450,0xdcf9,0xbdb4,
+0xdd80,0x5423,0x34ca,0xbe03,
+0x3528,0x9ad5,0x790b,0xbe30,
+0x46c1,0x94bb,0x4153,0xbe5c,
+0x5443,0x2e9e,0xdbfd,0xbe90,
+0x0373,0x49ca,0x48df,0xbed0,
+0xa9a6,0x804a,0xfd7f,0xbf1c,
+0xdb4c,0x53fc,0xfda0,0xbf83,
+0x1514,0xb55b,0xea18,0x3fe8
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short B[] = {
+0x3c61,0x556d,0xb352,0xe8e6,
+0x3c54,0x5b8a,0xea87,0xb950,
+0xbc8a,0xcea3,0xb253,0x2277,
+0xbc82,0x806c,0x9c77,0x3320,
+0x3cb5,0x5915,0xfceb,0x588a,
+0x3cb7,0xd68e,0x5f04,0xa2d1,
+0xbce0,0xefcd,0x8bc4,0xd22a,
+0xbcf1,0x2db5,0x138a,0xfbc7,
+0x3d07,0x76e1,0x762d,0x31e8,
+0x3d28,0x0d3c,0x26b3,0x281e,
+0xbd17,0xa948,0x2e6d,0x22a0,
+0xbd5c,0xbc45,0x8e73,0xe255,
+0xbd69,0x53e1,0x076a,0xb493,
+0x3d81,0xe7d3,0xf643,0x9fa3,
+0x3daf,0x101f,0x653c,0x457b,
+0x3dc1,0xe1a1,0xf158,0x7865,
+0xbdb4,0xdcf9,0xd450,0x4c0c,
+0xbe03,0x34ca,0x5423,0xdd80,
+0xbe30,0x790b,0x9ad5,0x3528,
+0xbe5c,0x4153,0x94bb,0x46c1,
+0xbe90,0xdbfd,0x2e9e,0x5443,
+0xbed0,0x48df,0x49ca,0x0373,
+0xbf1c,0xfd7f,0x804a,0xa9a6,
+0xbf83,0xfda0,0x53fc,0xdb4c,
+0x3fe8,0xea18,0xb55b,0x1514
+};
+#endif
+
+/* i1.c */
+#ifdef ANSIPROT
+extern double chbevl ( double, void *, int );
+extern double exp ( double );
+extern double sqrt ( double );
+extern double fabs ( double );
+#else
+double chbevl(), exp(), sqrt(), fabs();
+#endif
+
+double i1(x)
+double x;
+{
+double y, z;
+
+z = fabs(x);
+if( z <= 8.0 )
+ {
+ y = (z/2.0) - 2.0;
+ z = chbevl( y, A, 29 ) * z * exp(z);
+ }
+else
+ {
+ z = exp(z) * chbevl( 32.0/z - 2.0, B, 25 ) / sqrt(z);
+ }
+if( x < 0.0 )
+ z = -z;
+return( z );
+}
+
+/* i1e() */
+
+double i1e( x )
+double x;
+{
+double y, z;
+
+z = fabs(x);
+if( z <= 8.0 )
+ {
+ y = (z/2.0) - 2.0;
+ z = chbevl( y, A, 29 ) * z;
+ }
+else
+ {
+ z = chbevl( 32.0/z - 2.0, B, 25 ) / sqrt(z);
+ }
+if( x < 0.0 )
+ z = -z;
+return( z );
+}
diff --git a/libm/double/igam.c b/libm/double/igam.c
new file mode 100644
index 000000000..a1d0bab36
--- /dev/null
+++ b/libm/double/igam.c
@@ -0,0 +1,210 @@
+/* igam.c
+ *
+ * Incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, y, igam();
+ *
+ * y = igam( a, x );
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ * x
+ * -
+ * 1 | | -t a-1
+ * igam(a,x) = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * 0
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 200000 3.6e-14 2.9e-15
+ * IEEE 0,100 300000 9.9e-14 1.5e-14
+ */
+ /* igamc()
+ *
+ * Complemented incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, y, igamc();
+ *
+ * y = igamc( a, x );
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ *
+ * igamc(a,x) = 1 - igam(a,x)
+ *
+ * inf.
+ * -
+ * 1 | | -t a-1
+ * = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * x
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ * ACCURACY:
+ *
+ * Tested at random a, x.
+ * a x Relative error:
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0.5,100 0,100 200000 1.9e-14 1.7e-15
+ * IEEE 0.01,0.5 0,100 200000 1.4e-13 1.6e-15
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1985, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double lgam ( double );
+extern double exp ( double );
+extern double log ( double );
+extern double fabs ( double );
+extern double igam ( double, double );
+extern double igamc ( double, double );
+#else
+double lgam(), exp(), log(), fabs(), igam(), igamc();
+#endif
+
+extern double MACHEP, MAXLOG;
+static double big = 4.503599627370496e15;
+static double biginv = 2.22044604925031308085e-16;
+
+double igamc( a, x )
+double a, x;
+{
+double ans, ax, c, yc, r, t, y, z;
+double pk, pkm1, pkm2, qk, qkm1, qkm2;
+
+if( (x <= 0) || ( a <= 0) )
+ return( 1.0 );
+
+if( (x < 1.0) || (x < a) )
+ return( 1.0 - igam(a,x) );
+
+ax = a * log(x) - x - lgam(a);
+if( ax < -MAXLOG )
+ {
+ mtherr( "igamc", UNDERFLOW );
+ return( 0.0 );
+ }
+ax = exp(ax);
+
+/* continued fraction */
+y = 1.0 - a;
+z = x + y + 1.0;
+c = 0.0;
+pkm2 = 1.0;
+qkm2 = x;
+pkm1 = x + 1.0;
+qkm1 = z * x;
+ans = pkm1/qkm1;
+
+do
+ {
+ c += 1.0;
+ y += 1.0;
+ z += 2.0;
+ yc = y * c;
+ pk = pkm1 * z - pkm2 * yc;
+ qk = qkm1 * z - qkm2 * yc;
+ if( qk != 0 )
+ {
+ r = pk/qk;
+ t = fabs( (ans - r)/r );
+ ans = r;
+ }
+ else
+ t = 1.0;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+ if( fabs(pk) > big )
+ {
+ pkm2 *= biginv;
+ pkm1 *= biginv;
+ qkm2 *= biginv;
+ qkm1 *= biginv;
+ }
+ }
+while( t > MACHEP );
+
+return( ans * ax );
+}
+
+
+
+/* left tail of incomplete gamma function:
+ *
+ * inf. k
+ * a -x - x
+ * x e > ----------
+ * - -
+ * k=0 | (a+k+1)
+ *
+ */
+
+double igam( a, x )
+double a, x;
+{
+double ans, ax, c, r;
+
+if( (x <= 0) || ( a <= 0) )
+ return( 0.0 );
+
+if( (x > 1.0) && (x > a ) )
+ return( 1.0 - igamc(a,x) );
+
+/* Compute x**a * exp(-x) / gamma(a) */
+ax = a * log(x) - x - lgam(a);
+if( ax < -MAXLOG )
+ {
+ mtherr( "igam", UNDERFLOW );
+ return( 0.0 );
+ }
+ax = exp(ax);
+
+/* power series */
+r = a;
+c = 1.0;
+ans = 1.0;
+
+do
+ {
+ r += 1.0;
+ c *= x/r;
+ ans += c;
+ }
+while( c/ans > MACHEP );
+
+return( ans * ax/a );
+}
diff --git a/libm/double/igami.c b/libm/double/igami.c
new file mode 100644
index 000000000..e93ba2a14
--- /dev/null
+++ b/libm/double/igami.c
@@ -0,0 +1,187 @@
+/* igami()
+ *
+ * Inverse of complemented imcomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, x, p, igami();
+ *
+ * x = igami( a, p );
+ *
+ * DESCRIPTION:
+ *
+ * Given p, the function finds x such that
+ *
+ * igamc( a, x ) = p.
+ *
+ * Starting with the approximate value
+ *
+ * 3
+ * x = a t
+ *
+ * where
+ *
+ * t = 1 - d - ndtri(p) sqrt(d)
+ *
+ * and
+ *
+ * d = 1/9a,
+ *
+ * the routine performs up to 10 Newton iterations to find the
+ * root of igamc(a,x) - p = 0.
+ *
+ * ACCURACY:
+ *
+ * Tested at random a, p in the intervals indicated.
+ *
+ * a p Relative error:
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0.5,100 0,0.5 100000 1.0e-14 1.7e-15
+ * IEEE 0.01,0.5 0,0.5 100000 9.0e-14 3.4e-15
+ * IEEE 0.5,10000 0,0.5 20000 2.3e-13 3.8e-14
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+extern double MACHEP, MAXNUM, MAXLOG, MINLOG;
+#ifdef ANSIPROT
+extern double igamc ( double, double );
+extern double ndtri ( double );
+extern double exp ( double );
+extern double fabs ( double );
+extern double log ( double );
+extern double sqrt ( double );
+extern double lgam ( double );
+#else
+double igamc(), ndtri(), exp(), fabs(), log(), sqrt(), lgam();
+#endif
+
+double igami( a, y0 )
+double a, y0;
+{
+double x0, x1, x, yl, yh, y, d, lgm, dithresh;
+int i, dir;
+
+/* bound the solution */
+x0 = MAXNUM;
+yl = 0;
+x1 = 0;
+yh = 1.0;
+dithresh = 5.0 * MACHEP;
+
+/* approximation to inverse function */
+d = 1.0/(9.0*a);
+y = ( 1.0 - d - ndtri(y0) * sqrt(d) );
+x = a * y * y * y;
+
+lgm = lgam(a);
+
+for( i=0; i<10; i++ )
+ {
+ if( x > x0 || x < x1 )
+ goto ihalve;
+ y = igamc(a,x);
+ if( y < yl || y > yh )
+ goto ihalve;
+ if( y < y0 )
+ {
+ x0 = x;
+ yl = y;
+ }
+ else
+ {
+ x1 = x;
+ yh = y;
+ }
+/* compute the derivative of the function at this point */
+ d = (a - 1.0) * log(x) - x - lgm;
+ if( d < -MAXLOG )
+ goto ihalve;
+ d = -exp(d);
+/* compute the step to the next approximation of x */
+ d = (y - y0)/d;
+ if( fabs(d/x) < MACHEP )
+ goto done;
+ x = x - d;
+ }
+
+/* Resort to interval halving if Newton iteration did not converge. */
+ihalve:
+
+d = 0.0625;
+if( x0 == MAXNUM )
+ {
+ if( x <= 0.0 )
+ x = 1.0;
+ while( x0 == MAXNUM )
+ {
+ x = (1.0 + d) * x;
+ y = igamc( a, x );
+ if( y < y0 )
+ {
+ x0 = x;
+ yl = y;
+ break;
+ }
+ d = d + d;
+ }
+ }
+d = 0.5;
+dir = 0;
+
+for( i=0; i<400; i++ )
+ {
+ x = x1 + d * (x0 - x1);
+ y = igamc( a, x );
+ lgm = (x0 - x1)/(x1 + x0);
+ if( fabs(lgm) < dithresh )
+ break;
+ lgm = (y - y0)/y0;
+ if( fabs(lgm) < dithresh )
+ break;
+ if( x <= 0.0 )
+ break;
+ if( y >= y0 )
+ {
+ x1 = x;
+ yh = y;
+ if( dir < 0 )
+ {
+ dir = 0;
+ d = 0.5;
+ }
+ else if( dir > 1 )
+ d = 0.5 * d + 0.5;
+ else
+ d = (y0 - yl)/(yh - yl);
+ dir += 1;
+ }
+ else
+ {
+ x0 = x;
+ yl = y;
+ if( dir > 0 )
+ {
+ dir = 0;
+ d = 0.5;
+ }
+ else if( dir < -1 )
+ d = 0.5 * d;
+ else
+ d = (y0 - yl)/(yh - yl);
+ dir -= 1;
+ }
+ }
+if( x == 0.0 )
+ mtherr( "igami", UNDERFLOW );
+
+done:
+return( x );
+}
diff --git a/libm/double/incbet.c b/libm/double/incbet.c
new file mode 100644
index 000000000..ec236747d
--- /dev/null
+++ b/libm/double/incbet.c
@@ -0,0 +1,409 @@
+/* incbet.c
+ *
+ * Incomplete beta integral
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, incbet();
+ *
+ * y = incbet( a, b, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns incomplete beta integral of the arguments, evaluated
+ * from zero to x. The function is defined as
+ *
+ * x
+ * - -
+ * | (a+b) | | a-1 b-1
+ * ----------- | t (1-t) dt.
+ * - - | |
+ * | (a) | (b) -
+ * 0
+ *
+ * The domain of definition is 0 <= x <= 1. In this
+ * implementation a and b are restricted to positive values.
+ * The integral from x to 1 may be obtained by the symmetry
+ * relation
+ *
+ * 1 - incbet( a, b, x ) = incbet( b, a, 1-x ).
+ *
+ * The integral is evaluated by a continued fraction expansion
+ * or, when b*x is small, by a power series.
+ *
+ * ACCURACY:
+ *
+ * Tested at uniformly distributed random points (a,b,x) with a and b
+ * in "domain" and x between 0 and 1.
+ * Relative error
+ * arithmetic domain # trials peak rms
+ * IEEE 0,5 10000 6.9e-15 4.5e-16
+ * IEEE 0,85 250000 2.2e-13 1.7e-14
+ * IEEE 0,1000 30000 5.3e-12 6.3e-13
+ * IEEE 0,10000 250000 9.3e-11 7.1e-12
+ * IEEE 0,100000 10000 8.7e-10 4.8e-11
+ * Outputs smaller than the IEEE gradual underflow threshold
+ * were excluded from these statistics.
+ *
+ * ERROR MESSAGES:
+ * message condition value returned
+ * incbet domain x<0, x>1 0.0
+ * incbet underflow 0.0
+ */
+
+
+/*
+Cephes Math Library, Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef DEC
+#define MAXGAM 34.84425627277176174
+#else
+#define MAXGAM 171.624376956302725
+#endif
+
+extern double MACHEP, MINLOG, MAXLOG;
+#ifdef ANSIPROT
+extern double gamma ( double );
+extern double lgam ( double );
+extern double exp ( double );
+extern double log ( double );
+extern double pow ( double, double );
+extern double fabs ( double );
+static double incbcf(double, double, double);
+static double incbd(double, double, double);
+static double pseries(double, double, double);
+#else
+double gamma(), lgam(), exp(), log(), pow(), fabs();
+static double incbcf(), incbd(), pseries();
+#endif
+
+static double big = 4.503599627370496e15;
+static double biginv = 2.22044604925031308085e-16;
+
+
+double incbet( aa, bb, xx )
+double aa, bb, xx;
+{
+double a, b, t, x, xc, w, y;
+int flag;
+
+if( aa <= 0.0 || bb <= 0.0 )
+ goto domerr;
+
+if( (xx <= 0.0) || ( xx >= 1.0) )
+ {
+ if( xx == 0.0 )
+ return(0.0);
+ if( xx == 1.0 )
+ return( 1.0 );
+domerr:
+ mtherr( "incbet", DOMAIN );
+ return( 0.0 );
+ }
+
+flag = 0;
+if( (bb * xx) <= 1.0 && xx <= 0.95)
+ {
+ t = pseries(aa, bb, xx);
+ goto done;
+ }
+
+w = 1.0 - xx;
+
+/* Reverse a and b if x is greater than the mean. */
+if( xx > (aa/(aa+bb)) )
+ {
+ flag = 1;
+ a = bb;
+ b = aa;
+ xc = xx;
+ x = w;
+ }
+else
+ {
+ a = aa;
+ b = bb;
+ xc = w;
+ x = xx;
+ }
+
+if( flag == 1 && (b * x) <= 1.0 && x <= 0.95)
+ {
+ t = pseries(a, b, x);
+ goto done;
+ }
+
+/* Choose expansion for better convergence. */
+y = x * (a+b-2.0) - (a-1.0);
+if( y < 0.0 )
+ w = incbcf( a, b, x );
+else
+ w = incbd( a, b, x ) / xc;
+
+/* Multiply w by the factor
+ a b _ _ _
+ x (1-x) | (a+b) / ( a | (a) | (b) ) . */
+
+y = a * log(x);
+t = b * log(xc);
+if( (a+b) < MAXGAM && fabs(y) < MAXLOG && fabs(t) < MAXLOG )
+ {
+ t = pow(xc,b);
+ t *= pow(x,a);
+ t /= a;
+ t *= w;
+ t *= gamma(a+b) / (gamma(a) * gamma(b));
+ goto done;
+ }
+/* Resort to logarithms. */
+y += t + lgam(a+b) - lgam(a) - lgam(b);
+y += log(w/a);
+if( y < MINLOG )
+ t = 0.0;
+else
+ t = exp(y);
+
+done:
+
+if( flag == 1 )
+ {
+ if( t <= MACHEP )
+ t = 1.0 - MACHEP;
+ else
+ t = 1.0 - t;
+ }
+return( t );
+}
+
+/* Continued fraction expansion #1
+ * for incomplete beta integral
+ */
+
+static double incbcf( a, b, x )
+double a, b, x;
+{
+double xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
+double k1, k2, k3, k4, k5, k6, k7, k8;
+double r, t, ans, thresh;
+int n;
+
+k1 = a;
+k2 = a + b;
+k3 = a;
+k4 = a + 1.0;
+k5 = 1.0;
+k6 = b - 1.0;
+k7 = k4;
+k8 = a + 2.0;
+
+pkm2 = 0.0;
+qkm2 = 1.0;
+pkm1 = 1.0;
+qkm1 = 1.0;
+ans = 1.0;
+r = 1.0;
+n = 0;
+thresh = 3.0 * MACHEP;
+do
+ {
+
+ xk = -( x * k1 * k2 )/( k3 * k4 );
+ pk = pkm1 + pkm2 * xk;
+ qk = qkm1 + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ xk = ( x * k5 * k6 )/( k7 * k8 );
+ pk = pkm1 + pkm2 * xk;
+ qk = qkm1 + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ if( qk != 0 )
+ r = pk/qk;
+ if( r != 0 )
+ {
+ t = fabs( (ans - r)/r );
+ ans = r;
+ }
+ else
+ t = 1.0;
+
+ if( t < thresh )
+ goto cdone;
+
+ k1 += 1.0;
+ k2 += 1.0;
+ k3 += 2.0;
+ k4 += 2.0;
+ k5 += 1.0;
+ k6 -= 1.0;
+ k7 += 2.0;
+ k8 += 2.0;
+
+ if( (fabs(qk) + fabs(pk)) > big )
+ {
+ pkm2 *= biginv;
+ pkm1 *= biginv;
+ qkm2 *= biginv;
+ qkm1 *= biginv;
+ }
+ if( (fabs(qk) < biginv) || (fabs(pk) < biginv) )
+ {
+ pkm2 *= big;
+ pkm1 *= big;
+ qkm2 *= big;
+ qkm1 *= big;
+ }
+ }
+while( ++n < 300 );
+
+cdone:
+return(ans);
+}
+
+
+/* Continued fraction expansion #2
+ * for incomplete beta integral
+ */
+
+static double incbd( a, b, x )
+double a, b, x;
+{
+double xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
+double k1, k2, k3, k4, k5, k6, k7, k8;
+double r, t, ans, z, thresh;
+int n;
+
+k1 = a;
+k2 = b - 1.0;
+k3 = a;
+k4 = a + 1.0;
+k5 = 1.0;
+k6 = a + b;
+k7 = a + 1.0;;
+k8 = a + 2.0;
+
+pkm2 = 0.0;
+qkm2 = 1.0;
+pkm1 = 1.0;
+qkm1 = 1.0;
+z = x / (1.0-x);
+ans = 1.0;
+r = 1.0;
+n = 0;
+thresh = 3.0 * MACHEP;
+do
+ {
+
+ xk = -( z * k1 * k2 )/( k3 * k4 );
+ pk = pkm1 + pkm2 * xk;
+ qk = qkm1 + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ xk = ( z * k5 * k6 )/( k7 * k8 );
+ pk = pkm1 + pkm2 * xk;
+ qk = qkm1 + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ if( qk != 0 )
+ r = pk/qk;
+ if( r != 0 )
+ {
+ t = fabs( (ans - r)/r );
+ ans = r;
+ }
+ else
+ t = 1.0;
+
+ if( t < thresh )
+ goto cdone;
+
+ k1 += 1.0;
+ k2 -= 1.0;
+ k3 += 2.0;
+ k4 += 2.0;
+ k5 += 1.0;
+ k6 += 1.0;
+ k7 += 2.0;
+ k8 += 2.0;
+
+ if( (fabs(qk) + fabs(pk)) > big )
+ {
+ pkm2 *= biginv;
+ pkm1 *= biginv;
+ qkm2 *= biginv;
+ qkm1 *= biginv;
+ }
+ if( (fabs(qk) < biginv) || (fabs(pk) < biginv) )
+ {
+ pkm2 *= big;
+ pkm1 *= big;
+ qkm2 *= big;
+ qkm1 *= big;
+ }
+ }
+while( ++n < 300 );
+cdone:
+return(ans);
+}
+
+/* Power series for incomplete beta integral.
+ Use when b*x is small and x not too close to 1. */
+
+static double pseries( a, b, x )
+double a, b, x;
+{
+double s, t, u, v, n, t1, z, ai;
+
+ai = 1.0 / a;
+u = (1.0 - b) * x;
+v = u / (a + 1.0);
+t1 = v;
+t = u;
+n = 2.0;
+s = 0.0;
+z = MACHEP * ai;
+while( fabs(v) > z )
+ {
+ u = (n - b) * x / n;
+ t *= u;
+ v = t / (a + n);
+ s += v;
+ n += 1.0;
+ }
+s += t1;
+s += ai;
+
+u = a * log(x);
+if( (a+b) < MAXGAM && fabs(u) < MAXLOG )
+ {
+ t = gamma(a+b)/(gamma(a)*gamma(b));
+ s = s * t * pow(x,a);
+ }
+else
+ {
+ t = lgam(a+b) - lgam(a) - lgam(b) + u + log(s);
+ if( t < MINLOG )
+ s = 0.0;
+ else
+ s = exp(t);
+ }
+return(s);
+}
diff --git a/libm/double/incbi.c b/libm/double/incbi.c
new file mode 100644
index 000000000..817219c4a
--- /dev/null
+++ b/libm/double/incbi.c
@@ -0,0 +1,313 @@
+/* incbi()
+ *
+ * Inverse of imcomplete beta integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double a, b, x, y, incbi();
+ *
+ * x = incbi( a, b, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given y, the function finds x such that
+ *
+ * incbet( a, b, x ) = y .
+ *
+ * The routine performs interval halving or Newton iterations to find the
+ * root of incbet(a,b,x) - y = 0.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * x a,b
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0,1 .5,10000 50000 5.8e-12 1.3e-13
+ * IEEE 0,1 .25,100 100000 1.8e-13 3.9e-15
+ * IEEE 0,1 0,5 50000 1.1e-12 5.5e-15
+ * VAX 0,1 .5,100 25000 3.5e-14 1.1e-15
+ * With a and b constrained to half-integer or integer values:
+ * IEEE 0,1 .5,10000 50000 5.8e-12 1.1e-13
+ * IEEE 0,1 .5,100 100000 1.7e-14 7.9e-16
+ * With a = .5, b constrained to half-integer or integer values:
+ * IEEE 0,1 .5,10000 10000 8.3e-11 1.0e-11
+ */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1996, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+extern double MACHEP, MAXNUM, MAXLOG, MINLOG;
+#ifdef ANSIPROT
+extern double ndtri ( double );
+extern double exp ( double );
+extern double fabs ( double );
+extern double log ( double );
+extern double sqrt ( double );
+extern double lgam ( double );
+extern double incbet ( double, double, double );
+#else
+double ndtri(), exp(), fabs(), log(), sqrt(), lgam(), incbet();
+#endif
+
+double incbi( aa, bb, yy0 )
+double aa, bb, yy0;
+{
+double a, b, y0, d, y, x, x0, x1, lgm, yp, di, dithresh, yl, yh, xt;
+int i, rflg, dir, nflg;
+
+
+i = 0;
+if( yy0 <= 0 )
+ return(0.0);
+if( yy0 >= 1.0 )
+ return(1.0);
+x0 = 0.0;
+yl = 0.0;
+x1 = 1.0;
+yh = 1.0;
+nflg = 0;
+
+if( aa <= 1.0 || bb <= 1.0 )
+ {
+ dithresh = 1.0e-6;
+ rflg = 0;
+ a = aa;
+ b = bb;
+ y0 = yy0;
+ x = a/(a+b);
+ y = incbet( a, b, x );
+ goto ihalve;
+ }
+else
+ {
+ dithresh = 1.0e-4;
+ }
+/* approximation to inverse function */
+
+yp = -ndtri(yy0);
+
+if( yy0 > 0.5 )
+ {
+ rflg = 1;
+ a = bb;
+ b = aa;
+ y0 = 1.0 - yy0;
+ yp = -yp;
+ }
+else
+ {
+ rflg = 0;
+ a = aa;
+ b = bb;
+ y0 = yy0;
+ }
+
+lgm = (yp * yp - 3.0)/6.0;
+x = 2.0/( 1.0/(2.0*a-1.0) + 1.0/(2.0*b-1.0) );
+d = yp * sqrt( x + lgm ) / x
+ - ( 1.0/(2.0*b-1.0) - 1.0/(2.0*a-1.0) )
+ * (lgm + 5.0/6.0 - 2.0/(3.0*x));
+d = 2.0 * d;
+if( d < MINLOG )
+ {
+ x = 1.0;
+ goto under;
+ }
+x = a/( a + b * exp(d) );
+y = incbet( a, b, x );
+yp = (y - y0)/y0;
+if( fabs(yp) < 0.2 )
+ goto newt;
+
+/* Resort to interval halving if not close enough. */
+ihalve:
+
+dir = 0;
+di = 0.5;
+for( i=0; i<100; i++ )
+ {
+ if( i != 0 )
+ {
+ x = x0 + di * (x1 - x0);
+ if( x == 1.0 )
+ x = 1.0 - MACHEP;
+ if( x == 0.0 )
+ {
+ di = 0.5;
+ x = x0 + di * (x1 - x0);
+ if( x == 0.0 )
+ goto under;
+ }
+ y = incbet( a, b, x );
+ yp = (x1 - x0)/(x1 + x0);
+ if( fabs(yp) < dithresh )
+ goto newt;
+ yp = (y-y0)/y0;
+ if( fabs(yp) < dithresh )
+ goto newt;
+ }
+ if( y < y0 )
+ {
+ x0 = x;
+ yl = y;
+ if( dir < 0 )
+ {
+ dir = 0;
+ di = 0.5;
+ }
+ else if( dir > 3 )
+ di = 1.0 - (1.0 - di) * (1.0 - di);
+ else if( dir > 1 )
+ di = 0.5 * di + 0.5;
+ else
+ di = (y0 - y)/(yh - yl);
+ dir += 1;
+ if( x0 > 0.75 )
+ {
+ if( rflg == 1 )
+ {
+ rflg = 0;
+ a = aa;
+ b = bb;
+ y0 = yy0;
+ }
+ else
+ {
+ rflg = 1;
+ a = bb;
+ b = aa;
+ y0 = 1.0 - yy0;
+ }
+ x = 1.0 - x;
+ y = incbet( a, b, x );
+ x0 = 0.0;
+ yl = 0.0;
+ x1 = 1.0;
+ yh = 1.0;
+ goto ihalve;
+ }
+ }
+ else
+ {
+ x1 = x;
+ if( rflg == 1 && x1 < MACHEP )
+ {
+ x = 0.0;
+ goto done;
+ }
+ yh = y;
+ if( dir > 0 )
+ {
+ dir = 0;
+ di = 0.5;
+ }
+ else if( dir < -3 )
+ di = di * di;
+ else if( dir < -1 )
+ di = 0.5 * di;
+ else
+ di = (y - y0)/(yh - yl);
+ dir -= 1;
+ }
+ }
+mtherr( "incbi", PLOSS );
+if( x0 >= 1.0 )
+ {
+ x = 1.0 - MACHEP;
+ goto done;
+ }
+if( x <= 0.0 )
+ {
+under:
+ mtherr( "incbi", UNDERFLOW );
+ x = 0.0;
+ goto done;
+ }
+
+newt:
+
+if( nflg )
+ goto done;
+nflg = 1;
+lgm = lgam(a+b) - lgam(a) - lgam(b);
+
+for( i=0; i<8; i++ )
+ {
+ /* Compute the function at this point. */
+ if( i != 0 )
+ y = incbet(a,b,x);
+ if( y < yl )
+ {
+ x = x0;
+ y = yl;
+ }
+ else if( y > yh )
+ {
+ x = x1;
+ y = yh;
+ }
+ else if( y < y0 )
+ {
+ x0 = x;
+ yl = y;
+ }
+ else
+ {
+ x1 = x;
+ yh = y;
+ }
+ if( x == 1.0 || x == 0.0 )
+ break;
+ /* Compute the derivative of the function at this point. */
+ d = (a - 1.0) * log(x) + (b - 1.0) * log(1.0-x) + lgm;
+ if( d < MINLOG )
+ goto done;
+ if( d > MAXLOG )
+ break;
+ d = exp(d);
+ /* Compute the step to the next approximation of x. */
+ d = (y - y0)/d;
+ xt = x - d;
+ if( xt <= x0 )
+ {
+ y = (x - x0) / (x1 - x0);
+ xt = x0 + 0.5 * y * (x - x0);
+ if( xt <= 0.0 )
+ break;
+ }
+ if( xt >= x1 )
+ {
+ y = (x1 - x) / (x1 - x0);
+ xt = x1 - 0.5 * y * (x1 - x);
+ if( xt >= 1.0 )
+ break;
+ }
+ x = xt;
+ if( fabs(d/x) < 128.0 * MACHEP )
+ goto done;
+ }
+/* Did not converge. */
+dithresh = 256.0 * MACHEP;
+goto ihalve;
+
+done:
+
+if( rflg )
+ {
+ if( x <= MACHEP )
+ x = 1.0 - MACHEP;
+ else
+ x = 1.0 - x;
+ }
+return( x );
+}
diff --git a/libm/double/isnan.c b/libm/double/isnan.c
new file mode 100644
index 000000000..8ae83bcba
--- /dev/null
+++ b/libm/double/isnan.c
@@ -0,0 +1,237 @@
+/* isnan()
+ * signbit()
+ * isfinite()
+ *
+ * Floating point numeric utilities
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double ceil(), floor(), frexp(), ldexp();
+ * int signbit(), isnan(), isfinite();
+ * double x, y;
+ * int expnt, n;
+ *
+ * y = floor(x);
+ * y = ceil(x);
+ * y = frexp( x, &expnt );
+ * y = ldexp( x, n );
+ * n = signbit(x);
+ * n = isnan(x);
+ * n = isfinite(x);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * All four routines return a double precision floating point
+ * result.
+ *
+ * floor() returns the largest integer less than or equal to x.
+ * It truncates toward minus infinity.
+ *
+ * ceil() returns the smallest integer greater than or equal
+ * to x. It truncates toward plus infinity.
+ *
+ * frexp() extracts the exponent from x. It returns an integer
+ * power of two to expnt and the significand between 0.5 and 1
+ * to y. Thus x = y * 2**expn.
+ *
+ * ldexp() multiplies x by 2**n.
+ *
+ * signbit(x) returns 1 if the sign bit of x is 1, else 0.
+ *
+ * These functions are part of the standard C run time library
+ * for many but not all C compilers. The ones supplied are
+ * written in C for either DEC or IEEE arithmetic. They should
+ * be used only if your compiler library does not already have
+ * them.
+ *
+ * The IEEE versions assume that denormal numbers are implemented
+ * in the arithmetic. Some modifications will be required if
+ * the arithmetic has abrupt rather than gradual underflow.
+ */
+
+
+/*
+Cephes Math Library Release 2.3: March, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef UNK
+/* ceil(), floor(), frexp(), ldexp() may need to be rewritten. */
+#undef UNK
+#if BIGENDIAN
+#define MIEEE 1
+#else
+#define IBMPC 1
+#endif
+#endif
+
+
+/* Return 1 if the sign bit of x is 1, else 0. */
+
+int signbit(x)
+double x;
+{
+union
+ {
+ double d;
+ short s[4];
+ int i[2];
+ } u;
+
+u.d = x;
+
+if( sizeof(int) == 4 )
+ {
+#ifdef IBMPC
+ return( u.i[1] < 0 );
+#endif
+#ifdef DEC
+ return( u.s[3] < 0 );
+#endif
+#ifdef MIEEE
+ return( u.i[0] < 0 );
+#endif
+ }
+else
+ {
+#ifdef IBMPC
+ return( u.s[3] < 0 );
+#endif
+#ifdef DEC
+ return( u.s[3] < 0 );
+#endif
+#ifdef MIEEE
+ return( u.s[0] < 0 );
+#endif
+ }
+}
+
+
+/* Return 1 if x is a number that is Not a Number, else return 0. */
+
+int isnan(x)
+double x;
+{
+#ifdef NANS
+union
+ {
+ double d;
+ unsigned short s[4];
+ unsigned int i[2];
+ } u;
+
+u.d = x;
+
+if( sizeof(int) == 4 )
+ {
+#ifdef IBMPC
+ if( ((u.i[1] & 0x7ff00000) == 0x7ff00000)
+ && (((u.i[1] & 0x000fffff) != 0) || (u.i[0] != 0)))
+ return 1;
+#endif
+#ifdef DEC
+ if( (u.s[1] & 0x7fff) == 0)
+ {
+ if( (u.s[2] | u.s[1] | u.s[0]) != 0 )
+ return(1);
+ }
+#endif
+#ifdef MIEEE
+ if( ((u.i[0] & 0x7ff00000) == 0x7ff00000)
+ && (((u.i[0] & 0x000fffff) != 0) || (u.i[1] != 0)))
+ return 1;
+#endif
+ return(0);
+ }
+else
+ { /* size int not 4 */
+#ifdef IBMPC
+ if( (u.s[3] & 0x7ff0) == 0x7ff0)
+ {
+ if( ((u.s[3] & 0x000f) | u.s[2] | u.s[1] | u.s[0]) != 0 )
+ return(1);
+ }
+#endif
+#ifdef DEC
+ if( (u.s[3] & 0x7fff) == 0)
+ {
+ if( (u.s[2] | u.s[1] | u.s[0]) != 0 )
+ return(1);
+ }
+#endif
+#ifdef MIEEE
+ if( (u.s[0] & 0x7ff0) == 0x7ff0)
+ {
+ if( ((u.s[0] & 0x000f) | u.s[1] | u.s[2] | u.s[3]) != 0 )
+ return(1);
+ }
+#endif
+ return(0);
+ } /* size int not 4 */
+
+#else
+/* No NANS. */
+return(0);
+#endif
+}
+
+
+/* Return 1 if x is not infinite and is not a NaN. */
+
+int isfinite(x)
+double x;
+{
+#ifdef INFINITIES
+union
+ {
+ double d;
+ unsigned short s[4];
+ unsigned int i[2];
+ } u;
+
+u.d = x;
+
+if( sizeof(int) == 4 )
+ {
+#ifdef IBMPC
+ if( (u.i[1] & 0x7ff00000) != 0x7ff00000)
+ return 1;
+#endif
+#ifdef DEC
+ if( (u.s[3] & 0x7fff) != 0)
+ return 1;
+#endif
+#ifdef MIEEE
+ if( (u.i[0] & 0x7ff00000) != 0x7ff00000)
+ return 1;
+#endif
+ return(0);
+ }
+else
+ {
+#ifdef IBMPC
+ if( (u.s[3] & 0x7ff0) != 0x7ff0)
+ return 1;
+#endif
+#ifdef DEC
+ if( (u.s[3] & 0x7fff) != 0)
+ return 1;
+#endif
+#ifdef MIEEE
+ if( (u.s[0] & 0x7ff0) != 0x7ff0)
+ return 1;
+#endif
+ return(0);
+ }
+#else
+/* No INFINITY. */
+return(1);
+#endif
+}
diff --git a/libm/double/iv.c b/libm/double/iv.c
new file mode 100644
index 000000000..ec0e96244
--- /dev/null
+++ b/libm/double/iv.c
@@ -0,0 +1,116 @@
+/* iv.c
+ *
+ * Modified Bessel function of noninteger order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, iv();
+ *
+ * y = iv( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order v of the
+ * argument. If x is negative, v must be integer valued.
+ *
+ * The function is defined as Iv(x) = Jv( ix ). It is
+ * here computed in terms of the confluent hypergeometric
+ * function, according to the formula
+ *
+ * v -x
+ * Iv(x) = (x/2) e hyperg( v+0.5, 2v+1, 2x ) / gamma(v+1)
+ *
+ * If v is a negative integer, then v is replaced by -v.
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (v, x), with v between 0 and
+ * 30, x between 0 and 28.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 2000 3.1e-15 5.4e-16
+ * IEEE 0,30 10000 1.7e-14 2.7e-15
+ *
+ * Accuracy is diminished if v is near a negative integer.
+ *
+ * See also hyperg.c.
+ *
+ */
+ /* iv.c */
+/* Modified Bessel function of noninteger order */
+/* If x < 0, then v must be an integer. */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double hyperg ( double, double, double );
+extern double exp ( double );
+extern double gamma ( double );
+extern double log ( double );
+extern double fabs ( double );
+extern double floor ( double );
+#else
+double hyperg(), exp(), gamma(), log(), fabs(), floor();
+#endif
+extern double MACHEP, MAXNUM;
+
+double iv( v, x )
+double v, x;
+{
+int sign;
+double t, ax;
+
+/* If v is a negative integer, invoke symmetry */
+t = floor(v);
+if( v < 0.0 )
+ {
+ if( t == v )
+ {
+ v = -v; /* symmetry */
+ t = -t;
+ }
+ }
+/* If x is negative, require v to be an integer */
+sign = 1;
+if( x < 0.0 )
+ {
+ if( t != v )
+ {
+ mtherr( "iv", DOMAIN );
+ return( 0.0 );
+ }
+ if( v != 2.0 * floor(v/2.0) )
+ sign = -1;
+ }
+
+/* Avoid logarithm singularity */
+if( x == 0.0 )
+ {
+ if( v == 0.0 )
+ return( 1.0 );
+ if( v < 0.0 )
+ {
+ mtherr( "iv", OVERFLOW );
+ return( MAXNUM );
+ }
+ else
+ return( 0.0 );
+ }
+
+ax = fabs(x);
+t = v * log( 0.5 * ax ) - x;
+t = sign * exp(t) / gamma( v + 1.0 );
+ax = v + 0.5;
+return( t * hyperg( ax, 2.0 * ax, 2.0 * x ) );
+}
diff --git a/libm/double/j0.c b/libm/double/j0.c
new file mode 100644
index 000000000..c0f1bd4b8
--- /dev/null
+++ b/libm/double/j0.c
@@ -0,0 +1,543 @@
+/* j0.c
+ *
+ * Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, j0();
+ *
+ * y = j0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order zero of the argument.
+ *
+ * The domain is divided into the intervals [0, 5] and
+ * (5, infinity). In the first interval the following rational
+ * approximation is used:
+ *
+ *
+ * 2 2
+ * (w - r ) (w - r ) P (w) / Q (w)
+ * 1 2 3 8
+ *
+ * 2
+ * where w = x and the two r's are zeros of the function.
+ *
+ * In the second interval, the Hankel asymptotic expansion
+ * is employed with two rational functions of degree 6/6
+ * and 7/7.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 10000 4.4e-17 6.3e-18
+ * IEEE 0, 30 60000 4.2e-16 1.1e-16
+ *
+ */
+ /* y0.c
+ *
+ * Bessel function of the second kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y0();
+ *
+ * y = y0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind, of order
+ * zero, of the argument.
+ *
+ * The domain is divided into the intervals [0, 5] and
+ * (5, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute
+ * y0(x) = R(x) + 2 * log(x) * j0(x) / PI.
+ * Thus a call to j0() is required.
+ *
+ * In the second interval, the Hankel asymptotic expansion
+ * is employed with two rational functions of degree 6/6
+ * and 7/7.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error, when y0(x) < 1; else relative error:
+ *
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 9400 7.0e-17 7.9e-18
+ * IEEE 0, 30 30000 1.3e-15 1.6e-16
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+/* Note: all coefficients satisfy the relative error criterion
+ * except YP, YQ which are designed for absolute error. */
+
+#include <math.h>
+
+#ifdef UNK
+static double PP[7] = {
+ 7.96936729297347051624E-4,
+ 8.28352392107440799803E-2,
+ 1.23953371646414299388E0,
+ 5.44725003058768775090E0,
+ 8.74716500199817011941E0,
+ 5.30324038235394892183E0,
+ 9.99999999999999997821E-1,
+};
+static double PQ[7] = {
+ 9.24408810558863637013E-4,
+ 8.56288474354474431428E-2,
+ 1.25352743901058953537E0,
+ 5.47097740330417105182E0,
+ 8.76190883237069594232E0,
+ 5.30605288235394617618E0,
+ 1.00000000000000000218E0,
+};
+#endif
+#ifdef DEC
+static unsigned short PP[28] = {
+0035520,0164604,0140733,0054470,
+0037251,0122605,0115356,0107170,
+0040236,0124412,0071500,0056303,
+0040656,0047737,0045720,0045263,
+0041013,0172143,0045004,0142103,
+0040651,0132045,0026241,0026406,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short PQ[28] = {
+0035562,0052006,0070034,0134666,
+0037257,0057055,0055242,0123424,
+0040240,0071626,0046630,0032371,
+0040657,0011077,0032013,0012731,
+0041014,0030307,0050331,0006414,
+0040651,0145457,0065021,0150304,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short PP[28] = {
+0x6b27,0x983b,0x1d30,0x3f4a,
+0xd1cf,0xb35d,0x34b0,0x3fb5,
+0x0b98,0x4e68,0xd521,0x3ff3,
+0x0956,0xe97a,0xc9fb,0x4015,
+0x9888,0x6940,0x7e8c,0x4021,
+0x25a1,0xa594,0x3684,0x4015,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short PQ[28] = {
+0x9737,0xce03,0x4a80,0x3f4e,
+0x54e3,0xab54,0xebc5,0x3fb5,
+0x069f,0xc9b3,0x0e72,0x3ff4,
+0x62bb,0xe681,0xe247,0x4015,
+0x21a1,0xea1b,0x8618,0x4021,
+0x3a19,0xed42,0x3965,0x4015,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short PP[28] = {
+0x3f4a,0x1d30,0x983b,0x6b27,
+0x3fb5,0x34b0,0xb35d,0xd1cf,
+0x3ff3,0xd521,0x4e68,0x0b98,
+0x4015,0xc9fb,0xe97a,0x0956,
+0x4021,0x7e8c,0x6940,0x9888,
+0x4015,0x3684,0xa594,0x25a1,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short PQ[28] = {
+0x3f4e,0x4a80,0xce03,0x9737,
+0x3fb5,0xebc5,0xab54,0x54e3,
+0x3ff4,0x0e72,0xc9b3,0x069f,
+0x4015,0xe247,0xe681,0x62bb,
+0x4021,0x8618,0xea1b,0x21a1,
+0x4015,0x3965,0xed42,0x3a19,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+
+#ifdef UNK
+static double QP[8] = {
+-1.13663838898469149931E-2,
+-1.28252718670509318512E0,
+-1.95539544257735972385E1,
+-9.32060152123768231369E1,
+-1.77681167980488050595E2,
+-1.47077505154951170175E2,
+-5.14105326766599330220E1,
+-6.05014350600728481186E0,
+};
+static double QQ[7] = {
+/* 1.00000000000000000000E0,*/
+ 6.43178256118178023184E1,
+ 8.56430025976980587198E2,
+ 3.88240183605401609683E3,
+ 7.24046774195652478189E3,
+ 5.93072701187316984827E3,
+ 2.06209331660327847417E3,
+ 2.42005740240291393179E2,
+};
+#endif
+#ifdef DEC
+static unsigned short QP[32] = {
+0136472,0035021,0142451,0141115,
+0140244,0024731,0150620,0105642,
+0141234,0067177,0124161,0060141,
+0141672,0064572,0151557,0043036,
+0142061,0127141,0003127,0043517,
+0142023,0011727,0060271,0144544,
+0141515,0122142,0126620,0143150,
+0140701,0115306,0106715,0007344,
+};
+static unsigned short QQ[28] = {
+/*0040200,0000000,0000000,0000000,*/
+0041600,0121272,0004741,0026544,
+0042526,0015605,0105654,0161771,
+0043162,0123155,0165644,0062645,
+0043342,0041675,0167576,0130756,
+0043271,0052720,0165631,0154214,
+0043000,0160576,0034614,0172024,
+0042162,0000570,0030500,0051235,
+};
+#endif
+#ifdef IBMPC
+static unsigned short QP[32] = {
+0x384a,0x38a5,0x4742,0xbf87,
+0x1174,0x3a32,0x853b,0xbff4,
+0x2c0c,0xf50e,0x8dcf,0xc033,
+0xe8c4,0x5a6d,0x4d2f,0xc057,
+0xe8ea,0x20ca,0x35cc,0xc066,
+0x392d,0xec17,0x627a,0xc062,
+0x18cd,0x55b2,0xb48c,0xc049,
+0xa1dd,0xd1b9,0x3358,0xc018,
+};
+static unsigned short QQ[28] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x25ac,0x413c,0x1457,0x4050,
+0x9c7f,0xb175,0xc370,0x408a,
+0x8cb5,0xbd74,0x54cd,0x40ae,
+0xd63e,0xbdef,0x4877,0x40bc,
+0x3b11,0x1d73,0x2aba,0x40b7,
+0x9e82,0xc731,0x1c2f,0x40a0,
+0x0a54,0x0628,0x402f,0x406e,
+};
+#endif
+#ifdef MIEEE
+static unsigned short QP[32] = {
+0xbf87,0x4742,0x38a5,0x384a,
+0xbff4,0x853b,0x3a32,0x1174,
+0xc033,0x8dcf,0xf50e,0x2c0c,
+0xc057,0x4d2f,0x5a6d,0xe8c4,
+0xc066,0x35cc,0x20ca,0xe8ea,
+0xc062,0x627a,0xec17,0x392d,
+0xc049,0xb48c,0x55b2,0x18cd,
+0xc018,0x3358,0xd1b9,0xa1dd,
+};
+static unsigned short QQ[28] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4050,0x1457,0x413c,0x25ac,
+0x408a,0xc370,0xb175,0x9c7f,
+0x40ae,0x54cd,0xbd74,0x8cb5,
+0x40bc,0x4877,0xbdef,0xd63e,
+0x40b7,0x2aba,0x1d73,0x3b11,
+0x40a0,0x1c2f,0xc731,0x9e82,
+0x406e,0x402f,0x0628,0x0a54,
+};
+#endif
+
+
+#ifdef UNK
+static double YP[8] = {
+ 1.55924367855235737965E4,
+-1.46639295903971606143E7,
+ 5.43526477051876500413E9,
+-9.82136065717911466409E11,
+ 8.75906394395366999549E13,
+-3.46628303384729719441E15,
+ 4.42733268572569800351E16,
+-1.84950800436986690637E16,
+};
+static double YQ[7] = {
+/* 1.00000000000000000000E0,*/
+ 1.04128353664259848412E3,
+ 6.26107330137134956842E5,
+ 2.68919633393814121987E8,
+ 8.64002487103935000337E10,
+ 2.02979612750105546709E13,
+ 3.17157752842975028269E15,
+ 2.50596256172653059228E17,
+};
+#endif
+#ifdef DEC
+static unsigned short YP[32] = {
+0043563,0120677,0042264,0046166,
+0146137,0140371,0113444,0042260,
+0050241,0175707,0100502,0063344,
+0152144,0125737,0007265,0164526,
+0053637,0051621,0163035,0060546,
+0155105,0004416,0107306,0060023,
+0056035,0045133,0030132,0000024,
+0155603,0065132,0144061,0131732,
+};
+static unsigned short YQ[28] = {
+/*0040200,0000000,0000000,0000000,*/
+0042602,0024422,0135557,0162663,
+0045030,0155665,0044075,0160135,
+0047200,0035432,0105446,0104005,
+0051240,0167331,0056063,0022743,
+0053223,0127746,0025764,0012160,
+0055064,0044206,0177532,0145545,
+0056536,0111375,0163715,0127201,
+};
+#endif
+#ifdef IBMPC
+static unsigned short YP[32] = {
+0x898f,0xe896,0x7437,0x40ce,
+0x8896,0x32e4,0xf81f,0xc16b,
+0x4cdd,0xf028,0x3f78,0x41f4,
+0xbd2b,0xe1d6,0x957b,0xc26c,
+0xac2d,0x3cc3,0xea72,0x42d3,
+0xcc02,0xd1d8,0xa121,0xc328,
+0x4003,0x660b,0xa94b,0x4363,
+0x367b,0x5906,0x6d4b,0xc350,
+};
+static unsigned short YQ[28] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xfcb6,0x576d,0x4522,0x4090,
+0xbc0c,0xa907,0x1b76,0x4123,
+0xd101,0x5164,0x0763,0x41b0,
+0x64bc,0x2b86,0x1ddb,0x4234,
+0x828e,0xc57e,0x75fc,0x42b2,
+0x596d,0xdfeb,0x8910,0x4326,
+0xb5d0,0xbcf9,0xd25f,0x438b,
+};
+#endif
+#ifdef MIEEE
+static unsigned short YP[32] = {
+0x40ce,0x7437,0xe896,0x898f,
+0xc16b,0xf81f,0x32e4,0x8896,
+0x41f4,0x3f78,0xf028,0x4cdd,
+0xc26c,0x957b,0xe1d6,0xbd2b,
+0x42d3,0xea72,0x3cc3,0xac2d,
+0xc328,0xa121,0xd1d8,0xcc02,
+0x4363,0xa94b,0x660b,0x4003,
+0xc350,0x6d4b,0x5906,0x367b,
+};
+static unsigned short YQ[28] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4090,0x4522,0x576d,0xfcb6,
+0x4123,0x1b76,0xa907,0xbc0c,
+0x41b0,0x0763,0x5164,0xd101,
+0x4234,0x1ddb,0x2b86,0x64bc,
+0x42b2,0x75fc,0xc57e,0x828e,
+0x4326,0x8910,0xdfeb,0x596d,
+0x438b,0xd25f,0xbcf9,0xb5d0,
+};
+#endif
+
+#ifdef UNK
+/* 5.783185962946784521175995758455807035071 */
+static double DR1 = 5.78318596294678452118E0;
+/* 30.47126234366208639907816317502275584842 */
+static double DR2 = 3.04712623436620863991E1;
+#endif
+
+#ifdef DEC
+static unsigned short R1[] = {0040671,0007734,0001061,0056734};
+#define DR1 *(double *)R1
+static unsigned short R2[] = {0041363,0142445,0030416,0165567};
+#define DR2 *(double *)R2
+#endif
+
+#ifdef IBMPC
+static unsigned short R1[] = {0x2bbb,0x8046,0x21fb,0x4017};
+#define DR1 *(double *)R1
+static unsigned short R2[] = {0xdd6f,0xa621,0x78a4,0x403e};
+#define DR2 *(double *)R2
+#endif
+
+#ifdef MIEEE
+static unsigned short R1[] = {0x4017,0x21fb,0x8046,0x2bbb};
+#define DR1 *(double *)R1
+static unsigned short R2[] = {0x403e,0x78a4,0xa621,0xdd6f};
+#define DR2 *(double *)R2
+#endif
+
+#ifdef UNK
+static double RP[4] = {
+-4.79443220978201773821E9,
+ 1.95617491946556577543E12,
+-2.49248344360967716204E14,
+ 9.70862251047306323952E15,
+};
+static double RQ[8] = {
+/* 1.00000000000000000000E0,*/
+ 4.99563147152651017219E2,
+ 1.73785401676374683123E5,
+ 4.84409658339962045305E7,
+ 1.11855537045356834862E10,
+ 2.11277520115489217587E12,
+ 3.10518229857422583814E14,
+ 3.18121955943204943306E16,
+ 1.71086294081043136091E18,
+};
+#endif
+#ifdef DEC
+static unsigned short RP[16] = {
+0150216,0161235,0064344,0014450,
+0052343,0135216,0035624,0144153,
+0154142,0130247,0003310,0003667,
+0055411,0173703,0047772,0176635,
+};
+static unsigned short RQ[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0042371,0144025,0032265,0136137,
+0044451,0133131,0132420,0151466,
+0046470,0144641,0072540,0030636,
+0050446,0126600,0045042,0044243,
+0052365,0172633,0110301,0071063,
+0054215,0032424,0062272,0043513,
+0055742,0005013,0171731,0072335,
+0057275,0170646,0036663,0013134,
+};
+#endif
+#ifdef IBMPC
+static unsigned short RP[16] = {
+0x8325,0xad1c,0xdc53,0xc1f1,
+0x990d,0xc772,0x7751,0x427c,
+0x00f7,0xe0d9,0x5614,0xc2ec,
+0x5fb4,0x69ff,0x3ef8,0x4341,
+};
+static unsigned short RQ[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xb78c,0xa696,0x3902,0x407f,
+0x1a67,0x36a2,0x36cb,0x4105,
+0x0634,0x2eac,0x1934,0x4187,
+0x4914,0x0944,0xd5b0,0x4204,
+0x2e46,0x7218,0xbeb3,0x427e,
+0x48e9,0x8c97,0xa6a2,0x42f1,
+0x2e9c,0x7e7b,0x4141,0x435c,
+0x62cc,0xc7b6,0xbe34,0x43b7,
+};
+#endif
+#ifdef MIEEE
+static unsigned short RP[16] = {
+0xc1f1,0xdc53,0xad1c,0x8325,
+0x427c,0x7751,0xc772,0x990d,
+0xc2ec,0x5614,0xe0d9,0x00f7,
+0x4341,0x3ef8,0x69ff,0x5fb4,
+};
+static unsigned short RQ[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x407f,0x3902,0xa696,0xb78c,
+0x4105,0x36cb,0x36a2,0x1a67,
+0x4187,0x1934,0x2eac,0x0634,
+0x4204,0xd5b0,0x0944,0x4914,
+0x427e,0xbeb3,0x7218,0x2e46,
+0x42f1,0xa6a2,0x8c97,0x48e9,
+0x435c,0x4141,0x7e7b,0x2e9c,
+0x43b7,0xbe34,0xc7b6,0x62cc,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double log ( double );
+extern double sin ( double );
+extern double cos ( double );
+extern double sqrt ( double );
+double j0 ( double );
+#else
+double polevl(), p1evl(), log(), sin(), cos(), sqrt();
+double j0();
+#endif
+extern double TWOOPI, SQ2OPI, PIO4;
+
+double j0(x)
+double x;
+{
+double w, z, p, q, xn;
+
+if( x < 0 )
+ x = -x;
+
+if( x <= 5.0 )
+ {
+ z = x * x;
+ if( x < 1.0e-5 )
+ return( 1.0 - z/4.0 );
+
+ p = (z - DR1) * (z - DR2);
+ p = p * polevl( z, RP, 3)/p1evl( z, RQ, 8 );
+ return( p );
+ }
+
+w = 5.0/x;
+q = 25.0/(x*x);
+p = polevl( q, PP, 6)/polevl( q, PQ, 6 );
+q = polevl( q, QP, 7)/p1evl( q, QQ, 7 );
+xn = x - PIO4;
+p = p * cos(xn) - w * q * sin(xn);
+return( p * SQ2OPI / sqrt(x) );
+}
+
+/* y0() 2 */
+/* Bessel function of second kind, order zero */
+
+/* Rational approximation coefficients YP[], YQ[] are used here.
+ * The function computed is y0(x) - 2 * log(x) * j0(x) / PI,
+ * whose value at x = 0 is 2 * ( log(0.5) + EUL ) / PI
+ * = 0.073804295108687225.
+ */
+
+/*
+#define PIO4 .78539816339744830962
+#define SQ2OPI .79788456080286535588
+*/
+extern double MAXNUM;
+
+double y0(x)
+double x;
+{
+double w, z, p, q, xn;
+
+if( x <= 5.0 )
+ {
+ if( x <= 0.0 )
+ {
+ mtherr( "y0", DOMAIN );
+ return( -MAXNUM );
+ }
+ z = x * x;
+ w = polevl( z, YP, 7) / p1evl( z, YQ, 7 );
+ w += TWOOPI * log(x) * j0(x);
+ return( w );
+ }
+
+w = 5.0/x;
+z = 25.0 / (x * x);
+p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
+q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
+xn = x - PIO4;
+p = p * sin(xn) + w * q * cos(xn);
+return( p * SQ2OPI / sqrt(x) );
+}
diff --git a/libm/double/j1.c b/libm/double/j1.c
new file mode 100644
index 000000000..95e46ea79
--- /dev/null
+++ b/libm/double/j1.c
@@ -0,0 +1,515 @@
+/* j1.c
+ *
+ * Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, j1();
+ *
+ * y = j1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order one of the argument.
+ *
+ * The domain is divided into the intervals [0, 8] and
+ * (8, infinity). In the first interval a 24 term Chebyshev
+ * expansion is used. In the second, the asymptotic
+ * trigonometric representation is employed using two
+ * rational functions of degree 5/5.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 10000 4.0e-17 1.1e-17
+ * IEEE 0, 30 30000 2.6e-16 1.1e-16
+ *
+ *
+ */
+ /* y1.c
+ *
+ * Bessel function of second kind of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y1();
+ *
+ * y = y1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind of order one
+ * of the argument.
+ *
+ * The domain is divided into the intervals [0, 8] and
+ * (8, infinity). In the first interval a 25 term Chebyshev
+ * expansion is used, and a call to j1() is required.
+ * In the second, the asymptotic trigonometric representation
+ * is employed using two rational functions of degree 5/5.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 10000 8.6e-17 1.3e-17
+ * IEEE 0, 30 30000 1.0e-15 1.3e-16
+ *
+ * (error criterion relative when |y1| > 1).
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+/*
+#define PIO4 .78539816339744830962
+#define THPIO4 2.35619449019234492885
+#define SQ2OPI .79788456080286535588
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double RP[4] = {
+-8.99971225705559398224E8,
+ 4.52228297998194034323E11,
+-7.27494245221818276015E13,
+ 3.68295732863852883286E15,
+};
+static double RQ[8] = {
+/* 1.00000000000000000000E0,*/
+ 6.20836478118054335476E2,
+ 2.56987256757748830383E5,
+ 8.35146791431949253037E7,
+ 2.21511595479792499675E10,
+ 4.74914122079991414898E12,
+ 7.84369607876235854894E14,
+ 8.95222336184627338078E16,
+ 5.32278620332680085395E18,
+};
+#endif
+#ifdef DEC
+static unsigned short RP[16] = {
+0147526,0110742,0063322,0077052,
+0051722,0112720,0065034,0061530,
+0153604,0052227,0033147,0105650,
+0055121,0055025,0032276,0022015,
+};
+static unsigned short RQ[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0042433,0032610,0155604,0033473,
+0044572,0173320,0067270,0006616,
+0046637,0045246,0162225,0006606,
+0050645,0004773,0157577,0053004,
+0052612,0033734,0001667,0176501,
+0054462,0054121,0173147,0121367,
+0056237,0002777,0121451,0176007,
+0057623,0136253,0131601,0044710,
+};
+#endif
+#ifdef IBMPC
+static unsigned short RP[16] = {
+0x4fc5,0x4cda,0xd23c,0xc1ca,
+0x8c6b,0x0d43,0x52ba,0x425a,
+0xf175,0xe6cc,0x8a92,0xc2d0,
+0xc482,0xa697,0x2b42,0x432a,
+};
+static unsigned short RQ[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x86e7,0x1b70,0x66b1,0x4083,
+0x01b2,0x0dd7,0x5eda,0x410f,
+0xa1b1,0xdc92,0xe954,0x4193,
+0xeac1,0x7bef,0xa13f,0x4214,
+0xffa8,0x8076,0x46fb,0x4291,
+0xf45f,0x3ecc,0x4b0a,0x4306,
+0x3f81,0xf465,0xe0bf,0x4373,
+0x2939,0x7670,0x7795,0x43d2,
+};
+#endif
+#ifdef MIEEE
+static unsigned short RP[16] = {
+0xc1ca,0xd23c,0x4cda,0x4fc5,
+0x425a,0x52ba,0x0d43,0x8c6b,
+0xc2d0,0x8a92,0xe6cc,0xf175,
+0x432a,0x2b42,0xa697,0xc482,
+};
+static unsigned short RQ[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4083,0x66b1,0x1b70,0x86e7,
+0x410f,0x5eda,0x0dd7,0x01b2,
+0x4193,0xe954,0xdc92,0xa1b1,
+0x4214,0xa13f,0x7bef,0xeac1,
+0x4291,0x46fb,0x8076,0xffa8,
+0x4306,0x4b0a,0x3ecc,0xf45f,
+0x4373,0xe0bf,0xf465,0x3f81,
+0x43d2,0x7795,0x7670,0x2939,
+};
+#endif
+
+#ifdef UNK
+static double PP[7] = {
+ 7.62125616208173112003E-4,
+ 7.31397056940917570436E-2,
+ 1.12719608129684925192E0,
+ 5.11207951146807644818E0,
+ 8.42404590141772420927E0,
+ 5.21451598682361504063E0,
+ 1.00000000000000000254E0,
+};
+static double PQ[7] = {
+ 5.71323128072548699714E-4,
+ 6.88455908754495404082E-2,
+ 1.10514232634061696926E0,
+ 5.07386386128601488557E0,
+ 8.39985554327604159757E0,
+ 5.20982848682361821619E0,
+ 9.99999999999999997461E-1,
+};
+#endif
+#ifdef DEC
+static unsigned short PP[28] = {
+0035507,0144542,0061543,0024326,
+0037225,0145105,0017766,0022661,
+0040220,0043766,0010254,0133255,
+0040643,0113047,0142611,0151521,
+0041006,0144344,0055351,0074261,
+0040646,0156520,0120574,0006416,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short PQ[28] = {
+0035425,0142330,0115041,0165514,
+0037214,0177352,0145105,0052026,
+0040215,0072515,0141207,0073255,
+0040642,0056427,0137222,0106405,
+0041006,0062716,0166427,0165450,
+0040646,0133352,0035425,0123304,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short PP[28] = {
+0x651b,0x4c6c,0xf92c,0x3f48,
+0xc4b6,0xa3fe,0xb948,0x3fb2,
+0x96d6,0xc215,0x08fe,0x3ff2,
+0x3a6a,0xf8b1,0x72c4,0x4014,
+0x2f16,0x8b5d,0xd91c,0x4020,
+0x81a2,0x142f,0xdbaa,0x4014,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short PQ[28] = {
+0x3d69,0x1344,0xb89b,0x3f42,
+0xaa83,0x5948,0x9fdd,0x3fb1,
+0xeed6,0xb850,0xaea9,0x3ff1,
+0x51a1,0xf7d2,0x4ba2,0x4014,
+0xfd65,0xdda2,0xccb9,0x4020,
+0xb4d9,0x4762,0xd6dd,0x4014,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short PP[28] = {
+0x3f48,0xf92c,0x4c6c,0x651b,
+0x3fb2,0xb948,0xa3fe,0xc4b6,
+0x3ff2,0x08fe,0xc215,0x96d6,
+0x4014,0x72c4,0xf8b1,0x3a6a,
+0x4020,0xd91c,0x8b5d,0x2f16,
+0x4014,0xdbaa,0x142f,0x81a2,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short PQ[28] = {
+0x3f42,0xb89b,0x1344,0x3d69,
+0x3fb1,0x9fdd,0x5948,0xaa83,
+0x3ff1,0xaea9,0xb850,0xeed6,
+0x4014,0x4ba2,0xf7d2,0x51a1,
+0x4020,0xccb9,0xdda2,0xfd65,
+0x4014,0xd6dd,0x4762,0xb4d9,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+
+#ifdef UNK
+static double QP[8] = {
+ 5.10862594750176621635E-2,
+ 4.98213872951233449420E0,
+ 7.58238284132545283818E1,
+ 3.66779609360150777800E2,
+ 7.10856304998926107277E2,
+ 5.97489612400613639965E2,
+ 2.11688757100572135698E2,
+ 2.52070205858023719784E1,
+};
+static double QQ[7] = {
+/* 1.00000000000000000000E0,*/
+ 7.42373277035675149943E1,
+ 1.05644886038262816351E3,
+ 4.98641058337653607651E3,
+ 9.56231892404756170795E3,
+ 7.99704160447350683650E3,
+ 2.82619278517639096600E3,
+ 3.36093607810698293419E2,
+};
+#endif
+#ifdef DEC
+static unsigned short QP[32] = {
+0037121,0037723,0055605,0151004,
+0040637,0066656,0031554,0077264,
+0041627,0122714,0153170,0161466,
+0042267,0061712,0036520,0140145,
+0042461,0133315,0131573,0071176,
+0042425,0057525,0147500,0013201,
+0042123,0130122,0061245,0154131,
+0041311,0123772,0064254,0172650,
+};
+static unsigned short QQ[28] = {
+/*0040200,0000000,0000000,0000000,*/
+0041624,0074603,0002112,0101670,
+0042604,0007135,0010162,0175565,
+0043233,0151510,0157757,0172010,
+0043425,0064506,0112006,0104276,
+0043371,0164125,0032271,0164242,
+0043060,0121425,0122750,0136013,
+0042250,0005773,0053472,0146267,
+};
+#endif
+#ifdef IBMPC
+static unsigned short QP[32] = {
+0xba40,0x6b70,0x27fa,0x3faa,
+0x8fd6,0xc66d,0xedb5,0x4013,
+0x1c67,0x9acf,0xf4b9,0x4052,
+0x180d,0x47aa,0xec79,0x4076,
+0x6e50,0xb66f,0x36d9,0x4086,
+0x02d0,0xb9e8,0xabea,0x4082,
+0xbb0b,0x4c54,0x760a,0x406a,
+0x9eb5,0x4d15,0x34ff,0x4039,
+};
+static unsigned short QQ[28] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x5077,0x6089,0x8f30,0x4052,
+0x5f6f,0xa20e,0x81cb,0x4090,
+0xfe81,0x1bfd,0x7a69,0x40b3,
+0xd118,0xd280,0xad28,0x40c2,
+0x3d14,0xa697,0x3d0a,0x40bf,
+0x1781,0xb4bd,0x1462,0x40a6,
+0x5997,0x6ae7,0x017f,0x4075,
+};
+#endif
+#ifdef MIEEE
+static unsigned short QP[32] = {
+0x3faa,0x27fa,0x6b70,0xba40,
+0x4013,0xedb5,0xc66d,0x8fd6,
+0x4052,0xf4b9,0x9acf,0x1c67,
+0x4076,0xec79,0x47aa,0x180d,
+0x4086,0x36d9,0xb66f,0x6e50,
+0x4082,0xabea,0xb9e8,0x02d0,
+0x406a,0x760a,0x4c54,0xbb0b,
+0x4039,0x34ff,0x4d15,0x9eb5,
+};
+static unsigned short QQ[28] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4052,0x8f30,0x6089,0x5077,
+0x4090,0x81cb,0xa20e,0x5f6f,
+0x40b3,0x7a69,0x1bfd,0xfe81,
+0x40c2,0xad28,0xd280,0xd118,
+0x40bf,0x3d0a,0xa697,0x3d14,
+0x40a6,0x1462,0xb4bd,0x1781,
+0x4075,0x017f,0x6ae7,0x5997,
+};
+#endif
+
+#ifdef UNK
+static double YP[6] = {
+ 1.26320474790178026440E9,
+-6.47355876379160291031E11,
+ 1.14509511541823727583E14,
+-8.12770255501325109621E15,
+ 2.02439475713594898196E17,
+-7.78877196265950026825E17,
+};
+static double YQ[8] = {
+/* 1.00000000000000000000E0,*/
+ 5.94301592346128195359E2,
+ 2.35564092943068577943E5,
+ 7.34811944459721705660E7,
+ 1.87601316108706159478E10,
+ 3.88231277496238566008E12,
+ 6.20557727146953693363E14,
+ 6.87141087355300489866E16,
+ 3.97270608116560655612E18,
+};
+#endif
+#ifdef DEC
+static unsigned short YP[24] = {
+0047626,0112763,0013715,0133045,
+0152026,0134552,0142033,0024411,
+0053720,0045245,0102210,0077565,
+0155347,0000321,0136415,0102031,
+0056463,0146550,0055633,0032605,
+0157054,0171012,0167361,0054265,
+};
+static unsigned short YQ[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0042424,0111515,0044773,0153014,
+0044546,0005405,0171307,0075774,
+0046614,0023575,0047105,0063556,
+0050613,0143034,0101533,0156026,
+0052541,0175367,0166514,0114257,
+0054415,0014466,0134350,0171154,
+0056164,0017436,0025075,0022101,
+0057534,0103614,0103663,0121772,
+};
+#endif
+#ifdef IBMPC
+static unsigned short YP[24] = {
+0xb6c5,0x62f9,0xd2be,0x41d2,
+0x6521,0x5883,0xd72d,0xc262,
+0x0fef,0xb091,0x0954,0x42da,
+0xb083,0x37a1,0xe01a,0xc33c,
+0x66b1,0x0b73,0x79ad,0x4386,
+0x2b17,0x5dde,0x9e41,0xc3a5,
+};
+static unsigned short YQ[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x7ac2,0xa93f,0x9269,0x4082,
+0xef7f,0xbe58,0xc160,0x410c,
+0xacee,0xa9c8,0x84ef,0x4191,
+0x7b83,0x906b,0x78c3,0x4211,
+0x9316,0xfda9,0x3f5e,0x428c,
+0x1e4e,0xd71d,0xa326,0x4301,
+0xa488,0xc547,0x83e3,0x436e,
+0x747f,0x90f6,0x90f1,0x43cb,
+};
+#endif
+#ifdef MIEEE
+static unsigned short YP[24] = {
+0x41d2,0xd2be,0x62f9,0xb6c5,
+0xc262,0xd72d,0x5883,0x6521,
+0x42da,0x0954,0xb091,0x0fef,
+0xc33c,0xe01a,0x37a1,0xb083,
+0x4386,0x79ad,0x0b73,0x66b1,
+0xc3a5,0x9e41,0x5dde,0x2b17,
+};
+static unsigned short YQ[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4082,0x9269,0xa93f,0x7ac2,
+0x410c,0xc160,0xbe58,0xef7f,
+0x4191,0x84ef,0xa9c8,0xacee,
+0x4211,0x78c3,0x906b,0x7b83,
+0x428c,0x3f5e,0xfda9,0x9316,
+0x4301,0xa326,0xd71d,0x1e4e,
+0x436e,0x83e3,0xc547,0xa488,
+0x43cb,0x90f1,0x90f6,0x747f,
+};
+#endif
+
+
+#ifdef UNK
+static double Z1 = 1.46819706421238932572E1;
+static double Z2 = 4.92184563216946036703E1;
+#endif
+
+#ifdef DEC
+static unsigned short DZ1[] = {0041152,0164532,0006114,0010540};
+static unsigned short DZ2[] = {0041504,0157663,0001625,0020621};
+#define Z1 (*(double *)DZ1)
+#define Z2 (*(double *)DZ2)
+#endif
+
+#ifdef IBMPC
+static unsigned short DZ1[] = {0x822c,0x4189,0x5d2b,0x402d};
+static unsigned short DZ2[] = {0xa432,0x6072,0x9bf6,0x4048};
+#define Z1 (*(double *)DZ1)
+#define Z2 (*(double *)DZ2)
+#endif
+
+#ifdef MIEEE
+static unsigned short DZ1[] = {0x402d,0x5d2b,0x4189,0x822c};
+static unsigned short DZ2[] = {0x4048,0x9bf6,0x6072,0xa432};
+#define Z1 (*(double *)DZ1)
+#define Z2 (*(double *)DZ2)
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double log ( double );
+extern double sin ( double );
+extern double cos ( double );
+extern double sqrt ( double );
+double j1 ( double );
+#else
+double polevl(), p1evl(), log(), sin(), cos(), sqrt();
+double j1();
+#endif
+extern double TWOOPI, THPIO4, SQ2OPI;
+
+double j1(x)
+double x;
+{
+double w, z, p, q, xn;
+
+w = x;
+if( x < 0 )
+ w = -x;
+
+if( w <= 5.0 )
+ {
+ z = x * x;
+ w = polevl( z, RP, 3 ) / p1evl( z, RQ, 8 );
+ w = w * x * (z - Z1) * (z - Z2);
+ return( w );
+ }
+
+w = 5.0/x;
+z = w * w;
+p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
+q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
+xn = x - THPIO4;
+p = p * cos(xn) - w * q * sin(xn);
+return( p * SQ2OPI / sqrt(x) );
+}
+
+
+extern double MAXNUM;
+
+double y1(x)
+double x;
+{
+double w, z, p, q, xn;
+
+if( x <= 5.0 )
+ {
+ if( x <= 0.0 )
+ {
+ mtherr( "y1", DOMAIN );
+ return( -MAXNUM );
+ }
+ z = x * x;
+ w = x * (polevl( z, YP, 5 ) / p1evl( z, YQ, 8 ));
+ w += TWOOPI * ( j1(x) * log(x) - 1.0/x );
+ return( w );
+ }
+
+w = 5.0/x;
+z = w * w;
+p = polevl( z, PP, 6)/polevl( z, PQ, 6 );
+q = polevl( z, QP, 7)/p1evl( z, QQ, 7 );
+xn = x - THPIO4;
+p = p * sin(xn) + w * q * cos(xn);
+return( p * SQ2OPI / sqrt(x) );
+}
diff --git a/libm/double/jn.c b/libm/double/jn.c
new file mode 100644
index 000000000..ee05395aa
--- /dev/null
+++ b/libm/double/jn.c
@@ -0,0 +1,133 @@
+/* jn.c
+ *
+ * Bessel function of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double x, y, jn();
+ *
+ * y = jn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The ratio of jn(x) to j0(x) is computed by backward
+ * recurrence. First the ratio jn/jn-1 is found by a
+ * continued fraction expansion. Then the recurrence
+ * relating successive orders is applied until j0 or j1 is
+ * reached.
+ *
+ * If n = 0 or 1 the routine for j0 or j1 is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic range # trials peak rms
+ * DEC 0, 30 5500 6.9e-17 9.3e-18
+ * IEEE 0, 30 5000 4.4e-16 7.9e-17
+ *
+ *
+ * Not suitable for large n or x. Use jv() instead.
+ *
+ */
+
+/* jn.c
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+#include <math.h>
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double j0 ( double );
+extern double j1 ( double );
+#else
+double fabs(), j0(), j1();
+#endif
+extern double MACHEP;
+
+double jn( n, x )
+int n;
+double x;
+{
+double pkm2, pkm1, pk, xk, r, ans;
+int k, sign;
+
+if( n < 0 )
+ {
+ n = -n;
+ if( (n & 1) == 0 ) /* -1**n */
+ sign = 1;
+ else
+ sign = -1;
+ }
+else
+ sign = 1;
+
+if( x < 0.0 )
+ {
+ if( n & 1 )
+ sign = -sign;
+ x = -x;
+ }
+
+if( n == 0 )
+ return( sign * j0(x) );
+if( n == 1 )
+ return( sign * j1(x) );
+if( n == 2 )
+ return( sign * (2.0 * j1(x) / x - j0(x)) );
+
+if( x < MACHEP )
+ return( 0.0 );
+
+/* continued fraction */
+#ifdef DEC
+k = 56;
+#else
+k = 53;
+#endif
+
+pk = 2 * (n + k);
+ans = pk;
+xk = x * x;
+
+do
+ {
+ pk -= 2.0;
+ ans = pk - (xk/ans);
+ }
+while( --k > 0 );
+ans = x/ans;
+
+/* backward recurrence */
+
+pk = 1.0;
+pkm1 = 1.0/ans;
+k = n-1;
+r = 2 * k;
+
+do
+ {
+ pkm2 = (pkm1 * r - pk * x) / x;
+ pk = pkm1;
+ pkm1 = pkm2;
+ r -= 2.0;
+ }
+while( --k > 0 );
+
+if( fabs(pk) > fabs(pkm1) )
+ ans = j1(x)/pk;
+else
+ ans = j0(x)/pkm1;
+return( sign * ans );
+}
diff --git a/libm/double/jv.c b/libm/double/jv.c
new file mode 100644
index 000000000..5b8af3663
--- /dev/null
+++ b/libm/double/jv.c
@@ -0,0 +1,884 @@
+/* jv.c
+ *
+ * Bessel function of noninteger order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, jv();
+ *
+ * y = jv( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order v of the argument,
+ * where v is real. Negative x is allowed if v is an integer.
+ *
+ * Several expansions are included: the ascending power
+ * series, the Hankel expansion, and two transitional
+ * expansions for large v. If v is not too large, it
+ * is reduced by recurrence to a region of best accuracy.
+ * The transitional expansions give 12D accuracy for v > 500.
+ *
+ *
+ *
+ * ACCURACY:
+ * Results for integer v are indicated by *, where x and v
+ * both vary from -125 to +125. Otherwise,
+ * x ranges from 0 to 125, v ranges as indicated by "domain."
+ * Error criterion is absolute, except relative when |jv()| > 1.
+ *
+ * arithmetic v domain x domain # trials peak rms
+ * IEEE 0,125 0,125 100000 4.6e-15 2.2e-16
+ * IEEE -125,0 0,125 40000 5.4e-11 3.7e-13
+ * IEEE 0,500 0,500 20000 4.4e-15 4.0e-16
+ * Integer v:
+ * IEEE -125,125 -125,125 50000 3.5e-15* 1.9e-16*
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+#define DEBUG 0
+
+#ifdef DEC
+#define MAXGAM 34.84425627277176174
+#else
+#define MAXGAM 171.624376956302725
+#endif
+
+#ifdef ANSIPROT
+extern int airy ( double, double *, double *, double *, double * );
+extern double fabs ( double );
+extern double floor ( double );
+extern double frexp ( double, int * );
+extern double polevl ( double, void *, int );
+extern double j0 ( double );
+extern double j1 ( double );
+extern double sqrt ( double );
+extern double cbrt ( double );
+extern double exp ( double );
+extern double log ( double );
+extern double sin ( double );
+extern double cos ( double );
+extern double acos ( double );
+extern double pow ( double, double );
+extern double gamma ( double );
+extern double lgam ( double );
+static double recur(double *, double, double *, int);
+static double jvs(double, double);
+static double hankel(double, double);
+static double jnx(double, double);
+static double jnt(double, double);
+#else
+int airy();
+double fabs(), floor(), frexp(), polevl(), j0(), j1(), sqrt(), cbrt();
+double exp(), log(), sin(), cos(), acos(), pow(), gamma(), lgam();
+static double recur(), jvs(), hankel(), jnx(), jnt();
+#endif
+
+extern double MAXNUM, MACHEP, MINLOG, MAXLOG;
+#define BIG 1.44115188075855872E+17
+
+double jv( n, x )
+double n, x;
+{
+double k, q, t, y, an;
+int i, sign, nint;
+
+nint = 0; /* Flag for integer n */
+sign = 1; /* Flag for sign inversion */
+an = fabs( n );
+y = floor( an );
+if( y == an )
+ {
+ nint = 1;
+ i = an - 16384.0 * floor( an/16384.0 );
+ if( n < 0.0 )
+ {
+ if( i & 1 )
+ sign = -sign;
+ n = an;
+ }
+ if( x < 0.0 )
+ {
+ if( i & 1 )
+ sign = -sign;
+ x = -x;
+ }
+ if( n == 0.0 )
+ return( j0(x) );
+ if( n == 1.0 )
+ return( sign * j1(x) );
+ }
+
+if( (x < 0.0) && (y != an) )
+ {
+ mtherr( "Jv", DOMAIN );
+ y = 0.0;
+ goto done;
+ }
+
+y = fabs(x);
+
+if( y < MACHEP )
+ goto underf;
+
+k = 3.6 * sqrt(y);
+t = 3.6 * sqrt(an);
+if( (y < t) && (an > 21.0) )
+ return( sign * jvs(n,x) );
+if( (an < k) && (y > 21.0) )
+ return( sign * hankel(n,x) );
+
+if( an < 500.0 )
+ {
+/* Note: if x is too large, the continued
+ * fraction will fail; but then the
+ * Hankel expansion can be used.
+ */
+ if( nint != 0 )
+ {
+ k = 0.0;
+ q = recur( &n, x, &k, 1 );
+ if( k == 0.0 )
+ {
+ y = j0(x)/q;
+ goto done;
+ }
+ if( k == 1.0 )
+ {
+ y = j1(x)/q;
+ goto done;
+ }
+ }
+
+if( an > 2.0 * y )
+ goto rlarger;
+
+ if( (n >= 0.0) && (n < 20.0)
+ && (y > 6.0) && (y < 20.0) )
+ {
+/* Recur backwards from a larger value of n
+ */
+rlarger:
+ k = n;
+
+ y = y + an + 1.0;
+ if( y < 30.0 )
+ y = 30.0;
+ y = n + floor(y-n);
+ q = recur( &y, x, &k, 0 );
+ y = jvs(y,x) * q;
+ goto done;
+ }
+
+ if( k <= 30.0 )
+ {
+ k = 2.0;
+ }
+ else if( k < 90.0 )
+ {
+ k = (3*k)/4;
+ }
+ if( an > (k + 3.0) )
+ {
+ if( n < 0.0 )
+ k = -k;
+ q = n - floor(n);
+ k = floor(k) + q;
+ if( n > 0.0 )
+ q = recur( &n, x, &k, 1 );
+ else
+ {
+ t = k;
+ k = n;
+ q = recur( &t, x, &k, 1 );
+ k = t;
+ }
+ if( q == 0.0 )
+ {
+underf:
+ y = 0.0;
+ goto done;
+ }
+ }
+ else
+ {
+ k = n;
+ q = 1.0;
+ }
+
+/* boundary between convergence of
+ * power series and Hankel expansion
+ */
+ y = fabs(k);
+ if( y < 26.0 )
+ t = (0.0083*y + 0.09)*y + 12.9;
+ else
+ t = 0.9 * y;
+
+ if( x > t )
+ y = hankel(k,x);
+ else
+ y = jvs(k,x);
+#if DEBUG
+printf( "y = %.16e, recur q = %.16e\n", y, q );
+#endif
+ if( n > 0.0 )
+ y /= q;
+ else
+ y *= q;
+ }
+
+else
+ {
+/* For large n, use the uniform expansion
+ * or the transitional expansion.
+ * But if x is of the order of n**2,
+ * these may blow up, whereas the
+ * Hankel expansion will then work.
+ */
+ if( n < 0.0 )
+ {
+ mtherr( "Jv", TLOSS );
+ y = 0.0;
+ goto done;
+ }
+ t = x/n;
+ t /= n;
+ if( t > 0.3 )
+ y = hankel(n,x);
+ else
+ y = jnx(n,x);
+ }
+
+done: return( sign * y);
+}
+
+/* Reduce the order by backward recurrence.
+ * AMS55 #9.1.27 and 9.1.73.
+ */
+
+static double recur( n, x, newn, cancel )
+double *n;
+double x;
+double *newn;
+int cancel;
+{
+double pkm2, pkm1, pk, qkm2, qkm1;
+/* double pkp1; */
+double k, ans, qk, xk, yk, r, t, kf;
+static double big = BIG;
+int nflag, ctr;
+
+/* continued fraction for Jn(x)/Jn-1(x) */
+if( *n < 0.0 )
+ nflag = 1;
+else
+ nflag = 0;
+
+fstart:
+
+#if DEBUG
+printf( "recur: n = %.6e, newn = %.6e, cfrac = ", *n, *newn );
+#endif
+
+pkm2 = 0.0;
+qkm2 = 1.0;
+pkm1 = x;
+qkm1 = *n + *n;
+xk = -x * x;
+yk = qkm1;
+ans = 1.0;
+ctr = 0;
+do
+ {
+ yk += 2.0;
+ pk = pkm1 * yk + pkm2 * xk;
+ qk = qkm1 * yk + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+ if( qk != 0 )
+ r = pk/qk;
+ else
+ r = 0.0;
+ if( r != 0 )
+ {
+ t = fabs( (ans - r)/r );
+ ans = r;
+ }
+ else
+ t = 1.0;
+
+ if( ++ctr > 1000 )
+ {
+ mtherr( "jv", UNDERFLOW );
+ goto done;
+ }
+ if( t < MACHEP )
+ goto done;
+
+ if( fabs(pk) > big )
+ {
+ pkm2 /= big;
+ pkm1 /= big;
+ qkm2 /= big;
+ qkm1 /= big;
+ }
+ }
+while( t > MACHEP );
+
+done:
+
+#if DEBUG
+printf( "%.6e\n", ans );
+#endif
+
+/* Change n to n-1 if n < 0 and the continued fraction is small
+ */
+if( nflag > 0 )
+ {
+ if( fabs(ans) < 0.125 )
+ {
+ nflag = -1;
+ *n = *n - 1.0;
+ goto fstart;
+ }
+ }
+
+
+kf = *newn;
+
+/* backward recurrence
+ * 2k
+ * J (x) = --- J (x) - J (x)
+ * k-1 x k k+1
+ */
+
+pk = 1.0;
+pkm1 = 1.0/ans;
+k = *n - 1.0;
+r = 2 * k;
+do
+ {
+ pkm2 = (pkm1 * r - pk * x) / x;
+ /* pkp1 = pk; */
+ pk = pkm1;
+ pkm1 = pkm2;
+ r -= 2.0;
+/*
+ t = fabs(pkp1) + fabs(pk);
+ if( (k > (kf + 2.5)) && (fabs(pkm1) < 0.25*t) )
+ {
+ k -= 1.0;
+ t = x*x;
+ pkm2 = ( (r*(r+2.0)-t)*pk - r*x*pkp1 )/t;
+ pkp1 = pk;
+ pk = pkm1;
+ pkm1 = pkm2;
+ r -= 2.0;
+ }
+*/
+ k -= 1.0;
+ }
+while( k > (kf + 0.5) );
+
+/* Take the larger of the last two iterates
+ * on the theory that it may have less cancellation error.
+ */
+
+if( cancel )
+ {
+ if( (kf >= 0.0) && (fabs(pk) > fabs(pkm1)) )
+ {
+ k += 1.0;
+ pkm2 = pk;
+ }
+ }
+*newn = k;
+#if DEBUG
+printf( "newn %.6e rans %.6e\n", k, pkm2 );
+#endif
+return( pkm2 );
+}
+
+
+
+/* Ascending power series for Jv(x).
+ * AMS55 #9.1.10.
+ */
+
+extern double PI;
+extern int sgngam;
+
+static double jvs( n, x )
+double n, x;
+{
+double t, u, y, z, k;
+int ex;
+
+z = -x * x / 4.0;
+u = 1.0;
+y = u;
+k = 1.0;
+t = 1.0;
+
+while( t > MACHEP )
+ {
+ u *= z / (k * (n+k));
+ y += u;
+ k += 1.0;
+ if( y != 0 )
+ t = fabs( u/y );
+ }
+#if DEBUG
+printf( "power series=%.5e ", y );
+#endif
+t = frexp( 0.5*x, &ex );
+ex = ex * n;
+if( (ex > -1023)
+ && (ex < 1023)
+ && (n > 0.0)
+ && (n < (MAXGAM-1.0)) )
+ {
+ t = pow( 0.5*x, n ) / gamma( n + 1.0 );
+#if DEBUG
+printf( "pow(.5*x, %.4e)/gamma(n+1)=%.5e\n", n, t );
+#endif
+ y *= t;
+ }
+else
+ {
+#if DEBUG
+ z = n * log(0.5*x);
+ k = lgam( n+1.0 );
+ t = z - k;
+ printf( "log pow=%.5e, lgam(%.4e)=%.5e\n", z, n+1.0, k );
+#else
+ t = n * log(0.5*x) - lgam(n + 1.0);
+#endif
+ if( y < 0 )
+ {
+ sgngam = -sgngam;
+ y = -y;
+ }
+ t += log(y);
+#if DEBUG
+printf( "log y=%.5e\n", log(y) );
+#endif
+ if( t < -MAXLOG )
+ {
+ return( 0.0 );
+ }
+ if( t > MAXLOG )
+ {
+ mtherr( "Jv", OVERFLOW );
+ return( MAXNUM );
+ }
+ y = sgngam * exp( t );
+ }
+return(y);
+}
+
+/* Hankel's asymptotic expansion
+ * for large x.
+ * AMS55 #9.2.5.
+ */
+
+static double hankel( n, x )
+double n, x;
+{
+double t, u, z, k, sign, conv;
+double p, q, j, m, pp, qq;
+int flag;
+
+m = 4.0*n*n;
+j = 1.0;
+z = 8.0 * x;
+k = 1.0;
+p = 1.0;
+u = (m - 1.0)/z;
+q = u;
+sign = 1.0;
+conv = 1.0;
+flag = 0;
+t = 1.0;
+pp = 1.0e38;
+qq = 1.0e38;
+
+while( t > MACHEP )
+ {
+ k += 2.0;
+ j += 1.0;
+ sign = -sign;
+ u *= (m - k * k)/(j * z);
+ p += sign * u;
+ k += 2.0;
+ j += 1.0;
+ u *= (m - k * k)/(j * z);
+ q += sign * u;
+ t = fabs(u/p);
+ if( t < conv )
+ {
+ conv = t;
+ qq = q;
+ pp = p;
+ flag = 1;
+ }
+/* stop if the terms start getting larger */
+ if( (flag != 0) && (t > conv) )
+ {
+#if DEBUG
+ printf( "Hankel: convergence to %.4E\n", conv );
+#endif
+ goto hank1;
+ }
+ }
+
+hank1:
+u = x - (0.5*n + 0.25) * PI;
+t = sqrt( 2.0/(PI*x) ) * ( pp * cos(u) - qq * sin(u) );
+#if DEBUG
+printf( "hank: %.6e\n", t );
+#endif
+return( t );
+}
+
+
+/* Asymptotic expansion for large n.
+ * AMS55 #9.3.35.
+ */
+
+static double lambda[] = {
+ 1.0,
+ 1.041666666666666666666667E-1,
+ 8.355034722222222222222222E-2,
+ 1.282265745563271604938272E-1,
+ 2.918490264641404642489712E-1,
+ 8.816272674437576524187671E-1,
+ 3.321408281862767544702647E+0,
+ 1.499576298686255465867237E+1,
+ 7.892301301158651813848139E+1,
+ 4.744515388682643231611949E+2,
+ 3.207490090890661934704328E+3
+};
+static double mu[] = {
+ 1.0,
+ -1.458333333333333333333333E-1,
+ -9.874131944444444444444444E-2,
+ -1.433120539158950617283951E-1,
+ -3.172272026784135480967078E-1,
+ -9.424291479571202491373028E-1,
+ -3.511203040826354261542798E+0,
+ -1.572726362036804512982712E+1,
+ -8.228143909718594444224656E+1,
+ -4.923553705236705240352022E+2,
+ -3.316218568547972508762102E+3
+};
+static double P1[] = {
+ -2.083333333333333333333333E-1,
+ 1.250000000000000000000000E-1
+};
+static double P2[] = {
+ 3.342013888888888888888889E-1,
+ -4.010416666666666666666667E-1,
+ 7.031250000000000000000000E-2
+};
+static double P3[] = {
+ -1.025812596450617283950617E+0,
+ 1.846462673611111111111111E+0,
+ -8.912109375000000000000000E-1,
+ 7.324218750000000000000000E-2
+};
+static double P4[] = {
+ 4.669584423426247427983539E+0,
+ -1.120700261622299382716049E+1,
+ 8.789123535156250000000000E+0,
+ -2.364086914062500000000000E+0,
+ 1.121520996093750000000000E-1
+};
+static double P5[] = {
+ -2.8212072558200244877E1,
+ 8.4636217674600734632E1,
+ -9.1818241543240017361E1,
+ 4.2534998745388454861E1,
+ -7.3687943594796316964E0,
+ 2.27108001708984375E-1
+};
+static double P6[] = {
+ 2.1257013003921712286E2,
+ -7.6525246814118164230E2,
+ 1.0599904525279998779E3,
+ -6.9957962737613254123E2,
+ 2.1819051174421159048E2,
+ -2.6491430486951555525E1,
+ 5.7250142097473144531E-1
+};
+static double P7[] = {
+ -1.9194576623184069963E3,
+ 8.0617221817373093845E3,
+ -1.3586550006434137439E4,
+ 1.1655393336864533248E4,
+ -5.3056469786134031084E3,
+ 1.2009029132163524628E3,
+ -1.0809091978839465550E2,
+ 1.7277275025844573975E0
+};
+
+
+static double jnx( n, x )
+double n, x;
+{
+double zeta, sqz, zz, zp, np;
+double cbn, n23, t, z, sz;
+double pp, qq, z32i, zzi;
+double ak, bk, akl, bkl;
+int sign, doa, dob, nflg, k, s, tk, tkp1, m;
+static double u[8];
+static double ai, aip, bi, bip;
+
+/* Test for x very close to n.
+ * Use expansion for transition region if so.
+ */
+cbn = cbrt(n);
+z = (x - n)/cbn;
+if( fabs(z) <= 0.7 )
+ return( jnt(n,x) );
+
+z = x/n;
+zz = 1.0 - z*z;
+if( zz == 0.0 )
+ return(0.0);
+
+if( zz > 0.0 )
+ {
+ sz = sqrt( zz );
+ t = 1.5 * (log( (1.0+sz)/z ) - sz ); /* zeta ** 3/2 */
+ zeta = cbrt( t * t );
+ nflg = 1;
+ }
+else
+ {
+ sz = sqrt(-zz);
+ t = 1.5 * (sz - acos(1.0/z));
+ zeta = -cbrt( t * t );
+ nflg = -1;
+ }
+z32i = fabs(1.0/t);
+sqz = cbrt(t);
+
+/* Airy function */
+n23 = cbrt( n * n );
+t = n23 * zeta;
+
+#if DEBUG
+printf("zeta %.5E, Airy(%.5E)\n", zeta, t );
+#endif
+airy( t, &ai, &aip, &bi, &bip );
+
+/* polynomials in expansion */
+u[0] = 1.0;
+zzi = 1.0/zz;
+u[1] = polevl( zzi, P1, 1 )/sz;
+u[2] = polevl( zzi, P2, 2 )/zz;
+u[3] = polevl( zzi, P3, 3 )/(sz*zz);
+pp = zz*zz;
+u[4] = polevl( zzi, P4, 4 )/pp;
+u[5] = polevl( zzi, P5, 5 )/(pp*sz);
+pp *= zz;
+u[6] = polevl( zzi, P6, 6 )/pp;
+u[7] = polevl( zzi, P7, 7 )/(pp*sz);
+
+#if DEBUG
+for( k=0; k<=7; k++ )
+ printf( "u[%d] = %.5E\n", k, u[k] );
+#endif
+
+pp = 0.0;
+qq = 0.0;
+np = 1.0;
+/* flags to stop when terms get larger */
+doa = 1;
+dob = 1;
+akl = MAXNUM;
+bkl = MAXNUM;
+
+for( k=0; k<=3; k++ )
+ {
+ tk = 2 * k;
+ tkp1 = tk + 1;
+ zp = 1.0;
+ ak = 0.0;
+ bk = 0.0;
+ for( s=0; s<=tk; s++ )
+ {
+ if( doa )
+ {
+ if( (s & 3) > 1 )
+ sign = nflg;
+ else
+ sign = 1;
+ ak += sign * mu[s] * zp * u[tk-s];
+ }
+
+ if( dob )
+ {
+ m = tkp1 - s;
+ if( ((m+1) & 3) > 1 )
+ sign = nflg;
+ else
+ sign = 1;
+ bk += sign * lambda[s] * zp * u[m];
+ }
+ zp *= z32i;
+ }
+
+ if( doa )
+ {
+ ak *= np;
+ t = fabs(ak);
+ if( t < akl )
+ {
+ akl = t;
+ pp += ak;
+ }
+ else
+ doa = 0;
+ }
+
+ if( dob )
+ {
+ bk += lambda[tkp1] * zp * u[0];
+ bk *= -np/sqz;
+ t = fabs(bk);
+ if( t < bkl )
+ {
+ bkl = t;
+ qq += bk;
+ }
+ else
+ dob = 0;
+ }
+#if DEBUG
+ printf("a[%d] %.5E, b[%d] %.5E\n", k, ak, k, bk );
+#endif
+ if( np < MACHEP )
+ break;
+ np /= n*n;
+ }
+
+/* normalizing factor ( 4*zeta/(1 - z**2) )**1/4 */
+t = 4.0 * zeta/zz;
+t = sqrt( sqrt(t) );
+
+t *= ai*pp/cbrt(n) + aip*qq/(n23*n);
+return(t);
+}
+
+/* Asymptotic expansion for transition region,
+ * n large and x close to n.
+ * AMS55 #9.3.23.
+ */
+
+static double PF2[] = {
+ -9.0000000000000000000e-2,
+ 8.5714285714285714286e-2
+};
+static double PF3[] = {
+ 1.3671428571428571429e-1,
+ -5.4920634920634920635e-2,
+ -4.4444444444444444444e-3
+};
+static double PF4[] = {
+ 1.3500000000000000000e-3,
+ -1.6036054421768707483e-1,
+ 4.2590187590187590188e-2,
+ 2.7330447330447330447e-3
+};
+static double PG1[] = {
+ -2.4285714285714285714e-1,
+ 1.4285714285714285714e-2
+};
+static double PG2[] = {
+ -9.0000000000000000000e-3,
+ 1.9396825396825396825e-1,
+ -1.1746031746031746032e-2
+};
+static double PG3[] = {
+ 1.9607142857142857143e-2,
+ -1.5983694083694083694e-1,
+ 6.3838383838383838384e-3
+};
+
+
+static double jnt( n, x )
+double n, x;
+{
+double z, zz, z3;
+double cbn, n23, cbtwo;
+double ai, aip, bi, bip; /* Airy functions */
+double nk, fk, gk, pp, qq;
+double F[5], G[4];
+int k;
+
+cbn = cbrt(n);
+z = (x - n)/cbn;
+cbtwo = cbrt( 2.0 );
+
+/* Airy function */
+zz = -cbtwo * z;
+airy( zz, &ai, &aip, &bi, &bip );
+
+/* polynomials in expansion */
+zz = z * z;
+z3 = zz * z;
+F[0] = 1.0;
+F[1] = -z/5.0;
+F[2] = polevl( z3, PF2, 1 ) * zz;
+F[3] = polevl( z3, PF3, 2 );
+F[4] = polevl( z3, PF4, 3 ) * z;
+G[0] = 0.3 * zz;
+G[1] = polevl( z3, PG1, 1 );
+G[2] = polevl( z3, PG2, 2 ) * z;
+G[3] = polevl( z3, PG3, 2 ) * zz;
+#if DEBUG
+for( k=0; k<=4; k++ )
+ printf( "F[%d] = %.5E\n", k, F[k] );
+for( k=0; k<=3; k++ )
+ printf( "G[%d] = %.5E\n", k, G[k] );
+#endif
+pp = 0.0;
+qq = 0.0;
+nk = 1.0;
+n23 = cbrt( n * n );
+
+for( k=0; k<=4; k++ )
+ {
+ fk = F[k]*nk;
+ pp += fk;
+ if( k != 4 )
+ {
+ gk = G[k]*nk;
+ qq += gk;
+ }
+#if DEBUG
+ printf("fk[%d] %.5E, gk[%d] %.5E\n", k, fk, k, gk );
+#endif
+ nk /= n23;
+ }
+
+fk = cbtwo * ai * pp/cbn + cbrt(4.0) * aip * qq/n;
+return(fk);
+}
diff --git a/libm/double/k0.c b/libm/double/k0.c
new file mode 100644
index 000000000..7d09cb4a1
--- /dev/null
+++ b/libm/double/k0.c
@@ -0,0 +1,333 @@
+/* k0.c
+ *
+ * Modified Bessel function, third kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k0();
+ *
+ * y = k0( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of the third kind
+ * of order zero of the argument.
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at 2000 random points between 0 and 8. Peak absolute
+ * error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 3100 1.3e-16 2.1e-17
+ * IEEE 0, 30 30000 1.2e-15 1.6e-16
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * K0 domain x <= 0 MAXNUM
+ *
+ */
+ /* k0e()
+ *
+ * Modified Bessel function, third kind, order zero,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k0e();
+ *
+ * y = k0e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order zero of the argument.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 1.4e-15 1.4e-16
+ * See k0().
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for K0(x) + log(x/2) I0(x)
+ * in the interval [0,2]. The odd order coefficients are all
+ * zero; only the even order coefficients are listed.
+ *
+ * lim(x->0){ K0(x) + log(x/2) I0(x) } = -EUL.
+ */
+
+#ifdef UNK
+static double A[] =
+{
+ 1.37446543561352307156E-16,
+ 4.25981614279661018399E-14,
+ 1.03496952576338420167E-11,
+ 1.90451637722020886025E-9,
+ 2.53479107902614945675E-7,
+ 2.28621210311945178607E-5,
+ 1.26461541144692592338E-3,
+ 3.59799365153615016266E-2,
+ 3.44289899924628486886E-1,
+-5.35327393233902768720E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short A[] = {
+0023036,0073417,0032477,0165673,
+0025077,0154126,0016046,0012517,
+0027066,0011342,0035211,0005041,
+0031002,0160233,0037454,0050224,
+0032610,0012747,0037712,0173741,
+0034277,0144007,0172147,0162375,
+0035645,0140563,0125431,0165626,
+0037023,0057662,0125124,0102051,
+0037660,0043304,0004411,0166707,
+0140011,0005467,0047227,0130370
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short A[] = {
+0xfd77,0xe6a7,0xcee1,0x3ca3,
+0xc2aa,0xc384,0xfb0a,0x3d27,
+0x2144,0x4751,0xc25c,0x3da6,
+0x8a13,0x67e5,0x5c13,0x3e20,
+0x5efc,0xe7f9,0x02bc,0x3e91,
+0xfca0,0xfe8c,0xf900,0x3ef7,
+0x3d73,0x7563,0xb82e,0x3f54,
+0x9085,0x554a,0x6bf6,0x3fa2,
+0x3db9,0x8121,0x08d8,0x3fd6,
+0xf61f,0xe9d2,0x2166,0xbfe1
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short A[] = {
+0x3ca3,0xcee1,0xe6a7,0xfd77,
+0x3d27,0xfb0a,0xc384,0xc2aa,
+0x3da6,0xc25c,0x4751,0x2144,
+0x3e20,0x5c13,0x67e5,0x8a13,
+0x3e91,0x02bc,0xe7f9,0x5efc,
+0x3ef7,0xf900,0xfe8c,0xfca0,
+0x3f54,0xb82e,0x7563,0x3d73,
+0x3fa2,0x6bf6,0x554a,0x9085,
+0x3fd6,0x08d8,0x8121,0x3db9,
+0xbfe1,0x2166,0xe9d2,0xf61f
+};
+#endif
+
+
+
+/* Chebyshev coefficients for exp(x) sqrt(x) K0(x)
+ * in the inverted interval [2,infinity].
+ *
+ * lim(x->inf){ exp(x) sqrt(x) K0(x) } = sqrt(pi/2).
+ */
+
+#ifdef UNK
+static double B[] = {
+ 5.30043377268626276149E-18,
+-1.64758043015242134646E-17,
+ 5.21039150503902756861E-17,
+-1.67823109680541210385E-16,
+ 5.51205597852431940784E-16,
+-1.84859337734377901440E-15,
+ 6.34007647740507060557E-15,
+-2.22751332699166985548E-14,
+ 8.03289077536357521100E-14,
+-2.98009692317273043925E-13,
+ 1.14034058820847496303E-12,
+-4.51459788337394416547E-12,
+ 1.85594911495471785253E-11,
+-7.95748924447710747776E-11,
+ 3.57739728140030116597E-10,
+-1.69753450938905987466E-9,
+ 8.57403401741422608519E-9,
+-4.66048989768794782956E-8,
+ 2.76681363944501510342E-7,
+-1.83175552271911948767E-6,
+ 1.39498137188764993662E-5,
+-1.28495495816278026384E-4,
+ 1.56988388573005337491E-3,
+-3.14481013119645005427E-2,
+ 2.44030308206595545468E0
+};
+#endif
+
+#ifdef DEC
+static unsigned short B[] = {
+0021703,0106456,0076144,0173406,
+0122227,0173144,0116011,0030033,
+0022560,0044562,0006506,0067642,
+0123101,0076243,0123273,0131013,
+0023436,0157713,0056243,0141331,
+0124005,0032207,0063726,0164664,
+0024344,0066342,0051756,0162300,
+0124710,0121365,0154053,0077022,
+0025264,0161166,0066246,0077420,
+0125647,0141671,0006443,0103212,
+0026240,0076431,0077147,0160445,
+0126636,0153741,0174002,0105031,
+0027243,0040102,0035375,0163073,
+0127656,0176256,0113476,0044653,
+0030304,0125544,0006377,0130104,
+0130751,0047257,0110537,0127324,
+0031423,0046400,0014772,0012164,
+0132110,0025240,0155247,0112570,
+0032624,0105314,0007437,0021574,
+0133365,0155243,0174306,0116506,
+0034152,0004776,0061643,0102504,
+0135006,0136277,0036104,0175023,
+0035715,0142217,0162474,0115022,
+0137000,0147671,0065177,0134356,
+0040434,0026754,0175163,0044070
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short B[] = {
+0x9ee1,0xcf8c,0x71a5,0x3c58,
+0x2603,0x9381,0xfecc,0xbc72,
+0xcdf4,0x41a8,0x092e,0x3c8e,
+0x7641,0x74d7,0x2f94,0xbca8,
+0x785b,0x6b94,0xdbf9,0x3cc3,
+0xdd36,0xecfa,0xa690,0xbce0,
+0xdc98,0x4a7d,0x8d9c,0x3cfc,
+0x6fc2,0xbb05,0x145e,0xbd19,
+0xcfe2,0xcd94,0x9c4e,0x3d36,
+0x70d1,0x21a4,0xf877,0xbd54,
+0xfc25,0x2fcc,0x0fa3,0x3d74,
+0x5143,0x3f00,0xdafc,0xbd93,
+0xbcc7,0x475f,0x6808,0x3db4,
+0xc935,0xd2e7,0xdf95,0xbdd5,
+0xf608,0x819f,0x956c,0x3df8,
+0xf5db,0xf22b,0x29d5,0xbe1d,
+0x428e,0x033f,0x69a0,0x3e42,
+0xf2af,0x1b54,0x0554,0xbe69,
+0xe46f,0x81e3,0x9159,0x3e92,
+0xd3a9,0x7f18,0xbb54,0xbebe,
+0x70a9,0xcc74,0x413f,0x3eed,
+0x9f42,0xe788,0xd797,0xbf20,
+0x9342,0xfca7,0xb891,0x3f59,
+0xf71e,0x2d4f,0x19f7,0xbfa0,
+0x6907,0x9f4e,0x85bd,0x4003
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short B[] = {
+0x3c58,0x71a5,0xcf8c,0x9ee1,
+0xbc72,0xfecc,0x9381,0x2603,
+0x3c8e,0x092e,0x41a8,0xcdf4,
+0xbca8,0x2f94,0x74d7,0x7641,
+0x3cc3,0xdbf9,0x6b94,0x785b,
+0xbce0,0xa690,0xecfa,0xdd36,
+0x3cfc,0x8d9c,0x4a7d,0xdc98,
+0xbd19,0x145e,0xbb05,0x6fc2,
+0x3d36,0x9c4e,0xcd94,0xcfe2,
+0xbd54,0xf877,0x21a4,0x70d1,
+0x3d74,0x0fa3,0x2fcc,0xfc25,
+0xbd93,0xdafc,0x3f00,0x5143,
+0x3db4,0x6808,0x475f,0xbcc7,
+0xbdd5,0xdf95,0xd2e7,0xc935,
+0x3df8,0x956c,0x819f,0xf608,
+0xbe1d,0x29d5,0xf22b,0xf5db,
+0x3e42,0x69a0,0x033f,0x428e,
+0xbe69,0x0554,0x1b54,0xf2af,
+0x3e92,0x9159,0x81e3,0xe46f,
+0xbebe,0xbb54,0x7f18,0xd3a9,
+0x3eed,0x413f,0xcc74,0x70a9,
+0xbf20,0xd797,0xe788,0x9f42,
+0x3f59,0xb891,0xfca7,0x9342,
+0xbfa0,0x19f7,0x2d4f,0xf71e,
+0x4003,0x85bd,0x9f4e,0x6907
+};
+#endif
+
+/* k0.c */
+#ifdef ANSIPROT
+extern double chbevl ( double, void *, int );
+extern double exp ( double );
+extern double i0 ( double );
+extern double log ( double );
+extern double sqrt ( double );
+#else
+double chbevl(), exp(), i0(), log(), sqrt();
+#endif
+extern double PI;
+extern double MAXNUM;
+
+double k0(x)
+double x;
+{
+double y, z;
+
+if( x <= 0.0 )
+ {
+ mtherr( "k0", DOMAIN );
+ return( MAXNUM );
+ }
+
+if( x <= 2.0 )
+ {
+ y = x * x - 2.0;
+ y = chbevl( y, A, 10 ) - log( 0.5 * x ) * i0(x);
+ return( y );
+ }
+z = 8.0/x - 2.0;
+y = exp(-x) * chbevl( z, B, 25 ) / sqrt(x);
+return(y);
+}
+
+
+
+
+double k0e( x )
+double x;
+{
+double y;
+
+if( x <= 0.0 )
+ {
+ mtherr( "k0e", DOMAIN );
+ return( MAXNUM );
+ }
+
+if( x <= 2.0 )
+ {
+ y = x * x - 2.0;
+ y = chbevl( y, A, 10 ) - log( 0.5 * x ) * i0(x);
+ return( y * exp(x) );
+ }
+
+y = chbevl( 8.0/x - 2.0, B, 25 ) / sqrt(x);
+return(y);
+}
diff --git a/libm/double/k1.c b/libm/double/k1.c
new file mode 100644
index 000000000..a96305355
--- /dev/null
+++ b/libm/double/k1.c
@@ -0,0 +1,335 @@
+/* k1.c
+ *
+ * Modified Bessel function, third kind, order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k1();
+ *
+ * y = k1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the modified Bessel function of the third kind
+ * of order one of the argument.
+ *
+ * The range is partitioned into the two intervals [0,2] and
+ * (2, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 3300 8.9e-17 2.2e-17
+ * IEEE 0, 30 30000 1.2e-15 1.6e-16
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * k1 domain x <= 0 MAXNUM
+ *
+ */
+ /* k1e.c
+ *
+ * Modified Bessel function, third kind, order one,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, k1e();
+ *
+ * y = k1e( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order one of the argument:
+ *
+ * k1e(x) = exp(x) * k1(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 7.8e-16 1.2e-16
+ * See k1().
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for x(K1(x) - log(x/2) I1(x))
+ * in the interval [0,2].
+ *
+ * lim(x->0){ x(K1(x) - log(x/2) I1(x)) } = 1.
+ */
+
+#ifdef UNK
+static double A[] =
+{
+-7.02386347938628759343E-18,
+-2.42744985051936593393E-15,
+-6.66690169419932900609E-13,
+-1.41148839263352776110E-10,
+-2.21338763073472585583E-8,
+-2.43340614156596823496E-6,
+-1.73028895751305206302E-4,
+-6.97572385963986435018E-3,
+-1.22611180822657148235E-1,
+-3.53155960776544875667E-1,
+ 1.52530022733894777053E0
+};
+#endif
+
+#ifdef DEC
+static unsigned short A[] = {
+0122001,0110501,0164746,0151255,
+0124056,0165213,0150034,0147377,
+0126073,0124026,0167207,0001044,
+0130033,0030735,0141061,0033116,
+0131676,0020350,0121341,0107175,
+0133443,0046631,0062031,0070716,
+0135065,0067427,0026435,0164022,
+0136344,0112234,0165752,0006222,
+0137373,0015622,0017016,0155636,
+0137664,0150333,0125730,0067240,
+0040303,0036411,0130200,0043120
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short A[] = {
+0xda56,0x3d3c,0x3228,0xbc60,
+0x99e0,0x7a03,0xdd51,0xbce5,
+0xe045,0xddd0,0x7502,0xbd67,
+0x26ca,0xb846,0x663b,0xbde3,
+0x31d0,0x145c,0xc41d,0xbe57,
+0x2e3a,0x2c83,0x69b3,0xbec4,
+0xbd02,0xe5a3,0xade2,0xbf26,
+0x4192,0x9d7d,0x9293,0xbf7c,
+0xdb74,0x43c1,0x6372,0xbfbf,
+0x0dd4,0x757b,0x9a1b,0xbfd6,
+0x08ca,0x3610,0x67a1,0x3ff8
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short A[] = {
+0xbc60,0x3228,0x3d3c,0xda56,
+0xbce5,0xdd51,0x7a03,0x99e0,
+0xbd67,0x7502,0xddd0,0xe045,
+0xbde3,0x663b,0xb846,0x26ca,
+0xbe57,0xc41d,0x145c,0x31d0,
+0xbec4,0x69b3,0x2c83,0x2e3a,
+0xbf26,0xade2,0xe5a3,0xbd02,
+0xbf7c,0x9293,0x9d7d,0x4192,
+0xbfbf,0x6372,0x43c1,0xdb74,
+0xbfd6,0x9a1b,0x757b,0x0dd4,
+0x3ff8,0x67a1,0x3610,0x08ca
+};
+#endif
+
+
+
+/* Chebyshev coefficients for exp(x) sqrt(x) K1(x)
+ * in the interval [2,infinity].
+ *
+ * lim(x->inf){ exp(x) sqrt(x) K1(x) } = sqrt(pi/2).
+ */
+
+#ifdef UNK
+static double B[] =
+{
+-5.75674448366501715755E-18,
+ 1.79405087314755922667E-17,
+-5.68946255844285935196E-17,
+ 1.83809354436663880070E-16,
+-6.05704724837331885336E-16,
+ 2.03870316562433424052E-15,
+-7.01983709041831346144E-15,
+ 2.47715442448130437068E-14,
+-8.97670518232499435011E-14,
+ 3.34841966607842919884E-13,
+-1.28917396095102890680E-12,
+ 5.13963967348173025100E-12,
+-2.12996783842756842877E-11,
+ 9.21831518760500529508E-11,
+-4.19035475934189648750E-10,
+ 2.01504975519703286596E-9,
+-1.03457624656780970260E-8,
+ 5.74108412545004946722E-8,
+-3.50196060308781257119E-7,
+ 2.40648494783721712015E-6,
+-1.93619797416608296024E-5,
+ 1.95215518471351631108E-4,
+-2.85781685962277938680E-3,
+ 1.03923736576817238437E-1,
+ 2.72062619048444266945E0
+};
+#endif
+
+#ifdef DEC
+static unsigned short B[] = {
+0121724,0061352,0013041,0150076,
+0022245,0074324,0016172,0173232,
+0122603,0030250,0135670,0165221,
+0023123,0165362,0023561,0060124,
+0123456,0112436,0141654,0073623,
+0024022,0163557,0077564,0006753,
+0124374,0165221,0131014,0026524,
+0024737,0017512,0144250,0175451,
+0125312,0021456,0123136,0076633,
+0025674,0077720,0020125,0102607,
+0126265,0067543,0007744,0043701,
+0026664,0152702,0033002,0074202,
+0127273,0055234,0120016,0071733,
+0027712,0133200,0042441,0075515,
+0130346,0057000,0015456,0074470,
+0031012,0074441,0051636,0111155,
+0131461,0136444,0177417,0002101,
+0032166,0111743,0032176,0021410,
+0132674,0001224,0076555,0027060,
+0033441,0077430,0135226,0106663,
+0134242,0065610,0167155,0113447,
+0035114,0131304,0043664,0102163,
+0136073,0045065,0171465,0122123,
+0037324,0152767,0147401,0017732,
+0040456,0017275,0050061,0062120,
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short B[] = {
+0x3a08,0x42c4,0x8c5d,0xbc5a,
+0x5ed3,0x838f,0xaf1a,0x3c74,
+0x1d52,0x1777,0x6615,0xbc90,
+0x2c0b,0x44ee,0x7d5e,0x3caa,
+0x8ef2,0xd875,0xd2a3,0xbcc5,
+0x81bd,0xefee,0x5ced,0x3ce2,
+0x85ab,0x3641,0x9d52,0xbcff,
+0x1f65,0x5915,0xe3e9,0x3d1b,
+0xcfb3,0xd4cb,0x4465,0xbd39,
+0xb0b1,0x040a,0x8ffa,0x3d57,
+0x88f8,0x61fc,0xadec,0xbd76,
+0x4f10,0x46c0,0x9ab8,0x3d96,
+0xce7b,0x9401,0x6b53,0xbdb7,
+0x2f6a,0x08a4,0x56d0,0x3dd9,
+0xcf27,0x0365,0xcbc0,0xbdfc,
+0xd24e,0x2a73,0x4f24,0x3e21,
+0xe088,0x9fe1,0x37a4,0xbe46,
+0xc461,0x668f,0xd27c,0x3e6e,
+0xa5c6,0x8fad,0x8052,0xbe97,
+0xd1b6,0x1752,0x2fe3,0x3ec4,
+0xb2e5,0x1dcd,0x4d71,0xbef4,
+0x908e,0x88f6,0x9658,0x3f29,
+0xb48a,0xbe66,0x6946,0xbf67,
+0x23fb,0xf9e0,0x9abe,0x3fba,
+0x2c8a,0xaa06,0xc3d7,0x4005
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short B[] = {
+0xbc5a,0x8c5d,0x42c4,0x3a08,
+0x3c74,0xaf1a,0x838f,0x5ed3,
+0xbc90,0x6615,0x1777,0x1d52,
+0x3caa,0x7d5e,0x44ee,0x2c0b,
+0xbcc5,0xd2a3,0xd875,0x8ef2,
+0x3ce2,0x5ced,0xefee,0x81bd,
+0xbcff,0x9d52,0x3641,0x85ab,
+0x3d1b,0xe3e9,0x5915,0x1f65,
+0xbd39,0x4465,0xd4cb,0xcfb3,
+0x3d57,0x8ffa,0x040a,0xb0b1,
+0xbd76,0xadec,0x61fc,0x88f8,
+0x3d96,0x9ab8,0x46c0,0x4f10,
+0xbdb7,0x6b53,0x9401,0xce7b,
+0x3dd9,0x56d0,0x08a4,0x2f6a,
+0xbdfc,0xcbc0,0x0365,0xcf27,
+0x3e21,0x4f24,0x2a73,0xd24e,
+0xbe46,0x37a4,0x9fe1,0xe088,
+0x3e6e,0xd27c,0x668f,0xc461,
+0xbe97,0x8052,0x8fad,0xa5c6,
+0x3ec4,0x2fe3,0x1752,0xd1b6,
+0xbef4,0x4d71,0x1dcd,0xb2e5,
+0x3f29,0x9658,0x88f6,0x908e,
+0xbf67,0x6946,0xbe66,0xb48a,
+0x3fba,0x9abe,0xf9e0,0x23fb,
+0x4005,0xc3d7,0xaa06,0x2c8a
+};
+#endif
+
+#ifdef ANSIPROT
+extern double chbevl ( double, void *, int );
+extern double exp ( double );
+extern double i1 ( double );
+extern double log ( double );
+extern double sqrt ( double );
+#else
+double chbevl(), exp(), i1(), log(), sqrt();
+#endif
+extern double PI;
+extern double MINLOG, MAXNUM;
+
+double k1(x)
+double x;
+{
+double y, z;
+
+z = 0.5 * x;
+if( z <= 0.0 )
+ {
+ mtherr( "k1", DOMAIN );
+ return( MAXNUM );
+ }
+
+if( x <= 2.0 )
+ {
+ y = x * x - 2.0;
+ y = log(z) * i1(x) + chbevl( y, A, 11 ) / x;
+ return( y );
+ }
+
+return( exp(-x) * chbevl( 8.0/x - 2.0, B, 25 ) / sqrt(x) );
+}
+
+
+
+
+double k1e( x )
+double x;
+{
+double y;
+
+if( x <= 0.0 )
+ {
+ mtherr( "k1e", DOMAIN );
+ return( MAXNUM );
+ }
+
+if( x <= 2.0 )
+ {
+ y = x * x - 2.0;
+ y = log( 0.5 * x ) * i1(x) + chbevl( y, A, 11 ) / x;
+ return( y * exp(x) );
+ }
+
+return( chbevl( 8.0/x - 2.0, B, 25 ) / sqrt(x) );
+}
diff --git a/libm/double/kn.c b/libm/double/kn.c
new file mode 100644
index 000000000..72a1c1a53
--- /dev/null
+++ b/libm/double/kn.c
@@ -0,0 +1,255 @@
+/* kn.c
+ *
+ * Modified Bessel function, third kind, integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, kn();
+ * int n;
+ *
+ * y = kn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of the third kind
+ * of order n of the argument.
+ *
+ * The range is partitioned into the two intervals [0,9.55] and
+ * (9.55, infinity). An ascending power series is used in the
+ * low range, and an asymptotic expansion in the high range.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 3000 1.3e-9 5.8e-11
+ * IEEE 0,30 90000 1.8e-8 3.0e-10
+ *
+ * Error is high only near the crossover point x = 9.55
+ * between the two expansions used.
+ */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
+*/
+
+
+/*
+Algorithm for Kn.
+ n-1
+ -n - (n-k-1)! 2 k
+K (x) = 0.5 (x/2) > -------- (-x /4)
+ n - k!
+ k=0
+
+ inf. 2 k
+ n n - (x /4)
+ + (-1) 0.5(x/2) > {p(k+1) + p(n+k+1) - 2log(x/2)} ---------
+ - k! (n+k)!
+ k=0
+
+where p(m) is the psi function: p(1) = -EUL and
+
+ m-1
+ -
+ p(m) = -EUL + > 1/k
+ -
+ k=1
+
+For large x,
+ 2 2 2
+ u-1 (u-1 )(u-3 )
+K (z) = sqrt(pi/2z) exp(-z) { 1 + ------- + ------------ + ...}
+ v 1 2
+ 1! (8z) 2! (8z)
+asymptotically, where
+
+ 2
+ u = 4 v .
+
+*/
+
+#include <math.h>
+
+#define EUL 5.772156649015328606065e-1
+#define MAXFAC 31
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double exp ( double );
+extern double log ( double );
+extern double sqrt ( double );
+#else
+double fabs(), exp(), log(), sqrt();
+#endif
+extern double MACHEP, MAXNUM, MAXLOG, PI;
+
+double kn( nn, x )
+int nn;
+double x;
+{
+double k, kf, nk1f, nkf, zn, t, s, z0, z;
+double ans, fn, pn, pk, zmn, tlg, tox;
+int i, n;
+
+if( nn < 0 )
+ n = -nn;
+else
+ n = nn;
+
+if( n > MAXFAC )
+ {
+overf:
+ mtherr( "kn", OVERFLOW );
+ return( MAXNUM );
+ }
+
+if( x <= 0.0 )
+ {
+ if( x < 0.0 )
+ mtherr( "kn", DOMAIN );
+ else
+ mtherr( "kn", SING );
+ return( MAXNUM );
+ }
+
+
+if( x > 9.55 )
+ goto asymp;
+
+ans = 0.0;
+z0 = 0.25 * x * x;
+fn = 1.0;
+pn = 0.0;
+zmn = 1.0;
+tox = 2.0/x;
+
+if( n > 0 )
+ {
+ /* compute factorial of n and psi(n) */
+ pn = -EUL;
+ k = 1.0;
+ for( i=1; i<n; i++ )
+ {
+ pn += 1.0/k;
+ k += 1.0;
+ fn *= k;
+ }
+
+ zmn = tox;
+
+ if( n == 1 )
+ {
+ ans = 1.0/x;
+ }
+ else
+ {
+ nk1f = fn/n;
+ kf = 1.0;
+ s = nk1f;
+ z = -z0;
+ zn = 1.0;
+ for( i=1; i<n; i++ )
+ {
+ nk1f = nk1f/(n-i);
+ kf = kf * i;
+ zn *= z;
+ t = nk1f * zn / kf;
+ s += t;
+ if( (MAXNUM - fabs(t)) < fabs(s) )
+ goto overf;
+ if( (tox > 1.0) && ((MAXNUM/tox) < zmn) )
+ goto overf;
+ zmn *= tox;
+ }
+ s *= 0.5;
+ t = fabs(s);
+ if( (zmn > 1.0) && ((MAXNUM/zmn) < t) )
+ goto overf;
+ if( (t > 1.0) && ((MAXNUM/t) < zmn) )
+ goto overf;
+ ans = s * zmn;
+ }
+ }
+
+
+tlg = 2.0 * log( 0.5 * x );
+pk = -EUL;
+if( n == 0 )
+ {
+ pn = pk;
+ t = 1.0;
+ }
+else
+ {
+ pn = pn + 1.0/n;
+ t = 1.0/fn;
+ }
+s = (pk+pn-tlg)*t;
+k = 1.0;
+do
+ {
+ t *= z0 / (k * (k+n));
+ pk += 1.0/k;
+ pn += 1.0/(k+n);
+ s += (pk+pn-tlg)*t;
+ k += 1.0;
+ }
+while( fabs(t/s) > MACHEP );
+
+s = 0.5 * s / zmn;
+if( n & 1 )
+ s = -s;
+ans += s;
+
+return(ans);
+
+
+
+/* Asymptotic expansion for Kn(x) */
+/* Converges to 1.4e-17 for x > 18.4 */
+
+asymp:
+
+if( x > MAXLOG )
+ {
+ mtherr( "kn", UNDERFLOW );
+ return(0.0);
+ }
+k = n;
+pn = 4.0 * k * k;
+pk = 1.0;
+z0 = 8.0 * x;
+fn = 1.0;
+t = 1.0;
+s = t;
+nkf = MAXNUM;
+i = 0;
+do
+ {
+ z = pn - pk * pk;
+ t = t * z /(fn * z0);
+ nk1f = fabs(t);
+ if( (i >= n) && (nk1f > nkf) )
+ {
+ goto adone;
+ }
+ nkf = nk1f;
+ s += t;
+ fn += 1.0;
+ pk += 2.0;
+ i += 1;
+ }
+while( fabs(t/s) > MACHEP );
+
+adone:
+ans = exp(-x) * sqrt( PI/(2.0*x) ) * s;
+return(ans);
+}
diff --git a/libm/double/kolmogorov.c b/libm/double/kolmogorov.c
new file mode 100644
index 000000000..0d6fe92bd
--- /dev/null
+++ b/libm/double/kolmogorov.c
@@ -0,0 +1,243 @@
+
+/* Re Kolmogorov statistics, here is Birnbaum and Tingey's formula for the
+ distribution of D+, the maximum of all positive deviations between a
+ theoretical distribution function P(x) and an empirical one Sn(x)
+ from n samples.
+
+ +
+ D = sup [P(x) - S (x)]
+ n -inf < x < inf n
+
+
+ [n(1-e)]
+ + - v-1 n-v
+ Pr{D > e} = > C e (e + v/n) (1 - e - v/n)
+ n - n v
+ v=0
+
+ [n(1-e)] is the largest integer not exceeding n(1-e).
+ nCv is the number of combinations of n things taken v at a time. */
+
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double pow ( double, double );
+extern double floor ( double );
+extern double lgam ( double );
+extern double exp ( double );
+extern double sqrt ( double );
+extern double log ( double );
+extern double fabs ( double );
+double smirnov ( int, double );
+double kolmogorov ( double );
+#else
+double pow (), floor (), lgam (), exp (), sqrt (), log (), fabs ();
+double smirnov (), kolmogorov ();
+#endif
+extern double MAXLOG;
+
+/* Exact Smirnov statistic, for one-sided test. */
+double
+smirnov (n, e)
+ int n;
+ double e;
+{
+ int v, nn;
+ double evn, omevn, p, t, c, lgamnp1;
+
+ if (n <= 0 || e < 0.0 || e > 1.0)
+ return (-1.0);
+ nn = floor ((double) n * (1.0 - e));
+ p = 0.0;
+ if (n < 1013)
+ {
+ c = 1.0;
+ for (v = 0; v <= nn; v++)
+ {
+ evn = e + ((double) v) / n;
+ p += c * pow (evn, (double) (v - 1))
+ * pow (1.0 - evn, (double) (n - v));
+ /* Next combinatorial term; worst case error = 4e-15. */
+ c *= ((double) (n - v)) / (v + 1);
+ }
+ }
+ else
+ {
+ lgamnp1 = lgam ((double) (n + 1));
+ for (v = 0; v <= nn; v++)
+ {
+ evn = e + ((double) v) / n;
+ omevn = 1.0 - evn;
+ if (fabs (omevn) > 0.0)
+ {
+ t = lgamnp1
+ - lgam ((double) (v + 1))
+ - lgam ((double) (n - v + 1))
+ + (v - 1) * log (evn)
+ + (n - v) * log (omevn);
+ if (t > -MAXLOG)
+ p += exp (t);
+ }
+ }
+ }
+ return (p * e);
+}
+
+
+/* Kolmogorov's limiting distribution of two-sided test, returns
+ probability that sqrt(n) * max deviation > y,
+ or that max deviation > y/sqrt(n).
+ The approximation is useful for the tail of the distribution
+ when n is large. */
+double
+kolmogorov (y)
+ double y;
+{
+ double p, t, r, sign, x;
+
+ x = -2.0 * y * y;
+ sign = 1.0;
+ p = 0.0;
+ r = 1.0;
+ do
+ {
+ t = exp (x * r * r);
+ p += sign * t;
+ if (t == 0.0)
+ break;
+ r += 1.0;
+ sign = -sign;
+ }
+ while ((t / p) > 1.1e-16);
+ return (p + p);
+}
+
+/* Functional inverse of Smirnov distribution
+ finds e such that smirnov(n,e) = p. */
+double
+smirnovi (n, p)
+ int n;
+ double p;
+{
+ double e, t, dpde;
+
+ if (p <= 0.0 || p > 1.0)
+ {
+ mtherr ("smirnovi", DOMAIN);
+ return 0.0;
+ }
+ /* Start with approximation p = exp(-2 n e^2). */
+ e = sqrt (-log (p) / (2.0 * n));
+ do
+ {
+ /* Use approximate derivative in Newton iteration. */
+ t = -2.0 * n * e;
+ dpde = 2.0 * t * exp (t * e);
+ if (fabs (dpde) > 0.0)
+ t = (p - smirnov (n, e)) / dpde;
+ else
+ {
+ mtherr ("smirnovi", UNDERFLOW);
+ return 0.0;
+ }
+ e = e + t;
+ if (e >= 1.0 || e <= 0.0)
+ {
+ mtherr ("smirnovi", OVERFLOW);
+ return 0.0;
+ }
+ }
+ while (fabs (t / e) > 1e-10);
+ return (e);
+}
+
+
+/* Functional inverse of Kolmogorov statistic for two-sided test.
+ Finds y such that kolmogorov(y) = p.
+ If e = smirnovi (n,p), then kolmogi(2 * p) / sqrt(n) should
+ be close to e. */
+double
+kolmogi (p)
+ double p;
+{
+ double y, t, dpdy;
+
+ if (p <= 0.0 || p > 1.0)
+ {
+ mtherr ("kolmogi", DOMAIN);
+ return 0.0;
+ }
+ /* Start with approximation p = 2 exp(-2 y^2). */
+ y = sqrt (-0.5 * log (0.5 * p));
+ do
+ {
+ /* Use approximate derivative in Newton iteration. */
+ t = -2.0 * y;
+ dpdy = 4.0 * t * exp (t * y);
+ if (fabs (dpdy) > 0.0)
+ t = (p - kolmogorov (y)) / dpdy;
+ else
+ {
+ mtherr ("kolmogi", UNDERFLOW);
+ return 0.0;
+ }
+ y = y + t;
+ }
+ while (fabs (t / y) > 1e-10);
+ return (y);
+}
+
+
+#ifdef SALONE
+/* Type in a number. */
+void
+getnum (s, px)
+ char *s;
+ double *px;
+{
+ char str[30];
+
+ printf (" %s (%.15e) ? ", s, *px);
+ gets (str);
+ if (str[0] == '\0' || str[0] == '\n')
+ return;
+ sscanf (str, "%lf", px);
+ printf ("%.15e\n", *px);
+}
+
+/* Type in values, get answers. */
+void
+main ()
+{
+ int n;
+ double e, p, ps, pk, ek, y;
+
+ n = 5;
+ e = 0.0;
+ p = 0.1;
+loop:
+ ps = n;
+ getnum ("n", &ps);
+ n = ps;
+ if (n <= 0)
+ {
+ printf ("? Operator error.\n");
+ goto loop;
+ }
+ /*
+ getnum ("e", &e);
+ ps = smirnov (n, e);
+ y = sqrt ((double) n) * e;
+ printf ("y = %.4e\n", y);
+ pk = kolmogorov (y);
+ printf ("Smirnov = %.15e, Kolmogorov/2 = %.15e\n", ps, pk / 2.0);
+*/
+ getnum ("p", &p);
+ e = smirnovi (n, p);
+ printf ("Smirnov e = %.15e\n", e);
+ y = kolmogi (2.0 * p);
+ ek = y / sqrt ((double) n);
+ printf ("Kolmogorov e = %.15e\n", ek);
+ goto loop;
+}
+#endif
diff --git a/libm/double/levnsn.c b/libm/double/levnsn.c
new file mode 100644
index 000000000..3fda5d6bd
--- /dev/null
+++ b/libm/double/levnsn.c
@@ -0,0 +1,82 @@
+/* Levnsn.c */
+/* Levinson-Durbin LPC
+ *
+ * | R0 R1 R2 ... RN-1 | | A1 | | -R1 |
+ * | R1 R0 R1 ... RN-2 | | A2 | | -R2 |
+ * | R2 R1 R0 ... RN-3 | | A3 | = | -R3 |
+ * | ... | | ...| | ... |
+ * | RN-1 RN-2... R0 | | AN | | -RN |
+ *
+ * Ref: John Makhoul, "Linear Prediction, A Tutorial Review"
+ * Proc. IEEE Vol. 63, PP 561-580 April, 1975.
+ *
+ * R is the input autocorrelation function. R0 is the zero lag
+ * term. A is the output array of predictor coefficients. Note
+ * that a filter impulse response has a coefficient of 1.0 preceding
+ * A1. E is an array of mean square error for each prediction order
+ * 1 to N. REFL is an output array of the reflection coefficients.
+ */
+
+#define abs(x) ( (x) < 0 ? -(x) : (x) )
+
+int levnsn( n, r, a, e, refl )
+int n;
+double r[], a[], e[], refl[];
+{
+int k, km1, i, kmi, j;
+double ai, akk, err, err1, r0, t, akmi;
+double *pa, *pr;
+
+for( i=0; i<n; i++ )
+ {
+ a[i] = 0.0;
+ e[i] = 0.0;
+ refl[i] = 0.0;
+ }
+r0 = r[0];
+e[0] = r0;
+err = r0;
+
+akk = -r[1]/err;
+err = (1.0 - akk*akk) * err;
+e[1] = err;
+a[1] = akk;
+refl[1] = akk;
+
+if( err < 1.0e-2 )
+ return 0;
+
+for( k=2; k<n; k++ )
+ {
+ t = 0.0;
+ pa = &a[1];
+ pr = &r[k-1];
+ for( j=1; j<k; j++ )
+ t += *pa++ * *pr--;
+ akk = -( r[k] + t )/err;
+ refl[k] = akk;
+ km1 = k/2;
+ for( j=1; j<=km1; j++ )
+ {
+ kmi = k-j;
+ ai = a[j];
+ akmi = a[kmi];
+ a[j] = ai + akk*akmi;
+ if( i == kmi )
+ goto nxtk;
+ a[kmi] = akmi + akk*ai;
+ }
+nxtk:
+ a[k] = akk;
+ err1 = (1.0 - akk*akk)*err;
+ e[k] = err1;
+ if( err1 < 0 )
+ err1 = -err1;
+/* err1 = abs(err1);*/
+/* if( (err1 < 1.0e-2) || (err1 >= err) )*/
+ if( err1 < 1.0e-2 )
+ return 0;
+ err = err1;
+ }
+ return 0;
+}
diff --git a/libm/double/log.c b/libm/double/log.c
new file mode 100644
index 000000000..2fdea17a7
--- /dev/null
+++ b/libm/double/log.c
@@ -0,0 +1,341 @@
+/* log.c
+ *
+ * Natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, log();
+ *
+ * y = log( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the logarithm
+ * of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting z = 2(x-1)/x+1),
+ *
+ * log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 150000 1.44e-16 5.06e-17
+ * IEEE +-MAXNUM 30000 1.20e-16 4.78e-17
+ * DEC 0, 10 170000 1.8e-17 6.3e-18
+ *
+ * In the tests over the interval [+-MAXNUM], the logarithms
+ * of the random arguments were uniformly distributed over
+ * [0, MAXLOG].
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity: x = 0; returns -INFINITY
+ * log domain: x < 0; returns NAN
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+static char fname[] = {"log"};
+
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ */
+#ifdef UNK
+static double P[] = {
+ 1.01875663804580931796E-4,
+ 4.97494994976747001425E-1,
+ 4.70579119878881725854E0,
+ 1.44989225341610930846E1,
+ 1.79368678507819816313E1,
+ 7.70838733755885391666E0,
+};
+static double Q[] = {
+/* 1.00000000000000000000E0, */
+ 1.12873587189167450590E1,
+ 4.52279145837532221105E1,
+ 8.29875266912776603211E1,
+ 7.11544750618563894466E1,
+ 2.31251620126765340583E1,
+};
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0037777,0127270,0162547,0057274,
+0041001,0054665,0164317,0005341,
+0041451,0034104,0031640,0105773,
+0041677,0011276,0123617,0160135,
+0041701,0126603,0053215,0117250,
+0041420,0115777,0135206,0030232,
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041220,0144332,0045272,0174241,
+0041742,0164566,0035720,0130431,
+0042246,0126327,0166065,0116357,
+0042372,0033420,0157525,0124560,
+0042271,0167002,0066537,0172303,
+0041730,0164777,0113711,0044407,
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x1bb0,0x93c3,0xb4c2,0x3f1a,
+0x52f2,0x3f56,0xd6f5,0x3fdf,
+0x6911,0xed92,0xd2ba,0x4012,
+0xeb2e,0xc63e,0xff72,0x402c,
+0xc84d,0x924b,0xefd6,0x4031,
+0xdcf8,0x7d7e,0xd563,0x401e,
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xef8e,0xae97,0x9320,0x4026,
+0xc033,0x4e19,0x9d2c,0x4046,
+0xbdbd,0xa326,0xbf33,0x4054,
+0xae21,0xeb5e,0xc9e2,0x4051,
+0x25b2,0x9e1f,0x200a,0x4037,
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f1a,0xb4c2,0x93c3,0x1bb0,
+0x3fdf,0xd6f5,0x3f56,0x52f2,
+0x4012,0xd2ba,0xed92,0x6911,
+0x402c,0xff72,0xc63e,0xeb2e,
+0x4031,0xefd6,0x924b,0xc84d,
+0x401e,0xd563,0x7d7e,0xdcf8,
+};
+static unsigned short Q[] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4026,0x9320,0xae97,0xef8e,
+0x4046,0x9d2c,0x4e19,0xc033,
+0x4054,0xbf33,0xa326,0xbdbd,
+0x4051,0xc9e2,0xeb5e,0xae21,
+0x4037,0x200a,0x9e1f,0x25b2,
+};
+#endif
+
+/* Coefficients for log(x) = z + z**3 P(z)/Q(z),
+ * where z = 2(x-1)/(x+1)
+ * 1/sqrt(2) <= x < sqrt(2)
+ */
+
+#ifdef UNK
+static double R[3] = {
+-7.89580278884799154124E-1,
+ 1.63866645699558079767E1,
+-6.41409952958715622951E1,
+};
+static double S[3] = {
+/* 1.00000000000000000000E0,*/
+-3.56722798256324312549E1,
+ 3.12093766372244180303E2,
+-7.69691943550460008604E2,
+};
+#endif
+#ifdef DEC
+static unsigned short R[12] = {
+0140112,0020756,0161540,0072035,
+0041203,0013743,0114023,0155527,
+0141600,0044060,0104421,0050400,
+};
+static unsigned short S[12] = {
+/*0040200,0000000,0000000,0000000,*/
+0141416,0130152,0017543,0064122,
+0042234,0006000,0104527,0020155,
+0142500,0066110,0146631,0174731,
+};
+#endif
+#ifdef IBMPC
+static unsigned short R[12] = {
+0x0e84,0xdc6c,0x443d,0xbfe9,
+0x7b6b,0x7302,0x62fc,0x4030,
+0x2a20,0x1122,0x0906,0xc050,
+};
+static unsigned short S[12] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x6d0a,0x43ec,0xd60d,0xc041,
+0xe40e,0x112a,0x8180,0x4073,
+0x3f3b,0x19b3,0x0d89,0xc088,
+};
+#endif
+#ifdef MIEEE
+static unsigned short R[12] = {
+0xbfe9,0x443d,0xdc6c,0x0e84,
+0x4030,0x62fc,0x7302,0x7b6b,
+0xc050,0x0906,0x1122,0x2a20,
+};
+static unsigned short S[12] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0xc041,0xd60d,0x43ec,0x6d0a,
+0x4073,0x8180,0x112a,0xe40e,
+0xc088,0x0d89,0x19b3,0x3f3b,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double frexp(), ldexp(), polevl(), p1evl();
+int isnan(), isfinite();
+#endif
+#define SQRTH 0.70710678118654752440
+extern double INFINITY, NAN;
+
+double log(x)
+double x;
+{
+int e;
+#ifdef DEC
+short *q;
+#endif
+double y, z;
+
+#ifdef NANS
+if( isnan(x) )
+ return(x);
+#endif
+#ifdef INFINITIES
+if( x == INFINITY )
+ return(x);
+#endif
+/* Test for domain */
+if( x <= 0.0 )
+ {
+ if( x == 0.0 )
+ {
+ mtherr( fname, SING );
+ return( -INFINITY );
+ }
+ else
+ {
+ mtherr( fname, DOMAIN );
+ return( NAN );
+ }
+ }
+
+/* separate mantissa from exponent */
+
+#ifdef DEC
+q = (short *)&x;
+e = *q; /* short containing exponent */
+e = ((e >> 7) & 0377) - 0200; /* the exponent */
+*q &= 0177; /* strip exponent from x */
+*q |= 040000; /* x now between 0.5 and 1 */
+#endif
+
+/* Note, frexp is used so that denormal numbers
+ * will be handled properly.
+ */
+#ifdef IBMPC
+x = frexp( x, &e );
+/*
+q = (short *)&x;
+q += 3;
+e = *q;
+e = ((e >> 4) & 0x0fff) - 0x3fe;
+*q &= 0x0f;
+*q |= 0x3fe0;
+*/
+#endif
+
+/* Equivalent C language standard library function: */
+#ifdef UNK
+x = frexp( x, &e );
+#endif
+
+#ifdef MIEEE
+x = frexp( x, &e );
+#endif
+
+
+
+/* logarithm using log(x) = z + z**3 P(z)/Q(z),
+ * where z = 2(x-1)/x+1)
+ */
+
+if( (e > 2) || (e < -2) )
+{
+if( x < SQRTH )
+ { /* 2( 2x-1 )/( 2x+1 ) */
+ e -= 1;
+ z = x - 0.5;
+ y = 0.5 * z + 0.5;
+ }
+else
+ { /* 2 (x-1)/(x+1) */
+ z = x - 0.5;
+ z -= 0.5;
+ y = 0.5 * x + 0.5;
+ }
+
+x = z / y;
+
+
+/* rational form */
+z = x*x;
+z = x * ( z * polevl( z, R, 2 ) / p1evl( z, S, 3 ) );
+y = e;
+z = z - y * 2.121944400546905827679e-4;
+z = z + x;
+z = z + e * 0.693359375;
+goto ldone;
+}
+
+
+
+/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+
+if( x < SQRTH )
+ {
+ e -= 1;
+ x = ldexp( x, 1 ) - 1.0; /* 2x - 1 */
+ }
+else
+ {
+ x = x - 1.0;
+ }
+
+
+/* rational form */
+z = x*x;
+#if DEC
+y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 6 ) );
+#else
+y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 5 ) );
+#endif
+if( e )
+ y = y - e * 2.121944400546905827679e-4;
+y = y - ldexp( z, -1 ); /* y - 0.5 * z */
+z = x + y;
+if( e )
+ z = z + e * 0.693359375;
+
+ldone:
+
+return( z );
+}
diff --git a/libm/double/log10.c b/libm/double/log10.c
new file mode 100644
index 000000000..7dc72e253
--- /dev/null
+++ b/libm/double/log10.c
@@ -0,0 +1,250 @@
+/* log10.c
+ *
+ * Common logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, log10();
+ *
+ * y = log10( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns logarithm to the base 10 of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. The logarithm of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 30000 1.5e-16 5.0e-17
+ * IEEE 0, MAXNUM 30000 1.4e-16 4.8e-17
+ * DEC 1, MAXNUM 50000 2.5e-17 6.0e-18
+ *
+ * In the tests over the interval [1, MAXNUM], the logarithms
+ * of the random arguments were uniformly distributed over
+ * [0, MAXLOG].
+ *
+ * ERROR MESSAGES:
+ *
+ * log10 singularity: x = 0; returns -INFINITY
+ * log10 domain: x < 0; returns NAN
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+static char fname[] = {"log10"};
+
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ */
+#ifdef UNK
+static double P[] = {
+ 4.58482948458143443514E-5,
+ 4.98531067254050724270E-1,
+ 6.56312093769992875930E0,
+ 2.97877425097986925891E1,
+ 6.06127134467767258030E1,
+ 5.67349287391754285487E1,
+ 1.98892446572874072159E1
+};
+static double Q[] = {
+/* 1.00000000000000000000E0, */
+ 1.50314182634250003249E1,
+ 8.27410449222435217021E1,
+ 2.20664384982121929218E2,
+ 3.07254189979530058263E2,
+ 2.14955586696422947765E2,
+ 5.96677339718622216300E1
+};
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0034500,0046473,0051374,0135174,
+0037777,0037566,0145712,0150321,
+0040722,0002426,0031543,0123107,
+0041356,0046513,0170752,0004346,
+0041562,0071553,0023536,0163343,
+0041542,0170221,0024316,0114216,
+0041237,0016454,0046611,0104602
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041160,0100260,0067736,0102424,
+0041645,0075552,0036563,0147072,
+0042134,0125025,0021132,0025320,
+0042231,0120211,0046030,0103271,
+0042126,0172241,0052151,0120426,
+0041556,0125702,0072116,0047103
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x974f,0x6a5f,0x09a7,0x3f08,
+0x5a1a,0xd979,0xe7ee,0x3fdf,
+0x74c9,0xc66c,0x40a2,0x401a,
+0x411d,0x7e3d,0xc9a9,0x403d,
+0xdcdc,0x64eb,0x4e6d,0x404e,
+0xd312,0x2519,0x5e12,0x404c,
+0x3130,0x89b1,0xe3a5,0x4033
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xd0a2,0x0dfb,0x1016,0x402e,
+0x79c7,0x47ae,0xaf6d,0x4054,
+0x455a,0xa44b,0x9542,0x406b,
+0x10d7,0x2983,0x3411,0x4073,
+0x3423,0x2a8d,0xde94,0x406a,
+0xc9c8,0x4e89,0xd578,0x404d
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f08,0x09a7,0x6a5f,0x974f,
+0x3fdf,0xe7ee,0xd979,0x5a1a,
+0x401a,0x40a2,0xc66c,0x74c9,
+0x403d,0xc9a9,0x7e3d,0x411d,
+0x404e,0x4e6d,0x64eb,0xdcdc,
+0x404c,0x5e12,0x2519,0xd312,
+0x4033,0xe3a5,0x89b1,0x3130
+};
+static unsigned short Q[] = {
+0x402e,0x1016,0x0dfb,0xd0a2,
+0x4054,0xaf6d,0x47ae,0x79c7,
+0x406b,0x9542,0xa44b,0x455a,
+0x4073,0x3411,0x2983,0x10d7,
+0x406a,0xde94,0x2a8d,0x3423,
+0x404d,0xd578,0x4e89,0xc9c8
+};
+#endif
+
+#define SQRTH 0.70710678118654752440
+#define L102A 3.0078125E-1
+#define L102B 2.48745663981195213739E-4
+#define L10EA 4.3359375E-1
+#define L10EB 7.00731903251827651129E-4
+
+#ifdef ANSIPROT
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double frexp(), ldexp(), polevl(), p1evl();
+int isnan(), isfinite();
+#endif
+extern double LOGE2, SQRT2, INFINITY, NAN;
+
+double log10(x)
+double x;
+{
+VOLATILE double z;
+double y;
+#ifdef DEC
+short *q;
+#endif
+int e;
+
+#ifdef NANS
+if( isnan(x) )
+ return(x);
+#endif
+#ifdef INFINITIES
+if( x == INFINITY )
+ return(x);
+#endif
+/* Test for domain */
+if( x <= 0.0 )
+ {
+ if( x == 0.0 )
+ {
+ mtherr( fname, SING );
+ return( -INFINITY );
+ }
+ else
+ {
+ mtherr( fname, DOMAIN );
+ return( NAN );
+ }
+ }
+
+/* separate mantissa from exponent */
+
+#ifdef DEC
+q = (short *)&x;
+e = *q; /* short containing exponent */
+e = ((e >> 7) & 0377) - 0200; /* the exponent */
+*q &= 0177; /* strip exponent from x */
+*q |= 040000; /* x now between 0.5 and 1 */
+#endif
+
+#ifdef IBMPC
+x = frexp( x, &e );
+/*
+q = (short *)&x;
+q += 3;
+e = *q;
+e = ((e >> 4) & 0x0fff) - 0x3fe;
+*q &= 0x0f;
+*q |= 0x3fe0;
+*/
+#endif
+
+/* Equivalent C language standard library function: */
+#ifdef UNK
+x = frexp( x, &e );
+#endif
+
+#ifdef MIEEE
+x = frexp( x, &e );
+#endif
+
+/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+
+if( x < SQRTH )
+ {
+ e -= 1;
+ x = ldexp( x, 1 ) - 1.0; /* 2x - 1 */
+ }
+else
+ {
+ x = x - 1.0;
+ }
+
+
+/* rational form */
+z = x*x;
+y = x * ( z * polevl( x, P, 6 ) / p1evl( x, Q, 6 ) );
+y = y - ldexp( z, -1 ); /* y - 0.5 * x**2 */
+
+/* multiply log of fraction by log10(e)
+ * and base 2 exponent by log10(2)
+ */
+z = (x + y) * L10EB; /* accumulate terms in order of size */
+z += y * L10EA;
+z += x * L10EA;
+z += e * L102B;
+z += e * L102A;
+
+
+return( z );
+}
diff --git a/libm/double/log2.c b/libm/double/log2.c
new file mode 100644
index 000000000..e73782712
--- /dev/null
+++ b/libm/double/log2.c
@@ -0,0 +1,348 @@
+/* log2.c
+ *
+ * Base 2 logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, log2();
+ *
+ * y = log2( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base 2 logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the base e
+ * logarithm of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting z = 2(x-1)/x+1),
+ *
+ * log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 30000 2.0e-16 5.5e-17
+ * IEEE exp(+-700) 40000 1.3e-16 4.6e-17
+ *
+ * In the tests over the interval [exp(+-700)], the logarithms
+ * of the random arguments were uniformly distributed.
+ *
+ * ERROR MESSAGES:
+ *
+ * log2 singularity: x = 0; returns -INFINITY
+ * log2 domain: x < 0; returns NAN
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+static char fname[] = {"log2"};
+
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ */
+#ifdef UNK
+static double P[] = {
+ 1.01875663804580931796E-4,
+ 4.97494994976747001425E-1,
+ 4.70579119878881725854E0,
+ 1.44989225341610930846E1,
+ 1.79368678507819816313E1,
+ 7.70838733755885391666E0,
+};
+static double Q[] = {
+/* 1.00000000000000000000E0, */
+ 1.12873587189167450590E1,
+ 4.52279145837532221105E1,
+ 8.29875266912776603211E1,
+ 7.11544750618563894466E1,
+ 2.31251620126765340583E1,
+};
+#define LOG2EA 0.44269504088896340735992
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0037777,0127270,0162547,0057274,
+0041001,0054665,0164317,0005341,
+0041451,0034104,0031640,0105773,
+0041677,0011276,0123617,0160135,
+0041701,0126603,0053215,0117250,
+0041420,0115777,0135206,0030232,
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041220,0144332,0045272,0174241,
+0041742,0164566,0035720,0130431,
+0042246,0126327,0166065,0116357,
+0042372,0033420,0157525,0124560,
+0042271,0167002,0066537,0172303,
+0041730,0164777,0113711,0044407,
+};
+static unsigned short L[5] = {0037742,0124354,0122560,0057703};
+#define LOG2EA (*(double *)(&L[0]))
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x1bb0,0x93c3,0xb4c2,0x3f1a,
+0x52f2,0x3f56,0xd6f5,0x3fdf,
+0x6911,0xed92,0xd2ba,0x4012,
+0xeb2e,0xc63e,0xff72,0x402c,
+0xc84d,0x924b,0xefd6,0x4031,
+0xdcf8,0x7d7e,0xd563,0x401e,
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xef8e,0xae97,0x9320,0x4026,
+0xc033,0x4e19,0x9d2c,0x4046,
+0xbdbd,0xa326,0xbf33,0x4054,
+0xae21,0xeb5e,0xc9e2,0x4051,
+0x25b2,0x9e1f,0x200a,0x4037,
+};
+static unsigned short L[5] = {0x0bf8,0x94ae,0x551d,0x3fdc};
+#define LOG2EA (*(double *)(&L[0]))
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3f1a,0xb4c2,0x93c3,0x1bb0,
+0x3fdf,0xd6f5,0x3f56,0x52f2,
+0x4012,0xd2ba,0xed92,0x6911,
+0x402c,0xff72,0xc63e,0xeb2e,
+0x4031,0xefd6,0x924b,0xc84d,
+0x401e,0xd563,0x7d7e,0xdcf8,
+};
+static unsigned short Q[] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4026,0x9320,0xae97,0xef8e,
+0x4046,0x9d2c,0x4e19,0xc033,
+0x4054,0xbf33,0xa326,0xbdbd,
+0x4051,0xc9e2,0xeb5e,0xae21,
+0x4037,0x200a,0x9e1f,0x25b2,
+};
+static unsigned short L[5] = {0x3fdc,0x551d,0x94ae,0x0bf8};
+#define LOG2EA (*(double *)(&L[0]))
+#endif
+
+/* Coefficients for log(x) = z + z**3 P(z)/Q(z),
+ * where z = 2(x-1)/(x+1)
+ * 1/sqrt(2) <= x < sqrt(2)
+ */
+
+#ifdef UNK
+static double R[3] = {
+-7.89580278884799154124E-1,
+ 1.63866645699558079767E1,
+-6.41409952958715622951E1,
+};
+static double S[3] = {
+/* 1.00000000000000000000E0,*/
+-3.56722798256324312549E1,
+ 3.12093766372244180303E2,
+-7.69691943550460008604E2,
+};
+/* log2(e) - 1 */
+#define LOG2EA 0.44269504088896340735992
+#endif
+#ifdef DEC
+static unsigned short R[12] = {
+0140112,0020756,0161540,0072035,
+0041203,0013743,0114023,0155527,
+0141600,0044060,0104421,0050400,
+};
+static unsigned short S[12] = {
+/*0040200,0000000,0000000,0000000,*/
+0141416,0130152,0017543,0064122,
+0042234,0006000,0104527,0020155,
+0142500,0066110,0146631,0174731,
+};
+/* log2(e) - 1 */
+#define LOG2EA 0.44269504088896340735992L
+#endif
+#ifdef IBMPC
+static unsigned short R[12] = {
+0x0e84,0xdc6c,0x443d,0xbfe9,
+0x7b6b,0x7302,0x62fc,0x4030,
+0x2a20,0x1122,0x0906,0xc050,
+};
+static unsigned short S[12] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x6d0a,0x43ec,0xd60d,0xc041,
+0xe40e,0x112a,0x8180,0x4073,
+0x3f3b,0x19b3,0x0d89,0xc088,
+};
+#endif
+#ifdef MIEEE
+static unsigned short R[12] = {
+0xbfe9,0x443d,0xdc6c,0x0e84,
+0x4030,0x62fc,0x7302,0x7b6b,
+0xc050,0x0906,0x1122,0x2a20,
+};
+static unsigned short S[12] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0xc041,0xd60d,0x43ec,0x6d0a,
+0x4073,0x8180,0x112a,0xe40e,
+0xc088,0x0d89,0x19b3,0x3f3b,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double frexp(), ldexp(), polevl(), p1evl();
+int isnan(), isfinite();
+#endif
+#define SQRTH 0.70710678118654752440
+extern double LOGE2, INFINITY, NAN;
+
+double log2(x)
+double x;
+{
+int e;
+double y;
+VOLATILE double z;
+#ifdef DEC
+short *q;
+#endif
+
+#ifdef NANS
+if( isnan(x) )
+ return(x);
+#endif
+#ifdef INFINITIES
+if( x == INFINITY )
+ return(x);
+#endif
+/* Test for domain */
+if( x <= 0.0 )
+ {
+ if( x == 0.0 )
+ {
+ mtherr( fname, SING );
+ return( -INFINITY );
+ }
+ else
+ {
+ mtherr( fname, DOMAIN );
+ return( NAN );
+ }
+ }
+
+/* separate mantissa from exponent */
+
+#ifdef DEC
+q = (short *)&x;
+e = *q; /* short containing exponent */
+e = ((e >> 7) & 0377) - 0200; /* the exponent */
+*q &= 0177; /* strip exponent from x */
+*q |= 040000; /* x now between 0.5 and 1 */
+#endif
+
+/* Note, frexp is used so that denormal numbers
+ * will be handled properly.
+ */
+#ifdef IBMPC
+x = frexp( x, &e );
+/*
+q = (short *)&x;
+q += 3;
+e = *q;
+e = ((e >> 4) & 0x0fff) - 0x3fe;
+*q &= 0x0f;
+*q |= 0x3fe0;
+*/
+#endif
+
+/* Equivalent C language standard library function: */
+#ifdef UNK
+x = frexp( x, &e );
+#endif
+
+#ifdef MIEEE
+x = frexp( x, &e );
+#endif
+
+
+/* logarithm using log(x) = z + z**3 P(z)/Q(z),
+ * where z = 2(x-1)/x+1)
+ */
+
+if( (e > 2) || (e < -2) )
+{
+if( x < SQRTH )
+ { /* 2( 2x-1 )/( 2x+1 ) */
+ e -= 1;
+ z = x - 0.5;
+ y = 0.5 * z + 0.5;
+ }
+else
+ { /* 2 (x-1)/(x+1) */
+ z = x - 0.5;
+ z -= 0.5;
+ y = 0.5 * x + 0.5;
+ }
+
+x = z / y;
+z = x*x;
+y = x * ( z * polevl( z, R, 2 ) / p1evl( z, S, 3 ) );
+goto ldone;
+}
+
+
+
+/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+
+if( x < SQRTH )
+ {
+ e -= 1;
+ x = ldexp( x, 1 ) - 1.0; /* 2x - 1 */
+ }
+else
+ {
+ x = x - 1.0;
+ }
+
+z = x*x;
+#if DEC
+y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 6 ) ) - ldexp( z, -1 );
+#else
+y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 5 ) ) - ldexp( z, -1 );
+#endif
+
+ldone:
+
+/* Multiply log of fraction by log2(e)
+ * and base 2 exponent by 1
+ *
+ * ***CAUTION***
+ *
+ * This sequence of operations is critical and it may
+ * be horribly defeated by some compiler optimizers.
+ */
+z = y * LOG2EA;
+z += x * LOG2EA;
+z += y;
+z += x;
+z += e;
+return( z );
+}
diff --git a/libm/double/lrand.c b/libm/double/lrand.c
new file mode 100644
index 000000000..cfdaa9f28
--- /dev/null
+++ b/libm/double/lrand.c
@@ -0,0 +1,86 @@
+/* lrand.c
+ *
+ * Pseudorandom number generator
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long y, drand();
+ *
+ * drand( &y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Yields a long integer random number.
+ *
+ * The three-generator congruential algorithm by Brian
+ * Wichmann and David Hill (BYTE magazine, March, 1987,
+ * pp 127-8) is used. The period, given by them, is
+ * 6953607871644.
+ *
+ *
+ */
+
+
+
+#include <math.h>
+
+
+/* Three-generator random number algorithm
+ * of Brian Wichmann and David Hill
+ * BYTE magazine, March, 1987 pp 127-8
+ *
+ * The period, given by them, is (p-1)(q-1)(r-1)/4 = 6.95e12.
+ */
+
+static int sx = 1;
+static int sy = 10000;
+static int sz = 3000;
+
+/* This function implements the three
+ * congruential generators.
+ */
+
+long lrand()
+{
+int r, s;
+unsigned long ans;
+
+/*
+if( arg )
+ {
+ sx = 1;
+ sy = 10000;
+ sz = 3000;
+ }
+*/
+
+/* sx = sx * 171 mod 30269 */
+r = sx/177;
+s = sx - 177 * r;
+sx = 171 * s - 2 * r;
+if( sx < 0 )
+ sx += 30269;
+
+
+/* sy = sy * 172 mod 30307 */
+r = sy/176;
+s = sy - 176 * r;
+sy = 172 * s - 35 * r;
+if( sy < 0 )
+ sy += 30307;
+
+/* sz = 170 * sz mod 30323 */
+r = sz/178;
+s = sz - 178 * r;
+sz = 170 * s - 63 * r;
+if( sz < 0 )
+ sz += 30323;
+
+ans = sx * sy * sz;
+return(ans);
+}
+
diff --git a/libm/double/lsqrt.c b/libm/double/lsqrt.c
new file mode 100644
index 000000000..bf85a54f1
--- /dev/null
+++ b/libm/double/lsqrt.c
@@ -0,0 +1,85 @@
+/* lsqrt.c
+ *
+ * Integer square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long x, y;
+ * long lsqrt();
+ *
+ * y = lsqrt( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns a long integer square root of the long integer
+ * argument. The computation is by binary long division.
+ *
+ * The largest possible result is lsqrt(2,147,483,647)
+ * = 46341.
+ *
+ * If x < 0, the square root of |x| is returned, and an
+ * error message is printed.
+ *
+ *
+ * ACCURACY:
+ *
+ * An extra, roundoff, bit is computed; hence the result
+ * is the nearest integer to the actual square root.
+ * NOTE: only DEC arithmetic is currently supported.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.0: April, 1987
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+long lsqrt(x)
+long x;
+{
+long num, sq;
+long temp;
+int i, j, k, n;
+
+if( x < 0 )
+ {
+ mtherr( "lsqrt", DOMAIN );
+ x = -x;
+ }
+
+num = 0;
+sq = 0;
+k = 24;
+n = 4;
+
+for( j=0; j<4; j++ )
+ {
+ num |= (x >> k) & 0xff; /* bring in next byte of arg */
+ if( j == 3 ) /* do roundoff bit at end */
+ n = 5;
+ for( i=0; i<n; i++ )
+ {
+ num <<= 2; /* next 2 bits of arg */
+ sq <<= 1; /* shift up answer */
+ temp = (sq << 1) + 256; /* trial divisor */
+ temp = num - temp;
+ if( temp >= 0 )
+ {
+ num = temp; /* it went in */
+ sq += 256; /* answer bit = 1 */
+ }
+ }
+ k -= 8; /* shift count to get next byte of arg */
+ }
+
+sq += 256; /* add roundoff bit */
+sq >>= 9; /* truncate */
+return( sq );
+}
diff --git a/libm/double/ltstd.c b/libm/double/ltstd.c
new file mode 100644
index 000000000..f47fc3907
--- /dev/null
+++ b/libm/double/ltstd.c
@@ -0,0 +1,469 @@
+/* ltstd.c */
+/* Function test routine.
+ * Requires long double type check routine and double precision function
+ * under test. Indicate function name and range in #define statements
+ * below. Modifications for two argument functions and absolute
+ * rather than relative accuracy report are indicated.
+ */
+
+#include <stdio.h>
+/* int printf(), gets(), sscanf(); */
+
+#include <math.h>
+#ifdef ANSIPROT
+int drand ( void );
+int dprec ( void );
+int ldprec ( void );
+double exp ( double );
+double sqrt ( double );
+double fabs ( double );
+double floor ( double );
+long double sqrtl ( long double );
+long double fabsl ( long double );
+#else
+int drand();
+int dprec(), ldprec();
+double exp(), sqrt(), fabs(), floor();
+long double sqrtl(), fabsl();
+#endif
+
+#define RELERR 1
+#define ONEARG 0
+#define ONEINT 0
+#define TWOARG 0
+#define TWOINT 0
+#define THREEARG 1
+#define THREEINT 0
+#define FOURARG 0
+#define VECARG 0
+#define FOURANS 0
+#define TWOANS 0
+#define PROB 0
+#define EXPSCALE 0
+#define EXPSC2 0
+/* insert function to be tested here: */
+#define FUNC hyperg
+double FUNC();
+#define QFUNC hypergl
+long double QFUNC();
+/*extern int aiconf;*/
+
+extern double MAXLOG;
+extern double MINLOG;
+extern double MAXNUM;
+#define LTS 3.258096538
+/* insert low end and width of test interval */
+#define LOW 0.0
+#define WIDTH 30.0
+#define LOWA 0.0
+#define WIDTHA 30.0
+/* 1.073741824e9 */
+/* 2.147483648e9 */
+long double qone = 1.0L;
+static long double q1, q2, q3, qa, qb, qc, qz, qy1, qy2, qy3, qy4;
+static double y2, y3, y4, a, b, c, x, y, z, e;
+static long double qe, qmax, qrmsa, qave;
+volatile double v;
+static long double lp[3], lq[3];
+static double dp[3], dq[3];
+
+char strave[20];
+char strrms[20];
+char strmax[20];
+double underthresh = 2.22507385850720138309E-308; /* 2^-1022 */
+
+void main()
+{
+char s[80];
+int i, j, k;
+long m, n;
+
+merror = 0;
+ldprec(); /* set up coprocessor. */
+/*aiconf = -1;*/ /* configure Airy function */
+x = 1.0;
+z = x * x;
+qmax = 0.0L;
+sprintf(strmax, "%.4Le", qmax );
+qrmsa = 0.0L;
+qave = 0.0L;
+
+#if 1
+printf(" Start at random number #:" );
+gets( s );
+sscanf( s, "%ld", &n );
+printf("%ld\n", n );
+#else
+n = 0;
+#endif
+
+for( m=0; m<n; m++ )
+ drand( &x );
+n = 0;
+m = 0;
+x = floor( x );
+
+loop:
+
+for( i=0; i<500; i++ )
+{
+n++;
+m++;
+
+#if ONEARG || TWOARG || THREEARG || FOURARG
+/*ldprec();*/ /* set up floating point coprocessor */
+/* make random number in desired range */
+drand( &x );
+x = WIDTH * ( x - 1.0 ) + LOW;
+#if EXPSCALE
+x = exp(x);
+drand( &a );
+a = 1.0e-13 * x * a;
+if( x > 0.0 )
+ x -= a;
+else
+ x += a;
+#endif
+#if ONEINT
+k = x;
+x = k;
+#endif
+v = x;
+q1 = v; /* double number to q type */
+#endif
+
+/* do again if second argument required */
+
+#if TWOARG || THREEARG || FOURARG
+drand( &a );
+a = WIDTHA * ( a - 1.0 ) + LOWA;
+/*a /= 50.0;*/
+#if EXPSC2
+a = exp(a);
+drand( &y2 );
+y2 = 1.0e-13 * y2 * a;
+if( a > 0.0 )
+ a -= y2;
+else
+ a += y2;
+#endif
+#if TWOINT || THREEINT
+k = a + 0.25;
+a = k;
+#endif
+v = a;
+qy4 = v;
+#endif
+
+#if THREEARG || FOURARG
+drand( &b );
+#if PROB
+/*
+b = b - 1.0;
+b = a * b;
+*/
+#if 1
+/* This makes b <= a, for bdtr. */
+b = (a - LOWA) * ( b - 1.0 ) + LOWA;
+if( b > 1.0 && a > 1.0 )
+ b -= 1.0;
+else
+ {
+ a += 1.0;
+ k = a;
+ a = k;
+ v = a;
+ qy4 = v;
+ }
+#else
+b = WIDTHA * ( b - 1.0 ) + LOWA;
+#endif
+
+/* Half-integer a and b */
+/*
+a = 0.5*floor(2.0*a+1.0);
+b = 0.5*floor(2.0*b+1.0);
+*/
+v = a;
+qy4 = v;
+/*x = (a / (a+b));*/
+
+#else
+b = WIDTHA * ( b - 1.0 ) + LOWA;
+#endif
+#if THREEINT
+j = b + 0.25;
+b = j;
+#endif
+v = b;
+qb = v;
+#endif
+
+#if FOURARG
+drand( &c );
+c = WIDTHA * ( c - 1.0 ) + LOWA;
+/* for hyp2f1 to ensure c-a-b > -1 */
+/*
+z = c-a-b;
+if( z < -1.0 )
+ c -= 1.6 * z;
+*/
+v = c;
+qc = v;
+#endif
+
+#if VECARG
+for( j=0; j<3; j++)
+ {
+ drand( &x );
+ x = WIDTH * ( x - 1.0 ) + LOW;
+ v = x;
+ dp[j] = v;
+ q1 = v; /* double number to q type */
+ lp[j] = q1;
+ drand( &x );
+ x = WIDTH * ( x - 1.0 ) + LOW;
+ v = x;
+ dq[j] = v;
+ q1 = v; /* double number to q type */
+ lq[j] = q1;
+ }
+#endif /* VECARG */
+
+/*printf("%.16E %.16E\n", a, x);*/
+/* compute function under test */
+/* Set to double precision */
+/*dprec();*/
+#if ONEARG
+#if FOURANS
+/*FUNC( x, &z, &y2, &y3, &y4 );*/
+FUNC( x, &y4, &y2, &y3, &z );
+#else
+#if TWOANS
+FUNC( x, &z, &y2 );
+/*FUNC( x, &y2, &z );*/
+#else
+#if ONEINT
+z = FUNC( k );
+#else
+z = FUNC( x );
+#endif
+#endif
+#endif
+#endif
+
+#if TWOARG
+#if TWOINT
+z = FUNC( k, x );
+/*z = FUNC( x, k );*/
+/*z = FUNC( a, x );*/
+#else
+#if FOURANS
+FUNC( a, x, &z, &y2, &y3, &y4 );
+#else
+z = FUNC( a, x );
+#endif
+#endif
+#endif
+
+#if THREEARG
+#if THREEINT
+z = FUNC( j, k, x );
+#else
+z = FUNC( a, b, x );
+#endif
+#endif
+
+#if FOURARG
+z = FUNC( a, b, c, x );
+#endif
+
+#if VECARG
+z = FUNC( dp, dq );
+#endif
+
+q2 = z;
+/* handle detected overflow */
+if( (z == MAXNUM) || (z == -MAXNUM) )
+ {
+ printf("detected overflow ");
+#if FOURARG
+ printf("%.4E %.4E %.4E %.4E %.4E %6ld \n",
+ a, b, c, x, y, n);
+#else
+ printf("%.16E %.4E %.4E %6ld \n", x, a, z, n);
+#endif
+ e = 0.0;
+ m -= 1;
+ goto endlup;
+ }
+/* Skip high precision if underflow. */
+if( merror == UNDERFLOW )
+ goto underf;
+
+/* compute high precision function */
+/*ldprec();*/
+#if ONEARG
+#if FOURANS
+/*qy4 = QFUNC( q1, qz, qy2, qy3 );*/
+qz = QFUNC( q1, qy4, qy2, qy3 );
+#else
+#if TWOANS
+qy2 = QFUNC( q1, qz );
+/*qz = QFUNC( q1, qy2 );*/
+#else
+/* qy4 = 0.0L;*/
+/* qy4 = 1.0L;*/
+/*qz = QFUNC( qy4, q1 );*/
+/*qz = QFUNC( 1, q1 );*/
+qz = QFUNC( q1 ); /* normal */
+#endif
+#endif
+#endif
+
+#if TWOARG
+#if TWOINT
+qz = QFUNC( k, q1 );
+/*qz = QFUNC( q1, qy4 );*/
+/*qz = QFUNC( qy4, q1 );*/
+#else
+#if FOURANS
+qc = QFUNC( qy4, q1, qz, qy2, qy3 );
+#else
+/*qy4 = 0.0L;;*/
+/*qy4 = 1.0L );*/
+qz = QFUNC( qy4, q1 );
+#endif
+#endif
+#endif
+
+#if THREEARG
+#if THREEINT
+qz = QFUNC( j, k, q1 );
+#else
+qz = QFUNC( qy4, qb, q1 );
+#endif
+#endif
+
+#if FOURARG
+qz = QFUNC( qy4, qb, qc, q1 );
+#endif
+
+#if VECARG
+qz = QFUNC( lp, lq );
+#endif
+
+y = qz; /* correct answer, in double precision */
+
+/* get absolute error, in extended precision */
+qe = q2 - qz;
+e = qe; /* the error in double precision */
+
+/* handle function result equal to zero
+ or underflowed. */
+if( qz == 0.0L || merror == UNDERFLOW || fabs(z) < underthresh )
+ {
+underf:
+ merror = 0;
+/* Don't bother to print anything. */
+#if 0
+ printf("ans 0 ");
+#if ONEARG
+ printf("%.8E %.8E %.4E %6ld \n", x, y, e, n);
+#endif
+
+#if TWOARG
+#if TWOINT
+ printf("%d %.8E %.8E %.4E %6ld \n", k, x, y, e, n);
+#else
+ printf("%.6E %.6E %.6E %.4E %6ld \n", a, x, y, e, n);
+#endif
+#endif
+
+#if THREEARG
+ printf("%.6E %.6E %.6E %.6E %.4E %6ld \n", a, b, x, y, e, n);
+#endif
+
+#if FOURARG
+ printf("%.4E %.4E %.4E %.4E %.4E %.4E %6ld \n",
+ a, b, c, x, y, e, n);
+#endif
+#endif /* 0 */
+ qe = 0.0L;
+ e = 0.0;
+ m -= 1;
+ goto endlup;
+ }
+
+else
+
+/* relative error */
+
+/* comment out the following two lines if absolute accuracy report */
+
+#if RELERR
+ qe = qe / qz;
+#else
+ {
+ q2 = qz;
+ q2 = fabsl(q2);
+ if( q2 > 1.0L )
+ qe = qe / qz;
+ }
+#endif
+
+qave = qave + qe;
+/* absolute value of error */
+qe = fabs(qe);
+
+/* peak detect the error */
+if( qe > qmax )
+ {
+ qmax = qe;
+ sprintf(strmax, "%.4Le", qmax );
+#if ONEARG
+ printf("%.8E %.8E %s %6ld \n", x, y, strmax, n);
+#endif
+#if TWOARG
+#if TWOINT
+ printf("%d %.8E %.8E %s %6ld \n", k, x, y, strmax, n);
+#else
+ printf("%.6E %.6E %.6E %s %6ld \n", a, x, y, strmax, n);
+#endif
+#endif
+#if THREEARG
+ printf("%.6E %.6E %.6E %.6E %s %6ld \n", a, b, x, y, strmax, n);
+#endif
+#if FOURARG
+ printf("%.4E %.4E %.4E %.4E %.4E %s %6ld \n",
+ a, b, c, x, y, strmax, n);
+#endif
+#if VECARG
+ printf("%.8E %s %6ld \n", y, strmax, n);
+#endif
+ }
+
+/* accumulate rms error */
+/* rmsa += e * e; accumulate the square of the error */
+q2 = qe * qe;
+qrmsa = qrmsa + q2;
+endlup: ;
+/*ldprec();*/
+}
+
+/* report every 500 trials */
+/* rms = sqrt( rmsa/m ); */
+q1 = m;
+q2 = qrmsa / q1;
+q2 = sqrtl(q2);
+sprintf(strrms, "%.4Le", q2 );
+
+q2 = qave / q1;
+sprintf(strave, "%.4Le", q2 );
+/*
+printf("%6ld max = %s rms = %s ave = %s \n", m, strmax, strrms, strave );
+*/
+printf("%6ld max = %s rms = %s ave = %s \r", m, strmax, strrms, strave );
+fflush(stdout);
+goto loop;
+}
diff --git a/libm/double/minv.c b/libm/double/minv.c
new file mode 100644
index 000000000..df788fecf
--- /dev/null
+++ b/libm/double/minv.c
@@ -0,0 +1,61 @@
+/* minv.c
+ *
+ * Matrix inversion
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n, errcod;
+ * double A[n*n], X[n*n];
+ * double B[n];
+ * int IPS[n];
+ * int minv();
+ *
+ * errcod = minv( A, X, n, B, IPS );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the inverse of the n by n matrix A. The result goes
+ * to X. B and IPS are scratch pad arrays of length n.
+ * The contents of matrix A are destroyed.
+ *
+ * The routine returns nonzero on error; error messages are printed
+ * by subroutine simq().
+ *
+ */
+
+minv( A, X, n, B, IPS )
+double A[], X[];
+int n;
+double B[];
+int IPS[];
+{
+double *pX;
+int i, j, k;
+
+for( i=1; i<n; i++ )
+ B[i] = 0.0;
+B[0] = 1.0;
+/* Reduce the matrix and solve for first right hand side vector */
+pX = X;
+k = simq( A, B, pX, n, 1, IPS );
+if( k )
+ return(-1);
+/* Solve for the remaining right hand side vectors */
+for( i=1; i<n; i++ )
+ {
+ B[i-1] = 0.0;
+ B[i] = 1.0;
+ pX += n;
+ k = simq( A, B, pX, n, -1, IPS );
+ if( k )
+ return(-1);
+ }
+/* Transpose the array of solution vectors */
+mtransp( n, X, X );
+return(0);
+}
+
diff --git a/libm/double/mod2pi.c b/libm/double/mod2pi.c
new file mode 100644
index 000000000..057954a9b
--- /dev/null
+++ b/libm/double/mod2pi.c
@@ -0,0 +1,122 @@
+/* Program to test range reduction of trigonometry functions
+ *
+ * -- Steve Moshier
+ */
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double floor ( double );
+extern double ldexp ( double, int );
+extern double sin ( double );
+#else
+double floor(), ldexp(), sin();
+#endif
+
+#define TPI 6.283185307179586476925
+
+main()
+{
+char s[40];
+double a, n, t, x, y, z;
+int lflg;
+
+x = TPI/4.0;
+t = 1.0;
+
+loop:
+
+t = 2.0 * t;
+
+/* Stop testing at a point beyond which the integer part of
+ * x/2pi cannot be represented exactly by a double precision number.
+ * The library trigonometry functions will probably give up long before
+ * this point is reached.
+ */
+if( t > 1.0e16 )
+ exit(0);
+
+/* Adjust the following to choose a nontrivial x
+ * where test function(x) has a slope of about 1 or more.
+ */
+x = TPI * t + 0.5;
+
+z = x;
+lflg = 0;
+
+inlup:
+
+/* floor() returns the largest integer less than its argument.
+ * If you do not have this, or AINT(), then you may convert x/TPI
+ * to a long integer and then back to double; but in that case
+ * x will be limited to the largest value that will fit into a
+ * long integer.
+ */
+n = floor( z/TPI );
+
+/* Carefully subtract 2 pi n from x.
+ * This is done by subtracting n * 2**k in such a way that there
+ * is no arithmetic cancellation error at any step. The k are the
+ * bits in the number 2 pi.
+ *
+ * If you do not have ldexp(), then you may multiply or
+ * divide n by an appropriate power of 2 after each step.
+ * For example:
+ * a = z - 4*n;
+ * a -= 2*n;
+ * n /= 4;
+ * a -= n; n/4
+ * n /= 8;
+ * a -= n; n/32
+ * etc.
+ * This will only work if division by a power of 2 is exact.
+ */
+
+a = z - ldexp(n, 2); /* 4n */
+a -= ldexp( n, 1); /* 2n */
+a -= ldexp( n, -2 ); /* n/4 */
+a -= ldexp( n, -5 ); /* n/32 */
+a -= ldexp( n, -9 ); /* n/512 */
+a += ldexp( n, -15 ); /* add n/32768 */
+a -= ldexp( n, -17 ); /* n/131072 */
+a -= ldexp( n, -18 );
+a -= ldexp( n, -20 );
+a -= ldexp( n, -22 );
+a -= ldexp( n, -24 );
+a -= ldexp( n, -28 );
+a -= ldexp( n, -32 );
+a -= ldexp( n, -37 );
+a -= ldexp( n, -39 );
+a -= ldexp( n, -40 );
+a -= ldexp( n, -42 );
+a -= ldexp( n, -46 );
+a -= ldexp( n, -47 );
+
+/* Subtract what is left of 2 pi n after all the above reductions.
+ */
+a -= 2.44929359829470635445e-16 * n;
+
+/* If the test is extended too far, it is possible
+ * to have chosen the wrong value of n. The following
+ * will fix that, but at some reduction in accuracy.
+ */
+if( (a > TPI) || (a < -1e-11) )
+ {
+ z = a;
+ lflg += 1;
+ printf( "Warning! Reduction failed on first try.\n" );
+ goto inlup;
+ }
+if( a < 0.0 )
+ {
+ printf( "Warning! Reduced value < 0\n" );
+ a += TPI;
+ }
+
+/* Compute the test function at x and at a = x mod 2 pi.
+ */
+y = sin(x);
+z = sin(a);
+printf( "sin(%.15e) error = %.3e\n", x, y-z );
+goto loop;
+}
+
diff --git a/libm/double/monot.c b/libm/double/monot.c
new file mode 100644
index 000000000..bb00c5f28
--- /dev/null
+++ b/libm/double/monot.c
@@ -0,0 +1,308 @@
+
+/* monot.c
+ Floating point function test vectors.
+
+ Arguments and function values are synthesized for NPTS points in
+ the vicinity of each given tabulated test point. The points are
+ chosen to be near and on either side of the likely function algorithm
+ domain boundaries. Since the function programs change their methods
+ at these points, major coding errors or monotonicity failures might be
+ detected.
+
+ August, 1998
+ S. L. Moshier */
+
+
+#include <stdio.h>
+
+/* Avoid including math.h. */
+double frexp (double, int *);
+double ldexp (double, int);
+
+/* Number of test points to generate on each side of tabulated point. */
+#define NPTS 100
+
+/* Functions of one variable. */
+double exp (double);
+double log (double);
+double sin (double);
+double cos (double);
+double tan (double);
+double atan (double);
+double asin (double);
+double acos (double);
+double sinh (double);
+double cosh (double);
+double tanh (double);
+double asinh (double);
+double acosh (double);
+double atanh (double);
+double gamma (double);
+double fabs (double);
+double floor (double);
+
+struct oneargument
+ {
+ char *name; /* Name of the function. */
+ double (*func) (double);
+ double arg1; /* Function argument, assumed exact. */
+ double answer1; /* Exact, close to function value. */
+ double answer2; /* answer1 + answer2 has extended precision. */
+ double derivative; /* dy/dx evaluated at x = arg1. */
+ int thresh; /* Error report threshold. 2 = 1 ULP approx. */
+ };
+
+/* Add this to error threshold test[i].thresh. */
+#define OKERROR 0
+
+/* Unit of relative error in test[i].thresh. */
+static double MACHEP = 1.1102230246251565404e-16;
+/* extern double MACHEP; */
+
+
+struct oneargument test1[] =
+{
+ {"exp", exp, 1.0, 2.7182769775390625,
+ 4.85091998273536028747e-6, 2.71828182845904523536, 2},
+ {"exp", exp, -1.0, 3.678741455078125e-1,
+ 5.29566362982159552377e-6, 3.678794411714423215955e-1, 2},
+ {"exp", exp, 0.5, 1.648712158203125,
+ 9.1124970031468486507878e-6, 1.64872127070012814684865, 2},
+ {"exp", exp, -0.5, 6.065216064453125e-1,
+ 9.0532673209236037995e-6, 6.0653065971263342360e-1, 2},
+ {"exp", exp, 2.0, 7.3890533447265625,
+ 2.75420408772723042746e-6, 7.38905609893065022723, 2},
+ {"exp", exp, -2.0, 1.353302001953125e-1,
+ 5.08304130019189399949e-6, 1.3533528323661269189e-1, 2},
+ {"log", log, 1.41421356237309492343, 3.465728759765625e-1,
+ 7.1430341006605745676897e-7, 7.0710678118654758708668e-1, 2},
+ {"log", log, 7.07106781186547461715e-1, -3.46588134765625e-1,
+ 1.45444856522566402246e-5, 1.41421356237309517417, 2},
+ {"sin", sin, 7.85398163397448278999e-1, 7.0709228515625e-1,
+ 1.4496030297502751942956e-5, 7.071067811865475460497e-1, 2},
+ {"sin", sin, -7.85398163397448501044e-1, -7.071075439453125e-1,
+ 7.62758764840238811175e-7, 7.07106781186547389040e-1, 2},
+ {"sin", sin, 1.570796326794896558, 9.999847412109375e-1,
+ 1.52587890625e-5, 6.12323399573676588613e-17, 2},
+ {"sin", sin, -1.57079632679489678004, -1.0,
+ 1.29302922820150306903e-32, -1.60812264967663649223e-16, 2},
+ {"sin", sin, 4.712388980384689674, -1.0,
+ 1.68722975549458979398e-32, -1.83697019872102976584e-16, 2},
+ {"sin", sin, -4.71238898038468989604, 9.999847412109375e-1,
+ 1.52587890625e-5, 3.83475850529283315008e-17, 2},
+ {"cos", cos, 3.92699081698724139500E-1, 9.23873901367187500000E-1,
+ 5.63114409926198633370E-6, -3.82683432365089757586E-1, 2},
+ {"cos", cos, 7.85398163397448278999E-1, 7.07092285156250000000E-1,
+ 1.44960302975460497458E-5, -7.07106781186547502752E-1, 2},
+ {"cos", cos, 1.17809724509617241850E0, 3.82675170898437500000E-1,
+ 8.26146665231415693919E-6, -9.23879532511286738554E-1, 2},
+ {"cos", cos, 1.96349540849362069750E0, -3.82690429687500000000E-1,
+ 6.99732241029898567203E-6, -9.23879532511286785419E-1, 2},
+ {"cos", cos, 2.35619449019234483700E0, -7.07107543945312500000E-1,
+ 7.62758765040545859856E-7, -7.07106781186547589348E-1, 2},
+ {"cos", cos, 2.74889357189106897650E0, -9.23889160156250000000E-1,
+ 9.62764496328487887036E-6, -3.82683432365089870728E-1, 2},
+ {"cos", cos, 3.14159265358979311600E0, -1.00000000000000000000E0,
+ 7.49879891330928797323E-33, -1.22464679914735317723E-16, 2},
+ {"tan", tan, 7.85398163397448278999E-1, 9.999847412109375e-1,
+ 1.52587890624387676600E-5, 1.99999999999999987754E0, 2},
+ {"tan", tan, 1.17809724509617241850E0, 2.41419982910156250000E0,
+ 1.37332715322352112604E-5, 6.82842712474618858345E0, 2},
+ {"tan", tan, 1.96349540849362069750E0, -2.41421508789062500000E0,
+ 1.52551752942854759743E-6, 6.82842712474619262118E0, 2},
+ {"tan", tan, 2.35619449019234483700E0, -1.00001525878906250000E0,
+ 1.52587890623163029801E-5, 2.00000000000000036739E0, 2},
+ {"tan", tan, 2.74889357189106897650E0, -4.14215087890625000000E-1,
+ 1.52551752982565655126E-6, 1.17157287525381000640E0, 2},
+ {"atan", atan, 4.14213562373094923430E-1, 3.92684936523437500000E-1,
+ 1.41451752865477964149E-5, 8.53553390593273837869E-1, 2},
+ {"atan", atan, 1.0, 7.85385131835937500000E-1,
+ 1.30315615108096156608E-5, 0.5, 2},
+ {"atan", atan, 2.41421356237309492343E0, 1.17808532714843750000E0,
+ 1.19179477349460632350E-5, 1.46446609406726250782E-1, 2},
+ {"atan", atan, -2.41421356237309514547E0, -1.17810058593750000000E0,
+ 3.34084132752141908545E-6, 1.46446609406726227789E-1, 2},
+ {"atan", atan, -1.0, -7.85400390625000000000E-1,
+ 2.22722755169038433915E-6, 0.5, 2},
+ {"atan", atan, -4.14213562373095145475E-1, -3.92700195312500000000E-1,
+ 1.11361377576267665972E-6, 8.53553390593273703853E-1, 2},
+ {"asin", asin, 3.82683432365089615246E-1, 3.92684936523437500000E-1,
+ 1.41451752864854321970E-5, 1.08239220029239389286E0, 2},
+ {"asin", asin, 0.5, 5.23590087890625000000E-1,
+ 8.68770767387307710723E-6, 1.15470053837925152902E0, 2},
+ {"asin", asin, 7.07106781186547461715E-1, 7.85385131835937500000E-1,
+ 1.30315615107209645016E-5, 1.41421356237309492343E0, 2},
+ {"asin", asin, 9.23879532511286738483E-1, 1.17808532714843750000E0,
+ 1.19179477349183147612E-5, 2.61312592975275276483E0, 2},
+ {"asin", asin, -0.5, -5.23605346679687500000E-1,
+ 6.57108138862692289277E-6, 1.15470053837925152902E0, 2},
+ {"acos", acos, 1.95090322016128192573E-1, 1.37443542480468750000E0,
+ 1.13611408471185777914E-5, -1.01959115820831832232E0, 2},
+ {"acos", acos, 3.82683432365089615246E-1, 1.17808532714843750000E0,
+ 1.19179477351337991247E-5, -1.08239220029239389286E0, 2},
+ {"acos", acos, 0.5, 1.04719543457031250000E0,
+ 2.11662628524615421446E-6, -1.15470053837925152902E0, 2},
+ {"acos", acos, 7.07106781186547461715E-1, 7.85385131835937500000E-1,
+ 1.30315615108982668201E-5, -1.41421356237309492343E0, 2},
+ {"acos", acos, 9.23879532511286738483E-1, 3.92684936523437500000E-1,
+ 1.41451752867009165605E-5, -2.61312592975275276483E0, 2},
+ {"acos", acos, 9.80785280403230430579E-1, 1.96334838867187500000E-1,
+ 1.47019821746724723933E-5, -5.12583089548300990774E0, 2},
+ {"acos", acos, -0.5, 2.09439086914062500000E0,
+ 4.23325257049230842892E-6, -1.15470053837925152902E0, 2},
+ {"sinh", sinh, 1.0, 1.17518615722656250000E0,
+ 1.50364172389568823819E-5, 1.54308063481524377848E0, 2},
+ {"sinh", sinh, 7.09089565712818057364E2, 4.49423283712885057274E307,
+ 4.25947714184369757620E208, 4.49423283712885057274E307, 2},
+ {"sinh", sinh, 2.22044604925031308085E-16, 0.00000000000000000000E0,
+ 2.22044604925031308085E-16, 1.00000000000000000000E0, 2},
+ {"cosh", cosh, 7.09089565712818057364E2, 4.49423283712885057274E307,
+ 4.25947714184369757620E208, 4.49423283712885057274E307, 2},
+ {"cosh", cosh, 1.0, 1.54307556152343750000E0,
+ 5.07329180627847790562E-6, 1.17520119364380145688E0, 2},
+ {"cosh", cosh, 0.5, 1.12762451171875000000E0,
+ 1.45348763078522622516E-6, 5.21095305493747361622E-1, 2},
+ {"tanh", tanh, 0.5, 4.62112426757812500000E-1,
+ 4.73050219725850231848E-6, 7.86447732965927410150E-1, 2},
+ {"tanh", tanh, 5.49306144334054780032E-1, 4.99984741210937500000E-1,
+ 1.52587890624507506378E-5, 7.50000000000000049249E-1, 2},
+ {"tanh", tanh, 0.625, 5.54595947265625000000E-1,
+ 3.77508375729399903910E-6, 6.92419147969988069631E-1, 2},
+ {"asinh", asinh, 0.5, 4.81201171875000000000E-1,
+ 1.06531846034474977589E-5, 8.94427190999915878564E-1, 2},
+ {"asinh", asinh, 1.0, 8.81362915039062500000E-1,
+ 1.06719804805252326093E-5, 7.07106781186547524401E-1, 2},
+ {"asinh", asinh, 2.0, 1.44363403320312500000E0,
+ 1.44197568534249327674E-6, 4.47213595499957939282E-1, 2},
+ {"acosh", acosh, 2.0, 1.31695556640625000000E0,
+ 2.33051856670862504635E-6, 5.77350269189625764509E-1, 2},
+ {"acosh", acosh, 1.5, 9.62417602539062500000E-1,
+ 6.04758014439499551783E-6, 8.94427190999915878564E-1, 2},
+ {"acosh", acosh, 1.03125, 2.49343872070312500000E-1,
+ 9.62177257298785143908E-6, 3.96911150685467059809E0, 2},
+ {"atanh", atanh, 0.5, 5.49301147460937500000E-1,
+ 4.99687311734569762262E-6, 1.33333333333333333333E0, 2},
+#if 0
+ {"gamma", gamma, 1.0, 1.0,
+ 0.0, -5.772156649015328606e-1, 2},
+ {"gamma", gamma, 2.0, 1.0,
+ 0.0, 4.2278433509846713939e-1, 2},
+ {"gamma", gamma, 3.0, 2.0,
+ 0.0, 1.845568670196934279, 2},
+ {"gamma", gamma, 4.0, 6.0,
+ 0.0, 7.536706010590802836, 2},
+#endif
+ {"null", NULL, 0.0, 0.0, 0.0, 2},
+};
+
+/* These take care of extra-precise floating point register problems. */
+volatile double volat1;
+volatile double volat2;
+
+
+/* Return the next nearest floating point value to X
+ in the direction of UPDOWN (+1 or -1).
+ (Fails if X is denormalized.) */
+
+double
+nextval (x, updown)
+ double x;
+ int updown;
+{
+ double m;
+ int i;
+
+ volat1 = x;
+ m = 0.25 * MACHEP * volat1 * updown;
+ volat2 = volat1 + m;
+ if (volat2 != volat1)
+ printf ("successor failed\n");
+
+ for (i = 2; i < 10; i++)
+ {
+ volat2 = volat1 + i * m;
+ if (volat1 != volat2)
+ return volat2;
+ }
+
+ printf ("nextval failed\n");
+ return volat1;
+}
+
+
+
+
+int
+main ()
+{
+ double (*fun1) (double);
+ int i, j, errs, tests;
+ double x, x0, y, dy, err;
+
+ /* Set math coprocessor to double precision. */
+ /* dprec (); */
+ errs = 0;
+ tests = 0;
+ i = 0;
+
+ for (;;)
+ {
+ fun1 = test1[i].func;
+ if (fun1 == NULL)
+ break;
+ volat1 = test1[i].arg1;
+ x0 = volat1;
+ x = volat1;
+ for (j = 0; j <= NPTS; j++)
+ {
+ volat1 = x - x0;
+ dy = volat1 * test1[i].derivative;
+ dy = test1[i].answer2 + dy;
+ volat1 = test1[i].answer1 + dy;
+ volat2 = (*(fun1)) (x);
+ if (volat2 != volat1)
+ {
+ /* Report difference between program result
+ and extended precision function value. */
+ err = volat2 - test1[i].answer1;
+ err = err - dy;
+ err = err / volat1;
+ if (fabs (err) > ((OKERROR + test1[i].thresh) * MACHEP))
+ {
+ printf ("%d %s(%.16e) = %.16e, rel err = %.3e\n",
+ j, test1[i].name, x, volat2, err);
+ errs += 1;
+ }
+ }
+ x = nextval (x, 1);
+ tests += 1;
+ }
+
+ x = x0;
+ x = nextval (x, -1);
+ for (j = 1; j < NPTS; j++)
+ {
+ volat1 = x - x0;
+ dy = volat1 * test1[i].derivative;
+ dy = test1[i].answer2 + dy;
+ volat1 = test1[i].answer1 + dy;
+ volat2 = (*(fun1)) (x);
+ if (volat2 != volat1)
+ {
+ err = volat2 - test1[i].answer1;
+ err = err - dy;
+ err = err / volat1;
+ if (fabs (err) > ((OKERROR + test1[i].thresh) * MACHEP))
+ {
+ printf ("%d %s(%.16e) = %.16e, rel err = %.3e\n",
+ j, test1[i].name, x, volat2, err);
+ errs += 1;
+ }
+ }
+ x = nextval (x, -1);
+ tests += 1;
+ }
+ i += 1;
+ }
+ printf ("%d errors in %d tests\n", errs, tests);
+}
diff --git a/libm/double/mtherr.c b/libm/double/mtherr.c
new file mode 100644
index 000000000..ed3d26d51
--- /dev/null
+++ b/libm/double/mtherr.c
@@ -0,0 +1,102 @@
+/* mtherr.c
+ *
+ * Library common error handling routine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * char *fctnam;
+ * int code;
+ * int mtherr();
+ *
+ * mtherr( fctnam, code );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This routine may be called to report one of the following
+ * error conditions (in the include file math.h).
+ *
+ * Mnemonic Value Significance
+ *
+ * DOMAIN 1 argument domain error
+ * SING 2 function singularity
+ * OVERFLOW 3 overflow range error
+ * UNDERFLOW 4 underflow range error
+ * TLOSS 5 total loss of precision
+ * PLOSS 6 partial loss of precision
+ * EDOM 33 Unix domain error code
+ * ERANGE 34 Unix range error code
+ *
+ * The default version of the file prints the function name,
+ * passed to it by the pointer fctnam, followed by the
+ * error condition. The display is directed to the standard
+ * output device. The routine then returns to the calling
+ * program. Users may wish to modify the program to abort by
+ * calling exit() under severe error conditions such as domain
+ * errors.
+ *
+ * Since all error conditions pass control to this function,
+ * the display may be easily changed, eliminated, or directed
+ * to an error logging device.
+ *
+ * SEE ALSO:
+ *
+ * math.h
+ *
+ */
+
+/*
+Cephes Math Library Release 2.0: April, 1987
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <stdio.h>
+#include <math.h>
+
+int merror = 0;
+
+/* Notice: the order of appearance of the following
+ * messages is bound to the error codes defined
+ * in math.h.
+ */
+static char *ermsg[7] = {
+"unknown", /* error code 0 */
+"domain", /* error code 1 */
+"singularity", /* et seq. */
+"overflow",
+"underflow",
+"total loss of precision",
+"partial loss of precision"
+};
+
+
+int mtherr( name, code )
+char *name;
+int code;
+{
+
+/* Display string passed by calling program,
+ * which is supposed to be the name of the
+ * function in which the error occurred:
+ */
+printf( "\n%s ", name );
+
+/* Set global error message word */
+merror = code;
+
+/* Display error message defined
+ * by the code argument.
+ */
+if( (code <= 0) || (code >= 7) )
+ code = 0;
+printf( "%s error\n", ermsg[code] );
+
+/* Return to calling
+ * program
+ */
+return( 0 );
+}
diff --git a/libm/double/mtransp.c b/libm/double/mtransp.c
new file mode 100644
index 000000000..b4a54dd0f
--- /dev/null
+++ b/libm/double/mtransp.c
@@ -0,0 +1,61 @@
+/* mtransp.c
+ *
+ * Matrix transpose
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * double A[n*n], T[n*n];
+ *
+ * mtransp( n, A, T );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * T[r][c] = A[c][r]
+ *
+ *
+ * Transposes the n by n square matrix A and puts the result in T.
+ * The output, T, may occupy the same storage as A.
+ *
+ *
+ *
+ */
+
+
+mtransp( n, A, T )
+int n;
+double *A, *T;
+{
+int i, j, np1;
+double *pAc, *pAr, *pTc, *pTr, *pA0, *pT0;
+double x, y;
+
+np1 = n+1;
+pA0 = A;
+pT0 = T;
+for( i=0; i<n-1; i++ ) /* row index */
+ {
+ pAc = pA0; /* next diagonal element of input */
+ pAr = pAc + n; /* next row down underneath the diagonal element */
+ pTc = pT0; /* next diagonal element of the output */
+ pTr = pTc + n; /* next row underneath */
+ *pTc++ = *pAc++; /* copy the diagonal element */
+ for( j=i+1; j<n; j++ ) /* column index */
+ {
+ x = *pAr;
+ *pTr = *pAc++;
+ *pTc++ = x;
+ pAr += n;
+ pTr += n;
+ }
+ pA0 += np1; /* &A[n*i+i] for next i */
+ pT0 += np1; /* &T[n*i+i] for next i */
+ }
+*pT0 = *pA0; /* copy the diagonal element */
+}
+
diff --git a/libm/double/mtst.c b/libm/double/mtst.c
new file mode 100644
index 000000000..2559d2340
--- /dev/null
+++ b/libm/double/mtst.c
@@ -0,0 +1,464 @@
+/* mtst.c
+ Consistency tests for math functions.
+ To get strict rounding rules on a 386 or 68000 computer,
+ define SETPREC to 1.
+
+ With NTRIALS=10000, the following are typical results for
+ IEEE double precision arithmetic.
+
+Consistency test of math functions.
+Max and rms relative errors for 10000 random arguments.
+x = cbrt( cube(x) ): max = 0.00E+00 rms = 0.00E+00
+x = atan( tan(x) ): max = 2.21E-16 rms = 3.27E-17
+x = sin( asin(x) ): max = 2.13E-16 rms = 2.95E-17
+x = sqrt( square(x) ): max = 0.00E+00 rms = 0.00E+00
+x = log( exp(x) ): max = 1.11E-16 A rms = 4.35E-18 A
+x = tanh( atanh(x) ): max = 2.22E-16 rms = 2.43E-17
+x = asinh( sinh(x) ): max = 2.05E-16 rms = 3.49E-18
+x = acosh( cosh(x) ): max = 1.43E-15 A rms = 1.54E-17 A
+x = log10( exp10(x) ): max = 5.55E-17 A rms = 1.27E-18 A
+x = pow( pow(x,a),1/a ): max = 7.60E-14 rms = 1.05E-15
+x = cos( acos(x) ): max = 2.22E-16 A rms = 6.90E-17 A
+*/
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
+*/
+
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+#ifndef NTRIALS
+#define NTRIALS 10000
+#endif
+
+#define SETPREC 1
+#define STRTST 0
+
+#define WTRIALS (NTRIALS/5)
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double sqrt ( double );
+extern double cbrt ( double );
+extern double exp ( double );
+extern double log ( double );
+extern double exp10 ( double );
+extern double log10 ( double );
+extern double tan ( double );
+extern double atan ( double );
+extern double sin ( double );
+extern double asin ( double );
+extern double cos ( double );
+extern double acos ( double );
+extern double pow ( double, double );
+extern double tanh ( double );
+extern double atanh ( double );
+extern double sinh ( double );
+extern double asinh ( double x );
+extern double cosh ( double );
+extern double acosh ( double );
+extern double gamma ( double );
+extern double lgam ( double );
+#else
+double fabs(), sqrt(), cbrt(), exp(), log();
+double exp10(), log10(), tan(), atan();
+double sin(), asin(), cos(), acos(), pow();
+double tanh(), atanh(), sinh(), asinh(), cosh(), acosh();
+double gamma(), lgam();
+#endif
+
+/* C9X spells lgam lgamma. */
+#define GLIBC2 0
+#if GLIBC2
+double lgamma (double);
+#endif
+
+#if SETPREC
+int dprec();
+#endif
+
+int drand();
+/* void exit(); */
+/* int printf(); */
+
+
+/* Provide inverses for square root and cube root: */
+double square(x)
+double x;
+{
+return( x * x );
+}
+
+double cube(x)
+double x;
+{
+return( x * x * x );
+}
+
+/* lookup table for each function */
+struct fundef
+ {
+ char *nam1; /* the function */
+ double (*name )();
+ char *nam2; /* its inverse */
+ double (*inv )();
+ int nargs; /* number of function arguments */
+ int tstyp; /* type code of the function */
+ long ctrl; /* relative error flag */
+ double arg1w; /* width of domain for 1st arg */
+ double arg1l; /* lower bound domain 1st arg */
+ long arg1f; /* flags, e.g. integer arg */
+ double arg2w; /* same info for args 2, 3, 4 */
+ double arg2l;
+ long arg2f;
+/*
+ double arg3w;
+ double arg3l;
+ long arg3f;
+ double arg4w;
+ double arg4l;
+ long arg4f;
+*/
+ };
+
+
+/* fundef.ctrl bits: */
+#define RELERR 1
+
+/* fundef.tstyp test types: */
+#define POWER 1
+#define ELLIP 2
+#define GAMMA 3
+#define WRONK1 4
+#define WRONK2 5
+#define WRONK3 6
+
+/* fundef.argNf argument flag bits: */
+#define INT 2
+#define EXPSCAL 4
+
+extern double MINLOG;
+extern double MAXLOG;
+extern double PI;
+extern double PIO2;
+/*
+define MINLOG -170.0
+define MAXLOG +170.0
+define PI 3.14159265358979323846
+define PIO2 1.570796326794896619
+*/
+
+#define NTESTS 12
+struct fundef defs[NTESTS] = {
+{" cube", cube, " cbrt", cbrt, 1, 0, 1, 2002.0, -1001.0, 0,
+0.0, 0.0, 0},
+{" tan", tan, " atan", atan, 1, 0, 1, 0.0, 0.0, 0,
+0.0, 0.0, 0},
+{" asin", asin, " sin", sin, 1, 0, 1, 2.0, -1.0, 0,
+0.0, 0.0, 0},
+{"square", square, " sqrt", sqrt, 1, 0, 1, 170.0, -85.0, EXPSCAL,
+0.0, 0.0, 0},
+{" exp", exp, " log", log, 1, 0, 0, 340.0, -170.0, 0,
+0.0, 0.0, 0},
+{" atanh", atanh, " tanh", tanh, 1, 0, 1, 2.0, -1.0, 0,
+0.0, 0.0, 0},
+{" sinh", sinh, " asinh", asinh, 1, 0, 1, 340.0, 0.0, 0,
+0.0, 0.0, 0},
+{" cosh", cosh, " acosh", acosh, 1, 0, 0, 340.0, 0.0, 0,
+0.0, 0.0, 0},
+{" exp10", exp10, " log10", log10, 1, 0, 0, 340.0, -170.0, 0,
+0.0, 0.0, 0},
+{"pow", pow, "pow", pow, 2, POWER, 1, 21.0, 0.0, 0,
+42.0, -21.0, 0},
+{" acos", acos, " cos", cos, 1, 0, 0, 2.0, -1.0, 0,
+0.0, 0.0, 0},
+#if GLIBC2
+{ "gamma", gamma, "lgamma", lgamma, 1, GAMMA, 0, 34.0, 0.0, 0,
+0.0, 0.0, 0},
+#else
+{ "gamma", gamma, "lgam", lgam, 1, GAMMA, 0, 34.0, 0.0, 0,
+0.0, 0.0, 0},
+#endif
+};
+
+static char *headrs[] = {
+"x = %s( %s(x) ): ",
+"x = %s( %s(x,a),1/a ): ", /* power */
+"Legendre %s, %s: ", /* ellip */
+"%s(x) = log(%s(x)): ", /* gamma */
+"Wronksian of %s, %s: ",
+"Wronksian of %s, %s: ",
+"Wronksian of %s, %s: "
+};
+
+static double yy1 = 0.0;
+static double y2 = 0.0;
+static double y3 = 0.0;
+static double y4 = 0.0;
+static double a = 0.0;
+static double x = 0.0;
+static double y = 0.0;
+static double z = 0.0;
+static double e = 0.0;
+static double max = 0.0;
+static double rmsa = 0.0;
+static double rms = 0.0;
+static double ave = 0.0;
+
+
+int main()
+{
+double (*fun )();
+double (*ifun )();
+struct fundef *d;
+int i, k, itst;
+int m, ntr;
+
+#if SETPREC
+dprec(); /* set coprocessor precision */
+#endif
+ntr = NTRIALS;
+printf( "Consistency test of math functions.\n" );
+printf( "Max and rms relative errors for %d random arguments.\n",
+ ntr );
+
+/* Initialize machine dependent parameters: */
+defs[1].arg1w = PI;
+defs[1].arg1l = -PI/2.0;
+/* Microsoft C has trouble with denormal numbers. */
+#if 0
+defs[3].arg1w = MAXLOG;
+defs[3].arg1l = -MAXLOG/2.0;
+defs[4].arg1w = 2*MAXLOG;
+defs[4].arg1l = -MAXLOG;
+#endif
+defs[6].arg1w = 2.0*MAXLOG;
+defs[6].arg1l = -MAXLOG;
+defs[7].arg1w = MAXLOG;
+defs[7].arg1l = 0.0;
+
+
+/* Outer loop, on the test number: */
+
+for( itst=STRTST; itst<NTESTS; itst++ )
+{
+d = &defs[itst];
+k = 0;
+m = 0;
+max = 0.0;
+rmsa = 0.0;
+ave = 0.0;
+fun = d->name;
+ifun = d->inv;
+
+/* Absolute error criterion starts with gamma function
+ * (put all such at end of table)
+ */
+if( d->tstyp == GAMMA )
+ printf( "Absolute error criterion (but relative if >1):\n" );
+
+/* Smaller number of trials for Wronksians
+ * (put them at end of list)
+ */
+if( d->tstyp == WRONK1 )
+ {
+ ntr = WTRIALS;
+ printf( "Absolute error and only %d trials:\n", ntr );
+ }
+
+printf( headrs[d->tstyp], d->nam2, d->nam1 );
+
+for( i=0; i<ntr; i++ )
+{
+m++;
+
+/* make random number(s) in desired range(s) */
+switch( d->nargs )
+{
+
+default:
+goto illegn;
+
+case 2:
+drand( &a );
+a = d->arg2w * ( a - 1.0 ) + d->arg2l;
+if( d->arg2f & EXPSCAL )
+ {
+ a = exp(a);
+ drand( &y2 );
+ a -= 1.0e-13 * a * y2;
+ }
+if( d->arg2f & INT )
+ {
+ k = a + 0.25;
+ a = k;
+ }
+
+case 1:
+drand( &x );
+x = d->arg1w * ( x - 1.0 ) + d->arg1l;
+if( d->arg1f & EXPSCAL )
+ {
+ x = exp(x);
+ drand( &a );
+ x += 1.0e-13 * x * a;
+ }
+}
+
+
+/* compute function under test */
+switch( d->nargs )
+ {
+ case 1:
+ switch( d->tstyp )
+ {
+ case ELLIP:
+ yy1 = ( *(fun) )(x);
+ y2 = ( *(fun) )(1.0-x);
+ y3 = ( *(ifun) )(x);
+ y4 = ( *(ifun) )(1.0-x);
+ break;
+
+#if 1
+ case GAMMA:
+#if GLIBC2
+ y = lgamma(x);
+#else
+ y = lgam(x);
+#endif
+ x = log( gamma(x) );
+ break;
+#endif
+ default:
+ z = ( *(fun) )(x);
+ y = ( *(ifun) )(z);
+ }
+ break;
+
+ case 2:
+ if( d->arg2f & INT )
+ {
+ switch( d->tstyp )
+ {
+ case WRONK1:
+ yy1 = (*fun)( k, x ); /* jn */
+ y2 = (*fun)( k+1, x );
+ y3 = (*ifun)( k, x ); /* yn */
+ y4 = (*ifun)( k+1, x );
+ break;
+
+ case WRONK2:
+ yy1 = (*fun)( a, x ); /* iv */
+ y2 = (*fun)( a+1.0, x );
+ y3 = (*ifun)( k, x ); /* kn */
+ y4 = (*ifun)( k+1, x );
+ break;
+
+ default:
+ z = (*fun)( k, x );
+ y = (*ifun)( k, z );
+ }
+ }
+ else
+ {
+ if( d->tstyp == POWER )
+ {
+ z = (*fun)( x, a );
+ y = (*ifun)( z, 1.0/a );
+ }
+ else
+ {
+ z = (*fun)( a, x );
+ y = (*ifun)( a, z );
+ }
+ }
+ break;
+
+
+ default:
+illegn:
+ printf( "Illegal nargs= %d", d->nargs );
+ exit(1);
+ }
+
+switch( d->tstyp )
+ {
+ case WRONK1:
+ e = (y2*y3 - yy1*y4) - 2.0/(PI*x); /* Jn, Yn */
+ break;
+
+ case WRONK2:
+ e = (y2*y3 + yy1*y4) - 1.0/x; /* In, Kn */
+ break;
+
+ case ELLIP:
+ e = (yy1-y3)*y4 + y3*y2 - PIO2;
+ break;
+
+ default:
+ e = y - x;
+ break;
+ }
+
+if( d->ctrl & RELERR )
+ e /= x;
+else
+ {
+ if( fabs(x) > 1.0 )
+ e /= x;
+ }
+
+ave += e;
+/* absolute value of error */
+if( e < 0 )
+ e = -e;
+
+/* peak detect the error */
+if( e > max )
+ {
+ max = e;
+
+ if( e > 1.0e-10 )
+ {
+ printf("x %.6E z %.6E y %.6E max %.4E\n",
+ x, z, y, max);
+ if( d->tstyp == POWER )
+ {
+ printf( "a %.6E\n", a );
+ }
+ if( d->tstyp >= WRONK1 )
+ {
+ printf( "yy1 %.4E y2 %.4E y3 %.4E y4 %.4E k %d x %.4E\n",
+ yy1, y2, y3, y4, k, x );
+ }
+ }
+
+/*
+ printf("%.8E %.8E %.4E %6ld \n", x, y, max, n);
+ printf("%d %.8E %.8E %.4E %6ld \n", k, x, y, max, n);
+ printf("%.6E %.6E %.6E %.4E %6ld \n", a, x, y, max, n);
+ printf("%.6E %.6E %.6E %.6E %.4E %6ld \n", a, b, x, y, max, n);
+ printf("%.4E %.4E %.4E %.4E %.4E %.4E %6ld \n",
+ a, b, c, x, y, max, n);
+*/
+ }
+
+/* accumulate rms error */
+e *= 1.0e16; /* adjust range */
+rmsa += e * e; /* accumulate the square of the error */
+}
+
+/* report after NTRIALS trials */
+rms = 1.0e-16 * sqrt( rmsa/m );
+if(d->ctrl & RELERR)
+ printf(" max = %.2E rms = %.2E\n", max, rms );
+else
+ printf(" max = %.2E A rms = %.2E A\n", max, rms );
+} /* loop on itst */
+
+exit(0);
+}
diff --git a/libm/double/nbdtr.c b/libm/double/nbdtr.c
new file mode 100644
index 000000000..9930a4087
--- /dev/null
+++ b/libm/double/nbdtr.c
@@ -0,0 +1,222 @@
+/* nbdtr.c
+ *
+ * Negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtr();
+ *
+ * y = nbdtr( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the negative
+ * binomial distribution:
+ *
+ * k
+ * -- ( n+j-1 ) n j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=0
+ *
+ * In a sequence of Bernoulli trials, this is the probability
+ * that k or fewer failures precede the nth success.
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p), with p between 0 and 1.
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 100000 1.7e-13 8.8e-15
+ * See also incbet.c.
+ *
+ */
+ /* nbdtrc.c
+ *
+ * Complemented negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtrc();
+ *
+ * y = nbdtrc( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the negative
+ * binomial distribution:
+ *
+ * inf
+ * -- ( n+j-1 ) n j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=k+1
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,p), with p between 0 and 1.
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 100000 1.7e-13 8.8e-15
+ * See also incbet.c.
+ */
+
+/* nbdtrc
+ *
+ * Complemented negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtrc();
+ *
+ * y = nbdtrc( k, n, p );
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the negative
+ * binomial distribution:
+ *
+ * inf
+ * -- ( n+j-1 ) n j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=k+1
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ * ACCURACY:
+ *
+ * See incbet.c.
+ */
+ /* nbdtri
+ *
+ * Functional inverse of negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * double p, y, nbdtri();
+ *
+ * p = nbdtri( k, n, y );
+ *
+ * DESCRIPTION:
+ *
+ * Finds the argument p such that nbdtr(k,n,p) is equal to y.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,y), with y between 0 and 1.
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 100000 1.5e-14 8.5e-16
+ * See also incbi.c.
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double incbet ( double, double, double );
+extern double incbi ( double, double, double );
+#else
+double incbet(), incbi();
+#endif
+
+double nbdtrc( k, n, p )
+int k, n;
+double p;
+{
+double dk, dn;
+
+if( (p < 0.0) || (p > 1.0) )
+ goto domerr;
+if( k < 0 )
+ {
+domerr:
+ mtherr( "nbdtr", DOMAIN );
+ return( 0.0 );
+ }
+
+dk = k+1;
+dn = n;
+return( incbet( dk, dn, 1.0 - p ) );
+}
+
+
+
+double nbdtr( k, n, p )
+int k, n;
+double p;
+{
+double dk, dn;
+
+if( (p < 0.0) || (p > 1.0) )
+ goto domerr;
+if( k < 0 )
+ {
+domerr:
+ mtherr( "nbdtr", DOMAIN );
+ return( 0.0 );
+ }
+dk = k+1;
+dn = n;
+return( incbet( dn, dk, p ) );
+}
+
+
+
+double nbdtri( k, n, p )
+int k, n;
+double p;
+{
+double dk, dn, w;
+
+if( (p < 0.0) || (p > 1.0) )
+ goto domerr;
+if( k < 0 )
+ {
+domerr:
+ mtherr( "nbdtri", DOMAIN );
+ return( 0.0 );
+ }
+dk = k+1;
+dn = n;
+w = incbi( dn, dk, p );
+return( w );
+}
diff --git a/libm/double/ndtr.c b/libm/double/ndtr.c
new file mode 100644
index 000000000..75d59ab54
--- /dev/null
+++ b/libm/double/ndtr.c
@@ -0,0 +1,481 @@
+/* ndtr.c
+ *
+ * Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, ndtr();
+ *
+ * y = ndtr( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the Gaussian probability density
+ * function, integrated from minus infinity to x:
+ *
+ * x
+ * -
+ * 1 | | 2
+ * ndtr(x) = --------- | exp( - t /2 ) dt
+ * sqrt(2pi) | |
+ * -
+ * -inf.
+ *
+ * = ( 1 + erf(z) ) / 2
+ * = erfc(z) / 2
+ *
+ * where z = x/sqrt(2). Computation is via the functions
+ * erf and erfc.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -13,0 8000 2.1e-15 4.8e-16
+ * IEEE -13,0 30000 3.4e-14 6.7e-15
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * erfc underflow x > 37.519379347 0.0
+ *
+ */
+ /* erf.c
+ *
+ * Error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, erf();
+ *
+ * y = erf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The integral is
+ *
+ * x
+ * -
+ * 2 | | 2
+ * erf(x) = -------- | exp( - t ) dt.
+ * sqrt(pi) | |
+ * -
+ * 0
+ *
+ * The magnitude of x is limited to 9.231948545 for DEC
+ * arithmetic; 1 or -1 is returned outside this range.
+ *
+ * For 0 <= |x| < 1, erf(x) = x * P4(x**2)/Q5(x**2); otherwise
+ * erf(x) = 1 - erfc(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,1 14000 4.7e-17 1.5e-17
+ * IEEE 0,1 30000 3.7e-16 1.0e-16
+ *
+ */
+ /* erfc.c
+ *
+ * Complementary error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, erfc();
+ *
+ * y = erfc( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * 1 - erf(x) =
+ *
+ * inf.
+ * -
+ * 2 | | 2
+ * erfc(x) = -------- | exp( - t ) dt
+ * sqrt(pi) | |
+ * -
+ * x
+ *
+ *
+ * For small x, erfc(x) = 1 - erf(x); otherwise rational
+ * approximations are computed.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 9.2319 12000 5.1e-16 1.2e-16
+ * IEEE 0,26.6417 30000 5.7e-14 1.5e-14
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * erfc underflow x > 9.231948545 (DEC) 0.0
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1988, 1992, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+extern double SQRTH;
+extern double MAXLOG;
+
+
+#ifdef UNK
+static double P[] = {
+ 2.46196981473530512524E-10,
+ 5.64189564831068821977E-1,
+ 7.46321056442269912687E0,
+ 4.86371970985681366614E1,
+ 1.96520832956077098242E2,
+ 5.26445194995477358631E2,
+ 9.34528527171957607540E2,
+ 1.02755188689515710272E3,
+ 5.57535335369399327526E2
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 1.32281951154744992508E1,
+ 8.67072140885989742329E1,
+ 3.54937778887819891062E2,
+ 9.75708501743205489753E2,
+ 1.82390916687909736289E3,
+ 2.24633760818710981792E3,
+ 1.65666309194161350182E3,
+ 5.57535340817727675546E2
+};
+static double R[] = {
+ 5.64189583547755073984E-1,
+ 1.27536670759978104416E0,
+ 5.01905042251180477414E0,
+ 6.16021097993053585195E0,
+ 7.40974269950448939160E0,
+ 2.97886665372100240670E0
+};
+static double S[] = {
+/* 1.00000000000000000000E0,*/
+ 2.26052863220117276590E0,
+ 9.39603524938001434673E0,
+ 1.20489539808096656605E1,
+ 1.70814450747565897222E1,
+ 9.60896809063285878198E0,
+ 3.36907645100081516050E0
+};
+static double T[] = {
+ 9.60497373987051638749E0,
+ 9.00260197203842689217E1,
+ 2.23200534594684319226E3,
+ 7.00332514112805075473E3,
+ 5.55923013010394962768E4
+};
+static double U[] = {
+/* 1.00000000000000000000E0,*/
+ 3.35617141647503099647E1,
+ 5.21357949780152679795E2,
+ 4.59432382970980127987E3,
+ 2.26290000613890934246E4,
+ 4.92673942608635921086E4
+};
+
+#define UTHRESH 37.519379347
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0030207,0054445,0011173,0021706,
+0040020,0067272,0030661,0122075,
+0040756,0151236,0173053,0067042,
+0041502,0106175,0062555,0151457,
+0042104,0102525,0047401,0003667,
+0042403,0116176,0011446,0075303,
+0042551,0120723,0061641,0123275,
+0042600,0070651,0007264,0134516,
+0042413,0061102,0167507,0176625
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041123,0123257,0165741,0017142,
+0041655,0065027,0173413,0115450,
+0042261,0074011,0021573,0004150,
+0042563,0166530,0013662,0007200,
+0042743,0176427,0162443,0105214,
+0043014,0062546,0153727,0123772,
+0042717,0012470,0006227,0067424,
+0042413,0061103,0003042,0013254
+};
+static unsigned short R[] = {
+0040020,0067272,0101024,0155421,
+0040243,0037467,0056706,0026462,
+0040640,0116017,0120665,0034315,
+0040705,0020162,0143350,0060137,
+0040755,0016234,0134304,0130157,
+0040476,0122700,0051070,0015473
+};
+static unsigned short S[] = {
+/*0040200,0000000,0000000,0000000,*/
+0040420,0126200,0044276,0070413,
+0041026,0053051,0007302,0063746,
+0041100,0144203,0174051,0061151,
+0041210,0123314,0126343,0177646,
+0041031,0137125,0051431,0033011,
+0040527,0117362,0152661,0066201
+};
+static unsigned short T[] = {
+0041031,0126770,0170672,0166101,
+0041664,0006522,0072360,0031770,
+0043013,0100025,0162641,0126671,
+0043332,0155231,0161627,0076200,
+0044131,0024115,0021020,0117343
+};
+static unsigned short U[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041406,0037461,0177575,0032714,
+0042402,0053350,0123061,0153557,
+0043217,0111227,0032007,0164217,
+0043660,0145000,0004013,0160114,
+0044100,0071544,0167107,0125471
+};
+#define UTHRESH 14.0
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x6479,0xa24f,0xeb24,0x3df0,
+0x3488,0x4636,0x0dd7,0x3fe2,
+0x6dc4,0xdec5,0xda53,0x401d,
+0xba66,0xacad,0x518f,0x4048,
+0x20f7,0xa9e0,0x90aa,0x4068,
+0xcf58,0xc264,0x738f,0x4080,
+0x34d8,0x6c74,0x343a,0x408d,
+0x972a,0x21d6,0x0e35,0x4090,
+0xffb3,0x5de8,0x6c48,0x4081
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x23cc,0xfd7c,0x74d5,0x402a,
+0x7365,0xfee1,0xad42,0x4055,
+0x610d,0x246f,0x2f01,0x4076,
+0x41d0,0x02f6,0x7dab,0x408e,
+0x7151,0xfca4,0x7fa2,0x409c,
+0xf4ff,0xdafa,0x8cac,0x40a1,
+0xede2,0x0192,0xe2a7,0x4099,
+0x42d6,0x60c4,0x6c48,0x4081
+};
+static unsigned short R[] = {
+0x9b62,0x5042,0x0dd7,0x3fe2,
+0xc5a6,0xebb8,0x67e6,0x3ff4,
+0xa71a,0xf436,0x1381,0x4014,
+0x0c0c,0x58dd,0xa40e,0x4018,
+0x960e,0x9718,0xa393,0x401d,
+0x0367,0x0a47,0xd4b8,0x4007
+};
+static unsigned short S[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xce21,0x0917,0x1590,0x4002,
+0x4cfd,0x21d8,0xcac5,0x4022,
+0x2c4d,0x7f05,0x1910,0x4028,
+0x7ff5,0x959c,0x14d9,0x4031,
+0x26c1,0xaa63,0x37ca,0x4023,
+0x2d90,0x5ab6,0xf3de,0x400a
+};
+static unsigned short T[] = {
+0x5d88,0x1e37,0x35bf,0x4023,
+0x067f,0x4e9e,0x81aa,0x4056,
+0x35b7,0xbcb4,0x7002,0x40a1,
+0xef90,0x3c72,0x5b53,0x40bb,
+0x13dc,0xa442,0x2509,0x40eb
+};
+static unsigned short U[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xa6ba,0x3fef,0xc7e6,0x4040,
+0x3aee,0x14c6,0x4add,0x4080,
+0xfd12,0xe680,0xf252,0x40b1,
+0x7c0a,0x0101,0x1940,0x40d6,
+0xf567,0x9dc8,0x0e6c,0x40e8
+};
+#define UTHRESH 37.519379347
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3df0,0xeb24,0xa24f,0x6479,
+0x3fe2,0x0dd7,0x4636,0x3488,
+0x401d,0xda53,0xdec5,0x6dc4,
+0x4048,0x518f,0xacad,0xba66,
+0x4068,0x90aa,0xa9e0,0x20f7,
+0x4080,0x738f,0xc264,0xcf58,
+0x408d,0x343a,0x6c74,0x34d8,
+0x4090,0x0e35,0x21d6,0x972a,
+0x4081,0x6c48,0x5de8,0xffb3
+};
+static unsigned short Q[] = {
+0x402a,0x74d5,0xfd7c,0x23cc,
+0x4055,0xad42,0xfee1,0x7365,
+0x4076,0x2f01,0x246f,0x610d,
+0x408e,0x7dab,0x02f6,0x41d0,
+0x409c,0x7fa2,0xfca4,0x7151,
+0x40a1,0x8cac,0xdafa,0xf4ff,
+0x4099,0xe2a7,0x0192,0xede2,
+0x4081,0x6c48,0x60c4,0x42d6
+};
+static unsigned short R[] = {
+0x3fe2,0x0dd7,0x5042,0x9b62,
+0x3ff4,0x67e6,0xebb8,0xc5a6,
+0x4014,0x1381,0xf436,0xa71a,
+0x4018,0xa40e,0x58dd,0x0c0c,
+0x401d,0xa393,0x9718,0x960e,
+0x4007,0xd4b8,0x0a47,0x0367
+};
+static unsigned short S[] = {
+0x4002,0x1590,0x0917,0xce21,
+0x4022,0xcac5,0x21d8,0x4cfd,
+0x4028,0x1910,0x7f05,0x2c4d,
+0x4031,0x14d9,0x959c,0x7ff5,
+0x4023,0x37ca,0xaa63,0x26c1,
+0x400a,0xf3de,0x5ab6,0x2d90
+};
+static unsigned short T[] = {
+0x4023,0x35bf,0x1e37,0x5d88,
+0x4056,0x81aa,0x4e9e,0x067f,
+0x40a1,0x7002,0xbcb4,0x35b7,
+0x40bb,0x5b53,0x3c72,0xef90,
+0x40eb,0x2509,0xa442,0x13dc
+};
+static unsigned short U[] = {
+0x4040,0xc7e6,0x3fef,0xa6ba,
+0x4080,0x4add,0x14c6,0x3aee,
+0x40b1,0xf252,0xe680,0xfd12,
+0x40d6,0x1940,0x0101,0x7c0a,
+0x40e8,0x0e6c,0x9dc8,0xf567
+};
+#define UTHRESH 37.519379347
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double exp ( double );
+extern double log ( double );
+extern double fabs ( double );
+double erf ( double );
+double erfc ( double );
+#else
+double polevl(), p1evl(), exp(), log(), fabs();
+double erf(), erfc();
+#endif
+
+double ndtr(a)
+double a;
+{
+double x, y, z;
+
+x = a * SQRTH;
+z = fabs(x);
+
+if( z < SQRTH )
+ y = 0.5 + 0.5 * erf(x);
+
+else
+ {
+ y = 0.5 * erfc(z);
+
+ if( x > 0 )
+ y = 1.0 - y;
+ }
+
+return(y);
+}
+
+
+double erfc(a)
+double a;
+{
+double p,q,x,y,z;
+
+
+if( a < 0.0 )
+ x = -a;
+else
+ x = a;
+
+if( x < 1.0 )
+ return( 1.0 - erf(a) );
+
+z = -a * a;
+
+if( z < -MAXLOG )
+ {
+under:
+ mtherr( "erfc", UNDERFLOW );
+ if( a < 0 )
+ return( 2.0 );
+ else
+ return( 0.0 );
+ }
+
+z = exp(z);
+
+if( x < 8.0 )
+ {
+ p = polevl( x, P, 8 );
+ q = p1evl( x, Q, 8 );
+ }
+else
+ {
+ p = polevl( x, R, 5 );
+ q = p1evl( x, S, 6 );
+ }
+y = (z * p)/q;
+
+if( a < 0 )
+ y = 2.0 - y;
+
+if( y == 0.0 )
+ goto under;
+
+return(y);
+}
+
+
+
+double erf(x)
+double x;
+{
+double y, z;
+
+if( fabs(x) > 1.0 )
+ return( 1.0 - erfc(x) );
+z = x * x;
+y = x * polevl( z, T, 4 ) / p1evl( z, U, 5 );
+return( y );
+
+}
diff --git a/libm/double/ndtri.c b/libm/double/ndtri.c
new file mode 100644
index 000000000..948e36c50
--- /dev/null
+++ b/libm/double/ndtri.c
@@ -0,0 +1,417 @@
+/* ndtri.c
+ *
+ * Inverse of Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, ndtri();
+ *
+ * x = ndtri( y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the argument, x, for which the area under the
+ * Gaussian probability density function (integrated from
+ * minus infinity to x) is equal to y.
+ *
+ *
+ * For small arguments 0 < y < exp(-2), the program computes
+ * z = sqrt( -2.0 * log(y) ); then the approximation is
+ * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).
+ * There are two rational functions P/Q, one for 0 < y < exp(-32)
+ * and the other for y up to exp(-2). For larger arguments,
+ * w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0.125, 1 5500 9.5e-17 2.1e-17
+ * DEC 6e-39, 0.135 3500 5.7e-17 1.3e-17
+ * IEEE 0.125, 1 20000 7.2e-16 1.3e-16
+ * IEEE 3e-308, 0.135 50000 4.6e-16 9.8e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ndtri domain x <= 0 -MAXNUM
+ * ndtri domain x >= 1 MAXNUM
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+extern double MAXNUM;
+
+#ifdef UNK
+/* sqrt(2pi) */
+static double s2pi = 2.50662827463100050242E0;
+#endif
+
+#ifdef DEC
+static unsigned short s2p[] = {0040440,0066230,0177661,0034055};
+#define s2pi *(double *)s2p
+#endif
+
+#ifdef IBMPC
+static unsigned short s2p[] = {0x2706,0x1ff6,0x0d93,0x4004};
+#define s2pi *(double *)s2p
+#endif
+
+#ifdef MIEEE
+static unsigned short s2p[] = {
+0x4004,0x0d93,0x1ff6,0x2706
+};
+#define s2pi *(double *)s2p
+#endif
+
+/* approximation for 0 <= |y - 0.5| <= 3/8 */
+#ifdef UNK
+static double P0[5] = {
+-5.99633501014107895267E1,
+ 9.80010754185999661536E1,
+-5.66762857469070293439E1,
+ 1.39312609387279679503E1,
+-1.23916583867381258016E0,
+};
+static double Q0[8] = {
+/* 1.00000000000000000000E0,*/
+ 1.95448858338141759834E0,
+ 4.67627912898881538453E0,
+ 8.63602421390890590575E1,
+-2.25462687854119370527E2,
+ 2.00260212380060660359E2,
+-8.20372256168333339912E1,
+ 1.59056225126211695515E1,
+-1.18331621121330003142E0,
+};
+#endif
+#ifdef DEC
+static unsigned short P0[20] = {
+0141557,0155170,0071360,0120550,
+0041704,0000214,0172417,0067307,
+0141542,0132204,0040066,0156723,
+0041136,0163161,0157276,0007747,
+0140236,0116374,0073666,0051764,
+};
+static unsigned short Q0[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0040372,0026256,0110403,0123707,
+0040625,0122024,0020277,0026661,
+0041654,0134161,0124134,0007244,
+0142141,0073162,0133021,0131371,
+0042110,0041235,0043516,0057767,
+0141644,0011417,0036155,0137305,
+0041176,0076556,0004043,0125430,
+0140227,0073347,0152776,0067251,
+};
+#endif
+#ifdef IBMPC
+static unsigned short P0[20] = {
+0x142d,0x0e5e,0xfb4f,0xc04d,
+0xedd9,0x9ea1,0x8011,0x4058,
+0xdbba,0x8806,0x5690,0xc04c,
+0xc1fd,0x3bd7,0xdcce,0x402b,
+0xca7e,0x8ef6,0xd39f,0xbff3,
+};
+static unsigned short Q0[36] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x74f9,0xd220,0x4595,0x3fff,
+0xe5b6,0x8417,0xb482,0x4012,
+0x81d4,0x350b,0x970e,0x4055,
+0x365f,0x56c2,0x2ece,0xc06c,
+0xcbff,0xa8e9,0x0853,0x4069,
+0xb7d9,0xe78d,0x8261,0xc054,
+0x7563,0xc104,0xcfad,0x402f,
+0xcdd5,0xfabf,0xeedc,0xbff2,
+};
+#endif
+#ifdef MIEEE
+static unsigned short P0[20] = {
+0xc04d,0xfb4f,0x0e5e,0x142d,
+0x4058,0x8011,0x9ea1,0xedd9,
+0xc04c,0x5690,0x8806,0xdbba,
+0x402b,0xdcce,0x3bd7,0xc1fd,
+0xbff3,0xd39f,0x8ef6,0xca7e,
+};
+static unsigned short Q0[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x3fff,0x4595,0xd220,0x74f9,
+0x4012,0xb482,0x8417,0xe5b6,
+0x4055,0x970e,0x350b,0x81d4,
+0xc06c,0x2ece,0x56c2,0x365f,
+0x4069,0x0853,0xa8e9,0xcbff,
+0xc054,0x8261,0xe78d,0xb7d9,
+0x402f,0xcfad,0xc104,0x7563,
+0xbff2,0xeedc,0xfabf,0xcdd5,
+};
+#endif
+
+
+/* Approximation for interval z = sqrt(-2 log y ) between 2 and 8
+ * i.e., y between exp(-2) = .135 and exp(-32) = 1.27e-14.
+ */
+#ifdef UNK
+static double P1[9] = {
+ 4.05544892305962419923E0,
+ 3.15251094599893866154E1,
+ 5.71628192246421288162E1,
+ 4.40805073893200834700E1,
+ 1.46849561928858024014E1,
+ 2.18663306850790267539E0,
+-1.40256079171354495875E-1,
+-3.50424626827848203418E-2,
+-8.57456785154685413611E-4,
+};
+static double Q1[8] = {
+/* 1.00000000000000000000E0,*/
+ 1.57799883256466749731E1,
+ 4.53907635128879210584E1,
+ 4.13172038254672030440E1,
+ 1.50425385692907503408E1,
+ 2.50464946208309415979E0,
+-1.42182922854787788574E-1,
+-3.80806407691578277194E-2,
+-9.33259480895457427372E-4,
+};
+#endif
+#ifdef DEC
+static unsigned short P1[36] = {
+0040601,0143074,0150744,0073326,
+0041374,0031554,0113253,0146016,
+0041544,0123272,0012463,0176771,
+0041460,0051160,0103560,0156511,
+0041152,0172624,0117772,0030755,
+0040413,0170713,0151545,0176413,
+0137417,0117512,0022154,0131671,
+0137017,0104257,0071432,0007072,
+0135540,0143363,0063137,0036166,
+};
+static unsigned short Q1[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0041174,0075325,0004736,0120326,
+0041465,0110044,0047561,0045567,
+0041445,0042321,0012142,0030340,
+0041160,0127074,0166076,0141051,
+0040440,0046055,0040745,0150400,
+0137421,0114146,0067330,0010621,
+0137033,0175162,0025555,0114351,
+0135564,0122773,0145750,0030357,
+};
+#endif
+#ifdef IBMPC
+static unsigned short P1[36] = {
+0x8edb,0x9a3c,0x38c7,0x4010,
+0x7982,0x92d5,0x866d,0x403f,
+0x7fbf,0x42a6,0x94d7,0x404c,
+0x1ba9,0x10ee,0x0a4e,0x4046,
+0x463e,0x93ff,0x5eb2,0x402d,
+0xbfa1,0x7a6c,0x7e39,0x4001,
+0x9677,0x448d,0xf3e9,0xbfc1,
+0x41c7,0xee63,0xf115,0xbfa1,
+0xe78f,0x6ccb,0x18de,0xbf4c,
+};
+static unsigned short Q1[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xd41b,0xa13b,0x8f5a,0x402f,
+0x296f,0x89ee,0xb204,0x4046,
+0x461c,0x228c,0xa89a,0x4044,
+0xd845,0x9d87,0x15c7,0x402e,
+0xba20,0xa83c,0x0985,0x4004,
+0x0232,0xcddb,0x330c,0xbfc2,
+0xb31d,0x456d,0x7f4e,0xbfa3,
+0x061e,0x797d,0x94bf,0xbf4e,
+};
+#endif
+#ifdef MIEEE
+static unsigned short P1[36] = {
+0x4010,0x38c7,0x9a3c,0x8edb,
+0x403f,0x866d,0x92d5,0x7982,
+0x404c,0x94d7,0x42a6,0x7fbf,
+0x4046,0x0a4e,0x10ee,0x1ba9,
+0x402d,0x5eb2,0x93ff,0x463e,
+0x4001,0x7e39,0x7a6c,0xbfa1,
+0xbfc1,0xf3e9,0x448d,0x9677,
+0xbfa1,0xf115,0xee63,0x41c7,
+0xbf4c,0x18de,0x6ccb,0xe78f,
+};
+static unsigned short Q1[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x402f,0x8f5a,0xa13b,0xd41b,
+0x4046,0xb204,0x89ee,0x296f,
+0x4044,0xa89a,0x228c,0x461c,
+0x402e,0x15c7,0x9d87,0xd845,
+0x4004,0x0985,0xa83c,0xba20,
+0xbfc2,0x330c,0xcddb,0x0232,
+0xbfa3,0x7f4e,0x456d,0xb31d,
+0xbf4e,0x94bf,0x797d,0x061e,
+};
+#endif
+
+/* Approximation for interval z = sqrt(-2 log y ) between 8 and 64
+ * i.e., y between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890.
+ */
+
+#ifdef UNK
+static double P2[9] = {
+ 3.23774891776946035970E0,
+ 6.91522889068984211695E0,
+ 3.93881025292474443415E0,
+ 1.33303460815807542389E0,
+ 2.01485389549179081538E-1,
+ 1.23716634817820021358E-2,
+ 3.01581553508235416007E-4,
+ 2.65806974686737550832E-6,
+ 6.23974539184983293730E-9,
+};
+static double Q2[8] = {
+/* 1.00000000000000000000E0,*/
+ 6.02427039364742014255E0,
+ 3.67983563856160859403E0,
+ 1.37702099489081330271E0,
+ 2.16236993594496635890E-1,
+ 1.34204006088543189037E-2,
+ 3.28014464682127739104E-4,
+ 2.89247864745380683936E-6,
+ 6.79019408009981274425E-9,
+};
+#endif
+#ifdef DEC
+static unsigned short P2[36] = {
+0040517,0033507,0036236,0125641,
+0040735,0044616,0014473,0140133,
+0040574,0012567,0114535,0102541,
+0040252,0120340,0143474,0150135,
+0037516,0051057,0115361,0031211,
+0036512,0131204,0101511,0125144,
+0035236,0016627,0043160,0140216,
+0033462,0060512,0060141,0010641,
+0031326,0062541,0101304,0077706,
+};
+static unsigned short Q2[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0040700,0143322,0132137,0040501,
+0040553,0101155,0053221,0140257,
+0040260,0041071,0052573,0010004,
+0037535,0066472,0177261,0162330,
+0036533,0160475,0066666,0036132,
+0035253,0174533,0027771,0044027,
+0033502,0016147,0117666,0063671,
+0031351,0047455,0141663,0054751,
+};
+#endif
+#ifdef IBMPC
+static unsigned short P2[36] = {
+0xd574,0xe793,0xe6e8,0x4009,
+0x780b,0xc327,0xa931,0x401b,
+0xb0ac,0xf32b,0x82ae,0x400f,
+0x9a0c,0x18e7,0x541c,0x3ff5,
+0x2651,0xf35e,0xca45,0x3fc9,
+0x354d,0x9069,0x5650,0x3f89,
+0x1812,0xe8ce,0xc3b2,0x3f33,
+0x2234,0x4c0c,0x4c29,0x3ec6,
+0x8ff9,0x3058,0xccac,0x3e3a,
+};
+static unsigned short Q2[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xe828,0x568b,0x18da,0x4018,
+0x3816,0xaad2,0x704d,0x400d,
+0x6200,0x2aaf,0x0847,0x3ff6,
+0x3c9b,0x5fd6,0xada7,0x3fcb,
+0xc78b,0xadb6,0x7c27,0x3f8b,
+0x2903,0x65ff,0x7f2b,0x3f35,
+0xccf7,0xf3f6,0x438c,0x3ec8,
+0x6b3d,0xb876,0x29e5,0x3e3d,
+};
+#endif
+#ifdef MIEEE
+static unsigned short P2[36] = {
+0x4009,0xe6e8,0xe793,0xd574,
+0x401b,0xa931,0xc327,0x780b,
+0x400f,0x82ae,0xf32b,0xb0ac,
+0x3ff5,0x541c,0x18e7,0x9a0c,
+0x3fc9,0xca45,0xf35e,0x2651,
+0x3f89,0x5650,0x9069,0x354d,
+0x3f33,0xc3b2,0xe8ce,0x1812,
+0x3ec6,0x4c29,0x4c0c,0x2234,
+0x3e3a,0xccac,0x3058,0x8ff9,
+};
+static unsigned short Q2[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4018,0x18da,0x568b,0xe828,
+0x400d,0x704d,0xaad2,0x3816,
+0x3ff6,0x0847,0x2aaf,0x6200,
+0x3fcb,0xada7,0x5fd6,0x3c9b,
+0x3f8b,0x7c27,0xadb6,0xc78b,
+0x3f35,0x7f2b,0x65ff,0x2903,
+0x3ec8,0x438c,0xf3f6,0xccf7,
+0x3e3d,0x29e5,0xb876,0x6b3d,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double log ( double );
+extern double sqrt ( double );
+#else
+double polevl(), p1evl(), log(), sqrt();
+#endif
+
+double ndtri(y0)
+double y0;
+{
+double x, y, z, y2, x0, x1;
+int code;
+
+if( y0 <= 0.0 )
+ {
+ mtherr( "ndtri", DOMAIN );
+ return( -MAXNUM );
+ }
+if( y0 >= 1.0 )
+ {
+ mtherr( "ndtri", DOMAIN );
+ return( MAXNUM );
+ }
+code = 1;
+y = y0;
+if( y > (1.0 - 0.13533528323661269189) ) /* 0.135... = exp(-2) */
+ {
+ y = 1.0 - y;
+ code = 0;
+ }
+
+if( y > 0.13533528323661269189 )
+ {
+ y = y - 0.5;
+ y2 = y * y;
+ x = y + y * (y2 * polevl( y2, P0, 4)/p1evl( y2, Q0, 8 ));
+ x = x * s2pi;
+ return(x);
+ }
+
+x = sqrt( -2.0 * log(y) );
+x0 = x - log(x)/x;
+
+z = 1.0/x;
+if( x < 8.0 ) /* y > exp(-32) = 1.2664165549e-14 */
+ x1 = z * polevl( z, P1, 8 )/p1evl( z, Q1, 8 );
+else
+ x1 = z * polevl( z, P2, 8 )/p1evl( z, Q2, 8 );
+x = x0 - x1;
+if( code != 0 )
+ x = -x;
+return( x );
+}
diff --git a/libm/double/paranoia.c b/libm/double/paranoia.c
new file mode 100644
index 000000000..49ff72623
--- /dev/null
+++ b/libm/double/paranoia.c
@@ -0,0 +1,2156 @@
+/* A C version of Kahan's Floating Point Test "Paranoia"
+
+ Thos Sumner, UCSF, Feb. 1985
+ David Gay, BTL, Jan. 1986
+
+ This is a rewrite from the Pascal version by
+
+ B. A. Wichmann, 18 Jan. 1985
+
+ (and does NOT exhibit good C programming style).
+
+(C) Apr 19 1983 in BASIC version by:
+ Professor W. M. Kahan,
+ 567 Evans Hall
+ Electrical Engineering & Computer Science Dept.
+ University of California
+ Berkeley, California 94720
+ USA
+
+converted to Pascal by:
+ B. A. Wichmann
+ National Physical Laboratory
+ Teddington Middx
+ TW11 OLW
+ UK
+
+converted to C by:
+
+ David M. Gay and Thos Sumner
+ AT&T Bell Labs Computer Center, Rm. U-76
+ 600 Mountainn Avenue University of California
+ Murray Hill, NJ 07974 San Francisco, CA 94143
+ USA USA
+
+with simultaneous corrections to the Pascal source (reflected
+in the Pascal source available over netlib).
+
+Reports of results on various systems from all the versions
+of Paranoia are being collected by Richard Karpinski at the
+same address as Thos Sumner. This includes sample outputs,
+bug reports, and criticisms.
+
+You may copy this program freely if you acknowledge its source.
+Comments on the Pascal version to NPL, please.
+
+
+The C version catches signals from floating-point exceptions.
+If signal(SIGFPE,...) is unavailable in your environment, you may
+#define NOSIGNAL to comment out the invocations of signal.
+
+This source file is too big for some C compilers, but may be split
+into pieces. Comments containing "SPLIT" suggest convenient places
+for this splitting. At the end of these comments is an "ed script"
+(for the UNIX(tm) editor ed) that will do this splitting.
+
+By #defining Single when you compile this source, you may obtain
+a single-precision C version of Paranoia.
+
+
+The following is from the introductory commentary from Wichmann's work:
+
+The BASIC program of Kahan is written in Microsoft BASIC using many
+facilities which have no exact analogy in Pascal. The Pascal
+version below cannot therefore be exactly the same. Rather than be
+a minimal transcription of the BASIC program, the Pascal coding
+follows the conventional style of block-structured languages. Hence
+the Pascal version could be useful in producing versions in other
+structured languages.
+
+Rather than use identifiers of minimal length (which therefore have
+little mnemonic significance), the Pascal version uses meaningful
+identifiers as follows [Note: A few changes have been made for C]:
+
+
+BASIC C BASIC C BASIC C
+
+ A J S StickyBit
+ A1 AInverse J0 NoErrors T
+ B Radix [Failure] T0 Underflow
+ B1 BInverse J1 NoErrors T2 ThirtyTwo
+ B2 RadixD2 [SeriousDefect] T5 OneAndHalf
+ B9 BMinusU2 J2 NoErrors T7 TwentySeven
+ C [Defect] T8 TwoForty
+ C1 CInverse J3 NoErrors U OneUlp
+ D [Flaw] U0 UnderflowThreshold
+ D4 FourD K PageNo U1
+ E0 L Milestone U2
+ E1 M V
+ E2 Exp2 N V0
+ E3 N1 V8
+ E5 MinSqEr O Zero V9
+ E6 SqEr O1 One W
+ E7 MaxSqEr O2 Two X
+ E8 O3 Three X1
+ E9 O4 Four X8
+ F1 MinusOne O5 Five X9 Random1
+ F2 Half O8 Eight Y
+ F3 Third O9 Nine Y1
+ F6 P Precision Y2
+ F9 Q Y9 Random2
+ G1 GMult Q8 Z
+ G2 GDiv Q9 Z0 PseudoZero
+ G3 GAddSub R Z1
+ H R1 RMult Z2
+ H1 HInverse R2 RDiv Z9
+ I R3 RAddSub
+ IO NoTrials R4 RSqrt
+ I3 IEEE R9 Random9
+
+ SqRWrng
+
+All the variables in BASIC are true variables and in consequence,
+the program is more difficult to follow since the "constants" must
+be determined (the glossary is very helpful). The Pascal version
+uses Real constants, but checks are added to ensure that the values
+are correctly converted by the compiler.
+
+The major textual change to the Pascal version apart from the
+identifiersis that named procedures are used, inserting parameters
+wherehelpful. New procedures are also introduced. The
+correspondence is as follows:
+
+
+BASIC Pascal
+lines
+
+ 90- 140 Pause
+ 170- 250 Instructions
+ 380- 460 Heading
+ 480- 670 Characteristics
+ 690- 870 History
+2940-2950 Random
+3710-3740 NewD
+4040-4080 DoesYequalX
+4090-4110 PrintIfNPositive
+4640-4850 TestPartialUnderflow
+
+=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=
+
+Below is an "ed script" that splits para.c into 10 files
+of the form part[1-8].c, subs.c, and msgs.c, plus a header
+file, paranoia.h, that these files require.
+r paranoia.c
+$
+?SPLIT
++,$w msgs.c
+.,$d
+?SPLIT
+.d
++d
+-,$w subs.c
+-,$d
+?part8
++d
+?include
+.,$w part8.c
+.,$d
+-d
+?part7
++d
+?include
+.,$w part7.c
+.,$d
+-d
+?part6
++d
+?include
+.,$w part6.c
+.,$d
+-d
+?part5
++d
+?include
+.,$w part5.c
+.,$d
+-d
+?part4
++d
+?include
+.,$w part4.c
+.,$d
+-d
+?part3
++d
+?include
+.,$w part3.c
+.,$d
+-d
+?part2
++d
+?include
+.,$w part2.c
+.,$d
+?SPLIT
+.d
+1,/^#include/-1d
+1,$w part1.c
+/Computed constants/,$d
+1,$s/^int/extern &/
+1,$s/^FLOAT/extern &/
+1,$s! = .*!;!
+/^Guard/,/^Round/s/^/extern /
+/^jmp_buf/s/^/extern /
+/^Sig_type/s/^/extern /
+a
+extern int sigfpe();
+.
+w paranoia.h
+q
+
+*/
+
+#include <stdio.h>
+#ifndef NOSIGNAL
+#include <signal.h>
+#endif
+#include <setjmp.h>
+
+extern double fabs(), floor(), log(), pow(), sqrt();
+
+#ifdef Single
+#define FLOAT float
+#define FABS(x) (float)fabs((double)(x))
+#define FLOOR(x) (float)floor((double)(x))
+#define LOG(x) (float)log((double)(x))
+#define POW(x,y) (float)pow((double)(x),(double)(y))
+#define SQRT(x) (float)sqrt((double)(x))
+#else
+#define FLOAT double
+#define FABS(x) fabs(x)
+#define FLOOR(x) floor(x)
+#define LOG(x) log(x)
+#define POW(x,y) pow(x,y)
+#define SQRT(x) sqrt(x)
+#endif
+
+jmp_buf ovfl_buf;
+typedef int (*Sig_type)();
+Sig_type sigsave;
+
+#define KEYBOARD 0
+
+FLOAT Radix, BInvrse, RadixD2, BMinusU2;
+FLOAT Sign(), Random();
+
+/*Small floating point constants.*/
+FLOAT Zero = 0.0;
+FLOAT Half = 0.5;
+FLOAT One = 1.0;
+FLOAT Two = 2.0;
+FLOAT Three = 3.0;
+FLOAT Four = 4.0;
+FLOAT Five = 5.0;
+FLOAT Eight = 8.0;
+FLOAT Nine = 9.0;
+FLOAT TwentySeven = 27.0;
+FLOAT ThirtyTwo = 32.0;
+FLOAT TwoForty = 240.0;
+FLOAT MinusOne = -1.0;
+FLOAT OneAndHalf = 1.5;
+/*Integer constants*/
+int NoTrials = 20; /*Number of tests for commutativity. */
+#define False 0
+#define True 1
+
+/* Definitions for declared types
+ Guard == (Yes, No);
+ Rounding == (Chopped, Rounded, Other);
+ Message == packed array [1..40] of char;
+ Class == (Flaw, Defect, Serious, Failure);
+ */
+#define Yes 1
+#define No 0
+#define Chopped 2
+#define Rounded 1
+#define Other 0
+#define Flaw 3
+#define Defect 2
+#define Serious 1
+#define Failure 0
+typedef int Guard, Rounding, Class;
+typedef char Message;
+
+/* Declarations of Variables */
+int Indx;
+char ch[8];
+FLOAT AInvrse, A1;
+FLOAT C, CInvrse;
+FLOAT D, FourD;
+FLOAT E0, E1, Exp2, E3, MinSqEr;
+FLOAT SqEr, MaxSqEr, E9;
+FLOAT Third;
+FLOAT F6, F9;
+FLOAT H, HInvrse;
+int I;
+FLOAT StickyBit, J;
+FLOAT MyZero;
+FLOAT Precision;
+FLOAT Q, Q9;
+FLOAT R, Random9;
+FLOAT T, Underflow, S;
+FLOAT OneUlp, UfThold, U1, U2;
+FLOAT V, V0, V9;
+FLOAT W;
+FLOAT X, X1, X2, X8, Random1;
+FLOAT Y, Y1, Y2, Random2;
+FLOAT Z, PseudoZero, Z1, Z2, Z9;
+volatile FLOAT VV;
+int ErrCnt[4];
+int fpecount;
+int Milestone;
+int PageNo;
+int M, N, N1;
+Guard GMult, GDiv, GAddSub;
+Rounding RMult, RDiv, RAddSub, RSqrt;
+int Break, Done, NotMonot, Monot, Anomaly, IEEE,
+ SqRWrng, UfNGrad;
+/* Computed constants. */
+/*U1 gap below 1.0, i.e, 1.0-U1 is next number below 1.0 */
+/*U2 gap above 1.0, i.e, 1.0+U2 is next number above 1.0 */
+
+/* floating point exception receiver */
+sigfpe()
+{
+ fpecount++;
+ printf("\n* * * FLOATING-POINT ERROR * * *\n");
+ fflush(stdout);
+ if (sigsave) {
+#ifndef NOSIGNAL
+ signal(SIGFPE, sigsave);
+#endif
+ sigsave = 0;
+ longjmp(ovfl_buf, 1);
+ }
+ abort();
+}
+
+main()
+{
+ /* Set coprocessor to double precision, no arith traps. */
+ /* __setfpucw(0x127f);*/
+ dprec();
+ /* First two assignments use integer right-hand sides. */
+ Zero = 0;
+ One = 1;
+ Two = One + One;
+ Three = Two + One;
+ Four = Three + One;
+ Five = Four + One;
+ Eight = Four + Four;
+ Nine = Three * Three;
+ TwentySeven = Nine * Three;
+ ThirtyTwo = Four * Eight;
+ TwoForty = Four * Five * Three * Four;
+ MinusOne = -One;
+ Half = One / Two;
+ OneAndHalf = One + Half;
+ ErrCnt[Failure] = 0;
+ ErrCnt[Serious] = 0;
+ ErrCnt[Defect] = 0;
+ ErrCnt[Flaw] = 0;
+ PageNo = 1;
+ /*=============================================*/
+ Milestone = 0;
+ /*=============================================*/
+#ifndef NOSIGNAL
+ signal(SIGFPE, sigfpe);
+#endif
+ Instructions();
+ Pause();
+ Heading();
+ Pause();
+ Characteristics();
+ Pause();
+ History();
+ Pause();
+ /*=============================================*/
+ Milestone = 7;
+ /*=============================================*/
+ printf("Program is now RUNNING tests on small integers:\n");
+
+ TstCond (Failure, (Zero + Zero == Zero) && (One - One == Zero)
+ && (One > Zero) && (One + One == Two),
+ "0+0 != 0, 1-1 != 0, 1 <= 0, or 1+1 != 2");
+ Z = - Zero;
+ if (Z == 0.0) {
+ U1 = 0.001;
+ Radix = 1;
+ TstPtUf();
+ }
+ else {
+ ErrCnt[Failure] = ErrCnt[Failure] + 1;
+ printf("Comparison alleges that -0.0 is Non-zero!\n");
+ }
+ TstCond (Failure, (Three == Two + One) && (Four == Three + One)
+ && (Four + Two * (- Two) == Zero)
+ && (Four - Three - One == Zero),
+ "3 != 2+1, 4 != 3+1, 4+2*(-2) != 0, or 4-3-1 != 0");
+ TstCond (Failure, (MinusOne == (0 - One))
+ && (MinusOne + One == Zero ) && (One + MinusOne == Zero)
+ && (MinusOne + FABS(One) == Zero)
+ && (MinusOne + MinusOne * MinusOne == Zero),
+ "-1+1 != 0, (-1)+abs(1) != 0, or -1+(-1)*(-1) != 0");
+ TstCond (Failure, Half + MinusOne + Half == Zero,
+ "1/2 + (-1) + 1/2 != 0");
+ /*=============================================*/
+ /*SPLIT
+ part2();
+ part3();
+ part4();
+ part5();
+ part6();
+ part7();
+ part8();
+ }
+#include "paranoia.h"
+part2(){
+*/
+ Milestone = 10;
+ /*=============================================*/
+ TstCond (Failure, (Nine == Three * Three)
+ && (TwentySeven == Nine * Three) && (Eight == Four + Four)
+ && (ThirtyTwo == Eight * Four)
+ && (ThirtyTwo - TwentySeven - Four - One == Zero),
+ "9 != 3*3, 27 != 9*3, 32 != 8*4, or 32-27-4-1 != 0");
+ TstCond (Failure, (Five == Four + One) &&
+ (TwoForty == Four * Five * Three * Four)
+ && (TwoForty / Three - Four * Four * Five == Zero)
+ && ( TwoForty / Four - Five * Three * Four == Zero)
+ && ( TwoForty / Five - Four * Three * Four == Zero),
+ "5 != 4+1, 240/3 != 80, 240/4 != 60, or 240/5 != 48");
+ if (ErrCnt[Failure] == 0) {
+ printf("-1, 0, 1/2, 1, 2, 3, 4, 5, 9, 27, 32 & 240 are O.K.\n");
+ printf("\n");
+ }
+ printf("Searching for Radix and Precision.\n");
+ W = One;
+ do {
+ W = W + W;
+ Y = W + One;
+ Z = Y - W;
+ Y = Z - One;
+ } while (MinusOne + FABS(Y) < Zero);
+ /*.. now W is just big enough that |((W+1)-W)-1| >= 1 ...*/
+ Precision = Zero;
+ Y = One;
+ do {
+ Radix = W + Y;
+ Y = Y + Y;
+ Radix = Radix - W;
+ } while ( Radix == Zero);
+ if (Radix < Two) Radix = One;
+ printf("Radix = %f .\n", Radix);
+ if (Radix != 1) {
+ W = One;
+ do {
+ Precision = Precision + One;
+ W = W * Radix;
+ Y = W + One;
+ } while ((Y - W) == One);
+ }
+ /*... now W == Radix^Precision is barely too big to satisfy (W+1)-W == 1
+ ...*/
+ U1 = One / W;
+ U2 = Radix * U1;
+ printf("Closest relative separation found is U1 = %.7e .\n\n", U1);
+ printf("Recalculating radix and precision.");
+
+ /*save old values*/
+ E0 = Radix;
+ E1 = U1;
+ E9 = U2;
+ E3 = Precision;
+
+ X = Four / Three;
+ Third = X - One;
+ F6 = Half - Third;
+ X = F6 + F6;
+ X = FABS(X - Third);
+ if (X < U2) X = U2;
+
+ /*... now X = (unknown no.) ulps of 1+...*/
+ do {
+ U2 = X;
+ Y = Half * U2 + ThirtyTwo * U2 * U2;
+ Y = One + Y;
+ X = Y - One;
+ } while ( ! ((U2 <= X) || (X <= Zero)));
+
+ /*... now U2 == 1 ulp of 1 + ... */
+ X = Two / Three;
+ F6 = X - Half;
+ Third = F6 + F6;
+ X = Third - Half;
+ X = FABS(X + F6);
+ if (X < U1) X = U1;
+
+ /*... now X == (unknown no.) ulps of 1 -... */
+ do {
+ U1 = X;
+ Y = Half * U1 + ThirtyTwo * U1 * U1;
+ Y = Half - Y;
+ X = Half + Y;
+ Y = Half - X;
+ X = Half + Y;
+ } while ( ! ((U1 <= X) || (X <= Zero)));
+ /*... now U1 == 1 ulp of 1 - ... */
+ if (U1 == E1) printf("confirms closest relative separation U1 .\n");
+ else printf("gets better closest relative separation U1 = %.7e .\n", U1);
+ W = One / U1;
+ F9 = (Half - U1) + Half;
+ Radix = FLOOR(0.01 + U2 / U1);
+ if (Radix == E0) printf("Radix confirmed.\n");
+ else printf("MYSTERY: recalculated Radix = %.7e .\n", Radix);
+ TstCond (Defect, Radix <= Eight + Eight,
+ "Radix is too big: roundoff problems");
+ TstCond (Flaw, (Radix == Two) || (Radix == 10)
+ || (Radix == One), "Radix is not as good as 2 or 10");
+ /*=============================================*/
+ Milestone = 20;
+ /*=============================================*/
+ TstCond (Failure, F9 - Half < Half,
+ "(1-U1)-1/2 < 1/2 is FALSE, prog. fails?");
+ X = F9;
+ I = 1;
+ Y = X - Half;
+ Z = Y - Half;
+ TstCond (Failure, (X != One)
+ || (Z == Zero), "Comparison is fuzzy,X=1 but X-1/2-1/2 != 0");
+ X = One + U2;
+ I = 0;
+ /*=============================================*/
+ Milestone = 25;
+ /*=============================================*/
+ /*... BMinusU2 = nextafter(Radix, 0) */
+ BMinusU2 = Radix - One;
+ BMinusU2 = (BMinusU2 - U2) + One;
+ /* Purify Integers */
+ if (Radix != One) {
+ X = - TwoForty * LOG(U1) / LOG(Radix);
+ Y = FLOOR(Half + X);
+ if (FABS(X - Y) * Four < One) X = Y;
+ Precision = X / TwoForty;
+ Y = FLOOR(Half + Precision);
+ if (FABS(Precision - Y) * TwoForty < Half) Precision = Y;
+ }
+ if ((Precision != FLOOR(Precision)) || (Radix == One)) {
+ printf("Precision cannot be characterized by an Integer number\n");
+ printf("of significant digits but, by itself, this is a minor flaw.\n");
+ }
+ if (Radix == One)
+ printf("logarithmic encoding has precision characterized solely by U1.\n");
+ else printf("The number of significant digits of the Radix is %f .\n",
+ Precision);
+ TstCond (Serious, U2 * Nine * Nine * TwoForty < One,
+ "Precision worse than 5 decimal figures ");
+ /*=============================================*/
+ Milestone = 30;
+ /*=============================================*/
+ /* Test for extra-precise subepressions */
+ X = FABS(((Four / Three - One) - One / Four) * Three - One / Four);
+ do {
+ Z2 = X;
+ X = (One + (Half * Z2 + ThirtyTwo * Z2 * Z2)) - One;
+ } while ( ! ((Z2 <= X) || (X <= Zero)));
+ X = Y = Z = FABS((Three / Four - Two / Three) * Three - One / Four);
+ do {
+ Z1 = Z;
+ Z = (One / Two - ((One / Two - (Half * Z1 + ThirtyTwo * Z1 * Z1))
+ + One / Two)) + One / Two;
+ } while ( ! ((Z1 <= Z) || (Z <= Zero)));
+ do {
+ do {
+ Y1 = Y;
+ Y = (Half - ((Half - (Half * Y1 + ThirtyTwo * Y1 * Y1)) + Half
+ )) + Half;
+ } while ( ! ((Y1 <= Y) || (Y <= Zero)));
+ X1 = X;
+ X = ((Half * X1 + ThirtyTwo * X1 * X1) - F9) + F9;
+ } while ( ! ((X1 <= X) || (X <= Zero)));
+ if ((X1 != Y1) || (X1 != Z1)) {
+ BadCond(Serious, "Disagreements among the values X1, Y1, Z1,\n");
+ printf("respectively %.7e, %.7e, %.7e,\n", X1, Y1, Z1);
+ printf("are symptoms of inconsistencies introduced\n");
+ printf("by extra-precise evaluation of arithmetic subexpressions.\n");
+ notify("Possibly some part of this");
+ if ((X1 == U1) || (Y1 == U1) || (Z1 == U1)) printf(
+ "That feature is not tested further by this program.\n") ;
+ }
+ else {
+ if ((Z1 != U1) || (Z2 != U2)) {
+ if ((Z1 >= U1) || (Z2 >= U2)) {
+ BadCond(Failure, "");
+ notify("Precision");
+ printf("\tU1 = %.7e, Z1 - U1 = %.7e\n",U1,Z1-U1);
+ printf("\tU2 = %.7e, Z2 - U2 = %.7e\n",U2,Z2-U2);
+ }
+ else {
+ if ((Z1 <= Zero) || (Z2 <= Zero)) {
+ printf("Because of unusual Radix = %f", Radix);
+ printf(", or exact rational arithmetic a result\n");
+ printf("Z1 = %.7e, or Z2 = %.7e ", Z1, Z2);
+ notify("of an\nextra-precision");
+ }
+ if (Z1 != Z2 || Z1 > Zero) {
+ X = Z1 / U1;
+ Y = Z2 / U2;
+ if (Y > X) X = Y;
+ Q = - LOG(X);
+ printf("Some subexpressions appear to be calculated extra\n");
+ printf("precisely with about %g extra B-digits, i.e.\n",
+ (Q / LOG(Radix)));
+ printf("roughly %g extra significant decimals.\n",
+ Q / LOG(10.));
+ }
+ printf("That feature is not tested further by this program.\n");
+ }
+ }
+ }
+ Pause();
+ /*=============================================*/
+ /*SPLIT
+ }
+#include "paranoia.h"
+part3(){
+*/
+ Milestone = 35;
+ /*=============================================*/
+ if (Radix >= Two) {
+ X = W / (Radix * Radix);
+ Y = X + One;
+ Z = Y - X;
+ T = Z + U2;
+ X = T - Z;
+ TstCond (Failure, X == U2,
+ "Subtraction is not normalized X=Y,X+Z != Y+Z!");
+ if (X == U2) printf(
+ "Subtraction appears to be normalized, as it should be.");
+ }
+ printf("\nChecking for guard digit in *, /, and -.\n");
+ Y = F9 * One;
+ Z = One * F9;
+ X = F9 - Half;
+ Y = (Y - Half) - X;
+ Z = (Z - Half) - X;
+ X = One + U2;
+ T = X * Radix;
+ R = Radix * X;
+ X = T - Radix;
+ X = X - Radix * U2;
+ T = R - Radix;
+ T = T - Radix * U2;
+ X = X * (Radix - One);
+ T = T * (Radix - One);
+ if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)) GMult = Yes;
+ else {
+ GMult = No;
+ TstCond (Serious, False,
+ "* lacks a Guard Digit, so 1*X != X");
+ }
+ Z = Radix * U2;
+ X = One + Z;
+ Y = FABS((X + Z) - X * X) - U2;
+ X = One - U2;
+ Z = FABS((X - U2) - X * X) - U1;
+ TstCond (Failure, (Y <= Zero)
+ && (Z <= Zero), "* gets too many final digits wrong.\n");
+ Y = One - U2;
+ X = One + U2;
+ Z = One / Y;
+ Y = Z - X;
+ X = One / Three;
+ Z = Three / Nine;
+ X = X - Z;
+ T = Nine / TwentySeven;
+ Z = Z - T;
+ TstCond(Defect, X == Zero && Y == Zero && Z == Zero,
+ "Division lacks a Guard Digit, so error can exceed 1 ulp\n\
+or 1/3 and 3/9 and 9/27 may disagree");
+ Y = F9 / One;
+ X = F9 - Half;
+ Y = (Y - Half) - X;
+ X = One + U2;
+ T = X / One;
+ X = T - X;
+ if ((X == Zero) && (Y == Zero) && (Z == Zero)) GDiv = Yes;
+ else {
+ GDiv = No;
+ TstCond (Serious, False,
+ "Division lacks a Guard Digit, so X/1 != X");
+ }
+ X = One / (One + U2);
+ Y = X - Half - Half;
+ TstCond (Serious, Y < Zero,
+ "Computed value of 1/1.000..1 >= 1");
+ X = One - U2;
+ Y = One + Radix * U2;
+ Z = X * Radix;
+ T = Y * Radix;
+ R = Z / Radix;
+ StickyBit = T / Radix;
+ X = R - X;
+ Y = StickyBit - Y;
+ TstCond (Failure, X == Zero && Y == Zero,
+ "* and/or / gets too many last digits wrong");
+ Y = One - U1;
+ X = One - F9;
+ Y = One - Y;
+ T = Radix - U2;
+ Z = Radix - BMinusU2;
+ T = Radix - T;
+ if ((X == U1) && (Y == U1) && (Z == U2) && (T == U2)) GAddSub = Yes;
+ else {
+ GAddSub = No;
+ TstCond (Serious, False,
+ "- lacks Guard Digit, so cancellation is obscured");
+ }
+ if (F9 != One && F9 - One >= Zero) {
+ BadCond(Serious, "comparison alleges (1-U1) < 1 although\n");
+ printf(" subtration yields (1-U1) - 1 = 0 , thereby vitiating\n");
+ printf(" such precautions against division by zero as\n");
+ printf(" ... if (X == 1.0) {.....} else {.../(X-1.0)...}\n");
+ }
+ if (GMult == Yes && GDiv == Yes && GAddSub == Yes) printf(
+ " *, /, and - appear to have guard digits, as they should.\n");
+ /*=============================================*/
+ Milestone = 40;
+ /*=============================================*/
+ Pause();
+ printf("Checking rounding on multiply, divide and add/subtract.\n");
+ RMult = Other;
+ RDiv = Other;
+ RAddSub = Other;
+ RadixD2 = Radix / Two;
+ A1 = Two;
+ Done = False;
+ do {
+ AInvrse = Radix;
+ do {
+ X = AInvrse;
+ AInvrse = AInvrse / A1;
+ } while ( ! (FLOOR(AInvrse) != AInvrse));
+ Done = (X == One) || (A1 > Three);
+ if (! Done) A1 = Nine + One;
+ } while ( ! (Done));
+ if (X == One) A1 = Radix;
+ AInvrse = One / A1;
+ X = A1;
+ Y = AInvrse;
+ Done = False;
+ do {
+ Z = X * Y - Half;
+ TstCond (Failure, Z == Half,
+ "X * (1/X) differs from 1");
+ Done = X == Radix;
+ X = Radix;
+ Y = One / X;
+ } while ( ! (Done));
+ Y2 = One + U2;
+ Y1 = One - U2;
+ X = OneAndHalf - U2;
+ Y = OneAndHalf + U2;
+ Z = (X - U2) * Y2;
+ T = Y * Y1;
+ Z = Z - X;
+ T = T - X;
+ X = X * Y2;
+ Y = (Y + U2) * Y1;
+ X = X - OneAndHalf;
+ Y = Y - OneAndHalf;
+ if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T <= Zero)) {
+ X = (OneAndHalf + U2) * Y2;
+ Y = OneAndHalf - U2 - U2;
+ Z = OneAndHalf + U2 + U2;
+ T = (OneAndHalf - U2) * Y1;
+ X = X - (Z + U2);
+ StickyBit = Y * Y1;
+ S = Z * Y2;
+ T = T - Y;
+ Y = (U2 - Y) + StickyBit;
+ Z = S - (Z + U2 + U2);
+ StickyBit = (Y2 + U2) * Y1;
+ Y1 = Y2 * Y1;
+ StickyBit = StickyBit - Y2;
+ Y1 = Y1 - Half;
+ if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)
+ && ( StickyBit == Zero) && (Y1 == Half)) {
+ RMult = Rounded;
+ printf("Multiplication appears to round correctly.\n");
+ }
+ else if ((X + U2 == Zero) && (Y < Zero) && (Z + U2 == Zero)
+ && (T < Zero) && (StickyBit + U2 == Zero)
+ && (Y1 < Half)) {
+ RMult = Chopped;
+ printf("Multiplication appears to chop.\n");
+ }
+ else printf("* is neither chopped nor correctly rounded.\n");
+ if ((RMult == Rounded) && (GMult == No)) notify("Multiplication");
+ }
+ else printf("* is neither chopped nor correctly rounded.\n");
+ /*=============================================*/
+ Milestone = 45;
+ /*=============================================*/
+ Y2 = One + U2;
+ Y1 = One - U2;
+ Z = OneAndHalf + U2 + U2;
+ X = Z / Y2;
+ T = OneAndHalf - U2 - U2;
+ Y = (T - U2) / Y1;
+ Z = (Z + U2) / Y2;
+ X = X - OneAndHalf;
+ Y = Y - T;
+ T = T / Y1;
+ Z = Z - (OneAndHalf + U2);
+ T = (U2 - OneAndHalf) + T;
+ if (! ((X > Zero) || (Y > Zero) || (Z > Zero) || (T > Zero))) {
+ X = OneAndHalf / Y2;
+ Y = OneAndHalf - U2;
+ Z = OneAndHalf + U2;
+ X = X - Y;
+ T = OneAndHalf / Y1;
+ Y = Y / Y1;
+ T = T - (Z + U2);
+ Y = Y - Z;
+ Z = Z / Y2;
+ Y1 = (Y2 + U2) / Y2;
+ Z = Z - OneAndHalf;
+ Y2 = Y1 - Y2;
+ Y1 = (F9 - U1) / F9;
+ if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)
+ && (Y2 == Zero) && (Y2 == Zero)
+ && (Y1 - Half == F9 - Half )) {
+ RDiv = Rounded;
+ printf("Division appears to round correctly.\n");
+ if (GDiv == No) notify("Division");
+ }
+ else if ((X < Zero) && (Y < Zero) && (Z < Zero) && (T < Zero)
+ && (Y2 < Zero) && (Y1 - Half < F9 - Half)) {
+ RDiv = Chopped;
+ printf("Division appears to chop.\n");
+ }
+ }
+ if (RDiv == Other) printf("/ is neither chopped nor correctly rounded.\n");
+ BInvrse = One / Radix;
+ TstCond (Failure, (BInvrse * Radix - Half == Half),
+ "Radix * ( 1 / Radix ) differs from 1");
+ /*=============================================*/
+ /*SPLIT
+ }
+#include "paranoia.h"
+part4(){
+*/
+ Milestone = 50;
+ /*=============================================*/
+ TstCond (Failure, ((F9 + U1) - Half == Half)
+ && ((BMinusU2 + U2 ) - One == Radix - One),
+ "Incomplete carry-propagation in Addition");
+ X = One - U1 * U1;
+ Y = One + U2 * (One - U2);
+ Z = F9 - Half;
+ X = (X - Half) - Z;
+ Y = Y - One;
+ if ((X == Zero) && (Y == Zero)) {
+ RAddSub = Chopped;
+ printf("Add/Subtract appears to be chopped.\n");
+ }
+ if (GAddSub == Yes) {
+ X = (Half + U2) * U2;
+ Y = (Half - U2) * U2;
+ X = One + X;
+ Y = One + Y;
+ X = (One + U2) - X;
+ Y = One - Y;
+ if ((X == Zero) && (Y == Zero)) {
+ X = (Half + U2) * U1;
+ Y = (Half - U2) * U1;
+ X = One - X;
+ Y = One - Y;
+ X = F9 - X;
+ Y = One - Y;
+ if ((X == Zero) && (Y == Zero)) {
+ RAddSub = Rounded;
+ printf("Addition/Subtraction appears to round correctly.\n");
+ if (GAddSub == No) notify("Add/Subtract");
+ }
+ else printf("Addition/Subtraction neither rounds nor chops.\n");
+ }
+ else printf("Addition/Subtraction neither rounds nor chops.\n");
+ }
+ else printf("Addition/Subtraction neither rounds nor chops.\n");
+ S = One;
+ X = One + Half * (One + Half);
+ Y = (One + U2) * Half;
+ Z = X - Y;
+ T = Y - X;
+ StickyBit = Z + T;
+ if (StickyBit != Zero) {
+ S = Zero;
+ BadCond(Flaw, "(X - Y) + (Y - X) is non zero!\n");
+ }
+ StickyBit = Zero;
+ if ((GMult == Yes) && (GDiv == Yes) && (GAddSub == Yes)
+ && (RMult == Rounded) && (RDiv == Rounded)
+ && (RAddSub == Rounded) && (FLOOR(RadixD2) == RadixD2)) {
+ printf("Checking for sticky bit.\n");
+ X = (Half + U1) * U2;
+ Y = Half * U2;
+ Z = One + Y;
+ T = One + X;
+ if ((Z - One <= Zero) && (T - One >= U2)) {
+ Z = T + Y;
+ Y = Z - X;
+ if ((Z - T >= U2) && (Y - T == Zero)) {
+ X = (Half + U1) * U1;
+ Y = Half * U1;
+ Z = One - Y;
+ T = One - X;
+ if ((Z - One == Zero) && (T - F9 == Zero)) {
+ Z = (Half - U1) * U1;
+ T = F9 - Z;
+ Q = F9 - Y;
+ if ((T - F9 == Zero) && (F9 - U1 - Q == Zero)) {
+ Z = (One + U2) * OneAndHalf;
+ T = (OneAndHalf + U2) - Z + U2;
+ X = One + Half / Radix;
+ Y = One + Radix * U2;
+ Z = X * Y;
+ if (T == Zero && X + Radix * U2 - Z == Zero) {
+ if (Radix != Two) {
+ X = Two + U2;
+ Y = X / Two;
+ if ((Y - One == Zero)) StickyBit = S;
+ }
+ else StickyBit = S;
+ }
+ }
+ }
+ }
+ }
+ }
+ if (StickyBit == One) printf("Sticky bit apparently used correctly.\n");
+ else printf("Sticky bit used incorrectly or not at all.\n");
+ TstCond (Flaw, !(GMult == No || GDiv == No || GAddSub == No ||
+ RMult == Other || RDiv == Other || RAddSub == Other),
+ "lack(s) of guard digits or failure(s) to correctly round or chop\n\
+(noted above) count as one flaw in the final tally below");
+ /*=============================================*/
+ Milestone = 60;
+ /*=============================================*/
+ printf("\n");
+ printf("Does Multiplication commute? ");
+ printf("Testing on %d random pairs.\n", NoTrials);
+ Random9 = SQRT(3.0);
+ Random1 = Third;
+ I = 1;
+ do {
+ X = Random();
+ Y = Random();
+ Z9 = Y * X;
+ Z = X * Y;
+ Z9 = Z - Z9;
+ I = I + 1;
+ } while ( ! ((I > NoTrials) || (Z9 != Zero)));
+ if (I == NoTrials) {
+ Random1 = One + Half / Three;
+ Random2 = (U2 + U1) + One;
+ Z = Random1 * Random2;
+ Y = Random2 * Random1;
+ Z9 = (One + Half / Three) * ((U2 + U1) + One) - (One + Half /
+ Three) * ((U2 + U1) + One);
+ }
+ if (! ((I == NoTrials) || (Z9 == Zero)))
+ BadCond(Defect, "X * Y == Y * X trial fails.\n");
+ else printf(" No failures found in %d integer pairs.\n", NoTrials);
+ /*=============================================*/
+ Milestone = 70;
+ /*=============================================*/
+ printf("\nRunning test of square root(x).\n");
+ TstCond (Failure, (Zero == SQRT(Zero))
+ && (- Zero == SQRT(- Zero))
+ && (One == SQRT(One)), "Square root of 0.0, -0.0 or 1.0 wrong");
+ MinSqEr = Zero;
+ MaxSqEr = Zero;
+ J = Zero;
+ X = Radix;
+ OneUlp = U2;
+ SqXMinX (Serious);
+ X = BInvrse;
+ OneUlp = BInvrse * U1;
+ SqXMinX (Serious);
+ X = U1;
+ OneUlp = U1 * U1;
+ SqXMinX (Serious);
+ if (J != Zero) Pause();
+ printf("Testing if sqrt(X * X) == X for %d Integers X.\n", NoTrials);
+ J = Zero;
+ X = Two;
+ Y = Radix;
+ if ((Radix != One)) do {
+ X = Y;
+ Y = Radix * Y;
+ } while ( ! ((Y - X >= NoTrials)));
+ OneUlp = X * U2;
+ I = 1;
+ while (I < 10) {
+ X = X + One;
+ SqXMinX (Defect);
+ if (J > Zero) break;
+ I = I + 1;
+ }
+ printf("Test for sqrt monotonicity.\n");
+ I = - 1;
+ X = BMinusU2;
+ Y = Radix;
+ Z = Radix + Radix * U2;
+ NotMonot = False;
+ Monot = False;
+ while ( ! (NotMonot || Monot)) {
+ I = I + 1;
+ X = SQRT(X);
+ Q = SQRT(Y);
+ Z = SQRT(Z);
+ if ((X > Q) || (Q > Z)) NotMonot = True;
+ else {
+ Q = FLOOR(Q + Half);
+ if ((I > 0) || (Radix == Q * Q)) Monot = True;
+ else if (I > 0) {
+ if (I > 1) Monot = True;
+ else {
+ Y = Y * BInvrse;
+ X = Y - U1;
+ Z = Y + U1;
+ }
+ }
+ else {
+ Y = Q;
+ X = Y - U2;
+ Z = Y + U2;
+ }
+ }
+ }
+ if (Monot) printf("sqrt has passed a test for Monotonicity.\n");
+ else {
+ BadCond(Defect, "");
+ printf("sqrt(X) is non-monotonic for X near %.7e .\n", Y);
+ }
+ /*=============================================*/
+ /*SPLIT
+ }
+#include "paranoia.h"
+part5(){
+*/
+ Milestone = 80;
+ /*=============================================*/
+ MinSqEr = MinSqEr + Half;
+ MaxSqEr = MaxSqEr - Half;
+ Y = (SQRT(One + U2) - One) / U2;
+ SqEr = (Y - One) + U2 / Eight;
+ if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+ SqEr = Y + U2 / Eight;
+ if (SqEr < MinSqEr) MinSqEr = SqEr;
+ Y = ((SQRT(F9) - U2) - (One - U2)) / U1;
+ SqEr = Y + U1 / Eight;
+ if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+ SqEr = (Y + One) + U1 / Eight;
+ if (SqEr < MinSqEr) MinSqEr = SqEr;
+ OneUlp = U2;
+ X = OneUlp;
+ for( Indx = 1; Indx <= 3; ++Indx) {
+ Y = SQRT((X + U1 + X) + F9);
+ Y = ((Y - U2) - ((One - U2) + X)) / OneUlp;
+ Z = ((U1 - X) + F9) * Half * X * X / OneUlp;
+ SqEr = (Y + Half) + Z;
+ if (SqEr < MinSqEr) MinSqEr = SqEr;
+ SqEr = (Y - Half) + Z;
+ if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+ if (((Indx == 1) || (Indx == 3)))
+ X = OneUlp * Sign (X) * FLOOR(Eight / (Nine * SQRT(OneUlp)));
+ else {
+ OneUlp = U1;
+ X = - OneUlp;
+ }
+ }
+ /*=============================================*/
+ Milestone = 85;
+ /*=============================================*/
+ SqRWrng = False;
+ Anomaly = False;
+ if (Radix != One) {
+ printf("Testing whether sqrt is rounded or chopped.\n");
+ D = FLOOR(Half + POW(Radix, One + Precision - FLOOR(Precision)));
+ /* ... == Radix^(1 + fract) if (Precision == Integer + fract. */
+ X = D / Radix;
+ Y = D / A1;
+ if ((X != FLOOR(X)) || (Y != FLOOR(Y))) {
+ Anomaly = True;
+ }
+ else {
+ X = Zero;
+ Z2 = X;
+ Y = One;
+ Y2 = Y;
+ Z1 = Radix - One;
+ FourD = Four * D;
+ do {
+ if (Y2 > Z2) {
+ Q = Radix;
+ Y1 = Y;
+ do {
+ X1 = FABS(Q + FLOOR(Half - Q / Y1) * Y1);
+ Q = Y1;
+ Y1 = X1;
+ } while ( ! (X1 <= Zero));
+ if (Q <= One) {
+ Z2 = Y2;
+ Z = Y;
+ }
+ }
+ Y = Y + Two;
+ X = X + Eight;
+ Y2 = Y2 + X;
+ if (Y2 >= FourD) Y2 = Y2 - FourD;
+ } while ( ! (Y >= D));
+ X8 = FourD - Z2;
+ Q = (X8 + Z * Z) / FourD;
+ X8 = X8 / Eight;
+ if (Q != FLOOR(Q)) Anomaly = True;
+ else {
+ Break = False;
+ do {
+ X = Z1 * Z;
+ X = X - FLOOR(X / Radix) * Radix;
+ if (X == One)
+ Break = True;
+ else
+ Z1 = Z1 - One;
+ } while ( ! (Break || (Z1 <= Zero)));
+ if ((Z1 <= Zero) && (! Break)) Anomaly = True;
+ else {
+ if (Z1 > RadixD2) Z1 = Z1 - Radix;
+ do {
+ NewD();
+ } while ( ! (U2 * D >= F9));
+ if (D * Radix - D != W - D) Anomaly = True;
+ else {
+ Z2 = D;
+ I = 0;
+ Y = D + (One + Z) * Half;
+ X = D + Z + Q;
+ SR3750();
+ Y = D + (One - Z) * Half + D;
+ X = D - Z + D;
+ X = X + Q + X;
+ SR3750();
+ NewD();
+ if (D - Z2 != W - Z2) Anomaly = True;
+ else {
+ Y = (D - Z2) + (Z2 + (One - Z) * Half);
+ X = (D - Z2) + (Z2 - Z + Q);
+ SR3750();
+ Y = (One + Z) * Half;
+ X = Q;
+ SR3750();
+ if (I == 0) Anomaly = True;
+ }
+ }
+ }
+ }
+ }
+ if ((I == 0) || Anomaly) {
+ BadCond(Failure, "Anomalous arithmetic with Integer < ");
+ printf("Radix^Precision = %.7e\n", W);
+ printf(" fails test whether sqrt rounds or chops.\n");
+ SqRWrng = True;
+ }
+ }
+ if (! Anomaly) {
+ if (! ((MinSqEr < Zero) || (MaxSqEr > Zero))) {
+ RSqrt = Rounded;
+ printf("Square root appears to be correctly rounded.\n");
+ }
+ else {
+ if ((MaxSqEr + U2 > U2 - Half) || (MinSqEr > Half)
+ || (MinSqEr + Radix < Half)) SqRWrng = True;
+ else {
+ RSqrt = Chopped;
+ printf("Square root appears to be chopped.\n");
+ }
+ }
+ }
+ if (SqRWrng) {
+ printf("Square root is neither chopped nor correctly rounded.\n");
+ printf("Observed errors run from %.7e ", MinSqEr - Half);
+ printf("to %.7e ulps.\n", Half + MaxSqEr);
+ TstCond (Serious, MaxSqEr - MinSqEr < Radix * Radix,
+ "sqrt gets too many last digits wrong");
+ }
+ /*=============================================*/
+ Milestone = 90;
+ /*=============================================*/
+ Pause();
+ printf("Testing powers Z^i for small Integers Z and i.\n");
+ N = 0;
+ /* ... test powers of zero. */
+ I = 0;
+ Z = -Zero;
+ M = 3.0;
+ Break = False;
+ do {
+ X = One;
+ SR3980();
+ if (I <= 10) {
+ I = 1023;
+ SR3980();
+ }
+ if (Z == MinusOne) Break = True;
+ else {
+ Z = MinusOne;
+ PrintIfNPositive();
+ N = 0;
+ /* .. if(-1)^N is invalid, replace MinusOne by One. */
+ I = - 4;
+ }
+ } while ( ! Break);
+ PrintIfNPositive();
+ N1 = N;
+ N = 0;
+ Z = A1;
+ M = FLOOR(Two * LOG(W) / LOG(A1));
+ Break = False;
+ do {
+ X = Z;
+ I = 1;
+ SR3980();
+ if (Z == AInvrse) Break = True;
+ else Z = AInvrse;
+ } while ( ! (Break));
+ /*=============================================*/
+ Milestone = 100;
+ /*=============================================*/
+ /* Powers of Radix have been tested, */
+ /* next try a few primes */
+ M = NoTrials;
+ Z = Three;
+ do {
+ X = Z;
+ I = 1;
+ SR3980();
+ do {
+ Z = Z + Two;
+ } while ( Three * FLOOR(Z / Three) == Z );
+ } while ( Z < Eight * Three );
+ if (N > 0) {
+ printf("Errors like this may invalidate financial calculations\n");
+ printf("\tinvolving interest rates.\n");
+ }
+ PrintIfNPositive();
+ N += N1;
+ if (N == 0) printf("... no discrepancis found.\n");
+ if (N > 0) Pause();
+ else printf("\n");
+ /*=============================================*/
+ /*SPLIT
+ }
+#include "paranoia.h"
+part6(){
+*/
+ Milestone = 110;
+ /*=============================================*/
+ printf("Seeking Underflow thresholds UfThold and E0.\n");
+ D = U1;
+ if (Precision != FLOOR(Precision)) {
+ D = BInvrse;
+ X = Precision;
+ do {
+ D = D * BInvrse;
+ X = X - One;
+ } while ( X > Zero);
+ }
+ Y = One;
+ Z = D;
+ /* ... D is power of 1/Radix < 1. */
+ do {
+ C = Y;
+ Y = Z;
+ Z = Y * Y;
+ VV = Z;
+ } while ((Y > Z) && (VV + VV > VV));
+ Y = C;
+ Z = Y * D;
+ do {
+ C = Y;
+ Y = Z;
+ Z = Y * D;
+ VV = Z;
+ } while ((Y > Z) && (VV + VV > VV));
+ if (Radix < Two) HInvrse = Two;
+ else HInvrse = Radix;
+ H = One / HInvrse;
+ /* ... 1/HInvrse == H == Min(1/Radix, 1/2) */
+ CInvrse = One / C;
+ E0 = C;
+ Z = E0 * H;
+ /* ...1/Radix^(BIG Integer) << 1 << CInvrse == 1/C */
+ do {
+ Y = E0;
+ E0 = Z;
+ Z = E0 * H;
+ VV = Z;
+ } while ((E0 > VV) && (VV + VV > VV));
+ UfThold = E0;
+ E1 = Zero;
+ Q = Zero;
+ E9 = U2;
+ S = One + E9;
+ D = C * S;
+ if (D <= C) {
+ E9 = Radix * U2;
+ S = One + E9;
+ D = C * S;
+ if (D <= C) {
+ BadCond(Failure, "multiplication gets too many last digits wrong.\n");
+ Underflow = E0;
+ Y1 = Zero;
+ PseudoZero = Z;
+ Pause();
+ }
+ }
+ else {
+ Underflow = D;
+ PseudoZero = Underflow * H;
+ UfThold = Zero;
+ do {
+ Y1 = Underflow;
+ Underflow = PseudoZero;
+ if (E1 + E1 <= E1) {
+ Y2 = Underflow * HInvrse;
+ E1 = FABS(Y1 - Y2);
+ Q = Y1;
+ if ((UfThold == Zero) && (Y1 != Y2)) UfThold = Y1;
+ }
+ PseudoZero = PseudoZero * H;
+ VV = PseudoZero;
+ } while ((Underflow > VV)
+ && (VV + VV > VV));
+ }
+ /* Comment line 4530 .. 4560 */
+ if (PseudoZero != Zero) {
+ printf("\n");
+ Z = PseudoZero;
+ /* ... Test PseudoZero for "phoney- zero" violates */
+ /* ... PseudoZero < Underflow or PseudoZero < PseudoZero + PseudoZero
+ ... */
+ if (PseudoZero <= Zero) {
+ BadCond(Failure, "Positive expressions can underflow to an\n");
+ printf("allegedly negative value\n");
+ printf("PseudoZero that prints out as: %g .\n", PseudoZero);
+ X = - PseudoZero;
+ if (X <= Zero) {
+ printf("But -PseudoZero, which should be\n");
+ printf("positive, isn't; it prints out as %g .\n", X);
+ }
+ }
+ else {
+ BadCond(Flaw, "Underflow can stick at an allegedly positive\n");
+ printf("value PseudoZero that prints out as %g .\n", PseudoZero);
+ }
+ TstPtUf();
+ }
+ /*=============================================*/
+ Milestone = 120;
+ /*=============================================*/
+ if (CInvrse * Y > CInvrse * Y1) {
+ S = H * S;
+ E0 = Underflow;
+ }
+ if (! ((E1 == Zero) || (E1 == E0))) {
+ BadCond(Defect, "");
+ if (E1 < E0) {
+ printf("Products underflow at a higher");
+ printf(" threshold than differences.\n");
+ if (PseudoZero == Zero)
+ E0 = E1;
+ }
+ else {
+ printf("Difference underflows at a higher");
+ printf(" threshold than products.\n");
+ }
+ }
+ printf("Smallest strictly positive number found is E0 = %g .\n", E0);
+ Z = E0;
+ TstPtUf();
+ Underflow = E0;
+ if (N == 1) Underflow = Y;
+ I = 4;
+ if (E1 == Zero) I = 3;
+ if (UfThold == Zero) I = I - 2;
+ UfNGrad = True;
+ switch (I) {
+ case 1:
+ UfThold = Underflow;
+ if ((CInvrse * Q) != ((CInvrse * Y) * S)) {
+ UfThold = Y;
+ BadCond(Failure, "Either accuracy deteriorates as numbers\n");
+ printf("approach a threshold = %.17e\n", UfThold);;
+ printf(" coming down from %.17e\n", C);
+ printf(" or else multiplication gets too many last digits wrong.\n");
+ }
+ Pause();
+ break;
+
+ case 2:
+ BadCond(Failure, "Underflow confuses Comparison which alleges that\n");
+ printf("Q == Y while denying that |Q - Y| == 0; these values\n");
+ printf("print out as Q = %.17e, Y = %.17e .\n", Q, Y);
+ printf ("|Q - Y| = %.17e .\n" , FABS(Q - Y2));
+ UfThold = Q;
+ break;
+
+ case 3:
+ X = X;
+ break;
+
+ case 4:
+ if ((Q == UfThold) && (E1 == E0)
+ && (FABS( UfThold - E1 / E9) <= E1)) {
+ UfNGrad = False;
+ printf("Underflow is gradual; it incurs Absolute Error =\n");
+ printf("(roundoff in UfThold) < E0.\n");
+ Y = E0 * CInvrse;
+ Y = Y * (OneAndHalf + U2);
+ X = CInvrse * (One + U2);
+ Y = Y / X;
+ IEEE = (Y == E0);
+ }
+ }
+ if (UfNGrad) {
+ printf("\n");
+ R = SQRT(Underflow / UfThold);
+ if (R <= H) {
+ Z = R * UfThold;
+ X = Z * (One + R * H * (One + H));
+ }
+ else {
+ Z = UfThold;
+ X = Z * (One + H * H * (One + H));
+ }
+ if (! ((X == Z) || (X - Z != Zero))) {
+ BadCond(Flaw, "");
+ printf("X = %.17e\n\tis not equal to Z = %.17e .\n", X, Z);
+ Z9 = X - Z;
+ printf("yet X - Z yields %.17e .\n", Z9);
+ printf(" Should this NOT signal Underflow, ");
+ printf("this is a SERIOUS DEFECT\nthat causes ");
+ printf("confusion when innocent statements like\n");;
+ printf(" if (X == Z) ... else");
+ printf(" ... (f(X) - f(Z)) / (X - Z) ...\n");
+ printf("encounter Division by Zero although actually\n");
+ printf("X / Z = 1 + %g .\n", (X / Z - Half) - Half);
+ }
+ }
+ printf("The Underflow threshold is %.17e, %s\n", UfThold,
+ " below which");
+ printf("calculation may suffer larger Relative error than ");
+ printf("merely roundoff.\n");
+ Y2 = U1 * U1;
+ Y = Y2 * Y2;
+ Y2 = Y * U1;
+ if (Y2 <= UfThold) {
+ if (Y > E0) {
+ BadCond(Defect, "");
+ I = 5;
+ }
+ else {
+ BadCond(Serious, "");
+ I = 4;
+ }
+ printf("Range is too narrow; U1^%d Underflows.\n", I);
+ }
+ /*=============================================*/
+ /*SPLIT
+ }
+#include "paranoia.h"
+part7(){
+*/
+ Milestone = 130;
+ /*=============================================*/
+ Y = - FLOOR(Half - TwoForty * LOG(UfThold) / LOG(HInvrse)) / TwoForty;
+ Y2 = Y + Y;
+ printf("Since underflow occurs below the threshold\n");
+ printf("UfThold = (%.17e) ^ (%.17e)\nonly underflow ", HInvrse, Y);
+ printf("should afflict the expression\n\t(%.17e) ^ (%.17e);\n", HInvrse, Y);
+ V9 = POW(HInvrse, Y2);
+ printf("actually calculating yields: %.17e .\n", V9);
+ if (! ((V9 >= Zero) && (V9 <= (Radix + Radix + E9) * UfThold))) {
+ BadCond(Serious, "this is not between 0 and underflow\n");
+ printf(" threshold = %.17e .\n", UfThold);
+ }
+ else if (! (V9 > UfThold * (One + E9)))
+ printf("This computed value is O.K.\n");
+ else {
+ BadCond(Defect, "this is not between 0 and underflow\n");
+ printf(" threshold = %.17e .\n", UfThold);
+ }
+ /*=============================================*/
+ Milestone = 140;
+ /*=============================================*/
+ printf("\n");
+ /* ...calculate Exp2 == exp(2) == 7.389056099... */
+ X = Zero;
+ I = 2;
+ Y = Two * Three;
+ Q = Zero;
+ N = 0;
+ do {
+ Z = X;
+ I = I + 1;
+ Y = Y / (I + I);
+ R = Y + Q;
+ X = Z + R;
+ Q = (Z - X) + R;
+ } while(X > Z);
+ Z = (OneAndHalf + One / Eight) + X / (OneAndHalf * ThirtyTwo);
+ X = Z * Z;
+ Exp2 = X * X;
+ X = F9;
+ Y = X - U1;
+ printf("Testing X^((X + 1) / (X - 1)) vs. exp(2) = %.17e as X -> 1.\n",
+ Exp2);
+ for(I = 1;;) {
+ Z = X - BInvrse;
+ Z = (X + One) / (Z - (One - BInvrse));
+ Q = POW(X, Z) - Exp2;
+ if (FABS(Q) > TwoForty * U2) {
+ N = 1;
+ V9 = (X - BInvrse) - (One - BInvrse);
+ BadCond(Defect, "Calculated");
+ printf(" %.17e for\n", POW(X,Z));
+ printf("\t(1 + (%.17e) ^ (%.17e);\n", V9, Z);
+ printf("\tdiffers from correct value by %.17e .\n", Q);
+ printf("\tThis much error may spoil financial\n");
+ printf("\tcalculations involving tiny interest rates.\n");
+ break;
+ }
+ else {
+ Z = (Y - X) * Two + Y;
+ X = Y;
+ Y = Z;
+ Z = One + (X - F9)*(X - F9);
+ if (Z > One && I < NoTrials) I++;
+ else {
+ if (X > One) {
+ if (N == 0)
+ printf("Accuracy seems adequate.\n");
+ break;
+ }
+ else {
+ X = One + U2;
+ Y = U2 + U2;
+ Y += X;
+ I = 1;
+ }
+ }
+ }
+ }
+ /*=============================================*/
+ Milestone = 150;
+ /*=============================================*/
+ printf("Testing powers Z^Q at four nearly extreme values.\n");
+ N = 0;
+ Z = A1;
+ Q = FLOOR(Half - LOG(C) / LOG(A1));
+ Break = False;
+ do {
+ X = CInvrse;
+ Y = POW(Z, Q);
+ IsYeqX();
+ Q = - Q;
+ X = C;
+ Y = POW(Z, Q);
+ IsYeqX();
+ if (Z < One) Break = True;
+ else Z = AInvrse;
+ } while ( ! (Break));
+ PrintIfNPositive();
+ if (N == 0) printf(" ... no discrepancies found.\n");
+ printf("\n");
+
+ /*=============================================*/
+ Milestone = 160;
+ /*=============================================*/
+ Pause();
+ printf("Searching for Overflow threshold:\n");
+ printf("This may generate an error.\n");
+ sigsave = sigfpe;
+ I = 0;
+ Y = - CInvrse;
+ V9 = HInvrse * Y;
+ if (setjmp(ovfl_buf)) goto overflow;
+ do {
+ V = Y;
+ Y = V9;
+ V9 = HInvrse * Y;
+ } while(V9 < Y);
+ I = 1;
+overflow:
+ Z = V9;
+ printf("Can `Z = -Y' overflow?\n");
+ printf("Trying it on Y = %.17e .\n", Y);
+ V9 = - Y;
+ V0 = V9;
+ if (V - Y == V + V0) printf("Seems O.K.\n");
+ else {
+ printf("finds a ");
+ BadCond(Flaw, "-(-Y) differs from Y.\n");
+ }
+ if (Z != Y) {
+ BadCond(Serious, "");
+ printf("overflow past %.17e\n\tshrinks to %.17e .\n", Y, Z);
+ }
+ Y = V * (HInvrse * U2 - HInvrse);
+ Z = Y + ((One - HInvrse) * U2) * V;
+ if (Z < V0) Y = Z;
+ if (Y < V0) V = Y;
+ if (V0 - V < V0) V = V0;
+ printf("Overflow threshold is V = %.17e .\n", V);
+ if (I) printf("Overflow saturates at V0 = %.17e .\n", V0);
+ else printf("There is no saturation value because \
+the system traps on overflow.\n");
+ V9 = V * One;
+ printf("No Overflow should be signaled for V * 1 = %.17e\n", V9);
+ V9 = V / One;
+ printf(" nor for V / 1 = %.17e .\n", V9);
+ printf("Any overflow signal separating this * from the one\n");
+ printf("above is a DEFECT.\n");
+ /*=============================================*/
+ Milestone = 170;
+ /*=============================================*/
+ if (!(-V < V && -V0 < V0 && -UfThold < V && UfThold < V)) {
+ BadCond(Failure, "Comparisons involving ");
+ printf("+-%g, +-%g\nand +-%g are confused by Overflow.",
+ V, V0, UfThold);
+ }
+ /*=============================================*/
+ Milestone = 175;
+ /*=============================================*/
+ printf("\n");
+ for(Indx = 1; Indx <= 3; ++Indx) {
+ switch (Indx) {
+ case 1: Z = UfThold; break;
+ case 2: Z = E0; break;
+ case 3: Z = PseudoZero; break;
+ }
+ if (Z != Zero) {
+ V9 = SQRT(Z);
+ Y = V9 * V9;
+ if (Y / (One - Radix * E9) < Z
+ || Y > (One + Radix + E9) * Z) {
+ if (V9 > U1) BadCond(Serious, "");
+ else BadCond(Defect, "");
+ printf("Comparison alleges that what prints as Z = %.17e\n", Z);
+ printf(" is too far from sqrt(Z) ^ 2 = %.17e .\n", Y);
+ }
+ }
+ }
+ /*=============================================*/
+ Milestone = 180;
+ /*=============================================*/
+ for(Indx = 1; Indx <= 2; ++Indx) {
+ if (Indx == 1) Z = V;
+ else Z = V0;
+ V9 = SQRT(Z);
+ X = (One - Radix * E9) * V9;
+ V9 = V9 * X;
+ if (((V9 < (One - Two * Radix * E9) * Z) || (V9 > Z))) {
+ Y = V9;
+ if (X < W) BadCond(Serious, "");
+ else BadCond(Defect, "");
+ printf("Comparison alleges that Z = %17e\n", Z);
+ printf(" is too far from sqrt(Z) ^ 2 (%.17e) .\n", Y);
+ }
+ }
+ /*=============================================*/
+ /*SPLIT
+ }
+#include "paranoia.h"
+part8(){
+*/
+ Milestone = 190;
+ /*=============================================*/
+ Pause();
+ X = UfThold * V;
+ Y = Radix * Radix;
+ if (X*Y < One || X > Y) {
+ if (X * Y < U1 || X > Y/U1) BadCond(Defect, "Badly");
+ else BadCond(Flaw, "");
+
+ printf(" unbalanced range; UfThold * V = %.17e\n\t%s\n",
+ X, "is too far from 1.\n");
+ }
+ /*=============================================*/
+ Milestone = 200;
+ /*=============================================*/
+ for (Indx = 1; Indx <= 5; ++Indx) {
+ X = F9;
+ switch (Indx) {
+ case 2: X = One + U2; break;
+ case 3: X = V; break;
+ case 4: X = UfThold; break;
+ case 5: X = Radix;
+ }
+ Y = X;
+ sigsave = sigfpe;
+ if (setjmp(ovfl_buf))
+ printf(" X / X traps when X = %g\n", X);
+ else {
+ V9 = (Y / X - Half) - Half;
+ if (V9 == Zero) continue;
+ if (V9 == - U1 && Indx < 5) BadCond(Flaw, "");
+ else BadCond(Serious, "");
+ printf(" X / X differs from 1 when X = %.17e\n", X);
+ printf(" instead, X / X - 1/2 - 1/2 = %.17e .\n", V9);
+ }
+ }
+ /*=============================================*/
+ Milestone = 210;
+ /*=============================================*/
+ MyZero = Zero;
+ printf("\n");
+ printf("What message and/or values does Division by Zero produce?\n") ;
+#ifndef NOPAUSE
+ printf("This can interupt your program. You can ");
+ printf("skip this part if you wish.\n");
+ printf("Do you wish to compute 1 / 0? ");
+ fflush(stdout);
+ read (KEYBOARD, ch, 8);
+ if ((ch[0] == 'Y') || (ch[0] == 'y')) {
+#endif
+ sigsave = sigfpe;
+ printf(" Trying to compute 1 / 0 produces ...");
+ if (!setjmp(ovfl_buf)) printf(" %.7e .\n", One / MyZero);
+#ifndef NOPAUSE
+ }
+ else printf("O.K.\n");
+ printf("\nDo you wish to compute 0 / 0? ");
+ fflush(stdout);
+ read (KEYBOARD, ch, 80);
+ if ((ch[0] == 'Y') || (ch[0] == 'y')) {
+#endif
+ sigsave = sigfpe;
+ printf("\n Trying to compute 0 / 0 produces ...");
+ if (!setjmp(ovfl_buf)) printf(" %.7e .\n", Zero / MyZero);
+#ifndef NOPAUSE
+ }
+ else printf("O.K.\n");
+#endif
+ /*=============================================*/
+ Milestone = 220;
+ /*=============================================*/
+ Pause();
+ printf("\n");
+ {
+ static char *msg[] = {
+ "FAILUREs encountered =",
+ "SERIOUS DEFECTs discovered =",
+ "DEFECTs discovered =",
+ "FLAWs discovered =" };
+ int i;
+ for(i = 0; i < 4; i++) if (ErrCnt[i])
+ printf("The number of %-29s %d.\n",
+ msg[i], ErrCnt[i]);
+ }
+ printf("\n");
+ if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[Defect]
+ + ErrCnt[Flaw]) > 0) {
+ if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[
+ Defect] == 0) && (ErrCnt[Flaw] > 0)) {
+ printf("The arithmetic diagnosed seems ");
+ printf("satisfactory though flawed.\n");
+ }
+ if ((ErrCnt[Failure] + ErrCnt[Serious] == 0)
+ && ( ErrCnt[Defect] > 0)) {
+ printf("The arithmetic diagnosed may be acceptable\n");
+ printf("despite inconvenient Defects.\n");
+ }
+ if ((ErrCnt[Failure] + ErrCnt[Serious]) > 0) {
+ printf("The arithmetic diagnosed has ");
+ printf("unacceptable serious defects.\n");
+ }
+ if (ErrCnt[Failure] > 0) {
+ printf("Fatal FAILURE may have spoiled this");
+ printf(" program's subsequent diagnoses.\n");
+ }
+ }
+ else {
+ printf("No failures, defects nor flaws have been discovered.\n");
+ if (! ((RMult == Rounded) && (RDiv == Rounded)
+ && (RAddSub == Rounded) && (RSqrt == Rounded)))
+ printf("The arithmetic diagnosed seems satisfactory.\n");
+ else {
+ if (StickyBit >= One &&
+ (Radix - Two) * (Radix - Nine - One) == Zero) {
+ printf("Rounding appears to conform to ");
+ printf("the proposed IEEE standard P");
+ if ((Radix == Two) &&
+ ((Precision - Four * Three * Two) *
+ ( Precision - TwentySeven -
+ TwentySeven + One) == Zero))
+ printf("754");
+ else printf("854");
+ if (IEEE) printf(".\n");
+ else {
+ printf(",\nexcept for possibly Double Rounding");
+ printf(" during Gradual Underflow.\n");
+ }
+ }
+ printf("The arithmetic diagnosed appears to be excellent!\n");
+ }
+ }
+ if (fpecount)
+ printf("\nA total of %d floating point exceptions were registered.\n",
+ fpecount);
+ printf("END OF TEST.\n");
+ }
+
+/*SPLIT subs.c
+#include "paranoia.h"
+*/
+
+/* Sign */
+
+FLOAT Sign (X)
+FLOAT X;
+{ return X >= 0. ? 1.0 : -1.0; }
+
+/* Pause */
+
+Pause()
+{
+ char ch[8];
+
+#ifndef NOPAUSE
+ printf("\nTo continue, press RETURN");
+ fflush(stdout);
+ read(KEYBOARD, ch, 8);
+#endif
+ printf("\nDiagnosis resumes after milestone Number %d", Milestone);
+ printf(" Page: %d\n\n", PageNo);
+ ++Milestone;
+ ++PageNo;
+ }
+
+ /* TstCond */
+
+TstCond (K, Valid, T)
+int K, Valid;
+char *T;
+{ if (! Valid) { BadCond(K,T); printf(".\n"); } }
+
+BadCond(K, T)
+int K;
+char *T;
+{
+ static char *msg[] = { "FAILURE", "SERIOUS DEFECT", "DEFECT", "FLAW" };
+
+ ErrCnt [K] = ErrCnt [K] + 1;
+ printf("%s: %s", msg[K], T);
+ }
+
+/* Random */
+/* Random computes
+ X = (Random1 + Random9)^5
+ Random1 = X - FLOOR(X) + 0.000005 * X;
+ and returns the new value of Random1
+*/
+
+FLOAT Random()
+{
+ FLOAT X, Y;
+
+ X = Random1 + Random9;
+ Y = X * X;
+ Y = Y * Y;
+ X = X * Y;
+ Y = X - FLOOR(X);
+ Random1 = Y + X * 0.000005;
+ return(Random1);
+ }
+
+/* SqXMinX */
+
+SqXMinX (ErrKind)
+int ErrKind;
+{
+ FLOAT XA, XB;
+
+ XB = X * BInvrse;
+ XA = X - XB;
+ SqEr = ((SQRT(X * X) - XB) - XA) / OneUlp;
+ if (SqEr != Zero) {
+ if (SqEr < MinSqEr) MinSqEr = SqEr;
+ if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+ J = J + 1.0;
+ BadCond(ErrKind, "\n");
+ printf("sqrt( %.17e) - %.17e = %.17e\n", X * X, X, OneUlp * SqEr);
+ printf("\tinstead of correct value 0 .\n");
+ }
+ }
+
+/* NewD */
+
+NewD()
+{
+ X = Z1 * Q;
+ X = FLOOR(Half - X / Radix) * Radix + X;
+ Q = (Q - X * Z) / Radix + X * X * (D / Radix);
+ Z = Z - Two * X * D;
+ if (Z <= Zero) {
+ Z = - Z;
+ Z1 = - Z1;
+ }
+ D = Radix * D;
+ }
+
+/* SR3750 */
+
+SR3750()
+{
+ if (! ((X - Radix < Z2 - Radix) || (X - Z2 > W - Z2))) {
+ I = I + 1;
+ X2 = SQRT(X * D);
+ Y2 = (X2 - Z2) - (Y - Z2);
+ X2 = X8 / (Y - Half);
+ X2 = X2 - Half * X2 * X2;
+ SqEr = (Y2 + Half) + (Half - X2);
+ if (SqEr < MinSqEr) MinSqEr = SqEr;
+ SqEr = Y2 - X2;
+ if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+ }
+ }
+
+/* IsYeqX */
+
+IsYeqX()
+{
+ if (Y != X) {
+ if (N <= 0) {
+ if (Z == Zero && Q <= Zero)
+ printf("WARNING: computing\n");
+ else BadCond(Defect, "computing\n");
+ printf("\t(%.17e) ^ (%.17e)\n", Z, Q);
+ printf("\tyielded %.17e;\n", Y);
+ printf("\twhich compared unequal to correct %.17e ;\n",
+ X);
+ printf("\t\tthey differ by %.17e .\n", Y - X);
+ }
+ N = N + 1; /* ... count discrepancies. */
+ }
+ }
+
+/* SR3980 */
+
+SR3980()
+{
+ do {
+ Q = (FLOAT) I;
+ Y = POW(Z, Q);
+ IsYeqX();
+ if (++I > M) break;
+ X = Z * X;
+ } while ( X < W );
+ }
+
+/* PrintIfNPositive */
+
+PrintIfNPositive()
+{
+ if (N > 0) printf("Similar discrepancies have occurred %d times.\n", N);
+ }
+
+/* TstPtUf */
+
+TstPtUf()
+{
+ N = 0;
+ if (Z != Zero) {
+ printf("Since comparison denies Z = 0, evaluating ");
+ printf("(Z + Z) / Z should be safe.\n");
+ sigsave = sigfpe;
+ if (setjmp(ovfl_buf)) goto very_serious;
+ Q9 = (Z + Z) / Z;
+ printf("What the machine gets for (Z + Z) / Z is %.17e .\n",
+ Q9);
+ if (FABS(Q9 - Two) < Radix * U2) {
+ printf("This is O.K., provided Over/Underflow");
+ printf(" has NOT just been signaled.\n");
+ }
+ else {
+ if ((Q9 < One) || (Q9 > Two)) {
+very_serious:
+ N = 1;
+ ErrCnt [Serious] = ErrCnt [Serious] + 1;
+ printf("This is a VERY SERIOUS DEFECT!\n");
+ }
+ else {
+ N = 1;
+ ErrCnt [Defect] = ErrCnt [Defect] + 1;
+ printf("This is a DEFECT!\n");
+ }
+ }
+ V9 = Z * One;
+ Random1 = V9;
+ V9 = One * Z;
+ Random2 = V9;
+ V9 = Z / One;
+ if ((Z == Random1) && (Z == Random2) && (Z == V9)) {
+ if (N > 0) Pause();
+ }
+ else {
+ N = 1;
+ BadCond(Defect, "What prints as Z = ");
+ printf("%.17e\n\tcompares different from ", Z);
+ if (Z != Random1) printf("Z * 1 = %.17e ", Random1);
+ if (! ((Z == Random2)
+ || (Random2 == Random1)))
+ printf("1 * Z == %g\n", Random2);
+ if (! (Z == V9)) printf("Z / 1 = %.17e\n", V9);
+ if (Random2 != Random1) {
+ ErrCnt [Defect] = ErrCnt [Defect] + 1;
+ BadCond(Defect, "Multiplication does not commute!\n");
+ printf("\tComparison alleges that 1 * Z = %.17e\n",
+ Random2);
+ printf("\tdiffers from Z * 1 = %.17e\n", Random1);
+ }
+ Pause();
+ }
+ }
+ }
+
+notify(s)
+char *s;
+{
+ printf("%s test appears to be inconsistent...\n", s);
+ printf(" PLEASE NOTIFY KARPINKSI!\n");
+ }
+
+/*SPLIT msgs.c */
+
+/* Instructions */
+
+msglist(s)
+char **s;
+{ while(*s) printf("%s\n", *s++); }
+
+Instructions()
+{
+ static char *instr[] = {
+ "Lest this program stop prematurely, i.e. before displaying\n",
+ " `END OF TEST',\n",
+ "try to persuade the computer NOT to terminate execution when an",
+ "error like Over/Underflow or Division by Zero occurs, but rather",
+ "to persevere with a surrogate value after, perhaps, displaying some",
+ "warning. If persuasion avails naught, don't despair but run this",
+ "program anyway to see how many milestones it passes, and then",
+ "amend it to make further progress.\n",
+ "Answer questions with Y, y, N or n (unless otherwise indicated).\n",
+ 0};
+
+ msglist(instr);
+ }
+
+/* Heading */
+
+Heading()
+{
+ static char *head[] = {
+ "Users are invited to help debug and augment this program so it will",
+ "cope with unanticipated and newly uncovered arithmetic pathologies.\n",
+ "Please send suggestions and interesting results to",
+ "\tRichard Karpinski",
+ "\tComputer Center U-76",
+ "\tUniversity of California",
+ "\tSan Francisco, CA 94143-0704, USA\n",
+ "In doing so, please include the following information:",
+#ifdef Single
+ "\tPrecision:\tsingle;",
+#else
+ "\tPrecision:\tdouble;",
+#endif
+ "\tVersion:\t27 January 1986;",
+ "\tComputer:\n",
+ "\tCompiler:\n",
+ "\tOptimization level:\n",
+ "\tOther relevant compiler options:",
+ 0};
+
+ msglist(head);
+ }
+
+/* Characteristics */
+
+Characteristics()
+{
+ static char *chars[] = {
+ "Running this program should reveal these characteristics:",
+ " Radix = 1, 2, 4, 8, 10, 16, 100, 256 ...",
+ " Precision = number of significant digits carried.",
+ " U2 = Radix/Radix^Precision = One Ulp",
+ "\t(OneUlpnit in the Last Place) of 1.000xxx .",
+ " U1 = 1/Radix^Precision = One Ulp of numbers a little less than 1.0 .",
+ " Adequacy of guard digits for Mult., Div. and Subt.",
+ " Whether arithmetic is chopped, correctly rounded, or something else",
+ "\tfor Mult., Div., Add/Subt. and Sqrt.",
+ " Whether a Sticky Bit used correctly for rounding.",
+ " UnderflowThreshold = an underflow threshold.",
+ " E0 and PseudoZero tell whether underflow is abrupt, gradual, or fuzzy.",
+ " V = an overflow threshold, roughly.",
+ " V0 tells, roughly, whether Infinity is represented.",
+ " Comparisions are checked for consistency with subtraction",
+ "\tand for contamination with pseudo-zeros.",
+ " Sqrt is tested. Y^X is not tested.",
+ " Extra-precise subexpressions are revealed but NOT YET tested.",
+ " Decimal-Binary conversion is NOT YET tested for accuracy.",
+ 0};
+
+ msglist(chars);
+ }
+
+History()
+
+{ /* History */
+ /* Converted from Brian Wichmann's Pascal version to C by Thos Sumner,
+ with further massaging by David M. Gay. */
+
+ static char *hist[] = {
+ "The program attempts to discriminate among",
+ " FLAWs, like lack of a sticky bit,",
+ " Serious DEFECTs, like lack of a guard digit, and",
+ " FAILUREs, like 2+2 == 5 .",
+ "Failures may confound subsequent diagnoses.\n",
+ "The diagnostic capabilities of this program go beyond an earlier",
+ "program called `MACHAR', which can be found at the end of the",
+ "book `Software Manual for the Elementary Functions' (1980) by",
+ "W. J. Cody and W. Waite. Although both programs try to discover",
+ "the Radix, Precision and range (over/underflow thresholds)",
+ "of the arithmetic, this program tries to cope with a wider variety",
+ "of pathologies, and to say how well the arithmetic is implemented.",
+ "\nThe program is based upon a conventional radix representation for",
+ "floating-point numbers, but also allows logarithmic encoding",
+ "as used by certain early WANG machines.\n",
+ "BASIC version of this program (C) 1983 by Prof. W. M. Kahan;",
+ "see source comments for more history.",
+ 0};
+
+ msglist(hist);
+ }
diff --git a/libm/double/pdtr.c b/libm/double/pdtr.c
new file mode 100644
index 000000000..5b4ae4054
--- /dev/null
+++ b/libm/double/pdtr.c
@@ -0,0 +1,184 @@
+/* pdtr.c
+ *
+ * Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * double m, y, pdtr();
+ *
+ * y = pdtr( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the first k terms of the Poisson
+ * distribution:
+ *
+ * k j
+ * -- -m m
+ * > e --
+ * -- j!
+ * j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the relation
+ *
+ * y = pdtr( k, m ) = igamc( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ */
+ /* pdtrc()
+ *
+ * Complemented poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * double m, y, pdtrc();
+ *
+ * y = pdtrc( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the Poisson
+ * distribution:
+ *
+ * inf. j
+ * -- -m m
+ * > e --
+ * -- j!
+ * j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the formula
+ *
+ * y = pdtrc( k, m ) = igam( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam.c.
+ *
+ */
+ /* pdtri()
+ *
+ * Inverse Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * double m, y, pdtr();
+ *
+ * m = pdtri( k, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Poisson variable x such that the integral
+ * from 0 to x of the Poisson density is equal to the
+ * given probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ * m = igami( k+1, y ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igami.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * pdtri domain y < 0 or y >= 1 0.0
+ * k < 0
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double igam ( double, double );
+extern double igamc ( double, double );
+extern double igami ( double, double );
+#else
+double igam(), igamc(), igami();
+#endif
+
+double pdtrc( k, m )
+int k;
+double m;
+{
+double v;
+
+if( (k < 0) || (m <= 0.0) )
+ {
+ mtherr( "pdtrc", DOMAIN );
+ return( 0.0 );
+ }
+v = k+1;
+return( igam( v, m ) );
+}
+
+
+
+double pdtr( k, m )
+int k;
+double m;
+{
+double v;
+
+if( (k < 0) || (m <= 0.0) )
+ {
+ mtherr( "pdtr", DOMAIN );
+ return( 0.0 );
+ }
+v = k+1;
+return( igamc( v, m ) );
+}
+
+
+double pdtri( k, y )
+int k;
+double y;
+{
+double v;
+
+if( (k < 0) || (y < 0.0) || (y >= 1.0) )
+ {
+ mtherr( "pdtri", DOMAIN );
+ return( 0.0 );
+ }
+v = k+1;
+v = igami( v, y );
+return( v );
+}
diff --git a/libm/double/planck.c b/libm/double/planck.c
new file mode 100644
index 000000000..834c85dff
--- /dev/null
+++ b/libm/double/planck.c
@@ -0,0 +1,223 @@
+/* planck.c
+ *
+ * Integral of Planck's black body radiation formula
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double lambda, T, y, plancki();
+ *
+ * y = plancki( lambda, T );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the definite integral, from wavelength 0 to lambda,
+ * of Planck's radiation formula
+ * -5
+ * c1 lambda
+ * E = ------------------
+ * c2/(lambda T)
+ * e - 1
+ *
+ * Physical constants c1 = 3.7417749e-16 and c2 = 0.01438769 are built in
+ * to the function program. They are scaled to provide a result
+ * in watts per square meter. Argument T represents temperature in degrees
+ * Kelvin; lambda is wavelength in meters.
+ *
+ * The integral is expressed in closed form, in terms of polylogarithms
+ * (see polylog.c).
+ *
+ * The total area under the curve is
+ * (-1/8) (42 zeta(4) - 12 pi^2 zeta(2) + pi^4 ) c1 (T/c2)^4
+ * = (pi^4 / 15) c1 (T/c2)^4
+ * = 5.6705032e-8 T^4
+ * where sigma = 5.6705032e-8 W m^2 K^-4 is the Stefan-Boltzmann constant.
+ *
+ *
+ * ACCURACY:
+ *
+ * The left tail of the function experiences some relative error
+ * amplification in computing the dominant term exp(-c2/(lambda T)).
+ * For the right-hand tail see planckc, below.
+ *
+ * Relative error.
+ * The domain refers to lambda T / c2.
+ * arithmetic domain # trials peak rms
+ * IEEE 0.1, 10 50000 7.1e-15 5.4e-16
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8: July, 1999
+Copyright 1999 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double polylog (int, double);
+extern double exp (double);
+extern double log1p (double); /* log(1+x) */
+extern double expm1 (double); /* exp(x) - 1 */
+double planckc(double, double);
+double plancki(double, double);
+#else
+double polylog(), exp(), log1p(), expm1();
+double planckc(), plancki();
+#endif
+
+/* NIST value (1999): 2 pi h c^2 = 3.741 7749(22) × 10-16 W m2 */
+double planck_c1 = 3.7417749e-16;
+/* NIST value (1999): h c / k = 0.014 387 69 m K */
+double planck_c2 = 0.01438769;
+
+
+double
+plancki(w, T)
+ double w, T;
+{
+ double b, h, y, bw;
+
+ b = T / planck_c2;
+ bw = b * w;
+
+ if (bw > 0.59375)
+ {
+ y = b * b;
+ h = y * y;
+ /* Right tail. */
+ y = planckc (w, T);
+ /* pi^4 / 15 */
+ y = 6.493939402266829149096 * planck_c1 * h - y;
+ return y;
+ }
+
+ h = exp(-planck_c2/(w*T));
+ y = 6. * polylog (4, h) * bw;
+ y = (y + 6. * polylog (3, h)) * bw;
+ y = (y + 3. * polylog (2, h)) * bw;
+ y = (y - log1p (-h)) * bw;
+ h = w * w;
+ h = h * h;
+ y = y * (planck_c1 / h);
+ return y;
+}
+
+/* planckc
+ *
+ * Complemented Planck radiation integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double lambda, T, y, planckc();
+ *
+ * y = planckc( lambda, T );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Integral from w to infinity (area under right hand tail)
+ * of Planck's radiation formula.
+ *
+ * The program for large lambda uses an asymptotic series in inverse
+ * powers of the wavelength.
+ *
+ * ACCURACY:
+ *
+ * Relative error.
+ * The domain refers to lambda T / c2.
+ * arithmetic domain # trials peak rms
+ * IEEE 0.6, 10 50000 1.1e-15 2.2e-16
+ *
+ */
+
+double
+planckc (w, T)
+ double w;
+ double T;
+{
+ double b, d, p, u, y;
+
+ b = T / planck_c2;
+ d = b*w;
+ if (d <= 0.59375)
+ {
+ y = 6.493939402266829149096 * planck_c1 * b*b*b*b;
+ return (y - plancki(w,T));
+ }
+ u = 1.0/d;
+ p = u * u;
+#if 0
+ y = 236364091.*p/365866013534056632601804800000.;
+ y = (y - 15458917./475677107995483570176000000.)*p;
+ y = (y + 174611./123104841613737984000000.)*p;
+ y = (y - 43867./643745871363538944000.)*p;
+ y = ((y + 3617./1081289781411840000.)*p - 1./5928123801600.)*p;
+ y = ((y + 691./78460462080000.)*p - 1./2075673600.)*p;
+ y = ((((y + 1./35481600.)*p - 1.0/544320.)*p + 1.0/6720.)*p - 1./40.)*p;
+ y = y + log(d * expm1(u));
+ y = y - 5.*u/8. + 1./3.;
+#else
+ y = -236364091.*p/45733251691757079075225600000.;
+ y = (y + 77683./352527500984795136000000.)*p;
+ y = (y - 174611./18465726242060697600000.)*p;
+ y = (y + 43867./107290978560589824000.)*p;
+ y = ((y - 3617./202741834014720000.)*p + 1./1270312243200.)*p;
+ y = ((y - 691./19615115520000.)*p + 1./622702080.)*p;
+ y = ((((y - 1./13305600.)*p + 1./272160.)*p - 1./5040.)*p + 1./60.)*p;
+ y = y - 0.125*u + 1./3.;
+#endif
+ y = y * planck_c1 * b / (w*w*w);
+ return y;
+}
+
+
+/* planckd
+ *
+ * Planck's black body radiation formula
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double lambda, T, y, planckd();
+ *
+ * y = planckd( lambda, T );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates Planck's radiation formula
+ * -5
+ * c1 lambda
+ * E = ------------------
+ * c2/(lambda T)
+ * e - 1
+ *
+ */
+
+double
+planckd(w, T)
+ double w, T;
+{
+ return (planck_c2 / ((w*w*w*w*w) * (exp(planck_c2/(w*T)) - 1.0)));
+}
+
+
+/* Wavelength, w, of maximum radiation at given temperature T.
+ c2/wT = constant
+ Wein displacement law.
+ */
+double
+planckw(T)
+ double T;
+{
+ return (planck_c2 / (4.96511423174427630 * T));
+}
diff --git a/libm/double/polevl.c b/libm/double/polevl.c
new file mode 100644
index 000000000..4d050fbfc
--- /dev/null
+++ b/libm/double/polevl.c
@@ -0,0 +1,97 @@
+/* polevl.c
+ * p1evl.c
+ *
+ * Evaluate polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * double x, y, coef[N+1], polevl[];
+ *
+ * y = polevl( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates polynomial of degree N:
+ *
+ * 2 N
+ * y = C + C x + C x +...+ C x
+ * 0 1 2 N
+ *
+ * Coefficients are stored in reverse order:
+ *
+ * coef[0] = C , ..., coef[N] = C .
+ * N 0
+ *
+ * The function p1evl() assumes that coef[N] = 1.0 and is
+ * omitted from the array. Its calling arguments are
+ * otherwise the same as polevl().
+ *
+ *
+ * SPEED:
+ *
+ * In the interest of speed, there are no checks for out
+ * of bounds arithmetic. This routine is used by most of
+ * the functions in the library. Depending on available
+ * equipment features, the user may wish to rewrite the
+ * program in microcode or assembly language.
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.1: December, 1988
+Copyright 1984, 1987, 1988 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+double polevl( x, coef, N )
+double x;
+double coef[];
+int N;
+{
+double ans;
+int i;
+double *p;
+
+p = coef;
+ans = *p++;
+i = N;
+
+do
+ ans = ans * x + *p++;
+while( --i );
+
+return( ans );
+}
+
+/* p1evl() */
+/* N
+ * Evaluate polynomial when coefficient of x is 1.0.
+ * Otherwise same as polevl.
+ */
+
+double p1evl( x, coef, N )
+double x;
+double coef[];
+int N;
+{
+double ans;
+double *p;
+int i;
+
+p = coef;
+ans = x + *p++;
+i = N-1;
+
+do
+ ans = ans * x + *p++;
+while( --i );
+
+return( ans );
+}
diff --git a/libm/double/polmisc.c b/libm/double/polmisc.c
new file mode 100644
index 000000000..7d517ae69
--- /dev/null
+++ b/libm/double/polmisc.c
@@ -0,0 +1,309 @@
+
+/* Square root, sine, cosine, and arctangent of polynomial.
+ * See polyn.c for data structures and discussion.
+ */
+
+#include <stdio.h>
+#include <math.h>
+#ifdef ANSIPROT
+extern double atan2 ( double, double );
+extern double sqrt ( double );
+extern double fabs ( double );
+extern double sin ( double );
+extern double cos ( double );
+extern void polclr ( double *a, int n );
+extern void polmov ( double *a, int na, double *b );
+extern void polmul ( double a[], int na, double b[], int nb, double c[] );
+extern void poladd ( double a[], int na, double b[], int nb, double c[] );
+extern void polsub ( double a[], int na, double b[], int nb, double c[] );
+extern int poldiv ( double a[], int na, double b[], int nb, double c[] );
+extern void polsbt ( double a[], int na, double b[], int nb, double c[] );
+extern void * malloc ( long );
+extern void free ( void * );
+#else
+double atan2(), sqrt(), fabs(), sin(), cos();
+void polclr(), polmov(), polsbt(), poladd(), polsub(), polmul();
+int poldiv();
+void * malloc();
+void free ();
+#endif
+
+/* Highest degree of polynomial to be handled
+ by the polyn.c subroutine package. */
+#define N 16
+/* Highest degree actually initialized at runtime. */
+extern int MAXPOL;
+
+/* Taylor series coefficients for various functions
+ */
+double patan[N+1] = {
+ 0.0, 1.0, 0.0, -1.0/3.0, 0.0,
+ 1.0/5.0, 0.0, -1.0/7.0, 0.0, 1.0/9.0, 0.0, -1.0/11.0,
+ 0.0, 1.0/13.0, 0.0, -1.0/15.0, 0.0 };
+
+double psin[N+1] = {
+ 0.0, 1.0, 0.0, -1.0/6.0, 0.0, 1.0/120.0, 0.0,
+ -1.0/5040.0, 0.0, 1.0/362880.0, 0.0, -1.0/39916800.0,
+ 0.0, 1.0/6227020800.0, 0.0, -1.0/1.307674368e12, 0.0};
+
+double pcos[N+1] = {
+ 1.0, 0.0, -1.0/2.0, 0.0, 1.0/24.0, 0.0,
+ -1.0/720.0, 0.0, 1.0/40320.0, 0.0, -1.0/3628800.0, 0.0,
+ 1.0/479001600.0, 0.0, -1.0/8.7179291e10, 0.0, 1.0/2.0922789888e13};
+
+double pasin[N+1] = {
+ 0.0, 1.0, 0.0, 1.0/6.0, 0.0,
+ 3.0/40.0, 0.0, 15.0/336.0, 0.0, 105.0/3456.0, 0.0, 945.0/42240.0,
+ 0.0, 10395.0/599040.0 , 0.0, 135135.0/9676800.0 , 0.0
+};
+
+/* Square root of 1 + x. */
+double psqrt[N+1] = {
+ 1.0, 1./2., -1./8., 1./16., -5./128., 7./256., -21./1024., 33./2048.,
+ -429./32768., 715./65536., -2431./262144., 4199./524288., -29393./4194304.,
+ 52003./8388608., -185725./33554432., 334305./67108864.,
+ -9694845./2147483648.};
+
+/* Arctangent of the ratio num/den of two polynomials.
+ */
+void
+polatn( num, den, ans, nn )
+ double num[], den[], ans[];
+ int nn;
+{
+ double a, t;
+ double *polq, *polu, *polt;
+ int i;
+
+ if (nn > N)
+ {
+ mtherr ("polatn", OVERFLOW);
+ return;
+ }
+ /* arctan( a + b ) = arctan(a) + arctan( b/(1 + ab + a**2) ) */
+ t = num[0];
+ a = den[0];
+ if( (t == 0.0) && (a == 0.0 ) )
+ {
+ t = num[1];
+ a = den[1];
+ }
+ t = atan2( t, a ); /* arctan(num/den), the ANSI argument order */
+ polq = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ polu = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ polt = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ polclr( polq, MAXPOL );
+ i = poldiv( den, nn, num, nn, polq );
+ a = polq[0]; /* a */
+ polq[0] = 0.0; /* b */
+ polmov( polq, nn, polu ); /* b */
+ /* Form the polynomial
+ 1 + ab + a**2
+ where a is a scalar. */
+ for( i=0; i<=nn; i++ )
+ polu[i] *= a;
+ polu[0] += 1.0 + a * a;
+ poldiv( polu, nn, polq, nn, polt ); /* divide into b */
+ polsbt( polt, nn, patan, nn, polu ); /* arctan(b) */
+ polu[0] += t; /* plus arctan(a) */
+ polmov( polu, nn, ans );
+ free( polt );
+ free( polu );
+ free( polq );
+}
+
+
+
+/* Square root of a polynomial.
+ * Assumes the lowest degree nonzero term is dominant
+ * and of even degree. An error message is given
+ * if the Newton iteration does not converge.
+ */
+void
+polsqt( pol, ans, nn )
+ double pol[], ans[];
+ int nn;
+{
+ double t;
+ double *x, *y;
+ int i, n;
+#if 0
+ double z[N+1];
+ double u;
+#endif
+
+ if (nn > N)
+ {
+ mtherr ("polatn", OVERFLOW);
+ return;
+ }
+ x = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ y = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ polmov( pol, nn, x );
+ polclr( y, MAXPOL );
+
+ /* Find lowest degree nonzero term. */
+ t = 0.0;
+ for( n=0; n<nn; n++ )
+ {
+ if( x[n] != 0.0 )
+ goto nzero;
+ }
+ polmov( y, nn, ans );
+ return;
+
+nzero:
+
+ if( n > 0 )
+ {
+ if (n & 1)
+ {
+ printf("error, sqrt of odd polynomial\n");
+ return;
+ }
+ /* Divide by x^n. */
+ y[n] = x[n];
+ poldiv (y, nn, pol, N, x);
+ }
+
+ t = x[0];
+ for( i=1; i<=nn; i++ )
+ x[i] /= t;
+ x[0] = 0.0;
+ /* series development sqrt(1+x) = 1 + x / 2 - x**2 / 8 + x**3 / 16
+ hopes that first (constant) term is greater than what follows */
+ polsbt( x, nn, psqrt, nn, y);
+ t = sqrt( t );
+ for( i=0; i<=nn; i++ )
+ y[i] *= t;
+
+ /* If first nonzero coefficient was at degree n > 0, multiply by
+ x^(n/2). */
+ if (n > 0)
+ {
+ polclr (x, MAXPOL);
+ x[n/2] = 1.0;
+ polmul (x, nn, y, nn, y);
+ }
+#if 0
+/* Newton iterations */
+for( n=0; n<10; n++ )
+ {
+ poldiv( y, nn, pol, nn, z );
+ poladd( y, nn, z, nn, y );
+ for( i=0; i<=nn; i++ )
+ y[i] *= 0.5;
+ for( i=0; i<=nn; i++ )
+ {
+ u = fabs( y[i] - z[i] );
+ if( u > 1.0e-15 )
+ goto more;
+ }
+ goto done;
+more: ;
+ }
+printf( "square root did not converge\n" );
+done:
+#endif /* 0 */
+
+polmov( y, nn, ans );
+free( y );
+free( x );
+}
+
+
+
+/* Sine of a polynomial.
+ * The computation uses
+ * sin(a+b) = sin(a) cos(b) + cos(a) sin(b)
+ * where a is the constant term of the polynomial and
+ * b is the sum of the rest of the terms.
+ * Since sin(b) and cos(b) are computed by series expansions,
+ * the value of b should be small.
+ */
+void
+polsin( x, y, nn )
+ double x[], y[];
+ int nn;
+{
+ double a, sc;
+ double *w, *c;
+ int i;
+
+ if (nn > N)
+ {
+ mtherr ("polatn", OVERFLOW);
+ return;
+ }
+ w = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ c = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ polmov( x, nn, w );
+ polclr( c, MAXPOL );
+ polclr( y, nn );
+ /* a, in the description, is x[0]. b is the polynomial x - x[0]. */
+ a = w[0];
+ /* c = cos (b) */
+ w[0] = 0.0;
+ polsbt( w, nn, pcos, nn, c );
+ sc = sin(a);
+ /* sin(a) cos (b) */
+ for( i=0; i<=nn; i++ )
+ c[i] *= sc;
+ /* y = sin (b) */
+ polsbt( w, nn, psin, nn, y );
+ sc = cos(a);
+ /* cos(a) sin(b) */
+ for( i=0; i<=nn; i++ )
+ y[i] *= sc;
+ poladd( c, nn, y, nn, y );
+ free( c );
+ free( w );
+}
+
+
+/* Cosine of a polynomial.
+ * The computation uses
+ * cos(a+b) = cos(a) cos(b) - sin(a) sin(b)
+ * where a is the constant term of the polynomial and
+ * b is the sum of the rest of the terms.
+ * Since sin(b) and cos(b) are computed by series expansions,
+ * the value of b should be small.
+ */
+void
+polcos( x, y, nn )
+ double x[], y[];
+ int nn;
+{
+ double a, sc;
+ double *w, *c;
+ int i;
+ double sin(), cos();
+
+ if (nn > N)
+ {
+ mtherr ("polatn", OVERFLOW);
+ return;
+ }
+ w = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ c = (double * )malloc( (MAXPOL+1) * sizeof (double) );
+ polmov( x, nn, w );
+ polclr( c, MAXPOL );
+ polclr( y, nn );
+ a = w[0];
+ w[0] = 0.0;
+ /* c = cos(b) */
+ polsbt( w, nn, pcos, nn, c );
+ sc = cos(a);
+ /* cos(a) cos(b) */
+ for( i=0; i<=nn; i++ )
+ c[i] *= sc;
+ /* y = sin(b) */
+ polsbt( w, nn, psin, nn, y );
+ sc = sin(a);
+ /* sin(a) sin(b) */
+ for( i=0; i<=nn; i++ )
+ y[i] *= sc;
+ polsub( y, nn, c, nn, y );
+ free( c );
+ free( w );
+}
diff --git a/libm/double/polrt.c b/libm/double/polrt.c
new file mode 100644
index 000000000..b1cd88087
--- /dev/null
+++ b/libm/double/polrt.c
@@ -0,0 +1,227 @@
+/* polrt.c
+ *
+ * Find roots of a polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct
+ * {
+ * double r;
+ * double i;
+ * }cmplx;
+ *
+ * double xcof[], cof[];
+ * int m;
+ * cmplx root[];
+ *
+ * polrt( xcof, cof, m, root )
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Iterative determination of the roots of a polynomial of
+ * degree m whose coefficient vector is xcof[]. The
+ * coefficients are arranged in ascending order; i.e., the
+ * coefficient of x**m is xcof[m].
+ *
+ * The array cof[] is working storage the same size as xcof[].
+ * root[] is the output array containing the complex roots.
+ *
+ *
+ * ACCURACY:
+ *
+ * Termination depends on evaluation of the polynomial at
+ * the trial values of the roots. The values of multiple roots
+ * or of roots that are nearly equal may have poor relative
+ * accuracy after the first root in the neighborhood has been
+ * found.
+ *
+ */
+
+/* polrt */
+/* Complex roots of real polynomial */
+/* number of coefficients is m + 1 ( i.e., m is degree of polynomial) */
+
+#include <math.h>
+/*
+typedef struct
+ {
+ double r;
+ double i;
+ }cmplx;
+*/
+#ifdef ANSIPROT
+extern double fabs ( double );
+#else
+double fabs();
+#endif
+
+int polrt( xcof, cof, m, root )
+double xcof[], cof[];
+int m;
+cmplx root[];
+{
+register double *p, *q;
+int i, j, nsav, n, n1, n2, nroot, iter, retry;
+int final;
+double mag, cofj;
+cmplx x0, x, xsav, dx, t, t1, u, ud;
+
+final = 0;
+n = m;
+if( n <= 0 )
+ return(1);
+if( n > 36 )
+ return(2);
+if( xcof[m] == 0.0 )
+ return(4);
+
+n1 = n;
+n2 = n;
+nroot = 0;
+nsav = n;
+q = &xcof[0];
+p = &cof[n];
+for( j=0; j<=nsav; j++ )
+ *p-- = *q++; /* cof[ n-j ] = xcof[j];*/
+xsav.r = 0.0;
+xsav.i = 0.0;
+
+nxtrut:
+x0.r = 0.00500101;
+x0.i = 0.01000101;
+retry = 0;
+
+tryagn:
+retry += 1;
+x.r = x0.r;
+
+x0.r = -10.0 * x0.i;
+x0.i = -10.0 * x.r;
+
+x.r = x0.r;
+x.i = x0.i;
+
+finitr:
+iter = 0;
+
+while( iter < 500 )
+{
+u.r = cof[n];
+if( u.r == 0.0 )
+ { /* this root is zero */
+ x.r = 0;
+ n1 -= 1;
+ n2 -= 1;
+ goto zerrut;
+ }
+u.i = 0;
+ud.r = 0;
+ud.i = 0;
+t.r = 1.0;
+t.i = 0;
+p = &cof[n-1];
+for( i=0; i<n; i++ )
+ {
+ t1.r = x.r * t.r - x.i * t.i;
+ t1.i = x.r * t.i + x.i * t.r;
+ cofj = *p--; /* evaluate polynomial */
+ u.r += cofj * t1.r;
+ u.i += cofj * t1.i;
+ cofj = cofj * (i+1); /* derivative */
+ ud.r += cofj * t.r;
+ ud.i -= cofj * t.i;
+ t.r = t1.r;
+ t.i = t1.i;
+ }
+
+mag = ud.r * ud.r + ud.i * ud.i;
+if( mag == 0.0 )
+ {
+ if( !final )
+ goto tryagn;
+ x.r = xsav.r;
+ x.i = xsav.i;
+ goto findon;
+ }
+dx.r = (u.i * ud.i - u.r * ud.r)/mag;
+x.r += dx.r;
+dx.i = -(u.r * ud.i + u.i * ud.r)/mag;
+x.i += dx.i;
+if( (fabs(dx.i) + fabs(dx.r)) < 1.0e-6 )
+ goto lupdon;
+iter += 1;
+} /* while iter < 500 */
+
+if( final )
+ goto lupdon;
+if( retry < 5 )
+ goto tryagn;
+return(3);
+
+lupdon:
+/* Swap original and reduced polynomials */
+q = &xcof[nsav];
+p = &cof[0];
+for( j=0; j<=n2; j++ )
+ {
+ cofj = *q;
+ *q-- = *p;
+ *p++ = cofj;
+ }
+i = n;
+n = n1;
+n1 = i;
+
+if( !final )
+ {
+ final = 1;
+ if( fabs(x.i/x.r) < 1.0e-4 )
+ x.i = 0.0;
+ xsav.r = x.r;
+ xsav.i = x.i;
+ goto finitr; /* do final iteration on original polynomial */
+ }
+
+findon:
+final = 0;
+if( fabs(x.i/x.r) >= 1.0e-5 )
+ {
+ cofj = x.r + x.r;
+ mag = x.r * x.r + x.i * x.i;
+ n -= 2;
+ }
+else
+ { /* root is real */
+zerrut:
+ x.i = 0;
+ cofj = x.r;
+ mag = 0;
+ n -= 1;
+ }
+/* divide working polynomial cof(z) by z - x */
+p = &cof[1];
+*p += cofj * *(p-1);
+for( j=1; j<n; j++ )
+ {
+ *(p+1) += cofj * *p - mag * *(p-1);
+ p++;
+ }
+
+setrut:
+root[nroot].r = x.r;
+root[nroot].i = x.i;
+nroot += 1;
+if( mag != 0.0 )
+ {
+ x.i = -x.i;
+ mag = 0;
+ goto setrut; /* fill in the complex conjugate root */
+ }
+if( n > 0 )
+ goto nxtrut;
+return(0);
+}
diff --git a/libm/double/polylog.c b/libm/double/polylog.c
new file mode 100644
index 000000000..c21e04449
--- /dev/null
+++ b/libm/double/polylog.c
@@ -0,0 +1,467 @@
+/* polylog.c
+ *
+ * Polylogarithms
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, polylog();
+ * int n;
+ *
+ * y = polylog( n, x );
+ *
+ *
+ * The polylogarithm of order n is defined by the series
+ *
+ *
+ * inf k
+ * - x
+ * Li (x) = > --- .
+ * n - n
+ * k=1 k
+ *
+ *
+ * For x = 1,
+ *
+ * inf
+ * - 1
+ * Li (1) = > --- = Riemann zeta function (n) .
+ * n - n
+ * k=1 k
+ *
+ *
+ * When n = 2, the function is the dilogarithm, related to Spence's integral:
+ *
+ * x 1-x
+ * - -
+ * | | -ln(1-t) | | ln t
+ * Li (x) = | -------- dt = | ------ dt = spence(1-x) .
+ * 2 | | t | | 1 - t
+ * - -
+ * 0 1
+ *
+ *
+ * See also the program cpolylog.c for the complex polylogarithm,
+ * whose definition is extended to x > 1.
+ *
+ * References:
+ *
+ * Lewin, L., _Polylogarithms and Associated Functions_,
+ * North Holland, 1981.
+ *
+ * Lewin, L., ed., _Structural Properties of Polylogarithms_,
+ * American Mathematical Society, 1991.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain n # trials peak rms
+ * IEEE 0, 1 2 50000 6.2e-16 8.0e-17
+ * IEEE 0, 1 3 100000 2.5e-16 6.6e-17
+ * IEEE 0, 1 4 30000 1.7e-16 4.9e-17
+ * IEEE 0, 1 5 30000 5.1e-16 7.8e-17
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: July, 1999
+Copyright 1999 by Stephen L. Moshier
+*/
+
+#include <math.h>
+extern double PI;
+
+/* polylog(4, 1-x) = zeta(4) - x zeta(3) + x^2 A4(x)/B4(x)
+ 0 <= x <= 0.125
+ Theoretical peak absolute error 4.5e-18 */
+#if UNK
+static double A4[13] = {
+ 3.056144922089490701751E-2,
+ 3.243086484162581557457E-1,
+ 2.877847281461875922565E-1,
+ 7.091267785886180663385E-2,
+ 6.466460072456621248630E-3,
+ 2.450233019296542883275E-4,
+ 4.031655364627704957049E-6,
+ 2.884169163909467997099E-8,
+ 8.680067002466594858347E-11,
+ 1.025983405866370985438E-13,
+ 4.233468313538272640380E-17,
+ 4.959422035066206902317E-21,
+ 1.059365867585275714599E-25,
+};
+static double B4[12] = {
+ /* 1.000000000000000000000E0, */
+ 2.821262403600310974875E0,
+ 1.780221124881327022033E0,
+ 3.778888211867875721773E-1,
+ 3.193887040074337940323E-2,
+ 1.161252418498096498304E-3,
+ 1.867362374829870620091E-5,
+ 1.319022779715294371091E-7,
+ 3.942755256555603046095E-10,
+ 4.644326968986396928092E-13,
+ 1.913336021014307074861E-16,
+ 2.240041814626069927477E-20,
+ 4.784036597230791011855E-25,
+};
+#endif
+#if DEC
+static short A4[52] = {
+0036772,0056001,0016601,0164507,
+0037646,0005710,0076603,0176456,
+0037623,0054205,0013532,0026476,
+0037221,0035252,0101064,0065407,
+0036323,0162231,0042033,0107244,
+0035200,0073170,0106141,0136543,
+0033607,0043647,0163672,0055340,
+0031767,0137614,0173376,0072313,
+0027676,0160156,0161276,0034203,
+0025347,0003752,0123106,0064266,
+0022503,0035770,0160173,0177501,
+0017273,0056226,0033704,0132530,
+0013403,0022244,0175205,0052161,
+};
+static short B4[48] = {
+ /*0040200,0000000,0000000,0000000, */
+0040464,0107620,0027471,0071672,
+0040343,0157111,0025601,0137255,
+0037701,0075244,0140412,0160220,
+0037002,0151125,0036572,0057163,
+0035630,0032452,0050727,0161653,
+0034234,0122515,0034323,0172615,
+0032415,0120405,0123660,0003160,
+0030330,0140530,0161045,0150177,
+0026002,0134747,0014542,0002510,
+0023134,0113666,0035730,0035732,
+0017723,0110343,0041217,0007764,
+0014024,0007412,0175575,0160230,
+};
+#endif
+#if IBMPC
+static short A4[52] = {
+0x3d29,0x23b0,0x4b80,0x3f9f,
+0x7fa6,0x0fb0,0xc179,0x3fd4,
+0x45a8,0xa2eb,0x6b10,0x3fd2,
+0x8d61,0x5046,0x2755,0x3fb2,
+0x71d4,0x2883,0x7c93,0x3f7a,
+0x37ac,0x118c,0x0ecf,0x3f30,
+0x4b5c,0xfcf7,0xe8f4,0x3ed0,
+0xce99,0x9edf,0xf7f1,0x3e5e,
+0xc710,0xdc57,0xdc0d,0x3dd7,
+0xcd17,0x54c8,0xe0fd,0x3d3c,
+0x7fe8,0x1c0f,0x677f,0x3c88,
+0x96ab,0xc6f8,0x6b92,0x3bb7,
+0xaa8e,0x9f50,0x6494,0x3ac0,
+};
+static short B4[48] = {
+ /*0x0000,0x0000,0x0000,0x3ff0,*/
+0x2e77,0x05e7,0x91f2,0x4006,
+0x37d6,0x2570,0x7bc9,0x3ffc,
+0x5c12,0x9821,0x2f54,0x3fd8,
+0x4bce,0xa7af,0x5a4a,0x3fa0,
+0xfc75,0x4a3a,0x06a5,0x3f53,
+0x7eb2,0xa71a,0x94a9,0x3ef3,
+0x00ce,0xb4f6,0xb420,0x3e81,
+0xba10,0x1c44,0x182b,0x3dfb,
+0x40a9,0xe32c,0x573c,0x3d60,
+0x077b,0xc77b,0x92f6,0x3cab,
+0xe1fe,0x6851,0x721c,0x3bda,
+0xbc13,0x5f6f,0x81e1,0x3ae2,
+};
+#endif
+#if MIEEE
+static short A4[52] = {
+0x3f9f,0x4b80,0x23b0,0x3d29,
+0x3fd4,0xc179,0x0fb0,0x7fa6,
+0x3fd2,0x6b10,0xa2eb,0x45a8,
+0x3fb2,0x2755,0x5046,0x8d61,
+0x3f7a,0x7c93,0x2883,0x71d4,
+0x3f30,0x0ecf,0x118c,0x37ac,
+0x3ed0,0xe8f4,0xfcf7,0x4b5c,
+0x3e5e,0xf7f1,0x9edf,0xce99,
+0x3dd7,0xdc0d,0xdc57,0xc710,
+0x3d3c,0xe0fd,0x54c8,0xcd17,
+0x3c88,0x677f,0x1c0f,0x7fe8,
+0x3bb7,0x6b92,0xc6f8,0x96ab,
+0x3ac0,0x6494,0x9f50,0xaa8e,
+};
+static short B4[48] = {
+ /*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4006,0x91f2,0x05e7,0x2e77,
+0x3ffc,0x7bc9,0x2570,0x37d6,
+0x3fd8,0x2f54,0x9821,0x5c12,
+0x3fa0,0x5a4a,0xa7af,0x4bce,
+0x3f53,0x06a5,0x4a3a,0xfc75,
+0x3ef3,0x94a9,0xa71a,0x7eb2,
+0x3e81,0xb420,0xb4f6,0x00ce,
+0x3dfb,0x182b,0x1c44,0xba10,
+0x3d60,0x573c,0xe32c,0x40a9,
+0x3cab,0x92f6,0xc77b,0x077b,
+0x3bda,0x721c,0x6851,0xe1fe,
+0x3ae2,0x81e1,0x5f6f,0xbc13,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double spence ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double zetac ( double );
+extern double pow ( double, double );
+extern double powi ( double, int );
+extern double log ( double );
+extern double fac ( int i );
+extern double fabs (double);
+double polylog (int, double);
+#else
+extern double spence(), polevl(), p1evl(), zetac();
+extern double pow(), powi(), log();
+extern double fac(); /* factorial */
+extern double fabs();
+double polylog();
+#endif
+extern double MACHEP;
+
+double
+polylog (n, x)
+ int n;
+ double x;
+{
+ double h, k, p, s, t, u, xc, z;
+ int i, j;
+
+/* This recurrence provides formulas for n < 2.
+
+ d 1
+ -- Li (x) = --- Li (x) .
+ dx n x n-1
+
+*/
+
+ if (n == -1)
+ {
+ p = 1.0 - x;
+ u = x / p;
+ s = u * u + u;
+ return s;
+ }
+
+ if (n == 0)
+ {
+ s = x / (1.0 - x);
+ return s;
+ }
+
+ /* Not implemented for n < -1.
+ Not defined for x > 1. Use cpolylog if you need that. */
+ if (x > 1.0 || n < -1)
+ {
+ mtherr("polylog", DOMAIN);
+ return 0.0;
+ }
+
+ if (n == 1)
+ {
+ s = -log (1.0 - x);
+ return s;
+ }
+
+ /* Argument +1 */
+ if (x == 1.0 && n > 1)
+ {
+ s = zetac ((double) n) + 1.0;
+ return s;
+ }
+
+ /* Argument -1.
+ 1-n
+ Li (-z) = - (1 - 2 ) Li (z)
+ n n
+ */
+ if (x == -1.0 && n > 1)
+ {
+ /* Li_n(1) = zeta(n) */
+ s = zetac ((double) n) + 1.0;
+ s = s * (powi (2.0, 1 - n) - 1.0);
+ return s;
+ }
+
+/* Inversion formula:
+ * [n/2] n-2r
+ * n 1 n - log (z)
+ * Li (-z) + (-1) Li (-1/z) = - --- log (z) + 2 > ----------- Li (-1)
+ * n n n! - (n - 2r)! 2r
+ * r=1
+ */
+ if (x < -1.0 && n > 1)
+ {
+ double q, w;
+ int r;
+
+ w = log (-x);
+ s = 0.0;
+ for (r = 1; r <= n / 2; r++)
+ {
+ j = 2 * r;
+ p = polylog (j, -1.0);
+ j = n - j;
+ if (j == 0)
+ {
+ s = s + p;
+ break;
+ }
+ q = (double) j;
+ q = pow (w, q) * p / fac (j);
+ s = s + q;
+ }
+ s = 2.0 * s;
+ q = polylog (n, 1.0 / x);
+ if (n & 1)
+ q = -q;
+ s = s - q;
+ s = s - pow (w, (double) n) / fac (n);
+ return s;
+ }
+
+ if (n == 2)
+ {
+ if (x < 0.0 || x > 1.0)
+ return (spence (1.0 - x));
+ }
+
+
+
+ /* The power series converges slowly when x is near 1. For n = 3, this
+ identity helps:
+
+ Li (-x/(1-x)) + Li (1-x) + Li (x)
+ 3 3 3
+ 2 2 3
+ = Li (1) + (pi /6) log(1-x) - (1/2) log(x) log (1-x) + (1/6) log (1-x)
+ 3
+ */
+
+ if (n == 3)
+ {
+ p = x * x * x;
+ if (x > 0.8)
+ {
+ u = log(x);
+ s = p / 6.0;
+ xc = 1.0 - x;
+ s = s - 0.5 * u * u * log(xc);
+ s = s + PI * PI * u / 6.0;
+ s = s - polylog (3, -xc/x);
+ s = s - polylog (3, xc);
+ s = s + zetac(3.0);
+ s = s + 1.0;
+ return s;
+ }
+ /* Power series */
+ t = p / 27.0;
+ t = t + .125 * x * x;
+ t = t + x;
+
+ s = 0.0;
+ k = 4.0;
+ do
+ {
+ p = p * x;
+ h = p / (k * k * k);
+ s = s + h;
+ k += 1.0;
+ }
+ while (fabs(h/s) > 1.1e-16);
+ return (s + t);
+ }
+
+if (n == 4)
+ {
+ if (x >= 0.875)
+ {
+ u = 1.0 - x;
+ s = polevl(u, A4, 12) / p1evl(u, B4, 12);
+ s = s * u * u - 1.202056903159594285400 * u;
+ s += 1.0823232337111381915160;
+ return s;
+ }
+ goto pseries;
+ }
+
+
+ if (x < 0.75)
+ goto pseries;
+
+
+/* This expansion in powers of log(x) is especially useful when
+ x is near 1.
+
+ See also the pari gp calculator.
+
+ inf j
+ - z(n-j) (log(x))
+ polylog(n,x) = > -----------------
+ - j!
+ j=0
+
+ where
+
+ z(j) = Riemann zeta function (j), j != 1
+
+ n-1
+ -
+ z(1) = -log(-log(x)) + > 1/k
+ -
+ k=1
+ */
+
+ z = log(x);
+ h = -log(-z);
+ for (i = 1; i < n; i++)
+ h = h + 1.0/i;
+ p = 1.0;
+ s = zetac((double)n) + 1.0;
+ for (j=1; j<=n+1; j++)
+ {
+ p = p * z / j;
+ if (j == n-1)
+ s = s + h * p;
+ else
+ s = s + (zetac((double)(n-j)) + 1.0) * p;
+ }
+ j = n + 3;
+ z = z * z;
+ for(;;)
+ {
+ p = p * z / ((j-1)*j);
+ h = (zetac((double)(n-j)) + 1.0);
+ h = h * p;
+ s = s + h;
+ if (fabs(h/s) < MACHEP)
+ break;
+ j += 2;
+ }
+ return s;
+
+
+pseries:
+
+ p = x * x * x;
+ k = 3.0;
+ s = 0.0;
+ do
+ {
+ p = p * x;
+ k += 1.0;
+ h = p / powi(k, n);
+ s = s + h;
+ }
+ while (fabs(h/s) > MACHEP);
+ s += x * x * x / powi(3.0,n);
+ s += x * x / powi(2.0,n);
+ s += x;
+ return s;
+}
diff --git a/libm/double/polyn.c b/libm/double/polyn.c
new file mode 100644
index 000000000..2927e77f0
--- /dev/null
+++ b/libm/double/polyn.c
@@ -0,0 +1,471 @@
+/* polyn.c
+ * polyr.c
+ * Arithmetic operations on polynomials
+ *
+ * In the following descriptions a, b, c are polynomials of degree
+ * na, nb, nc respectively. The degree of a polynomial cannot
+ * exceed a run-time value MAXPOL. An operation that attempts
+ * to use or generate a polynomial of higher degree may produce a
+ * result that suffers truncation at degree MAXPOL. The value of
+ * MAXPOL is set by calling the function
+ *
+ * polini( maxpol );
+ *
+ * where maxpol is the desired maximum degree. This must be
+ * done prior to calling any of the other functions in this module.
+ * Memory for internal temporary polynomial storage is allocated
+ * by polini().
+ *
+ * Each polynomial is represented by an array containing its
+ * coefficients, together with a separately declared integer equal
+ * to the degree of the polynomial. The coefficients appear in
+ * ascending order; that is,
+ *
+ * 2 na
+ * a(x) = a[0] + a[1] * x + a[2] * x + ... + a[na] * x .
+ *
+ *
+ *
+ * sum = poleva( a, na, x ); Evaluate polynomial a(t) at t = x.
+ * polprt( a, na, D ); Print the coefficients of a to D digits.
+ * polclr( a, na ); Set a identically equal to zero, up to a[na].
+ * polmov( a, na, b ); Set b = a.
+ * poladd( a, na, b, nb, c ); c = b + a, nc = max(na,nb)
+ * polsub( a, na, b, nb, c ); c = b - a, nc = max(na,nb)
+ * polmul( a, na, b, nb, c ); c = b * a, nc = na+nb
+ *
+ *
+ * Division:
+ *
+ * i = poldiv( a, na, b, nb, c ); c = b / a, nc = MAXPOL
+ *
+ * returns i = the degree of the first nonzero coefficient of a.
+ * The computed quotient c must be divided by x^i. An error message
+ * is printed if a is identically zero.
+ *
+ *
+ * Change of variables:
+ * If a and b are polynomials, and t = a(x), then
+ * c(t) = b(a(x))
+ * is a polynomial found by substituting a(x) for t. The
+ * subroutine call for this is
+ *
+ * polsbt( a, na, b, nb, c );
+ *
+ *
+ * Notes:
+ * poldiv() is an integer routine; poleva() is double.
+ * Any of the arguments a, b, c may refer to the same array.
+ *
+ */
+
+#include <stdio.h>
+#include <math.h>
+#if ANSIPROT
+void exit (int);
+extern void * malloc ( long );
+extern void free ( void * );
+void polclr ( double *, int );
+void polmov ( double *, int, double * );
+void polmul ( double *, int, double *, int, double * );
+int poldiv ( double *, int, double *, int, double * );
+#else
+void exit();
+void * malloc();
+void free ();
+void polclr(), polmov(), poldiv(), polmul();
+#endif
+#ifndef NULL
+#define NULL 0
+#endif
+
+/* near pointer version of malloc() */
+/*
+#define malloc _nmalloc
+#define free _nfree
+*/
+
+/* Pointers to internal arrays. Note poldiv() allocates
+ * and deallocates some temporary arrays every time it is called.
+ */
+static double *pt1 = 0;
+static double *pt2 = 0;
+static double *pt3 = 0;
+
+/* Maximum degree of polynomial. */
+int MAXPOL = 0;
+extern int MAXPOL;
+
+/* Number of bytes (chars) in maximum size polynomial. */
+static int psize = 0;
+
+
+/* Initialize max degree of polynomials
+ * and allocate temporary storage.
+ */
+void polini( maxdeg )
+int maxdeg;
+{
+
+MAXPOL = maxdeg;
+psize = (maxdeg + 1) * sizeof(double);
+
+/* Release previously allocated memory, if any. */
+if( pt3 )
+ free(pt3);
+if( pt2 )
+ free(pt2);
+if( pt1 )
+ free(pt1);
+
+/* Allocate new arrays */
+pt1 = (double * )malloc(psize); /* used by polsbt */
+pt2 = (double * )malloc(psize); /* used by polsbt */
+pt3 = (double * )malloc(psize); /* used by polmul */
+
+/* Report if failure */
+if( (pt1 == NULL) || (pt2 == NULL) || (pt3 == NULL) )
+ {
+ mtherr( "polini", ERANGE );
+ exit(1);
+ }
+}
+
+
+
+/* Print the coefficients of a, with d decimal precision.
+ */
+static char *form = "abcdefghijk";
+
+void polprt( a, na, d )
+double a[];
+int na, d;
+{
+int i, j, d1;
+char *p;
+
+/* Create format descriptor string for the printout.
+ * Do this partly by hand, since sprintf() may be too
+ * bug-ridden to accomplish this feat by itself.
+ */
+p = form;
+*p++ = '%';
+d1 = d + 8;
+sprintf( p, "%d ", d1 );
+p += 1;
+if( d1 >= 10 )
+ p += 1;
+*p++ = '.';
+sprintf( p, "%d ", d );
+p += 1;
+if( d >= 10 )
+ p += 1;
+*p++ = 'e';
+*p++ = ' ';
+*p++ = '\0';
+
+
+/* Now do the printing.
+ */
+d1 += 1;
+j = 0;
+for( i=0; i<=na; i++ )
+ {
+/* Detect end of available line */
+ j += d1;
+ if( j >= 78 )
+ {
+ printf( "\n" );
+ j = d1;
+ }
+ printf( form, a[i] );
+ }
+printf( "\n" );
+}
+
+
+
+/* Set a = 0.
+ */
+void polclr( a, n )
+register double *a;
+int n;
+{
+int i;
+
+if( n > MAXPOL )
+ n = MAXPOL;
+for( i=0; i<=n; i++ )
+ *a++ = 0.0;
+}
+
+
+
+/* Set b = a.
+ */
+void polmov( a, na, b )
+register double *a, *b;
+int na;
+{
+int i;
+
+if( na > MAXPOL )
+ na = MAXPOL;
+
+for( i=0; i<= na; i++ )
+ {
+ *b++ = *a++;
+ }
+}
+
+
+/* c = b * a.
+ */
+void polmul( a, na, b, nb, c )
+double a[], b[], c[];
+int na, nb;
+{
+int i, j, k, nc;
+double x;
+
+nc = na + nb;
+polclr( pt3, MAXPOL );
+
+for( i=0; i<=na; i++ )
+ {
+ x = a[i];
+ for( j=0; j<=nb; j++ )
+ {
+ k = i + j;
+ if( k > MAXPOL )
+ break;
+ pt3[k] += x * b[j];
+ }
+ }
+
+if( nc > MAXPOL )
+ nc = MAXPOL;
+for( i=0; i<=nc; i++ )
+ c[i] = pt3[i];
+}
+
+
+
+
+/* c = b + a.
+ */
+void poladd( a, na, b, nb, c )
+double a[], b[], c[];
+int na, nb;
+{
+int i, n;
+
+
+if( na > nb )
+ n = na;
+else
+ n = nb;
+
+if( n > MAXPOL )
+ n = MAXPOL;
+
+for( i=0; i<=n; i++ )
+ {
+ if( i > na )
+ c[i] = b[i];
+ else if( i > nb )
+ c[i] = a[i];
+ else
+ c[i] = b[i] + a[i];
+ }
+}
+
+/* c = b - a.
+ */
+void polsub( a, na, b, nb, c )
+double a[], b[], c[];
+int na, nb;
+{
+int i, n;
+
+
+if( na > nb )
+ n = na;
+else
+ n = nb;
+
+if( n > MAXPOL )
+ n = MAXPOL;
+
+for( i=0; i<=n; i++ )
+ {
+ if( i > na )
+ c[i] = b[i];
+ else if( i > nb )
+ c[i] = -a[i];
+ else
+ c[i] = b[i] - a[i];
+ }
+}
+
+
+
+/* c = b/a
+ */
+int poldiv( a, na, b, nb, c )
+double a[], b[], c[];
+int na, nb;
+{
+double quot;
+double *ta, *tb, *tq;
+int i, j, k, sing;
+
+sing = 0;
+
+/* Allocate temporary arrays. This would be quicker
+ * if done automatically on the stack, but stack space
+ * may be hard to obtain on a small computer.
+ */
+ta = (double * )malloc( psize );
+polclr( ta, MAXPOL );
+polmov( a, na, ta );
+
+tb = (double * )malloc( psize );
+polclr( tb, MAXPOL );
+polmov( b, nb, tb );
+
+tq = (double * )malloc( psize );
+polclr( tq, MAXPOL );
+
+/* What to do if leading (constant) coefficient
+ * of denominator is zero.
+ */
+if( a[0] == 0.0 )
+ {
+ for( i=0; i<=na; i++ )
+ {
+ if( ta[i] != 0.0 )
+ goto nzero;
+ }
+ mtherr( "poldiv", SING );
+ goto done;
+
+nzero:
+/* Reduce the degree of the denominator. */
+ for( i=0; i<na; i++ )
+ ta[i] = ta[i+1];
+ ta[na] = 0.0;
+
+ if( b[0] != 0.0 )
+ {
+/* Optional message:
+ printf( "poldiv singularity, divide quotient by x\n" );
+*/
+ sing += 1;
+ }
+ else
+ {
+/* Reduce degree of numerator. */
+ for( i=0; i<nb; i++ )
+ tb[i] = tb[i+1];
+ tb[nb] = 0.0;
+ }
+/* Call self, using reduced polynomials. */
+ sing += poldiv( ta, na, tb, nb, c );
+ goto done;
+ }
+
+/* Long division algorithm. ta[0] is nonzero.
+ */
+for( i=0; i<=MAXPOL; i++ )
+ {
+ quot = tb[i]/ta[0];
+ for( j=0; j<=MAXPOL; j++ )
+ {
+ k = j + i;
+ if( k > MAXPOL )
+ break;
+ tb[k] -= quot * ta[j];
+ }
+ tq[i] = quot;
+ }
+/* Send quotient to output array. */
+polmov( tq, MAXPOL, c );
+
+done:
+
+/* Restore allocated memory. */
+free(tq);
+free(tb);
+free(ta);
+return( sing );
+}
+
+
+
+
+/* Change of variables
+ * Substitute a(y) for the variable x in b(x).
+ * x = a(y)
+ * c(x) = b(x) = b(a(y)).
+ */
+
+void polsbt( a, na, b, nb, c )
+double a[], b[], c[];
+int na, nb;
+{
+int i, j, k, n2;
+double x;
+
+/* 0th degree term:
+ */
+polclr( pt1, MAXPOL );
+pt1[0] = b[0];
+
+polclr( pt2, MAXPOL );
+pt2[0] = 1.0;
+n2 = 0;
+
+for( i=1; i<=nb; i++ )
+ {
+/* Form ith power of a. */
+ polmul( a, na, pt2, n2, pt2 );
+ n2 += na;
+ x = b[i];
+/* Add the ith coefficient of b times the ith power of a. */
+ for( j=0; j<=n2; j++ )
+ {
+ if( j > MAXPOL )
+ break;
+ pt1[j] += x * pt2[j];
+ }
+ }
+
+k = n2 + nb;
+if( k > MAXPOL )
+ k = MAXPOL;
+for( i=0; i<=k; i++ )
+ c[i] = pt1[i];
+}
+
+
+
+
+/* Evaluate polynomial a(t) at t = x.
+ */
+double poleva( a, na, x )
+double a[];
+int na;
+double x;
+{
+double s;
+int i;
+
+s = a[na];
+for( i=na-1; i>=0; i-- )
+ {
+ s = s * x + a[i];
+ }
+return(s);
+}
+
diff --git a/libm/double/polyr.c b/libm/double/polyr.c
new file mode 100644
index 000000000..81ca817e3
--- /dev/null
+++ b/libm/double/polyr.c
@@ -0,0 +1,533 @@
+
+/* Arithmetic operations on polynomials with rational coefficients
+ *
+ * In the following descriptions a, b, c are polynomials of degree
+ * na, nb, nc respectively. The degree of a polynomial cannot
+ * exceed a run-time value MAXPOL. An operation that attempts
+ * to use or generate a polynomial of higher degree may produce a
+ * result that suffers truncation at degree MAXPOL. The value of
+ * MAXPOL is set by calling the function
+ *
+ * polini( maxpol );
+ *
+ * where maxpol is the desired maximum degree. This must be
+ * done prior to calling any of the other functions in this module.
+ * Memory for internal temporary polynomial storage is allocated
+ * by polini().
+ *
+ * Each polynomial is represented by an array containing its
+ * coefficients, together with a separately declared integer equal
+ * to the degree of the polynomial. The coefficients appear in
+ * ascending order; that is,
+ *
+ * 2 na
+ * a(x) = a[0] + a[1] * x + a[2] * x + ... + a[na] * x .
+ *
+ *
+ *
+ * `a', `b', `c' are arrays of fracts.
+ * poleva( a, na, &x, &sum ); Evaluate polynomial a(t) at t = x.
+ * polprt( a, na, D ); Print the coefficients of a to D digits.
+ * polclr( a, na ); Set a identically equal to zero, up to a[na].
+ * polmov( a, na, b ); Set b = a.
+ * poladd( a, na, b, nb, c ); c = b + a, nc = max(na,nb)
+ * polsub( a, na, b, nb, c ); c = b - a, nc = max(na,nb)
+ * polmul( a, na, b, nb, c ); c = b * a, nc = na+nb
+ *
+ *
+ * Division:
+ *
+ * i = poldiv( a, na, b, nb, c ); c = b / a, nc = MAXPOL
+ *
+ * returns i = the degree of the first nonzero coefficient of a.
+ * The computed quotient c must be divided by x^i. An error message
+ * is printed if a is identically zero.
+ *
+ *
+ * Change of variables:
+ * If a and b are polynomials, and t = a(x), then
+ * c(t) = b(a(x))
+ * is a polynomial found by substituting a(x) for t. The
+ * subroutine call for this is
+ *
+ * polsbt( a, na, b, nb, c );
+ *
+ *
+ * Notes:
+ * poldiv() is an integer routine; poleva() is double.
+ * Any of the arguments a, b, c may refer to the same array.
+ *
+ */
+
+#include <stdio.h>
+#include <math.h>
+#ifndef NULL
+#define NULL 0
+#endif
+typedef struct{
+ double n;
+ double d;
+ }fract;
+
+#ifdef ANSIPROT
+extern void radd ( fract *, fract *, fract * );
+extern void rsub ( fract *, fract *, fract * );
+extern void rmul ( fract *, fract *, fract * );
+extern void rdiv ( fract *, fract *, fract * );
+void polmov ( fract *, int, fract * );
+void polmul ( fract *, int, fract *, int, fract * );
+int poldiv ( fract *, int, fract *, int, fract * );
+void * malloc ( long );
+void free ( void * );
+#else
+void radd(), rsub(), rmul(), rdiv();
+void polmov(), polmul();
+int poldiv();
+void * malloc();
+void free ();
+#endif
+
+/* near pointer version of malloc() */
+/*
+#define malloc _nmalloc
+#define free _nfree
+*/
+/* Pointers to internal arrays. Note poldiv() allocates
+ * and deallocates some temporary arrays every time it is called.
+ */
+static fract *pt1 = 0;
+static fract *pt2 = 0;
+static fract *pt3 = 0;
+
+/* Maximum degree of polynomial. */
+int MAXPOL = 0;
+extern int MAXPOL;
+
+/* Number of bytes (chars) in maximum size polynomial. */
+static int psize = 0;
+
+
+/* Initialize max degree of polynomials
+ * and allocate temporary storage.
+ */
+void polini( maxdeg )
+int maxdeg;
+{
+
+MAXPOL = maxdeg;
+psize = (maxdeg + 1) * sizeof(fract);
+
+/* Release previously allocated memory, if any. */
+if( pt3 )
+ free(pt3);
+if( pt2 )
+ free(pt2);
+if( pt1 )
+ free(pt1);
+
+/* Allocate new arrays */
+pt1 = (fract * )malloc(psize); /* used by polsbt */
+pt2 = (fract * )malloc(psize); /* used by polsbt */
+pt3 = (fract * )malloc(psize); /* used by polmul */
+
+/* Report if failure */
+if( (pt1 == NULL) || (pt2 == NULL) || (pt3 == NULL) )
+ {
+ mtherr( "polini", ERANGE );
+ exit(1);
+ }
+}
+
+
+
+/* Print the coefficients of a, with d decimal precision.
+ */
+static char *form = "abcdefghijk";
+
+void polprt( a, na, d )
+fract a[];
+int na, d;
+{
+int i, j, d1;
+char *p;
+
+/* Create format descriptor string for the printout.
+ * Do this partly by hand, since sprintf() may be too
+ * bug-ridden to accomplish this feat by itself.
+ */
+p = form;
+*p++ = '%';
+d1 = d + 8;
+sprintf( p, "%d ", d1 );
+p += 1;
+if( d1 >= 10 )
+ p += 1;
+*p++ = '.';
+sprintf( p, "%d ", d );
+p += 1;
+if( d >= 10 )
+ p += 1;
+*p++ = 'e';
+*p++ = ' ';
+*p++ = '\0';
+
+
+/* Now do the printing.
+ */
+d1 += 1;
+j = 0;
+for( i=0; i<=na; i++ )
+ {
+/* Detect end of available line */
+ j += d1;
+ if( j >= 78 )
+ {
+ printf( "\n" );
+ j = d1;
+ }
+ printf( form, a[i].n );
+ j += d1;
+ if( j >= 78 )
+ {
+ printf( "\n" );
+ j = d1;
+ }
+ printf( form, a[i].d );
+ }
+printf( "\n" );
+}
+
+
+
+/* Set a = 0.
+ */
+void polclr( a, n )
+fract a[];
+int n;
+{
+int i;
+
+if( n > MAXPOL )
+ n = MAXPOL;
+for( i=0; i<=n; i++ )
+ {
+ a[i].n = 0.0;
+ a[i].d = 1.0;
+ }
+}
+
+
+
+/* Set b = a.
+ */
+void polmov( a, na, b )
+fract a[], b[];
+int na;
+{
+int i;
+
+if( na > MAXPOL )
+ na = MAXPOL;
+
+for( i=0; i<= na; i++ )
+ {
+ b[i].n = a[i].n;
+ b[i].d = a[i].d;
+ }
+}
+
+
+/* c = b * a.
+ */
+void polmul( a, na, b, nb, c )
+fract a[], b[], c[];
+int na, nb;
+{
+int i, j, k, nc;
+fract temp;
+fract *p;
+
+nc = na + nb;
+polclr( pt3, MAXPOL );
+
+p = &a[0];
+for( i=0; i<=na; i++ )
+ {
+ for( j=0; j<=nb; j++ )
+ {
+ k = i + j;
+ if( k > MAXPOL )
+ break;
+ rmul( p, &b[j], &temp ); /*pt3[k] += a[i] * b[j];*/
+ radd( &temp, &pt3[k], &pt3[k] );
+ }
+ ++p;
+ }
+
+if( nc > MAXPOL )
+ nc = MAXPOL;
+for( i=0; i<=nc; i++ )
+ {
+ c[i].n = pt3[i].n;
+ c[i].d = pt3[i].d;
+ }
+}
+
+
+
+
+/* c = b + a.
+ */
+void poladd( a, na, b, nb, c )
+fract a[], b[], c[];
+int na, nb;
+{
+int i, n;
+
+
+if( na > nb )
+ n = na;
+else
+ n = nb;
+
+if( n > MAXPOL )
+ n = MAXPOL;
+
+for( i=0; i<=n; i++ )
+ {
+ if( i > na )
+ {
+ c[i].n = b[i].n;
+ c[i].d = b[i].d;
+ }
+ else if( i > nb )
+ {
+ c[i].n = a[i].n;
+ c[i].d = a[i].d;
+ }
+ else
+ {
+ radd( &a[i], &b[i], &c[i] ); /*c[i] = b[i] + a[i];*/
+ }
+ }
+}
+
+/* c = b - a.
+ */
+void polsub( a, na, b, nb, c )
+fract a[], b[], c[];
+int na, nb;
+{
+int i, n;
+
+
+if( na > nb )
+ n = na;
+else
+ n = nb;
+
+if( n > MAXPOL )
+ n = MAXPOL;
+
+for( i=0; i<=n; i++ )
+ {
+ if( i > na )
+ {
+ c[i].n = b[i].n;
+ c[i].d = b[i].d;
+ }
+ else if( i > nb )
+ {
+ c[i].n = -a[i].n;
+ c[i].d = a[i].d;
+ }
+ else
+ {
+ rsub( &a[i], &b[i], &c[i] ); /*c[i] = b[i] - a[i];*/
+ }
+ }
+}
+
+
+
+/* c = b/a
+ */
+int poldiv( a, na, b, nb, c )
+fract a[], b[], c[];
+int na, nb;
+{
+fract *ta, *tb, *tq;
+fract quot;
+fract temp;
+int i, j, k, sing;
+
+sing = 0;
+
+/* Allocate temporary arrays. This would be quicker
+ * if done automatically on the stack, but stack space
+ * may be hard to obtain on a small computer.
+ */
+ta = (fract * )malloc( psize );
+polclr( ta, MAXPOL );
+polmov( a, na, ta );
+
+tb = (fract * )malloc( psize );
+polclr( tb, MAXPOL );
+polmov( b, nb, tb );
+
+tq = (fract * )malloc( psize );
+polclr( tq, MAXPOL );
+
+/* What to do if leading (constant) coefficient
+ * of denominator is zero.
+ */
+if( a[0].n == 0.0 )
+ {
+ for( i=0; i<=na; i++ )
+ {
+ if( ta[i].n != 0.0 )
+ goto nzero;
+ }
+ mtherr( "poldiv", SING );
+ goto done;
+
+nzero:
+/* Reduce the degree of the denominator. */
+ for( i=0; i<na; i++ )
+ {
+ ta[i].n = ta[i+1].n;
+ ta[i].d = ta[i+1].d;
+ }
+ ta[na].n = 0.0;
+ ta[na].d = 1.0;
+
+ if( b[0].n != 0.0 )
+ {
+/* Optional message:
+ printf( "poldiv singularity, divide quotient by x\n" );
+*/
+ sing += 1;
+ }
+ else
+ {
+/* Reduce degree of numerator. */
+ for( i=0; i<nb; i++ )
+ {
+ tb[i].n = tb[i+1].n;
+ tb[i].d = tb[i+1].d;
+ }
+ tb[nb].n = 0.0;
+ tb[nb].d = 1.0;
+ }
+/* Call self, using reduced polynomials. */
+ sing += poldiv( ta, na, tb, nb, c );
+ goto done;
+ }
+
+/* Long division algorithm. ta[0] is nonzero.
+ */
+for( i=0; i<=MAXPOL; i++ )
+ {
+ rdiv( &ta[0], &tb[i], &quot ); /*quot = tb[i]/ta[0];*/
+ for( j=0; j<=MAXPOL; j++ )
+ {
+ k = j + i;
+ if( k > MAXPOL )
+ break;
+
+ rmul( &ta[j], &quot, &temp ); /*tb[k] -= quot * ta[j];*/
+ rsub( &temp, &tb[k], &tb[k] );
+ }
+ tq[i].n = quot.n;
+ tq[i].d = quot.d;
+ }
+/* Send quotient to output array. */
+polmov( tq, MAXPOL, c );
+
+done:
+
+/* Restore allocated memory. */
+free(tq);
+free(tb);
+free(ta);
+return( sing );
+}
+
+
+
+
+/* Change of variables
+ * Substitute a(y) for the variable x in b(x).
+ * x = a(y)
+ * c(x) = b(x) = b(a(y)).
+ */
+
+void polsbt( a, na, b, nb, c )
+fract a[], b[], c[];
+int na, nb;
+{
+int i, j, k, n2;
+fract temp;
+fract *p;
+
+/* 0th degree term:
+ */
+polclr( pt1, MAXPOL );
+pt1[0].n = b[0].n;
+pt1[0].d = b[0].d;
+
+polclr( pt2, MAXPOL );
+pt2[0].n = 1.0;
+pt2[0].d = 1.0;
+n2 = 0;
+p = &b[1];
+
+for( i=1; i<=nb; i++ )
+ {
+/* Form ith power of a. */
+ polmul( a, na, pt2, n2, pt2 );
+ n2 += na;
+/* Add the ith coefficient of b times the ith power of a. */
+ for( j=0; j<=n2; j++ )
+ {
+ if( j > MAXPOL )
+ break;
+ rmul( &pt2[j], p, &temp ); /*pt1[j] += b[i] * pt2[j];*/
+ radd( &temp, &pt1[j], &pt1[j] );
+ }
+ ++p;
+ }
+
+k = n2 + nb;
+if( k > MAXPOL )
+ k = MAXPOL;
+for( i=0; i<=k; i++ )
+ {
+ c[i].n = pt1[i].n;
+ c[i].d = pt1[i].d;
+ }
+}
+
+
+
+
+/* Evaluate polynomial a(t) at t = x.
+ */
+void poleva( a, na, x, s )
+fract a[];
+int na;
+fract *x;
+fract *s;
+{
+int i;
+fract temp;
+
+s->n = a[na].n;
+s->d = a[na].d;
+for( i=na-1; i>=0; i-- )
+ {
+ rmul( s, x, &temp ); /*s = s * x + a[i];*/
+ radd( &a[i], &temp, s );
+ }
+}
+
diff --git a/libm/double/pow.c b/libm/double/pow.c
new file mode 100644
index 000000000..768ad1062
--- /dev/null
+++ b/libm/double/pow.c
@@ -0,0 +1,756 @@
+/* pow.c
+ *
+ * Power function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, z, pow();
+ *
+ * z = pow( x, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes x raised to the yth power. Analytically,
+ *
+ * x**y = exp( y log(x) ).
+ *
+ * Following Cody and Waite, this program uses a lookup table
+ * of 2**-i/16 and pseudo extended precision arithmetic to
+ * obtain an extra three bits of accuracy in both the logarithm
+ * and the exponential.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -26,26 30000 4.2e-16 7.7e-17
+ * DEC -26,26 60000 4.8e-17 9.1e-18
+ * 1/26 < x < 26, with log(x) uniformly distributed.
+ * -26 < y < 26, y uniformly distributed.
+ * IEEE 0,8700 30000 1.5e-14 2.1e-15
+ * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * pow overflow x**y > MAXNUM INFINITY
+ * pow underflow x**y < 1/MAXNUM 0.0
+ * pow domain x<0 and y noninteger 0.0
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+static char fname[] = {"pow"};
+
+#define SQRTH 0.70710678118654752440
+
+#ifdef UNK
+static double P[] = {
+ 4.97778295871696322025E-1,
+ 3.73336776063286838734E0,
+ 7.69994162726912503298E0,
+ 4.66651806774358464979E0
+};
+static double Q[] = {
+/* 1.00000000000000000000E0, */
+ 9.33340916416696166113E0,
+ 2.79999886606328401649E1,
+ 3.35994905342304405431E1,
+ 1.39995542032307539578E1
+};
+/* 2^(-i/16), IEEE precision */
+static double A[] = {
+ 1.00000000000000000000E0,
+ 9.57603280698573700036E-1,
+ 9.17004043204671215328E-1,
+ 8.78126080186649726755E-1,
+ 8.40896415253714502036E-1,
+ 8.05245165974627141736E-1,
+ 7.71105412703970372057E-1,
+ 7.38413072969749673113E-1,
+ 7.07106781186547572737E-1,
+ 6.77127773468446325644E-1,
+ 6.48419777325504820276E-1,
+ 6.20928906036742001007E-1,
+ 5.94603557501360513449E-1,
+ 5.69394317378345782288E-1,
+ 5.45253866332628844837E-1,
+ 5.22136891213706877402E-1,
+ 5.00000000000000000000E-1
+};
+static double B[] = {
+ 0.00000000000000000000E0,
+ 1.64155361212281360176E-17,
+ 4.09950501029074826006E-17,
+ 3.97491740484881042808E-17,
+-4.83364665672645672553E-17,
+ 1.26912513974441574796E-17,
+ 1.99100761573282305549E-17,
+-1.52339103990623557348E-17,
+ 0.00000000000000000000E0
+};
+static double R[] = {
+ 1.49664108433729301083E-5,
+ 1.54010762792771901396E-4,
+ 1.33335476964097721140E-3,
+ 9.61812908476554225149E-3,
+ 5.55041086645832347466E-2,
+ 2.40226506959099779976E-1,
+ 6.93147180559945308821E-1
+};
+
+#define douba(k) A[k]
+#define doubb(k) B[k]
+#define MEXP 16383.0
+#ifdef DENORMAL
+#define MNEXP -17183.0
+#else
+#define MNEXP -16383.0
+#endif
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0037776,0156313,0175332,0163602,
+0040556,0167577,0052366,0174245,
+0040766,0062753,0175707,0055564,
+0040625,0052035,0131344,0155636,
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041025,0052644,0154404,0105155,
+0041337,0177772,0007016,0047646,
+0041406,0062740,0154273,0020020,
+0041137,0177054,0106127,0044555,
+};
+static unsigned short A[] = {
+0040200,0000000,0000000,0000000,
+0040165,0022575,0012444,0103314,
+0040152,0140306,0163735,0022071,
+0040140,0146336,0166052,0112341,
+0040127,0042374,0145326,0116553,
+0040116,0022214,0012437,0102201,
+0040105,0063452,0010525,0003333,
+0040075,0004243,0117530,0006067,
+0040065,0002363,0031771,0157145,
+0040055,0054076,0165102,0120513,
+0040045,0177326,0124661,0050471,
+0040036,0172462,0060221,0120422,
+0040030,0033760,0050615,0134251,
+0040021,0141723,0071653,0010703,
+0040013,0112701,0161752,0105727,
+0040005,0125303,0063714,0044173,
+0040000,0000000,0000000,0000000
+};
+static unsigned short B[] = {
+0000000,0000000,0000000,0000000,
+0021473,0040265,0153315,0140671,
+0121074,0062627,0042146,0176454,
+0121413,0003524,0136332,0066212,
+0121767,0046404,0166231,0012553,
+0121257,0015024,0002357,0043574,
+0021736,0106532,0043060,0056206,
+0121310,0020334,0165705,0035326,
+0000000,0000000,0000000,0000000
+};
+
+static unsigned short R[] = {
+0034173,0014076,0137624,0115771,
+0035041,0076763,0003744,0111311,
+0035656,0141766,0041127,0074351,
+0036435,0112533,0073611,0116664,
+0037143,0054106,0134040,0152223,
+0037565,0176757,0176026,0025551,
+0040061,0071027,0173721,0147572
+};
+
+/*
+static double R[] = {
+0.14928852680595608186e-4,
+0.15400290440989764601e-3,
+0.13333541313585784703e-2,
+0.96181290595172416964e-2,
+0.55504108664085595326e-1,
+0.24022650695909537056e0,
+0.69314718055994529629e0
+};
+*/
+#define douba(k) (*(double *)&A[(k)<<2])
+#define doubb(k) (*(double *)&B[(k)<<2])
+#define MEXP 2031.0
+#define MNEXP -2031.0
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x5cf0,0x7f5b,0xdb99,0x3fdf,
+0xdf15,0xea9e,0xddef,0x400d,
+0xeb6f,0x7f78,0xccbd,0x401e,
+0x9b74,0xb65c,0xaa83,0x4012,
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x914e,0x9b20,0xaab4,0x4022,
+0xc9f5,0x41c1,0xffff,0x403b,
+0x6402,0x1b17,0xccbc,0x4040,
+0xe92e,0x918a,0xffc5,0x402b,
+};
+static unsigned short A[] = {
+0x0000,0x0000,0x0000,0x3ff0,
+0x90da,0xa2a4,0xa4af,0x3fee,
+0xa487,0xdcfb,0x5818,0x3fed,
+0x529c,0xdd85,0x199b,0x3fec,
+0xd3ad,0x995a,0xe89f,0x3fea,
+0xf090,0x82a3,0xc491,0x3fe9,
+0xa0db,0x422a,0xace5,0x3fe8,
+0x0187,0x73eb,0xa114,0x3fe7,
+0x3bcd,0x667f,0xa09e,0x3fe6,
+0x5429,0xdd48,0xab07,0x3fe5,
+0x2a27,0xd536,0xbfda,0x3fe4,
+0x3422,0x4c12,0xdea6,0x3fe3,
+0xb715,0x0a31,0x06fe,0x3fe3,
+0x6238,0x6e75,0x387a,0x3fe2,
+0x517b,0x3c7d,0x72b8,0x3fe1,
+0x890f,0x6cf9,0xb558,0x3fe0,
+0x0000,0x0000,0x0000,0x3fe0
+};
+static unsigned short B[] = {
+0x0000,0x0000,0x0000,0x0000,
+0x3707,0xd75b,0xed02,0x3c72,
+0xcc81,0x345d,0xa1cd,0x3c87,
+0x4b27,0x5686,0xe9f1,0x3c86,
+0x6456,0x13b2,0xdd34,0xbc8b,
+0x42e2,0xafec,0x4397,0x3c6d,
+0x82e4,0xd231,0xf46a,0x3c76,
+0x8a76,0xb9d7,0x9041,0xbc71,
+0x0000,0x0000,0x0000,0x0000
+};
+static unsigned short R[] = {
+0x937f,0xd7f2,0x6307,0x3eef,
+0x9259,0x60fc,0x2fbe,0x3f24,
+0xef1d,0xc84a,0xd87e,0x3f55,
+0x33b7,0x6ef1,0xb2ab,0x3f83,
+0x1a92,0xd704,0x6b08,0x3fac,
+0xc56d,0xff82,0xbfbd,0x3fce,
+0x39ef,0xfefa,0x2e42,0x3fe6
+};
+
+#define douba(k) (*(double *)&A[(k)<<2])
+#define doubb(k) (*(double *)&B[(k)<<2])
+#define MEXP 16383.0
+#ifdef DENORMAL
+#define MNEXP -17183.0
+#else
+#define MNEXP -16383.0
+#endif
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0x3fdf,0xdb99,0x7f5b,0x5cf0,
+0x400d,0xddef,0xea9e,0xdf15,
+0x401e,0xccbd,0x7f78,0xeb6f,
+0x4012,0xaa83,0xb65c,0x9b74
+};
+static unsigned short Q[] = {
+0x4022,0xaab4,0x9b20,0x914e,
+0x403b,0xffff,0x41c1,0xc9f5,
+0x4040,0xccbc,0x1b17,0x6402,
+0x402b,0xffc5,0x918a,0xe92e
+};
+static unsigned short A[] = {
+0x3ff0,0x0000,0x0000,0x0000,
+0x3fee,0xa4af,0xa2a4,0x90da,
+0x3fed,0x5818,0xdcfb,0xa487,
+0x3fec,0x199b,0xdd85,0x529c,
+0x3fea,0xe89f,0x995a,0xd3ad,
+0x3fe9,0xc491,0x82a3,0xf090,
+0x3fe8,0xace5,0x422a,0xa0db,
+0x3fe7,0xa114,0x73eb,0x0187,
+0x3fe6,0xa09e,0x667f,0x3bcd,
+0x3fe5,0xab07,0xdd48,0x5429,
+0x3fe4,0xbfda,0xd536,0x2a27,
+0x3fe3,0xdea6,0x4c12,0x3422,
+0x3fe3,0x06fe,0x0a31,0xb715,
+0x3fe2,0x387a,0x6e75,0x6238,
+0x3fe1,0x72b8,0x3c7d,0x517b,
+0x3fe0,0xb558,0x6cf9,0x890f,
+0x3fe0,0x0000,0x0000,0x0000
+};
+static unsigned short B[] = {
+0x0000,0x0000,0x0000,0x0000,
+0x3c72,0xed02,0xd75b,0x3707,
+0x3c87,0xa1cd,0x345d,0xcc81,
+0x3c86,0xe9f1,0x5686,0x4b27,
+0xbc8b,0xdd34,0x13b2,0x6456,
+0x3c6d,0x4397,0xafec,0x42e2,
+0x3c76,0xf46a,0xd231,0x82e4,
+0xbc71,0x9041,0xb9d7,0x8a76,
+0x0000,0x0000,0x0000,0x0000
+};
+static unsigned short R[] = {
+0x3eef,0x6307,0xd7f2,0x937f,
+0x3f24,0x2fbe,0x60fc,0x9259,
+0x3f55,0xd87e,0xc84a,0xef1d,
+0x3f83,0xb2ab,0x6ef1,0x33b7,
+0x3fac,0x6b08,0xd704,0x1a92,
+0x3fce,0xbfbd,0xff82,0xc56d,
+0x3fe6,0x2e42,0xfefa,0x39ef
+};
+
+#define douba(k) (*(double *)&A[(k)<<2])
+#define doubb(k) (*(double *)&B[(k)<<2])
+#define MEXP 16383.0
+#ifdef DENORMAL
+#define MNEXP -17183.0
+#else
+#define MNEXP -16383.0
+#endif
+#endif
+
+/* log2(e) - 1 */
+#define LOG2EA 0.44269504088896340736
+
+#define F W
+#define Fa Wa
+#define Fb Wb
+#define G W
+#define Ga Wa
+#define Gb u
+#define H W
+#define Ha Wb
+#define Hb Wb
+
+#ifdef ANSIPROT
+extern double floor ( double );
+extern double fabs ( double );
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double powi ( double, int );
+extern int signbit ( double );
+extern int isnan ( double );
+extern int isfinite ( double );
+static double reduc ( double );
+#else
+double floor(), fabs(), frexp(), ldexp();
+double polevl(), p1evl(), powi();
+int signbit(), isnan(), isfinite();
+static double reduc();
+#endif
+extern double MAXNUM;
+#ifdef INFINITIES
+extern double INFINITY;
+#endif
+#ifdef NANS
+extern double NAN;
+#endif
+#ifdef MINUSZERO
+extern double NEGZERO;
+#endif
+
+double pow( x, y )
+double x, y;
+{
+double w, z, W, Wa, Wb, ya, yb, u;
+/* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
+double aw, ay, wy;
+int e, i, nflg, iyflg, yoddint;
+
+if( y == 0.0 )
+ return( 1.0 );
+#ifdef NANS
+if( isnan(x) )
+ return( x );
+if( isnan(y) )
+ return( y );
+#endif
+if( y == 1.0 )
+ return( x );
+
+
+#ifdef INFINITIES
+if( !isfinite(y) && (x == 1.0 || x == -1.0) )
+ {
+ mtherr( "pow", DOMAIN );
+#ifdef NANS
+ return( NAN );
+#else
+ return( INFINITY );
+#endif
+ }
+#endif
+
+if( x == 1.0 )
+ return( 1.0 );
+
+if( y >= MAXNUM )
+ {
+#ifdef INFINITIES
+ if( x > 1.0 )
+ return( INFINITY );
+#else
+ if( x > 1.0 )
+ return( MAXNUM );
+#endif
+ if( x > 0.0 && x < 1.0 )
+ return( 0.0);
+ if( x < -1.0 )
+ {
+#ifdef INFINITIES
+ return( INFINITY );
+#else
+ return( MAXNUM );
+#endif
+ }
+ if( x > -1.0 && x < 0.0 )
+ return( 0.0 );
+ }
+if( y <= -MAXNUM )
+ {
+ if( x > 1.0 )
+ return( 0.0 );
+#ifdef INFINITIES
+ if( x > 0.0 && x < 1.0 )
+ return( INFINITY );
+#else
+ if( x > 0.0 && x < 1.0 )
+ return( MAXNUM );
+#endif
+ if( x < -1.0 )
+ return( 0.0 );
+#ifdef INFINITIES
+ if( x > -1.0 && x < 0.0 )
+ return( INFINITY );
+#else
+ if( x > -1.0 && x < 0.0 )
+ return( MAXNUM );
+#endif
+ }
+if( x >= MAXNUM )
+ {
+#if INFINITIES
+ if( y > 0.0 )
+ return( INFINITY );
+#else
+ if( y > 0.0 )
+ return( MAXNUM );
+#endif
+ return(0.0);
+ }
+/* Set iyflg to 1 if y is an integer. */
+iyflg = 0;
+w = floor(y);
+if( w == y )
+ iyflg = 1;
+
+/* Test for odd integer y. */
+yoddint = 0;
+if( iyflg )
+ {
+ ya = fabs(y);
+ ya = floor(0.5 * ya);
+ yb = 0.5 * fabs(w);
+ if( ya != yb )
+ yoddint = 1;
+ }
+
+if( x <= -MAXNUM )
+ {
+ if( y > 0.0 )
+ {
+#ifdef INFINITIES
+ if( yoddint )
+ return( -INFINITY );
+ return( INFINITY );
+#else
+ if( yoddint )
+ return( -MAXNUM );
+ return( MAXNUM );
+#endif
+ }
+ if( y < 0.0 )
+ {
+#ifdef MINUSZERO
+ if( yoddint )
+ return( NEGZERO );
+#endif
+ return( 0.0 );
+ }
+ }
+
+nflg = 0; /* flag = 1 if x<0 raised to integer power */
+if( x <= 0.0 )
+ {
+ if( x == 0.0 )
+ {
+ if( y < 0.0 )
+ {
+#ifdef MINUSZERO
+ if( signbit(x) && yoddint )
+ return( -INFINITY );
+#endif
+#ifdef INFINITIES
+ return( INFINITY );
+#else
+ return( MAXNUM );
+#endif
+ }
+ if( y > 0.0 )
+ {
+#ifdef MINUSZERO
+ if( signbit(x) && yoddint )
+ return( NEGZERO );
+#endif
+ return( 0.0 );
+ }
+ return( 1.0 );
+ }
+ else
+ {
+ if( iyflg == 0 )
+ { /* noninteger power of negative number */
+ mtherr( fname, DOMAIN );
+#ifdef NANS
+ return(NAN);
+#else
+ return(0.0L);
+#endif
+ }
+ nflg = 1;
+ }
+ }
+
+/* Integer power of an integer. */
+
+if( iyflg )
+ {
+ i = w;
+ w = floor(x);
+ if( (w == x) && (fabs(y) < 32768.0) )
+ {
+ w = powi( x, (int) y );
+ return( w );
+ }
+ }
+
+if( nflg )
+ x = fabs(x);
+
+/* For results close to 1, use a series expansion. */
+w = x - 1.0;
+aw = fabs(w);
+ay = fabs(y);
+wy = w * y;
+ya = fabs(wy);
+if((aw <= 1.0e-3 && ay <= 1.0)
+ || (ya <= 1.0e-3 && ay >= 1.0))
+ {
+ z = (((((w*(y-5.)/720. + 1./120.)*w*(y-4.) + 1./24.)*w*(y-3.)
+ + 1./6.)*w*(y-2.) + 0.5)*w*(y-1.) )*wy + wy + 1.;
+ goto done;
+ }
+/* These are probably too much trouble. */
+#if 0
+w = y * log(x);
+if (aw > 1.0e-3 && fabs(w) < 1.0e-3)
+ {
+ z = ((((((
+ w/7. + 1.)*w/6. + 1.)*w/5. + 1.)*w/4. + 1.)*w/3. + 1.)*w/2. + 1.)*w + 1.;
+ goto done;
+ }
+
+if(ya <= 1.0e-3 && aw <= 1.0e-4)
+ {
+ z = (((((
+ wy*1./720.
+ + (-w*1./48. + 1./120.) )*wy
+ + ((w*17./144. - 1./12.)*w + 1./24.) )*wy
+ + (((-w*5./16. + 7./24.)*w - 1./4.)*w + 1./6.) )*wy
+ + ((((w*137./360. - 5./12.)*w + 11./24.)*w - 1./2.)*w + 1./2.) )*wy
+ + (((((-w*1./6. + 1./5.)*w - 1./4)*w + 1./3.)*w -1./2.)*w ) )*wy
+ + wy + 1.0;
+ goto done;
+ }
+#endif
+
+/* separate significand from exponent */
+x = frexp( x, &e );
+
+#if 0
+/* For debugging, check for gross overflow. */
+if( (e * y) > (MEXP + 1024) )
+ goto overflow;
+#endif
+
+/* Find significand of x in antilog table A[]. */
+i = 1;
+if( x <= douba(9) )
+ i = 9;
+if( x <= douba(i+4) )
+ i += 4;
+if( x <= douba(i+2) )
+ i += 2;
+if( x >= douba(1) )
+ i = -1;
+i += 1;
+
+
+/* Find (x - A[i])/A[i]
+ * in order to compute log(x/A[i]):
+ *
+ * log(x) = log( a x/a ) = log(a) + log(x/a)
+ *
+ * log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a
+ */
+x -= douba(i);
+x -= doubb(i/2);
+x /= douba(i);
+
+
+/* rational approximation for log(1+v):
+ *
+ * log(1+v) = v - v**2/2 + v**3 P(v) / Q(v)
+ */
+z = x*x;
+w = x * ( z * polevl( x, P, 3 ) / p1evl( x, Q, 4 ) );
+w = w - ldexp( z, -1 ); /* w - 0.5 * z */
+
+/* Convert to base 2 logarithm:
+ * multiply by log2(e)
+ */
+w = w + LOG2EA * w;
+/* Note x was not yet added in
+ * to above rational approximation,
+ * so do it now, while multiplying
+ * by log2(e).
+ */
+z = w + LOG2EA * x;
+z = z + x;
+
+/* Compute exponent term of the base 2 logarithm. */
+w = -i;
+w = ldexp( w, -4 ); /* divide by 16 */
+w += e;
+/* Now base 2 log of x is w + z. */
+
+/* Multiply base 2 log by y, in extended precision. */
+
+/* separate y into large part ya
+ * and small part yb less than 1/16
+ */
+ya = reduc(y);
+yb = y - ya;
+
+
+F = z * y + w * yb;
+Fa = reduc(F);
+Fb = F - Fa;
+
+G = Fa + w * ya;
+Ga = reduc(G);
+Gb = G - Ga;
+
+H = Fb + Gb;
+Ha = reduc(H);
+w = ldexp( Ga+Ha, 4 );
+
+/* Test the power of 2 for overflow */
+if( w > MEXP )
+ {
+#ifndef INFINITIES
+ mtherr( fname, OVERFLOW );
+#endif
+#ifdef INFINITIES
+ if( nflg && yoddint )
+ return( -INFINITY );
+ return( INFINITY );
+#else
+ if( nflg && yoddint )
+ return( -MAXNUM );
+ return( MAXNUM );
+#endif
+ }
+
+if( w < (MNEXP - 1) )
+ {
+#ifndef DENORMAL
+ mtherr( fname, UNDERFLOW );
+#endif
+#ifdef MINUSZERO
+ if( nflg && yoddint )
+ return( NEGZERO );
+#endif
+ return( 0.0 );
+ }
+
+e = w;
+Hb = H - Ha;
+
+if( Hb > 0.0 )
+ {
+ e += 1;
+ Hb -= 0.0625;
+ }
+
+/* Now the product y * log2(x) = Hb + e/16.0.
+ *
+ * Compute base 2 exponential of Hb,
+ * where -0.0625 <= Hb <= 0.
+ */
+z = Hb * polevl( Hb, R, 6 ); /* z = 2**Hb - 1 */
+
+/* Express e/16 as an integer plus a negative number of 16ths.
+ * Find lookup table entry for the fractional power of 2.
+ */
+if( e < 0 )
+ i = 0;
+else
+ i = 1;
+i = e/16 + i;
+e = 16*i - e;
+w = douba( e );
+z = w + w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */
+z = ldexp( z, i ); /* multiply by integer power of 2 */
+
+done:
+
+/* Negate if odd integer power of negative number */
+if( nflg && yoddint )
+ {
+#ifdef MINUSZERO
+ if( z == 0.0 )
+ z = NEGZERO;
+ else
+#endif
+ z = -z;
+ }
+return( z );
+}
+
+
+/* Find a multiple of 1/16 that is within 1/16 of x. */
+static double reduc(x)
+double x;
+{
+double t;
+
+t = ldexp( x, 4 );
+t = floor( t );
+t = ldexp( t, -4 );
+return(t);
+}
diff --git a/libm/double/powi.c b/libm/double/powi.c
new file mode 100644
index 000000000..46d9a1400
--- /dev/null
+++ b/libm/double/powi.c
@@ -0,0 +1,186 @@
+/* powi.c
+ *
+ * Real raised to integer power
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, powi();
+ * int n;
+ *
+ * y = powi( x, n );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns argument x raised to the nth power.
+ * The routine efficiently decomposes n as a sum of powers of
+ * two. The desired power is a product of two-to-the-kth
+ * powers of x. Thus to compute the 32767 power of x requires
+ * 28 multiplications instead of 32767 multiplications.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error:
+ * arithmetic x domain n domain # trials peak rms
+ * DEC .04,26 -26,26 100000 2.7e-16 4.3e-17
+ * IEEE .04,26 -26,26 50000 2.0e-15 3.8e-16
+ * IEEE 1,2 -1022,1023 50000 8.6e-14 1.6e-14
+ *
+ * Returns MAXNUM on overflow, zero on underflow.
+ *
+ */
+
+/* powi.c */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double log ( double );
+extern double frexp ( double, int * );
+extern int signbit ( double );
+#else
+double log(), frexp();
+int signbit();
+#endif
+extern double NEGZERO, INFINITY, MAXNUM, MAXLOG, MINLOG, LOGE2;
+
+double powi( x, nn )
+double x;
+int nn;
+{
+int n, e, sign, asign, lx;
+double w, y, s;
+
+/* See pow.c for these tests. */
+if( x == 0.0 )
+ {
+ if( nn == 0 )
+ return( 1.0 );
+ else if( nn < 0 )
+ return( INFINITY );
+ else
+ {
+ if( nn & 1 )
+ return( x );
+ else
+ return( 0.0 );
+ }
+ }
+
+if( nn == 0 )
+ return( 1.0 );
+
+if( nn == -1 )
+ return( 1.0/x );
+
+if( x < 0.0 )
+ {
+ asign = -1;
+ x = -x;
+ }
+else
+ asign = 0;
+
+
+if( nn < 0 )
+ {
+ sign = -1;
+ n = -nn;
+ }
+else
+ {
+ sign = 1;
+ n = nn;
+ }
+
+/* Even power will be positive. */
+if( (n & 1) == 0 )
+ asign = 0;
+
+/* Overflow detection */
+
+/* Calculate approximate logarithm of answer */
+s = frexp( x, &lx );
+e = (lx - 1)*n;
+if( (e == 0) || (e > 64) || (e < -64) )
+ {
+ s = (s - 7.0710678118654752e-1) / (s + 7.0710678118654752e-1);
+ s = (2.9142135623730950 * s - 0.5 + lx) * nn * LOGE2;
+ }
+else
+ {
+ s = LOGE2 * e;
+ }
+
+if( s > MAXLOG )
+ {
+ mtherr( "powi", OVERFLOW );
+ y = INFINITY;
+ goto done;
+ }
+
+#if DENORMAL
+if( s < MINLOG )
+ {
+ y = 0.0;
+ goto done;
+ }
+
+/* Handle tiny denormal answer, but with less accuracy
+ * since roundoff error in 1.0/x will be amplified.
+ * The precise demarcation should be the gradual underflow threshold.
+ */
+if( (s < (-MAXLOG+2.0)) && (sign < 0) )
+ {
+ x = 1.0/x;
+ sign = -sign;
+ }
+#else
+/* do not produce denormal answer */
+if( s < -MAXLOG )
+ return(0.0);
+#endif
+
+
+/* First bit of the power */
+if( n & 1 )
+ y = x;
+
+else
+ y = 1.0;
+
+w = x;
+n >>= 1;
+while( n )
+ {
+ w = w * w; /* arg to the 2-to-the-kth power */
+ if( n & 1 ) /* if that bit is set, then include in product */
+ y *= w;
+ n >>= 1;
+ }
+
+if( sign < 0 )
+ y = 1.0/y;
+
+done:
+
+if( asign )
+ {
+ /* odd power of negative number */
+ if( y == 0.0 )
+ y = NEGZERO;
+ else
+ y = -y;
+ }
+return(y);
+}
diff --git a/libm/double/psi.c b/libm/double/psi.c
new file mode 100644
index 000000000..6da2aa0c2
--- /dev/null
+++ b/libm/double/psi.c
@@ -0,0 +1,201 @@
+/* psi.c
+ *
+ * Psi (digamma) function
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, psi();
+ *
+ * y = psi( x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * d -
+ * psi(x) = -- ln | (x)
+ * dx
+ *
+ * is the logarithmic derivative of the gamma function.
+ * For integer x,
+ * n-1
+ * -
+ * psi(n) = -EUL + > 1/k.
+ * -
+ * k=1
+ *
+ * This formula is used for 0 < n <= 10. If x is negative, it
+ * is transformed to a positive argument by the reflection
+ * formula psi(1-x) = psi(x) + pi cot(pi x).
+ * For general positive x, the argument is made greater than 10
+ * using the recurrence psi(x+1) = psi(x) + 1/x.
+ * Then the following asymptotic expansion is applied:
+ *
+ * inf. B
+ * - 2k
+ * psi(x) = log(x) - 1/2x - > -------
+ * - 2k
+ * k=1 2k x
+ *
+ * where the B2k are Bernoulli numbers.
+ *
+ * ACCURACY:
+ * Relative error (except absolute when |psi| < 1):
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 2500 1.7e-16 2.0e-17
+ * IEEE 0,30 30000 1.3e-15 1.4e-16
+ * IEEE -30,0 40000 1.5e-15 2.2e-16
+ *
+ * ERROR MESSAGES:
+ * message condition value returned
+ * psi singularity x integer <=0 MAXNUM
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double A[] = {
+ 8.33333333333333333333E-2,
+-2.10927960927960927961E-2,
+ 7.57575757575757575758E-3,
+-4.16666666666666666667E-3,
+ 3.96825396825396825397E-3,
+-8.33333333333333333333E-3,
+ 8.33333333333333333333E-2
+};
+#endif
+
+#ifdef DEC
+static unsigned short A[] = {
+0037252,0125252,0125252,0125253,
+0136654,0145314,0126312,0146255,
+0036370,0037017,0101740,0174076,
+0136210,0104210,0104210,0104211,
+0036202,0004040,0101010,0020202,
+0136410,0104210,0104210,0104211,
+0037252,0125252,0125252,0125253
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short A[] = {
+0x5555,0x5555,0x5555,0x3fb5,
+0x5996,0x9599,0x9959,0xbf95,
+0x1f08,0xf07c,0x07c1,0x3f7f,
+0x1111,0x1111,0x1111,0xbf71,
+0x0410,0x1041,0x4104,0x3f70,
+0x1111,0x1111,0x1111,0xbf81,
+0x5555,0x5555,0x5555,0x3fb5
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short A[] = {
+0x3fb5,0x5555,0x5555,0x5555,
+0xbf95,0x9959,0x9599,0x5996,
+0x3f7f,0x07c1,0xf07c,0x1f08,
+0xbf71,0x1111,0x1111,0x1111,
+0x3f70,0x4104,0x1041,0x0410,
+0xbf81,0x1111,0x1111,0x1111,
+0x3fb5,0x5555,0x5555,0x5555
+};
+#endif
+
+#define EUL 0.57721566490153286061
+
+#ifdef ANSIPROT
+extern double floor ( double );
+extern double log ( double );
+extern double tan ( double );
+extern double polevl ( double, void *, int );
+#else
+double floor(), log(), tan(), polevl();
+#endif
+extern double PI, MAXNUM;
+
+
+double psi(x)
+double x;
+{
+double p, q, nz, s, w, y, z;
+int i, n, negative;
+
+negative = 0;
+nz = 0.0;
+
+if( x <= 0.0 )
+ {
+ negative = 1;
+ q = x;
+ p = floor(q);
+ if( p == q )
+ {
+ mtherr( "psi", SING );
+ return( MAXNUM );
+ }
+/* Remove the zeros of tan(PI x)
+ * by subtracting the nearest integer from x
+ */
+ nz = q - p;
+ if( nz != 0.5 )
+ {
+ if( nz > 0.5 )
+ {
+ p += 1.0;
+ nz = q - p;
+ }
+ nz = PI/tan(PI*nz);
+ }
+ else
+ {
+ nz = 0.0;
+ }
+ x = 1.0 - x;
+ }
+
+/* check for positive integer up to 10 */
+if( (x <= 10.0) && (x == floor(x)) )
+ {
+ y = 0.0;
+ n = x;
+ for( i=1; i<n; i++ )
+ {
+ w = i;
+ y += 1.0/w;
+ }
+ y -= EUL;
+ goto done;
+ }
+
+s = x;
+w = 0.0;
+while( s < 10.0 )
+ {
+ w += 1.0/s;
+ s += 1.0;
+ }
+
+if( s < 1.0e17 )
+ {
+ z = 1.0/(s * s);
+ y = z * polevl( z, A, 6 );
+ }
+else
+ y = 0.0;
+
+y = log(s) - (0.5/s) - y - w;
+
+done:
+
+if( negative )
+ {
+ y -= nz;
+ }
+
+return(y);
+}
diff --git a/libm/double/revers.c b/libm/double/revers.c
new file mode 100644
index 000000000..370bdb5d6
--- /dev/null
+++ b/libm/double/revers.c
@@ -0,0 +1,156 @@
+/* revers.c
+ *
+ * Reversion of power series
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * extern int MAXPOL;
+ * int n;
+ * double x[n+1], y[n+1];
+ *
+ * polini(n);
+ * revers( y, x, n );
+ *
+ * Note, polini() initializes the polynomial arithmetic subroutines;
+ * see polyn.c.
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ *
+ * inf
+ * - i
+ * y(x) = > a x
+ * - i
+ * i=1
+ *
+ * then
+ *
+ * inf
+ * - j
+ * x(y) = > A y ,
+ * - j
+ * j=1
+ *
+ * where
+ * 1
+ * A = ---
+ * 1 a
+ * 1
+ *
+ * etc. The coefficients of x(y) are found by expanding
+ *
+ * inf inf
+ * - - i
+ * x(y) = > A > a x
+ * - j - i
+ * j=1 i=1
+ *
+ * and setting each coefficient of x , higher than the first,
+ * to zero.
+ *
+ *
+ *
+ * RESTRICTIONS:
+ *
+ * y[0] must be zero, and y[1] must be nonzero.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+extern int MAXPOL; /* initialized by polini() */
+
+#ifdef ANSIPROT
+/* See polyn.c. */
+void polmov ( double *, int, double * );
+void polclr ( double *, int );
+void poladd ( double *, int, double *, int, double * );
+void polmul ( double *, int, double *, int, double * );
+void * malloc ( long );
+void free ( void * );
+#else
+void polmov(), polclr(), poladd(), polmul();
+void * malloc();
+void free ();
+#endif
+
+void revers( y, x, n)
+double y[], x[];
+int n;
+{
+double *yn, *yp, *ysum;
+int j;
+
+if( y[1] == 0.0 )
+ mtherr( "revers", DOMAIN );
+/* printf( "revers: y[1] = 0\n" );*/
+j = (MAXPOL + 1) * sizeof(double);
+yn = (double *)malloc(j);
+yp = (double *)malloc(j);
+ysum = (double *)malloc(j);
+
+polmov( y, n, yn );
+polclr( ysum, n );
+x[0] = 0.0;
+x[1] = 1.0/y[1];
+for( j=2; j<=n; j++ )
+ {
+/* A_(j-1) times the expansion of y^(j-1) */
+ polmul( &x[j-1], 0, yn, n, yp );
+/* The expansion of the sum of A_k y^k up to k=j-1 */
+ poladd( yp, n, ysum, n, ysum );
+/* The expansion of y^j */
+ polmul( yn, n, y, n, yn );
+/* The coefficient A_j to make the sum up to k=j equal to zero */
+ x[j] = -ysum[j]/yn[j];
+ }
+free(yn);
+free(yp);
+free(ysum);
+}
+
+
+#if 0
+/* Demonstration program
+ */
+#define N 10
+double y[N], x[N];
+double fac();
+
+main()
+{
+double a, odd;
+int i;
+
+polini( N-1 );
+a = 1.0;
+y[0] = 0.0;
+odd = 1.0;
+for( i=1; i<N; i++ )
+ {
+/* sin(x) */
+/*
+ if( i & 1 )
+ {
+ y[i] = odd/fac(i);
+ odd = -odd;
+ }
+ else
+ y[i] = 0.0;
+*/
+ y[i] = 1.0/fac(i);
+ }
+revers( y, x, N-1 );
+for( i=0; i<N; i++ )
+ printf( "%2d %.10e %.10e\n", i, x[i], y[i] );
+}
+#endif
diff --git a/libm/double/rgamma.c b/libm/double/rgamma.c
new file mode 100644
index 000000000..1d6ff3840
--- /dev/null
+++ b/libm/double/rgamma.c
@@ -0,0 +1,209 @@
+/* rgamma.c
+ *
+ * Reciprocal gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, rgamma();
+ *
+ * y = rgamma( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns one divided by the gamma function of the argument.
+ *
+ * The function is approximated by a Chebyshev expansion in
+ * the interval [0,1]. Range reduction is by recurrence
+ * for arguments between -34.034 and +34.84425627277176174.
+ * 1/MAXNUM is returned for positive arguments outside this
+ * range. For arguments less than -34.034 the cosecant
+ * reflection formula is applied; lograrithms are employed
+ * to avoid unnecessary overflow.
+ *
+ * The reciprocal gamma function has no singularities,
+ * but overflow and underflow may occur for large arguments.
+ * These conditions return either MAXNUM or 1/MAXNUM with
+ * appropriate sign.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -30,+30 4000 1.2e-16 1.8e-17
+ * IEEE -30,+30 30000 1.1e-15 2.0e-16
+ * For arguments less than -34.034 the peak error is on the
+ * order of 5e-15 (DEC), excepting overflow or underflow.
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1985, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for reciprocal gamma function
+ * in interval 0 to 1. Function is 1/(x gamma(x)) - 1
+ */
+
+#ifdef UNK
+static double R[] = {
+ 3.13173458231230000000E-17,
+-6.70718606477908000000E-16,
+ 2.20039078172259550000E-15,
+ 2.47691630348254132600E-13,
+-6.60074100411295197440E-12,
+ 5.13850186324226978840E-11,
+ 1.08965386454418662084E-9,
+-3.33964630686836942556E-8,
+ 2.68975996440595483619E-7,
+ 2.96001177518801696639E-6,
+-8.04814124978471142852E-5,
+ 4.16609138709688864714E-4,
+ 5.06579864028608725080E-3,
+-6.41925436109158228810E-2,
+-4.98558728684003594785E-3,
+ 1.27546015610523951063E-1
+};
+#endif
+
+#ifdef DEC
+static unsigned short R[] = {
+0022420,0066376,0176751,0071636,
+0123501,0051114,0042104,0131153,
+0024036,0107013,0126504,0033361,
+0025613,0070040,0035174,0162316,
+0126750,0037060,0077775,0122202,
+0027541,0177143,0037675,0105150,
+0030625,0141311,0075005,0115436,
+0132017,0067714,0125033,0014721,
+0032620,0063707,0105256,0152643,
+0033506,0122235,0072757,0170053,
+0134650,0144041,0015617,0016143,
+0035332,0066125,0000776,0006215,
+0036245,0177377,0137173,0131432,
+0137203,0073541,0055645,0141150,
+0136243,0057043,0026226,0017362,
+0037402,0115554,0033441,0012310
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short R[] = {
+0x2e74,0xdfbd,0x0d9f,0x3c82,
+0x964d,0x8888,0x2a49,0xbcc8,
+0x86de,0x75a8,0xd1c1,0x3ce3,
+0x9c9a,0x074f,0x6e04,0x3d51,
+0xb490,0x0fff,0x07c6,0xbd9d,
+0xb14d,0x67f7,0x3fcc,0x3dcc,
+0xb364,0x2f40,0xb859,0x3e12,
+0x633a,0x9543,0xedf9,0xbe61,
+0xdab4,0xf155,0x0cf8,0x3e92,
+0xfe05,0xaebd,0xd493,0x3ec8,
+0xe38c,0x2371,0x1904,0xbf15,
+0xc192,0xa03f,0x4d8a,0x3f3b,
+0x7663,0xf7cf,0xbfdf,0x3f74,
+0xb84d,0x2b74,0x6eec,0xbfb0,
+0xc3de,0x6592,0x6bc4,0xbf74,
+0x2299,0x86e4,0x536d,0x3fc0
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short R[] = {
+0x3c82,0x0d9f,0xdfbd,0x2e74,
+0xbcc8,0x2a49,0x8888,0x964d,
+0x3ce3,0xd1c1,0x75a8,0x86de,
+0x3d51,0x6e04,0x074f,0x9c9a,
+0xbd9d,0x07c6,0x0fff,0xb490,
+0x3dcc,0x3fcc,0x67f7,0xb14d,
+0x3e12,0xb859,0x2f40,0xb364,
+0xbe61,0xedf9,0x9543,0x633a,
+0x3e92,0x0cf8,0xf155,0xdab4,
+0x3ec8,0xd493,0xaebd,0xfe05,
+0xbf15,0x1904,0x2371,0xe38c,
+0x3f3b,0x4d8a,0xa03f,0xc192,
+0x3f74,0xbfdf,0xf7cf,0x7663,
+0xbfb0,0x6eec,0x2b74,0xb84d,
+0xbf74,0x6bc4,0x6592,0xc3de,
+0x3fc0,0x536d,0x86e4,0x2299
+};
+#endif
+
+static char name[] = "rgamma";
+
+#ifdef ANSIPROT
+extern double chbevl ( double, void *, int );
+extern double exp ( double );
+extern double log ( double );
+extern double sin ( double );
+extern double lgam ( double );
+#else
+double chbevl(), exp(), log(), sin(), lgam();
+#endif
+extern double PI, MAXLOG, MAXNUM;
+
+
+double rgamma(x)
+double x;
+{
+double w, y, z;
+int sign;
+
+if( x > 34.84425627277176174)
+ {
+ mtherr( name, UNDERFLOW );
+ return(1.0/MAXNUM);
+ }
+if( x < -34.034 )
+ {
+ w = -x;
+ z = sin( PI*w );
+ if( z == 0.0 )
+ return(0.0);
+ if( z < 0.0 )
+ {
+ sign = 1;
+ z = -z;
+ }
+ else
+ sign = -1;
+
+ y = log( w * z ) - log(PI) + lgam(w);
+ if( y < -MAXLOG )
+ {
+ mtherr( name, UNDERFLOW );
+ return( sign * 1.0 / MAXNUM );
+ }
+ if( y > MAXLOG )
+ {
+ mtherr( name, OVERFLOW );
+ return( sign * MAXNUM );
+ }
+ return( sign * exp(y));
+ }
+z = 1.0;
+w = x;
+
+while( w > 1.0 ) /* Downward recurrence */
+ {
+ w -= 1.0;
+ z *= w;
+ }
+while( w < 0.0 ) /* Upward recurrence */
+ {
+ z /= w;
+ w += 1.0;
+ }
+if( w == 0.0 ) /* Nonpositive integer */
+ return(0.0);
+if( w == 1.0 ) /* Other integer */
+ return( 1.0/z );
+
+y = w * ( 1.0 + chbevl( 4.0*w-2.0, R, 16 ) ) / z;
+return(y);
+}
diff --git a/libm/double/round.c b/libm/double/round.c
new file mode 100644
index 000000000..df4564a0f
--- /dev/null
+++ b/libm/double/round.c
@@ -0,0 +1,70 @@
+/* round.c
+ *
+ * Round double to nearest or even integer valued double
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, round();
+ *
+ * y = round(x);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the nearest integer to x as a double precision
+ * floating point result. If x ends in 0.5 exactly, the
+ * nearest even integer is chosen.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * If x is greater than 1/(2*MACHEP), its closest machine
+ * representation is already an integer, so rounding does
+ * not change it.
+ */
+
+/*
+Cephes Math Library Release 2.1: January, 1989
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+#include <math.h>
+#ifdef ANSIPROT
+double floor ( double );
+#else
+double floor();
+#endif
+
+double round(x)
+double x;
+{
+double y, r;
+
+/* Largest integer <= x */
+y = floor(x);
+
+/* Fractional part */
+r = x - y;
+
+/* Round up to nearest. */
+if( r > 0.5 )
+ goto rndup;
+
+/* Round to even */
+if( r == 0.5 )
+ {
+ r = y - 2.0 * floor( 0.5 * y );
+ if( r == 1.0 )
+ {
+rndup:
+ y += 1.0;
+ }
+ }
+
+/* Else round down. */
+return(y);
+}
diff --git a/libm/double/setprec.c b/libm/double/setprec.c
new file mode 100644
index 000000000..a5222ae73
--- /dev/null
+++ b/libm/double/setprec.c
@@ -0,0 +1,10 @@
+/* Null stubs for coprocessor precision settings */
+
+int
+sprec() {return 0; }
+
+int
+dprec() {return 0; }
+
+int
+ldprec() {return 0; }
diff --git a/libm/double/shichi.c b/libm/double/shichi.c
new file mode 100644
index 000000000..a1497fc34
--- /dev/null
+++ b/libm/double/shichi.c
@@ -0,0 +1,599 @@
+/* shichi.c
+ *
+ * Hyperbolic sine and cosine integrals
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, Chi, Shi, shichi();
+ *
+ * shichi( x, &Chi, &Shi );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integrals
+ *
+ * x
+ * -
+ * | | cosh t - 1
+ * Chi(x) = eul + ln x + | ----------- dt,
+ * | | t
+ * -
+ * 0
+ *
+ * x
+ * -
+ * | | sinh t
+ * Shi(x) = | ------ dt
+ * | | t
+ * -
+ * 0
+ *
+ * where eul = 0.57721566490153286061 is Euler's constant.
+ * The integrals are evaluated by power series for x < 8
+ * and by Chebyshev expansions for x between 8 and 88.
+ * For large x, both functions approach exp(x)/2x.
+ * Arguments greater than 88 in magnitude return MAXNUM.
+ *
+ *
+ * ACCURACY:
+ *
+ * Test interval 0 to 88.
+ * Relative error:
+ * arithmetic function # trials peak rms
+ * DEC Shi 3000 9.1e-17
+ * IEEE Shi 30000 6.9e-16 1.6e-16
+ * Absolute error, except relative when |Chi| > 1:
+ * DEC Chi 2500 9.3e-17
+ * IEEE Chi 30000 8.4e-16 1.4e-16
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef UNK
+/* x exp(-x) shi(x), inverted interval 8 to 18 */
+static double S1[] = {
+ 1.83889230173399459482E-17,
+-9.55485532279655569575E-17,
+ 2.04326105980879882648E-16,
+ 1.09896949074905343022E-15,
+-1.31313534344092599234E-14,
+ 5.93976226264314278932E-14,
+-3.47197010497749154755E-14,
+-1.40059764613117131000E-12,
+ 9.49044626224223543299E-12,
+-1.61596181145435454033E-11,
+-1.77899784436430310321E-10,
+ 1.35455469767246947469E-9,
+-1.03257121792819495123E-9,
+-3.56699611114982536845E-8,
+ 1.44818877384267342057E-7,
+ 7.82018215184051295296E-7,
+-5.39919118403805073710E-6,
+-3.12458202168959833422E-5,
+ 8.90136741950727517826E-5,
+ 2.02558474743846862168E-3,
+ 2.96064440855633256972E-2,
+ 1.11847751047257036625E0
+};
+
+/* x exp(-x) shi(x), inverted interval 18 to 88 */
+static double S2[] = {
+-1.05311574154850938805E-17,
+ 2.62446095596355225821E-17,
+ 8.82090135625368160657E-17,
+-3.38459811878103047136E-16,
+-8.30608026366935789136E-16,
+ 3.93397875437050071776E-15,
+ 1.01765565969729044505E-14,
+-4.21128170307640802703E-14,
+-1.60818204519802480035E-13,
+ 3.34714954175994481761E-13,
+ 2.72600352129153073807E-12,
+ 1.66894954752839083608E-12,
+-3.49278141024730899554E-11,
+-1.58580661666482709598E-10,
+-1.79289437183355633342E-10,
+ 1.76281629144264523277E-9,
+ 1.69050228879421288846E-8,
+ 1.25391771228487041649E-7,
+ 1.16229947068677338732E-6,
+ 1.61038260117376323993E-5,
+ 3.49810375601053973070E-4,
+ 1.28478065259647610779E-2,
+ 1.03665722588798326712E0
+};
+#endif
+
+#ifdef DEC
+static unsigned short S1[] = {
+0022251,0115635,0165120,0006574,
+0122734,0050751,0020305,0101356,
+0023153,0111154,0011103,0177462,
+0023636,0060321,0060253,0124246,
+0124554,0106655,0152525,0166400,
+0025205,0140145,0171006,0106556,
+0125034,0056427,0004205,0176022,
+0126305,0016731,0025011,0134453,
+0027046,0172453,0112604,0116235,
+0127216,0022071,0116600,0137667,
+0130103,0115126,0071104,0052535,
+0030672,0025450,0010071,0141414,
+0130615,0165136,0132137,0177737,
+0132031,0031611,0074436,0175407,
+0032433,0077602,0104345,0060076,
+0033121,0165741,0167177,0172433,
+0133665,0025262,0174621,0022612,
+0134403,0006761,0124566,0145405,
+0034672,0126332,0034737,0116744,
+0036004,0137654,0037332,0131766,
+0036762,0104466,0121445,0124326,
+0040217,0025105,0062145,0042640
+};
+
+static unsigned short S2[] = {
+0122102,0041774,0016051,0055137,
+0022362,0010125,0007651,0015773,
+0022713,0062551,0040227,0071645,
+0123303,0015732,0025731,0146570,
+0123557,0064016,0002067,0067711,
+0024215,0136214,0132374,0124234,
+0024467,0051425,0071066,0064210,
+0125075,0124305,0135123,0024170,
+0125465,0010261,0005560,0034232,
+0025674,0066602,0030724,0174557,
+0026477,0151520,0051510,0067250,
+0026352,0161076,0113154,0116271,
+0127431,0116470,0177465,0127274,
+0130056,0056174,0170315,0013321,
+0130105,0020575,0075327,0036710,
+0030762,0043625,0113046,0125035,
+0031621,0033211,0154354,0022077,
+0032406,0121555,0074270,0041141,
+0033234,0000116,0041611,0173743,
+0034207,0013263,0174715,0115563,
+0035267,0063300,0175753,0117266,
+0036522,0077633,0033255,0136200,
+0040204,0130457,0014454,0166254
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short S1[] = {
+0x01b0,0xbd4a,0x3373,0x3c75,
+0xb05e,0x2418,0x8a3d,0xbc9b,
+0x7fe6,0x8248,0x724d,0x3cad,
+0x7515,0x2c15,0xcc1a,0x3cd3,
+0xbda0,0xbaaa,0x91b5,0xbd0d,
+0xd1ae,0xbe40,0xb80c,0x3d30,
+0xbf82,0xe110,0x8ba2,0xbd23,
+0x3725,0x2541,0xa3bb,0xbd78,
+0x9394,0x72b0,0xdea5,0x3da4,
+0x17f7,0x33b0,0xc487,0xbdb1,
+0x8aac,0xce48,0x734a,0xbde8,
+0x3862,0x0207,0x4565,0x3e17,
+0xfffc,0xd68b,0xbd4b,0xbe11,
+0xdf61,0x2f23,0x2671,0xbe63,
+0xac08,0x511c,0x6ff0,0x3e83,
+0xfea3,0x3dcf,0x3d7c,0x3eaa,
+0x24b1,0x5f32,0xa556,0xbed6,
+0xd961,0x352e,0x61be,0xbf00,
+0xf3bd,0x473b,0x559b,0x3f17,
+0x567f,0x87db,0x97f5,0x3f60,
+0xb51b,0xd464,0x5126,0x3f9e,
+0xa8b4,0xac8c,0xe548,0x3ff1
+};
+
+static unsigned short S2[] = {
+0x2b4c,0x8385,0x487f,0xbc68,
+0x237f,0xa1f5,0x420a,0x3c7e,
+0xee75,0x2812,0x6cad,0x3c99,
+0x39af,0x457b,0x637b,0xbcb8,
+0xedf9,0xc086,0xed01,0xbccd,
+0x9513,0x969f,0xb791,0x3cf1,
+0xcd11,0xae46,0xea62,0x3d06,
+0x650f,0xb74a,0xb518,0xbd27,
+0x0713,0x216e,0xa216,0xbd46,
+0x9f2e,0x463a,0x8db0,0x3d57,
+0x0dd5,0x0a69,0xfa6a,0x3d87,
+0x9397,0xd2cd,0x5c47,0x3d7d,
+0xb5d8,0x1fe6,0x33a7,0xbdc3,
+0xa2da,0x9e19,0xcb8f,0xbde5,
+0xe7b9,0xaf5a,0xa42f,0xbde8,
+0xd544,0xb2c4,0x48f2,0x3e1e,
+0x8488,0x3b1d,0x26d1,0x3e52,
+0x084c,0xaf17,0xd46d,0x3e80,
+0x3efc,0xc871,0x8009,0x3eb3,
+0xb36e,0x7f39,0xe2d6,0x3ef0,
+0x73d7,0x1f7d,0xecd8,0x3f36,
+0xb790,0x66d5,0x4ff3,0x3f8a,
+0x9d96,0xe325,0x9625,0x3ff0
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short S1[] = {
+0x3c75,0x3373,0xbd4a,0x01b0,
+0xbc9b,0x8a3d,0x2418,0xb05e,
+0x3cad,0x724d,0x8248,0x7fe6,
+0x3cd3,0xcc1a,0x2c15,0x7515,
+0xbd0d,0x91b5,0xbaaa,0xbda0,
+0x3d30,0xb80c,0xbe40,0xd1ae,
+0xbd23,0x8ba2,0xe110,0xbf82,
+0xbd78,0xa3bb,0x2541,0x3725,
+0x3da4,0xdea5,0x72b0,0x9394,
+0xbdb1,0xc487,0x33b0,0x17f7,
+0xbde8,0x734a,0xce48,0x8aac,
+0x3e17,0x4565,0x0207,0x3862,
+0xbe11,0xbd4b,0xd68b,0xfffc,
+0xbe63,0x2671,0x2f23,0xdf61,
+0x3e83,0x6ff0,0x511c,0xac08,
+0x3eaa,0x3d7c,0x3dcf,0xfea3,
+0xbed6,0xa556,0x5f32,0x24b1,
+0xbf00,0x61be,0x352e,0xd961,
+0x3f17,0x559b,0x473b,0xf3bd,
+0x3f60,0x97f5,0x87db,0x567f,
+0x3f9e,0x5126,0xd464,0xb51b,
+0x3ff1,0xe548,0xac8c,0xa8b4
+};
+
+static unsigned short S2[] = {
+0xbc68,0x487f,0x8385,0x2b4c,
+0x3c7e,0x420a,0xa1f5,0x237f,
+0x3c99,0x6cad,0x2812,0xee75,
+0xbcb8,0x637b,0x457b,0x39af,
+0xbccd,0xed01,0xc086,0xedf9,
+0x3cf1,0xb791,0x969f,0x9513,
+0x3d06,0xea62,0xae46,0xcd11,
+0xbd27,0xb518,0xb74a,0x650f,
+0xbd46,0xa216,0x216e,0x0713,
+0x3d57,0x8db0,0x463a,0x9f2e,
+0x3d87,0xfa6a,0x0a69,0x0dd5,
+0x3d7d,0x5c47,0xd2cd,0x9397,
+0xbdc3,0x33a7,0x1fe6,0xb5d8,
+0xbde5,0xcb8f,0x9e19,0xa2da,
+0xbde8,0xa42f,0xaf5a,0xe7b9,
+0x3e1e,0x48f2,0xb2c4,0xd544,
+0x3e52,0x26d1,0x3b1d,0x8488,
+0x3e80,0xd46d,0xaf17,0x084c,
+0x3eb3,0x8009,0xc871,0x3efc,
+0x3ef0,0xe2d6,0x7f39,0xb36e,
+0x3f36,0xecd8,0x1f7d,0x73d7,
+0x3f8a,0x4ff3,0x66d5,0xb790,
+0x3ff0,0x9625,0xe325,0x9d96
+};
+#endif
+
+
+#ifdef UNK
+/* x exp(-x) chin(x), inverted interval 8 to 18 */
+static double C1[] = {
+-8.12435385225864036372E-18,
+ 2.17586413290339214377E-17,
+ 5.22624394924072204667E-17,
+-9.48812110591690559363E-16,
+ 5.35546311647465209166E-15,
+-1.21009970113732918701E-14,
+-6.00865178553447437951E-14,
+ 7.16339649156028587775E-13,
+-2.93496072607599856104E-12,
+-1.40359438136491256904E-12,
+ 8.76302288609054966081E-11,
+-4.40092476213282340617E-10,
+-1.87992075640569295479E-10,
+ 1.31458150989474594064E-8,
+-4.75513930924765465590E-8,
+-2.21775018801848880741E-7,
+ 1.94635531373272490962E-6,
+ 4.33505889257316408893E-6,
+-6.13387001076494349496E-5,
+-3.13085477492997465138E-4,
+ 4.97164789823116062801E-4,
+ 2.64347496031374526641E-2,
+ 1.11446150876699213025E0
+};
+
+/* x exp(-x) chin(x), inverted interval 18 to 88 */
+static double C2[] = {
+ 8.06913408255155572081E-18,
+-2.08074168180148170312E-17,
+-5.98111329658272336816E-17,
+ 2.68533951085945765591E-16,
+ 4.52313941698904694774E-16,
+-3.10734917335299464535E-15,
+-4.42823207332531972288E-15,
+ 3.49639695410806959872E-14,
+ 6.63406731718911586609E-14,
+-3.71902448093119218395E-13,
+-1.27135418132338309016E-12,
+ 2.74851141935315395333E-12,
+ 2.33781843985453438400E-11,
+ 2.71436006377612442764E-11,
+-2.56600180000355990529E-10,
+-1.61021375163803438552E-9,
+-4.72543064876271773512E-9,
+-3.00095178028681682282E-9,
+ 7.79387474390914922337E-8,
+ 1.06942765566401507066E-6,
+ 1.59503164802313196374E-5,
+ 3.49592575153777996871E-4,
+ 1.28475387530065247392E-2,
+ 1.03665693917934275131E0
+};
+#endif
+
+#ifdef DEC
+static unsigned short C1[] = {
+0122025,0157055,0021702,0021427,
+0022310,0130043,0123265,0022340,
+0022561,0002231,0017746,0013043,
+0123610,0136375,0002352,0024467,
+0024300,0171555,0141300,0000446,
+0124531,0176777,0126210,0035616,
+0125207,0046604,0167760,0077132,
+0026111,0120666,0026606,0064143,
+0126516,0103615,0054127,0005436,
+0126305,0104721,0025415,0004134,
+0027700,0131556,0164725,0157553,
+0130361,0170602,0077274,0055406,
+0130116,0131420,0125472,0017231,
+0031541,0153747,0177312,0056304,
+0132114,0035517,0041545,0043151,
+0132556,0020415,0110044,0172442,
+0033402,0117041,0031152,0010364,
+0033621,0072737,0050647,0013720,
+0134600,0121366,0140010,0063265,
+0135244,0022637,0013756,0044742,
+0035402,0052052,0006523,0043564,
+0036730,0106660,0020277,0162146,
+0040216,0123254,0135147,0005724
+};
+
+static unsigned short C2[] = {
+0022024,0154550,0104311,0144257,
+0122277,0165037,0133443,0155601,
+0122611,0165102,0157053,0055252,
+0023232,0146235,0153511,0113222,
+0023402,0057340,0145304,0010471,
+0124137,0164171,0113071,0100002,
+0124237,0105473,0056130,0022022,
+0025035,0073266,0056746,0164433,
+0025225,0061313,0055600,0165407,
+0125721,0056312,0107613,0051215,
+0126262,0166534,0115336,0066653,
+0026501,0064307,0127442,0065573,
+0027315,0121375,0142020,0045356,
+0027356,0140764,0070641,0046570,
+0130215,0010503,0146335,0177737,
+0130735,0047134,0015215,0163665,
+0131242,0056523,0155276,0050053,
+0131116,0034515,0050707,0163512,
+0032247,0057507,0107545,0032007,
+0033217,0104501,0021706,0025047,
+0034205,0146413,0033746,0076562,
+0035267,0044605,0065355,0002772,
+0036522,0077173,0130716,0170304,
+0040204,0130454,0130571,0027270
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short C1[] = {
+0x4463,0xa478,0xbbc5,0xbc62,
+0xa49c,0x74d6,0x1604,0x3c79,
+0xc2c4,0x23fc,0x2093,0x3c8e,
+0x4527,0xa09d,0x179f,0xbcd1,
+0x0025,0xb858,0x1e6d,0x3cf8,
+0x0772,0xf591,0x3fbf,0xbd0b,
+0x0fcb,0x9dfe,0xe9b0,0xbd30,
+0xcd0c,0xc5b0,0x3436,0x3d69,
+0xe164,0xab0a,0xd0f1,0xbd89,
+0xa10c,0x2561,0xb13a,0xbd78,
+0xbbed,0xdd3a,0x166d,0x3dd8,
+0x8b61,0x4fd7,0x3e30,0xbdfe,
+0x43d3,0x1567,0xd662,0xbde9,
+0x4b98,0xffd9,0x3afc,0x3e4c,
+0xa8cd,0xe86c,0x8769,0xbe69,
+0x9ea4,0xb204,0xc421,0xbe8d,
+0x421f,0x264d,0x53c4,0x3ec0,
+0xe2fa,0xea34,0x2ebb,0x3ed2,
+0x0cd7,0xd801,0x145e,0xbf10,
+0xc93c,0xe2fd,0x84b3,0xbf34,
+0x68ef,0x41aa,0x4a85,0x3f40,
+0xfc8d,0x0417,0x11b6,0x3f9b,
+0xe17b,0x974c,0xd4d5,0x3ff1
+};
+
+static unsigned short C2[] = {
+0x3916,0x1119,0x9b2d,0x3c62,
+0x7b70,0xf6e4,0xfd43,0xbc77,
+0x6b55,0x5bc5,0x3d48,0xbc91,
+0x32d2,0xbae9,0x5993,0x3cb3,
+0x8227,0x1958,0x4bdc,0x3cc0,
+0x3000,0x32c7,0xfd0f,0xbceb,
+0x0482,0x6b8b,0xf167,0xbcf3,
+0xdd23,0xcbbc,0xaed6,0x3d23,
+0x1d61,0x6b70,0xac59,0x3d32,
+0x6a52,0x51f1,0x2b99,0xbd5a,
+0xcdb5,0x935b,0x5dab,0xbd76,
+0x4d6f,0xf5e4,0x2d18,0x3d88,
+0x095e,0xb882,0xb45f,0x3db9,
+0x29af,0x8e34,0xd83e,0x3dbd,
+0xbffc,0x799b,0xa228,0xbdf1,
+0xbcf7,0x8351,0xa9cb,0xbe1b,
+0xca05,0x7b57,0x4baa,0xbe34,
+0xfce9,0xaa38,0xc729,0xbe29,
+0xa681,0xf1ec,0xebe8,0x3e74,
+0xc545,0x2478,0xf128,0x3eb1,
+0xcfae,0x66fc,0xb9a1,0x3ef0,
+0xa0bf,0xad5d,0xe930,0x3f36,
+0xde19,0x7639,0x4fcf,0x3f8a,
+0x25d7,0x962f,0x9625,0x3ff0
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short C1[] = {
+0xbc62,0xbbc5,0xa478,0x4463,
+0x3c79,0x1604,0x74d6,0xa49c,
+0x3c8e,0x2093,0x23fc,0xc2c4,
+0xbcd1,0x179f,0xa09d,0x4527,
+0x3cf8,0x1e6d,0xb858,0x0025,
+0xbd0b,0x3fbf,0xf591,0x0772,
+0xbd30,0xe9b0,0x9dfe,0x0fcb,
+0x3d69,0x3436,0xc5b0,0xcd0c,
+0xbd89,0xd0f1,0xab0a,0xe164,
+0xbd78,0xb13a,0x2561,0xa10c,
+0x3dd8,0x166d,0xdd3a,0xbbed,
+0xbdfe,0x3e30,0x4fd7,0x8b61,
+0xbde9,0xd662,0x1567,0x43d3,
+0x3e4c,0x3afc,0xffd9,0x4b98,
+0xbe69,0x8769,0xe86c,0xa8cd,
+0xbe8d,0xc421,0xb204,0x9ea4,
+0x3ec0,0x53c4,0x264d,0x421f,
+0x3ed2,0x2ebb,0xea34,0xe2fa,
+0xbf10,0x145e,0xd801,0x0cd7,
+0xbf34,0x84b3,0xe2fd,0xc93c,
+0x3f40,0x4a85,0x41aa,0x68ef,
+0x3f9b,0x11b6,0x0417,0xfc8d,
+0x3ff1,0xd4d5,0x974c,0xe17b
+};
+
+static unsigned short C2[] = {
+0x3c62,0x9b2d,0x1119,0x3916,
+0xbc77,0xfd43,0xf6e4,0x7b70,
+0xbc91,0x3d48,0x5bc5,0x6b55,
+0x3cb3,0x5993,0xbae9,0x32d2,
+0x3cc0,0x4bdc,0x1958,0x8227,
+0xbceb,0xfd0f,0x32c7,0x3000,
+0xbcf3,0xf167,0x6b8b,0x0482,
+0x3d23,0xaed6,0xcbbc,0xdd23,
+0x3d32,0xac59,0x6b70,0x1d61,
+0xbd5a,0x2b99,0x51f1,0x6a52,
+0xbd76,0x5dab,0x935b,0xcdb5,
+0x3d88,0x2d18,0xf5e4,0x4d6f,
+0x3db9,0xb45f,0xb882,0x095e,
+0x3dbd,0xd83e,0x8e34,0x29af,
+0xbdf1,0xa228,0x799b,0xbffc,
+0xbe1b,0xa9cb,0x8351,0xbcf7,
+0xbe34,0x4baa,0x7b57,0xca05,
+0xbe29,0xc729,0xaa38,0xfce9,
+0x3e74,0xebe8,0xf1ec,0xa681,
+0x3eb1,0xf128,0x2478,0xc545,
+0x3ef0,0xb9a1,0x66fc,0xcfae,
+0x3f36,0xe930,0xad5d,0xa0bf,
+0x3f8a,0x4fcf,0x7639,0xde19,
+0x3ff0,0x9625,0x962f,0x25d7
+};
+#endif
+
+
+
+/* Sine and cosine integrals */
+
+#ifdef ANSIPROT
+extern double log ( double );
+extern double exp ( double );
+extern double fabs ( double );
+extern double chbevl ( double, void *, int );
+#else
+double log(), exp(), fabs(), chbevl();
+#endif
+#define EUL 0.57721566490153286061
+extern double MACHEP, MAXNUM, PIO2;
+
+int shichi( x, si, ci )
+double x;
+double *si, *ci;
+{
+double k, z, c, s, a;
+short sign;
+
+if( x < 0.0 )
+ {
+ sign = -1;
+ x = -x;
+ }
+else
+ sign = 0;
+
+
+if( x == 0.0 )
+ {
+ *si = 0.0;
+ *ci = -MAXNUM;
+ return( 0 );
+ }
+
+if( x >= 8.0 )
+ goto chb;
+
+z = x * x;
+
+/* Direct power series expansion */
+
+a = 1.0;
+s = 1.0;
+c = 0.0;
+k = 2.0;
+
+do
+ {
+ a *= z/k;
+ c += a/k;
+ k += 1.0;
+ a /= k;
+ s += a/k;
+ k += 1.0;
+ }
+while( fabs(a/s) > MACHEP );
+
+s *= x;
+goto done;
+
+
+chb:
+
+if( x < 18.0 )
+ {
+ a = (576.0/x - 52.0)/10.0;
+ k = exp(x) / x;
+ s = k * chbevl( a, S1, 22 );
+ c = k * chbevl( a, C1, 23 );
+ goto done;
+ }
+
+if( x <= 88.0 )
+ {
+ a = (6336.0/x - 212.0)/70.0;
+ k = exp(x) / x;
+ s = k * chbevl( a, S2, 23 );
+ c = k * chbevl( a, C2, 24 );
+ goto done;
+ }
+else
+ {
+ if( sign )
+ *si = -MAXNUM;
+ else
+ *si = MAXNUM;
+ *ci = MAXNUM;
+ return(0);
+ }
+done:
+if( sign )
+ s = -s;
+
+*si = s;
+
+*ci = EUL + log(x) + c;
+return(0);
+}
diff --git a/libm/double/sici.c b/libm/double/sici.c
new file mode 100644
index 000000000..b00b9c449
--- /dev/null
+++ b/libm/double/sici.c
@@ -0,0 +1,675 @@
+/* sici.c
+ *
+ * Sine and cosine integrals
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, Ci, Si, sici();
+ *
+ * sici( x, &Si, &Ci );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the integrals
+ *
+ * x
+ * -
+ * | cos t - 1
+ * Ci(x) = eul + ln x + | --------- dt,
+ * | t
+ * -
+ * 0
+ * x
+ * -
+ * | sin t
+ * Si(x) = | ----- dt
+ * | t
+ * -
+ * 0
+ *
+ * where eul = 0.57721566490153286061 is Euler's constant.
+ * The integrals are approximated by rational functions.
+ * For x > 8 auxiliary functions f(x) and g(x) are employed
+ * such that
+ *
+ * Ci(x) = f(x) sin(x) - g(x) cos(x)
+ * Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)
+ *
+ *
+ * ACCURACY:
+ * Test interval = [0,50].
+ * Absolute error, except relative when > 1:
+ * arithmetic function # trials peak rms
+ * IEEE Si 30000 4.4e-16 7.3e-17
+ * IEEE Ci 30000 6.9e-16 5.1e-17
+ * DEC Si 5000 4.4e-17 9.0e-18
+ * DEC Ci 5300 7.9e-17 5.2e-18
+ */
+
+/*
+Cephes Math Library Release 2.1: January, 1989
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double SN[] = {
+-8.39167827910303881427E-11,
+ 4.62591714427012837309E-8,
+-9.75759303843632795789E-6,
+ 9.76945438170435310816E-4,
+-4.13470316229406538752E-2,
+ 1.00000000000000000302E0,
+};
+static double SD[] = {
+ 2.03269266195951942049E-12,
+ 1.27997891179943299903E-9,
+ 4.41827842801218905784E-7,
+ 9.96412122043875552487E-5,
+ 1.42085239326149893930E-2,
+ 9.99999999999999996984E-1,
+};
+#endif
+#ifdef DEC
+static unsigned short SN[] = {
+0127670,0104362,0167505,0035161,
+0032106,0127177,0032131,0056461,
+0134043,0132213,0000476,0172351,
+0035600,0006331,0064761,0032665,
+0137051,0055601,0044667,0017645,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short SD[] = {
+0026417,0004674,0052064,0001573,
+0030657,0165501,0014666,0131526,
+0032755,0032133,0034147,0024124,
+0034720,0173167,0166624,0154477,
+0036550,0145336,0063534,0063220,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short SN[] = {
+0xa74e,0x5de8,0x111e,0xbdd7,
+0x2ba6,0xe68b,0xd5cf,0x3e68,
+0xde9d,0x6027,0x7691,0xbee4,
+0x26b7,0x2d3e,0x019b,0x3f50,
+0xe3f5,0x2936,0x2b70,0xbfa5,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short SD[] = {
+0x806f,0x8a86,0xe137,0x3d81,
+0xd66b,0x2336,0xfd68,0x3e15,
+0xe50a,0x670c,0xa68b,0x3e9d,
+0x9b28,0xfdb2,0x1ece,0x3f1a,
+0x8cd2,0xcceb,0x195b,0x3f8d,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short SN[] = {
+0xbdd7,0x111e,0x5de8,0xa74e,
+0x3e68,0xd5cf,0xe68b,0x2ba6,
+0xbee4,0x7691,0x6027,0xde9d,
+0x3f50,0x019b,0x2d3e,0x26b7,
+0xbfa5,0x2b70,0x2936,0xe3f5,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short SD[] = {
+0x3d81,0xe137,0x8a86,0x806f,
+0x3e15,0xfd68,0x2336,0xd66b,
+0x3e9d,0xa68b,0x670c,0xe50a,
+0x3f1a,0x1ece,0xfdb2,0x9b28,
+0x3f8d,0x195b,0xcceb,0x8cd2,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+#ifdef UNK
+static double CN[] = {
+ 2.02524002389102268789E-11,
+-1.35249504915790756375E-8,
+ 3.59325051419993077021E-6,
+-4.74007206873407909465E-4,
+ 2.89159652607555242092E-2,
+-1.00000000000000000080E0,
+};
+static double CD[] = {
+ 4.07746040061880559506E-12,
+ 3.06780997581887812692E-9,
+ 1.23210355685883423679E-6,
+ 3.17442024775032769882E-4,
+ 5.10028056236446052392E-2,
+ 4.00000000000000000080E0,
+};
+#endif
+#ifdef DEC
+static unsigned short CN[] = {
+0027262,0022131,0160257,0020166,
+0131550,0055534,0077637,0000557,
+0033561,0021622,0161463,0026575,
+0135370,0102053,0116333,0000466,
+0036754,0160454,0122022,0024622,
+0140200,0000000,0000000,0000000,
+};
+static unsigned short CD[] = {
+0026617,0073177,0107543,0104425,
+0031122,0150573,0156453,0041517,
+0033245,0057301,0077706,0110510,
+0035246,0067130,0165424,0044543,
+0037120,0164121,0061206,0053657,
+0040600,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short CN[] = {
+0xe40f,0x3c15,0x448b,0x3db6,
+0xe02e,0x8ff3,0x0b6b,0xbe4d,
+0x65b0,0x5c66,0x2472,0x3ece,
+0x6027,0x739b,0x1085,0xbf3f,
+0x4532,0x9482,0x9c25,0x3f9d,
+0x0000,0x0000,0x0000,0xbff0,
+};
+static unsigned short CD[] = {
+0x7123,0xf1ec,0xeecf,0x3d91,
+0x686a,0x7ba5,0x5a2f,0x3e2a,
+0xd229,0x2ff8,0xabd8,0x3eb4,
+0x892c,0x1d62,0xcdcb,0x3f34,
+0xcaf6,0x2c50,0x1d0a,0x3faa,
+0x0000,0x0000,0x0000,0x4010,
+};
+#endif
+#ifdef MIEEE
+static unsigned short CN[] = {
+0x3db6,0x448b,0x3c15,0xe40f,
+0xbe4d,0x0b6b,0x8ff3,0xe02e,
+0x3ece,0x2472,0x5c66,0x65b0,
+0xbf3f,0x1085,0x739b,0x6027,
+0x3f9d,0x9c25,0x9482,0x4532,
+0xbff0,0x0000,0x0000,0x0000,
+};
+static unsigned short CD[] = {
+0x3d91,0xeecf,0xf1ec,0x7123,
+0x3e2a,0x5a2f,0x7ba5,0x686a,
+0x3eb4,0xabd8,0x2ff8,0xd229,
+0x3f34,0xcdcb,0x1d62,0x892c,
+0x3faa,0x1d0a,0x2c50,0xcaf6,
+0x4010,0x0000,0x0000,0x0000,
+};
+#endif
+
+
+#ifdef UNK
+static double FN4[] = {
+ 4.23612862892216586994E0,
+ 5.45937717161812843388E0,
+ 1.62083287701538329132E0,
+ 1.67006611831323023771E-1,
+ 6.81020132472518137426E-3,
+ 1.08936580650328664411E-4,
+ 5.48900223421373614008E-7,
+};
+static double FD4[] = {
+/* 1.00000000000000000000E0,*/
+ 8.16496634205391016773E0,
+ 7.30828822505564552187E0,
+ 1.86792257950184183883E0,
+ 1.78792052963149907262E-1,
+ 7.01710668322789753610E-3,
+ 1.10034357153915731354E-4,
+ 5.48900252756255700982E-7,
+};
+#endif
+#ifdef DEC
+static unsigned short FN4[] = {
+0040607,0107135,0120133,0153471,
+0040656,0131467,0140424,0017567,
+0040317,0073563,0121610,0002511,
+0037453,0001710,0000040,0006334,
+0036337,0024033,0176003,0171425,
+0034744,0072341,0121657,0126035,
+0033023,0054042,0154652,0000451,
+};
+static unsigned short FD4[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041002,0121663,0137500,0177450,
+0040751,0156577,0042213,0061552,
+0040357,0014026,0045465,0147265,
+0037467,0012503,0110413,0131772,
+0036345,0167701,0155706,0160551,
+0034746,0141076,0162250,0123547,
+0033023,0054043,0056706,0151050,
+};
+#endif
+#ifdef IBMPC
+static unsigned short FN4[] = {
+0x7ae7,0xb40b,0xf1cb,0x4010,
+0x83ef,0xf822,0xd666,0x4015,
+0x00a9,0x7471,0xeeee,0x3ff9,
+0x019c,0x0004,0x6079,0x3fc5,
+0x7e63,0x7f80,0xe503,0x3f7b,
+0xf584,0x3475,0x8e9c,0x3f1c,
+0x4025,0x5b35,0x6b04,0x3ea2,
+};
+static unsigned short FD4[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x1fe5,0x77e8,0x5476,0x4020,
+0x6c6d,0xe891,0x3baf,0x401d,
+0xb9d7,0xc966,0xe302,0x3ffd,
+0x767f,0x7221,0xe2a8,0x3fc6,
+0xdc2d,0x3b78,0xbdf8,0x3f7c,
+0x14ed,0xdc95,0xd847,0x3f1c,
+0xda45,0x6bb8,0x6b04,0x3ea2,
+};
+#endif
+#ifdef MIEEE
+static unsigned short FN4[] = {
+0x4010,0xf1cb,0xb40b,0x7ae7,
+0x4015,0xd666,0xf822,0x83ef,
+0x3ff9,0xeeee,0x7471,0x00a9,
+0x3fc5,0x6079,0x0004,0x019c,
+0x3f7b,0xe503,0x7f80,0x7e63,
+0x3f1c,0x8e9c,0x3475,0xf584,
+0x3ea2,0x6b04,0x5b35,0x4025,
+};
+static unsigned short FD4[] = {
+/* 0x3ff0,0x0000,0x0000,0x0000,*/
+0x4020,0x5476,0x77e8,0x1fe5,
+0x401d,0x3baf,0xe891,0x6c6d,
+0x3ffd,0xe302,0xc966,0xb9d7,
+0x3fc6,0xe2a8,0x7221,0x767f,
+0x3f7c,0xbdf8,0x3b78,0xdc2d,
+0x3f1c,0xd847,0xdc95,0x14ed,
+0x3ea2,0x6b04,0x6bb8,0xda45,
+};
+#endif
+
+#ifdef UNK
+static double FN8[] = {
+ 4.55880873470465315206E-1,
+ 7.13715274100146711374E-1,
+ 1.60300158222319456320E-1,
+ 1.16064229408124407915E-2,
+ 3.49556442447859055605E-4,
+ 4.86215430826454749482E-6,
+ 3.20092790091004902806E-8,
+ 9.41779576128512936592E-11,
+ 9.70507110881952024631E-14,
+};
+static double FD8[] = {
+/* 1.00000000000000000000E0,*/
+ 9.17463611873684053703E-1,
+ 1.78685545332074536321E-1,
+ 1.22253594771971293032E-2,
+ 3.58696481881851580297E-4,
+ 4.92435064317881464393E-6,
+ 3.21956939101046018377E-8,
+ 9.43720590350276732376E-11,
+ 9.70507110881952025725E-14,
+};
+#endif
+#ifdef DEC
+static unsigned short FN8[] = {
+0037751,0064467,0142332,0164573,
+0040066,0133013,0050352,0071102,
+0037444,0022671,0102157,0013535,
+0036476,0024335,0136423,0146444,
+0035267,0042253,0164110,0110460,
+0033643,0022626,0062535,0060320,
+0032011,0075223,0010110,0153413,
+0027717,0014572,0011360,0014034,
+0025332,0104755,0004563,0152354,
+};
+static unsigned short FD8[] = {
+/*0040200,0000000,0000000,0000000,*/
+0040152,0157345,0030104,0075616,
+0037466,0174527,0172740,0071060,
+0036510,0046337,0144272,0156552,
+0035274,0007555,0042537,0015572,
+0033645,0035731,0112465,0026474,
+0032012,0043612,0030613,0030123,
+0027717,0103277,0004564,0151000,
+0025332,0104755,0004563,0152354,
+};
+#endif
+#ifdef IBMPC
+static unsigned short FN8[] = {
+0x5d2f,0xf89b,0x2d26,0x3fdd,
+0x4e48,0x6a1d,0xd6c1,0x3fe6,
+0xe2ec,0x308d,0x84b7,0x3fc4,
+0x79a4,0xb7a2,0xc51b,0x3f87,
+0x1226,0x7d09,0xe895,0x3f36,
+0xac1a,0xccab,0x64b2,0x3ed4,
+0x1ae1,0x6209,0x2f52,0x3e61,
+0x0304,0x425e,0xe32f,0x3dd9,
+0x7a9d,0xa12e,0x513d,0x3d3b,
+};
+static unsigned short FD8[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x8f72,0xa608,0x5bdc,0x3fed,
+0x0e46,0xfebc,0xdf2a,0x3fc6,
+0x5bad,0xf917,0x099b,0x3f89,
+0xe36f,0xa8ab,0x81ed,0x3f37,
+0xa5a8,0x32a6,0xa77b,0x3ed4,
+0x660a,0x4631,0x48f1,0x3e61,
+0x9a40,0xe12e,0xf0d7,0x3dd9,
+0x7a9d,0xa12e,0x513d,0x3d3b,
+};
+#endif
+#ifdef MIEEE
+static unsigned short FN8[] = {
+0x3fdd,0x2d26,0xf89b,0x5d2f,
+0x3fe6,0xd6c1,0x6a1d,0x4e48,
+0x3fc4,0x84b7,0x308d,0xe2ec,
+0x3f87,0xc51b,0xb7a2,0x79a4,
+0x3f36,0xe895,0x7d09,0x1226,
+0x3ed4,0x64b2,0xccab,0xac1a,
+0x3e61,0x2f52,0x6209,0x1ae1,
+0x3dd9,0xe32f,0x425e,0x0304,
+0x3d3b,0x513d,0xa12e,0x7a9d,
+};
+static unsigned short FD8[] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x3fed,0x5bdc,0xa608,0x8f72,
+0x3fc6,0xdf2a,0xfebc,0x0e46,
+0x3f89,0x099b,0xf917,0x5bad,
+0x3f37,0x81ed,0xa8ab,0xe36f,
+0x3ed4,0xa77b,0x32a6,0xa5a8,
+0x3e61,0x48f1,0x4631,0x660a,
+0x3dd9,0xf0d7,0xe12e,0x9a40,
+0x3d3b,0x513d,0xa12e,0x7a9d,
+};
+#endif
+
+#ifdef UNK
+static double GN4[] = {
+ 8.71001698973114191777E-2,
+ 6.11379109952219284151E-1,
+ 3.97180296392337498885E-1,
+ 7.48527737628469092119E-2,
+ 5.38868681462177273157E-3,
+ 1.61999794598934024525E-4,
+ 1.97963874140963632189E-6,
+ 7.82579040744090311069E-9,
+};
+static double GD4[] = {
+/* 1.00000000000000000000E0,*/
+ 1.64402202413355338886E0,
+ 6.66296701268987968381E-1,
+ 9.88771761277688796203E-2,
+ 6.22396345441768420760E-3,
+ 1.73221081474177119497E-4,
+ 2.02659182086343991969E-6,
+ 7.82579218933534490868E-9,
+};
+#endif
+#ifdef DEC
+static unsigned short GN4[] = {
+0037262,0060622,0164572,0157515,
+0040034,0101527,0061263,0147204,
+0037713,0055467,0037475,0144512,
+0037231,0046151,0035234,0045261,
+0036260,0111624,0150617,0053536,
+0035051,0157175,0016675,0155456,
+0033404,0154757,0041211,0000055,
+0031406,0071060,0130322,0033322,
+};
+static unsigned short GD4[] = {
+/* 0040200,0000000,0000000,0000000,*/
+0040322,0067520,0046707,0053275,
+0040052,0111153,0126542,0005516,
+0037312,0100035,0167121,0014552,
+0036313,0171143,0137176,0014213,
+0035065,0121256,0012033,0150603,
+0033410,0000225,0013121,0071643,
+0031406,0071062,0131152,0150454,
+};
+#endif
+#ifdef IBMPC
+static unsigned short GN4[] = {
+0x5bea,0x5d2f,0x4c32,0x3fb6,
+0x79d1,0xec56,0x906a,0x3fe3,
+0xb929,0xe7e7,0x6b66,0x3fd9,
+0x8956,0x2753,0x298d,0x3fb3,
+0xeaec,0x9a31,0x1272,0x3f76,
+0xbb66,0xa3b7,0x3bcf,0x3f25,
+0x2006,0xe851,0x9b3d,0x3ec0,
+0x46da,0x161a,0xce46,0x3e40,
+};
+static unsigned short GD4[] = {
+/* 0x0000,0x0000,0x0000,0x3ff0,*/
+0xead8,0x09b8,0x4dea,0x3ffa,
+0x416a,0x75ac,0x524d,0x3fe5,
+0x232d,0xbdca,0x5003,0x3fb9,
+0xc311,0x77cf,0x7e4c,0x3f79,
+0x7a30,0xc283,0xb455,0x3f26,
+0x2e74,0xa2ca,0x0012,0x3ec1,
+0x5a26,0x564d,0xce46,0x3e40,
+};
+#endif
+#ifdef MIEEE
+static unsigned short GN4[] = {
+0x3fb6,0x4c32,0x5d2f,0x5bea,
+0x3fe3,0x906a,0xec56,0x79d1,
+0x3fd9,0x6b66,0xe7e7,0xb929,
+0x3fb3,0x298d,0x2753,0x8956,
+0x3f76,0x1272,0x9a31,0xeaec,
+0x3f25,0x3bcf,0xa3b7,0xbb66,
+0x3ec0,0x9b3d,0xe851,0x2006,
+0x3e40,0xce46,0x161a,0x46da,
+};
+static unsigned short GD4[] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x3ffa,0x4dea,0x09b8,0xead8,
+0x3fe5,0x524d,0x75ac,0x416a,
+0x3fb9,0x5003,0xbdca,0x232d,
+0x3f79,0x7e4c,0x77cf,0xc311,
+0x3f26,0xb455,0xc283,0x7a30,
+0x3ec1,0x0012,0xa2ca,0x2e74,
+0x3e40,0xce46,0x564d,0x5a26,
+};
+#endif
+
+#ifdef UNK
+static double GN8[] = {
+ 6.97359953443276214934E-1,
+ 3.30410979305632063225E-1,
+ 3.84878767649974295920E-2,
+ 1.71718239052347903558E-3,
+ 3.48941165502279436777E-5,
+ 3.47131167084116673800E-7,
+ 1.70404452782044526189E-9,
+ 3.85945925430276600453E-12,
+ 3.14040098946363334640E-15,
+};
+static double GD8[] = {
+/* 1.00000000000000000000E0,*/
+ 1.68548898811011640017E0,
+ 4.87852258695304967486E-1,
+ 4.67913194259625806320E-2,
+ 1.90284426674399523638E-3,
+ 3.68475504442561108162E-5,
+ 3.57043223443740838771E-7,
+ 1.72693748966316146736E-9,
+ 3.87830166023954706752E-12,
+ 3.14040098946363335242E-15,
+};
+#endif
+#ifdef DEC
+static unsigned short GN8[] = {
+0040062,0103056,0110624,0033123,
+0037651,0025640,0136266,0145647,
+0037035,0122566,0137770,0061777,
+0035741,0011424,0065311,0013370,
+0034422,0055505,0134324,0016755,
+0032672,0056530,0022565,0014747,
+0030752,0031674,0114735,0013162,
+0026607,0145353,0022020,0123625,
+0024142,0045054,0060033,0016505,
+};
+static unsigned short GD8[] = {
+/*0040200,0000000,0000000,0000000,*/
+0040327,0137032,0064331,0136425,
+0037771,0143705,0070300,0105711,
+0037077,0124101,0025275,0035356,
+0035771,0064333,0145103,0105357,
+0034432,0106301,0105311,0010713,
+0032677,0127645,0120034,0157551,
+0030755,0054466,0010743,0105566,
+0026610,0072242,0142530,0135744,
+0024142,0045054,0060033,0016505,
+};
+#endif
+#ifdef IBMPC
+static unsigned short GN8[] = {
+0x86ca,0xd232,0x50c5,0x3fe6,
+0xd975,0x1796,0x2574,0x3fd5,
+0x0c80,0xd7ff,0xb4ae,0x3fa3,
+0x22df,0x8d59,0x2262,0x3f5c,
+0x83be,0xb71a,0x4b68,0x3f02,
+0xa33d,0x04ae,0x4bab,0x3e97,
+0xa2ce,0x933b,0x4677,0x3e1d,
+0x14f3,0x6482,0xf95d,0x3d90,
+0x63a9,0x8c03,0x4945,0x3cec,
+};
+static unsigned short GD8[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x37a3,0x4d1b,0xf7c3,0x3ffa,
+0x1179,0xae18,0x38f8,0x3fdf,
+0xa75e,0x2557,0xf508,0x3fa7,
+0x715e,0x7948,0x2d1b,0x3f5f,
+0x2239,0x3159,0x5198,0x3f03,
+0x9bed,0xb403,0xf5f4,0x3e97,
+0x716f,0xc23c,0xab26,0x3e1d,
+0x177c,0x58ab,0x0e94,0x3d91,
+0x63a9,0x8c03,0x4945,0x3cec,
+};
+#endif
+#ifdef MIEEE
+static unsigned short GN8[] = {
+0x3fe6,0x50c5,0xd232,0x86ca,
+0x3fd5,0x2574,0x1796,0xd975,
+0x3fa3,0xb4ae,0xd7ff,0x0c80,
+0x3f5c,0x2262,0x8d59,0x22df,
+0x3f02,0x4b68,0xb71a,0x83be,
+0x3e97,0x4bab,0x04ae,0xa33d,
+0x3e1d,0x4677,0x933b,0xa2ce,
+0x3d90,0xf95d,0x6482,0x14f3,
+0x3cec,0x4945,0x8c03,0x63a9,
+};
+static unsigned short GD8[] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x3ffa,0xf7c3,0x4d1b,0x37a3,
+0x3fdf,0x38f8,0xae18,0x1179,
+0x3fa7,0xf508,0x2557,0xa75e,
+0x3f5f,0x2d1b,0x7948,0x715e,
+0x3f03,0x5198,0x3159,0x2239,
+0x3e97,0xf5f4,0xb403,0x9bed,
+0x3e1d,0xab26,0xc23c,0x716f,
+0x3d91,0x0e94,0x58ab,0x177c,
+0x3cec,0x4945,0x8c03,0x63a9,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double log ( double );
+extern double sin ( double );
+extern double cos ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+#else
+double log(), sin(), cos(), polevl(), p1evl();
+#endif
+#define EUL 0.57721566490153286061
+extern double MAXNUM, PIO2, MACHEP;
+
+
+int sici( x, si, ci )
+double x;
+double *si, *ci;
+{
+double z, c, s, f, g;
+short sign;
+
+if( x < 0.0 )
+ {
+ sign = -1;
+ x = -x;
+ }
+else
+ sign = 0;
+
+
+if( x == 0.0 )
+ {
+ *si = 0.0;
+ *ci = -MAXNUM;
+ return( 0 );
+ }
+
+
+if( x > 1.0e9 )
+ {
+ *si = PIO2 - cos(x)/x;
+ *ci = sin(x)/x;
+ return( 0 );
+ }
+
+
+
+if( x > 4.0 )
+ goto asympt;
+
+z = x * x;
+s = x * polevl( z, SN, 5 ) / polevl( z, SD, 5 );
+c = z * polevl( z, CN, 5 ) / polevl( z, CD, 5 );
+
+if( sign )
+ s = -s;
+*si = s;
+*ci = EUL + log(x) + c; /* real part if x < 0 */
+return(0);
+
+
+
+/* The auxiliary functions are:
+ *
+ *
+ * *si = *si - PIO2;
+ * c = cos(x);
+ * s = sin(x);
+ *
+ * t = *ci * s - *si * c;
+ * a = *ci * c + *si * s;
+ *
+ * *si = t;
+ * *ci = -a;
+ */
+
+
+asympt:
+
+s = sin(x);
+c = cos(x);
+z = 1.0/(x*x);
+if( x < 8.0 )
+ {
+ f = polevl( z, FN4, 6 ) / (x * p1evl( z, FD4, 7 ));
+ g = z * polevl( z, GN4, 7 ) / p1evl( z, GD4, 7 );
+ }
+else
+ {
+ f = polevl( z, FN8, 8 ) / (x * p1evl( z, FD8, 8 ));
+ g = z * polevl( z, GN8, 8 ) / p1evl( z, GD8, 9 );
+ }
+*si = PIO2 - f * c - g * s;
+if( sign )
+ *si = -( *si );
+*ci = f * s - g * c;
+
+return(0);
+}
diff --git a/libm/double/simpsn.c b/libm/double/simpsn.c
new file mode 100644
index 000000000..4eb19460b
--- /dev/null
+++ b/libm/double/simpsn.c
@@ -0,0 +1,81 @@
+/* simpsn.c */
+/* simpsn.c
+ * Numerical integration of function tabulated
+ * at equally spaced arguments
+ */
+
+/* Coefficients for Cote integration formulas */
+
+/* Note: these numbers were computed using 40-decimal precision. */
+
+#define NCOTE 8
+
+/* 6th order formula */
+/*
+static double simcon[] =
+{
+ 4.88095238095238095E-2,
+ 2.57142857142857142857E-1,
+ 3.2142857142857142857E-2,
+ 3.2380952380952380952E-1,
+};
+*/
+
+/* 8th order formula */
+static double simcon[] =
+{
+ 3.488536155202821869E-2,
+ 2.076895943562610229E-1,
+ -3.27336860670194003527E-2,
+ 3.7022927689594356261E-1,
+ -1.6014109347442680776E-1,
+};
+
+/* 10th order formula */
+/*
+static double simcon[] =
+{
+ 2.68341483619261397039E-2,
+ 1.77535941424830313719E-1,
+ -8.1043570626903960237E-2,
+ 4.5494628827962161295E-1,
+ -4.3515512265512265512E-1,
+ 7.1376463043129709796E-1,
+};
+*/
+
+/* simpsn.c 2 */
+/* 20th order formula */
+/*
+static double simcon[] =
+{
+ 1.182527324903160319E-2,
+ 1.14137717644606974987E-1,
+ -2.36478370511426964E-1,
+ 1.20618689348187566E+0,
+ -3.7710317267153304677E+0,
+ 1.03367982199398011435E+1,
+ -2.270881584397951229796E+1,
+ 4.1828057422193554603E+1,
+ -6.4075279490154004651555E+1,
+ 8.279728347247285172085E+1,
+ -9.0005367135242894657916E+1,
+};
+*/
+
+/* simpsn.c 3 */
+double simpsn( f, delta )
+double f[]; /* tabulated function */
+double delta; /* spacing of arguments */
+{
+extern double simcon[];
+double ans;
+int i;
+
+
+ans = simcon[NCOTE/2] * f[NCOTE/2];
+for( i=0; i < NCOTE/2; i++ )
+ ans += simcon[i] * ( f[i] + f[NCOTE-i] );
+
+return( ans * delta * NCOTE );
+}
diff --git a/libm/double/simq.c b/libm/double/simq.c
new file mode 100644
index 000000000..96d63e521
--- /dev/null
+++ b/libm/double/simq.c
@@ -0,0 +1,180 @@
+/* simq.c
+ *
+ * Solution of simultaneous linear equations AX = B
+ * by Gaussian elimination with partial pivoting
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double A[n*n], B[n], X[n];
+ * int n, flag;
+ * int IPS[];
+ * int simq();
+ *
+ * ercode = simq( A, B, X, n, flag, IPS );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * B, X, IPS are vectors of length n.
+ * A is an n x n matrix (i.e., a vector of length n*n),
+ * stored row-wise: that is, A(i,j) = A[ij],
+ * where ij = i*n + j, which is the transpose of the normal
+ * column-wise storage.
+ *
+ * The contents of matrix A are destroyed.
+ *
+ * Set flag=0 to solve.
+ * Set flag=-1 to do a new back substitution for different B vector
+ * using the same A matrix previously reduced when flag=0.
+ *
+ * The routine returns nonzero on error; messages are printed.
+ *
+ *
+ * ACCURACY:
+ *
+ * Depends on the conditioning (range of eigenvalues) of matrix A.
+ *
+ *
+ * REFERENCE:
+ *
+ * Computer Solution of Linear Algebraic Systems,
+ * by George E. Forsythe and Cleve B. Moler; Prentice-Hall, 1967.
+ *
+ */
+
+/* simq 2 */
+
+#include <stdio.h>
+#define fabs(x) ((x) < 0 ? -(x) : (x))
+
+int simq( A, B, X, n, flag, IPS )
+double A[], B[], X[];
+int n, flag;
+int IPS[];
+{
+int i, j, ij, ip, ipj, ipk, ipn;
+int idxpiv, iback;
+int k, kp, kp1, kpk, kpn;
+int nip, nkp, nm1;
+double em, q, rownrm, big, size, pivot, sum;
+
+nm1 = n-1;
+if( flag < 0 )
+ goto solve;
+
+/* Initialize IPS and X */
+
+ij=0;
+for( i=0; i<n; i++ )
+ {
+ IPS[i] = i;
+ rownrm = 0.0;
+ for( j=0; j<n; j++ )
+ {
+ q = fabs( A[ij] );
+ if( rownrm < q )
+ rownrm = q;
+ ++ij;
+ }
+ if( rownrm == 0.0 )
+ {
+ printf("SIMQ ROWNRM=0");
+ return(1);
+ }
+ X[i] = 1.0/rownrm;
+ }
+
+/* simq 3 */
+/* Gaussian elimination with partial pivoting */
+
+for( k=0; k<nm1; k++ )
+ {
+ big= 0.0;
+ idxpiv = 0;
+ for( i=k; i<n; i++ )
+ {
+ ip = IPS[i];
+ ipk = n*ip + k;
+ size = fabs( A[ipk] ) * X[ip];
+ if( size > big )
+ {
+ big = size;
+ idxpiv = i;
+ }
+ }
+
+ if( big == 0.0 )
+ {
+ printf( "SIMQ BIG=0" );
+ return(2);
+ }
+ if( idxpiv != k )
+ {
+ j = IPS[k];
+ IPS[k] = IPS[idxpiv];
+ IPS[idxpiv] = j;
+ }
+ kp = IPS[k];
+ kpk = n*kp + k;
+ pivot = A[kpk];
+ kp1 = k+1;
+ for( i=kp1; i<n; i++ )
+ {
+ ip = IPS[i];
+ ipk = n*ip + k;
+ em = -A[ipk]/pivot;
+ A[ipk] = -em;
+ nip = n*ip;
+ nkp = n*kp;
+ for( j=kp1; j<n; j++ )
+ {
+ ipj = nip + j;
+ A[ipj] = A[ipj] + em * A[nkp + j];
+ }
+ }
+ }
+kpn = n * IPS[n-1] + n - 1; /* last element of IPS[n] th row */
+if( A[kpn] == 0.0 )
+ {
+ printf( "SIMQ A[kpn]=0");
+ return(3);
+ }
+
+/* simq 4 */
+/* back substitution */
+
+solve:
+ip = IPS[0];
+X[0] = B[ip];
+for( i=1; i<n; i++ )
+ {
+ ip = IPS[i];
+ ipj = n * ip;
+ sum = 0.0;
+ for( j=0; j<i; j++ )
+ {
+ sum += A[ipj] * X[j];
+ ++ipj;
+ }
+ X[i] = B[ip] - sum;
+ }
+
+ipn = n * IPS[n-1] + n - 1;
+X[n-1] = X[n-1]/A[ipn];
+
+for( iback=1; iback<n; iback++ )
+ {
+/* i goes (n-1),...,1 */
+ i = nm1 - iback;
+ ip = IPS[i];
+ nip = n*ip;
+ sum = 0.0;
+ for( j=i+1; j<n; j++ )
+ sum += A[nip+j] * X[j];
+ X[i] = (X[i] - sum)/A[nip+i];
+ }
+return(0);
+}
diff --git a/libm/double/sin.c b/libm/double/sin.c
new file mode 100644
index 000000000..24746d79d
--- /dev/null
+++ b/libm/double/sin.c
@@ -0,0 +1,387 @@
+/* sin.c
+ *
+ * Circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, sin();
+ *
+ * y = sin( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of pi/4. The reduction
+ * error is nearly eliminated by contriving an extended precision
+ * modular arithmetic.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the sine is approximated by
+ * x + x**3 P(x**2).
+ * Between pi/4 and pi/2 the cosine is represented as
+ * 1 - x**2 Q(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 10 150000 3.0e-17 7.8e-18
+ * IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sin total loss x > 1.073741824e9 0.0
+ *
+ * Partial loss of accuracy begins to occur at x = 2**30
+ * = 1.074e9. The loss is not gradual, but jumps suddenly to
+ * about 1 part in 10e7. Results may be meaningless for
+ * x > 2**49 = 5.6e14. The routine as implemented flags a
+ * TLOSS error for x > 2**30 and returns 0.0.
+ */
+ /* cos.c
+ *
+ * Circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cos();
+ *
+ * y = cos( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of pi/4. The reduction
+ * error is nearly eliminated by contriving an extended precision
+ * modular arithmetic.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the cosine is approximated by
+ * 1 - x**2 Q(x**2).
+ * Between pi/4 and pi/2 the sine is represented as
+ * x + x**3 P(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1.07e9,+1.07e9 130000 2.1e-16 5.4e-17
+ * DEC 0,+1.07e9 17000 3.0e-17 7.2e-18
+ */
+
+/* sin.c */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1985, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double sincof[] = {
+ 1.58962301576546568060E-10,
+-2.50507477628578072866E-8,
+ 2.75573136213857245213E-6,
+-1.98412698295895385996E-4,
+ 8.33333333332211858878E-3,
+-1.66666666666666307295E-1,
+};
+static double coscof[6] = {
+-1.13585365213876817300E-11,
+ 2.08757008419747316778E-9,
+-2.75573141792967388112E-7,
+ 2.48015872888517045348E-5,
+-1.38888888888730564116E-3,
+ 4.16666666666665929218E-2,
+};
+static double DP1 = 7.85398125648498535156E-1;
+static double DP2 = 3.77489470793079817668E-8;
+static double DP3 = 2.69515142907905952645E-15;
+/* static double lossth = 1.073741824e9; */
+#endif
+
+#ifdef DEC
+static unsigned short sincof[] = {
+0030056,0143750,0177214,0163153,
+0131727,0027455,0044510,0175352,
+0033470,0167432,0131752,0042414,
+0135120,0006400,0146776,0174027,
+0036410,0104210,0104207,0137202,
+0137452,0125252,0125252,0125103,
+};
+static unsigned short coscof[24] = {
+0127107,0151115,0002060,0152325,
+0031017,0072353,0155161,0174053,
+0132623,0171173,0172542,0057056,
+0034320,0006400,0147102,0023652,
+0135666,0005540,0133012,0076213,
+0037052,0125252,0125252,0125126,
+};
+/* 7.853981629014015197753906250000E-1 */
+static unsigned short P1[] = {0040111,0007732,0120000,0000000,};
+/* 4.960467869796758577649598009884E-10 */
+static unsigned short P2[] = {0030410,0055060,0100000,0000000,};
+/* 2.860594363054915898381331279295E-18 */
+static unsigned short P3[] = {0021523,0011431,0105056,0001560,};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+#ifdef IBMPC
+static unsigned short sincof[] = {
+0x9ccd,0x1fd1,0xd8fd,0x3de5,
+0x1f5d,0xa929,0xe5e5,0xbe5a,
+0x48a1,0x567d,0x1de3,0x3ec7,
+0xdf03,0x19bf,0x01a0,0xbf2a,
+0xf7d0,0x1110,0x1111,0x3f81,
+0x5548,0x5555,0x5555,0xbfc5,
+};
+static unsigned short coscof[24] = {
+0x1a9b,0xa086,0xfa49,0xbda8,
+0x3f05,0x7b4e,0xee9d,0x3e21,
+0x4bc6,0x7eac,0x7e4f,0xbe92,
+0x44f5,0x19c8,0x01a0,0x3efa,
+0x4f91,0x16c1,0xc16c,0xbf56,
+0x554b,0x5555,0x5555,0x3fa5,
+};
+/*
+ 7.85398125648498535156E-1,
+ 3.77489470793079817668E-8,
+ 2.69515142907905952645E-15,
+*/
+static unsigned short P1[] = {0x0000,0x4000,0x21fb,0x3fe9};
+static unsigned short P2[] = {0x0000,0x0000,0x442d,0x3e64};
+static unsigned short P3[] = {0x5170,0x98cc,0x4698,0x3ce8};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+#ifdef MIEEE
+static unsigned short sincof[] = {
+0x3de5,0xd8fd,0x1fd1,0x9ccd,
+0xbe5a,0xe5e5,0xa929,0x1f5d,
+0x3ec7,0x1de3,0x567d,0x48a1,
+0xbf2a,0x01a0,0x19bf,0xdf03,
+0x3f81,0x1111,0x1110,0xf7d0,
+0xbfc5,0x5555,0x5555,0x5548,
+};
+static unsigned short coscof[24] = {
+0xbda8,0xfa49,0xa086,0x1a9b,
+0x3e21,0xee9d,0x7b4e,0x3f05,
+0xbe92,0x7e4f,0x7eac,0x4bc6,
+0x3efa,0x01a0,0x19c8,0x44f5,
+0xbf56,0xc16c,0x16c1,0x4f91,
+0x3fa5,0x5555,0x5555,0x554b,
+};
+static unsigned short P1[] = {0x3fe9,0x21fb,0x4000,0x0000};
+static unsigned short P2[] = {0x3e64,0x442d,0x0000,0x0000};
+static unsigned short P3[] = {0x3ce8,0x4698,0x98cc,0x5170};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double floor ( double );
+extern double ldexp ( double, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+#else
+double polevl(), floor(), ldexp();
+int isnan(), isfinite();
+#endif
+extern double PIO4;
+static double lossth = 1.073741824e9;
+#ifdef NANS
+extern double NAN;
+#endif
+#ifdef INFINITIES
+extern double INFINITY;
+#endif
+
+
+double sin(x)
+double x;
+{
+double y, z, zz;
+int j, sign;
+
+#ifdef MINUSZERO
+if( x == 0.0 )
+ return(x);
+#endif
+#ifdef NANS
+if( isnan(x) )
+ return(x);
+if( !isfinite(x) )
+ {
+ mtherr( "sin", DOMAIN );
+ return(NAN);
+ }
+#endif
+/* make argument positive but save the sign */
+sign = 1;
+if( x < 0 )
+ {
+ x = -x;
+ sign = -1;
+ }
+
+if( x > lossth )
+ {
+ mtherr( "sin", TLOSS );
+ return(0.0);
+ }
+
+y = floor( x/PIO4 ); /* integer part of x/PIO4 */
+
+/* strip high bits of integer part to prevent integer overflow */
+z = ldexp( y, -4 );
+z = floor(z); /* integer part of y/8 */
+z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
+
+j = z; /* convert to integer for tests on the phase angle */
+/* map zeros to origin */
+if( j & 1 )
+ {
+ j += 1;
+ y += 1.0;
+ }
+j = j & 07; /* octant modulo 360 degrees */
+/* reflect in x axis */
+if( j > 3)
+ {
+ sign = -sign;
+ j -= 4;
+ }
+
+/* Extended precision modular arithmetic */
+z = ((x - y * DP1) - y * DP2) - y * DP3;
+
+zz = z * z;
+
+if( (j==1) || (j==2) )
+ {
+ y = 1.0 - ldexp(zz,-1) + zz * zz * polevl( zz, coscof, 5 );
+ }
+else
+ {
+/* y = z + z * (zz * polevl( zz, sincof, 5 ));*/
+ y = z + z * z * z * polevl( zz, sincof, 5 );
+ }
+
+if(sign < 0)
+ y = -y;
+
+return(y);
+}
+
+
+
+
+
+double cos(x)
+double x;
+{
+double y, z, zz;
+long i;
+int j, sign;
+
+#ifdef NANS
+if( isnan(x) )
+ return(x);
+if( !isfinite(x) )
+ {
+ mtherr( "cos", DOMAIN );
+ return(NAN);
+ }
+#endif
+
+/* make argument positive */
+sign = 1;
+if( x < 0 )
+ x = -x;
+
+if( x > lossth )
+ {
+ mtherr( "cos", TLOSS );
+ return(0.0);
+ }
+
+y = floor( x/PIO4 );
+z = ldexp( y, -4 );
+z = floor(z); /* integer part of y/8 */
+z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
+
+/* integer and fractional part modulo one octant */
+i = z;
+if( i & 1 ) /* map zeros to origin */
+ {
+ i += 1;
+ y += 1.0;
+ }
+j = i & 07;
+if( j > 3)
+ {
+ j -=4;
+ sign = -sign;
+ }
+
+if( j > 1 )
+ sign = -sign;
+
+/* Extended precision modular arithmetic */
+z = ((x - y * DP1) - y * DP2) - y * DP3;
+
+zz = z * z;
+
+if( (j==1) || (j==2) )
+ {
+/* y = z + z * (zz * polevl( zz, sincof, 5 ));*/
+ y = z + z * z * z * polevl( zz, sincof, 5 );
+ }
+else
+ {
+ y = 1.0 - ldexp(zz,-1) + zz * zz * polevl( zz, coscof, 5 );
+ }
+
+if(sign < 0)
+ y = -y;
+
+return(y);
+}
+
+
+
+
+
+/* Degrees, minutes, seconds to radians: */
+
+/* 1 arc second, in radians = 4.8481368110953599358991410e-5 */
+#ifdef DEC
+static unsigned short P648[] = {034513,054170,0176773,0116043,};
+#define P64800 *(double *)P648
+#else
+static double P64800 = 4.8481368110953599358991410e-5;
+#endif
+
+double radian(d,m,s)
+double d,m,s;
+{
+
+return( ((d*60.0 + m)*60.0 + s)*P64800 );
+}
diff --git a/libm/double/sincos.c b/libm/double/sincos.c
new file mode 100644
index 000000000..8a4a3784c
--- /dev/null
+++ b/libm/double/sincos.c
@@ -0,0 +1,364 @@
+/* sincos.c
+ *
+ * Circular sine and cosine of argument in degrees
+ * Table lookup and interpolation algorithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, sine, cosine, flg, sincos();
+ *
+ * sincos( x, &sine, &cosine, flg );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns both the sine and the cosine of the argument x.
+ * Several different compile time options and minimax
+ * approximations are supplied to permit tailoring the
+ * tradeoff between computation speed and accuracy.
+ *
+ * Since range reduction is time consuming, the reduction
+ * of x modulo 360 degrees is also made optional.
+ *
+ * sin(i) is internally tabulated for 0 <= i <= 90 degrees.
+ * Approximation polynomials, ranging from linear interpolation
+ * to cubics in (x-i)**2, compute the sine and cosine
+ * of the residual x-i which is between -0.5 and +0.5 degree.
+ * In the case of the high accuracy options, the residual
+ * and the tabulated values are combined using the trigonometry
+ * formulas for sin(A+B) and cos(A+B).
+ *
+ * Compile time options are supplied for 5, 11, or 17 decimal
+ * relative accuracy (ACC5, ACC11, ACC17 respectively).
+ * A subroutine flag argument "flg" chooses betwen this
+ * accuracy and table lookup only (peak absolute error
+ * = 0.0087).
+ *
+ * If the argument flg = 1, then the tabulated value is
+ * returned for the nearest whole number of degrees. The
+ * approximation polynomials are not computed. At
+ * x = 0.5 deg, the absolute error is then sin(0.5) = 0.0087.
+ *
+ * An intermediate speed and precision can be obtained using
+ * the compile time option LINTERP and flg = 1. This yields
+ * a linear interpolation using a slope estimated from the sine
+ * or cosine at the nearest integer argument. The peak absolute
+ * error with this option is 3.8e-5. Relative error at small
+ * angles is about 1e-5.
+ *
+ * If flg = 0, then the approximation polynomials are computed
+ * and applied.
+ *
+ *
+ *
+ * SPEED:
+ *
+ * Relative speed comparisons follow for 6MHz IBM AT clone
+ * and Microsoft C version 4.0. These figures include
+ * software overhead of do loop and function calls.
+ * Since system hardware and software vary widely, the
+ * numbers should be taken as representative only.
+ *
+ * flg=0 flg=0 flg=1 flg=1
+ * ACC11 ACC5 LINTERP Lookup only
+ * In-line 8087 (/FPi)
+ * sin(), cos() 1.0 1.0 1.0 1.0
+ *
+ * In-line 8087 (/FPi)
+ * sincos() 1.1 1.4 1.9 3.0
+ *
+ * Software (/FPa)
+ * sin(), cos() 0.19 0.19 0.19 0.19
+ *
+ * Software (/FPa)
+ * sincos() 0.39 0.50 0.73 1.7
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * The accurate approximations are designed with a relative error
+ * criterion. The absolute error is greatest at x = 0.5 degree.
+ * It decreases from a local maximum at i+0.5 degrees to full
+ * machine precision at each integer i degrees. With the
+ * ACC5 option, the relative error of 6.3e-6 is equivalent to
+ * an absolute angular error of 0.01 arc second in the argument
+ * at x = i+0.5 degrees. For small angles < 0.5 deg, the ACC5
+ * accuracy is 6.3e-6 (.00063%) of reading; i.e., the absolute
+ * error decreases in proportion to the argument. This is true
+ * for both the sine and cosine approximations, since the latter
+ * is for the function 1 - cos(x).
+ *
+ * If absolute error is of most concern, use the compile time
+ * option ABSERR to obtain an absolute error of 2.7e-8 for ACC5
+ * precision. This is about half the absolute error of the
+ * relative precision option. In this case the relative error
+ * for small angles will increase to 9.5e-6 -- a reasonable
+ * tradeoff.
+ */
+
+
+#include <math.h>
+
+/* Define one of the following to be 1:
+ */
+#define ACC5 1
+#define ACC11 0
+#define ACC17 0
+
+/* Option for linear interpolation when flg = 1
+ */
+#define LINTERP 1
+
+/* Option for absolute error criterion
+ */
+#define ABSERR 1
+
+/* Option to include modulo 360 function:
+ */
+#define MOD360 0
+
+/*
+Cephes Math Library Release 2.1
+Copyright 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+/* Table of sin(i degrees)
+ * for 0 <= i <= 90
+ */
+static double sintbl[92] = {
+ 0.00000000000000000000E0,
+ 1.74524064372835128194E-2,
+ 3.48994967025009716460E-2,
+ 5.23359562429438327221E-2,
+ 6.97564737441253007760E-2,
+ 8.71557427476581735581E-2,
+ 1.04528463267653471400E-1,
+ 1.21869343405147481113E-1,
+ 1.39173100960065444112E-1,
+ 1.56434465040230869010E-1,
+ 1.73648177666930348852E-1,
+ 1.90808995376544812405E-1,
+ 2.07911690817759337102E-1,
+ 2.24951054343864998051E-1,
+ 2.41921895599667722560E-1,
+ 2.58819045102520762349E-1,
+ 2.75637355816999185650E-1,
+ 2.92371704722736728097E-1,
+ 3.09016994374947424102E-1,
+ 3.25568154457156668714E-1,
+ 3.42020143325668733044E-1,
+ 3.58367949545300273484E-1,
+ 3.74606593415912035415E-1,
+ 3.90731128489273755062E-1,
+ 4.06736643075800207754E-1,
+ 4.22618261740699436187E-1,
+ 4.38371146789077417453E-1,
+ 4.53990499739546791560E-1,
+ 4.69471562785890775959E-1,
+ 4.84809620246337029075E-1,
+ 5.00000000000000000000E-1,
+ 5.15038074910054210082E-1,
+ 5.29919264233204954047E-1,
+ 5.44639035015027082224E-1,
+ 5.59192903470746830160E-1,
+ 5.73576436351046096108E-1,
+ 5.87785252292473129169E-1,
+ 6.01815023152048279918E-1,
+ 6.15661475325658279669E-1,
+ 6.29320391049837452706E-1,
+ 6.42787609686539326323E-1,
+ 6.56059028990507284782E-1,
+ 6.69130606358858213826E-1,
+ 6.81998360062498500442E-1,
+ 6.94658370458997286656E-1,
+ 7.07106781186547524401E-1,
+ 7.19339800338651139356E-1,
+ 7.31353701619170483288E-1,
+ 7.43144825477394235015E-1,
+ 7.54709580222771997943E-1,
+ 7.66044443118978035202E-1,
+ 7.77145961456970879980E-1,
+ 7.88010753606721956694E-1,
+ 7.98635510047292846284E-1,
+ 8.09016994374947424102E-1,
+ 8.19152044288991789684E-1,
+ 8.29037572555041692006E-1,
+ 8.38670567945424029638E-1,
+ 8.48048096156425970386E-1,
+ 8.57167300702112287465E-1,
+ 8.66025403784438646764E-1,
+ 8.74619707139395800285E-1,
+ 8.82947592858926942032E-1,
+ 8.91006524188367862360E-1,
+ 8.98794046299166992782E-1,
+ 9.06307787036649963243E-1,
+ 9.13545457642600895502E-1,
+ 9.20504853452440327397E-1,
+ 9.27183854566787400806E-1,
+ 9.33580426497201748990E-1,
+ 9.39692620785908384054E-1,
+ 9.45518575599316810348E-1,
+ 9.51056516295153572116E-1,
+ 9.56304755963035481339E-1,
+ 9.61261695938318861916E-1,
+ 9.65925826289068286750E-1,
+ 9.70295726275996472306E-1,
+ 9.74370064785235228540E-1,
+ 9.78147600733805637929E-1,
+ 9.81627183447663953497E-1,
+ 9.84807753012208059367E-1,
+ 9.87688340595137726190E-1,
+ 9.90268068741570315084E-1,
+ 9.92546151641322034980E-1,
+ 9.94521895368273336923E-1,
+ 9.96194698091745532295E-1,
+ 9.97564050259824247613E-1,
+ 9.98629534754573873784E-1,
+ 9.99390827019095730006E-1,
+ 9.99847695156391239157E-1,
+ 1.00000000000000000000E0,
+ 9.99847695156391239157E-1,
+};
+
+#ifdef ANSIPROT
+double floor ( double );
+#else
+double floor();
+#endif
+
+int sincos(x, s, c, flg)
+double x;
+double *s, *c;
+int flg;
+{
+int ix, ssign, csign, xsign;
+double y, z, sx, sz, cx, cz;
+
+/* Make argument nonnegative.
+ */
+xsign = 1;
+if( x < 0.0 )
+ {
+ xsign = -1;
+ x = -x;
+ }
+
+
+#if MOD360
+x = x - 360.0 * floor( x/360.0 );
+#endif
+
+/* Find nearest integer to x.
+ * Note there should be a domain error test here,
+ * but this is omitted to gain speed.
+ */
+ix = x + 0.5;
+z = x - ix; /* the residual */
+
+/* Look up the sine and cosine of the integer.
+ */
+if( ix <= 180 )
+ {
+ ssign = 1;
+ csign = 1;
+ }
+else
+ {
+ ssign = -1;
+ csign = -1;
+ ix -= 180;
+ }
+
+if( ix > 90 )
+ {
+ csign = -csign;
+ ix = 180 - ix;
+ }
+
+sx = sintbl[ix];
+if( ssign < 0 )
+ sx = -sx;
+cx = sintbl[ 90-ix ];
+if( csign < 0 )
+ cx = -cx;
+
+/* If the flag argument is set, then just return
+ * the tabulated values for arg to the nearest whole degree.
+ */
+if( flg )
+ {
+#if LINTERP
+ y = sx + 1.74531263774940077459e-2 * z * cx;
+ cx -= 1.74531263774940077459e-2 * z * sx;
+ sx = y;
+#endif
+ if( xsign < 0 )
+ sx = -sx;
+ *s = sx; /* sine */
+ *c = cx; /* cosine */
+ return 0;
+ }
+
+
+if( ssign < 0 )
+ sx = -sx;
+if( csign < 0 )
+ cx = -cx;
+
+/* Find sine and cosine
+ * of the residual angle between -0.5 and +0.5 degree.
+ */
+#if ACC5
+#if ABSERR
+/* absolute error = 2.769e-8: */
+sz = 1.74531263774940077459e-2 * z;
+/* absolute error = 4.146e-11: */
+cz = 1.0 - 1.52307909153324666207e-4 * z * z;
+#else
+/* relative error = 6.346e-6: */
+sz = 1.74531817576426662296e-2 * z;
+/* relative error = 3.173e-6: */
+cz = 1.0 - 1.52308226602566149927e-4 * z * z;
+#endif
+#else
+y = z * z;
+#endif
+
+
+#if ACC11
+sz = ( -8.86092781698004819918e-7 * y
+ + 1.74532925198378577601e-2 ) * z;
+
+cz = 1.0 - ( -3.86631403698859047896e-9 * y
+ + 1.52308709893047593702e-4 ) * y;
+#endif
+
+
+#if ACC17
+sz = (( 1.34959795251974073996e-11 * y
+ - 8.86096155697856783296e-7 ) * y
+ + 1.74532925199432957214e-2 ) * z;
+
+cz = 1.0 - (( 3.92582397764340914444e-14 * y
+ - 3.86632385155548605680e-9 ) * y
+ + 1.52308709893354299569e-4 ) * y;
+#endif
+
+
+/* Combine the tabulated part and the calculated part
+ * by trigonometry.
+ */
+y = sx * cz + cx * sz;
+if( xsign < 0 )
+ y = - y;
+*s = y; /* sine */
+
+*c = cx * cz - sx * sz; /* cosine */
+return 0;
+}
diff --git a/libm/double/sindg.c b/libm/double/sindg.c
new file mode 100644
index 000000000..8057ab68d
--- /dev/null
+++ b/libm/double/sindg.c
@@ -0,0 +1,308 @@
+/* sindg.c
+ *
+ * Circular sine of angle in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, sindg();
+ *
+ * y = sindg( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of 45 degrees.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the sine is approximated by
+ * x + x**3 P(x**2).
+ * Between pi/4 and pi/2 the cosine is represented as
+ * 1 - x**2 P(x**2).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC +-1000 3100 3.3e-17 9.0e-18
+ * IEEE +-1000 30000 2.3e-16 5.6e-17
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sindg total loss x > 8.0e14 (DEC) 0.0
+ * x > 1.0e14 (IEEE)
+ *
+ */
+ /* cosdg.c
+ *
+ * Circular cosine of angle in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cosdg();
+ *
+ * y = cosdg( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of 45 degrees.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the cosine is approximated by
+ * 1 - x**2 P(x**2).
+ * Between pi/4 and pi/2 the sine is represented as
+ * x + x**3 P(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC +-1000 3400 3.5e-17 9.1e-18
+ * IEEE +-1000 30000 2.1e-16 5.7e-17
+ * See also sin().
+ *
+ */
+
+/* Cephes Math Library Release 2.0: April, 1987
+ * Copyright 1985, 1987 by Stephen L. Moshier
+ * Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */
+
+#include <math.h>
+
+#ifdef UNK
+static double sincof[] = {
+ 1.58962301572218447952E-10,
+-2.50507477628503540135E-8,
+ 2.75573136213856773549E-6,
+-1.98412698295895384658E-4,
+ 8.33333333332211858862E-3,
+-1.66666666666666307295E-1
+};
+static double coscof[] = {
+ 1.13678171382044553091E-11,
+-2.08758833757683644217E-9,
+ 2.75573155429816611547E-7,
+-2.48015872936186303776E-5,
+ 1.38888888888806666760E-3,
+-4.16666666666666348141E-2,
+ 4.99999999999999999798E-1
+};
+static double PI180 = 1.74532925199432957692E-2; /* pi/180 */
+static double lossth = 1.0e14;
+#endif
+
+#ifdef DEC
+static unsigned short sincof[] = {
+0030056,0143750,0177170,0073013,
+0131727,0027455,0044510,0132205,
+0033470,0167432,0131752,0042263,
+0135120,0006400,0146776,0174027,
+0036410,0104210,0104207,0137202,
+0137452,0125252,0125252,0125103
+};
+static unsigned short coscof[] = {
+0027107,0176030,0153315,0110312,
+0131017,0072476,0007450,0123243,
+0032623,0171174,0070066,0146445,
+0134320,0006400,0147355,0163313,
+0035666,0005540,0133012,0165067,
+0137052,0125252,0125252,0125206,
+0040000,0000000,0000000,0000000
+};
+static unsigned short P1[] = {0036616,0175065,0011224,0164711};
+#define PI180 *(double *)P1
+static double lossth = 8.0e14;
+#endif
+
+#ifdef IBMPC
+static unsigned short sincof[] = {
+0x0ec1,0x1fcf,0xd8fd,0x3de5,
+0x1691,0xa929,0xe5e5,0xbe5a,
+0x4896,0x567d,0x1de3,0x3ec7,
+0xdf03,0x19bf,0x01a0,0xbf2a,
+0xf7d0,0x1110,0x1111,0x3f81,
+0x5548,0x5555,0x5555,0xbfc5
+};
+static unsigned short coscof[] = {
+0xb219,0x1ad9,0xff83,0x3da8,
+0x14d4,0xc1e5,0xeea7,0xbe21,
+0xd9a5,0x8e06,0x7e4f,0x3e92,
+0xbcd9,0x19dd,0x01a0,0xbefa,
+0x5d47,0x16c1,0xc16c,0x3f56,
+0x5551,0x5555,0x5555,0xbfa5,
+0x0000,0x0000,0x0000,0x3fe0
+};
+
+static unsigned short P1[] = {0x9d39,0xa252,0xdf46,0x3f91};
+#define PI180 *(double *)P1
+static double lossth = 1.0e14;
+#endif
+
+#ifdef MIEEE
+static unsigned short sincof[] = {
+0x3de5,0xd8fd,0x1fcf,0x0ec1,
+0xbe5a,0xe5e5,0xa929,0x1691,
+0x3ec7,0x1de3,0x567d,0x4896,
+0xbf2a,0x01a0,0x19bf,0xdf03,
+0x3f81,0x1111,0x1110,0xf7d0,
+0xbfc5,0x5555,0x5555,0x5548
+};
+static unsigned short coscof[] = {
+0x3da8,0xff83,0x1ad9,0xb219,
+0xbe21,0xeea7,0xc1e5,0x14d4,
+0x3e92,0x7e4f,0x8e06,0xd9a5,
+0xbefa,0x01a0,0x19dd,0xbcd9,
+0x3f56,0xc16c,0x16c1,0x5d47,
+0xbfa5,0x5555,0x5555,0x5551,
+0x3fe0,0x0000,0x0000,0x0000
+};
+
+static unsigned short P1[] = {
+0x3f91,0xdf46,0xa252,0x9d39
+};
+#define PI180 *(double *)P1
+static double lossth = 1.0e14;
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double floor ( double );
+extern double ldexp ( double, int );
+#else
+double polevl(), floor(), ldexp();
+#endif
+extern double PIO4;
+
+double sindg(x)
+double x;
+{
+double y, z, zz;
+int j, sign;
+
+/* make argument positive but save the sign */
+sign = 1;
+if( x < 0 )
+ {
+ x = -x;
+ sign = -1;
+ }
+
+if( x > lossth )
+ {
+ mtherr( "sindg", TLOSS );
+ return(0.0);
+ }
+
+y = floor( x/45.0 ); /* integer part of x/PIO4 */
+
+/* strip high bits of integer part to prevent integer overflow */
+z = ldexp( y, -4 );
+z = floor(z); /* integer part of y/8 */
+z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
+
+j = z; /* convert to integer for tests on the phase angle */
+/* map zeros to origin */
+if( j & 1 )
+ {
+ j += 1;
+ y += 1.0;
+ }
+j = j & 07; /* octant modulo 360 degrees */
+/* reflect in x axis */
+if( j > 3)
+ {
+ sign = -sign;
+ j -= 4;
+ }
+
+z = x - y * 45.0; /* x mod 45 degrees */
+z *= PI180; /* multiply by pi/180 to convert to radians */
+zz = z * z;
+
+if( (j==1) || (j==2) )
+ {
+ y = 1.0 - zz * polevl( zz, coscof, 6 );
+ }
+else
+ {
+ y = z + z * (zz * polevl( zz, sincof, 5 ));
+ }
+
+if(sign < 0)
+ y = -y;
+
+return(y);
+}
+
+
+
+
+
+double cosdg(x)
+double x;
+{
+double y, z, zz;
+int j, sign;
+
+/* make argument positive */
+sign = 1;
+if( x < 0 )
+ x = -x;
+
+if( x > lossth )
+ {
+ mtherr( "cosdg", TLOSS );
+ return(0.0);
+ }
+
+y = floor( x/45.0 );
+z = ldexp( y, -4 );
+z = floor(z); /* integer part of y/8 */
+z = y - ldexp( z, 4 ); /* y - 16 * (y/16) */
+
+/* integer and fractional part modulo one octant */
+j = z;
+if( j & 1 ) /* map zeros to origin */
+ {
+ j += 1;
+ y += 1.0;
+ }
+j = j & 07;
+if( j > 3)
+ {
+ j -=4;
+ sign = -sign;
+ }
+
+if( j > 1 )
+ sign = -sign;
+
+z = x - y * 45.0; /* x mod 45 degrees */
+z *= PI180; /* multiply by pi/180 to convert to radians */
+
+zz = z * z;
+
+if( (j==1) || (j==2) )
+ {
+ y = z + z * (zz * polevl( zz, sincof, 5 ));
+ }
+else
+ {
+ y = 1.0 - zz * polevl( zz, coscof, 6 );
+ }
+
+if(sign < 0)
+ y = -y;
+
+return(y);
+}
diff --git a/libm/double/sinh.c b/libm/double/sinh.c
new file mode 100644
index 000000000..545bd6826
--- /dev/null
+++ b/libm/double/sinh.c
@@ -0,0 +1,148 @@
+/* sinh.c
+ *
+ * Hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, sinh();
+ *
+ * y = sinh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic sine of argument in the range MINLOG to
+ * MAXLOG.
+ *
+ * The range is partitioned into two segments. If |x| <= 1, a
+ * rational function of the form x + x**3 P(x)/Q(x) is employed.
+ * Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC +- 88 50000 4.0e-17 7.7e-18
+ * IEEE +-MAXLOG 30000 2.6e-16 5.7e-17
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+-7.89474443963537015605E-1,
+-1.63725857525983828727E2,
+-1.15614435765005216044E4,
+-3.51754964808151394800E5
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+-2.77711081420602794433E2,
+ 3.61578279834431989373E4,
+-2.11052978884890840399E6
+};
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0140112,0015377,0042731,0163255,
+0142043,0134721,0146177,0123761,
+0143464,0122706,0034353,0006017,
+0144653,0140536,0157665,0054045
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0142212,0155404,0133513,0022040,
+0044015,0036723,0173271,0011053,
+0145400,0150407,0023710,0001034
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x3cd6,0xe8bb,0x435f,0xbfe9,
+0xf4fe,0x398f,0x773a,0xc064,
+0x6182,0xc71d,0x94b8,0xc0c6,
+0xab05,0xdbf6,0x782b,0xc115
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x6484,0x96e9,0x5b60,0xc071,
+0x2245,0x7ed7,0xa7ba,0x40e1,
+0x0044,0xe4f9,0x1a20,0xc140
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0xbfe9,0x435f,0xe8bb,0x3cd6,
+0xc064,0x773a,0x398f,0xf4fe,
+0xc0c6,0x94b8,0xc71d,0x6182,
+0xc115,0x782b,0xdbf6,0xab05
+};
+static unsigned short Q[] = {
+0xc071,0x5b60,0x96e9,0x6484,
+0x40e1,0xa7ba,0x7ed7,0x2245,
+0xc140,0x1a20,0xe4f9,0x0044
+};
+#endif
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double exp ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+#else
+double fabs(), exp(), polevl(), p1evl();
+#endif
+extern double INFINITY, MINLOG, MAXLOG, LOGE2;
+
+double sinh(x)
+double x;
+{
+double a;
+
+#ifdef MINUSZERO
+if( x == 0.0 )
+ return(x);
+#endif
+a = fabs(x);
+if( (x > (MAXLOG + LOGE2)) || (x > -(MINLOG-LOGE2) ) )
+ {
+ mtherr( "sinh", DOMAIN );
+ if( x > 0 )
+ return( INFINITY );
+ else
+ return( -INFINITY );
+ }
+if( a > 1.0 )
+ {
+ if( a >= (MAXLOG - LOGE2) )
+ {
+ a = exp(0.5*a);
+ a = (0.5 * a) * a;
+ if( x < 0 )
+ a = -a;
+ return(a);
+ }
+ a = exp(a);
+ a = 0.5*a - (0.5/a);
+ if( x < 0 )
+ a = -a;
+ return(a);
+ }
+
+a *= a;
+return( x + x * a * (polevl(a,P,3)/p1evl(a,Q,3)) );
+}
diff --git a/libm/double/spence.c b/libm/double/spence.c
new file mode 100644
index 000000000..e2a56176b
--- /dev/null
+++ b/libm/double/spence.c
@@ -0,0 +1,205 @@
+/* spence.c
+ *
+ * Dilogarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, spence();
+ *
+ * y = spence( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the integral
+ *
+ * x
+ * -
+ * | | log t
+ * spence(x) = - | ----- dt
+ * | | t - 1
+ * -
+ * 1
+ *
+ * for x >= 0. A rational approximation gives the integral in
+ * the interval (0.5, 1.5). Transformation formulas for 1/x
+ * and 1-x are employed outside the basic expansion range.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,4 30000 3.9e-15 5.4e-16
+ * DEC 0,4 3000 2.5e-16 4.5e-17
+ *
+ *
+ */
+
+/* spence.c */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1985, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double A[8] = {
+ 4.65128586073990045278E-5,
+ 7.31589045238094711071E-3,
+ 1.33847639578309018650E-1,
+ 8.79691311754530315341E-1,
+ 2.71149851196553469920E0,
+ 4.25697156008121755724E0,
+ 3.29771340985225106936E0,
+ 1.00000000000000000126E0,
+};
+static double B[8] = {
+ 6.90990488912553276999E-4,
+ 2.54043763932544379113E-2,
+ 2.82974860602568089943E-1,
+ 1.41172597751831069617E0,
+ 3.63800533345137075418E0,
+ 5.03278880143316990390E0,
+ 3.54771340985225096217E0,
+ 9.99999999999999998740E-1,
+};
+#endif
+#ifdef DEC
+static unsigned short A[32] = {
+0034503,0013315,0034120,0157771,
+0036357,0135043,0016766,0150637,
+0037411,0007533,0005212,0161475,
+0040141,0031563,0023217,0120331,
+0040455,0104461,0007002,0155522,
+0040610,0034434,0065721,0120465,
+0040523,0006674,0105671,0054427,
+0040200,0000000,0000000,0000000,
+};
+static unsigned short B[32] = {
+0035465,0021626,0032367,0144157,
+0036720,0016326,0134431,0000406,
+0037620,0161024,0133701,0120766,
+0040264,0131557,0152055,0064512,
+0040550,0152424,0051166,0034272,
+0040641,0006233,0014672,0111572,
+0040543,0006674,0105671,0054425,
+0040200,0000000,0000000,0000000,
+};
+#endif
+#ifdef IBMPC
+static unsigned short A[32] = {
+0x1bff,0xa70a,0x62d9,0x3f08,
+0xda34,0x63be,0xf744,0x3f7d,
+0x5c68,0x6151,0x21eb,0x3fc1,
+0xf41b,0x64d1,0x266e,0x3fec,
+0x5b6a,0x21c0,0xb126,0x4005,
+0x3427,0x8d7a,0x0723,0x4011,
+0x2b23,0x9177,0x61b7,0x400a,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+static unsigned short B[32] = {
+0xf90e,0xc69e,0xa472,0x3f46,
+0x2021,0xd723,0x039a,0x3f9a,
+0x343f,0x96f8,0x1c42,0x3fd2,
+0xad29,0xfa85,0x966d,0x3ff6,
+0xc717,0x8a4e,0x1aa2,0x400d,
+0x526f,0x6337,0x2193,0x4014,
+0x2b23,0x9177,0x61b7,0x400c,
+0x0000,0x0000,0x0000,0x3ff0,
+};
+#endif
+#ifdef MIEEE
+static unsigned short A[32] = {
+0x3f08,0x62d9,0xa70a,0x1bff,
+0x3f7d,0xf744,0x63be,0xda34,
+0x3fc1,0x21eb,0x6151,0x5c68,
+0x3fec,0x266e,0x64d1,0xf41b,
+0x4005,0xb126,0x21c0,0x5b6a,
+0x4011,0x0723,0x8d7a,0x3427,
+0x400a,0x61b7,0x9177,0x2b23,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+static unsigned short B[32] = {
+0x3f46,0xa472,0xc69e,0xf90e,
+0x3f9a,0x039a,0xd723,0x2021,
+0x3fd2,0x1c42,0x96f8,0x343f,
+0x3ff6,0x966d,0xfa85,0xad29,
+0x400d,0x1aa2,0x8a4e,0xc717,
+0x4014,0x2193,0x6337,0x526f,
+0x400c,0x61b7,0x9177,0x2b23,
+0x3ff0,0x0000,0x0000,0x0000,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double log ( double );
+extern double polevl ( double, void *, int );
+#else
+double fabs(), log(), polevl();
+#endif
+extern double PI, MACHEP;
+
+double spence(x)
+double x;
+{
+double w, y, z;
+int flag;
+
+if( x < 0.0 )
+ {
+ mtherr( "spence", DOMAIN );
+ return(0.0);
+ }
+
+if( x == 1.0 )
+ return( 0.0 );
+
+if( x == 0.0 )
+ return( PI*PI/6.0 );
+
+flag = 0;
+
+if( x > 2.0 )
+ {
+ x = 1.0/x;
+ flag |= 2;
+ }
+
+if( x > 1.5 )
+ {
+ w = (1.0/x) - 1.0;
+ flag |= 2;
+ }
+
+else if( x < 0.5 )
+ {
+ w = -x;
+ flag |= 1;
+ }
+
+else
+ w = x - 1.0;
+
+
+y = -w * polevl( w, A, 7) / polevl( w, B, 7 );
+
+if( flag & 1 )
+ y = (PI * PI)/6.0 - log(x) * log(1.0-x) - y;
+
+if( flag & 2 )
+ {
+ z = log(x);
+ y = -0.5 * z * z - y;
+ }
+
+return( y );
+}
diff --git a/libm/double/sqrt.c b/libm/double/sqrt.c
new file mode 100644
index 000000000..92bbce53b
--- /dev/null
+++ b/libm/double/sqrt.c
@@ -0,0 +1,178 @@
+/* sqrt.c
+ *
+ * Square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, sqrt();
+ *
+ * y = sqrt( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the square root of x.
+ *
+ * Range reduction involves isolating the power of two of the
+ * argument and using a polynomial approximation to obtain
+ * a rough value for the square root. Then Heron's iteration
+ * is used three times to converge to an accurate value.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 10 60000 2.1e-17 7.9e-18
+ * IEEE 0,1.7e308 30000 1.7e-16 6.3e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sqrt domain x < 0 0.0
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1988, 2000 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double frexp ( double, int * );
+extern double ldexp ( double, int );
+#else
+double frexp(), ldexp();
+#endif
+extern double SQRT2; /* SQRT2 = 1.41421356237309504880 */
+
+double sqrt(x)
+double x;
+{
+int e;
+#ifndef UNK
+short *q;
+#endif
+double z, w;
+
+if( x <= 0.0 )
+ {
+ if( x < 0.0 )
+ mtherr( "sqrt", DOMAIN );
+ return( 0.0 );
+ }
+w = x;
+/* separate exponent and significand */
+#ifdef UNK
+z = frexp( x, &e );
+#endif
+#ifdef DEC
+q = (short *)&x;
+e = ((*q >> 7) & 0377) - 0200;
+*q &= 0177;
+*q |= 040000;
+z = x;
+#endif
+
+/* Note, frexp and ldexp are used in order to
+ * handle denormal numbers properly.
+ */
+#ifdef IBMPC
+z = frexp( x, &e );
+q = (short *)&x;
+q += 3;
+/*
+e = ((*q >> 4) & 0x0fff) - 0x3fe;
+*q &= 0x000f;
+*q |= 0x3fe0;
+z = x;
+*/
+#endif
+#ifdef MIEEE
+z = frexp( x, &e );
+q = (short *)&x;
+/*
+e = ((*q >> 4) & 0x0fff) - 0x3fe;
+*q &= 0x000f;
+*q |= 0x3fe0;
+z = x;
+*/
+#endif
+
+/* approximate square root of number between 0.5 and 1
+ * relative error of approximation = 7.47e-3
+ */
+x = 4.173075996388649989089E-1 + 5.9016206709064458299663E-1 * z;
+
+/* adjust for odd powers of 2 */
+if( (e & 1) != 0 )
+ x *= SQRT2;
+
+/* re-insert exponent */
+#ifdef UNK
+x = ldexp( x, (e >> 1) );
+#endif
+#ifdef DEC
+*q += ((e >> 1) & 0377) << 7;
+*q &= 077777;
+#endif
+#ifdef IBMPC
+x = ldexp( x, (e >> 1) );
+/*
+*q += ((e >>1) & 0x7ff) << 4;
+*q &= 077777;
+*/
+#endif
+#ifdef MIEEE
+x = ldexp( x, (e >> 1) );
+/*
+*q += ((e >>1) & 0x7ff) << 4;
+*q &= 077777;
+*/
+#endif
+
+/* Newton iterations: */
+#ifdef UNK
+x = 0.5*(x + w/x);
+x = 0.5*(x + w/x);
+x = 0.5*(x + w/x);
+#endif
+
+/* Note, assume the square root cannot be denormal,
+ * so it is safe to use integer exponent operations here.
+ */
+#ifdef DEC
+x += w/x;
+*q -= 0200;
+x += w/x;
+*q -= 0200;
+x += w/x;
+*q -= 0200;
+#endif
+#ifdef IBMPC
+x += w/x;
+*q -= 0x10;
+x += w/x;
+*q -= 0x10;
+x += w/x;
+*q -= 0x10;
+#endif
+#ifdef MIEEE
+x += w/x;
+*q -= 0x10;
+x += w/x;
+*q -= 0x10;
+x += w/x;
+*q -= 0x10;
+#endif
+
+return(x);
+}
diff --git a/libm/double/stdtr.c b/libm/double/stdtr.c
new file mode 100644
index 000000000..743e01704
--- /dev/null
+++ b/libm/double/stdtr.c
@@ -0,0 +1,225 @@
+/* stdtr.c
+ *
+ * Student's t distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double t, stdtr();
+ * short k;
+ *
+ * y = stdtr( k, t );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the integral from minus infinity to t of the Student
+ * t distribution with integer k > 0 degrees of freedom:
+ *
+ * t
+ * -
+ * | |
+ * - | 2 -(k+1)/2
+ * | ( (k+1)/2 ) | ( x )
+ * ---------------------- | ( 1 + --- ) dx
+ * - | ( k )
+ * sqrt( k pi ) | ( k/2 ) |
+ * | |
+ * -
+ * -inf.
+ *
+ * Relation to incomplete beta integral:
+ *
+ * 1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
+ * where
+ * z = k/(k + t**2).
+ *
+ * For t < -2, this is the method of computation. For higher t,
+ * a direct method is derived from integration by parts.
+ * Since the function is symmetric about t=0, the area under the
+ * right tail of the density is found by calling the function
+ * with -t instead of t.
+ *
+ * ACCURACY:
+ *
+ * Tested at random 1 <= k <= 25. The "domain" refers to t.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -100,-2 50000 5.9e-15 1.4e-15
+ * IEEE -2,100 500000 2.7e-15 4.9e-17
+ */
+
+/* stdtri.c
+ *
+ * Functional inverse of Student's t distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double p, t, stdtri();
+ * int k;
+ *
+ * t = stdtri( k, p );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given probability p, finds the argument t such that stdtr(k,t)
+ * is equal to p.
+ *
+ * ACCURACY:
+ *
+ * Tested at random 1 <= k <= 100. The "domain" refers to p:
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE .001,.999 25000 5.7e-15 8.0e-16
+ * IEEE 10^-6,.001 25000 2.0e-12 2.9e-14
+ */
+
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+extern double PI, MACHEP, MAXNUM;
+#ifdef ANSIPROT
+extern double sqrt ( double );
+extern double atan ( double );
+extern double incbet ( double, double, double );
+extern double incbi ( double, double, double );
+extern double fabs ( double );
+#else
+double sqrt(), atan(), incbet(), incbi(), fabs();
+#endif
+
+double stdtr( k, t )
+int k;
+double t;
+{
+double x, rk, z, f, tz, p, xsqk;
+int j;
+
+if( k <= 0 )
+ {
+ mtherr( "stdtr", DOMAIN );
+ return(0.0);
+ }
+
+if( t == 0 )
+ return( 0.5 );
+
+if( t < -2.0 )
+ {
+ rk = k;
+ z = rk / (rk + t * t);
+ p = 0.5 * incbet( 0.5*rk, 0.5, z );
+ return( p );
+ }
+
+/* compute integral from -t to + t */
+
+if( t < 0 )
+ x = -t;
+else
+ x = t;
+
+rk = k; /* degrees of freedom */
+z = 1.0 + ( x * x )/rk;
+
+/* test if k is odd or even */
+if( (k & 1) != 0)
+ {
+
+ /* computation for odd k */
+
+ xsqk = x/sqrt(rk);
+ p = atan( xsqk );
+ if( k > 1 )
+ {
+ f = 1.0;
+ tz = 1.0;
+ j = 3;
+ while( (j<=(k-2)) && ( (tz/f) > MACHEP ) )
+ {
+ tz *= (j-1)/( z * j );
+ f += tz;
+ j += 2;
+ }
+ p += f * xsqk/z;
+ }
+ p *= 2.0/PI;
+ }
+
+
+else
+ {
+
+ /* computation for even k */
+
+ f = 1.0;
+ tz = 1.0;
+ j = 2;
+
+ while( ( j <= (k-2) ) && ( (tz/f) > MACHEP ) )
+ {
+ tz *= (j - 1)/( z * j );
+ f += tz;
+ j += 2;
+ }
+ p = f * x/sqrt(z*rk);
+ }
+
+/* common exit */
+
+
+if( t < 0 )
+ p = -p; /* note destruction of relative accuracy */
+
+ p = 0.5 + 0.5 * p;
+return(p);
+}
+
+double stdtri( k, p )
+int k;
+double p;
+{
+double t, rk, z;
+int rflg;
+
+if( k <= 0 || p <= 0.0 || p >= 1.0 )
+ {
+ mtherr( "stdtri", DOMAIN );
+ return(0.0);
+ }
+
+rk = k;
+
+if( p > 0.25 && p < 0.75 )
+ {
+ if( p == 0.5 )
+ return( 0.0 );
+ z = 1.0 - 2.0 * p;
+ z = incbi( 0.5, 0.5*rk, fabs(z) );
+ t = sqrt( rk*z/(1.0-z) );
+ if( p < 0.5 )
+ t = -t;
+ return( t );
+ }
+rflg = -1;
+if( p >= 0.5)
+ {
+ p = 1.0 - p;
+ rflg = 1;
+ }
+z = incbi( 0.5*rk, 0.5, 2.0*p );
+
+if( MAXNUM * z < rk )
+ return(rflg* MAXNUM);
+t = sqrt( rk/z - rk );
+return( rflg * t );
+}
diff --git a/libm/double/struve.c b/libm/double/struve.c
new file mode 100644
index 000000000..fabf0735e
--- /dev/null
+++ b/libm/double/struve.c
@@ -0,0 +1,312 @@
+/* struve.c
+ *
+ * Struve function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, struve();
+ *
+ * y = struve( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the Struve function Hv(x) of order v, argument x.
+ * Negative x is rejected unless v is an integer.
+ *
+ * This module also contains the hypergeometric functions 1F2
+ * and 3F0 and a routine for the Bessel function Yv(x) with
+ * noninteger v.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Not accurately characterized, but spot checked against tables.
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.81: June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+#include <math.h>
+#define DEBUG 0
+#ifdef ANSIPROT
+extern double gamma ( double );
+extern double pow ( double, double );
+extern double sqrt ( double );
+extern double yn ( int, double );
+extern double jv ( double, double );
+extern double fabs ( double );
+extern double floor ( double );
+extern double sin ( double );
+extern double cos ( double );
+double yv ( double, double );
+double onef2 (double, double, double, double, double * );
+double threef0 (double, double, double, double, double * );
+#else
+double gamma(), pow(), sqrt(), yn(), yv(), jv(), fabs(), floor();
+double sin(), cos();
+double onef2(), threef0();
+#endif
+static double stop = 1.37e-17;
+extern double MACHEP;
+
+double onef2( a, b, c, x, err )
+double a, b, c, x;
+double *err;
+{
+double n, a0, sum, t;
+double an, bn, cn, max, z;
+
+an = a;
+bn = b;
+cn = c;
+a0 = 1.0;
+sum = 1.0;
+n = 1.0;
+t = 1.0;
+max = 0.0;
+
+do
+ {
+ if( an == 0 )
+ goto done;
+ if( bn == 0 )
+ goto error;
+ if( cn == 0 )
+ goto error;
+ if( (a0 > 1.0e34) || (n > 200) )
+ goto error;
+ a0 *= (an * x) / (bn * cn * n);
+ sum += a0;
+ an += 1.0;
+ bn += 1.0;
+ cn += 1.0;
+ n += 1.0;
+ z = fabs( a0 );
+ if( z > max )
+ max = z;
+ if( sum != 0 )
+ t = fabs( a0 / sum );
+ else
+ t = z;
+ }
+while( t > stop );
+
+done:
+
+*err = fabs( MACHEP*max /sum );
+
+#if DEBUG
+ printf(" onef2 cancellation error %.5E\n", *err );
+#endif
+
+goto xit;
+
+error:
+#if DEBUG
+printf("onef2 does not converge\n");
+#endif
+*err = 1.0e38;
+
+xit:
+
+#if DEBUG
+printf("onef2( %.2E %.2E %.2E %.5E ) = %.3E %.6E\n", a, b, c, x, n, sum);
+#endif
+return(sum);
+}
+
+
+
+
+double threef0( a, b, c, x, err )
+double a, b, c, x;
+double *err;
+{
+double n, a0, sum, t, conv, conv1;
+double an, bn, cn, max, z;
+
+an = a;
+bn = b;
+cn = c;
+a0 = 1.0;
+sum = 1.0;
+n = 1.0;
+t = 1.0;
+max = 0.0;
+conv = 1.0e38;
+conv1 = conv;
+
+do
+ {
+ if( an == 0.0 )
+ goto done;
+ if( bn == 0.0 )
+ goto done;
+ if( cn == 0.0 )
+ goto done;
+ if( (a0 > 1.0e34) || (n > 200) )
+ goto error;
+ a0 *= (an * bn * cn * x) / n;
+ an += 1.0;
+ bn += 1.0;
+ cn += 1.0;
+ n += 1.0;
+ z = fabs( a0 );
+ if( z > max )
+ max = z;
+ if( z >= conv )
+ {
+ if( (z < max) && (z > conv1) )
+ goto done;
+ }
+ conv1 = conv;
+ conv = z;
+ sum += a0;
+ if( sum != 0 )
+ t = fabs( a0 / sum );
+ else
+ t = z;
+ }
+while( t > stop );
+
+done:
+
+t = fabs( MACHEP*max/sum );
+#if DEBUG
+ printf(" threef0 cancellation error %.5E\n", t );
+#endif
+
+max = fabs( conv/sum );
+if( max > t )
+ t = max;
+#if DEBUG
+ printf(" threef0 convergence %.5E\n", max );
+#endif
+
+goto xit;
+
+error:
+#if DEBUG
+printf("threef0 does not converge\n");
+#endif
+t = 1.0e38;
+
+xit:
+
+#if DEBUG
+printf("threef0( %.2E %.2E %.2E %.5E ) = %.3E %.6E\n", a, b, c, x, n, sum);
+#endif
+
+*err = t;
+return(sum);
+}
+
+
+
+
+extern double PI;
+
+double struve( v, x )
+double v, x;
+{
+double y, ya, f, g, h, t;
+double onef2err, threef0err;
+
+f = floor(v);
+if( (v < 0) && ( v-f == 0.5 ) )
+ {
+ y = jv( -v, x );
+ f = 1.0 - f;
+ g = 2.0 * floor(f/2.0);
+ if( g != f )
+ y = -y;
+ return(y);
+ }
+t = 0.25*x*x;
+f = fabs(x);
+g = 1.5 * fabs(v);
+if( (f > 30.0) && (f > g) )
+ {
+ onef2err = 1.0e38;
+ y = 0.0;
+ }
+else
+ {
+ y = onef2( 1.0, 1.5, 1.5+v, -t, &onef2err );
+ }
+
+if( (f < 18.0) || (x < 0.0) )
+ {
+ threef0err = 1.0e38;
+ ya = 0.0;
+ }
+else
+ {
+ ya = threef0( 1.0, 0.5, 0.5-v, -1.0/t, &threef0err );
+ }
+
+f = sqrt( PI );
+h = pow( 0.5*x, v-1.0 );
+
+if( onef2err <= threef0err )
+ {
+ g = gamma( v + 1.5 );
+ y = y * h * t / ( 0.5 * f * g );
+ return(y);
+ }
+else
+ {
+ g = gamma( v + 0.5 );
+ ya = ya * h / ( f * g );
+ ya = ya + yv( v, x );
+ return(ya);
+ }
+}
+
+
+
+
+/* Bessel function of noninteger order
+ */
+
+double yv( v, x )
+double v, x;
+{
+double y, t;
+int n;
+
+y = floor( v );
+if( y == v )
+ {
+ n = v;
+ y = yn( n, x );
+ return( y );
+ }
+t = PI * v;
+y = (cos(t) * jv( v, x ) - jv( -v, x ))/sin(t);
+return( y );
+}
+
+/* Crossover points between ascending series and asymptotic series
+ * for Struve function
+ *
+ * v x
+ *
+ * 0 19.2
+ * 1 18.95
+ * 2 19.15
+ * 3 19.3
+ * 5 19.7
+ * 10 21.35
+ * 20 26.35
+ * 30 32.31
+ * 40 40.0
+ */
diff --git a/libm/double/tan.c b/libm/double/tan.c
new file mode 100644
index 000000000..603f4b6a9
--- /dev/null
+++ b/libm/double/tan.c
@@ -0,0 +1,304 @@
+/* tan.c
+ *
+ * Circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, tan();
+ *
+ * y = tan( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular tangent of the radian argument x.
+ *
+ * Range reduction is modulo pi/4. A rational function
+ * x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC +-1.07e9 44000 4.1e-17 1.0e-17
+ * IEEE +-1.07e9 30000 2.9e-16 8.1e-17
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * tan total loss x > 1.073741824e9 0.0
+ *
+ */
+ /* cot.c
+ *
+ * Circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cot();
+ *
+ * y = cot( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular cotangent of the radian argument x.
+ *
+ * Range reduction is modulo pi/4. A rational function
+ * x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-1.07e9 30000 2.9e-16 8.2e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * cot total loss x > 1.073741824e9 0.0
+ * cot singularity x = 0 INFINITY
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+yright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+-1.30936939181383777646E4,
+ 1.15351664838587416140E6,
+-1.79565251976484877988E7
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 1.36812963470692954678E4,
+-1.32089234440210967447E6,
+ 2.50083801823357915839E7,
+-5.38695755929454629881E7
+};
+static double DP1 = 7.853981554508209228515625E-1;
+static double DP2 = 7.94662735614792836714E-9;
+static double DP3 = 3.06161699786838294307E-17;
+static double lossth = 1.073741824e9;
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0143514,0113306,0111171,0174674,
+0045214,0147545,0027744,0167346,
+0146210,0177526,0114514,0105660
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0043525,0142457,0072633,0025617,
+0145241,0036742,0140525,0162256,
+0046276,0146176,0013526,0143573,
+0146515,0077401,0162762,0150607
+};
+/* 7.853981629014015197753906250000E-1 */
+static unsigned short P1[] = {0040111,0007732,0120000,0000000,};
+/* 4.960467869796758577649598009884E-10 */
+static unsigned short P2[] = {0030410,0055060,0100000,0000000,};
+/* 2.860594363054915898381331279295E-18 */
+static unsigned short P3[] = {0021523,0011431,0105056,0001560,};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+static double lossth = 1.073741824e9;
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x3f38,0xd24f,0x92d8,0xc0c9,
+0x9ddd,0xa5fc,0x99ec,0x4131,
+0x9176,0xd329,0x1fea,0xc171
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x6572,0xeeb3,0xb8a5,0x40ca,
+0xbc96,0x582a,0x27bc,0xc134,
+0xd8ef,0xc2ea,0xd98f,0x4177,
+0x5a31,0x3cbe,0xafe0,0xc189
+};
+/*
+ 7.85398125648498535156E-1,
+ 3.77489470793079817668E-8,
+ 2.69515142907905952645E-15,
+*/
+static unsigned short P1[] = {0x0000,0x4000,0x21fb,0x3fe9};
+static unsigned short P2[] = {0x0000,0x0000,0x442d,0x3e64};
+static unsigned short P3[] = {0x5170,0x98cc,0x4698,0x3ce8};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+static double lossth = 1.073741824e9;
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0xc0c9,0x92d8,0xd24f,0x3f38,
+0x4131,0x99ec,0xa5fc,0x9ddd,
+0xc171,0x1fea,0xd329,0x9176
+};
+static unsigned short Q[] = {
+0x40ca,0xb8a5,0xeeb3,0x6572,
+0xc134,0x27bc,0x582a,0xbc96,
+0x4177,0xd98f,0xc2ea,0xd8ef,
+0xc189,0xafe0,0x3cbe,0x5a31
+};
+static unsigned short P1[] = {
+0x3fe9,0x21fb,0x4000,0x0000
+};
+static unsigned short P2[] = {
+0x3e64,0x442d,0x0000,0x0000
+};
+static unsigned short P3[] = {
+0x3ce8,0x4698,0x98cc,0x5170,
+};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+static double lossth = 1.073741824e9;
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double floor ( double );
+extern double ldexp ( double, int );
+extern int isnan ( double );
+extern int isfinite ( double );
+static double tancot(double, int);
+#else
+double polevl(), p1evl(), floor(), ldexp();
+static double tancot();
+int isnan(), isfinite();
+#endif
+extern double PIO4;
+extern double INFINITY;
+extern double NAN;
+
+double tan(x)
+double x;
+{
+#ifdef MINUSZERO
+if( x == 0.0 )
+ return(x);
+#endif
+#ifdef NANS
+if( isnan(x) )
+ return(x);
+if( !isfinite(x) )
+ {
+ mtherr( "tan", DOMAIN );
+ return(NAN);
+ }
+#endif
+return( tancot(x,0) );
+}
+
+
+double cot(x)
+double x;
+{
+
+if( x == 0.0 )
+ {
+ mtherr( "cot", SING );
+ return( INFINITY );
+ }
+return( tancot(x,1) );
+}
+
+
+static double tancot( xx, cotflg )
+double xx;
+int cotflg;
+{
+double x, y, z, zz;
+int j, sign;
+
+/* make argument positive but save the sign */
+if( xx < 0 )
+ {
+ x = -xx;
+ sign = -1;
+ }
+else
+ {
+ x = xx;
+ sign = 1;
+ }
+
+if( x > lossth )
+ {
+ if( cotflg )
+ mtherr( "cot", TLOSS );
+ else
+ mtherr( "tan", TLOSS );
+ return(0.0);
+ }
+
+/* compute x mod PIO4 */
+y = floor( x/PIO4 );
+
+/* strip high bits of integer part */
+z = ldexp( y, -3 );
+z = floor(z); /* integer part of y/8 */
+z = y - ldexp( z, 3 ); /* y - 16 * (y/16) */
+
+/* integer and fractional part modulo one octant */
+j = z;
+
+/* map zeros and singularities to origin */
+if( j & 1 )
+ {
+ j += 1;
+ y += 1.0;
+ }
+
+z = ((x - y * DP1) - y * DP2) - y * DP3;
+
+zz = z * z;
+
+if( zz > 1.0e-14 )
+ y = z + z * (zz * polevl( zz, P, 2 )/p1evl(zz, Q, 4));
+else
+ y = z;
+
+if( j & 2 )
+ {
+ if( cotflg )
+ y = -y;
+ else
+ y = -1.0/y;
+ }
+else
+ {
+ if( cotflg )
+ y = 1.0/y;
+ }
+
+if( sign < 0 )
+ y = -y;
+
+return( y );
+}
diff --git a/libm/double/tandg.c b/libm/double/tandg.c
new file mode 100644
index 000000000..92fd1e56b
--- /dev/null
+++ b/libm/double/tandg.c
@@ -0,0 +1,267 @@
+/* tandg.c
+ *
+ * Circular tangent of argument in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, tandg();
+ *
+ * y = tandg( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular tangent of the argument x in degrees.
+ *
+ * Range reduction is modulo pi/4. A rational function
+ * x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,10 8000 3.4e-17 1.2e-17
+ * IEEE 0,10 30000 3.2e-16 8.4e-17
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * tandg total loss x > 8.0e14 (DEC) 0.0
+ * x > 1.0e14 (IEEE)
+ * tandg singularity x = 180 k + 90 MAXNUM
+ */
+ /* cotdg.c
+ *
+ * Circular cotangent of argument in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, cotdg();
+ *
+ * y = cotdg( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular cotangent of the argument x in degrees.
+ *
+ * Range reduction is modulo pi/4. A rational function
+ * x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * cotdg total loss x > 8.0e14 (DEC) 0.0
+ * x > 1.0e14 (IEEE)
+ * cotdg singularity x = 180 k MAXNUM
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+-1.30936939181383777646E4,
+ 1.15351664838587416140E6,
+-1.79565251976484877988E7
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 1.36812963470692954678E4,
+-1.32089234440210967447E6,
+ 2.50083801823357915839E7,
+-5.38695755929454629881E7
+};
+static double PI180 = 1.74532925199432957692E-2;
+static double lossth = 1.0e14;
+#endif
+
+#ifdef DEC
+static unsigned short P[] = {
+0143514,0113306,0111171,0174674,
+0045214,0147545,0027744,0167346,
+0146210,0177526,0114514,0105660
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0043525,0142457,0072633,0025617,
+0145241,0036742,0140525,0162256,
+0046276,0146176,0013526,0143573,
+0146515,0077401,0162762,0150607
+};
+static unsigned short P1[] = {0036616,0175065,0011224,0164711};
+#define PI180 *(double *)P1
+static double lossth = 8.0e14;
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x3f38,0xd24f,0x92d8,0xc0c9,
+0x9ddd,0xa5fc,0x99ec,0x4131,
+0x9176,0xd329,0x1fea,0xc171
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x6572,0xeeb3,0xb8a5,0x40ca,
+0xbc96,0x582a,0x27bc,0xc134,
+0xd8ef,0xc2ea,0xd98f,0x4177,
+0x5a31,0x3cbe,0xafe0,0xc189
+};
+static unsigned short P1[] = {0x9d39,0xa252,0xdf46,0x3f91};
+#define PI180 *(double *)P1
+static double lossth = 1.0e14;
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0xc0c9,0x92d8,0xd24f,0x3f38,
+0x4131,0x99ec,0xa5fc,0x9ddd,
+0xc171,0x1fea,0xd329,0x9176
+};
+static unsigned short Q[] = {
+0x40ca,0xb8a5,0xeeb3,0x6572,
+0xc134,0x27bc,0x582a,0xbc96,
+0x4177,0xd98f,0xc2ea,0xd8ef,
+0xc189,0xafe0,0x3cbe,0x5a31
+};
+static unsigned short P1[] = {
+0x3f91,0xdf46,0xa252,0x9d39
+};
+#define PI180 *(double *)P1
+static double lossth = 1.0e14;
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double floor ( double );
+extern double ldexp ( double, int );
+static double tancot( double, int );
+#else
+double polevl(), p1evl(), floor(), ldexp();
+static double tancot();
+#endif
+extern double MAXNUM;
+extern double PIO4;
+
+
+double tandg(x)
+double x;
+{
+
+return( tancot(x,0) );
+}
+
+
+double cotdg(x)
+double x;
+{
+
+return( tancot(x,1) );
+}
+
+
+static double tancot( xx, cotflg )
+double xx;
+int cotflg;
+{
+double x, y, z, zz;
+int j, sign;
+
+/* make argument positive but save the sign */
+if( xx < 0 )
+ {
+ x = -xx;
+ sign = -1;
+ }
+else
+ {
+ x = xx;
+ sign = 1;
+ }
+
+if( x > lossth )
+ {
+ mtherr( "tandg", TLOSS );
+ return(0.0);
+ }
+
+/* compute x mod PIO4 */
+y = floor( x/45.0 );
+
+/* strip high bits of integer part */
+z = ldexp( y, -3 );
+z = floor(z); /* integer part of y/8 */
+z = y - ldexp( z, 3 ); /* y - 16 * (y/16) */
+
+/* integer and fractional part modulo one octant */
+j = z;
+
+/* map zeros and singularities to origin */
+if( j & 1 )
+ {
+ j += 1;
+ y += 1.0;
+ }
+
+z = x - y * 45.0;
+z *= PI180;
+
+zz = z * z;
+
+if( zz > 1.0e-14 )
+ y = z + z * (zz * polevl( zz, P, 2 )/p1evl(zz, Q, 4));
+else
+ y = z;
+
+if( j & 2 )
+ {
+ if( cotflg )
+ y = -y;
+ else
+ {
+ if( y != 0.0 )
+ {
+ y = -1.0/y;
+ }
+ else
+ {
+ mtherr( "tandg", SING );
+ y = MAXNUM;
+ }
+ }
+ }
+else
+ {
+ if( cotflg )
+ {
+ if( y != 0.0 )
+ y = 1.0/y;
+ else
+ {
+ mtherr( "cotdg", SING );
+ y = MAXNUM;
+ }
+ }
+ }
+
+if( sign < 0 )
+ y = -y;
+
+return( y );
+}
diff --git a/libm/double/tanh.c b/libm/double/tanh.c
new file mode 100644
index 000000000..910a4188e
--- /dev/null
+++ b/libm/double/tanh.c
@@ -0,0 +1,141 @@
+/* tanh.c
+ *
+ * Hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, tanh();
+ *
+ * y = tanh( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic tangent of argument in the range MINLOG to
+ * MAXLOG.
+ *
+ * A rational function is used for |x| < 0.625. The form
+ * x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
+ * Otherwise,
+ * tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -2,2 50000 3.3e-17 6.4e-18
+ * IEEE -2,2 30000 2.5e-16 5.8e-17
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1995, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static double P[] = {
+-9.64399179425052238628E-1,
+-9.92877231001918586564E1,
+-1.61468768441708447952E3
+};
+static double Q[] = {
+/* 1.00000000000000000000E0,*/
+ 1.12811678491632931402E2,
+ 2.23548839060100448583E3,
+ 4.84406305325125486048E3
+};
+#endif
+#ifdef DEC
+static unsigned short P[] = {
+0140166,0161335,0053753,0075126,
+0141706,0111520,0070463,0040552,
+0142711,0153001,0101300,0025430
+};
+static unsigned short Q[] = {
+/*0040200,0000000,0000000,0000000,*/
+0041741,0117624,0051300,0156060,
+0043013,0133720,0071251,0127717,
+0043227,0060201,0021020,0020136
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x6f4b,0xaafd,0xdc5b,0xbfee,
+0x682d,0x0e26,0xd26a,0xc058,
+0x0563,0x3058,0x3ac0,0xc099
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x1b86,0x8a58,0x33f2,0x405c,
+0x35fa,0x0e55,0x76fa,0x40a1,
+0x040c,0x2442,0xec10,0x40b2
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short P[] = {
+0xbfee,0xdc5b,0xaafd,0x6f4b,
+0xc058,0xd26a,0x0e26,0x682d,
+0xc099,0x3ac0,0x3058,0x0563
+};
+static unsigned short Q[] = {
+0x405c,0x33f2,0x8a58,0x1b86,
+0x40a1,0x76fa,0x0e55,0x35fa,
+0x40b2,0xec10,0x2442,0x040c
+};
+#endif
+
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double exp ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+#else
+double fabs(), exp(), polevl(), p1evl();
+#endif
+extern double MAXLOG;
+
+double tanh(x)
+double x;
+{
+double s, z;
+
+#ifdef MINUSZERO
+if( x == 0.0 )
+ return(x);
+#endif
+z = fabs(x);
+if( z > 0.5 * MAXLOG )
+ {
+ if( x > 0 )
+ return( 1.0 );
+ else
+ return( -1.0 );
+ }
+if( z >= 0.625 )
+ {
+ s = exp(2.0*z);
+ z = 1.0 - 2.0/(s + 1.0);
+ if( x < 0 )
+ z = -z;
+ }
+else
+ {
+ if( x == 0.0 )
+ return(x);
+ s = x * x;
+ z = polevl( s, P, 2 )/p1evl(s, Q, 3);
+ z = x * s * z;
+ z = x + z;
+ }
+return( z );
+}
diff --git a/libm/double/time-it.c b/libm/double/time-it.c
new file mode 100644
index 000000000..32d07db4e
--- /dev/null
+++ b/libm/double/time-it.c
@@ -0,0 +1,38 @@
+/* Reports run time, in seconds, for a command.
+ The command argument can have multiple words, but then
+ it has to be quoted, as for example
+
+ time-it "command < file1 > file2"
+
+ The time interval resolution is one whole second. */
+
+
+#include <time.h>
+int system ();
+int printf ();
+
+int
+main (argv, argc)
+ int argv;
+ char **argc;
+{
+ time_t t0, t1;
+
+ if (argv < 2)
+ {
+ printf ("Usage: time-it name_of_program_to_be_timed\n");
+ exit (1);
+ }
+ time (&t0);
+ /* Wait til the clock changes before starting. */
+ do
+ {
+ time (&t1);
+ }
+ while (t1 == t0);
+ system (argc[1]);
+ t0 = t1;
+ time (&t1);
+ printf ("%ld seconds.\n", t1 - t0);
+ exit (0);
+}
diff --git a/libm/double/unity.c b/libm/double/unity.c
new file mode 100644
index 000000000..9223e0edf
--- /dev/null
+++ b/libm/double/unity.c
@@ -0,0 +1,138 @@
+/* unity.c
+ *
+ * Relative error approximations for function arguments near
+ * unity.
+ *
+ * log1p(x) = log(1+x)
+ * expm1(x) = exp(x) - 1
+ * cosm1(x) = cos(x) - 1
+ *
+ */
+
+#include <math.h>
+
+#ifdef ANSIPROT
+extern int isnan (double);
+extern int isfinite (double);
+extern double log ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double exp ( double );
+extern double cos ( double );
+#else
+double log(), polevl(), p1evl(), exp(), cos();
+int isnan(), isfinite();
+#endif
+extern double INFINITY;
+
+/* log1p(x) = log(1 + x) */
+
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 2.32e-20
+ */
+static double LP[] = {
+ 4.5270000862445199635215E-5,
+ 4.9854102823193375972212E-1,
+ 6.5787325942061044846969E0,
+ 2.9911919328553073277375E1,
+ 6.0949667980987787057556E1,
+ 5.7112963590585538103336E1,
+ 2.0039553499201281259648E1,
+};
+static double LQ[] = {
+/* 1.0000000000000000000000E0,*/
+ 1.5062909083469192043167E1,
+ 8.3047565967967209469434E1,
+ 2.2176239823732856465394E2,
+ 3.0909872225312059774938E2,
+ 2.1642788614495947685003E2,
+ 6.0118660497603843919306E1,
+};
+
+#define SQRTH 0.70710678118654752440
+#define SQRT2 1.41421356237309504880
+
+double log1p(x)
+double x;
+{
+double z;
+
+z = 1.0 + x;
+if( (z < SQRTH) || (z > SQRT2) )
+ return( log(z) );
+z = x*x;
+z = -0.5 * z + x * ( z * polevl( x, LP, 6 ) / p1evl( x, LQ, 6 ) );
+return (x + z);
+}
+
+
+
+/* expm1(x) = exp(x) - 1 */
+
+/* e^x = 1 + 2x P(x^2)/( Q(x^2) - P(x^2) )
+ * -0.5 <= x <= 0.5
+ */
+
+static double EP[3] = {
+ 1.2617719307481059087798E-4,
+ 3.0299440770744196129956E-2,
+ 9.9999999999999999991025E-1,
+};
+static double EQ[4] = {
+ 3.0019850513866445504159E-6,
+ 2.5244834034968410419224E-3,
+ 2.2726554820815502876593E-1,
+ 2.0000000000000000000897E0,
+};
+
+double expm1(x)
+double x;
+{
+double r, xx;
+
+#ifdef NANS
+if( isnan(x) )
+ return(x);
+#endif
+#ifdef INFINITIES
+if( x == INFINITY )
+ return(INFINITY);
+if( x == -INFINITY )
+ return(-1.0);
+#endif
+if( (x < -0.5) || (x > 0.5) )
+ return( exp(x) - 1.0 );
+xx = x * x;
+r = x * polevl( xx, EP, 2 );
+r = r/( polevl( xx, EQ, 3 ) - r );
+return (r + r);
+}
+
+
+
+/* cosm1(x) = cos(x) - 1 */
+
+static double coscof[7] = {
+ 4.7377507964246204691685E-14,
+-1.1470284843425359765671E-11,
+ 2.0876754287081521758361E-9,
+-2.7557319214999787979814E-7,
+ 2.4801587301570552304991E-5,
+-1.3888888888888872993737E-3,
+ 4.1666666666666666609054E-2,
+};
+
+extern double PIO4;
+
+double cosm1(x)
+double x;
+{
+double xx;
+
+if( (x < -PIO4) || (x > PIO4) )
+ return( cos(x) - 1.0 );
+xx = x * x;
+xx = -0.5*xx + xx * xx * polevl( xx, coscof, 6 );
+return xx;
+}
diff --git a/libm/double/yn.c b/libm/double/yn.c
new file mode 100644
index 000000000..0c569a925
--- /dev/null
+++ b/libm/double/yn.c
@@ -0,0 +1,114 @@
+/* yn.c
+ *
+ * Bessel function of second kind of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, yn();
+ * int n;
+ *
+ * y = yn( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The function is evaluated by forward recurrence on
+ * n, starting with values computed by the routines
+ * y0() and y1().
+ *
+ * If n = 0 or 1 the routine for y0 or y1 is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Absolute error, except relative
+ * when y > 1:
+ * arithmetic domain # trials peak rms
+ * DEC 0, 30 2200 2.9e-16 5.3e-17
+ * IEEE 0, 30 30000 3.4e-15 4.3e-16
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * yn singularity x = 0 MAXNUM
+ * yn overflow MAXNUM
+ *
+ * Spot checked against tables for x, n between 0 and 100.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double y0 ( double );
+extern double y1 ( double );
+extern double log ( double );
+#else
+double y0(), y1(), log();
+#endif
+extern double MAXNUM, MAXLOG;
+
+double yn( n, x )
+int n;
+double x;
+{
+double an, anm1, anm2, r;
+int k, sign;
+
+if( n < 0 )
+ {
+ n = -n;
+ if( (n & 1) == 0 ) /* -1**n */
+ sign = 1;
+ else
+ sign = -1;
+ }
+else
+ sign = 1;
+
+
+if( n == 0 )
+ return( sign * y0(x) );
+if( n == 1 )
+ return( sign * y1(x) );
+
+/* test for overflow */
+if( x <= 0.0 )
+ {
+ mtherr( "yn", SING );
+ return( -MAXNUM );
+ }
+
+/* forward recurrence on n */
+
+anm2 = y0(x);
+anm1 = y1(x);
+k = 1;
+r = 2 * k;
+do
+ {
+ an = r * anm1 / x - anm2;
+ anm2 = anm1;
+ anm1 = an;
+ r += 2.0;
+ ++k;
+ }
+while( k < n );
+
+
+return( sign * an );
+}
diff --git a/libm/double/zeta.c b/libm/double/zeta.c
new file mode 100644
index 000000000..a49c619d5
--- /dev/null
+++ b/libm/double/zeta.c
@@ -0,0 +1,189 @@
+/* zeta.c
+ *
+ * Riemann zeta function of two arguments
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, q, y, zeta();
+ *
+ * y = zeta( x, q );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *
+ * inf.
+ * - -x
+ * zeta(x,q) = > (k+q)
+ * -
+ * k=0
+ *
+ * where x > 1 and q is not a negative integer or zero.
+ * The Euler-Maclaurin summation formula is used to obtain
+ * the expansion
+ *
+ * n
+ * - -x
+ * zeta(x,q) = > (k+q)
+ * -
+ * k=1
+ *
+ * 1-x inf. B x(x+1)...(x+2j)
+ * (n+q) 1 - 2j
+ * + --------- - ------- + > --------------------
+ * x-1 x - x+2j+1
+ * 2(n+q) j=1 (2j)! (n+q)
+ *
+ * where the B2j are Bernoulli numbers. Note that (see zetac.c)
+ * zeta(x,1) = zetac(x) + 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ *
+ * REFERENCE:
+ *
+ * Gradshteyn, I. S., and I. M. Ryzhik, Tables of Integrals,
+ * Series, and Products, p. 1073; Academic Press, 1980.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern double fabs ( double );
+extern double pow ( double, double );
+extern double floor ( double );
+#else
+double fabs(), pow(), floor();
+#endif
+extern double MAXNUM, MACHEP;
+
+/* Expansion coefficients
+ * for Euler-Maclaurin summation formula
+ * (2k)! / B2k
+ * where B2k are Bernoulli numbers
+ */
+static double A[] = {
+12.0,
+-720.0,
+30240.0,
+-1209600.0,
+47900160.0,
+-1.8924375803183791606e9, /*1.307674368e12/691*/
+7.47242496e10,
+-2.950130727918164224e12, /*1.067062284288e16/3617*/
+1.1646782814350067249e14, /*5.109094217170944e18/43867*/
+-4.5979787224074726105e15, /*8.028576626982912e20/174611*/
+1.8152105401943546773e17, /*1.5511210043330985984e23/854513*/
+-7.1661652561756670113e18 /*1.6938241367317436694528e27/236364091*/
+};
+/* 30 Nov 86 -- error in third coefficient fixed */
+
+
+double zeta(x,q)
+double x,q;
+{
+int i;
+double a, b, k, s, t, w;
+
+if( x == 1.0 )
+ goto retinf;
+
+if( x < 1.0 )
+ {
+domerr:
+ mtherr( "zeta", DOMAIN );
+ return(0.0);
+ }
+
+if( q <= 0.0 )
+ {
+ if(q == floor(q))
+ {
+ mtherr( "zeta", SING );
+retinf:
+ return( MAXNUM );
+ }
+ if( x != floor(x) )
+ goto domerr; /* because q^-x not defined */
+ }
+
+/* Euler-Maclaurin summation formula */
+/*
+if( x < 25.0 )
+*/
+{
+/* Permit negative q but continue sum until n+q > +9 .
+ * This case should be handled by a reflection formula.
+ * If q<0 and x is an integer, there is a relation to
+ * the polygamma function.
+ */
+s = pow( q, -x );
+a = q;
+i = 0;
+b = 0.0;
+while( (i < 9) || (a <= 9.0) )
+ {
+ i += 1;
+ a += 1.0;
+ b = pow( a, -x );
+ s += b;
+ if( fabs(b/s) < MACHEP )
+ goto done;
+ }
+
+w = a;
+s += b*w/(x-1.0);
+s -= 0.5 * b;
+a = 1.0;
+k = 0.0;
+for( i=0; i<12; i++ )
+ {
+ a *= x + k;
+ b /= w;
+ t = a*b/A[i];
+ s = s + t;
+ t = fabs(t/s);
+ if( t < MACHEP )
+ goto done;
+ k += 1.0;
+ a *= x + k;
+ b /= w;
+ k += 1.0;
+ }
+done:
+return(s);
+}
+
+
+
+/* Basic sum of inverse powers */
+/*
+pseres:
+
+s = pow( q, -x );
+a = q;
+do
+ {
+ a += 2.0;
+ b = pow( a, -x );
+ s += b;
+ }
+while( b/s > MACHEP );
+
+b = pow( 2.0, -x );
+s = (s + b)/(1.0-b);
+return(s);
+*/
+}
diff --git a/libm/double/zetac.c b/libm/double/zetac.c
new file mode 100644
index 000000000..cc28590b3
--- /dev/null
+++ b/libm/double/zetac.c
@@ -0,0 +1,599 @@
+ /* zetac.c
+ *
+ * Riemann zeta function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, zetac();
+ *
+ * y = zetac( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *
+ * inf.
+ * - -x
+ * zetac(x) = > k , x > 1,
+ * -
+ * k=2
+ *
+ * is related to the Riemann zeta function by
+ *
+ * Riemann zeta(x) = zetac(x) + 1.
+ *
+ * Extension of the function definition for x < 1 is implemented.
+ * Zero is returned for x > log2(MAXNUM).
+ *
+ * An overflow error may occur for large negative x, due to the
+ * gamma function in the reflection formula.
+ *
+ * ACCURACY:
+ *
+ * Tabulated values have full machine accuracy.
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 1,50 10000 9.8e-16 1.3e-16
+ * DEC 1,50 2000 1.1e-16 1.9e-17
+ *
+ *
+ */
+
+/*
+Cephes Math Library Release 2.8: June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+extern double MAXNUM, PI;
+
+/* Riemann zeta(x) - 1
+ * for integer arguments between 0 and 30.
+ */
+#ifdef UNK
+static double azetac[] = {
+-1.50000000000000000000E0,
+ 1.70141183460469231730E38, /* infinity. */
+ 6.44934066848226436472E-1,
+ 2.02056903159594285400E-1,
+ 8.23232337111381915160E-2,
+ 3.69277551433699263314E-2,
+ 1.73430619844491397145E-2,
+ 8.34927738192282683980E-3,
+ 4.07735619794433937869E-3,
+ 2.00839282608221441785E-3,
+ 9.94575127818085337146E-4,
+ 4.94188604119464558702E-4,
+ 2.46086553308048298638E-4,
+ 1.22713347578489146752E-4,
+ 6.12481350587048292585E-5,
+ 3.05882363070204935517E-5,
+ 1.52822594086518717326E-5,
+ 7.63719763789976227360E-6,
+ 3.81729326499983985646E-6,
+ 1.90821271655393892566E-6,
+ 9.53962033872796113152E-7,
+ 4.76932986787806463117E-7,
+ 2.38450502727732990004E-7,
+ 1.19219925965311073068E-7,
+ 5.96081890512594796124E-8,
+ 2.98035035146522801861E-8,
+ 1.49015548283650412347E-8,
+ 7.45071178983542949198E-9,
+ 3.72533402478845705482E-9,
+ 1.86265972351304900640E-9,
+ 9.31327432419668182872E-10
+};
+#endif
+
+#ifdef DEC
+static unsigned short azetac[] = {
+0140300,0000000,0000000,0000000,
+0077777,0177777,0177777,0177777,
+0040045,0015146,0022460,0076462,
+0037516,0164001,0036001,0104116,
+0037250,0114425,0061754,0022033,
+0037027,0040616,0145174,0146670,
+0036616,0011411,0100444,0104437,
+0036410,0145550,0051474,0161067,
+0036205,0115527,0141434,0133506,
+0036003,0117475,0100553,0053403,
+0035602,0056147,0045567,0027703,
+0035401,0106157,0111054,0145242,
+0035201,0002455,0113151,0101015,
+0035000,0126235,0004273,0157260,
+0034600,0071127,0112647,0005261,
+0034400,0045736,0057610,0157550,
+0034200,0031146,0172621,0074172,
+0034000,0020603,0115503,0032007,
+0033600,0013114,0124672,0023135,
+0033400,0007330,0043715,0151117,
+0033200,0004742,0145043,0033514,
+0033000,0003225,0152624,0004411,
+0032600,0002143,0033166,0035746,
+0032400,0001354,0074234,0026143,
+0032200,0000762,0147776,0170220,
+0032000,0000514,0072452,0130631,
+0031600,0000335,0114266,0063315,
+0031400,0000223,0132710,0041045,
+0031200,0000142,0073202,0153426,
+0031000,0000101,0121400,0152065,
+0030600,0000053,0140525,0072761
+};
+#endif
+
+#ifdef IBMPC
+static unsigned short azetac[] = {
+0x0000,0x0000,0x0000,0xbff8,
+0xffff,0xffff,0xffff,0x7fef,
+0x0fa6,0xc4a6,0xa34c,0x3fe4,
+0x310a,0x2780,0xdd00,0x3fc9,
+0x8483,0xac7d,0x1322,0x3fb5,
+0x99b7,0xd94f,0xe831,0x3fa2,
+0x9124,0x3024,0xc261,0x3f91,
+0x9c47,0x0a67,0x196d,0x3f81,
+0x96e9,0xf863,0xb36a,0x3f70,
+0x6ae0,0xb02d,0x73e7,0x3f60,
+0xe5f8,0xe96e,0x4b8c,0x3f50,
+0x9954,0xf245,0x318d,0x3f40,
+0x3042,0xb2cd,0x20a5,0x3f30,
+0x7bd6,0xa117,0x1593,0x3f20,
+0xe156,0xf2b4,0x0e4a,0x3f10,
+0x1bed,0xcbf1,0x097b,0x3f00,
+0x2f0f,0xdeb2,0x064c,0x3ef0,
+0x6681,0x7368,0x0430,0x3ee0,
+0x44cc,0x9537,0x02c9,0x3ed0,
+0xba4a,0x08f9,0x01db,0x3ec0,
+0x66ea,0x5944,0x013c,0x3eb0,
+0x8121,0xbab2,0x00d2,0x3ea0,
+0xc77d,0x66ce,0x008c,0x3e90,
+0x858c,0x8f13,0x005d,0x3e80,
+0xde12,0x59ff,0x003e,0x3e70,
+0x5633,0x8ea5,0x0029,0x3e60,
+0xccda,0xb316,0x001b,0x3e50,
+0x0845,0x76b9,0x0012,0x3e40,
+0x5ae3,0x4ed0,0x000c,0x3e30,
+0x1a87,0x3460,0x0008,0x3e20,
+0xaebe,0x782a,0x0005,0x3e10
+};
+#endif
+
+#ifdef MIEEE
+static unsigned short azetac[] = {
+0xbff8,0x0000,0x0000,0x0000,
+0x7fef,0xffff,0xffff,0xffff,
+0x3fe4,0xa34c,0xc4a6,0x0fa6,
+0x3fc9,0xdd00,0x2780,0x310a,
+0x3fb5,0x1322,0xac7d,0x8483,
+0x3fa2,0xe831,0xd94f,0x99b7,
+0x3f91,0xc261,0x3024,0x9124,
+0x3f81,0x196d,0x0a67,0x9c47,
+0x3f70,0xb36a,0xf863,0x96e9,
+0x3f60,0x73e7,0xb02d,0x6ae0,
+0x3f50,0x4b8c,0xe96e,0xe5f8,
+0x3f40,0x318d,0xf245,0x9954,
+0x3f30,0x20a5,0xb2cd,0x3042,
+0x3f20,0x1593,0xa117,0x7bd6,
+0x3f10,0x0e4a,0xf2b4,0xe156,
+0x3f00,0x097b,0xcbf1,0x1bed,
+0x3ef0,0x064c,0xdeb2,0x2f0f,
+0x3ee0,0x0430,0x7368,0x6681,
+0x3ed0,0x02c9,0x9537,0x44cc,
+0x3ec0,0x01db,0x08f9,0xba4a,
+0x3eb0,0x013c,0x5944,0x66ea,
+0x3ea0,0x00d2,0xbab2,0x8121,
+0x3e90,0x008c,0x66ce,0xc77d,
+0x3e80,0x005d,0x8f13,0x858c,
+0x3e70,0x003e,0x59ff,0xde12,
+0x3e60,0x0029,0x8ea5,0x5633,
+0x3e50,0x001b,0xb316,0xccda,
+0x3e40,0x0012,0x76b9,0x0845,
+0x3e30,0x000c,0x4ed0,0x5ae3,
+0x3e20,0x0008,0x3460,0x1a87,
+0x3e10,0x0005,0x782a,0xaebe
+};
+#endif
+
+
+/* 2**x (1 - 1/x) (zeta(x) - 1) = P(1/x)/Q(1/x), 1 <= x <= 10 */
+#ifdef UNK
+static double P[9] = {
+ 5.85746514569725319540E11,
+ 2.57534127756102572888E11,
+ 4.87781159567948256438E10,
+ 5.15399538023885770696E9,
+ 3.41646073514754094281E8,
+ 1.60837006880656492731E7,
+ 5.92785467342109522998E5,
+ 1.51129169964938823117E4,
+ 2.01822444485997955865E2,
+};
+static double Q[8] = {
+/* 1.00000000000000000000E0,*/
+ 3.90497676373371157516E11,
+ 5.22858235368272161797E10,
+ 5.64451517271280543351E9,
+ 3.39006746015350418834E8,
+ 1.79410371500126453702E7,
+ 5.66666825131384797029E5,
+ 1.60382976810944131506E4,
+ 1.96436237223387314144E2,
+};
+#endif
+#ifdef DEC
+static unsigned short P[36] = {
+0052010,0060466,0101211,0134657,
+0051557,0154353,0135060,0064411,
+0051065,0133157,0133514,0133633,
+0050231,0114735,0035036,0111344,
+0047242,0164327,0146036,0033545,
+0046165,0065364,0130045,0011005,
+0045020,0134427,0075073,0134107,
+0043554,0021653,0000440,0177426,
+0042111,0151213,0134312,0021402,
+};
+static unsigned short Q[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0051665,0153363,0054252,0137010,
+0051102,0143645,0121415,0036107,
+0050250,0034073,0131133,0036465,
+0047241,0123250,0150037,0070012,
+0046210,0160426,0111463,0116507,
+0045012,0054255,0031674,0173612,
+0043572,0114460,0151520,0012221,
+0042104,0067655,0037037,0137421,
+};
+#endif
+#ifdef IBMPC
+static unsigned short P[36] = {
+0x3736,0xd051,0x0c26,0x4261,
+0x0d21,0x7746,0xfb1d,0x424d,
+0x96f3,0xf6e9,0xb6cd,0x4226,
+0xd25c,0xa743,0x333b,0x41f3,
+0xc6ed,0xf983,0x5d1a,0x41b4,
+0xa241,0x9604,0xad5e,0x416e,
+0x7709,0xef47,0x1722,0x4122,
+0x1fe3,0x6024,0x8475,0x40cd,
+0x4460,0x7719,0x3a51,0x4069,
+};
+static unsigned short Q[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x57c1,0x6b15,0xbade,0x4256,
+0xa789,0xb461,0x58f4,0x4228,
+0x67a7,0x764b,0x0707,0x41f5,
+0xee01,0x1a03,0x34d5,0x41b4,
+0x73a9,0xd266,0x1c22,0x4171,
+0x9ef1,0xa677,0x4b15,0x4121,
+0x0292,0x1a6a,0x5326,0x40cf,
+0xf7e2,0xa7c3,0x8df5,0x4068,
+};
+#endif
+#ifdef MIEEE
+static unsigned short P[36] = {
+0x4261,0x0c26,0xd051,0x3736,
+0x424d,0xfb1d,0x7746,0x0d21,
+0x4226,0xb6cd,0xf6e9,0x96f3,
+0x41f3,0x333b,0xa743,0xd25c,
+0x41b4,0x5d1a,0xf983,0xc6ed,
+0x416e,0xad5e,0x9604,0xa241,
+0x4122,0x1722,0xef47,0x7709,
+0x40cd,0x8475,0x6024,0x1fe3,
+0x4069,0x3a51,0x7719,0x4460,
+};
+static unsigned short Q[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4256,0xbade,0x6b15,0x57c1,
+0x4228,0x58f4,0xb461,0xa789,
+0x41f5,0x0707,0x764b,0x67a7,
+0x41b4,0x34d5,0x1a03,0xee01,
+0x4171,0x1c22,0xd266,0x73a9,
+0x4121,0x4b15,0xa677,0x9ef1,
+0x40cf,0x5326,0x1a6a,0x0292,
+0x4068,0x8df5,0xa7c3,0xf7e2,
+};
+#endif
+
+/* log(zeta(x) - 1 - 2**-x), 10 <= x <= 50 */
+#ifdef UNK
+static double A[11] = {
+ 8.70728567484590192539E6,
+ 1.76506865670346462757E8,
+ 2.60889506707483264896E10,
+ 5.29806374009894791647E11,
+ 2.26888156119238241487E13,
+ 3.31884402932705083599E14,
+ 5.13778997975868230192E15,
+-1.98123688133907171455E15,
+-9.92763810039983572356E16,
+ 7.82905376180870586444E16,
+ 9.26786275768927717187E16,
+};
+static double B[10] = {
+/* 1.00000000000000000000E0,*/
+-7.92625410563741062861E6,
+-1.60529969932920229676E8,
+-2.37669260975543221788E10,
+-4.80319584350455169857E11,
+-2.07820961754173320170E13,
+-2.96075404507272223680E14,
+-4.86299103694609136686E15,
+ 5.34589509675789930199E15,
+ 5.71464111092297631292E16,
+-1.79915597658676556828E16,
+};
+#endif
+#ifdef DEC
+static unsigned short A[44] = {
+0046004,0156325,0126302,0131567,
+0047050,0052177,0015271,0136466,
+0050702,0060271,0070727,0171112,
+0051766,0132727,0064363,0145042,
+0053245,0012466,0056000,0117230,
+0054226,0166155,0174275,0170213,
+0055222,0003127,0112544,0101322,
+0154741,0036625,0010346,0053767,
+0156260,0054653,0154052,0031113,
+0056213,0011152,0021000,0007111,
+0056244,0120534,0040576,0163262,
+};
+static unsigned short B[40] = {
+/*0040200,0000000,0000000,0000000,*/
+0145761,0161734,0033026,0015520,
+0147031,0013743,0017355,0036703,
+0150661,0011720,0061061,0136402,
+0151737,0125216,0070274,0164414,
+0153227,0032653,0127211,0145250,
+0154206,0121666,0123774,0042035,
+0155212,0033352,0125154,0132533,
+0055227,0170201,0110775,0072132,
+0056113,0003133,0127132,0122303,
+0155577,0126351,0141462,0171037,
+};
+#endif
+#ifdef IBMPC
+static unsigned short A[44] = {
+0x566f,0xb598,0x9b9a,0x4160,
+0x37a7,0xe357,0x0a8f,0x41a5,
+0xfe49,0x2e3a,0x4c17,0x4218,
+0x7944,0xed1e,0xd6ba,0x425e,
+0x13d3,0xcb80,0xa2a6,0x42b4,
+0xbe11,0xbf17,0xdd8d,0x42f2,
+0x905a,0xf2ac,0x40ca,0x4332,
+0xcaff,0xa21c,0x27b2,0xc31c,
+0x4649,0x7b05,0x0b35,0xc376,
+0x01c9,0x4440,0x624d,0x4371,
+0xdcd6,0x882f,0x942b,0x4374,
+};
+static unsigned short B[40] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xc36a,0x86c2,0x3c7b,0xc15e,
+0xa7b8,0x63dd,0x22fc,0xc1a3,
+0x37a0,0x0c46,0x227a,0xc216,
+0x9d22,0xce17,0xf551,0xc25b,
+0x3955,0x75d1,0xe6b5,0xc2b2,
+0x8884,0xd4ff,0xd476,0xc2f0,
+0x96ab,0x554d,0x46dd,0xc331,
+0xae8b,0x323f,0xfe10,0x4332,
+0x5498,0x75cb,0x60cb,0x4369,
+0x5e44,0x3866,0xf59d,0xc34f,
+};
+#endif
+#ifdef MIEEE
+static unsigned short A[44] = {
+0x4160,0x9b9a,0xb598,0x566f,
+0x41a5,0x0a8f,0xe357,0x37a7,
+0x4218,0x4c17,0x2e3a,0xfe49,
+0x425e,0xd6ba,0xed1e,0x7944,
+0x42b4,0xa2a6,0xcb80,0x13d3,
+0x42f2,0xdd8d,0xbf17,0xbe11,
+0x4332,0x40ca,0xf2ac,0x905a,
+0xc31c,0x27b2,0xa21c,0xcaff,
+0xc376,0x0b35,0x7b05,0x4649,
+0x4371,0x624d,0x4440,0x01c9,
+0x4374,0x942b,0x882f,0xdcd6,
+};
+static unsigned short B[40] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0xc15e,0x3c7b,0x86c2,0xc36a,
+0xc1a3,0x22fc,0x63dd,0xa7b8,
+0xc216,0x227a,0x0c46,0x37a0,
+0xc25b,0xf551,0xce17,0x9d22,
+0xc2b2,0xe6b5,0x75d1,0x3955,
+0xc2f0,0xd476,0xd4ff,0x8884,
+0xc331,0x46dd,0x554d,0x96ab,
+0x4332,0xfe10,0x323f,0xae8b,
+0x4369,0x60cb,0x75cb,0x5498,
+0xc34f,0xf59d,0x3866,0x5e44,
+};
+#endif
+
+/* (1-x) (zeta(x) - 1), 0 <= x <= 1 */
+
+#ifdef UNK
+static double R[6] = {
+-3.28717474506562731748E-1,
+ 1.55162528742623950834E1,
+-2.48762831680821954401E2,
+ 1.01050368053237678329E3,
+ 1.26726061410235149405E4,
+-1.11578094770515181334E5,
+};
+static double S[5] = {
+/* 1.00000000000000000000E0,*/
+ 1.95107674914060531512E1,
+ 3.17710311750646984099E2,
+ 3.03835500874445748734E3,
+ 2.03665876435770579345E4,
+ 7.43853965136767874343E4,
+};
+#endif
+#ifdef DEC
+static unsigned short R[24] = {
+0137650,0046650,0022502,0040316,
+0041170,0041222,0057666,0142216,
+0142170,0141510,0167741,0075646,
+0042574,0120074,0046505,0106053,
+0043506,0001154,0130073,0101413,
+0144331,0166414,0020560,0131652,
+};
+static unsigned short S[20] = {
+/*0040200,0000000,0000000,0000000,*/
+0041234,0013015,0042073,0113570,
+0042236,0155353,0077325,0077445,
+0043075,0162656,0016646,0031723,
+0043637,0016454,0157636,0071126,
+0044221,0044262,0140365,0146434,
+};
+#endif
+#ifdef IBMPC
+static unsigned short R[24] = {
+0x481a,0x04a8,0x09b5,0xbfd5,
+0xd892,0x4bf6,0x0852,0x402f,
+0x2f75,0x1dfc,0x1869,0xc06f,
+0xb185,0x89a8,0x9407,0x408f,
+0x7061,0x9607,0xc04d,0x40c8,
+0x1675,0x842e,0x3da1,0xc0fb,
+};
+static unsigned short S[20] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x72ef,0xa887,0x82c1,0x4033,
+0xafe5,0x6fda,0xdb5d,0x4073,
+0xc67a,0xc3b4,0xbcb5,0x40a7,
+0xce4b,0x9bf3,0xe3a5,0x40d3,
+0xb9a3,0x581e,0x2916,0x40f2,
+};
+#endif
+#ifdef MIEEE
+static unsigned short R[24] = {
+0xbfd5,0x09b5,0x04a8,0x481a,
+0x402f,0x0852,0x4bf6,0xd892,
+0xc06f,0x1869,0x1dfc,0x2f75,
+0x408f,0x9407,0x89a8,0xb185,
+0x40c8,0xc04d,0x9607,0x7061,
+0xc0fb,0x3da1,0x842e,0x1675,
+};
+static unsigned short S[20] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4033,0x82c1,0xa887,0x72ef,
+0x4073,0xdb5d,0x6fda,0xafe5,
+0x40a7,0xbcb5,0xc3b4,0xc67a,
+0x40d3,0xe3a5,0x9bf3,0xce4b,
+0x40f2,0x2916,0x581e,0xb9a3,
+};
+#endif
+
+#define MAXL2 127
+
+/*
+ * Riemann zeta function, minus one
+ */
+#ifdef ANSIPROT
+extern double sin ( double );
+extern double floor ( double );
+extern double gamma ( double );
+extern double pow ( double, double );
+extern double exp ( double );
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+double zetac ( double );
+#else
+double sin(), floor(), gamma(), pow(), exp();
+double polevl(), p1evl(), zetac();
+#endif
+extern double MACHEP;
+
+double zetac(x)
+double x;
+{
+int i;
+double a, b, s, w;
+
+if( x < 0.0 )
+ {
+#ifdef DEC
+ if( x < -30.8148 )
+#else
+ if( x < -170.6243 )
+#endif
+ {
+ mtherr( "zetac", OVERFLOW );
+ return(0.0);
+ }
+ s = 1.0 - x;
+ w = zetac( s );
+ b = sin(0.5*PI*x) * pow(2.0*PI, x) * gamma(s) * (1.0 + w) / PI;
+ return(b - 1.0);
+ }
+
+if( x >= MAXL2 )
+ return(0.0); /* because first term is 2**-x */
+
+/* Tabulated values for integer argument */
+w = floor(x);
+if( w == x )
+ {
+ i = x;
+ if( i < 31 )
+ {
+#ifdef UNK
+ return( azetac[i] );
+#else
+ return( *(double *)&azetac[4*i] );
+#endif
+ }
+ }
+
+
+if( x < 1.0 )
+ {
+ w = 1.0 - x;
+ a = polevl( x, R, 5 ) / ( w * p1evl( x, S, 5 ));
+ return( a );
+ }
+
+if( x == 1.0 )
+ {
+ mtherr( "zetac", SING );
+ return( MAXNUM );
+ }
+
+if( x <= 10.0 )
+ {
+ b = pow( 2.0, x ) * (x - 1.0);
+ w = 1.0/x;
+ s = (x * polevl( w, P, 8 )) / (b * p1evl( w, Q, 8 ));
+ return( s );
+ }
+
+if( x <= 50.0 )
+ {
+ b = pow( 2.0, -x );
+ w = polevl( x, A, 10 ) / p1evl( x, B, 10 );
+ w = exp(w) + b;
+ return(w);
+ }
+
+
+/* Basic sum of inverse powers */
+
+
+s = 0.0;
+a = 1.0;
+do
+ {
+ a += 2.0;
+ b = pow( a, -x );
+ s += b;
+ }
+while( b/s > MACHEP );
+
+b = pow( 2.0, -x );
+s = (s + b)/(1.0-b);
+return(s);
+}
diff --git a/libm/float/Makefile b/libm/float/Makefile
new file mode 100644
index 000000000..389ac1a5d
--- /dev/null
+++ b/libm/float/Makefile
@@ -0,0 +1,62 @@
+# Makefile for uClibc's math library
+#
+# Copyright (C) 2001 by Lineo, inc.
+#
+# This program is free software; you can redistribute it and/or modify it under
+# the terms of the GNU Library General Public License as published by the Free
+# Software Foundation; either version 2 of the License, or (at your option) any
+# later version.
+#
+# This program is distributed in the hope that it will be useful, but WITHOUT
+# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+# FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more
+# details.
+#
+# You should have received a copy of the GNU Library General Public License
+# along with this program; if not, write to the Free Software Foundation, Inc.,
+# 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+#
+# Derived in part from the Linux-8086 C library, the GNU C Library, and several
+# other sundry sources. Files within this library are copyright by their
+# respective copyright holders.
+
+TOPDIR=../../
+include $(TOPDIR)Rules.mak
+
+LIBM=../libm.a
+TARGET_CC= $(TOPDIR)/extra/gcc-uClibc/$(TARGET_ARCH)-uclibc-gcc
+
+CSRC= acoshf.c airyf.c asinf.c asinhf.c atanf.c \
+ atanhf.c bdtrf.c betaf.c cbrtf.c chbevlf.c chdtrf.c \
+ clogf.c cmplxf.c constf.c coshf.c dawsnf.c ellief.c \
+ ellikf.c ellpef.c ellpkf.c ellpjf.c expf.c exp2f.c \
+ exp10f.c expnf.c facf.c fdtrf.c floorf.c fresnlf.c \
+ gammaf.c gdtrf.c hypergf.c hyp2f1f.c igamf.c igamif.c \
+ incbetf.c incbif.c i0f.c i1f.c ivf.c j0f.c j1f.c \
+ jnf.c jvf.c k0f.c k1f.c knf.c logf.c log2f.c \
+ log10f.c nbdtrf.c ndtrf.c ndtrif.c pdtrf.c polynf.c \
+ powif.c powf.c psif.c rgammaf.c shichif.c sicif.c \
+ sindgf.c sinf.c sinhf.c spencef.c sqrtf.c stdtrf.c \
+ struvef.c tandgf.c tanf.c tanhf.c ynf.c zetaf.c \
+ zetacf.c polevlf.c setprec.c mtherr.c
+COBJS=$(patsubst %.c,%.o, $(CSRC))
+
+
+OBJS=$(COBJS)
+
+all: $(OBJS) $(LIBM)
+
+$(LIBM): ar-target
+
+ar-target: $(OBJS)
+ $(AR) $(ARFLAGS) $(LIBM) $(OBJS)
+
+$(COBJS): %.o : %.c
+ $(TARGET_CC) $(CFLAGS) -c $< -o $@
+ $(STRIPTOOL) -x -R .note -R .comment $*.o
+
+$(OBJ): Makefile
+
+clean:
+ rm -f *.[oa] *~ core
+
diff --git a/libm/float/README.txt b/libm/float/README.txt
new file mode 100644
index 000000000..30a10b083
--- /dev/null
+++ b/libm/float/README.txt
@@ -0,0 +1,4721 @@
+/* acoshf.c
+ *
+ * Inverse hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, acoshf();
+ *
+ * y = acoshf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic cosine of argument.
+ *
+ * If 1 <= x < 1.5, a polynomial approximation
+ *
+ * sqrt(z) * P(z)
+ *
+ * where z = x-1, is used. Otherwise,
+ *
+ * acosh(x) = log( x + sqrt( (x-1)(x+1) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 1,3 100000 1.8e-7 3.9e-8
+ * IEEE 1,2000 100000 3.0e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * acoshf domain |x| < 1 0.0
+ *
+ */
+
+/* airy.c
+ *
+ * Airy function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, ai, aip, bi, bip;
+ * int airyf();
+ *
+ * airyf( x, _&ai, _&aip, _&bi, _&bip );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Solution of the differential equation
+ *
+ * y"(x) = xy.
+ *
+ * The function returns the two independent solutions Ai, Bi
+ * and their first derivatives Ai'(x), Bi'(x).
+ *
+ * Evaluation is by power series summation for small x,
+ * by rational minimax approximations for large x.
+ *
+ *
+ *
+ * ACCURACY:
+ * Error criterion is absolute when function <= 1, relative
+ * when function > 1, except * denotes relative error criterion.
+ * For large negative x, the absolute error increases as x^1.5.
+ * For large positive x, the relative error increases as x^1.5.
+ *
+ * Arithmetic domain function # trials peak rms
+ * IEEE -10, 0 Ai 50000 7.0e-7 1.2e-7
+ * IEEE 0, 10 Ai 50000 9.9e-6* 6.8e-7*
+ * IEEE -10, 0 Ai' 50000 2.4e-6 3.5e-7
+ * IEEE 0, 10 Ai' 50000 8.7e-6* 6.2e-7*
+ * IEEE -10, 10 Bi 100000 2.2e-6 2.6e-7
+ * IEEE -10, 10 Bi' 50000 2.2e-6 3.5e-7
+ *
+ */
+
+/* asinf.c
+ *
+ * Inverse circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, asinf();
+ *
+ * y = asinf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
+ *
+ * A polynomial of the form x + x**3 P(x**2)
+ * is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is
+ * transformed by the identity
+ *
+ * asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1, 1 100000 2.5e-7 5.0e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * asinf domain |x| > 1 0.0
+ *
+ */
+ /* acosf()
+ *
+ * Inverse circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, acosf();
+ *
+ * y = acosf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose cosine
+ * is x.
+ *
+ * Analytically, acos(x) = pi/2 - asin(x). However if |x| is
+ * near 1, there is cancellation error in subtracting asin(x)
+ * from pi/2. Hence if x < -0.5,
+ *
+ * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
+ *
+ * or if x > +0.5,
+ *
+ * acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1, 1 100000 1.4e-7 4.2e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * acosf domain |x| > 1 0.0
+ */
+
+/* asinhf.c
+ *
+ * Inverse hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, asinhf();
+ *
+ * y = asinhf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic sine of argument.
+ *
+ * If |x| < 0.5, the function is approximated by a rational
+ * form x + x**3 P(x)/Q(x). Otherwise,
+ *
+ * asinh(x) = log( x + sqrt(1 + x*x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -3,3 100000 2.4e-7 4.1e-8
+ *
+ */
+
+/* atanf.c
+ *
+ * Inverse circular tangent
+ * (arctangent)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, atanf();
+ *
+ * y = atanf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose tangent
+ * is x.
+ *
+ * Range reduction is from four intervals into the interval
+ * from zero to tan( pi/8 ). A polynomial approximates
+ * the function in this basic interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10, 10 100000 1.9e-7 4.1e-8
+ *
+ */
+ /* atan2f()
+ *
+ * Quadrant correct inverse circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, z, atan2f();
+ *
+ * z = atan2f( y, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle whose tangent is y/x.
+ * Define compile time symbol ANSIC = 1 for ANSI standard,
+ * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
+ * 0 to 2PI, args (x,y).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10, 10 100000 1.9e-7 4.1e-8
+ * See atan.c.
+ *
+ */
+
+/* atanhf.c
+ *
+ * Inverse hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, atanhf();
+ *
+ * y = atanhf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic tangent of argument in the range
+ * MINLOGF to MAXLOGF.
+ *
+ * If |x| < 0.5, a polynomial approximation is used.
+ * Otherwise,
+ * atanh(x) = 0.5 * log( (1+x)/(1-x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1,1 100000 1.4e-7 3.1e-8
+ *
+ */
+
+/* bdtrf.c
+ *
+ * Binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * float p, y, bdtrf();
+ *
+ * y = bdtrf( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the Binomial
+ * probability density:
+ *
+ * k
+ * -- ( n ) j n-j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error (p varies from 0 to 1):
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 2000 6.9e-5 1.1e-5
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtrf domain k < 0 0.0
+ * n < k
+ * x < 0, x > 1
+ *
+ */
+ /* bdtrcf()
+ *
+ * Complemented binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * float p, y, bdtrcf();
+ *
+ * y = bdtrcf( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 through n of the Binomial
+ * probability density:
+ *
+ * n
+ * -- ( n ) j n-j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error (p varies from 0 to 1):
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 2000 6.0e-5 1.2e-5
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtrcf domain x<0, x>1, n<k 0.0
+ */
+ /* bdtrif()
+ *
+ * Inverse binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * float p, y, bdtrif();
+ *
+ * p = bdtrf( k, n, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the event probability p such that the sum of the
+ * terms 0 through k of the Binomial probability density
+ * is equal to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relation
+ *
+ * 1 - p = incbi( n-k, k+1, y ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error (p varies from 0 to 1):
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 2000 3.5e-5 3.3e-6
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtrif domain k < 0, n <= k 0.0
+ * x < 0, x > 1
+ *
+ */
+
+/* betaf.c
+ *
+ * Beta function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, y, betaf();
+ *
+ * y = betaf( a, b );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * - -
+ * | (a) | (b)
+ * beta( a, b ) = -----------.
+ * -
+ * | (a+b)
+ *
+ * For large arguments the logarithm of the function is
+ * evaluated using lgam(), then exponentiated.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 10000 4.0e-5 6.0e-6
+ * IEEE -20,0 10000 4.9e-3 5.4e-5
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * betaf overflow log(beta) > MAXLOG 0.0
+ * a or b <0 integer 0.0
+ *
+ */
+
+/* cbrtf.c
+ *
+ * Cube root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, cbrtf();
+ *
+ * y = cbrtf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the cube root of the argument, which may be negative.
+ *
+ * Range reduction involves determining the power of 2 of
+ * the argument. A polynomial of degree 2 applied to the
+ * mantissa, and multiplication by the cube root of 1, 2, or 4
+ * approximates the root to within about 0.1%. Then Newton's
+ * iteration is used to converge to an accurate result.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,1e38 100000 7.6e-8 2.7e-8
+ *
+ */
+
+/* chbevlf.c
+ *
+ * Evaluate Chebyshev series
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * float x, y, coef[N], chebevlf();
+ *
+ * y = chbevlf( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the series
+ *
+ * N-1
+ * - '
+ * y = > coef[i] T (x/2)
+ * - i
+ * i=0
+ *
+ * of Chebyshev polynomials Ti at argument x/2.
+ *
+ * Coefficients are stored in reverse order, i.e. the zero
+ * order term is last in the array. Note N is the number of
+ * coefficients, not the order.
+ *
+ * If coefficients are for the interval a to b, x must
+ * have been transformed to x -> 2(2x - b - a)/(b-a) before
+ * entering the routine. This maps x from (a, b) to (-1, 1),
+ * over which the Chebyshev polynomials are defined.
+ *
+ * If the coefficients are for the inverted interval, in
+ * which (a, b) is mapped to (1/b, 1/a), the transformation
+ * required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
+ * this becomes x -> 4a/x - 1.
+ *
+ *
+ *
+ * SPEED:
+ *
+ * Taking advantage of the recurrence properties of the
+ * Chebyshev polynomials, the routine requires one more
+ * addition per loop than evaluating a nested polynomial of
+ * the same degree.
+ *
+ */
+
+/* chdtrf.c
+ *
+ * Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float df, x, y, chdtrf();
+ *
+ * y = chdtrf( df, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the left hand tail (from 0 to x)
+ * of the Chi square probability density function with
+ * v degrees of freedom.
+ *
+ *
+ * inf.
+ * -
+ * 1 | | v/2-1 -t/2
+ * P( x | v ) = ----------- | t e dt
+ * v/2 - | |
+ * 2 | (v/2) -
+ * x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ * y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 3.2e-5 5.0e-6
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtrf domain x < 0 or v < 1 0.0
+ */
+ /* chdtrcf()
+ *
+ * Complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float v, x, y, chdtrcf();
+ *
+ * y = chdtrcf( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the right hand tail (from x to
+ * infinity) of the Chi square probability density function
+ * with v degrees of freedom:
+ *
+ *
+ * inf.
+ * -
+ * 1 | | v/2-1 -t/2
+ * P( x | v ) = ----------- | t e dt
+ * v/2 - | |
+ * 2 | (v/2) -
+ * x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ * y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 2.7e-5 3.2e-6
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtrc domain x < 0 or v < 1 0.0
+ */
+ /* chdtrif()
+ *
+ * Inverse of complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float df, x, y, chdtrif();
+ *
+ * x = chdtrif( df, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Chi-square argument x such that the integral
+ * from x to infinity of the Chi-square density is equal
+ * to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ * x/2 = igami( df/2, y );
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 10000 2.2e-5 8.5e-7
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtri domain y < 0 or y > 1 0.0
+ * v < 1
+ *
+ */
+
+/* clogf.c
+ *
+ * Complex natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void clogf();
+ * cmplxf z, w;
+ *
+ * clogf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns complex logarithm to the base e (2.718...) of
+ * the complex argument x.
+ *
+ * If z = x + iy, r = sqrt( x**2 + y**2 ),
+ * then
+ * w = log(r) + i arctan(y/x).
+ *
+ * The arctangent ranges from -PI to +PI.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.9e-6 6.2e-8
+ *
+ * Larger relative error can be observed for z near 1 +i0.
+ * In IEEE arithmetic the peak absolute error is 3.1e-7.
+ *
+ */
+ /* cexpf()
+ *
+ * Complex exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cexpf();
+ * cmplxf z, w;
+ *
+ * cexpf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the exponential of the complex argument z
+ * into the complex result w.
+ *
+ * If
+ * z = x + iy,
+ * r = exp(x),
+ *
+ * then
+ *
+ * w = r cos y + i r sin y.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.4e-7 4.5e-8
+ *
+ */
+ /* csinf()
+ *
+ * Complex circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csinf();
+ * cmplxf z, w;
+ *
+ * csinf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * w = sin x cosh y + i cos x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.9e-7 5.5e-8
+ *
+ */
+ /* ccosf()
+ *
+ * Complex circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccosf();
+ * cmplxf z, w;
+ *
+ * ccosf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * w = cos x cosh y - i sin x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.8e-7 5.5e-8
+ */
+ /* ctanf()
+ *
+ * Complex circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ctanf();
+ * cmplxf z, w;
+ *
+ * ctanf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * sin 2x + i sinh 2y
+ * w = --------------------.
+ * cos 2x + cosh 2y
+ *
+ * On the real axis the denominator is zero at odd multiples
+ * of PI/2. The denominator is evaluated by its Taylor
+ * series near these points.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 3.3e-7 5.1e-8
+ */
+ /* ccotf()
+ *
+ * Complex circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccotf();
+ * cmplxf z, w;
+ *
+ * ccotf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * sin 2x - i sinh 2y
+ * w = --------------------.
+ * cosh 2y - cos 2x
+ *
+ * On the real axis, the denominator has zeros at even
+ * multiples of PI/2. Near these points it is evaluated
+ * by a Taylor series.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 3.6e-7 5.7e-8
+ * Also tested by ctan * ccot = 1 + i0.
+ */
+ /* casinf()
+ *
+ * Complex circular arc sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void casinf();
+ * cmplxf z, w;
+ *
+ * casinf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Inverse complex sine:
+ *
+ * 2
+ * w = -i clog( iz + csqrt( 1 - z ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.1e-5 1.5e-6
+ * Larger relative error can be observed for z near zero.
+ *
+ */
+ /* cacosf()
+ *
+ * Complex circular arc cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cacosf();
+ * cmplxf z, w;
+ *
+ * cacosf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * w = arccos z = PI/2 - arcsin z.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 9.2e-6 1.2e-6
+ *
+ */
+ /* catan()
+ *
+ * Complex circular arc tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void catan();
+ * cmplxf z, w;
+ *
+ * catan( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ * 1 ( 2x )
+ * Re w = - arctan(-----------) + k PI
+ * 2 ( 2 2)
+ * (1 - x - y )
+ *
+ * ( 2 2)
+ * 1 (x + (y+1) )
+ * Im w = - log(------------)
+ * 4 ( 2 2)
+ * (x + (y-1) )
+ *
+ * Where k is an arbitrary integer.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 2.3e-6 5.2e-8
+ *
+ */
+
+/* cmplxf.c
+ *
+ * Complex number arithmetic
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct {
+ * float r; real part
+ * float i; imaginary part
+ * }cmplxf;
+ *
+ * cmplxf *a, *b, *c;
+ *
+ * caddf( a, b, c ); c = b + a
+ * csubf( a, b, c ); c = b - a
+ * cmulf( a, b, c ); c = b * a
+ * cdivf( a, b, c ); c = b / a
+ * cnegf( c ); c = -c
+ * cmovf( b, c ); c = b
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Addition:
+ * c.r = b.r + a.r
+ * c.i = b.i + a.i
+ *
+ * Subtraction:
+ * c.r = b.r - a.r
+ * c.i = b.i - a.i
+ *
+ * Multiplication:
+ * c.r = b.r * a.r - b.i * a.i
+ * c.i = b.r * a.i + b.i * a.r
+ *
+ * Division:
+ * d = a.r * a.r + a.i * a.i
+ * c.r = (b.r * a.r + b.i * a.i)/d
+ * c.i = (b.i * a.r - b.r * a.i)/d
+ * ACCURACY:
+ *
+ * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
+ * error 3.1e-17, rms 1.2e-17. The test (y/z) * (z/y) = 1 had
+ * peak relative error 8.3e-17, rms 2.1e-17.
+ *
+ * Tests in the rectangle {-10,+10}:
+ * Relative error:
+ * arithmetic function # trials peak rms
+ * IEEE cadd 30000 5.9e-8 2.6e-8
+ * IEEE csub 30000 6.0e-8 2.6e-8
+ * IEEE cmul 30000 1.1e-7 3.7e-8
+ * IEEE cdiv 30000 2.1e-7 5.7e-8
+ */
+
+/* cabsf()
+ *
+ * Complex absolute value
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float cabsf();
+ * cmplxf z;
+ * float a;
+ *
+ * a = cabsf( &z );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy
+ *
+ * then
+ *
+ * a = sqrt( x**2 + y**2 ).
+ *
+ * Overflow and underflow are avoided by testing the magnitudes
+ * of x and y before squaring. If either is outside half of
+ * the floating point full scale range, both are rescaled.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.2e-7 3.4e-8
+ */
+ /* csqrtf()
+ *
+ * Complex square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csqrtf();
+ * cmplxf z, w;
+ *
+ * csqrtf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy, r = |z|, then
+ *
+ * 1/2
+ * Im w = [ (r - x)/2 ] ,
+ *
+ * Re w = y / 2 Im w.
+ *
+ *
+ * Note that -w is also a square root of z. The solution
+ * reported is always in the upper half plane.
+ *
+ * Because of the potential for cancellation error in r - x,
+ * the result is sharpened by doing a Heron iteration
+ * (see sqrt.c) in complex arithmetic.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 100000 1.8e-7 4.2e-8
+ *
+ */
+
+/* coshf.c
+ *
+ * Hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, coshf();
+ *
+ * y = coshf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic cosine of argument in the range MINLOGF to
+ * MAXLOGF.
+ *
+ * cosh(x) = ( exp(x) + exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-MAXLOGF 100000 1.2e-7 2.8e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * coshf overflow |x| > MAXLOGF MAXNUMF
+ *
+ *
+ */
+
+/* dawsnf.c
+ *
+ * Dawson's Integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, dawsnf();
+ *
+ * y = dawsnf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ * x
+ * -
+ * 2 | | 2
+ * dawsn(x) = exp( -x ) | exp( t ) dt
+ * | |
+ * -
+ * 0
+ *
+ * Three different rational approximations are employed, for
+ * the intervals 0 to 3.25; 3.25 to 6.25; and 6.25 up.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,10 50000 4.4e-7 6.3e-8
+ *
+ *
+ */
+
+/* ellief.c
+ *
+ * Incomplete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float phi, m, y, ellief();
+ *
+ * y = ellief( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ * phi
+ * -
+ * | |
+ * | 2
+ * E(phi\m) = | sqrt( 1 - m sin t ) dt
+ * |
+ * | |
+ * -
+ * 0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random arguments with phi in [0, 2] and m in
+ * [0, 1].
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,2 10000 4.5e-7 7.4e-8
+ *
+ *
+ */
+
+/* ellikf.c
+ *
+ * Incomplete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float phi, m, y, ellikf();
+ *
+ * y = ellikf( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ * phi
+ * -
+ * | |
+ * | dt
+ * F(phi\m) = | ------------------
+ * | 2
+ * | | sqrt( 1 - m sin t )
+ * -
+ * 0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with phi in [0, 2] and m in
+ * [0, 1].
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,2 10000 2.9e-7 5.8e-8
+ *
+ *
+ */
+
+/* ellpef.c
+ *
+ * Complete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float m1, y, ellpef();
+ *
+ * y = ellpef( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ * pi/2
+ * -
+ * | | 2
+ * E(m) = | sqrt( 1 - m sin t ) dt
+ * | |
+ * -
+ * 0
+ *
+ * Where m = 1 - m1, using the approximation
+ *
+ * P(x) - x log x Q(x).
+ *
+ * Though there are no singularities, the argument m1 is used
+ * rather than m for compatibility with ellpk().
+ *
+ * E(1) = 1; E(0) = pi/2.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 1 30000 1.1e-7 3.9e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ellpef domain x<0, x>1 0.0
+ *
+ */
+
+/* ellpjf.c
+ *
+ * Jacobian Elliptic Functions
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float u, m, sn, cn, dn, phi;
+ * int ellpj();
+ *
+ * ellpj( u, m, _&sn, _&cn, _&dn, _&phi );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
+ * and dn(u|m) of parameter m between 0 and 1, and real
+ * argument u.
+ *
+ * These functions are periodic, with quarter-period on the
+ * real axis equal to the complete elliptic integral
+ * ellpk(1.0-m).
+ *
+ * Relation to incomplete elliptic integral:
+ * If u = ellik(phi,m), then sn(u|m) = sin(phi),
+ * and cn(u|m) = cos(phi). Phi is called the amplitude of u.
+ *
+ * Computation is by means of the arithmetic-geometric mean
+ * algorithm, except when m is within 1e-9 of 0 or 1. In the
+ * latter case with m close to 1, the approximation applies
+ * only for phi < pi/2.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with u between 0 and 10, m between
+ * 0 and 1.
+ *
+ * Absolute error (* = relative error):
+ * arithmetic function # trials peak rms
+ * IEEE sn 10000 1.7e-6 2.2e-7
+ * IEEE cn 10000 1.6e-6 2.2e-7
+ * IEEE dn 10000 1.4e-3 1.9e-5
+ * IEEE phi 10000 3.9e-7* 6.7e-8*
+ *
+ * Peak error observed in consistency check using addition
+ * theorem for sn(u+v) was 4e-16 (absolute). Also tested by
+ * the above relation to the incomplete elliptic integral.
+ * Accuracy deteriorates when u is large.
+ *
+ */
+
+/* ellpkf.c
+ *
+ * Complete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float m1, y, ellpkf();
+ *
+ * y = ellpkf( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ * pi/2
+ * -
+ * | |
+ * | dt
+ * K(m) = | ------------------
+ * | 2
+ * | | sqrt( 1 - m sin t )
+ * -
+ * 0
+ *
+ * where m = 1 - m1, using the approximation
+ *
+ * P(x) - log x Q(x).
+ *
+ * The argument m1 is used rather than m so that the logarithmic
+ * singularity at m = 1 will be shifted to the origin; this
+ * preserves maximum accuracy.
+ *
+ * K(0) = pi/2.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,1 30000 1.3e-7 3.4e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ellpkf domain x<0, x>1 0.0
+ *
+ */
+
+/* exp10f.c
+ *
+ * Base 10 exponential function
+ * (Common antilogarithm)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, exp10f();
+ *
+ * y = exp10f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 10 raised to the x power.
+ *
+ * Range reduction is accomplished by expressing the argument
+ * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
+ * A polynomial approximates 10**f.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -38,+38 100000 9.8e-8 2.8e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp10 underflow x < -MAXL10 0.0
+ * exp10 overflow x > MAXL10 MAXNUM
+ *
+ * IEEE single arithmetic: MAXL10 = 38.230809449325611792.
+ *
+ */
+
+/* exp2f.c
+ *
+ * Base 2 exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, exp2f();
+ *
+ * y = exp2f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 2 raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ * x k f
+ * 2 = 2 2.
+ *
+ * A polynomial approximates 2**x in the basic range [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -127,+127 100000 1.7e-7 2.8e-8
+ *
+ *
+ * See exp.c for comments on error amplification.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp underflow x < -MAXL2 0.0
+ * exp overflow x > MAXL2 MAXNUMF
+ *
+ * For IEEE arithmetic, MAXL2 = 127.
+ */
+
+/* expf.c
+ *
+ * Exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, expf();
+ *
+ * y = expf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns e (2.71828...) raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *
+ * x k f
+ * e = 2 e.
+ *
+ * A polynomial is used to approximate exp(f)
+ * in the basic range [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +- MAXLOG 100000 1.7e-7 2.8e-8
+ *
+ *
+ * Error amplification in the exponential function can be
+ * a serious matter. The error propagation involves
+ * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
+ * which shows that a 1 lsb error in representing X produces
+ * a relative error of X times 1 lsb in the function.
+ * While the routine gives an accurate result for arguments
+ * that are exactly represented by a double precision
+ * computer number, the result contains amplified roundoff
+ * error for large arguments not exactly represented.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * expf underflow x < MINLOGF 0.0
+ * expf overflow x > MAXLOGF MAXNUMF
+ *
+ */
+
+/* expnf.c
+ *
+ * Exponential integral En
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * float x, y, expnf();
+ *
+ * y = expnf( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the exponential integral
+ *
+ * inf.
+ * -
+ * | | -xt
+ * | e
+ * E (x) = | ---- dt.
+ * n | n
+ * | | t
+ * -
+ * 1
+ *
+ *
+ * Both n and x must be nonnegative.
+ *
+ * The routine employs either a power series, a continued
+ * fraction, or an asymptotic formula depending on the
+ * relative values of n and x.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 10000 5.6e-7 1.2e-7
+ *
+ */
+
+/* facf.c
+ *
+ * Factorial function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float y, facf();
+ * int i;
+ *
+ * y = facf( i );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns factorial of i = 1 * 2 * 3 * ... * i.
+ * fac(0) = 1.0.
+ *
+ * Due to machine arithmetic bounds the largest value of
+ * i accepted is 33 in single precision arithmetic.
+ * Greater values, or negative ones,
+ * produce an error message and return MAXNUM.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * For i < 34 the values are simply tabulated, and have
+ * full machine accuracy.
+ *
+ */
+
+/* fdtrf.c
+ *
+ * F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * float x, y, fdtrf();
+ *
+ * y = fdtrf( df1, df2, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density). This is the density
+ * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
+ * variables having Chi square distributions with df1
+ * and df2 degrees of freedom, respectively.
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ * P(x) = incbet( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
+ *
+ *
+ * The arguments a and b are greater than zero, and x
+ * x is nonnegative.
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 2.2e-5 1.1e-6
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrf domain a<0, b<0, x<0 0.0
+ *
+ */
+ /* fdtrcf()
+ *
+ * Complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * float x, y, fdtrcf();
+ *
+ * y = fdtrcf( df1, df2, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from x to infinity under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density).
+ *
+ *
+ * inf.
+ * -
+ * 1 | | a-1 b-1
+ * 1-P(x) = ------ | t (1-t) dt
+ * B(a,b) | |
+ * -
+ * x
+ *
+ * (See fdtr.c.)
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 7.3e-5 1.2e-5
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrcf domain a<0, b<0, x<0 0.0
+ *
+ */
+ /* fdtrif()
+ *
+ * Inverse of complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float df1, df2, x, y, fdtrif();
+ *
+ * x = fdtrif( df1, df2, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the F density argument x such that the integral
+ * from x to infinity of the F density is equal to the
+ * given probability y.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relations
+ *
+ * z = incbi( df2/2, df1/2, y )
+ * x = df2 (1-z) / (df1 z).
+ *
+ * Note: the following relations hold for the inverse of
+ * the uncomplemented F distribution:
+ *
+ * z = incbi( df1/2, df2/2, y )
+ * x = df2 z / (df1 (1-z)).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * arithmetic domain # trials peak rms
+ * Absolute error:
+ * IEEE 0,100 5000 4.0e-5 3.2e-6
+ * Relative error:
+ * IEEE 0,100 5000 1.2e-3 1.8e-5
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrif domain y <= 0 or y > 1 0.0
+ * v < 1
+ *
+ */
+
+/* ceilf()
+ * floorf()
+ * frexpf()
+ * ldexpf()
+ *
+ * Single precision floating point numeric utilities
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y;
+ * float ceilf(), floorf(), frexpf(), ldexpf();
+ * int expnt, n;
+ *
+ * y = floorf(x);
+ * y = ceilf(x);
+ * y = frexpf( x, &expnt );
+ * y = ldexpf( x, n );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * All four routines return a single precision floating point
+ * result.
+ *
+ * sfloor() returns the largest integer less than or equal to x.
+ * It truncates toward minus infinity.
+ *
+ * sceil() returns the smallest integer greater than or equal
+ * to x. It truncates toward plus infinity.
+ *
+ * sfrexp() extracts the exponent from x. It returns an integer
+ * power of two to expnt and the significand between 0.5 and 1
+ * to y. Thus x = y * 2**expn.
+ *
+ * sldexp() multiplies x by 2**n.
+ *
+ * These functions are part of the standard C run time library
+ * for many but not all C compilers. The ones supplied are
+ * written in C for either DEC or IEEE arithmetic. They should
+ * be used only if your compiler library does not already have
+ * them.
+ *
+ * The IEEE versions assume that denormal numbers are implemented
+ * in the arithmetic. Some modifications will be required if
+ * the arithmetic has abrupt rather than gradual underflow.
+ */
+
+/* fresnlf.c
+ *
+ * Fresnel integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, S, C;
+ * void fresnlf();
+ *
+ * fresnlf( x, _&S, _&C );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the Fresnel integrals
+ *
+ * x
+ * -
+ * | |
+ * C(x) = | cos(pi/2 t**2) dt,
+ * | |
+ * -
+ * 0
+ *
+ * x
+ * -
+ * | |
+ * S(x) = | sin(pi/2 t**2) dt.
+ * | |
+ * -
+ * 0
+ *
+ *
+ * The integrals are evaluated by power series for small x.
+ * For x >= 1 auxiliary functions f(x) and g(x) are employed
+ * such that
+ *
+ * C(x) = 0.5 + f(x) sin( pi/2 x**2 ) - g(x) cos( pi/2 x**2 )
+ * S(x) = 0.5 - f(x) cos( pi/2 x**2 ) - g(x) sin( pi/2 x**2 )
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error.
+ *
+ * Arithmetic function domain # trials peak rms
+ * IEEE S(x) 0, 10 30000 1.1e-6 1.9e-7
+ * IEEE C(x) 0, 10 30000 1.1e-6 2.0e-7
+ */
+
+/* gammaf.c
+ *
+ * Gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, gammaf();
+ * extern int sgngamf;
+ *
+ * y = gammaf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns gamma function of the argument. The result is
+ * correctly signed, and the sign (+1 or -1) is also
+ * returned in a global (extern) variable named sgngamf.
+ * This same variable is also filled in by the logarithmic
+ * gamma function lgam().
+ *
+ * Arguments between 0 and 10 are reduced by recurrence and the
+ * function is approximated by a polynomial function covering
+ * the interval (2,3). Large arguments are handled by Stirling's
+ * formula. Negative arguments are made positive using
+ * a reflection formula.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,-33 100,000 5.7e-7 1.0e-7
+ * IEEE -33,0 100,000 6.1e-7 1.2e-7
+ *
+ *
+ */
+/* lgamf()
+ *
+ * Natural logarithm of gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, lgamf();
+ * extern int sgngamf;
+ *
+ * y = lgamf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of the absolute
+ * value of the gamma function of the argument.
+ * The sign (+1 or -1) of the gamma function is returned in a
+ * global (extern) variable named sgngamf.
+ *
+ * For arguments greater than 6.5, the logarithm of the gamma
+ * function is approximated by the logarithmic version of
+ * Stirling's formula. Arguments between 0 and +6.5 are reduced by
+ * by recurrence to the interval [.75,1.25] or [1.5,2.5] of a rational
+ * approximation. The cosecant reflection formula is employed for
+ * arguments less than zero.
+ *
+ * Arguments greater than MAXLGM = 2.035093e36 return MAXNUM and an
+ * error message.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ *
+ * arithmetic domain # trials peak rms
+ * IEEE -100,+100 500,000 7.4e-7 6.8e-8
+ * The error criterion was relative when the function magnitude
+ * was greater than one but absolute when it was less than one.
+ * The routine has low relative error for positive arguments.
+ *
+ * The following test used the relative error criterion.
+ * IEEE -2, +3 100000 4.0e-7 5.6e-8
+ *
+ */
+
+/* gdtrf.c
+ *
+ * Gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, x, y, gdtrf();
+ *
+ * y = gdtrf( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from zero to x of the gamma probability
+ * density function:
+ *
+ *
+ * x
+ * b -
+ * a | | b-1 -at
+ * y = ----- | t e dt
+ * - | |
+ * | (b) -
+ * 0
+ *
+ * The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igam( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 5.8e-5 3.0e-6
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * gdtrf domain x < 0 0.0
+ *
+ */
+ /* gdtrcf.c
+ *
+ * Complemented gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, x, y, gdtrcf();
+ *
+ * y = gdtrcf( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from x to infinity of the gamma
+ * probability density function:
+ *
+ *
+ * inf.
+ * b -
+ * a | | b-1 -at
+ * y = ----- | t e dt
+ * - | |
+ * | (b) -
+ * x
+ *
+ * The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igamc( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 9.1e-5 1.5e-5
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * gdtrcf domain x < 0 0.0
+ *
+ */
+
+/* hyp2f1f.c
+ *
+ * Gauss hypergeometric function F
+ * 2 1
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, c, x, y, hyp2f1f();
+ *
+ * y = hyp2f1f( a, b, c, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * hyp2f1( a, b, c, x ) = F ( a, b; c; x )
+ * 2 1
+ *
+ * inf.
+ * - a(a+1)...(a+k) b(b+1)...(b+k) k+1
+ * = 1 + > ----------------------------- x .
+ * - c(c+1)...(c+k) (k+1)!
+ * k = 0
+ *
+ * Cases addressed are
+ * Tests and escapes for negative integer a, b, or c
+ * Linear transformation if c - a or c - b negative integer
+ * Special case c = a or c = b
+ * Linear transformation for x near +1
+ * Transformation for x < -0.5
+ * Psi function expansion if x > 0.5 and c - a - b integer
+ * Conditionally, a recurrence on c to make c-a-b > 0
+ *
+ * |x| > 1 is rejected.
+ *
+ * The parameters a, b, c are considered to be integer
+ * valued if they are within 1.0e-6 of the nearest integer.
+ *
+ * ACCURACY:
+ *
+ * Relative error (-1 < x < 1):
+ * arithmetic domain # trials peak rms
+ * IEEE 0,3 30000 5.8e-4 4.3e-6
+ */
+
+/* hypergf.c
+ *
+ * Confluent hypergeometric function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, x, y, hypergf();
+ *
+ * y = hypergf( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the confluent hypergeometric function
+ *
+ * 1 2
+ * a x a(a+1) x
+ * F ( a,b;x ) = 1 + ---- + --------- + ...
+ * 1 1 b 1! b(b+1) 2!
+ *
+ * Many higher transcendental functions are special cases of
+ * this power series.
+ *
+ * As is evident from the formula, b must not be a negative
+ * integer or zero unless a is an integer with 0 >= a > b.
+ *
+ * The routine attempts both a direct summation of the series
+ * and an asymptotic expansion. In each case error due to
+ * roundoff, cancellation, and nonconvergence is estimated.
+ * The result with smaller estimated error is returned.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a, b, x), all three variables
+ * ranging from 0 to 30.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,5 10000 6.6e-7 1.3e-7
+ * IEEE 0,30 30000 1.1e-5 6.5e-7
+ *
+ * Larger errors can be observed when b is near a negative
+ * integer or zero. Certain combinations of arguments yield
+ * serious cancellation error in the power series summation
+ * and also are not in the region of near convergence of the
+ * asymptotic series. An error message is printed if the
+ * self-estimated relative error is greater than 1.0e-3.
+ *
+ */
+
+/* i0f.c
+ *
+ * Modified Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, i0();
+ *
+ * y = i0f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order zero of the
+ * argument.
+ *
+ * The function is defined as i0(x) = j0( ix ).
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 100000 4.0e-7 7.9e-8
+ *
+ */
+ /* i0ef.c
+ *
+ * Modified Bessel function of order zero,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, i0ef();
+ *
+ * y = i0ef( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order zero of the argument.
+ *
+ * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 100000 3.7e-7 7.0e-8
+ * See i0f().
+ *
+ */
+
+/* i1f.c
+ *
+ * Modified Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, i1f();
+ *
+ * y = i1f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order one of the
+ * argument.
+ *
+ * The function is defined as i1(x) = -i j1( ix ).
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 100000 1.5e-6 1.6e-7
+ *
+ *
+ */
+ /* i1ef.c
+ *
+ * Modified Bessel function of order one,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, i1ef();
+ *
+ * y = i1ef( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order one of the argument.
+ *
+ * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 1.5e-6 1.5e-7
+ * See i1().
+ *
+ */
+
+/* igamf.c
+ *
+ * Incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, x, y, igamf();
+ *
+ * y = igamf( a, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ * x
+ * -
+ * 1 | | -t a-1
+ * igam(a,x) = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * 0
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 20000 7.8e-6 5.9e-7
+ *
+ */
+ /* igamcf()
+ *
+ * Complemented incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, x, y, igamcf();
+ *
+ * y = igamcf( a, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ *
+ * igamc(a,x) = 1 - igam(a,x)
+ *
+ * inf.
+ * -
+ * 1 | | -t a-1
+ * = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * x
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 30000 7.8e-6 5.9e-7
+ *
+ */
+
+/* igamif()
+ *
+ * Inverse of complemented imcomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, x, y, igamif();
+ *
+ * x = igamif( a, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given y, the function finds x such that
+ *
+ * igamc( a, x ) = y.
+ *
+ * Starting with the approximate value
+ *
+ * 3
+ * x = a t
+ *
+ * where
+ *
+ * t = 1 - d - ndtri(y) sqrt(d)
+ *
+ * and
+ *
+ * d = 1/9a,
+ *
+ * the routine performs up to 10 Newton iterations to find the
+ * root of igamc(a,x) - y = 0.
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested for a ranging from 0 to 100 and x from 0 to 1.
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 1.0e-5 1.5e-6
+ *
+ */
+
+/* incbetf.c
+ *
+ * Incomplete beta integral
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, x, y, incbetf();
+ *
+ * y = incbetf( a, b, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns incomplete beta integral of the arguments, evaluated
+ * from zero to x. The function is defined as
+ *
+ * x
+ * - -
+ * | (a+b) | | a-1 b-1
+ * ----------- | t (1-t) dt.
+ * - - | |
+ * | (a) | (b) -
+ * 0
+ *
+ * The domain of definition is 0 <= x <= 1. In this
+ * implementation a and b are restricted to positive values.
+ * The integral from x to 1 may be obtained by the symmetry
+ * relation
+ *
+ * 1 - incbet( a, b, x ) = incbet( b, a, 1-x ).
+ *
+ * The integral is evaluated by a continued fraction expansion.
+ * If a < 1, the function calls itself recursively after a
+ * transformation to increase a to a+1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,x) with a and b in the indicated
+ * interval and x between 0 and 1.
+ *
+ * arithmetic domain # trials peak rms
+ * Relative error:
+ * IEEE 0,30 10000 3.7e-5 5.1e-6
+ * IEEE 0,100 10000 1.7e-4 2.5e-5
+ * The useful domain for relative error is limited by underflow
+ * of the single precision exponential function.
+ * Absolute error:
+ * IEEE 0,30 100000 2.2e-5 9.6e-7
+ * IEEE 0,100 10000 6.5e-5 3.7e-6
+ *
+ * Larger errors may occur for extreme ratios of a and b.
+ *
+ * ERROR MESSAGES:
+ * message condition value returned
+ * incbetf domain x<0, x>1 0.0
+ */
+
+/* incbif()
+ *
+ * Inverse of imcomplete beta integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, x, y, incbif();
+ *
+ * x = incbif( a, b, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given y, the function finds x such that
+ *
+ * incbet( a, b, x ) = y.
+ *
+ * the routine performs up to 10 Newton iterations to find the
+ * root of incbet(a,b,x) - y = 0.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * x a,b
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0,1 0,100 5000 2.8e-4 8.3e-6
+ *
+ * Overflow and larger errors may occur for one of a or b near zero
+ * and the other large.
+ */
+
+/* ivf.c
+ *
+ * Modified Bessel function of noninteger order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float v, x, y, ivf();
+ *
+ * y = ivf( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order v of the
+ * argument. If x is negative, v must be integer valued.
+ *
+ * The function is defined as Iv(x) = Jv( ix ). It is
+ * here computed in terms of the confluent hypergeometric
+ * function, according to the formula
+ *
+ * v -x
+ * Iv(x) = (x/2) e hyperg( v+0.5, 2v+1, 2x ) / gamma(v+1)
+ *
+ * If v is a negative integer, then v is replaced by -v.
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (v, x), with v between 0 and
+ * 30, x between 0 and 28.
+ * arithmetic domain # trials peak rms
+ * Relative error:
+ * IEEE 0,15 3000 4.7e-6 5.4e-7
+ * Absolute error (relative when function > 1)
+ * IEEE 0,30 5000 8.5e-6 1.3e-6
+ *
+ * Accuracy is diminished if v is near a negative integer.
+ * The useful domain for relative error is limited by overflow
+ * of the single precision exponential function.
+ *
+ * See also hyperg.c.
+ *
+ */
+
+/* j0f.c
+ *
+ * Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, j0f();
+ *
+ * y = j0f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order zero of the argument.
+ *
+ * The domain is divided into the intervals [0, 2] and
+ * (2, infinity). In the first interval the following polynomial
+ * approximation is used:
+ *
+ *
+ * 2 2 2
+ * (w - r ) (w - r ) (w - r ) P(w)
+ * 1 2 3
+ *
+ * 2
+ * where w = x and the three r's are zeros of the function.
+ *
+ * In the second interval, the modulus and phase are approximated
+ * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
+ * and Phase(x) = x + 1/x R(1/x^2) - pi/4. The function is
+ *
+ * j0(x) = Modulus(x) cos( Phase(x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 2 100000 1.3e-7 3.6e-8
+ * IEEE 2, 32 100000 1.9e-7 5.4e-8
+ *
+ */
+ /* y0f.c
+ *
+ * Bessel function of the second kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, y0f();
+ *
+ * y = y0f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind, of order
+ * zero, of the argument.
+ *
+ * The domain is divided into the intervals [0, 2] and
+ * (2, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute
+ *
+ * 2 2 2
+ * y0(x) = (w - r ) (w - r ) (w - r ) R(x) + 2/pi ln(x) j0(x).
+ * 1 2 3
+ *
+ * Thus a call to j0() is required. The three zeros are removed
+ * from R(x) to improve its numerical stability.
+ *
+ * In the second interval, the modulus and phase are approximated
+ * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
+ * and Phase(x) = x + 1/x S(1/x^2) - pi/4. Then the function is
+ *
+ * y0(x) = Modulus(x) sin( Phase(x) ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error, when y0(x) < 1; else relative error:
+ *
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 2 100000 2.4e-7 3.4e-8
+ * IEEE 2, 32 100000 1.8e-7 5.3e-8
+ *
+ */
+
+/* j1f.c
+ *
+ * Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, j1f();
+ *
+ * y = j1f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order one of the argument.
+ *
+ * The domain is divided into the intervals [0, 2] and
+ * (2, infinity). In the first interval a polynomial approximation
+ * 2
+ * (w - r ) x P(w)
+ * 1
+ * 2
+ * is used, where w = x and r is the first zero of the function.
+ *
+ * In the second interval, the modulus and phase are approximated
+ * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
+ * and Phase(x) = x + 1/x R(1/x^2) - 3pi/4. The function is
+ *
+ * j0(x) = Modulus(x) cos( Phase(x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 2 100000 1.2e-7 2.5e-8
+ * IEEE 2, 32 100000 2.0e-7 5.3e-8
+ *
+ *
+ */
+ /* y1.c
+ *
+ * Bessel function of second kind of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y1();
+ *
+ * y = y1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind of order one
+ * of the argument.
+ *
+ * The domain is divided into the intervals [0, 2] and
+ * (2, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute
+ *
+ * 2
+ * y0(x) = (w - r ) x R(x^2) + 2/pi (ln(x) j1(x) - 1/x) .
+ * 1
+ *
+ * Thus a call to j1() is required.
+ *
+ * In the second interval, the modulus and phase are approximated
+ * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
+ * and Phase(x) = x + 1/x S(1/x^2) - 3pi/4. Then the function is
+ *
+ * y0(x) = Modulus(x) sin( Phase(x) ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 2 100000 2.2e-7 4.6e-8
+ * IEEE 2, 32 100000 1.9e-7 5.3e-8
+ *
+ * (error criterion relative when |y1| > 1).
+ *
+ */
+
+/* jnf.c
+ *
+ * Bessel function of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * float x, y, jnf();
+ *
+ * y = jnf( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The ratio of jn(x) to j0(x) is computed by backward
+ * recurrence. First the ratio jn/jn-1 is found by a
+ * continued fraction expansion. Then the recurrence
+ * relating successive orders is applied until j0 or j1 is
+ * reached.
+ *
+ * If n = 0 or 1 the routine for j0 or j1 is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic range # trials peak rms
+ * IEEE 0, 15 30000 3.6e-7 3.6e-8
+ *
+ *
+ * Not suitable for large n or x. Use jvf() instead.
+ *
+ */
+
+/* jvf.c
+ *
+ * Bessel function of noninteger order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float v, x, y, jvf();
+ *
+ * y = jvf( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order v of the argument,
+ * where v is real. Negative x is allowed if v is an integer.
+ *
+ * Several expansions are included: the ascending power
+ * series, the Hankel expansion, and two transitional
+ * expansions for large v. If v is not too large, it
+ * is reduced by recurrence to a region of best accuracy.
+ *
+ * The single precision routine accepts negative v, but with
+ * reduced accuracy.
+ *
+ *
+ *
+ * ACCURACY:
+ * Results for integer v are indicated by *.
+ * Error criterion is absolute, except relative when |jv()| > 1.
+ *
+ * arithmetic domain # trials peak rms
+ * v x
+ * IEEE 0,125 0,125 30000 2.0e-6 2.0e-7
+ * IEEE -17,0 0,125 30000 1.1e-5 4.0e-7
+ * IEEE -100,0 0,125 3000 1.5e-4 7.8e-6
+ */
+
+/* k0f.c
+ *
+ * Modified Bessel function, third kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, k0f();
+ *
+ * y = k0f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of the third kind
+ * of order zero of the argument.
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at 2000 random points between 0 and 8. Peak absolute
+ * error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 7.8e-7 8.5e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * K0 domain x <= 0 MAXNUM
+ *
+ */
+ /* k0ef()
+ *
+ * Modified Bessel function, third kind, order zero,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, k0ef();
+ *
+ * y = k0ef( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order zero of the argument.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 8.1e-7 7.8e-8
+ * See k0().
+ *
+ */
+
+/* k1f.c
+ *
+ * Modified Bessel function, third kind, order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, k1f();
+ *
+ * y = k1f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the modified Bessel function of the third kind
+ * of order one of the argument.
+ *
+ * The range is partitioned into the two intervals [0,2] and
+ * (2, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 4.6e-7 7.6e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * k1 domain x <= 0 MAXNUM
+ *
+ */
+ /* k1ef.c
+ *
+ * Modified Bessel function, third kind, order one,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, k1ef();
+ *
+ * y = k1ef( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order one of the argument:
+ *
+ * k1e(x) = exp(x) * k1(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 4.9e-7 6.7e-8
+ * See k1().
+ *
+ */
+
+/* knf.c
+ *
+ * Modified Bessel function, third kind, integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, knf();
+ * int n;
+ *
+ * y = knf( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of the third kind
+ * of order n of the argument.
+ *
+ * The range is partitioned into the two intervals [0,9.55] and
+ * (9.55, infinity). An ascending power series is used in the
+ * low range, and an asymptotic expansion in the high range.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error, relative when function > 1:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 10000 2.0e-4 3.8e-6
+ *
+ * Error is high only near the crossover point x = 9.55
+ * between the two expansions used.
+ */
+
+/* log10f.c
+ *
+ * Common logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, log10f();
+ *
+ * y = log10f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns logarithm to the base 10 of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. The logarithm of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 100000 1.3e-7 3.4e-8
+ * IEEE 0, MAXNUMF 100000 1.3e-7 2.6e-8
+ *
+ * In the tests over the interval [0, MAXNUM], the logarithms
+ * of the random arguments were uniformly distributed over
+ * [-MAXL10, MAXL10].
+ *
+ * ERROR MESSAGES:
+ *
+ * log10f singularity: x = 0; returns -MAXL10
+ * log10f domain: x < 0; returns -MAXL10
+ * MAXL10 = 38.230809449325611792
+ */
+
+/* log2f.c
+ *
+ * Base 2 logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, log2f();
+ *
+ * y = log2f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base 2 logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the base e
+ * logarithm of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting z = 2(x-1)/x+1),
+ *
+ * log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE exp(+-88) 100000 1.1e-7 2.4e-8
+ * IEEE 0.5, 2.0 100000 1.1e-7 3.0e-8
+ *
+ * In the tests over the interval [exp(+-88)], the logarithms
+ * of the random arguments were uniformly distributed.
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity: x = 0; returns MINLOGF/log(2)
+ * log domain: x < 0; returns MINLOGF/log(2)
+ */
+
+/* logf.c
+ *
+ * Natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, logf();
+ *
+ * y = logf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the logarithm
+ * of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 100000 7.6e-8 2.7e-8
+ * IEEE 1, MAXNUMF 100000 2.6e-8
+ *
+ * In the tests over the interval [1, MAXNUM], the logarithms
+ * of the random arguments were uniformly distributed over
+ * [0, MAXLOGF].
+ *
+ * ERROR MESSAGES:
+ *
+ * logf singularity: x = 0; returns MINLOG
+ * logf domain: x < 0; returns MINLOG
+ */
+
+/* mtherr.c
+ *
+ * Library common error handling routine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * char *fctnam;
+ * int code;
+ * void mtherr();
+ *
+ * mtherr( fctnam, code );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This routine may be called to report one of the following
+ * error conditions (in the include file math.h).
+ *
+ * Mnemonic Value Significance
+ *
+ * DOMAIN 1 argument domain error
+ * SING 2 function singularity
+ * OVERFLOW 3 overflow range error
+ * UNDERFLOW 4 underflow range error
+ * TLOSS 5 total loss of precision
+ * PLOSS 6 partial loss of precision
+ * EDOM 33 Unix domain error code
+ * ERANGE 34 Unix range error code
+ *
+ * The default version of the file prints the function name,
+ * passed to it by the pointer fctnam, followed by the
+ * error condition. The display is directed to the standard
+ * output device. The routine then returns to the calling
+ * program. Users may wish to modify the program to abort by
+ * calling exit() under severe error conditions such as domain
+ * errors.
+ *
+ * Since all error conditions pass control to this function,
+ * the display may be easily changed, eliminated, or directed
+ * to an error logging device.
+ *
+ * SEE ALSO:
+ *
+ * math.h
+ *
+ */
+
+/* nbdtrf.c
+ *
+ * Negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * float p, y, nbdtrf();
+ *
+ * y = nbdtrf( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the negative
+ * binomial distribution:
+ *
+ * k
+ * -- ( n+j-1 ) n j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=0
+ *
+ * In a sequence of Bernoulli trials, this is the probability
+ * that k or fewer failures precede the nth success.
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 1.5e-4 1.9e-5
+ *
+ */
+ /* nbdtrcf.c
+ *
+ * Complemented negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * float p, y, nbdtrcf();
+ *
+ * y = nbdtrcf( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the negative
+ * binomial distribution:
+ *
+ * inf
+ * -- ( n+j-1 ) n j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=k+1
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 1.4e-4 2.0e-5
+ *
+ */
+
+/* ndtrf.c
+ *
+ * Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, ndtrf();
+ *
+ * y = ndtrf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the Gaussian probability density
+ * function, integrated from minus infinity to x:
+ *
+ * x
+ * -
+ * 1 | | 2
+ * ndtr(x) = --------- | exp( - t /2 ) dt
+ * sqrt(2pi) | |
+ * -
+ * -inf.
+ *
+ * = ( 1 + erf(z) ) / 2
+ * = erfc(z) / 2
+ *
+ * where z = x/sqrt(2). Computation is via the functions
+ * erf and erfc.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -13,0 50000 1.5e-5 2.6e-6
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * See erfcf().
+ *
+ */
+ /* erff.c
+ *
+ * Error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, erff();
+ *
+ * y = erff( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The integral is
+ *
+ * x
+ * -
+ * 2 | | 2
+ * erf(x) = -------- | exp( - t ) dt.
+ * sqrt(pi) | |
+ * -
+ * 0
+ *
+ * The magnitude of x is limited to 9.231948545 for DEC
+ * arithmetic; 1 or -1 is returned outside this range.
+ *
+ * For 0 <= |x| < 1, erf(x) = x * P(x**2); otherwise
+ * erf(x) = 1 - erfc(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -9.3,9.3 50000 1.7e-7 2.8e-8
+ *
+ */
+ /* erfcf.c
+ *
+ * Complementary error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, erfcf();
+ *
+ * y = erfcf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * 1 - erf(x) =
+ *
+ * inf.
+ * -
+ * 2 | | 2
+ * erfc(x) = -------- | exp( - t ) dt
+ * sqrt(pi) | |
+ * -
+ * x
+ *
+ *
+ * For small x, erfc(x) = 1 - erf(x); otherwise polynomial
+ * approximations 1/x P(1/x**2) are computed.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -9.3,9.3 50000 3.9e-6 7.2e-7
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * erfcf underflow x**2 > MAXLOGF 0.0
+ *
+ *
+ */
+
+/* ndtrif.c
+ *
+ * Inverse of Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, ndtrif();
+ *
+ * x = ndtrif( y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the argument, x, for which the area under the
+ * Gaussian probability density function (integrated from
+ * minus infinity to x) is equal to y.
+ *
+ *
+ * For small arguments 0 < y < exp(-2), the program computes
+ * z = sqrt( -2.0 * log(y) ); then the approximation is
+ * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).
+ * There are two rational functions P/Q, one for 0 < y < exp(-32)
+ * and the other for y up to exp(-2). For larger arguments,
+ * w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 1e-38, 1 30000 3.6e-7 5.0e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ndtrif domain x <= 0 -MAXNUM
+ * ndtrif domain x >= 1 MAXNUM
+ *
+ */
+
+/* pdtrf.c
+ *
+ * Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * float m, y, pdtrf();
+ *
+ * y = pdtrf( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the first k terms of the Poisson
+ * distribution:
+ *
+ * k j
+ * -- -m m
+ * > e --
+ * -- j!
+ * j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the relation
+ *
+ * y = pdtr( k, m ) = igamc( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 6.9e-5 8.0e-6
+ *
+ */
+ /* pdtrcf()
+ *
+ * Complemented poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * float m, y, pdtrcf();
+ *
+ * y = pdtrcf( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the Poisson
+ * distribution:
+ *
+ * inf. j
+ * -- -m m
+ * > e --
+ * -- j!
+ * j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the formula
+ *
+ * y = pdtrc( k, m ) = igam( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 8.4e-5 1.2e-5
+ *
+ */
+ /* pdtrif()
+ *
+ * Inverse Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * float m, y, pdtrf();
+ *
+ * m = pdtrif( k, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Poisson variable x such that the integral
+ * from 0 to x of the Poisson density is equal to the
+ * given probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ * m = igami( k+1, y ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 8.7e-6 1.4e-6
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * pdtri domain y < 0 or y >= 1 0.0
+ * k < 0
+ *
+ */
+
+/* polevlf.c
+ * p1evlf.c
+ *
+ * Evaluate polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * float x, y, coef[N+1], polevlf[];
+ *
+ * y = polevlf( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates polynomial of degree N:
+ *
+ * 2 N
+ * y = C + C x + C x +...+ C x
+ * 0 1 2 N
+ *
+ * Coefficients are stored in reverse order:
+ *
+ * coef[0] = C , ..., coef[N] = C .
+ * N 0
+ *
+ * The function p1evl() assumes that coef[N] = 1.0 and is
+ * omitted from the array. Its calling arguments are
+ * otherwise the same as polevl().
+ *
+ *
+ * SPEED:
+ *
+ * In the interest of speed, there are no checks for out
+ * of bounds arithmetic. This routine is used by most of
+ * the functions in the library. Depending on available
+ * equipment features, the user may wish to rewrite the
+ * program in microcode or assembly language.
+ *
+ */
+
+/* polynf.c
+ * polyrf.c
+ * Arithmetic operations on polynomials
+ *
+ * In the following descriptions a, b, c are polynomials of degree
+ * na, nb, nc respectively. The degree of a polynomial cannot
+ * exceed a run-time value MAXPOLF. An operation that attempts
+ * to use or generate a polynomial of higher degree may produce a
+ * result that suffers truncation at degree MAXPOL. The value of
+ * MAXPOL is set by calling the function
+ *
+ * polinif( maxpol );
+ *
+ * where maxpol is the desired maximum degree. This must be
+ * done prior to calling any of the other functions in this module.
+ * Memory for internal temporary polynomial storage is allocated
+ * by polinif().
+ *
+ * Each polynomial is represented by an array containing its
+ * coefficients, together with a separately declared integer equal
+ * to the degree of the polynomial. The coefficients appear in
+ * ascending order; that is,
+ *
+ * 2 na
+ * a(x) = a[0] + a[1] * x + a[2] * x + ... + a[na] * x .
+ *
+ *
+ *
+ * sum = poleva( a, na, x ); Evaluate polynomial a(t) at t = x.
+ * polprtf( a, na, D ); Print the coefficients of a to D digits.
+ * polclrf( a, na ); Set a identically equal to zero, up to a[na].
+ * polmovf( a, na, b ); Set b = a.
+ * poladdf( a, na, b, nb, c ); c = b + a, nc = max(na,nb)
+ * polsubf( a, na, b, nb, c ); c = b - a, nc = max(na,nb)
+ * polmulf( a, na, b, nb, c ); c = b * a, nc = na+nb
+ *
+ *
+ * Division:
+ *
+ * i = poldivf( a, na, b, nb, c ); c = b / a, nc = MAXPOL
+ *
+ * returns i = the degree of the first nonzero coefficient of a.
+ * The computed quotient c must be divided by x^i. An error message
+ * is printed if a is identically zero.
+ *
+ *
+ * Change of variables:
+ * If a and b are polynomials, and t = a(x), then
+ * c(t) = b(a(x))
+ * is a polynomial found by substituting a(x) for t. The
+ * subroutine call for this is
+ *
+ * polsbtf( a, na, b, nb, c );
+ *
+ *
+ * Notes:
+ * poldivf() is an integer routine; polevaf() is float.
+ * Any of the arguments a, b, c may refer to the same array.
+ *
+ */
+
+/* powf.c
+ *
+ * Power function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, z, powf();
+ *
+ * z = powf( x, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes x raised to the yth power. Analytically,
+ *
+ * x**y = exp( y log(x) ).
+ *
+ * Following Cody and Waite, this program uses a lookup table
+ * of 2**-i/16 and pseudo extended precision arithmetic to
+ * obtain an extra three bits of accuracy in both the logarithm
+ * and the exponential.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,10 100,000 1.4e-7 3.6e-8
+ * 1/10 < x < 10, x uniformly distributed.
+ * -10 < y < 10, y uniformly distributed.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * powf overflow x**y > MAXNUMF MAXNUMF
+ * powf underflow x**y < 1/MAXNUMF 0.0
+ * powf domain x<0 and y noninteger 0.0
+ *
+ */
+
+/* powif.c
+ *
+ * Real raised to integer power
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, powif();
+ * int n;
+ *
+ * y = powif( x, n );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns argument x raised to the nth power.
+ * The routine efficiently decomposes n as a sum of powers of
+ * two. The desired power is a product of two-to-the-kth
+ * powers of x. Thus to compute the 32767 power of x requires
+ * 28 multiplications instead of 32767 multiplications.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error:
+ * arithmetic x domain n domain # trials peak rms
+ * IEEE .04,26 -26,26 100000 1.1e-6 2.0e-7
+ * IEEE 1,2 -128,128 100000 1.1e-5 1.0e-6
+ *
+ * Returns MAXNUMF on overflow, zero on underflow.
+ *
+ */
+
+/* psif.c
+ *
+ * Psi (digamma) function
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, psif();
+ *
+ * y = psif( x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * d -
+ * psi(x) = -- ln | (x)
+ * dx
+ *
+ * is the logarithmic derivative of the gamma function.
+ * For integer x,
+ * n-1
+ * -
+ * psi(n) = -EUL + > 1/k.
+ * -
+ * k=1
+ *
+ * This formula is used for 0 < n <= 10. If x is negative, it
+ * is transformed to a positive argument by the reflection
+ * formula psi(1-x) = psi(x) + pi cot(pi x).
+ * For general positive x, the argument is made greater than 10
+ * using the recurrence psi(x+1) = psi(x) + 1/x.
+ * Then the following asymptotic expansion is applied:
+ *
+ * inf. B
+ * - 2k
+ * psi(x) = log(x) - 1/2x - > -------
+ * - 2k
+ * k=1 2k x
+ *
+ * where the B2k are Bernoulli numbers.
+ *
+ * ACCURACY:
+ * Absolute error, relative when |psi| > 1 :
+ * arithmetic domain # trials peak rms
+ * IEEE -33,0 30000 8.2e-7 1.2e-7
+ * IEEE 0,33 100000 7.3e-7 7.7e-8
+ *
+ * ERROR MESSAGES:
+ * message condition value returned
+ * psi singularity x integer <=0 MAXNUMF
+ */
+
+/* rgammaf.c
+ *
+ * Reciprocal gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, rgammaf();
+ *
+ * y = rgammaf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns one divided by the gamma function of the argument.
+ *
+ * The function is approximated by a Chebyshev expansion in
+ * the interval [0,1]. Range reduction is by recurrence
+ * for arguments between -34.034 and +34.84425627277176174.
+ * 1/MAXNUMF is returned for positive arguments outside this
+ * range.
+ *
+ * The reciprocal gamma function has no singularities,
+ * but overflow and underflow may occur for large arguments.
+ * These conditions return either MAXNUMF or 1/MAXNUMF with
+ * appropriate sign.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -34,+34 100000 8.9e-7 1.1e-7
+ */
+
+/* shichif.c
+ *
+ * Hyperbolic sine and cosine integrals
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, Chi, Shi;
+ *
+ * shichi( x, &Chi, &Shi );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integrals
+ *
+ * x
+ * -
+ * | | cosh t - 1
+ * Chi(x) = eul + ln x + | ----------- dt,
+ * | | t
+ * -
+ * 0
+ *
+ * x
+ * -
+ * | | sinh t
+ * Shi(x) = | ------ dt
+ * | | t
+ * -
+ * 0
+ *
+ * where eul = 0.57721566490153286061 is Euler's constant.
+ * The integrals are evaluated by power series for x < 8
+ * and by Chebyshev expansions for x between 8 and 88.
+ * For large x, both functions approach exp(x)/2x.
+ * Arguments greater than 88 in magnitude return MAXNUM.
+ *
+ *
+ * ACCURACY:
+ *
+ * Test interval 0 to 88.
+ * Relative error:
+ * arithmetic function # trials peak rms
+ * IEEE Shi 20000 3.5e-7 7.0e-8
+ * Absolute error, except relative when |Chi| > 1:
+ * IEEE Chi 20000 3.8e-7 7.6e-8
+ */
+
+/* sicif.c
+ *
+ * Sine and cosine integrals
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, Ci, Si;
+ *
+ * sicif( x, &Si, &Ci );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the integrals
+ *
+ * x
+ * -
+ * | cos t - 1
+ * Ci(x) = eul + ln x + | --------- dt,
+ * | t
+ * -
+ * 0
+ * x
+ * -
+ * | sin t
+ * Si(x) = | ----- dt
+ * | t
+ * -
+ * 0
+ *
+ * where eul = 0.57721566490153286061 is Euler's constant.
+ * The integrals are approximated by rational functions.
+ * For x > 8 auxiliary functions f(x) and g(x) are employed
+ * such that
+ *
+ * Ci(x) = f(x) sin(x) - g(x) cos(x)
+ * Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)
+ *
+ *
+ * ACCURACY:
+ * Test interval = [0,50].
+ * Absolute error, except relative when > 1:
+ * arithmetic function # trials peak rms
+ * IEEE Si 30000 2.1e-7 4.3e-8
+ * IEEE Ci 30000 3.9e-7 2.2e-8
+ */
+
+/* sindgf.c
+ *
+ * Circular sine of angle in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, sindgf();
+ *
+ * y = sindgf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of 45 degrees.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the sine is approximated by
+ * x + x**3 P(x**2).
+ * Between pi/4 and pi/2 the cosine is represented as
+ * 1 - x**2 Q(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-3600 100,000 1.2e-7 3.0e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sin total loss x > 2^24 0.0
+ *
+ */
+
+/* cosdgf.c
+ *
+ * Circular cosine of angle in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, cosdgf();
+ *
+ * y = cosdgf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of 45 degrees.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the cosine is approximated by
+ * 1 - x**2 Q(x**2).
+ * Between pi/4 and pi/2 the sine is represented as
+ * x + x**3 P(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -8192,+8192 100,000 3.0e-7 3.0e-8
+ */
+
+/* sinf.c
+ *
+ * Circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, sinf();
+ *
+ * y = sinf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of pi/4. The reduction
+ * error is nearly eliminated by contriving an extended precision
+ * modular arithmetic.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the sine is approximated by
+ * x + x**3 P(x**2).
+ * Between pi/4 and pi/2 the cosine is represented as
+ * 1 - x**2 Q(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -4096,+4096 100,000 1.2e-7 3.0e-8
+ * IEEE -8192,+8192 100,000 3.0e-7 3.0e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sin total loss x > 2^24 0.0
+ *
+ * Partial loss of accuracy begins to occur at x = 2^13
+ * = 8192. Results may be meaningless for x >= 2^24
+ * The routine as implemented flags a TLOSS error
+ * for x >= 2^24 and returns 0.0.
+ */
+
+/* cosf.c
+ *
+ * Circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, cosf();
+ *
+ * y = cosf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of pi/4. The reduction
+ * error is nearly eliminated by contriving an extended precision
+ * modular arithmetic.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the cosine is approximated by
+ * 1 - x**2 Q(x**2).
+ * Between pi/4 and pi/2 the sine is represented as
+ * x + x**3 P(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -8192,+8192 100,000 3.0e-7 3.0e-8
+ */
+
+/* sinhf.c
+ *
+ * Hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, sinhf();
+ *
+ * y = sinhf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic sine of argument in the range MINLOGF to
+ * MAXLOGF.
+ *
+ * The range is partitioned into two segments. If |x| <= 1, a
+ * polynomial approximation is used.
+ * Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-MAXLOG 100000 1.1e-7 2.9e-8
+ *
+ */
+
+/* spencef.c
+ *
+ * Dilogarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, spencef();
+ *
+ * y = spencef( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the integral
+ *
+ * x
+ * -
+ * | | log t
+ * spence(x) = - | ----- dt
+ * | | t - 1
+ * -
+ * 1
+ *
+ * for x >= 0. A rational approximation gives the integral in
+ * the interval (0.5, 1.5). Transformation formulas for 1/x
+ * and 1-x are employed outside the basic expansion range.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,4 30000 4.4e-7 6.3e-8
+ *
+ *
+ */
+
+/* sqrtf.c
+ *
+ * Square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, sqrtf();
+ *
+ * y = sqrtf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the square root of x.
+ *
+ * Range reduction involves isolating the power of two of the
+ * argument and using a polynomial approximation to obtain
+ * a rough value for the square root. Then Heron's iteration
+ * is used three times to converge to an accurate value.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,1.e38 100000 8.7e-8 2.9e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sqrtf domain x < 0 0.0
+ *
+ */
+
+/* stdtrf.c
+ *
+ * Student's t distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float t, stdtrf();
+ * short k;
+ *
+ * y = stdtrf( k, t );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the integral from minus infinity to t of the Student
+ * t distribution with integer k > 0 degrees of freedom:
+ *
+ * t
+ * -
+ * | |
+ * - | 2 -(k+1)/2
+ * | ( (k+1)/2 ) | ( x )
+ * ---------------------- | ( 1 + --- ) dx
+ * - | ( k )
+ * sqrt( k pi ) | ( k/2 ) |
+ * | |
+ * -
+ * -inf.
+ *
+ * Relation to incomplete beta integral:
+ *
+ * 1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
+ * where
+ * z = k/(k + t**2).
+ *
+ * For t < -1, this is the method of computation. For higher t,
+ * a direct method is derived from integration by parts.
+ * Since the function is symmetric about t=0, the area under the
+ * right tail of the density is found by calling the function
+ * with -t instead of t.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +/- 100 5000 2.3e-5 2.9e-6
+ */
+
+/* struvef.c
+ *
+ * Struve function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float v, x, y, struvef();
+ *
+ * y = struvef( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the Struve function Hv(x) of order v, argument x.
+ * Negative x is rejected unless v is an integer.
+ *
+ * This module also contains the hypergeometric functions 1F2
+ * and 3F0 and a routine for the Bessel function Yv(x) with
+ * noninteger v.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * v varies from 0 to 10.
+ * Absolute error (relative error when |Hv(x)| > 1):
+ * arithmetic domain # trials peak rms
+ * IEEE -10,10 100000 9.0e-5 4.0e-6
+ *
+ */
+
+/* tandgf.c
+ *
+ * Circular tangent of angle in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, tandgf();
+ *
+ * y = tandgf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular tangent of the radian argument x.
+ *
+ * Range reduction is into intervals of 45 degrees.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-2^24 50000 2.4e-7 4.8e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * tanf total loss x > 2^24 0.0
+ *
+ */
+ /* cotdgf.c
+ *
+ * Circular cotangent of angle in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, cotdgf();
+ *
+ * y = cotdgf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of 45 degrees.
+ * A common routine computes either the tangent or cotangent.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-2^24 50000 2.4e-7 4.8e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * cot total loss x > 2^24 0.0
+ * cot singularity x = 0 MAXNUMF
+ *
+ */
+
+/* tanf.c
+ *
+ * Circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, tanf();
+ *
+ * y = tanf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular tangent of the radian argument x.
+ *
+ * Range reduction is modulo pi/4. A polynomial approximation
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-4096 100000 3.3e-7 4.5e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * tanf total loss x > 2^24 0.0
+ *
+ */
+ /* cotf.c
+ *
+ * Circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, cotf();
+ *
+ * y = cotf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular cotangent of the radian argument x.
+ * A common routine computes either the tangent or cotangent.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-4096 100000 3.0e-7 4.5e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * cot total loss x > 2^24 0.0
+ * cot singularity x = 0 MAXNUMF
+ *
+ */
+
+/* tanhf.c
+ *
+ * Hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, tanhf();
+ *
+ * y = tanhf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic tangent of argument in the range MINLOG to
+ * MAXLOG.
+ *
+ * A polynomial approximation is used for |x| < 0.625.
+ * Otherwise,
+ *
+ * tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -2,2 100000 1.3e-7 2.6e-8
+ *
+ */
+
+/* ynf.c
+ *
+ * Bessel function of second kind of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, ynf();
+ * int n;
+ *
+ * y = ynf( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The function is evaluated by forward recurrence on
+ * n, starting with values computed by the routines
+ * y0() and y1().
+ *
+ * If n = 0 or 1 the routine for y0 or y1 is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Absolute error, except relative when y > 1:
+ *
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 10000 2.3e-6 3.4e-7
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * yn singularity x = 0 MAXNUMF
+ * yn overflow MAXNUMF
+ *
+ * Spot checked against tables for x, n between 0 and 100.
+ *
+ */
+
+ /* zetacf.c
+ *
+ * Riemann zeta function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, zetacf();
+ *
+ * y = zetacf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *
+ * inf.
+ * - -x
+ * zetac(x) = > k , x > 1,
+ * -
+ * k=2
+ *
+ * is related to the Riemann zeta function by
+ *
+ * Riemann zeta(x) = zetac(x) + 1.
+ *
+ * Extension of the function definition for x < 1 is implemented.
+ * Zero is returned for x > log2(MAXNUM).
+ *
+ * An overflow error may occur for large negative x, due to the
+ * gamma function in the reflection formula.
+ *
+ * ACCURACY:
+ *
+ * Tabulated values have full machine accuracy.
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 1,50 30000 5.5e-7 7.5e-8
+ *
+ *
+ */
+
+/* zetaf.c
+ *
+ * Riemann zeta function of two arguments
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, q, y, zetaf();
+ *
+ * y = zetaf( x, q );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *
+ * inf.
+ * - -x
+ * zeta(x,q) = > (k+q)
+ * -
+ * k=0
+ *
+ * where x > 1 and q is not a negative integer or zero.
+ * The Euler-Maclaurin summation formula is used to obtain
+ * the expansion
+ *
+ * n
+ * - -x
+ * zeta(x,q) = > (k+q)
+ * -
+ * k=1
+ *
+ * 1-x inf. B x(x+1)...(x+2j)
+ * (n+q) 1 - 2j
+ * + --------- - ------- + > --------------------
+ * x-1 x - x+2j+1
+ * 2(n+q) j=1 (2j)! (n+q)
+ *
+ * where the B2j are Bernoulli numbers. Note that (see zetac.c)
+ * zeta(x,1) = zetac(x) + 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,25 10000 6.9e-7 1.0e-7
+ *
+ * Large arguments may produce underflow in powf(), in which
+ * case the results are inaccurate.
+ *
+ * REFERENCE:
+ *
+ * Gradshteyn, I. S., and I. M. Ryzhik, Tables of Integrals,
+ * Series, and Products, p. 1073; Academic Press, 1980.
+ *
+ */
diff --git a/libm/float/acoshf.c b/libm/float/acoshf.c
new file mode 100644
index 000000000..c45206125
--- /dev/null
+++ b/libm/float/acoshf.c
@@ -0,0 +1,97 @@
+/* acoshf.c
+ *
+ * Inverse hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, acoshf();
+ *
+ * y = acoshf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic cosine of argument.
+ *
+ * If 1 <= x < 1.5, a polynomial approximation
+ *
+ * sqrt(z) * P(z)
+ *
+ * where z = x-1, is used. Otherwise,
+ *
+ * acosh(x) = log( x + sqrt( (x-1)(x+1) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 1,3 100000 1.8e-7 3.9e-8
+ * IEEE 1,2000 100000 3.0e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * acoshf domain |x| < 1 0.0
+ *
+ */
+
+/* acosh.c */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Single precision inverse hyperbolic cosine
+ * test interval: [1.0, 1.5]
+ * trials: 10000
+ * peak relative error: 1.7e-7
+ * rms relative error: 5.0e-8
+ *
+ * Copyright (C) 1989 by Stephen L. Moshier. All rights reserved.
+ */
+#include <math.h>
+extern float LOGE2F;
+
+float sqrtf( float );
+float logf( float );
+
+float acoshf( float xx )
+{
+float x, z;
+
+x = xx;
+if( x < 1.0 )
+ {
+ mtherr( "acoshf", DOMAIN );
+ return(0.0);
+ }
+
+if( x > 1500.0 )
+ return( logf(x) + LOGE2F );
+
+z = x - 1.0;
+
+if( z < 0.5 )
+ {
+ z =
+ (((( 1.7596881071E-3 * z
+ - 7.5272886713E-3) * z
+ + 2.6454905019E-2) * z
+ - 1.1784741703E-1) * z
+ + 1.4142135263E0) * sqrtf( z );
+ }
+else
+ {
+ z = sqrtf( z*(x+1.0) );
+ z = logf(x + z);
+ }
+return( z );
+}
diff --git a/libm/float/airyf.c b/libm/float/airyf.c
new file mode 100644
index 000000000..a84a5c861
--- /dev/null
+++ b/libm/float/airyf.c
@@ -0,0 +1,377 @@
+/* airy.c
+ *
+ * Airy function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, ai, aip, bi, bip;
+ * int airyf();
+ *
+ * airyf( x, _&ai, _&aip, _&bi, _&bip );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Solution of the differential equation
+ *
+ * y"(x) = xy.
+ *
+ * The function returns the two independent solutions Ai, Bi
+ * and their first derivatives Ai'(x), Bi'(x).
+ *
+ * Evaluation is by power series summation for small x,
+ * by rational minimax approximations for large x.
+ *
+ *
+ *
+ * ACCURACY:
+ * Error criterion is absolute when function <= 1, relative
+ * when function > 1, except * denotes relative error criterion.
+ * For large negative x, the absolute error increases as x^1.5.
+ * For large positive x, the relative error increases as x^1.5.
+ *
+ * Arithmetic domain function # trials peak rms
+ * IEEE -10, 0 Ai 50000 7.0e-7 1.2e-7
+ * IEEE 0, 10 Ai 50000 9.9e-6* 6.8e-7*
+ * IEEE -10, 0 Ai' 50000 2.4e-6 3.5e-7
+ * IEEE 0, 10 Ai' 50000 8.7e-6* 6.2e-7*
+ * IEEE -10, 10 Bi 100000 2.2e-6 2.6e-7
+ * IEEE -10, 10 Bi' 50000 2.2e-6 3.5e-7
+ *
+ */
+ /* airy.c */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+static float c1 = 0.35502805388781723926;
+static float c2 = 0.258819403792806798405;
+static float sqrt3 = 1.732050807568877293527;
+static float sqpii = 5.64189583547756286948E-1;
+extern float PIF;
+
+extern float MAXNUMF, MACHEPF;
+#define MAXAIRY 25.77
+
+/* Note, these expansions are for double precision accuracy;
+ * they have not yet been redesigned for single precision.
+ */
+static float AN[8] = {
+ 3.46538101525629032477e-1,
+ 1.20075952739645805542e1,
+ 7.62796053615234516538e1,
+ 1.68089224934630576269e2,
+ 1.59756391350164413639e2,
+ 7.05360906840444183113e1,
+ 1.40264691163389668864e1,
+ 9.99999999999999995305e-1,
+};
+static float AD[8] = {
+ 5.67594532638770212846e-1,
+ 1.47562562584847203173e1,
+ 8.45138970141474626562e1,
+ 1.77318088145400459522e2,
+ 1.64234692871529701831e2,
+ 7.14778400825575695274e1,
+ 1.40959135607834029598e1,
+ 1.00000000000000000470e0,
+};
+
+
+static float APN[8] = {
+ 6.13759184814035759225e-1,
+ 1.47454670787755323881e1,
+ 8.20584123476060982430e1,
+ 1.71184781360976385540e2,
+ 1.59317847137141783523e2,
+ 6.99778599330103016170e1,
+ 1.39470856980481566958e1,
+ 1.00000000000000000550e0,
+};
+static float APD[8] = {
+ 3.34203677749736953049e-1,
+ 1.11810297306158156705e1,
+ 7.11727352147859965283e1,
+ 1.58778084372838313640e2,
+ 1.53206427475809220834e2,
+ 6.86752304592780337944e1,
+ 1.38498634758259442477e1,
+ 9.99999999999999994502e-1,
+};
+
+static float BN16[5] = {
+-2.53240795869364152689e-1,
+ 5.75285167332467384228e-1,
+-3.29907036873225371650e-1,
+ 6.44404068948199951727e-2,
+-3.82519546641336734394e-3,
+};
+static float BD16[5] = {
+/* 1.00000000000000000000e0,*/
+-7.15685095054035237902e0,
+ 1.06039580715664694291e1,
+-5.23246636471251500874e0,
+ 9.57395864378383833152e-1,
+-5.50828147163549611107e-2,
+};
+
+static float BPPN[5] = {
+ 4.65461162774651610328e-1,
+-1.08992173800493920734e0,
+ 6.38800117371827987759e-1,
+-1.26844349553102907034e-1,
+ 7.62487844342109852105e-3,
+};
+static float BPPD[5] = {
+/* 1.00000000000000000000e0,*/
+-8.70622787633159124240e0,
+ 1.38993162704553213172e1,
+-7.14116144616431159572e0,
+ 1.34008595960680518666e0,
+-7.84273211323341930448e-2,
+};
+
+static float AFN[9] = {
+-1.31696323418331795333e-1,
+-6.26456544431912369773e-1,
+-6.93158036036933542233e-1,
+-2.79779981545119124951e-1,
+-4.91900132609500318020e-2,
+-4.06265923594885404393e-3,
+-1.59276496239262096340e-4,
+-2.77649108155232920844e-6,
+-1.67787698489114633780e-8,
+};
+static float AFD[9] = {
+/* 1.00000000000000000000e0,*/
+ 1.33560420706553243746e1,
+ 3.26825032795224613948e1,
+ 2.67367040941499554804e1,
+ 9.18707402907259625840e0,
+ 1.47529146771666414581e0,
+ 1.15687173795188044134e-1,
+ 4.40291641615211203805e-3,
+ 7.54720348287414296618e-5,
+ 4.51850092970580378464e-7,
+};
+
+static float AGN[11] = {
+ 1.97339932091685679179e-2,
+ 3.91103029615688277255e-1,
+ 1.06579897599595591108e0,
+ 9.39169229816650230044e-1,
+ 3.51465656105547619242e-1,
+ 6.33888919628925490927e-2,
+ 5.85804113048388458567e-3,
+ 2.82851600836737019778e-4,
+ 6.98793669997260967291e-6,
+ 8.11789239554389293311e-8,
+ 3.41551784765923618484e-10,
+};
+static float AGD[10] = {
+/* 1.00000000000000000000e0,*/
+ 9.30892908077441974853e0,
+ 1.98352928718312140417e1,
+ 1.55646628932864612953e1,
+ 5.47686069422975497931e0,
+ 9.54293611618961883998e-1,
+ 8.64580826352392193095e-2,
+ 4.12656523824222607191e-3,
+ 1.01259085116509135510e-4,
+ 1.17166733214413521882e-6,
+ 4.91834570062930015649e-9,
+};
+
+static float APFN[9] = {
+ 1.85365624022535566142e-1,
+ 8.86712188052584095637e-1,
+ 9.87391981747398547272e-1,
+ 4.01241082318003734092e-1,
+ 7.10304926289631174579e-2,
+ 5.90618657995661810071e-3,
+ 2.33051409401776799569e-4,
+ 4.08718778289035454598e-6,
+ 2.48379932900442457853e-8,
+};
+static float APFD[9] = {
+/* 1.00000000000000000000e0,*/
+ 1.47345854687502542552e1,
+ 3.75423933435489594466e1,
+ 3.14657751203046424330e1,
+ 1.09969125207298778536e1,
+ 1.78885054766999417817e0,
+ 1.41733275753662636873e-1,
+ 5.44066067017226003627e-3,
+ 9.39421290654511171663e-5,
+ 5.65978713036027009243e-7,
+};
+
+static float APGN[11] = {
+-3.55615429033082288335e-2,
+-6.37311518129435504426e-1,
+-1.70856738884312371053e0,
+-1.50221872117316635393e0,
+-5.63606665822102676611e-1,
+-1.02101031120216891789e-1,
+-9.48396695961445269093e-3,
+-4.60325307486780994357e-4,
+-1.14300836484517375919e-5,
+-1.33415518685547420648e-7,
+-5.63803833958893494476e-10,
+};
+static float APGD[11] = {
+/* 1.00000000000000000000e0,*/
+ 9.85865801696130355144e0,
+ 2.16401867356585941885e1,
+ 1.73130776389749389525e1,
+ 6.17872175280828766327e0,
+ 1.08848694396321495475e0,
+ 9.95005543440888479402e-2,
+ 4.78468199683886610842e-3,
+ 1.18159633322838625562e-4,
+ 1.37480673554219441465e-6,
+ 5.79912514929147598821e-9,
+};
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+float polevlf(float, float *, int);
+float p1evlf(float, float *, int);
+float sinf(float), cosf(float), expf(float), sqrtf(float);
+
+int airyf( float xx, float *ai, float *aip, float *bi, float *bip )
+{
+float x, z, zz, t, f, g, uf, ug, k, zeta, theta;
+int domflg;
+
+x = xx;
+domflg = 0;
+if( x > MAXAIRY )
+ {
+ *ai = 0;
+ *aip = 0;
+ *bi = MAXNUMF;
+ *bip = MAXNUMF;
+ return(-1);
+ }
+
+if( x < -2.09 )
+ {
+ domflg = 15;
+ t = sqrtf(-x);
+ zeta = -2.0 * x * t / 3.0;
+ t = sqrtf(t);
+ k = sqpii / t;
+ z = 1.0/zeta;
+ zz = z * z;
+ uf = 1.0 + zz * polevlf( zz, AFN, 8 ) / p1evlf( zz, AFD, 9 );
+ ug = z * polevlf( zz, AGN, 10 ) / p1evlf( zz, AGD, 10 );
+ theta = zeta + 0.25 * PIF;
+ f = sinf( theta );
+ g = cosf( theta );
+ *ai = k * (f * uf - g * ug);
+ *bi = k * (g * uf + f * ug);
+ uf = 1.0 + zz * polevlf( zz, APFN, 8 ) / p1evlf( zz, APFD, 9 );
+ ug = z * polevlf( zz, APGN, 10 ) / p1evlf( zz, APGD, 10 );
+ k = sqpii * t;
+ *aip = -k * (g * uf + f * ug);
+ *bip = k * (f * uf - g * ug);
+ return(0);
+ }
+
+if( x >= 2.09 ) /* cbrt(9) */
+ {
+ domflg = 5;
+ t = sqrtf(x);
+ zeta = 2.0 * x * t / 3.0;
+ g = expf( zeta );
+ t = sqrtf(t);
+ k = 2.0 * t * g;
+ z = 1.0/zeta;
+ f = polevlf( z, AN, 7 ) / polevlf( z, AD, 7 );
+ *ai = sqpii * f / k;
+ k = -0.5 * sqpii * t / g;
+ f = polevlf( z, APN, 7 ) / polevlf( z, APD, 7 );
+ *aip = f * k;
+
+ if( x > 8.3203353 ) /* zeta > 16 */
+ {
+ f = z * polevlf( z, BN16, 4 ) / p1evlf( z, BD16, 5 );
+ k = sqpii * g;
+ *bi = k * (1.0 + f) / t;
+ f = z * polevlf( z, BPPN, 4 ) / p1evlf( z, BPPD, 5 );
+ *bip = k * t * (1.0 + f);
+ return(0);
+ }
+ }
+
+f = 1.0;
+g = x;
+t = 1.0;
+uf = 1.0;
+ug = x;
+k = 1.0;
+z = x * x * x;
+while( t > MACHEPF )
+ {
+ uf *= z;
+ k += 1.0;
+ uf /=k;
+ ug *= z;
+ k += 1.0;
+ ug /=k;
+ uf /=k;
+ f += uf;
+ k += 1.0;
+ ug /=k;
+ g += ug;
+ t = fabsf(uf/f);
+ }
+uf = c1 * f;
+ug = c2 * g;
+if( (domflg & 1) == 0 )
+ *ai = uf - ug;
+if( (domflg & 2) == 0 )
+ *bi = sqrt3 * (uf + ug);
+
+/* the deriviative of ai */
+k = 4.0;
+uf = x * x/2.0;
+ug = z/3.0;
+f = uf;
+g = 1.0 + ug;
+uf /= 3.0;
+t = 1.0;
+
+while( t > MACHEPF )
+ {
+ uf *= z;
+ ug /=k;
+ k += 1.0;
+ ug *= z;
+ uf /=k;
+ f += uf;
+ k += 1.0;
+ ug /=k;
+ uf /=k;
+ g += ug;
+ k += 1.0;
+ t = fabsf(ug/g);
+ }
+
+uf = c1 * f;
+ug = c2 * g;
+if( (domflg & 4) == 0 )
+ *aip = uf - ug;
+if( (domflg & 8) == 0 )
+ *bip = sqrt3 * (uf + ug);
+return(0);
+}
diff --git a/libm/float/asinf.c b/libm/float/asinf.c
new file mode 100644
index 000000000..c96d75acb
--- /dev/null
+++ b/libm/float/asinf.c
@@ -0,0 +1,186 @@
+/* asinf.c
+ *
+ * Inverse circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, asinf();
+ *
+ * y = asinf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
+ *
+ * A polynomial of the form x + x**3 P(x**2)
+ * is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is
+ * transformed by the identity
+ *
+ * asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1, 1 100000 2.5e-7 5.0e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * asinf domain |x| > 1 0.0
+ *
+ */
+ /* acosf()
+ *
+ * Inverse circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, acosf();
+ *
+ * y = acosf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose cosine
+ * is x.
+ *
+ * Analytically, acos(x) = pi/2 - asin(x). However if |x| is
+ * near 1, there is cancellation error in subtracting asin(x)
+ * from pi/2. Hence if x < -0.5,
+ *
+ * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
+ *
+ * or if x > +0.5,
+ *
+ * acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1, 1 100000 1.4e-7 4.2e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * acosf domain |x| > 1 0.0
+ */
+
+/* asin.c */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Single precision circular arcsine
+ * test interval: [-0.5, +0.5]
+ * trials: 10000
+ * peak relative error: 6.7e-8
+ * rms relative error: 2.5e-8
+ */
+#include <math.h>
+extern float PIF, PIO2F;
+
+float sqrtf( float );
+
+float asinf( float xx )
+{
+float a, x, z;
+int sign, flag;
+
+x = xx;
+
+if( x > 0 )
+ {
+ sign = 1;
+ a = x;
+ }
+else
+ {
+ sign = -1;
+ a = -x;
+ }
+
+if( a > 1.0 )
+ {
+ mtherr( "asinf", DOMAIN );
+ return( 0.0 );
+ }
+
+if( a < 1.0e-4 )
+ {
+ z = a;
+ goto done;
+ }
+
+if( a > 0.5 )
+ {
+ z = 0.5 * (1.0 - a);
+ x = sqrtf( z );
+ flag = 1;
+ }
+else
+ {
+ x = a;
+ z = x * x;
+ flag = 0;
+ }
+
+z =
+(((( 4.2163199048E-2 * z
+ + 2.4181311049E-2) * z
+ + 4.5470025998E-2) * z
+ + 7.4953002686E-2) * z
+ + 1.6666752422E-1) * z * x
+ + x;
+
+if( flag != 0 )
+ {
+ z = z + z;
+ z = PIO2F - z;
+ }
+done:
+if( sign < 0 )
+ z = -z;
+return( z );
+}
+
+
+
+
+float acosf( float x )
+{
+
+if( x < -1.0 )
+ goto domerr;
+
+if( x < -0.5)
+ return( PIF - 2.0 * asinf( sqrtf(0.5*(1.0+x)) ) );
+
+if( x > 1.0 )
+ {
+domerr: mtherr( "acosf", DOMAIN );
+ return( 0.0 );
+ }
+
+if( x > 0.5 )
+ return( 2.0 * asinf( sqrtf(0.5*(1.0-x) ) ) );
+
+return( PIO2F - asinf(x) );
+}
+
diff --git a/libm/float/asinhf.c b/libm/float/asinhf.c
new file mode 100644
index 000000000..d3fbe10a7
--- /dev/null
+++ b/libm/float/asinhf.c
@@ -0,0 +1,88 @@
+/* asinhf.c
+ *
+ * Inverse hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, asinhf();
+ *
+ * y = asinhf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic sine of argument.
+ *
+ * If |x| < 0.5, the function is approximated by a rational
+ * form x + x**3 P(x)/Q(x). Otherwise,
+ *
+ * asinh(x) = log( x + sqrt(1 + x*x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -3,3 100000 2.4e-7 4.1e-8
+ *
+ */
+
+/* asinh.c */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Single precision inverse hyperbolic sine
+ * test interval: [-0.5, +0.5]
+ * trials: 10000
+ * peak relative error: 8.8e-8
+ * rms relative error: 3.2e-8
+ */
+#include <math.h>
+extern float LOGE2F;
+
+float logf( float );
+float sqrtf( float );
+
+float asinhf( float xx )
+{
+float x, z;
+
+if( xx < 0 )
+ x = -xx;
+else
+ x = xx;
+
+if( x > 1500.0 )
+ {
+ z = logf(x) + LOGE2F;
+ goto done;
+ }
+z = x * x;
+if( x < 0.5 )
+ {
+ z =
+ ((( 2.0122003309E-2 * z
+ - 4.2699340972E-2) * z
+ + 7.4847586088E-2) * z
+ - 1.6666288134E-1) * z * x
+ + x;
+ }
+else
+ {
+ z = sqrtf( z + 1.0 );
+ z = logf( x + z );
+ }
+done:
+if( xx < 0 )
+ z = -z;
+return( z );
+}
+
diff --git a/libm/float/atanf.c b/libm/float/atanf.c
new file mode 100644
index 000000000..321e3be39
--- /dev/null
+++ b/libm/float/atanf.c
@@ -0,0 +1,190 @@
+/* atanf.c
+ *
+ * Inverse circular tangent
+ * (arctangent)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, atanf();
+ *
+ * y = atanf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose tangent
+ * is x.
+ *
+ * Range reduction is from four intervals into the interval
+ * from zero to tan( pi/8 ). A polynomial approximates
+ * the function in this basic interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10, 10 100000 1.9e-7 4.1e-8
+ *
+ */
+ /* atan2f()
+ *
+ * Quadrant correct inverse circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, z, atan2f();
+ *
+ * z = atan2f( y, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle whose tangent is y/x.
+ * Define compile time symbol ANSIC = 1 for ANSI standard,
+ * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
+ * 0 to 2PI, args (x,y).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10, 10 100000 1.9e-7 4.1e-8
+ * See atan.c.
+ *
+ */
+
+/* atan.c */
+
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Single precision circular arcsine
+ * test interval: [-tan(pi/8), +tan(pi/8)]
+ * trials: 10000
+ * peak relative error: 7.7e-8
+ * rms relative error: 2.9e-8
+ */
+#include <math.h>
+extern float PIF, PIO2F, PIO4F;
+
+float atanf( float xx )
+{
+float x, y, z;
+int sign;
+
+x = xx;
+
+/* make argument positive and save the sign */
+if( xx < 0.0 )
+ {
+ sign = -1;
+ x = -xx;
+ }
+else
+ {
+ sign = 1;
+ x = xx;
+ }
+/* range reduction */
+if( x > 2.414213562373095 ) /* tan 3pi/8 */
+ {
+ y = PIO2F;
+ x = -( 1.0/x );
+ }
+
+else if( x > 0.4142135623730950 ) /* tan pi/8 */
+ {
+ y = PIO4F;
+ x = (x-1.0)/(x+1.0);
+ }
+else
+ y = 0.0;
+
+z = x * x;
+y +=
+((( 8.05374449538e-2 * z
+ - 1.38776856032E-1) * z
+ + 1.99777106478E-1) * z
+ - 3.33329491539E-1) * z * x
+ + x;
+
+if( sign < 0 )
+ y = -y;
+
+return( y );
+}
+
+
+
+
+float atan2f( float y, float x )
+{
+float z, w;
+int code;
+
+
+code = 0;
+
+if( x < 0.0 )
+ code = 2;
+if( y < 0.0 )
+ code |= 1;
+
+if( x == 0.0 )
+ {
+ if( code & 1 )
+ {
+#if ANSIC
+ return( -PIO2F );
+#else
+ return( 3.0*PIO2F );
+#endif
+ }
+ if( y == 0.0 )
+ return( 0.0 );
+ return( PIO2F );
+ }
+
+if( y == 0.0 )
+ {
+ if( code & 2 )
+ return( PIF );
+ return( 0.0 );
+ }
+
+
+switch( code )
+ {
+ default:
+#if ANSIC
+ case 0:
+ case 1: w = 0.0; break;
+ case 2: w = PIF; break;
+ case 3: w = -PIF; break;
+#else
+ case 0: w = 0.0; break;
+ case 1: w = 2.0 * PIF; break;
+ case 2:
+ case 3: w = PIF; break;
+#endif
+ }
+
+z = atanf( y/x );
+
+return( w + z );
+}
+
diff --git a/libm/float/atanhf.c b/libm/float/atanhf.c
new file mode 100644
index 000000000..dfadad09e
--- /dev/null
+++ b/libm/float/atanhf.c
@@ -0,0 +1,92 @@
+/* atanhf.c
+ *
+ * Inverse hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, atanhf();
+ *
+ * y = atanhf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic tangent of argument in the range
+ * MINLOGF to MAXLOGF.
+ *
+ * If |x| < 0.5, a polynomial approximation is used.
+ * Otherwise,
+ * atanh(x) = 0.5 * log( (1+x)/(1-x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1,1 100000 1.4e-7 3.1e-8
+ *
+ */
+
+/* atanh.c */
+
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright (C) 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Single precision inverse hyperbolic tangent
+ * test interval: [-0.5, +0.5]
+ * trials: 10000
+ * peak relative error: 8.2e-8
+ * rms relative error: 3.0e-8
+ */
+#include <math.h>
+extern float MAXNUMF;
+
+float logf( float );
+
+float atanhf( float xx )
+{
+float x, z;
+
+x = xx;
+if( x < 0 )
+ z = -x;
+else
+ z = x;
+if( z >= 1.0 )
+ {
+ if( x == 1.0 )
+ return( MAXNUMF );
+ if( x == -1.0 )
+ return( -MAXNUMF );
+ mtherr( "atanhl", DOMAIN );
+ return( MAXNUMF );
+ }
+
+if( z < 1.0e-4 )
+ return(x);
+
+if( z < 0.5 )
+ {
+ z = x * x;
+ z =
+ (((( 1.81740078349E-1 * z
+ + 8.24370301058E-2) * z
+ + 1.46691431730E-1) * z
+ + 1.99782164500E-1) * z
+ + 3.33337300303E-1) * z * x
+ + x;
+ }
+else
+ {
+ z = 0.5 * logf( (1.0+x)/(1.0-x) );
+ }
+return( z );
+}
diff --git a/libm/float/bdtrf.c b/libm/float/bdtrf.c
new file mode 100644
index 000000000..e063f1c77
--- /dev/null
+++ b/libm/float/bdtrf.c
@@ -0,0 +1,247 @@
+/* bdtrf.c
+ *
+ * Binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * float p, y, bdtrf();
+ *
+ * y = bdtrf( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the Binomial
+ * probability density:
+ *
+ * k
+ * -- ( n ) j n-j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error (p varies from 0 to 1):
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 2000 6.9e-5 1.1e-5
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtrf domain k < 0 0.0
+ * n < k
+ * x < 0, x > 1
+ *
+ */
+ /* bdtrcf()
+ *
+ * Complemented binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * float p, y, bdtrcf();
+ *
+ * y = bdtrcf( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 through n of the Binomial
+ * probability density:
+ *
+ * n
+ * -- ( n ) j n-j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error (p varies from 0 to 1):
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 2000 6.0e-5 1.2e-5
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtrcf domain x<0, x>1, n<k 0.0
+ */
+ /* bdtrif()
+ *
+ * Inverse binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * float p, y, bdtrif();
+ *
+ * p = bdtrf( k, n, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the event probability p such that the sum of the
+ * terms 0 through k of the Binomial probability density
+ * is equal to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relation
+ *
+ * 1 - p = incbi( n-k, k+1, y ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error (p varies from 0 to 1):
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 2000 3.5e-5 3.3e-6
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtrif domain k < 0, n <= k 0.0
+ * x < 0, x > 1
+ *
+ */
+
+/* bdtr() */
+
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+#ifdef ANSIC
+float incbetf(float, float, float), powf(float, float);
+float incbif( float, float, float );
+#else
+float incbetf(), powf(), incbif();
+#endif
+
+float bdtrcf( int k, int n, float pp )
+{
+float p, dk, dn;
+
+p = pp;
+if( (p < 0.0) || (p > 1.0) )
+ goto domerr;
+if( k < 0 )
+ return( 1.0 );
+
+if( n < k )
+ {
+domerr:
+ mtherr( "bdtrcf", DOMAIN );
+ return( 0.0 );
+ }
+
+if( k == n )
+ return( 0.0 );
+dn = n - k;
+if( k == 0 )
+ {
+ dk = 1.0 - powf( 1.0-p, dn );
+ }
+else
+ {
+ dk = k + 1;
+ dk = incbetf( dk, dn, p );
+ }
+return( dk );
+}
+
+
+
+float bdtrf( int k, int n, float pp )
+{
+float p, dk, dn;
+
+p = pp;
+if( (p < 0.0) || (p > 1.0) )
+ goto domerr;
+if( (k < 0) || (n < k) )
+ {
+domerr:
+ mtherr( "bdtrf", DOMAIN );
+ return( 0.0 );
+ }
+
+if( k == n )
+ return( 1.0 );
+
+dn = n - k;
+if( k == 0 )
+ {
+ dk = powf( 1.0-p, dn );
+ }
+else
+ {
+ dk = k + 1;
+ dk = incbetf( dn, dk, 1.0 - p );
+ }
+return( dk );
+}
+
+
+float bdtrif( int k, int n, float yy )
+{
+float y, dk, dn, p;
+
+y = yy;
+if( (y < 0.0) || (y > 1.0) )
+ goto domerr;
+if( (k < 0) || (n <= k) )
+ {
+domerr:
+ mtherr( "bdtrif", DOMAIN );
+ return( 0.0 );
+ }
+
+dn = n - k;
+if( k == 0 )
+ {
+ p = 1.0 - powf( y, 1.0/dn );
+ }
+else
+ {
+ dk = k + 1;
+ p = 1.0 - incbif( dn, dk, y );
+ }
+return( p );
+}
diff --git a/libm/float/betaf.c b/libm/float/betaf.c
new file mode 100644
index 000000000..7a1963191
--- /dev/null
+++ b/libm/float/betaf.c
@@ -0,0 +1,122 @@
+/* betaf.c
+ *
+ * Beta function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, y, betaf();
+ *
+ * y = betaf( a, b );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * - -
+ * | (a) | (b)
+ * beta( a, b ) = -----------.
+ * -
+ * | (a+b)
+ *
+ * For large arguments the logarithm of the function is
+ * evaluated using lgam(), then exponentiated.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 10000 4.0e-5 6.0e-6
+ * IEEE -20,0 10000 4.9e-3 5.4e-5
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * betaf overflow log(beta) > MAXLOG 0.0
+ * a or b <0 integer 0.0
+ *
+ */
+
+/* beta.c */
+
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#define MAXGAM 34.84425627277176174
+
+
+extern float MAXLOGF, MAXNUMF;
+extern int sgngamf;
+
+#ifdef ANSIC
+float gammaf(float), lgamf(float), expf(float), floorf(float);
+#else
+float gammaf(), lgamf(), expf(), floorf();
+#endif
+
+float betaf( float aa, float bb )
+{
+float a, b, y;
+int sign;
+
+sign = 1;
+a = aa;
+b = bb;
+if( a <= 0.0 )
+ {
+ if( a == floorf(a) )
+ goto over;
+ }
+if( b <= 0.0 )
+ {
+ if( b == floorf(b) )
+ goto over;
+ }
+
+
+y = a + b;
+if( fabsf(y) > MAXGAM )
+ {
+ y = lgamf(y);
+ sign *= sgngamf; /* keep track of the sign */
+ y = lgamf(b) - y;
+ sign *= sgngamf;
+ y = lgamf(a) + y;
+ sign *= sgngamf;
+ if( y > MAXLOGF )
+ {
+over:
+ mtherr( "betaf", OVERFLOW );
+ return( sign * MAXNUMF );
+ }
+ return( sign * expf(y) );
+ }
+
+y = gammaf(y);
+if( y == 0.0 )
+ goto over;
+
+if( a > b )
+ {
+ y = gammaf(a)/y;
+ y *= gammaf(b);
+ }
+else
+ {
+ y = gammaf(b)/y;
+ y *= gammaf(a);
+ }
+
+return(y);
+}
diff --git a/libm/float/cbrtf.c b/libm/float/cbrtf.c
new file mode 100644
index 000000000..ca9b433d9
--- /dev/null
+++ b/libm/float/cbrtf.c
@@ -0,0 +1,119 @@
+/* cbrtf.c
+ *
+ * Cube root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, cbrtf();
+ *
+ * y = cbrtf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the cube root of the argument, which may be negative.
+ *
+ * Range reduction involves determining the power of 2 of
+ * the argument. A polynomial of degree 2 applied to the
+ * mantissa, and multiplication by the cube root of 1, 2, or 4
+ * approximates the root to within about 0.1%. Then Newton's
+ * iteration is used to converge to an accurate result.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,1e38 100000 7.6e-8 2.7e-8
+ *
+ */
+ /* cbrt.c */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+static float CBRT2 = 1.25992104989487316477;
+static float CBRT4 = 1.58740105196819947475;
+
+
+float frexpf(float, int *), ldexpf(float, int);
+
+float cbrtf( float xx )
+{
+int e, rem, sign;
+float x, z;
+
+x = xx;
+if( x == 0 )
+ return( 0.0 );
+if( x > 0 )
+ sign = 1;
+else
+ {
+ sign = -1;
+ x = -x;
+ }
+
+z = x;
+/* extract power of 2, leaving
+ * mantissa between 0.5 and 1
+ */
+x = frexpf( x, &e );
+
+/* Approximate cube root of number between .5 and 1,
+ * peak relative error = 9.2e-6
+ */
+x = (((-0.13466110473359520655053 * x
+ + 0.54664601366395524503440 ) * x
+ - 0.95438224771509446525043 ) * x
+ + 1.1399983354717293273738 ) * x
+ + 0.40238979564544752126924;
+
+/* exponent divided by 3 */
+if( e >= 0 )
+ {
+ rem = e;
+ e /= 3;
+ rem -= 3*e;
+ if( rem == 1 )
+ x *= CBRT2;
+ else if( rem == 2 )
+ x *= CBRT4;
+ }
+
+
+/* argument less than 1 */
+
+else
+ {
+ e = -e;
+ rem = e;
+ e /= 3;
+ rem -= 3*e;
+ if( rem == 1 )
+ x /= CBRT2;
+ else if( rem == 2 )
+ x /= CBRT4;
+ e = -e;
+ }
+
+/* multiply by power of 2 */
+x = ldexpf( x, e );
+
+/* Newton iteration */
+x -= ( x - (z/(x*x)) ) * 0.333333333333;
+
+if( sign < 0 )
+ x = -x;
+return(x);
+}
diff --git a/libm/float/chbevlf.c b/libm/float/chbevlf.c
new file mode 100644
index 000000000..343d00a22
--- /dev/null
+++ b/libm/float/chbevlf.c
@@ -0,0 +1,86 @@
+/* chbevlf.c
+ *
+ * Evaluate Chebyshev series
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * float x, y, coef[N], chebevlf();
+ *
+ * y = chbevlf( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the series
+ *
+ * N-1
+ * - '
+ * y = > coef[i] T (x/2)
+ * - i
+ * i=0
+ *
+ * of Chebyshev polynomials Ti at argument x/2.
+ *
+ * Coefficients are stored in reverse order, i.e. the zero
+ * order term is last in the array. Note N is the number of
+ * coefficients, not the order.
+ *
+ * If coefficients are for the interval a to b, x must
+ * have been transformed to x -> 2(2x - b - a)/(b-a) before
+ * entering the routine. This maps x from (a, b) to (-1, 1),
+ * over which the Chebyshev polynomials are defined.
+ *
+ * If the coefficients are for the inverted interval, in
+ * which (a, b) is mapped to (1/b, 1/a), the transformation
+ * required is x -> 2(2ab/x - b - a)/(b-a). If b is infinity,
+ * this becomes x -> 4a/x - 1.
+ *
+ *
+ *
+ * SPEED:
+ *
+ * Taking advantage of the recurrence properties of the
+ * Chebyshev polynomials, the routine requires one more
+ * addition per loop than evaluating a nested polynomial of
+ * the same degree.
+ *
+ */
+ /* chbevl.c */
+
+/*
+Cephes Math Library Release 2.0: April, 1987
+Copyright 1985, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#ifdef ANSIC
+float chbevlf( float x, float *array, int n )
+#else
+float chbevlf( x, array, n )
+float x;
+float *array;
+int n;
+#endif
+{
+float b0, b1, b2, *p;
+int i;
+
+p = array;
+b0 = *p++;
+b1 = 0.0;
+i = n - 1;
+
+do
+ {
+ b2 = b1;
+ b1 = b0;
+ b0 = x * b1 - b2 + *p++;
+ }
+while( --i );
+
+return( 0.5*(b0-b2) );
+}
diff --git a/libm/float/chdtrf.c b/libm/float/chdtrf.c
new file mode 100644
index 000000000..53bd3d961
--- /dev/null
+++ b/libm/float/chdtrf.c
@@ -0,0 +1,210 @@
+/* chdtrf.c
+ *
+ * Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float df, x, y, chdtrf();
+ *
+ * y = chdtrf( df, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the left hand tail (from 0 to x)
+ * of the Chi square probability density function with
+ * v degrees of freedom.
+ *
+ *
+ * inf.
+ * -
+ * 1 | | v/2-1 -t/2
+ * P( x | v ) = ----------- | t e dt
+ * v/2 - | |
+ * 2 | (v/2) -
+ * x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ * y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 3.2e-5 5.0e-6
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtrf domain x < 0 or v < 1 0.0
+ */
+ /* chdtrcf()
+ *
+ * Complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float v, x, y, chdtrcf();
+ *
+ * y = chdtrcf( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the right hand tail (from x to
+ * infinity) of the Chi square probability density function
+ * with v degrees of freedom:
+ *
+ *
+ * inf.
+ * -
+ * 1 | | v/2-1 -t/2
+ * P( x | v ) = ----------- | t e dt
+ * v/2 - | |
+ * 2 | (v/2) -
+ * x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ * y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 2.7e-5 3.2e-6
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtrc domain x < 0 or v < 1 0.0
+ */
+ /* chdtrif()
+ *
+ * Inverse of complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float df, x, y, chdtrif();
+ *
+ * x = chdtrif( df, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Chi-square argument x such that the integral
+ * from x to infinity of the Chi-square density is equal
+ * to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ * x/2 = igami( df/2, y );
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 10000 2.2e-5 8.5e-7
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtri domain y < 0 or y > 1 0.0
+ * v < 1
+ *
+ */
+
+/* chdtr() */
+
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+#ifdef ANSIC
+float igamcf(float, float), igamf(float, float), igamif(float, float);
+#else
+float igamcf(), igamf(), igamif();
+#endif
+
+float chdtrcf(float dff, float xx)
+{
+float df, x;
+
+df = dff;
+x = xx;
+
+if( (x < 0.0) || (df < 1.0) )
+ {
+ mtherr( "chdtrcf", DOMAIN );
+ return(0.0);
+ }
+return( igamcf( 0.5*df, 0.5*x ) );
+}
+
+
+float chdtrf(float dff, float xx)
+{
+float df, x;
+
+df = dff;
+x = xx;
+if( (x < 0.0) || (df < 1.0) )
+ {
+ mtherr( "chdtrf", DOMAIN );
+ return(0.0);
+ }
+return( igamf( 0.5*df, 0.5*x ) );
+}
+
+
+float chdtrif( float dff, float yy )
+{
+float y, df, x;
+
+y = yy;
+df = dff;
+if( (y < 0.0) || (y > 1.0) || (df < 1.0) )
+ {
+ mtherr( "chdtrif", DOMAIN );
+ return(0.0);
+ }
+
+x = igamif( 0.5 * df, y );
+return( 2.0 * x );
+}
diff --git a/libm/float/clogf.c b/libm/float/clogf.c
new file mode 100644
index 000000000..5f4944eba
--- /dev/null
+++ b/libm/float/clogf.c
@@ -0,0 +1,669 @@
+/* clogf.c
+ *
+ * Complex natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void clogf();
+ * cmplxf z, w;
+ *
+ * clogf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns complex logarithm to the base e (2.718...) of
+ * the complex argument x.
+ *
+ * If z = x + iy, r = sqrt( x**2 + y**2 ),
+ * then
+ * w = log(r) + i arctan(y/x).
+ *
+ * The arctangent ranges from -PI to +PI.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.9e-6 6.2e-8
+ *
+ * Larger relative error can be observed for z near 1 +i0.
+ * In IEEE arithmetic the peak absolute error is 3.1e-7.
+ *
+ */
+
+#include <math.h>
+extern float MAXNUMF, MACHEPF, PIF, PIO2F;
+#ifdef ANSIC
+float cabsf(cmplxf *), sqrtf(float), logf(float), atan2f(float, float);
+float expf(float), sinf(float), cosf(float);
+float coshf(float), sinhf(float), asinf(float);
+float ctansf(cmplxf *), redupif(float);
+void cchshf( float, float *, float * );
+void caddf( cmplxf *, cmplxf *, cmplxf * );
+void csqrtf( cmplxf *, cmplxf * );
+#else
+float cabsf(), sqrtf(), logf(), atan2f();
+float expf(), sinf(), cosf();
+float coshf(), sinhf(), asinf();
+float ctansf(), redupif();
+void cchshf(), csqrtf(), caddf();
+#endif
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+void clogf( z, w )
+register cmplxf *z, *w;
+{
+float p, rr;
+
+/*rr = sqrtf( z->r * z->r + z->i * z->i );*/
+rr = cabsf(z);
+p = logf(rr);
+#if ANSIC
+rr = atan2f( z->i, z->r );
+#else
+rr = atan2f( z->r, z->i );
+if( rr > PIF )
+ rr -= PIF + PIF;
+#endif
+w->i = rr;
+w->r = p;
+}
+ /* cexpf()
+ *
+ * Complex exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cexpf();
+ * cmplxf z, w;
+ *
+ * cexpf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the exponential of the complex argument z
+ * into the complex result w.
+ *
+ * If
+ * z = x + iy,
+ * r = exp(x),
+ *
+ * then
+ *
+ * w = r cos y + i r sin y.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.4e-7 4.5e-8
+ *
+ */
+
+void cexpf( z, w )
+register cmplxf *z, *w;
+{
+float r;
+
+r = expf( z->r );
+w->r = r * cosf( z->i );
+w->i = r * sinf( z->i );
+}
+ /* csinf()
+ *
+ * Complex circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csinf();
+ * cmplxf z, w;
+ *
+ * csinf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * w = sin x cosh y + i cos x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.9e-7 5.5e-8
+ *
+ */
+
+void csinf( z, w )
+register cmplxf *z, *w;
+{
+float ch, sh;
+
+cchshf( z->i, &ch, &sh );
+w->r = sinf( z->r ) * ch;
+w->i = cosf( z->r ) * sh;
+}
+
+
+
+/* calculate cosh and sinh */
+
+void cchshf( float xx, float *c, float *s )
+{
+float x, e, ei;
+
+x = xx;
+if( fabsf(x) <= 0.5f )
+ {
+ *c = coshf(x);
+ *s = sinhf(x);
+ }
+else
+ {
+ e = expf(x);
+ ei = 0.5f/e;
+ e = 0.5f * e;
+ *s = e - ei;
+ *c = e + ei;
+ }
+}
+
+ /* ccosf()
+ *
+ * Complex circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccosf();
+ * cmplxf z, w;
+ *
+ * ccosf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * w = cos x cosh y - i sin x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.8e-7 5.5e-8
+ */
+
+void ccosf( z, w )
+register cmplxf *z, *w;
+{
+float ch, sh;
+
+cchshf( z->i, &ch, &sh );
+w->r = cosf( z->r ) * ch;
+w->i = -sinf( z->r ) * sh;
+}
+ /* ctanf()
+ *
+ * Complex circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ctanf();
+ * cmplxf z, w;
+ *
+ * ctanf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * sin 2x + i sinh 2y
+ * w = --------------------.
+ * cos 2x + cosh 2y
+ *
+ * On the real axis the denominator is zero at odd multiples
+ * of PI/2. The denominator is evaluated by its Taylor
+ * series near these points.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 3.3e-7 5.1e-8
+ */
+
+void ctanf( z, w )
+register cmplxf *z, *w;
+{
+float d;
+
+d = cosf( 2.0f * z->r ) + coshf( 2.0f * z->i );
+
+if( fabsf(d) < 0.25f )
+ d = ctansf(z);
+
+if( d == 0.0f )
+ {
+ mtherr( "ctanf", OVERFLOW );
+ w->r = MAXNUMF;
+ w->i = MAXNUMF;
+ return;
+ }
+
+w->r = sinf( 2.0f * z->r ) / d;
+w->i = sinhf( 2.0f * z->i ) / d;
+}
+ /* ccotf()
+ *
+ * Complex circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccotf();
+ * cmplxf z, w;
+ *
+ * ccotf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * sin 2x - i sinh 2y
+ * w = --------------------.
+ * cosh 2y - cos 2x
+ *
+ * On the real axis, the denominator has zeros at even
+ * multiples of PI/2. Near these points it is evaluated
+ * by a Taylor series.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 3.6e-7 5.7e-8
+ * Also tested by ctan * ccot = 1 + i0.
+ */
+
+void ccotf( z, w )
+register cmplxf *z, *w;
+{
+float d;
+
+
+d = coshf(2.0f * z->i) - cosf(2.0f * z->r);
+
+if( fabsf(d) < 0.25f )
+ d = ctansf(z);
+
+if( d == 0.0f )
+ {
+ mtherr( "ccotf", OVERFLOW );
+ w->r = MAXNUMF;
+ w->i = MAXNUMF;
+ return;
+ }
+
+d = 1.0f/d;
+w->r = sinf( 2.0f * z->r ) * d;
+w->i = -sinhf( 2.0f * z->i ) * d;
+}
+
+/* Program to subtract nearest integer multiple of PI */
+/* extended precision value of PI: */
+
+static float DP1 = 3.140625;
+static float DP2 = 9.67502593994140625E-4;
+static float DP3 = 1.509957990978376432E-7;
+
+
+float redupif(float xx)
+{
+float x, t;
+long i;
+
+x = xx;
+t = x/PIF;
+if( t >= 0.0f )
+ t += 0.5f;
+else
+ t -= 0.5f;
+
+i = t; /* the multiple */
+t = i;
+t = ((x - t * DP1) - t * DP2) - t * DP3;
+return(t);
+}
+
+/* Taylor series expansion for cosh(2y) - cos(2x) */
+
+float ctansf(z)
+cmplxf *z;
+{
+float f, x, x2, y, y2, rn, t, d;
+
+x = fabsf( 2.0f * z->r );
+y = fabsf( 2.0f * z->i );
+
+x = redupif(x);
+
+x = x * x;
+y = y * y;
+x2 = 1.0f;
+y2 = 1.0f;
+f = 1.0f;
+rn = 0.0f;
+d = 0.0f;
+do
+ {
+ rn += 1.0f;
+ f *= rn;
+ rn += 1.0f;
+ f *= rn;
+ x2 *= x;
+ y2 *= y;
+ t = y2 + x2;
+ t /= f;
+ d += t;
+
+ rn += 1.0f;
+ f *= rn;
+ rn += 1.0f;
+ f *= rn;
+ x2 *= x;
+ y2 *= y;
+ t = y2 - x2;
+ t /= f;
+ d += t;
+ }
+while( fabsf(t/d) > MACHEPF );
+return(d);
+}
+ /* casinf()
+ *
+ * Complex circular arc sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void casinf();
+ * cmplxf z, w;
+ *
+ * casinf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Inverse complex sine:
+ *
+ * 2
+ * w = -i clog( iz + csqrt( 1 - z ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.1e-5 1.5e-6
+ * Larger relative error can be observed for z near zero.
+ *
+ */
+
+void casinf( z, w )
+cmplxf *z, *w;
+{
+float x, y;
+static cmplxf ca, ct, zz, z2;
+/*
+float cn, n;
+static float a, b, s, t, u, v, y2;
+static cmplxf sum;
+*/
+
+x = z->r;
+y = z->i;
+
+if( y == 0.0f )
+ {
+ if( fabsf(x) > 1.0f )
+ {
+ w->r = PIO2F;
+ w->i = 0.0f;
+ mtherr( "casinf", DOMAIN );
+ }
+ else
+ {
+ w->r = asinf(x);
+ w->i = 0.0f;
+ }
+ return;
+ }
+
+/* Power series expansion */
+/*
+b = cabsf(z);
+if( b < 0.125 )
+{
+z2.r = (x - y) * (x + y);
+z2.i = 2.0 * x * y;
+
+cn = 1.0;
+n = 1.0;
+ca.r = x;
+ca.i = y;
+sum.r = x;
+sum.i = y;
+do
+ {
+ ct.r = z2.r * ca.r - z2.i * ca.i;
+ ct.i = z2.r * ca.i + z2.i * ca.r;
+ ca.r = ct.r;
+ ca.i = ct.i;
+
+ cn *= n;
+ n += 1.0;
+ cn /= n;
+ n += 1.0;
+ b = cn/n;
+
+ ct.r *= b;
+ ct.i *= b;
+ sum.r += ct.r;
+ sum.i += ct.i;
+ b = fabsf(ct.r) + fabsf(ct.i);
+ }
+while( b > MACHEPF );
+w->r = sum.r;
+w->i = sum.i;
+return;
+}
+*/
+
+
+ca.r = x;
+ca.i = y;
+
+ct.r = -ca.i; /* iz */
+ct.i = ca.r;
+
+ /* sqrt( 1 - z*z) */
+/* cmul( &ca, &ca, &zz ) */
+zz.r = (ca.r - ca.i) * (ca.r + ca.i); /*x * x - y * y */
+zz.i = 2.0f * ca.r * ca.i;
+
+zz.r = 1.0f - zz.r;
+zz.i = -zz.i;
+csqrtf( &zz, &z2 );
+
+caddf( &z2, &ct, &zz );
+clogf( &zz, &zz );
+w->r = zz.i; /* mult by 1/i = -i */
+w->i = -zz.r;
+return;
+}
+ /* cacosf()
+ *
+ * Complex circular arc cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cacosf();
+ * cmplxf z, w;
+ *
+ * cacosf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * w = arccos z = PI/2 - arcsin z.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 9.2e-6 1.2e-6
+ *
+ */
+
+void cacosf( z, w )
+cmplxf *z, *w;
+{
+
+casinf( z, w );
+w->r = PIO2F - w->r;
+w->i = -w->i;
+}
+ /* catan()
+ *
+ * Complex circular arc tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void catan();
+ * cmplxf z, w;
+ *
+ * catan( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ * 1 ( 2x )
+ * Re w = - arctan(-----------) + k PI
+ * 2 ( 2 2)
+ * (1 - x - y )
+ *
+ * ( 2 2)
+ * 1 (x + (y+1) )
+ * Im w = - log(------------)
+ * 4 ( 2 2)
+ * (x + (y-1) )
+ *
+ * Where k is an arbitrary integer.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 2.3e-6 5.2e-8
+ *
+ */
+
+void catanf( z, w )
+cmplxf *z, *w;
+{
+float a, t, x, x2, y;
+
+x = z->r;
+y = z->i;
+
+if( (x == 0.0f) && (y > 1.0f) )
+ goto ovrf;
+
+x2 = x * x;
+a = 1.0f - x2 - (y * y);
+if( a == 0.0f )
+ goto ovrf;
+
+#if ANSIC
+t = 0.5f * atan2f( 2.0f * x, a );
+#else
+t = 0.5f * atan2f( a, 2.0f * x );
+#endif
+w->r = redupif( t );
+
+t = y - 1.0f;
+a = x2 + (t * t);
+if( a == 0.0f )
+ goto ovrf;
+
+t = y + 1.0f;
+a = (x2 + (t * t))/a;
+w->i = 0.25f*logf(a);
+return;
+
+ovrf:
+mtherr( "catanf", OVERFLOW );
+w->r = MAXNUMF;
+w->i = MAXNUMF;
+}
diff --git a/libm/float/cmplxf.c b/libm/float/cmplxf.c
new file mode 100644
index 000000000..949b94e3d
--- /dev/null
+++ b/libm/float/cmplxf.c
@@ -0,0 +1,407 @@
+/* cmplxf.c
+ *
+ * Complex number arithmetic
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct {
+ * float r; real part
+ * float i; imaginary part
+ * }cmplxf;
+ *
+ * cmplxf *a, *b, *c;
+ *
+ * caddf( a, b, c ); c = b + a
+ * csubf( a, b, c ); c = b - a
+ * cmulf( a, b, c ); c = b * a
+ * cdivf( a, b, c ); c = b / a
+ * cnegf( c ); c = -c
+ * cmovf( b, c ); c = b
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Addition:
+ * c.r = b.r + a.r
+ * c.i = b.i + a.i
+ *
+ * Subtraction:
+ * c.r = b.r - a.r
+ * c.i = b.i - a.i
+ *
+ * Multiplication:
+ * c.r = b.r * a.r - b.i * a.i
+ * c.i = b.r * a.i + b.i * a.r
+ *
+ * Division:
+ * d = a.r * a.r + a.i * a.i
+ * c.r = (b.r * a.r + b.i * a.i)/d
+ * c.i = (b.i * a.r - b.r * a.i)/d
+ * ACCURACY:
+ *
+ * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
+ * error 3.1e-17, rms 1.2e-17. The test (y/z) * (z/y) = 1 had
+ * peak relative error 8.3e-17, rms 2.1e-17.
+ *
+ * Tests in the rectangle {-10,+10}:
+ * Relative error:
+ * arithmetic function # trials peak rms
+ * IEEE cadd 30000 5.9e-8 2.6e-8
+ * IEEE csub 30000 6.0e-8 2.6e-8
+ * IEEE cmul 30000 1.1e-7 3.7e-8
+ * IEEE cdiv 30000 2.1e-7 5.7e-8
+ */
+ /* cmplx.c
+ * complex number arithmetic
+ */
+
+
+/*
+Cephes Math Library Release 2.1: December, 1988
+Copyright 1984, 1987, 1988 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+extern float MAXNUMF, MACHEPF, PIF, PIO2F;
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+#ifdef ANSIC
+float sqrtf(float), frexpf(float, int *);
+float ldexpf(float, int);
+float cabsf(cmplxf *), atan2f(float, float), cosf(float), sinf(float);
+#else
+float sqrtf(), frexpf(), ldexpf();
+float cabsf(), atan2f(), cosf(), sinf();
+#endif
+/*
+typedef struct
+ {
+ float r;
+ float i;
+ }cmplxf;
+*/
+cmplxf czerof = {0.0, 0.0};
+extern cmplxf czerof;
+cmplxf conef = {1.0, 0.0};
+extern cmplxf conef;
+
+/* c = b + a */
+
+void caddf( a, b, c )
+register cmplxf *a, *b;
+cmplxf *c;
+{
+
+c->r = b->r + a->r;
+c->i = b->i + a->i;
+}
+
+
+/* c = b - a */
+
+void csubf( a, b, c )
+register cmplxf *a, *b;
+cmplxf *c;
+{
+
+c->r = b->r - a->r;
+c->i = b->i - a->i;
+}
+
+/* c = b * a */
+
+void cmulf( a, b, c )
+register cmplxf *a, *b;
+cmplxf *c;
+{
+register float y;
+
+y = b->r * a->r - b->i * a->i;
+c->i = b->r * a->i + b->i * a->r;
+c->r = y;
+}
+
+
+
+/* c = b / a */
+
+void cdivf( a, b, c )
+register cmplxf *a, *b;
+cmplxf *c;
+{
+float y, p, q, w;
+
+
+y = a->r * a->r + a->i * a->i;
+p = b->r * a->r + b->i * a->i;
+q = b->i * a->r - b->r * a->i;
+
+if( y < 1.0f )
+ {
+ w = MAXNUMF * y;
+ if( (fabsf(p) > w) || (fabsf(q) > w) || (y == 0.0f) )
+ {
+ c->r = MAXNUMF;
+ c->i = MAXNUMF;
+ mtherr( "cdivf", OVERFLOW );
+ return;
+ }
+ }
+c->r = p/y;
+c->i = q/y;
+}
+
+
+/* b = a */
+
+void cmovf( a, b )
+register short *a, *b;
+{
+int i;
+
+
+i = 8;
+do
+ *b++ = *a++;
+while( --i );
+}
+
+
+void cnegf( a )
+register cmplxf *a;
+{
+
+a->r = -a->r;
+a->i = -a->i;
+}
+
+/* cabsf()
+ *
+ * Complex absolute value
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float cabsf();
+ * cmplxf z;
+ * float a;
+ *
+ * a = cabsf( &z );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy
+ *
+ * then
+ *
+ * a = sqrt( x**2 + y**2 ).
+ *
+ * Overflow and underflow are avoided by testing the magnitudes
+ * of x and y before squaring. If either is outside half of
+ * the floating point full scale range, both are rescaled.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 30000 1.2e-7 3.4e-8
+ */
+
+
+/*
+Cephes Math Library Release 2.1: January, 1989
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+/*
+typedef struct
+ {
+ float r;
+ float i;
+ }cmplxf;
+*/
+/* square root of max and min numbers */
+#define SMAX 1.3043817825332782216E+19
+#define SMIN 7.6664670834168704053E-20
+#define PREC 12
+#define MAXEXPF 128
+
+
+#define SMAXT (2.0f * SMAX)
+#define SMINT (0.5f * SMIN)
+
+float cabsf( z )
+register cmplxf *z;
+{
+float x, y, b, re, im;
+int ex, ey, e;
+
+re = fabsf( z->r );
+im = fabsf( z->i );
+
+if( re == 0.0f )
+ {
+ return( im );
+ }
+if( im == 0.0f )
+ {
+ return( re );
+ }
+
+/* Get the exponents of the numbers */
+x = frexpf( re, &ex );
+y = frexpf( im, &ey );
+
+/* Check if one number is tiny compared to the other */
+e = ex - ey;
+if( e > PREC )
+ return( re );
+if( e < -PREC )
+ return( im );
+
+/* Find approximate exponent e of the geometric mean. */
+e = (ex + ey) >> 1;
+
+/* Rescale so mean is about 1 */
+x = ldexpf( re, -e );
+y = ldexpf( im, -e );
+
+/* Hypotenuse of the right triangle */
+b = sqrtf( x * x + y * y );
+
+/* Compute the exponent of the answer. */
+y = frexpf( b, &ey );
+ey = e + ey;
+
+/* Check it for overflow and underflow. */
+if( ey > MAXEXPF )
+ {
+ mtherr( "cabsf", OVERFLOW );
+ return( MAXNUMF );
+ }
+if( ey < -MAXEXPF )
+ return(0.0f);
+
+/* Undo the scaling */
+b = ldexpf( b, e );
+return( b );
+}
+ /* csqrtf()
+ *
+ * Complex square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csqrtf();
+ * cmplxf z, w;
+ *
+ * csqrtf( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy, r = |z|, then
+ *
+ * 1/2
+ * Im w = [ (r - x)/2 ] ,
+ *
+ * Re w = y / 2 Im w.
+ *
+ *
+ * Note that -w is also a square root of z. The solution
+ * reported is always in the upper half plane.
+ *
+ * Because of the potential for cancellation error in r - x,
+ * the result is sharpened by doing a Heron iteration
+ * (see sqrt.c) in complex arithmetic.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,+10 100000 1.8e-7 4.2e-8
+ *
+ */
+
+
+void csqrtf( z, w )
+cmplxf *z, *w;
+{
+cmplxf q, s;
+float x, y, r, t;
+
+x = z->r;
+y = z->i;
+
+if( y == 0.0f )
+ {
+ if( x < 0.0f )
+ {
+ w->r = 0.0f;
+ w->i = sqrtf(-x);
+ return;
+ }
+ else
+ {
+ w->r = sqrtf(x);
+ w->i = 0.0f;
+ return;
+ }
+ }
+
+if( x == 0.0f )
+ {
+ r = fabsf(y);
+ r = sqrtf(0.5f*r);
+ if( y > 0 )
+ w->r = r;
+ else
+ w->r = -r;
+ w->i = r;
+ return;
+ }
+
+/* Approximate sqrt(x^2+y^2) - x = y^2/2x - y^4/24x^3 + ... .
+ * The relative error in the first term is approximately y^2/12x^2 .
+ */
+if( (fabsf(y) < fabsf(0.015f*x))
+ && (x > 0) )
+ {
+ t = 0.25f*y*(y/x);
+ }
+else
+ {
+ r = cabsf(z);
+ t = 0.5f*(r - x);
+ }
+
+r = sqrtf(t);
+q.i = r;
+q.r = 0.5f*y/r;
+
+/* Heron iteration in complex arithmetic:
+ * q = (q + z/q)/2
+ */
+cdivf( &q, z, &s );
+caddf( &q, &s, w );
+w->r *= 0.5f;
+w->i *= 0.5f;
+}
+
diff --git a/libm/float/constf.c b/libm/float/constf.c
new file mode 100644
index 000000000..bf6b6f657
--- /dev/null
+++ b/libm/float/constf.c
@@ -0,0 +1,20 @@
+
+#ifdef DEC
+/* MAXNUMF = 2^127 * (1 - 2^-24) */
+float MAXNUMF = 1.7014117331926442990585209174225846272e38;
+float MAXLOGF = 88.02969187150841;
+float MINLOGF = -88.7228391116729996; /* log(2^-128) */
+#else
+/* MAXNUMF = 2^128 * (1 - 2^-24) */
+float MAXNUMF = 3.4028234663852885981170418348451692544e38;
+float MAXLOGF = 88.72283905206835;
+float MINLOGF = -103.278929903431851103; /* log(2^-149) */
+#endif
+
+float LOG2EF = 1.44269504088896341;
+float LOGE2F = 0.693147180559945309;
+float SQRTHF = 0.707106781186547524;
+float PIF = 3.141592653589793238;
+float PIO2F = 1.5707963267948966192;
+float PIO4F = 0.7853981633974483096;
+float MACHEPF = 5.9604644775390625E-8;
diff --git a/libm/float/coshf.c b/libm/float/coshf.c
new file mode 100644
index 000000000..2b44fdeb3
--- /dev/null
+++ b/libm/float/coshf.c
@@ -0,0 +1,67 @@
+/* coshf.c
+ *
+ * Hyperbolic cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, coshf();
+ *
+ * y = coshf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic cosine of argument in the range MINLOGF to
+ * MAXLOGF.
+ *
+ * cosh(x) = ( exp(x) + exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-MAXLOGF 100000 1.2e-7 2.8e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * coshf overflow |x| > MAXLOGF MAXNUMF
+ *
+ *
+ */
+
+/* cosh.c */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1985, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+extern float MAXLOGF, MAXNUMF;
+
+float expf(float);
+
+float coshf(float xx)
+{
+float x, y;
+
+x = xx;
+if( x < 0 )
+ x = -x;
+if( x > MAXLOGF )
+ {
+ mtherr( "coshf", OVERFLOW );
+ return( MAXNUMF );
+ }
+y = expf(x);
+y = y + 1.0/y;
+return( 0.5*y );
+}
diff --git a/libm/float/dawsnf.c b/libm/float/dawsnf.c
new file mode 100644
index 000000000..d00607719
--- /dev/null
+++ b/libm/float/dawsnf.c
@@ -0,0 +1,168 @@
+/* dawsnf.c
+ *
+ * Dawson's Integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, dawsnf();
+ *
+ * y = dawsnf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ * x
+ * -
+ * 2 | | 2
+ * dawsn(x) = exp( -x ) | exp( t ) dt
+ * | |
+ * -
+ * 0
+ *
+ * Three different rational approximations are employed, for
+ * the intervals 0 to 3.25; 3.25 to 6.25; and 6.25 up.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,10 50000 4.4e-7 6.3e-8
+ *
+ *
+ */
+
+/* dawsn.c */
+
+
+/*
+Cephes Math Library Release 2.1: January, 1989
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+/* Dawson's integral, interval 0 to 3.25 */
+static float AN[10] = {
+ 1.13681498971755972054E-11,
+ 8.49262267667473811108E-10,
+ 1.94434204175553054283E-8,
+ 9.53151741254484363489E-7,
+ 3.07828309874913200438E-6,
+ 3.52513368520288738649E-4,
+-8.50149846724410912031E-4,
+ 4.22618223005546594270E-2,
+-9.17480371773452345351E-2,
+ 9.99999999999999994612E-1,
+};
+static float AD[11] = {
+ 2.40372073066762605484E-11,
+ 1.48864681368493396752E-9,
+ 5.21265281010541664570E-8,
+ 1.27258478273186970203E-6,
+ 2.32490249820789513991E-5,
+ 3.25524741826057911661E-4,
+ 3.48805814657162590916E-3,
+ 2.79448531198828973716E-2,
+ 1.58874241960120565368E-1,
+ 5.74918629489320327824E-1,
+ 1.00000000000000000539E0,
+};
+
+/* interval 3.25 to 6.25 */
+static float BN[11] = {
+ 5.08955156417900903354E-1,
+-2.44754418142697847934E-1,
+ 9.41512335303534411857E-2,
+-2.18711255142039025206E-2,
+ 3.66207612329569181322E-3,
+-4.23209114460388756528E-4,
+ 3.59641304793896631888E-5,
+-2.14640351719968974225E-6,
+ 9.10010780076391431042E-8,
+-2.40274520828250956942E-9,
+ 3.59233385440928410398E-11,
+};
+static float BD[10] = {
+/* 1.00000000000000000000E0,*/
+-6.31839869873368190192E-1,
+ 2.36706788228248691528E-1,
+-5.31806367003223277662E-2,
+ 8.48041718586295374409E-3,
+-9.47996768486665330168E-4,
+ 7.81025592944552338085E-5,
+-4.55875153252442634831E-6,
+ 1.89100358111421846170E-7,
+-4.91324691331920606875E-9,
+ 7.18466403235734541950E-11,
+};
+
+/* 6.25 to infinity */
+static float CN[5] = {
+-5.90592860534773254987E-1,
+ 6.29235242724368800674E-1,
+-1.72858975380388136411E-1,
+ 1.64837047825189632310E-2,
+-4.86827613020462700845E-4,
+};
+static float CD[5] = {
+/* 1.00000000000000000000E0,*/
+-2.69820057197544900361E0,
+ 1.73270799045947845857E0,
+-3.93708582281939493482E-1,
+ 3.44278924041233391079E-2,
+-9.73655226040941223894E-4,
+};
+
+
+extern float PIF, MACHEPF;
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+#ifdef ANSIC
+float polevlf(float, float *, int);
+float p1evlf(float, float *, int);
+#else
+float polevlf(), p1evlf();
+#endif
+
+float dawsnf( float xxx )
+{
+float xx, x, y;
+int sign;
+
+xx = xxx;
+sign = 1;
+if( xx < 0.0 )
+ {
+ sign = -1;
+ xx = -xx;
+ }
+
+if( xx < 3.25 )
+ {
+ x = xx*xx;
+ y = xx * polevlf( x, AN, 9 )/polevlf( x, AD, 10 );
+ return( sign * y );
+ }
+
+
+x = 1.0/(xx*xx);
+
+if( xx < 6.25 )
+ {
+ y = 1.0/xx + x * polevlf( x, BN, 10) / (p1evlf( x, BD, 10) * xx);
+ return( sign * 0.5 * y );
+ }
+
+
+if( xx > 1.0e9 )
+ return( (sign * 0.5)/xx );
+
+/* 6.25 to infinity */
+y = 1.0/xx + x * polevlf( x, CN, 4) / (p1evlf( x, CD, 5) * xx);
+return( sign * 0.5 * y );
+}
diff --git a/libm/float/ellief.c b/libm/float/ellief.c
new file mode 100644
index 000000000..5c3f822df
--- /dev/null
+++ b/libm/float/ellief.c
@@ -0,0 +1,115 @@
+/* ellief.c
+ *
+ * Incomplete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float phi, m, y, ellief();
+ *
+ * y = ellief( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ * phi
+ * -
+ * | |
+ * | 2
+ * E(phi\m) = | sqrt( 1 - m sin t ) dt
+ * |
+ * | |
+ * -
+ * 0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random arguments with phi in [0, 2] and m in
+ * [0, 1].
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,2 10000 4.5e-7 7.4e-8
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Incomplete elliptic integral of second kind */
+
+#include <math.h>
+
+extern float PIF, PIO2F, MACHEPF;
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#ifdef ANSIC
+float sqrtf(float), logf(float), sinf(float), tanf(float), atanf(float);
+float ellpef(float), ellpkf(float);
+#else
+float sqrtf(), logf(), sinf(), tanf(), atanf();
+float ellpef(), ellpkf();
+#endif
+
+
+float ellief( float phia, float ma )
+{
+float phi, m, a, b, c, e, temp;
+float lphi, t;
+int d, mod;
+
+phi = phia;
+m = ma;
+if( m == 0.0 )
+ return( phi );
+if( m == 1.0 )
+ return( sinf(phi) );
+lphi = phi;
+if( lphi < 0.0 )
+ lphi = -lphi;
+a = 1.0;
+b = 1.0 - m;
+b = sqrtf(b);
+c = sqrtf(m);
+d = 1;
+e = 0.0;
+t = tanf( lphi );
+mod = (lphi + PIO2F)/PIF;
+
+while( fabsf(c/a) > MACHEPF )
+ {
+ temp = b/a;
+ lphi = lphi + atanf(t*temp) + mod * PIF;
+ mod = (lphi + PIO2F)/PIF;
+ t = t * ( 1.0 + temp )/( 1.0 - temp * t * t );
+ c = 0.5 * ( a - b );
+ temp = sqrtf( a * b );
+ a = 0.5 * ( a + b );
+ b = temp;
+ d += d;
+ e += c * sinf(lphi);
+ }
+
+b = 1.0 - m;
+temp = ellpef(b)/ellpkf(b);
+temp *= (atanf(t) + mod * PIF)/(d * a);
+temp += e;
+if( phi < 0.0 )
+ temp = -temp;
+return( temp );
+}
diff --git a/libm/float/ellikf.c b/libm/float/ellikf.c
new file mode 100644
index 000000000..8ec890926
--- /dev/null
+++ b/libm/float/ellikf.c
@@ -0,0 +1,113 @@
+/* ellikf.c
+ *
+ * Incomplete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float phi, m, y, ellikf();
+ *
+ * y = ellikf( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ * phi
+ * -
+ * | |
+ * | dt
+ * F(phi\m) = | ------------------
+ * | 2
+ * | | sqrt( 1 - m sin t )
+ * -
+ * 0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with phi in [0, 2] and m in
+ * [0, 1].
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,2 10000 2.9e-7 5.8e-8
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Incomplete elliptic integral of first kind */
+
+#include <math.h>
+extern float PIF, PIO2F, MACHEPF;
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#ifdef ANSIC
+float sqrtf(float), logf(float), sinf(float), tanf(float), atanf(float);
+#else
+float sqrtf(), logf(), sinf(), tanf(), atanf();
+#endif
+
+
+float ellikf( float phia, float ma )
+{
+float phi, m, a, b, c, temp;
+float t;
+int d, mod, sign;
+
+phi = phia;
+m = ma;
+if( m == 0.0 )
+ return( phi );
+if( phi < 0.0 )
+ {
+ phi = -phi;
+ sign = -1;
+ }
+else
+ sign = 0;
+a = 1.0;
+b = 1.0 - m;
+if( b == 0.0 )
+ return( logf( tanf( 0.5*(PIO2F + phi) ) ) );
+b = sqrtf(b);
+c = sqrtf(m);
+d = 1;
+t = tanf( phi );
+mod = (phi + PIO2F)/PIF;
+
+while( fabsf(c/a) > MACHEPF )
+ {
+ temp = b/a;
+ phi = phi + atanf(t*temp) + mod * PIF;
+ mod = (phi + PIO2F)/PIF;
+ t = t * ( 1.0 + temp )/( 1.0 - temp * t * t );
+ c = ( a - b )/2.0;
+ temp = sqrtf( a * b );
+ a = ( a + b )/2.0;
+ b = temp;
+ d += d;
+ }
+
+temp = (atanf(t) + mod * PIF)/(d * a);
+if( sign < 0 )
+ temp = -temp;
+return( temp );
+}
diff --git a/libm/float/ellpef.c b/libm/float/ellpef.c
new file mode 100644
index 000000000..645bc55ba
--- /dev/null
+++ b/libm/float/ellpef.c
@@ -0,0 +1,105 @@
+/* ellpef.c
+ *
+ * Complete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float m1, y, ellpef();
+ *
+ * y = ellpef( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ * pi/2
+ * -
+ * | | 2
+ * E(m) = | sqrt( 1 - m sin t ) dt
+ * | |
+ * -
+ * 0
+ *
+ * Where m = 1 - m1, using the approximation
+ *
+ * P(x) - x log x Q(x).
+ *
+ * Though there are no singularities, the argument m1 is used
+ * rather than m for compatibility with ellpk().
+ *
+ * E(1) = 1; E(0) = pi/2.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 1 30000 1.1e-7 3.9e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ellpef domain x<0, x>1 0.0
+ *
+ */
+
+/* ellpe.c */
+
+/* Elliptic integral of second kind */
+
+/*
+Cephes Math Library, Release 2.1: February, 1989
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+
+static float P[] = {
+ 1.53552577301013293365E-4,
+ 2.50888492163602060990E-3,
+ 8.68786816565889628429E-3,
+ 1.07350949056076193403E-2,
+ 7.77395492516787092951E-3,
+ 7.58395289413514708519E-3,
+ 1.15688436810574127319E-2,
+ 2.18317996015557253103E-2,
+ 5.68051945617860553470E-2,
+ 4.43147180560990850618E-1,
+ 1.00000000000000000299E0
+};
+static float Q[] = {
+ 3.27954898576485872656E-5,
+ 1.00962792679356715133E-3,
+ 6.50609489976927491433E-3,
+ 1.68862163993311317300E-2,
+ 2.61769742454493659583E-2,
+ 3.34833904888224918614E-2,
+ 4.27180926518931511717E-2,
+ 5.85936634471101055642E-2,
+ 9.37499997197644278445E-2,
+ 2.49999999999888314361E-1
+};
+
+float polevlf(float, float *, int), logf(float);
+float ellpef( float xx)
+{
+float x;
+
+x = xx;
+if( (x <= 0.0) || (x > 1.0) )
+ {
+ if( x == 0.0 )
+ return( 1.0 );
+ mtherr( "ellpef", DOMAIN );
+ return( 0.0 );
+ }
+return( polevlf(x,P,10) - logf(x) * (x * polevlf(x,Q,9)) );
+}
diff --git a/libm/float/ellpjf.c b/libm/float/ellpjf.c
new file mode 100644
index 000000000..552f5ffe4
--- /dev/null
+++ b/libm/float/ellpjf.c
@@ -0,0 +1,161 @@
+/* ellpjf.c
+ *
+ * Jacobian Elliptic Functions
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float u, m, sn, cn, dn, phi;
+ * int ellpj();
+ *
+ * ellpj( u, m, _&sn, _&cn, _&dn, _&phi );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
+ * and dn(u|m) of parameter m between 0 and 1, and real
+ * argument u.
+ *
+ * These functions are periodic, with quarter-period on the
+ * real axis equal to the complete elliptic integral
+ * ellpk(1.0-m).
+ *
+ * Relation to incomplete elliptic integral:
+ * If u = ellik(phi,m), then sn(u|m) = sin(phi),
+ * and cn(u|m) = cos(phi). Phi is called the amplitude of u.
+ *
+ * Computation is by means of the arithmetic-geometric mean
+ * algorithm, except when m is within 1e-9 of 0 or 1. In the
+ * latter case with m close to 1, the approximation applies
+ * only for phi < pi/2.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with u between 0 and 10, m between
+ * 0 and 1.
+ *
+ * Absolute error (* = relative error):
+ * arithmetic function # trials peak rms
+ * IEEE sn 10000 1.7e-6 2.2e-7
+ * IEEE cn 10000 1.6e-6 2.2e-7
+ * IEEE dn 10000 1.4e-3 1.9e-5
+ * IEEE phi 10000 3.9e-7* 6.7e-8*
+ *
+ * Peak error observed in consistency check using addition
+ * theorem for sn(u+v) was 4e-16 (absolute). Also tested by
+ * the above relation to the incomplete elliptic integral.
+ * Accuracy deteriorates when u is large.
+ *
+ */
+
+/* ellpj.c */
+
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+extern float PIO2F, MACHEPF;
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#ifdef ANSIC
+float sqrtf(float), sinf(float), cosf(float), asinf(float), tanhf(float);
+float sinhf(float), coshf(float), atanf(float), expf(float);
+#else
+float sqrtf(), sinf(), cosf(), asinf(), tanhf();
+float sinhf(), coshf(), atanf(), expf();
+#endif
+
+int ellpjf( float uu, float mm,
+ float *sn, float *cn, float *dn, float *ph )
+{
+float u, m, ai, b, phi, t, twon;
+float a[10], c[10];
+int i;
+
+u = uu;
+m = mm;
+/* Check for special cases */
+
+if( m < 0.0 || m > 1.0 )
+ {
+ mtherr( "ellpjf", DOMAIN );
+ return(-1);
+ }
+if( m < 1.0e-5 )
+ {
+ t = sinf(u);
+ b = cosf(u);
+ ai = 0.25 * m * (u - t*b);
+ *sn = t - ai*b;
+ *cn = b + ai*t;
+ *ph = u - ai;
+ *dn = 1.0 - 0.5*m*t*t;
+ return(0);
+ }
+
+if( m >= 0.99999 )
+ {
+ ai = 0.25 * (1.0-m);
+ b = coshf(u);
+ t = tanhf(u);
+ phi = 1.0/b;
+ twon = b * sinhf(u);
+ *sn = t + ai * (twon - u)/(b*b);
+ *ph = 2.0*atanf(expf(u)) - PIO2F + ai*(twon - u)/b;
+ ai *= t * phi;
+ *cn = phi - ai * (twon - u);
+ *dn = phi + ai * (twon + u);
+ return(0);
+ }
+
+
+/* A. G. M. scale */
+a[0] = 1.0;
+b = sqrtf(1.0 - m);
+c[0] = sqrtf(m);
+twon = 1.0;
+i = 0;
+
+while( fabsf( (c[i]/a[i]) ) > MACHEPF )
+ {
+ if( i > 8 )
+ {
+/* mtherr( "ellpjf", OVERFLOW );*/
+ break;
+ }
+ ai = a[i];
+ ++i;
+ c[i] = 0.5 * ( ai - b );
+ t = sqrtf( ai * b );
+ a[i] = 0.5 * ( ai + b );
+ b = t;
+ twon += twon;
+ }
+
+
+/* backward recurrence */
+phi = twon * a[i] * u;
+do
+ {
+ t = c[i] * sinf(phi) / a[i];
+ b = phi;
+ phi = 0.5 * (asinf(t) + phi);
+ }
+while( --i );
+
+*sn = sinf(phi);
+t = cosf(phi);
+*cn = t;
+*dn = t/cosf(phi-b);
+*ph = phi;
+return(0);
+}
diff --git a/libm/float/ellpkf.c b/libm/float/ellpkf.c
new file mode 100644
index 000000000..2cc13d90a
--- /dev/null
+++ b/libm/float/ellpkf.c
@@ -0,0 +1,128 @@
+/* ellpkf.c
+ *
+ * Complete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float m1, y, ellpkf();
+ *
+ * y = ellpkf( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ * pi/2
+ * -
+ * | |
+ * | dt
+ * K(m) = | ------------------
+ * | 2
+ * | | sqrt( 1 - m sin t )
+ * -
+ * 0
+ *
+ * where m = 1 - m1, using the approximation
+ *
+ * P(x) - log x Q(x).
+ *
+ * The argument m1 is used rather than m so that the logarithmic
+ * singularity at m = 1 will be shifted to the origin; this
+ * preserves maximum accuracy.
+ *
+ * K(0) = pi/2.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,1 30000 1.3e-7 3.4e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ellpkf domain x<0, x>1 0.0
+ *
+ */
+
+/* ellpk.c */
+
+
+/*
+Cephes Math Library, Release 2.0: April, 1987
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+static float P[] =
+{
+ 1.37982864606273237150E-4,
+ 2.28025724005875567385E-3,
+ 7.97404013220415179367E-3,
+ 9.85821379021226008714E-3,
+ 6.87489687449949877925E-3,
+ 6.18901033637687613229E-3,
+ 8.79078273952743772254E-3,
+ 1.49380448916805252718E-2,
+ 3.08851465246711995998E-2,
+ 9.65735902811690126535E-2,
+ 1.38629436111989062502E0
+};
+
+static float Q[] =
+{
+ 2.94078955048598507511E-5,
+ 9.14184723865917226571E-4,
+ 5.94058303753167793257E-3,
+ 1.54850516649762399335E-2,
+ 2.39089602715924892727E-2,
+ 3.01204715227604046988E-2,
+ 3.73774314173823228969E-2,
+ 4.88280347570998239232E-2,
+ 7.03124996963957469739E-2,
+ 1.24999999999870820058E-1,
+ 4.99999999999999999821E-1
+};
+static float C1 = 1.3862943611198906188E0; /* log(4) */
+
+extern float MACHEPF, MAXNUMF;
+
+float polevlf(float, float *, int);
+float p1evlf(float, float *, int);
+float logf(float);
+float ellpkf(float xx)
+{
+float x;
+
+x = xx;
+if( (x < 0.0) || (x > 1.0) )
+ {
+ mtherr( "ellpkf", DOMAIN );
+ return( 0.0 );
+ }
+
+if( x > MACHEPF )
+ {
+ return( polevlf(x,P,10) - logf(x) * polevlf(x,Q,10) );
+ }
+else
+ {
+ if( x == 0.0 )
+ {
+ mtherr( "ellpkf", SING );
+ return( MAXNUMF );
+ }
+ else
+ {
+ return( C1 - 0.5 * logf(x) );
+ }
+ }
+}
diff --git a/libm/float/exp10f.c b/libm/float/exp10f.c
new file mode 100644
index 000000000..c7c62c567
--- /dev/null
+++ b/libm/float/exp10f.c
@@ -0,0 +1,115 @@
+/* exp10f.c
+ *
+ * Base 10 exponential function
+ * (Common antilogarithm)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, exp10f();
+ *
+ * y = exp10f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 10 raised to the x power.
+ *
+ * Range reduction is accomplished by expressing the argument
+ * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
+ * A polynomial approximates 10**f.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -38,+38 100000 9.8e-8 2.8e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp10 underflow x < -MAXL10 0.0
+ * exp10 overflow x > MAXL10 MAXNUM
+ *
+ * IEEE single arithmetic: MAXL10 = 38.230809449325611792.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+static float P[] = {
+ 2.063216740311022E-001,
+ 5.420251702225484E-001,
+ 1.171292686296281E+000,
+ 2.034649854009453E+000,
+ 2.650948748208892E+000,
+ 2.302585167056758E+000
+};
+
+/*static float LOG102 = 3.01029995663981195214e-1;*/
+static float LOG210 = 3.32192809488736234787e0;
+static float LG102A = 3.00781250000000000000E-1;
+static float LG102B = 2.48745663981195213739E-4;
+static float MAXL10 = 38.230809449325611792;
+
+
+
+
+extern float MAXNUMF;
+
+float floorf(float), ldexpf(float, int), polevlf(float, float *, int);
+
+float exp10f(float xx)
+{
+float x, px, qx;
+short n;
+
+x = xx;
+if( x > MAXL10 )
+ {
+ mtherr( "exp10f", OVERFLOW );
+ return( MAXNUMF );
+ }
+
+if( x < -MAXL10 ) /* Would like to use MINLOG but can't */
+ {
+ mtherr( "exp10f", UNDERFLOW );
+ return(0.0);
+ }
+
+/* The following is necessary because range reduction blows up: */
+if( x == 0 )
+ return(1.0);
+
+/* Express 10**x = 10**g 2**n
+ * = 10**g 10**( n log10(2) )
+ * = 10**( g + n log10(2) )
+ */
+px = x * LOG210;
+qx = floorf( px + 0.5 );
+n = qx;
+x -= qx * LG102A;
+x -= qx * LG102B;
+
+/* rational approximation for exponential
+ * of the fractional part:
+ * 10**x - 1 = 2x P(x**2)/( Q(x**2) - P(x**2) )
+ */
+px = 1.0 + x * polevlf( x, P, 5 );
+
+/* multiply by power of 2 */
+x = ldexpf( px, n );
+
+return(x);
+}
diff --git a/libm/float/exp2f.c b/libm/float/exp2f.c
new file mode 100644
index 000000000..0de21decd
--- /dev/null
+++ b/libm/float/exp2f.c
@@ -0,0 +1,116 @@
+/* exp2f.c
+ *
+ * Base 2 exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, exp2f();
+ *
+ * y = exp2f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 2 raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ * x k f
+ * 2 = 2 2.
+ *
+ * A polynomial approximates 2**x in the basic range [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -127,+127 100000 1.7e-7 2.8e-8
+ *
+ *
+ * See exp.c for comments on error amplification.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp underflow x < -MAXL2 0.0
+ * exp overflow x > MAXL2 MAXNUMF
+ *
+ * For IEEE arithmetic, MAXL2 = 127.
+ */
+
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+
+#include <math.h>
+static char fname[] = {"exp2f"};
+
+static float P[] = {
+ 1.535336188319500E-004,
+ 1.339887440266574E-003,
+ 9.618437357674640E-003,
+ 5.550332471162809E-002,
+ 2.402264791363012E-001,
+ 6.931472028550421E-001
+};
+#define MAXL2 127.0
+#define MINL2 -127.0
+
+
+
+extern float MAXNUMF;
+
+float polevlf(float, float *, int), floorf(float), ldexpf(float, int);
+
+float exp2f( float xx )
+{
+float x, px;
+int i0;
+
+x = xx;
+if( x > MAXL2)
+ {
+ mtherr( fname, OVERFLOW );
+ return( MAXNUMF );
+ }
+
+if( x < MINL2 )
+ {
+ mtherr( fname, UNDERFLOW );
+ return(0.0);
+ }
+
+/* The following is necessary because range reduction blows up: */
+if( x == 0 )
+ return(1.0);
+
+/* separate into integer and fractional parts */
+px = floorf(x);
+i0 = px;
+x = x - px;
+
+if( x > 0.5 )
+ {
+ i0 += 1;
+ x -= 1.0;
+ }
+
+/* rational approximation
+ * exp2(x) = 1.0 + xP(x)
+ */
+px = 1.0 + x * polevlf( x, P, 5 );
+
+/* scale by power of 2 */
+px = ldexpf( px, i0 );
+return(px);
+}
diff --git a/libm/float/expf.c b/libm/float/expf.c
new file mode 100644
index 000000000..073678b99
--- /dev/null
+++ b/libm/float/expf.c
@@ -0,0 +1,122 @@
+/* expf.c
+ *
+ * Exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, expf();
+ *
+ * y = expf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns e (2.71828...) raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *
+ * x k f
+ * e = 2 e.
+ *
+ * A polynomial is used to approximate exp(f)
+ * in the basic range [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +- MAXLOG 100000 1.7e-7 2.8e-8
+ *
+ *
+ * Error amplification in the exponential function can be
+ * a serious matter. The error propagation involves
+ * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
+ * which shows that a 1 lsb error in representing X produces
+ * a relative error of X times 1 lsb in the function.
+ * While the routine gives an accurate result for arguments
+ * that are exactly represented by a double precision
+ * computer number, the result contains amplified roundoff
+ * error for large arguments not exactly represented.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * expf underflow x < MINLOGF 0.0
+ * expf overflow x > MAXLOGF MAXNUMF
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Single precision exponential function.
+ * test interval: [-0.5, +0.5]
+ * trials: 80000
+ * peak relative error: 7.6e-8
+ * rms relative error: 2.8e-8
+ */
+#include <math.h>
+extern float LOG2EF, MAXLOGF, MINLOGF, MAXNUMF;
+
+static float C1 = 0.693359375;
+static float C2 = -2.12194440e-4;
+
+
+
+float floorf( float ), ldexpf( float, int );
+
+float expf( float xx )
+{
+float x, z;
+int n;
+
+x = xx;
+
+
+if( x > MAXLOGF)
+ {
+ mtherr( "expf", OVERFLOW );
+ return( MAXNUMF );
+ }
+
+if( x < MINLOGF )
+ {
+ mtherr( "expf", UNDERFLOW );
+ return(0.0);
+ }
+
+/* Express e**x = e**g 2**n
+ * = e**g e**( n loge(2) )
+ * = e**( g + n loge(2) )
+ */
+z = floorf( LOG2EF * x + 0.5 ); /* floor() truncates toward -infinity. */
+x -= z * C1;
+x -= z * C2;
+n = z;
+
+z = x * x;
+/* Theoretical peak relative error in [-0.5, +0.5] is 4.2e-9. */
+z =
+((((( 1.9875691500E-4 * x
+ + 1.3981999507E-3) * x
+ + 8.3334519073E-3) * x
+ + 4.1665795894E-2) * x
+ + 1.6666665459E-1) * x
+ + 5.0000001201E-1) * z
+ + x
+ + 1.0;
+
+/* multiply by power of 2 */
+x = ldexpf( z, n );
+
+return( x );
+}
diff --git a/libm/float/expnf.c b/libm/float/expnf.c
new file mode 100644
index 000000000..ebf0ccb3e
--- /dev/null
+++ b/libm/float/expnf.c
@@ -0,0 +1,207 @@
+/* expnf.c
+ *
+ * Exponential integral En
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * float x, y, expnf();
+ *
+ * y = expnf( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the exponential integral
+ *
+ * inf.
+ * -
+ * | | -xt
+ * | e
+ * E (x) = | ---- dt.
+ * n | n
+ * | | t
+ * -
+ * 1
+ *
+ *
+ * Both n and x must be nonnegative.
+ *
+ * The routine employs either a power series, a continued
+ * fraction, or an asymptotic formula depending on the
+ * relative values of n and x.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 10000 5.6e-7 1.2e-7
+ *
+ */
+
+/* expn.c */
+
+/* Cephes Math Library Release 2.2: July, 1992
+ * Copyright 1985, 1992 by Stephen L. Moshier
+ * Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */
+
+#include <math.h>
+
+#define EUL 0.57721566490153286060
+#define BIG 16777216.
+extern float MAXNUMF, MACHEPF, MAXLOGF;
+#ifdef ANSIC
+float powf(float, float), gammaf(float), logf(float), expf(float);
+#else
+float powf(), gammaf(), logf(), expf();
+#endif
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+
+float expnf( int n, float xx )
+{
+float x, ans, r, t, yk, xk;
+float pk, pkm1, pkm2, qk, qkm1, qkm2;
+float psi, z;
+int i, k;
+static float big = BIG;
+
+
+x = xx;
+if( n < 0 )
+ goto domerr;
+
+if( x < 0 )
+ {
+domerr: mtherr( "expnf", DOMAIN );
+ return( MAXNUMF );
+ }
+
+if( x > MAXLOGF )
+ return( 0.0 );
+
+if( x == 0.0 )
+ {
+ if( n < 2 )
+ {
+ mtherr( "expnf", SING );
+ return( MAXNUMF );
+ }
+ else
+ return( 1.0/(n-1.0) );
+ }
+
+if( n == 0 )
+ return( expf(-x)/x );
+
+/* expn.c */
+/* Expansion for large n */
+
+if( n > 5000 )
+ {
+ xk = x + n;
+ yk = 1.0 / (xk * xk);
+ t = n;
+ ans = yk * t * (6.0 * x * x - 8.0 * t * x + t * t);
+ ans = yk * (ans + t * (t - 2.0 * x));
+ ans = yk * (ans + t);
+ ans = (ans + 1.0) * expf( -x ) / xk;
+ goto done;
+ }
+
+if( x > 1.0 )
+ goto cfrac;
+
+/* expn.c */
+
+/* Power series expansion */
+
+psi = -EUL - logf(x);
+for( i=1; i<n; i++ )
+ psi = psi + 1.0/i;
+
+z = -x;
+xk = 0.0;
+yk = 1.0;
+pk = 1.0 - n;
+if( n == 1 )
+ ans = 0.0;
+else
+ ans = 1.0/pk;
+do
+ {
+ xk += 1.0;
+ yk *= z/xk;
+ pk += 1.0;
+ if( pk != 0.0 )
+ {
+ ans += yk/pk;
+ }
+ if( ans != 0.0 )
+ t = fabsf(yk/ans);
+ else
+ t = 1.0;
+ }
+while( t > MACHEPF );
+k = xk;
+t = n;
+r = n - 1;
+ans = (powf(z, r) * psi / gammaf(t)) - ans;
+goto done;
+
+/* expn.c */
+/* continued fraction */
+cfrac:
+k = 1;
+pkm2 = 1.0;
+qkm2 = x;
+pkm1 = 1.0;
+qkm1 = x + n;
+ans = pkm1/qkm1;
+
+do
+ {
+ k += 1;
+ if( k & 1 )
+ {
+ yk = 1.0;
+ xk = n + (k-1)/2;
+ }
+ else
+ {
+ yk = x;
+ xk = k/2;
+ }
+ pk = pkm1 * yk + pkm2 * xk;
+ qk = qkm1 * yk + qkm2 * xk;
+ if( qk != 0 )
+ {
+ r = pk/qk;
+ t = fabsf( (ans - r)/r );
+ ans = r;
+ }
+ else
+ t = 1.0;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+if( fabsf(pk) > big )
+ {
+ pkm2 *= MACHEPF;
+ pkm1 *= MACHEPF;
+ qkm2 *= MACHEPF;
+ qkm1 *= MACHEPF;
+ }
+ }
+while( t > MACHEPF );
+
+ans *= expf( -x );
+
+done:
+return( ans );
+}
+
diff --git a/libm/float/facf.c b/libm/float/facf.c
new file mode 100644
index 000000000..c69738897
--- /dev/null
+++ b/libm/float/facf.c
@@ -0,0 +1,106 @@
+/* facf.c
+ *
+ * Factorial function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float y, facf();
+ * int i;
+ *
+ * y = facf( i );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns factorial of i = 1 * 2 * 3 * ... * i.
+ * fac(0) = 1.0.
+ *
+ * Due to machine arithmetic bounds the largest value of
+ * i accepted is 33 in single precision arithmetic.
+ * Greater values, or negative ones,
+ * produce an error message and return MAXNUM.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * For i < 34 the values are simply tabulated, and have
+ * full machine accuracy.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.0: April, 1987
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+/* Factorials of integers from 0 through 33 */
+static float factbl[] = {
+ 1.00000000000000000000E0,
+ 1.00000000000000000000E0,
+ 2.00000000000000000000E0,
+ 6.00000000000000000000E0,
+ 2.40000000000000000000E1,
+ 1.20000000000000000000E2,
+ 7.20000000000000000000E2,
+ 5.04000000000000000000E3,
+ 4.03200000000000000000E4,
+ 3.62880000000000000000E5,
+ 3.62880000000000000000E6,
+ 3.99168000000000000000E7,
+ 4.79001600000000000000E8,
+ 6.22702080000000000000E9,
+ 8.71782912000000000000E10,
+ 1.30767436800000000000E12,
+ 2.09227898880000000000E13,
+ 3.55687428096000000000E14,
+ 6.40237370572800000000E15,
+ 1.21645100408832000000E17,
+ 2.43290200817664000000E18,
+ 5.10909421717094400000E19,
+ 1.12400072777760768000E21,
+ 2.58520167388849766400E22,
+ 6.20448401733239439360E23,
+ 1.55112100433309859840E25,
+ 4.03291461126605635584E26,
+ 1.0888869450418352160768E28,
+ 3.04888344611713860501504E29,
+ 8.841761993739701954543616E30,
+ 2.6525285981219105863630848E32,
+ 8.22283865417792281772556288E33,
+ 2.6313083693369353016721801216E35,
+ 8.68331761881188649551819440128E36
+};
+#define MAXFACF 33
+
+extern float MAXNUMF;
+
+#ifdef ANSIC
+float facf( int i )
+#else
+float facf(i)
+int i;
+#endif
+{
+
+if( i < 0 )
+ {
+ mtherr( "facf", SING );
+ return( MAXNUMF );
+ }
+
+if( i > MAXFACF )
+ {
+ mtherr( "facf", OVERFLOW );
+ return( MAXNUMF );
+ }
+
+/* Get answer from table for small i. */
+return( factbl[i] );
+}
diff --git a/libm/float/fdtrf.c b/libm/float/fdtrf.c
new file mode 100644
index 000000000..5fdc6d81d
--- /dev/null
+++ b/libm/float/fdtrf.c
@@ -0,0 +1,214 @@
+/* fdtrf.c
+ *
+ * F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * float x, y, fdtrf();
+ *
+ * y = fdtrf( df1, df2, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density). This is the density
+ * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
+ * variables having Chi square distributions with df1
+ * and df2 degrees of freedom, respectively.
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ * P(x) = incbet( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
+ *
+ *
+ * The arguments a and b are greater than zero, and x
+ * x is nonnegative.
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 2.2e-5 1.1e-6
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrf domain a<0, b<0, x<0 0.0
+ *
+ */
+ /* fdtrcf()
+ *
+ * Complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * float x, y, fdtrcf();
+ *
+ * y = fdtrcf( df1, df2, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from x to infinity under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density).
+ *
+ *
+ * inf.
+ * -
+ * 1 | | a-1 b-1
+ * 1-P(x) = ------ | t (1-t) dt
+ * B(a,b) | |
+ * -
+ * x
+ *
+ * (See fdtr.c.)
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 7.3e-5 1.2e-5
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrcf domain a<0, b<0, x<0 0.0
+ *
+ */
+ /* fdtrif()
+ *
+ * Inverse of complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float df1, df2, x, y, fdtrif();
+ *
+ * x = fdtrif( df1, df2, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the F density argument x such that the integral
+ * from x to infinity of the F density is equal to the
+ * given probability y.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relations
+ *
+ * z = incbi( df2/2, df1/2, y )
+ * x = df2 (1-z) / (df1 z).
+ *
+ * Note: the following relations hold for the inverse of
+ * the uncomplemented F distribution:
+ *
+ * z = incbi( df1/2, df2/2, y )
+ * x = df2 z / (df1 (1-z)).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * arithmetic domain # trials peak rms
+ * Absolute error:
+ * IEEE 0,100 5000 4.0e-5 3.2e-6
+ * Relative error:
+ * IEEE 0,100 5000 1.2e-3 1.8e-5
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrif domain y <= 0 or y > 1 0.0
+ * v < 1
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+#ifdef ANSIC
+float incbetf(float, float, float);
+float incbif(float, float, float);
+#else
+float incbetf(), incbif();
+#endif
+
+float fdtrcf( int ia, int ib, float xx )
+{
+float x, a, b, w;
+
+x = xx;
+if( (ia < 1) || (ib < 1) || (x < 0.0) )
+ {
+ mtherr( "fdtrcf", DOMAIN );
+ return( 0.0 );
+ }
+a = ia;
+b = ib;
+w = b / (b + a * x);
+return( incbetf( 0.5*b, 0.5*a, w ) );
+}
+
+
+
+float fdtrf( int ia, int ib, int xx )
+{
+float x, a, b, w;
+
+x = xx;
+if( (ia < 1) || (ib < 1) || (x < 0.0) )
+ {
+ mtherr( "fdtrf", DOMAIN );
+ return( 0.0 );
+ }
+a = ia;
+b = ib;
+w = a * x;
+w = w / (b + w);
+return( incbetf( 0.5*a, 0.5*b, w) );
+}
+
+
+float fdtrif( int ia, int ib, float yy )
+{
+float y, a, b, w, x;
+
+y = yy;
+if( (ia < 1) || (ib < 1) || (y <= 0.0) || (y > 1.0) )
+ {
+ mtherr( "fdtrif", DOMAIN );
+ return( 0.0 );
+ }
+a = ia;
+b = ib;
+w = incbif( 0.5*b, 0.5*a, y );
+x = (b - b*w)/(a*w);
+return(x);
+}
diff --git a/libm/float/floorf.c b/libm/float/floorf.c
new file mode 100644
index 000000000..7a2f3530d
--- /dev/null
+++ b/libm/float/floorf.c
@@ -0,0 +1,526 @@
+/* ceilf()
+ * floorf()
+ * frexpf()
+ * ldexpf()
+ * signbitf()
+ * isnanf()
+ * isfinitef()
+ *
+ * Single precision floating point numeric utilities
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y;
+ * float ceilf(), floorf(), frexpf(), ldexpf();
+ * int signbit(), isnan(), isfinite();
+ * int expnt, n;
+ *
+ * y = floorf(x);
+ * y = ceilf(x);
+ * y = frexpf( x, &expnt );
+ * y = ldexpf( x, n );
+ * n = signbit(x);
+ * n = isnan(x);
+ * n = isfinite(x);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * All four routines return a single precision floating point
+ * result.
+ *
+ * sfloor() returns the largest integer less than or equal to x.
+ * It truncates toward minus infinity.
+ *
+ * sceil() returns the smallest integer greater than or equal
+ * to x. It truncates toward plus infinity.
+ *
+ * sfrexp() extracts the exponent from x. It returns an integer
+ * power of two to expnt and the significand between 0.5 and 1
+ * to y. Thus x = y * 2**expn.
+ *
+ * ldexpf() multiplies x by 2**n.
+ *
+ * signbit(x) returns 1 if the sign bit of x is 1, else 0.
+ *
+ * These functions are part of the standard C run time library
+ * for many but not all C compilers. The ones supplied are
+ * written in C for either DEC or IEEE arithmetic. They should
+ * be used only if your compiler library does not already have
+ * them.
+ *
+ * The IEEE versions assume that denormal numbers are implemented
+ * in the arithmetic. Some modifications will be required if
+ * the arithmetic has abrupt rather than gradual underflow.
+ */
+
+
+/*
+Cephes Math Library Release 2.1: December, 1988
+Copyright 1984, 1987, 1988 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+#ifdef DEC
+#undef DENORMAL
+#define DENORMAL 0
+#endif
+
+#ifdef UNK
+#undef UNK
+#if BIGENDIAN
+#define MIEEE 1
+#else
+#define IBMPC 1
+#endif
+/*
+char *unkmsg = "ceil(), floor(), frexp(), ldexp() must be rewritten!\n";
+*/
+#endif
+
+#define EXPMSK 0x807f
+#define MEXP 255
+#define NBITS 24
+
+
+extern float MAXNUMF; /* (2^24 - 1) * 2^103 */
+#ifdef ANSIC
+float floorf(float);
+#else
+float floorf();
+#endif
+
+float ceilf( float x )
+{
+float y;
+
+#ifdef UNK
+printf( "%s\n", unkmsg );
+return(0.0);
+#endif
+
+y = floorf( (float )x );
+if( y < x )
+ y += 1.0;
+return(y);
+}
+
+
+
+
+/* Bit clearing masks: */
+
+static unsigned short bmask[] = {
+0xffff,
+0xfffe,
+0xfffc,
+0xfff8,
+0xfff0,
+0xffe0,
+0xffc0,
+0xff80,
+0xff00,
+0xfe00,
+0xfc00,
+0xf800,
+0xf000,
+0xe000,
+0xc000,
+0x8000,
+0x0000,
+};
+
+
+
+float floorf( float x )
+{
+unsigned short *p;
+union
+ {
+ float y;
+ unsigned short i[2];
+ } u;
+int e;
+
+#ifdef UNK
+printf( "%s\n", unkmsg );
+return(0.0);
+#endif
+
+u.y = x;
+/* find the exponent (power of 2) */
+#ifdef DEC
+p = &u.i[0];
+e = (( *p >> 7) & 0377) - 0201;
+p += 3;
+#endif
+
+#ifdef IBMPC
+p = &u.i[1];
+e = (( *p >> 7) & 0xff) - 0x7f;
+p -= 1;
+#endif
+
+#ifdef MIEEE
+p = &u.i[0];
+e = (( *p >> 7) & 0xff) - 0x7f;
+p += 1;
+#endif
+
+if( e < 0 )
+ {
+ if( u.y < 0 )
+ return( -1.0 );
+ else
+ return( 0.0 );
+ }
+
+e = (NBITS -1) - e;
+/* clean out 16 bits at a time */
+while( e >= 16 )
+ {
+#ifdef IBMPC
+ *p++ = 0;
+#endif
+
+#ifdef DEC
+ *p-- = 0;
+#endif
+
+#ifdef MIEEE
+ *p-- = 0;
+#endif
+ e -= 16;
+ }
+
+/* clear the remaining bits */
+if( e > 0 )
+ *p &= bmask[e];
+
+if( (x < 0) && (u.y != x) )
+ u.y -= 1.0;
+
+return(u.y);
+}
+
+
+
+float frexpf( float x, int *pw2 )
+{
+union
+ {
+ float y;
+ unsigned short i[2];
+ } u;
+int i, k;
+short *q;
+
+u.y = x;
+
+#ifdef UNK
+printf( "%s\n", unkmsg );
+return(0.0);
+#endif
+
+#ifdef IBMPC
+q = &u.i[1];
+#endif
+
+#ifdef DEC
+q = &u.i[0];
+#endif
+
+#ifdef MIEEE
+q = &u.i[0];
+#endif
+
+/* find the exponent (power of 2) */
+
+i = ( *q >> 7) & 0xff;
+if( i == 0 )
+ {
+ if( u.y == 0.0 )
+ {
+ *pw2 = 0;
+ return(0.0);
+ }
+/* Number is denormal or zero */
+#if DENORMAL
+/* Handle denormal number. */
+ do
+ {
+ u.y *= 2.0;
+ i -= 1;
+ k = ( *q >> 7) & 0xff;
+ }
+ while( k == 0 );
+ i = i + k;
+#else
+ *pw2 = 0;
+ return( 0.0 );
+#endif /* DENORMAL */
+ }
+i -= 0x7e;
+*pw2 = i;
+*q &= 0x807f; /* strip all exponent bits */
+*q |= 0x3f00; /* mantissa between 0.5 and 1 */
+return( u.y );
+}
+
+
+
+
+
+float ldexpf( float x, int pw2 )
+{
+union
+ {
+ float y;
+ unsigned short i[2];
+ } u;
+short *q;
+int e;
+
+#ifdef UNK
+printf( "%s\n", unkmsg );
+return(0.0);
+#endif
+
+u.y = x;
+#ifdef DEC
+q = &u.i[0];
+#endif
+
+#ifdef IBMPC
+q = &u.i[1];
+#endif
+#ifdef MIEEE
+q = &u.i[0];
+#endif
+while( (e = ( *q >> 7) & 0xff) == 0 )
+ {
+ if( u.y == (float )0.0 )
+ {
+ return( 0.0 );
+ }
+/* Input is denormal. */
+ if( pw2 > 0 )
+ {
+ u.y *= 2.0;
+ pw2 -= 1;
+ }
+ if( pw2 < 0 )
+ {
+ if( pw2 < -24 )
+ return( 0.0 );
+ u.y *= 0.5;
+ pw2 += 1;
+ }
+ if( pw2 == 0 )
+ return(u.y);
+ }
+
+e += pw2;
+
+/* Handle overflow */
+if( e > MEXP )
+ {
+ return( MAXNUMF );
+ }
+
+*q &= 0x807f;
+
+/* Handle denormalized results */
+if( e < 1 )
+ {
+#if DENORMAL
+ if( e < -24 )
+ return( 0.0 );
+ *q |= 0x80; /* Set LSB of exponent. */
+ /* For denormals, significant bits may be lost even
+ when dividing by 2. Construct 2^-(1-e) so the result
+ is obtained with only one multiplication. */
+ u.y *= ldexpf(1.0f, e - 1);
+ return(u.y);
+#else
+ return( 0.0 );
+#endif
+ }
+*q |= (e & 0xff) << 7;
+return(u.y);
+}
+
+
+/* Return 1 if the sign bit of x is 1, else 0. */
+
+int signbitf(x)
+float x;
+{
+union
+ {
+ float f;
+ short s[4];
+ int i;
+ } u;
+
+u.f = x;
+
+if( sizeof(int) == 4 )
+ {
+#ifdef IBMPC
+ return( u.i < 0 );
+#endif
+#ifdef DEC
+ return( u.s[1] < 0 );
+#endif
+#ifdef MIEEE
+ return( u.i < 0 );
+#endif
+ }
+else
+ {
+#ifdef IBMPC
+ return( u.s[1] < 0 );
+#endif
+#ifdef DEC
+ return( u.s[1] < 0 );
+#endif
+#ifdef MIEEE
+ return( u.s[0] < 0 );
+#endif
+ }
+}
+
+
+/* Return 1 if x is a number that is Not a Number, else return 0. */
+
+int isnanf(x)
+float x;
+{
+#ifdef NANS
+union
+ {
+ float f;
+ unsigned short s[2];
+ unsigned int i;
+ } u;
+
+u.f = x;
+
+if( sizeof(int) == 4 )
+ {
+#ifdef IBMPC
+ if( ((u.i & 0x7f800000) == 0x7f800000)
+ && ((u.i & 0x007fffff) != 0) )
+ return 1;
+#endif
+#ifdef DEC
+ if( (u.s[1] & 0x7f80) == 0)
+ {
+ if( (u.s[1] | u.s[0]) != 0 )
+ return(1);
+ }
+#endif
+#ifdef MIEEE
+ if( ((u.i & 0x7f800000) == 0x7f800000)
+ && ((u.i & 0x007fffff) != 0) )
+ return 1;
+#endif
+ return(0);
+ }
+else
+ { /* size int not 4 */
+#ifdef IBMPC
+ if( (u.s[1] & 0x7f80) == 0x7f80)
+ {
+ if( ((u.s[1] & 0x007f) | u.s[0]) != 0 )
+ return(1);
+ }
+#endif
+#ifdef DEC
+ if( (u.s[1] & 0x7f80) == 0)
+ {
+ if( (u.s[1] | u.s[0]) != 0 )
+ return(1);
+ }
+#endif
+#ifdef MIEEE
+ if( (u.s[0] & 0x7f80) == 0x7f80)
+ {
+ if( ((u.s[0] & 0x000f) | u.s[1]) != 0 )
+ return(1);
+ }
+#endif
+ return(0);
+ } /* size int not 4 */
+
+#else
+/* No NANS. */
+return(0);
+#endif
+}
+
+
+/* Return 1 if x is not infinite and is not a NaN. */
+
+int isfinitef(x)
+float x;
+{
+#ifdef INFINITIES
+union
+ {
+ float f;
+ unsigned short s[2];
+ unsigned int i;
+ } u;
+
+u.f = x;
+
+if( sizeof(int) == 4 )
+ {
+#ifdef IBMPC
+ if( (u.i & 0x7f800000) != 0x7f800000)
+ return 1;
+#endif
+#ifdef DEC
+ if( (u.s[1] & 0x7f80) == 0)
+ {
+ if( (u.s[1] | u.s[0]) != 0 )
+ return(1);
+ }
+#endif
+#ifdef MIEEE
+ if( (u.i & 0x7f800000) != 0x7f800000)
+ return 1;
+#endif
+ return(0);
+ }
+else
+ {
+#ifdef IBMPC
+ if( (u.s[1] & 0x7f80) != 0x7f80)
+ return 1;
+#endif
+#ifdef DEC
+ if( (u.s[1] & 0x7f80) == 0)
+ {
+ if( (u.s[1] | u.s[0]) != 0 )
+ return(1);
+ }
+#endif
+#ifdef MIEEE
+ if( (u.s[0] & 0x7f80) != 0x7f80)
+ return 1;
+#endif
+ return(0);
+ }
+#else
+/* No INFINITY. */
+return(1);
+#endif
+}
diff --git a/libm/float/fresnlf.c b/libm/float/fresnlf.c
new file mode 100644
index 000000000..d6ae773b1
--- /dev/null
+++ b/libm/float/fresnlf.c
@@ -0,0 +1,173 @@
+/* fresnlf.c
+ *
+ * Fresnel integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, S, C;
+ * void fresnlf();
+ *
+ * fresnlf( x, _&S, _&C );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the Fresnel integrals
+ *
+ * x
+ * -
+ * | |
+ * C(x) = | cos(pi/2 t**2) dt,
+ * | |
+ * -
+ * 0
+ *
+ * x
+ * -
+ * | |
+ * S(x) = | sin(pi/2 t**2) dt.
+ * | |
+ * -
+ * 0
+ *
+ *
+ * The integrals are evaluated by power series for small x.
+ * For x >= 1 auxiliary functions f(x) and g(x) are employed
+ * such that
+ *
+ * C(x) = 0.5 + f(x) sin( pi/2 x**2 ) - g(x) cos( pi/2 x**2 )
+ * S(x) = 0.5 - f(x) cos( pi/2 x**2 ) - g(x) sin( pi/2 x**2 )
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error.
+ *
+ * Arithmetic function domain # trials peak rms
+ * IEEE S(x) 0, 10 30000 1.1e-6 1.9e-7
+ * IEEE C(x) 0, 10 30000 1.1e-6 2.0e-7
+ */
+
+/*
+Cephes Math Library Release 2.1: January, 1989
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+/* S(x) for small x */
+static float sn[7] = {
+ 1.647629463788700E-009,
+-1.522754752581096E-007,
+ 8.424748808502400E-006,
+-3.120693124703272E-004,
+ 7.244727626597022E-003,
+-9.228055941124598E-002,
+ 5.235987735681432E-001
+};
+
+/* C(x) for small x */
+static float cn[7] = {
+ 1.416802502367354E-008,
+-1.157231412229871E-006,
+ 5.387223446683264E-005,
+-1.604381798862293E-003,
+ 2.818489036795073E-002,
+-2.467398198317899E-001,
+ 9.999999760004487E-001
+};
+
+
+/* Auxiliary function f(x) */
+static float fn[8] = {
+-1.903009855649792E+012,
+ 1.355942388050252E+011,
+-4.158143148511033E+009,
+ 7.343848463587323E+007,
+-8.732356681548485E+005,
+ 8.560515466275470E+003,
+-1.032877601091159E+002,
+ 2.999401847870011E+000
+};
+
+/* Auxiliary function g(x) */
+static float gn[8] = {
+-1.860843997624650E+011,
+ 1.278350673393208E+010,
+-3.779387713202229E+008,
+ 6.492611570598858E+006,
+-7.787789623358162E+004,
+ 8.602931494734327E+002,
+-1.493439396592284E+001,
+ 9.999841934744914E-001
+};
+
+
+extern float PIF, PIO2F;
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#ifdef ANSIC
+float polevlf( float, float *, int );
+float cosf(float), sinf(float);
+#else
+float polevlf(), cosf(), sinf();
+#endif
+
+void fresnlf( float xxa, float *ssa, float *cca )
+{
+float f, g, cc, ss, c, s, t, u, x, x2;
+
+x = xxa;
+x = fabsf(x);
+x2 = x * x;
+if( x2 < 2.5625 )
+ {
+ t = x2 * x2;
+ ss = x * x2 * polevlf( t, sn, 6);
+ cc = x * polevlf( t, cn, 6);
+ goto done;
+ }
+
+if( x > 36974.0 )
+ {
+ cc = 0.5;
+ ss = 0.5;
+ goto done;
+ }
+
+
+/* Asymptotic power series auxiliary functions
+ * for large argument
+ */
+ x2 = x * x;
+ t = PIF * x2;
+ u = 1.0/(t * t);
+ t = 1.0/t;
+ f = 1.0 - u * polevlf( u, fn, 7);
+ g = t * polevlf( u, gn, 7);
+
+ t = PIO2F * x2;
+ c = cosf(t);
+ s = sinf(t);
+ t = PIF * x;
+ cc = 0.5 + (f * s - g * c)/t;
+ ss = 0.5 - (f * c + g * s)/t;
+
+done:
+if( xxa < 0.0 )
+ {
+ cc = -cc;
+ ss = -ss;
+ }
+
+*cca = cc;
+*ssa = ss;
+#if !ANSIC
+return 0;
+#endif
+}
diff --git a/libm/float/gammaf.c b/libm/float/gammaf.c
new file mode 100644
index 000000000..e8c4694c4
--- /dev/null
+++ b/libm/float/gammaf.c
@@ -0,0 +1,423 @@
+/* gammaf.c
+ *
+ * Gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, gammaf();
+ * extern int sgngamf;
+ *
+ * y = gammaf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns gamma function of the argument. The result is
+ * correctly signed, and the sign (+1 or -1) is also
+ * returned in a global (extern) variable named sgngamf.
+ * This same variable is also filled in by the logarithmic
+ * gamma function lgam().
+ *
+ * Arguments between 0 and 10 are reduced by recurrence and the
+ * function is approximated by a polynomial function covering
+ * the interval (2,3). Large arguments are handled by Stirling's
+ * formula. Negative arguments are made positive using
+ * a reflection formula.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,-33 100,000 5.7e-7 1.0e-7
+ * IEEE -33,0 100,000 6.1e-7 1.2e-7
+ *
+ *
+ */
+/* lgamf()
+ *
+ * Natural logarithm of gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, lgamf();
+ * extern int sgngamf;
+ *
+ * y = lgamf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of the absolute
+ * value of the gamma function of the argument.
+ * The sign (+1 or -1) of the gamma function is returned in a
+ * global (extern) variable named sgngamf.
+ *
+ * For arguments greater than 6.5, the logarithm of the gamma
+ * function is approximated by the logarithmic version of
+ * Stirling's formula. Arguments between 0 and +6.5 are reduced by
+ * by recurrence to the interval [.75,1.25] or [1.5,2.5] of a rational
+ * approximation. The cosecant reflection formula is employed for
+ * arguments less than zero.
+ *
+ * Arguments greater than MAXLGM = 2.035093e36 return MAXNUM and an
+ * error message.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ *
+ * arithmetic domain # trials peak rms
+ * IEEE -100,+100 500,000 7.4e-7 6.8e-8
+ * The error criterion was relative when the function magnitude
+ * was greater than one but absolute when it was less than one.
+ * The routine has low relative error for positive arguments.
+ *
+ * The following test used the relative error criterion.
+ * IEEE -2, +3 100000 4.0e-7 5.6e-8
+ *
+ */
+
+/* gamma.c */
+/* gamma function */
+
+/*
+Cephes Math Library Release 2.7: July, 1998
+Copyright 1984, 1987, 1989, 1992, 1998 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+/* define MAXGAM 34.84425627277176174 */
+
+/* Stirling's formula for the gamma function
+ * gamma(x) = sqrt(2 pi) x^(x-.5) exp(-x) ( 1 + 1/x P(1/x) )
+ * .028 < 1/x < .1
+ * relative error < 1.9e-11
+ */
+static float STIR[] = {
+-2.705194986674176E-003,
+ 3.473255786154910E-003,
+ 8.333331788340907E-002,
+};
+static float MAXSTIR = 26.77;
+static float SQTPIF = 2.50662827463100050242; /* sqrt( 2 pi ) */
+
+int sgngamf = 0;
+extern int sgngamf;
+extern float MAXLOGF, MAXNUMF, PIF;
+
+#ifdef ANSIC
+float expf(float);
+float logf(float);
+float powf( float, float );
+float sinf(float);
+float gammaf(float);
+float floorf(float);
+static float stirf(float);
+float polevlf( float, float *, int );
+float p1evlf( float, float *, int );
+#else
+float expf(), logf(), powf(), sinf(), floorf();
+float polevlf(), p1evlf();
+static float stirf();
+#endif
+
+/* Gamma function computed by Stirling's formula,
+ * sqrt(2 pi) x^(x-.5) exp(-x) (1 + 1/x P(1/x))
+ * The polynomial STIR is valid for 33 <= x <= 172.
+ */
+static float stirf( float xx )
+{
+float x, y, w, v;
+
+x = xx;
+w = 1.0/x;
+w = 1.0 + w * polevlf( w, STIR, 2 );
+y = expf( -x );
+if( x > MAXSTIR )
+ { /* Avoid overflow in pow() */
+ v = powf( x, 0.5 * x - 0.25 );
+ y *= v;
+ y *= v;
+ }
+else
+ {
+ y = powf( x, x - 0.5 ) * y;
+ }
+y = SQTPIF * y * w;
+return( y );
+}
+
+
+/* gamma(x+2), 0 < x < 1 */
+static float P[] = {
+ 1.536830450601906E-003,
+ 5.397581592950993E-003,
+ 4.130370201859976E-003,
+ 7.232307985516519E-002,
+ 8.203960091619193E-002,
+ 4.117857447645796E-001,
+ 4.227867745131584E-001,
+ 9.999999822945073E-001,
+};
+
+float gammaf( float xx )
+{
+float p, q, x, z, nz;
+int i, direction, negative;
+
+x = xx;
+sgngamf = 1;
+negative = 0;
+nz = 0.0;
+if( x < 0.0 )
+ {
+ negative = 1;
+ q = -x;
+ p = floorf(q);
+ if( p == q )
+ goto goverf;
+ i = p;
+ if( (i & 1) == 0 )
+ sgngamf = -1;
+ nz = q - p;
+ if( nz > 0.5 )
+ {
+ p += 1.0;
+ nz = q - p;
+ }
+ nz = q * sinf( PIF * nz );
+ if( nz == 0.0 )
+ {
+goverf:
+ mtherr( "gamma", OVERFLOW );
+ return( sgngamf * MAXNUMF);
+ }
+ if( nz < 0 )
+ nz = -nz;
+ x = q;
+ }
+if( x >= 10.0 )
+ {
+ z = stirf(x);
+ }
+if( x < 2.0 )
+ direction = 1;
+else
+ direction = 0;
+z = 1.0;
+while( x >= 3.0 )
+ {
+ x -= 1.0;
+ z *= x;
+ }
+/*
+while( x < 0.0 )
+ {
+ if( x > -1.E-4 )
+ goto small;
+ z *=x;
+ x += 1.0;
+ }
+*/
+while( x < 2.0 )
+ {
+ if( x < 1.e-4 )
+ goto small;
+ z *=x;
+ x += 1.0;
+ }
+
+if( direction )
+ z = 1.0/z;
+
+if( x == 2.0 )
+ return(z);
+
+x -= 2.0;
+p = z * polevlf( x, P, 7 );
+
+gdone:
+
+if( negative )
+ {
+ p = sgngamf * PIF/(nz * p );
+ }
+return(p);
+
+small:
+if( x == 0.0 )
+ {
+ mtherr( "gamma", SING );
+ return( MAXNUMF );
+ }
+else
+ {
+ p = z / ((1.0 + 0.5772156649015329 * x) * x);
+ goto gdone;
+ }
+}
+
+
+
+
+/* log gamma(x+2), -.5 < x < .5 */
+static float B[] = {
+ 6.055172732649237E-004,
+-1.311620815545743E-003,
+ 2.863437556468661E-003,
+-7.366775108654962E-003,
+ 2.058355474821512E-002,
+-6.735323259371034E-002,
+ 3.224669577325661E-001,
+ 4.227843421859038E-001
+};
+
+/* log gamma(x+1), -.25 < x < .25 */
+static float C[] = {
+ 1.369488127325832E-001,
+-1.590086327657347E-001,
+ 1.692415923504637E-001,
+-2.067882815621965E-001,
+ 2.705806208275915E-001,
+-4.006931650563372E-001,
+ 8.224670749082976E-001,
+-5.772156501719101E-001
+};
+
+/* log( sqrt( 2*pi ) ) */
+static float LS2PI = 0.91893853320467274178;
+#define MAXLGM 2.035093e36
+static float PIINV = 0.318309886183790671538;
+
+/* Logarithm of gamma function */
+
+
+float lgamf( float xx )
+{
+float p, q, w, z, x;
+float nx, tx;
+int i, direction;
+
+sgngamf = 1;
+
+x = xx;
+if( x < 0.0 )
+ {
+ q = -x;
+ w = lgamf(q); /* note this modifies sgngam! */
+ p = floorf(q);
+ if( p == q )
+ goto loverf;
+ i = p;
+ if( (i & 1) == 0 )
+ sgngamf = -1;
+ else
+ sgngamf = 1;
+ z = q - p;
+ if( z > 0.5 )
+ {
+ p += 1.0;
+ z = p - q;
+ }
+ z = q * sinf( PIF * z );
+ if( z == 0.0 )
+ goto loverf;
+ z = -logf( PIINV*z ) - w;
+ return( z );
+ }
+
+if( x < 6.5 )
+ {
+ direction = 0;
+ z = 1.0;
+ tx = x;
+ nx = 0.0;
+ if( x >= 1.5 )
+ {
+ while( tx > 2.5 )
+ {
+ nx -= 1.0;
+ tx = x + nx;
+ z *=tx;
+ }
+ x += nx - 2.0;
+iv1r5:
+ p = x * polevlf( x, B, 7 );
+ goto cont;
+ }
+ if( x >= 1.25 )
+ {
+ z *= x;
+ x -= 1.0; /* x + 1 - 2 */
+ direction = 1;
+ goto iv1r5;
+ }
+ if( x >= 0.75 )
+ {
+ x -= 1.0;
+ p = x * polevlf( x, C, 7 );
+ q = 0.0;
+ goto contz;
+ }
+ while( tx < 1.5 )
+ {
+ if( tx == 0.0 )
+ goto loverf;
+ z *=tx;
+ nx += 1.0;
+ tx = x + nx;
+ }
+ direction = 1;
+ x += nx - 2.0;
+ p = x * polevlf( x, B, 7 );
+
+cont:
+ if( z < 0.0 )
+ {
+ sgngamf = -1;
+ z = -z;
+ }
+ else
+ {
+ sgngamf = 1;
+ }
+ q = logf(z);
+ if( direction )
+ q = -q;
+contz:
+ return( p + q );
+ }
+
+if( x > MAXLGM )
+ {
+loverf:
+ mtherr( "lgamf", OVERFLOW );
+ return( sgngamf * MAXNUMF );
+ }
+
+/* Note, though an asymptotic formula could be used for x >= 3,
+ * there is cancellation error in the following if x < 6.5. */
+q = LS2PI - x;
+q += ( x - 0.5 ) * logf(x);
+
+if( x <= 1.0e4 )
+ {
+ z = 1.0/x;
+ p = z * z;
+ q += (( 6.789774945028216E-004 * p
+ - 2.769887652139868E-003 ) * p
+ + 8.333316229807355E-002 ) * z;
+ }
+return( q );
+}
diff --git a/libm/float/gdtrf.c b/libm/float/gdtrf.c
new file mode 100644
index 000000000..e7e02026b
--- /dev/null
+++ b/libm/float/gdtrf.c
@@ -0,0 +1,144 @@
+/* gdtrf.c
+ *
+ * Gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, x, y, gdtrf();
+ *
+ * y = gdtrf( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from zero to x of the gamma probability
+ * density function:
+ *
+ *
+ * x
+ * b -
+ * a | | b-1 -at
+ * y = ----- | t e dt
+ * - | |
+ * | (b) -
+ * 0
+ *
+ * The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igam( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 5.8e-5 3.0e-6
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * gdtrf domain x < 0 0.0
+ *
+ */
+ /* gdtrcf.c
+ *
+ * Complemented gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, x, y, gdtrcf();
+ *
+ * y = gdtrcf( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from x to infinity of the gamma
+ * probability density function:
+ *
+ *
+ * inf.
+ * b -
+ * a | | b-1 -at
+ * y = ----- | t e dt
+ * - | |
+ * | (b) -
+ * x
+ *
+ * The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igamc( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 9.1e-5 1.5e-5
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * gdtrcf domain x < 0 0.0
+ *
+ */
+
+/* gdtr() */
+
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+#ifdef ANSIC
+float igamf(float, float), igamcf(float, float);
+#else
+float igamf(), igamcf();
+#endif
+
+
+
+float gdtrf( float aa, float bb, float xx )
+{
+float a, b, x;
+
+a = aa;
+b = bb;
+x = xx;
+
+
+if( x < 0.0 )
+ {
+ mtherr( "gdtrf", DOMAIN );
+ return( 0.0 );
+ }
+return( igamf( b, a * x ) );
+}
+
+
+
+float gdtrcf( float aa, float bb, float xx )
+{
+float a, b, x;
+
+a = aa;
+b = bb;
+x = xx;
+if( x < 0.0 )
+ {
+ mtherr( "gdtrcf", DOMAIN );
+ return( 0.0 );
+ }
+return( igamcf( b, a * x ) );
+}
diff --git a/libm/float/hyp2f1f.c b/libm/float/hyp2f1f.c
new file mode 100644
index 000000000..01fe54928
--- /dev/null
+++ b/libm/float/hyp2f1f.c
@@ -0,0 +1,442 @@
+/* hyp2f1f.c
+ *
+ * Gauss hypergeometric function F
+ * 2 1
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, c, x, y, hyp2f1f();
+ *
+ * y = hyp2f1f( a, b, c, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * hyp2f1( a, b, c, x ) = F ( a, b; c; x )
+ * 2 1
+ *
+ * inf.
+ * - a(a+1)...(a+k) b(b+1)...(b+k) k+1
+ * = 1 + > ----------------------------- x .
+ * - c(c+1)...(c+k) (k+1)!
+ * k = 0
+ *
+ * Cases addressed are
+ * Tests and escapes for negative integer a, b, or c
+ * Linear transformation if c - a or c - b negative integer
+ * Special case c = a or c = b
+ * Linear transformation for x near +1
+ * Transformation for x < -0.5
+ * Psi function expansion if x > 0.5 and c - a - b integer
+ * Conditionally, a recurrence on c to make c-a-b > 0
+ *
+ * |x| > 1 is rejected.
+ *
+ * The parameters a, b, c are considered to be integer
+ * valued if they are within 1.0e-6 of the nearest integer.
+ *
+ * ACCURACY:
+ *
+ * Relative error (-1 < x < 1):
+ * arithmetic domain # trials peak rms
+ * IEEE 0,3 30000 5.8e-4 4.3e-6
+ */
+
+/* hyp2f1 */
+
+
+/*
+Cephes Math Library Release 2.2: November, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+#define EPS 1.0e-5
+#define EPS2 1.0e-5
+#define ETHRESH 1.0e-5
+
+extern float MAXNUMF, MACHEPF;
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#ifdef ANSIC
+float powf(float, float);
+static float hys2f1f(float, float, float, float, float *);
+static float hyt2f1f(float, float, float, float, float *);
+float gammaf(float), logf(float), expf(float), psif(float);
+float floorf(float);
+#else
+float powf(), gammaf(), logf(), expf(), psif();
+float floorf();
+static float hyt2f1f(), hys2f1f();
+#endif
+
+#define roundf(x) (floorf((x)+(float )0.5))
+
+
+
+
+float hyp2f1f( float aa, float bb, float cc, float xx )
+{
+float a, b, c, x;
+float d, d1, d2, e;
+float p, q, r, s, y, ax;
+float ia, ib, ic, id, err;
+int flag, i, aid;
+
+a = aa;
+b = bb;
+c = cc;
+x = xx;
+err = 0.0;
+ax = fabsf(x);
+s = 1.0 - x;
+flag = 0;
+ia = roundf(a); /* nearest integer to a */
+ib = roundf(b);
+
+if( a <= 0 )
+ {
+ if( fabsf(a-ia) < EPS ) /* a is a negative integer */
+ flag |= 1;
+ }
+
+if( b <= 0 )
+ {
+ if( fabsf(b-ib) < EPS ) /* b is a negative integer */
+ flag |= 2;
+ }
+
+if( ax < 1.0 )
+ {
+ if( fabsf(b-c) < EPS ) /* b = c */
+ {
+ y = powf( s, -a ); /* s to the -a power */
+ goto hypdon;
+ }
+ if( fabsf(a-c) < EPS ) /* a = c */
+ {
+ y = powf( s, -b ); /* s to the -b power */
+ goto hypdon;
+ }
+ }
+
+
+
+if( c <= 0.0 )
+ {
+ ic = roundf(c); /* nearest integer to c */
+ if( fabsf(c-ic) < EPS ) /* c is a negative integer */
+ {
+ /* check if termination before explosion */
+ if( (flag & 1) && (ia > ic) )
+ goto hypok;
+ if( (flag & 2) && (ib > ic) )
+ goto hypok;
+ goto hypdiv;
+ }
+ }
+
+if( flag ) /* function is a polynomial */
+ goto hypok;
+
+if( ax > 1.0 ) /* series diverges */
+ goto hypdiv;
+
+p = c - a;
+ia = roundf(p);
+if( (ia <= 0.0) && (fabsf(p-ia) < EPS) ) /* negative int c - a */
+ flag |= 4;
+
+r = c - b;
+ib = roundf(r); /* nearest integer to r */
+if( (ib <= 0.0) && (fabsf(r-ib) < EPS) ) /* negative int c - b */
+ flag |= 8;
+
+d = c - a - b;
+id = roundf(d); /* nearest integer to d */
+q = fabsf(d-id);
+
+if( fabsf(ax-1.0) < EPS ) /* |x| == 1.0 */
+ {
+ if( x > 0.0 )
+ {
+ if( flag & 12 ) /* negative int c-a or c-b */
+ {
+ if( d >= 0.0 )
+ goto hypf;
+ else
+ goto hypdiv;
+ }
+ if( d <= 0.0 )
+ goto hypdiv;
+ y = gammaf(c)*gammaf(d)/(gammaf(p)*gammaf(r));
+ goto hypdon;
+ }
+
+ if( d <= -1.0 )
+ goto hypdiv;
+ }
+
+/* Conditionally make d > 0 by recurrence on c
+ * AMS55 #15.2.27
+ */
+if( d < 0.0 )
+ {
+/* Try the power series first */
+ y = hyt2f1f( a, b, c, x, &err );
+ if( err < ETHRESH )
+ goto hypdon;
+/* Apply the recurrence if power series fails */
+ err = 0.0;
+ aid = 2 - id;
+ e = c + aid;
+ d2 = hyp2f1f(a,b,e,x);
+ d1 = hyp2f1f(a,b,e+1.0,x);
+ q = a + b + 1.0;
+ for( i=0; i<aid; i++ )
+ {
+ r = e - 1.0;
+ y = (e*(r-(2.0*e-q)*x)*d2 + (e-a)*(e-b)*x*d1)/(e*r*s);
+ e = r;
+ d1 = d2;
+ d2 = y;
+ }
+ goto hypdon;
+ }
+
+
+if( flag & 12 )
+ goto hypf; /* negative integer c-a or c-b */
+
+hypok:
+y = hyt2f1f( a, b, c, x, &err );
+
+hypdon:
+if( err > ETHRESH )
+ {
+ mtherr( "hyp2f1", PLOSS );
+/* printf( "Estimated err = %.2e\n", err );*/
+ }
+return(y);
+
+/* The transformation for c-a or c-b negative integer
+ * AMS55 #15.3.3
+ */
+hypf:
+y = powf( s, d ) * hys2f1f( c-a, c-b, c, x, &err );
+goto hypdon;
+
+/* The alarm exit */
+hypdiv:
+mtherr( "hyp2f1f", OVERFLOW );
+return( MAXNUMF );
+}
+
+
+
+
+/* Apply transformations for |x| near 1
+ * then call the power series
+ */
+static float hyt2f1f( float aa, float bb, float cc, float xx, float *loss )
+{
+float a, b, c, x;
+float p, q, r, s, t, y, d, err, err1;
+float ax, id, d1, d2, e, y1;
+int i, aid;
+
+a = aa;
+b = bb;
+c = cc;
+x = xx;
+err = 0.0;
+s = 1.0 - x;
+if( x < -0.5 )
+ {
+ if( b > a )
+ y = powf( s, -a ) * hys2f1f( a, c-b, c, -x/s, &err );
+
+ else
+ y = powf( s, -b ) * hys2f1f( c-a, b, c, -x/s, &err );
+
+ goto done;
+ }
+
+
+
+d = c - a - b;
+id = roundf(d); /* nearest integer to d */
+
+if( x > 0.8 )
+{
+
+if( fabsf(d-id) > EPS2 ) /* test for integer c-a-b */
+ {
+/* Try the power series first */
+ y = hys2f1f( a, b, c, x, &err );
+ if( err < ETHRESH )
+ goto done;
+/* If power series fails, then apply AMS55 #15.3.6 */
+ q = hys2f1f( a, b, 1.0-d, s, &err );
+ q *= gammaf(d) /(gammaf(c-a) * gammaf(c-b));
+ r = powf(s,d) * hys2f1f( c-a, c-b, d+1.0, s, &err1 );
+ r *= gammaf(-d)/(gammaf(a) * gammaf(b));
+ y = q + r;
+
+ q = fabsf(q); /* estimate cancellation error */
+ r = fabsf(r);
+ if( q > r )
+ r = q;
+ err += err1 + (MACHEPF*r)/y;
+
+ y *= gammaf(c);
+ goto done;
+ }
+else
+ {
+/* Psi function expansion, AMS55 #15.3.10, #15.3.11, #15.3.12 */
+ if( id >= 0.0 )
+ {
+ e = d;
+ d1 = d;
+ d2 = 0.0;
+ aid = id;
+ }
+ else
+ {
+ e = -d;
+ d1 = 0.0;
+ d2 = d;
+ aid = -id;
+ }
+
+ ax = logf(s);
+
+ /* sum for t = 0 */
+ y = psif(1.0) + psif(1.0+e) - psif(a+d1) - psif(b+d1) - ax;
+ y /= gammaf(e+1.0);
+
+ p = (a+d1) * (b+d1) * s / gammaf(e+2.0); /* Poch for t=1 */
+ t = 1.0;
+ do
+ {
+ r = psif(1.0+t) + psif(1.0+t+e) - psif(a+t+d1)
+ - psif(b+t+d1) - ax;
+ q = p * r;
+ y += q;
+ p *= s * (a+t+d1) / (t+1.0);
+ p *= (b+t+d1) / (t+1.0+e);
+ t += 1.0;
+ }
+ while( fabsf(q/y) > EPS );
+
+
+ if( id == 0.0 )
+ {
+ y *= gammaf(c)/(gammaf(a)*gammaf(b));
+ goto psidon;
+ }
+
+ y1 = 1.0;
+
+ if( aid == 1 )
+ goto nosum;
+
+ t = 0.0;
+ p = 1.0;
+ for( i=1; i<aid; i++ )
+ {
+ r = 1.0-e+t;
+ p *= s * (a+t+d2) * (b+t+d2) / r;
+ t += 1.0;
+ p /= t;
+ y1 += p;
+ }
+
+
+nosum:
+ p = gammaf(c);
+ y1 *= gammaf(e) * p / (gammaf(a+d1) * gammaf(b+d1));
+ y *= p / (gammaf(a+d2) * gammaf(b+d2));
+ if( (aid & 1) != 0 )
+ y = -y;
+
+ q = powf( s, id ); /* s to the id power */
+ if( id > 0.0 )
+ y *= q;
+ else
+ y1 *= q;
+
+ y += y1;
+psidon:
+ goto done;
+ }
+}
+
+
+/* Use defining power series if no special cases */
+y = hys2f1f( a, b, c, x, &err );
+
+done:
+*loss = err;
+return(y);
+}
+
+
+
+
+
+/* Defining power series expansion of Gauss hypergeometric function */
+
+static float hys2f1f( float aa, float bb, float cc, float xx, float *loss )
+{
+int i;
+float a, b, c, x;
+float f, g, h, k, m, s, u, umax;
+
+
+a = aa;
+b = bb;
+c = cc;
+x = xx;
+i = 0;
+umax = 0.0;
+f = a;
+g = b;
+h = c;
+k = 0.0;
+s = 1.0;
+u = 1.0;
+
+do
+ {
+ if( fabsf(h) < EPS )
+ return( MAXNUMF );
+ m = k + 1.0;
+ u = u * ((f+k) * (g+k) * x / ((h+k) * m));
+ s += u;
+ k = fabsf(u); /* remember largest term summed */
+ if( k > umax )
+ umax = k;
+ k = m;
+ if( ++i > 10000 ) /* should never happen */
+ {
+ *loss = 1.0;
+ return(s);
+ }
+ }
+while( fabsf(u/s) > MACHEPF );
+
+/* return estimated relative error */
+*loss = (MACHEPF*umax)/fabsf(s) + (MACHEPF*i);
+
+return(s);
+}
+
+
diff --git a/libm/float/hypergf.c b/libm/float/hypergf.c
new file mode 100644
index 000000000..60d0eb4c5
--- /dev/null
+++ b/libm/float/hypergf.c
@@ -0,0 +1,384 @@
+/* hypergf.c
+ *
+ * Confluent hypergeometric function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, x, y, hypergf();
+ *
+ * y = hypergf( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the confluent hypergeometric function
+ *
+ * 1 2
+ * a x a(a+1) x
+ * F ( a,b;x ) = 1 + ---- + --------- + ...
+ * 1 1 b 1! b(b+1) 2!
+ *
+ * Many higher transcendental functions are special cases of
+ * this power series.
+ *
+ * As is evident from the formula, b must not be a negative
+ * integer or zero unless a is an integer with 0 >= a > b.
+ *
+ * The routine attempts both a direct summation of the series
+ * and an asymptotic expansion. In each case error due to
+ * roundoff, cancellation, and nonconvergence is estimated.
+ * The result with smaller estimated error is returned.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a, b, x), all three variables
+ * ranging from 0 to 30.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,5 10000 6.6e-7 1.3e-7
+ * IEEE 0,30 30000 1.1e-5 6.5e-7
+ *
+ * Larger errors can be observed when b is near a negative
+ * integer or zero. Certain combinations of arguments yield
+ * serious cancellation error in the power series summation
+ * and also are not in the region of near convergence of the
+ * asymptotic series. An error message is printed if the
+ * self-estimated relative error is greater than 1.0e-3.
+ *
+ */
+
+/* hyperg.c */
+
+
+/*
+Cephes Math Library Release 2.1: November, 1988
+Copyright 1984, 1987, 1988 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+extern float MAXNUMF, MACHEPF;
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#ifdef ANSIC
+float expf(float);
+float hyp2f0f(float, float, float, int, float *);
+static float hy1f1af(float, float, float, float *);
+static float hy1f1pf(float, float, float, float *);
+float logf(float), gammaf(float), lgamf(float);
+#else
+float expf(), hyp2f0f();
+float logf(), gammaf(), lgamf();
+static float hy1f1pf(), hy1f1af();
+#endif
+
+float hypergf( float aa, float bb, float xx )
+{
+float a, b, x, asum, psum, acanc, pcanc, temp;
+
+
+a = aa;
+b = bb;
+x = xx;
+/* See if a Kummer transformation will help */
+temp = b - a;
+if( fabsf(temp) < 0.001 * fabsf(a) )
+ return( expf(x) * hypergf( temp, b, -x ) );
+
+psum = hy1f1pf( a, b, x, &pcanc );
+if( pcanc < 1.0e-6 )
+ goto done;
+
+
+/* try asymptotic series */
+
+asum = hy1f1af( a, b, x, &acanc );
+
+
+/* Pick the result with less estimated error */
+
+if( acanc < pcanc )
+ {
+ pcanc = acanc;
+ psum = asum;
+ }
+
+done:
+if( pcanc > 1.0e-3 )
+ mtherr( "hyperg", PLOSS );
+
+return( psum );
+}
+
+
+
+
+/* Power series summation for confluent hypergeometric function */
+
+
+static float hy1f1pf( float aa, float bb, float xx, float *err )
+{
+float a, b, x, n, a0, sum, t, u, temp;
+float an, bn, maxt, pcanc;
+
+a = aa;
+b = bb;
+x = xx;
+/* set up for power series summation */
+an = a;
+bn = b;
+a0 = 1.0;
+sum = 1.0;
+n = 1.0;
+t = 1.0;
+maxt = 0.0;
+
+
+while( t > MACHEPF )
+ {
+ if( bn == 0 ) /* check bn first since if both */
+ {
+ mtherr( "hypergf", SING );
+ return( MAXNUMF ); /* an and bn are zero it is */
+ }
+ if( an == 0 ) /* a singularity */
+ return( sum );
+ if( n > 200 )
+ goto pdone;
+ u = x * ( an / (bn * n) );
+
+ /* check for blowup */
+ temp = fabsf(u);
+ if( (temp > 1.0 ) && (maxt > (MAXNUMF/temp)) )
+ {
+ pcanc = 1.0; /* estimate 100% error */
+ goto blowup;
+ }
+
+ a0 *= u;
+ sum += a0;
+ t = fabsf(a0);
+ if( t > maxt )
+ maxt = t;
+/*
+ if( (maxt/fabsf(sum)) > 1.0e17 )
+ {
+ pcanc = 1.0;
+ goto blowup;
+ }
+*/
+ an += 1.0;
+ bn += 1.0;
+ n += 1.0;
+ }
+
+pdone:
+
+/* estimate error due to roundoff and cancellation */
+if( sum != 0.0 )
+ maxt /= fabsf(sum);
+maxt *= MACHEPF; /* this way avoids multiply overflow */
+pcanc = fabsf( MACHEPF * n + maxt );
+
+blowup:
+
+*err = pcanc;
+
+return( sum );
+}
+
+
+/* hy1f1a() */
+/* asymptotic formula for hypergeometric function:
+ *
+ * ( -a
+ * -- ( |z|
+ * | (b) ( -------- 2f0( a, 1+a-b, -1/x )
+ * ( --
+ * ( | (b-a)
+ *
+ *
+ * x a-b )
+ * e |x| )
+ * + -------- 2f0( b-a, 1-a, 1/x ) )
+ * -- )
+ * | (a) )
+ */
+
+static float hy1f1af( float aa, float bb, float xx, float *err )
+{
+float a, b, x, h1, h2, t, u, temp, acanc, asum, err1, err2;
+
+a = aa;
+b = bb;
+x = xx;
+if( x == 0 )
+ {
+ acanc = 1.0;
+ asum = MAXNUMF;
+ goto adone;
+ }
+temp = logf( fabsf(x) );
+t = x + temp * (a-b);
+u = -temp * a;
+
+if( b > 0 )
+ {
+ temp = lgamf(b);
+ t += temp;
+ u += temp;
+ }
+
+h1 = hyp2f0f( a, a-b+1, -1.0/x, 1, &err1 );
+
+temp = expf(u) / gammaf(b-a);
+h1 *= temp;
+err1 *= temp;
+
+h2 = hyp2f0f( b-a, 1.0-a, 1.0/x, 2, &err2 );
+
+if( a < 0 )
+ temp = expf(t) / gammaf(a);
+else
+ temp = expf( t - lgamf(a) );
+
+h2 *= temp;
+err2 *= temp;
+
+if( x < 0.0 )
+ asum = h1;
+else
+ asum = h2;
+
+acanc = fabsf(err1) + fabsf(err2);
+
+
+if( b < 0 )
+ {
+ temp = gammaf(b);
+ asum *= temp;
+ acanc *= fabsf(temp);
+ }
+
+
+if( asum != 0.0 )
+ acanc /= fabsf(asum);
+
+acanc *= 30.0; /* fudge factor, since error of asymptotic formula
+ * often seems this much larger than advertised */
+
+adone:
+
+
+*err = acanc;
+return( asum );
+}
+
+/* hyp2f0() */
+
+float hyp2f0f(float aa, float bb, float xx, int type, float *err)
+{
+float a, b, x, a0, alast, t, tlast, maxt;
+float n, an, bn, u, sum, temp;
+
+a = aa;
+b = bb;
+x = xx;
+an = a;
+bn = b;
+a0 = 1.0;
+alast = 1.0;
+sum = 0.0;
+n = 1.0;
+t = 1.0;
+tlast = 1.0e9;
+maxt = 0.0;
+
+do
+ {
+ if( an == 0 )
+ goto pdone;
+ if( bn == 0 )
+ goto pdone;
+
+ u = an * (bn * x / n);
+
+ /* check for blowup */
+ temp = fabsf(u);
+ if( (temp > 1.0 ) && (maxt > (MAXNUMF/temp)) )
+ goto error;
+
+ a0 *= u;
+ t = fabsf(a0);
+
+ /* terminating condition for asymptotic series */
+ if( t > tlast )
+ goto ndone;
+
+ tlast = t;
+ sum += alast; /* the sum is one term behind */
+ alast = a0;
+
+ if( n > 200 )
+ goto ndone;
+
+ an += 1.0;
+ bn += 1.0;
+ n += 1.0;
+ if( t > maxt )
+ maxt = t;
+ }
+while( t > MACHEPF );
+
+
+pdone: /* series converged! */
+
+/* estimate error due to roundoff and cancellation */
+*err = fabsf( MACHEPF * (n + maxt) );
+
+alast = a0;
+goto done;
+
+ndone: /* series did not converge */
+
+/* The following "Converging factors" are supposed to improve accuracy,
+ * but do not actually seem to accomplish very much. */
+
+n -= 1.0;
+x = 1.0/x;
+
+switch( type ) /* "type" given as subroutine argument */
+{
+case 1:
+ alast *= ( 0.5 + (0.125 + 0.25*b - 0.5*a + 0.25*x - 0.25*n)/x );
+ break;
+
+case 2:
+ alast *= 2.0/3.0 - b + 2.0*a + x - n;
+ break;
+
+default:
+ ;
+}
+
+/* estimate error due to roundoff, cancellation, and nonconvergence */
+*err = MACHEPF * (n + maxt) + fabsf( a0 );
+
+
+done:
+sum += alast;
+return( sum );
+
+/* series blew up: */
+error:
+*err = MAXNUMF;
+mtherr( "hypergf", TLOSS );
+return( sum );
+}
diff --git a/libm/float/i0f.c b/libm/float/i0f.c
new file mode 100644
index 000000000..bb62cf60a
--- /dev/null
+++ b/libm/float/i0f.c
@@ -0,0 +1,160 @@
+/* i0f.c
+ *
+ * Modified Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, i0();
+ *
+ * y = i0f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order zero of the
+ * argument.
+ *
+ * The function is defined as i0(x) = j0( ix ).
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 100000 4.0e-7 7.9e-8
+ *
+ */
+ /* i0ef.c
+ *
+ * Modified Bessel function of order zero,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, i0ef();
+ *
+ * y = i0ef( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order zero of the argument.
+ *
+ * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 100000 3.7e-7 7.0e-8
+ * See i0f().
+ *
+ */
+
+/* i0.c */
+
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for exp(-x) I0(x)
+ * in the interval [0,8].
+ *
+ * lim(x->0){ exp(-x) I0(x) } = 1.
+ */
+
+static float A[] =
+{
+-1.30002500998624804212E-8f,
+ 6.04699502254191894932E-8f,
+-2.67079385394061173391E-7f,
+ 1.11738753912010371815E-6f,
+-4.41673835845875056359E-6f,
+ 1.64484480707288970893E-5f,
+-5.75419501008210370398E-5f,
+ 1.88502885095841655729E-4f,
+-5.76375574538582365885E-4f,
+ 1.63947561694133579842E-3f,
+-4.32430999505057594430E-3f,
+ 1.05464603945949983183E-2f,
+-2.37374148058994688156E-2f,
+ 4.93052842396707084878E-2f,
+-9.49010970480476444210E-2f,
+ 1.71620901522208775349E-1f,
+-3.04682672343198398683E-1f,
+ 6.76795274409476084995E-1f
+};
+
+
+/* Chebyshev coefficients for exp(-x) sqrt(x) I0(x)
+ * in the inverted interval [8,infinity].
+ *
+ * lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).
+ */
+
+static float B[] =
+{
+ 3.39623202570838634515E-9f,
+ 2.26666899049817806459E-8f,
+ 2.04891858946906374183E-7f,
+ 2.89137052083475648297E-6f,
+ 6.88975834691682398426E-5f,
+ 3.36911647825569408990E-3f,
+ 8.04490411014108831608E-1f
+};
+
+
+float chbevlf(float, float *, int), expf(float), sqrtf(float);
+
+float i0f( float x )
+{
+float y;
+
+if( x < 0 )
+ x = -x;
+if( x <= 8.0f )
+ {
+ y = 0.5f*x - 2.0f;
+ return( expf(x) * chbevlf( y, A, 18 ) );
+ }
+
+return( expf(x) * chbevlf( 32.0f/x - 2.0f, B, 7 ) / sqrtf(x) );
+}
+
+
+
+float chbevlf(float, float *, int), expf(float), sqrtf(float);
+
+float i0ef( float x )
+{
+float y;
+
+if( x < 0 )
+ x = -x;
+if( x <= 8.0f )
+ {
+ y = 0.5f*x - 2.0f;
+ return( chbevlf( y, A, 18 ) );
+ }
+
+return( chbevlf( 32.0f/x - 2.0f, B, 7 ) / sqrtf(x) );
+}
diff --git a/libm/float/i1f.c b/libm/float/i1f.c
new file mode 100644
index 000000000..e9741e1da
--- /dev/null
+++ b/libm/float/i1f.c
@@ -0,0 +1,177 @@
+/* i1f.c
+ *
+ * Modified Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, i1f();
+ *
+ * y = i1f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order one of the
+ * argument.
+ *
+ * The function is defined as i1(x) = -i j1( ix ).
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 100000 1.5e-6 1.6e-7
+ *
+ *
+ */
+ /* i1ef.c
+ *
+ * Modified Bessel function of order one,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, i1ef();
+ *
+ * y = i1ef( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of order one of the argument.
+ *
+ * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 1.5e-6 1.5e-7
+ * See i1().
+ *
+ */
+
+/* i1.c 2 */
+
+
+/*
+Cephes Math Library Release 2.0: March, 1987
+Copyright 1985, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for exp(-x) I1(x) / x
+ * in the interval [0,8].
+ *
+ * lim(x->0){ exp(-x) I1(x) / x } = 1/2.
+ */
+
+static float A[] =
+{
+ 9.38153738649577178388E-9f,
+-4.44505912879632808065E-8f,
+ 2.00329475355213526229E-7f,
+-8.56872026469545474066E-7f,
+ 3.47025130813767847674E-6f,
+-1.32731636560394358279E-5f,
+ 4.78156510755005422638E-5f,
+-1.61760815825896745588E-4f,
+ 5.12285956168575772895E-4f,
+-1.51357245063125314899E-3f,
+ 4.15642294431288815669E-3f,
+-1.05640848946261981558E-2f,
+ 2.47264490306265168283E-2f,
+-5.29459812080949914269E-2f,
+ 1.02643658689847095384E-1f,
+-1.76416518357834055153E-1f,
+ 2.52587186443633654823E-1f
+};
+
+
+/* Chebyshev coefficients for exp(-x) sqrt(x) I1(x)
+ * in the inverted interval [8,infinity].
+ *
+ * lim(x->inf){ exp(-x) sqrt(x) I1(x) } = 1/sqrt(2pi).
+ */
+
+static float B[] =
+{
+-3.83538038596423702205E-9f,
+-2.63146884688951950684E-8f,
+-2.51223623787020892529E-7f,
+-3.88256480887769039346E-6f,
+-1.10588938762623716291E-4f,
+-9.76109749136146840777E-3f,
+ 7.78576235018280120474E-1f
+};
+
+/* i1.c */
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#ifdef ANSIC
+float chbevlf(float, float *, int);
+float expf(float), sqrtf(float);
+#else
+float chbevlf(), expf(), sqrtf();
+#endif
+
+
+float i1f(float xx)
+{
+float x, y, z;
+
+x = xx;
+z = fabsf(x);
+if( z <= 8.0f )
+ {
+ y = 0.5f*z - 2.0f;
+ z = chbevlf( y, A, 17 ) * z * expf(z);
+ }
+else
+ {
+ z = expf(z) * chbevlf( 32.0f/z - 2.0f, B, 7 ) / sqrtf(z);
+ }
+if( x < 0.0f )
+ z = -z;
+return( z );
+}
+
+/* i1e() */
+
+float i1ef( float xx )
+{
+float x, y, z;
+
+x = xx;
+z = fabsf(x);
+if( z <= 8.0f )
+ {
+ y = 0.5f*z - 2.0f;
+ z = chbevlf( y, A, 17 ) * z;
+ }
+else
+ {
+ z = chbevlf( 32.0f/z - 2.0f, B, 7 ) / sqrtf(z);
+ }
+if( x < 0.0f )
+ z = -z;
+return( z );
+}
diff --git a/libm/float/igamf.c b/libm/float/igamf.c
new file mode 100644
index 000000000..c54225df4
--- /dev/null
+++ b/libm/float/igamf.c
@@ -0,0 +1,223 @@
+/* igamf.c
+ *
+ * Incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, x, y, igamf();
+ *
+ * y = igamf( a, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ * x
+ * -
+ * 1 | | -t a-1
+ * igam(a,x) = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * 0
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 20000 7.8e-6 5.9e-7
+ *
+ */
+ /* igamcf()
+ *
+ * Complemented incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, x, y, igamcf();
+ *
+ * y = igamcf( a, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ *
+ * igamc(a,x) = 1 - igam(a,x)
+ *
+ * inf.
+ * -
+ * 1 | | -t a-1
+ * = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * x
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 30000 7.8e-6 5.9e-7
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1985, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+/* BIG = 1/MACHEPF */
+#define BIG 16777216.
+
+extern float MACHEPF, MAXLOGF;
+
+#ifdef ANSIC
+float lgamf(float), expf(float), logf(float), igamf(float, float);
+#else
+float lgamf(), expf(), logf(), igamf();
+#endif
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+
+
+float igamcf( float aa, float xx )
+{
+float a, x, ans, c, yc, ax, y, z;
+float pk, pkm1, pkm2, qk, qkm1, qkm2;
+float r, t;
+static float big = BIG;
+
+a = aa;
+x = xx;
+if( (x <= 0) || ( a <= 0) )
+ return( 1.0 );
+
+if( (x < 1.0) || (x < a) )
+ return( 1.0 - igamf(a,x) );
+
+ax = a * logf(x) - x - lgamf(a);
+if( ax < -MAXLOGF )
+ {
+ mtherr( "igamcf", UNDERFLOW );
+ return( 0.0 );
+ }
+ax = expf(ax);
+
+/* continued fraction */
+y = 1.0 - a;
+z = x + y + 1.0;
+c = 0.0;
+pkm2 = 1.0;
+qkm2 = x;
+pkm1 = x + 1.0;
+qkm1 = z * x;
+ans = pkm1/qkm1;
+
+do
+ {
+ c += 1.0;
+ y += 1.0;
+ z += 2.0;
+ yc = y * c;
+ pk = pkm1 * z - pkm2 * yc;
+ qk = qkm1 * z - qkm2 * yc;
+ if( qk != 0 )
+ {
+ r = pk/qk;
+ t = fabsf( (ans - r)/r );
+ ans = r;
+ }
+ else
+ t = 1.0;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+ if( fabsf(pk) > big )
+ {
+ pkm2 *= MACHEPF;
+ pkm1 *= MACHEPF;
+ qkm2 *= MACHEPF;
+ qkm1 *= MACHEPF;
+ }
+ }
+while( t > MACHEPF );
+
+return( ans * ax );
+}
+
+
+
+/* left tail of incomplete gamma function:
+ *
+ * inf. k
+ * a -x - x
+ * x e > ----------
+ * - -
+ * k=0 | (a+k+1)
+ *
+ */
+
+float igamf( float aa, float xx )
+{
+float a, x, ans, ax, c, r;
+
+a = aa;
+x = xx;
+if( (x <= 0) || ( a <= 0) )
+ return( 0.0 );
+
+if( (x > 1.0) && (x > a ) )
+ return( 1.0 - igamcf(a,x) );
+
+/* Compute x**a * exp(-x) / gamma(a) */
+ax = a * logf(x) - x - lgamf(a);
+if( ax < -MAXLOGF )
+ {
+ mtherr( "igamf", UNDERFLOW );
+ return( 0.0 );
+ }
+ax = expf(ax);
+
+/* power series */
+r = a;
+c = 1.0;
+ans = 1.0;
+
+do
+ {
+ r += 1.0;
+ c *= x/r;
+ ans += c;
+ }
+while( c/ans > MACHEPF );
+
+return( ans * ax/a );
+}
diff --git a/libm/float/igamif.c b/libm/float/igamif.c
new file mode 100644
index 000000000..5a33b4982
--- /dev/null
+++ b/libm/float/igamif.c
@@ -0,0 +1,112 @@
+/* igamif()
+ *
+ * Inverse of complemented imcomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, x, y, igamif();
+ *
+ * x = igamif( a, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given y, the function finds x such that
+ *
+ * igamc( a, x ) = y.
+ *
+ * Starting with the approximate value
+ *
+ * 3
+ * x = a t
+ *
+ * where
+ *
+ * t = 1 - d - ndtri(y) sqrt(d)
+ *
+ * and
+ *
+ * d = 1/9a,
+ *
+ * the routine performs up to 10 Newton iterations to find the
+ * root of igamc(a,x) - y = 0.
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested for a ranging from 0 to 100 and x from 0 to 1.
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 1.0e-5 1.5e-6
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+extern float MACHEPF, MAXLOGF;
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#ifdef ANSIC
+float igamcf(float, float);
+float ndtrif(float), expf(float), logf(float), sqrtf(float), lgamf(float);
+#else
+float igamcf();
+float ndtrif(), expf(), logf(), sqrtf(), lgamf();
+#endif
+
+
+float igamif( float aa, float yy0 )
+{
+float a, y0, d, y, x0, lgm;
+int i;
+
+a = aa;
+y0 = yy0;
+/* approximation to inverse function */
+d = 1.0/(9.0*a);
+y = ( 1.0 - d - ndtrif(y0) * sqrtf(d) );
+x0 = a * y * y * y;
+
+lgm = lgamf(a);
+
+for( i=0; i<10; i++ )
+ {
+ if( x0 <= 0.0 )
+ {
+ mtherr( "igamif", UNDERFLOW );
+ return(0.0);
+ }
+ y = igamcf(a,x0);
+/* compute the derivative of the function at this point */
+ d = (a - 1.0) * logf(x0) - x0 - lgm;
+ if( d < -MAXLOGF )
+ {
+ mtherr( "igamif", UNDERFLOW );
+ goto done;
+ }
+ d = -expf(d);
+/* compute the step to the next approximation of x */
+ if( d == 0.0 )
+ goto done;
+ d = (y - y0)/d;
+ x0 = x0 - d;
+ if( i < 3 )
+ continue;
+ if( fabsf(d/x0) < (2.0 * MACHEPF) )
+ goto done;
+ }
+
+done:
+return( x0 );
+}
diff --git a/libm/float/incbetf.c b/libm/float/incbetf.c
new file mode 100644
index 000000000..fed9aae4b
--- /dev/null
+++ b/libm/float/incbetf.c
@@ -0,0 +1,424 @@
+/* incbetf.c
+ *
+ * Incomplete beta integral
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, x, y, incbetf();
+ *
+ * y = incbetf( a, b, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns incomplete beta integral of the arguments, evaluated
+ * from zero to x. The function is defined as
+ *
+ * x
+ * - -
+ * | (a+b) | | a-1 b-1
+ * ----------- | t (1-t) dt.
+ * - - | |
+ * | (a) | (b) -
+ * 0
+ *
+ * The domain of definition is 0 <= x <= 1. In this
+ * implementation a and b are restricted to positive values.
+ * The integral from x to 1 may be obtained by the symmetry
+ * relation
+ *
+ * 1 - incbet( a, b, x ) = incbet( b, a, 1-x ).
+ *
+ * The integral is evaluated by a continued fraction expansion.
+ * If a < 1, the function calls itself recursively after a
+ * transformation to increase a to a+1.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,x) with a and b in the indicated
+ * interval and x between 0 and 1.
+ *
+ * arithmetic domain # trials peak rms
+ * Relative error:
+ * IEEE 0,30 10000 3.7e-5 5.1e-6
+ * IEEE 0,100 10000 1.7e-4 2.5e-5
+ * The useful domain for relative error is limited by underflow
+ * of the single precision exponential function.
+ * Absolute error:
+ * IEEE 0,30 100000 2.2e-5 9.6e-7
+ * IEEE 0,100 10000 6.5e-5 3.7e-6
+ *
+ * Larger errors may occur for extreme ratios of a and b.
+ *
+ * ERROR MESSAGES:
+ * message condition value returned
+ * incbetf domain x<0, x>1 0.0
+ */
+
+
+/*
+Cephes Math Library, Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+#ifdef ANSIC
+float lgamf(float), expf(float), logf(float);
+static float incbdf(float, float, float);
+static float incbcff(float, float, float);
+float incbpsf(float, float, float);
+#else
+float lgamf(), expf(), logf();
+float incbpsf();
+static float incbcff(), incbdf();
+#endif
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+/* BIG = 1/MACHEPF */
+#define BIG 16777216.
+extern float MACHEPF, MAXLOGF;
+#define MINLOGF (-MAXLOGF)
+
+float incbetf( float aaa, float bbb, float xxx )
+{
+float aa, bb, xx, ans, a, b, t, x, onemx;
+int flag;
+
+aa = aaa;
+bb = bbb;
+xx = xxx;
+if( (xx <= 0.0) || ( xx >= 1.0) )
+ {
+ if( xx == 0.0 )
+ return(0.0);
+ if( xx == 1.0 )
+ return( 1.0 );
+ mtherr( "incbetf", DOMAIN );
+ return( 0.0 );
+ }
+
+onemx = 1.0 - xx;
+
+
+/* transformation for small aa */
+
+if( aa <= 1.0 )
+ {
+ ans = incbetf( aa+1.0, bb, xx );
+ t = aa*logf(xx) + bb*logf( 1.0-xx )
+ + lgamf(aa+bb) - lgamf(aa+1.0) - lgamf(bb);
+ if( t > MINLOGF )
+ ans += expf(t);
+ return( ans );
+ }
+
+
+/* see if x is greater than the mean */
+
+if( xx > (aa/(aa+bb)) )
+ {
+ flag = 1;
+ a = bb;
+ b = aa;
+ t = xx;
+ x = onemx;
+ }
+else
+ {
+ flag = 0;
+ a = aa;
+ b = bb;
+ t = onemx;
+ x = xx;
+ }
+
+/* transformation for small aa */
+/*
+if( a <= 1.0 )
+ {
+ ans = a*logf(x) + b*logf( onemx )
+ + lgamf(a+b) - lgamf(a+1.0) - lgamf(b);
+ t = incbetf( a+1.0, b, x );
+ if( ans > MINLOGF )
+ t += expf(ans);
+ goto bdone;
+ }
+*/
+/* Choose expansion for optimal convergence */
+
+
+if( b > 10.0 )
+ {
+if( fabsf(b*x/a) < 0.3 )
+ {
+ t = incbpsf( a, b, x );
+ goto bdone;
+ }
+ }
+
+ans = x * (a+b-2.0)/(a-1.0);
+if( ans < 1.0 )
+ {
+ ans = incbcff( a, b, x );
+ t = b * logf( t );
+ }
+else
+ {
+ ans = incbdf( a, b, x );
+ t = (b-1.0) * logf(t);
+ }
+
+t += a*logf(x) + lgamf(a+b) - lgamf(a) - lgamf(b);
+t += logf( ans/a );
+
+if( t < MINLOGF )
+ {
+ t = 0.0;
+ if( flag == 0 )
+ {
+ mtherr( "incbetf", UNDERFLOW );
+ }
+ }
+else
+ {
+ t = expf(t);
+ }
+bdone:
+
+if( flag )
+ t = 1.0 - t;
+
+return( t );
+}
+
+/* Continued fraction expansion #1
+ * for incomplete beta integral
+ */
+
+static float incbcff( float aa, float bb, float xx )
+{
+float a, b, x, xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
+float k1, k2, k3, k4, k5, k6, k7, k8;
+float r, t, ans;
+static float big = BIG;
+int n;
+
+a = aa;
+b = bb;
+x = xx;
+k1 = a;
+k2 = a + b;
+k3 = a;
+k4 = a + 1.0;
+k5 = 1.0;
+k6 = b - 1.0;
+k7 = k4;
+k8 = a + 2.0;
+
+pkm2 = 0.0;
+qkm2 = 1.0;
+pkm1 = 1.0;
+qkm1 = 1.0;
+ans = 1.0;
+r = 0.0;
+n = 0;
+do
+ {
+
+ xk = -( x * k1 * k2 )/( k3 * k4 );
+ pk = pkm1 + pkm2 * xk;
+ qk = qkm1 + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ xk = ( x * k5 * k6 )/( k7 * k8 );
+ pk = pkm1 + pkm2 * xk;
+ qk = qkm1 + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ if( qk != 0 )
+ r = pk/qk;
+ if( r != 0 )
+ {
+ t = fabsf( (ans - r)/r );
+ ans = r;
+ }
+ else
+ t = 1.0;
+
+ if( t < MACHEPF )
+ goto cdone;
+
+ k1 += 1.0;
+ k2 += 1.0;
+ k3 += 2.0;
+ k4 += 2.0;
+ k5 += 1.0;
+ k6 -= 1.0;
+ k7 += 2.0;
+ k8 += 2.0;
+
+ if( (fabsf(qk) + fabsf(pk)) > big )
+ {
+ pkm2 *= MACHEPF;
+ pkm1 *= MACHEPF;
+ qkm2 *= MACHEPF;
+ qkm1 *= MACHEPF;
+ }
+ if( (fabsf(qk) < MACHEPF) || (fabsf(pk) < MACHEPF) )
+ {
+ pkm2 *= big;
+ pkm1 *= big;
+ qkm2 *= big;
+ qkm1 *= big;
+ }
+ }
+while( ++n < 100 );
+
+cdone:
+return(ans);
+}
+
+
+/* Continued fraction expansion #2
+ * for incomplete beta integral
+ */
+
+static float incbdf( float aa, float bb, float xx )
+{
+float a, b, x, xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
+float k1, k2, k3, k4, k5, k6, k7, k8;
+float r, t, ans, z;
+static float big = BIG;
+int n;
+
+a = aa;
+b = bb;
+x = xx;
+k1 = a;
+k2 = b - 1.0;
+k3 = a;
+k4 = a + 1.0;
+k5 = 1.0;
+k6 = a + b;
+k7 = a + 1.0;;
+k8 = a + 2.0;
+
+pkm2 = 0.0;
+qkm2 = 1.0;
+pkm1 = 1.0;
+qkm1 = 1.0;
+z = x / (1.0-x);
+ans = 1.0;
+r = 0.0;
+n = 0;
+do
+ {
+
+ xk = -( z * k1 * k2 )/( k3 * k4 );
+ pk = pkm1 + pkm2 * xk;
+ qk = qkm1 + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ xk = ( z * k5 * k6 )/( k7 * k8 );
+ pk = pkm1 + pkm2 * xk;
+ qk = qkm1 + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ if( qk != 0 )
+ r = pk/qk;
+ if( r != 0 )
+ {
+ t = fabsf( (ans - r)/r );
+ ans = r;
+ }
+ else
+ t = 1.0;
+
+ if( t < MACHEPF )
+ goto cdone;
+
+ k1 += 1.0;
+ k2 -= 1.0;
+ k3 += 2.0;
+ k4 += 2.0;
+ k5 += 1.0;
+ k6 += 1.0;
+ k7 += 2.0;
+ k8 += 2.0;
+
+ if( (fabsf(qk) + fabsf(pk)) > big )
+ {
+ pkm2 *= MACHEPF;
+ pkm1 *= MACHEPF;
+ qkm2 *= MACHEPF;
+ qkm1 *= MACHEPF;
+ }
+ if( (fabsf(qk) < MACHEPF) || (fabsf(pk) < MACHEPF) )
+ {
+ pkm2 *= big;
+ pkm1 *= big;
+ qkm2 *= big;
+ qkm1 *= big;
+ }
+ }
+while( ++n < 100 );
+
+cdone:
+return(ans);
+}
+
+
+/* power series */
+float incbpsf( float aa, float bb, float xx )
+{
+float a, b, x, t, u, y, s;
+
+a = aa;
+b = bb;
+x = xx;
+
+y = a * logf(x) + (b-1.0)*logf(1.0-x) - logf(a);
+y -= lgamf(a) + lgamf(b);
+y += lgamf(a+b);
+
+
+t = x / (1.0 - x);
+s = 0.0;
+u = 1.0;
+do
+ {
+ b -= 1.0;
+ if( b == 0.0 )
+ break;
+ a += 1.0;
+ u *= t*b/a;
+ s += u;
+ }
+while( fabsf(u) > MACHEPF );
+
+if( y < MINLOGF )
+ {
+ mtherr( "incbetf", UNDERFLOW );
+ s = 0.0;
+ }
+else
+ s = expf(y) * (1.0 + s);
+/*printf( "incbpsf: %.4e\n", s );*/
+return(s);
+}
diff --git a/libm/float/incbif.c b/libm/float/incbif.c
new file mode 100644
index 000000000..4d8c0652e
--- /dev/null
+++ b/libm/float/incbif.c
@@ -0,0 +1,197 @@
+/* incbif()
+ *
+ * Inverse of imcomplete beta integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, b, x, y, incbif();
+ *
+ * x = incbif( a, b, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given y, the function finds x such that
+ *
+ * incbet( a, b, x ) = y.
+ *
+ * the routine performs up to 10 Newton iterations to find the
+ * root of incbet(a,b,x) - y = 0.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * x a,b
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0,1 0,100 5000 2.8e-4 8.3e-6
+ *
+ * Overflow and larger errors may occur for one of a or b near zero
+ * and the other large.
+ */
+
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+extern float MACHEPF, MINLOGF;
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#ifdef ANSIC
+float incbetf(float, float, float);
+float ndtrif(float), expf(float), logf(float), sqrtf(float), lgamf(float);
+#else
+float incbetf();
+float ndtrif(), expf(), logf(), sqrtf(), lgamf();
+#endif
+
+float incbif( float aaa, float bbb, float yyy0 )
+{
+float aa, bb, yy0, a, b, y0;
+float d, y, x, x0, x1, lgm, yp, di;
+int i, rflg;
+
+
+aa = aaa;
+bb = bbb;
+yy0 = yyy0;
+if( yy0 <= 0 )
+ return(0.0);
+if( yy0 >= 1.0 )
+ return(1.0);
+
+/* approximation to inverse function */
+
+yp = -ndtrif(yy0);
+
+if( yy0 > 0.5 )
+ {
+ rflg = 1;
+ a = bb;
+ b = aa;
+ y0 = 1.0 - yy0;
+ yp = -yp;
+ }
+else
+ {
+ rflg = 0;
+ a = aa;
+ b = bb;
+ y0 = yy0;
+ }
+
+
+if( (aa <= 1.0) || (bb <= 1.0) )
+ {
+ y = 0.5 * yp * yp;
+ }
+else
+ {
+ lgm = (yp * yp - 3.0)* 0.16666666666666667;
+ x0 = 2.0/( 1.0/(2.0*a-1.0) + 1.0/(2.0*b-1.0) );
+ y = yp * sqrtf( x0 + lgm ) / x0
+ - ( 1.0/(2.0*b-1.0) - 1.0/(2.0*a-1.0) )
+ * (lgm + 0.833333333333333333 - 2.0/(3.0*x0));
+ y = 2.0 * y;
+ if( y < MINLOGF )
+ {
+ x0 = 1.0;
+ goto under;
+ }
+ }
+
+x = a/( a + b * expf(y) );
+y = incbetf( a, b, x );
+yp = (y - y0)/y0;
+if( fabsf(yp) < 0.1 )
+ goto newt;
+
+/* Resort to interval halving if not close enough */
+x0 = 0.0;
+x1 = 1.0;
+di = 0.5;
+
+for( i=0; i<20; i++ )
+ {
+ if( i != 0 )
+ {
+ x = di * x1 + (1.0-di) * x0;
+ y = incbetf( a, b, x );
+ yp = (y - y0)/y0;
+ if( fabsf(yp) < 1.0e-3 )
+ goto newt;
+ }
+
+ if( y < y0 )
+ {
+ x0 = x;
+ di = 0.5;
+ }
+ else
+ {
+ x1 = x;
+ di *= di;
+ if( di == 0.0 )
+ di = 0.5;
+ }
+ }
+
+if( x0 == 0.0 )
+ {
+under:
+ mtherr( "incbif", UNDERFLOW );
+ goto done;
+ }
+
+newt:
+
+x0 = x;
+lgm = lgamf(a+b) - lgamf(a) - lgamf(b);
+
+for( i=0; i<10; i++ )
+ {
+/* compute the function at this point */
+ if( i != 0 )
+ y = incbetf(a,b,x0);
+/* compute the derivative of the function at this point */
+ d = (a - 1.0) * logf(x0) + (b - 1.0) * logf(1.0-x0) + lgm;
+ if( d < MINLOGF )
+ {
+ x0 = 0.0;
+ goto under;
+ }
+ d = expf(d);
+/* compute the step to the next approximation of x */
+ d = (y - y0)/d;
+ x = x0;
+ x0 = x0 - d;
+ if( x0 <= 0.0 )
+ {
+ x0 = 0.0;
+ goto under;
+ }
+ if( x0 >= 1.0 )
+ {
+ x0 = 1.0;
+ goto under;
+ }
+ if( i < 2 )
+ continue;
+ if( fabsf(d/x0) < 256.0 * MACHEPF )
+ goto done;
+ }
+
+done:
+if( rflg )
+ x0 = 1.0 - x0;
+return( x0 );
+}
diff --git a/libm/float/ivf.c b/libm/float/ivf.c
new file mode 100644
index 000000000..b7ab2b619
--- /dev/null
+++ b/libm/float/ivf.c
@@ -0,0 +1,114 @@
+/* ivf.c
+ *
+ * Modified Bessel function of noninteger order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float v, x, y, ivf();
+ *
+ * y = ivf( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of order v of the
+ * argument. If x is negative, v must be integer valued.
+ *
+ * The function is defined as Iv(x) = Jv( ix ). It is
+ * here computed in terms of the confluent hypergeometric
+ * function, according to the formula
+ *
+ * v -x
+ * Iv(x) = (x/2) e hyperg( v+0.5, 2v+1, 2x ) / gamma(v+1)
+ *
+ * If v is a negative integer, then v is replaced by -v.
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (v, x), with v between 0 and
+ * 30, x between 0 and 28.
+ * arithmetic domain # trials peak rms
+ * Relative error:
+ * IEEE 0,15 3000 4.7e-6 5.4e-7
+ * Absolute error (relative when function > 1)
+ * IEEE 0,30 5000 8.5e-6 1.3e-6
+ *
+ * Accuracy is diminished if v is near a negative integer.
+ * The useful domain for relative error is limited by overflow
+ * of the single precision exponential function.
+ *
+ * See also hyperg.c.
+ *
+ */
+ /* iv.c */
+/* Modified Bessel function of noninteger order */
+/* If x < 0, then v must be an integer. */
+
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+extern float MAXNUMF;
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+float hypergf(float, float, float);
+float expf(float), gammaf(float), logf(float), floorf(float);
+
+float ivf( float v, float x )
+{
+int sign;
+float t, ax;
+
+/* If v is a negative integer, invoke symmetry */
+t = floorf(v);
+if( v < 0.0 )
+ {
+ if( t == v )
+ {
+ v = -v; /* symmetry */
+ t = -t;
+ }
+ }
+/* If x is negative, require v to be an integer */
+sign = 1;
+if( x < 0.0 )
+ {
+ if( t != v )
+ {
+ mtherr( "ivf", DOMAIN );
+ return( 0.0 );
+ }
+ if( v != 2.0 * floorf(v/2.0) )
+ sign = -1;
+ }
+
+/* Avoid logarithm singularity */
+if( x == 0.0 )
+ {
+ if( v == 0.0 )
+ return( 1.0 );
+ if( v < 0.0 )
+ {
+ mtherr( "ivf", OVERFLOW );
+ return( MAXNUMF );
+ }
+ else
+ return( 0.0 );
+ }
+
+ax = fabsf(x);
+t = v * logf( 0.5 * ax ) - x;
+t = sign * expf(t) / gammaf( v + 1.0 );
+ax = v + 0.5;
+return( t * hypergf( ax, 2.0 * ax, 2.0 * x ) );
+}
diff --git a/libm/float/j0f.c b/libm/float/j0f.c
new file mode 100644
index 000000000..2b0d4a5a4
--- /dev/null
+++ b/libm/float/j0f.c
@@ -0,0 +1,228 @@
+/* j0f.c
+ *
+ * Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, j0f();
+ *
+ * y = j0f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order zero of the argument.
+ *
+ * The domain is divided into the intervals [0, 2] and
+ * (2, infinity). In the first interval the following polynomial
+ * approximation is used:
+ *
+ *
+ * 2 2 2
+ * (w - r ) (w - r ) (w - r ) P(w)
+ * 1 2 3
+ *
+ * 2
+ * where w = x and the three r's are zeros of the function.
+ *
+ * In the second interval, the modulus and phase are approximated
+ * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
+ * and Phase(x) = x + 1/x R(1/x^2) - pi/4. The function is
+ *
+ * j0(x) = Modulus(x) cos( Phase(x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 2 100000 1.3e-7 3.6e-8
+ * IEEE 2, 32 100000 1.9e-7 5.4e-8
+ *
+ */
+ /* y0f.c
+ *
+ * Bessel function of the second kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, y0f();
+ *
+ * y = y0f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind, of order
+ * zero, of the argument.
+ *
+ * The domain is divided into the intervals [0, 2] and
+ * (2, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute
+ *
+ * 2 2 2
+ * y0(x) = (w - r ) (w - r ) (w - r ) R(x) + 2/pi ln(x) j0(x).
+ * 1 2 3
+ *
+ * Thus a call to j0() is required. The three zeros are removed
+ * from R(x) to improve its numerical stability.
+ *
+ * In the second interval, the modulus and phase are approximated
+ * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
+ * and Phase(x) = x + 1/x S(1/x^2) - pi/4. Then the function is
+ *
+ * y0(x) = Modulus(x) sin( Phase(x) ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error, when y0(x) < 1; else relative error:
+ *
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 2 100000 2.4e-7 3.4e-8
+ * IEEE 2, 32 100000 1.8e-7 5.3e-8
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+static float MO[8] = {
+-6.838999669318810E-002f,
+ 1.864949361379502E-001f,
+-2.145007480346739E-001f,
+ 1.197549369473540E-001f,
+-3.560281861530129E-003f,
+-4.969382655296620E-002f,
+-3.355424622293709E-006f,
+ 7.978845717621440E-001f
+};
+
+static float PH[8] = {
+ 3.242077816988247E+001f,
+-3.630592630518434E+001f,
+ 1.756221482109099E+001f,
+-4.974978466280903E+000f,
+ 1.001973420681837E+000f,
+-1.939906941791308E-001f,
+ 6.490598792654666E-002f,
+-1.249992184872738E-001f
+};
+
+static float YP[5] = {
+ 9.454583683980369E-008f,
+-9.413212653797057E-006f,
+ 5.344486707214273E-004f,
+-1.584289289821316E-002f,
+ 1.707584643733568E-001f
+};
+
+float YZ1 = 0.43221455686510834878f;
+float YZ2 = 22.401876406482861405f;
+float YZ3 = 64.130620282338755553f;
+
+static float DR1 = 5.78318596294678452118f;
+/*
+static float DR2 = 30.4712623436620863991;
+static float DR3 = 74.887006790695183444889;
+*/
+
+static float JP[5] = {
+-6.068350350393235E-008f,
+ 6.388945720783375E-006f,
+-3.969646342510940E-004f,
+ 1.332913422519003E-002f,
+-1.729150680240724E-001f
+};
+extern float PIO4F;
+
+
+float polevlf(float, float *, int);
+float logf(float), sinf(float), cosf(float), sqrtf(float);
+
+float j0f( float xx )
+{
+float x, w, z, p, q, xn;
+
+
+if( xx < 0 )
+ x = -xx;
+else
+ x = xx;
+
+if( x <= 2.0f )
+ {
+ z = x * x;
+ if( x < 1.0e-3f )
+ return( 1.0f - 0.25f*z );
+
+ p = (z-DR1) * polevlf( z, JP, 4);
+ return( p );
+ }
+
+q = 1.0f/x;
+w = sqrtf(q);
+
+p = w * polevlf( q, MO, 7);
+w = q*q;
+xn = q * polevlf( w, PH, 7) - PIO4F;
+p = p * cosf(xn + x);
+return(p);
+}
+
+/* y0() 2 */
+/* Bessel function of second kind, order zero */
+
+/* Rational approximation coefficients YP[] are used for x < 6.5.
+ * The function computed is y0(x) - 2 ln(x) j0(x) / pi,
+ * whose value at x = 0 is 2 * ( log(0.5) + EUL ) / pi
+ * = 0.073804295108687225 , EUL is Euler's constant.
+ */
+
+static float TWOOPI = 0.636619772367581343075535f; /* 2/pi */
+extern float MAXNUMF;
+
+float y0f( float xx )
+{
+float x, w, z, p, q, xn;
+
+
+x = xx;
+if( x <= 2.0f )
+ {
+ if( x <= 0.0f )
+ {
+ mtherr( "y0f", DOMAIN );
+ return( -MAXNUMF );
+ }
+ z = x * x;
+/* w = (z-YZ1)*(z-YZ2)*(z-YZ3) * polevlf( z, YP, 4);*/
+ w = (z-YZ1) * polevlf( z, YP, 4);
+ w += TWOOPI * logf(x) * j0f(x);
+ return( w );
+ }
+
+q = 1.0f/x;
+w = sqrtf(q);
+
+p = w * polevlf( q, MO, 7);
+w = q*q;
+xn = q * polevlf( w, PH, 7) - PIO4F;
+p = p * sinf(xn + x);
+return( p );
+}
diff --git a/libm/float/j0tst.c b/libm/float/j0tst.c
new file mode 100644
index 000000000..e5a5607d7
--- /dev/null
+++ b/libm/float/j0tst.c
@@ -0,0 +1,43 @@
+float z[20] = {
+2.4048254489898681641,
+5.5200781822204589844,
+8.6537275314331054687,
+11.791533470153808594,
+14.930917739868164062,
+18.071063995361328125,
+21.211637496948242188,
+24.352472305297851563,
+27.493478775024414062,
+30.634607315063476562,
+33.775821685791015625,
+36.9170989990234375,
+40.0584259033203125,
+43.19979095458984375,
+46.3411865234375,
+49.482608795166015625,
+52.624050140380859375,
+55.76551055908203125,
+58.906982421875,
+62.04846954345703125,
+};
+
+/* #if ANSIC */
+#if __STDC__
+float j0f(float);
+#else
+float j0f();
+#endif
+
+int main()
+{
+float y;
+int i;
+
+for (i = 0; i< 20; i++)
+ {
+ y = j0f(z[i]);
+ printf("%.9e\n", y);
+ }
+exit(0);
+}
+
diff --git a/libm/float/j1f.c b/libm/float/j1f.c
new file mode 100644
index 000000000..4306e9747
--- /dev/null
+++ b/libm/float/j1f.c
@@ -0,0 +1,211 @@
+/* j1f.c
+ *
+ * Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, j1f();
+ *
+ * y = j1f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order one of the argument.
+ *
+ * The domain is divided into the intervals [0, 2] and
+ * (2, infinity). In the first interval a polynomial approximation
+ * 2
+ * (w - r ) x P(w)
+ * 1
+ * 2
+ * is used, where w = x and r is the first zero of the function.
+ *
+ * In the second interval, the modulus and phase are approximated
+ * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
+ * and Phase(x) = x + 1/x R(1/x^2) - 3pi/4. The function is
+ *
+ * j0(x) = Modulus(x) cos( Phase(x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 2 100000 1.2e-7 2.5e-8
+ * IEEE 2, 32 100000 2.0e-7 5.3e-8
+ *
+ *
+ */
+ /* y1.c
+ *
+ * Bessel function of second kind of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y1();
+ *
+ * y = y1( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind of order one
+ * of the argument.
+ *
+ * The domain is divided into the intervals [0, 2] and
+ * (2, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute
+ *
+ * 2
+ * y0(x) = (w - r ) x R(x^2) + 2/pi (ln(x) j1(x) - 1/x) .
+ * 1
+ *
+ * Thus a call to j1() is required.
+ *
+ * In the second interval, the modulus and phase are approximated
+ * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
+ * and Phase(x) = x + 1/x S(1/x^2) - 3pi/4. Then the function is
+ *
+ * y0(x) = Modulus(x) sin( Phase(x) ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 2 100000 2.2e-7 4.6e-8
+ * IEEE 2, 32 100000 1.9e-7 5.3e-8
+ *
+ * (error criterion relative when |y1| > 1).
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+
+static float JP[5] = {
+-4.878788132172128E-009f,
+ 6.009061827883699E-007f,
+-4.541343896997497E-005f,
+ 1.937383947804541E-003f,
+-3.405537384615824E-002f
+};
+
+static float YP[5] = {
+ 8.061978323326852E-009f,
+-9.496460629917016E-007f,
+ 6.719543806674249E-005f,
+-2.641785726447862E-003f,
+ 4.202369946500099E-002f
+};
+
+static float MO1[8] = {
+ 6.913942741265801E-002f,
+-2.284801500053359E-001f,
+ 3.138238455499697E-001f,
+-2.102302420403875E-001f,
+ 5.435364690523026E-003f,
+ 1.493389585089498E-001f,
+ 4.976029650847191E-006f,
+ 7.978845453073848E-001f
+};
+
+static float PH1[8] = {
+-4.497014141919556E+001f,
+ 5.073465654089319E+001f,
+-2.485774108720340E+001f,
+ 7.222973196770240E+000f,
+-1.544842782180211E+000f,
+ 3.503787691653334E-001f,
+-1.637986776941202E-001f,
+ 3.749989509080821E-001f
+};
+
+static float YO1 = 4.66539330185668857532f;
+static float Z1 = 1.46819706421238932572E1f;
+
+static float THPIO4F = 2.35619449019234492885f; /* 3*pi/4 */
+static float TWOOPI = 0.636619772367581343075535f; /* 2/pi */
+extern float PIO4;
+
+
+float polevlf(float, float *, int);
+float logf(float), sinf(float), cosf(float), sqrtf(float);
+
+float j1f( float xx )
+{
+float x, w, z, p, q, xn;
+
+
+x = xx;
+if( x < 0 )
+ x = -xx;
+
+if( x <= 2.0f )
+ {
+ z = x * x;
+ p = (z-Z1) * x * polevlf( z, JP, 4 );
+ return( p );
+ }
+
+q = 1.0f/x;
+w = sqrtf(q);
+
+p = w * polevlf( q, MO1, 7);
+w = q*q;
+xn = q * polevlf( w, PH1, 7) - THPIO4F;
+p = p * cosf(xn + x);
+return(p);
+}
+
+
+
+
+extern float MAXNUMF;
+
+float y1f( float xx )
+{
+float x, w, z, p, q, xn;
+
+
+x = xx;
+if( x <= 2.0f )
+ {
+ if( x <= 0.0f )
+ {
+ mtherr( "y1f", DOMAIN );
+ return( -MAXNUMF );
+ }
+ z = x * x;
+ w = (z - YO1) * x * polevlf( z, YP, 4 );
+ w += TWOOPI * ( j1f(x) * logf(x) - 1.0f/x );
+ return( w );
+ }
+
+q = 1.0f/x;
+w = sqrtf(q);
+
+p = w * polevlf( q, MO1, 7);
+w = q*q;
+xn = q * polevlf( w, PH1, 7) - THPIO4F;
+p = p * sinf(xn + x);
+return(p);
+}
diff --git a/libm/float/jnf.c b/libm/float/jnf.c
new file mode 100644
index 000000000..de358e0ef
--- /dev/null
+++ b/libm/float/jnf.c
@@ -0,0 +1,124 @@
+/* jnf.c
+ *
+ * Bessel function of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * float x, y, jnf();
+ *
+ * y = jnf( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The ratio of jn(x) to j0(x) is computed by backward
+ * recurrence. First the ratio jn/jn-1 is found by a
+ * continued fraction expansion. Then the recurrence
+ * relating successive orders is applied until j0 or j1 is
+ * reached.
+ *
+ * If n = 0 or 1 the routine for j0 or j1 is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic range # trials peak rms
+ * IEEE 0, 15 30000 3.6e-7 3.6e-8
+ *
+ *
+ * Not suitable for large n or x. Use jvf() instead.
+ *
+ */
+
+/* jn.c
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+#include <math.h>
+
+extern float MACHEPF;
+
+float j0f(float), j1f(float);
+
+float jnf( int n, float xx )
+{
+float x, pkm2, pkm1, pk, xk, r, ans, xinv, sign;
+int k;
+
+x = xx;
+sign = 1.0;
+if( n < 0 )
+ {
+ n = -n;
+ if( (n & 1) != 0 ) /* -1**n */
+ sign = -1.0;
+ }
+
+if( n == 0 )
+ return( sign * j0f(x) );
+if( n == 1 )
+ return( sign * j1f(x) );
+if( n == 2 )
+ return( sign * (2.0 * j1f(x) / x - j0f(x)) );
+
+/*
+if( x < MACHEPF )
+ return( 0.0 );
+*/
+
+/* continued fraction */
+k = 24;
+pk = 2 * (n + k);
+ans = pk;
+xk = x * x;
+
+do
+ {
+ pk -= 2.0;
+ ans = pk - (xk/ans);
+ }
+while( --k > 0 );
+/*ans = x/ans;*/
+
+/* backward recurrence */
+
+pk = 1.0;
+/*pkm1 = 1.0/ans;*/
+xinv = 1.0/x;
+pkm1 = ans * xinv;
+k = n-1;
+r = (float )(2 * k);
+
+do
+ {
+ pkm2 = (pkm1 * r - pk * x) * xinv;
+ pk = pkm1;
+ pkm1 = pkm2;
+ r -= 2.0;
+ }
+while( --k > 0 );
+
+r = pk;
+if( r < 0 )
+ r = -r;
+ans = pkm1;
+if( ans < 0 )
+ ans = -ans;
+
+if( r > ans ) /* if( fabs(pk) > fabs(pkm1) ) */
+ ans = sign * j1f(x)/pk;
+else
+ ans = sign * j0f(x)/pkm1;
+return( ans );
+}
diff --git a/libm/float/jvf.c b/libm/float/jvf.c
new file mode 100644
index 000000000..268a8e4eb
--- /dev/null
+++ b/libm/float/jvf.c
@@ -0,0 +1,848 @@
+/* jvf.c
+ *
+ * Bessel function of noninteger order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float v, x, y, jvf();
+ *
+ * y = jvf( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order v of the argument,
+ * where v is real. Negative x is allowed if v is an integer.
+ *
+ * Several expansions are included: the ascending power
+ * series, the Hankel expansion, and two transitional
+ * expansions for large v. If v is not too large, it
+ * is reduced by recurrence to a region of best accuracy.
+ *
+ * The single precision routine accepts negative v, but with
+ * reduced accuracy.
+ *
+ *
+ *
+ * ACCURACY:
+ * Results for integer v are indicated by *.
+ * Error criterion is absolute, except relative when |jv()| > 1.
+ *
+ * arithmetic domain # trials peak rms
+ * v x
+ * IEEE 0,125 0,125 30000 2.0e-6 2.0e-7
+ * IEEE -17,0 0,125 30000 1.1e-5 4.0e-7
+ * IEEE -100,0 0,125 3000 1.5e-4 7.8e-6
+ */
+
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+#define DEBUG 0
+
+extern float MAXNUMF, MACHEPF, MINLOGF, MAXLOGF, PIF;
+extern int sgngamf;
+
+/* BIG = 1/MACHEPF */
+#define BIG 16777216.
+
+#ifdef ANSIC
+float floorf(float), j0f(float), j1f(float);
+static float jnxf(float, float);
+static float jvsf(float, float);
+static float hankelf(float, float);
+static float jntf(float, float);
+static float recurf( float *, float, float * );
+float sqrtf(float), sinf(float), cosf(float);
+float lgamf(float), expf(float), logf(float), powf(float, float);
+float gammaf(float), cbrtf(float), acosf(float);
+int airyf(float, float *, float *, float *, float *);
+float polevlf(float, float *, int);
+#else
+float floorf(), j0f(), j1f();
+float sqrtf(), sinf(), cosf();
+float lgamf(), expf(), logf(), powf(), gammaf();
+float cbrtf(), polevlf(), acosf();
+void airyf();
+static float recurf(), jvsf(), hankelf(), jnxf(), jntf(), jvsf();
+#endif
+
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+float jvf( float nn, float xx )
+{
+float n, x, k, q, t, y, an, sign;
+int i, nint;
+
+n = nn;
+x = xx;
+nint = 0; /* Flag for integer n */
+sign = 1.0; /* Flag for sign inversion */
+an = fabsf( n );
+y = floorf( an );
+if( y == an )
+ {
+ nint = 1;
+ i = an - 16384.0 * floorf( an/16384.0 );
+ if( n < 0.0 )
+ {
+ if( i & 1 )
+ sign = -sign;
+ n = an;
+ }
+ if( x < 0.0 )
+ {
+ if( i & 1 )
+ sign = -sign;
+ x = -x;
+ }
+ if( n == 0.0 )
+ return( j0f(x) );
+ if( n == 1.0 )
+ return( sign * j1f(x) );
+ }
+
+if( (x < 0.0) && (y != an) )
+ {
+ mtherr( "jvf", DOMAIN );
+ y = 0.0;
+ goto done;
+ }
+
+y = fabsf(x);
+
+if( y < MACHEPF )
+ goto underf;
+
+/* Easy cases - x small compared to n */
+t = 3.6 * sqrtf(an);
+if( y < t )
+ return( sign * jvsf(n,x) );
+
+/* x large compared to n */
+k = 3.6 * sqrtf(y);
+if( (an < k) && (y > 6.0) )
+ return( sign * hankelf(n,x) );
+
+if( (n > -100) && (n < 14.0) )
+ {
+/* Note: if x is too large, the continued
+ * fraction will fail; but then the
+ * Hankel expansion can be used.
+ */
+ if( nint != 0 )
+ {
+ k = 0.0;
+ q = recurf( &n, x, &k );
+ if( k == 0.0 )
+ {
+ y = j0f(x)/q;
+ goto done;
+ }
+ if( k == 1.0 )
+ {
+ y = j1f(x)/q;
+ goto done;
+ }
+ }
+
+ if( n >= 0.0 )
+ {
+/* Recur backwards from a larger value of n
+ */
+ if( y > 1.3 * an )
+ goto recurdwn;
+ if( an > 1.3 * y )
+ goto recurdwn;
+ k = n;
+ y = 2.0*(y+an+1.0);
+ if( (y - n) > 33.0 )
+ y = n + 33.0;
+ y = n + floorf(y-n);
+ q = recurf( &y, x, &k );
+ y = jvsf(y,x) * q;
+ goto done;
+ }
+recurdwn:
+ if( an > (k + 3.0) )
+ {
+/* Recur backwards from n to k
+ */
+ if( n < 0.0 )
+ k = -k;
+ q = n - floorf(n);
+ k = floorf(k) + q;
+ if( n > 0.0 )
+ q = recurf( &n, x, &k );
+ else
+ {
+ t = k;
+ k = n;
+ q = recurf( &t, x, &k );
+ k = t;
+ }
+ if( q == 0.0 )
+ {
+underf:
+ y = 0.0;
+ goto done;
+ }
+ }
+ else
+ {
+ k = n;
+ q = 1.0;
+ }
+
+/* boundary between convergence of
+ * power series and Hankel expansion
+ */
+ t = fabsf(k);
+ if( t < 26.0 )
+ t = (0.0083*t + 0.09)*t + 12.9;
+ else
+ t = 0.9 * t;
+
+ if( y > t ) /* y = |x| */
+ y = hankelf(k,x);
+ else
+ y = jvsf(k,x);
+#if DEBUG
+printf( "y = %.16e, q = %.16e\n", y, q );
+#endif
+ if( n > 0.0 )
+ y /= q;
+ else
+ y *= q;
+ }
+
+else
+ {
+/* For large positive n, use the uniform expansion
+ * or the transitional expansion.
+ * But if x is of the order of n**2,
+ * these may blow up, whereas the
+ * Hankel expansion will then work.
+ */
+ if( n < 0.0 )
+ {
+ mtherr( "jvf", TLOSS );
+ y = 0.0;
+ goto done;
+ }
+ t = y/an;
+ t /= an;
+ if( t > 0.3 )
+ y = hankelf(n,x);
+ else
+ y = jnxf(n,x);
+ }
+
+done: return( sign * y);
+}
+
+/* Reduce the order by backward recurrence.
+ * AMS55 #9.1.27 and 9.1.73.
+ */
+
+static float recurf( float *n, float xx, float *newn )
+{
+float x, pkm2, pkm1, pk, pkp1, qkm2, qkm1;
+float k, ans, qk, xk, yk, r, t, kf, xinv;
+static float big = BIG;
+int nflag, ctr;
+
+x = xx;
+/* continued fraction for Jn(x)/Jn-1(x) */
+if( *n < 0.0 )
+ nflag = 1;
+else
+ nflag = 0;
+
+fstart:
+
+#if DEBUG
+printf( "n = %.6e, newn = %.6e, cfrac = ", *n, *newn );
+#endif
+
+pkm2 = 0.0;
+qkm2 = 1.0;
+pkm1 = x;
+qkm1 = *n + *n;
+xk = -x * x;
+yk = qkm1;
+ans = 1.0;
+ctr = 0;
+do
+ {
+ yk += 2.0;
+ pk = pkm1 * yk + pkm2 * xk;
+ qk = qkm1 * yk + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+ if( qk != 0 )
+ r = pk/qk;
+ else
+ r = 0.0;
+ if( r != 0 )
+ {
+ t = fabsf( (ans - r)/r );
+ ans = r;
+ }
+ else
+ t = 1.0;
+
+ if( t < MACHEPF )
+ goto done;
+
+ if( fabsf(pk) > big )
+ {
+ pkm2 *= MACHEPF;
+ pkm1 *= MACHEPF;
+ qkm2 *= MACHEPF;
+ qkm1 *= MACHEPF;
+ }
+ }
+while( t > MACHEPF );
+
+done:
+
+#if DEBUG
+printf( "%.6e\n", ans );
+#endif
+
+/* Change n to n-1 if n < 0 and the continued fraction is small
+ */
+if( nflag > 0 )
+ {
+ if( fabsf(ans) < 0.125 )
+ {
+ nflag = -1;
+ *n = *n - 1.0;
+ goto fstart;
+ }
+ }
+
+
+kf = *newn;
+
+/* backward recurrence
+ * 2k
+ * J (x) = --- J (x) - J (x)
+ * k-1 x k k+1
+ */
+
+pk = 1.0;
+pkm1 = 1.0/ans;
+k = *n - 1.0;
+r = 2 * k;
+xinv = 1.0/x;
+do
+ {
+ pkm2 = (pkm1 * r - pk * x) * xinv;
+ pkp1 = pk;
+ pk = pkm1;
+ pkm1 = pkm2;
+ r -= 2.0;
+#if 0
+ t = fabsf(pkp1) + fabsf(pk);
+ if( (k > (kf + 2.5)) && (fabsf(pkm1) < 0.25*t) )
+ {
+ k -= 1.0;
+ t = x*x;
+ pkm2 = ( (r*(r+2.0)-t)*pk - r*x*pkp1 )/t;
+ pkp1 = pk;
+ pk = pkm1;
+ pkm1 = pkm2;
+ r -= 2.0;
+ }
+#endif
+ k -= 1.0;
+ }
+while( k > (kf + 0.5) );
+
+#if 0
+/* Take the larger of the last two iterates
+ * on the theory that it may have less cancellation error.
+ */
+if( (kf >= 0.0) && (fabsf(pk) > fabsf(pkm1)) )
+ {
+ k += 1.0;
+ pkm2 = pk;
+ }
+#endif
+
+*newn = k;
+#if DEBUG
+printf( "newn %.6e\n", k );
+#endif
+return( pkm2 );
+}
+
+
+
+/* Ascending power series for Jv(x).
+ * AMS55 #9.1.10.
+ */
+
+static float jvsf( float nn, float xx )
+{
+float n, x, t, u, y, z, k, ay;
+
+#if DEBUG
+printf( "jvsf: " );
+#endif
+n = nn;
+x = xx;
+z = -0.25 * x * x;
+u = 1.0;
+y = u;
+k = 1.0;
+t = 1.0;
+
+while( t > MACHEPF )
+ {
+ u *= z / (k * (n+k));
+ y += u;
+ k += 1.0;
+ t = fabsf(u);
+ if( (ay = fabsf(y)) > 1.0 )
+ t /= ay;
+ }
+
+if( x < 0.0 )
+ {
+ y = y * powf( 0.5 * x, n ) / gammaf( n + 1.0 );
+ }
+else
+ {
+ t = n * logf(0.5*x) - lgamf(n + 1.0);
+ if( t < -MAXLOGF )
+ {
+ return( 0.0 );
+ }
+ if( t > MAXLOGF )
+ {
+ t = logf(y) + t;
+ if( t > MAXLOGF )
+ {
+ mtherr( "jvf", OVERFLOW );
+ return( MAXNUMF );
+ }
+ else
+ {
+ y = sgngamf * expf(t);
+ return(y);
+ }
+ }
+ y = sgngamf * y * expf( t );
+ }
+#if DEBUG
+printf( "y = %.8e\n", y );
+#endif
+return(y);
+}
+
+/* Hankel's asymptotic expansion
+ * for large x.
+ * AMS55 #9.2.5.
+ */
+static float hankelf( float nn, float xx )
+{
+float n, x, t, u, z, k, sign, conv;
+float p, q, j, m, pp, qq;
+int flag;
+
+#if DEBUG
+printf( "hankelf: " );
+#endif
+n = nn;
+x = xx;
+m = 4.0*n*n;
+j = 1.0;
+z = 8.0 * x;
+k = 1.0;
+p = 1.0;
+u = (m - 1.0)/z;
+q = u;
+sign = 1.0;
+conv = 1.0;
+flag = 0;
+t = 1.0;
+pp = 1.0e38;
+qq = 1.0e38;
+
+while( t > MACHEPF )
+ {
+ k += 2.0;
+ j += 1.0;
+ sign = -sign;
+ u *= (m - k * k)/(j * z);
+ p += sign * u;
+ k += 2.0;
+ j += 1.0;
+ u *= (m - k * k)/(j * z);
+ q += sign * u;
+ t = fabsf(u/p);
+ if( t < conv )
+ {
+ conv = t;
+ qq = q;
+ pp = p;
+ flag = 1;
+ }
+/* stop if the terms start getting larger */
+ if( (flag != 0) && (t > conv) )
+ {
+#if DEBUG
+ printf( "Hankel: convergence to %.4E\n", conv );
+#endif
+ goto hank1;
+ }
+ }
+
+hank1:
+u = x - (0.5*n + 0.25) * PIF;
+t = sqrtf( 2.0/(PIF*x) ) * ( pp * cosf(u) - qq * sinf(u) );
+return( t );
+}
+
+
+/* Asymptotic expansion for large n.
+ * AMS55 #9.3.35.
+ */
+
+static float lambda[] = {
+ 1.0,
+ 1.041666666666666666666667E-1,
+ 8.355034722222222222222222E-2,
+ 1.282265745563271604938272E-1,
+ 2.918490264641404642489712E-1,
+ 8.816272674437576524187671E-1,
+ 3.321408281862767544702647E+0,
+ 1.499576298686255465867237E+1,
+ 7.892301301158651813848139E+1,
+ 4.744515388682643231611949E+2,
+ 3.207490090890661934704328E+3
+};
+static float mu[] = {
+ 1.0,
+ -1.458333333333333333333333E-1,
+ -9.874131944444444444444444E-2,
+ -1.433120539158950617283951E-1,
+ -3.172272026784135480967078E-1,
+ -9.424291479571202491373028E-1,
+ -3.511203040826354261542798E+0,
+ -1.572726362036804512982712E+1,
+ -8.228143909718594444224656E+1,
+ -4.923553705236705240352022E+2,
+ -3.316218568547972508762102E+3
+};
+static float P1[] = {
+ -2.083333333333333333333333E-1,
+ 1.250000000000000000000000E-1
+};
+static float P2[] = {
+ 3.342013888888888888888889E-1,
+ -4.010416666666666666666667E-1,
+ 7.031250000000000000000000E-2
+};
+static float P3[] = {
+ -1.025812596450617283950617E+0,
+ 1.846462673611111111111111E+0,
+ -8.912109375000000000000000E-1,
+ 7.324218750000000000000000E-2
+};
+static float P4[] = {
+ 4.669584423426247427983539E+0,
+ -1.120700261622299382716049E+1,
+ 8.789123535156250000000000E+0,
+ -2.364086914062500000000000E+0,
+ 1.121520996093750000000000E-1
+};
+static float P5[] = {
+ -2.8212072558200244877E1,
+ 8.4636217674600734632E1,
+ -9.1818241543240017361E1,
+ 4.2534998745388454861E1,
+ -7.3687943594796316964E0,
+ 2.27108001708984375E-1
+};
+static float P6[] = {
+ 2.1257013003921712286E2,
+ -7.6525246814118164230E2,
+ 1.0599904525279998779E3,
+ -6.9957962737613254123E2,
+ 2.1819051174421159048E2,
+ -2.6491430486951555525E1,
+ 5.7250142097473144531E-1
+};
+static float P7[] = {
+ -1.9194576623184069963E3,
+ 8.0617221817373093845E3,
+ -1.3586550006434137439E4,
+ 1.1655393336864533248E4,
+ -5.3056469786134031084E3,
+ 1.2009029132163524628E3,
+ -1.0809091978839465550E2,
+ 1.7277275025844573975E0
+};
+
+
+static float jnxf( float nn, float xx )
+{
+float n, x, zeta, sqz, zz, zp, np;
+float cbn, n23, t, z, sz;
+float pp, qq, z32i, zzi;
+float ak, bk, akl, bkl;
+int sign, doa, dob, nflg, k, s, tk, tkp1, m;
+static float u[8];
+static float ai, aip, bi, bip;
+
+n = nn;
+x = xx;
+/* Test for x very close to n.
+ * Use expansion for transition region if so.
+ */
+cbn = cbrtf(n);
+z = (x - n)/cbn;
+if( (fabsf(z) <= 0.7) || (n < 0.0) )
+ return( jntf(n,x) );
+z = x/n;
+zz = 1.0 - z*z;
+if( zz == 0.0 )
+ return(0.0);
+
+if( zz > 0.0 )
+ {
+ sz = sqrtf( zz );
+ t = 1.5 * (logf( (1.0+sz)/z ) - sz ); /* zeta ** 3/2 */
+ zeta = cbrtf( t * t );
+ nflg = 1;
+ }
+else
+ {
+ sz = sqrtf(-zz);
+ t = 1.5 * (sz - acosf(1.0/z));
+ zeta = -cbrtf( t * t );
+ nflg = -1;
+ }
+z32i = fabsf(1.0/t);
+sqz = cbrtf(t);
+
+/* Airy function */
+n23 = cbrtf( n * n );
+t = n23 * zeta;
+
+#if DEBUG
+printf("zeta %.5E, Airyf(%.5E)\n", zeta, t );
+#endif
+airyf( t, &ai, &aip, &bi, &bip );
+
+/* polynomials in expansion */
+u[0] = 1.0;
+zzi = 1.0/zz;
+u[1] = polevlf( zzi, P1, 1 )/sz;
+u[2] = polevlf( zzi, P2, 2 )/zz;
+u[3] = polevlf( zzi, P3, 3 )/(sz*zz);
+pp = zz*zz;
+u[4] = polevlf( zzi, P4, 4 )/pp;
+u[5] = polevlf( zzi, P5, 5 )/(pp*sz);
+pp *= zz;
+u[6] = polevlf( zzi, P6, 6 )/pp;
+u[7] = polevlf( zzi, P7, 7 )/(pp*sz);
+
+#if DEBUG
+for( k=0; k<=7; k++ )
+ printf( "u[%d] = %.5E\n", k, u[k] );
+#endif
+
+pp = 0.0;
+qq = 0.0;
+np = 1.0;
+/* flags to stop when terms get larger */
+doa = 1;
+dob = 1;
+akl = MAXNUMF;
+bkl = MAXNUMF;
+
+for( k=0; k<=3; k++ )
+ {
+ tk = 2 * k;
+ tkp1 = tk + 1;
+ zp = 1.0;
+ ak = 0.0;
+ bk = 0.0;
+ for( s=0; s<=tk; s++ )
+ {
+ if( doa )
+ {
+ if( (s & 3) > 1 )
+ sign = nflg;
+ else
+ sign = 1;
+ ak += sign * mu[s] * zp * u[tk-s];
+ }
+
+ if( dob )
+ {
+ m = tkp1 - s;
+ if( ((m+1) & 3) > 1 )
+ sign = nflg;
+ else
+ sign = 1;
+ bk += sign * lambda[s] * zp * u[m];
+ }
+ zp *= z32i;
+ }
+
+ if( doa )
+ {
+ ak *= np;
+ t = fabsf(ak);
+ if( t < akl )
+ {
+ akl = t;
+ pp += ak;
+ }
+ else
+ doa = 0;
+ }
+
+ if( dob )
+ {
+ bk += lambda[tkp1] * zp * u[0];
+ bk *= -np/sqz;
+ t = fabsf(bk);
+ if( t < bkl )
+ {
+ bkl = t;
+ qq += bk;
+ }
+ else
+ dob = 0;
+ }
+#if DEBUG
+ printf("a[%d] %.5E, b[%d] %.5E\n", k, ak, k, bk );
+#endif
+ if( np < MACHEPF )
+ break;
+ np /= n*n;
+ }
+
+/* normalizing factor ( 4*zeta/(1 - z**2) )**1/4 */
+t = 4.0 * zeta/zz;
+t = sqrtf( sqrtf(t) );
+
+t *= ai*pp/cbrtf(n) + aip*qq/(n23*n);
+return(t);
+}
+
+/* Asymptotic expansion for transition region,
+ * n large and x close to n.
+ * AMS55 #9.3.23.
+ */
+
+static float PF2[] = {
+ -9.0000000000000000000e-2,
+ 8.5714285714285714286e-2
+};
+static float PF3[] = {
+ 1.3671428571428571429e-1,
+ -5.4920634920634920635e-2,
+ -4.4444444444444444444e-3
+};
+static float PF4[] = {
+ 1.3500000000000000000e-3,
+ -1.6036054421768707483e-1,
+ 4.2590187590187590188e-2,
+ 2.7330447330447330447e-3
+};
+static float PG1[] = {
+ -2.4285714285714285714e-1,
+ 1.4285714285714285714e-2
+};
+static float PG2[] = {
+ -9.0000000000000000000e-3,
+ 1.9396825396825396825e-1,
+ -1.1746031746031746032e-2
+};
+static float PG3[] = {
+ 1.9607142857142857143e-2,
+ -1.5983694083694083694e-1,
+ 6.3838383838383838384e-3
+};
+
+
+static float jntf( float nn, float xx )
+{
+float n, x, z, zz, z3;
+float cbn, n23, cbtwo;
+float ai, aip, bi, bip; /* Airy functions */
+float nk, fk, gk, pp, qq;
+float F[5], G[4];
+int k;
+
+n = nn;
+x = xx;
+cbn = cbrtf(n);
+z = (x - n)/cbn;
+cbtwo = cbrtf( 2.0 );
+
+/* Airy function */
+zz = -cbtwo * z;
+airyf( zz, &ai, &aip, &bi, &bip );
+
+/* polynomials in expansion */
+zz = z * z;
+z3 = zz * z;
+F[0] = 1.0;
+F[1] = -z/5.0;
+F[2] = polevlf( z3, PF2, 1 ) * zz;
+F[3] = polevlf( z3, PF3, 2 );
+F[4] = polevlf( z3, PF4, 3 ) * z;
+G[0] = 0.3 * zz;
+G[1] = polevlf( z3, PG1, 1 );
+G[2] = polevlf( z3, PG2, 2 ) * z;
+G[3] = polevlf( z3, PG3, 2 ) * zz;
+#if DEBUG
+for( k=0; k<=4; k++ )
+ printf( "F[%d] = %.5E\n", k, F[k] );
+for( k=0; k<=3; k++ )
+ printf( "G[%d] = %.5E\n", k, G[k] );
+#endif
+pp = 0.0;
+qq = 0.0;
+nk = 1.0;
+n23 = cbrtf( n * n );
+
+for( k=0; k<=4; k++ )
+ {
+ fk = F[k]*nk;
+ pp += fk;
+ if( k != 4 )
+ {
+ gk = G[k]*nk;
+ qq += gk;
+ }
+#if DEBUG
+ printf("fk[%d] %.5E, gk[%d] %.5E\n", k, fk, k, gk );
+#endif
+ nk /= n23;
+ }
+
+fk = cbtwo * ai * pp/cbn + cbrtf(4.0) * aip * qq/n;
+return(fk);
+}
diff --git a/libm/float/k0f.c b/libm/float/k0f.c
new file mode 100644
index 000000000..e0e0698ac
--- /dev/null
+++ b/libm/float/k0f.c
@@ -0,0 +1,175 @@
+/* k0f.c
+ *
+ * Modified Bessel function, third kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, k0f();
+ *
+ * y = k0f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of the third kind
+ * of order zero of the argument.
+ *
+ * The range is partitioned into the two intervals [0,8] and
+ * (8, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at 2000 random points between 0 and 8. Peak absolute
+ * error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 7.8e-7 8.5e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * K0 domain x <= 0 MAXNUM
+ *
+ */
+ /* k0ef()
+ *
+ * Modified Bessel function, third kind, order zero,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, k0ef();
+ *
+ * y = k0ef( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order zero of the argument.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 8.1e-7 7.8e-8
+ * See k0().
+ *
+ */
+
+/*
+Cephes Math Library Release 2.0: April, 1987
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for K0(x) + log(x/2) I0(x)
+ * in the interval [0,2]. The odd order coefficients are all
+ * zero; only the even order coefficients are listed.
+ *
+ * lim(x->0){ K0(x) + log(x/2) I0(x) } = -EUL.
+ */
+
+static float A[] =
+{
+ 1.90451637722020886025E-9f,
+ 2.53479107902614945675E-7f,
+ 2.28621210311945178607E-5f,
+ 1.26461541144692592338E-3f,
+ 3.59799365153615016266E-2f,
+ 3.44289899924628486886E-1f,
+-5.35327393233902768720E-1f
+};
+
+
+
+/* Chebyshev coefficients for exp(x) sqrt(x) K0(x)
+ * in the inverted interval [2,infinity].
+ *
+ * lim(x->inf){ exp(x) sqrt(x) K0(x) } = sqrt(pi/2).
+ */
+
+static float B[] = {
+-1.69753450938905987466E-9f,
+ 8.57403401741422608519E-9f,
+-4.66048989768794782956E-8f,
+ 2.76681363944501510342E-7f,
+-1.83175552271911948767E-6f,
+ 1.39498137188764993662E-5f,
+-1.28495495816278026384E-4f,
+ 1.56988388573005337491E-3f,
+-3.14481013119645005427E-2f,
+ 2.44030308206595545468E0f
+};
+
+/* k0.c */
+
+extern float MAXNUMF;
+
+#ifdef ANSIC
+float chbevlf(float, float *, int);
+float expf(float), i0f(float), logf(float), sqrtf(float);
+#else
+float chbevlf(), expf(), i0f(), logf(), sqrtf();
+#endif
+
+
+float k0f( float xx )
+{
+float x, y, z;
+
+x = xx;
+if( x <= 0.0f )
+ {
+ mtherr( "k0f", DOMAIN );
+ return( MAXNUMF );
+ }
+
+if( x <= 2.0f )
+ {
+ y = x * x - 2.0f;
+ y = chbevlf( y, A, 7 ) - logf( 0.5f * x ) * i0f(x);
+ return( y );
+ }
+z = 8.0f/x - 2.0f;
+y = expf(-x) * chbevlf( z, B, 10 ) / sqrtf(x);
+return(y);
+}
+
+
+
+float k0ef( float xx )
+{
+float x, y;
+
+
+x = xx;
+if( x <= 0.0f )
+ {
+ mtherr( "k0ef", DOMAIN );
+ return( MAXNUMF );
+ }
+
+if( x <= 2.0f )
+ {
+ y = x * x - 2.0f;
+ y = chbevlf( y, A, 7 ) - logf( 0.5f * x ) * i0f(x);
+ return( y * expf(x) );
+ }
+
+y = chbevlf( 8.0f/x - 2.0f, B, 10 ) / sqrtf(x);
+return(y);
+}
diff --git a/libm/float/k1f.c b/libm/float/k1f.c
new file mode 100644
index 000000000..d5b9bdfce
--- /dev/null
+++ b/libm/float/k1f.c
@@ -0,0 +1,174 @@
+/* k1f.c
+ *
+ * Modified Bessel function, third kind, order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, k1f();
+ *
+ * y = k1f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the modified Bessel function of the third kind
+ * of order one of the argument.
+ *
+ * The range is partitioned into the two intervals [0,2] and
+ * (2, infinity). Chebyshev polynomial expansions are employed
+ * in each interval.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 4.6e-7 7.6e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * k1 domain x <= 0 MAXNUM
+ *
+ */
+ /* k1ef.c
+ *
+ * Modified Bessel function, third kind, order one,
+ * exponentially scaled
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, k1ef();
+ *
+ * y = k1ef( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns exponentially scaled modified Bessel function
+ * of the third kind of order one of the argument:
+ *
+ * k1e(x) = exp(x) * k1(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 30000 4.9e-7 6.7e-8
+ * See k1().
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for x(K1(x) - log(x/2) I1(x))
+ * in the interval [0,2].
+ *
+ * lim(x->0){ x(K1(x) - log(x/2) I1(x)) } = 1.
+ */
+
+#define MINNUMF 6.0e-39
+static float A[] =
+{
+-2.21338763073472585583E-8f,
+-2.43340614156596823496E-6f,
+-1.73028895751305206302E-4f,
+-6.97572385963986435018E-3f,
+-1.22611180822657148235E-1f,
+-3.53155960776544875667E-1f,
+ 1.52530022733894777053E0f
+};
+
+
+
+
+/* Chebyshev coefficients for exp(x) sqrt(x) K1(x)
+ * in the interval [2,infinity].
+ *
+ * lim(x->inf){ exp(x) sqrt(x) K1(x) } = sqrt(pi/2).
+ */
+
+static float B[] =
+{
+ 2.01504975519703286596E-9f,
+-1.03457624656780970260E-8f,
+ 5.74108412545004946722E-8f,
+-3.50196060308781257119E-7f,
+ 2.40648494783721712015E-6f,
+-1.93619797416608296024E-5f,
+ 1.95215518471351631108E-4f,
+-2.85781685962277938680E-3f,
+ 1.03923736576817238437E-1f,
+ 2.72062619048444266945E0f
+};
+
+
+
+extern float MAXNUMF;
+#ifdef ANSIC
+float chbevlf(float, float *, int);
+float expf(float), i1f(float), logf(float), sqrtf(float);
+#else
+float chbevlf(), expf(), i1f(), logf(), sqrtf();
+#endif
+
+float k1f(float xx)
+{
+float x, y;
+
+x = xx;
+if( x <= MINNUMF )
+ {
+ mtherr( "k1f", DOMAIN );
+ return( MAXNUMF );
+ }
+
+if( x <= 2.0f )
+ {
+ y = x * x - 2.0f;
+ y = logf( 0.5f * x ) * i1f(x) + chbevlf( y, A, 7 ) / x;
+ return( y );
+ }
+
+return( expf(-x) * chbevlf( 8.0f/x - 2.0f, B, 10 ) / sqrtf(x) );
+
+}
+
+
+
+float k1ef( float xx )
+{
+float x, y;
+
+x = xx;
+if( x <= 0.0f )
+ {
+ mtherr( "k1ef", DOMAIN );
+ return( MAXNUMF );
+ }
+
+if( x <= 2.0f )
+ {
+ y = x * x - 2.0f;
+ y = logf( 0.5f * x ) * i1f(x) + chbevlf( y, A, 7 ) / x;
+ return( y * expf(x) );
+ }
+
+return( chbevlf( 8.0f/x - 2.0f, B, 10 ) / sqrtf(x) );
+
+}
diff --git a/libm/float/knf.c b/libm/float/knf.c
new file mode 100644
index 000000000..85e297390
--- /dev/null
+++ b/libm/float/knf.c
@@ -0,0 +1,252 @@
+/* knf.c
+ *
+ * Modified Bessel function, third kind, integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, knf();
+ * int n;
+ *
+ * y = knf( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns modified Bessel function of the third kind
+ * of order n of the argument.
+ *
+ * The range is partitioned into the two intervals [0,9.55] and
+ * (9.55, infinity). An ascending power series is used in the
+ * low range, and an asymptotic expansion in the high range.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error, relative when function > 1:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 10000 2.0e-4 3.8e-6
+ *
+ * Error is high only near the crossover point x = 9.55
+ * between the two expansions used.
+ */
+
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+
+*/
+
+
+/*
+Algorithm for Kn.
+ n-1
+ -n - (n-k-1)! 2 k
+K (x) = 0.5 (x/2) > -------- (-x /4)
+ n - k!
+ k=0
+
+ inf. 2 k
+ n n - (x /4)
+ + (-1) 0.5(x/2) > {p(k+1) + p(n+k+1) - 2log(x/2)} ---------
+ - k! (n+k)!
+ k=0
+
+where p(m) is the psi function: p(1) = -EUL and
+
+ m-1
+ -
+ p(m) = -EUL + > 1/k
+ -
+ k=1
+
+For large x,
+ 2 2 2
+ u-1 (u-1 )(u-3 )
+K (z) = sqrt(pi/2z) exp(-z) { 1 + ------- + ------------ + ...}
+ v 1 2
+ 1! (8z) 2! (8z)
+asymptotically, where
+
+ 2
+ u = 4 v .
+
+*/
+
+#include <math.h>
+
+#define EUL 5.772156649015328606065e-1
+#define MAXFAC 31
+extern float MACHEPF, MAXNUMF, MAXLOGF, PIF;
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+float expf(float), logf(float), sqrtf(float);
+
+float knf( int nnn, float xx )
+{
+float x, k, kf, nk1f, nkf, zn, t, s, z0, z;
+float ans, fn, pn, pk, zmn, tlg, tox;
+int i, n, nn;
+
+nn = nnn;
+x = xx;
+if( nn < 0 )
+ n = -nn;
+else
+ n = nn;
+
+if( n > MAXFAC )
+ {
+overf:
+ mtherr( "knf", OVERFLOW );
+ return( MAXNUMF );
+ }
+
+if( x <= 0.0 )
+ {
+ if( x < 0.0 )
+ mtherr( "knf", DOMAIN );
+ else
+ mtherr( "knf", SING );
+ return( MAXNUMF );
+ }
+
+
+if( x > 9.55 )
+ goto asymp;
+
+ans = 0.0;
+z0 = 0.25 * x * x;
+fn = 1.0;
+pn = 0.0;
+zmn = 1.0;
+tox = 2.0/x;
+
+if( n > 0 )
+ {
+ /* compute factorial of n and psi(n) */
+ pn = -EUL;
+ k = 1.0;
+ for( i=1; i<n; i++ )
+ {
+ pn += 1.0/k;
+ k += 1.0;
+ fn *= k;
+ }
+
+ zmn = tox;
+
+ if( n == 1 )
+ {
+ ans = 1.0/x;
+ }
+ else
+ {
+ nk1f = fn/n;
+ kf = 1.0;
+ s = nk1f;
+ z = -z0;
+ zn = 1.0;
+ for( i=1; i<n; i++ )
+ {
+ nk1f = nk1f/(n-i);
+ kf = kf * i;
+ zn *= z;
+ t = nk1f * zn / kf;
+ s += t;
+ if( (MAXNUMF - fabsf(t)) < fabsf(s) )
+ goto overf;
+ if( (tox > 1.0) && ((MAXNUMF/tox) < zmn) )
+ goto overf;
+ zmn *= tox;
+ }
+ s *= 0.5;
+ t = fabsf(s);
+ if( (zmn > 1.0) && ((MAXNUMF/zmn) < t) )
+ goto overf;
+ if( (t > 1.0) && ((MAXNUMF/t) < zmn) )
+ goto overf;
+ ans = s * zmn;
+ }
+ }
+
+
+tlg = 2.0 * logf( 0.5 * x );
+pk = -EUL;
+if( n == 0 )
+ {
+ pn = pk;
+ t = 1.0;
+ }
+else
+ {
+ pn = pn + 1.0/n;
+ t = 1.0/fn;
+ }
+s = (pk+pn-tlg)*t;
+k = 1.0;
+do
+ {
+ t *= z0 / (k * (k+n));
+ pk += 1.0/k;
+ pn += 1.0/(k+n);
+ s += (pk+pn-tlg)*t;
+ k += 1.0;
+ }
+while( fabsf(t/s) > MACHEPF );
+
+s = 0.5 * s / zmn;
+if( n & 1 )
+ s = -s;
+ans += s;
+
+return(ans);
+
+
+
+/* Asymptotic expansion for Kn(x) */
+/* Converges to 1.4e-17 for x > 18.4 */
+
+asymp:
+
+if( x > MAXLOGF )
+ {
+ mtherr( "knf", UNDERFLOW );
+ return(0.0);
+ }
+k = n;
+pn = 4.0 * k * k;
+pk = 1.0;
+z0 = 8.0 * x;
+fn = 1.0;
+t = 1.0;
+s = t;
+nkf = MAXNUMF;
+i = 0;
+do
+ {
+ z = pn - pk * pk;
+ t = t * z /(fn * z0);
+ nk1f = fabsf(t);
+ if( (i >= n) && (nk1f > nkf) )
+ {
+ goto adone;
+ }
+ nkf = nk1f;
+ s += t;
+ fn += 1.0;
+ pk += 2.0;
+ i += 1;
+ }
+while( fabsf(t/s) > MACHEPF );
+
+adone:
+ans = expf(-x) * sqrtf( PIF/(2.0*x) ) * s;
+return(ans);
+}
diff --git a/libm/float/log10f.c b/libm/float/log10f.c
new file mode 100644
index 000000000..6cb2e4d87
--- /dev/null
+++ b/libm/float/log10f.c
@@ -0,0 +1,129 @@
+/* log10f.c
+ *
+ * Common logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, log10f();
+ *
+ * y = log10f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns logarithm to the base 10 of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. The logarithm of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 100000 1.3e-7 3.4e-8
+ * IEEE 0, MAXNUMF 100000 1.3e-7 2.6e-8
+ *
+ * In the tests over the interval [0, MAXNUM], the logarithms
+ * of the random arguments were uniformly distributed over
+ * [-MAXL10, MAXL10].
+ *
+ * ERROR MESSAGES:
+ *
+ * log10f singularity: x = 0; returns -MAXL10
+ * log10f domain: x < 0; returns -MAXL10
+ * MAXL10 = 38.230809449325611792
+ */
+
+/*
+Cephes Math Library Release 2.1: December, 1988
+Copyright 1984, 1987, 1988 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+static char fname[] = {"log10"};
+
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ */
+static float P[] = {
+ 7.0376836292E-2,
+-1.1514610310E-1,
+ 1.1676998740E-1,
+-1.2420140846E-1,
+ 1.4249322787E-1,
+-1.6668057665E-1,
+ 2.0000714765E-1,
+-2.4999993993E-1,
+ 3.3333331174E-1
+};
+
+
+#define SQRTH 0.70710678118654752440
+#define L102A 3.0078125E-1
+#define L102B 2.48745663981195213739E-4
+#define L10EA 4.3359375E-1
+#define L10EB 7.00731903251827651129E-4
+
+static float MAXL10 = 38.230809449325611792;
+
+float frexpf(float, int *), polevlf(float, float *, int);
+
+float log10f(float xx)
+{
+float x, y, z;
+int e;
+
+x = xx;
+/* Test for domain */
+if( x <= 0.0 )
+ {
+ if( x == 0.0 )
+ mtherr( fname, SING );
+ else
+ mtherr( fname, DOMAIN );
+ return( -MAXL10 );
+ }
+
+/* separate mantissa from exponent */
+
+x = frexpf( x, &e );
+
+/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x) */
+
+if( x < SQRTH )
+ {
+ e -= 1;
+ x = 2.0*x - 1.0;
+ }
+else
+ {
+ x = x - 1.0;
+ }
+
+
+/* rational form */
+z = x*x;
+y = x * ( z * polevlf( x, P, 8 ) );
+y = y - 0.5 * z; /* y - 0.5 * x**2 */
+
+/* multiply log of fraction by log10(e)
+ * and base 2 exponent by log10(2)
+ */
+z = (x + y) * L10EB; /* accumulate terms in order of size */
+z += y * L10EA;
+z += x * L10EA;
+x = e;
+z += x * L102B;
+z += x * L102A;
+
+
+return( z );
+}
diff --git a/libm/float/log2f.c b/libm/float/log2f.c
new file mode 100644
index 000000000..5cd5f4838
--- /dev/null
+++ b/libm/float/log2f.c
@@ -0,0 +1,129 @@
+/* log2f.c
+ *
+ * Base 2 logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, log2f();
+ *
+ * y = log2f( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base 2 logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the base e
+ * logarithm of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting z = 2(x-1)/x+1),
+ *
+ * log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE exp(+-88) 100000 1.1e-7 2.4e-8
+ * IEEE 0.5, 2.0 100000 1.1e-7 3.0e-8
+ *
+ * In the tests over the interval [exp(+-88)], the logarithms
+ * of the random arguments were uniformly distributed.
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity: x = 0; returns MINLOGF/log(2)
+ * log domain: x < 0; returns MINLOGF/log(2)
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+static char fname[] = {"log2"};
+
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ */
+
+static float P[] = {
+ 7.0376836292E-2,
+-1.1514610310E-1,
+ 1.1676998740E-1,
+-1.2420140846E-1,
+ 1.4249322787E-1,
+-1.6668057665E-1,
+ 2.0000714765E-1,
+-2.4999993993E-1,
+ 3.3333331174E-1
+};
+
+#define LOG2EA 0.44269504088896340735992
+#define SQRTH 0.70710678118654752440
+extern float MINLOGF, LOGE2F;
+
+float frexpf(float, int *), polevlf(float, float *, int);
+
+float log2f(float xx)
+{
+float x, y, z;
+int e;
+
+x = xx;
+/* Test for domain */
+if( x <= 0.0 )
+ {
+ if( x == 0.0 )
+ mtherr( fname, SING );
+ else
+ mtherr( fname, DOMAIN );
+ return( MINLOGF/LOGE2F );
+ }
+
+/* separate mantissa from exponent */
+x = frexpf( x, &e );
+
+
+/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+
+if( x < SQRTH )
+ {
+ e -= 1;
+ x = 2.0*x - 1.0;
+ }
+else
+ {
+ x = x - 1.0;
+ }
+
+z = x*x;
+y = x * ( z * polevlf( x, P, 8 ) );
+y = y - 0.5 * z; /* y - 0.5 * x**2 */
+
+
+/* Multiply log of fraction by log2(e)
+ * and base 2 exponent by 1
+ *
+ * ***CAUTION***
+ *
+ * This sequence of operations is critical and it may
+ * be horribly defeated by some compiler optimizers.
+ */
+z = y * LOG2EA;
+z += x * LOG2EA;
+z += y;
+z += x;
+z += (float )e;
+return( z );
+}
diff --git a/libm/float/logf.c b/libm/float/logf.c
new file mode 100644
index 000000000..750138564
--- /dev/null
+++ b/libm/float/logf.c
@@ -0,0 +1,128 @@
+/* logf.c
+ *
+ * Natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, logf();
+ *
+ * y = logf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the logarithm
+ * of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 100000 7.6e-8 2.7e-8
+ * IEEE 1, MAXNUMF 100000 2.6e-8
+ *
+ * In the tests over the interval [1, MAXNUM], the logarithms
+ * of the random arguments were uniformly distributed over
+ * [0, MAXLOGF].
+ *
+ * ERROR MESSAGES:
+ *
+ * logf singularity: x = 0; returns MINLOG
+ * logf domain: x < 0; returns MINLOG
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Single precision natural logarithm
+ * test interval: [sqrt(2)/2, sqrt(2)]
+ * trials: 10000
+ * peak relative error: 7.1e-8
+ * rms relative error: 2.7e-8
+ */
+
+#include <math.h>
+extern float MINLOGF, SQRTHF;
+
+
+float frexpf( float, int * );
+
+float logf( float xx )
+{
+register float y;
+float x, z, fe;
+int e;
+
+x = xx;
+fe = 0.0;
+/* Test for domain */
+if( x <= 0.0 )
+ {
+ if( x == 0.0 )
+ mtherr( "logf", SING );
+ else
+ mtherr( "logf", DOMAIN );
+ return( MINLOGF );
+ }
+
+x = frexpf( x, &e );
+if( x < SQRTHF )
+ {
+ e -= 1;
+ x = x + x - 1.0; /* 2x - 1 */
+ }
+else
+ {
+ x = x - 1.0;
+ }
+z = x * x;
+/* 3.4e-9 */
+/*
+p = logfcof;
+y = *p++ * x;
+for( i=0; i<8; i++ )
+ {
+ y += *p++;
+ y *= x;
+ }
+y *= z;
+*/
+
+y =
+(((((((( 7.0376836292E-2 * x
+- 1.1514610310E-1) * x
++ 1.1676998740E-1) * x
+- 1.2420140846E-1) * x
++ 1.4249322787E-1) * x
+- 1.6668057665E-1) * x
++ 2.0000714765E-1) * x
+- 2.4999993993E-1) * x
++ 3.3333331174E-1) * x * z;
+
+if( e )
+ {
+ fe = e;
+ y += -2.12194440e-4 * fe;
+ }
+
+y += -0.5 * z; /* y - 0.5 x^2 */
+z = x + y; /* ... + x */
+
+if( e )
+ z += 0.693359375 * fe;
+
+return( z );
+}
diff --git a/libm/float/mtherr.c b/libm/float/mtherr.c
new file mode 100644
index 000000000..d67dc042e
--- /dev/null
+++ b/libm/float/mtherr.c
@@ -0,0 +1,99 @@
+/* mtherr.c
+ *
+ * Library common error handling routine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * char *fctnam;
+ * int code;
+ * void mtherr();
+ *
+ * mtherr( fctnam, code );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This routine may be called to report one of the following
+ * error conditions (in the include file math.h).
+ *
+ * Mnemonic Value Significance
+ *
+ * DOMAIN 1 argument domain error
+ * SING 2 function singularity
+ * OVERFLOW 3 overflow range error
+ * UNDERFLOW 4 underflow range error
+ * TLOSS 5 total loss of precision
+ * PLOSS 6 partial loss of precision
+ * EDOM 33 Unix domain error code
+ * ERANGE 34 Unix range error code
+ *
+ * The default version of the file prints the function name,
+ * passed to it by the pointer fctnam, followed by the
+ * error condition. The display is directed to the standard
+ * output device. The routine then returns to the calling
+ * program. Users may wish to modify the program to abort by
+ * calling exit() under severe error conditions such as domain
+ * errors.
+ *
+ * Since all error conditions pass control to this function,
+ * the display may be easily changed, eliminated, or directed
+ * to an error logging device.
+ *
+ * SEE ALSO:
+ *
+ * math.h
+ *
+ */
+
+/*
+Cephes Math Library Release 2.0: April, 1987
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+/* Notice: the order of appearance of the following
+ * messages is bound to the error codes defined
+ * in math.h.
+ */
+static char *ermsg[7] = {
+"unknown", /* error code 0 */
+"domain", /* error code 1 */
+"singularity", /* et seq. */
+"overflow",
+"underflow",
+"total loss of precision",
+"partial loss of precision"
+};
+
+
+void printf();
+
+int mtherr( name, code )
+char *name;
+int code;
+{
+
+/* Display string passed by calling program,
+ * which is supposed to be the name of the
+ * function in which the error occurred:
+ */
+printf( "\n%s ", name );
+ /* exit(2); */
+
+/* Display error message defined
+ * by the code argument.
+ */
+if( (code <= 0) || (code >= 6) )
+ code = 0;
+printf( "%s error\n", ermsg[code] );
+
+/* Return to calling
+ * program
+ */
+return 0;
+}
diff --git a/libm/float/nantst.c b/libm/float/nantst.c
new file mode 100644
index 000000000..7edd992ae
--- /dev/null
+++ b/libm/float/nantst.c
@@ -0,0 +1,54 @@
+float inf = 1.0f/0.0f;
+float nnn = 1.0f/0.0f - 1.0f/0.0f;
+float fin = 1.0f;
+float neg = -1.0f;
+float nn2;
+
+int isnanf(), isfinitef(), signbitf();
+
+void pvalue (char *str, float x)
+{
+union
+ {
+ float f;
+ unsigned int i;
+ }u;
+
+printf("%s ", str);
+u.f = x;
+printf("%08x\n", u.i);
+}
+
+
+int
+main()
+{
+
+if (!isnanf(nnn))
+ abort();
+pvalue("nnn", nnn);
+pvalue("inf", inf);
+nn2 = inf - inf;
+pvalue("inf - inf", nn2);
+if (isnanf(fin))
+ abort();
+if (isnanf(inf))
+ abort();
+if (!isfinitef(fin))
+ abort();
+if (isfinitef(nnn))
+ abort();
+if (isfinitef(inf))
+ abort();
+if (!signbitf(neg))
+ abort();
+if (signbitf(fin))
+ abort();
+if (signbitf(inf))
+ abort();
+/*
+if (signbitf(nnn))
+ abort();
+ */
+exit (0);
+}
diff --git a/libm/float/nbdtrf.c b/libm/float/nbdtrf.c
new file mode 100644
index 000000000..e9b02753b
--- /dev/null
+++ b/libm/float/nbdtrf.c
@@ -0,0 +1,141 @@
+/* nbdtrf.c
+ *
+ * Negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * float p, y, nbdtrf();
+ *
+ * y = nbdtrf( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the negative
+ * binomial distribution:
+ *
+ * k
+ * -- ( n+j-1 ) n j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=0
+ *
+ * In a sequence of Bernoulli trials, this is the probability
+ * that k or fewer failures precede the nth success.
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 1.5e-4 1.9e-5
+ *
+ */
+ /* nbdtrcf.c
+ *
+ * Complemented negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * float p, y, nbdtrcf();
+ *
+ * y = nbdtrcf( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the negative
+ * binomial distribution:
+ *
+ * inf
+ * -- ( n+j-1 ) n j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=k+1
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 1.4e-4 2.0e-5
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+#ifdef ANSIC
+float incbetf(float, float, float);
+#else
+float incbetf();
+#endif
+
+
+float nbdtrcf( int k, int n, float pp )
+{
+float dk, dn, p;
+
+p = pp;
+if( (p < 0.0) || (p > 1.0) )
+ goto domerr;
+if( k < 0 )
+ {
+domerr:
+ mtherr( "nbdtrf", DOMAIN );
+ return( 0.0 );
+ }
+
+dk = k+1;
+dn = n;
+return( incbetf( dk, dn, 1.0 - p ) );
+}
+
+
+
+float nbdtrf( int k, int n, float pp )
+{
+float dk, dn, p;
+
+p = pp;
+if( (p < 0.0) || (p > 1.0) )
+ goto domerr;
+if( k < 0 )
+ {
+domerr:
+ mtherr( "nbdtrf", DOMAIN );
+ return( 0.0 );
+ }
+dk = k+1;
+dn = n;
+return( incbetf( dn, dk, p ) );
+}
diff --git a/libm/float/ndtrf.c b/libm/float/ndtrf.c
new file mode 100644
index 000000000..c08d69eca
--- /dev/null
+++ b/libm/float/ndtrf.c
@@ -0,0 +1,281 @@
+/* ndtrf.c
+ *
+ * Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, ndtrf();
+ *
+ * y = ndtrf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the Gaussian probability density
+ * function, integrated from minus infinity to x:
+ *
+ * x
+ * -
+ * 1 | | 2
+ * ndtr(x) = --------- | exp( - t /2 ) dt
+ * sqrt(2pi) | |
+ * -
+ * -inf.
+ *
+ * = ( 1 + erf(z) ) / 2
+ * = erfc(z) / 2
+ *
+ * where z = x/sqrt(2). Computation is via the functions
+ * erf and erfc.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -13,0 50000 1.5e-5 2.6e-6
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * See erfcf().
+ *
+ */
+ /* erff.c
+ *
+ * Error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, erff();
+ *
+ * y = erff( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The integral is
+ *
+ * x
+ * -
+ * 2 | | 2
+ * erf(x) = -------- | exp( - t ) dt.
+ * sqrt(pi) | |
+ * -
+ * 0
+ *
+ * The magnitude of x is limited to 9.231948545 for DEC
+ * arithmetic; 1 or -1 is returned outside this range.
+ *
+ * For 0 <= |x| < 1, erf(x) = x * P(x**2); otherwise
+ * erf(x) = 1 - erfc(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -9.3,9.3 50000 1.7e-7 2.8e-8
+ *
+ */
+ /* erfcf.c
+ *
+ * Complementary error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, erfcf();
+ *
+ * y = erfcf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * 1 - erf(x) =
+ *
+ * inf.
+ * -
+ * 2 | | 2
+ * erfc(x) = -------- | exp( - t ) dt
+ * sqrt(pi) | |
+ * -
+ * x
+ *
+ *
+ * For small x, erfc(x) = 1 - erf(x); otherwise polynomial
+ * approximations 1/x P(1/x**2) are computed.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -9.3,9.3 50000 3.9e-6 7.2e-7
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * erfcf underflow x**2 > MAXLOGF 0.0
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1988 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+extern float MAXLOGF, SQRTHF;
+
+
+/* erfc(x) = exp(-x^2) P(1/x), 1 < x < 2 */
+static float P[] = {
+ 2.326819970068386E-002,
+-1.387039388740657E-001,
+ 3.687424674597105E-001,
+-5.824733027278666E-001,
+ 6.210004621745983E-001,
+-4.944515323274145E-001,
+ 3.404879937665872E-001,
+-2.741127028184656E-001,
+ 5.638259427386472E-001
+};
+
+/* erfc(x) = exp(-x^2) 1/x P(1/x^2), 2 < x < 14 */
+static float R[] = {
+-1.047766399936249E+001,
+ 1.297719955372516E+001,
+-7.495518717768503E+000,
+ 2.921019019210786E+000,
+-1.015265279202700E+000,
+ 4.218463358204948E-001,
+-2.820767439740514E-001,
+ 5.641895067754075E-001
+};
+
+/* erf(x) = x P(x^2), 0 < x < 1 */
+static float T[] = {
+ 7.853861353153693E-005,
+-8.010193625184903E-004,
+ 5.188327685732524E-003,
+-2.685381193529856E-002,
+ 1.128358514861418E-001,
+-3.761262582423300E-001,
+ 1.128379165726710E+000
+};
+
+/*#define UTHRESH 37.519379347*/
+
+#define UTHRESH 14.0
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#ifdef ANSIC
+float polevlf(float, float *, int);
+float expf(float), logf(float), erff(float), erfcf(float);
+#else
+float polevlf(), expf(), logf(), erff(), erfcf();
+#endif
+
+
+
+float ndtrf(float aa)
+{
+float x, y, z;
+
+x = aa;
+x *= SQRTHF;
+z = fabsf(x);
+
+if( z < SQRTHF )
+ y = 0.5 + 0.5 * erff(x);
+else
+ {
+ y = 0.5 * erfcf(z);
+
+ if( x > 0 )
+ y = 1.0 - y;
+ }
+
+return(y);
+}
+
+
+float erfcf(float aa)
+{
+float a, p,q,x,y,z;
+
+
+a = aa;
+x = fabsf(a);
+
+if( x < 1.0 )
+ return( 1.0 - erff(a) );
+
+z = -a * a;
+
+if( z < -MAXLOGF )
+ {
+under:
+ mtherr( "erfcf", UNDERFLOW );
+ if( a < 0 )
+ return( 2.0 );
+ else
+ return( 0.0 );
+ }
+
+z = expf(z);
+q = 1.0/x;
+y = q * q;
+if( x < 2.0 )
+ {
+ p = polevlf( y, P, 8 );
+ }
+else
+ {
+ p = polevlf( y, R, 7 );
+ }
+
+y = z * q * p;
+
+if( a < 0 )
+ y = 2.0 - y;
+
+if( y == 0.0 )
+ goto under;
+
+return(y);
+}
+
+
+float erff(float xx)
+{
+float x, y, z;
+
+x = xx;
+if( fabsf(x) > 1.0 )
+ return( 1.0 - erfcf(x) );
+
+z = x * x;
+y = x * polevlf( z, T, 6 );
+return( y );
+
+}
diff --git a/libm/float/ndtrif.c b/libm/float/ndtrif.c
new file mode 100644
index 000000000..3e33bc2c5
--- /dev/null
+++ b/libm/float/ndtrif.c
@@ -0,0 +1,186 @@
+/* ndtrif.c
+ *
+ * Inverse of Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, ndtrif();
+ *
+ * x = ndtrif( y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the argument, x, for which the area under the
+ * Gaussian probability density function (integrated from
+ * minus infinity to x) is equal to y.
+ *
+ *
+ * For small arguments 0 < y < exp(-2), the program computes
+ * z = sqrt( -2.0 * log(y) ); then the approximation is
+ * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).
+ * There are two rational functions P/Q, one for 0 < y < exp(-32)
+ * and the other for y up to exp(-2). For larger arguments,
+ * w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 1e-38, 1 30000 3.6e-7 5.0e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ndtrif domain x <= 0 -MAXNUM
+ * ndtrif domain x >= 1 MAXNUM
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+extern float MAXNUMF;
+
+/* sqrt(2pi) */
+static float s2pi = 2.50662827463100050242;
+
+/* approximation for 0 <= |y - 0.5| <= 3/8 */
+static float P0[5] = {
+-5.99633501014107895267E1,
+ 9.80010754185999661536E1,
+-5.66762857469070293439E1,
+ 1.39312609387279679503E1,
+-1.23916583867381258016E0,
+};
+static float Q0[8] = {
+/* 1.00000000000000000000E0,*/
+ 1.95448858338141759834E0,
+ 4.67627912898881538453E0,
+ 8.63602421390890590575E1,
+-2.25462687854119370527E2,
+ 2.00260212380060660359E2,
+-8.20372256168333339912E1,
+ 1.59056225126211695515E1,
+-1.18331621121330003142E0,
+};
+
+/* Approximation for interval z = sqrt(-2 log y ) between 2 and 8
+ * i.e., y between exp(-2) = .135 and exp(-32) = 1.27e-14.
+ */
+static float P1[9] = {
+ 4.05544892305962419923E0,
+ 3.15251094599893866154E1,
+ 5.71628192246421288162E1,
+ 4.40805073893200834700E1,
+ 1.46849561928858024014E1,
+ 2.18663306850790267539E0,
+-1.40256079171354495875E-1,
+-3.50424626827848203418E-2,
+-8.57456785154685413611E-4,
+};
+static float Q1[8] = {
+/* 1.00000000000000000000E0,*/
+ 1.57799883256466749731E1,
+ 4.53907635128879210584E1,
+ 4.13172038254672030440E1,
+ 1.50425385692907503408E1,
+ 2.50464946208309415979E0,
+-1.42182922854787788574E-1,
+-3.80806407691578277194E-2,
+-9.33259480895457427372E-4,
+};
+
+
+/* Approximation for interval z = sqrt(-2 log y ) between 8 and 64
+ * i.e., y between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890.
+ */
+
+static float P2[9] = {
+ 3.23774891776946035970E0,
+ 6.91522889068984211695E0,
+ 3.93881025292474443415E0,
+ 1.33303460815807542389E0,
+ 2.01485389549179081538E-1,
+ 1.23716634817820021358E-2,
+ 3.01581553508235416007E-4,
+ 2.65806974686737550832E-6,
+ 6.23974539184983293730E-9,
+};
+static float Q2[8] = {
+/* 1.00000000000000000000E0,*/
+ 6.02427039364742014255E0,
+ 3.67983563856160859403E0,
+ 1.37702099489081330271E0,
+ 2.16236993594496635890E-1,
+ 1.34204006088543189037E-2,
+ 3.28014464682127739104E-4,
+ 2.89247864745380683936E-6,
+ 6.79019408009981274425E-9,
+};
+
+#ifdef ANSIC
+float polevlf(float, float *, int);
+float p1evlf(float, float *, int);
+float logf(float), sqrtf(float);
+#else
+float polevlf(), p1evlf(), logf(), sqrtf();
+#endif
+
+
+float ndtrif(float yy0)
+{
+float y0, x, y, z, y2, x0, x1;
+int code;
+
+y0 = yy0;
+if( y0 <= 0.0 )
+ {
+ mtherr( "ndtrif", DOMAIN );
+ return( -MAXNUMF );
+ }
+if( y0 >= 1.0 )
+ {
+ mtherr( "ndtrif", DOMAIN );
+ return( MAXNUMF );
+ }
+code = 1;
+y = y0;
+if( y > (1.0 - 0.13533528323661269189) ) /* 0.135... = exp(-2) */
+ {
+ y = 1.0 - y;
+ code = 0;
+ }
+
+if( y > 0.13533528323661269189 )
+ {
+ y = y - 0.5;
+ y2 = y * y;
+ x = y + y * (y2 * polevlf( y2, P0, 4)/p1evlf( y2, Q0, 8 ));
+ x = x * s2pi;
+ return(x);
+ }
+
+x = sqrtf( -2.0 * logf(y) );
+x0 = x - logf(x)/x;
+
+z = 1.0/x;
+if( x < 8.0 ) /* y > exp(-32) = 1.2664165549e-14 */
+ x1 = z * polevlf( z, P1, 8 )/p1evlf( z, Q1, 8 );
+else
+ x1 = z * polevlf( z, P2, 8 )/p1evlf( z, Q2, 8 );
+x = x0 - x1;
+if( code != 0 )
+ x = -x;
+return( x );
+}
diff --git a/libm/float/pdtrf.c b/libm/float/pdtrf.c
new file mode 100644
index 000000000..17a05ee13
--- /dev/null
+++ b/libm/float/pdtrf.c
@@ -0,0 +1,188 @@
+/* pdtrf.c
+ *
+ * Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * float m, y, pdtrf();
+ *
+ * y = pdtrf( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the first k terms of the Poisson
+ * distribution:
+ *
+ * k j
+ * -- -m m
+ * > e --
+ * -- j!
+ * j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the relation
+ *
+ * y = pdtr( k, m ) = igamc( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 6.9e-5 8.0e-6
+ *
+ */
+ /* pdtrcf()
+ *
+ * Complemented poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * float m, y, pdtrcf();
+ *
+ * y = pdtrcf( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the Poisson
+ * distribution:
+ *
+ * inf. j
+ * -- -m m
+ * > e --
+ * -- j!
+ * j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the formula
+ *
+ * y = pdtrc( k, m ) = igam( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 8.4e-5 1.2e-5
+ *
+ */
+ /* pdtrif()
+ *
+ * Inverse Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * float m, y, pdtrf();
+ *
+ * m = pdtrif( k, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Poisson variable x such that the integral
+ * from 0 to x of the Poisson density is equal to the
+ * given probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ * m = igami( k+1, y ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100 5000 8.7e-6 1.4e-6
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * pdtri domain y < 0 or y >= 1 0.0
+ * k < 0
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+#ifdef ANSIC
+float igamf(float, float), igamcf(float, float), igamif(float, float);
+#else
+float igamf(), igamcf(), igamif();
+#endif
+
+
+float pdtrcf( int k, float mm )
+{
+float v, m;
+
+m = mm;
+if( (k < 0) || (m <= 0.0) )
+ {
+ mtherr( "pdtrcf", DOMAIN );
+ return( 0.0 );
+ }
+v = k+1;
+return( igamf( v, m ) );
+}
+
+
+
+float pdtrf( int k, float mm )
+{
+float v, m;
+
+m = mm;
+if( (k < 0) || (m <= 0.0) )
+ {
+ mtherr( "pdtr", DOMAIN );
+ return( 0.0 );
+ }
+v = k+1;
+return( igamcf( v, m ) );
+}
+
+
+float pdtrif( int k, float yy )
+{
+float v, y;
+
+y = yy;
+if( (k < 0) || (y < 0.0) || (y >= 1.0) )
+ {
+ mtherr( "pdtrif", DOMAIN );
+ return( 0.0 );
+ }
+v = k+1;
+v = igamif( v, y );
+return( v );
+}
diff --git a/libm/float/polevlf.c b/libm/float/polevlf.c
new file mode 100644
index 000000000..7d7b4d0b7
--- /dev/null
+++ b/libm/float/polevlf.c
@@ -0,0 +1,99 @@
+/* polevlf.c
+ * p1evlf.c
+ *
+ * Evaluate polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * float x, y, coef[N+1], polevlf[];
+ *
+ * y = polevlf( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates polynomial of degree N:
+ *
+ * 2 N
+ * y = C + C x + C x +...+ C x
+ * 0 1 2 N
+ *
+ * Coefficients are stored in reverse order:
+ *
+ * coef[0] = C , ..., coef[N] = C .
+ * N 0
+ *
+ * The function p1evl() assumes that coef[N] = 1.0 and is
+ * omitted from the array. Its calling arguments are
+ * otherwise the same as polevl().
+ *
+ *
+ * SPEED:
+ *
+ * In the interest of speed, there are no checks for out
+ * of bounds arithmetic. This routine is used by most of
+ * the functions in the library. Depending on available
+ * equipment features, the user may wish to rewrite the
+ * program in microcode or assembly language.
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.1: December, 1988
+Copyright 1984, 1987, 1988 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+float polevlf( float xx, float *coef, int N )
+{
+float ans, x;
+float *p;
+int i;
+
+x = xx;
+p = coef;
+ans = *p++;
+
+/*
+for( i=0; i<N; i++ )
+ ans = ans * x + *p++;
+*/
+
+i = N;
+do
+ ans = ans * x + *p++;
+while( --i );
+
+return( ans );
+}
+
+/* p1evl() */
+/* N
+ * Evaluate polynomial when coefficient of x is 1.0.
+ * Otherwise same as polevl.
+ */
+
+float p1evlf( float xx, float *coef, int N )
+{
+float ans, x;
+float *p;
+int i;
+
+x = xx;
+p = coef;
+ans = x + *p++;
+i = N-1;
+
+do
+ ans = ans * x + *p++;
+while( --i );
+
+return( ans );
+}
diff --git a/libm/float/polynf.c b/libm/float/polynf.c
new file mode 100644
index 000000000..48c6675d4
--- /dev/null
+++ b/libm/float/polynf.c
@@ -0,0 +1,520 @@
+/* polynf.c
+ * polyrf.c
+ * Arithmetic operations on polynomials
+ *
+ * In the following descriptions a, b, c are polynomials of degree
+ * na, nb, nc respectively. The degree of a polynomial cannot
+ * exceed a run-time value MAXPOLF. An operation that attempts
+ * to use or generate a polynomial of higher degree may produce a
+ * result that suffers truncation at degree MAXPOL. The value of
+ * MAXPOL is set by calling the function
+ *
+ * polinif( maxpol );
+ *
+ * where maxpol is the desired maximum degree. This must be
+ * done prior to calling any of the other functions in this module.
+ * Memory for internal temporary polynomial storage is allocated
+ * by polinif().
+ *
+ * Each polynomial is represented by an array containing its
+ * coefficients, together with a separately declared integer equal
+ * to the degree of the polynomial. The coefficients appear in
+ * ascending order; that is,
+ *
+ * 2 na
+ * a(x) = a[0] + a[1] * x + a[2] * x + ... + a[na] * x .
+ *
+ *
+ *
+ * sum = poleva( a, na, x ); Evaluate polynomial a(t) at t = x.
+ * polprtf( a, na, D ); Print the coefficients of a to D digits.
+ * polclrf( a, na ); Set a identically equal to zero, up to a[na].
+ * polmovf( a, na, b ); Set b = a.
+ * poladdf( a, na, b, nb, c ); c = b + a, nc = max(na,nb)
+ * polsubf( a, na, b, nb, c ); c = b - a, nc = max(na,nb)
+ * polmulf( a, na, b, nb, c ); c = b * a, nc = na+nb
+ *
+ *
+ * Division:
+ *
+ * i = poldivf( a, na, b, nb, c ); c = b / a, nc = MAXPOL
+ *
+ * returns i = the degree of the first nonzero coefficient of a.
+ * The computed quotient c must be divided by x^i. An error message
+ * is printed if a is identically zero.
+ *
+ *
+ * Change of variables:
+ * If a and b are polynomials, and t = a(x), then
+ * c(t) = b(a(x))
+ * is a polynomial found by substituting a(x) for t. The
+ * subroutine call for this is
+ *
+ * polsbtf( a, na, b, nb, c );
+ *
+ *
+ * Notes:
+ * poldivf() is an integer routine; polevaf() is float.
+ * Any of the arguments a, b, c may refer to the same array.
+ *
+ */
+
+#ifndef NULL
+#define NULL 0
+#endif
+#include <math.h>
+
+#ifdef ANSIC
+void printf(), sprintf(), exit();
+void free(void *);
+void *malloc(int);
+#else
+void printf(), sprintf(), free(), exit();
+void *malloc();
+#endif
+/* near pointer version of malloc() */
+/*#define malloc _nmalloc*/
+/*#define free _nfree*/
+
+/* Pointers to internal arrays. Note poldiv() allocates
+ * and deallocates some temporary arrays every time it is called.
+ */
+static float *pt1 = 0;
+static float *pt2 = 0;
+static float *pt3 = 0;
+
+/* Maximum degree of polynomial. */
+int MAXPOLF = 0;
+extern int MAXPOLF;
+
+/* Number of bytes (chars) in maximum size polynomial. */
+static int psize = 0;
+
+
+/* Initialize max degree of polynomials
+ * and allocate temporary storage.
+ */
+#ifdef ANSIC
+void polinif( int maxdeg )
+#else
+int polinif( maxdeg )
+int maxdeg;
+#endif
+{
+
+MAXPOLF = maxdeg;
+psize = (maxdeg + 1) * sizeof(float);
+
+/* Release previously allocated memory, if any. */
+if( pt3 )
+ free(pt3);
+if( pt2 )
+ free(pt2);
+if( pt1 )
+ free(pt1);
+
+/* Allocate new arrays */
+pt1 = (float * )malloc(psize); /* used by polsbtf */
+pt2 = (float * )malloc(psize); /* used by polsbtf */
+pt3 = (float * )malloc(psize); /* used by polmul */
+
+/* Report if failure */
+if( (pt1 == NULL) || (pt2 == NULL) || (pt3 == NULL) )
+ {
+ mtherr( "polinif", ERANGE );
+ exit(1);
+ }
+#if !ANSIC
+return 0;
+#endif
+}
+
+
+
+/* Print the coefficients of a, with d decimal precision.
+ */
+static char *form = "abcdefghijk";
+
+#ifdef ANSIC
+void polprtf( float *a, int na, int d )
+#else
+int polprtf( a, na, d )
+float a[];
+int na, d;
+#endif
+{
+int i, j, d1;
+char *p;
+
+/* Create format descriptor string for the printout.
+ * Do this partly by hand, since sprintf() may be too
+ * bug-ridden to accomplish this feat by itself.
+ */
+p = form;
+*p++ = '%';
+d1 = d + 8;
+(void )sprintf( p, "%d ", d1 );
+p += 1;
+if( d1 >= 10 )
+ p += 1;
+*p++ = '.';
+(void )sprintf( p, "%d ", d );
+p += 1;
+if( d >= 10 )
+ p += 1;
+*p++ = 'e';
+*p++ = ' ';
+*p++ = '\0';
+
+
+/* Now do the printing.
+ */
+d1 += 1;
+j = 0;
+for( i=0; i<=na; i++ )
+ {
+/* Detect end of available line */
+ j += d1;
+ if( j >= 78 )
+ {
+ printf( "\n" );
+ j = d1;
+ }
+ printf( form, a[i] );
+ }
+printf( "\n" );
+#if !ANSIC
+return 0;
+#endif
+}
+
+
+
+/* Set a = 0.
+ */
+#ifdef ANSIC
+void polclrf( register float *a, int n )
+#else
+int polclrf( a, n )
+register float *a;
+int n;
+#endif
+{
+int i;
+
+if( n > MAXPOLF )
+ n = MAXPOLF;
+for( i=0; i<=n; i++ )
+ *a++ = 0.0;
+#if !ANSIC
+return 0;
+#endif
+}
+
+
+
+/* Set b = a.
+ */
+#ifdef ANSIC
+void polmovf( register float *a, int na, register float *b )
+#else
+int polmovf( a, na, b )
+register float *a, *b;
+int na;
+#endif
+{
+int i;
+
+if( na > MAXPOLF )
+ na = MAXPOLF;
+
+for( i=0; i<= na; i++ )
+ {
+ *b++ = *a++;
+ }
+#if !ANSIC
+return 0;
+#endif
+}
+
+
+/* c = b * a.
+ */
+#ifdef ANSIC
+void polmulf( float a[], int na, float b[], int nb, float c[] )
+#else
+int polmulf( a, na, b, nb, c )
+float a[], b[], c[];
+int na, nb;
+#endif
+{
+int i, j, k, nc;
+float x;
+
+nc = na + nb;
+polclrf( pt3, MAXPOLF );
+
+for( i=0; i<=na; i++ )
+ {
+ x = a[i];
+ for( j=0; j<=nb; j++ )
+ {
+ k = i + j;
+ if( k > MAXPOLF )
+ break;
+ pt3[k] += x * b[j];
+ }
+ }
+
+if( nc > MAXPOLF )
+ nc = MAXPOLF;
+for( i=0; i<=nc; i++ )
+ c[i] = pt3[i];
+#if !ANSIC
+return 0;
+#endif
+}
+
+
+
+
+/* c = b + a.
+ */
+#ifdef ANSIC
+void poladdf( float a[], int na, float b[], int nb, float c[] )
+#else
+int poladdf( a, na, b, nb, c )
+float a[], b[], c[];
+int na, nb;
+#endif
+{
+int i, n;
+
+
+if( na > nb )
+ n = na;
+else
+ n = nb;
+
+if( n > MAXPOLF )
+ n = MAXPOLF;
+
+for( i=0; i<=n; i++ )
+ {
+ if( i > na )
+ c[i] = b[i];
+ else if( i > nb )
+ c[i] = a[i];
+ else
+ c[i] = b[i] + a[i];
+ }
+#if !ANSIC
+return 0;
+#endif
+}
+
+/* c = b - a.
+ */
+#ifdef ANSIC
+void polsubf( float a[], int na, float b[], int nb, float c[] )
+#else
+int polsubf( a, na, b, nb, c )
+float a[], b[], c[];
+int na, nb;
+#endif
+{
+int i, n;
+
+
+if( na > nb )
+ n = na;
+else
+ n = nb;
+
+if( n > MAXPOLF )
+ n = MAXPOLF;
+
+for( i=0; i<=n; i++ )
+ {
+ if( i > na )
+ c[i] = b[i];
+ else if( i > nb )
+ c[i] = -a[i];
+ else
+ c[i] = b[i] - a[i];
+ }
+#if !ANSIC
+return 0;
+#endif
+}
+
+
+
+/* c = b/a
+ */
+#ifdef ANSIC
+int poldivf( float a[], int na, float b[], int nb, float c[] )
+#else
+int poldivf( a, na, b, nb, c )
+float a[], b[], c[];
+int na, nb;
+#endif
+{
+float quot;
+float *ta, *tb, *tq;
+int i, j, k, sing;
+
+sing = 0;
+
+/* Allocate temporary arrays. This would be quicker
+ * if done automatically on the stack, but stack space
+ * may be hard to obtain on a small computer.
+ */
+ta = (float * )malloc( psize );
+polclrf( ta, MAXPOLF );
+polmovf( a, na, ta );
+
+tb = (float * )malloc( psize );
+polclrf( tb, MAXPOLF );
+polmovf( b, nb, tb );
+
+tq = (float * )malloc( psize );
+polclrf( tq, MAXPOLF );
+
+/* What to do if leading (constant) coefficient
+ * of denominator is zero.
+ */
+if( a[0] == 0.0 )
+ {
+ for( i=0; i<=na; i++ )
+ {
+ if( ta[i] != 0.0 )
+ goto nzero;
+ }
+ mtherr( "poldivf", SING );
+ goto done;
+
+nzero:
+/* Reduce the degree of the denominator. */
+ for( i=0; i<na; i++ )
+ ta[i] = ta[i+1];
+ ta[na] = 0.0;
+
+ if( b[0] != 0.0 )
+ {
+/* Optional message:
+ printf( "poldivf singularity, divide quotient by x\n" );
+*/
+ sing += 1;
+ }
+ else
+ {
+/* Reduce degree of numerator. */
+ for( i=0; i<nb; i++ )
+ tb[i] = tb[i+1];
+ tb[nb] = 0.0;
+ }
+/* Call self, using reduced polynomials. */
+ sing += poldivf( ta, na, tb, nb, c );
+ goto done;
+ }
+
+/* Long division algorithm. ta[0] is nonzero.
+ */
+for( i=0; i<=MAXPOLF; i++ )
+ {
+ quot = tb[i]/ta[0];
+ for( j=0; j<=MAXPOLF; j++ )
+ {
+ k = j + i;
+ if( k > MAXPOLF )
+ break;
+ tb[k] -= quot * ta[j];
+ }
+ tq[i] = quot;
+ }
+/* Send quotient to output array. */
+polmovf( tq, MAXPOLF, c );
+
+done:
+
+/* Restore allocated memory. */
+free(tq);
+free(tb);
+free(ta);
+return( sing );
+}
+
+
+
+
+/* Change of variables
+ * Substitute a(y) for the variable x in b(x).
+ * x = a(y)
+ * c(x) = b(x) = b(a(y)).
+ */
+
+#ifdef ANSIC
+void polsbtf( float a[], int na, float b[], int nb, float c[] )
+#else
+int polsbtf( a, na, b, nb, c )
+float a[], b[], c[];
+int na, nb;
+#endif
+{
+int i, j, k, n2;
+float x;
+
+/* 0th degree term:
+ */
+polclrf( pt1, MAXPOLF );
+pt1[0] = b[0];
+
+polclrf( pt2, MAXPOLF );
+pt2[0] = 1.0;
+n2 = 0;
+
+for( i=1; i<=nb; i++ )
+ {
+/* Form ith power of a. */
+ polmulf( a, na, pt2, n2, pt2 );
+ n2 += na;
+ x = b[i];
+/* Add the ith coefficient of b times the ith power of a. */
+ for( j=0; j<=n2; j++ )
+ {
+ if( j > MAXPOLF )
+ break;
+ pt1[j] += x * pt2[j];
+ }
+ }
+
+k = n2 + nb;
+if( k > MAXPOLF )
+ k = MAXPOLF;
+for( i=0; i<=k; i++ )
+ c[i] = pt1[i];
+#if !ANSIC
+return 0;
+#endif
+}
+
+
+
+
+/* Evaluate polynomial a(t) at t = x.
+ */
+float polevaf( float *a, int na, float xx )
+{
+float x, s;
+int i;
+
+x = xx;
+s = a[na];
+for( i=na-1; i>=0; i-- )
+ {
+ s = s * x + a[i];
+ }
+return(s);
+}
+
diff --git a/libm/float/powf.c b/libm/float/powf.c
new file mode 100644
index 000000000..367a39ad4
--- /dev/null
+++ b/libm/float/powf.c
@@ -0,0 +1,338 @@
+/* powf.c
+ *
+ * Power function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, z, powf();
+ *
+ * z = powf( x, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes x raised to the yth power. Analytically,
+ *
+ * x**y = exp( y log(x) ).
+ *
+ * Following Cody and Waite, this program uses a lookup table
+ * of 2**-i/16 and pseudo extended precision arithmetic to
+ * obtain an extra three bits of accuracy in both the logarithm
+ * and the exponential.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,10 100,000 1.4e-7 3.6e-8
+ * 1/10 < x < 10, x uniformly distributed.
+ * -10 < y < 10, y uniformly distributed.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * powf overflow x**y > MAXNUMF MAXNUMF
+ * powf underflow x**y < 1/MAXNUMF 0.0
+ * powf domain x<0 and y noninteger 0.0
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1988 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+static char fname[] = {"powf"};
+
+
+/* 2^(-i/16)
+ * The decimal values are rounded to 24-bit precision
+ */
+static float A[] = {
+ 1.00000000000000000000E0,
+ 9.57603275775909423828125E-1,
+ 9.17004048824310302734375E-1,
+ 8.78126084804534912109375E-1,
+ 8.40896427631378173828125E-1,
+ 8.05245161056518554687500E-1,
+ 7.71105408668518066406250E-1,
+ 7.38413095474243164062500E-1,
+ 7.07106769084930419921875E-1,
+ 6.77127778530120849609375E-1,
+ 6.48419797420501708984375E-1,
+ 6.20928883552551269531250E-1,
+ 5.94603538513183593750000E-1,
+ 5.69394290447235107421875E-1,
+ 5.45253872871398925781250E-1,
+ 5.22136867046356201171875E-1,
+ 5.00000000000000000000E-1
+};
+/* continuation, for even i only
+ * 2^(i/16) = A[i] + B[i/2]
+ */
+static float B[] = {
+ 0.00000000000000000000E0,
+-5.61963907099083340520586E-9,
+-1.23776636307969995237668E-8,
+ 4.03545234539989593104537E-9,
+ 1.21016171044789693621048E-8,
+-2.00949968760174979411038E-8,
+ 1.89881769396087499852802E-8,
+-6.53877009617774467211965E-9,
+ 0.00000000000000000000E0
+};
+
+/* 1 / A[i]
+ * The decimal values are full precision
+ */
+static float Ainv[] = {
+ 1.00000000000000000000000E0,
+ 1.04427378242741384032197E0,
+ 1.09050773266525765920701E0,
+ 1.13878863475669165370383E0,
+ 1.18920711500272106671750E0,
+ 1.24185781207348404859368E0,
+ 1.29683955465100966593375E0,
+ 1.35425554693689272829801E0,
+ 1.41421356237309504880169E0,
+ 1.47682614593949931138691E0,
+ 1.54221082540794082361229E0,
+ 1.61049033194925430817952E0,
+ 1.68179283050742908606225E0,
+ 1.75625216037329948311216E0,
+ 1.83400808640934246348708E0,
+ 1.91520656139714729387261E0,
+ 2.00000000000000000000000E0
+};
+
+#ifdef DEC
+#define MEXP 2032.0
+#define MNEXP -2032.0
+#else
+#define MEXP 2048.0
+#define MNEXP -2400.0
+#endif
+
+/* log2(e) - 1 */
+#define LOG2EA 0.44269504088896340736F
+extern float MAXNUMF;
+
+#define F W
+#define Fa Wa
+#define Fb Wb
+#define G W
+#define Ga Wa
+#define Gb u
+#define H W
+#define Ha Wb
+#define Hb Wb
+
+
+#ifdef ANSIC
+float floorf( float );
+float frexpf( float, int *);
+float ldexpf( float, int );
+float powif( float, int );
+#else
+float floorf(), frexpf(), ldexpf(), powif();
+#endif
+
+/* Find a multiple of 1/16 that is within 1/16 of x. */
+#define reduc(x) 0.0625 * floorf( 16 * (x) )
+
+#ifdef ANSIC
+float powf( float x, float y )
+#else
+float powf( x, y )
+float x, y;
+#endif
+{
+float u, w, z, W, Wa, Wb, ya, yb;
+/* float F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
+int e, i, nflg;
+
+
+nflg = 0; /* flag = 1 if x<0 raised to integer power */
+w = floorf(y);
+if( w < 0 )
+ z = -w;
+else
+ z = w;
+if( (w == y) && (z < 32768.0) )
+ {
+ i = w;
+ w = powif( x, i );
+ return( w );
+ }
+
+
+if( x <= 0.0F )
+ {
+ if( x == 0.0 )
+ {
+ if( y == 0.0 )
+ return( 1.0 ); /* 0**0 */
+ else
+ return( 0.0 ); /* 0**y */
+ }
+ else
+ {
+ if( w != y )
+ { /* noninteger power of negative number */
+ mtherr( fname, DOMAIN );
+ return(0.0);
+ }
+ nflg = 1;
+ if( x < 0 )
+ x = -x;
+ }
+ }
+
+/* separate significand from exponent */
+x = frexpf( x, &e );
+
+/* find significand in antilog table A[] */
+i = 1;
+if( x <= A[9] )
+ i = 9;
+if( x <= A[i+4] )
+ i += 4;
+if( x <= A[i+2] )
+ i += 2;
+if( x >= A[1] )
+ i = -1;
+i += 1;
+
+
+/* Find (x - A[i])/A[i]
+ * in order to compute log(x/A[i]):
+ *
+ * log(x) = log( a x/a ) = log(a) + log(x/a)
+ *
+ * log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a
+ */
+x -= A[i];
+x -= B[ i >> 1 ];
+x *= Ainv[i];
+
+
+/* rational approximation for log(1+v):
+ *
+ * log(1+v) = v - 0.5 v^2 + v^3 P(v)
+ * Theoretical relative error of the approximation is 3.5e-11
+ * on the interval 2^(1/16) - 1 > v > 2^(-1/16) - 1
+ */
+z = x*x;
+w = (((-0.1663883081054895 * x
+ + 0.2003770364206271) * x
+ - 0.2500006373383951) * x
+ + 0.3333331095506474) * x * z;
+w -= 0.5 * z;
+
+/* Convert to base 2 logarithm:
+ * multiply by log2(e)
+ */
+w = w + LOG2EA * w;
+/* Note x was not yet added in
+ * to above rational approximation,
+ * so do it now, while multiplying
+ * by log2(e).
+ */
+z = w + LOG2EA * x;
+z = z + x;
+
+/* Compute exponent term of the base 2 logarithm. */
+w = -i;
+w *= 0.0625; /* divide by 16 */
+w += e;
+/* Now base 2 log of x is w + z. */
+
+/* Multiply base 2 log by y, in extended precision. */
+
+/* separate y into large part ya
+ * and small part yb less than 1/16
+ */
+ya = reduc(y);
+yb = y - ya;
+
+
+F = z * y + w * yb;
+Fa = reduc(F);
+Fb = F - Fa;
+
+G = Fa + w * ya;
+Ga = reduc(G);
+Gb = G - Ga;
+
+H = Fb + Gb;
+Ha = reduc(H);
+w = 16 * (Ga + Ha);
+
+/* Test the power of 2 for overflow */
+if( w > MEXP )
+ {
+ mtherr( fname, OVERFLOW );
+ return( MAXNUMF );
+ }
+
+if( w < MNEXP )
+ {
+ mtherr( fname, UNDERFLOW );
+ return( 0.0 );
+ }
+
+e = w;
+Hb = H - Ha;
+
+if( Hb > 0.0 )
+ {
+ e += 1;
+ Hb -= 0.0625;
+ }
+
+/* Now the product y * log2(x) = Hb + e/16.0.
+ *
+ * Compute base 2 exponential of Hb,
+ * where -0.0625 <= Hb <= 0.
+ * Theoretical relative error of the approximation is 2.8e-12.
+ */
+/* z = 2**Hb - 1 */
+z = ((( 9.416993633606397E-003 * Hb
+ + 5.549356188719141E-002) * Hb
+ + 2.402262883964191E-001) * Hb
+ + 6.931471791490764E-001) * Hb;
+
+/* Express e/16 as an integer plus a negative number of 16ths.
+ * Find lookup table entry for the fractional power of 2.
+ */
+if( e < 0 )
+ i = -( -e >> 4 );
+else
+ i = (e >> 4) + 1;
+e = (i << 4) - e;
+w = A[e];
+z = w + w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */
+z = ldexpf( z, i ); /* multiply by integer power of 2 */
+
+if( nflg )
+ {
+/* For negative x,
+ * find out if the integer exponent
+ * is odd or even.
+ */
+ w = 2 * floorf( (float) 0.5 * w );
+ if( w != y )
+ z = -z; /* odd exponent */
+ }
+
+return( z );
+}
diff --git a/libm/float/powif.c b/libm/float/powif.c
new file mode 100644
index 000000000..d226896ba
--- /dev/null
+++ b/libm/float/powif.c
@@ -0,0 +1,156 @@
+/* powif.c
+ *
+ * Real raised to integer power
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, powif();
+ * int n;
+ *
+ * y = powif( x, n );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns argument x raised to the nth power.
+ * The routine efficiently decomposes n as a sum of powers of
+ * two. The desired power is a product of two-to-the-kth
+ * powers of x. Thus to compute the 32767 power of x requires
+ * 28 multiplications instead of 32767 multiplications.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error:
+ * arithmetic x domain n domain # trials peak rms
+ * IEEE .04,26 -26,26 100000 1.1e-6 2.0e-7
+ * IEEE 1,2 -128,128 100000 1.1e-5 1.0e-6
+ *
+ * Returns MAXNUMF on overflow, zero on underflow.
+ *
+ */
+
+/* powi.c */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+extern float MAXNUMF, MAXLOGF, MINLOGF, LOGE2F;
+
+float frexpf( float, int * );
+
+float powif( float x, int nn )
+{
+int n, e, sign, asign, lx;
+float w, y, s;
+
+if( x == 0.0 )
+ {
+ if( nn == 0 )
+ return( 1.0 );
+ else if( nn < 0 )
+ return( MAXNUMF );
+ else
+ return( 0.0 );
+ }
+
+if( nn == 0 )
+ return( 1.0 );
+
+
+if( x < 0.0 )
+ {
+ asign = -1;
+ x = -x;
+ }
+else
+ asign = 0;
+
+
+if( nn < 0 )
+ {
+ sign = -1;
+ n = -nn;
+/*
+ x = 1.0/x;
+*/
+ }
+else
+ {
+ sign = 0;
+ n = nn;
+ }
+
+/* Overflow detection */
+
+/* Calculate approximate logarithm of answer */
+s = frexpf( x, &lx );
+e = (lx - 1)*n;
+if( (e == 0) || (e > 64) || (e < -64) )
+ {
+ s = (s - 7.0710678118654752e-1) / (s + 7.0710678118654752e-1);
+ s = (2.9142135623730950 * s - 0.5 + lx) * nn * LOGE2F;
+ }
+else
+ {
+ s = LOGE2F * e;
+ }
+
+if( s > MAXLOGF )
+ {
+ mtherr( "powi", OVERFLOW );
+ y = MAXNUMF;
+ goto done;
+ }
+
+if( s < MINLOGF )
+ return(0.0);
+
+/* Handle tiny denormal answer, but with less accuracy
+ * since roundoff error in 1.0/x will be amplified.
+ * The precise demarcation should be the gradual underflow threshold.
+ */
+if( s < (-MAXLOGF+2.0) )
+ {
+ x = 1.0/x;
+ sign = 0;
+ }
+
+/* First bit of the power */
+if( n & 1 )
+ y = x;
+
+else
+ {
+ y = 1.0;
+ asign = 0;
+ }
+
+w = x;
+n >>= 1;
+while( n )
+ {
+ w = w * w; /* arg to the 2-to-the-kth power */
+ if( n & 1 ) /* if that bit is set, then include in product */
+ y *= w;
+ n >>= 1;
+ }
+
+
+done:
+
+if( asign )
+ y = -y; /* odd power of negative number */
+if( sign )
+ y = 1.0/y;
+return(y);
+}
diff --git a/libm/float/powtst.c b/libm/float/powtst.c
new file mode 100644
index 000000000..ff4845de2
--- /dev/null
+++ b/libm/float/powtst.c
@@ -0,0 +1,41 @@
+#include <stdio.h>
+#include <math.h>
+extern float MAXNUMF, MAXLOGF, MINLOGF;
+
+int
+main()
+{
+float exp1, minnum, x, y, z, e;
+exp1 = expf(1.0F);
+
+minnum = powif(2.0F,-149);
+
+x = exp1;
+y = MINLOGF + logf(0.501);
+/*y = MINLOGF - 0.405;*/
+z = powf(x,y);
+e = (z - minnum) / minnum;
+printf("%.16e %.16e\n", z, e);
+
+x = exp1;
+y = MAXLOGF;
+z = powf(x,y);
+e = (z - MAXNUMF) / MAXNUMF;
+printf("%.16e %.16e\n", z, e);
+
+x = MAXNUMF;
+y = 1.0F/MAXLOGF;
+z = powf(x,y);
+e = (z - exp1) / exp1;
+printf("%.16e %.16e\n", z, e);
+
+
+x = exp1;
+y = MINLOGF;
+z = powf(x,y);
+e = (z - minnum) / minnum;
+printf("%.16e %.16e\n", z, e);
+
+
+exit(0);
+}
diff --git a/libm/float/psif.c b/libm/float/psif.c
new file mode 100644
index 000000000..2d9187c67
--- /dev/null
+++ b/libm/float/psif.c
@@ -0,0 +1,153 @@
+/* psif.c
+ *
+ * Psi (digamma) function
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, psif();
+ *
+ * y = psif( x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * d -
+ * psi(x) = -- ln | (x)
+ * dx
+ *
+ * is the logarithmic derivative of the gamma function.
+ * For integer x,
+ * n-1
+ * -
+ * psi(n) = -EUL + > 1/k.
+ * -
+ * k=1
+ *
+ * This formula is used for 0 < n <= 10. If x is negative, it
+ * is transformed to a positive argument by the reflection
+ * formula psi(1-x) = psi(x) + pi cot(pi x).
+ * For general positive x, the argument is made greater than 10
+ * using the recurrence psi(x+1) = psi(x) + 1/x.
+ * Then the following asymptotic expansion is applied:
+ *
+ * inf. B
+ * - 2k
+ * psi(x) = log(x) - 1/2x - > -------
+ * - 2k
+ * k=1 2k x
+ *
+ * where the B2k are Bernoulli numbers.
+ *
+ * ACCURACY:
+ * Absolute error, relative when |psi| > 1 :
+ * arithmetic domain # trials peak rms
+ * IEEE -33,0 30000 8.2e-7 1.2e-7
+ * IEEE 0,33 100000 7.3e-7 7.7e-8
+ *
+ * ERROR MESSAGES:
+ * message condition value returned
+ * psi singularity x integer <=0 MAXNUMF
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+
+static float A[] = {
+-4.16666666666666666667E-3,
+ 3.96825396825396825397E-3,
+-8.33333333333333333333E-3,
+ 8.33333333333333333333E-2
+};
+
+
+#define EUL 0.57721566490153286061
+
+extern float PIF, MAXNUMF;
+
+
+
+float floorf(float), logf(float), tanf(float);
+float polevlf(float, float *, int);
+
+float psif(float xx)
+{
+float p, q, nz, x, s, w, y, z;
+int i, n, negative;
+
+
+x = xx;
+nz = 0.0;
+negative = 0;
+if( x <= 0.0 )
+ {
+ negative = 1;
+ q = x;
+ p = floorf(q);
+ if( p == q )
+ {
+ mtherr( "psif", SING );
+ return( MAXNUMF );
+ }
+ nz = q - p;
+ if( nz != 0.5 )
+ {
+ if( nz > 0.5 )
+ {
+ p += 1.0;
+ nz = q - p;
+ }
+ nz = PIF/tanf(PIF*nz);
+ }
+ else
+ {
+ nz = 0.0;
+ }
+ x = 1.0 - x;
+ }
+
+/* check for positive integer up to 10 */
+if( (x <= 10.0) && (x == floorf(x)) )
+ {
+ y = 0.0;
+ n = x;
+ for( i=1; i<n; i++ )
+ {
+ w = i;
+ y += 1.0/w;
+ }
+ y -= EUL;
+ goto done;
+ }
+
+s = x;
+w = 0.0;
+while( s < 10.0 )
+ {
+ w += 1.0/s;
+ s += 1.0;
+ }
+
+if( s < 1.0e8 )
+ {
+ z = 1.0/(s * s);
+ y = z * polevlf( z, A, 3 );
+ }
+else
+ y = 0.0;
+
+y = logf(s) - (0.5/s) - y - w;
+
+done:
+if( negative )
+ {
+ y -= nz;
+ }
+return(y);
+}
diff --git a/libm/float/rgammaf.c b/libm/float/rgammaf.c
new file mode 100644
index 000000000..5afa25e91
--- /dev/null
+++ b/libm/float/rgammaf.c
@@ -0,0 +1,130 @@
+/* rgammaf.c
+ *
+ * Reciprocal gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, rgammaf();
+ *
+ * y = rgammaf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns one divided by the gamma function of the argument.
+ *
+ * The function is approximated by a Chebyshev expansion in
+ * the interval [0,1]. Range reduction is by recurrence
+ * for arguments between -34.034 and +34.84425627277176174.
+ * 1/MAXNUMF is returned for positive arguments outside this
+ * range.
+ *
+ * The reciprocal gamma function has no singularities,
+ * but overflow and underflow may occur for large arguments.
+ * These conditions return either MAXNUMF or 1/MAXNUMF with
+ * appropriate sign.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -34,+34 100000 8.9e-7 1.1e-7
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1985, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+/* Chebyshev coefficients for reciprocal gamma function
+ * in interval 0 to 1. Function is 1/(x gamma(x)) - 1
+ */
+
+static float R[] = {
+ 1.08965386454418662084E-9,
+-3.33964630686836942556E-8,
+ 2.68975996440595483619E-7,
+ 2.96001177518801696639E-6,
+-8.04814124978471142852E-5,
+ 4.16609138709688864714E-4,
+ 5.06579864028608725080E-3,
+-6.41925436109158228810E-2,
+-4.98558728684003594785E-3,
+ 1.27546015610523951063E-1
+};
+
+
+static char name[] = "rgammaf";
+
+extern float PIF, MAXLOGF, MAXNUMF;
+
+
+
+float chbevlf(float, float *, int);
+float expf(float), logf(float), sinf(float), lgamf(float);
+
+float rgammaf(float xx)
+{
+float x, w, y, z;
+int sign;
+
+x = xx;
+if( x > 34.84425627277176174)
+ {
+ mtherr( name, UNDERFLOW );
+ return(1.0/MAXNUMF);
+ }
+if( x < -34.034 )
+ {
+ w = -x;
+ z = sinf( PIF*w );
+ if( z == 0.0 )
+ return(0.0);
+ if( z < 0.0 )
+ {
+ sign = 1;
+ z = -z;
+ }
+ else
+ sign = -1;
+
+ y = logf( w * z / PIF ) + lgamf(w);
+ if( y < -MAXLOGF )
+ {
+ mtherr( name, UNDERFLOW );
+ return( sign * 1.0 / MAXNUMF );
+ }
+ if( y > MAXLOGF )
+ {
+ mtherr( name, OVERFLOW );
+ return( sign * MAXNUMF );
+ }
+ return( sign * expf(y));
+ }
+z = 1.0;
+w = x;
+
+while( w > 1.0 ) /* Downward recurrence */
+ {
+ w -= 1.0;
+ z *= w;
+ }
+while( w < 0.0 ) /* Upward recurrence */
+ {
+ z /= w;
+ w += 1.0;
+ }
+if( w == 0.0 ) /* Nonpositive integer */
+ return(0.0);
+if( w == 1.0 ) /* Other integer */
+ return( 1.0/z );
+
+y = w * ( 1.0 + chbevlf( 4.0*w-2.0, R, 10 ) ) / z;
+return(y);
+}
diff --git a/libm/float/setprec.c b/libm/float/setprec.c
new file mode 100644
index 000000000..a5222ae73
--- /dev/null
+++ b/libm/float/setprec.c
@@ -0,0 +1,10 @@
+/* Null stubs for coprocessor precision settings */
+
+int
+sprec() {return 0; }
+
+int
+dprec() {return 0; }
+
+int
+ldprec() {return 0; }
diff --git a/libm/float/shichif.c b/libm/float/shichif.c
new file mode 100644
index 000000000..ae98021a9
--- /dev/null
+++ b/libm/float/shichif.c
@@ -0,0 +1,212 @@
+/* shichif.c
+ *
+ * Hyperbolic sine and cosine integrals
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, Chi, Shi;
+ *
+ * shichi( x, &Chi, &Shi );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integrals
+ *
+ * x
+ * -
+ * | | cosh t - 1
+ * Chi(x) = eul + ln x + | ----------- dt,
+ * | | t
+ * -
+ * 0
+ *
+ * x
+ * -
+ * | | sinh t
+ * Shi(x) = | ------ dt
+ * | | t
+ * -
+ * 0
+ *
+ * where eul = 0.57721566490153286061 is Euler's constant.
+ * The integrals are evaluated by power series for x < 8
+ * and by Chebyshev expansions for x between 8 and 88.
+ * For large x, both functions approach exp(x)/2x.
+ * Arguments greater than 88 in magnitude return MAXNUM.
+ *
+ *
+ * ACCURACY:
+ *
+ * Test interval 0 to 88.
+ * Relative error:
+ * arithmetic function # trials peak rms
+ * IEEE Shi 20000 3.5e-7 7.0e-8
+ * Absolute error, except relative when |Chi| > 1:
+ * IEEE Chi 20000 3.8e-7 7.6e-8
+ */
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+/* x exp(-x) shi(x), inverted interval 8 to 18 */
+static float S1[] = {
+-3.56699611114982536845E-8,
+ 1.44818877384267342057E-7,
+ 7.82018215184051295296E-7,
+-5.39919118403805073710E-6,
+-3.12458202168959833422E-5,
+ 8.90136741950727517826E-5,
+ 2.02558474743846862168E-3,
+ 2.96064440855633256972E-2,
+ 1.11847751047257036625E0
+};
+
+/* x exp(-x) shi(x), inverted interval 18 to 88 */
+static float S2[] = {
+ 1.69050228879421288846E-8,
+ 1.25391771228487041649E-7,
+ 1.16229947068677338732E-6,
+ 1.61038260117376323993E-5,
+ 3.49810375601053973070E-4,
+ 1.28478065259647610779E-2,
+ 1.03665722588798326712E0
+};
+
+
+/* x exp(-x) chin(x), inverted interval 8 to 18 */
+static float C1[] = {
+ 1.31458150989474594064E-8,
+-4.75513930924765465590E-8,
+-2.21775018801848880741E-7,
+ 1.94635531373272490962E-6,
+ 4.33505889257316408893E-6,
+-6.13387001076494349496E-5,
+-3.13085477492997465138E-4,
+ 4.97164789823116062801E-4,
+ 2.64347496031374526641E-2,
+ 1.11446150876699213025E0
+};
+
+/* x exp(-x) chin(x), inverted interval 18 to 88 */
+static float C2[] = {
+-3.00095178028681682282E-9,
+ 7.79387474390914922337E-8,
+ 1.06942765566401507066E-6,
+ 1.59503164802313196374E-5,
+ 3.49592575153777996871E-4,
+ 1.28475387530065247392E-2,
+ 1.03665693917934275131E0
+};
+
+
+
+/* Sine and cosine integrals */
+
+#define EUL 0.57721566490153286061
+extern float MACHEPF, MAXNUMF;
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#ifdef ANSIC
+float logf(float ), expf(float), chbevlf(float, float *, int);
+#else
+float logf(), expf(), chbevlf();
+#endif
+
+
+
+int shichif( float xx, float *si, float *ci )
+{
+float x, k, z, c, s, a;
+short sign;
+
+x = xx;
+if( x < 0.0 )
+ {
+ sign = -1;
+ x = -x;
+ }
+else
+ sign = 0;
+
+
+if( x == 0.0 )
+ {
+ *si = 0.0;
+ *ci = -MAXNUMF;
+ return( 0 );
+ }
+
+if( x >= 8.0 )
+ goto chb;
+
+z = x * x;
+
+/* Direct power series expansion */
+
+a = 1.0;
+s = 1.0;
+c = 0.0;
+k = 2.0;
+
+do
+ {
+ a *= z/k;
+ c += a/k;
+ k += 1.0;
+ a /= k;
+ s += a/k;
+ k += 1.0;
+ }
+while( fabsf(a/s) > MACHEPF );
+
+s *= x;
+goto done;
+
+
+chb:
+
+if( x < 18.0 )
+ {
+ a = (576.0/x - 52.0)/10.0;
+ k = expf(x) / x;
+ s = k * chbevlf( a, S1, 9 );
+ c = k * chbevlf( a, C1, 10 );
+ goto done;
+ }
+
+if( x <= 88.0 )
+ {
+ a = (6336.0/x - 212.0)/70.0;
+ k = expf(x) / x;
+ s = k * chbevlf( a, S2, 7 );
+ c = k * chbevlf( a, C2, 7 );
+ goto done;
+ }
+else
+ {
+ if( sign )
+ *si = -MAXNUMF;
+ else
+ *si = MAXNUMF;
+ *ci = MAXNUMF;
+ return(0);
+ }
+done:
+if( sign )
+ s = -s;
+
+*si = s;
+
+*ci = EUL + logf(x) + c;
+return(0);
+}
diff --git a/libm/float/sicif.c b/libm/float/sicif.c
new file mode 100644
index 000000000..04633ee68
--- /dev/null
+++ b/libm/float/sicif.c
@@ -0,0 +1,279 @@
+/* sicif.c
+ *
+ * Sine and cosine integrals
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, Ci, Si;
+ *
+ * sicif( x, &Si, &Ci );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates the integrals
+ *
+ * x
+ * -
+ * | cos t - 1
+ * Ci(x) = eul + ln x + | --------- dt,
+ * | t
+ * -
+ * 0
+ * x
+ * -
+ * | sin t
+ * Si(x) = | ----- dt
+ * | t
+ * -
+ * 0
+ *
+ * where eul = 0.57721566490153286061 is Euler's constant.
+ * The integrals are approximated by rational functions.
+ * For x > 8 auxiliary functions f(x) and g(x) are employed
+ * such that
+ *
+ * Ci(x) = f(x) sin(x) - g(x) cos(x)
+ * Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)
+ *
+ *
+ * ACCURACY:
+ * Test interval = [0,50].
+ * Absolute error, except relative when > 1:
+ * arithmetic function # trials peak rms
+ * IEEE Si 30000 2.1e-7 4.3e-8
+ * IEEE Ci 30000 3.9e-7 2.2e-8
+ */
+
+/*
+Cephes Math Library Release 2.1: January, 1989
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+static float SN[] = {
+-8.39167827910303881427E-11,
+ 4.62591714427012837309E-8,
+-9.75759303843632795789E-6,
+ 9.76945438170435310816E-4,
+-4.13470316229406538752E-2,
+ 1.00000000000000000302E0,
+};
+static float SD[] = {
+ 2.03269266195951942049E-12,
+ 1.27997891179943299903E-9,
+ 4.41827842801218905784E-7,
+ 9.96412122043875552487E-5,
+ 1.42085239326149893930E-2,
+ 9.99999999999999996984E-1,
+};
+
+static float CN[] = {
+ 2.02524002389102268789E-11,
+-1.35249504915790756375E-8,
+ 3.59325051419993077021E-6,
+-4.74007206873407909465E-4,
+ 2.89159652607555242092E-2,
+-1.00000000000000000080E0,
+};
+static float CD[] = {
+ 4.07746040061880559506E-12,
+ 3.06780997581887812692E-9,
+ 1.23210355685883423679E-6,
+ 3.17442024775032769882E-4,
+ 5.10028056236446052392E-2,
+ 4.00000000000000000080E0,
+};
+
+
+static float FN4[] = {
+ 4.23612862892216586994E0,
+ 5.45937717161812843388E0,
+ 1.62083287701538329132E0,
+ 1.67006611831323023771E-1,
+ 6.81020132472518137426E-3,
+ 1.08936580650328664411E-4,
+ 5.48900223421373614008E-7,
+};
+static float FD4[] = {
+/* 1.00000000000000000000E0,*/
+ 8.16496634205391016773E0,
+ 7.30828822505564552187E0,
+ 1.86792257950184183883E0,
+ 1.78792052963149907262E-1,
+ 7.01710668322789753610E-3,
+ 1.10034357153915731354E-4,
+ 5.48900252756255700982E-7,
+};
+
+
+static float FN8[] = {
+ 4.55880873470465315206E-1,
+ 7.13715274100146711374E-1,
+ 1.60300158222319456320E-1,
+ 1.16064229408124407915E-2,
+ 3.49556442447859055605E-4,
+ 4.86215430826454749482E-6,
+ 3.20092790091004902806E-8,
+ 9.41779576128512936592E-11,
+ 9.70507110881952024631E-14,
+};
+static float FD8[] = {
+/* 1.00000000000000000000E0,*/
+ 9.17463611873684053703E-1,
+ 1.78685545332074536321E-1,
+ 1.22253594771971293032E-2,
+ 3.58696481881851580297E-4,
+ 4.92435064317881464393E-6,
+ 3.21956939101046018377E-8,
+ 9.43720590350276732376E-11,
+ 9.70507110881952025725E-14,
+};
+
+static float GN4[] = {
+ 8.71001698973114191777E-2,
+ 6.11379109952219284151E-1,
+ 3.97180296392337498885E-1,
+ 7.48527737628469092119E-2,
+ 5.38868681462177273157E-3,
+ 1.61999794598934024525E-4,
+ 1.97963874140963632189E-6,
+ 7.82579040744090311069E-9,
+};
+static float GD4[] = {
+/* 1.00000000000000000000E0,*/
+ 1.64402202413355338886E0,
+ 6.66296701268987968381E-1,
+ 9.88771761277688796203E-2,
+ 6.22396345441768420760E-3,
+ 1.73221081474177119497E-4,
+ 2.02659182086343991969E-6,
+ 7.82579218933534490868E-9,
+};
+
+static float GN8[] = {
+ 6.97359953443276214934E-1,
+ 3.30410979305632063225E-1,
+ 3.84878767649974295920E-2,
+ 1.71718239052347903558E-3,
+ 3.48941165502279436777E-5,
+ 3.47131167084116673800E-7,
+ 1.70404452782044526189E-9,
+ 3.85945925430276600453E-12,
+ 3.14040098946363334640E-15,
+};
+static float GD8[] = {
+/* 1.00000000000000000000E0,*/
+ 1.68548898811011640017E0,
+ 4.87852258695304967486E-1,
+ 4.67913194259625806320E-2,
+ 1.90284426674399523638E-3,
+ 3.68475504442561108162E-5,
+ 3.57043223443740838771E-7,
+ 1.72693748966316146736E-9,
+ 3.87830166023954706752E-12,
+ 3.14040098946363335242E-15,
+};
+
+#define EUL 0.57721566490153286061
+extern float MAXNUMF, PIO2F, MACHEPF;
+
+
+
+#ifdef ANSIC
+float logf(float), sinf(float), cosf(float);
+float polevlf(float, float *, int);
+float p1evlf(float, float *, int);
+#else
+float logf(), sinf(), cosf(), polevlf(), p1evlf();
+#endif
+
+
+int sicif( float xx, float *si, float *ci )
+{
+float x, z, c, s, f, g;
+int sign;
+
+x = xx;
+if( x < 0.0 )
+ {
+ sign = -1;
+ x = -x;
+ }
+else
+ sign = 0;
+
+
+if( x == 0.0 )
+ {
+ *si = 0.0;
+ *ci = -MAXNUMF;
+ return( 0 );
+ }
+
+
+if( x > 1.0e9 )
+ {
+ *si = PIO2F - cosf(x)/x;
+ *ci = sinf(x)/x;
+ return( 0 );
+ }
+
+
+
+if( x > 4.0 )
+ goto asympt;
+
+z = x * x;
+s = x * polevlf( z, SN, 5 ) / polevlf( z, SD, 5 );
+c = z * polevlf( z, CN, 5 ) / polevlf( z, CD, 5 );
+
+if( sign )
+ s = -s;
+*si = s;
+*ci = EUL + logf(x) + c; /* real part if x < 0 */
+return(0);
+
+
+
+/* The auxiliary functions are:
+ *
+ *
+ * *si = *si - PIO2;
+ * c = cos(x);
+ * s = sin(x);
+ *
+ * t = *ci * s - *si * c;
+ * a = *ci * c + *si * s;
+ *
+ * *si = t;
+ * *ci = -a;
+ */
+
+
+asympt:
+
+s = sinf(x);
+c = cosf(x);
+z = 1.0/(x*x);
+if( x < 8.0 )
+ {
+ f = polevlf( z, FN4, 6 ) / (x * p1evlf( z, FD4, 7 ));
+ g = z * polevlf( z, GN4, 7 ) / p1evlf( z, GD4, 7 );
+ }
+else
+ {
+ f = polevlf( z, FN8, 8 ) / (x * p1evlf( z, FD8, 8 ));
+ g = z * polevlf( z, GN8, 8 ) / p1evlf( z, GD8, 9 );
+ }
+*si = PIO2F - f * c - g * s;
+if( sign )
+ *si = -( *si );
+*ci = f * s - g * c;
+
+return(0);
+}
diff --git a/libm/float/sindgf.c b/libm/float/sindgf.c
new file mode 100644
index 000000000..a3f5851c8
--- /dev/null
+++ b/libm/float/sindgf.c
@@ -0,0 +1,232 @@
+/* sindgf.c
+ *
+ * Circular sine of angle in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, sindgf();
+ *
+ * y = sindgf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of 45 degrees.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the sine is approximated by
+ * x + x**3 P(x**2).
+ * Between pi/4 and pi/2 the cosine is represented as
+ * 1 - x**2 Q(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-3600 100,000 1.2e-7 3.0e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sin total loss x > 2^24 0.0
+ *
+ */
+
+/* cosdgf.c
+ *
+ * Circular cosine of angle in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, cosdgf();
+ *
+ * y = cosdgf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of 45 degrees.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the cosine is approximated by
+ * 1 - x**2 Q(x**2).
+ * Between pi/4 and pi/2 the sine is represented as
+ * x + x**3 P(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -8192,+8192 100,000 3.0e-7 3.0e-8
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1985, 1987, 1988, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+/* Single precision circular sine
+ * test interval: [-pi/4, +pi/4]
+ * trials: 10000
+ * peak relative error: 6.8e-8
+ * rms relative error: 2.6e-8
+ */
+#include <math.h>
+
+
+/*static float FOPI = 1.27323954473516;*/
+
+extern float PIO4F;
+
+/* These are for a 24-bit significand: */
+static float T24M1 = 16777215.;
+
+static float PI180 = 0.0174532925199432957692; /* pi/180 */
+
+float sindgf( float xx )
+{
+float x, y, z;
+long j;
+int sign;
+
+sign = 1;
+x = xx;
+if( xx < 0 )
+ {
+ sign = -1;
+ x = -xx;
+ }
+if( x > T24M1 )
+ {
+ mtherr( "sindgf", TLOSS );
+ return(0.0);
+ }
+j = 0.022222222222222222222 * x; /* integer part of x/45 */
+y = j;
+/* map zeros to origin */
+if( j & 1 )
+ {
+ j += 1;
+ y += 1.0;
+ }
+j &= 7; /* octant modulo 360 degrees */
+/* reflect in x axis */
+if( j > 3)
+ {
+ sign = -sign;
+ j -= 4;
+ }
+
+x = x - y * 45.0;
+x *= PI180; /* multiply by pi/180 to convert to radians */
+
+z = x * x;
+if( (j==1) || (j==2) )
+ {
+/*
+ y = ((( 2.4462803166E-5 * z
+ - 1.3887580023E-3) * z
+ + 4.1666650433E-2) * z
+ - 4.9999999968E-1) * z
+ + 1.0;
+*/
+
+/* measured relative error in +/- pi/4 is 7.8e-8 */
+ y = (( 2.443315711809948E-005 * z
+ - 1.388731625493765E-003) * z
+ + 4.166664568298827E-002) * z * z;
+ y -= 0.5 * z;
+ y += 1.0;
+ }
+else
+ {
+/* Theoretical relative error = 3.8e-9 in [-pi/4, +pi/4] */
+ y = ((-1.9515295891E-4 * z
+ + 8.3321608736E-3) * z
+ - 1.6666654611E-1) * z * x;
+ y += x;
+ }
+
+if(sign < 0)
+ y = -y;
+return( y);
+}
+
+
+/* Single precision circular cosine
+ * test interval: [-pi/4, +pi/4]
+ * trials: 10000
+ * peak relative error: 8.3e-8
+ * rms relative error: 2.2e-8
+ */
+
+float cosdgf( float xx )
+{
+register float x, y, z;
+int j, sign;
+
+/* make argument positive */
+sign = 1;
+x = xx;
+if( x < 0 )
+ x = -x;
+
+if( x > T24M1 )
+ {
+ mtherr( "cosdgf", TLOSS );
+ return(0.0);
+ }
+
+j = 0.02222222222222222222222 * x; /* integer part of x/PIO4 */
+y = j;
+/* integer and fractional part modulo one octant */
+if( j & 1 ) /* map zeros to origin */
+ {
+ j += 1;
+ y += 1.0;
+ }
+j &= 7;
+if( j > 3)
+ {
+ j -=4;
+ sign = -sign;
+ }
+
+if( j > 1 )
+ sign = -sign;
+
+x = x - y * 45.0; /* x mod 45 degrees */
+x *= PI180; /* multiply by pi/180 to convert to radians */
+
+z = x * x;
+
+if( (j==1) || (j==2) )
+ {
+ y = (((-1.9515295891E-4 * z
+ + 8.3321608736E-3) * z
+ - 1.6666654611E-1) * z * x)
+ + x;
+ }
+else
+ {
+ y = (( 2.443315711809948E-005 * z
+ - 1.388731625493765E-003) * z
+ + 4.166664568298827E-002) * z * z;
+ y -= 0.5 * z;
+ y += 1.0;
+ }
+if(sign < 0)
+ y = -y;
+return( y );
+}
+
diff --git a/libm/float/sinf.c b/libm/float/sinf.c
new file mode 100644
index 000000000..2f1bb45b8
--- /dev/null
+++ b/libm/float/sinf.c
@@ -0,0 +1,283 @@
+/* sinf.c
+ *
+ * Circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, sinf();
+ *
+ * y = sinf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of pi/4. The reduction
+ * error is nearly eliminated by contriving an extended precision
+ * modular arithmetic.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the sine is approximated by
+ * x + x**3 P(x**2).
+ * Between pi/4 and pi/2 the cosine is represented as
+ * 1 - x**2 Q(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -4096,+4096 100,000 1.2e-7 3.0e-8
+ * IEEE -8192,+8192 100,000 3.0e-7 3.0e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sin total loss x > 2^24 0.0
+ *
+ * Partial loss of accuracy begins to occur at x = 2^13
+ * = 8192. Results may be meaningless for x >= 2^24
+ * The routine as implemented flags a TLOSS error
+ * for x >= 2^24 and returns 0.0.
+ */
+
+/* cosf.c
+ *
+ * Circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, cosf();
+ *
+ * y = cosf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of pi/4. The reduction
+ * error is nearly eliminated by contriving an extended precision
+ * modular arithmetic.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the cosine is approximated by
+ * 1 - x**2 Q(x**2).
+ * Between pi/4 and pi/2 the sine is represented as
+ * x + x**3 P(x**2).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -8192,+8192 100,000 3.0e-7 3.0e-8
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1985, 1987, 1988, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+/* Single precision circular sine
+ * test interval: [-pi/4, +pi/4]
+ * trials: 10000
+ * peak relative error: 6.8e-8
+ * rms relative error: 2.6e-8
+ */
+#include <math.h>
+
+
+static float FOPI = 1.27323954473516;
+
+extern float PIO4F;
+/* Note, these constants are for a 32-bit significand: */
+/*
+static float DP1 = 0.7853851318359375;
+static float DP2 = 1.30315311253070831298828125e-5;
+static float DP3 = 3.03855025325309630e-11;
+static float lossth = 65536.;
+*/
+
+/* These are for a 24-bit significand: */
+static float DP1 = 0.78515625;
+static float DP2 = 2.4187564849853515625e-4;
+static float DP3 = 3.77489497744594108e-8;
+static float lossth = 8192.;
+static float T24M1 = 16777215.;
+
+static float sincof[] = {
+-1.9515295891E-4,
+ 8.3321608736E-3,
+-1.6666654611E-1
+};
+static float coscof[] = {
+ 2.443315711809948E-005,
+-1.388731625493765E-003,
+ 4.166664568298827E-002
+};
+
+float sinf( float xx )
+{
+float *p;
+float x, y, z;
+register unsigned long j;
+register int sign;
+
+sign = 1;
+x = xx;
+if( xx < 0 )
+ {
+ sign = -1;
+ x = -xx;
+ }
+if( x > T24M1 )
+ {
+ mtherr( "sinf", TLOSS );
+ return(0.0);
+ }
+j = FOPI * x; /* integer part of x/(PI/4) */
+y = j;
+/* map zeros to origin */
+if( j & 1 )
+ {
+ j += 1;
+ y += 1.0;
+ }
+j &= 7; /* octant modulo 360 degrees */
+/* reflect in x axis */
+if( j > 3)
+ {
+ sign = -sign;
+ j -= 4;
+ }
+
+if( x > lossth )
+ {
+ mtherr( "sinf", PLOSS );
+ x = x - y * PIO4F;
+ }
+else
+ {
+/* Extended precision modular arithmetic */
+ x = ((x - y * DP1) - y * DP2) - y * DP3;
+ }
+/*einits();*/
+z = x * x;
+if( (j==1) || (j==2) )
+ {
+/* measured relative error in +/- pi/4 is 7.8e-8 */
+/*
+ y = (( 2.443315711809948E-005 * z
+ - 1.388731625493765E-003) * z
+ + 4.166664568298827E-002) * z * z;
+*/
+ p = coscof;
+ y = *p++;
+ y = y * z + *p++;
+ y = y * z + *p++;
+ y *= z * z;
+ y -= 0.5 * z;
+ y += 1.0;
+ }
+else
+ {
+/* Theoretical relative error = 3.8e-9 in [-pi/4, +pi/4] */
+/*
+ y = ((-1.9515295891E-4 * z
+ + 8.3321608736E-3) * z
+ - 1.6666654611E-1) * z * x;
+ y += x;
+*/
+ p = sincof;
+ y = *p++;
+ y = y * z + *p++;
+ y = y * z + *p++;
+ y *= z * x;
+ y += x;
+ }
+/*einitd();*/
+if(sign < 0)
+ y = -y;
+return( y);
+}
+
+
+/* Single precision circular cosine
+ * test interval: [-pi/4, +pi/4]
+ * trials: 10000
+ * peak relative error: 8.3e-8
+ * rms relative error: 2.2e-8
+ */
+
+float cosf( float xx )
+{
+float x, y, z;
+int j, sign;
+
+/* make argument positive */
+sign = 1;
+x = xx;
+if( x < 0 )
+ x = -x;
+
+if( x > T24M1 )
+ {
+ mtherr( "cosf", TLOSS );
+ return(0.0);
+ }
+
+j = FOPI * x; /* integer part of x/PIO4 */
+y = j;
+/* integer and fractional part modulo one octant */
+if( j & 1 ) /* map zeros to origin */
+ {
+ j += 1;
+ y += 1.0;
+ }
+j &= 7;
+if( j > 3)
+ {
+ j -=4;
+ sign = -sign;
+ }
+
+if( j > 1 )
+ sign = -sign;
+
+if( x > lossth )
+ {
+ mtherr( "cosf", PLOSS );
+ x = x - y * PIO4F;
+ }
+else
+/* Extended precision modular arithmetic */
+ x = ((x - y * DP1) - y * DP2) - y * DP3;
+
+z = x * x;
+
+if( (j==1) || (j==2) )
+ {
+ y = (((-1.9515295891E-4 * z
+ + 8.3321608736E-3) * z
+ - 1.6666654611E-1) * z * x)
+ + x;
+ }
+else
+ {
+ y = (( 2.443315711809948E-005 * z
+ - 1.388731625493765E-003) * z
+ + 4.166664568298827E-002) * z * z;
+ y -= 0.5 * z;
+ y += 1.0;
+ }
+if(sign < 0)
+ y = -y;
+return( y );
+}
+
diff --git a/libm/float/sinhf.c b/libm/float/sinhf.c
new file mode 100644
index 000000000..e8baaf4fa
--- /dev/null
+++ b/libm/float/sinhf.c
@@ -0,0 +1,87 @@
+/* sinhf.c
+ *
+ * Hyperbolic sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, sinhf();
+ *
+ * y = sinhf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic sine of argument in the range MINLOGF to
+ * MAXLOGF.
+ *
+ * The range is partitioned into two segments. If |x| <= 1, a
+ * polynomial approximation is used.
+ * Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-MAXLOG 100000 1.1e-7 2.9e-8
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Single precision hyperbolic sine
+ * test interval: [-1, +1]
+ * trials: 10000
+ * peak relative error: 9.0e-8
+ * rms relative error: 3.0e-8
+ */
+#include <math.h>
+extern float MAXLOGF, MAXNUMF;
+
+float expf( float );
+
+float sinhf( float xx )
+{
+register float z;
+float x;
+
+x = xx;
+if( xx < 0 )
+ z = -x;
+else
+ z = x;
+
+if( z > MAXLOGF )
+ {
+ mtherr( "sinhf", DOMAIN );
+ if( x > 0 )
+ return( MAXNUMF );
+ else
+ return( -MAXNUMF );
+ }
+if( z > 1.0 )
+ {
+ z = expf(z);
+ z = 0.5*z - (0.5/z);
+ if( x < 0 )
+ z = -z;
+ }
+else
+ {
+ z = x * x;
+ z =
+ (( 2.03721912945E-4 * z
+ + 8.33028376239E-3) * z
+ + 1.66667160211E-1) * z * x
+ + x;
+ }
+return( z );
+}
diff --git a/libm/float/spencef.c b/libm/float/spencef.c
new file mode 100644
index 000000000..52799babe
--- /dev/null
+++ b/libm/float/spencef.c
@@ -0,0 +1,135 @@
+/* spencef.c
+ *
+ * Dilogarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, spencef();
+ *
+ * y = spencef( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the integral
+ *
+ * x
+ * -
+ * | | log t
+ * spence(x) = - | ----- dt
+ * | | t - 1
+ * -
+ * 1
+ *
+ * for x >= 0. A rational approximation gives the integral in
+ * the interval (0.5, 1.5). Transformation formulas for 1/x
+ * and 1-x are employed outside the basic expansion range.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,4 30000 4.4e-7 6.3e-8
+ *
+ *
+ */
+
+/* spence.c */
+
+
+/*
+Cephes Math Library Release 2.1: January, 1989
+Copyright 1985, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+static float A[8] = {
+ 4.65128586073990045278E-5,
+ 7.31589045238094711071E-3,
+ 1.33847639578309018650E-1,
+ 8.79691311754530315341E-1,
+ 2.71149851196553469920E0,
+ 4.25697156008121755724E0,
+ 3.29771340985225106936E0,
+ 1.00000000000000000126E0,
+};
+static float B[8] = {
+ 6.90990488912553276999E-4,
+ 2.54043763932544379113E-2,
+ 2.82974860602568089943E-1,
+ 1.41172597751831069617E0,
+ 3.63800533345137075418E0,
+ 5.03278880143316990390E0,
+ 3.54771340985225096217E0,
+ 9.99999999999999998740E-1,
+};
+
+extern float PIF, MACHEPF;
+
+/* pi * pi / 6 */
+#define PIFS 1.64493406684822643647
+
+
+float logf(float), polevlf(float, float *, int);
+float spencef(float xx)
+{
+float x, w, y, z;
+int flag;
+
+x = xx;
+if( x < 0.0 )
+ {
+ mtherr( "spencef", DOMAIN );
+ return(0.0);
+ }
+
+if( x == 1.0 )
+ return( 0.0 );
+
+if( x == 0.0 )
+ return( PIFS );
+
+flag = 0;
+
+if( x > 2.0 )
+ {
+ x = 1.0/x;
+ flag |= 2;
+ }
+
+if( x > 1.5 )
+ {
+ w = (1.0/x) - 1.0;
+ flag |= 2;
+ }
+
+else if( x < 0.5 )
+ {
+ w = -x;
+ flag |= 1;
+ }
+
+else
+ w = x - 1.0;
+
+
+y = -w * polevlf( w, A, 7) / polevlf( w, B, 7 );
+
+if( flag & 1 )
+ y = PIFS - logf(x) * logf(1.0-x) - y;
+
+if( flag & 2 )
+ {
+ z = logf(x);
+ y = -0.5 * z * z - y;
+ }
+
+return( y );
+}
diff --git a/libm/float/sqrtf.c b/libm/float/sqrtf.c
new file mode 100644
index 000000000..bc75a907b
--- /dev/null
+++ b/libm/float/sqrtf.c
@@ -0,0 +1,140 @@
+/* sqrtf.c
+ *
+ * Square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, sqrtf();
+ *
+ * y = sqrtf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the square root of x.
+ *
+ * Range reduction involves isolating the power of two of the
+ * argument and using a polynomial approximation to obtain
+ * a rough value for the square root. Then Heron's iteration
+ * is used three times to converge to an accurate value.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,1.e38 100000 8.7e-8 2.9e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sqrtf domain x < 0 0.0
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Single precision square root
+ * test interval: [sqrt(2)/2, sqrt(2)]
+ * trials: 30000
+ * peak relative error: 8.8e-8
+ * rms relative error: 3.3e-8
+ *
+ * test interval: [0.01, 100.0]
+ * trials: 50000
+ * peak relative error: 8.7e-8
+ * rms relative error: 3.3e-8
+ *
+ * Copyright (C) 1989 by Stephen L. Moshier. All rights reserved.
+ */
+#include <math.h>
+
+#ifdef ANSIC
+float frexpf( float, int * );
+float ldexpf( float, int );
+
+float sqrtf( float xx )
+#else
+float frexpf(), ldexpf();
+
+float sqrtf(xx)
+float xx;
+#endif
+{
+float f, x, y;
+int e;
+
+f = xx;
+if( f <= 0.0 )
+ {
+ if( f < 0.0 )
+ mtherr( "sqrtf", DOMAIN );
+ return( 0.0 );
+ }
+
+x = frexpf( f, &e ); /* f = x * 2**e, 0.5 <= x < 1.0 */
+/* If power of 2 is odd, double x and decrement the power of 2. */
+if( e & 1 )
+ {
+ x = x + x;
+ e -= 1;
+ }
+
+e >>= 1; /* The power of 2 of the square root. */
+
+if( x > 1.41421356237 )
+ {
+/* x is between sqrt(2) and 2. */
+ x = x - 2.0;
+ y =
+ ((((( -9.8843065718E-4 * x
+ + 7.9479950957E-4) * x
+ - 3.5890535377E-3) * x
+ + 1.1028809744E-2) * x
+ - 4.4195203560E-2) * x
+ + 3.5355338194E-1) * x
+ + 1.41421356237E0;
+ goto sqdon;
+ }
+
+if( x > 0.707106781187 )
+ {
+/* x is between sqrt(2)/2 and sqrt(2). */
+ x = x - 1.0;
+ y =
+ ((((( 1.35199291026E-2 * x
+ - 2.26657767832E-2) * x
+ + 2.78720776889E-2) * x
+ - 3.89582788321E-2) * x
+ + 6.24811144548E-2) * x
+ - 1.25001503933E-1) * x * x
+ + 0.5 * x
+ + 1.0;
+ goto sqdon;
+ }
+
+/* x is between 0.5 and sqrt(2)/2. */
+x = x - 0.5;
+y =
+((((( -3.9495006054E-1 * x
+ + 5.1743034569E-1) * x
+ - 4.3214437330E-1) * x
+ + 3.5310730460E-1) * x
+ - 3.5354581892E-1) * x
+ + 7.0710676017E-1) * x
+ + 7.07106781187E-1;
+
+sqdon:
+y = ldexpf( y, e ); /* y = y * 2**e */
+return( y);
+}
diff --git a/libm/float/stdtrf.c b/libm/float/stdtrf.c
new file mode 100644
index 000000000..76b14c1f6
--- /dev/null
+++ b/libm/float/stdtrf.c
@@ -0,0 +1,154 @@
+/* stdtrf.c
+ *
+ * Student's t distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float t, stdtrf();
+ * short k;
+ *
+ * y = stdtrf( k, t );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the integral from minus infinity to t of the Student
+ * t distribution with integer k > 0 degrees of freedom:
+ *
+ * t
+ * -
+ * | |
+ * - | 2 -(k+1)/2
+ * | ( (k+1)/2 ) | ( x )
+ * ---------------------- | ( 1 + --- ) dx
+ * - | ( k )
+ * sqrt( k pi ) | ( k/2 ) |
+ * | |
+ * -
+ * -inf.
+ *
+ * Relation to incomplete beta integral:
+ *
+ * 1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
+ * where
+ * z = k/(k + t**2).
+ *
+ * For t < -1, this is the method of computation. For higher t,
+ * a direct method is derived from integration by parts.
+ * Since the function is symmetric about t=0, the area under the
+ * right tail of the density is found by calling the function
+ * with -t instead of t.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +/- 100 5000 2.3e-5 2.9e-6
+ */
+
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+extern float PIF, MACHEPF;
+
+#ifdef ANSIC
+float sqrtf(float), atanf(float), incbetf(float, float, float);
+#else
+float sqrtf(), atanf(), incbetf();
+#endif
+
+
+
+float stdtrf( int k, float tt )
+{
+float t, x, rk, z, f, tz, p, xsqk;
+int j;
+
+t = tt;
+if( k <= 0 )
+ {
+ mtherr( "stdtrf", DOMAIN );
+ return(0.0);
+ }
+
+if( t == 0 )
+ return( 0.5 );
+
+if( t < -1.0 )
+ {
+ rk = k;
+ z = rk / (rk + t * t);
+ p = 0.5 * incbetf( 0.5*rk, 0.5, z );
+ return( p );
+ }
+
+/* compute integral from -t to + t */
+
+if( t < 0 )
+ x = -t;
+else
+ x = t;
+
+rk = k; /* degrees of freedom */
+z = 1.0 + ( x * x )/rk;
+
+/* test if k is odd or even */
+if( (k & 1) != 0)
+ {
+
+ /* computation for odd k */
+
+ xsqk = x/sqrtf(rk);
+ p = atanf( xsqk );
+ if( k > 1 )
+ {
+ f = 1.0;
+ tz = 1.0;
+ j = 3;
+ while( (j<=(k-2)) && ( (tz/f) > MACHEPF ) )
+ {
+ tz *= (j-1)/( z * j );
+ f += tz;
+ j += 2;
+ }
+ p += f * xsqk/z;
+ }
+ p *= 2.0/PIF;
+ }
+
+
+else
+ {
+
+ /* computation for even k */
+
+ f = 1.0;
+ tz = 1.0;
+ j = 2;
+
+ while( ( j <= (k-2) ) && ( (tz/f) > MACHEPF ) )
+ {
+ tz *= (j - 1)/( z * j );
+ f += tz;
+ j += 2;
+ }
+ p = f * x/sqrtf(z*rk);
+ }
+
+/* common exit */
+
+
+if( t < 0 )
+ p = -p; /* note destruction of relative accuracy */
+
+ p = 0.5 + 0.5 * p;
+return(p);
+}
diff --git a/libm/float/struvef.c b/libm/float/struvef.c
new file mode 100644
index 000000000..4cf8854ed
--- /dev/null
+++ b/libm/float/struvef.c
@@ -0,0 +1,315 @@
+/* struvef.c
+ *
+ * Struve function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float v, x, y, struvef();
+ *
+ * y = struvef( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the Struve function Hv(x) of order v, argument x.
+ * Negative x is rejected unless v is an integer.
+ *
+ * This module also contains the hypergeometric functions 1F2
+ * and 3F0 and a routine for the Bessel function Yv(x) with
+ * noninteger v.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * v varies from 0 to 10.
+ * Absolute error (relative error when |Hv(x)| > 1):
+ * arithmetic domain # trials peak rms
+ * IEEE -10,10 100000 9.0e-5 4.0e-6
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+#define DEBUG 0
+
+extern float MACHEPF, MAXNUMF, PIF;
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+#ifdef ANSIC
+float gammaf(float), powf(float, float), sqrtf(float);
+float yvf(float, float);
+float floorf(float), ynf(int, float);
+float jvf(float, float);
+float sinf(float), cosf(float);
+#else
+float gammaf(), powf(), sqrtf(), yvf();
+float floorf(), ynf(), jvf(), sinf(), cosf();
+#endif
+
+float onef2f( float aa, float bb, float cc, float xx, float *err )
+{
+float a, b, c, x, n, a0, sum, t;
+float an, bn, cn, max, z;
+
+a = aa;
+b = bb;
+c = cc;
+x = xx;
+an = a;
+bn = b;
+cn = c;
+a0 = 1.0;
+sum = 1.0;
+n = 1.0;
+t = 1.0;
+max = 0.0;
+
+do
+ {
+ if( an == 0 )
+ goto done;
+ if( bn == 0 )
+ goto error;
+ if( cn == 0 )
+ goto error;
+ if( (a0 > 1.0e34) || (n > 200) )
+ goto error;
+ a0 *= (an * x) / (bn * cn * n);
+ sum += a0;
+ an += 1.0;
+ bn += 1.0;
+ cn += 1.0;
+ n += 1.0;
+ z = fabsf( a0 );
+ if( z > max )
+ max = z;
+ if( sum != 0 )
+ t = fabsf( a0 / sum );
+ else
+ t = z;
+ }
+while( t > MACHEPF );
+
+done:
+
+*err = fabsf( MACHEPF*max /sum );
+
+#if DEBUG
+ printf(" onef2f cancellation error %.5E\n", *err );
+#endif
+
+goto xit;
+
+error:
+#if DEBUG
+printf("onef2f does not converge\n");
+#endif
+*err = MAXNUMF;
+
+xit:
+
+#if DEBUG
+printf("onef2( %.2E %.2E %.2E %.5E ) = %.3E %.6E\n", a, b, c, x, n, sum);
+#endif
+return(sum);
+}
+
+
+
+float threef0f( float aa, float bb, float cc, float xx, float *err )
+{
+float a, b, c, x, n, a0, sum, t, conv, conv1;
+float an, bn, cn, max, z;
+
+a = aa;
+b = bb;
+c = cc;
+x = xx;
+an = a;
+bn = b;
+cn = c;
+a0 = 1.0;
+sum = 1.0;
+n = 1.0;
+t = 1.0;
+max = 0.0;
+conv = 1.0e38;
+conv1 = conv;
+
+do
+ {
+ if( an == 0.0 )
+ goto done;
+ if( bn == 0.0 )
+ goto done;
+ if( cn == 0.0 )
+ goto done;
+ if( (a0 > 1.0e34) || (n > 200) )
+ goto error;
+ a0 *= (an * bn * cn * x) / n;
+ an += 1.0;
+ bn += 1.0;
+ cn += 1.0;
+ n += 1.0;
+ z = fabsf( a0 );
+ if( z > max )
+ max = z;
+ if( z >= conv )
+ {
+ if( (z < max) && (z > conv1) )
+ goto done;
+ }
+ conv1 = conv;
+ conv = z;
+ sum += a0;
+ if( sum != 0 )
+ t = fabsf( a0 / sum );
+ else
+ t = z;
+ }
+while( t > MACHEPF );
+
+done:
+
+t = fabsf( MACHEPF*max/sum );
+#if DEBUG
+ printf(" threef0f cancellation error %.5E\n", t );
+#endif
+
+max = fabsf( conv/sum );
+if( max > t )
+ t = max;
+#if DEBUG
+ printf(" threef0f convergence %.5E\n", max );
+#endif
+
+goto xit;
+
+error:
+#if DEBUG
+printf("threef0f does not converge\n");
+#endif
+t = MAXNUMF;
+
+xit:
+
+#if DEBUG
+printf("threef0f( %.2E %.2E %.2E %.5E ) = %.3E %.6E\n", a, b, c, x, n, sum);
+#endif
+
+*err = t;
+return(sum);
+}
+
+
+
+
+float struvef( float vv, float xx )
+{
+float v, x, y, ya, f, g, h, t;
+float onef2err, threef0err;
+
+v = vv;
+x = xx;
+f = floorf(v);
+if( (v < 0) && ( v-f == 0.5 ) )
+ {
+ y = jvf( -v, x );
+ f = 1.0 - f;
+ g = 2.0 * floorf(0.5*f);
+ if( g != f )
+ y = -y;
+ return(y);
+ }
+t = 0.25*x*x;
+f = fabsf(x);
+g = 1.5 * fabsf(v);
+if( (f > 30.0) && (f > g) )
+ {
+ onef2err = MAXNUMF;
+ y = 0.0;
+ }
+else
+ {
+ y = onef2f( 1.0, 1.5, 1.5+v, -t, &onef2err );
+ }
+
+if( (f < 18.0) || (x < 0.0) )
+ {
+ threef0err = MAXNUMF;
+ ya = 0.0;
+ }
+else
+ {
+ ya = threef0f( 1.0, 0.5, 0.5-v, -1.0/t, &threef0err );
+ }
+
+f = sqrtf( PIF );
+h = powf( 0.5*x, v-1.0 );
+
+if( onef2err <= threef0err )
+ {
+ g = gammaf( v + 1.5 );
+ y = y * h * t / ( 0.5 * f * g );
+ return(y);
+ }
+else
+ {
+ g = gammaf( v + 0.5 );
+ ya = ya * h / ( f * g );
+ ya = ya + yvf( v, x );
+ return(ya);
+ }
+}
+
+
+
+
+/* Bessel function of noninteger order
+ */
+
+float yvf( float vv, float xx )
+{
+float v, x, y, t;
+int n;
+
+v = vv;
+x = xx;
+y = floorf( v );
+if( y == v )
+ {
+ n = v;
+ y = ynf( n, x );
+ return( y );
+ }
+t = PIF * v;
+y = (cosf(t) * jvf( v, x ) - jvf( -v, x ))/sinf(t);
+return( y );
+}
+
+/* Crossover points between ascending series and asymptotic series
+ * for Struve function
+ *
+ * v x
+ *
+ * 0 19.2
+ * 1 18.95
+ * 2 19.15
+ * 3 19.3
+ * 5 19.7
+ * 10 21.35
+ * 20 26.35
+ * 30 32.31
+ * 40 40.0
+ */
diff --git a/libm/float/tandgf.c b/libm/float/tandgf.c
new file mode 100644
index 000000000..dc55ad5e4
--- /dev/null
+++ b/libm/float/tandgf.c
@@ -0,0 +1,206 @@
+/* tandgf.c
+ *
+ * Circular tangent of angle in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, tandgf();
+ *
+ * y = tandgf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular tangent of the radian argument x.
+ *
+ * Range reduction is into intervals of 45 degrees.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-2^24 50000 2.4e-7 4.8e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * tanf total loss x > 2^24 0.0
+ *
+ */
+ /* cotdgf.c
+ *
+ * Circular cotangent of angle in degrees
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, cotdgf();
+ *
+ * y = cotdgf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of 45 degrees.
+ * A common routine computes either the tangent or cotangent.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-2^24 50000 2.4e-7 4.8e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * cot total loss x > 2^24 0.0
+ * cot singularity x = 0 MAXNUMF
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Single precision circular tangent
+ * test interval: [-pi/4, +pi/4]
+ * trials: 10000
+ * peak relative error: 8.7e-8
+ * rms relative error: 2.8e-8
+ */
+#include <math.h>
+
+extern float MAXNUMF;
+
+static float T24M1 = 16777215.;
+static float PI180 = 0.0174532925199432957692; /* pi/180 */
+
+static float tancotf( float xx, int cotflg )
+{
+float x, y, z, zz;
+long j;
+int sign;
+
+
+/* make argument positive but save the sign */
+if( xx < 0.0 )
+ {
+ x = -xx;
+ sign = -1;
+ }
+else
+ {
+ x = xx;
+ sign = 1;
+ }
+
+if( x > T24M1 )
+ {
+ if( cotflg )
+ mtherr( "cotdgf", TLOSS );
+ else
+ mtherr( "tandgf", TLOSS );
+ return(0.0);
+ }
+
+/* compute x mod PIO4 */
+j = 0.022222222222222222222 * x; /* integer part of x/45 */
+y = j;
+
+/* map zeros and singularities to origin */
+if( j & 1 )
+ {
+ j += 1;
+ y += 1.0;
+ }
+
+z = x - y * 45.0;
+z *= PI180; /* multiply by pi/180 to convert to radians */
+
+zz = z * z;
+
+if( x > 1.0e-4 )
+ {
+/* 1.7e-8 relative error in [-pi/4, +pi/4] */
+ y =
+ ((((( 9.38540185543E-3 * zz
+ + 3.11992232697E-3) * zz
+ + 2.44301354525E-2) * zz
+ + 5.34112807005E-2) * zz
+ + 1.33387994085E-1) * zz
+ + 3.33331568548E-1) * zz * z
+ + z;
+ }
+else
+ {
+ y = z;
+ }
+
+if( j & 2 )
+ {
+ if( cotflg )
+ y = -y;
+ else
+ {
+ if( y != 0.0 )
+ {
+ y = -1.0/y;
+ }
+ else
+ {
+ mtherr( "tandgf", SING );
+ y = MAXNUMF;
+ }
+ }
+ }
+else
+ {
+ if( cotflg )
+ {
+ if( y != 0.0 )
+ y = 1.0/y;
+ else
+ {
+ mtherr( "cotdgf", SING );
+ y = MAXNUMF;
+ }
+ }
+ }
+
+if( sign < 0 )
+ y = -y;
+
+return( y );
+}
+
+
+float tandgf( float x )
+{
+
+return( tancotf(x,0) );
+}
+
+float cotdgf( float x )
+{
+
+if( x == 0.0 )
+ {
+ mtherr( "cotdgf", SING );
+ return( MAXNUMF );
+ }
+return( tancotf(x,1) );
+}
+
diff --git a/libm/float/tanf.c b/libm/float/tanf.c
new file mode 100644
index 000000000..5bbf43075
--- /dev/null
+++ b/libm/float/tanf.c
@@ -0,0 +1,192 @@
+/* tanf.c
+ *
+ * Circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, tanf();
+ *
+ * y = tanf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular tangent of the radian argument x.
+ *
+ * Range reduction is modulo pi/4. A polynomial approximation
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-4096 100000 3.3e-7 4.5e-8
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * tanf total loss x > 2^24 0.0
+ *
+ */
+ /* cotf.c
+ *
+ * Circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, cotf();
+ *
+ * y = cotf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular cotangent of the radian argument x.
+ * A common routine computes either the tangent or cotangent.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-4096 100000 3.0e-7 4.5e-8
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * cot total loss x > 2^24 0.0
+ * cot singularity x = 0 MAXNUMF
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Single precision circular tangent
+ * test interval: [-pi/4, +pi/4]
+ * trials: 10000
+ * peak relative error: 8.7e-8
+ * rms relative error: 2.8e-8
+ */
+#include <math.h>
+
+extern float MAXNUMF;
+
+static float DP1 = 0.78515625;
+static float DP2 = 2.4187564849853515625e-4;
+static float DP3 = 3.77489497744594108e-8;
+float FOPI = 1.27323954473516; /* 4/pi */
+static float lossth = 8192.;
+/*static float T24M1 = 16777215.;*/
+
+
+static float tancotf( float xx, int cotflg )
+{
+float x, y, z, zz;
+long j;
+int sign;
+
+
+/* make argument positive but save the sign */
+if( xx < 0.0 )
+ {
+ x = -xx;
+ sign = -1;
+ }
+else
+ {
+ x = xx;
+ sign = 1;
+ }
+
+if( x > lossth )
+ {
+ if( cotflg )
+ mtherr( "cotf", TLOSS );
+ else
+ mtherr( "tanf", TLOSS );
+ return(0.0);
+ }
+
+/* compute x mod PIO4 */
+j = FOPI * x; /* integer part of x/(PI/4) */
+y = j;
+
+/* map zeros and singularities to origin */
+if( j & 1 )
+ {
+ j += 1;
+ y += 1.0;
+ }
+
+z = ((x - y * DP1) - y * DP2) - y * DP3;
+
+zz = z * z;
+
+if( x > 1.0e-4 )
+ {
+/* 1.7e-8 relative error in [-pi/4, +pi/4] */
+ y =
+ ((((( 9.38540185543E-3 * zz
+ + 3.11992232697E-3) * zz
+ + 2.44301354525E-2) * zz
+ + 5.34112807005E-2) * zz
+ + 1.33387994085E-1) * zz
+ + 3.33331568548E-1) * zz * z
+ + z;
+ }
+else
+ {
+ y = z;
+ }
+
+if( j & 2 )
+ {
+ if( cotflg )
+ y = -y;
+ else
+ y = -1.0/y;
+ }
+else
+ {
+ if( cotflg )
+ y = 1.0/y;
+ }
+
+if( sign < 0 )
+ y = -y;
+
+return( y );
+}
+
+
+float tanf( float x )
+{
+
+return( tancotf(x,0) );
+}
+
+float cotf( float x )
+{
+
+if( x == 0.0 )
+ {
+ mtherr( "cotf", SING );
+ return( MAXNUMF );
+ }
+return( tancotf(x,1) );
+}
+
diff --git a/libm/float/tanhf.c b/libm/float/tanhf.c
new file mode 100644
index 000000000..4636192c2
--- /dev/null
+++ b/libm/float/tanhf.c
@@ -0,0 +1,88 @@
+/* tanhf.c
+ *
+ * Hyperbolic tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, tanhf();
+ *
+ * y = tanhf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic tangent of argument in the range MINLOG to
+ * MAXLOG.
+ *
+ * A polynomial approximation is used for |x| < 0.625.
+ * Otherwise,
+ *
+ * tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -2,2 100000 1.3e-7 2.6e-8
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+/* Single precision hyperbolic tangent
+ * test interval: [-0.625, +0.625]
+ * trials: 10000
+ * peak relative error: 7.2e-8
+ * rms relative error: 2.6e-8
+ */
+#include <math.h>
+
+extern float MAXLOGF;
+
+float expf( float );
+
+float tanhf( float xx )
+{
+float x, z;
+
+if( xx < 0 )
+ x = -xx;
+else
+ x = xx;
+
+if( x > 0.5 * MAXLOGF )
+ {
+ if( xx > 0 )
+ return( 1.0 );
+ else
+ return( -1.0 );
+ }
+if( x >= 0.625 )
+ {
+ x = expf(x+x);
+ z = 1.0 - 2.0/(x + 1.0);
+ if( xx < 0 )
+ z = -z;
+ }
+else
+ {
+ z = x * x;
+ z =
+ (((( -5.70498872745E-3 * z
+ + 2.06390887954E-2) * z
+ - 5.37397155531E-2) * z
+ + 1.33314422036E-1) * z
+ - 3.33332819422E-1) * z * xx
+ + xx;
+ }
+return( z );
+}
diff --git a/libm/float/ynf.c b/libm/float/ynf.c
new file mode 100644
index 000000000..55d984b26
--- /dev/null
+++ b/libm/float/ynf.c
@@ -0,0 +1,120 @@
+/* ynf.c
+ *
+ * Bessel function of second kind of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, ynf();
+ * int n;
+ *
+ * y = ynf( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The function is evaluated by forward recurrence on
+ * n, starting with values computed by the routines
+ * y0() and y1().
+ *
+ * If n = 0 or 1 the routine for y0 or y1 is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Absolute error, except relative when y > 1:
+ *
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 10000 2.3e-6 3.4e-7
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * yn singularity x = 0 MAXNUMF
+ * yn overflow MAXNUMF
+ *
+ * Spot checked against tables for x, n between 0 and 100.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+extern float MAXNUMF, MAXLOGF;
+
+float y0f(float), y1f(float), logf(float);
+
+float ynf( int nn, float xx )
+{
+float x, an, anm1, anm2, r, xinv;
+int k, n, sign;
+
+x = xx;
+n = nn;
+if( n < 0 )
+ {
+ n = -n;
+ if( (n & 1) == 0 ) /* -1**n */
+ sign = 1;
+ else
+ sign = -1;
+ }
+else
+ sign = 1;
+
+
+if( n == 0 )
+ return( sign * y0f(x) );
+if( n == 1 )
+ return( sign * y1f(x) );
+
+/* test for overflow */
+if( x <= 0.0 )
+ {
+ mtherr( "ynf", SING );
+ return( -MAXNUMF );
+ }
+if( (x < 1.0) || (n > 29) )
+ {
+ an = (float )n;
+ r = an * logf( an/x );
+ if( r > MAXLOGF )
+ {
+ mtherr( "ynf", OVERFLOW );
+ return( -MAXNUMF );
+ }
+ }
+
+/* forward recurrence on n */
+
+anm2 = y0f(x);
+anm1 = y1f(x);
+k = 1;
+r = 2 * k;
+xinv = 1.0/x;
+do
+ {
+ an = r * anm1 * xinv - anm2;
+ anm2 = anm1;
+ anm1 = an;
+ r += 2.0;
+ ++k;
+ }
+while( k < n );
+
+
+return( sign * an );
+}
diff --git a/libm/float/zetacf.c b/libm/float/zetacf.c
new file mode 100644
index 000000000..da2ace6a4
--- /dev/null
+++ b/libm/float/zetacf.c
@@ -0,0 +1,266 @@
+ /* zetacf.c
+ *
+ * Riemann zeta function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, y, zetacf();
+ *
+ * y = zetacf( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *
+ * inf.
+ * - -x
+ * zetac(x) = > k , x > 1,
+ * -
+ * k=2
+ *
+ * is related to the Riemann zeta function by
+ *
+ * Riemann zeta(x) = zetac(x) + 1.
+ *
+ * Extension of the function definition for x < 1 is implemented.
+ * Zero is returned for x > log2(MAXNUM).
+ *
+ * An overflow error may occur for large negative x, due to the
+ * gamma function in the reflection formula.
+ *
+ * ACCURACY:
+ *
+ * Tabulated values have full machine accuracy.
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 1,50 30000 5.5e-7 7.5e-8
+ *
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+
+/* Riemann zeta(x) - 1
+ * for integer arguments between 0 and 30.
+ */
+static float azetacf[] = {
+-1.50000000000000000000E0,
+ 1.70141183460469231730E38, /* infinity. */
+ 6.44934066848226436472E-1,
+ 2.02056903159594285400E-1,
+ 8.23232337111381915160E-2,
+ 3.69277551433699263314E-2,
+ 1.73430619844491397145E-2,
+ 8.34927738192282683980E-3,
+ 4.07735619794433937869E-3,
+ 2.00839282608221441785E-3,
+ 9.94575127818085337146E-4,
+ 4.94188604119464558702E-4,
+ 2.46086553308048298638E-4,
+ 1.22713347578489146752E-4,
+ 6.12481350587048292585E-5,
+ 3.05882363070204935517E-5,
+ 1.52822594086518717326E-5,
+ 7.63719763789976227360E-6,
+ 3.81729326499983985646E-6,
+ 1.90821271655393892566E-6,
+ 9.53962033872796113152E-7,
+ 4.76932986787806463117E-7,
+ 2.38450502727732990004E-7,
+ 1.19219925965311073068E-7,
+ 5.96081890512594796124E-8,
+ 2.98035035146522801861E-8,
+ 1.49015548283650412347E-8,
+ 7.45071178983542949198E-9,
+ 3.72533402478845705482E-9,
+ 1.86265972351304900640E-9,
+ 9.31327432419668182872E-10
+};
+
+
+/* 2**x (1 - 1/x) (zeta(x) - 1) = P(1/x)/Q(1/x), 1 <= x <= 10 */
+static float P[9] = {
+ 5.85746514569725319540E11,
+ 2.57534127756102572888E11,
+ 4.87781159567948256438E10,
+ 5.15399538023885770696E9,
+ 3.41646073514754094281E8,
+ 1.60837006880656492731E7,
+ 5.92785467342109522998E5,
+ 1.51129169964938823117E4,
+ 2.01822444485997955865E2,
+};
+static float Q[8] = {
+/* 1.00000000000000000000E0,*/
+ 3.90497676373371157516E11,
+ 5.22858235368272161797E10,
+ 5.64451517271280543351E9,
+ 3.39006746015350418834E8,
+ 1.79410371500126453702E7,
+ 5.66666825131384797029E5,
+ 1.60382976810944131506E4,
+ 1.96436237223387314144E2,
+};
+
+/* log(zeta(x) - 1 - 2**-x), 10 <= x <= 50 */
+static float A[11] = {
+ 8.70728567484590192539E6,
+ 1.76506865670346462757E8,
+ 2.60889506707483264896E10,
+ 5.29806374009894791647E11,
+ 2.26888156119238241487E13,
+ 3.31884402932705083599E14,
+ 5.13778997975868230192E15,
+-1.98123688133907171455E15,
+-9.92763810039983572356E16,
+ 7.82905376180870586444E16,
+ 9.26786275768927717187E16,
+};
+static float B[10] = {
+/* 1.00000000000000000000E0,*/
+-7.92625410563741062861E6,
+-1.60529969932920229676E8,
+-2.37669260975543221788E10,
+-4.80319584350455169857E11,
+-2.07820961754173320170E13,
+-2.96075404507272223680E14,
+-4.86299103694609136686E15,
+ 5.34589509675789930199E15,
+ 5.71464111092297631292E16,
+-1.79915597658676556828E16,
+};
+
+/* (1-x) (zeta(x) - 1), 0 <= x <= 1 */
+
+static float R[6] = {
+-3.28717474506562731748E-1,
+ 1.55162528742623950834E1,
+-2.48762831680821954401E2,
+ 1.01050368053237678329E3,
+ 1.26726061410235149405E4,
+-1.11578094770515181334E5,
+};
+static float S[5] = {
+/* 1.00000000000000000000E0,*/
+ 1.95107674914060531512E1,
+ 3.17710311750646984099E2,
+ 3.03835500874445748734E3,
+ 2.03665876435770579345E4,
+ 7.43853965136767874343E4,
+};
+
+
+#define MAXL2 127
+
+/*
+ * Riemann zeta function, minus one
+ */
+
+extern float MACHEPF, PIO2F, MAXNUMF, PIF;
+
+#ifdef ANSIC
+extern float sinf ( float xx );
+extern float floorf ( float x );
+extern float gammaf ( float xx );
+extern float powf ( float x, float y );
+extern float expf ( float xx );
+extern float polevlf ( float xx, float *coef, int N );
+extern float p1evlf ( float xx, float *coef, int N );
+#else
+float sinf(), floorf(), gammaf(), powf(), expf();
+float polevlf(), p1evlf();
+#endif
+
+float zetacf(float xx)
+{
+int i;
+float x, a, b, s, w;
+
+x = xx;
+if( x < 0.0 )
+ {
+ if( x < -30.8148 )
+ {
+ mtherr( "zetacf", OVERFLOW );
+ return(0.0);
+ }
+ s = 1.0 - x;
+ w = zetacf( s );
+ b = sinf(PIO2F*x) * powf(2.0*PIF, x) * gammaf(s) * (1.0 + w) / PIF;
+ return(b - 1.0);
+ }
+
+if( x >= MAXL2 )
+ return(0.0); /* because first term is 2**-x */
+
+/* Tabulated values for integer argument */
+w = floorf(x);
+if( w == x )
+ {
+ i = x;
+ if( i < 31 )
+ {
+ return( azetacf[i] );
+ }
+ }
+
+
+if( x < 1.0 )
+ {
+ w = 1.0 - x;
+ a = polevlf( x, R, 5 ) / ( w * p1evlf( x, S, 5 ));
+ return( a );
+ }
+
+if( x == 1.0 )
+ {
+ mtherr( "zetacf", SING );
+ return( MAXNUMF );
+ }
+
+if( x <= 10.0 )
+ {
+ b = powf( 2.0, x ) * (x - 1.0);
+ w = 1.0/x;
+ s = (x * polevlf( w, P, 8 )) / (b * p1evlf( w, Q, 8 ));
+ return( s );
+ }
+
+if( x <= 50.0 )
+ {
+ b = powf( 2.0, -x );
+ w = polevlf( x, A, 10 ) / p1evlf( x, B, 10 );
+ w = expf(w) + b;
+ return(w);
+ }
+
+
+/* Basic sum of inverse powers */
+
+
+s = 0.0;
+a = 1.0;
+do
+ {
+ a += 2.0;
+ b = powf( a, -x );
+ s += b;
+ }
+while( b/s > MACHEPF );
+
+b = powf( 2.0, -x );
+s = (s + b)/(1.0-b);
+return(s);
+}
diff --git a/libm/float/zetaf.c b/libm/float/zetaf.c
new file mode 100644
index 000000000..d01f1d2b2
--- /dev/null
+++ b/libm/float/zetaf.c
@@ -0,0 +1,175 @@
+/* zetaf.c
+ *
+ * Riemann zeta function of two arguments
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float x, q, y, zetaf();
+ *
+ * y = zetaf( x, q );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ *
+ * inf.
+ * - -x
+ * zeta(x,q) = > (k+q)
+ * -
+ * k=0
+ *
+ * where x > 1 and q is not a negative integer or zero.
+ * The Euler-Maclaurin summation formula is used to obtain
+ * the expansion
+ *
+ * n
+ * - -x
+ * zeta(x,q) = > (k+q)
+ * -
+ * k=1
+ *
+ * 1-x inf. B x(x+1)...(x+2j)
+ * (n+q) 1 - 2j
+ * + --------- - ------- + > --------------------
+ * x-1 x - x+2j+1
+ * 2(n+q) j=1 (2j)! (n+q)
+ *
+ * where the B2j are Bernoulli numbers. Note that (see zetac.c)
+ * zeta(x,1) = zetac(x) + 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,25 10000 6.9e-7 1.0e-7
+ *
+ * Large arguments may produce underflow in powf(), in which
+ * case the results are inaccurate.
+ *
+ * REFERENCE:
+ *
+ * Gradshteyn, I. S., and I. M. Ryzhik, Tables of Integrals,
+ * Series, and Products, p. 1073; Academic Press, 1980.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+extern float MAXNUMF, MACHEPF;
+
+/* Expansion coefficients
+ * for Euler-Maclaurin summation formula
+ * (2k)! / B2k
+ * where B2k are Bernoulli numbers
+ */
+static float A[] = {
+12.0,
+-720.0,
+30240.0,
+-1209600.0,
+47900160.0,
+-1.8924375803183791606e9, /*1.307674368e12/691*/
+7.47242496e10,
+-2.950130727918164224e12, /*1.067062284288e16/3617*/
+1.1646782814350067249e14, /*5.109094217170944e18/43867*/
+-4.5979787224074726105e15, /*8.028576626982912e20/174611*/
+1.8152105401943546773e17, /*1.5511210043330985984e23/854513*/
+-7.1661652561756670113e18 /*1.6938241367317436694528e27/236364091*/
+};
+/* 30 Nov 86 -- error in third coefficient fixed */
+
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+
+float powf( float, float );
+float zetaf(float xx, float qq)
+{
+int i;
+float x, q, a, b, k, s, w, t;
+
+x = xx;
+q = qq;
+if( x == 1.0 )
+ return( MAXNUMF );
+
+if( x < 1.0 )
+ {
+ mtherr( "zetaf", DOMAIN );
+ return(0.0);
+ }
+
+
+/* Euler-Maclaurin summation formula */
+/*
+if( x < 25.0 )
+{
+*/
+w = 9.0;
+s = powf( q, -x );
+a = q;
+for( i=0; i<9; i++ )
+ {
+ a += 1.0;
+ b = powf( a, -x );
+ s += b;
+ if( b/s < MACHEPF )
+ goto done;
+ }
+
+w = a;
+s += b*w/(x-1.0);
+s -= 0.5 * b;
+a = 1.0;
+k = 0.0;
+for( i=0; i<12; i++ )
+ {
+ a *= x + k;
+ b /= w;
+ t = a*b/A[i];
+ s = s + t;
+ t = fabsf(t/s);
+ if( t < MACHEPF )
+ goto done;
+ k += 1.0;
+ a *= x + k;
+ b /= w;
+ k += 1.0;
+ }
+done:
+return(s);
+/*
+}
+*/
+
+
+/* Basic sum of inverse powers */
+/*
+pseres:
+
+s = powf( q, -x );
+a = q;
+do
+ {
+ a += 2.0;
+ b = powf( a, -x );
+ s += b;
+ }
+while( b/s > MACHEPF );
+
+b = powf( 2.0, -x );
+s = (s + b)/(1.0-b);
+return(s);
+*/
+}
diff --git a/libm/ldouble/Makefile b/libm/ldouble/Makefile
new file mode 100644
index 000000000..43395a140
--- /dev/null
+++ b/libm/ldouble/Makefile
@@ -0,0 +1,123 @@
+# Makefile for uClibc's math library
+#
+# Copyright (C) 2001 by Lineo, inc.
+#
+# This program is free software; you can redistribute it and/or modify it under
+# the terms of the GNU Library General Public License as published by the Free
+# Software Foundation; either version 2 of the License, or (at your option) any
+# later version.
+#
+# This program is distributed in the hope that it will be useful, but WITHOUT
+# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+# FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more
+# details.
+#
+# You should have received a copy of the GNU Library General Public License
+# along with this program; if not, write to the Free Software Foundation, Inc.,
+# 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+#
+# Derived in part from the Linux-8086 C library, the GNU C Library, and several
+# other sundry sources. Files within this library are copyright by their
+# respective copyright holders.
+
+TOPDIR=../../
+include $(TOPDIR)Rules.mak
+
+LIBM=../libm.a
+TARGET_CC= $(TOPDIR)/extra/gcc-uClibc/$(TARGET_ARCH)-uclibc-gcc
+
+CSRC=acoshl.c asinhl.c asinl.c atanhl.c atanl.c bdtrl.c btdtrl.c cbrtl.c \
+ chdtrl.c coshl.c ellpel.c ellpkl.c elliel.c ellikl.c ellpjl.c \
+ exp10l.c exp2l.c expl.c fdtrl.c gammal.c gdtrl.c igamil.c igaml.c \
+ incbetl.c incbil.c isnanl.c j0l.c j1l.c jnl.c ldrand.c log10l.c log2l.c \
+ logl.c nbdtrl.c ndtril.c ndtrl.c pdtrl.c powl.c powil.c sinhl.c sinl.c \
+ sqrtl.c stdtrl.c tanhl.c tanl.c unityl.c ynl.c \
+ floorl.c polevll.c mtherr.c #cmplxl.c clogl.c
+COBJS=$(patsubst %.c,%.o, $(CSRC))
+
+
+OBJS=$(COBJS)
+
+all: $(OBJS) $(LIBM)
+
+$(LIBM): ar-target
+
+ar-target: $(OBJS)
+ $(AR) $(ARFLAGS) $(LIBM) $(OBJS)
+
+$(COBJS): %.o : %.c
+ $(TARGET_CC) $(CFLAGS) -c $< -o $@
+ $(STRIPTOOL) -x -R .note -R .comment $*.o
+
+$(OBJ): Makefile
+
+clean:
+ rm -f *.[oa] *~ core
+
+
+
+#-----------------------------------------
+
+
+#all: mtstl lparanoi lcalc fltestl nantst testvect monotl libml.a
+
+mtstl: libml.a mtstl.o $(OBJS)
+ $(CC) $(CFLAGS) -o mtstl mtstl.o libml.a $(LIBS)
+
+mtstl.o: mtstl.c
+
+lparanoi: libml.a lparanoi.o setprec.o ieee.o econst.o $(OBJS)
+ $(CC) $(CFLAGS) -o lparanoi lparanoi.o setprec.o ieee.o econst.o libml.a $(LIBS)
+
+lparanoi.o: lparanoi.c
+ $(CC) $(CFLAGS) -Wno-implicit -c lparanoi.c
+
+econst.o: econst.c ehead.h
+
+lcalc: libml.a lcalc.o ieee.o econst.o $(OBJS)
+ $(CC) $(CFLAGS) -o lcalc lcalc.o ieee.o econst.o libml.a $(LIBS)
+
+lcalc.o: lcalc.c lcalc.h ehead.h
+
+ieee.o: ieee.c ehead.h
+
+# Use $(OBJS) in ar command for libml.a if possible; else *.o
+libml.a: $(OBJS) mconf.h
+ ar -rv libml.a $(OBJS)
+ ranlib libml.a
+
+
+fltestl: fltestl.c libml.a
+ $(CC) $(CFLAGS) -o fltestl fltestl.c libml.a
+
+fltestl.o: fltestl.c
+
+flrtstl: flrtstl.c libml.a
+ $(CC) $(CFLAGS) -o flrtstl flrtstl.c libml.a
+
+flrtstl.o: flrtstl.c
+
+nantst: nantst.c libml.a
+ $(CC) $(CFLAGS) -o nantst nantst.c libml.a
+
+nantst.o: nantst.c
+
+testvect: testvect.o libml.a
+ $(CC) $(CFLAGS) -o testvect testvect.o libml.a
+
+testvect.o: testvect.c
+ $(CC) -g -c -o testvect.o testvect.c
+
+monotl: monotl.o libml.a
+ $(CC) $(CFLAGS) -o monotl monotl.o libml.a
+
+monotl.o: monotl.c
+ $(CC) -g -c -o monotl.o monotl.c
+
+# Run test programs
+check: mtstl fltestl testvect monotl libml.a
+ -mtstl
+ -fltestl
+ -testvect
+ -monotl
+
diff --git a/libm/ldouble/README.txt b/libm/ldouble/README.txt
new file mode 100644
index 000000000..30fcaad36
--- /dev/null
+++ b/libm/ldouble/README.txt
@@ -0,0 +1,3502 @@
+/* acoshl.c
+ *
+ * Inverse hyperbolic cosine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, acoshl();
+ *
+ * y = acoshl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic cosine of argument.
+ *
+ * If 1 <= x < 1.5, a rational approximation
+ *
+ * sqrt(2z) * P(z)/Q(z)
+ *
+ * where z = x-1, is used. Otherwise,
+ *
+ * acosh(x) = log( x + sqrt( (x-1)(x+1) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 1,3 30000 2.0e-19 3.9e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * acoshl domain |x| < 1 0.0
+ *
+ */
+
+/* asinhl.c
+ *
+ * Inverse hyperbolic sine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, asinhl();
+ *
+ * y = asinhl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic sine of argument.
+ *
+ * If |x| < 0.5, the function is approximated by a rational
+ * form x + x**3 P(x)/Q(x). Otherwise,
+ *
+ * asinh(x) = log( x + sqrt(1 + x*x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -3,3 30000 1.7e-19 3.5e-20
+ *
+ */
+
+/* asinl.c
+ *
+ * Inverse circular sine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, asinl();
+ *
+ * y = asinl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
+ *
+ * A rational function of the form x + x**3 P(x**2)/Q(x**2)
+ * is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is
+ * transformed by the identity
+ *
+ * asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1, 1 30000 2.7e-19 4.8e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * asin domain |x| > 1 0.0
+ *
+ */
+ /* acosl()
+ *
+ * Inverse circular cosine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, acosl();
+ *
+ * y = acosl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose cosine
+ * is x.
+ *
+ * Analytically, acos(x) = pi/2 - asin(x). However if |x| is
+ * near 1, there is cancellation error in subtracting asin(x)
+ * from pi/2. Hence if x < -0.5,
+ *
+ * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
+ *
+ * or if x > +0.5,
+ *
+ * acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1, 1 30000 1.4e-19 3.5e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * asin domain |x| > 1 0.0
+ */
+
+/* atanhl.c
+ *
+ * Inverse hyperbolic tangent, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, atanhl();
+ *
+ * y = atanhl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic tangent of argument in the range
+ * MINLOGL to MAXLOGL.
+ *
+ * If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is
+ * employed. Otherwise,
+ * atanh(x) = 0.5 * log( (1+x)/(1-x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1,1 30000 1.1e-19 3.3e-20
+ *
+ */
+
+/* atanl.c
+ *
+ * Inverse circular tangent, long double precision
+ * (arctangent)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, atanl();
+ *
+ * y = atanl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose tangent
+ * is x.
+ *
+ * Range reduction is from four intervals into the interval
+ * from zero to tan( pi/8 ). The approximant uses a rational
+ * function of degree 3/4 of the form x + x**3 P(x)/Q(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10, 10 150000 1.3e-19 3.0e-20
+ *
+ */
+ /* atan2l()
+ *
+ * Quadrant correct inverse circular tangent,
+ * long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, z, atan2l();
+ *
+ * z = atan2l( y, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle whose tangent is y/x.
+ * Define compile time symbol ANSIC = 1 for ANSI standard,
+ * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
+ * 0 to 2PI, args (x,y).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10, 10 60000 1.7e-19 3.2e-20
+ * See atan.c.
+ *
+ */
+
+/* bdtrl.c
+ *
+ * Binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, bdtrl();
+ *
+ * y = bdtrl( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the Binomial
+ * probability density:
+ *
+ * k
+ * -- ( n ) j n-j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (k,n,p) with a and b between 0
+ * and 10000 and p between 0 and 1.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,10000 3000 1.6e-14 2.2e-15
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtrl domain k < 0 0.0
+ * n < k
+ * x < 0, x > 1
+ *
+ */
+ /* bdtrcl()
+ *
+ * Complemented binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, bdtrcl();
+ *
+ * y = bdtrcl( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 through n of the Binomial
+ * probability density:
+ *
+ * n
+ * -- ( n ) j n-j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See incbet.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtrcl domain x<0, x>1, n<k 0.0
+ */
+ /* bdtril()
+ *
+ * Inverse binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, bdtril();
+ *
+ * p = bdtril( k, n, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the event probability p such that the sum of the
+ * terms 0 through k of the Binomial probability density
+ * is equal to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relation
+ *
+ * 1 - p = incbi( n-k, k+1, y ).
+ *
+ * ACCURACY:
+ *
+ * See incbi.c.
+ * Tested at random k, n between 1 and 10000. The "domain" refers to p:
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,1 3500 2.0e-15 8.2e-17
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtril domain k < 0, n <= k 0.0
+ * x < 0, x > 1
+ */
+
+
+/* btdtrl.c
+ *
+ * Beta distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, b, x, y, btdtrl();
+ *
+ * y = btdtrl( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the beta density
+ * function:
+ *
+ *
+ * x
+ * - -
+ * | (a+b) | | a-1 b-1
+ * P(x) = ---------- | t (1-t) dt
+ * - - | |
+ * | (a) | (b) -
+ * 0
+ *
+ *
+ * The mean value of this distribution is a/(a+b). The variance
+ * is ab/[(a+b)^2 (a+b+1)].
+ *
+ * This function is identical to the incomplete beta integral
+ * function, incbetl(a, b, x).
+ *
+ * The complemented function is
+ *
+ * 1 - P(1-x) = incbetl( b, a, x );
+ *
+ *
+ * ACCURACY:
+ *
+ * See incbetl.c.
+ *
+ */
+
+/* cbrtl.c
+ *
+ * Cube root, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, cbrtl();
+ *
+ * y = cbrtl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the cube root of the argument, which may be negative.
+ *
+ * Range reduction involves determining the power of 2 of
+ * the argument. A polynomial of degree 2 applied to the
+ * mantissa, and multiplication by the cube root of 1, 2, or 4
+ * approximates the root to within about 0.1%. Then Newton's
+ * iteration is used three times to converge to an accurate
+ * result.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE .125,8 80000 7.0e-20 2.2e-20
+ * IEEE exp(+-707) 100000 7.0e-20 2.4e-20
+ *
+ */
+
+/* chdtrl.c
+ *
+ * Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double df, x, y, chdtrl();
+ *
+ * y = chdtrl( df, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the left hand tail (from 0 to x)
+ * of the Chi square probability density function with
+ * v degrees of freedom.
+ *
+ *
+ * inf.
+ * -
+ * 1 | | v/2-1 -t/2
+ * P( x | v ) = ----------- | t e dt
+ * v/2 - | |
+ * 2 | (v/2) -
+ * x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ * y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtr domain x < 0 or v < 1 0.0
+ */
+ /* chdtrcl()
+ *
+ * Complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double v, x, y, chdtrcl();
+ *
+ * y = chdtrcl( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the right hand tail (from x to
+ * infinity) of the Chi square probability density function
+ * with v degrees of freedom:
+ *
+ *
+ * inf.
+ * -
+ * 1 | | v/2-1 -t/2
+ * P( x | v ) = ----------- | t e dt
+ * v/2 - | |
+ * 2 | (v/2) -
+ * x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ * y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtrc domain x < 0 or v < 1 0.0
+ */
+ /* chdtril()
+ *
+ * Inverse of complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double df, x, y, chdtril();
+ *
+ * x = chdtril( df, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Chi-square argument x such that the integral
+ * from x to infinity of the Chi-square density is equal
+ * to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ * x/2 = igami( df/2, y );
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igami.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtri domain y < 0 or y > 1 0.0
+ * v < 1
+ *
+ */
+
+/* clogl.c
+ *
+ * Complex natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void clogl();
+ * cmplxl z, w;
+ *
+ * clogl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns complex logarithm to the base e (2.718...) of
+ * the complex argument x.
+ *
+ * If z = x + iy, r = sqrt( x**2 + y**2 ),
+ * then
+ * w = log(r) + i arctan(y/x).
+ *
+ * The arctangent ranges from -PI to +PI.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 7000 8.5e-17 1.9e-17
+ * IEEE -10,+10 30000 5.0e-15 1.1e-16
+ *
+ * Larger relative error can be observed for z near 1 +i0.
+ * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
+ * absolute error 1.0e-16.
+ */
+
+ /* cexpl()
+ *
+ * Complex exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cexpl();
+ * cmplxl z, w;
+ *
+ * cexpl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the exponential of the complex argument z
+ * into the complex result w.
+ *
+ * If
+ * z = x + iy,
+ * r = exp(x),
+ *
+ * then
+ *
+ * w = r cos y + i r sin y.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 8700 3.7e-17 1.1e-17
+ * IEEE -10,+10 30000 3.0e-16 8.7e-17
+ *
+ */
+ /* csinl()
+ *
+ * Complex circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csinl();
+ * cmplxl z, w;
+ *
+ * csinl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * w = sin x cosh y + i cos x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 8400 5.3e-17 1.3e-17
+ * IEEE -10,+10 30000 3.8e-16 1.0e-16
+ * Also tested by csin(casin(z)) = z.
+ *
+ */
+ /* ccosl()
+ *
+ * Complex circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccosl();
+ * cmplxl z, w;
+ *
+ * ccosl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * w = cos x cosh y - i sin x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 8400 4.5e-17 1.3e-17
+ * IEEE -10,+10 30000 3.8e-16 1.0e-16
+ */
+ /* ctanl()
+ *
+ * Complex circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ctanl();
+ * cmplxl z, w;
+ *
+ * ctanl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * sin 2x + i sinh 2y
+ * w = --------------------.
+ * cos 2x + cosh 2y
+ *
+ * On the real axis the denominator is zero at odd multiples
+ * of PI/2. The denominator is evaluated by its Taylor
+ * series near these points.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 5200 7.1e-17 1.6e-17
+ * IEEE -10,+10 30000 7.2e-16 1.2e-16
+ * Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
+ */
+ /* ccotl()
+ *
+ * Complex circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccotl();
+ * cmplxl z, w;
+ *
+ * ccotl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * sin 2x - i sinh 2y
+ * w = --------------------.
+ * cosh 2y - cos 2x
+ *
+ * On the real axis, the denominator has zeros at even
+ * multiples of PI/2. Near these points it is evaluated
+ * by a Taylor series.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 3000 6.5e-17 1.6e-17
+ * IEEE -10,+10 30000 9.2e-16 1.2e-16
+ * Also tested by ctan * ccot = 1 + i0.
+ */
+
+ /* casinl()
+ *
+ * Complex circular arc sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void casinl();
+ * cmplxl z, w;
+ *
+ * casinl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Inverse complex sine:
+ *
+ * 2
+ * w = -i clog( iz + csqrt( 1 - z ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 10100 2.1e-15 3.4e-16
+ * IEEE -10,+10 30000 2.2e-14 2.7e-15
+ * Larger relative error can be observed for z near zero.
+ * Also tested by csin(casin(z)) = z.
+ */
+ /* cacosl()
+ *
+ * Complex circular arc cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cacosl();
+ * cmplxl z, w;
+ *
+ * cacosl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * w = arccos z = PI/2 - arcsin z.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 5200 1.6e-15 2.8e-16
+ * IEEE -10,+10 30000 1.8e-14 2.2e-15
+ */
+
+ /* catanl()
+ *
+ * Complex circular arc tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void catanl();
+ * cmplxl z, w;
+ *
+ * catanl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ * 1 ( 2x )
+ * Re w = - arctan(-----------) + k PI
+ * 2 ( 2 2)
+ * (1 - x - y )
+ *
+ * ( 2 2)
+ * 1 (x + (y+1) )
+ * Im w = - log(------------)
+ * 4 ( 2 2)
+ * (x + (y-1) )
+ *
+ * Where k is an arbitrary integer.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 5900 1.3e-16 7.8e-18
+ * IEEE -10,+10 30000 2.3e-15 8.5e-17
+ * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
+ * had peak relative error 1.5e-16, rms relative error
+ * 2.9e-17. See also clog().
+ */
+
+/* cmplxl.c
+ *
+ * Complex number arithmetic
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct {
+ * long double r; real part
+ * long double i; imaginary part
+ * }cmplxl;
+ *
+ * cmplxl *a, *b, *c;
+ *
+ * caddl( a, b, c ); c = b + a
+ * csubl( a, b, c ); c = b - a
+ * cmull( a, b, c ); c = b * a
+ * cdivl( a, b, c ); c = b / a
+ * cnegl( c ); c = -c
+ * cmovl( b, c ); c = b
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Addition:
+ * c.r = b.r + a.r
+ * c.i = b.i + a.i
+ *
+ * Subtraction:
+ * c.r = b.r - a.r
+ * c.i = b.i - a.i
+ *
+ * Multiplication:
+ * c.r = b.r * a.r - b.i * a.i
+ * c.i = b.r * a.i + b.i * a.r
+ *
+ * Division:
+ * d = a.r * a.r + a.i * a.i
+ * c.r = (b.r * a.r + b.i * a.i)/d
+ * c.i = (b.i * a.r - b.r * a.i)/d
+ * ACCURACY:
+ *
+ * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
+ * error 3.1e-17, rms 1.2e-17. The test (y/z) * (z/y) = 1 had
+ * peak relative error 8.3e-17, rms 2.1e-17.
+ *
+ * Tests in the rectangle {-10,+10}:
+ * Relative error:
+ * arithmetic function # trials peak rms
+ * DEC cadd 10000 1.4e-17 3.4e-18
+ * IEEE cadd 100000 1.1e-16 2.7e-17
+ * DEC csub 10000 1.4e-17 4.5e-18
+ * IEEE csub 100000 1.1e-16 3.4e-17
+ * DEC cmul 3000 2.3e-17 8.7e-18
+ * IEEE cmul 100000 2.1e-16 6.9e-17
+ * DEC cdiv 18000 4.9e-17 1.3e-17
+ * IEEE cdiv 100000 3.7e-16 1.1e-16
+ */
+
+/* cabsl()
+ *
+ * Complex absolute value
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double cabsl();
+ * cmplxl z;
+ * long double a;
+ *
+ * a = cabs( &z );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy
+ *
+ * then
+ *
+ * a = sqrt( x**2 + y**2 ).
+ *
+ * Overflow and underflow are avoided by testing the magnitudes
+ * of x and y before squaring. If either is outside half of
+ * the floating point full scale range, both are rescaled.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -30,+30 30000 3.2e-17 9.2e-18
+ * IEEE -10,+10 100000 2.7e-16 6.9e-17
+ */
+ /* csqrtl()
+ *
+ * Complex square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csqrtl();
+ * cmplxl z, w;
+ *
+ * csqrtl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy, r = |z|, then
+ *
+ * 1/2
+ * Im w = [ (r - x)/2 ] ,
+ *
+ * Re w = y / 2 Im w.
+ *
+ *
+ * Note that -w is also a square root of z. The root chosen
+ * is always in the upper half plane.
+ *
+ * Because of the potential for cancellation error in r - x,
+ * the result is sharpened by doing a Heron iteration
+ * (see sqrt.c) in complex arithmetic.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 25000 3.2e-17 9.6e-18
+ * IEEE -10,+10 100000 3.2e-16 7.7e-17
+ *
+ * 2
+ * Also tested by csqrt( z ) = z, and tested by arguments
+ * close to the real axis.
+ */
+
+/* coshl.c
+ *
+ * Hyperbolic cosine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, coshl();
+ *
+ * y = coshl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic cosine of argument in the range MINLOGL to
+ * MAXLOGL.
+ *
+ * cosh(x) = ( exp(x) + exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-10000 30000 1.1e-19 2.8e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * cosh overflow |x| > MAXLOGL MAXNUML
+ *
+ *
+ */
+
+/* elliel.c
+ *
+ * Incomplete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double phi, m, y, elliel();
+ *
+ * y = elliel( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ * phi
+ * -
+ * | |
+ * | 2
+ * E(phi_\m) = | sqrt( 1 - m sin t ) dt
+ * |
+ * | |
+ * -
+ * 0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random arguments with phi in [-10, 10] and m in
+ * [0, 1].
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,10 50000 2.7e-18 2.3e-19
+ *
+ *
+ */
+
+/* ellikl.c
+ *
+ * Incomplete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double phi, m, y, ellikl();
+ *
+ * y = ellikl( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ * phi
+ * -
+ * | |
+ * | dt
+ * F(phi_\m) = | ------------------
+ * | 2
+ * | | sqrt( 1 - m sin t )
+ * -
+ * 0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with m in [0, 1] and phi as indicated.
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,10 30000 3.6e-18 4.1e-19
+ *
+ *
+ */
+
+/* ellpel.c
+ *
+ * Complete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double m1, y, ellpel();
+ *
+ * y = ellpel( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ * pi/2
+ * -
+ * | | 2
+ * E(m) = | sqrt( 1 - m sin t ) dt
+ * | |
+ * -
+ * 0
+ *
+ * Where m = 1 - m1, using the approximation
+ *
+ * P(x) - x log x Q(x).
+ *
+ * Though there are no singularities, the argument m1 is used
+ * rather than m for compatibility with ellpk().
+ *
+ * E(1) = 1; E(0) = pi/2.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 1 10000 1.1e-19 3.5e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ellpel domain x<0, x>1 0.0
+ *
+ */
+
+/* ellpjl.c
+ *
+ * Jacobian Elliptic Functions
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double u, m, sn, cn, dn, phi;
+ * int ellpjl();
+ *
+ * ellpjl( u, m, _&sn, _&cn, _&dn, _&phi );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
+ * and dn(u|m) of parameter m between 0 and 1, and real
+ * argument u.
+ *
+ * These functions are periodic, with quarter-period on the
+ * real axis equal to the complete elliptic integral
+ * ellpk(1.0-m).
+ *
+ * Relation to incomplete elliptic integral:
+ * If u = ellik(phi,m), then sn(u|m) = sin(phi),
+ * and cn(u|m) = cos(phi). Phi is called the amplitude of u.
+ *
+ * Computation is by means of the arithmetic-geometric mean
+ * algorithm, except when m is within 1e-12 of 0 or 1. In the
+ * latter case with m close to 1, the approximation applies
+ * only for phi < pi/2.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with u between 0 and 10, m between
+ * 0 and 1.
+ *
+ * Absolute error (* = relative error):
+ * arithmetic function # trials peak rms
+ * IEEE sn 10000 1.7e-18 2.3e-19
+ * IEEE cn 20000 1.6e-18 2.2e-19
+ * IEEE dn 10000 4.7e-15 2.7e-17
+ * IEEE phi 10000 4.0e-19* 6.6e-20*
+ *
+ * Accuracy deteriorates when u is large.
+ *
+ */
+
+/* ellpkl.c
+ *
+ * Complete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double m1, y, ellpkl();
+ *
+ * y = ellpkl( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ * pi/2
+ * -
+ * | |
+ * | dt
+ * K(m) = | ------------------
+ * | 2
+ * | | sqrt( 1 - m sin t )
+ * -
+ * 0
+ *
+ * where m = 1 - m1, using the approximation
+ *
+ * P(x) - log x Q(x).
+ *
+ * The argument m1 is used rather than m so that the logarithmic
+ * singularity at m = 1 will be shifted to the origin; this
+ * preserves maximum accuracy.
+ *
+ * K(0) = pi/2.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,1 10000 1.1e-19 3.3e-20
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ellpkl domain x<0, x>1 0.0
+ *
+ */
+
+/* exp10l.c
+ *
+ * Base 10 exponential function, long double precision
+ * (Common antilogarithm)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, exp10l()
+ *
+ * y = exp10l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 10 raised to the x power.
+ *
+ * Range reduction is accomplished by expressing the argument
+ * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
+ * The Pade' form
+ *
+ * 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ *
+ * is used to approximate 10**f.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-4900 30000 1.0e-19 2.7e-20
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp10l underflow x < -MAXL10 0.0
+ * exp10l overflow x > MAXL10 MAXNUM
+ *
+ * IEEE arithmetic: MAXL10 = 4932.0754489586679023819
+ *
+ */
+
+/* exp2l.c
+ *
+ * Base 2 exponential function, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, exp2l();
+ *
+ * y = exp2l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 2 raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ * x k f
+ * 2 = 2 2.
+ *
+ * A Pade' form
+ *
+ * 1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
+ *
+ * approximates 2**x in the basic range [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-16300 300000 9.1e-20 2.6e-20
+ *
+ *
+ * See exp.c for comments on error amplification.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp2l underflow x < -16382 0.0
+ * exp2l overflow x >= 16384 MAXNUM
+ *
+ */
+
+/* expl.c
+ *
+ * Exponential function, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, expl();
+ *
+ * y = expl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns e (2.71828...) raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *
+ * x k f
+ * e = 2 e.
+ *
+ * A Pade' form of degree 2/3 is used to approximate exp(f) - 1
+ * in the basic range [-0.5 ln 2, 0.5 ln 2].
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-10000 50000 1.12e-19 2.81e-20
+ *
+ *
+ * Error amplification in the exponential function can be
+ * a serious matter. The error propagation involves
+ * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
+ * which shows that a 1 lsb error in representing X produces
+ * a relative error of X times 1 lsb in the function.
+ * While the routine gives an accurate result for arguments
+ * that are exactly represented by a long double precision
+ * computer number, the result contains amplified roundoff
+ * error for large arguments not exactly represented.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp underflow x < MINLOG 0.0
+ * exp overflow x > MAXLOG MAXNUM
+ *
+ */
+
+/* fabsl.c
+ *
+ * Absolute value
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y;
+ *
+ * y = fabsl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the absolute value of the argument.
+ *
+ */
+
+/* fdtrl.c
+ *
+ * F distribution, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * long double x, y, fdtrl();
+ *
+ * y = fdtrl( df1, df2, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density). This is the density
+ * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
+ * variables having Chi square distributions with df1
+ * and df2 degrees of freedom, respectively.
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ * P(x) = incbetl( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
+ *
+ *
+ * The arguments a and b are greater than zero, and x
+ * x is nonnegative.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,x) in the indicated intervals.
+ * x a,b Relative error:
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0,1 1,100 10000 9.3e-18 2.9e-19
+ * IEEE 0,1 1,10000 10000 1.9e-14 2.9e-15
+ * IEEE 1,5 1,10000 10000 5.8e-15 1.4e-16
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrl domain a<0, b<0, x<0 0.0
+ *
+ */
+ /* fdtrcl()
+ *
+ * Complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * long double x, y, fdtrcl();
+ *
+ * y = fdtrcl( df1, df2, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from x to infinity under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density).
+ *
+ *
+ * inf.
+ * -
+ * 1 | | a-1 b-1
+ * 1-P(x) = ------ | t (1-t) dt
+ * B(a,b) | |
+ * -
+ * x
+ *
+ * (See fdtr.c.)
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * See incbet.c.
+ * Tested at random points (a,b,x).
+ *
+ * x a,b Relative error:
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0,1 0,100 10000 4.2e-18 3.3e-19
+ * IEEE 0,1 1,10000 10000 7.2e-15 2.6e-16
+ * IEEE 1,5 1,10000 10000 1.7e-14 3.0e-15
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrcl domain a<0, b<0, x<0 0.0
+ *
+ */
+ /* fdtril()
+ *
+ * Inverse of complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * long double x, p, fdtril();
+ *
+ * x = fdtril( df1, df2, p );
+ *
+ * DESCRIPTION:
+ *
+ * Finds the F density argument x such that the integral
+ * from x to infinity of the F density is equal to the
+ * given probability p.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relations
+ *
+ * z = incbi( df2/2, df1/2, p )
+ * x = df2 (1-z) / (df1 z).
+ *
+ * Note: the following relations hold for the inverse of
+ * the uncomplemented F distribution:
+ *
+ * z = incbi( df1/2, df2/2, p )
+ * x = df2 z / (df1 (1-z)).
+ *
+ * ACCURACY:
+ *
+ * See incbi.c.
+ * Tested at random points (a,b,p).
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * For p between .001 and 1:
+ * IEEE 1,100 40000 4.6e-18 2.7e-19
+ * IEEE 1,10000 30000 1.7e-14 1.4e-16
+ * For p between 10^-6 and .001:
+ * IEEE 1,100 20000 1.9e-15 3.9e-17
+ * IEEE 1,10000 30000 2.7e-15 4.0e-17
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtril domain p <= 0 or p > 1 0.0
+ * v < 1
+ */
+
+/* ceill()
+ * floorl()
+ * frexpl()
+ * ldexpl()
+ * fabsl()
+ *
+ * Floating point numeric utilities
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y;
+ * long double ceill(), floorl(), frexpl(), ldexpl(), fabsl();
+ * int expnt, n;
+ *
+ * y = floorl(x);
+ * y = ceill(x);
+ * y = frexpl( x, &expnt );
+ * y = ldexpl( x, n );
+ * y = fabsl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * All four routines return a long double precision floating point
+ * result.
+ *
+ * floorl() returns the largest integer less than or equal to x.
+ * It truncates toward minus infinity.
+ *
+ * ceill() returns the smallest integer greater than or equal
+ * to x. It truncates toward plus infinity.
+ *
+ * frexpl() extracts the exponent from x. It returns an integer
+ * power of two to expnt and the significand between 0.5 and 1
+ * to y. Thus x = y * 2**expn.
+ *
+ * ldexpl() multiplies x by 2**n.
+ *
+ * fabsl() returns the absolute value of its argument.
+ *
+ * These functions are part of the standard C run time library
+ * for some but not all C compilers. The ones supplied are
+ * written in C for IEEE arithmetic. They should
+ * be used only if your compiler library does not already have
+ * them.
+ *
+ * The IEEE versions assume that denormal numbers are implemented
+ * in the arithmetic. Some modifications will be required if
+ * the arithmetic has abrupt rather than gradual underflow.
+ */
+
+/* gammal.c
+ *
+ * Gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, gammal();
+ * extern int sgngam;
+ *
+ * y = gammal( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns gamma function of the argument. The result is
+ * correctly signed, and the sign (+1 or -1) is also
+ * returned in a global (extern) variable named sgngam.
+ * This variable is also filled in by the logarithmic gamma
+ * function lgam().
+ *
+ * Arguments |x| <= 13 are reduced by recurrence and the function
+ * approximated by a rational function of degree 7/8 in the
+ * interval (2,3). Large arguments are handled by Stirling's
+ * formula. Large negative arguments are made positive using
+ * a reflection formula.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -40,+40 10000 3.6e-19 7.9e-20
+ * IEEE -1755,+1755 10000 4.8e-18 6.5e-19
+ *
+ * Accuracy for large arguments is dominated by error in powl().
+ *
+ */
+/* lgaml()
+ *
+ * Natural logarithm of gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, lgaml();
+ * extern int sgngam;
+ *
+ * y = lgaml( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of the absolute
+ * value of the gamma function of the argument.
+ * The sign (+1 or -1) of the gamma function is returned in a
+ * global (extern) variable named sgngam.
+ *
+ * For arguments greater than 33, the logarithm of the gamma
+ * function is approximated by the logarithmic version of
+ * Stirling's formula using a polynomial approximation of
+ * degree 4. Arguments between -33 and +33 are reduced by
+ * recurrence to the interval [2,3] of a rational approximation.
+ * The cosecant reflection formula is employed for arguments
+ * less than -33.
+ *
+ * Arguments greater than MAXLGML (10^4928) return MAXNUML.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * arithmetic domain # trials peak rms
+ * IEEE -40, 40 100000 2.2e-19 4.6e-20
+ * IEEE 10^-2000,10^+2000 20000 1.6e-19 3.3e-20
+ * The error criterion was relative when the function magnitude
+ * was greater than one but absolute when it was less than one.
+ *
+ */
+
+/* gdtrl.c
+ *
+ * Gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, b, x, y, gdtrl();
+ *
+ * y = gdtrl( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from zero to x of the gamma probability
+ * density function:
+ *
+ *
+ * x
+ * b -
+ * a | | b-1 -at
+ * y = ----- | t e dt
+ * - | |
+ * | (b) -
+ * 0
+ *
+ * The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igam( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * gdtrl domain x < 0 0.0
+ *
+ */
+ /* gdtrcl.c
+ *
+ * Complemented gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, b, x, y, gdtrcl();
+ *
+ * y = gdtrcl( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from x to infinity of the gamma
+ * probability density function:
+ *
+ *
+ * inf.
+ * b -
+ * a | | b-1 -at
+ * y = ----- | t e dt
+ * - | |
+ * | (b) -
+ * x
+ *
+ * The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igamc( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * gdtrcl domain x < 0 0.0
+ *
+ */
+
+/*
+C
+C ..................................................................
+C
+C SUBROUTINE GELS
+C
+C PURPOSE
+C TO SOLVE A SYSTEM OF SIMULTANEOUS LINEAR EQUATIONS WITH
+C SYMMETRIC COEFFICIENT MATRIX UPPER TRIANGULAR PART OF WHICH
+C IS ASSUMED TO BE STORED COLUMNWISE.
+C
+C USAGE
+C CALL GELS(R,A,M,N,EPS,IER,AUX)
+C
+C DESCRIPTION OF PARAMETERS
+C R - M BY N RIGHT HAND SIDE MATRIX. (DESTROYED)
+C ON RETURN R CONTAINS THE SOLUTION OF THE EQUATIONS.
+C A - UPPER TRIANGULAR PART OF THE SYMMETRIC
+C M BY M COEFFICIENT MATRIX. (DESTROYED)
+C M - THE NUMBER OF EQUATIONS IN THE SYSTEM.
+C N - THE NUMBER OF RIGHT HAND SIDE VECTORS.
+C EPS - AN INPUT CONSTANT WHICH IS USED AS RELATIVE
+C TOLERANCE FOR TEST ON LOSS OF SIGNIFICANCE.
+C IER - RESULTING ERROR PARAMETER CODED AS FOLLOWS
+C IER=0 - NO ERROR,
+C IER=-1 - NO RESULT BECAUSE OF M LESS THAN 1 OR
+C PIVOT ELEMENT AT ANY ELIMINATION STEP
+C EQUAL TO 0,
+C IER=K - WARNING DUE TO POSSIBLE LOSS OF SIGNIFI-
+C CANCE INDICATED AT ELIMINATION STEP K+1,
+C WHERE PIVOT ELEMENT WAS LESS THAN OR
+C EQUAL TO THE INTERNAL TOLERANCE EPS TIMES
+C ABSOLUTELY GREATEST MAIN DIAGONAL
+C ELEMENT OF MATRIX A.
+C AUX - AN AUXILIARY STORAGE ARRAY WITH DIMENSION M-1.
+C
+C REMARKS
+C UPPER TRIANGULAR PART OF MATRIX A IS ASSUMED TO BE STORED
+C COLUMNWISE IN M*(M+1)/2 SUCCESSIVE STORAGE LOCATIONS, RIGHT
+C HAND SIDE MATRIX R COLUMNWISE IN N*M SUCCESSIVE STORAGE
+C LOCATIONS. ON RETURN SOLUTION MATRIX R IS STORED COLUMNWISE
+C TOO.
+C THE PROCEDURE GIVES RESULTS IF THE NUMBER OF EQUATIONS M IS
+C GREATER THAN 0 AND PIVOT ELEMENTS AT ALL ELIMINATION STEPS
+C ARE DIFFERENT FROM 0. HOWEVER WARNING IER=K - IF GIVEN -
+C INDICATES POSSIBLE LOSS OF SIGNIFICANCE. IN CASE OF A WELL
+C SCALED MATRIX A AND APPROPRIATE TOLERANCE EPS, IER=K MAY BE
+C INTERPRETED THAT MATRIX A HAS THE RANK K. NO WARNING IS
+C GIVEN IN CASE M=1.
+C ERROR PARAMETER IER=-1 DOES NOT NECESSARILY MEAN THAT
+C MATRIX A IS SINGULAR, AS ONLY MAIN DIAGONAL ELEMENTS
+C ARE USED AS PIVOT ELEMENTS. POSSIBLY SUBROUTINE GELG (WHICH
+C WORKS WITH TOTAL PIVOTING) WOULD BE ABLE TO FIND A SOLUTION.
+C
+C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
+C NONE
+C
+C METHOD
+C SOLUTION IS DONE BY MEANS OF GAUSS-ELIMINATION WITH
+C PIVOTING IN MAIN DIAGONAL, IN ORDER TO PRESERVE
+C SYMMETRY IN REMAINING COEFFICIENT MATRICES.
+C
+C ..................................................................
+C
+*/
+
+/* igamil()
+ *
+ * Inverse of complemented imcomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, x, y, igamil();
+ *
+ * x = igamil( a, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given y, the function finds x such that
+ *
+ * igamc( a, x ) = y.
+ *
+ * Starting with the approximate value
+ *
+ * 3
+ * x = a t
+ *
+ * where
+ *
+ * t = 1 - d - ndtri(y) sqrt(d)
+ *
+ * and
+ *
+ * d = 1/9a,
+ *
+ * the routine performs up to 10 Newton iterations to find the
+ * root of igamc(a,x) - y = 0.
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested for a ranging from 0.5 to 30 and x from 0 to 0.5.
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,0.5 3400 8.8e-16 1.3e-16
+ * IEEE 0,0.5 10000 1.1e-14 1.0e-15
+ *
+ */
+
+/* igaml.c
+ *
+ * Incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, x, y, igaml();
+ *
+ * y = igaml( a, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ * x
+ * -
+ * 1 | | -t a-1
+ * igam(a,x) = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * 0
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 4000 4.4e-15 6.3e-16
+ * IEEE 0,30 10000 3.6e-14 5.1e-15
+ *
+ */
+ /* igamcl()
+ *
+ * Complemented incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, x, y, igamcl();
+ *
+ * y = igamcl( a, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ *
+ * igamc(a,x) = 1 - igam(a,x)
+ *
+ * inf.
+ * -
+ * 1 | | -t a-1
+ * = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * x
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 2000 2.7e-15 4.0e-16
+ * IEEE 0,30 60000 1.4e-12 6.3e-15
+ *
+ */
+
+/* incbetl.c
+ *
+ * Incomplete beta integral
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, b, x, y, incbetl();
+ *
+ * y = incbetl( a, b, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns incomplete beta integral of the arguments, evaluated
+ * from zero to x. The function is defined as
+ *
+ * x
+ * - -
+ * | (a+b) | | a-1 b-1
+ * ----------- | t (1-t) dt.
+ * - - | |
+ * | (a) | (b) -
+ * 0
+ *
+ * The domain of definition is 0 <= x <= 1. In this
+ * implementation a and b are restricted to positive values.
+ * The integral from x to 1 may be obtained by the symmetry
+ * relation
+ *
+ * 1 - incbet( a, b, x ) = incbet( b, a, 1-x ).
+ *
+ * The integral is evaluated by a continued fraction expansion
+ * or, when b*x is small, by a power series.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,x) with x between 0 and 1.
+ * arithmetic domain # trials peak rms
+ * IEEE 0,5 20000 4.5e-18 2.4e-19
+ * IEEE 0,100 100000 3.9e-17 1.0e-17
+ * Half-integer a, b:
+ * IEEE .5,10000 100000 3.9e-14 4.4e-15
+ * Outputs smaller than the IEEE gradual underflow threshold
+ * were excluded from these statistics.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * incbetl domain x<0, x>1 0.0
+ */
+
+/* incbil()
+ *
+ * Inverse of imcomplete beta integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, b, x, y, incbil();
+ *
+ * x = incbil( a, b, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given y, the function finds x such that
+ *
+ * incbet( a, b, x ) = y.
+ *
+ * the routine performs up to 10 Newton iterations to find the
+ * root of incbet(a,b,x) - y = 0.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * x a,b
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0,1 .5,10000 10000 1.1e-14 1.4e-16
+ */
+
+/* j0l.c
+ *
+ * Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, j0l();
+ *
+ * y = j0l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of first kind, order zero of the argument.
+ *
+ * The domain is divided into the intervals [0, 9] and
+ * (9, infinity). In the first interval the rational approximation
+ * is (x^2 - r^2) (x^2 - s^2) (x^2 - t^2) P7(x^2) / Q8(x^2),
+ * where r, s, t are the first three zeros of the function.
+ * In the second interval the expansion is in terms of the
+ * modulus M0(x) = sqrt(J0(x)^2 + Y0(x)^2) and phase P0(x)
+ * = atan(Y0(x)/J0(x)). M0 is approximated by sqrt(1/x)P7(1/x)/Q7(1/x).
+ * The approximation to J0 is M0 * cos(x - pi/4 + 1/x P5(1/x^2)/Q6(1/x^2)).
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 100000 2.8e-19 7.4e-20
+ *
+ *
+ */
+ /* y0l.c
+ *
+ * Bessel function of the second kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y0l();
+ *
+ * y = y0l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind, of order
+ * zero, of the argument.
+ *
+ * The domain is divided into the intervals [0, 5>, [5,9> and
+ * [9, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute y0(x) = R(x) + 2/pi * log(x) * j0(x).
+ *
+ * In the second interval, the approximation is
+ * (x - p)(x - q)(x - r)(x - s)P7(x)/Q7(x)
+ * where p, q, r, s are zeros of y0(x).
+ *
+ * The third interval uses the same approximations to modulus
+ * and phase as j0(x), whence y0(x) = modulus * sin(phase).
+ *
+ * ACCURACY:
+ *
+ * Absolute error, when y0(x) < 1; else relative error:
+ *
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 100000 3.4e-19 7.6e-20
+ *
+ */
+
+/* j1l.c
+ *
+ * Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, j1l();
+ *
+ * y = j1l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order one of the argument.
+ *
+ * The domain is divided into the intervals [0, 9] and
+ * (9, infinity). In the first interval the rational approximation
+ * is (x^2 - r^2) (x^2 - s^2) (x^2 - t^2) x P8(x^2) / Q8(x^2),
+ * where r, s, t are the first three zeros of the function.
+ * In the second interval the expansion is in terms of the
+ * modulus M1(x) = sqrt(J1(x)^2 + Y1(x)^2) and phase P1(x)
+ * = atan(Y1(x)/J1(x)). M1 is approximated by sqrt(1/x)P7(1/x)/Q8(1/x).
+ * The approximation to j1 is M1 * cos(x - 3 pi/4 + 1/x P5(1/x^2)/Q6(1/x^2)).
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 40000 1.8e-19 5.0e-20
+ *
+ *
+ */
+ /* y1l.c
+ *
+ * Bessel function of the second kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y1l();
+ *
+ * y = y1l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind, of order
+ * zero, of the argument.
+ *
+ * The domain is divided into the intervals [0, 4.5>, [4.5,9> and
+ * [9, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute y0(x) = R(x) + 2/pi * log(x) * j0(x).
+ *
+ * In the second interval, the approximation is
+ * (x - p)(x - q)(x - r)(x - s)P9(x)/Q10(x)
+ * where p, q, r, s are zeros of y1(x).
+ *
+ * The third interval uses the same approximations to modulus
+ * and phase as j1(x), whence y1(x) = modulus * sin(phase).
+ *
+ * ACCURACY:
+ *
+ * Absolute error, when y0(x) < 1; else relative error:
+ *
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 36000 2.7e-19 5.3e-20
+ *
+ */
+
+/* jnl.c
+ *
+ * Bessel function of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * long double x, y, jnl();
+ *
+ * y = jnl( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The ratio of jn(x) to j0(x) is computed by backward
+ * recurrence. First the ratio jn/jn-1 is found by a
+ * continued fraction expansion. Then the recurrence
+ * relating successive orders is applied until j0 or j1 is
+ * reached.
+ *
+ * If n = 0 or 1 the routine for j0 or j1 is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE -30, 30 5000 3.3e-19 4.7e-20
+ *
+ *
+ * Not suitable for large n or x.
+ *
+ */
+
+/* ldrand.c
+ *
+ * Pseudorandom number generator
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double y;
+ * int ldrand();
+ *
+ * ldrand( &y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Yields a random number 1.0 <= y < 2.0.
+ *
+ * The three-generator congruential algorithm by Brian
+ * Wichmann and David Hill (BYTE magazine, March, 1987,
+ * pp 127-8) is used.
+ *
+ * Versions invoked by the different arithmetic compile
+ * time options IBMPC, and MIEEE, produce the same sequences.
+ *
+ */
+
+/* log10l.c
+ *
+ * Common logarithm, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, log10l();
+ *
+ * y = log10l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base 10 logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the logarithm
+ * of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting z = 2(x-1)/x+1),
+ *
+ * log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 30000 9.0e-20 2.6e-20
+ * IEEE exp(+-10000) 30000 6.0e-20 2.3e-20
+ *
+ * In the tests over the interval exp(+-10000), the logarithms
+ * of the random arguments were uniformly distributed over
+ * [-10000, +10000].
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity: x = 0; returns MINLOG
+ * log domain: x < 0; returns MINLOG
+ */
+
+/* log2l.c
+ *
+ * Base 2 logarithm, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, log2l();
+ *
+ * y = log2l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base 2 logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the (natural)
+ * logarithm of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting z = 2(x-1)/x+1),
+ *
+ * log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 30000 9.8e-20 2.7e-20
+ * IEEE exp(+-10000) 70000 5.4e-20 2.3e-20
+ *
+ * In the tests over the interval exp(+-10000), the logarithms
+ * of the random arguments were uniformly distributed over
+ * [-10000, +10000].
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity: x = 0; returns MINLOG
+ * log domain: x < 0; returns MINLOG
+ */
+
+/* logl.c
+ *
+ * Natural logarithm, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, logl();
+ *
+ * y = logl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the logarithm
+ * of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting z = 2(x-1)/x+1),
+ *
+ * log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 150000 8.71e-20 2.75e-20
+ * IEEE exp(+-10000) 100000 5.39e-20 2.34e-20
+ *
+ * In the tests over the interval exp(+-10000), the logarithms
+ * of the random arguments were uniformly distributed over
+ * [-10000, +10000].
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity: x = 0; returns MINLOG
+ * log domain: x < 0; returns MINLOG
+ */
+
+/* mtherr.c
+ *
+ * Library common error handling routine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * char *fctnam;
+ * int code;
+ * int mtherr();
+ *
+ * mtherr( fctnam, code );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This routine may be called to report one of the following
+ * error conditions (in the include file mconf.h).
+ *
+ * Mnemonic Value Significance
+ *
+ * DOMAIN 1 argument domain error
+ * SING 2 function singularity
+ * OVERFLOW 3 overflow range error
+ * UNDERFLOW 4 underflow range error
+ * TLOSS 5 total loss of precision
+ * PLOSS 6 partial loss of precision
+ * EDOM 33 Unix domain error code
+ * ERANGE 34 Unix range error code
+ *
+ * The default version of the file prints the function name,
+ * passed to it by the pointer fctnam, followed by the
+ * error condition. The display is directed to the standard
+ * output device. The routine then returns to the calling
+ * program. Users may wish to modify the program to abort by
+ * calling exit() under severe error conditions such as domain
+ * errors.
+ *
+ * Since all error conditions pass control to this function,
+ * the display may be easily changed, eliminated, or directed
+ * to an error logging device.
+ *
+ * SEE ALSO:
+ *
+ * mconf.h
+ *
+ */
+
+/* nbdtrl.c
+ *
+ * Negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, nbdtrl();
+ *
+ * y = nbdtrl( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the negative
+ * binomial distribution:
+ *
+ * k
+ * -- ( n+j-1 ) n j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=0
+ *
+ * In a sequence of Bernoulli trials, this is the probability
+ * that k or fewer failures precede the nth success.
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (k,n,p) with k and n between 1 and 10,000
+ * and p between 0 and 1.
+ *
+ * arithmetic domain # trials peak rms
+ * Absolute error:
+ * IEEE 0,10000 10000 9.8e-15 2.1e-16
+ *
+ */
+ /* nbdtrcl.c
+ *
+ * Complemented negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, nbdtrcl();
+ *
+ * y = nbdtrcl( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the negative
+ * binomial distribution:
+ *
+ * inf
+ * -- ( n+j-1 ) n j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=k+1
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See incbetl.c.
+ *
+ */
+ /* nbdtril
+ *
+ * Functional inverse of negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, nbdtril();
+ *
+ * p = nbdtril( k, n, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the argument p such that nbdtr(k,n,p) is equal to y.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,y), with y between 0 and 1.
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100
+ * See also incbil.c.
+ */
+
+/* ndtril.c
+ *
+ * Inverse of Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, ndtril();
+ *
+ * x = ndtril( y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the argument, x, for which the area under the
+ * Gaussian probability density function (integrated from
+ * minus infinity to x) is equal to y.
+ *
+ *
+ * For small arguments 0 < y < exp(-2), the program computes
+ * z = sqrt( -2 log(y) ); then the approximation is
+ * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z) .
+ * For larger arguments, x/sqrt(2 pi) = w + w^3 R(w^2)/S(w^2)) ,
+ * where w = y - 0.5 .
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * Arguments uniformly distributed:
+ * IEEE 0, 1 5000 7.8e-19 9.9e-20
+ * Arguments exponentially distributed:
+ * IEEE exp(-11355),-1 30000 1.7e-19 4.3e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ndtril domain x <= 0 -MAXNUML
+ * ndtril domain x >= 1 MAXNUML
+ *
+ */
+
+/* ndtril.c
+ *
+ * Inverse of Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, ndtril();
+ *
+ * x = ndtril( y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the argument, x, for which the area under the
+ * Gaussian probability density function (integrated from
+ * minus infinity to x) is equal to y.
+ *
+ *
+ * For small arguments 0 < y < exp(-2), the program computes
+ * z = sqrt( -2 log(y) ); then the approximation is
+ * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z) .
+ * For larger arguments, x/sqrt(2 pi) = w + w^3 R(w^2)/S(w^2)) ,
+ * where w = y - 0.5 .
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * Arguments uniformly distributed:
+ * IEEE 0, 1 5000 7.8e-19 9.9e-20
+ * Arguments exponentially distributed:
+ * IEEE exp(-11355),-1 30000 1.7e-19 4.3e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ndtril domain x <= 0 -MAXNUML
+ * ndtril domain x >= 1 MAXNUML
+ *
+ */
+
+/* pdtrl.c
+ *
+ * Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * long double m, y, pdtrl();
+ *
+ * y = pdtrl( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the first k terms of the Poisson
+ * distribution:
+ *
+ * k j
+ * -- -m m
+ * > e --
+ * -- j!
+ * j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the relation
+ *
+ * y = pdtr( k, m ) = igamc( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ */
+ /* pdtrcl()
+ *
+ * Complemented poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * long double m, y, pdtrcl();
+ *
+ * y = pdtrcl( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the Poisson
+ * distribution:
+ *
+ * inf. j
+ * -- -m m
+ * > e --
+ * -- j!
+ * j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the formula
+ *
+ * y = pdtrc( k, m ) = igam( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam.c.
+ *
+ */
+ /* pdtril()
+ *
+ * Inverse Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * long double m, y, pdtrl();
+ *
+ * m = pdtril( k, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Poisson variable x such that the integral
+ * from 0 to x of the Poisson density is equal to the
+ * given probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ * m = igami( k+1, y ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igami.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * pdtri domain y < 0 or y >= 1 0.0
+ * k < 0
+ *
+ */
+
+/* polevll.c
+ * p1evll.c
+ *
+ * Evaluate polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * long double x, y, coef[N+1], polevl[];
+ *
+ * y = polevll( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates polynomial of degree N:
+ *
+ * 2 N
+ * y = C + C x + C x +...+ C x
+ * 0 1 2 N
+ *
+ * Coefficients are stored in reverse order:
+ *
+ * coef[0] = C , ..., coef[N] = C .
+ * N 0
+ *
+ * The function p1evll() assumes that coef[N] = 1.0 and is
+ * omitted from the array. Its calling arguments are
+ * otherwise the same as polevll().
+ *
+ * This module also contains the following globally declared constants:
+ * MAXNUML = 1.189731495357231765021263853E4932L;
+ * MACHEPL = 5.42101086242752217003726400434970855712890625E-20L;
+ * MAXLOGL = 1.1356523406294143949492E4L;
+ * MINLOGL = -1.1355137111933024058873E4L;
+ * LOGE2L = 6.9314718055994530941723E-1L;
+ * LOG2EL = 1.4426950408889634073599E0L;
+ * PIL = 3.1415926535897932384626L;
+ * PIO2L = 1.5707963267948966192313L;
+ * PIO4L = 7.8539816339744830961566E-1L;
+ *
+ * SPEED:
+ *
+ * In the interest of speed, there are no checks for out
+ * of bounds arithmetic. This routine is used by most of
+ * the functions in the library. Depending on available
+ * equipment features, the user may wish to rewrite the
+ * program in microcode or assembly language.
+ *
+ */
+
+/* powil.c
+ *
+ * Real raised to integer power, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, powil();
+ * int n;
+ *
+ * y = powil( x, n );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns argument x raised to the nth power.
+ * The routine efficiently decomposes n as a sum of powers of
+ * two. The desired power is a product of two-to-the-kth
+ * powers of x. Thus to compute the 32767 power of x requires
+ * 28 multiplications instead of 32767 multiplications.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error:
+ * arithmetic x domain n domain # trials peak rms
+ * IEEE .001,1000 -1022,1023 50000 4.3e-17 7.8e-18
+ * IEEE 1,2 -1022,1023 20000 3.9e-17 7.6e-18
+ * IEEE .99,1.01 0,8700 10000 3.6e-16 7.2e-17
+ *
+ * Returns MAXNUM on overflow, zero on underflow.
+ *
+ */
+
+/* powl.c
+ *
+ * Power function, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, z, powl();
+ *
+ * z = powl( x, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes x raised to the yth power. Analytically,
+ *
+ * x**y = exp( y log(x) ).
+ *
+ * Following Cody and Waite, this program uses a lookup table
+ * of 2**-i/32 and pseudo extended precision arithmetic to
+ * obtain several extra bits of accuracy in both the logarithm
+ * and the exponential.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * The relative error of pow(x,y) can be estimated
+ * by y dl ln(2), where dl is the absolute error of
+ * the internally computed base 2 logarithm. At the ends
+ * of the approximation interval the logarithm equal 1/32
+ * and its relative error is about 1 lsb = 1.1e-19. Hence
+ * the predicted relative error in the result is 2.3e-21 y .
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ *
+ * IEEE +-1000 40000 2.8e-18 3.7e-19
+ * .001 < x < 1000, with log(x) uniformly distributed.
+ * -1000 < y < 1000, y uniformly distributed.
+ *
+ * IEEE 0,8700 60000 6.5e-18 1.0e-18
+ * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * pow overflow x**y > MAXNUM MAXNUM
+ * pow underflow x**y < 1/MAXNUM 0.0
+ * pow domain x<0 and y noninteger 0.0
+ *
+ */
+
+/* sinhl.c
+ *
+ * Hyperbolic sine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, sinhl();
+ *
+ * y = sinhl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic sine of argument in the range MINLOGL to
+ * MAXLOGL.
+ *
+ * The range is partitioned into two segments. If |x| <= 1, a
+ * rational function of the form x + x**3 P(x)/Q(x) is employed.
+ * Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -2,2 10000 1.5e-19 3.9e-20
+ * IEEE +-10000 30000 1.1e-19 2.8e-20
+ *
+ */
+
+/* sinl.c
+ *
+ * Circular sine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, sinl();
+ *
+ * y = sinl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of pi/4. The reduction
+ * error is nearly eliminated by contriving an extended precision
+ * modular arithmetic.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the sine is approximated by the Cody
+ * and Waite polynomial form
+ * x + x**3 P(x**2) .
+ * Between pi/4 and pi/2 the cosine is represented as
+ * 1 - .5 x**2 + x**4 Q(x**2) .
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-5.5e11 200,000 1.2e-19 2.9e-20
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sin total loss x > 2**39 0.0
+ *
+ * Loss of precision occurs for x > 2**39 = 5.49755813888e11.
+ * The routine as implemented flags a TLOSS error for
+ * x > 2**39 and returns 0.0.
+ */
+ /* cosl.c
+ *
+ * Circular cosine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, cosl();
+ *
+ * y = cosl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of pi/4. The reduction
+ * error is nearly eliminated by contriving an extended precision
+ * modular arithmetic.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the cosine is approximated by
+ * 1 - .5 x**2 + x**4 Q(x**2) .
+ * Between pi/4 and pi/2 the sine is represented by the Cody
+ * and Waite polynomial form
+ * x + x**3 P(x**2) .
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-5.5e11 50000 1.2e-19 2.9e-20
+ */
+
+/* sqrtl.c
+ *
+ * Square root, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, sqrtl();
+ *
+ * y = sqrtl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the square root of x.
+ *
+ * Range reduction involves isolating the power of two of the
+ * argument and using a polynomial approximation to obtain
+ * a rough value for the square root. Then Heron's iteration
+ * is used three times to converge to an accurate value.
+ *
+ * Note, some arithmetic coprocessors such as the 8087 and
+ * 68881 produce correctly rounded square roots, which this
+ * routine will not.
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,10 30000 8.1e-20 3.1e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sqrt domain x < 0 0.0
+ *
+ */
+
+/* stdtrl.c
+ *
+ * Student's t distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double p, t, stdtrl();
+ * int k;
+ *
+ * p = stdtrl( k, t );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the integral from minus infinity to t of the Student
+ * t distribution with integer k > 0 degrees of freedom:
+ *
+ * t
+ * -
+ * | |
+ * - | 2 -(k+1)/2
+ * | ( (k+1)/2 ) | ( x )
+ * ---------------------- | ( 1 + --- ) dx
+ * - | ( k )
+ * sqrt( k pi ) | ( k/2 ) |
+ * | |
+ * -
+ * -inf.
+ *
+ * Relation to incomplete beta integral:
+ *
+ * 1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
+ * where
+ * z = k/(k + t**2).
+ *
+ * For t < -1.6, this is the method of computation. For higher t,
+ * a direct method is derived from integration by parts.
+ * Since the function is symmetric about t=0, the area under the
+ * right tail of the density is found by calling the function
+ * with -t instead of t.
+ *
+ * ACCURACY:
+ *
+ * Tested at random 1 <= k <= 100. The "domain" refers to t.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -100,-1.6 10000 5.7e-18 9.8e-19
+ * IEEE -1.6,100 10000 3.8e-18 1.0e-19
+ */
+
+/* stdtril.c
+ *
+ * Functional inverse of Student's t distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double p, t, stdtril();
+ * int k;
+ *
+ * t = stdtril( k, p );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given probability p, finds the argument t such that stdtrl(k,t)
+ * is equal to p.
+ *
+ * ACCURACY:
+ *
+ * Tested at random 1 <= k <= 100. The "domain" refers to p:
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,1 3500 4.2e-17 4.1e-18
+ */
+
+/* tanhl.c
+ *
+ * Hyperbolic tangent, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, tanhl();
+ *
+ * y = tanhl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic tangent of argument in the range MINLOGL to
+ * MAXLOGL.
+ *
+ * A rational function is used for |x| < 0.625. The form
+ * x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
+ * Otherwise,
+ * tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -2,2 30000 1.3e-19 2.4e-20
+ *
+ */
+
+/* tanl.c
+ *
+ * Circular tangent, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, tanl();
+ *
+ * y = tanl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular tangent of the radian argument x.
+ *
+ * Range reduction is modulo pi/4. A rational function
+ * x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-1.07e9 30000 1.9e-19 4.8e-20
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * tan total loss x > 2^39 0.0
+ *
+ */
+ /* cotl.c
+ *
+ * Circular cotangent, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, cotl();
+ *
+ * y = cotl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular cotangent of the radian argument x.
+ *
+ * Range reduction is modulo pi/4. A rational function
+ * x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-1.07e9 30000 1.9e-19 5.1e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * cot total loss x > 2^39 0.0
+ * cot singularity x = 0 MAXNUM
+ *
+ */
+
+/* unityl.c
+ *
+ * Relative error approximations for function arguments near
+ * unity.
+ *
+ * log1p(x) = log(1+x)
+ * expm1(x) = exp(x) - 1
+ * cos1m(x) = cos(x) - 1
+ *
+ */
+
+/* ynl.c
+ *
+ * Bessel function of second kind of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, ynl();
+ * int n;
+ *
+ * y = ynl( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The function is evaluated by forward recurrence on
+ * n, starting with values computed by the routines
+ * y0l() and y1l().
+ *
+ * If n = 0 or 1 the routine for y0l or y1l is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Absolute error, except relative error when y > 1.
+ * x >= 0, -30 <= n <= +30.
+ * arithmetic domain # trials peak rms
+ * IEEE -30, 30 10000 1.3e-18 1.8e-19
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ynl singularity x = 0 MAXNUML
+ * ynl overflow MAXNUML
+ *
+ * Spot checked against tables for x, n between 0 and 100.
+ *
+ */
diff --git a/libm/ldouble/acoshl.c b/libm/ldouble/acoshl.c
new file mode 100644
index 000000000..96c46bf22
--- /dev/null
+++ b/libm/ldouble/acoshl.c
@@ -0,0 +1,167 @@
+/* acoshl.c
+ *
+ * Inverse hyperbolic cosine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, acoshl();
+ *
+ * y = acoshl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic cosine of argument.
+ *
+ * If 1 <= x < 1.5, a rational approximation
+ *
+ * sqrt(2z) * P(z)/Q(z)
+ *
+ * where z = x-1, is used. Otherwise,
+ *
+ * acosh(x) = log( x + sqrt( (x-1)(x+1) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 1,3 30000 2.0e-19 3.9e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * acoshl domain |x| < 1 0.0
+ *
+ */
+
+/* acosh.c */
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright 1984, 1991, 1998 by Stephen L. Moshier
+*/
+
+
+/* acosh(1+x) = sqrt(2x) * R(x), interval 0 < x < 0.5 */
+
+#include <math.h>
+
+#ifdef UNK
+static long double P[] = {
+ 2.9071989653343333587238E-5L,
+ 3.2906030801088967279449E-3L,
+ 6.3034445964862182128388E-2L,
+ 4.1587081802731351459504E-1L,
+ 1.0989714347599256302467E0L,
+ 9.9999999999999999999715E-1L,
+};
+static long double Q[] = {
+ 1.0443462486787584738322E-4L,
+ 6.0085845375571145826908E-3L,
+ 8.7750439986662958343370E-2L,
+ 4.9564621536841869854584E-1L,
+ 1.1823047680932589605190E0L,
+ 1.0000000000000000000028E0L,
+};
+#endif
+
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x4536,0x4dba,0x9f55,0xf3df,0x3fef, XPD
+0x23a5,0xf9aa,0x289c,0xd7a7,0x3ff6, XPD
+0x7e8b,0x8645,0x341f,0x8118,0x3ffb, XPD
+0x0fd5,0x937f,0x0515,0xd4ed,0x3ffd, XPD
+0x2364,0xc41b,0x1891,0x8cab,0x3fff, XPD
+0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
+};
+static short Q[] = {
+0x1e7c,0x4f16,0xe98c,0xdb03,0x3ff1, XPD
+0xc319,0xc272,0xa90a,0xc4e3,0x3ff7, XPD
+0x2f83,0x9e5e,0x80af,0xb3b6,0x3ffb, XPD
+0xe1e0,0xc97c,0x573a,0xfdc5,0x3ffd, XPD
+0xcdf2,0x6ec5,0xc33c,0x9755,0x3fff, XPD
+0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
+};
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0x3fef0000,0xf3df9f55,0x4dba4536,
+0x3ff60000,0xd7a7289c,0xf9aa23a5,
+0x3ffb0000,0x8118341f,0x86457e8b,
+0x3ffd0000,0xd4ed0515,0x937f0fd5,
+0x3fff0000,0x8cab1891,0xc41b2364,
+0x3fff0000,0x80000000,0x00000000,
+};
+static long Q[] = {
+0x3ff10000,0xdb03e98c,0x4f161e7c,
+0x3ff70000,0xc4e3a90a,0xc272c319,
+0x3ffb0000,0xb3b680af,0x9e5e2f83,
+0x3ffd0000,0xfdc5573a,0xc97ce1e0,
+0x3fff0000,0x9755c33c,0x6ec5cdf2,
+0x3fff0000,0x80000000,0x00000000,
+};
+#endif
+
+extern long double LOGE2L;
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+#ifdef NANS
+extern long double NANL;
+#endif
+#ifdef ANSIPROT
+extern long double logl ( long double );
+extern long double sqrtl ( long double );
+extern long double polevll ( long double, void *, int );
+extern int isnanl ( long double );
+#else
+long double logl(), sqrtl(), polevll(), isnanl();
+#endif
+
+long double acoshl(x)
+long double x;
+{
+long double a, z;
+
+#ifdef NANS
+if( isnanl(x) )
+ return(x);
+#endif
+if( x < 1.0L )
+ {
+ mtherr( "acoshl", DOMAIN );
+#ifdef NANS
+ return(NANL);
+#else
+ return(0.0L);
+#endif
+ }
+
+if( x > 1.0e10 )
+ {
+#ifdef INFINITIES
+ if( x == INFINITYL )
+ return( INFINITYL );
+#endif
+ return( logl(x) + LOGE2L );
+ }
+
+z = x - 1.0L;
+
+if( z < 0.5L )
+ {
+ a = sqrtl(2.0L*z) * (polevll(z, P, 5) / polevll(z, Q, 5) );
+ return( a );
+ }
+
+a = sqrtl( z*(x+1.0L) );
+return( logl(x + a) );
+}
diff --git a/libm/ldouble/arcdotl.c b/libm/ldouble/arcdotl.c
new file mode 100644
index 000000000..952f027c6
--- /dev/null
+++ b/libm/ldouble/arcdotl.c
@@ -0,0 +1,108 @@
+/* arcdot.c
+ *
+ * Angle between two vectors
+ *
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double p[3], q[3], arcdotl();
+ *
+ * y = arcdotl( p, q );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * For two vectors p, q, the angle A between them is given by
+ *
+ * p.q / (|p| |q|) = cos A .
+ *
+ * where "." represents inner product, "|x|" the length of vector x.
+ * If the angle is small, an expression in sin A is preferred.
+ * Set r = q - p. Then
+ *
+ * p.q = p.p + p.r ,
+ *
+ * |p|^2 = p.p ,
+ *
+ * |q|^2 = p.p + 2 p.r + r.r ,
+ *
+ * p.p^2 + 2 p.p p.r + p.r^2
+ * cos^2 A = ----------------------------
+ * p.p (p.p + 2 p.r + r.r)
+ *
+ * p.p + 2 p.r + p.r^2 / p.p
+ * = --------------------------- ,
+ * p.p + 2 p.r + r.r
+ *
+ * sin^2 A = 1 - cos^2 A
+ *
+ * r.r - p.r^2 / p.p
+ * = --------------------
+ * p.p + 2 p.r + r.r
+ *
+ * = (r.r - p.r^2 / p.p) / q.q .
+ *
+ * ACCURACY:
+ *
+ * About 1 ULP. See arcdot.c.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.3: November, 1995
+Copyright 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double sqrtl ( long double );
+extern long double acosl ( long double );
+extern long double asinl ( long double );
+extern long double atanl ( long double );
+#else
+long double sqrtl(), acosl(), asinl(), atanl();
+#endif
+extern long double PIL;
+
+long double arcdotl(p,q)
+long double p[], q[];
+{
+long double pp, pr, qq, rr, rt, pt, qt, pq;
+int i;
+
+pq = 0.0L;
+qq = 0.0L;
+pp = 0.0L;
+pr = 0.0L;
+rr = 0.0L;
+for (i=0; i<3; i++)
+ {
+ pt = p[i];
+ qt = q[i];
+ pq += pt * qt;
+ qq += qt * qt;
+ pp += pt * pt;
+ rt = qt - pt;
+ pr += pt * rt;
+ rr += rt * rt;
+ }
+if (rr == 0.0L || pp == 0.0L || qq == 0.0L)
+ return 0.0L;
+rt = (rr - (pr * pr) / pp) / qq;
+if (rt <= 0.75L)
+ {
+ rt = sqrtl(rt);
+ qt = asinl(rt);
+ if (pq < 0.0L)
+ qt = PIL - qt;
+ }
+else
+ {
+ pt = pq / sqrtl(pp*qq);
+ qt = acosl(pt);
+ }
+return qt;
+}
diff --git a/libm/ldouble/asinhl.c b/libm/ldouble/asinhl.c
new file mode 100644
index 000000000..025dfc29d
--- /dev/null
+++ b/libm/ldouble/asinhl.c
@@ -0,0 +1,156 @@
+/* asinhl.c
+ *
+ * Inverse hyperbolic sine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, asinhl();
+ *
+ * y = asinhl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic sine of argument.
+ *
+ * If |x| < 0.5, the function is approximated by a rational
+ * form x + x**3 P(x)/Q(x). Otherwise,
+ *
+ * asinh(x) = log( x + sqrt(1 + x*x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -3,3 30000 1.7e-19 3.5e-20
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright 1984, 1991, 1998 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef UNK
+static long double P[] = {
+-7.2157234864927687427374E-1L,
+-1.3005588097490352458918E1L,
+-5.9112383795679709212744E1L,
+-9.5372702442289028811361E1L,
+-4.9802880260861844539014E1L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0L,*/
+ 2.8754968540389640419671E1L,
+ 2.0990255691901160529390E2L,
+ 5.9265075560893800052658E2L,
+ 7.0670399135805956780660E2L,
+ 2.9881728156517107462943E2L,
+};
+#endif
+
+
+#ifdef IBMPC
+static short P[] = {
+0x8f42,0x2584,0xf727,0xb8b8,0xbffe, XPD
+0x9d56,0x7f7c,0xe38b,0xd016,0xc002, XPD
+0xc518,0xdc2d,0x14bc,0xec73,0xc004, XPD
+0x99fe,0xc18a,0xd2da,0xbebe,0xc005, XPD
+0xb46c,0x3c05,0x263e,0xc736,0xc004, XPD
+};
+static short Q[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0xdfed,0x33db,0x2cf2,0xe60a,0x4003, XPD
+0xf109,0x61ee,0x0df8,0xd1e7,0x4006, XPD
+0xf21e,0xda84,0xa5fa,0x9429,0x4008, XPD
+0x13fc,0xc4e2,0x0e31,0xb0ad,0x4008, XPD
+0x485c,0xad04,0x9cae,0x9568,0x4007, XPD
+};
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0xbffe0000,0xb8b8f727,0x25848f42,
+0xc0020000,0xd016e38b,0x7f7c9d56,
+0xc0040000,0xec7314bc,0xdc2dc518,
+0xc0050000,0xbebed2da,0xc18a99fe,
+0xc0040000,0xc736263e,0x3c05b46c,
+};
+static long Q[] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x40030000,0xe60a2cf2,0x33dbdfed,
+0x40060000,0xd1e70df8,0x61eef109,
+0x40080000,0x9429a5fa,0xda84f21e,
+0x40080000,0xb0ad0e31,0xc4e213fc,
+0x40070000,0x95689cae,0xad04485c,
+};
+#endif
+
+extern long double LOGE2L;
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+#ifdef ANSIPROT
+extern long double logl ( long double );
+extern long double sqrtl ( long double );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern int isnanl ( long double );
+extern int isfinitel ( long double );
+#else
+long double logl(), sqrtl(), polevll(), p1evll(), isnanl(), isfinitel();
+#endif
+
+long double asinhl(x)
+long double x;
+{
+long double a, z;
+int sign;
+
+#ifdef NANS
+if( isnanl(x) )
+ return(x);
+#endif
+#ifdef MINUSZERO
+if( x == 0.0L )
+ return(x);
+#endif
+#ifdef INFINITIES
+ if( !isfinitel(x) )
+ return(x);
+#endif
+if( x < 0.0L )
+ {
+ sign = -1;
+ x = -x;
+ }
+else
+ sign = 1;
+
+if( x > 1.0e10L )
+ {
+ return( sign * (logl(x) + LOGE2L) );
+ }
+
+z = x * x;
+if( x < 0.5L )
+ {
+ a = ( polevll(z, P, 4)/p1evll(z, Q, 5) ) * z;
+ a = a * x + x;
+ if( sign < 0 )
+ a = -a;
+ return(a);
+ }
+
+a = sqrtl( z + 1.0L );
+return( sign * logl(x + a) );
+}
diff --git a/libm/ldouble/asinl.c b/libm/ldouble/asinl.c
new file mode 100644
index 000000000..163f01055
--- /dev/null
+++ b/libm/ldouble/asinl.c
@@ -0,0 +1,249 @@
+/* asinl.c
+ *
+ * Inverse circular sine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, asinl();
+ *
+ * y = asinl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
+ *
+ * A rational function of the form x + x**3 P(x**2)/Q(x**2)
+ * is used for |x| in the interval [0, 0.5]. If |x| > 0.5 it is
+ * transformed by the identity
+ *
+ * asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1, 1 30000 2.7e-19 4.8e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * asinl domain |x| > 1 NANL
+ *
+ */
+ /* acosl()
+ *
+ * Inverse circular cosine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, acosl();
+ *
+ * y = acosl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose cosine
+ * is x.
+ *
+ * Analytically, acos(x) = pi/2 - asin(x). However if |x| is
+ * near 1, there is cancellation error in subtracting asin(x)
+ * from pi/2. Hence if x < -0.5,
+ *
+ * acos(x) = pi - 2.0 * asin( sqrt((1+x)/2) );
+ *
+ * or if x > +0.5,
+ *
+ * acos(x) = 2.0 * asin( sqrt((1-x)/2) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1, 1 30000 1.4e-19 3.5e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * acosl domain |x| > 1 NANL
+ */
+
+/* asin.c */
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright 1984, 1990, 1998 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static long double P[] = {
+ 3.7769340062433674871612E-3L,
+-6.1212919176969202969441E-1L,
+ 5.9303993515791417710775E0L,
+-1.8631697621590161441592E1L,
+ 2.3314603132141795720634E1L,
+-1.0087146579384916260197E1L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0L,*/
+-1.5684335624873146511217E1L,
+ 7.8702951549021104258866E1L,
+-1.7078401170625864261444E2L,
+ 1.6712291455718995937376E2L,
+-6.0522879476309497128868E1L,
+};
+#endif
+
+#ifdef IBMPC
+static short P[] = {
+0x59d1,0x3509,0x7009,0xf786,0x3ff6, XPD
+0xbe97,0x93e6,0x7fab,0x9cb4,0xbffe, XPD
+0x8bf5,0x6810,0xd4dc,0xbdc5,0x4001, XPD
+0x9bd4,0x8d86,0xb77b,0x950d,0xc003, XPD
+0x3b0f,0x9e25,0x4ea5,0xba84,0x4003, XPD
+0xea38,0xc6a9,0xf3cf,0xa164,0xc002, XPD
+};
+static short Q[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0x1229,0x8516,0x09e9,0xfaf3,0xc002, XPD
+0xb5c3,0xf36f,0xe943,0x9d67,0x4005, XPD
+0xe11a,0xbe0f,0xb4fd,0xaac8,0xc006, XPD
+0x4c69,0x1355,0x7754,0xa71f,0x4006, XPD
+0xded7,0xa9fe,0x6db7,0xf217,0xc004, XPD
+};
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0x3ff60000,0xf7867009,0x350959d1,
+0xbffe0000,0x9cb47fab,0x93e6be97,
+0x40010000,0xbdc5d4dc,0x68108bf5,
+0xc0030000,0x950db77b,0x8d869bd4,
+0x40030000,0xba844ea5,0x9e253b0f,
+0xc0020000,0xa164f3cf,0xc6a9ea38,
+};
+static long Q[] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0xc0020000,0xfaf309e9,0x85161229,
+0x40050000,0x9d67e943,0xf36fb5c3,
+0xc0060000,0xaac8b4fd,0xbe0fe11a,
+0x40060000,0xa71f7754,0x13554c69,
+0xc0040000,0xf2176db7,0xa9feded7,
+};
+#endif
+#ifdef NANS
+extern long double NANL;
+#endif
+#ifdef ANSIPROT
+extern long double ldexpl ( long double, int );
+extern long double sqrtl ( long double );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+long double asinl ( long double );
+#else
+long double ldexpl(), sqrtl(), polevll(), p1evll();
+long double asinl();
+#endif
+
+long double asinl(x)
+long double x;
+{
+long double a, p, z, zz;
+short sign, flag;
+extern long double PIO2L;
+
+if( x > 0 )
+ {
+ sign = 1;
+ a = x;
+ }
+else
+ {
+ sign = -1;
+ a = -x;
+ }
+
+if( a > 1.0L )
+ {
+ mtherr( "asinl", DOMAIN );
+#ifdef NANS
+ return( NANL );
+#else
+ return( 0.0L );
+#endif
+ }
+
+if( a < 1.0e-8L )
+ {
+ z = a;
+ goto done;
+ }
+
+if( a > 0.5L )
+ {
+ zz = 0.5L -a;
+ zz = ldexpl( zz + 0.5L, -1 );
+ z = sqrtl( zz );
+ flag = 1;
+ }
+else
+ {
+ z = a;
+ zz = z * z;
+ flag = 0;
+ }
+
+p = zz * polevll( zz, P, 5)/p1evll( zz, Q, 5);
+z = z * p + z;
+if( flag != 0 )
+ {
+ z = z + z;
+ z = PIO2L - z;
+ }
+done:
+if( sign < 0 )
+ z = -z;
+return(z);
+}
+
+
+extern long double PIO2L, PIL;
+
+long double acosl(x)
+long double x;
+{
+
+if( x < -1.0L )
+ goto domerr;
+
+if( x < -0.5L)
+ return( PIL - 2.0L * asinl( sqrtl(0.5L*(1.0L+x)) ) );
+
+if( x > 1.0L )
+ {
+domerr: mtherr( "acosl", DOMAIN );
+#ifdef NANS
+ return( NANL );
+#else
+ return( 0.0L );
+#endif
+ }
+
+if( x > 0.5L )
+ return( 2.0L * asinl( sqrtl(0.5L*(1.0L-x) ) ) );
+
+return( PIO2L - asinl(x) );
+}
diff --git a/libm/ldouble/atanhl.c b/libm/ldouble/atanhl.c
new file mode 100644
index 000000000..3dc7bd2eb
--- /dev/null
+++ b/libm/ldouble/atanhl.c
@@ -0,0 +1,163 @@
+/* atanhl.c
+ *
+ * Inverse hyperbolic tangent, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, atanhl();
+ *
+ * y = atanhl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns inverse hyperbolic tangent of argument in the range
+ * MINLOGL to MAXLOGL.
+ *
+ * If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is
+ * employed. Otherwise,
+ * atanh(x) = 0.5 * log( (1+x)/(1-x) ).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1,1 30000 1.1e-19 3.3e-20
+ *
+ */
+
+
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright (C) 1987, 1991, 1998 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static long double P[] = {
+ 2.9647757819596835680719E-3L,
+-8.0026596513099094380633E-1L,
+ 7.7920941408493040219831E0L,
+-2.4330686602187898836837E1L,
+ 3.0204265014595622991082E1L,
+-1.2961142942114056581210E1L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0L,*/
+-1.3729634163247557081869E1L,
+ 6.2320841104088512332185E1L,
+-1.2469344457045341444078E2L,
+ 1.1394285233959210574352E2L,
+-3.8883428826342169425890E1L,
+};
+#endif
+
+#ifdef IBMPC
+static short P[] = {
+0x3aa2,0x036b,0xaf06,0xc24c,0x3ff6, XPD
+0x528e,0x56e8,0x3af4,0xccde,0xbffe, XPD
+0x9d89,0xc9a1,0xd5cf,0xf958,0x4001, XPD
+0xa653,0x6cfa,0x3f04,0xc2a5,0xc003, XPD
+0xc651,0x2b3d,0x55b2,0xf1a2,0x4003, XPD
+0xd76d,0xf293,0xd76b,0xcf60,0xc002, XPD
+};
+static short Q[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0xd1b9,0x5314,0x94df,0xdbac,0xc002, XPD
+0x3caa,0x0517,0x8a92,0xf948,0x4004, XPD
+0x535e,0xaf5f,0x0b2a,0xf963,0xc005, XPD
+0xa6f9,0xb702,0xbd8a,0xe3e2,0x4005, XPD
+0xe136,0xf5ee,0xa190,0x9b88,0xc004, XPD
+};
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0x3ff60000,0xc24caf06,0x036b3aa2,
+0xbffe0000,0xccde3af4,0x56e8528e,
+0x40010000,0xf958d5cf,0xc9a19d89,
+0xc0030000,0xc2a53f04,0x6cfaa653,
+0x40030000,0xf1a255b2,0x2b3dc651,
+0xc0020000,0xcf60d76b,0xf293d76d,
+};
+static long Q[] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0xc0020000,0xdbac94df,0x5314d1b9,
+0x40040000,0xf9488a92,0x05173caa,
+0xc0050000,0xf9630b2a,0xaf5f535e,
+0x40050000,0xe3e2bd8a,0xb702a6f9,
+0xc0040000,0x9b88a190,0xf5eee136,
+};
+#endif
+
+extern long double MAXNUML;
+#ifdef ANSIPROT
+extern long double fabsl ( long double );
+extern long double logl ( long double );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+#else
+long double fabsl(), logl(), polevll(), p1evll();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+#ifdef NANS
+extern long double NANL;
+#endif
+
+long double atanhl(x)
+long double x;
+{
+long double s, z;
+
+#ifdef MINUSZERO
+if( x == 0.0L )
+ return(x);
+#endif
+z = fabsl(x);
+if( z >= 1.0L )
+ {
+ if( x == 1.0L )
+ {
+#ifdef INFINITIES
+ return( INFINITYL );
+#else
+ return( MAXNUML );
+#endif
+ }
+ if( x == -1.0L )
+ {
+#ifdef INFINITIES
+ return( -INFINITYL );
+#else
+ return( -MAXNUML );
+#endif
+ }
+ mtherr( "atanhl", DOMAIN );
+#ifdef NANS
+ return( NANL );
+#else
+ return( MAXNUML );
+#endif
+ }
+
+if( z < 1.0e-8L )
+ return(x);
+
+if( z < 0.5L )
+ {
+ z = x * x;
+ s = x + x * z * (polevll(z, P, 5) / p1evll(z, Q, 5));
+ return(s);
+ }
+
+return( 0.5L * logl((1.0L+x)/(1.0L-x)) );
+}
diff --git a/libm/ldouble/atanl.c b/libm/ldouble/atanl.c
new file mode 100644
index 000000000..9e6d9af3c
--- /dev/null
+++ b/libm/ldouble/atanl.c
@@ -0,0 +1,376 @@
+/* atanl.c
+ *
+ * Inverse circular tangent, long double precision
+ * (arctangent)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, atanl();
+ *
+ * y = atanl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle between -pi/2 and +pi/2 whose tangent
+ * is x.
+ *
+ * Range reduction is from four intervals into the interval
+ * from zero to tan( pi/8 ). The approximant uses a rational
+ * function of degree 3/4 of the form x + x**3 P(x)/Q(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10, 10 150000 1.3e-19 3.0e-20
+ *
+ */
+ /* atan2l()
+ *
+ * Quadrant correct inverse circular tangent,
+ * long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, z, atan2l();
+ *
+ * z = atan2l( y, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns radian angle whose tangent is y/x.
+ * Define compile time symbol ANSIC = 1 for ANSI standard,
+ * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range
+ * 0 to 2PI, args (x,y).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10, 10 60000 1.7e-19 3.2e-20
+ * See atan.c.
+ *
+ */
+
+/* atan.c */
+
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright 1984, 1990, 1998 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+#ifdef UNK
+static long double P[] = {
+-8.6863818178092187535440E-1L,
+-1.4683508633175792446076E1L,
+-6.3976888655834347413154E1L,
+-9.9988763777265819915721E1L,
+-5.0894116899623603312185E1L,
+};
+static long double Q[] = {
+/* 1.00000000000000000000E0L,*/
+ 2.2981886733594175366172E1L,
+ 1.4399096122250781605352E2L,
+ 3.6144079386152023162701E2L,
+ 3.9157570175111990631099E2L,
+ 1.5268235069887081006606E2L,
+};
+
+/* tan( 3*pi/8 ) */
+static long double T3P8 = 2.41421356237309504880169L;
+
+/* tan( pi/8 ) */
+static long double TP8 = 4.1421356237309504880169e-1L;
+#endif
+
+
+#ifdef IBMPC
+static unsigned short P[] = {
+0x8ece,0xce53,0x1266,0xde5f,0xbffe, XPD
+0x07e6,0xa061,0xa6bf,0xeaef,0xc002, XPD
+0x53ee,0xf291,0x557f,0xffe8,0xc004, XPD
+0xf9d6,0xeda6,0x3f3e,0xc7fa,0xc005, XPD
+0xb6c3,0x6abc,0x9361,0xcb93,0xc004, XPD
+};
+static unsigned short Q[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0x54d4,0x894e,0xe76e,0xb7da,0x4003, XPD
+0x76b9,0x7a46,0xafa2,0x8ffd,0x4006, XPD
+0xe3a9,0xe9c0,0x6bee,0xb4b8,0x4007, XPD
+0xabc1,0x50a7,0xb098,0xc3c9,0x4007, XPD
+0x891c,0x100d,0xae89,0x98ae,0x4006, XPD
+};
+
+/* tan( 3*pi/8 ) = 2.41421356237309504880 */
+static unsigned short T3P8A[] = {0x3242,0xfcef,0x7999,0x9a82,0x4000, XPD};
+#define T3P8 *(long double *)T3P8A
+
+/* tan( pi/8 ) = 0.41421356237309504880 */
+static unsigned short TP8A[] = {0x9211,0xe779,0xcccf,0xd413,0x3ffd, XPD};
+#define TP8 *(long double *)TP8A
+#endif
+
+#ifdef MIEEE
+static unsigned long P[] = {
+0xbffe0000,0xde5f1266,0xce538ece,
+0xc0020000,0xeaefa6bf,0xa06107e6,
+0xc0040000,0xffe8557f,0xf29153ee,
+0xc0050000,0xc7fa3f3e,0xeda6f9d6,
+0xc0040000,0xcb939361,0x6abcb6c3,
+};
+static unsigned long Q[] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x40030000,0xb7dae76e,0x894e54d4,
+0x40060000,0x8ffdafa2,0x7a4676b9,
+0x40070000,0xb4b86bee,0xe9c0e3a9,
+0x40070000,0xc3c9b098,0x50a7abc1,
+0x40060000,0x98aeae89,0x100d891c,
+};
+
+/* tan( 3*pi/8 ) = 2.41421356237309504880 */
+static long T3P8A[] = {0x40000000,0x9a827999,0xfcef3242};
+#define T3P8 *(long double *)T3P8A
+
+/* tan( pi/8 ) = 0.41421356237309504880 */
+static long TP8A[] = {0x3ffd0000,0xd413cccf,0xe7799211};
+#define TP8 *(long double *)TP8A
+#endif
+
+#ifdef ANSIPROT
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern long double fabsl ( long double );
+extern int signbitl ( long double );
+extern int isnanl ( long double );
+long double atanl ( long double );
+#else
+long double polevll(), p1evll(), fabsl(), signbitl(), isnanl();
+long double atanl();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+#ifdef NANS
+extern long double NANL;
+#endif
+#ifdef MINUSZERO
+extern long double NEGZEROL;
+#endif
+
+long double atanl(x)
+long double x;
+{
+extern long double PIO2L, PIO4L;
+long double y, z;
+short sign;
+
+#ifdef MINUSZERO
+if( x == 0.0L )
+ return(x);
+#endif
+#ifdef INFINITIES
+if( x == INFINITYL )
+ return( PIO2L );
+if( x == -INFINITYL )
+ return( -PIO2L );
+#endif
+/* make argument positive and save the sign */
+sign = 1;
+if( x < 0.0L )
+ {
+ sign = -1;
+ x = -x;
+ }
+
+/* range reduction */
+if( x > T3P8 )
+ {
+ y = PIO2L;
+ x = -( 1.0L/x );
+ }
+
+else if( x > TP8 )
+ {
+ y = PIO4L;
+ x = (x-1.0L)/(x+1.0L);
+ }
+else
+ y = 0.0L;
+
+/* rational form in x**2 */
+z = x * x;
+y = y + ( polevll( z, P, 4 ) / p1evll( z, Q, 5 ) ) * z * x + x;
+
+if( sign < 0 )
+ y = -y;
+
+return(y);
+}
+
+/* atan2 */
+
+
+extern long double PIL, PIO2L, MAXNUML;
+
+#if ANSIC
+long double atan2l( y, x )
+#else
+long double atan2l( x, y )
+#endif
+long double x, y;
+{
+long double z, w;
+short code;
+
+code = 0;
+
+if( x < 0.0L )
+ code = 2;
+if( y < 0.0L )
+ code |= 1;
+
+#ifdef NANS
+if( isnanl(x) )
+ return(x);
+if( isnanl(y) )
+ return(y);
+#endif
+#ifdef MINUSZERO
+if( y == 0.0L )
+ {
+ if( signbitl(y) )
+ {
+ if( x > 0.0L )
+ z = y;
+ else if( x < 0.0L )
+ z = -PIL;
+ else
+ {
+ if( signbitl(x) )
+ z = -PIL;
+ else
+ z = y;
+ }
+ }
+ else /* y is +0 */
+ {
+ if( x == 0.0L )
+ {
+ if( signbitl(x) )
+ z = PIL;
+ else
+ z = 0.0L;
+ }
+ else if( x > 0.0L )
+ z = 0.0L;
+ else
+ z = PIL;
+ }
+ return z;
+ }
+if( x == 0.0L )
+ {
+ if( y > 0.0L )
+ z = PIO2L;
+ else
+ z = -PIO2L;
+ return z;
+ }
+#endif /* MINUSZERO */
+#ifdef INFINITIES
+if( x == INFINITYL )
+ {
+ if( y == INFINITYL )
+ z = 0.25L * PIL;
+ else if( y == -INFINITYL )
+ z = -0.25L * PIL;
+ else if( y < 0.0L )
+ z = NEGZEROL;
+ else
+ z = 0.0L;
+ return z;
+ }
+if( x == -INFINITYL )
+ {
+ if( y == INFINITYL )
+ z = 0.75L * PIL;
+ else if( y == -INFINITYL )
+ z = -0.75L * PIL;
+ else if( y >= 0.0L )
+ z = PIL;
+ else
+ z = -PIL;
+ return z;
+ }
+if( y == INFINITYL )
+ return( PIO2L );
+if( y == -INFINITYL )
+ return( -PIO2L );
+#endif /* INFINITIES */
+
+#ifdef INFINITIES
+if( x == 0.0L )
+#else
+if( fabsl(x) <= (fabsl(y) / MAXNUML) )
+#endif
+ {
+ if( code & 1 )
+ {
+#if ANSIC
+ return( -PIO2L );
+#else
+ return( 3.0L*PIO2L );
+#endif
+ }
+ if( y == 0.0L )
+ return( 0.0L );
+ return( PIO2L );
+ }
+
+if( y == 0.0L )
+ {
+ if( code & 2 )
+ return( PIL );
+ return( 0.0L );
+ }
+
+
+switch( code )
+ {
+ default:
+#if ANSIC
+ case 0:
+ case 1: w = 0.0L; break;
+ case 2: w = PIL; break;
+ case 3: w = -PIL; break;
+#else
+ case 0: w = 0.0L; break;
+ case 1: w = 2.0L * PIL; break;
+ case 2:
+ case 3: w = PIL; break;
+#endif
+ }
+
+z = w + atanl( y/x );
+#ifdef MINUSZERO
+if( z == 0.0L && y < 0.0L )
+ z = NEGZEROL;
+#endif
+return( z );
+}
diff --git a/libm/ldouble/bdtrl.c b/libm/ldouble/bdtrl.c
new file mode 100644
index 000000000..aca9577d1
--- /dev/null
+++ b/libm/ldouble/bdtrl.c
@@ -0,0 +1,260 @@
+/* bdtrl.c
+ *
+ * Binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, bdtrl();
+ *
+ * y = bdtrl( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the Binomial
+ * probability density:
+ *
+ * k
+ * -- ( n ) j n-j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtr( k, n, p ) = incbet( n-k, k+1, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (k,n,p) with a and b between 0
+ * and 10000 and p between 0 and 1.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,10000 3000 1.6e-14 2.2e-15
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtrl domain k < 0 0.0
+ * n < k
+ * x < 0, x > 1
+ *
+ */
+ /* bdtrcl()
+ *
+ * Complemented binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, bdtrcl();
+ *
+ * y = bdtrcl( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 through n of the Binomial
+ * probability density:
+ *
+ * n
+ * -- ( n ) j n-j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = bdtrc( k, n, p ) = incbet( k+1, n-k, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See incbet.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtrcl domain x<0, x>1, n<k 0.0
+ */
+ /* bdtril()
+ *
+ * Inverse binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, bdtril();
+ *
+ * p = bdtril( k, n, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the event probability p such that the sum of the
+ * terms 0 through k of the Binomial probability density
+ * is equal to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relation
+ *
+ * 1 - p = incbi( n-k, k+1, y ).
+ *
+ * ACCURACY:
+ *
+ * See incbi.c.
+ * Tested at random k, n between 1 and 10000. The "domain" refers to p:
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,1 3500 2.0e-15 8.2e-17
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * bdtril domain k < 0, n <= k 0.0
+ * x < 0, x > 1
+ */
+
+/* bdtr() */
+
+
+/*
+Cephes Math Library Release 2.3: March, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double incbetl ( long double, long double, long double );
+extern long double incbil ( long double, long double, long double );
+extern long double powl ( long double, long double );
+extern long double expm1l ( long double );
+extern long double log1pl ( long double );
+#else
+long double incbetl(), incbil(), powl(), expm1l(), log1pl();
+#endif
+
+long double bdtrcl( k, n, p )
+int k, n;
+long double p;
+{
+long double dk, dn;
+
+if( (p < 0.0L) || (p > 1.0L) )
+ goto domerr;
+if( k < 0 )
+ return( 1.0L );
+
+if( n < k )
+ {
+domerr:
+ mtherr( "bdtrcl", DOMAIN );
+ return( 0.0L );
+ }
+
+if( k == n )
+ return( 0.0L );
+dn = n - k;
+if( k == 0 )
+ {
+ if( p < .01L )
+ dk = -expm1l( dn * log1pl(-p) );
+ else
+ dk = 1.0L - powl( 1.0L-p, dn );
+ }
+else
+ {
+ dk = k + 1;
+ dk = incbetl( dk, dn, p );
+ }
+return( dk );
+}
+
+
+
+long double bdtrl( k, n, p )
+int k, n;
+long double p;
+{
+long double dk, dn, q;
+
+if( (p < 0.0L) || (p > 1.0L) )
+ goto domerr;
+if( (k < 0) || (n < k) )
+ {
+domerr:
+ mtherr( "bdtrl", DOMAIN );
+ return( 0.0L );
+ }
+
+if( k == n )
+ return( 1.0L );
+
+q = 1.0L - p;
+dn = n - k;
+if( k == 0 )
+ {
+ dk = powl( q, dn );
+ }
+else
+ {
+ dk = k + 1;
+ dk = incbetl( dn, dk, q );
+ }
+return( dk );
+}
+
+
+long double bdtril( k, n, y )
+int k, n;
+long double y;
+{
+long double dk, dn, p;
+
+if( (y < 0.0L) || (y > 1.0L) )
+ goto domerr;
+if( (k < 0) || (n <= k) )
+ {
+domerr:
+ mtherr( "bdtril", DOMAIN );
+ return( 0.0L );
+ }
+
+dn = n - k;
+if( k == 0 )
+ {
+ if( y > 0.8L )
+ p = -expm1l( log1pl(y-1.0L) / dn );
+ else
+ p = 1.0L - powl( y, 1.0L/dn );
+ }
+else
+ {
+ dk = k + 1;
+ p = incbetl( dn, dk, y );
+ if( p > 0.5 )
+ p = incbil( dk, dn, 1.0L-y );
+ else
+ p = 1.0 - incbil( dn, dk, y );
+ }
+return( p );
+}
diff --git a/libm/ldouble/btdtrl.c b/libm/ldouble/btdtrl.c
new file mode 100644
index 000000000..cbc4515da
--- /dev/null
+++ b/libm/ldouble/btdtrl.c
@@ -0,0 +1,68 @@
+
+/* btdtrl.c
+ *
+ * Beta distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, b, x, y, btdtrl();
+ *
+ * y = btdtrl( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the beta density
+ * function:
+ *
+ *
+ * x
+ * - -
+ * | (a+b) | | a-1 b-1
+ * P(x) = ---------- | t (1-t) dt
+ * - - | |
+ * | (a) | (b) -
+ * 0
+ *
+ *
+ * The mean value of this distribution is a/(a+b). The variance
+ * is ab/[(a+b)^2 (a+b+1)].
+ *
+ * This function is identical to the incomplete beta integral
+ * function, incbetl(a, b, x).
+ *
+ * The complemented function is
+ *
+ * 1 - P(1-x) = incbetl( b, a, x );
+ *
+ *
+ * ACCURACY:
+ *
+ * See incbetl.c.
+ *
+ */
+
+/* btdtrl() */
+
+
+/*
+Cephes Math Library Release 2.0: April, 1987
+Copyright 1984, 1995 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+#include <math.h>
+#ifdef ANSIPROT
+extern long double incbetl ( long double, long double, long double );
+#else
+long double incbetl();
+#endif
+
+long double btdtrl( a, b, x )
+long double a, b, x;
+{
+
+return( incbetl( a, b, x ) );
+}
diff --git a/libm/ldouble/cbrtl.c b/libm/ldouble/cbrtl.c
new file mode 100644
index 000000000..89ed11a06
--- /dev/null
+++ b/libm/ldouble/cbrtl.c
@@ -0,0 +1,143 @@
+/* cbrtl.c
+ *
+ * Cube root, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, cbrtl();
+ *
+ * y = cbrtl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the cube root of the argument, which may be negative.
+ *
+ * Range reduction involves determining the power of 2 of
+ * the argument. A polynomial of degree 2 applied to the
+ * mantissa, and multiplication by the cube root of 1, 2, or 4
+ * approximates the root to within about 0.1%. Then Newton's
+ * iteration is used three times to converge to an accurate
+ * result.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE .125,8 80000 7.0e-20 2.2e-20
+ * IEEE exp(+-707) 100000 7.0e-20 2.4e-20
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.2: January, 1991
+Copyright 1984, 1991 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+static long double CBRT2 = 1.2599210498948731647672L;
+static long double CBRT4 = 1.5874010519681994747517L;
+static long double CBRT2I = 0.79370052598409973737585L;
+static long double CBRT4I = 0.62996052494743658238361L;
+
+#ifdef ANSIPROT
+extern long double frexpl ( long double, int * );
+extern long double ldexpl ( long double, int );
+extern int isnanl ( long double );
+#else
+long double frexpl(), ldexpl();
+extern int isnanl();
+#endif
+
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+
+long double cbrtl(x)
+long double x;
+{
+int e, rem, sign;
+long double z;
+
+
+#ifdef NANS
+if(isnanl(x))
+ return(x);
+#endif
+#ifdef INFINITIES
+if( x == INFINITYL)
+ return(x);
+if( x == -INFINITYL)
+ return(x);
+#endif
+if( x == 0 )
+ return( x );
+if( x > 0 )
+ sign = 1;
+else
+ {
+ sign = -1;
+ x = -x;
+ }
+
+z = x;
+/* extract power of 2, leaving
+ * mantissa between 0.5 and 1
+ */
+x = frexpl( x, &e );
+
+/* Approximate cube root of number between .5 and 1,
+ * peak relative error = 1.2e-6
+ */
+x = (((( 1.3584464340920900529734e-1L * x
+ - 6.3986917220457538402318e-1L) * x
+ + 1.2875551670318751538055e0L) * x
+ - 1.4897083391357284957891e0L) * x
+ + 1.3304961236013647092521e0L) * x
+ + 3.7568280825958912391243e-1L;
+
+/* exponent divided by 3 */
+if( e >= 0 )
+ {
+ rem = e;
+ e /= 3;
+ rem -= 3*e;
+ if( rem == 1 )
+ x *= CBRT2;
+ else if( rem == 2 )
+ x *= CBRT4;
+ }
+else
+ { /* argument less than 1 */
+ e = -e;
+ rem = e;
+ e /= 3;
+ rem -= 3*e;
+ if( rem == 1 )
+ x *= CBRT2I;
+ else if( rem == 2 )
+ x *= CBRT4I;
+ e = -e;
+ }
+
+/* multiply by power of 2 */
+x = ldexpl( x, e );
+
+/* Newton iteration */
+
+x -= ( x - (z/(x*x)) )*0.3333333333333333333333L;
+x -= ( x - (z/(x*x)) )*0.3333333333333333333333L;
+
+if( sign < 0 )
+ x = -x;
+return(x);
+}
diff --git a/libm/ldouble/chdtrl.c b/libm/ldouble/chdtrl.c
new file mode 100644
index 000000000..e55361e1f
--- /dev/null
+++ b/libm/ldouble/chdtrl.c
@@ -0,0 +1,200 @@
+/* chdtrl.c
+ *
+ * Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double df, x, y, chdtrl();
+ *
+ * y = chdtrl( df, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the left hand tail (from 0 to x)
+ * of the Chi square probability density function with
+ * v degrees of freedom.
+ *
+ *
+ * inf.
+ * -
+ * 1 | | v/2-1 -t/2
+ * P( x | v ) = ----------- | t e dt
+ * v/2 - | |
+ * 2 | (v/2) -
+ * x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ * y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtr domain x < 0 or v < 1 0.0
+ */
+ /* chdtrcl()
+ *
+ * Complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double v, x, y, chdtrcl();
+ *
+ * y = chdtrcl( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the right hand tail (from x to
+ * infinity) of the Chi square probability density function
+ * with v degrees of freedom:
+ *
+ *
+ * inf.
+ * -
+ * 1 | | v/2-1 -t/2
+ * P( x | v ) = ----------- | t e dt
+ * v/2 - | |
+ * 2 | (v/2) -
+ * x
+ *
+ * where x is the Chi-square variable.
+ *
+ * The incomplete gamma integral is used, according to the
+ * formula
+ *
+ * y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).
+ *
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtrc domain x < 0 or v < 1 0.0
+ */
+ /* chdtril()
+ *
+ * Inverse of complemented Chi-square distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double df, x, y, chdtril();
+ *
+ * x = chdtril( df, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Chi-square argument x such that the integral
+ * from x to infinity of the Chi-square density is equal
+ * to the given cumulative probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ * x/2 = igami( df/2, y );
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igami.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * chdtri domain y < 0 or y > 1 0.0
+ * v < 1
+ *
+ */
+
+/* chdtr() */
+
+
+/*
+Cephes Math Library Release 2.3: March, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double igamcl ( long double, long double );
+extern long double igaml ( long double, long double );
+extern long double igamil ( long double, long double );
+#else
+long double igamcl(), igaml(), igamil();
+#endif
+
+long double chdtrcl(df,x)
+long double df, x;
+{
+
+if( (x < 0.0L) || (df < 1.0L) )
+ {
+ mtherr( "chdtrcl", DOMAIN );
+ return(0.0L);
+ }
+return( igamcl( 0.5L*df, 0.5L*x ) );
+}
+
+
+
+long double chdtrl(df,x)
+long double df, x;
+{
+
+if( (x < 0.0L) || (df < 1.0L) )
+ {
+ mtherr( "chdtrl", DOMAIN );
+ return(0.0L);
+ }
+return( igaml( 0.5L*df, 0.5L*x ) );
+}
+
+
+
+long double chdtril( df, y )
+long double df, y;
+{
+long double x;
+
+if( (y < 0.0L) || (y > 1.0L) || (df < 1.0L) )
+ {
+ mtherr( "chdtril", DOMAIN );
+ return(0.0L);
+ }
+
+x = igamil( 0.5L * df, y );
+return( 2.0L * x );
+}
diff --git a/libm/ldouble/clogl.c b/libm/ldouble/clogl.c
new file mode 100644
index 000000000..b3e6b25fb
--- /dev/null
+++ b/libm/ldouble/clogl.c
@@ -0,0 +1,720 @@
+/* clogl.c
+ *
+ * Complex natural logarithm
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void clogl();
+ * cmplxl z, w;
+ *
+ * clogl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns complex logarithm to the base e (2.718...) of
+ * the complex argument x.
+ *
+ * If z = x + iy, r = sqrt( x**2 + y**2 ),
+ * then
+ * w = log(r) + i arctan(y/x).
+ *
+ * The arctangent ranges from -PI to +PI.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 7000 8.5e-17 1.9e-17
+ * IEEE -10,+10 30000 5.0e-15 1.1e-16
+ *
+ * Larger relative error can be observed for z near 1 +i0.
+ * In IEEE arithmetic the peak absolute error is 5.2e-16, rms
+ * absolute error 1.0e-16.
+ */
+
+#include <math.h>
+#ifdef ANSIPROT
+static void cchshl ( long double x, long double *c, long double *s );
+static long double redupil ( long double x );
+static long double ctansl ( cmplxl *z );
+long double cabsl ( cmplxl *x );
+void csqrtl ( cmplxl *x, cmplxl *y );
+void caddl ( cmplxl *x, cmplxl *y, cmplxl *z );
+extern long double fabsl ( long double );
+extern long double sqrtl ( long double );
+extern long double logl ( long double );
+extern long double expl ( long double );
+extern long double atan2l ( long double, long double );
+extern long double coshl ( long double );
+extern long double sinhl ( long double );
+extern long double asinl ( long double );
+extern long double sinl ( long double );
+extern long double cosl ( long double );
+void clogl ( cmplxl *, cmplxl *);
+void casinl ( cmplxl *, cmplxl *);
+#else
+static void cchshl();
+static long double redupil();
+static long double ctansl();
+long double cabsl(), fabsl(), sqrtl();
+lnog double logl(), expl(), atan2l(), coshl(), sinhl();
+long double asinl(), sinl(), cosl();
+void caddl(), csqrtl(), clogl(), casinl();
+#endif
+
+extern long double MAXNUML, MACHEPL, PIL, PIO2L;
+
+void clogl( z, w )
+register cmplxl *z, *w;
+{
+long double p, rr;
+
+/*rr = sqrt( z->r * z->r + z->i * z->i );*/
+rr = cabsl(z);
+p = logl(rr);
+#if ANSIC
+rr = atan2l( z->i, z->r );
+#else
+rr = atan2l( z->r, z->i );
+if( rr > PIL )
+ rr -= PIL + PIL;
+#endif
+w->i = rr;
+w->r = p;
+}
+ /* cexpl()
+ *
+ * Complex exponential function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cexpl();
+ * cmplxl z, w;
+ *
+ * cexpl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the exponential of the complex argument z
+ * into the complex result w.
+ *
+ * If
+ * z = x + iy,
+ * r = exp(x),
+ *
+ * then
+ *
+ * w = r cos y + i r sin y.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 8700 3.7e-17 1.1e-17
+ * IEEE -10,+10 30000 3.0e-16 8.7e-17
+ *
+ */
+
+void cexpl( z, w )
+register cmplxl *z, *w;
+{
+long double r;
+
+r = expl( z->r );
+w->r = r * cosl( z->i );
+w->i = r * sinl( z->i );
+}
+ /* csinl()
+ *
+ * Complex circular sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csinl();
+ * cmplxl z, w;
+ *
+ * csinl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * w = sin x cosh y + i cos x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 8400 5.3e-17 1.3e-17
+ * IEEE -10,+10 30000 3.8e-16 1.0e-16
+ * Also tested by csin(casin(z)) = z.
+ *
+ */
+
+void csinl( z, w )
+register cmplxl *z, *w;
+{
+long double ch, sh;
+
+cchshl( z->i, &ch, &sh );
+w->r = sinl( z->r ) * ch;
+w->i = cosl( z->r ) * sh;
+}
+
+
+
+/* calculate cosh and sinh */
+
+static void cchshl( x, c, s )
+long double x, *c, *s;
+{
+long double e, ei;
+
+if( fabsl(x) <= 0.5L )
+ {
+ *c = coshl(x);
+ *s = sinhl(x);
+ }
+else
+ {
+ e = expl(x);
+ ei = 0.5L/e;
+ e = 0.5L * e;
+ *s = e - ei;
+ *c = e + ei;
+ }
+}
+
+ /* ccosl()
+ *
+ * Complex circular cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccosl();
+ * cmplxl z, w;
+ *
+ * ccosl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * w = cos x cosh y - i sin x sinh y.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 8400 4.5e-17 1.3e-17
+ * IEEE -10,+10 30000 3.8e-16 1.0e-16
+ */
+
+void ccosl( z, w )
+register cmplxl *z, *w;
+{
+long double ch, sh;
+
+cchshl( z->i, &ch, &sh );
+w->r = cosl( z->r ) * ch;
+w->i = -sinl( z->r ) * sh;
+}
+ /* ctanl()
+ *
+ * Complex circular tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ctanl();
+ * cmplxl z, w;
+ *
+ * ctanl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * sin 2x + i sinh 2y
+ * w = --------------------.
+ * cos 2x + cosh 2y
+ *
+ * On the real axis the denominator is zero at odd multiples
+ * of PI/2. The denominator is evaluated by its Taylor
+ * series near these points.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 5200 7.1e-17 1.6e-17
+ * IEEE -10,+10 30000 7.2e-16 1.2e-16
+ * Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
+ */
+
+void ctanl( z, w )
+register cmplxl *z, *w;
+{
+long double d;
+
+d = cosl( 2.0L * z->r ) + coshl( 2.0L * z->i );
+
+if( fabsl(d) < 0.25L )
+ d = ctansl(z);
+
+if( d == 0.0L )
+ {
+ mtherr( "ctan", OVERFLOW );
+ w->r = MAXNUML;
+ w->i = MAXNUML;
+ return;
+ }
+
+w->r = sinl( 2.0L * z->r ) / d;
+w->i = sinhl( 2.0L * z->i ) / d;
+}
+ /* ccotl()
+ *
+ * Complex circular cotangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void ccotl();
+ * cmplxl z, w;
+ *
+ * ccotl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ *
+ * sin 2x - i sinh 2y
+ * w = --------------------.
+ * cosh 2y - cos 2x
+ *
+ * On the real axis, the denominator has zeros at even
+ * multiples of PI/2. Near these points it is evaluated
+ * by a Taylor series.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 3000 6.5e-17 1.6e-17
+ * IEEE -10,+10 30000 9.2e-16 1.2e-16
+ * Also tested by ctan * ccot = 1 + i0.
+ */
+
+void ccotl( z, w )
+register cmplxl *z, *w;
+{
+long double d;
+
+d = coshl(2.0L * z->i) - cosl(2.0L * z->r);
+
+if( fabsl(d) < 0.25L )
+ d = ctansl(z);
+
+if( d == 0.0L )
+ {
+ mtherr( "ccot", OVERFLOW );
+ w->r = MAXNUML;
+ w->i = MAXNUML;
+ return;
+ }
+
+w->r = sinl( 2.0L * z->r ) / d;
+w->i = -sinhl( 2.0L * z->i ) / d;
+}
+
+/* Program to subtract nearest integer multiple of PI */
+/* extended precision value of PI: */
+#ifdef UNK
+static double DP1 = 3.14159265160560607910E0;
+static double DP2 = 1.98418714791870343106E-9;
+static double DP3 = 1.14423774522196636802E-17;
+#endif
+
+#ifdef DEC
+static unsigned short P1[] = {0040511,0007732,0120000,0000000,};
+static unsigned short P2[] = {0031010,0055060,0100000,0000000,};
+static unsigned short P3[] = {0022123,0011431,0105056,0001560,};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+#ifdef IBMPC
+static unsigned short P1[] = {0x0000,0x5400,0x21fb,0x4009};
+static unsigned short P2[] = {0x0000,0x1000,0x0b46,0x3e21};
+static unsigned short P3[] = {0xc06e,0x3145,0x6263,0x3c6a};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+#ifdef MIEEE
+static unsigned short P1[] = {
+0x4009,0x21fb,0x5400,0x0000
+};
+static unsigned short P2[] = {
+0x3e21,0x0b46,0x1000,0x0000
+};
+static unsigned short P3[] = {
+0x3c6a,0x6263,0x3145,0xc06e
+};
+#define DP1 *(double *)P1
+#define DP2 *(double *)P2
+#define DP3 *(double *)P3
+#endif
+
+static long double redupil(x)
+long double x;
+{
+long double t;
+long i;
+
+t = x/PIL;
+if( t >= 0.0L )
+ t += 0.5L;
+else
+ t -= 0.5L;
+
+i = t; /* the multiple */
+t = i;
+t = ((x - t * DP1) - t * DP2) - t * DP3;
+return(t);
+}
+
+/* Taylor series expansion for cosh(2y) - cos(2x) */
+
+static long double ctansl(z)
+cmplxl *z;
+{
+long double f, x, x2, y, y2, rn, t;
+long double d;
+
+x = fabsl( 2.0L * z->r );
+y = fabsl( 2.0L * z->i );
+
+x = redupil(x);
+
+x = x * x;
+y = y * y;
+x2 = 1.0L;
+y2 = 1.0L;
+f = 1.0L;
+rn = 0.0;
+d = 0.0;
+do
+ {
+ rn += 1.0L;
+ f *= rn;
+ rn += 1.0L;
+ f *= rn;
+ x2 *= x;
+ y2 *= y;
+ t = y2 + x2;
+ t /= f;
+ d += t;
+
+ rn += 1.0L;
+ f *= rn;
+ rn += 1.0L;
+ f *= rn;
+ x2 *= x;
+ y2 *= y;
+ t = y2 - x2;
+ t /= f;
+ d += t;
+ }
+while( fabsl(t/d) > MACHEPL );
+return(d);
+}
+ /* casinl()
+ *
+ * Complex circular arc sine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void casinl();
+ * cmplxl z, w;
+ *
+ * casinl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Inverse complex sine:
+ *
+ * 2
+ * w = -i clog( iz + csqrt( 1 - z ) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 10100 2.1e-15 3.4e-16
+ * IEEE -10,+10 30000 2.2e-14 2.7e-15
+ * Larger relative error can be observed for z near zero.
+ * Also tested by csin(casin(z)) = z.
+ */
+
+void casinl( z, w )
+cmplxl *z, *w;
+{
+static cmplxl ca, ct, zz, z2;
+long double x, y;
+
+x = z->r;
+y = z->i;
+
+if( y == 0.0L )
+ {
+ if( fabsl(x) > 1.0L )
+ {
+ w->r = PIO2L;
+ w->i = 0.0L;
+ mtherr( "casinl", DOMAIN );
+ }
+ else
+ {
+ w->r = asinl(x);
+ w->i = 0.0L;
+ }
+ return;
+ }
+
+/* Power series expansion */
+/*
+b = cabsl(z);
+if( b < 0.125L )
+{
+z2.r = (x - y) * (x + y);
+z2.i = 2.0L * x * y;
+
+cn = 1.0L;
+n = 1.0L;
+ca.r = x;
+ca.i = y;
+sum.r = x;
+sum.i = y;
+do
+ {
+ ct.r = z2.r * ca.r - z2.i * ca.i;
+ ct.i = z2.r * ca.i + z2.i * ca.r;
+ ca.r = ct.r;
+ ca.i = ct.i;
+
+ cn *= n;
+ n += 1.0L;
+ cn /= n;
+ n += 1.0L;
+ b = cn/n;
+
+ ct.r *= b;
+ ct.i *= b;
+ sum.r += ct.r;
+ sum.i += ct.i;
+ b = fabsl(ct.r) + fabs(ct.i);
+ }
+while( b > MACHEPL );
+w->r = sum.r;
+w->i = sum.i;
+return;
+}
+*/
+
+
+ca.r = x;
+ca.i = y;
+
+ct.r = -ca.i; /* iz */
+ct.i = ca.r;
+
+ /* sqrt( 1 - z*z) */
+/* cmul( &ca, &ca, &zz ) */
+zz.r = (ca.r - ca.i) * (ca.r + ca.i); /*x * x - y * y */
+zz.i = 2.0L * ca.r * ca.i;
+
+zz.r = 1.0L - zz.r;
+zz.i = -zz.i;
+csqrtl( &zz, &z2 );
+
+caddl( &z2, &ct, &zz );
+clogl( &zz, &zz );
+w->r = zz.i; /* mult by 1/i = -i */
+w->i = -zz.r;
+return;
+}
+ /* cacosl()
+ *
+ * Complex circular arc cosine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void cacosl();
+ * cmplxl z, w;
+ *
+ * cacosl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * w = arccos z = PI/2 - arcsin z.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 5200 1.6e-15 2.8e-16
+ * IEEE -10,+10 30000 1.8e-14 2.2e-15
+ */
+
+void cacosl( z, w )
+cmplxl *z, *w;
+{
+
+casinl( z, w );
+w->r = PIO2L - w->r;
+w->i = -w->i;
+}
+ /* catanl()
+ *
+ * Complex circular arc tangent
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void catanl();
+ * cmplxl z, w;
+ *
+ * catanl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * If
+ * z = x + iy,
+ *
+ * then
+ * 1 ( 2x )
+ * Re w = - arctan(-----------) + k PI
+ * 2 ( 2 2)
+ * (1 - x - y )
+ *
+ * ( 2 2)
+ * 1 (x + (y+1) )
+ * Im w = - log(------------)
+ * 4 ( 2 2)
+ * (x + (y-1) )
+ *
+ * Where k is an arbitrary integer.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 5900 1.3e-16 7.8e-18
+ * IEEE -10,+10 30000 2.3e-15 8.5e-17
+ * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
+ * had peak relative error 1.5e-16, rms relative error
+ * 2.9e-17. See also clog().
+ */
+
+void catanl( z, w )
+cmplxl *z, *w;
+{
+long double a, t, x, x2, y;
+
+x = z->r;
+y = z->i;
+
+if( (x == 0.0L) && (y > 1.0L) )
+ goto ovrf;
+
+x2 = x * x;
+a = 1.0L - x2 - (y * y);
+if( a == 0.0L )
+ goto ovrf;
+
+#if ANSIC
+t = atan2l( 2.0L * x, a ) * 0.5L;
+#else
+t = atan2l( a, 2.0 * x ) * 0.5L;
+#endif
+w->r = redupil( t );
+
+t = y - 1.0L;
+a = x2 + (t * t);
+if( a == 0.0L )
+ goto ovrf;
+
+t = y + 1.0L;
+a = (x2 + (t * t))/a;
+w->i = logl(a)/4.0;
+return;
+
+ovrf:
+mtherr( "catanl", OVERFLOW );
+w->r = MAXNUML;
+w->i = MAXNUML;
+}
diff --git a/libm/ldouble/cmplxl.c b/libm/ldouble/cmplxl.c
new file mode 100644
index 000000000..ef130618d
--- /dev/null
+++ b/libm/ldouble/cmplxl.c
@@ -0,0 +1,461 @@
+/* cmplxl.c
+ *
+ * Complex number arithmetic
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * typedef struct {
+ * long double r; real part
+ * long double i; imaginary part
+ * }cmplxl;
+ *
+ * cmplxl *a, *b, *c;
+ *
+ * caddl( a, b, c ); c = b + a
+ * csubl( a, b, c ); c = b - a
+ * cmull( a, b, c ); c = b * a
+ * cdivl( a, b, c ); c = b / a
+ * cnegl( c ); c = -c
+ * cmovl( b, c ); c = b
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Addition:
+ * c.r = b.r + a.r
+ * c.i = b.i + a.i
+ *
+ * Subtraction:
+ * c.r = b.r - a.r
+ * c.i = b.i - a.i
+ *
+ * Multiplication:
+ * c.r = b.r * a.r - b.i * a.i
+ * c.i = b.r * a.i + b.i * a.r
+ *
+ * Division:
+ * d = a.r * a.r + a.i * a.i
+ * c.r = (b.r * a.r + b.i * a.i)/d
+ * c.i = (b.i * a.r - b.r * a.i)/d
+ * ACCURACY:
+ *
+ * In DEC arithmetic, the test (1/z) * z = 1 had peak relative
+ * error 3.1e-17, rms 1.2e-17. The test (y/z) * (z/y) = 1 had
+ * peak relative error 8.3e-17, rms 2.1e-17.
+ *
+ * Tests in the rectangle {-10,+10}:
+ * Relative error:
+ * arithmetic function # trials peak rms
+ * DEC cadd 10000 1.4e-17 3.4e-18
+ * IEEE cadd 100000 1.1e-16 2.7e-17
+ * DEC csub 10000 1.4e-17 4.5e-18
+ * IEEE csub 100000 1.1e-16 3.4e-17
+ * DEC cmul 3000 2.3e-17 8.7e-18
+ * IEEE cmul 100000 2.1e-16 6.9e-17
+ * DEC cdiv 18000 4.9e-17 1.3e-17
+ * IEEE cdiv 100000 3.7e-16 1.1e-16
+ */
+ /* cmplx.c
+ * complex number arithmetic
+ */
+
+
+/*
+Cephes Math Library Release 2.3: March, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+/*
+typedef struct
+ {
+ long double r;
+ long double i;
+ }cmplxl;
+*/
+
+#ifdef ANSIPROT
+extern long double fabsl ( long double );
+extern long double cabsl ( cmplxl * );
+extern long double sqrtl ( long double );
+extern long double atan2l ( long double, long double );
+extern long double cosl ( long double );
+extern long double sinl ( long double );
+extern long double frexpl ( long double, int * );
+extern long double ldexpl ( long double, int );
+extern int isnanl ( long double );
+void cdivl ( cmplxl *, cmplxl *, cmplxl * );
+void caddl ( cmplxl *, cmplxl *, cmplxl * );
+#else
+long double fabsl(), cabsl(), sqrtl(), atan2l(), cosl(), sinl();
+long double frexpl(), ldexpl();
+int isnanl();
+void cdivl(), caddl();
+#endif
+
+
+extern double MAXNUML, MACHEPL, PIL, PIO2L, INFINITYL, NANL;
+cmplx czerol = {0.0L, 0.0L};
+cmplx conel = {1.0L, 0.0L};
+
+
+/* c = b + a */
+
+void caddl( a, b, c )
+register cmplxl *a, *b;
+cmplxl *c;
+{
+
+c->r = b->r + a->r;
+c->i = b->i + a->i;
+}
+
+
+/* c = b - a */
+
+void csubl( a, b, c )
+register cmplxl *a, *b;
+cmplxl *c;
+{
+
+c->r = b->r - a->r;
+c->i = b->i - a->i;
+}
+
+/* c = b * a */
+
+void cmull( a, b, c )
+register cmplxl *a, *b;
+cmplxl *c;
+{
+long double y;
+
+y = b->r * a->r - b->i * a->i;
+c->i = b->r * a->i + b->i * a->r;
+c->r = y;
+}
+
+
+
+/* c = b / a */
+
+void cdivl( a, b, c )
+register cmplxl *a, *b;
+cmplxl *c;
+{
+long double y, p, q, w;
+
+
+y = a->r * a->r + a->i * a->i;
+p = b->r * a->r + b->i * a->i;
+q = b->i * a->r - b->r * a->i;
+
+if( y < 1.0L )
+ {
+ w = MAXNUML * y;
+ if( (fabsl(p) > w) || (fabsl(q) > w) || (y == 0.0L) )
+ {
+ c->r = INFINITYL;
+ c->i = INFINITYL;
+ mtherr( "cdivl", OVERFLOW );
+ return;
+ }
+ }
+c->r = p/y;
+c->i = q/y;
+}
+
+
+/* b = a
+ Caution, a `short' is assumed to be 16 bits wide. */
+
+void cmovl( a, b )
+void *a, *b;
+{
+register short *pa, *pb;
+int i;
+
+pa = (short *) a;
+pb = (short *) b;
+i = 16;
+do
+ *pb++ = *pa++;
+while( --i );
+}
+
+
+void cnegl( a )
+register cmplxl *a;
+{
+
+a->r = -a->r;
+a->i = -a->i;
+}
+
+/* cabsl()
+ *
+ * Complex absolute value
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double cabsl();
+ * cmplxl z;
+ * long double a;
+ *
+ * a = cabs( &z );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy
+ *
+ * then
+ *
+ * a = sqrt( x**2 + y**2 ).
+ *
+ * Overflow and underflow are avoided by testing the magnitudes
+ * of x and y before squaring. If either is outside half of
+ * the floating point full scale range, both are rescaled.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -30,+30 30000 3.2e-17 9.2e-18
+ * IEEE -10,+10 100000 2.7e-16 6.9e-17
+ */
+
+
+/*
+Cephes Math Library Release 2.1: January, 1989
+Copyright 1984, 1987, 1989 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+/*
+typedef struct
+ {
+ long double r;
+ long double i;
+ }cmplxl;
+*/
+
+#ifdef UNK
+#define PRECL 32
+#define MAXEXPL 16384
+#define MINEXPL -16384
+#endif
+#ifdef IBMPC
+#define PRECL 32
+#define MAXEXPL 16384
+#define MINEXPL -16384
+#endif
+#ifdef MIEEE
+#define PRECL 32
+#define MAXEXPL 16384
+#define MINEXPL -16384
+#endif
+
+
+long double cabsl( z )
+register cmplxl *z;
+{
+long double x, y, b, re, im;
+int ex, ey, e;
+
+#ifdef INFINITIES
+/* Note, cabs(INFINITY,NAN) = INFINITY. */
+if( z->r == INFINITYL || z->i == INFINITYL
+ || z->r == -INFINITYL || z->i == -INFINITYL )
+ return( INFINITYL );
+#endif
+
+#ifdef NANS
+if( isnanl(z->r) )
+ return(z->r);
+if( isnanl(z->i) )
+ return(z->i);
+#endif
+
+re = fabsl( z->r );
+im = fabsl( z->i );
+
+if( re == 0.0 )
+ return( im );
+if( im == 0.0 )
+ return( re );
+
+/* Get the exponents of the numbers */
+x = frexpl( re, &ex );
+y = frexpl( im, &ey );
+
+/* Check if one number is tiny compared to the other */
+e = ex - ey;
+if( e > PRECL )
+ return( re );
+if( e < -PRECL )
+ return( im );
+
+/* Find approximate exponent e of the geometric mean. */
+e = (ex + ey) >> 1;
+
+/* Rescale so mean is about 1 */
+x = ldexpl( re, -e );
+y = ldexpl( im, -e );
+
+/* Hypotenuse of the right triangle */
+b = sqrtl( x * x + y * y );
+
+/* Compute the exponent of the answer. */
+y = frexpl( b, &ey );
+ey = e + ey;
+
+/* Check it for overflow and underflow. */
+if( ey > MAXEXPL )
+ {
+ mtherr( "cabsl", OVERFLOW );
+ return( INFINITYL );
+ }
+if( ey < MINEXPL )
+ return(0.0L);
+
+/* Undo the scaling */
+b = ldexpl( b, e );
+return( b );
+}
+ /* csqrtl()
+ *
+ * Complex square root
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * void csqrtl();
+ * cmplxl z, w;
+ *
+ * csqrtl( &z, &w );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * If z = x + iy, r = |z|, then
+ *
+ * 1/2
+ * Im w = [ (r - x)/2 ] ,
+ *
+ * Re w = y / 2 Im w.
+ *
+ *
+ * Note that -w is also a square root of z. The root chosen
+ * is always in the upper half plane.
+ *
+ * Because of the potential for cancellation error in r - x,
+ * the result is sharpened by doing a Heron iteration
+ * (see sqrt.c) in complex arithmetic.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC -10,+10 25000 3.2e-17 9.6e-18
+ * IEEE -10,+10 100000 3.2e-16 7.7e-17
+ *
+ * 2
+ * Also tested by csqrt( z ) = z, and tested by arguments
+ * close to the real axis.
+ */
+
+
+void csqrtl( z, w )
+cmplxl *z, *w;
+{
+cmplxl q, s;
+long double x, y, r, t;
+
+x = z->r;
+y = z->i;
+
+if( y == 0.0L )
+ {
+ if( x < 0.0L )
+ {
+ w->r = 0.0L;
+ w->i = sqrtl(-x);
+ return;
+ }
+ else
+ {
+ w->r = sqrtl(x);
+ w->i = 0.0L;
+ return;
+ }
+ }
+
+
+if( x == 0.0L )
+ {
+ r = fabsl(y);
+ r = sqrtl(0.5L*r);
+ if( y > 0.0L )
+ w->r = r;
+ else
+ w->r = -r;
+ w->i = r;
+ return;
+ }
+
+/* Approximate sqrt(x^2+y^2) - x = y^2/2x - y^4/24x^3 + ... .
+ * The relative error in the first term is approximately y^2/12x^2 .
+ */
+if( (fabsl(y) < 2.e-4L * fabsl(x))
+ && (x > 0) )
+ {
+ t = 0.25L*y*(y/x);
+ }
+else
+ {
+ r = cabsl(z);
+ t = 0.5L*(r - x);
+ }
+
+r = sqrtl(t);
+q.i = r;
+q.r = y/(2.0L*r);
+/* Heron iteration in complex arithmetic */
+cdivl( &q, z, &s );
+caddl( &q, &s, w );
+w->r *= 0.5L;
+w->i *= 0.5L;
+
+cdivl( &q, z, &s );
+caddl( &q, &s, w );
+w->r *= 0.5L;
+w->i *= 0.5L;
+}
+
+
+long double hypotl( x, y )
+long double x, y;
+{
+cmplxl z;
+
+z.r = x;
+z.i = y;
+return( cabsl(&z) );
+}
diff --git a/libm/ldouble/coshl.c b/libm/ldouble/coshl.c
new file mode 100644
index 000000000..46212ae44
--- /dev/null
+++ b/libm/ldouble/coshl.c
@@ -0,0 +1,89 @@
+/* coshl.c
+ *
+ * Hyperbolic cosine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, coshl();
+ *
+ * y = coshl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic cosine of argument in the range MINLOGL to
+ * MAXLOGL.
+ *
+ * cosh(x) = ( exp(x) + exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-10000 30000 1.1e-19 2.8e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * cosh overflow |x| > MAXLOGL+LOGE2L INFINITYL
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright 1985, 1991, 1998 by Stephen L. Moshier
+*/
+
+#include <math.h>
+extern long double MAXLOGL, MAXNUML, LOGE2L;
+#ifdef ANSIPROT
+extern long double expl ( long double );
+extern int isnanl ( long double );
+#else
+long double expl(), isnanl();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+#ifdef NANS
+extern long double NANL;
+#endif
+
+long double coshl(x)
+long double x;
+{
+long double y;
+
+#ifdef NANS
+if( isnanl(x) )
+ return(x);
+#endif
+if( x < 0 )
+ x = -x;
+if( x > (MAXLOGL + LOGE2L) )
+ {
+ mtherr( "coshl", OVERFLOW );
+#ifdef INFINITIES
+ return( INFINITYL );
+#else
+ return( MAXNUML );
+#endif
+ }
+if( x >= (MAXLOGL - LOGE2L) )
+ {
+ y = expl(0.5L * x);
+ y = (0.5L * y) * y;
+ return(y);
+ }
+y = expl(x);
+y = 0.5L * (y + 1.0L / y);
+return( y );
+}
diff --git a/libm/ldouble/econst.c b/libm/ldouble/econst.c
new file mode 100644
index 000000000..cfddbe3e2
--- /dev/null
+++ b/libm/ldouble/econst.c
@@ -0,0 +1,96 @@
+/* econst.c */
+/* e type constants used by high precision check routines */
+
+#include "ehead.h"
+
+
+#if NE == 10
+/* 0.0 */
+unsigned short ezero[NE] =
+ {0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,};
+
+/* 5.0E-1 */
+unsigned short ehalf[NE] =
+ {0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3ffe,};
+
+/* 1.0E0 */
+unsigned short eone[NE] =
+ {0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff,};
+
+/* 2.0E0 */
+unsigned short etwo[NE] =
+ {0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4000,};
+
+/* 3.2E1 */
+unsigned short e32[NE] =
+ {0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4004,};
+
+/* 6.93147180559945309417232121458176568075500134360255E-1 */
+unsigned short elog2[NE] =
+ {0x40f3, 0xf6af, 0x03f2, 0xb398,
+ 0xc9e3, 0x79ab, 0150717, 0013767, 0130562, 0x3ffe,};
+
+/* 1.41421356237309504880168872420969807856967187537695E0 */
+unsigned short esqrt2[NE] =
+ {0x1d6f, 0xbe9f, 0x754a, 0x89b3,
+ 0x597d, 0x6484, 0174736, 0171463, 0132404, 0x3fff,};
+
+/* 3.14159265358979323846264338327950288419716939937511E0 */
+unsigned short epi[NE] =
+ {0x2902, 0x1cd1, 0x80dc, 0x628b,
+ 0xc4c6, 0xc234, 0020550, 0155242, 0144417, 0040000,};
+
+/* 5.7721566490153286060651209008240243104215933593992E-1 */
+unsigned short eeul[NE] = {
+0xd1be,0xc7a4,0076660,0063743,0111704,0x3ffe,};
+
+#else
+
+/* 0.0 */
+unsigned short ezero[NE] = {
+0, 0000000,0000000,0000000,0000000,0000000,};
+/* 5.0E-1 */
+unsigned short ehalf[NE] = {
+0, 0000000,0000000,0000000,0100000,0x3ffe,};
+/* 1.0E0 */
+unsigned short eone[NE] = {
+0, 0000000,0000000,0000000,0100000,0x3fff,};
+/* 2.0E0 */
+unsigned short etwo[NE] = {
+0, 0000000,0000000,0000000,0100000,0040000,};
+/* 3.2E1 */
+unsigned short e32[NE] = {
+0, 0000000,0000000,0000000,0100000,0040004,};
+/* 6.93147180559945309417232121458176568075500134360255E-1 */
+unsigned short elog2[NE] = {
+0xc9e4,0x79ab,0150717,0013767,0130562,0x3ffe,};
+/* 1.41421356237309504880168872420969807856967187537695E0 */
+unsigned short esqrt2[NE] = {
+0x597e,0x6484,0174736,0171463,0132404,0x3fff,};
+/* 2/sqrt(PI) =
+ * 1.12837916709551257389615890312154517168810125865800E0 */
+unsigned short eoneopi[NE] = {
+0x71d5,0x688d,0012333,0135202,0110156,0x3fff,};
+/* 3.14159265358979323846264338327950288419716939937511E0 */
+unsigned short epi[NE] = {
+0xc4c6,0xc234,0020550,0155242,0144417,0040000,};
+/* 5.7721566490153286060651209008240243104215933593992E-1 */
+unsigned short eeul[NE] = {
+0xd1be,0xc7a4,0076660,0063743,0111704,0x3ffe,};
+#endif
+extern unsigned short ezero[];
+extern unsigned short ehalf[];
+extern unsigned short eone[];
+extern unsigned short etwo[];
+extern unsigned short e32[];
+extern unsigned short elog2[];
+extern unsigned short esqrt2[];
+extern unsigned short eoneopi[];
+extern unsigned short epi[];
+extern unsigned short eeul[];
+
diff --git a/libm/ldouble/ehead.h b/libm/ldouble/ehead.h
new file mode 100644
index 000000000..785396dce
--- /dev/null
+++ b/libm/ldouble/ehead.h
@@ -0,0 +1,45 @@
+
+/* Include file for extended precision arithmetic programs.
+ */
+
+/* Number of 16 bit words in external x type format */
+#define NE 6
+/* #define NE 10 */
+
+/* Number of 16 bit words in internal format */
+#define NI (NE+3)
+
+/* Array offset to exponent */
+#define E 1
+
+/* Array offset to high guard word */
+#define M 2
+
+/* Number of bits of precision */
+#define NBITS ((NI-4)*16)
+
+/* Maximum number of decimal digits in ASCII conversion
+ * = NBITS*log10(2)
+ */
+#define NDEC (NBITS*8/27)
+
+/* The exponent of 1.0 */
+#define EXONE (0x3fff)
+
+
+void eadd(), esub(), emul(), ediv();
+int ecmp(), enormlz(), eshift();
+void eshup1(), eshup8(), eshup6(), eshdn1(), eshdn8(), eshdn6();
+void eabs(), eneg(), emov(), eclear(), einfin(), efloor();
+void eldexp(), efrexp(), eifrac(), ltoe();
+void esqrt(), elog(), eexp(), etanh(), epow();
+void asctoe(), asctoe24(), asctoe53(), asctoe64();
+void etoasc(), e24toasc(), e53toasc(), e64toasc();
+void etoe64(), etoe53(), etoe24(), e64toe(), e53toe(), e24toe();
+int mtherr();
+
+extern unsigned short ezero[], ehalf[], eone[], etwo[];
+extern unsigned short elog2[], esqrt2[];
+
+
+/* by Stephen L. Moshier. */
diff --git a/libm/ldouble/elliel.c b/libm/ldouble/elliel.c
new file mode 100644
index 000000000..851914454
--- /dev/null
+++ b/libm/ldouble/elliel.c
@@ -0,0 +1,146 @@
+/* elliel.c
+ *
+ * Incomplete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double phi, m, y, elliel();
+ *
+ * y = elliel( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ * phi
+ * -
+ * | |
+ * | 2
+ * E(phi_\m) = | sqrt( 1 - m sin t ) dt
+ * |
+ * | |
+ * -
+ * 0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random arguments with phi in [-10, 10] and m in
+ * [0, 1].
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,10 50000 2.7e-18 2.3e-19
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.3: November, 1995
+Copyright 1984, 1987, 1993, 1995 by Stephen L. Moshier
+*/
+
+/* Incomplete elliptic integral of second kind */
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double sqrtl ( long double );
+extern long double fabsl ( long double );
+extern long double logl ( long double );
+extern long double sinl ( long double );
+extern long double tanl ( long double );
+extern long double atanl ( long double );
+extern long double floorl ( long double );
+extern long double ellpel ( long double );
+extern long double ellpkl ( long double );
+long double elliel ( long double, long double );
+#else
+long double sqrtl(), fabsl(), logl(), sinl(), tanl(), atanl(), floorl();
+long double ellpel(), ellpkl(), elliel();
+#endif
+extern long double PIL, PIO2L, MACHEPL;
+
+
+long double elliel( phi, m )
+long double phi, m;
+{
+long double a, b, c, e, temp, lphi, t, E;
+int d, mod, npio2, sign;
+
+if( m == 0.0L )
+ return( phi );
+lphi = phi;
+npio2 = floorl( lphi/PIO2L );
+if( npio2 & 1 )
+ npio2 += 1;
+lphi = lphi - npio2 * PIO2L;
+if( lphi < 0.0L )
+ {
+ lphi = -lphi;
+ sign = -1;
+ }
+else
+ {
+ sign = 1;
+ }
+a = 1.0L - m;
+E = ellpel( a );
+if( a == 0.0L )
+ {
+ temp = sinl( lphi );
+ goto done;
+ }
+t = tanl( lphi );
+b = sqrtl(a);
+if( fabsl(t) > 10.0L )
+ {
+ /* Transform the amplitude */
+ e = 1.0L/(b*t);
+ /* ... but avoid multiple recursions. */
+ if( fabsl(e) < 10.0L )
+ {
+ e = atanl(e);
+ temp = E + m * sinl( lphi ) * sinl( e ) - elliel( e, m );
+ goto done;
+ }
+ }
+c = sqrtl(m);
+a = 1.0L;
+d = 1;
+e = 0.0L;
+mod = 0;
+
+while( fabsl(c/a) > MACHEPL )
+ {
+ temp = b/a;
+ lphi = lphi + atanl(t*temp) + mod * PIL;
+ mod = (lphi + PIO2L)/PIL;
+ t = t * ( 1.0L + temp )/( 1.0L - temp * t * t );
+ c = 0.5L*( a - b );
+ temp = sqrtl( a * b );
+ a = 0.5L*( a + b );
+ b = temp;
+ d += d;
+ e += c * sinl(lphi);
+ }
+
+temp = E / ellpkl( 1.0L - m );
+temp *= (atanl(t) + mod * PIL)/(d * a);
+temp += e;
+
+done:
+
+if( sign < 0 )
+ temp = -temp;
+temp += npio2 * E;
+return( temp );
+}
diff --git a/libm/ldouble/ellikl.c b/libm/ldouble/ellikl.c
new file mode 100644
index 000000000..4eeffe0f5
--- /dev/null
+++ b/libm/ldouble/ellikl.c
@@ -0,0 +1,148 @@
+/* ellikl.c
+ *
+ * Incomplete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double phi, m, y, ellikl();
+ *
+ * y = ellikl( phi, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ * phi
+ * -
+ * | |
+ * | dt
+ * F(phi_\m) = | ------------------
+ * | 2
+ * | | sqrt( 1 - m sin t )
+ * -
+ * 0
+ *
+ * of amplitude phi and modulus m, using the arithmetic -
+ * geometric mean algorithm.
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with m in [0, 1] and phi as indicated.
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -10,10 30000 3.6e-18 4.1e-19
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.3: November, 1995
+Copyright 1984, 1987, 1995 by Stephen L. Moshier
+*/
+
+/* Incomplete elliptic integral of first kind */
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double sqrtl ( long double );
+extern long double fabsl ( long double );
+extern long double logl ( long double );
+extern long double tanl ( long double );
+extern long double atanl ( long double );
+extern long double floorl ( long double );
+extern long double ellpkl ( long double );
+long double ellikl ( long double, long double );
+#else
+long double sqrtl(), fabsl(), logl(), tanl(), atanl(), floorl(), ellpkl();
+long double ellikl();
+#endif
+extern long double PIL, PIO2L, MACHEPL, MAXNUML;
+
+long double ellikl( phi, m )
+long double phi, m;
+{
+long double a, b, c, e, temp, t, K;
+int d, mod, sign, npio2;
+
+if( m == 0.0L )
+ return( phi );
+a = 1.0L - m;
+if( a == 0.0L )
+ {
+ if( fabsl(phi) >= PIO2L )
+ {
+ mtherr( "ellikl", SING );
+ return( MAXNUML );
+ }
+ return( logl( tanl( 0.5L*(PIO2L + phi) ) ) );
+ }
+npio2 = floorl( phi/PIO2L );
+if( npio2 & 1 )
+ npio2 += 1;
+if( npio2 )
+ {
+ K = ellpkl( a );
+ phi = phi - npio2 * PIO2L;
+ }
+else
+ K = 0.0L;
+if( phi < 0.0L )
+ {
+ phi = -phi;
+ sign = -1;
+ }
+else
+ sign = 0;
+b = sqrtl(a);
+t = tanl( phi );
+if( fabsl(t) > 10.0L )
+ {
+ /* Transform the amplitude */
+ e = 1.0L/(b*t);
+ /* ... but avoid multiple recursions. */
+ if( fabsl(e) < 10.0L )
+ {
+ e = atanl(e);
+ if( npio2 == 0 )
+ K = ellpkl( a );
+ temp = K - ellikl( e, m );
+ goto done;
+ }
+ }
+a = 1.0L;
+c = sqrtl(m);
+d = 1;
+mod = 0;
+
+while( fabsl(c/a) > MACHEPL )
+ {
+ temp = b/a;
+ phi = phi + atanl(t*temp) + mod * PIL;
+ mod = (phi + PIO2L)/PIL;
+ t = t * ( 1.0L + temp )/( 1.0L - temp * t * t );
+ c = 0.5L * ( a - b );
+ temp = sqrtl( a * b );
+ a = 0.5L * ( a + b );
+ b = temp;
+ d += d;
+ }
+
+temp = (atanl(t) + mod * PIL)/(d * a);
+
+done:
+if( sign < 0 )
+ temp = -temp;
+temp += npio2 * K;
+return( temp );
+}
diff --git a/libm/ldouble/ellpel.c b/libm/ldouble/ellpel.c
new file mode 100644
index 000000000..6965db066
--- /dev/null
+++ b/libm/ldouble/ellpel.c
@@ -0,0 +1,173 @@
+/* ellpel.c
+ *
+ * Complete elliptic integral of the second kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double m1, y, ellpel();
+ *
+ * y = ellpel( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ * pi/2
+ * -
+ * | | 2
+ * E(m) = | sqrt( 1 - m sin t ) dt
+ * | |
+ * -
+ * 0
+ *
+ * Where m = 1 - m1, using the approximation
+ *
+ * P(x) - x log x Q(x).
+ *
+ * Though there are no singularities, the argument m1 is used
+ * rather than m for compatibility with ellpk().
+ *
+ * E(1) = 1; E(0) = pi/2.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 1 10000 1.1e-19 3.5e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ellpel domain x<0, x>1 0.0
+ *
+ */
+
+/* ellpe.c */
+
+/* Elliptic integral of second kind */
+
+/*
+Cephes Math Library, Release 2.3: October, 1995
+Copyright 1984, 1987, 1989, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#if UNK
+static long double P[12] = {
+ 3.198937812032341294902E-5L,
+ 7.742523238588775116241E-4L,
+ 4.140384701571542000550E-3L,
+ 7.963509564694454269086E-3L,
+ 7.280911706839967541799E-3L,
+ 5.044067167184043853799E-3L,
+ 5.076832243257395296304E-3L,
+ 7.155775630578315248130E-3L,
+ 1.154485760526450950611E-2L,
+ 2.183137319801117971860E-2L,
+ 5.680519271556930583433E-2L,
+ 4.431471805599467050354E-1L,
+};
+static long double Q[12] = {
+ 6.393938134301205485085E-6L,
+ 2.741404591220851603273E-4L,
+ 2.480876752984331133799E-3L,
+ 8.770638497964078750003E-3L,
+ 1.676835725889463343319E-2L,
+ 2.281970801531577700830E-2L,
+ 2.767367465121309044166E-2L,
+ 3.364167778770018154356E-2L,
+ 4.272453406734691973083E-2L,
+ 5.859374951483909267451E-2L,
+ 9.374999999923942267270E-2L,
+ 2.499999999999998643587E-1L,
+};
+#endif
+#if IBMPC
+static short P[] = {
+0x7a78,0x5a02,0x554d,0x862c,0x3ff0, XPD
+0x34db,0xa965,0x31a3,0xcaf7,0x3ff4, XPD
+0xca6c,0x6c00,0x1071,0x87ac,0x3ff7, XPD
+0x4cdb,0x125d,0x6149,0x8279,0x3ff8, XPD
+0xadbd,0x3d8f,0xb6d5,0xee94,0x3ff7, XPD
+0x8189,0xcd0e,0xb3c2,0xa548,0x3ff7, XPD
+0x32b5,0xdd64,0x8e39,0xa65b,0x3ff7, XPD
+0x0344,0xc9db,0xff27,0xea7a,0x3ff7, XPD
+0xba2d,0x806a,0xa476,0xbd26,0x3ff8, XPD
+0xc3e0,0x30fa,0xb53d,0xb2d7,0x3ff9, XPD
+0x23b8,0x4d33,0x8fcf,0xe8ac,0x3ffa, XPD
+0xbc79,0xa39f,0x2fef,0xe2e4,0x3ffd, XPD
+};
+static short Q[] = {
+0x89f1,0xe234,0x82a6,0xd68b,0x3fed, XPD
+0x202a,0x96b3,0x8273,0x8fba,0x3ff3, XPD
+0xc183,0xfc45,0x3484,0xa296,0x3ff6, XPD
+0x683e,0xe201,0xb960,0x8fb2,0x3ff8, XPD
+0x721a,0x1b6a,0xcb41,0x895d,0x3ff9, XPD
+0x4eee,0x295f,0x6574,0xbaf0,0x3ff9, XPD
+0x3ade,0xc98f,0xe6f2,0xe2b3,0x3ff9, XPD
+0xd470,0x1784,0xdb1e,0x89cb,0x3ffa, XPD
+0xa649,0xe5c1,0xebc8,0xaeff,0x3ffa, XPD
+0x84c0,0xa8f5,0xffde,0xefff,0x3ffa, XPD
+0x5506,0xf94f,0xffff,0xbfff,0x3ffb, XPD
+0xd8e7,0xffff,0xffff,0xffff,0x3ffc, XPD
+};
+#endif
+#if MIEEE
+static long P[36] = {
+0x3ff00000,0x862c554d,0x5a027a78,
+0x3ff40000,0xcaf731a3,0xa96534db,
+0x3ff70000,0x87ac1071,0x6c00ca6c,
+0x3ff80000,0x82796149,0x125d4cdb,
+0x3ff70000,0xee94b6d5,0x3d8fadbd,
+0x3ff70000,0xa548b3c2,0xcd0e8189,
+0x3ff70000,0xa65b8e39,0xdd6432b5,
+0x3ff70000,0xea7aff27,0xc9db0344,
+0x3ff80000,0xbd26a476,0x806aba2d,
+0x3ff90000,0xb2d7b53d,0x30fac3e0,
+0x3ffa0000,0xe8ac8fcf,0x4d3323b8,
+0x3ffd0000,0xe2e42fef,0xa39fbc79,
+};
+static long Q[36] = {
+0x3fed0000,0xd68b82a6,0xe23489f1,
+0x3ff30000,0x8fba8273,0x96b3202a,
+0x3ff60000,0xa2963484,0xfc45c183,
+0x3ff80000,0x8fb2b960,0xe201683e,
+0x3ff90000,0x895dcb41,0x1b6a721a,
+0x3ff90000,0xbaf06574,0x295f4eee,
+0x3ff90000,0xe2b3e6f2,0xc98f3ade,
+0x3ffa0000,0x89cbdb1e,0x1784d470,
+0x3ffa0000,0xaeffebc8,0xe5c1a649,
+0x3ffa0000,0xefffffde,0xa8f584c0,
+0x3ffb0000,0xbfffffff,0xf94f5506,
+0x3ffc0000,0xffffffff,0xffffd8e7,
+};
+#endif
+
+#ifdef ANSIPROT
+extern long double polevll ( long double, void *, int );
+extern long double logl ( long double );
+#else
+long double polevll(), logl();
+#endif
+
+long double ellpel(x)
+long double x;
+{
+
+if( (x <= 0.0L) || (x > 1.0L) )
+ {
+ if( x == 0.0L )
+ return( 1.0L );
+ mtherr( "ellpel", DOMAIN );
+ return( 0.0L );
+ }
+return( 1.0L + x * polevll(x,P,11) - logl(x) * (x * polevll(x,Q,11)) );
+}
diff --git a/libm/ldouble/ellpjl.c b/libm/ldouble/ellpjl.c
new file mode 100644
index 000000000..bb57fe6a1
--- /dev/null
+++ b/libm/ldouble/ellpjl.c
@@ -0,0 +1,164 @@
+/* ellpjl.c
+ *
+ * Jacobian Elliptic Functions
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double u, m, sn, cn, dn, phi;
+ * int ellpjl();
+ *
+ * ellpjl( u, m, _&sn, _&cn, _&dn, _&phi );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * Evaluates the Jacobian elliptic functions sn(u|m), cn(u|m),
+ * and dn(u|m) of parameter m between 0 and 1, and real
+ * argument u.
+ *
+ * These functions are periodic, with quarter-period on the
+ * real axis equal to the complete elliptic integral
+ * ellpk(1.0-m).
+ *
+ * Relation to incomplete elliptic integral:
+ * If u = ellik(phi,m), then sn(u|m) = sin(phi),
+ * and cn(u|m) = cos(phi). Phi is called the amplitude of u.
+ *
+ * Computation is by means of the arithmetic-geometric mean
+ * algorithm, except when m is within 1e-12 of 0 or 1. In the
+ * latter case with m close to 1, the approximation applies
+ * only for phi < pi/2.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points with u between 0 and 10, m between
+ * 0 and 1.
+ *
+ * Absolute error (* = relative error):
+ * arithmetic function # trials peak rms
+ * IEEE sn 10000 1.7e-18 2.3e-19
+ * IEEE cn 20000 1.6e-18 2.2e-19
+ * IEEE dn 10000 4.7e-15 2.7e-17
+ * IEEE phi 10000 4.0e-19* 6.6e-20*
+ *
+ * Accuracy deteriorates when u is large.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.3: November, 1995
+Copyright 1984, 1987, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double sqrtl ( long double );
+extern long double fabsl ( long double );
+extern long double sinl ( long double );
+extern long double cosl ( long double );
+extern long double asinl ( long double );
+extern long double tanhl ( long double );
+extern long double sinhl ( long double );
+extern long double coshl ( long double );
+extern long double atanl ( long double );
+extern long double expl ( long double );
+#else
+long double sqrtl(), fabsl(), sinl(), cosl(), asinl(), tanhl();
+long double sinhl(), coshl(), atanl(), expl();
+#endif
+extern long double PIO2L, MACHEPL;
+
+int ellpjl( u, m, sn, cn, dn, ph )
+long double u, m;
+long double *sn, *cn, *dn, *ph;
+{
+long double ai, b, phi, t, twon;
+long double a[9], c[9];
+int i;
+
+
+/* Check for special cases */
+
+if( m < 0.0L || m > 1.0L )
+ {
+ mtherr( "ellpjl", DOMAIN );
+ *sn = 0.0L;
+ *cn = 0.0L;
+ *ph = 0.0L;
+ *dn = 0.0L;
+ return(-1);
+ }
+if( m < 1.0e-12L )
+ {
+ t = sinl(u);
+ b = cosl(u);
+ ai = 0.25L * m * (u - t*b);
+ *sn = t - ai*b;
+ *cn = b + ai*t;
+ *ph = u - ai;
+ *dn = 1.0L - 0.5L*m*t*t;
+ return(0);
+ }
+
+if( m >= 0.999999999999L )
+ {
+ ai = 0.25L * (1.0L-m);
+ b = coshl(u);
+ t = tanhl(u);
+ phi = 1.0L/b;
+ twon = b * sinhl(u);
+ *sn = t + ai * (twon - u)/(b*b);
+ *ph = 2.0L*atanl(expl(u)) - PIO2L + ai*(twon - u)/b;
+ ai *= t * phi;
+ *cn = phi - ai * (twon - u);
+ *dn = phi + ai * (twon + u);
+ return(0);
+ }
+
+
+/* A. G. M. scale */
+a[0] = 1.0L;
+b = sqrtl(1.0L - m);
+c[0] = sqrtl(m);
+twon = 1.0L;
+i = 0;
+
+while( fabsl(c[i]/a[i]) > MACHEPL )
+ {
+ if( i > 7 )
+ {
+ mtherr( "ellpjl", OVERFLOW );
+ goto done;
+ }
+ ai = a[i];
+ ++i;
+ c[i] = 0.5L * ( ai - b );
+ t = sqrtl( ai * b );
+ a[i] = 0.5L * ( ai + b );
+ b = t;
+ twon *= 2.0L;
+ }
+
+done:
+
+/* backward recurrence */
+phi = twon * a[i] * u;
+do
+ {
+ t = c[i] * sinl(phi) / a[i];
+ b = phi;
+ phi = 0.5L * (asinl(t) + phi);
+ }
+while( --i );
+
+*sn = sinl(phi);
+t = cosl(phi);
+*cn = t;
+*dn = t/cosl(phi-b);
+*ph = phi;
+return(0);
+}
diff --git a/libm/ldouble/ellpkl.c b/libm/ldouble/ellpkl.c
new file mode 100644
index 000000000..dd42ac861
--- /dev/null
+++ b/libm/ldouble/ellpkl.c
@@ -0,0 +1,203 @@
+/* ellpkl.c
+ *
+ * Complete elliptic integral of the first kind
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double m1, y, ellpkl();
+ *
+ * y = ellpkl( m1 );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Approximates the integral
+ *
+ *
+ *
+ * pi/2
+ * -
+ * | |
+ * | dt
+ * K(m) = | ------------------
+ * | 2
+ * | | sqrt( 1 - m sin t )
+ * -
+ * 0
+ *
+ * where m = 1 - m1, using the approximation
+ *
+ * P(x) - log x Q(x).
+ *
+ * The argument m1 is used rather than m so that the logarithmic
+ * singularity at m = 1 will be shifted to the origin; this
+ * preserves maximum accuracy.
+ *
+ * K(0) = pi/2.
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,1 10000 1.1e-19 3.3e-20
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ellpkl domain x<0, x>1 0.0
+ *
+ */
+
+/* ellpkl.c */
+
+
+/*
+Cephes Math Library, Release 2.3: October, 1995
+Copyright 1984, 1987, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#if UNK
+static long double P[13] = {
+ 1.247539729154838838628E-6L,
+ 2.149421654232011240659E-4L,
+ 2.265267575136470585139E-3L,
+ 6.723088676584254248821E-3L,
+ 8.092066790639263075808E-3L,
+ 5.664069509748147028621E-3L,
+ 4.579865994050801042865E-3L,
+ 5.797368411662027645234E-3L,
+ 8.767698209432225911803E-3L,
+ 1.493761594388688915057E-2L,
+ 3.088514457872042326871E-2L,
+ 9.657359027999314232753E-2L,
+ 1.386294361119890618992E0L,
+};
+static long double Q[12] = {
+ 5.568631677757315398993E-5L,
+ 1.036110372590318802997E-3L,
+ 5.500459122138244213579E-3L,
+ 1.337330436245904844528E-2L,
+ 2.033103735656990487115E-2L,
+ 2.522868345512332304268E-2L,
+ 3.026786461242788135379E-2L,
+ 3.738370118296930305919E-2L,
+ 4.882812208418620146046E-2L,
+ 7.031249999330222751046E-2L,
+ 1.249999999999978263154E-1L,
+ 4.999999999999999999924E-1L,
+};
+static long double C1 = 1.386294361119890618834L; /* log(4) */
+#endif
+#if IBMPC
+static short P[] = {
+0xf098,0xad01,0x2381,0xa771,0x3feb, XPD
+0xd6ed,0xea22,0x1922,0xe162,0x3ff2, XPD
+0x3733,0xe2f1,0xe226,0x9474,0x3ff6, XPD
+0x3031,0x3c9d,0x5aff,0xdc4d,0x3ff7, XPD
+0x9a46,0x4310,0x968e,0x8494,0x3ff8, XPD
+0xbe4c,0x3ff2,0xa8a7,0xb999,0x3ff7, XPD
+0xf35c,0x0eaf,0xb355,0x9612,0x3ff7, XPD
+0xbc56,0x8fd4,0xd9dd,0xbdf7,0x3ff7, XPD
+0xc01e,0x867f,0x6444,0x8fa6,0x3ff8, XPD
+0x4ba3,0x6392,0xe6fd,0xf4bc,0x3ff8, XPD
+0x62c3,0xbb12,0xd7bc,0xfd02,0x3ff9, XPD
+0x08fe,0x476c,0x5fdf,0xc5c8,0x3ffb, XPD
+0x79ad,0xd1cf,0x17f7,0xb172,0x3fff, XPD
+};
+static short Q[] = {
+0x96a4,0x8474,0xba33,0xe990,0x3ff0, XPD
+0xe5a7,0xa50e,0x1854,0x87ce,0x3ff5, XPD
+0x8999,0x72e3,0x3205,0xb43d,0x3ff7, XPD
+0x3255,0x13eb,0xb438,0xdb1b,0x3ff8, XPD
+0xb717,0x497f,0x4691,0xa68d,0x3ff9, XPD
+0x30be,0x8c6b,0x624b,0xceac,0x3ff9, XPD
+0xa858,0x2a0d,0x5014,0xf7f4,0x3ff9, XPD
+0x8615,0xbfa6,0xa6df,0x991f,0x3ffa, XPD
+0x103c,0xa076,0xff37,0xc7ff,0x3ffa, XPD
+0xf508,0xc515,0xffff,0x8fff,0x3ffb, XPD
+0x1af5,0xfffb,0xffff,0xffff,0x3ffb, XPD
+0x0000,0x0000,0x0000,0x8000,0x3ffe, XPD
+};
+static unsigned short ac1[] = {
+0x79ac,0xd1cf,0x17f7,0xb172,0x3fff, XPD
+};
+#define C1 (*(long double *)ac1)
+#endif
+
+#ifdef MIEEE
+static long P[39] = {
+0x3feb0000,0xa7712381,0xad01f098,
+0x3ff20000,0xe1621922,0xea22d6ed,
+0x3ff60000,0x9474e226,0xe2f13733,
+0x3ff70000,0xdc4d5aff,0x3c9d3031,
+0x3ff80000,0x8494968e,0x43109a46,
+0x3ff70000,0xb999a8a7,0x3ff2be4c,
+0x3ff70000,0x9612b355,0x0eaff35c,
+0x3ff70000,0xbdf7d9dd,0x8fd4bc56,
+0x3ff80000,0x8fa66444,0x867fc01e,
+0x3ff80000,0xf4bce6fd,0x63924ba3,
+0x3ff90000,0xfd02d7bc,0xbb1262c3,
+0x3ffb0000,0xc5c85fdf,0x476c08fe,
+0x3fff0000,0xb17217f7,0xd1cf79ad,
+};
+static long Q[36] = {
+0x3ff00000,0xe990ba33,0x847496a4,
+0x3ff50000,0x87ce1854,0xa50ee5a7,
+0x3ff70000,0xb43d3205,0x72e38999,
+0x3ff80000,0xdb1bb438,0x13eb3255,
+0x3ff90000,0xa68d4691,0x497fb717,
+0x3ff90000,0xceac624b,0x8c6b30be,
+0x3ff90000,0xf7f45014,0x2a0da858,
+0x3ffa0000,0x991fa6df,0xbfa68615,
+0x3ffa0000,0xc7ffff37,0xa076103c,
+0x3ffb0000,0x8fffffff,0xc515f508,
+0x3ffb0000,0xffffffff,0xfffb1af5,
+0x3ffe0000,0x80000000,0x00000000,
+};
+static unsigned long ac1[] = {
+0x3fff0000,0xb17217f7,0xd1cf79ac
+};
+#define C1 (*(long double *)ac1)
+#endif
+
+
+#ifdef ANSIPROT
+extern long double polevll ( long double, void *, int );
+extern long double logl ( long double );
+#else
+long double polevll(), logl();
+#endif
+extern long double MACHEPL, MAXNUML;
+
+long double ellpkl(x)
+long double x;
+{
+
+if( (x < 0.0L) || (x > 1.0L) )
+ {
+ mtherr( "ellpkl", DOMAIN );
+ return( 0.0L );
+ }
+
+if( x > MACHEPL )
+ {
+ return( polevll(x,P,12) - logl(x) * polevll(x,Q,11) );
+ }
+else
+ {
+ if( x == 0.0L )
+ {
+ mtherr( "ellpkl", SING );
+ return( MAXNUML );
+ }
+ else
+ {
+ return( C1 - 0.5L * logl(x) );
+ }
+ }
+}
diff --git a/libm/ldouble/exp10l.c b/libm/ldouble/exp10l.c
new file mode 100644
index 000000000..b837571b4
--- /dev/null
+++ b/libm/ldouble/exp10l.c
@@ -0,0 +1,192 @@
+/* exp10l.c
+ *
+ * Base 10 exponential function, long double precision
+ * (Common antilogarithm)
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, exp10l()
+ *
+ * y = exp10l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 10 raised to the x power.
+ *
+ * Range reduction is accomplished by expressing the argument
+ * as 10**x = 2**n 10**f, with |f| < 0.5 log10(2).
+ * The Pade' form
+ *
+ * 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ *
+ * is used to approximate 10**f.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-4900 30000 1.0e-19 2.7e-20
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp10l underflow x < -MAXL10 0.0
+ * exp10l overflow x > MAXL10 MAXNUM
+ *
+ * IEEE arithmetic: MAXL10 = 4932.0754489586679023819
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: January, 1991
+Copyright 1984, 1991 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+#ifdef UNK
+static long double P[] = {
+ 3.1341179396892496811523E1L,
+ 4.5618283154904699073999E3L,
+ 1.3433113468542797218610E5L,
+ 7.6025447914440301593592E5L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0,*/
+ 4.7705440288425157637739E2L,
+ 2.9732606548049614870598E4L,
+ 4.0843697951001026189583E5L,
+ 6.6034865026929015925608E5L,
+};
+/*static long double LOG102 = 3.0102999566398119521373889e-1L;*/
+static long double LOG210 = 3.3219280948873623478703L;
+static long double LG102A = 3.01025390625e-1L;
+static long double LG102B = 4.6050389811952137388947e-6L;
+#endif
+
+
+#ifdef IBMPC
+static short P[] = {
+0x399a,0x7dc7,0xbc43,0xfaba,0x4003, XPD
+0xb526,0xdf32,0xa063,0x8e8e,0x400b, XPD
+0x18da,0xafa1,0xc89e,0x832e,0x4010, XPD
+0x503d,0x9352,0xe7aa,0xb99b,0x4012, XPD
+};
+static short Q[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0x947d,0x7855,0xf6ac,0xee86,0x4007, XPD
+0x18cf,0x7749,0x368d,0xe849,0x400d, XPD
+0x85be,0x2560,0x9f58,0xc76e,0x4011, XPD
+0x6d3c,0x80c5,0xca67,0xa137,0x4012, XPD
+};
+/*
+static short L102[] = {0xf799,0xfbcf,0x9a84,0x9a20,0x3ffd, XPD};
+#define LOG102 *(long double *)L102
+*/
+static short L210[] = {0x8afe,0xcd1b,0x784b,0xd49a,0x4000, XPD};
+#define LOG210 *(long double *)L210
+static short L102A[] = {0x0000,0x0000,0x0000,0x9a20,0x3ffd, XPD};
+#define LG102A *(long double *)L102A
+static short L102B[] = {0x8f89,0xf798,0xfbcf,0x9a84,0x3fed, XPD};
+#define LG102B *(long double *)L102B
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0x40030000,0xfababc43,0x7dc7399a,
+0x400b0000,0x8e8ea063,0xdf32b526,
+0x40100000,0x832ec89e,0xafa118da,
+0x40120000,0xb99be7aa,0x9352503d,
+};
+static long Q[] = {
+/* 0x3fff0000,0x80000000,0x00000000, */
+0x40070000,0xee86f6ac,0x7855947d,
+0x400d0000,0xe849368d,0x774918cf,
+0x40110000,0xc76e9f58,0x256085be,
+0x40120000,0xa137ca67,0x80c56d3c,
+};
+/*
+static long L102[] = {0x3ffd0000,0x9a209a84,0xfbcff799};
+#define LOG102 *(long double *)L102
+*/
+static long L210[] = {0x40000000,0xd49a784b,0xcd1b8afe};
+#define LOG210 *(long double *)L210
+static long L102A[] = {0x3ffd0000,0x9a200000,0x00000000};
+#define LG102A *(long double *)L102A
+static long L102B[] = {0x3fed0000,0x9a84fbcf,0xf7988f89};
+#define LG102B *(long double *)L102B
+#endif
+
+static long double MAXL10 = 4.9320754489586679023819e3L;
+extern long double MAXNUML;
+#ifdef ANSIPROT
+extern long double floorl ( long double );
+extern long double ldexpl ( long double, int );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern int isnanl ( long double );
+#else
+long double floorl(), ldexpl(), polevll(), p1evll(), isnanl();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+
+long double exp10l(x)
+long double x;
+{
+long double px, xx;
+short n;
+
+#ifdef NANS
+if( isnanl(x) )
+ return(x);
+#endif
+if( x > MAXL10 )
+ {
+#ifdef INFINITIES
+ return( INFINITYL );
+#else
+ mtherr( "exp10l", OVERFLOW );
+ return( MAXNUML );
+#endif
+ }
+
+if( x < -MAXL10 ) /* Would like to use MINLOG but can't */
+ {
+#ifndef INFINITIES
+ mtherr( "exp10l", UNDERFLOW );
+#endif
+ return(0.0L);
+ }
+
+/* Express 10**x = 10**g 2**n
+ * = 10**g 10**( n log10(2) )
+ * = 10**( g + n log10(2) )
+ */
+px = floorl( LOG210 * x + 0.5L );
+n = px;
+x -= px * LG102A;
+x -= px * LG102B;
+
+/* rational approximation for exponential
+ * of the fractional part:
+ * 10**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ */
+xx = x * x;
+px = x * polevll( xx, P, 3 );
+x = px/( p1evll( xx, Q, 4 ) - px );
+x = 1.0L + ldexpl( x, 1 );
+
+/* multiply by power of 2 */
+x = ldexpl( x, n );
+return(x);
+}
diff --git a/libm/ldouble/exp2l.c b/libm/ldouble/exp2l.c
new file mode 100644
index 000000000..076f8bca5
--- /dev/null
+++ b/libm/ldouble/exp2l.c
@@ -0,0 +1,166 @@
+/* exp2l.c
+ *
+ * Base 2 exponential function, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, exp2l();
+ *
+ * y = exp2l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns 2 raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ * x k f
+ * 2 = 2 2.
+ *
+ * A Pade' form
+ *
+ * 1 + 2x P(x**2) / (Q(x**2) - x P(x**2) )
+ *
+ * approximates 2**x in the basic range [-0.5, 0.5].
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-16300 300000 9.1e-20 2.6e-20
+ *
+ *
+ * See exp.c for comments on error amplification.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp2l underflow x < -16382 0.0
+ * exp2l overflow x >= 16384 MAXNUM
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright 1984, 1991, 1998 by Stephen L. Moshier
+*/
+
+
+
+#include <math.h>
+
+#ifdef UNK
+static long double P[] = {
+ 6.0614853552242266094567E1L,
+ 3.0286971917562792508623E4L,
+ 2.0803843631901852422887E6L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0,*/
+ 1.7492876999891839021063E3L,
+ 3.2772515434906797273099E5L,
+ 6.0027204078348487957118E6L,
+};
+#endif
+
+
+#ifdef IBMPC
+static short P[] = {
+0xffd8,0x6ad6,0x9c2b,0xf275,0x4004, XPD
+0x3426,0x2dc5,0xf19f,0xec9d,0x400d, XPD
+0x7ec0,0xd041,0x02e7,0xfdf4,0x4013, XPD
+};
+static short Q[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0x575b,0x9b93,0x34d6,0xdaa9,0x4009, XPD
+0xe38d,0x6d74,0xa4f0,0xa005,0x4011, XPD
+0xb37e,0xcfba,0x40d0,0xb730,0x4015, XPD
+};
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0x40040000,0xf2759c2b,0x6ad6ffd8,
+0x400d0000,0xec9df19f,0x2dc53426,
+0x40130000,0xfdf402e7,0xd0417ec0,
+};
+static long Q[] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x40090000,0xdaa934d6,0x9b93575b,
+0x40110000,0xa005a4f0,0x6d74e38d,
+0x40150000,0xb73040d0,0xcfbab37e,
+};
+#endif
+
+#define MAXL2L 16384.0L
+#define MINL2L -16382.0L
+
+
+extern long double MAXNUML;
+#ifdef ANSIPROT
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern long double floorl ( long double );
+extern long double ldexpl ( long double, int );
+extern int isnanl ( long double );
+#else
+long double polevll(), p1evll(), floorl(), ldexpl(), isnanl();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+
+long double exp2l(x)
+long double x;
+{
+long double px, xx;
+int n;
+
+#ifdef NANS
+if( isnanl(x) )
+ return(x);
+#endif
+if( x > MAXL2L)
+ {
+#ifdef INFINITIES
+ return( INFINITYL );
+#else
+ mtherr( "exp2l", OVERFLOW );
+ return( MAXNUML );
+#endif
+ }
+
+if( x < MINL2L )
+ {
+#ifndef INFINITIES
+ mtherr( "exp2l", UNDERFLOW );
+#endif
+ return(0.0L);
+ }
+
+xx = x; /* save x */
+/* separate into integer and fractional parts */
+px = floorl(x+0.5L);
+n = px;
+x = x - px;
+
+/* rational approximation
+ * exp2(x) = 1.0 + 2xP(xx)/(Q(xx) - P(xx))
+ * where xx = x**2
+ */
+xx = x * x;
+px = x * polevll( xx, P, 2 );
+x = px / ( p1evll( xx, Q, 3 ) - px );
+x = 1.0L + ldexpl( x, 1 );
+
+/* scale by power of 2 */
+x = ldexpl( x, n );
+return(x);
+}
diff --git a/libm/ldouble/expl.c b/libm/ldouble/expl.c
new file mode 100644
index 000000000..524246987
--- /dev/null
+++ b/libm/ldouble/expl.c
@@ -0,0 +1,183 @@
+/* expl.c
+ *
+ * Exponential function, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, expl();
+ *
+ * y = expl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns e (2.71828...) raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *
+ * x k f
+ * e = 2 e.
+ *
+ * A Pade' form of degree 2/3 is used to approximate exp(f) - 1
+ * in the basic range [-0.5 ln 2, 0.5 ln 2].
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-10000 50000 1.12e-19 2.81e-20
+ *
+ *
+ * Error amplification in the exponential function can be
+ * a serious matter. The error propagation involves
+ * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
+ * which shows that a 1 lsb error in representing X produces
+ * a relative error of X times 1 lsb in the function.
+ * While the routine gives an accurate result for arguments
+ * that are exactly represented by a long double precision
+ * computer number, the result contains amplified roundoff
+ * error for large arguments not exactly represented.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * exp underflow x < MINLOG 0.0
+ * exp overflow x > MAXLOG MAXNUM
+ *
+ */
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright 1984, 1990, 1998 by Stephen L. Moshier
+*/
+
+
+/* Exponential function */
+
+#include <math.h>
+
+#ifdef UNK
+static long double P[3] = {
+ 1.2617719307481059087798E-4L,
+ 3.0299440770744196129956E-2L,
+ 9.9999999999999999991025E-1L,
+};
+static long double Q[4] = {
+ 3.0019850513866445504159E-6L,
+ 2.5244834034968410419224E-3L,
+ 2.2726554820815502876593E-1L,
+ 2.0000000000000000000897E0L,
+};
+static long double C1 = 6.9314575195312500000000E-1L;
+static long double C2 = 1.4286068203094172321215E-6L;
+#endif
+
+#ifdef DEC
+not supported in long double precision
+#endif
+
+#ifdef IBMPC
+static short P[] = {
+0x424e,0x225f,0x6eaf,0x844e,0x3ff2, XPD
+0xf39e,0x5163,0x8866,0xf836,0x3ff9, XPD
+0xfffe,0xffff,0xffff,0xffff,0x3ffe, XPD
+};
+static short Q[] = {
+0xff1e,0xb2fc,0xb5e1,0xc975,0x3fec, XPD
+0xff3e,0x45b5,0xcda8,0xa571,0x3ff6, XPD
+0x9ee1,0x3f03,0x4cc4,0xe8b8,0x3ffc, XPD
+0x0000,0x0000,0x0000,0x8000,0x4000, XPD
+};
+static short sc1[] = {0x0000,0x0000,0x0000,0xb172,0x3ffe, XPD};
+#define C1 (*(long double *)sc1)
+static short sc2[] = {0x4f1e,0xcd5e,0x8e7b,0xbfbe,0x3feb, XPD};
+#define C2 (*(long double *)sc2)
+#endif
+
+#ifdef MIEEE
+static long P[9] = {
+0x3ff20000,0x844e6eaf,0x225f424e,
+0x3ff90000,0xf8368866,0x5163f39e,
+0x3ffe0000,0xffffffff,0xfffffffe,
+};
+static long Q[12] = {
+0x3fec0000,0xc975b5e1,0xb2fcff1e,
+0x3ff60000,0xa571cda8,0x45b5ff3e,
+0x3ffc0000,0xe8b84cc4,0x3f039ee1,
+0x40000000,0x80000000,0x00000000,
+};
+static long sc1[] = {0x3ffe0000,0xb1720000,0x00000000};
+#define C1 (*(long double *)sc1)
+static long sc2[] = {0x3feb0000,0xbfbe8e7b,0xcd5e4f1e};
+#define C2 (*(long double *)sc2)
+#endif
+
+extern long double LOG2EL, MAXLOGL, MINLOGL, MAXNUML;
+#ifdef ANSIPROT
+extern long double polevll ( long double, void *, int );
+extern long double floorl ( long double );
+extern long double ldexpl ( long double, int );
+extern int isnanl ( long double );
+#else
+long double polevll(), floorl(), ldexpl(), isnanl();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+
+long double expl(x)
+long double x;
+{
+long double px, xx;
+int n;
+
+#ifdef NANS
+if( isnanl(x) )
+ return(x);
+#endif
+if( x > MAXLOGL)
+ {
+#ifdef INFINITIES
+ return( INFINITYL );
+#else
+ mtherr( "expl", OVERFLOW );
+ return( MAXNUML );
+#endif
+ }
+
+if( x < MINLOGL )
+ {
+#ifndef INFINITIES
+ mtherr( "expl", UNDERFLOW );
+#endif
+ return(0.0L);
+ }
+
+/* Express e**x = e**g 2**n
+ * = e**g e**( n loge(2) )
+ * = e**( g + n loge(2) )
+ */
+px = floorl( LOG2EL * x + 0.5L ); /* floor() truncates toward -infinity. */
+n = px;
+x -= px * C1;
+x -= px * C2;
+
+
+/* rational approximation for exponential
+ * of the fractional part:
+ * e**x = 1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ */
+xx = x * x;
+px = x * polevll( xx, P, 2 );
+x = px/( polevll( xx, Q, 3 ) - px );
+x = 1.0L + ldexpl( x, 1 );
+
+x = ldexpl( x, n );
+return(x);
+}
diff --git a/libm/ldouble/fdtrl.c b/libm/ldouble/fdtrl.c
new file mode 100644
index 000000000..da2f8910a
--- /dev/null
+++ b/libm/ldouble/fdtrl.c
@@ -0,0 +1,237 @@
+/* fdtrl.c
+ *
+ * F distribution, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * long double x, y, fdtrl();
+ *
+ * y = fdtrl( df1, df2, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from zero to x under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density). This is the density
+ * of x = (u1/df1)/(u2/df2), where u1 and u2 are random
+ * variables having Chi square distributions with df1
+ * and df2 degrees of freedom, respectively.
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ * P(x) = incbetl( df1/2, df2/2, (df1*x/(df2 + df1*x) ).
+ *
+ *
+ * The arguments a and b are greater than zero, and x
+ * x is nonnegative.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,x) in the indicated intervals.
+ * x a,b Relative error:
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0,1 1,100 10000 9.3e-18 2.9e-19
+ * IEEE 0,1 1,10000 10000 1.9e-14 2.9e-15
+ * IEEE 1,5 1,10000 10000 5.8e-15 1.4e-16
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrl domain a<0, b<0, x<0 0.0
+ *
+ */
+ /* fdtrcl()
+ *
+ * Complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * long double x, y, fdtrcl();
+ *
+ * y = fdtrcl( df1, df2, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area from x to infinity under the F density
+ * function (also known as Snedcor's density or the
+ * variance ratio density).
+ *
+ *
+ * inf.
+ * -
+ * 1 | | a-1 b-1
+ * 1-P(x) = ------ | t (1-t) dt
+ * B(a,b) | |
+ * -
+ * x
+ *
+ * (See fdtr.c.)
+ *
+ * The incomplete beta integral is used, according to the
+ * formula
+ *
+ * P(x) = incbet( df2/2, df1/2, (df2/(df2 + df1*x) ).
+ *
+ *
+ * ACCURACY:
+ *
+ * See incbet.c.
+ * Tested at random points (a,b,x).
+ *
+ * x a,b Relative error:
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0,1 0,100 10000 4.2e-18 3.3e-19
+ * IEEE 0,1 1,10000 10000 7.2e-15 2.6e-16
+ * IEEE 1,5 1,10000 10000 1.7e-14 3.0e-15
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtrcl domain a<0, b<0, x<0 0.0
+ *
+ */
+ /* fdtril()
+ *
+ * Inverse of complemented F distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int df1, df2;
+ * long double x, p, fdtril();
+ *
+ * x = fdtril( df1, df2, p );
+ *
+ * DESCRIPTION:
+ *
+ * Finds the F density argument x such that the integral
+ * from x to infinity of the F density is equal to the
+ * given probability p.
+ *
+ * This is accomplished using the inverse beta integral
+ * function and the relations
+ *
+ * z = incbi( df2/2, df1/2, p )
+ * x = df2 (1-z) / (df1 z).
+ *
+ * Note: the following relations hold for the inverse of
+ * the uncomplemented F distribution:
+ *
+ * z = incbi( df1/2, df2/2, p )
+ * x = df2 z / (df1 (1-z)).
+ *
+ * ACCURACY:
+ *
+ * See incbi.c.
+ * Tested at random points (a,b,p).
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * For p between .001 and 1:
+ * IEEE 1,100 40000 4.6e-18 2.7e-19
+ * IEEE 1,10000 30000 1.7e-14 1.4e-16
+ * For p between 10^-6 and .001:
+ * IEEE 1,100 20000 1.9e-15 3.9e-17
+ * IEEE 1,10000 30000 2.7e-15 4.0e-17
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * fdtril domain p <= 0 or p > 1 0.0
+ * v < 1
+ */
+
+
+/*
+Cephes Math Library Release 2.3: March, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double incbetl ( long double, long double, long double );
+extern long double incbil ( long double, long double, long double );
+#else
+long double incbetl(), incbil();
+#endif
+
+long double fdtrcl( ia, ib, x )
+int ia, ib;
+long double x;
+{
+long double a, b, w;
+
+if( (ia < 1) || (ib < 1) || (x < 0.0L) )
+ {
+ mtherr( "fdtrcl", DOMAIN );
+ return( 0.0L );
+ }
+a = ia;
+b = ib;
+w = b / (b + a * x);
+return( incbetl( 0.5L*b, 0.5L*a, w ) );
+}
+
+
+
+long double fdtrl( ia, ib, x )
+int ia, ib;
+long double x;
+{
+long double a, b, w;
+
+if( (ia < 1) || (ib < 1) || (x < 0.0L) )
+ {
+ mtherr( "fdtrl", DOMAIN );
+ return( 0.0L );
+ }
+a = ia;
+b = ib;
+w = a * x;
+w = w / (b + w);
+return( incbetl(0.5L*a, 0.5L*b, w) );
+}
+
+
+long double fdtril( ia, ib, y )
+int ia, ib;
+long double y;
+{
+long double a, b, w, x;
+
+if( (ia < 1) || (ib < 1) || (y <= 0.0L) || (y > 1.0L) )
+ {
+ mtherr( "fdtril", DOMAIN );
+ return( 0.0L );
+ }
+a = ia;
+b = ib;
+/* Compute probability for x = 0.5. */
+w = incbetl( 0.5L*b, 0.5L*a, 0.5L );
+/* If that is greater than y, then the solution w < .5.
+ Otherwise, solve at 1-y to remove cancellation in (b - b*w). */
+if( w > y || y < 0.001L)
+ {
+ w = incbil( 0.5L*b, 0.5L*a, y );
+ x = (b - b*w)/(a*w);
+ }
+else
+ {
+ w = incbil( 0.5L*a, 0.5L*b, 1.0L - y );
+ x = b*w/(a*(1.0L-w));
+ }
+return(x);
+}
diff --git a/libm/ldouble/floorl.c b/libm/ldouble/floorl.c
new file mode 100644
index 000000000..1abdfb2cd
--- /dev/null
+++ b/libm/ldouble/floorl.c
@@ -0,0 +1,432 @@
+/* ceill()
+ * floorl()
+ * frexpl()
+ * ldexpl()
+ * fabsl()
+ * signbitl()
+ * isnanl()
+ * isfinitel()
+ *
+ * Floating point numeric utilities
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double ceill(), floorl(), frexpl(), ldexpl(), fabsl();
+ * int signbitl(), isnanl(), isfinitel();
+ * long double x, y;
+ * int expnt, n;
+ *
+ * y = floorl(x);
+ * y = ceill(x);
+ * y = frexpl( x, &expnt );
+ * y = ldexpl( x, n );
+ * y = fabsl( x );
+ * n = signbitl(x);
+ * n = isnanl(x);
+ * n = isfinitel(x);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The following routines return a long double precision floating point
+ * result:
+ *
+ * floorl() returns the largest integer less than or equal to x.
+ * It truncates toward minus infinity.
+ *
+ * ceill() returns the smallest integer greater than or equal
+ * to x. It truncates toward plus infinity.
+ *
+ * frexpl() extracts the exponent from x. It returns an integer
+ * power of two to expnt and the significand between 0.5 and 1
+ * to y. Thus x = y * 2**expn.
+ *
+ * ldexpl() multiplies x by 2**n.
+ *
+ * fabsl() returns the absolute value of its argument.
+ *
+ * These functions are part of the standard C run time library
+ * for some but not all C compilers. The ones supplied are
+ * written in C for IEEE arithmetic. They should
+ * be used only if your compiler library does not already have
+ * them.
+ *
+ * The IEEE versions assume that denormal numbers are implemented
+ * in the arithmetic. Some modifications will be required if
+ * the arithmetic has abrupt rather than gradual underflow.
+ */
+
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright 1984, 1987, 1988, 1992, 1998 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+/* This is defined in mconf.h. */
+/* #define DENORMAL 1 */
+
+#ifdef UNK
+/* Change UNK into something else. */
+#undef UNK
+#if BIGENDIAN
+#define MIEEE 1
+#else
+#define IBMPC 1
+#endif
+#endif
+
+#ifdef IBMPC
+#define EXPMSK 0x800f
+#define MEXP 0x7ff
+#define NBITS 64
+#endif
+
+#ifdef MIEEE
+#define EXPMSK 0x800f
+#define MEXP 0x7ff
+#define NBITS 64
+#endif
+
+extern double MAXNUML;
+
+#ifdef ANSIPROT
+extern long double fabsl ( long double );
+extern long double floorl ( long double );
+extern int isnanl ( long double );
+#else
+long double fabsl(), floorl();
+int isnanl();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+#ifdef NANS
+extern long double NANL;
+#endif
+
+long double fabsl(x)
+long double x;
+{
+union
+ {
+ long double d;
+ short i[6];
+ } u;
+
+u.d = x;
+#ifdef IBMPC
+ u.i[4] &= 0x7fff;
+#endif
+#ifdef MIEEE
+ u.i[0] &= 0x7fff;
+#endif
+return( u.d );
+}
+
+
+
+long double ceill(x)
+long double x;
+{
+long double y;
+
+#ifdef UNK
+mtherr( "ceill", DOMAIN );
+return(0.0L);
+#endif
+#ifdef INFINITIES
+if(x == -INFINITYL)
+ return(x);
+#endif
+#ifdef MINUSZERO
+if(x == 0.0L)
+ return(x);
+#endif
+y = floorl(x);
+if( y < x )
+ y += 1.0L;
+return(y);
+}
+
+
+
+
+/* Bit clearing masks: */
+
+static unsigned short bmask[] = {
+0xffff,
+0xfffe,
+0xfffc,
+0xfff8,
+0xfff0,
+0xffe0,
+0xffc0,
+0xff80,
+0xff00,
+0xfe00,
+0xfc00,
+0xf800,
+0xf000,
+0xe000,
+0xc000,
+0x8000,
+0x0000,
+};
+
+
+
+
+long double floorl(x)
+long double x;
+{
+unsigned short *p;
+union
+ {
+ long double y;
+ unsigned short sh[6];
+ } u;
+int e;
+
+#ifdef UNK
+mtherr( "floor", DOMAIN );
+return(0.0L);
+#endif
+#ifdef INFINITIES
+if( x == INFINITYL )
+ return(x);
+#endif
+#ifdef MINUSZERO
+if(x == 0.0L)
+ return(x);
+#endif
+u.y = x;
+/* find the exponent (power of 2) */
+#ifdef IBMPC
+p = (unsigned short *)&u.sh[4];
+e = (*p & 0x7fff) - 0x3fff;
+p -= 4;
+#endif
+
+#ifdef MIEEE
+p = (unsigned short *)&u.sh[0];
+e = (*p & 0x7fff) - 0x3fff;
+p += 5;
+#endif
+
+if( e < 0 )
+ {
+ if( u.y < 0.0L )
+ return( -1.0L );
+ else
+ return( 0.0L );
+ }
+
+e = (NBITS -1) - e;
+/* clean out 16 bits at a time */
+while( e >= 16 )
+ {
+#ifdef IBMPC
+ *p++ = 0;
+#endif
+
+#ifdef MIEEE
+ *p-- = 0;
+#endif
+ e -= 16;
+ }
+
+/* clear the remaining bits */
+if( e > 0 )
+ *p &= bmask[e];
+
+if( (x < 0) && (u.y != x) )
+ u.y -= 1.0L;
+
+return(u.y);
+}
+
+
+
+long double frexpl( x, pw2 )
+long double x;
+int *pw2;
+{
+union
+ {
+ long double y;
+ unsigned short sh[6];
+ } u;
+int i, k;
+short *q;
+
+u.y = x;
+
+#ifdef NANS
+if(isnanl(x))
+ {
+ *pw2 = 0;
+ return(x);
+ }
+#endif
+#ifdef INFINITIES
+if(x == -INFINITYL)
+ {
+ *pw2 = 0;
+ return(x);
+ }
+#endif
+#ifdef MINUSZERO
+if(x == 0.0L)
+ {
+ *pw2 = 0;
+ return(x);
+ }
+#endif
+
+#ifdef UNK
+mtherr( "frexpl", DOMAIN );
+return(0.0L);
+#endif
+
+/* find the exponent (power of 2) */
+#ifdef IBMPC
+q = (short *)&u.sh[4];
+i = *q & 0x7fff;
+#endif
+
+#ifdef MIEEE
+q = (short *)&u.sh[0];
+i = *q & 0x7fff;
+#endif
+
+if( i == 0 )
+ {
+ if( u.y == 0.0L )
+ {
+ *pw2 = 0;
+ return(0.0L);
+ }
+/* Number is denormal or zero */
+#ifdef DENORMAL
+/* Handle denormal number. */
+do
+ {
+ u.y *= 2.0L;
+ i -= 1;
+ k = *q & 0x7fff;
+ }
+while( (k == 0) && (i > -66) );
+i = i + k;
+#else
+ *pw2 = 0;
+ return(0.0L);
+#endif /* DENORMAL */
+ }
+
+*pw2 = i - 0x3ffe;
+/* *q = 0x3ffe; */
+/* Preserve sign of argument. */
+*q &= 0x8000;
+*q |= 0x3ffe;
+return( u.y );
+}
+
+
+
+
+
+
+long double ldexpl( x, pw2 )
+long double x;
+int pw2;
+{
+union
+ {
+ long double y;
+ unsigned short sh[6];
+ } u;
+unsigned short *q;
+long e;
+
+#ifdef UNK
+mtherr( "ldexp", DOMAIN );
+return(0.0L);
+#endif
+
+u.y = x;
+#ifdef IBMPC
+q = (unsigned short *)&u.sh[4];
+#endif
+#ifdef MIEEE
+q = (unsigned short *)&u.sh[0];
+#endif
+while( (e = (*q & 0x7fffL)) == 0 )
+ {
+#ifdef DENORMAL
+ if( u.y == 0.0L )
+ {
+ return( 0.0L );
+ }
+/* Input is denormal. */
+ if( pw2 > 0 )
+ {
+ u.y *= 2.0L;
+ pw2 -= 1;
+ }
+ if( pw2 < 0 )
+ {
+ if( pw2 < -64 )
+ return(0.0L);
+ u.y *= 0.5L;
+ pw2 += 1;
+ }
+ if( pw2 == 0 )
+ return(u.y);
+#else
+ return( 0.0L );
+#endif
+ }
+
+e = e + pw2;
+
+/* Handle overflow */
+if( e > 0x7fffL )
+ {
+ return( MAXNUML );
+ }
+*q &= 0x8000;
+/* Handle denormalized results */
+if( e < 1 )
+ {
+#ifdef DENORMAL
+ if( e < -64 )
+ return(0.0L);
+
+#ifdef IBMPC
+ *(q-1) |= 0x8000;
+#endif
+#ifdef MIEEE
+ *(q+2) |= 0x8000;
+#endif
+
+ while( e < 1 )
+ {
+ u.y *= 0.5L;
+ e += 1;
+ }
+ e = 0;
+#else
+ return(0.0L);
+#endif
+ }
+
+*q |= (unsigned short) e & 0x7fff;
+return(u.y);
+}
+
diff --git a/libm/ldouble/flrtstl.c b/libm/ldouble/flrtstl.c
new file mode 100644
index 000000000..77a389324
--- /dev/null
+++ b/libm/ldouble/flrtstl.c
@@ -0,0 +1,104 @@
+long double floorl(), ldexpl(), frexpl();
+
+#define N 16382
+void prnum();
+int printf();
+void exit();
+
+void main()
+{
+long double x, f, y, last, z, z0, y1;
+int i, k, e, e0, errs;
+
+errs = 0;
+f = 0.1L;
+x = f;
+last = x;
+z0 = frexpl( x, &e0 );
+printf( "frexpl(%.2Le) = %.5Le, %d\n", x, z0, e0 );
+k = 0;
+for( i=0; i<N+5; i++ )
+ {
+ y = ldexpl( f, k );
+ if( y != x )
+ {
+ printf( "ldexpl(%.1Le, %d) = %.5Le, s.b. %.5Le\n",
+ f, k, y, x );
+ ++errs;
+ }
+ z = frexpl( y, &e );
+ if( (e != k+e0) || (z != z0) )
+ {
+ printf( "frexpl(%.1Le) = %.5Le, %d; s.b. %.5Le, %d\n",
+ y, z, e, z0, k+e0 );
+ ++errs;
+ }
+ x += x;
+ if( x == last )
+ break;
+ last = x;
+ k += 1;
+ }
+printf( "i = %d\n", k );
+prnum( "last y =", &y );
+printf("\n");
+
+f = 0.1L;
+x = f;
+last = x;
+k = 0;
+for( i=0; i<N+64; i++ )
+ {
+ y = ldexpl( f, k );
+ if( y != x )
+ {
+ printf( "ldexpl(%.1Le, %d) = %.5Le, s.b. %.5Le\n",
+ f, k, y, x );
+ ++errs;
+ }
+ z = frexpl( y, &e );
+ if(
+#if 1
+ (e > -N+1) &&
+#endif
+ ((e != k+e0) || (z != z0)) )
+ {
+ printf( "frexpl(%.1Le) = %.5Le, %d; s.b. %.5Le, %d\n",
+ y, z, e, z0, k+e0 );
+ ++errs;
+ }
+ y1 = ldexpl( z, e );
+ if( y1 != y )
+ {
+ printf( "ldexpl(%.1Le, %d) = %.5Le, s.b. %.5Le\n",
+ z, e, y1, y );
+ ++errs;
+ }
+
+ x *= 0.5L;
+ if( x == 0.0L )
+ break;
+ if( x == last )
+ break;
+ last = x;
+ k -= 1;
+ }
+printf( "i = %d\n", k );
+prnum( "last y =", &y );
+
+printf( "\n%d errors\n", errs );
+exit(0);
+}
+
+
+void prnum(str, x)
+char *str;
+unsigned short *x;
+{
+int i;
+
+printf( "%s ", str );
+printf( "%.5Le = ", *(long double *)x );
+for( i=0; i<5; i++ )
+ printf( "%04x ", *x++ );
+}
diff --git a/libm/ldouble/fltestl.c b/libm/ldouble/fltestl.c
new file mode 100644
index 000000000..963e92467
--- /dev/null
+++ b/libm/ldouble/fltestl.c
@@ -0,0 +1,265 @@
+/* fltest.c
+ * Test program for floor(), frexp(), ldexp()
+ */
+
+/*
+Cephes Math Library Release 2.1: December, 1988
+Copyright 1984, 1987, 1988 by Stephen L. Moshier (moshier@world.std.com)
+*/
+
+
+
+/*#include <math.h>*/
+#define MACHEPL 5.42101086242752217003726400434970855712890625E-20L
+#define N 16300
+
+void flierr();
+int printf();
+void exit();
+
+int
+main()
+{
+long double x, y, y0, z, f, x00, y00;
+int i, j, e, e0;
+int errfr, errld, errfl, underexp, err, errth, e00;
+long double frexpl(), ldexpl(), floorl();
+
+
+/*
+if( 1 )
+ goto flrtst;
+*/
+
+printf( "Testing frexpl() and ldexpl().\n" );
+errth = 0.0L;
+errfr = 0;
+errld = 0;
+underexp = 0;
+f = 1.0L;
+x00 = 2.0L;
+y00 = 0.5L;
+e00 = 2;
+
+for( j=0; j<20; j++ )
+{
+if( j == 10 )
+ {
+ f = 1.0L;
+ x00 = 2.0L;
+ e00 = 1;
+/* Find 2**(2**14) / 2 */
+ for( i=0; i<13; i++ )
+ {
+ x00 *= x00;
+ e00 += e00;
+ }
+ y00 = x00/2.0L;
+ x00 = x00 * y00;
+ e00 += e00;
+ y00 = 0.5L;
+ }
+x = x00 * f;
+y0 = y00 * f;
+e0 = e00;
+
+#if 1
+/* If ldexp, frexp support denormal numbers, this should work. */
+for( i=0; i<16448; i++ )
+#else
+for( i=0; i<16383; i++ )
+#endif
+ {
+ x /= 2.0L;
+ e0 -= 1;
+ if( x == 0.0L )
+ {
+ if( f == 1.0L )
+ underexp = e0;
+ y0 = 0.0L;
+ e0 = 0;
+ }
+ y = frexpl( x, &e );
+ if( (e0 < -16383) && (e != e0) )
+ {
+ if( e == (e0 - 1) )
+ {
+ e += 1;
+ y /= 2.0L;
+ }
+ if( e == (e0 + 1) )
+ {
+ e -= 1;
+ y *= 2.0L;
+ }
+ }
+ err = y - y0;
+ if( y0 != 0.0L )
+ err /= y0;
+ if( err < 0.0L )
+ err = -err;
+ if( e0 > -1023 )
+ errth = 0.0L;
+ else
+ {/* Denormal numbers may have rounding errors */
+ if( e0 == -16383 )
+ {
+ errth = 2.0L * MACHEPL;
+ }
+ else
+ {
+ errth *= 2.0L;
+ }
+ }
+
+ if( (x != 0.0L) && ((err > errth) || (e != e0)) )
+ {
+ printf( "Test %d: ", j+1 );
+ printf( " frexpl( %.20Le) =?= %.20Le * 2**%d;", x, y, e );
+ printf( " should be %.20Le * 2**%d\n", y0, e0 );
+ errfr += 1;
+ }
+ y = ldexpl( x, 1-e0 );
+ err = y - 1.0L;
+ if( err < 0.0L )
+ err = -err;
+ if( (err > errth) && ((x == 0.0L) && (y != 0.0L)) )
+ {
+ printf( "Test %d: ", j+1 );
+ printf( "ldexpl( %.15Le, %d ) =?= %.15Le;", x, 1-e0, y );
+ if( x != 0.0L )
+ printf( " should be %.15Le\n", f );
+ else
+ printf( " should be %.15Le\n", 0.0L );
+ errld += 1;
+ }
+ if( x == 0.0L )
+ {
+ break;
+ }
+ }
+f = f * 1.08005973889L;
+}
+
+if( (errld == 0) && (errfr == 0) )
+ {
+ printf( "No errors found.\n" );
+ }
+
+/*flrtst:*/
+
+printf( "Testing floorl().\n" );
+errfl = 0;
+
+f = 1.0L/MACHEPL;
+x00 = 1.0L;
+for( j=0; j<57; j++ )
+{
+x = x00 - 1.0L;
+for( i=0; i<128; i++ )
+ {
+ y = floorl(x);
+ if( y != x )
+ {
+ flierr( x, y, j );
+ errfl += 1;
+ }
+/* Warning! the if() statement is compiler dependent,
+ * since x-0.49 may be held in extra precision accumulator
+ * so would never compare equal to x! The subroutine call
+ * y = floor() forces z to be stored as a double and reloaded
+ * for the if() statement.
+ */
+ z = x - 0.49L;
+ y = floorl(z);
+ if( z == x )
+ break;
+ if( y != (x - 1.0L) )
+ {
+ flierr( z, y, j );
+ errfl += 1;
+ }
+
+ z = x + 0.49L;
+ y = floorl(z);
+ if( z != x )
+ {
+ if( y != x )
+ {
+ flierr( z, y, j );
+ errfl += 1;
+ }
+ }
+ x = -x;
+ y = floorl(x);
+ if( z != x )
+ {
+ if( y != x )
+ {
+ flierr( x, y, j );
+ errfl += 1;
+ }
+ }
+ z = x + 0.49L;
+ y = floorl(z);
+ if( z != x )
+ {
+ if( y != x )
+ {
+ flierr( z, y, j );
+ errfl += 1;
+ }
+ }
+ z = x - 0.49L;
+ y = floorl(z);
+ if( z != x )
+ {
+ if( y != (x - 1.0L) )
+ {
+ flierr( z, y, j );
+ errfl += 1;
+ }
+ }
+ x = -x;
+ x += 1.0L;
+ }
+x00 = x00 + x00;
+}
+y = floorl(0.0L);
+if( y != 0.0L )
+ {
+ flierr( 0.0L, y, 57 );
+ errfl += 1;
+ }
+y = floorl(-0.0L);
+if( y != 0.0L )
+ {
+ flierr( -0.0L, y, 58 );
+ errfl += 1;
+ }
+y = floorl(-1.0L);
+if( y != -1.0L )
+ {
+ flierr( -1.0L, y, 59 );
+ errfl += 1;
+ }
+y = floorl(-0.1L);
+if( y != -1.0l )
+ {
+ flierr( -0.1L, y, 60 );
+ errfl += 1;
+ }
+
+if( errfl == 0 )
+ printf( "No errors found in floorl().\n" );
+exit(0);
+return 0;
+}
+
+void flierr( x, y, k )
+long double x, y;
+int k;
+{
+printf( "Test %d: ", k+1 );
+printf( "floorl(%.15Le) =?= %.15Le\n", x, y );
+}
diff --git a/libm/ldouble/gammal.c b/libm/ldouble/gammal.c
new file mode 100644
index 000000000..de7ed89a2
--- /dev/null
+++ b/libm/ldouble/gammal.c
@@ -0,0 +1,764 @@
+/* gammal.c
+ *
+ * Gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, gammal();
+ * extern int sgngam;
+ *
+ * y = gammal( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns gamma function of the argument. The result is
+ * correctly signed, and the sign (+1 or -1) is also
+ * returned in a global (extern) variable named sgngam.
+ * This variable is also filled in by the logarithmic gamma
+ * function lgam().
+ *
+ * Arguments |x| <= 13 are reduced by recurrence and the function
+ * approximated by a rational function of degree 7/8 in the
+ * interval (2,3). Large arguments are handled by Stirling's
+ * formula. Large negative arguments are made positive using
+ * a reflection formula.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -40,+40 10000 3.6e-19 7.9e-20
+ * IEEE -1755,+1755 10000 4.8e-18 6.5e-19
+ *
+ * Accuracy for large arguments is dominated by error in powl().
+ *
+ */
+/* lgaml()
+ *
+ * Natural logarithm of gamma function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, lgaml();
+ * extern int sgngam;
+ *
+ * y = lgaml( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of the absolute
+ * value of the gamma function of the argument.
+ * The sign (+1 or -1) of the gamma function is returned in a
+ * global (extern) variable named sgngam.
+ *
+ * For arguments greater than 33, the logarithm of the gamma
+ * function is approximated by the logarithmic version of
+ * Stirling's formula using a polynomial approximation of
+ * degree 4. Arguments between -33 and +33 are reduced by
+ * recurrence to the interval [2,3] of a rational approximation.
+ * The cosecant reflection formula is employed for arguments
+ * less than -33.
+ *
+ * Arguments greater than MAXLGML (10^4928) return MAXNUML.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * arithmetic domain # trials peak rms
+ * IEEE -40, 40 100000 2.2e-19 4.6e-20
+ * IEEE 10^-2000,10^+2000 20000 1.6e-19 3.3e-20
+ * The error criterion was relative when the function magnitude
+ * was greater than one but absolute when it was less than one.
+ *
+ */
+
+/* gamma.c */
+/* gamma function */
+
+/*
+Copyright 1994 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+/*
+gamma(x+2) = gamma(x+2) P(x)/Q(x)
+0 <= x <= 1
+Relative error
+n=7, d=8
+Peak error = 1.83e-20
+Relative error spread = 8.4e-23
+*/
+#if UNK
+static long double P[8] = {
+ 4.212760487471622013093E-5L,
+ 4.542931960608009155600E-4L,
+ 4.092666828394035500949E-3L,
+ 2.385363243461108252554E-2L,
+ 1.113062816019361559013E-1L,
+ 3.629515436640239168939E-1L,
+ 8.378004301573126728826E-1L,
+ 1.000000000000000000009E0L,
+};
+static long double Q[9] = {
+-1.397148517476170440917E-5L,
+ 2.346584059160635244282E-4L,
+-1.237799246653152231188E-3L,
+-7.955933682494738320586E-4L,
+ 2.773706565840072979165E-2L,
+-4.633887671244534213831E-2L,
+-2.243510905670329164562E-1L,
+ 4.150160950588455434583E-1L,
+ 9.999999999999999999908E-1L,
+};
+#endif
+#if IBMPC
+static short P[] = {
+0x434a,0x3f22,0x2bda,0xb0b2,0x3ff0, XPD
+0xf5aa,0xe82f,0x335b,0xee2e,0x3ff3, XPD
+0xbe6c,0x3757,0xc717,0x861b,0x3ff7, XPD
+0x7f43,0x5196,0xb166,0xc368,0x3ff9, XPD
+0x9549,0x8eb5,0x8c3a,0xe3f4,0x3ffb, XPD
+0x8d75,0x23af,0xc8e4,0xb9d4,0x3ffd, XPD
+0x29cf,0x19b3,0x16c8,0xd67a,0x3ffe, XPD
+0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
+};
+static short Q[] = {
+0x5473,0x2de8,0x1268,0xea67,0xbfee, XPD
+0x334b,0xc2f0,0xa2dd,0xf60e,0x3ff2, XPD
+0xbeed,0x1853,0xa691,0xa23d,0xbff5, XPD
+0x296e,0x7cb1,0x5dfd,0xd08f,0xbff4, XPD
+0x0417,0x7989,0xd7bc,0xe338,0x3ff9, XPD
+0x3295,0x3698,0xd580,0xbdcd,0xbffa, XPD
+0x75ef,0x3ab7,0x4ad3,0xe5bc,0xbffc, XPD
+0xe458,0x2ec7,0xfd57,0xd47c,0x3ffd, XPD
+0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
+};
+#endif
+#if MIEEE
+static long P[24] = {
+0x3ff00000,0xb0b22bda,0x3f22434a,
+0x3ff30000,0xee2e335b,0xe82ff5aa,
+0x3ff70000,0x861bc717,0x3757be6c,
+0x3ff90000,0xc368b166,0x51967f43,
+0x3ffb0000,0xe3f48c3a,0x8eb59549,
+0x3ffd0000,0xb9d4c8e4,0x23af8d75,
+0x3ffe0000,0xd67a16c8,0x19b329cf,
+0x3fff0000,0x80000000,0x00000000,
+};
+static long Q[27] = {
+0xbfee0000,0xea671268,0x2de85473,
+0x3ff20000,0xf60ea2dd,0xc2f0334b,
+0xbff50000,0xa23da691,0x1853beed,
+0xbff40000,0xd08f5dfd,0x7cb1296e,
+0x3ff90000,0xe338d7bc,0x79890417,
+0xbffa0000,0xbdcdd580,0x36983295,
+0xbffc0000,0xe5bc4ad3,0x3ab775ef,
+0x3ffd0000,0xd47cfd57,0x2ec7e458,
+0x3fff0000,0x80000000,0x00000000,
+};
+#endif
+/*
+static long double P[] = {
+-3.01525602666895735709e0L,
+-3.25157411956062339893e1L,
+-2.92929976820724030353e2L,
+-1.70730828800510297666e3L,
+-7.96667499622741999770e3L,
+-2.59780216007146401957e4L,
+-5.99650230220855581642e4L,
+-7.15743521530849602425e4L
+};
+static long double Q[] = {
+ 1.00000000000000000000e0L,
+-1.67955233807178858919e1L,
+ 8.85946791747759881659e1L,
+ 5.69440799097468430177e1L,
+-1.98526250512761318471e3L,
+ 3.31667508019495079814e3L,
+ 1.60577839621734713377e4L,
+-2.97045081369399940529e4L,
+-7.15743521530849602412e4L
+};
+*/
+#define MAXGAML 1755.455L
+/*static long double LOGPI = 1.14472988584940017414L;*/
+
+/* Stirling's formula for the gamma function
+gamma(x) = sqrt(2 pi) x^(x-.5) exp(-x) (1 + 1/x P(1/x))
+z(x) = x
+13 <= x <= 1024
+Relative error
+n=8, d=0
+Peak error = 9.44e-21
+Relative error spread = 8.8e-4
+*/
+#if UNK
+static long double STIR[9] = {
+ 7.147391378143610789273E-4L,
+-2.363848809501759061727E-5L,
+-5.950237554056330156018E-4L,
+ 6.989332260623193171870E-5L,
+ 7.840334842744753003862E-4L,
+-2.294719747873185405699E-4L,
+-2.681327161876304418288E-3L,
+ 3.472222222230075327854E-3L,
+ 8.333333333333331800504E-2L,
+};
+#endif
+#if IBMPC
+static short STIR[] = {
+0x6ede,0x69f7,0x54e3,0xbb5d,0x3ff4, XPD
+0xc395,0x0295,0x4443,0xc64b,0xbfef, XPD
+0xba6f,0x7c59,0x5e47,0x9bfb,0xbff4, XPD
+0x5704,0x1a39,0xb11d,0x9293,0x3ff1, XPD
+0x30b7,0x1a21,0x98b2,0xcd87,0x3ff4, XPD
+0xbef3,0x7023,0x6a08,0xf09e,0xbff2, XPD
+0x3a1c,0x5ac8,0x3478,0xafb9,0xbff6, XPD
+0xc3c9,0x906e,0x38e3,0xe38e,0x3ff6, XPD
+0xa1d5,0xaaaa,0xaaaa,0xaaaa,0x3ffb, XPD
+};
+#endif
+#if MIEEE
+static long STIR[27] = {
+0x3ff40000,0xbb5d54e3,0x69f76ede,
+0xbfef0000,0xc64b4443,0x0295c395,
+0xbff40000,0x9bfb5e47,0x7c59ba6f,
+0x3ff10000,0x9293b11d,0x1a395704,
+0x3ff40000,0xcd8798b2,0x1a2130b7,
+0xbff20000,0xf09e6a08,0x7023bef3,
+0xbff60000,0xafb93478,0x5ac83a1c,
+0x3ff60000,0xe38e38e3,0x906ec3c9,
+0x3ffb0000,0xaaaaaaaa,0xaaaaa1d5,
+};
+#endif
+#define MAXSTIR 1024.0L
+static long double SQTPI = 2.50662827463100050242E0L;
+
+/* 1/gamma(x) = z P(z)
+ * z(x) = 1/x
+ * 0 < x < 0.03125
+ * Peak relative error 4.2e-23
+ */
+#if UNK
+static long double S[9] = {
+-1.193945051381510095614E-3L,
+ 7.220599478036909672331E-3L,
+-9.622023360406271645744E-3L,
+-4.219773360705915470089E-2L,
+ 1.665386113720805206758E-1L,
+-4.200263503403344054473E-2L,
+-6.558780715202540684668E-1L,
+ 5.772156649015328608253E-1L,
+ 1.000000000000000000000E0L,
+};
+#endif
+#if IBMPC
+static short S[] = {
+0xbaeb,0xd6d3,0x25e5,0x9c7e,0xbff5, XPD
+0xfe9a,0xceb4,0xc74e,0xec9a,0x3ff7, XPD
+0x9225,0xdfef,0xb0e9,0x9da5,0xbff8, XPD
+0x10b0,0xec17,0x87dc,0xacd7,0xbffa, XPD
+0x6b8d,0x7515,0x1905,0xaa89,0x3ffc, XPD
+0xf183,0x126b,0xf47d,0xac0a,0xbffa, XPD
+0x7bf6,0x57d1,0xa013,0xa7e7,0xbffe, XPD
+0xc7a9,0x7db0,0x67e3,0x93c4,0x3ffe, XPD
+0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
+};
+#endif
+#if MIEEE
+static long S[27] = {
+0xbff50000,0x9c7e25e5,0xd6d3baeb,
+0x3ff70000,0xec9ac74e,0xceb4fe9a,
+0xbff80000,0x9da5b0e9,0xdfef9225,
+0xbffa0000,0xacd787dc,0xec1710b0,
+0x3ffc0000,0xaa891905,0x75156b8d,
+0xbffa0000,0xac0af47d,0x126bf183,
+0xbffe0000,0xa7e7a013,0x57d17bf6,
+0x3ffe0000,0x93c467e3,0x7db0c7a9,
+0x3fff0000,0x80000000,0x00000000,
+};
+#endif
+/* 1/gamma(-x) = z P(z)
+ * z(x) = 1/x
+ * 0 < x < 0.03125
+ * Peak relative error 5.16e-23
+ * Relative error spread = 2.5e-24
+ */
+#if UNK
+static long double SN[9] = {
+ 1.133374167243894382010E-3L,
+ 7.220837261893170325704E-3L,
+ 9.621911155035976733706E-3L,
+-4.219773343731191721664E-2L,
+-1.665386113944413519335E-1L,
+-4.200263503402112910504E-2L,
+ 6.558780715202536547116E-1L,
+ 5.772156649015328608727E-1L,
+-1.000000000000000000000E0L,
+};
+#endif
+#if IBMPC
+static short SN[] = {
+0x5dd1,0x02de,0xb9f7,0x948d,0x3ff5, XPD
+0x989b,0xdd68,0xc5f1,0xec9c,0x3ff7, XPD
+0x2ca1,0x18f0,0x386f,0x9da5,0x3ff8, XPD
+0x783f,0x41dd,0x87d1,0xacd7,0xbffa, XPD
+0x7a5b,0xd76d,0x1905,0xaa89,0xbffc, XPD
+0x7f64,0x1234,0xf47d,0xac0a,0xbffa, XPD
+0x5e26,0x57d1,0xa013,0xa7e7,0x3ffe, XPD
+0xc7aa,0x7db0,0x67e3,0x93c4,0x3ffe, XPD
+0x0000,0x0000,0x0000,0x8000,0xbfff, XPD
+};
+#endif
+#if MIEEE
+static long SN[27] = {
+0x3ff50000,0x948db9f7,0x02de5dd1,
+0x3ff70000,0xec9cc5f1,0xdd68989b,
+0x3ff80000,0x9da5386f,0x18f02ca1,
+0xbffa0000,0xacd787d1,0x41dd783f,
+0xbffc0000,0xaa891905,0xd76d7a5b,
+0xbffa0000,0xac0af47d,0x12347f64,
+0x3ffe0000,0xa7e7a013,0x57d15e26,
+0x3ffe0000,0x93c467e3,0x7db0c7aa,
+0xbfff0000,0x80000000,0x00000000,
+};
+#endif
+
+int sgngaml = 0;
+extern int sgngaml;
+extern long double MAXLOGL, MAXNUML, PIL;
+/* #define PIL 3.14159265358979323846L */
+/* #define MAXNUML 1.189731495357231765021263853E4932L */
+
+#ifdef ANSIPROT
+extern long double fabsl ( long double );
+extern long double lgaml ( long double );
+extern long double logl ( long double );
+extern long double expl ( long double );
+extern long double gammal ( long double );
+extern long double sinl ( long double );
+extern long double floorl ( long double );
+extern long double powl ( long double, long double );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern int isnanl ( long double );
+extern int isfinitel ( long double );
+static long double stirf ( long double );
+#else
+long double fabsl(), lgaml(), logl(), expl(), gammal(), sinl();
+long double floorl(), powl(), polevll(), p1evll(), isnanl(), isfinitel();
+static long double stirf();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+#ifdef NANS
+extern long double NANL;
+#endif
+
+/* Gamma function computed by Stirling's formula.
+ */
+static long double stirf(x)
+long double x;
+{
+long double y, w, v;
+
+w = 1.0L/x;
+/* For large x, use rational coefficients from the analytical expansion. */
+if( x > 1024.0L )
+ w = (((((6.97281375836585777429E-5L * w
+ + 7.84039221720066627474E-4L) * w
+ - 2.29472093621399176955E-4L) * w
+ - 2.68132716049382716049E-3L) * w
+ + 3.47222222222222222222E-3L) * w
+ + 8.33333333333333333333E-2L) * w
+ + 1.0L;
+else
+ w = 1.0L + w * polevll( w, STIR, 8 );
+y = expl(x);
+if( x > MAXSTIR )
+ { /* Avoid overflow in pow() */
+ v = powl( x, 0.5L * x - 0.25L );
+ y = v * (v / y);
+ }
+else
+ {
+ y = powl( x, x - 0.5L ) / y;
+ }
+y = SQTPI * y * w;
+return( y );
+}
+
+
+
+long double gammal(x)
+long double x;
+{
+long double p, q, z;
+int i;
+
+sgngaml = 1;
+#ifdef NANS
+if( isnanl(x) )
+ return(NANL);
+#endif
+#ifdef INFINITIES
+if(x == INFINITYL)
+ return(INFINITYL);
+#ifdef NANS
+if(x == -INFINITYL)
+ goto gamnan;
+#endif
+#endif
+q = fabsl(x);
+
+if( q > 13.0L )
+ {
+ if( q > MAXGAML )
+ goto goverf;
+ if( x < 0.0L )
+ {
+ p = floorl(q);
+ if( p == q )
+ {
+gamnan:
+#ifdef NANS
+ mtherr( "gammal", DOMAIN );
+ return (NANL);
+#else
+ goto goverf;
+#endif
+ }
+ i = p;
+ if( (i & 1) == 0 )
+ sgngaml = -1;
+ z = q - p;
+ if( z > 0.5L )
+ {
+ p += 1.0L;
+ z = q - p;
+ }
+ z = q * sinl( PIL * z );
+ z = fabsl(z) * stirf(q);
+ if( z <= PIL/MAXNUML )
+ {
+goverf:
+#ifdef INFINITIES
+ return( sgngaml * INFINITYL);
+#else
+ mtherr( "gammal", OVERFLOW );
+ return( sgngaml * MAXNUML);
+#endif
+ }
+ z = PIL/z;
+ }
+ else
+ {
+ z = stirf(x);
+ }
+ return( sgngaml * z );
+ }
+
+z = 1.0L;
+while( x >= 3.0L )
+ {
+ x -= 1.0L;
+ z *= x;
+ }
+
+while( x < -0.03125L )
+ {
+ z /= x;
+ x += 1.0L;
+ }
+
+if( x <= 0.03125L )
+ goto small;
+
+while( x < 2.0L )
+ {
+ z /= x;
+ x += 1.0L;
+ }
+
+if( x == 2.0L )
+ return(z);
+
+x -= 2.0L;
+p = polevll( x, P, 7 );
+q = polevll( x, Q, 8 );
+return( z * p / q );
+
+small:
+if( x == 0.0L )
+ {
+ goto gamnan;
+ }
+else
+ {
+ if( x < 0.0L )
+ {
+ x = -x;
+ q = z / (x * polevll( x, SN, 8 ));
+ }
+ else
+ q = z / (x * polevll( x, S, 8 ));
+ }
+return q;
+}
+
+
+
+/* A[]: Stirling's formula expansion of log gamma
+ * B[], C[]: log gamma function between 2 and 3
+ */
+
+
+/* log gamma(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x A(1/x^2)
+ * x >= 8
+ * Peak relative error 1.51e-21
+ * Relative spread of error peaks 5.67e-21
+ */
+#if UNK
+static long double A[7] = {
+ 4.885026142432270781165E-3L,
+-1.880801938119376907179E-3L,
+ 8.412723297322498080632E-4L,
+-5.952345851765688514613E-4L,
+ 7.936507795855070755671E-4L,
+-2.777777777750349603440E-3L,
+ 8.333333333333331447505E-2L,
+};
+#endif
+#if IBMPC
+static short A[] = {
+0xd984,0xcc08,0x91c2,0xa012,0x3ff7, XPD
+0x3d91,0x0304,0x3da1,0xf685,0xbff5, XPD
+0x3bdc,0xaad1,0xd492,0xdc88,0x3ff4, XPD
+0x8b20,0x9fce,0x844e,0x9c09,0xbff4, XPD
+0xf8f2,0x30e5,0x0092,0xd00d,0x3ff4, XPD
+0x4d88,0x03a8,0x60b6,0xb60b,0xbff6, XPD
+0x9fcc,0xaaaa,0xaaaa,0xaaaa,0x3ffb, XPD
+};
+#endif
+#if MIEEE
+static long A[21] = {
+0x3ff70000,0xa01291c2,0xcc08d984,
+0xbff50000,0xf6853da1,0x03043d91,
+0x3ff40000,0xdc88d492,0xaad13bdc,
+0xbff40000,0x9c09844e,0x9fce8b20,
+0x3ff40000,0xd00d0092,0x30e5f8f2,
+0xbff60000,0xb60b60b6,0x03a84d88,
+0x3ffb0000,0xaaaaaaaa,0xaaaa9fcc,
+};
+#endif
+
+/* log gamma(x+2) = x B(x)/C(x)
+ * 0 <= x <= 1
+ * Peak relative error 7.16e-22
+ * Relative spread of error peaks 4.78e-20
+ */
+#if UNK
+static long double B[7] = {
+-2.163690827643812857640E3L,
+-8.723871522843511459790E4L,
+-1.104326814691464261197E6L,
+-6.111225012005214299996E6L,
+-1.625568062543700591014E7L,
+-2.003937418103815175475E7L,
+-8.875666783650703802159E6L,
+};
+static long double C[7] = {
+/* 1.000000000000000000000E0L,*/
+-5.139481484435370143617E2L,
+-3.403570840534304670537E4L,
+-6.227441164066219501697E5L,
+-4.814940379411882186630E6L,
+-1.785433287045078156959E7L,
+-3.138646407656182662088E7L,
+-2.099336717757895876142E7L,
+};
+#endif
+#if IBMPC
+static short B[] = {
+0x9557,0x4995,0x0da1,0x873b,0xc00a, XPD
+0xfe44,0x9af8,0x5b8c,0xaa63,0xc00f, XPD
+0x5aa8,0x7cf5,0x3684,0x86ce,0xc013, XPD
+0x259a,0x258c,0xf206,0xba7f,0xc015, XPD
+0xbe18,0x1ca3,0xc0a0,0xf80a,0xc016, XPD
+0x168f,0x2c42,0x6717,0x98e3,0xc017, XPD
+0x2051,0x9d55,0x92c8,0x876e,0xc016, XPD
+};
+static short C[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
+0xaa77,0xcf2f,0xae76,0x807c,0xc008, XPD
+0xb280,0x0d74,0xb55a,0x84f3,0xc00e, XPD
+0xa505,0xcd30,0x81dc,0x9809,0xc012, XPD
+0x3369,0x4246,0xb8c2,0x92f0,0xc015, XPD
+0x63cf,0x6aee,0xbe6f,0x8837,0xc017, XPD
+0x26bb,0xccc7,0xb009,0xef75,0xc017, XPD
+0x462b,0xbae8,0xab96,0xa02a,0xc017, XPD
+};
+#endif
+#if MIEEE
+static long B[21] = {
+0xc00a0000,0x873b0da1,0x49959557,
+0xc00f0000,0xaa635b8c,0x9af8fe44,
+0xc0130000,0x86ce3684,0x7cf55aa8,
+0xc0150000,0xba7ff206,0x258c259a,
+0xc0160000,0xf80ac0a0,0x1ca3be18,
+0xc0170000,0x98e36717,0x2c42168f,
+0xc0160000,0x876e92c8,0x9d552051,
+};
+static long C[21] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0xc0080000,0x807cae76,0xcf2faa77,
+0xc00e0000,0x84f3b55a,0x0d74b280,
+0xc0120000,0x980981dc,0xcd30a505,
+0xc0150000,0x92f0b8c2,0x42463369,
+0xc0170000,0x8837be6f,0x6aee63cf,
+0xc0170000,0xef75b009,0xccc726bb,
+0xc0170000,0xa02aab96,0xbae8462b,
+};
+#endif
+
+/* log( sqrt( 2*pi ) ) */
+static long double LS2PI = 0.91893853320467274178L;
+#define MAXLGM 1.04848146839019521116e+4928L
+
+
+/* Logarithm of gamma function */
+
+
+long double lgaml(x)
+long double x;
+{
+long double p, q, w, z, f, nx;
+int i;
+
+sgngaml = 1;
+#ifdef NANS
+if( isnanl(x) )
+ return(NANL);
+#endif
+#ifdef INFINITIES
+if( !isfinitel(x) )
+ return(INFINITYL);
+#endif
+if( x < -34.0L )
+ {
+ q = -x;
+ w = lgaml(q); /* note this modifies sgngam! */
+ p = floorl(q);
+ if( p == q )
+ {
+#ifdef INFINITIES
+ mtherr( "lgaml", SING );
+ return (INFINITYL);
+#else
+ goto loverf;
+#endif
+ }
+ i = p;
+ if( (i & 1) == 0 )
+ sgngaml = -1;
+ else
+ sgngaml = 1;
+ z = q - p;
+ if( z > 0.5L )
+ {
+ p += 1.0L;
+ z = p - q;
+ }
+ z = q * sinl( PIL * z );
+ if( z == 0.0L )
+ goto loverf;
+/* z = LOGPI - logl( z ) - w; */
+ z = logl( PIL/z ) - w;
+ return( z );
+ }
+
+if( x < 13.0L )
+ {
+ z = 1.0L;
+ nx = floorl( x + 0.5L );
+ f = x - nx;
+ while( x >= 3.0L )
+ {
+ nx -= 1.0L;
+ x = nx + f;
+ z *= x;
+ }
+ while( x < 2.0L )
+ {
+ if( fabsl(x) <= 0.03125 )
+ goto lsmall;
+ z /= nx + f;
+ nx += 1.0L;
+ x = nx + f;
+ }
+ if( z < 0.0L )
+ {
+ sgngaml = -1;
+ z = -z;
+ }
+ else
+ sgngaml = 1;
+ if( x == 2.0L )
+ return( logl(z) );
+ x = (nx - 2.0L) + f;
+ p = x * polevll( x, B, 6 ) / p1evll( x, C, 7);
+ return( logl(z) + p );
+ }
+
+if( x > MAXLGM )
+ {
+loverf:
+#ifdef INFINITIES
+ return( sgngaml * INFINITYL );
+#else
+ mtherr( "lgaml", OVERFLOW );
+ return( sgngaml * MAXNUML );
+#endif
+ }
+
+q = ( x - 0.5L ) * logl(x) - x + LS2PI;
+if( x > 1.0e10L )
+ return(q);
+p = 1.0L/(x*x);
+q += polevll( p, A, 6 ) / x;
+return( q );
+
+
+lsmall:
+if( x == 0.0L )
+ goto loverf;
+if( x < 0.0L )
+ {
+ x = -x;
+ q = z / (x * polevll( x, SN, 8 ));
+ }
+else
+ q = z / (x * polevll( x, S, 8 ));
+if( q < 0.0L )
+ {
+ sgngaml = -1;
+ q = -q;
+ }
+else
+ sgngaml = 1;
+q = logl( q );
+return(q);
+}
diff --git a/libm/ldouble/gdtrl.c b/libm/ldouble/gdtrl.c
new file mode 100644
index 000000000..9a41790cb
--- /dev/null
+++ b/libm/ldouble/gdtrl.c
@@ -0,0 +1,130 @@
+/* gdtrl.c
+ *
+ * Gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, b, x, y, gdtrl();
+ *
+ * y = gdtrl( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from zero to x of the gamma probability
+ * density function:
+ *
+ *
+ * x
+ * b -
+ * a | | b-1 -at
+ * y = ----- | t e dt
+ * - | |
+ * | (b) -
+ * 0
+ *
+ * The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igam( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * gdtrl domain x < 0 0.0
+ *
+ */
+ /* gdtrcl.c
+ *
+ * Complemented gamma distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, b, x, y, gdtrcl();
+ *
+ * y = gdtrcl( a, b, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the integral from x to infinity of the gamma
+ * probability density function:
+ *
+ *
+ * inf.
+ * b -
+ * a | | b-1 -at
+ * y = ----- | t e dt
+ * - | |
+ * | (b) -
+ * x
+ *
+ * The incomplete gamma integral is used, according to the
+ * relation
+ *
+ * y = igamc( b, ax ).
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * gdtrcl domain x < 0 0.0
+ *
+ */
+
+/* gdtrl() */
+
+
+/*
+Cephes Math Library Release 2.3: March, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double igaml ( long double, long double );
+extern long double igamcl ( long double, long double );
+#else
+long double igaml(), igamcl();
+#endif
+
+long double gdtrl( a, b, x )
+long double a, b, x;
+{
+
+if( x < 0.0L )
+ {
+ mtherr( "gdtrl", DOMAIN );
+ return( 0.0L );
+ }
+return( igaml( b, a * x ) );
+}
+
+
+
+long double gdtrcl( a, b, x )
+long double a, b, x;
+{
+
+if( x < 0.0L )
+ {
+ mtherr( "gdtrcl", DOMAIN );
+ return( 0.0L );
+ }
+return( igamcl( b, a * x ) );
+}
diff --git a/libm/ldouble/gelsl.c b/libm/ldouble/gelsl.c
new file mode 100644
index 000000000..d66ad55e9
--- /dev/null
+++ b/libm/ldouble/gelsl.c
@@ -0,0 +1,240 @@
+/*
+C
+C ..................................................................
+C
+C SUBROUTINE GELS
+C
+C PURPOSE
+C TO SOLVE A SYSTEM OF SIMULTANEOUS LINEAR EQUATIONS WITH
+C SYMMETRIC COEFFICIENT MATRIX UPPER TRIANGULAR PART OF WHICH
+C IS ASSUMED TO BE STORED COLUMNWISE.
+C
+C USAGE
+C CALL GELS(R,A,M,N,EPS,IER,AUX)
+C
+C DESCRIPTION OF PARAMETERS
+C R - M BY N RIGHT HAND SIDE MATRIX. (DESTROYED)
+C ON RETURN R CONTAINS THE SOLUTION OF THE EQUATIONS.
+C A - UPPER TRIANGULAR PART OF THE SYMMETRIC
+C M BY M COEFFICIENT MATRIX. (DESTROYED)
+C M - THE NUMBER OF EQUATIONS IN THE SYSTEM.
+C N - THE NUMBER OF RIGHT HAND SIDE VECTORS.
+C EPS - AN INPUT CONSTANT WHICH IS USED AS RELATIVE
+C TOLERANCE FOR TEST ON LOSS OF SIGNIFICANCE.
+C IER - RESULTING ERROR PARAMETER CODED AS FOLLOWS
+C IER=0 - NO ERROR,
+C IER=-1 - NO RESULT BECAUSE OF M LESS THAN 1 OR
+C PIVOT ELEMENT AT ANY ELIMINATION STEP
+C EQUAL TO 0,
+C IER=K - WARNING DUE TO POSSIBLE LOSS OF SIGNIFI-
+C CANCE INDICATED AT ELIMINATION STEP K+1,
+C WHERE PIVOT ELEMENT WAS LESS THAN OR
+C EQUAL TO THE INTERNAL TOLERANCE EPS TIMES
+C ABSOLUTELY GREATEST MAIN DIAGONAL
+C ELEMENT OF MATRIX A.
+C AUX - AN AUXILIARY STORAGE ARRAY WITH DIMENSION M-1.
+C
+C REMARKS
+C UPPER TRIANGULAR PART OF MATRIX A IS ASSUMED TO BE STORED
+C COLUMNWISE IN M*(M+1)/2 SUCCESSIVE STORAGE LOCATIONS, RIGHT
+C HAND SIDE MATRIX R COLUMNWISE IN N*M SUCCESSIVE STORAGE
+C LOCATIONS. ON RETURN SOLUTION MATRIX R IS STORED COLUMNWISE
+C TOO.
+C THE PROCEDURE GIVES RESULTS IF THE NUMBER OF EQUATIONS M IS
+C GREATER THAN 0 AND PIVOT ELEMENTS AT ALL ELIMINATION STEPS
+C ARE DIFFERENT FROM 0. HOWEVER WARNING IER=K - IF GIVEN -
+C INDICATES POSSIBLE LOSS OF SIGNIFICANCE. IN CASE OF A WELL
+C SCALED MATRIX A AND APPROPRIATE TOLERANCE EPS, IER=K MAY BE
+C INTERPRETED THAT MATRIX A HAS THE RANK K. NO WARNING IS
+C GIVEN IN CASE M=1.
+C ERROR PARAMETER IER=-1 DOES NOT NECESSARILY MEAN THAT
+C MATRIX A IS SINGULAR, AS ONLY MAIN DIAGONAL ELEMENTS
+C ARE USED AS PIVOT ELEMENTS. POSSIBLY SUBROUTINE GELG (WHICH
+C WORKS WITH TOTAL PIVOTING) WOULD BE ABLE TO FIND A SOLUTION.
+C
+C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
+C NONE
+C
+C METHOD
+C SOLUTION IS DONE BY MEANS OF GAUSS-ELIMINATION WITH
+C PIVOTING IN MAIN DIAGONAL, IN ORDER TO PRESERVE
+C SYMMETRY IN REMAINING COEFFICIENT MATRICES.
+C
+C ..................................................................
+C
+*/
+
+#include <stdio.h>
+#define fabsl(x) ( (x) < 0.0L ? -(x) : (x) )
+
+int gels( A, R, M, EPS, AUX )
+long double A[],R[];
+int M;
+long double EPS;
+long double AUX[];
+{
+int I, J, K, L, IER;
+int II, LL, LLD, LR, LT, LST, LLST, LEND;
+long double tb, piv, tol, pivi;
+
+IER = 0;
+if( M <= 0 )
+ {
+fatal:
+ IER = -1;
+ goto done;
+ }
+/* SEARCH FOR GREATEST MAIN DIAGONAL ELEMENT */
+
+/* Diagonal elements are at A(i,i) = 0, 2, 5, 9, 14, ...
+ * A(i,j) = A( i(i-1)/2 + j - 1 )
+ */
+piv = 0.0L;
+I = 0;
+J = 0;
+L = 0;
+for( K=1; K<=M; K++ )
+ {
+ L += K;
+ tb = fabsl( A[L-1] );
+ if( tb > piv )
+ {
+ piv = tb;
+ I = L;
+ J = K;
+ }
+ }
+tol = EPS * piv;
+
+/*
+C MAIN DIAGONAL ELEMENT A(I)=A(J,J) IS FIRST PIVOT ELEMENT.
+C PIV CONTAINS THE ABSOLUTE VALUE OF A(I).
+*/
+
+/* START ELIMINATION LOOP */
+LST = 0;
+LEND = M - 1;
+for( K=1; K<=M; K++ )
+ {
+/* TEST ON USEFULNESS OF SYMMETRIC ALGORITHM */
+ if( piv <= 0.0L )
+ {
+ printf( "gels: piv <= 0 at K = %d\n", K );
+ goto fatal;
+ }
+ if( IER == 0 )
+ {
+ if( piv <= tol )
+ {
+ IER = K;
+/*
+ goto done;
+*/
+ }
+ }
+ LT = J - K;
+ LST += K;
+
+/* PIVOT ROW REDUCTION AND ROW INTERCHANGE IN RIGHT HAND SIDE R */
+ pivi = 1.0L / A[I-1];
+ L = K;
+ LL = L + LT;
+ tb = pivi * R[LL-1];
+ R[LL-1] = R[L-1];
+ R[L-1] = tb;
+/* IS ELIMINATION TERMINATED */
+ if( K >= M )
+ break;
+/*
+C ROW AND COLUMN INTERCHANGE AND PIVOT ROW REDUCTION IN MATRIX A.
+C ELEMENTS OF PIVOT COLUMN ARE SAVED IN AUXILIARY VECTOR AUX.
+*/
+ LR = LST + (LT*(K+J-1))/2;
+ LL = LR;
+ L=LST;
+ for( II=K; II<=LEND; II++ )
+ {
+ L += II;
+ LL += 1;
+ if( L == LR )
+ {
+ A[LL-1] = A[LST-1];
+ tb = A[L-1];
+ goto lab13;
+ }
+ if( L > LR )
+ LL = L + LT;
+
+ tb = A[LL-1];
+ A[LL-1] = A[L-1];
+lab13:
+ AUX[II-1] = tb;
+ A[L-1] = pivi * tb;
+ }
+/* SAVE COLUMN INTERCHANGE INFORMATION */
+ A[LST-1] = LT;
+/* ELEMENT REDUCTION AND SEARCH FOR NEXT PIVOT */
+ piv = 0.0L;
+ LLST = LST;
+ LT = 0;
+ for( II=K; II<=LEND; II++ )
+ {
+ pivi = -AUX[II-1];
+ LL = LLST;
+ LT += 1;
+ for( LLD=II; LLD<=LEND; LLD++ )
+ {
+ LL += LLD;
+ L = LL + LT;
+ A[L-1] += pivi * A[LL-1];
+ }
+ LLST += II;
+ LR = LLST + LT;
+ tb =fabsl( A[LR-1] );
+ if( tb > piv )
+ {
+ piv = tb;
+ I = LR;
+ J = II + 1;
+ }
+ LR = K;
+ LL = LR + LT;
+ R[LL-1] += pivi * R[LR-1];
+ }
+ }
+/* END OF ELIMINATION LOOP */
+
+/* BACK SUBSTITUTION AND BACK INTERCHANGE */
+
+if( LEND <= 0 )
+ {
+ printf( "gels: LEND = %d\n", LEND );
+ if( LEND < 0 )
+ goto fatal;
+ goto done;
+ }
+II = M;
+for( I=2; I<=M; I++ )
+ {
+ LST -= II;
+ II -= 1;
+ L = A[LST-1] + 0.5L;
+ J = II;
+ tb = R[J-1];
+ LL = J;
+ K = LST;
+ for( LT=II; LT<=LEND; LT++ )
+ {
+ LL += 1;
+ K += LT;
+ tb -= A[K-1] * R[LL-1];
+ }
+ K = J + L;
+ R[J-1] = R[K-1];
+ R[K-1] = tb;
+ }
+done:
+if( IER )
+ printf( "gels error %d!\n", IER );
+return( IER );
+}
diff --git a/libm/ldouble/ieee.c b/libm/ldouble/ieee.c
new file mode 100644
index 000000000..584329b0c
--- /dev/null
+++ b/libm/ldouble/ieee.c
@@ -0,0 +1,4182 @@
+/* ieee.c
+ *
+ * Extended precision IEEE binary floating point arithmetic routines
+ *
+ * Numbers are stored in C language as arrays of 16-bit unsigned
+ * short integers. The arguments of the routines are pointers to
+ * the arrays.
+ *
+ *
+ * External e type data structure, simulates Intel 8087 chip
+ * temporary real format but possibly with a larger significand:
+ *
+ * NE-1 significand words (least significant word first,
+ * most significant bit is normally set)
+ * exponent (value = EXONE for 1.0,
+ * top bit is the sign)
+ *
+ *
+ * Internal data structure of a number (a "word" is 16 bits):
+ *
+ * ei[0] sign word (0 for positive, 0xffff for negative)
+ * ei[1] biased exponent (value = EXONE for the number 1.0)
+ * ei[2] high guard word (always zero after normalization)
+ * ei[3]
+ * to ei[NI-2] significand (NI-4 significand words,
+ * most significant word first,
+ * most significant bit is set)
+ * ei[NI-1] low guard word (0x8000 bit is rounding place)
+ *
+ *
+ *
+ * Routines for external format numbers
+ *
+ * asctoe( string, e ) ASCII string to extended double e type
+ * asctoe64( string, &d ) ASCII string to long double
+ * asctoe53( string, &d ) ASCII string to double
+ * asctoe24( string, &f ) ASCII string to single
+ * asctoeg( string, e, prec ) ASCII string to specified precision
+ * e24toe( &f, e ) IEEE single precision to e type
+ * e53toe( &d, e ) IEEE double precision to e type
+ * e64toe( &d, e ) IEEE long double precision to e type
+ * eabs(e) absolute value
+ * eadd( a, b, c ) c = b + a
+ * eclear(e) e = 0
+ * ecmp (a, b) Returns 1 if a > b, 0 if a == b,
+ * -1 if a < b, -2 if either a or b is a NaN.
+ * ediv( a, b, c ) c = b / a
+ * efloor( a, b ) truncate to integer, toward -infinity
+ * efrexp( a, exp, s ) extract exponent and significand
+ * eifrac( e, &l, frac ) e to long integer and e type fraction
+ * euifrac( e, &l, frac ) e to unsigned long integer and e type fraction
+ * einfin( e ) set e to infinity, leaving its sign alone
+ * eldexp( a, n, b ) multiply by 2**n
+ * emov( a, b ) b = a
+ * emul( a, b, c ) c = b * a
+ * eneg(e) e = -e
+ * eround( a, b ) b = nearest integer value to a
+ * esub( a, b, c ) c = b - a
+ * e24toasc( &f, str, n ) single to ASCII string, n digits after decimal
+ * e53toasc( &d, str, n ) double to ASCII string, n digits after decimal
+ * e64toasc( &d, str, n ) long double to ASCII string
+ * etoasc( e, str, n ) e to ASCII string, n digits after decimal
+ * etoe24( e, &f ) convert e type to IEEE single precision
+ * etoe53( e, &d ) convert e type to IEEE double precision
+ * etoe64( e, &d ) convert e type to IEEE long double precision
+ * ltoe( &l, e ) long (32 bit) integer to e type
+ * ultoe( &l, e ) unsigned long (32 bit) integer to e type
+ * eisneg( e ) 1 if sign bit of e != 0, else 0
+ * eisinf( e ) 1 if e has maximum exponent (non-IEEE)
+ * or is infinite (IEEE)
+ * eisnan( e ) 1 if e is a NaN
+ * esqrt( a, b ) b = square root of a
+ *
+ *
+ * Routines for internal format numbers
+ *
+ * eaddm( ai, bi ) add significands, bi = bi + ai
+ * ecleaz(ei) ei = 0
+ * ecleazs(ei) set ei = 0 but leave its sign alone
+ * ecmpm( ai, bi ) compare significands, return 1, 0, or -1
+ * edivm( ai, bi ) divide significands, bi = bi / ai
+ * emdnorm(ai,l,s,exp) normalize and round off
+ * emovi( a, ai ) convert external a to internal ai
+ * emovo( ai, a ) convert internal ai to external a
+ * emovz( ai, bi ) bi = ai, low guard word of bi = 0
+ * emulm( ai, bi ) multiply significands, bi = bi * ai
+ * enormlz(ei) left-justify the significand
+ * eshdn1( ai ) shift significand and guards down 1 bit
+ * eshdn8( ai ) shift down 8 bits
+ * eshdn6( ai ) shift down 16 bits
+ * eshift( ai, n ) shift ai n bits up (or down if n < 0)
+ * eshup1( ai ) shift significand and guards up 1 bit
+ * eshup8( ai ) shift up 8 bits
+ * eshup6( ai ) shift up 16 bits
+ * esubm( ai, bi ) subtract significands, bi = bi - ai
+ *
+ *
+ * The result is always normalized and rounded to NI-4 word precision
+ * after each arithmetic operation.
+ *
+ * Exception flags are NOT fully supported.
+ *
+ * Define INFINITY in mconf.h for support of infinity; otherwise a
+ * saturation arithmetic is implemented.
+ *
+ * Define NANS for support of Not-a-Number items; otherwise the
+ * arithmetic will never produce a NaN output, and might be confused
+ * by a NaN input.
+ * If NaN's are supported, the output of ecmp(a,b) is -2 if
+ * either a or b is a NaN. This means asking if(ecmp(a,b) < 0)
+ * may not be legitimate. Use if(ecmp(a,b) == -1) for less-than
+ * if in doubt.
+ * Signaling NaN's are NOT supported; they are treated the same
+ * as quiet NaN's.
+ *
+ * Denormals are always supported here where appropriate (e.g., not
+ * for conversion to DEC numbers).
+ */
+
+/*
+ * Revision history:
+ *
+ * 5 Jan 84 PDP-11 assembly language version
+ * 2 Mar 86 fixed bug in asctoq()
+ * 6 Dec 86 C language version
+ * 30 Aug 88 100 digit version, improved rounding
+ * 15 May 92 80-bit long double support
+ *
+ * Author: S. L. Moshier.
+ */
+
+#include <stdio.h>
+#include <math.h>
+#include "ehead.h"
+
+/* Change UNK into something else. */
+#ifdef UNK
+#undef UNK
+#if BIGENDIAN
+#define MIEEE 1
+#else
+#define IBMPC 1
+#endif
+#endif
+
+/* NaN's require infinity support. */
+#ifdef NANS
+#ifndef INFINITY
+#define INFINITY
+#endif
+#endif
+
+/* This handles 64-bit long ints. */
+#define LONGBITS (8 * sizeof(long))
+
+/* Control register for rounding precision.
+ * This can be set to 80 (if NE=6), 64, 56, 53, or 24 bits.
+ */
+int rndprc = NBITS;
+extern int rndprc;
+
+#ifdef ANSIPROT
+extern void eaddm ( unsigned short *, unsigned short * );
+extern void esubm ( unsigned short *, unsigned short * );
+extern void emdnorm ( unsigned short *, int, int, long, int );
+extern void asctoeg ( char *, unsigned short *, int );
+extern void enan ( unsigned short *, int );
+extern void asctoe24 ( char *, unsigned short * );
+extern void asctoe53 ( char *, unsigned short * );
+extern void asctoe64 ( char *, unsigned short * );
+extern void asctoe113 ( char *, unsigned short * );
+extern void eremain ( unsigned short *, unsigned short *, unsigned short * );
+extern void einit ( void );
+extern void eiremain ( unsigned short *, unsigned short * );
+extern int ecmp ( unsigned short *, unsigned short * );
+extern int edivm ( unsigned short *, unsigned short * );
+extern int emulm ( unsigned short *, unsigned short * );
+extern int eisneg ( unsigned short * );
+extern int eisinf ( unsigned short * );
+extern void emovi ( unsigned short *, unsigned short * );
+extern void emovo ( unsigned short *, unsigned short * );
+extern void emovz ( unsigned short *, unsigned short * );
+extern void ecleaz ( unsigned short * );
+extern void eadd1 ( unsigned short *, unsigned short *, unsigned short * );
+extern int eisnan ( unsigned short * );
+extern int eiisnan ( unsigned short * );
+static void toe24( unsigned short *, unsigned short * );
+static void toe53( unsigned short *, unsigned short * );
+static void toe64( unsigned short *, unsigned short * );
+static void toe113( unsigned short *, unsigned short * );
+void einfin ( unsigned short * );
+void eshdn1 ( unsigned short * );
+void eshup1 ( unsigned short * );
+void eshup6 ( unsigned short * );
+void eshdn6 ( unsigned short * );
+void eshup8 ( unsigned short * );
+void eshdn8 ( unsigned short * );
+void m16m ( unsigned short, unsigned short *, unsigned short * );
+int ecmpm ( unsigned short *, unsigned short * );
+int enormlz ( unsigned short * );
+void ecleazs ( unsigned short * );
+int eshift ( unsigned short *, int );
+void emov ( unsigned short *, unsigned short * );
+void eneg ( unsigned short * );
+void eclear ( unsigned short * );
+void efloor ( unsigned short *, unsigned short * );
+void eadd ( unsigned short *, unsigned short *, unsigned short * );
+void esub ( unsigned short *, unsigned short *, unsigned short * );
+void ediv ( unsigned short *, unsigned short *, unsigned short * );
+void emul ( unsigned short *, unsigned short *, unsigned short * );
+void e24toe ( unsigned short *, unsigned short * );
+void e53toe ( unsigned short *, unsigned short * );
+void e64toe ( unsigned short *, unsigned short * );
+void e113toe ( unsigned short *, unsigned short * );
+void etoasc ( unsigned short *, char *, int );
+static int eiisinf ( unsigned short * );
+#else
+void eaddm(), esubm(), emdnorm(), asctoeg(), enan();
+static void toe24(), toe53(), toe64(), toe113();
+void eremain(), einit(), eiremain();
+int ecmpm(), edivm(), emulm(), eisneg(), eisinf();
+void emovi(), emovo(), emovz(), ecleaz(), eadd1();
+/* void etodec(), todec(), dectoe(); */
+int eisnan(), eiisnan(), ecmpm(), enormlz(), eshift();
+void einfin(), eshdn1(), eshup1(), eshup6(), eshdn6();
+void eshup8(), eshdn8(), m16m();
+void eadd(), esub(), ediv(), emul();
+void ecleazs(), emov(), eneg(), eclear(), efloor();
+void e24toe(), e53toe(), e64toe(), e113toe(), etoasc();
+static int eiisinf();
+#endif
+
+
+void einit()
+{
+}
+
+/*
+; Clear out entire external format number.
+;
+; unsigned short x[];
+; eclear( x );
+*/
+
+void eclear( x )
+register unsigned short *x;
+{
+register int i;
+
+for( i=0; i<NE; i++ )
+ *x++ = 0;
+}
+
+
+
+/* Move external format number from a to b.
+ *
+ * emov( a, b );
+ */
+
+void emov( a, b )
+register unsigned short *a, *b;
+{
+register int i;
+
+for( i=0; i<NE; i++ )
+ *b++ = *a++;
+}
+
+
+/*
+; Absolute value of external format number
+;
+; short x[NE];
+; eabs( x );
+*/
+
+void eabs(x)
+unsigned short x[]; /* x is the memory address of a short */
+{
+
+x[NE-1] &= 0x7fff; /* sign is top bit of last word of external format */
+}
+
+
+
+
+/*
+; Negate external format number
+;
+; unsigned short x[NE];
+; eneg( x );
+*/
+
+void eneg(x)
+unsigned short x[];
+{
+
+#ifdef NANS
+if( eisnan(x) )
+ return;
+#endif
+x[NE-1] ^= 0x8000; /* Toggle the sign bit */
+}
+
+
+
+/* Return 1 if external format number is negative,
+ * else return zero.
+ */
+int eisneg(x)
+unsigned short x[];
+{
+
+#ifdef NANS
+if( eisnan(x) )
+ return( 0 );
+#endif
+if( x[NE-1] & 0x8000 )
+ return( 1 );
+else
+ return( 0 );
+}
+
+
+/* Return 1 if external format number has maximum possible exponent,
+ * else return zero.
+ */
+int eisinf(x)
+unsigned short x[];
+{
+
+if( (x[NE-1] & 0x7fff) == 0x7fff )
+ {
+#ifdef NANS
+ if( eisnan(x) )
+ return( 0 );
+#endif
+ return( 1 );
+ }
+else
+ return( 0 );
+}
+
+/* Check if e-type number is not a number.
+ */
+int eisnan(x)
+unsigned short x[];
+{
+
+#ifdef NANS
+int i;
+/* NaN has maximum exponent */
+if( (x[NE-1] & 0x7fff) != 0x7fff )
+ return (0);
+/* ... and non-zero significand field. */
+for( i=0; i<NE-1; i++ )
+ {
+ if( *x++ != 0 )
+ return (1);
+ }
+#endif
+return (0);
+}
+
+/*
+; Fill entire number, including exponent and significand, with
+; largest possible number. These programs implement a saturation
+; value that is an ordinary, legal number. A special value
+; "infinity" may also be implemented; this would require tests
+; for that value and implementation of special rules for arithmetic
+; operations involving inifinity.
+*/
+
+void einfin(x)
+register unsigned short *x;
+{
+register int i;
+
+#ifdef INFINITY
+for( i=0; i<NE-1; i++ )
+ *x++ = 0;
+*x |= 32767;
+#else
+for( i=0; i<NE-1; i++ )
+ *x++ = 0xffff;
+*x |= 32766;
+if( rndprc < NBITS )
+ {
+ if (rndprc == 113)
+ {
+ *(x - 9) = 0;
+ *(x - 8) = 0;
+ }
+ if( rndprc == 64 )
+ {
+ *(x-5) = 0;
+ }
+ if( rndprc == 53 )
+ {
+ *(x-4) = 0xf800;
+ }
+ else
+ {
+ *(x-4) = 0;
+ *(x-3) = 0;
+ *(x-2) = 0xff00;
+ }
+ }
+#endif
+}
+
+
+
+/* Move in external format number,
+ * converting it to internal format.
+ */
+void emovi( a, b )
+unsigned short *a, *b;
+{
+register unsigned short *p, *q;
+int i;
+
+q = b;
+p = a + (NE-1); /* point to last word of external number */
+/* get the sign bit */
+if( *p & 0x8000 )
+ *q++ = 0xffff;
+else
+ *q++ = 0;
+/* get the exponent */
+*q = *p--;
+*q++ &= 0x7fff; /* delete the sign bit */
+#ifdef INFINITY
+if( (*(q-1) & 0x7fff) == 0x7fff )
+ {
+#ifdef NANS
+ if( eisnan(a) )
+ {
+ *q++ = 0;
+ for( i=3; i<NI; i++ )
+ *q++ = *p--;
+ return;
+ }
+#endif
+ for( i=2; i<NI; i++ )
+ *q++ = 0;
+ return;
+ }
+#endif
+/* clear high guard word */
+*q++ = 0;
+/* move in the significand */
+for( i=0; i<NE-1; i++ )
+ *q++ = *p--;
+/* clear low guard word */
+*q = 0;
+}
+
+
+/* Move internal format number out,
+ * converting it to external format.
+ */
+void emovo( a, b )
+unsigned short *a, *b;
+{
+register unsigned short *p, *q;
+unsigned short i;
+
+p = a;
+q = b + (NE-1); /* point to output exponent */
+/* combine sign and exponent */
+i = *p++;
+if( i )
+ *q-- = *p++ | 0x8000;
+else
+ *q-- = *p++;
+#ifdef INFINITY
+if( *(p-1) == 0x7fff )
+ {
+#ifdef NANS
+ if( eiisnan(a) )
+ {
+ enan( b, NBITS );
+ return;
+ }
+#endif
+ einfin(b);
+ return;
+ }
+#endif
+/* skip over guard word */
+++p;
+/* move the significand */
+for( i=0; i<NE-1; i++ )
+ *q-- = *p++;
+}
+
+
+
+
+/* Clear out internal format number.
+ */
+
+void ecleaz( xi )
+register unsigned short *xi;
+{
+register int i;
+
+for( i=0; i<NI; i++ )
+ *xi++ = 0;
+}
+
+/* same, but don't touch the sign. */
+
+void ecleazs( xi )
+register unsigned short *xi;
+{
+register int i;
+
+++xi;
+for(i=0; i<NI-1; i++)
+ *xi++ = 0;
+}
+
+
+
+
+/* Move internal format number from a to b.
+ */
+void emovz( a, b )
+register unsigned short *a, *b;
+{
+register int i;
+
+for( i=0; i<NI-1; i++ )
+ *b++ = *a++;
+/* clear low guard word */
+*b = 0;
+}
+
+/* Return nonzero if internal format number is a NaN.
+ */
+
+int eiisnan (x)
+unsigned short x[];
+{
+int i;
+
+if( (x[E] & 0x7fff) == 0x7fff )
+ {
+ for( i=M+1; i<NI; i++ )
+ {
+ if( x[i] != 0 )
+ return(1);
+ }
+ }
+return(0);
+}
+
+#ifdef INFINITY
+/* Return nonzero if internal format number is infinite. */
+
+static int
+eiisinf (x)
+ unsigned short x[];
+{
+
+#ifdef NANS
+ if (eiisnan (x))
+ return (0);
+#endif
+ if ((x[E] & 0x7fff) == 0x7fff)
+ return (1);
+ return (0);
+}
+#endif
+
+/*
+; Compare significands of numbers in internal format.
+; Guard words are included in the comparison.
+;
+; unsigned short a[NI], b[NI];
+; cmpm( a, b );
+;
+; for the significands:
+; returns +1 if a > b
+; 0 if a == b
+; -1 if a < b
+*/
+int ecmpm( a, b )
+register unsigned short *a, *b;
+{
+int i;
+
+a += M; /* skip up to significand area */
+b += M;
+for( i=M; i<NI; i++ )
+ {
+ if( *a++ != *b++ )
+ goto difrnt;
+ }
+return(0);
+
+difrnt:
+if( *(--a) > *(--b) )
+ return(1);
+else
+ return(-1);
+}
+
+
+/*
+; Shift significand down by 1 bit
+*/
+
+void eshdn1(x)
+register unsigned short *x;
+{
+register unsigned short bits;
+int i;
+
+x += M; /* point to significand area */
+
+bits = 0;
+for( i=M; i<NI; i++ )
+ {
+ if( *x & 1 )
+ bits |= 1;
+ *x >>= 1;
+ if( bits & 2 )
+ *x |= 0x8000;
+ bits <<= 1;
+ ++x;
+ }
+}
+
+
+
+/*
+; Shift significand up by 1 bit
+*/
+
+void eshup1(x)
+register unsigned short *x;
+{
+register unsigned short bits;
+int i;
+
+x += NI-1;
+bits = 0;
+
+for( i=M; i<NI; i++ )
+ {
+ if( *x & 0x8000 )
+ bits |= 1;
+ *x <<= 1;
+ if( bits & 2 )
+ *x |= 1;
+ bits <<= 1;
+ --x;
+ }
+}
+
+
+
+/*
+; Shift significand down by 8 bits
+*/
+
+void eshdn8(x)
+register unsigned short *x;
+{
+register unsigned short newbyt, oldbyt;
+int i;
+
+x += M;
+oldbyt = 0;
+for( i=M; i<NI; i++ )
+ {
+ newbyt = *x << 8;
+ *x >>= 8;
+ *x |= oldbyt;
+ oldbyt = newbyt;
+ ++x;
+ }
+}
+
+/*
+; Shift significand up by 8 bits
+*/
+
+void eshup8(x)
+register unsigned short *x;
+{
+int i;
+register unsigned short newbyt, oldbyt;
+
+x += NI-1;
+oldbyt = 0;
+
+for( i=M; i<NI; i++ )
+ {
+ newbyt = *x >> 8;
+ *x <<= 8;
+ *x |= oldbyt;
+ oldbyt = newbyt;
+ --x;
+ }
+}
+
+/*
+; Shift significand up by 16 bits
+*/
+
+void eshup6(x)
+register unsigned short *x;
+{
+int i;
+register unsigned short *p;
+
+p = x + M;
+x += M + 1;
+
+for( i=M; i<NI-1; i++ )
+ *p++ = *x++;
+
+*p = 0;
+}
+
+/*
+; Shift significand down by 16 bits
+*/
+
+void eshdn6(x)
+register unsigned short *x;
+{
+int i;
+register unsigned short *p;
+
+x += NI-1;
+p = x + 1;
+
+for( i=M; i<NI-1; i++ )
+ *(--p) = *(--x);
+
+*(--p) = 0;
+}
+
+/*
+; Add significands
+; x + y replaces y
+*/
+
+void eaddm( x, y )
+unsigned short *x, *y;
+{
+register unsigned long a;
+int i;
+unsigned int carry;
+
+x += NI-1;
+y += NI-1;
+carry = 0;
+for( i=M; i<NI; i++ )
+ {
+ a = (unsigned long )(*x) + (unsigned long )(*y) + carry;
+ if( a & 0x10000 )
+ carry = 1;
+ else
+ carry = 0;
+ *y = (unsigned short )a;
+ --x;
+ --y;
+ }
+}
+
+/*
+; Subtract significands
+; y - x replaces y
+*/
+
+void esubm( x, y )
+unsigned short *x, *y;
+{
+unsigned long a;
+int i;
+unsigned int carry;
+
+x += NI-1;
+y += NI-1;
+carry = 0;
+for( i=M; i<NI; i++ )
+ {
+ a = (unsigned long )(*y) - (unsigned long )(*x) - carry;
+ if( a & 0x10000 )
+ carry = 1;
+ else
+ carry = 0;
+ *y = (unsigned short )a;
+ --x;
+ --y;
+ }
+}
+
+
+/* Divide significands */
+
+static unsigned short equot[NI] = {0}; /* was static */
+
+#if 0
+int edivm( den, num )
+unsigned short den[], num[];
+{
+int i;
+register unsigned short *p, *q;
+unsigned short j;
+
+p = &equot[0];
+*p++ = num[0];
+*p++ = num[1];
+
+for( i=M; i<NI; i++ )
+ {
+ *p++ = 0;
+ }
+
+/* Use faster compare and subtraction if denominator
+ * has only 15 bits of significane.
+ */
+p = &den[M+2];
+if( *p++ == 0 )
+ {
+ for( i=M+3; i<NI; i++ )
+ {
+ if( *p++ != 0 )
+ goto fulldiv;
+ }
+ if( (den[M+1] & 1) != 0 )
+ goto fulldiv;
+ eshdn1(num);
+ eshdn1(den);
+
+ p = &den[M+1];
+ q = &num[M+1];
+
+ for( i=0; i<NBITS+2; i++ )
+ {
+ if( *p <= *q )
+ {
+ *q -= *p;
+ j = 1;
+ }
+ else
+ {
+ j = 0;
+ }
+ eshup1(equot);
+ equot[NI-2] |= j;
+ eshup1(num);
+ }
+ goto divdon;
+ }
+
+/* The number of quotient bits to calculate is
+ * NBITS + 1 scaling guard bit + 1 roundoff bit.
+ */
+fulldiv:
+
+p = &equot[NI-2];
+for( i=0; i<NBITS+2; i++ )
+ {
+ if( ecmpm(den,num) <= 0 )
+ {
+ esubm(den, num);
+ j = 1; /* quotient bit = 1 */
+ }
+ else
+ j = 0;
+ eshup1(equot);
+ *p |= j;
+ eshup1(num);
+ }
+
+divdon:
+
+eshdn1( equot );
+eshdn1( equot );
+
+/* test for nonzero remainder after roundoff bit */
+p = &num[M];
+j = 0;
+for( i=M; i<NI; i++ )
+ {
+ j |= *p++;
+ }
+if( j )
+ j = 1;
+
+
+for( i=0; i<NI; i++ )
+ num[i] = equot[i];
+return( (int )j );
+}
+
+/* Multiply significands */
+int emulm( a, b )
+unsigned short a[], b[];
+{
+unsigned short *p, *q;
+int i, j, k;
+
+equot[0] = b[0];
+equot[1] = b[1];
+for( i=M; i<NI; i++ )
+ equot[i] = 0;
+
+p = &a[NI-2];
+k = NBITS;
+while( *p == 0 ) /* significand is not supposed to be all zero */
+ {
+ eshdn6(a);
+ k -= 16;
+ }
+if( (*p & 0xff) == 0 )
+ {
+ eshdn8(a);
+ k -= 8;
+ }
+
+q = &equot[NI-1];
+j = 0;
+for( i=0; i<k; i++ )
+ {
+ if( *p & 1 )
+ eaddm(b, equot);
+/* remember if there were any nonzero bits shifted out */
+ if( *q & 1 )
+ j |= 1;
+ eshdn1(a);
+ eshdn1(equot);
+ }
+
+for( i=0; i<NI; i++ )
+ b[i] = equot[i];
+
+/* return flag for lost nonzero bits */
+return(j);
+}
+
+#else
+
+/* Multiply significand of e-type number b
+by 16-bit quantity a, e-type result to c. */
+
+void m16m( a, b, c )
+unsigned short a;
+unsigned short b[], c[];
+{
+register unsigned short *pp;
+register unsigned long carry;
+unsigned short *ps;
+unsigned short p[NI];
+unsigned long aa, m;
+int i;
+
+aa = a;
+pp = &p[NI-2];
+*pp++ = 0;
+*pp = 0;
+ps = &b[NI-1];
+
+for( i=M+1; i<NI; i++ )
+ {
+ if( *ps == 0 )
+ {
+ --ps;
+ --pp;
+ *(pp-1) = 0;
+ }
+ else
+ {
+ m = (unsigned long) aa * *ps--;
+ carry = (m & 0xffff) + *pp;
+ *pp-- = (unsigned short )carry;
+ carry = (carry >> 16) + (m >> 16) + *pp;
+ *pp = (unsigned short )carry;
+ *(pp-1) = carry >> 16;
+ }
+ }
+for( i=M; i<NI; i++ )
+ c[i] = p[i];
+}
+
+
+/* Divide significands. Neither the numerator nor the denominator
+is permitted to have its high guard word nonzero. */
+
+
+int edivm( den, num )
+unsigned short den[], num[];
+{
+int i;
+register unsigned short *p;
+unsigned long tnum;
+unsigned short j, tdenm, tquot;
+unsigned short tprod[NI+1];
+
+p = &equot[0];
+*p++ = num[0];
+*p++ = num[1];
+
+for( i=M; i<NI; i++ )
+ {
+ *p++ = 0;
+ }
+eshdn1( num );
+tdenm = den[M+1];
+for( i=M; i<NI; i++ )
+ {
+ /* Find trial quotient digit (the radix is 65536). */
+ tnum = (((unsigned long) num[M]) << 16) + num[M+1];
+
+ /* Do not execute the divide instruction if it will overflow. */
+ if( (tdenm * ((unsigned long)0xffffL)) < tnum )
+ tquot = 0xffff;
+ else
+ tquot = tnum / tdenm;
+
+ /* Prove that the divide worked. */
+/*
+ tcheck = (unsigned long )tquot * tdenm;
+ if( tnum - tcheck > tdenm )
+ tquot = 0xffff;
+*/
+ /* Multiply denominator by trial quotient digit. */
+ m16m( tquot, den, tprod );
+ /* The quotient digit may have been overestimated. */
+ if( ecmpm( tprod, num ) > 0 )
+ {
+ tquot -= 1;
+ esubm( den, tprod );
+ if( ecmpm( tprod, num ) > 0 )
+ {
+ tquot -= 1;
+ esubm( den, tprod );
+ }
+ }
+/*
+ if( ecmpm( tprod, num ) > 0 )
+ {
+ eshow( "tprod", tprod );
+ eshow( "num ", num );
+ printf( "tnum = %08lx, tden = %04x, tquot = %04x\n",
+ tnum, den[M+1], tquot );
+ }
+*/
+ esubm( tprod, num );
+/*
+ if( ecmpm( num, den ) >= 0 )
+ {
+ eshow( "num ", num );
+ eshow( "den ", den );
+ printf( "tnum = %08lx, tden = %04x, tquot = %04x\n",
+ tnum, den[M+1], tquot );
+ }
+*/
+ equot[i] = tquot;
+ eshup6(num);
+ }
+/* test for nonzero remainder after roundoff bit */
+p = &num[M];
+j = 0;
+for( i=M; i<NI; i++ )
+ {
+ j |= *p++;
+ }
+if( j )
+ j = 1;
+
+for( i=0; i<NI; i++ )
+ num[i] = equot[i];
+
+return( (int )j );
+}
+
+
+
+/* Multiply significands */
+int emulm( a, b )
+unsigned short a[], b[];
+{
+unsigned short *p, *q;
+unsigned short pprod[NI];
+unsigned short j;
+int i;
+
+equot[0] = b[0];
+equot[1] = b[1];
+for( i=M; i<NI; i++ )
+ equot[i] = 0;
+
+j = 0;
+p = &a[NI-1];
+q = &equot[NI-1];
+for( i=M+1; i<NI; i++ )
+ {
+ if( *p == 0 )
+ {
+ --p;
+ }
+ else
+ {
+ m16m( *p--, b, pprod );
+ eaddm(pprod, equot);
+ }
+ j |= *q;
+ eshdn6(equot);
+ }
+
+for( i=0; i<NI; i++ )
+ b[i] = equot[i];
+
+/* return flag for lost nonzero bits */
+return( (int)j );
+}
+
+
+/*
+eshow(str, x)
+char *str;
+unsigned short *x;
+{
+int i;
+
+printf( "%s ", str );
+for( i=0; i<NI; i++ )
+ printf( "%04x ", *x++ );
+printf( "\n" );
+}
+*/
+#endif
+
+
+
+/*
+ * Normalize and round off.
+ *
+ * The internal format number to be rounded is "s".
+ * Input "lost" indicates whether the number is exact.
+ * This is the so-called sticky bit.
+ *
+ * Input "subflg" indicates whether the number was obtained
+ * by a subtraction operation. In that case if lost is nonzero
+ * then the number is slightly smaller than indicated.
+ *
+ * Input "exp" is the biased exponent, which may be negative.
+ * the exponent field of "s" is ignored but is replaced by
+ * "exp" as adjusted by normalization and rounding.
+ *
+ * Input "rcntrl" is the rounding control.
+ */
+
+static int rlast = -1;
+static int rw = 0;
+static unsigned short rmsk = 0;
+static unsigned short rmbit = 0;
+static unsigned short rebit = 0;
+static int re = 0;
+static unsigned short rbit[NI] = {0,0,0,0,0,0,0,0};
+
+void emdnorm( s, lost, subflg, exp, rcntrl )
+unsigned short s[];
+int lost;
+int subflg;
+long exp;
+int rcntrl;
+{
+int i, j;
+unsigned short r;
+
+/* Normalize */
+j = enormlz( s );
+
+/* a blank significand could mean either zero or infinity. */
+#ifndef INFINITY
+if( j > NBITS )
+ {
+ ecleazs( s );
+ return;
+ }
+#endif
+exp -= j;
+#ifndef INFINITY
+if( exp >= 32767L )
+ goto overf;
+#else
+if( (j > NBITS) && (exp < 32767L) )
+ {
+ ecleazs( s );
+ return;
+ }
+#endif
+if( exp < 0L )
+ {
+ if( exp > (long )(-NBITS-1) )
+ {
+ j = (int )exp;
+ i = eshift( s, j );
+ if( i )
+ lost = 1;
+ }
+ else
+ {
+ ecleazs( s );
+ return;
+ }
+ }
+/* Round off, unless told not to by rcntrl. */
+if( rcntrl == 0 )
+ goto mdfin;
+/* Set up rounding parameters if the control register changed. */
+if( rndprc != rlast )
+ {
+ ecleaz( rbit );
+ switch( rndprc )
+ {
+ default:
+ case NBITS:
+ rw = NI-1; /* low guard word */
+ rmsk = 0xffff;
+ rmbit = 0x8000;
+ rebit = 1;
+ re = rw - 1;
+ break;
+ case 113:
+ rw = 10;
+ rmsk = 0x7fff;
+ rmbit = 0x4000;
+ rebit = 0x8000;
+ re = rw;
+ break;
+ case 64:
+ rw = 7;
+ rmsk = 0xffff;
+ rmbit = 0x8000;
+ rebit = 1;
+ re = rw-1;
+ break;
+/* For DEC arithmetic */
+ case 56:
+ rw = 6;
+ rmsk = 0xff;
+ rmbit = 0x80;
+ rebit = 0x100;
+ re = rw;
+ break;
+ case 53:
+ rw = 6;
+ rmsk = 0x7ff;
+ rmbit = 0x0400;
+ rebit = 0x800;
+ re = rw;
+ break;
+ case 24:
+ rw = 4;
+ rmsk = 0xff;
+ rmbit = 0x80;
+ rebit = 0x100;
+ re = rw;
+ break;
+ }
+ rbit[re] = rebit;
+ rlast = rndprc;
+ }
+
+/* Shift down 1 temporarily if the data structure has an implied
+ * most significant bit and the number is denormal.
+ * For rndprc = 64 or NBITS, there is no implied bit.
+ * But Intel long double denormals lose one bit of significance even so.
+ */
+#ifdef IBMPC
+if( (exp <= 0) && (rndprc != NBITS) )
+#else
+if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) )
+#endif
+ {
+ lost |= s[NI-1] & 1;
+ eshdn1(s);
+ }
+/* Clear out all bits below the rounding bit,
+ * remembering in r if any were nonzero.
+ */
+r = s[rw] & rmsk;
+if( rndprc < NBITS )
+ {
+ i = rw + 1;
+ while( i < NI )
+ {
+ if( s[i] )
+ r |= 1;
+ s[i] = 0;
+ ++i;
+ }
+ }
+s[rw] &= ~rmsk;
+if( (r & rmbit) != 0 )
+ {
+ if( r == rmbit )
+ {
+ if( lost == 0 )
+ { /* round to even */
+ if( (s[re] & rebit) == 0 )
+ goto mddone;
+ }
+ else
+ {
+ if( subflg != 0 )
+ goto mddone;
+ }
+ }
+ eaddm( rbit, s );
+ }
+mddone:
+#ifdef IBMPC
+if( (exp <= 0) && (rndprc != NBITS) )
+#else
+if( (exp <= 0) && (rndprc != 64) && (rndprc != NBITS) )
+#endif
+ {
+ eshup1(s);
+ }
+if( s[2] != 0 )
+ { /* overflow on roundoff */
+ eshdn1(s);
+ exp += 1;
+ }
+mdfin:
+s[NI-1] = 0;
+if( exp >= 32767L )
+ {
+#ifndef INFINITY
+overf:
+#endif
+#ifdef INFINITY
+ s[1] = 32767;
+ for( i=2; i<NI-1; i++ )
+ s[i] = 0;
+#else
+ s[1] = 32766;
+ s[2] = 0;
+ for( i=M+1; i<NI-1; i++ )
+ s[i] = 0xffff;
+ s[NI-1] = 0;
+ if( (rndprc < 64) || (rndprc == 113) )
+ {
+ s[rw] &= ~rmsk;
+ if( rndprc == 24 )
+ {
+ s[5] = 0;
+ s[6] = 0;
+ }
+ }
+#endif
+ return;
+ }
+if( exp < 0 )
+ s[1] = 0;
+else
+ s[1] = (unsigned short )exp;
+}
+
+
+
+/*
+; Subtract external format numbers.
+;
+; unsigned short a[NE], b[NE], c[NE];
+; esub( a, b, c ); c = b - a
+*/
+
+static int subflg = 0;
+
+void esub( a, b, c )
+unsigned short *a, *b, *c;
+{
+
+#ifdef NANS
+if( eisnan(a) )
+ {
+ emov (a, c);
+ return;
+ }
+if( eisnan(b) )
+ {
+ emov(b,c);
+ return;
+ }
+/* Infinity minus infinity is a NaN.
+ * Test for subtracting infinities of the same sign.
+ */
+if( eisinf(a) && eisinf(b) && ((eisneg (a) ^ eisneg (b)) == 0))
+ {
+ mtherr( "esub", DOMAIN );
+ enan( c, NBITS );
+ return;
+ }
+#endif
+subflg = 1;
+eadd1( a, b, c );
+}
+
+
+/*
+; Add.
+;
+; unsigned short a[NE], b[NE], c[NE];
+; eadd( a, b, c ); c = b + a
+*/
+void eadd( a, b, c )
+unsigned short *a, *b, *c;
+{
+
+#ifdef NANS
+/* NaN plus anything is a NaN. */
+if( eisnan(a) )
+ {
+ emov(a,c);
+ return;
+ }
+if( eisnan(b) )
+ {
+ emov(b,c);
+ return;
+ }
+/* Infinity minus infinity is a NaN.
+ * Test for adding infinities of opposite signs.
+ */
+if( eisinf(a) && eisinf(b)
+ && ((eisneg(a) ^ eisneg(b)) != 0) )
+ {
+ mtherr( "eadd", DOMAIN );
+ enan( c, NBITS );
+ return;
+ }
+#endif
+subflg = 0;
+eadd1( a, b, c );
+}
+
+void eadd1( a, b, c )
+unsigned short *a, *b, *c;
+{
+unsigned short ai[NI], bi[NI], ci[NI];
+int i, lost, j, k;
+long lt, lta, ltb;
+
+#ifdef INFINITY
+if( eisinf(a) )
+ {
+ emov(a,c);
+ if( subflg )
+ eneg(c);
+ return;
+ }
+if( eisinf(b) )
+ {
+ emov(b,c);
+ return;
+ }
+#endif
+emovi( a, ai );
+emovi( b, bi );
+if( subflg )
+ ai[0] = ~ai[0];
+
+/* compare exponents */
+lta = ai[E];
+ltb = bi[E];
+lt = lta - ltb;
+if( lt > 0L )
+ { /* put the larger number in bi */
+ emovz( bi, ci );
+ emovz( ai, bi );
+ emovz( ci, ai );
+ ltb = bi[E];
+ lt = -lt;
+ }
+lost = 0;
+if( lt != 0L )
+ {
+ if( lt < (long )(-NBITS-1) )
+ goto done; /* answer same as larger addend */
+ k = (int )lt;
+ lost = eshift( ai, k ); /* shift the smaller number down */
+ }
+else
+ {
+/* exponents were the same, so must compare significands */
+ i = ecmpm( ai, bi );
+ if( i == 0 )
+ { /* the numbers are identical in magnitude */
+ /* if different signs, result is zero */
+ if( ai[0] != bi[0] )
+ {
+ eclear(c);
+ return;
+ }
+ /* if same sign, result is double */
+ /* double denomalized tiny number */
+ if( (bi[E] == 0) && ((bi[3] & 0x8000) == 0) )
+ {
+ eshup1( bi );
+ goto done;
+ }
+ /* add 1 to exponent unless both are zero! */
+ for( j=1; j<NI-1; j++ )
+ {
+ if( bi[j] != 0 )
+ {
+/* This could overflow, but let emovo take care of that. */
+ ltb += 1;
+ break;
+ }
+ }
+ bi[E] = (unsigned short )ltb;
+ goto done;
+ }
+ if( i > 0 )
+ { /* put the larger number in bi */
+ emovz( bi, ci );
+ emovz( ai, bi );
+ emovz( ci, ai );
+ }
+ }
+if( ai[0] == bi[0] )
+ {
+ eaddm( ai, bi );
+ subflg = 0;
+ }
+else
+ {
+ esubm( ai, bi );
+ subflg = 1;
+ }
+emdnorm( bi, lost, subflg, ltb, 64 );
+
+done:
+emovo( bi, c );
+}
+
+
+
+/*
+; Divide.
+;
+; unsigned short a[NE], b[NE], c[NE];
+; ediv( a, b, c ); c = b / a
+*/
+void ediv( a, b, c )
+unsigned short *a, *b, *c;
+{
+unsigned short ai[NI], bi[NI];
+int i, sign;
+long lt, lta, ltb;
+
+/* IEEE says if result is not a NaN, the sign is "-" if and only if
+ operands have opposite signs -- but flush -0 to 0 later if not IEEE. */
+sign = eisneg(a) ^ eisneg(b);
+
+#ifdef NANS
+/* Return any NaN input. */
+if( eisnan(a) )
+ {
+ emov(a,c);
+ return;
+ }
+if( eisnan(b) )
+ {
+ emov(b,c);
+ return;
+ }
+/* Zero over zero, or infinity over infinity, is a NaN. */
+if( ((ecmp(a,ezero) == 0) && (ecmp(b,ezero) == 0))
+ || (eisinf (a) && eisinf (b)) )
+ {
+ mtherr( "ediv", DOMAIN );
+ enan( c, NBITS );
+ return;
+ }
+#endif
+/* Infinity over anything else is infinity. */
+#ifdef INFINITY
+if( eisinf(b) )
+ {
+ einfin(c);
+ goto divsign;
+ }
+if( eisinf(a) )
+ {
+ eclear(c);
+ goto divsign;
+ }
+#endif
+emovi( a, ai );
+emovi( b, bi );
+lta = ai[E];
+ltb = bi[E];
+if( bi[E] == 0 )
+ { /* See if numerator is zero. */
+ for( i=1; i<NI-1; i++ )
+ {
+ if( bi[i] != 0 )
+ {
+ ltb -= enormlz( bi );
+ goto dnzro1;
+ }
+ }
+ eclear(c);
+ goto divsign;
+ }
+dnzro1:
+
+if( ai[E] == 0 )
+ { /* possible divide by zero */
+ for( i=1; i<NI-1; i++ )
+ {
+ if( ai[i] != 0 )
+ {
+ lta -= enormlz( ai );
+ goto dnzro2;
+ }
+ }
+ einfin(c);
+ mtherr( "ediv", SING );
+ goto divsign;
+ }
+dnzro2:
+
+i = edivm( ai, bi );
+/* calculate exponent */
+lt = ltb - lta + EXONE;
+emdnorm( bi, i, 0, lt, 64 );
+emovo( bi, c );
+
+divsign:
+
+if( sign )
+ *(c+(NE-1)) |= 0x8000;
+else
+ *(c+(NE-1)) &= ~0x8000;
+}
+
+
+
+/*
+; Multiply.
+;
+; unsigned short a[NE], b[NE], c[NE];
+; emul( a, b, c ); c = b * a
+*/
+void emul( a, b, c )
+unsigned short *a, *b, *c;
+{
+unsigned short ai[NI], bi[NI];
+int i, j, sign;
+long lt, lta, ltb;
+
+/* IEEE says if result is not a NaN, the sign is "-" if and only if
+ operands have opposite signs -- but flush -0 to 0 later if not IEEE. */
+sign = eisneg(a) ^ eisneg(b);
+
+#ifdef NANS
+/* NaN times anything is the same NaN. */
+if( eisnan(a) )
+ {
+ emov(a,c);
+ return;
+ }
+if( eisnan(b) )
+ {
+ emov(b,c);
+ return;
+ }
+/* Zero times infinity is a NaN. */
+if( (eisinf(a) && (ecmp(b,ezero) == 0))
+ || (eisinf(b) && (ecmp(a,ezero) == 0)) )
+ {
+ mtherr( "emul", DOMAIN );
+ enan( c, NBITS );
+ return;
+ }
+#endif
+/* Infinity times anything else is infinity. */
+#ifdef INFINITY
+if( eisinf(a) || eisinf(b) )
+ {
+ einfin(c);
+ goto mulsign;
+ }
+#endif
+emovi( a, ai );
+emovi( b, bi );
+lta = ai[E];
+ltb = bi[E];
+if( ai[E] == 0 )
+ {
+ for( i=1; i<NI-1; i++ )
+ {
+ if( ai[i] != 0 )
+ {
+ lta -= enormlz( ai );
+ goto mnzer1;
+ }
+ }
+ eclear(c);
+ goto mulsign;
+ }
+mnzer1:
+
+if( bi[E] == 0 )
+ {
+ for( i=1; i<NI-1; i++ )
+ {
+ if( bi[i] != 0 )
+ {
+ ltb -= enormlz( bi );
+ goto mnzer2;
+ }
+ }
+ eclear(c);
+ goto mulsign;
+ }
+mnzer2:
+
+/* Multiply significands */
+j = emulm( ai, bi );
+/* calculate exponent */
+lt = lta + ltb - (EXONE - 1);
+emdnorm( bi, j, 0, lt, 64 );
+emovo( bi, c );
+/* IEEE says sign is "-" if and only if operands have opposite signs. */
+mulsign:
+if( sign )
+ *(c+(NE-1)) |= 0x8000;
+else
+ *(c+(NE-1)) &= ~0x8000;
+}
+
+
+
+
+/*
+; Convert IEEE double precision to e type
+; double d;
+; unsigned short x[N+2];
+; e53toe( &d, x );
+*/
+void e53toe( pe, y )
+unsigned short *pe, *y;
+{
+#ifdef DEC
+
+dectoe( pe, y ); /* see etodec.c */
+
+#else
+
+register unsigned short r;
+register unsigned short *p, *e;
+unsigned short yy[NI];
+int denorm, k;
+
+e = pe;
+denorm = 0; /* flag if denormalized number */
+ecleaz(yy);
+#ifdef IBMPC
+e += 3;
+#endif
+r = *e;
+yy[0] = 0;
+if( r & 0x8000 )
+ yy[0] = 0xffff;
+yy[M] = (r & 0x0f) | 0x10;
+r &= ~0x800f; /* strip sign and 4 significand bits */
+#ifdef INFINITY
+if( r == 0x7ff0 )
+ {
+#ifdef NANS
+#ifdef IBMPC
+ if( ((pe[3] & 0xf) != 0) || (pe[2] != 0)
+ || (pe[1] != 0) || (pe[0] != 0) )
+ {
+ enan( y, NBITS );
+ return;
+ }
+#else
+ if( ((pe[0] & 0xf) != 0) || (pe[1] != 0)
+ || (pe[2] != 0) || (pe[3] != 0) )
+ {
+ enan( y, NBITS );
+ return;
+ }
+#endif
+#endif /* NANS */
+ eclear( y );
+ einfin( y );
+ if( yy[0] )
+ eneg(y);
+ return;
+ }
+#endif
+r >>= 4;
+/* If zero exponent, then the significand is denormalized.
+ * So, take back the understood high significand bit. */
+if( r == 0 )
+ {
+ denorm = 1;
+ yy[M] &= ~0x10;
+ }
+r += EXONE - 01777;
+yy[E] = r;
+p = &yy[M+1];
+#ifdef IBMPC
+*p++ = *(--e);
+*p++ = *(--e);
+*p++ = *(--e);
+#endif
+#ifdef MIEEE
+++e;
+*p++ = *e++;
+*p++ = *e++;
+*p++ = *e++;
+#endif
+(void )eshift( yy, -5 );
+if( denorm )
+ { /* if zero exponent, then normalize the significand */
+ if( (k = enormlz(yy)) > NBITS )
+ ecleazs(yy);
+ else
+ yy[E] -= (unsigned short )(k-1);
+ }
+emovo( yy, y );
+#endif /* not DEC */
+}
+
+void e64toe( pe, y )
+unsigned short *pe, *y;
+{
+unsigned short yy[NI];
+unsigned short *p, *q, *e;
+int i;
+
+e = pe;
+p = yy;
+for( i=0; i<NE-5; i++ )
+ *p++ = 0;
+#ifdef IBMPC
+for( i=0; i<5; i++ )
+ *p++ = *e++;
+#endif
+#ifdef DEC
+for( i=0; i<5; i++ )
+ *p++ = *e++;
+#endif
+#ifdef MIEEE
+p = &yy[0] + (NE-1);
+*p-- = *e++;
+++e;
+for( i=0; i<4; i++ )
+ *p-- = *e++;
+#endif
+
+#ifdef IBMPC
+/* For Intel long double, shift denormal significand up 1
+ -- but only if the top significand bit is zero. */
+if((yy[NE-1] & 0x7fff) == 0 && (yy[NE-2] & 0x8000) == 0)
+ {
+ unsigned short temp[NI+1];
+ emovi(yy, temp);
+ eshup1(temp);
+ emovo(temp,y);
+ return;
+ }
+#endif
+#ifdef INFINITY
+/* Point to the exponent field. */
+p = &yy[NE-1];
+if( *p == 0x7fff )
+ {
+#ifdef NANS
+#ifdef IBMPC
+ for( i=0; i<4; i++ )
+ {
+ if((i != 3 && pe[i] != 0)
+ /* Check for Intel long double infinity pattern. */
+ || (i == 3 && pe[i] != 0x8000))
+ {
+ enan( y, NBITS );
+ return;
+ }
+ }
+#else
+ for( i=1; i<=4; i++ )
+ {
+ if( pe[i] != 0 )
+ {
+ enan( y, NBITS );
+ return;
+ }
+ }
+#endif
+#endif /* NANS */
+ eclear( y );
+ einfin( y );
+ if( *p & 0x8000 )
+ eneg(y);
+ return;
+ }
+#endif
+p = yy;
+q = y;
+for( i=0; i<NE; i++ )
+ *q++ = *p++;
+}
+
+void e113toe(pe,y)
+unsigned short *pe, *y;
+{
+register unsigned short r;
+unsigned short *e, *p;
+unsigned short yy[NI];
+int i;
+
+e = pe;
+ecleaz(yy);
+#ifdef IBMPC
+e += 7;
+#endif
+r = *e;
+yy[0] = 0;
+if( r & 0x8000 )
+ yy[0] = 0xffff;
+r &= 0x7fff;
+#ifdef INFINITY
+if( r == 0x7fff )
+ {
+#ifdef NANS
+#ifdef IBMPC
+ for( i=0; i<7; i++ )
+ {
+ if( pe[i] != 0 )
+ {
+ enan( y, NBITS );
+ return;
+ }
+ }
+#else
+ for( i=1; i<8; i++ )
+ {
+ if( pe[i] != 0 )
+ {
+ enan( y, NBITS );
+ return;
+ }
+ }
+#endif
+#endif /* NANS */
+ eclear( y );
+ einfin( y );
+ if( *e & 0x8000 )
+ eneg(y);
+ return;
+ }
+#endif /* INFINITY */
+yy[E] = r;
+p = &yy[M + 1];
+#ifdef IBMPC
+for( i=0; i<7; i++ )
+ *p++ = *(--e);
+#endif
+#ifdef MIEEE
+++e;
+for( i=0; i<7; i++ )
+ *p++ = *e++;
+#endif
+/* If denormal, remove the implied bit; else shift down 1. */
+if( r == 0 )
+ {
+ yy[M] = 0;
+ }
+else
+ {
+ yy[M] = 1;
+ eshift( yy, -1 );
+ }
+emovo(yy,y);
+}
+
+
+/*
+; Convert IEEE single precision to e type
+; float d;
+; unsigned short x[N+2];
+; dtox( &d, x );
+*/
+void e24toe( pe, y )
+unsigned short *pe, *y;
+{
+register unsigned short r;
+register unsigned short *p, *e;
+unsigned short yy[NI];
+int denorm, k;
+
+e = pe;
+denorm = 0; /* flag if denormalized number */
+ecleaz(yy);
+#ifdef IBMPC
+e += 1;
+#endif
+#ifdef DEC
+e += 1;
+#endif
+r = *e;
+yy[0] = 0;
+if( r & 0x8000 )
+ yy[0] = 0xffff;
+yy[M] = (r & 0x7f) | 0200;
+r &= ~0x807f; /* strip sign and 7 significand bits */
+#ifdef INFINITY
+if( r == 0x7f80 )
+ {
+#ifdef NANS
+#ifdef MIEEE
+ if( ((pe[0] & 0x7f) != 0) || (pe[1] != 0) )
+ {
+ enan( y, NBITS );
+ return;
+ }
+#else
+ if( ((pe[1] & 0x7f) != 0) || (pe[0] != 0) )
+ {
+ enan( y, NBITS );
+ return;
+ }
+#endif
+#endif /* NANS */
+ eclear( y );
+ einfin( y );
+ if( yy[0] )
+ eneg(y);
+ return;
+ }
+#endif
+r >>= 7;
+/* If zero exponent, then the significand is denormalized.
+ * So, take back the understood high significand bit. */
+if( r == 0 )
+ {
+ denorm = 1;
+ yy[M] &= ~0200;
+ }
+r += EXONE - 0177;
+yy[E] = r;
+p = &yy[M+1];
+#ifdef IBMPC
+*p++ = *(--e);
+#endif
+#ifdef DEC
+*p++ = *(--e);
+#endif
+#ifdef MIEEE
+++e;
+*p++ = *e++;
+#endif
+(void )eshift( yy, -8 );
+if( denorm )
+ { /* if zero exponent, then normalize the significand */
+ if( (k = enormlz(yy)) > NBITS )
+ ecleazs(yy);
+ else
+ yy[E] -= (unsigned short )(k-1);
+ }
+emovo( yy, y );
+}
+
+void etoe113(x,e)
+unsigned short *x, *e;
+{
+unsigned short xi[NI];
+long exp;
+int rndsav;
+
+#ifdef NANS
+if( eisnan(x) )
+ {
+ enan( e, 113 );
+ return;
+ }
+#endif
+emovi( x, xi );
+exp = (long )xi[E];
+#ifdef INFINITY
+if( eisinf(x) )
+ goto nonorm;
+#endif
+/* round off to nearest or even */
+rndsav = rndprc;
+rndprc = 113;
+emdnorm( xi, 0, 0, exp, 64 );
+rndprc = rndsav;
+nonorm:
+toe113 (xi, e);
+}
+
+/* move out internal format to ieee long double */
+static void toe113(a,b)
+unsigned short *a, *b;
+{
+register unsigned short *p, *q;
+unsigned short i;
+
+#ifdef NANS
+if( eiisnan(a) )
+ {
+ enan( b, 113 );
+ return;
+ }
+#endif
+p = a;
+#ifdef MIEEE
+q = b;
+#else
+q = b + 7; /* point to output exponent */
+#endif
+
+/* If not denormal, delete the implied bit. */
+if( a[E] != 0 )
+ {
+ eshup1 (a);
+ }
+/* combine sign and exponent */
+i = *p++;
+#ifdef MIEEE
+if( i )
+ *q++ = *p++ | 0x8000;
+else
+ *q++ = *p++;
+#else
+if( i )
+ *q-- = *p++ | 0x8000;
+else
+ *q-- = *p++;
+#endif
+/* skip over guard word */
+++p;
+/* move the significand */
+#ifdef MIEEE
+for (i = 0; i < 7; i++)
+ *q++ = *p++;
+#else
+for (i = 0; i < 7; i++)
+ *q-- = *p++;
+#endif
+}
+
+
+void etoe64( x, e )
+unsigned short *x, *e;
+{
+unsigned short xi[NI];
+long exp;
+int rndsav;
+
+#ifdef NANS
+if( eisnan(x) )
+ {
+ enan( e, 64 );
+ return;
+ }
+#endif
+emovi( x, xi );
+exp = (long )xi[E]; /* adjust exponent for offset */
+#ifdef INFINITY
+if( eisinf(x) )
+ goto nonorm;
+#endif
+/* round off to nearest or even */
+rndsav = rndprc;
+rndprc = 64;
+emdnorm( xi, 0, 0, exp, 64 );
+rndprc = rndsav;
+nonorm:
+toe64( xi, e );
+}
+
+/* move out internal format to ieee long double */
+static void toe64( a, b )
+unsigned short *a, *b;
+{
+register unsigned short *p, *q;
+unsigned short i;
+
+#ifdef NANS
+if( eiisnan(a) )
+ {
+ enan( b, 64 );
+ return;
+ }
+#endif
+#ifdef IBMPC
+/* Shift Intel denormal significand down 1. */
+if( a[E] == 0 )
+ eshdn1(a);
+#endif
+p = a;
+#ifdef MIEEE
+q = b;
+#else
+q = b + 4; /* point to output exponent */
+#if 1
+/* NOTE: if data type is 96 bits wide, clear the last word here. */
+*(q+1)= 0;
+#endif
+#endif
+
+/* combine sign and exponent */
+i = *p++;
+#ifdef MIEEE
+if( i )
+ *q++ = *p++ | 0x8000;
+else
+ *q++ = *p++;
+*q++ = 0;
+#else
+if( i )
+ *q-- = *p++ | 0x8000;
+else
+ *q-- = *p++;
+#endif
+/* skip over guard word */
+++p;
+/* move the significand */
+#ifdef MIEEE
+for( i=0; i<4; i++ )
+ *q++ = *p++;
+#else
+#ifdef INFINITY
+if (eiisinf (a))
+ {
+ /* Intel long double infinity. */
+ *q-- = 0x8000;
+ *q-- = 0;
+ *q-- = 0;
+ *q = 0;
+ return;
+ }
+#endif
+for( i=0; i<4; i++ )
+ *q-- = *p++;
+#endif
+}
+
+
+/*
+; e type to IEEE double precision
+; double d;
+; unsigned short x[NE];
+; etoe53( x, &d );
+*/
+
+#ifdef DEC
+
+void etoe53( x, e )
+unsigned short *x, *e;
+{
+etodec( x, e ); /* see etodec.c */
+}
+
+static void toe53( x, y )
+unsigned short *x, *y;
+{
+todec( x, y );
+}
+
+#else
+
+void etoe53( x, e )
+unsigned short *x, *e;
+{
+unsigned short xi[NI];
+long exp;
+int rndsav;
+
+#ifdef NANS
+if( eisnan(x) )
+ {
+ enan( e, 53 );
+ return;
+ }
+#endif
+emovi( x, xi );
+exp = (long )xi[E] - (EXONE - 0x3ff); /* adjust exponent for offsets */
+#ifdef INFINITY
+if( eisinf(x) )
+ goto nonorm;
+#endif
+/* round off to nearest or even */
+rndsav = rndprc;
+rndprc = 53;
+emdnorm( xi, 0, 0, exp, 64 );
+rndprc = rndsav;
+nonorm:
+toe53( xi, e );
+}
+
+
+static void toe53( x, y )
+unsigned short *x, *y;
+{
+unsigned short i;
+unsigned short *p;
+
+
+#ifdef NANS
+if( eiisnan(x) )
+ {
+ enan( y, 53 );
+ return;
+ }
+#endif
+p = &x[0];
+#ifdef IBMPC
+y += 3;
+#endif
+*y = 0; /* output high order */
+if( *p++ )
+ *y = 0x8000; /* output sign bit */
+
+i = *p++;
+if( i >= (unsigned int )2047 )
+ { /* Saturate at largest number less than infinity. */
+#ifdef INFINITY
+ *y |= 0x7ff0;
+#ifdef IBMPC
+ *(--y) = 0;
+ *(--y) = 0;
+ *(--y) = 0;
+#endif
+#ifdef MIEEE
+ ++y;
+ *y++ = 0;
+ *y++ = 0;
+ *y++ = 0;
+#endif
+#else
+ *y |= (unsigned short )0x7fef;
+#ifdef IBMPC
+ *(--y) = 0xffff;
+ *(--y) = 0xffff;
+ *(--y) = 0xffff;
+#endif
+#ifdef MIEEE
+ ++y;
+ *y++ = 0xffff;
+ *y++ = 0xffff;
+ *y++ = 0xffff;
+#endif
+#endif
+ return;
+ }
+if( i == 0 )
+ {
+ (void )eshift( x, 4 );
+ }
+else
+ {
+ i <<= 4;
+ (void )eshift( x, 5 );
+ }
+i |= *p++ & (unsigned short )0x0f; /* *p = xi[M] */
+*y |= (unsigned short )i; /* high order output already has sign bit set */
+#ifdef IBMPC
+*(--y) = *p++;
+*(--y) = *p++;
+*(--y) = *p;
+#endif
+#ifdef MIEEE
+++y;
+*y++ = *p++;
+*y++ = *p++;
+*y++ = *p++;
+#endif
+}
+
+#endif /* not DEC */
+
+
+
+/*
+; e type to IEEE single precision
+; float d;
+; unsigned short x[N+2];
+; xtod( x, &d );
+*/
+void etoe24( x, e )
+unsigned short *x, *e;
+{
+long exp;
+unsigned short xi[NI];
+int rndsav;
+
+#ifdef NANS
+if( eisnan(x) )
+ {
+ enan( e, 24 );
+ return;
+ }
+#endif
+emovi( x, xi );
+exp = (long )xi[E] - (EXONE - 0177); /* adjust exponent for offsets */
+#ifdef INFINITY
+if( eisinf(x) )
+ goto nonorm;
+#endif
+/* round off to nearest or even */
+rndsav = rndprc;
+rndprc = 24;
+emdnorm( xi, 0, 0, exp, 64 );
+rndprc = rndsav;
+nonorm:
+toe24( xi, e );
+}
+
+static void toe24( x, y )
+unsigned short *x, *y;
+{
+unsigned short i;
+unsigned short *p;
+
+#ifdef NANS
+if( eiisnan(x) )
+ {
+ enan( y, 24 );
+ return;
+ }
+#endif
+p = &x[0];
+#ifdef IBMPC
+y += 1;
+#endif
+#ifdef DEC
+y += 1;
+#endif
+*y = 0; /* output high order */
+if( *p++ )
+ *y = 0x8000; /* output sign bit */
+
+i = *p++;
+if( i >= 255 )
+ { /* Saturate at largest number less than infinity. */
+#ifdef INFINITY
+ *y |= (unsigned short )0x7f80;
+#ifdef IBMPC
+ *(--y) = 0;
+#endif
+#ifdef DEC
+ *(--y) = 0;
+#endif
+#ifdef MIEEE
+ ++y;
+ *y = 0;
+#endif
+#else
+ *y |= (unsigned short )0x7f7f;
+#ifdef IBMPC
+ *(--y) = 0xffff;
+#endif
+#ifdef DEC
+ *(--y) = 0xffff;
+#endif
+#ifdef MIEEE
+ ++y;
+ *y = 0xffff;
+#endif
+#endif
+ return;
+ }
+if( i == 0 )
+ {
+ (void )eshift( x, 7 );
+ }
+else
+ {
+ i <<= 7;
+ (void )eshift( x, 8 );
+ }
+i |= *p++ & (unsigned short )0x7f; /* *p = xi[M] */
+*y |= i; /* high order output already has sign bit set */
+#ifdef IBMPC
+*(--y) = *p;
+#endif
+#ifdef DEC
+*(--y) = *p;
+#endif
+#ifdef MIEEE
+++y;
+*y = *p;
+#endif
+}
+
+
+/* Compare two e type numbers.
+ *
+ * unsigned short a[NE], b[NE];
+ * ecmp( a, b );
+ *
+ * returns +1 if a > b
+ * 0 if a == b
+ * -1 if a < b
+ * -2 if either a or b is a NaN.
+ */
+int ecmp( a, b )
+unsigned short *a, *b;
+{
+unsigned short ai[NI], bi[NI];
+register unsigned short *p, *q;
+register int i;
+int msign;
+
+#ifdef NANS
+if (eisnan (a) || eisnan (b))
+ return( -2 );
+#endif
+emovi( a, ai );
+p = ai;
+emovi( b, bi );
+q = bi;
+
+if( *p != *q )
+ { /* the signs are different */
+/* -0 equals + 0 */
+ for( i=1; i<NI-1; i++ )
+ {
+ if( ai[i] != 0 )
+ goto nzro;
+ if( bi[i] != 0 )
+ goto nzro;
+ }
+ return(0);
+nzro:
+ if( *p == 0 )
+ return( 1 );
+ else
+ return( -1 );
+ }
+/* both are the same sign */
+if( *p == 0 )
+ msign = 1;
+else
+ msign = -1;
+i = NI-1;
+do
+ {
+ if( *p++ != *q++ )
+ {
+ goto diff;
+ }
+ }
+while( --i > 0 );
+
+return(0); /* equality */
+
+
+
+diff:
+
+if( *(--p) > *(--q) )
+ return( msign ); /* p is bigger */
+else
+ return( -msign ); /* p is littler */
+}
+
+
+
+
+/* Find nearest integer to x = floor( x + 0.5 )
+ *
+ * unsigned short x[NE], y[NE]
+ * eround( x, y );
+ */
+void eround( x, y )
+unsigned short *x, *y;
+{
+
+eadd( ehalf, x, y );
+efloor( y, y );
+}
+
+
+
+
+/*
+; convert long (32-bit) integer to e type
+;
+; long l;
+; unsigned short x[NE];
+; ltoe( &l, x );
+; note &l is the memory address of l
+*/
+void ltoe( lp, y )
+long *lp; /* lp is the memory address of a long integer */
+unsigned short *y; /* y is the address of a short */
+{
+unsigned short yi[NI];
+unsigned long ll;
+int k;
+
+ecleaz( yi );
+if( *lp < 0 )
+ {
+ ll = (unsigned long )( -(*lp) ); /* make it positive */
+ yi[0] = 0xffff; /* put correct sign in the e type number */
+ }
+else
+ {
+ ll = (unsigned long )( *lp );
+ }
+/* move the long integer to yi significand area */
+if( sizeof(long) == 8 )
+ {
+ yi[M] = (unsigned short) (ll >> (LONGBITS - 16));
+ yi[M + 1] = (unsigned short) (ll >> (LONGBITS - 32));
+ yi[M + 2] = (unsigned short) (ll >> 16);
+ yi[M + 3] = (unsigned short) ll;
+ yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
+ }
+else
+ {
+ yi[M] = (unsigned short )(ll >> 16);
+ yi[M+1] = (unsigned short )ll;
+ yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */
+ }
+if( (k = enormlz( yi )) > NBITS ) /* normalize the significand */
+ ecleaz( yi ); /* it was zero */
+else
+ yi[E] -= (unsigned short )k; /* subtract shift count from exponent */
+emovo( yi, y ); /* output the answer */
+}
+
+/*
+; convert unsigned long (32-bit) integer to e type
+;
+; unsigned long l;
+; unsigned short x[NE];
+; ltox( &l, x );
+; note &l is the memory address of l
+*/
+void ultoe( lp, y )
+unsigned long *lp; /* lp is the memory address of a long integer */
+unsigned short *y; /* y is the address of a short */
+{
+unsigned short yi[NI];
+unsigned long ll;
+int k;
+
+ecleaz( yi );
+ll = *lp;
+
+/* move the long integer to ayi significand area */
+if( sizeof(long) == 8 )
+ {
+ yi[M] = (unsigned short) (ll >> (LONGBITS - 16));
+ yi[M + 1] = (unsigned short) (ll >> (LONGBITS - 32));
+ yi[M + 2] = (unsigned short) (ll >> 16);
+ yi[M + 3] = (unsigned short) ll;
+ yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
+ }
+else
+ {
+ yi[M] = (unsigned short )(ll >> 16);
+ yi[M+1] = (unsigned short )ll;
+ yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */
+ }
+if( (k = enormlz( yi )) > NBITS ) /* normalize the significand */
+ ecleaz( yi ); /* it was zero */
+else
+ yi[E] -= (unsigned short )k; /* subtract shift count from exponent */
+emovo( yi, y ); /* output the answer */
+}
+
+
+/*
+; Find long integer and fractional parts
+
+; long i;
+; unsigned short x[NE], frac[NE];
+; xifrac( x, &i, frac );
+
+ The integer output has the sign of the input. The fraction is
+ the positive fractional part of abs(x).
+*/
+void eifrac( x, i, frac )
+unsigned short *x;
+long *i;
+unsigned short *frac;
+{
+unsigned short xi[NI];
+int j, k;
+unsigned long ll;
+
+emovi( x, xi );
+k = (int )xi[E] - (EXONE - 1);
+if( k <= 0 )
+ {
+/* if exponent <= 0, integer = 0 and real output is fraction */
+ *i = 0L;
+ emovo( xi, frac );
+ return;
+ }
+if( k > (8 * sizeof(long) - 1) )
+ {
+/*
+; long integer overflow: output large integer
+; and correct fraction
+*/
+ j = 8 * sizeof(long) - 1;
+ if( xi[0] )
+ *i = (long) ((unsigned long) 1) << j;
+ else
+ *i = (long) (((unsigned long) (~(0L))) >> 1);
+ (void )eshift( xi, k );
+ }
+if( k > 16 )
+ {
+/*
+ Shift more than 16 bits: shift up k-16 mod 16
+ then shift by 16's.
+*/
+ j = k - ((k >> 4) << 4);
+ eshift (xi, j);
+ ll = xi[M];
+ k -= j;
+ do
+ {
+ eshup6 (xi);
+ ll = (ll << 16) | xi[M];
+ }
+ while ((k -= 16) > 0);
+ *i = ll;
+ if (xi[0])
+ *i = -(*i);
+ }
+else
+ {
+/* shift not more than 16 bits */
+ eshift( xi, k );
+ *i = (long )xi[M] & 0xffff;
+ if( xi[0] )
+ *i = -(*i);
+ }
+xi[0] = 0;
+xi[E] = EXONE - 1;
+xi[M] = 0;
+if( (k = enormlz( xi )) > NBITS )
+ ecleaz( xi );
+else
+ xi[E] -= (unsigned short )k;
+
+emovo( xi, frac );
+}
+
+
+/*
+; Find unsigned long integer and fractional parts
+
+; unsigned long i;
+; unsigned short x[NE], frac[NE];
+; xifrac( x, &i, frac );
+
+ A negative e type input yields integer output = 0
+ but correct fraction.
+*/
+void euifrac( x, i, frac )
+unsigned short *x;
+unsigned long *i;
+unsigned short *frac;
+{
+unsigned short xi[NI];
+int j, k;
+unsigned long ll;
+
+emovi( x, xi );
+k = (int )xi[E] - (EXONE - 1);
+if( k <= 0 )
+ {
+/* if exponent <= 0, integer = 0 and argument is fraction */
+ *i = 0L;
+ emovo( xi, frac );
+ return;
+ }
+if( k > (8 * sizeof(long)) )
+ {
+/*
+; long integer overflow: output large integer
+; and correct fraction
+*/
+ *i = ~(0L);
+ (void )eshift( xi, k );
+ }
+else if( k > 16 )
+ {
+/*
+ Shift more than 16 bits: shift up k-16 mod 16
+ then shift up by 16's.
+*/
+ j = k - ((k >> 4) << 4);
+ eshift (xi, j);
+ ll = xi[M];
+ k -= j;
+ do
+ {
+ eshup6 (xi);
+ ll = (ll << 16) | xi[M];
+ }
+ while ((k -= 16) > 0);
+ *i = ll;
+ }
+else
+ {
+/* shift not more than 16 bits */
+ eshift( xi, k );
+ *i = (long )xi[M] & 0xffff;
+ }
+
+if( xi[0] ) /* A negative value yields unsigned integer 0. */
+ *i = 0L;
+
+xi[0] = 0;
+xi[E] = EXONE - 1;
+xi[M] = 0;
+if( (k = enormlz( xi )) > NBITS )
+ ecleaz( xi );
+else
+ xi[E] -= (unsigned short )k;
+
+emovo( xi, frac );
+}
+
+
+
+/*
+; Shift significand
+;
+; Shifts significand area up or down by the number of bits
+; given by the variable sc.
+*/
+int eshift( x, sc )
+unsigned short *x;
+int sc;
+{
+unsigned short lost;
+unsigned short *p;
+
+if( sc == 0 )
+ return( 0 );
+
+lost = 0;
+p = x + NI-1;
+
+if( sc < 0 )
+ {
+ sc = -sc;
+ while( sc >= 16 )
+ {
+ lost |= *p; /* remember lost bits */
+ eshdn6(x);
+ sc -= 16;
+ }
+
+ while( sc >= 8 )
+ {
+ lost |= *p & 0xff;
+ eshdn8(x);
+ sc -= 8;
+ }
+
+ while( sc > 0 )
+ {
+ lost |= *p & 1;
+ eshdn1(x);
+ sc -= 1;
+ }
+ }
+else
+ {
+ while( sc >= 16 )
+ {
+ eshup6(x);
+ sc -= 16;
+ }
+
+ while( sc >= 8 )
+ {
+ eshup8(x);
+ sc -= 8;
+ }
+
+ while( sc > 0 )
+ {
+ eshup1(x);
+ sc -= 1;
+ }
+ }
+if( lost )
+ lost = 1;
+return( (int )lost );
+}
+
+
+
+/*
+; normalize
+;
+; Shift normalizes the significand area pointed to by argument
+; shift count (up = positive) is returned.
+*/
+int enormlz(x)
+unsigned short x[];
+{
+register unsigned short *p;
+int sc;
+
+sc = 0;
+p = &x[M];
+if( *p != 0 )
+ goto normdn;
+++p;
+if( *p & 0x8000 )
+ return( 0 ); /* already normalized */
+while( *p == 0 )
+ {
+ eshup6(x);
+ sc += 16;
+/* With guard word, there are NBITS+16 bits available.
+ * return true if all are zero.
+ */
+ if( sc > NBITS )
+ return( sc );
+ }
+/* see if high byte is zero */
+while( (*p & 0xff00) == 0 )
+ {
+ eshup8(x);
+ sc += 8;
+ }
+/* now shift 1 bit at a time */
+while( (*p & 0x8000) == 0)
+ {
+ eshup1(x);
+ sc += 1;
+ if( sc > (NBITS+16) )
+ {
+ mtherr( "enormlz", UNDERFLOW );
+ return( sc );
+ }
+ }
+return( sc );
+
+/* Normalize by shifting down out of the high guard word
+ of the significand */
+normdn:
+
+if( *p & 0xff00 )
+ {
+ eshdn8(x);
+ sc -= 8;
+ }
+while( *p != 0 )
+ {
+ eshdn1(x);
+ sc -= 1;
+
+ if( sc < -NBITS )
+ {
+ mtherr( "enormlz", OVERFLOW );
+ return( sc );
+ }
+ }
+return( sc );
+}
+
+
+
+
+/* Convert e type number to decimal format ASCII string.
+ * The constants are for 64 bit precision.
+ */
+
+#define NTEN 12
+#define MAXP 4096
+
+#if NE == 10
+static unsigned short etens[NTEN + 1][NE] =
+{
+ {0x6576, 0x4a92, 0x804a, 0x153f,
+ 0xc94c, 0x979a, 0x8a20, 0x5202, 0xc460, 0x7525,}, /* 10**4096 */
+ {0x6a32, 0xce52, 0x329a, 0x28ce,
+ 0xa74d, 0x5de4, 0xc53d, 0x3b5d, 0x9e8b, 0x5a92,}, /* 10**2048 */
+ {0x526c, 0x50ce, 0xf18b, 0x3d28,
+ 0x650d, 0x0c17, 0x8175, 0x7586, 0xc976, 0x4d48,},
+ {0x9c66, 0x58f8, 0xbc50, 0x5c54,
+ 0xcc65, 0x91c6, 0xa60e, 0xa0ae, 0xe319, 0x46a3,},
+ {0x851e, 0xeab7, 0x98fe, 0x901b,
+ 0xddbb, 0xde8d, 0x9df9, 0xebfb, 0xaa7e, 0x4351,},
+ {0x0235, 0x0137, 0x36b1, 0x336c,
+ 0xc66f, 0x8cdf, 0x80e9, 0x47c9, 0x93ba, 0x41a8,},
+ {0x50f8, 0x25fb, 0xc76b, 0x6b71,
+ 0x3cbf, 0xa6d5, 0xffcf, 0x1f49, 0xc278, 0x40d3,},
+ {0x0000, 0x0000, 0x0000, 0x0000,
+ 0xf020, 0xb59d, 0x2b70, 0xada8, 0x9dc5, 0x4069,},
+ {0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0400, 0xc9bf, 0x8e1b, 0x4034,},
+ {0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x2000, 0xbebc, 0x4019,},
+ {0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0x9c40, 0x400c,},
+ {0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0xc800, 0x4005,},
+ {0x0000, 0x0000, 0x0000, 0x0000,
+ 0x0000, 0x0000, 0x0000, 0x0000, 0xa000, 0x4002,}, /* 10**1 */
+};
+
+static unsigned short emtens[NTEN + 1][NE] =
+{
+ {0x2030, 0xcffc, 0xa1c3, 0x8123,
+ 0x2de3, 0x9fde, 0xd2ce, 0x04c8, 0xa6dd, 0x0ad8,}, /* 10**-4096 */
+ {0x8264, 0xd2cb, 0xf2ea, 0x12d4,
+ 0x4925, 0x2de4, 0x3436, 0x534f, 0xceae, 0x256b,}, /* 10**-2048 */
+ {0xf53f, 0xf698, 0x6bd3, 0x0158,
+ 0x87a6, 0xc0bd, 0xda57, 0x82a5, 0xa2a6, 0x32b5,},
+ {0xe731, 0x04d4, 0xe3f2, 0xd332,
+ 0x7132, 0xd21c, 0xdb23, 0xee32, 0x9049, 0x395a,},
+ {0xa23e, 0x5308, 0xfefb, 0x1155,
+ 0xfa91, 0x1939, 0x637a, 0x4325, 0xc031, 0x3cac,},
+ {0xe26d, 0xdbde, 0xd05d, 0xb3f6,
+ 0xac7c, 0xe4a0, 0x64bc, 0x467c, 0xddd0, 0x3e55,},
+ {0x2a20, 0x6224, 0x47b3, 0x98d7,
+ 0x3f23, 0xe9a5, 0xa539, 0xea27, 0xa87f, 0x3f2a,},
+ {0x0b5b, 0x4af2, 0xa581, 0x18ed,
+ 0x67de, 0x94ba, 0x4539, 0x1ead, 0xcfb1, 0x3f94,},
+ {0xbf71, 0xa9b3, 0x7989, 0xbe68,
+ 0x4c2e, 0xe15b, 0xc44d, 0x94be, 0xe695, 0x3fc9,},
+ {0x3d4d, 0x7c3d, 0x36ba, 0x0d2b,
+ 0xfdc2, 0xcefc, 0x8461, 0x7711, 0xabcc, 0x3fe4,},
+ {0xc155, 0xa4a8, 0x404e, 0x6113,
+ 0xd3c3, 0x652b, 0xe219, 0x1758, 0xd1b7, 0x3ff1,},
+ {0xd70a, 0x70a3, 0x0a3d, 0xa3d7,
+ 0x3d70, 0xd70a, 0x70a3, 0x0a3d, 0xa3d7, 0x3ff8,},
+ {0xcccd, 0xcccc, 0xcccc, 0xcccc,
+ 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0x3ffb,}, /* 10**-1 */
+};
+#else
+static unsigned short etens[NTEN+1][NE] = {
+{0xc94c,0x979a,0x8a20,0x5202,0xc460,0x7525,},/* 10**4096 */
+{0xa74d,0x5de4,0xc53d,0x3b5d,0x9e8b,0x5a92,},/* 10**2048 */
+{0x650d,0x0c17,0x8175,0x7586,0xc976,0x4d48,},
+{0xcc65,0x91c6,0xa60e,0xa0ae,0xe319,0x46a3,},
+{0xddbc,0xde8d,0x9df9,0xebfb,0xaa7e,0x4351,},
+{0xc66f,0x8cdf,0x80e9,0x47c9,0x93ba,0x41a8,},
+{0x3cbf,0xa6d5,0xffcf,0x1f49,0xc278,0x40d3,},
+{0xf020,0xb59d,0x2b70,0xada8,0x9dc5,0x4069,},
+{0x0000,0x0000,0x0400,0xc9bf,0x8e1b,0x4034,},
+{0x0000,0x0000,0x0000,0x2000,0xbebc,0x4019,},
+{0x0000,0x0000,0x0000,0x0000,0x9c40,0x400c,},
+{0x0000,0x0000,0x0000,0x0000,0xc800,0x4005,},
+{0x0000,0x0000,0x0000,0x0000,0xa000,0x4002,}, /* 10**1 */
+};
+
+static unsigned short emtens[NTEN+1][NE] = {
+{0x2de4,0x9fde,0xd2ce,0x04c8,0xa6dd,0x0ad8,}, /* 10**-4096 */
+{0x4925,0x2de4,0x3436,0x534f,0xceae,0x256b,}, /* 10**-2048 */
+{0x87a6,0xc0bd,0xda57,0x82a5,0xa2a6,0x32b5,},
+{0x7133,0xd21c,0xdb23,0xee32,0x9049,0x395a,},
+{0xfa91,0x1939,0x637a,0x4325,0xc031,0x3cac,},
+{0xac7d,0xe4a0,0x64bc,0x467c,0xddd0,0x3e55,},
+{0x3f24,0xe9a5,0xa539,0xea27,0xa87f,0x3f2a,},
+{0x67de,0x94ba,0x4539,0x1ead,0xcfb1,0x3f94,},
+{0x4c2f,0xe15b,0xc44d,0x94be,0xe695,0x3fc9,},
+{0xfdc2,0xcefc,0x8461,0x7711,0xabcc,0x3fe4,},
+{0xd3c3,0x652b,0xe219,0x1758,0xd1b7,0x3ff1,},
+{0x3d71,0xd70a,0x70a3,0x0a3d,0xa3d7,0x3ff8,},
+{0xcccd,0xcccc,0xcccc,0xcccc,0xcccc,0x3ffb,}, /* 10**-1 */
+};
+#endif
+
+void e24toasc( x, string, ndigs )
+unsigned short x[];
+char *string;
+int ndigs;
+{
+unsigned short w[NI];
+
+e24toe( x, w );
+etoasc( w, string, ndigs );
+}
+
+
+void e53toasc( x, string, ndigs )
+unsigned short x[];
+char *string;
+int ndigs;
+{
+unsigned short w[NI];
+
+e53toe( x, w );
+etoasc( w, string, ndigs );
+}
+
+
+void e64toasc( x, string, ndigs )
+unsigned short x[];
+char *string;
+int ndigs;
+{
+unsigned short w[NI];
+
+e64toe( x, w );
+etoasc( w, string, ndigs );
+}
+
+void e113toasc (x, string, ndigs)
+unsigned short x[];
+char *string;
+int ndigs;
+{
+unsigned short w[NI];
+
+e113toe (x, w);
+etoasc (w, string, ndigs);
+}
+
+
+void etoasc( x, string, ndigs )
+unsigned short x[];
+char *string;
+int ndigs;
+{
+long digit;
+unsigned short y[NI], t[NI], u[NI], w[NI];
+unsigned short *p, *r, *ten;
+unsigned short sign;
+int i, j, k, expon, rndsav;
+char *s, *ss;
+unsigned short m;
+
+rndsav = rndprc;
+#ifdef NANS
+if( eisnan(x) )
+ {
+ sprintf( string, " NaN " );
+ goto bxit;
+ }
+#endif
+rndprc = NBITS; /* set to full precision */
+emov( x, y ); /* retain external format */
+if( y[NE-1] & 0x8000 )
+ {
+ sign = 0xffff;
+ y[NE-1] &= 0x7fff;
+ }
+else
+ {
+ sign = 0;
+ }
+expon = 0;
+ten = &etens[NTEN][0];
+emov( eone, t );
+/* Test for zero exponent */
+if( y[NE-1] == 0 )
+ {
+ for( k=0; k<NE-1; k++ )
+ {
+ if( y[k] != 0 )
+ goto tnzro; /* denormalized number */
+ }
+ goto isone; /* legal all zeros */
+ }
+tnzro:
+
+/* Test for infinity.
+ */
+if( y[NE-1] == 0x7fff )
+ {
+ if( sign )
+ sprintf( string, " -Infinity " );
+ else
+ sprintf( string, " Infinity " );
+ goto bxit;
+ }
+
+/* Test for exponent nonzero but significand denormalized.
+ * This is an error condition.
+ */
+if( (y[NE-1] != 0) && ((y[NE-2] & 0x8000) == 0) )
+ {
+ mtherr( "etoasc", DOMAIN );
+ sprintf( string, "NaN" );
+ goto bxit;
+ }
+
+/* Compare to 1.0 */
+i = ecmp( eone, y );
+if( i == 0 )
+ goto isone;
+
+if( i < 0 )
+ { /* Number is greater than 1 */
+/* Convert significand to an integer and strip trailing decimal zeros. */
+ emov( y, u );
+ u[NE-1] = EXONE + NBITS - 1;
+
+ p = &etens[NTEN-4][0];
+ m = 16;
+do
+ {
+ ediv( p, u, t );
+ efloor( t, w );
+ for( j=0; j<NE-1; j++ )
+ {
+ if( t[j] != w[j] )
+ goto noint;
+ }
+ emov( t, u );
+ expon += (int )m;
+noint:
+ p += NE;
+ m >>= 1;
+ }
+while( m != 0 );
+
+/* Rescale from integer significand */
+ u[NE-1] += y[NE-1] - (unsigned int )(EXONE + NBITS - 1);
+ emov( u, y );
+/* Find power of 10 */
+ emov( eone, t );
+ m = MAXP;
+ p = &etens[0][0];
+ while( ecmp( ten, u ) <= 0 )
+ {
+ if( ecmp( p, u ) <= 0 )
+ {
+ ediv( p, u, u );
+ emul( p, t, t );
+ expon += (int )m;
+ }
+ m >>= 1;
+ if( m == 0 )
+ break;
+ p += NE;
+ }
+ }
+else
+ { /* Number is less than 1.0 */
+/* Pad significand with trailing decimal zeros. */
+ if( y[NE-1] == 0 )
+ {
+ while( (y[NE-2] & 0x8000) == 0 )
+ {
+ emul( ten, y, y );
+ expon -= 1;
+ }
+ }
+ else
+ {
+ emovi( y, w );
+ for( i=0; i<NDEC+1; i++ )
+ {
+ if( (w[NI-1] & 0x7) != 0 )
+ break;
+/* multiply by 10 */
+ emovz( w, u );
+ eshdn1( u );
+ eshdn1( u );
+ eaddm( w, u );
+ u[1] += 3;
+ while( u[2] != 0 )
+ {
+ eshdn1(u);
+ u[1] += 1;
+ }
+ if( u[NI-1] != 0 )
+ break;
+ if( eone[NE-1] <= u[1] )
+ break;
+ emovz( u, w );
+ expon -= 1;
+ }
+ emovo( w, y );
+ }
+ k = -MAXP;
+ p = &emtens[0][0];
+ r = &etens[0][0];
+ emov( y, w );
+ emov( eone, t );
+ while( ecmp( eone, w ) > 0 )
+ {
+ if( ecmp( p, w ) >= 0 )
+ {
+ emul( r, w, w );
+ emul( r, t, t );
+ expon += k;
+ }
+ k /= 2;
+ if( k == 0 )
+ break;
+ p += NE;
+ r += NE;
+ }
+ ediv( t, eone, t );
+ }
+isone:
+/* Find the first (leading) digit. */
+emovi( t, w );
+emovz( w, t );
+emovi( y, w );
+emovz( w, y );
+eiremain( t, y );
+digit = equot[NI-1];
+while( (digit == 0) && (ecmp(y,ezero) != 0) )
+ {
+ eshup1( y );
+ emovz( y, u );
+ eshup1( u );
+ eshup1( u );
+ eaddm( u, y );
+ eiremain( t, y );
+ digit = equot[NI-1];
+ expon -= 1;
+ }
+s = string;
+if( sign )
+ *s++ = '-';
+else
+ *s++ = ' ';
+/* Examine number of digits requested by caller. */
+if( ndigs < 0 )
+ ndigs = 0;
+if( ndigs > NDEC )
+ ndigs = NDEC;
+if( digit == 10 )
+ {
+ *s++ = '1';
+ *s++ = '.';
+ if( ndigs > 0 )
+ {
+ *s++ = '0';
+ ndigs -= 1;
+ }
+ expon += 1;
+ }
+else
+ {
+ *s++ = (char )digit + '0';
+ *s++ = '.';
+ }
+/* Generate digits after the decimal point. */
+for( k=0; k<=ndigs; k++ )
+ {
+/* multiply current number by 10, without normalizing */
+ eshup1( y );
+ emovz( y, u );
+ eshup1( u );
+ eshup1( u );
+ eaddm( u, y );
+ eiremain( t, y );
+ *s++ = (char )equot[NI-1] + '0';
+ }
+digit = equot[NI-1];
+--s;
+ss = s;
+/* round off the ASCII string */
+if( digit > 4 )
+ {
+/* Test for critical rounding case in ASCII output. */
+ if( digit == 5 )
+ {
+ emovo( y, t );
+ if( ecmp(t,ezero) != 0 )
+ goto roun; /* round to nearest */
+ if( (*(s-1) & 1) == 0 )
+ goto doexp; /* round to even */
+ }
+/* Round up and propagate carry-outs */
+roun:
+ --s;
+ k = *s & 0x7f;
+/* Carry out to most significant digit? */
+ if( k == '.' )
+ {
+ --s;
+ k = *s;
+ k += 1;
+ *s = (char )k;
+/* Most significant digit carries to 10? */
+ if( k > '9' )
+ {
+ expon += 1;
+ *s = '1';
+ }
+ goto doexp;
+ }
+/* Round up and carry out from less significant digits */
+ k += 1;
+ *s = (char )k;
+ if( k > '9' )
+ {
+ *s = '0';
+ goto roun;
+ }
+ }
+doexp:
+/*
+if( expon >= 0 )
+ sprintf( ss, "e+%d", expon );
+else
+ sprintf( ss, "e%d", expon );
+*/
+ sprintf( ss, "E%d", expon );
+bxit:
+rndprc = rndsav;
+}
+
+
+
+
+/*
+; ASCTOQ
+; ASCTOQ.MAC LATEST REV: 11 JAN 84
+; SLM, 3 JAN 78
+;
+; Convert ASCII string to quadruple precision floating point
+;
+; Numeric input is free field decimal number
+; with max of 15 digits with or without
+; decimal point entered as ASCII from teletype.
+; Entering E after the number followed by a second
+; number causes the second number to be interpreted
+; as a power of 10 to be multiplied by the first number
+; (i.e., "scientific" notation).
+;
+; Usage:
+; asctoq( string, q );
+*/
+
+/* ASCII to single */
+void asctoe24( s, y )
+char *s;
+unsigned short *y;
+{
+asctoeg( s, y, 24 );
+}
+
+
+/* ASCII to double */
+void asctoe53( s, y )
+char *s;
+unsigned short *y;
+{
+#ifdef DEC
+asctoeg( s, y, 56 );
+#else
+asctoeg( s, y, 53 );
+#endif
+}
+
+
+/* ASCII to long double */
+void asctoe64( s, y )
+char *s;
+unsigned short *y;
+{
+asctoeg( s, y, 64 );
+}
+
+/* ASCII to 128-bit long double */
+void asctoe113 (s, y)
+char *s;
+unsigned short *y;
+{
+asctoeg( s, y, 113 );
+}
+
+/* ASCII to super double */
+void asctoe( s, y )
+char *s;
+unsigned short *y;
+{
+asctoeg( s, y, NBITS );
+}
+
+/* Space to make a copy of the input string: */
+static char lstr[82] = {0};
+
+void asctoeg( ss, y, oprec )
+char *ss;
+unsigned short *y;
+int oprec;
+{
+unsigned short yy[NI], xt[NI], tt[NI];
+int esign, decflg, sgnflg, nexp, exp, prec, lost;
+int k, trail, c, rndsav;
+long lexp;
+unsigned short nsign, *p;
+char *sp, *s;
+
+/* Copy the input string. */
+s = ss;
+while( *s == ' ' ) /* skip leading spaces */
+ ++s;
+sp = lstr;
+for( k=0; k<79; k++ )
+ {
+ if( (*sp++ = *s++) == '\0' )
+ break;
+ }
+*sp = '\0';
+s = lstr;
+
+rndsav = rndprc;
+rndprc = NBITS; /* Set to full precision */
+lost = 0;
+nsign = 0;
+decflg = 0;
+sgnflg = 0;
+nexp = 0;
+exp = 0;
+prec = 0;
+ecleaz( yy );
+trail = 0;
+
+nxtcom:
+k = *s - '0';
+if( (k >= 0) && (k <= 9) )
+ {
+/* Ignore leading zeros */
+ if( (prec == 0) && (decflg == 0) && (k == 0) )
+ goto donchr;
+/* Identify and strip trailing zeros after the decimal point. */
+ if( (trail == 0) && (decflg != 0) )
+ {
+ sp = s;
+ while( (*sp >= '0') && (*sp <= '9') )
+ ++sp;
+/* Check for syntax error */
+ c = *sp & 0x7f;
+ if( (c != 'e') && (c != 'E') && (c != '\0')
+ && (c != '\n') && (c != '\r') && (c != ' ')
+ && (c != ',') )
+ goto error;
+ --sp;
+ while( *sp == '0' )
+ *sp-- = 'z';
+ trail = 1;
+ if( *s == 'z' )
+ goto donchr;
+ }
+/* If enough digits were given to more than fill up the yy register,
+ * continuing until overflow into the high guard word yy[2]
+ * guarantees that there will be a roundoff bit at the top
+ * of the low guard word after normalization.
+ */
+ if( yy[2] == 0 )
+ {
+ if( decflg )
+ nexp += 1; /* count digits after decimal point */
+ eshup1( yy ); /* multiply current number by 10 */
+ emovz( yy, xt );
+ eshup1( xt );
+ eshup1( xt );
+ eaddm( xt, yy );
+ ecleaz( xt );
+ xt[NI-2] = (unsigned short )k;
+ eaddm( xt, yy );
+ }
+ else
+ {
+ /* Mark any lost non-zero digit. */
+ lost |= k;
+ /* Count lost digits before the decimal point. */
+ if (decflg == 0)
+ nexp -= 1;
+ }
+ prec += 1;
+ goto donchr;
+ }
+
+switch( *s )
+ {
+ case 'z':
+ break;
+ case 'E':
+ case 'e':
+ goto expnt;
+ case '.': /* decimal point */
+ if( decflg )
+ goto error;
+ ++decflg;
+ break;
+ case '-':
+ nsign = 0xffff;
+ if( sgnflg )
+ goto error;
+ ++sgnflg;
+ break;
+ case '+':
+ if( sgnflg )
+ goto error;
+ ++sgnflg;
+ break;
+ case ',':
+ case ' ':
+ case '\0':
+ case '\n':
+ case '\r':
+ goto daldone;
+ case 'i':
+ case 'I':
+ goto infinite;
+ default:
+ error:
+#ifdef NANS
+ enan( yy, NI*16 );
+#else
+ mtherr( "asctoe", DOMAIN );
+ ecleaz(yy);
+#endif
+ goto aexit;
+ }
+donchr:
+++s;
+goto nxtcom;
+
+/* Exponent interpretation */
+expnt:
+
+esign = 1;
+exp = 0;
+++s;
+/* check for + or - */
+if( *s == '-' )
+ {
+ esign = -1;
+ ++s;
+ }
+if( *s == '+' )
+ ++s;
+while( (*s >= '0') && (*s <= '9') )
+ {
+ exp *= 10;
+ exp += *s++ - '0';
+ if (exp > 4977)
+ {
+ if (esign < 0)
+ goto zero;
+ else
+ goto infinite;
+ }
+ }
+if( esign < 0 )
+ exp = -exp;
+if( exp > 4932 )
+ {
+infinite:
+ ecleaz(yy);
+ yy[E] = 0x7fff; /* infinity */
+ goto aexit;
+ }
+if( exp < -4977 )
+ {
+zero:
+ ecleaz(yy);
+ goto aexit;
+ }
+
+daldone:
+nexp = exp - nexp;
+/* Pad trailing zeros to minimize power of 10, per IEEE spec. */
+while( (nexp > 0) && (yy[2] == 0) )
+ {
+ emovz( yy, xt );
+ eshup1( xt );
+ eshup1( xt );
+ eaddm( yy, xt );
+ eshup1( xt );
+ if( xt[2] != 0 )
+ break;
+ nexp -= 1;
+ emovz( xt, yy );
+ }
+if( (k = enormlz(yy)) > NBITS )
+ {
+ ecleaz(yy);
+ goto aexit;
+ }
+lexp = (EXONE - 1 + NBITS) - k;
+emdnorm( yy, lost, 0, lexp, 64 );
+/* convert to external format */
+
+
+/* Multiply by 10**nexp. If precision is 64 bits,
+ * the maximum relative error incurred in forming 10**n
+ * for 0 <= n <= 324 is 8.2e-20, at 10**180.
+ * For 0 <= n <= 999, the peak relative error is 1.4e-19 at 10**947.
+ * For 0 >= n >= -999, it is -1.55e-19 at 10**-435.
+ */
+lexp = yy[E];
+if( nexp == 0 )
+ {
+ k = 0;
+ goto expdon;
+ }
+esign = 1;
+if( nexp < 0 )
+ {
+ nexp = -nexp;
+ esign = -1;
+ if( nexp > 4096 )
+ { /* Punt. Can't handle this without 2 divides. */
+ emovi( etens[0], tt );
+ lexp -= tt[E];
+ k = edivm( tt, yy );
+ lexp += EXONE;
+ nexp -= 4096;
+ }
+ }
+p = &etens[NTEN][0];
+emov( eone, xt );
+exp = 1;
+do
+ {
+ if( exp & nexp )
+ emul( p, xt, xt );
+ p -= NE;
+ exp = exp + exp;
+ }
+while( exp <= MAXP );
+
+emovi( xt, tt );
+if( esign < 0 )
+ {
+ lexp -= tt[E];
+ k = edivm( tt, yy );
+ lexp += EXONE;
+ }
+else
+ {
+ lexp += tt[E];
+ k = emulm( tt, yy );
+ lexp -= EXONE - 1;
+ }
+
+expdon:
+
+/* Round and convert directly to the destination type */
+if( oprec == 53 )
+ lexp -= EXONE - 0x3ff;
+else if( oprec == 24 )
+ lexp -= EXONE - 0177;
+#ifdef DEC
+else if( oprec == 56 )
+ lexp -= EXONE - 0201;
+#endif
+rndprc = oprec;
+emdnorm( yy, k, 0, lexp, 64 );
+
+aexit:
+
+rndprc = rndsav;
+yy[0] = nsign;
+switch( oprec )
+ {
+#ifdef DEC
+ case 56:
+ todec( yy, y ); /* see etodec.c */
+ break;
+#endif
+ case 53:
+ toe53( yy, y );
+ break;
+ case 24:
+ toe24( yy, y );
+ break;
+ case 64:
+ toe64( yy, y );
+ break;
+ case 113:
+ toe113( yy, y );
+ break;
+ case NBITS:
+ emovo( yy, y );
+ break;
+ }
+}
+
+
+
+/* y = largest integer not greater than x
+ * (truncated toward minus infinity)
+ *
+ * unsigned short x[NE], y[NE]
+ *
+ * efloor( x, y );
+ */
+static unsigned short bmask[] = {
+0xffff,
+0xfffe,
+0xfffc,
+0xfff8,
+0xfff0,
+0xffe0,
+0xffc0,
+0xff80,
+0xff00,
+0xfe00,
+0xfc00,
+0xf800,
+0xf000,
+0xe000,
+0xc000,
+0x8000,
+0x0000,
+};
+
+void efloor( x, y )
+unsigned short x[], y[];
+{
+register unsigned short *p;
+int e, expon, i;
+unsigned short f[NE];
+
+emov( x, f ); /* leave in external format */
+expon = (int )f[NE-1];
+e = (expon & 0x7fff) - (EXONE - 1);
+if( e <= 0 )
+ {
+ eclear(y);
+ goto isitneg;
+ }
+/* number of bits to clear out */
+e = NBITS - e;
+emov( f, y );
+if( e <= 0 )
+ return;
+
+p = &y[0];
+while( e >= 16 )
+ {
+ *p++ = 0;
+ e -= 16;
+ }
+/* clear the remaining bits */
+*p &= bmask[e];
+/* truncate negatives toward minus infinity */
+isitneg:
+
+if( (unsigned short )expon & (unsigned short )0x8000 )
+ {
+ for( i=0; i<NE-1; i++ )
+ {
+ if( f[i] != y[i] )
+ {
+ esub( eone, y, y );
+ break;
+ }
+ }
+ }
+}
+
+
+/* unsigned short x[], s[];
+ * long *exp;
+ *
+ * efrexp( x, exp, s );
+ *
+ * Returns s and exp such that s * 2**exp = x and .5 <= s < 1.
+ * For example, 1.1 = 0.55 * 2**1
+ * Handles denormalized numbers properly using long integer exp.
+ */
+void efrexp( x, exp, s )
+unsigned short x[];
+long *exp;
+unsigned short s[];
+{
+unsigned short xi[NI];
+long li;
+
+emovi( x, xi );
+li = (long )((short )xi[1]);
+
+if( li == 0 )
+ {
+ li -= enormlz( xi );
+ }
+xi[1] = 0x3ffe;
+emovo( xi, s );
+*exp = li - 0x3ffe;
+}
+
+
+
+/* unsigned short x[], y[];
+ * long pwr2;
+ *
+ * eldexp( x, pwr2, y );
+ *
+ * Returns y = x * 2**pwr2.
+ */
+void eldexp( x, pwr2, y )
+unsigned short x[];
+long pwr2;
+unsigned short y[];
+{
+unsigned short xi[NI];
+long li;
+int i;
+
+emovi( x, xi );
+li = xi[1];
+li += pwr2;
+i = 0;
+emdnorm( xi, i, i, li, 64 );
+emovo( xi, y );
+}
+
+
+/* c = remainder after dividing b by a
+ * Least significant integer quotient bits left in equot[].
+ */
+void eremain( a, b, c )
+unsigned short a[], b[], c[];
+{
+unsigned short den[NI], num[NI];
+
+#ifdef NANS
+if( eisinf(b) || (ecmp(a,ezero) == 0) || eisnan(a) || eisnan(b))
+ {
+ enan( c, NBITS );
+ return;
+ }
+#endif
+if( ecmp(a,ezero) == 0 )
+ {
+ mtherr( "eremain", SING );
+ eclear( c );
+ return;
+ }
+emovi( a, den );
+emovi( b, num );
+eiremain( den, num );
+/* Sign of remainder = sign of quotient */
+if( a[0] == b[0] )
+ num[0] = 0;
+else
+ num[0] = 0xffff;
+emovo( num, c );
+}
+
+
+void eiremain( den, num )
+unsigned short den[], num[];
+{
+long ld, ln;
+unsigned short j;
+
+ld = den[E];
+ld -= enormlz( den );
+ln = num[E];
+ln -= enormlz( num );
+ecleaz( equot );
+while( ln >= ld )
+ {
+ if( ecmpm(den,num) <= 0 )
+ {
+ esubm(den, num);
+ j = 1;
+ }
+ else
+ {
+ j = 0;
+ }
+ eshup1(equot);
+ equot[NI-1] |= j;
+ eshup1(num);
+ ln -= 1;
+ }
+emdnorm( num, 0, 0, ln, 0 );
+}
+
+/* NaN bit patterns
+ */
+#ifdef MIEEE
+unsigned short nan113[8] = {
+ 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff};
+unsigned short nan64[6] = {0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff};
+unsigned short nan53[4] = {0x7fff, 0xffff, 0xffff, 0xffff};
+unsigned short nan24[2] = {0x7fff, 0xffff};
+#endif
+
+#ifdef IBMPC
+unsigned short nan113[8] = {0, 0, 0, 0, 0, 0, 0xc000, 0xffff};
+unsigned short nan64[6] = {0, 0, 0, 0xc000, 0xffff, 0};
+unsigned short nan53[4] = {0, 0, 0, 0xfff8};
+unsigned short nan24[2] = {0, 0xffc0};
+#endif
+
+
+void enan (nan, size)
+unsigned short *nan;
+int size;
+{
+int i, n;
+unsigned short *p;
+
+switch( size )
+ {
+#ifndef DEC
+ case 113:
+ n = 8;
+ p = nan113;
+ break;
+
+ case 64:
+ n = 6;
+ p = nan64;
+ break;
+
+ case 53:
+ n = 4;
+ p = nan53;
+ break;
+
+ case 24:
+ n = 2;
+ p = nan24;
+ break;
+
+ case NBITS:
+ for( i=0; i<NE-2; i++ )
+ *nan++ = 0;
+ *nan++ = 0xc000;
+ *nan++ = 0x7fff;
+ return;
+
+ case NI*16:
+ *nan++ = 0;
+ *nan++ = 0x7fff;
+ *nan++ = 0;
+ *nan++ = 0xc000;
+ for( i=4; i<NI; i++ )
+ *nan++ = 0;
+ return;
+#endif
+ default:
+ mtherr( "enan", DOMAIN );
+ return;
+ }
+for (i=0; i < n; i++)
+ *nan++ = *p++;
+}
+
+
+
+/* Longhand square root. */
+
+static int esqinited = 0;
+static unsigned short sqrndbit[NI];
+
+void esqrt( x, y )
+unsigned short *x, *y;
+{
+unsigned short temp[NI], num[NI], sq[NI], xx[NI];
+int i, j, k, n, nlups;
+long m, exp;
+
+if( esqinited == 0 )
+ {
+ ecleaz( sqrndbit );
+ sqrndbit[NI-2] = 1;
+ esqinited = 1;
+ }
+/* Check for arg <= 0 */
+i = ecmp( x, ezero );
+if( i <= 0 )
+ {
+#ifdef NANS
+ if (i == -2)
+ {
+ enan (y, NBITS);
+ return;
+ }
+#endif
+ eclear(y);
+ if( i < 0 )
+ mtherr( "esqrt", DOMAIN );
+ return;
+ }
+
+#ifdef INFINITY
+if( eisinf(x) )
+ {
+ eclear(y);
+ einfin(y);
+ return;
+ }
+#endif
+/* Bring in the arg and renormalize if it is denormal. */
+emovi( x, xx );
+m = (long )xx[1]; /* local long word exponent */
+if( m == 0 )
+ m -= enormlz( xx );
+
+/* Divide exponent by 2 */
+m -= 0x3ffe;
+exp = (unsigned short )( (m / 2) + 0x3ffe );
+
+/* Adjust if exponent odd */
+if( (m & 1) != 0 )
+ {
+ if( m > 0 )
+ exp += 1;
+ eshdn1( xx );
+ }
+
+ecleaz( sq );
+ecleaz( num );
+n = 8; /* get 8 bits of result per inner loop */
+nlups = rndprc;
+j = 0;
+
+while( nlups > 0 )
+ {
+/* bring in next word of arg */
+ if( j < NE )
+ num[NI-1] = xx[j+3];
+/* Do additional bit on last outer loop, for roundoff. */
+ if( nlups <= 8 )
+ n = nlups + 1;
+ for( i=0; i<n; i++ )
+ {
+/* Next 2 bits of arg */
+ eshup1( num );
+ eshup1( num );
+/* Shift up answer */
+ eshup1( sq );
+/* Make trial divisor */
+ for( k=0; k<NI; k++ )
+ temp[k] = sq[k];
+ eshup1( temp );
+ eaddm( sqrndbit, temp );
+/* Subtract and insert answer bit if it goes in */
+ if( ecmpm( temp, num ) <= 0 )
+ {
+ esubm( temp, num );
+ sq[NI-2] |= 1;
+ }
+ }
+ nlups -= n;
+ j += 1;
+ }
+
+/* Adjust for extra, roundoff loop done. */
+exp += (NBITS - 1) - rndprc;
+
+/* Sticky bit = 1 if the remainder is nonzero. */
+k = 0;
+for( i=3; i<NI; i++ )
+ k |= (int )num[i];
+
+/* Renormalize and round off. */
+emdnorm( sq, k, 0, exp, 64 );
+emovo( sq, y );
+}
diff --git a/libm/ldouble/igamil.c b/libm/ldouble/igamil.c
new file mode 100644
index 000000000..1abe503e9
--- /dev/null
+++ b/libm/ldouble/igamil.c
@@ -0,0 +1,193 @@
+/* igamil()
+ *
+ * Inverse of complemented imcomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, x, y, igamil();
+ *
+ * x = igamil( a, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given y, the function finds x such that
+ *
+ * igamc( a, x ) = y.
+ *
+ * Starting with the approximate value
+ *
+ * 3
+ * x = a t
+ *
+ * where
+ *
+ * t = 1 - d - ndtri(y) sqrt(d)
+ *
+ * and
+ *
+ * d = 1/9a,
+ *
+ * the routine performs up to 10 Newton iterations to find the
+ * root of igamc(a,x) - y = 0.
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested for a ranging from 0.5 to 30 and x from 0 to 0.5.
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,0.5 3400 8.8e-16 1.3e-16
+ * IEEE 0,0.5 10000 1.1e-14 1.0e-15
+ *
+ */
+
+/*
+Cephes Math Library Release 2.3: March, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+extern long double MACHEPL, MAXNUML, MAXLOGL, MINLOGL;
+#ifdef ANSIPROT
+extern long double ndtril ( long double );
+extern long double expl ( long double );
+extern long double fabsl ( long double );
+extern long double logl ( long double );
+extern long double sqrtl ( long double );
+extern long double lgaml ( long double );
+extern long double igamcl ( long double, long double );
+#else
+long double ndtril(), expl(), fabsl(), logl(), sqrtl(), lgaml();
+long double igamcl();
+#endif
+
+long double igamil( a, y0 )
+long double a, y0;
+{
+long double x0, x1, x, yl, yh, y, d, lgm, dithresh;
+int i, dir;
+
+/* bound the solution */
+x0 = MAXNUML;
+yl = 0.0L;
+x1 = 0.0L;
+yh = 1.0L;
+dithresh = 4.0 * MACHEPL;
+
+/* approximation to inverse function */
+d = 1.0L/(9.0L*a);
+y = ( 1.0L - d - ndtril(y0) * sqrtl(d) );
+x = a * y * y * y;
+
+lgm = lgaml(a);
+
+for( i=0; i<10; i++ )
+ {
+ if( x > x0 || x < x1 )
+ goto ihalve;
+ y = igamcl(a,x);
+ if( y < yl || y > yh )
+ goto ihalve;
+ if( y < y0 )
+ {
+ x0 = x;
+ yl = y;
+ }
+ else
+ {
+ x1 = x;
+ yh = y;
+ }
+/* compute the derivative of the function at this point */
+ d = (a - 1.0L) * logl(x0) - x0 - lgm;
+ if( d < -MAXLOGL )
+ goto ihalve;
+ d = -expl(d);
+/* compute the step to the next approximation of x */
+ d = (y - y0)/d;
+ x = x - d;
+ if( i < 3 )
+ continue;
+ if( fabsl(d/x) < dithresh )
+ goto done;
+ }
+
+/* Resort to interval halving if Newton iteration did not converge. */
+ihalve:
+
+d = 0.0625L;
+if( x0 == MAXNUML )
+ {
+ if( x <= 0.0L )
+ x = 1.0L;
+ while( x0 == MAXNUML )
+ {
+ x = (1.0L + d) * x;
+ y = igamcl( a, x );
+ if( y < y0 )
+ {
+ x0 = x;
+ yl = y;
+ break;
+ }
+ d = d + d;
+ }
+ }
+d = 0.5L;
+dir = 0;
+
+for( i=0; i<400; i++ )
+ {
+ x = x1 + d * (x0 - x1);
+ y = igamcl( a, x );
+ lgm = (x0 - x1)/(x1 + x0);
+ if( fabsl(lgm) < dithresh )
+ break;
+ lgm = (y - y0)/y0;
+ if( fabsl(lgm) < dithresh )
+ break;
+ if( x <= 0.0L )
+ break;
+ if( y > y0 )
+ {
+ x1 = x;
+ yh = y;
+ if( dir < 0 )
+ {
+ dir = 0;
+ d = 0.5L;
+ }
+ else if( dir > 1 )
+ d = 0.5L * d + 0.5L;
+ else
+ d = (y0 - yl)/(yh - yl);
+ dir += 1;
+ }
+ else
+ {
+ x0 = x;
+ yl = y;
+ if( dir > 0 )
+ {
+ dir = 0;
+ d = 0.5L;
+ }
+ else if( dir < -1 )
+ d = 0.5L * d;
+ else
+ d = (y0 - yl)/(yh - yl);
+ dir -= 1;
+ }
+ }
+if( x == 0.0L )
+ mtherr( "igamil", UNDERFLOW );
+
+done:
+return( x );
+}
diff --git a/libm/ldouble/igaml.c b/libm/ldouble/igaml.c
new file mode 100644
index 000000000..0e59c5404
--- /dev/null
+++ b/libm/ldouble/igaml.c
@@ -0,0 +1,220 @@
+/* igaml.c
+ *
+ * Incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, x, y, igaml();
+ *
+ * y = igaml( a, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ * x
+ * -
+ * 1 | | -t a-1
+ * igam(a,x) = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * 0
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 4000 4.4e-15 6.3e-16
+ * IEEE 0,30 10000 3.6e-14 5.1e-15
+ *
+ */
+ /* igamcl()
+ *
+ * Complemented incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, x, y, igamcl();
+ *
+ * y = igamcl( a, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ *
+ * igamc(a,x) = 1 - igam(a,x)
+ *
+ * inf.
+ * -
+ * 1 | | -t a-1
+ * = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * x
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * DEC 0,30 2000 2.7e-15 4.0e-16
+ * IEEE 0,30 60000 1.4e-12 6.3e-15
+ *
+ */
+
+/*
+Cephes Math Library Release 2.3: March, 1995
+Copyright 1985, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double lgaml ( long double );
+extern long double expl ( long double );
+extern long double logl ( long double );
+extern long double fabsl ( long double );
+extern long double gammal ( long double );
+long double igaml ( long double, long double );
+long double igamcl ( long double, long double );
+#else
+long double lgaml(), expl(), logl(), fabsl(), igaml(), gammal();
+long double igamcl();
+#endif
+
+#define BIG 9.223372036854775808e18L
+#define MAXGAML 1755.455L
+extern long double MACHEPL, MINLOGL;
+
+long double igamcl( a, x )
+long double a, x;
+{
+long double ans, c, yc, ax, y, z, r, t;
+long double pk, pkm1, pkm2, qk, qkm1, qkm2;
+
+if( (x <= 0.0L) || ( a <= 0.0L) )
+ return( 1.0L );
+
+if( (x < 1.0L) || (x < a) )
+ return( 1.0L - igaml(a,x) );
+
+ax = a * logl(x) - x - lgaml(a);
+if( ax < MINLOGL )
+ {
+ mtherr( "igamcl", UNDERFLOW );
+ return( 0.0L );
+ }
+ax = expl(ax);
+
+/* continued fraction */
+y = 1.0L - a;
+z = x + y + 1.0L;
+c = 0.0L;
+pkm2 = 1.0L;
+qkm2 = x;
+pkm1 = x + 1.0L;
+qkm1 = z * x;
+ans = pkm1/qkm1;
+
+do
+ {
+ c += 1.0L;
+ y += 1.0L;
+ z += 2.0L;
+ yc = y * c;
+ pk = pkm1 * z - pkm2 * yc;
+ qk = qkm1 * z - qkm2 * yc;
+ if( qk != 0.0L )
+ {
+ r = pk/qk;
+ t = fabsl( (ans - r)/r );
+ ans = r;
+ }
+ else
+ t = 1.0L;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+ if( fabsl(pk) > BIG )
+ {
+ pkm2 /= BIG;
+ pkm1 /= BIG;
+ qkm2 /= BIG;
+ qkm1 /= BIG;
+ }
+ }
+while( t > MACHEPL );
+
+return( ans * ax );
+}
+
+
+
+/* left tail of incomplete gamma function:
+ *
+ * inf. k
+ * a -x - x
+ * x e > ----------
+ * - -
+ * k=0 | (a+k+1)
+ *
+ */
+
+long double igaml( a, x )
+long double a, x;
+{
+long double ans, ax, c, r;
+
+if( (x <= 0.0L) || ( a <= 0.0L) )
+ return( 0.0L );
+
+if( (x > 1.0L) && (x > a ) )
+ return( 1.0L - igamcl(a,x) );
+
+ax = a * logl(x) - x - lgaml(a);
+if( ax < MINLOGL )
+ {
+ mtherr( "igaml", UNDERFLOW );
+ return( 0.0L );
+ }
+ax = expl(ax);
+
+/* power series */
+r = a;
+c = 1.0L;
+ans = 1.0L;
+
+do
+ {
+ r += 1.0L;
+ c *= x/r;
+ ans += c;
+ }
+while( c/ans > MACHEPL );
+
+return( ans * ax/a );
+}
diff --git a/libm/ldouble/incbetl.c b/libm/ldouble/incbetl.c
new file mode 100644
index 000000000..fc85ead4c
--- /dev/null
+++ b/libm/ldouble/incbetl.c
@@ -0,0 +1,406 @@
+/* incbetl.c
+ *
+ * Incomplete beta integral
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, b, x, y, incbetl();
+ *
+ * y = incbetl( a, b, x );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns incomplete beta integral of the arguments, evaluated
+ * from zero to x. The function is defined as
+ *
+ * x
+ * - -
+ * | (a+b) | | a-1 b-1
+ * ----------- | t (1-t) dt.
+ * - - | |
+ * | (a) | (b) -
+ * 0
+ *
+ * The domain of definition is 0 <= x <= 1. In this
+ * implementation a and b are restricted to positive values.
+ * The integral from x to 1 may be obtained by the symmetry
+ * relation
+ *
+ * 1 - incbet( a, b, x ) = incbet( b, a, 1-x ).
+ *
+ * The integral is evaluated by a continued fraction expansion
+ * or, when b*x is small, by a power series.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,x) with x between 0 and 1.
+ * arithmetic domain # trials peak rms
+ * IEEE 0,5 20000 4.5e-18 2.4e-19
+ * IEEE 0,100 100000 3.9e-17 1.0e-17
+ * Half-integer a, b:
+ * IEEE .5,10000 100000 3.9e-14 4.4e-15
+ * Outputs smaller than the IEEE gradual underflow threshold
+ * were excluded from these statistics.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * incbetl domain x<0, x>1 0.0
+ */
+
+
+/*
+Cephes Math Library, Release 2.3: January, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#define MAXGAML 1755.455L
+static long double big = 9.223372036854775808e18L;
+static long double biginv = 1.084202172485504434007e-19L;
+extern long double MACHEPL, MINLOGL, MAXLOGL;
+
+#ifdef ANSIPROT
+extern long double gammal ( long double );
+extern long double lgaml ( long double );
+extern long double expl ( long double );
+extern long double logl ( long double );
+extern long double fabsl ( long double );
+extern long double powl ( long double, long double );
+static long double incbcfl( long double, long double, long double );
+static long double incbdl( long double, long double, long double );
+static long double pseriesl( long double, long double, long double );
+#else
+long double gammal(), lgaml(), expl(), logl(), fabsl(), powl();
+static long double incbcfl(), incbdl(), pseriesl();
+#endif
+
+long double incbetl( aa, bb, xx )
+long double aa, bb, xx;
+{
+long double a, b, t, x, w, xc, y;
+int flag;
+
+if( aa <= 0.0L || bb <= 0.0L )
+ goto domerr;
+
+if( (xx <= 0.0L) || ( xx >= 1.0L) )
+ {
+ if( xx == 0.0L )
+ return( 0.0L );
+ if( xx == 1.0L )
+ return( 1.0L );
+domerr:
+ mtherr( "incbetl", DOMAIN );
+ return( 0.0L );
+ }
+
+flag = 0;
+if( (bb * xx) <= 1.0L && xx <= 0.95L)
+ {
+ t = pseriesl(aa, bb, xx);
+ goto done;
+ }
+
+w = 1.0L - xx;
+
+/* Reverse a and b if x is greater than the mean. */
+if( xx > (aa/(aa+bb)) )
+ {
+ flag = 1;
+ a = bb;
+ b = aa;
+ xc = xx;
+ x = w;
+ }
+else
+ {
+ a = aa;
+ b = bb;
+ xc = w;
+ x = xx;
+ }
+
+if( flag == 1 && (b * x) <= 1.0L && x <= 0.95L)
+ {
+ t = pseriesl(a, b, x);
+ goto done;
+ }
+
+/* Choose expansion for optimal convergence */
+y = x * (a+b-2.0L) - (a-1.0L);
+if( y < 0.0L )
+ w = incbcfl( a, b, x );
+else
+ w = incbdl( a, b, x ) / xc;
+
+/* Multiply w by the factor
+ a b _ _ _
+ x (1-x) | (a+b) / ( a | (a) | (b) ) . */
+
+y = a * logl(x);
+t = b * logl(xc);
+if( (a+b) < MAXGAML && fabsl(y) < MAXLOGL && fabsl(t) < MAXLOGL )
+ {
+ t = powl(xc,b);
+ t *= powl(x,a);
+ t /= a;
+ t *= w;
+ t *= gammal(a+b) / (gammal(a) * gammal(b));
+ goto done;
+ }
+else
+ {
+ /* Resort to logarithms. */
+ y += t + lgaml(a+b) - lgaml(a) - lgaml(b);
+ y += logl(w/a);
+ if( y < MINLOGL )
+ t = 0.0L;
+ else
+ t = expl(y);
+ }
+
+done:
+
+if( flag == 1 )
+ {
+ if( t <= MACHEPL )
+ t = 1.0L - MACHEPL;
+ else
+ t = 1.0L - t;
+ }
+return( t );
+}
+
+/* Continued fraction expansion #1
+ * for incomplete beta integral
+ */
+
+static long double incbcfl( a, b, x )
+long double a, b, x;
+{
+long double xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
+long double k1, k2, k3, k4, k5, k6, k7, k8;
+long double r, t, ans, thresh;
+int n;
+
+k1 = a;
+k2 = a + b;
+k3 = a;
+k4 = a + 1.0L;
+k5 = 1.0L;
+k6 = b - 1.0L;
+k7 = k4;
+k8 = a + 2.0L;
+
+pkm2 = 0.0L;
+qkm2 = 1.0L;
+pkm1 = 1.0L;
+qkm1 = 1.0L;
+ans = 1.0L;
+r = 1.0L;
+n = 0;
+thresh = 3.0L * MACHEPL;
+do
+ {
+
+ xk = -( x * k1 * k2 )/( k3 * k4 );
+ pk = pkm1 + pkm2 * xk;
+ qk = qkm1 + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ xk = ( x * k5 * k6 )/( k7 * k8 );
+ pk = pkm1 + pkm2 * xk;
+ qk = qkm1 + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ if( qk != 0.0L )
+ r = pk/qk;
+ if( r != 0.0L )
+ {
+ t = fabsl( (ans - r)/r );
+ ans = r;
+ }
+ else
+ t = 1.0L;
+
+ if( t < thresh )
+ goto cdone;
+
+ k1 += 1.0L;
+ k2 += 1.0L;
+ k3 += 2.0L;
+ k4 += 2.0L;
+ k5 += 1.0L;
+ k6 -= 1.0L;
+ k7 += 2.0L;
+ k8 += 2.0L;
+
+ if( (fabsl(qk) + fabsl(pk)) > big )
+ {
+ pkm2 *= biginv;
+ pkm1 *= biginv;
+ qkm2 *= biginv;
+ qkm1 *= biginv;
+ }
+ if( (fabsl(qk) < biginv) || (fabsl(pk) < biginv) )
+ {
+ pkm2 *= big;
+ pkm1 *= big;
+ qkm2 *= big;
+ qkm1 *= big;
+ }
+ }
+while( ++n < 400 );
+mtherr( "incbetl", PLOSS );
+
+cdone:
+return(ans);
+}
+
+
+/* Continued fraction expansion #2
+ * for incomplete beta integral
+ */
+
+static long double incbdl( a, b, x )
+long double a, b, x;
+{
+long double xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
+long double k1, k2, k3, k4, k5, k6, k7, k8;
+long double r, t, ans, z, thresh;
+int n;
+
+k1 = a;
+k2 = b - 1.0L;
+k3 = a;
+k4 = a + 1.0L;
+k5 = 1.0L;
+k6 = a + b;
+k7 = a + 1.0L;
+k8 = a + 2.0L;
+
+pkm2 = 0.0L;
+qkm2 = 1.0L;
+pkm1 = 1.0L;
+qkm1 = 1.0L;
+z = x / (1.0L-x);
+ans = 1.0L;
+r = 1.0L;
+n = 0;
+thresh = 3.0L * MACHEPL;
+do
+ {
+
+ xk = -( z * k1 * k2 )/( k3 * k4 );
+ pk = pkm1 + pkm2 * xk;
+ qk = qkm1 + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ xk = ( z * k5 * k6 )/( k7 * k8 );
+ pk = pkm1 + pkm2 * xk;
+ qk = qkm1 + qkm2 * xk;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+
+ if( qk != 0.0L )
+ r = pk/qk;
+ if( r != 0.0L )
+ {
+ t = fabsl( (ans - r)/r );
+ ans = r;
+ }
+ else
+ t = 1.0L;
+
+ if( t < thresh )
+ goto cdone;
+
+ k1 += 1.0L;
+ k2 -= 1.0L;
+ k3 += 2.0L;
+ k4 += 2.0L;
+ k5 += 1.0L;
+ k6 += 1.0L;
+ k7 += 2.0L;
+ k8 += 2.0L;
+
+ if( (fabsl(qk) + fabsl(pk)) > big )
+ {
+ pkm2 *= biginv;
+ pkm1 *= biginv;
+ qkm2 *= biginv;
+ qkm1 *= biginv;
+ }
+ if( (fabsl(qk) < biginv) || (fabsl(pk) < biginv) )
+ {
+ pkm2 *= big;
+ pkm1 *= big;
+ qkm2 *= big;
+ qkm1 *= big;
+ }
+ }
+while( ++n < 400 );
+mtherr( "incbetl", PLOSS );
+
+cdone:
+return(ans);
+}
+
+/* Power series for incomplete gamma integral.
+ Use when b*x is small. */
+
+static long double pseriesl( a, b, x )
+long double a, b, x;
+{
+long double s, t, u, v, n, t1, z, ai;
+
+ai = 1.0L / a;
+u = (1.0L - b) * x;
+v = u / (a + 1.0L);
+t1 = v;
+t = u;
+n = 2.0L;
+s = 0.0L;
+z = MACHEPL * ai;
+while( fabsl(v) > z )
+ {
+ u = (n - b) * x / n;
+ t *= u;
+ v = t / (a + n);
+ s += v;
+ n += 1.0L;
+ }
+s += t1;
+s += ai;
+
+u = a * logl(x);
+if( (a+b) < MAXGAML && fabsl(u) < MAXLOGL )
+ {
+ t = gammal(a+b)/(gammal(a)*gammal(b));
+ s = s * t * powl(x,a);
+ }
+else
+ {
+ t = lgaml(a+b) - lgaml(a) - lgaml(b) + u + logl(s);
+ if( t < MINLOGL )
+ s = 0.0L;
+ else
+ s = expl(t);
+ }
+return(s);
+}
diff --git a/libm/ldouble/incbil.c b/libm/ldouble/incbil.c
new file mode 100644
index 000000000..b7610706b
--- /dev/null
+++ b/libm/ldouble/incbil.c
@@ -0,0 +1,305 @@
+/* incbil()
+ *
+ * Inverse of imcomplete beta integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double a, b, x, y, incbil();
+ *
+ * x = incbil( a, b, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given y, the function finds x such that
+ *
+ * incbet( a, b, x ) = y.
+ *
+ * the routine performs up to 10 Newton iterations to find the
+ * root of incbet(a,b,x) - y = 0.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * x a,b
+ * arithmetic domain domain # trials peak rms
+ * IEEE 0,1 .5,10000 10000 1.1e-14 1.4e-16
+ */
+
+
+/*
+Cephes Math Library Release 2.3: March, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+extern long double MACHEPL, MAXNUML, MAXLOGL, MINLOGL;
+#ifdef ANSIPROT
+extern long double incbetl ( long double, long double, long double );
+extern long double expl ( long double );
+extern long double fabsl ( long double );
+extern long double logl ( long double );
+extern long double sqrtl ( long double );
+extern long double lgaml ( long double );
+extern long double ndtril ( long double );
+#else
+long double incbetl(), expl(), fabsl(), logl(), sqrtl(), lgaml();
+long double ndtril();
+#endif
+
+long double incbil( aa, bb, yy0 )
+long double aa, bb, yy0;
+{
+long double a, b, y0, d, y, x, x0, x1, lgm, yp, di, dithresh, yl, yh, xt;
+int i, rflg, dir, nflg;
+
+
+if( yy0 <= 0.0L )
+ return(0.0L);
+if( yy0 >= 1.0L )
+ return(1.0L);
+x0 = 0.0L;
+yl = 0.0L;
+x1 = 1.0L;
+yh = 1.0L;
+if( aa <= 1.0L || bb <= 1.0L )
+ {
+ dithresh = 1.0e-7L;
+ rflg = 0;
+ a = aa;
+ b = bb;
+ y0 = yy0;
+ x = a/(a+b);
+ y = incbetl( a, b, x );
+ nflg = 0;
+ goto ihalve;
+ }
+else
+ {
+ nflg = 0;
+ dithresh = 1.0e-4L;
+ }
+
+/* approximation to inverse function */
+
+yp = -ndtril( yy0 );
+
+if( yy0 > 0.5L )
+ {
+ rflg = 1;
+ a = bb;
+ b = aa;
+ y0 = 1.0L - yy0;
+ yp = -yp;
+ }
+else
+ {
+ rflg = 0;
+ a = aa;
+ b = bb;
+ y0 = yy0;
+ }
+
+lgm = (yp * yp - 3.0L)/6.0L;
+x = 2.0L/( 1.0L/(2.0L * a-1.0L) + 1.0L/(2.0L * b - 1.0L) );
+d = yp * sqrtl( x + lgm ) / x
+ - ( 1.0L/(2.0L * b - 1.0L) - 1.0L/(2.0L * a - 1.0L) )
+ * (lgm + (5.0L/6.0L) - 2.0L/(3.0L * x));
+d = 2.0L * d;
+if( d < MINLOGL )
+ {
+ x = 1.0L;
+ goto under;
+ }
+x = a/( a + b * expl(d) );
+y = incbetl( a, b, x );
+yp = (y - y0)/y0;
+if( fabsl(yp) < 0.2 )
+ goto newt;
+
+/* Resort to interval halving if not close enough. */
+ihalve:
+
+dir = 0;
+di = 0.5L;
+for( i=0; i<400; i++ )
+ {
+ if( i != 0 )
+ {
+ x = x0 + di * (x1 - x0);
+ if( x == 1.0L )
+ x = 1.0L - MACHEPL;
+ if( x == 0.0L )
+ {
+ di = 0.5;
+ x = x0 + di * (x1 - x0);
+ if( x == 0.0 )
+ goto under;
+ }
+ y = incbetl( a, b, x );
+ yp = (x1 - x0)/(x1 + x0);
+ if( fabsl(yp) < dithresh )
+ goto newt;
+ yp = (y-y0)/y0;
+ if( fabsl(yp) < dithresh )
+ goto newt;
+ }
+ if( y < y0 )
+ {
+ x0 = x;
+ yl = y;
+ if( dir < 0 )
+ {
+ dir = 0;
+ di = 0.5L;
+ }
+ else if( dir > 3 )
+ di = 1.0L - (1.0L - di) * (1.0L - di);
+ else if( dir > 1 )
+ di = 0.5L * di + 0.5L;
+ else
+ di = (y0 - y)/(yh - yl);
+ dir += 1;
+ if( x0 > 0.95L )
+ {
+ if( rflg == 1 )
+ {
+ rflg = 0;
+ a = aa;
+ b = bb;
+ y0 = yy0;
+ }
+ else
+ {
+ rflg = 1;
+ a = bb;
+ b = aa;
+ y0 = 1.0 - yy0;
+ }
+ x = 1.0L - x;
+ y = incbetl( a, b, x );
+ x0 = 0.0;
+ yl = 0.0;
+ x1 = 1.0;
+ yh = 1.0;
+ goto ihalve;
+ }
+ }
+ else
+ {
+ x1 = x;
+ if( rflg == 1 && x1 < MACHEPL )
+ {
+ x = 0.0L;
+ goto done;
+ }
+ yh = y;
+ if( dir > 0 )
+ {
+ dir = 0;
+ di = 0.5L;
+ }
+ else if( dir < -3 )
+ di = di * di;
+ else if( dir < -1 )
+ di = 0.5L * di;
+ else
+ di = (y - y0)/(yh - yl);
+ dir -= 1;
+ }
+ }
+mtherr( "incbil", PLOSS );
+if( x0 >= 1.0L )
+ {
+ x = 1.0L - MACHEPL;
+ goto done;
+ }
+if( x <= 0.0L )
+ {
+under:
+ mtherr( "incbil", UNDERFLOW );
+ x = 0.0L;
+ goto done;
+ }
+
+newt:
+
+if( nflg )
+ goto done;
+nflg = 1;
+lgm = lgaml(a+b) - lgaml(a) - lgaml(b);
+
+for( i=0; i<15; i++ )
+ {
+ /* Compute the function at this point. */
+ if( i != 0 )
+ y = incbetl(a,b,x);
+ if( y < yl )
+ {
+ x = x0;
+ y = yl;
+ }
+ else if( y > yh )
+ {
+ x = x1;
+ y = yh;
+ }
+ else if( y < y0 )
+ {
+ x0 = x;
+ yl = y;
+ }
+ else
+ {
+ x1 = x;
+ yh = y;
+ }
+ if( x == 1.0L || x == 0.0L )
+ break;
+ /* Compute the derivative of the function at this point. */
+ d = (a - 1.0L) * logl(x) + (b - 1.0L) * logl(1.0L - x) + lgm;
+ if( d < MINLOGL )
+ goto done;
+ if( d > MAXLOGL )
+ break;
+ d = expl(d);
+ /* Compute the step to the next approximation of x. */
+ d = (y - y0)/d;
+ xt = x - d;
+ if( xt <= x0 )
+ {
+ y = (x - x0) / (x1 - x0);
+ xt = x0 + 0.5L * y * (x - x0);
+ if( xt <= 0.0L )
+ break;
+ }
+ if( xt >= x1 )
+ {
+ y = (x1 - x) / (x1 - x0);
+ xt = x1 - 0.5L * y * (x1 - x);
+ if( xt >= 1.0L )
+ break;
+ }
+ x = xt;
+ if( fabsl(d/x) < (128.0L * MACHEPL) )
+ goto done;
+ }
+/* Did not converge. */
+dithresh = 256.0L * MACHEPL;
+goto ihalve;
+
+done:
+if( rflg )
+ {
+ if( x <= MACHEPL )
+ x = 1.0L - MACHEPL;
+ else
+ x = 1.0L - x;
+ }
+return( x );
+}
diff --git a/libm/ldouble/isnanl.c b/libm/ldouble/isnanl.c
new file mode 100644
index 000000000..44158ecc7
--- /dev/null
+++ b/libm/ldouble/isnanl.c
@@ -0,0 +1,186 @@
+/* isnanl()
+ * isfinitel()
+ * signbitl()
+ *
+ * Floating point IEEE special number tests
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int signbitl(), isnanl(), isfinitel();
+ * long double x, y;
+ *
+ * n = signbitl(x);
+ * n = isnanl(x);
+ * n = isfinitel(x);
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * These functions are part of the standard C run time library
+ * for some but not all C compilers. The ones supplied are
+ * written in C for IEEE arithmetic. They should
+ * be used only if your compiler library does not already have
+ * them.
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.7: June, 1998
+Copyright 1992, 1998 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+/* This is defined in mconf.h. */
+/* #define DENORMAL 1 */
+
+#ifdef UNK
+/* Change UNK into something else. */
+#undef UNK
+#if BIGENDIAN
+#define MIEEE 1
+#else
+#define IBMPC 1
+#endif
+#endif
+
+
+/* Return 1 if the sign bit of x is 1, else 0. */
+
+int signbitl(x)
+long double x;
+{
+union
+ {
+ long double d;
+ short s[6];
+ int i[3];
+ } u;
+
+u.d = x;
+
+if( sizeof(int) == 4 )
+ {
+#ifdef IBMPC
+ return( u.s[4] < 0 );
+#endif
+#ifdef MIEEE
+ return( u.i[0] < 0 );
+#endif
+ }
+else
+ {
+#ifdef IBMPC
+ return( u.s[4] < 0 );
+#endif
+#ifdef MIEEE
+ return( u.s[0] < 0 );
+#endif
+ }
+}
+
+
+/* Return 1 if x is a number that is Not a Number, else return 0. */
+
+int isnanl(x)
+long double x;
+{
+#ifdef NANS
+union
+ {
+ long double d;
+ unsigned short s[6];
+ unsigned int i[3];
+ } u;
+
+u.d = x;
+
+if( sizeof(int) == 4 )
+ {
+#ifdef IBMPC
+ if( ((u.s[4] & 0x7fff) == 0x7fff)
+ && (((u.i[1] & 0x7fffffff)!= 0) || (u.i[0] != 0)))
+ return 1;
+#endif
+#ifdef MIEEE
+ if( ((u.i[0] & 0x7fff0000) == 0x7fff0000)
+ && (((u.i[1] & 0x7fffffff) != 0) || (u.i[2] != 0)))
+ return 1;
+#endif
+ return(0);
+ }
+else
+ { /* size int not 4 */
+#ifdef IBMPC
+ if( (u.s[4] & 0x7fff) == 0x7fff)
+ {
+ if((u.s[3] & 0x7fff) | u.s[2] | u.s[1] | u.s[0])
+ return(1);
+ }
+#endif
+#ifdef MIEEE
+ if( (u.s[0] & 0x7fff) == 0x7fff)
+ {
+ if((u.s[2] & 0x7fff) | u.s[3] | u.s[4] | u.s[5])
+ return(1);
+ }
+#endif
+ return(0);
+ } /* size int not 4 */
+
+#else
+/* No NANS. */
+return(0);
+#endif
+}
+
+
+/* Return 1 if x is not infinite and is not a NaN. */
+
+int isfinitel(x)
+long double x;
+{
+#ifdef INFINITIES
+union
+ {
+ long double d;
+ unsigned short s[6];
+ unsigned int i[3];
+ } u;
+
+u.d = x;
+
+if( sizeof(int) == 4 )
+ {
+#ifdef IBMPC
+ if( (u.s[4] & 0x7fff) != 0x7fff)
+ return 1;
+#endif
+#ifdef MIEEE
+ if( (u.i[0] & 0x7fff0000) != 0x7fff0000)
+ return 1;
+#endif
+ return(0);
+ }
+else
+ {
+#ifdef IBMPC
+ if( (u.s[4] & 0x7fff) != 0x7fff)
+ return 1;
+#endif
+#ifdef MIEEE
+ if( (u.s[0] & 0x7fff) != 0x7fff)
+ return 1;
+#endif
+ return(0);
+ }
+#else
+/* No INFINITY. */
+return(1);
+#endif
+}
diff --git a/libm/ldouble/j0l.c b/libm/ldouble/j0l.c
new file mode 100644
index 000000000..a30a65a4f
--- /dev/null
+++ b/libm/ldouble/j0l.c
@@ -0,0 +1,541 @@
+/* j0l.c
+ *
+ * Bessel function of order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, j0l();
+ *
+ * y = j0l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of first kind, order zero of the argument.
+ *
+ * The domain is divided into the intervals [0, 9] and
+ * (9, infinity). In the first interval the rational approximation
+ * is (x^2 - r^2) (x^2 - s^2) (x^2 - t^2) P7(x^2) / Q8(x^2),
+ * where r, s, t are the first three zeros of the function.
+ * In the second interval the expansion is in terms of the
+ * modulus M0(x) = sqrt(J0(x)^2 + Y0(x)^2) and phase P0(x)
+ * = atan(Y0(x)/J0(x)). M0 is approximated by sqrt(1/x)P7(1/x)/Q7(1/x).
+ * The approximation to J0 is M0 * cos(x - pi/4 + 1/x P5(1/x^2)/Q6(1/x^2)).
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 100000 2.8e-19 7.4e-20
+ *
+ *
+ */
+ /* y0l.c
+ *
+ * Bessel function of the second kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y0l();
+ *
+ * y = y0l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind, of order
+ * zero, of the argument.
+ *
+ * The domain is divided into the intervals [0, 5>, [5,9> and
+ * [9, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute y0(x) = R(x) + 2/pi * log(x) * j0(x).
+ *
+ * In the second interval, the approximation is
+ * (x - p)(x - q)(x - r)(x - s)P7(x)/Q7(x)
+ * where p, q, r, s are zeros of y0(x).
+ *
+ * The third interval uses the same approximations to modulus
+ * and phase as j0(x), whence y0(x) = modulus * sin(phase).
+ *
+ * ACCURACY:
+ *
+ * Absolute error, when y0(x) < 1; else relative error:
+ *
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 100000 3.4e-19 7.6e-20
+ *
+ */
+
+/* Copyright 1994 by Stephen L. Moshier (moshier@world.std.com). */
+
+#include <math.h>
+
+/*
+j0(x) = (x^2-JZ1)(x^2-JZ2)(x^2-JZ3)P(x**2)/Q(x**2)
+0 <= x <= 9
+Relative error
+n=7, d=8
+Peak error = 8.49e-22
+Relative error spread = 2.2e-3
+*/
+#if UNK
+static long double j0n[8] = {
+ 1.296848754518641770562E0L,
+-3.239201943301299801018E3L,
+ 3.490002040733471400107E6L,
+-2.076797068740966813173E9L,
+ 7.283696461857171054941E11L,
+-1.487926133645291056388E14L,
+ 1.620335009643150402368E16L,
+-7.173386747526788067407E17L,
+};
+static long double j0d[8] = {
+/* 1.000000000000000000000E0L,*/
+ 2.281959869176887763845E3L,
+ 2.910386840401647706984E6L,
+ 2.608400226578100610991E9L,
+ 1.752689035792859338860E12L,
+ 8.879132373286001289461E14L,
+ 3.265560832845194013669E17L,
+ 7.881340554308432241892E19L,
+ 9.466475654163919450528E21L,
+};
+#endif
+#if IBMPC
+static short j0n[] = {
+0xf759,0x4208,0x23d6,0xa5ff,0x3fff, XPD
+0xa9a8,0xe62b,0x3b28,0xca73,0xc00a, XPD
+0xfe10,0xb608,0x4829,0xd503,0x4014, XPD
+0x008c,0x7b60,0xd119,0xf792,0xc01d, XPD
+0x943a,0x69b7,0x36ca,0xa996,0x4026, XPD
+0x1b0b,0x6331,0x7add,0x8753,0xc02e, XPD
+0x4018,0xad26,0x71ba,0xe643,0x4034, XPD
+0xb96c,0xc486,0xfb95,0x9f47,0xc03a, XPD
+};
+static short j0d[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
+0xbdfe,0xc832,0x5b9f,0x8e9f,0x400a, XPD
+0xe1a0,0x923f,0xcb5c,0xb1a2,0x4014, XPD
+0x66d2,0x93fe,0x0762,0x9b79,0x401e, XPD
+0xfed1,0x086d,0x3425,0xcc0a,0x4027, XPD
+0x0841,0x8cb6,0x5a46,0xc9e3,0x4030, XPD
+0x3d2c,0xed55,0x20e1,0x9105,0x4039, XPD
+0xfdce,0xa4ca,0x2ed8,0x88b8,0x4041, XPD
+0x00ac,0xfb2b,0x6f62,0x804b,0x4048, XPD
+};
+#endif
+#if MIEEE
+static long j0n[24] = {
+0x3fff0000,0xa5ff23d6,0x4208f759,
+0xc00a0000,0xca733b28,0xe62ba9a8,
+0x40140000,0xd5034829,0xb608fe10,
+0xc01d0000,0xf792d119,0x7b60008c,
+0x40260000,0xa99636ca,0x69b7943a,
+0xc02e0000,0x87537add,0x63311b0b,
+0x40340000,0xe64371ba,0xad264018,
+0xc03a0000,0x9f47fb95,0xc486b96c,
+};
+static long j0d[24] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x400a0000,0x8e9f5b9f,0xc832bdfe,
+0x40140000,0xb1a2cb5c,0x923fe1a0,
+0x401e0000,0x9b790762,0x93fe66d2,
+0x40270000,0xcc0a3425,0x086dfed1,
+0x40300000,0xc9e35a46,0x8cb60841,
+0x40390000,0x910520e1,0xed553d2c,
+0x40410000,0x88b82ed8,0xa4cafdce,
+0x40480000,0x804b6f62,0xfb2b00ac,
+};
+#endif
+/*
+sqrt(j0^2(1/x^2) + y0^2(1/x^2)) = z P(z**2)/Q(z**2)
+z(x) = 1/sqrt(x)
+Relative error
+n=7, d=7
+Peak error = 1.80e-20
+Relative error spread = 5.1e-2
+*/
+#if UNK
+static long double modulusn[8] = {
+ 3.947542376069224461532E-1L,
+ 6.864682945702134624126E0L,
+ 1.021369773577974343844E1L,
+ 7.626141421290849630523E0L,
+ 2.842537511425216145635E0L,
+ 7.162842530423205720962E-1L,
+ 9.036664453160200052296E-2L,
+ 8.461833426898867839659E-3L,
+};
+static long double modulusd[7] = {
+/* 1.000000000000000000000E0L,*/
+ 9.117176038171821115904E0L,
+ 1.301235226061478261481E1L,
+ 9.613002539386213788182E0L,
+ 3.569671060989910901903E0L,
+ 8.983920141407590632423E-1L,
+ 1.132577931332212304986E-1L,
+ 1.060533546154121770442E-2L,
+};
+#endif
+#if IBMPC
+static short modulusn[] = {
+0x8559,0xf552,0x3a38,0xca1d,0x3ffd, XPD
+0x38a3,0xa663,0x7b91,0xdbab,0x4001, XPD
+0xb343,0x2673,0x4e51,0xa36b,0x4002, XPD
+0x5e4b,0xe3af,0x59bb,0xf409,0x4001, XPD
+0xb1cd,0x4e5e,0x2274,0xb5ec,0x4000, XPD
+0xcfe9,0x74e0,0x67a1,0xb75e,0x3ffe, XPD
+0x6b78,0x4cc6,0x25b7,0xb912,0x3ffb, XPD
+0xcb2b,0x4b73,0x8075,0x8aa3,0x3ff8, XPD
+};
+static short modulusd[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
+0x4498,0x3d2a,0xf3fb,0x91df,0x4002, XPD
+0x5e3d,0xb5f4,0x9848,0xd032,0x4002, XPD
+0xb837,0x3075,0xdbc0,0x99ce,0x4002, XPD
+0x775a,0x1b79,0x7d9c,0xe475,0x4000, XPD
+0x7e3f,0xb8dd,0x04df,0xe5fd,0x3ffe, XPD
+0xed5a,0x31cd,0xb3ac,0xe7f3,0x3ffb, XPD
+0x8a83,0x1b80,0x003e,0xadc2,0x3ff8, XPD
+};
+#endif
+#if MIEEE
+static long modulusn[24] = {
+0x3ffd0000,0xca1d3a38,0xf5528559,
+0x40010000,0xdbab7b91,0xa66338a3,
+0x40020000,0xa36b4e51,0x2673b343,
+0x40010000,0xf40959bb,0xe3af5e4b,
+0x40000000,0xb5ec2274,0x4e5eb1cd,
+0x3ffe0000,0xb75e67a1,0x74e0cfe9,
+0x3ffb0000,0xb91225b7,0x4cc66b78,
+0x3ff80000,0x8aa38075,0x4b73cb2b,
+};
+static long modulusd[21] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x40020000,0x91dff3fb,0x3d2a4498,
+0x40020000,0xd0329848,0xb5f45e3d,
+0x40020000,0x99cedbc0,0x3075b837,
+0x40000000,0xe4757d9c,0x1b79775a,
+0x3ffe0000,0xe5fd04df,0xb8dd7e3f,
+0x3ffb0000,0xe7f3b3ac,0x31cded5a,
+0x3ff80000,0xadc2003e,0x1b808a83,
+};
+#endif
+/*
+atan(y0(x)/j0(x)) = x - pi/4 + x P(x**2)/Q(x**2)
+Absolute error
+n=5, d=6
+Peak error = 2.80e-21
+Relative error spread = 5.5e-1
+*/
+#if UNK
+static long double phasen[6] = {
+-7.356766355393571519038E-1L,
+-5.001635199922493694706E-1L,
+-7.737323518141516881715E-2L,
+-3.998893155826990642730E-3L,
+-7.496317036829964150970E-5L,
+-4.290885090773112963542E-7L,
+};
+static long double phased[6] = {
+/* 1.000000000000000000000E0L,*/
+ 7.377856408614376072745E0L,
+ 4.285043297797736118069E0L,
+ 6.348446472935245102890E-1L,
+ 3.229866782185025048457E-2L,
+ 6.014932317342190404134E-4L,
+ 3.432708072618490390095E-6L,
+};
+#endif
+#if IBMPC
+static short phasen[] = {
+0x5106,0x12a6,0x4dd2,0xbc55,0xbffe, XPD
+0x1e30,0x04da,0xb769,0x800a,0xbffe, XPD
+0x8d8a,0x84e7,0xdbd5,0x9e75,0xbffb, XPD
+0xe514,0x8866,0x25a9,0x8309,0xbff7, XPD
+0xdc17,0x325e,0x8baf,0x9d35,0xbff1, XPD
+0x4c2f,0x2dd8,0x79c3,0xe65d,0xbfe9, XPD
+};
+static short phased[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
+0xf3e9,0xb2a5,0x6652,0xec17,0x4001, XPD
+0x4b69,0x3f87,0x131f,0x891f,0x4001, XPD
+0x6f25,0x2a95,0x2dc6,0xa285,0x3ffe, XPD
+0x37bf,0xfcc8,0x9b9f,0x844b,0x3ffa, XPD
+0xac5c,0x4806,0x8709,0x9dad,0x3ff4, XPD
+0x4c8c,0x2dd8,0x79c3,0xe65d,0x3fec, XPD
+};
+#endif
+#if MIEEE
+static long phasen[18] = {
+0xbffe0000,0xbc554dd2,0x12a65106,
+0xbffe0000,0x800ab769,0x04da1e30,
+0xbffb0000,0x9e75dbd5,0x84e78d8a,
+0xbff70000,0x830925a9,0x8866e514,
+0xbff10000,0x9d358baf,0x325edc17,
+0xbfe90000,0xe65d79c3,0x2dd84c2f,
+};
+static long phased[18] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x40010000,0xec176652,0xb2a5f3e9,
+0x40010000,0x891f131f,0x3f874b69,
+0x3ffe0000,0xa2852dc6,0x2a956f25,
+0x3ffa0000,0x844b9b9f,0xfcc837bf,
+0x3ff40000,0x9dad8709,0x4806ac5c,
+0x3fec0000,0xe65d79c3,0x2dd84c8c,
+};
+#endif
+#define JZ1 5.783185962946784521176L
+#define JZ2 30.47126234366208639908L
+#define JZ3 7.488700679069518344489e1L
+
+#define PIO4L 0.78539816339744830961566L
+#ifdef ANSIPROT
+extern long double sqrtl ( long double );
+extern long double fabsl ( long double );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern long double cosl ( long double );
+extern long double sinl ( long double );
+extern long double logl ( long double );
+long double j0l ( long double );
+#else
+long double sqrtl(), fabsl(), polevll(), p1evll(), cosl(), sinl(), logl();
+long double j0l();
+#endif
+
+long double j0l(x)
+long double x;
+{
+long double xx, y, z, modulus, phase;
+
+xx = x * x;
+if( xx < 81.0L )
+ {
+ y = (xx - JZ1) * (xx - JZ2) * (xx -JZ3);
+ y *= polevll( xx, j0n, 7 ) / p1evll( xx, j0d, 8 );
+ return y;
+ }
+
+y = fabsl(x);
+xx = 1.0/xx;
+phase = polevll( xx, phasen, 5 ) / p1evll( xx, phased, 6 );
+
+z = 1.0/y;
+modulus = polevll( z, modulusn, 7 ) / p1evll( z, modulusd, 7 );
+
+y = modulus * cosl( y - PIO4L + z*phase) / sqrtl(y);
+return y;
+}
+
+
+/*
+y0(x) = 2/pi * log(x) * j0(x) + P(z**2)/Q(z**2)
+0 <= x <= 5
+Absolute error
+n=7, d=7
+Peak error = 8.55e-22
+Relative error spread = 2.7e-1
+*/
+#if UNK
+static long double y0n[8] = {
+ 1.556909814120445353691E4L,
+-1.464324149797947303151E7L,
+ 5.427926320587133391307E9L,
+-9.808510181632626683952E11L,
+ 8.747842804834934784972E13L,
+-3.461898868011666236539E15L,
+ 4.421767595991969611983E16L,
+-1.847183690384811186958E16L,
+};
+static long double y0d[7] = {
+/* 1.000000000000000000000E0L,*/
+ 1.040792201755841697889E3L,
+ 6.256391154086099882302E5L,
+ 2.686702051957904669677E8L,
+ 8.630939306572281881328E10L,
+ 2.027480766502742538763E13L,
+ 3.167750475899536301562E15L,
+ 2.502813268068711844040E17L,
+};
+#endif
+#if IBMPC
+static short y0n[] = {
+0x126c,0x20be,0x647f,0xf344,0x400c, XPD
+0x2ec0,0x7b95,0x297f,0xdf70,0xc016, XPD
+0x2fdd,0x4b27,0xca98,0xa1c3,0x401f, XPD
+0x3e3c,0xb343,0x46c9,0xe45f,0xc026, XPD
+0xb219,0x37ba,0x5142,0x9f1f,0x402d, XPD
+0x23c9,0x6b29,0x4244,0xc4c9,0xc032, XPD
+0x501f,0x6264,0xbdf4,0x9d17,0x4036, XPD
+0x5fbd,0x0171,0x135a,0x8340,0xc035, XPD
+};
+static short y0d[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
+0x9057,0x7f25,0x59b7,0x8219,0x4009, XPD
+0xd938,0xb6b2,0x71d8,0x98be,0x4012, XPD
+0x97a4,0x90fa,0xa7e9,0x801c,0x401b, XPD
+0x553b,0x4dc8,0x8695,0xa0c3,0x4023, XPD
+0x6732,0x8c1b,0xc5ab,0x9384,0x402b, XPD
+0x04d3,0xa629,0xd61d,0xb410,0x4032, XPD
+0x241a,0x8f2b,0x629a,0xde4b,0x4038, XPD
+};
+#endif
+#if MIEEE
+static long y0n[24] = {
+0x400c0000,0xf344647f,0x20be126c,
+0xc0160000,0xdf70297f,0x7b952ec0,
+0x401f0000,0xa1c3ca98,0x4b272fdd,
+0xc0260000,0xe45f46c9,0xb3433e3c,
+0x402d0000,0x9f1f5142,0x37bab219,
+0xc0320000,0xc4c94244,0x6b2923c9,
+0x40360000,0x9d17bdf4,0x6264501f,
+0xc0350000,0x8340135a,0x01715fbd,
+};
+static long y0d[21] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x40090000,0x821959b7,0x7f259057,
+0x40120000,0x98be71d8,0xb6b2d938,
+0x401b0000,0x801ca7e9,0x90fa97a4,
+0x40230000,0xa0c38695,0x4dc8553b,
+0x402b0000,0x9384c5ab,0x8c1b6732,
+0x40320000,0xb410d61d,0xa62904d3,
+0x40380000,0xde4b629a,0x8f2b241a,
+};
+#endif
+/*
+y0(x) = (x-Y0Z1)(x-Y0Z2)(x-Y0Z3)(x-Y0Z4)P(x)/Q(x)
+4.5 <= x <= 9
+Absolute error
+n=9, d=9
+Peak error = 2.35e-20
+Relative error spread = 7.8e-13
+*/
+#if UNK
+static long double y059n[10] = {
+ 2.368715538373384869796E-2L,
+-1.472923738545276751402E0L,
+ 2.525993724177105060507E1L,
+ 7.727403527387097461580E1L,
+-4.578271827238477598563E3L,
+ 7.051411242092171161986E3L,
+ 1.951120419910720443331E5L,
+ 6.515211089266670755622E5L,
+-1.164760792144532266855E5L,
+-5.566567444353735925323E5L,
+};
+static long double y059d[9] = {
+/* 1.000000000000000000000E0L,*/
+-6.235501989189125881723E1L,
+ 2.224790285641017194158E3L,
+-5.103881883748705381186E4L,
+ 8.772616606054526158657E5L,
+-1.096162986826467060921E7L,
+ 1.083335477747278958468E8L,
+-7.045635226159434678833E8L,
+ 3.518324187204647941098E9L,
+ 1.173085288957116938494E9L,
+};
+#endif
+#if IBMPC
+static short y059n[] = {
+0x992f,0xab45,0x90b6,0xc20b,0x3ff9, XPD
+0x1207,0x46ea,0xc3db,0xbc88,0xbfff, XPD
+0x5504,0x035a,0x59fa,0xca14,0x4003, XPD
+0xd5a3,0xf673,0x4e59,0x9a8c,0x4005, XPD
+0x62e0,0xc25b,0x2cb3,0x8f12,0xc00b, XPD
+0xe8fa,0x4b44,0x4a39,0xdc5b,0x400b, XPD
+0x49e2,0xfb52,0x02af,0xbe8a,0x4010, XPD
+0x8c07,0x29e3,0x11be,0x9f10,0x4012, XPD
+0xfd54,0xb2fe,0x0a23,0xe37e,0xc00f, XPD
+0xf90c,0x3510,0x0be9,0x87e7,0xc012, XPD
+};
+static short y059d[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
+0xdebf,0xa468,0x8a55,0xf96b,0xc004, XPD
+0xad09,0x8e6a,0xa502,0x8b0c,0x400a, XPD
+0xa28c,0x5563,0xd19f,0xc75e,0xc00e, XPD
+0xe8b6,0xd705,0xda91,0xd62c,0x4012, XPD
+0xec8a,0x4697,0xddde,0xa742,0xc016, XPD
+0x27ff,0xca92,0x3d78,0xcea1,0x4019, XPD
+0xe26b,0x76b9,0x250a,0xa7fb,0xc01c, XPD
+0xceb6,0x3463,0x5ddb,0xd1b5,0x401e, XPD
+0x3b3b,0xea0b,0xb8d1,0x8bd7,0x401d, XPD
+};
+#endif
+#if MIEEE
+static long y059n[30] = {
+0x3ff90000,0xc20b90b6,0xab45992f,
+0xbfff0000,0xbc88c3db,0x46ea1207,
+0x40030000,0xca1459fa,0x035a5504,
+0x40050000,0x9a8c4e59,0xf673d5a3,
+0xc00b0000,0x8f122cb3,0xc25b62e0,
+0x400b0000,0xdc5b4a39,0x4b44e8fa,
+0x40100000,0xbe8a02af,0xfb5249e2,
+0x40120000,0x9f1011be,0x29e38c07,
+0xc00f0000,0xe37e0a23,0xb2fefd54,
+0xc0120000,0x87e70be9,0x3510f90c,
+};
+static long y059d[27] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0xc0040000,0xf96b8a55,0xa468debf,
+0x400a0000,0x8b0ca502,0x8e6aad09,
+0xc00e0000,0xc75ed19f,0x5563a28c,
+0x40120000,0xd62cda91,0xd705e8b6,
+0xc0160000,0xa742ddde,0x4697ec8a,
+0x40190000,0xcea13d78,0xca9227ff,
+0xc01c0000,0xa7fb250a,0x76b9e26b,
+0x401e0000,0xd1b55ddb,0x3463ceb6,
+0x401d0000,0x8bd7b8d1,0xea0b3b3b,
+};
+#endif
+#define TWOOPI 6.36619772367581343075535E-1L
+#define Y0Z1 3.957678419314857868376e0L
+#define Y0Z2 7.086051060301772697624e0L
+#define Y0Z3 1.022234504349641701900e1L
+#define Y0Z4 1.336109747387276347827e1L
+/* #define MAXNUML 1.189731495357231765021e4932L */
+extern long double MAXNUML;
+
+long double y0l(x)
+long double x;
+{
+long double xx, y, z, modulus, phase;
+
+if( x < 0.0 )
+ {
+ return (-MAXNUML);
+ }
+xx = x * x;
+if( xx < 81.0L )
+ {
+ if( xx < 20.25L )
+ {
+ y = TWOOPI * logl(x) * j0l(x);
+ y += polevll( xx, y0n, 7 ) / p1evll( xx, y0d, 7 );
+ }
+ else
+ {
+ y = (x - Y0Z1)*(x - Y0Z2)*(x - Y0Z3)*(x - Y0Z4);
+ y *= polevll( x, y059n, 9 ) / p1evll( x, y059d, 9 );
+ }
+ return y;
+ }
+
+y = fabsl(x);
+xx = 1.0/xx;
+phase = polevll( xx, phasen, 5 ) / p1evll( xx, phased, 6 );
+
+z = 1.0/y;
+modulus = polevll( z, modulusn, 7 ) / p1evll( z, modulusd, 7 );
+
+y = modulus * sinl( y - PIO4L + z*phase) / sqrtl(y);
+return y;
+}
diff --git a/libm/ldouble/j1l.c b/libm/ldouble/j1l.c
new file mode 100644
index 000000000..83428473e
--- /dev/null
+++ b/libm/ldouble/j1l.c
@@ -0,0 +1,551 @@
+/* j1l.c
+ *
+ * Bessel function of order one
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, j1l();
+ *
+ * y = j1l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order one of the argument.
+ *
+ * The domain is divided into the intervals [0, 9] and
+ * (9, infinity). In the first interval the rational approximation
+ * is (x^2 - r^2) (x^2 - s^2) (x^2 - t^2) x P8(x^2) / Q8(x^2),
+ * where r, s, t are the first three zeros of the function.
+ * In the second interval the expansion is in terms of the
+ * modulus M1(x) = sqrt(J1(x)^2 + Y1(x)^2) and phase P1(x)
+ * = atan(Y1(x)/J1(x)). M1 is approximated by sqrt(1/x)P7(1/x)/Q8(1/x).
+ * The approximation to j1 is M1 * cos(x - 3 pi/4 + 1/x P5(1/x^2)/Q6(1/x^2)).
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 40000 1.8e-19 5.0e-20
+ *
+ *
+ */
+ /* y1l.c
+ *
+ * Bessel function of the second kind, order zero
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, y1l();
+ *
+ * y = y1l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of the second kind, of order
+ * zero, of the argument.
+ *
+ * The domain is divided into the intervals [0, 4.5>, [4.5,9> and
+ * [9, infinity). In the first interval a rational approximation
+ * R(x) is employed to compute y0(x) = R(x) + 2/pi * log(x) * j0(x).
+ *
+ * In the second interval, the approximation is
+ * (x - p)(x - q)(x - r)(x - s)P9(x)/Q10(x)
+ * where p, q, r, s are zeros of y1(x).
+ *
+ * The third interval uses the same approximations to modulus
+ * and phase as j1(x), whence y1(x) = modulus * sin(phase).
+ *
+ * ACCURACY:
+ *
+ * Absolute error, when y0(x) < 1; else relative error:
+ *
+ * arithmetic domain # trials peak rms
+ * IEEE 0, 30 36000 2.7e-19 5.3e-20
+ *
+ */
+
+/* Copyright 1994 by Stephen L. Moshier (moshier@world.std.com). */
+
+#include <math.h>
+
+/*
+j1(x) = (x^2-r0^2)(x^2-r1^2)(x^2-r2^2) x P(x**2)/Q(x**2)
+0 <= x <= 9
+Relative error
+n=8, d=8
+Peak error = 2e-21
+*/
+#if UNK
+static long double j1n[9] = {
+-2.63469779622127762897E-4L,
+ 9.31329762279632791262E-1L,
+-1.46280142797793933909E3L,
+ 1.32000129539331214495E6L,
+-7.41183271195454042842E8L,
+ 2.626500686552841932403E11L,
+-5.68263073022183470933E13L,
+ 6.80006297997263446982E15L,
+-3.41470097444474566748E17L,
+};
+static long double j1d[8] = {
+/* 1.00000000000000000000E0L,*/
+ 2.95267951972943745733E3L,
+ 4.78723926343829674773E6L,
+ 5.37544732957807543920E9L,
+ 4.46866213886267829490E12L,
+ 2.76959756375961607085E15L,
+ 1.23367806884831151194E18L,
+ 3.57325874689695599524E20L,
+ 5.10779045516141578461E22L,
+};
+#endif
+#if IBMPC
+static short j1n[] = {
+0xf72f,0x18cc,0x50b2,0x8a22,0xbff3, XPD
+0x6dc3,0xc850,0xa096,0xee6b,0x3ffe, XPD
+0x29f3,0x496b,0xa54c,0xb6d9,0xc009, XPD
+0x38f5,0xf72b,0x0a5c,0xa122,0x4013, XPD
+0x1ac8,0xc825,0x3c9c,0xb0b6,0xc01c, XPD
+0x038e,0xbd23,0xa7fa,0xf49c,0x4024, XPD
+0x636c,0x4d29,0x9f71,0xcebb,0xc02c, XPD
+0xd3c2,0xf8f0,0xf852,0xc144,0x4033, XPD
+0xd8d8,0x7311,0xa7d2,0x97a4,0xc039, XPD
+};
+static short j1d[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
+0xbaf9,0x146e,0xdf50,0xb88a,0x400a, XPD
+0x6a17,0xe162,0x4e86,0x9218,0x4015, XPD
+0x6041,0xc9fe,0x6890,0xa033,0x401f, XPD
+0xb498,0xfdd5,0x209e,0x820e,0x4029, XPD
+0x0122,0x56c0,0xf2ef,0x9d6e,0x4032, XPD
+0xe6c0,0xa725,0x3d56,0x88f7,0x403b, XPD
+0x665d,0xb178,0x242e,0x9af7,0x4043, XPD
+0xdd67,0xf5b3,0x0522,0xad0f,0x404a, XPD
+};
+#endif
+#if MIEEE
+static long j1n[27] = {
+0xbff30000,0x8a2250b2,0x18ccf72f,
+0x3ffe0000,0xee6ba096,0xc8506dc3,
+0xc0090000,0xb6d9a54c,0x496b29f3,
+0x40130000,0xa1220a5c,0xf72b38f5,
+0xc01c0000,0xb0b63c9c,0xc8251ac8,
+0x40240000,0xf49ca7fa,0xbd23038e,
+0xc02c0000,0xcebb9f71,0x4d29636c,
+0x40330000,0xc144f852,0xf8f0d3c2,
+0xc0390000,0x97a4a7d2,0x7311d8d8,
+};
+static long j1d[24] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x400a0000,0xb88adf50,0x146ebaf9,
+0x40150000,0x92184e86,0xe1626a17,
+0x401f0000,0xa0336890,0xc9fe6041,
+0x40290000,0x820e209e,0xfdd5b498,
+0x40320000,0x9d6ef2ef,0x56c00122,
+0x403b0000,0x88f73d56,0xa725e6c0,
+0x40430000,0x9af7242e,0xb178665d,
+0x404a0000,0xad0f0522,0xf5b3dd67,
+};
+#endif
+/*
+sqrt(j0^2(1/x^2) + y0^2(1/x^2)) = z P(z**2)/Q(z**2)
+z(x) = 1/sqrt(x)
+Relative error
+n=7, d=8
+Peak error = 1.35e=20
+Relative error spread = 9.9e0
+*/
+#if UNK
+static long double modulusn[8] = {
+-5.041742205078442098874E0L,
+ 3.918474430130242177355E-1L,
+ 2.527521168680500659056E0L,
+ 7.172146812845906480743E0L,
+ 2.859499532295180940060E0L,
+ 1.014671139779858141347E0L,
+ 1.255798064266130869132E-1L,
+ 1.596507617085714650238E-2L,
+};
+static long double modulusd[8] = {
+/* 1.000000000000000000000E0L,*/
+-6.233092094568239317498E0L,
+-9.214128701852838347002E-1L,
+ 2.531772200570435289832E0L,
+ 8.755081357265851765640E0L,
+ 3.554340386955608261463E0L,
+ 1.267949948774331531237E0L,
+ 1.573909467558180942219E-1L,
+ 2.000925566825407466160E-2L,
+};
+#endif
+#if IBMPC
+static short modulusn[] = {
+0x3d53,0xb598,0xf3bf,0xa155,0xc001, XPD
+0x3111,0x863a,0x3a61,0xc8a0,0x3ffd, XPD
+0x7d55,0xdb8c,0xe825,0xa1c2,0x4000, XPD
+0xe5e2,0x6914,0x3a08,0xe582,0x4001, XPD
+0x71e6,0x88a5,0x0a53,0xb702,0x4000, XPD
+0x2cb0,0xc657,0xbe70,0x81e0,0x3fff, XPD
+0x6de4,0x8fae,0xfe26,0x8097,0x3ffc, XPD
+0xa905,0x05fb,0x3101,0x82c9,0x3ff9, XPD
+};
+static short modulusd[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
+0x2603,0x640e,0x7d8d,0xc775,0xc001, XPD
+0x77b5,0x8f2d,0xb6bf,0xebe1,0xbffe, XPD
+0x6420,0x97ce,0x8e44,0xa208,0x4000, XPD
+0x0260,0x746b,0xd030,0x8c14,0x4002, XPD
+0x77b6,0x34e2,0x501a,0xe37a,0x4000, XPD
+0x37ce,0x79ae,0x2f15,0xa24c,0x3fff, XPD
+0xfc82,0x02c7,0x17a4,0xa12b,0x3ffc, XPD
+0x1237,0xcc6c,0x7356,0xa3ea,0x3ff9, XPD
+};
+#endif
+#if MIEEE
+static long modulusn[24] = {
+0xc0010000,0xa155f3bf,0xb5983d53,
+0x3ffd0000,0xc8a03a61,0x863a3111,
+0x40000000,0xa1c2e825,0xdb8c7d55,
+0x40010000,0xe5823a08,0x6914e5e2,
+0x40000000,0xb7020a53,0x88a571e6,
+0x3fff0000,0x81e0be70,0xc6572cb0,
+0x3ffc0000,0x8097fe26,0x8fae6de4,
+0x3ff90000,0x82c93101,0x05fba905,
+};
+static long modulusd[24] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0xc0010000,0xc7757d8d,0x640e2603,
+0xbffe0000,0xebe1b6bf,0x8f2d77b5,
+0x40000000,0xa2088e44,0x97ce6420,
+0x40020000,0x8c14d030,0x746b0260,
+0x40000000,0xe37a501a,0x34e277b6,
+0x3fff0000,0xa24c2f15,0x79ae37ce,
+0x3ffc0000,0xa12b17a4,0x02c7fc82,
+0x3ff90000,0xa3ea7356,0xcc6c1237,
+};
+#endif
+/*
+atan(y1(x)/j1(x)) = x - 3pi/4 + z P(z**2)/Q(z**2)
+z(x) = 1/x
+Absolute error
+n=5, d=6
+Peak error = 4.83e-21
+Relative error spread = 1.9e0
+*/
+#if UNK
+static long double phasen[6] = {
+ 2.010456367705144783933E0L,
+ 1.587378144541918176658E0L,
+ 2.682837461073751055565E-1L,
+ 1.472572645054468815027E-2L,
+ 2.884976126715926258586E-4L,
+ 1.708502235134706284899E-6L,
+};
+static long double phased[6] = {
+/* 1.000000000000000000000E0L,*/
+ 6.809332495854873089362E0L,
+ 4.518597941618813112665E0L,
+ 7.320149039410806471101E-1L,
+ 3.960155028960712309814E-2L,
+ 7.713202197319040439861E-4L,
+ 4.556005960359216767984E-6L,
+};
+#endif
+#if IBMPC
+static short phasen[] = {
+0xebc0,0x5506,0x512f,0x80ab,0x4000, XPD
+0x6050,0x98aa,0x3500,0xcb2f,0x3fff, XPD
+0xe907,0x28b9,0x7cb7,0x895c,0x3ffd, XPD
+0xa830,0xf4a3,0x2c60,0xf144,0x3ff8, XPD
+0xf74f,0xbe87,0x7e7d,0x9741,0x3ff3, XPD
+0x540c,0xc1d5,0xb096,0xe54f,0x3feb, XPD
+};
+static short phased[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
+0xefe3,0x292c,0x0d43,0xd9e6,0x4001, XPD
+0xb1f2,0xe0d2,0x5ab5,0x9098,0x4001, XPD
+0xc39e,0x9c8c,0x5428,0xbb65,0x3ffe, XPD
+0x98f8,0xd610,0x3c35,0xa235,0x3ffa, XPD
+0xa853,0x55fb,0x6c79,0xca32,0x3ff4, XPD
+0x8d72,0x2be3,0xcb0f,0x98df,0x3fed, XPD
+};
+#endif
+#if MIEEE
+static long phasen[18] = {
+0x40000000,0x80ab512f,0x5506ebc0,
+0x3fff0000,0xcb2f3500,0x98aa6050,
+0x3ffd0000,0x895c7cb7,0x28b9e907,
+0x3ff80000,0xf1442c60,0xf4a3a830,
+0x3ff30000,0x97417e7d,0xbe87f74f,
+0x3feb0000,0xe54fb096,0xc1d5540c,
+};
+static long phased[18] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x40010000,0xd9e60d43,0x292cefe3,
+0x40010000,0x90985ab5,0xe0d2b1f2,
+0x3ffe0000,0xbb655428,0x9c8cc39e,
+0x3ffa0000,0xa2353c35,0xd61098f8,
+0x3ff40000,0xca326c79,0x55fba853,
+0x3fed0000,0x98dfcb0f,0x2be38d72,
+};
+#endif
+#define JZ1 1.46819706421238932572e1L
+#define JZ2 4.92184563216946036703e1L
+#define JZ3 1.03499453895136580332e2L
+
+#define THPIO4L 2.35619449019234492885L
+#ifdef ANSIPROT
+extern long double sqrtl ( long double );
+extern long double fabsl ( long double );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern long double cosl ( long double );
+extern long double sinl ( long double );
+extern long double logl ( long double );
+long double j1l (long double );
+#else
+long double sqrtl(), fabsl(), polevll(), p1evll(), cosl(), sinl(), logl();
+long double j1l();
+#endif
+
+long double j1l(x)
+long double x;
+{
+long double xx, y, z, modulus, phase;
+
+xx = x * x;
+if( xx < 81.0L )
+ {
+ y = (xx - JZ1) * (xx - JZ2) * (xx - JZ3);
+ y *= x * polevll( xx, j1n, 8 ) / p1evll( xx, j1d, 8 );
+ return y;
+ }
+
+y = fabsl(x);
+xx = 1.0/xx;
+phase = polevll( xx, phasen, 5 ) / p1evll( xx, phased, 6 );
+
+z = 1.0/y;
+modulus = polevll( z, modulusn, 7 ) / p1evll( z, modulusd, 8 );
+
+y = modulus * cosl( y - THPIO4L + z*phase) / sqrtl(y);
+if( x < 0 )
+ y = -y;
+return y;
+}
+
+/*
+y1(x) = 2/pi * (log(x) * j1(x) - 1/x) + R(x^2) z P(z**2)/Q(z**2)
+0 <= x <= 4.5
+z(x) = x
+Absolute error
+n=6, d=7
+Peak error = 7.25e-22
+Relative error spread = 4.5e-2
+*/
+#if UNK
+static long double y1n[7] = {
+-1.288901054372751879531E5L,
+ 9.914315981558815369372E7L,
+-2.906793378120403577274E10L,
+ 3.954354656937677136266E12L,
+-2.445982226888344140154E14L,
+ 5.685362960165615942886E15L,
+-2.158855258453711703120E16L,
+};
+static long double y1d[7] = {
+/* 1.000000000000000000000E0L,*/
+ 8.926354644853231136073E2L,
+ 4.679841933793707979659E5L,
+ 1.775133253792677466651E8L,
+ 5.089532584184822833416E10L,
+ 1.076474894829072923244E13L,
+ 1.525917240904692387994E15L,
+ 1.101136026928555260168E17L,
+};
+#endif
+#if IBMPC
+static short y1n[] = {
+0x5b16,0xf7f8,0x0d7e,0xfbbd,0xc00f, XPD
+0x53e4,0x194c,0xbefa,0xbd19,0x4019, XPD
+0x7607,0xa687,0xaf0a,0xd892,0xc021, XPD
+0x5633,0xaa6b,0x79e5,0xe62c,0x4028, XPD
+0x69fd,0x1242,0xf62d,0xde75,0xc02e, XPD
+0x7f8b,0x4757,0x75bd,0xa196,0x4033, XPD
+0x3a10,0x0848,0x5930,0x9965,0xc035, XPD
+};
+static short y1d[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
+0xdd1a,0x3b8e,0xab73,0xdf28,0x4008, XPD
+0x298c,0x29ef,0x0630,0xe482,0x4011, XPD
+0x0e86,0x117b,0x36d6,0xa94a,0x401a, XPD
+0x57e0,0x1d92,0x90a9,0xbd99,0x4022, XPD
+0xaaf0,0x342b,0xd098,0x9ca5,0x402a, XPD
+0x8c6a,0x397e,0x0963,0xad7a,0x4031, XPD
+0x7302,0xb91b,0xde7e,0xc399,0x4037, XPD
+};
+#endif
+#if MIEEE
+static long y1n[21] = {
+0xc00f0000,0xfbbd0d7e,0xf7f85b16,
+0x40190000,0xbd19befa,0x194c53e4,
+0xc0210000,0xd892af0a,0xa6877607,
+0x40280000,0xe62c79e5,0xaa6b5633,
+0xc02e0000,0xde75f62d,0x124269fd,
+0x40330000,0xa19675bd,0x47577f8b,
+0xc0350000,0x99655930,0x08483a10,
+};
+static long y1d[21] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x40080000,0xdf28ab73,0x3b8edd1a,
+0x40110000,0xe4820630,0x29ef298c,
+0x401a0000,0xa94a36d6,0x117b0e86,
+0x40220000,0xbd9990a9,0x1d9257e0,
+0x402a0000,0x9ca5d098,0x342baaf0,
+0x40310000,0xad7a0963,0x397e8c6a,
+0x40370000,0xc399de7e,0xb91b7302,
+};
+#endif
+/*
+y1(x) = (x-YZ1)(x-YZ2)(x-YZ3)(x-YZ4)R(x) P(z)/Q(z)
+z(x) = x
+4.5 <= x <= 9
+Absolute error
+n=9, d=10
+Peak error = 3.27e-22
+Relative error spread = 4.5e-2
+*/
+#if UNK
+static long double y159n[10] = {
+-6.806634906054210550896E-1L,
+ 4.306669585790359450532E1L,
+-9.230477746767243316014E2L,
+ 6.171186628598134035237E3L,
+ 2.096869860275353982829E4L,
+-1.238961670382216747944E5L,
+-1.781314136808997406109E6L,
+-1.803400156074242435454E6L,
+-1.155761550219364178627E6L,
+ 3.112221202330688509818E5L,
+};
+static long double y159d[10] = {
+/* 1.000000000000000000000E0L,*/
+-6.181482377814679766978E1L,
+ 2.238187927382180589099E3L,
+-5.225317824142187494326E4L,
+ 9.217235006983512475118E5L,
+-1.183757638771741974521E7L,
+ 1.208072488974110742912E8L,
+-8.193431077523942651173E8L,
+ 4.282669747880013349981E9L,
+-1.171523459555524458808E9L,
+ 1.078445545755236785692E8L,
+};
+#endif
+#if IBMPC
+static short y159n[] = {
+0xb5e5,0xbb42,0xf667,0xae3f,0xbffe, XPD
+0xfdf1,0x41e5,0x4beb,0xac44,0x4004, XPD
+0xe917,0x8486,0x0ebd,0xe6c3,0xc008, XPD
+0xdf40,0x226b,0x7e37,0xc0d9,0x400b, XPD
+0xb2bf,0x4296,0x65af,0xa3d1,0x400d, XPD
+0xa33b,0x8229,0x1561,0xf1fc,0xc00f, XPD
+0xcd43,0x2f50,0x1118,0xd972,0xc013, XPD
+0x3811,0xa3da,0x413f,0xdc24,0xc013, XPD
+0xf62f,0xd968,0x8c66,0x8d15,0xc013, XPD
+0x539b,0xf305,0xc3d8,0x97f6,0x4011, XPD
+};
+static short y159d[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
+0x1a6c,0x1c93,0x612a,0xf742,0xc004, XPD
+0xd0fe,0x2487,0x01c0,0x8be3,0x400a, XPD
+0xbed4,0x3ad5,0x2da1,0xcc1d,0xc00e, XPD
+0x3c4f,0xdc46,0xb802,0xe107,0x4012, XPD
+0xe5e5,0x4172,0x8863,0xb4a0,0xc016, XPD
+0x6de5,0xb797,0xea1c,0xe66b,0x4019, XPD
+0xa46a,0x0273,0xbc0f,0xc358,0xc01c, XPD
+0x8e0e,0xe148,0x5ab3,0xff44,0x401e, XPD
+0xb3ad,0x1c6d,0x0f07,0x8ba8,0xc01d, XPD
+0xa231,0x6ab0,0x7952,0xcdb2,0x4019, XPD
+};
+#endif
+#if MIEEE
+static long y159n[30] = {
+0xbffe0000,0xae3ff667,0xbb42b5e5,
+0x40040000,0xac444beb,0x41e5fdf1,
+0xc0080000,0xe6c30ebd,0x8486e917,
+0x400b0000,0xc0d97e37,0x226bdf40,
+0x400d0000,0xa3d165af,0x4296b2bf,
+0xc00f0000,0xf1fc1561,0x8229a33b,
+0xc0130000,0xd9721118,0x2f50cd43,
+0xc0130000,0xdc24413f,0xa3da3811,
+0xc0130000,0x8d158c66,0xd968f62f,
+0x40110000,0x97f6c3d8,0xf305539b,
+};
+static long y159d[30] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0xc0040000,0xf742612a,0x1c931a6c,
+0x400a0000,0x8be301c0,0x2487d0fe,
+0xc00e0000,0xcc1d2da1,0x3ad5bed4,
+0x40120000,0xe107b802,0xdc463c4f,
+0xc0160000,0xb4a08863,0x4172e5e5,
+0x40190000,0xe66bea1c,0xb7976de5,
+0xc01c0000,0xc358bc0f,0x0273a46a,
+0x401e0000,0xff445ab3,0xe1488e0e,
+0xc01d0000,0x8ba80f07,0x1c6db3ad,
+0x40190000,0xcdb27952,0x6ab0a231,
+};
+#endif
+
+extern long double MAXNUML;
+/* #define MAXNUML 1.18973149535723176502e4932L */
+#define TWOOPI 6.36619772367581343075535e-1L
+#define THPIO4 2.35619449019234492885L
+#define Y1Z1 2.19714132603101703515e0L
+#define Y1Z2 5.42968104079413513277e0L
+#define Y1Z3 8.59600586833116892643e0L
+#define Y1Z4 1.17491548308398812434e1L
+
+long double y1l(x)
+long double x;
+{
+long double xx, y, z, modulus, phase;
+
+if( x < 0.0 )
+ {
+ return (-MAXNUML);
+ }
+z = 1.0/x;
+xx = x * x;
+if( xx < 81.0L )
+ {
+ if( xx < 20.25L )
+ {
+ y = TWOOPI * (logl(x) * j1l(x) - z);
+ y += x * polevll( xx, y1n, 6 ) / p1evll( xx, y1d, 7 );
+ }
+ else
+ {
+ y = (x - Y1Z1)*(x - Y1Z2)*(x - Y1Z3)*(x - Y1Z4);
+ y *= polevll( x, y159n, 9 ) / p1evll( x, y159d, 10 );
+ }
+ return y;
+ }
+
+xx = 1.0/xx;
+phase = polevll( xx, phasen, 5 ) / p1evll( xx, phased, 6 );
+
+modulus = polevll( z, modulusn, 7 ) / p1evll( z, modulusd, 8 );
+
+z = modulus * sinl( x - THPIO4L + z*phase) / sqrtl(x);
+return z;
+}
diff --git a/libm/ldouble/jnl.c b/libm/ldouble/jnl.c
new file mode 100644
index 000000000..1b24c50c7
--- /dev/null
+++ b/libm/ldouble/jnl.c
@@ -0,0 +1,130 @@
+/* jnl.c
+ *
+ * Bessel function of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int n;
+ * long double x, y, jnl();
+ *
+ * y = jnl( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The ratio of jn(x) to j0(x) is computed by backward
+ * recurrence. First the ratio jn/jn-1 is found by a
+ * continued fraction expansion. Then the recurrence
+ * relating successive orders is applied until j0 or j1 is
+ * reached.
+ *
+ * If n = 0 or 1 the routine for j0 or j1 is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Absolute error:
+ * arithmetic domain # trials peak rms
+ * IEEE -30, 30 5000 3.3e-19 4.7e-20
+ *
+ *
+ * Not suitable for large n or x.
+ *
+ */
+
+/* jn.c
+Cephes Math Library Release 2.0: April, 1987
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+#include <math.h>
+
+extern long double MACHEPL;
+#ifdef ANSIPROT
+extern long double fabsl ( long double );
+extern long double j0l ( long double );
+extern long double j1l ( long double );
+#else
+long double fabsl(), j0l(), j1l();
+#endif
+
+long double jnl( n, x )
+int n;
+long double x;
+{
+long double pkm2, pkm1, pk, xk, r, ans;
+int k, sign;
+
+if( n < 0 )
+ {
+ n = -n;
+ if( (n & 1) == 0 ) /* -1**n */
+ sign = 1;
+ else
+ sign = -1;
+ }
+else
+ sign = 1;
+
+if( x < 0.0L )
+ {
+ if( n & 1 )
+ sign = -sign;
+ x = -x;
+ }
+
+
+if( n == 0 )
+ return( sign * j0l(x) );
+if( n == 1 )
+ return( sign * j1l(x) );
+if( n == 2 )
+ return( sign * (2.0L * j1l(x) / x - j0l(x)) );
+
+if( x < MACHEPL )
+ return( 0.0L );
+
+/* continued fraction */
+k = 53;
+pk = 2 * (n + k);
+ans = pk;
+xk = x * x;
+
+do
+ {
+ pk -= 2.0L;
+ ans = pk - (xk/ans);
+ }
+while( --k > 0 );
+ans = x/ans;
+
+/* backward recurrence */
+
+pk = 1.0L;
+pkm1 = 1.0L/ans;
+k = n-1;
+r = 2 * k;
+
+do
+ {
+ pkm2 = (pkm1 * r - pk * x) / x;
+ pk = pkm1;
+ pkm1 = pkm2;
+ r -= 2.0L;
+ }
+while( --k > 0 );
+
+if( fabsl(pk) > fabsl(pkm1) )
+ ans = j1l(x)/pk;
+else
+ ans = j0l(x)/pkm1;
+return( sign * ans );
+}
diff --git a/libm/ldouble/lcalc.c b/libm/ldouble/lcalc.c
new file mode 100644
index 000000000..87250952f
--- /dev/null
+++ b/libm/ldouble/lcalc.c
@@ -0,0 +1,1484 @@
+/* calc.c */
+/* Keyboard command interpreter */
+/* by Stephen L. Moshier */
+
+/* Include functions for IEEE special values */
+#define NANS 1
+
+/* length of command line: */
+#define LINLEN 128
+
+#define XON 0x11
+#define XOFF 0x13
+
+#define SALONE 1
+#define DECPDP 0
+#define INTLOGIN 0
+#define INTHELP 1
+#ifndef TRUE
+#define TRUE 1
+#endif
+
+/* Initialize squirrel printf: */
+#define INIPRINTF 0
+
+#if DECPDP
+#define TRUE 1
+#endif
+
+#include <stdio.h>
+#include <string.h>
+static char idterp[] = {
+"\n\nSteve Moshier's command interpreter V1.3\n"};
+#define ISLOWER(c) ((c >= 'a') && (c <= 'z'))
+#define ISUPPER(c) ((c >= 'A') && (c <= 'Z'))
+#define ISALPHA(c) (ISLOWER(c) || ISUPPER(c))
+#define ISDIGIT(c) ((c >= '0') && (c <= '9'))
+#define ISATF(c) (((c >= 'a')&&(c <= 'f')) || ((c >= 'A')&&(c <= 'F')))
+#define ISXDIGIT(c) (ISDIGIT(c) || ISATF(c))
+#define ISOCTAL(c) ((c >= '0') && (c < '8'))
+#define ISALNUM(c) (ISALPHA(c) || (ISDIGIT(c))
+FILE *fopen();
+
+#include "lcalc.h"
+#include "ehead.h"
+
+/* space for working precision numbers */
+static long double vs[22];
+
+/* the symbol table of temporary variables: */
+
+#define NTEMP 4
+struct varent temp[NTEMP] = {
+{"T", OPR | TEMP, &vs[14]},
+{"T", OPR | TEMP, &vs[15]},
+{"T", OPR | TEMP, &vs[16]},
+{"\0", OPR | TEMP, &vs[17]}
+};
+
+/* the symbol table of operators */
+/* EOL is interpreted on null, newline, or ; */
+struct symbol oprtbl[] = {
+{"BOL", OPR | BOL, 0},
+{"EOL", OPR | EOL, 0},
+{"-", OPR | UMINUS, 8},
+/*"~", OPR | COMP, 8,*/
+{",", OPR | EOE, 1},
+{"=", OPR | EQU, 2},
+/*"|", OPR | LOR, 3,*/
+/*"^", OPR | LXOR, 4,*/
+/*"&", OPR | LAND, 5,*/
+{"+", OPR | PLUS, 6},
+{"-", OPR | MINUS, 6},
+{"*", OPR | MULT, 7},
+{"/", OPR | DIV, 7},
+/*"%", OPR | MOD, 7,*/
+{"(", OPR | LPAREN, 11},
+{")", OPR | RPAREN, 11},
+{"\0", ILLEG, 0}
+};
+
+#define NOPR 8
+
+/* the symbol table of indirect variables: */
+extern long double PIL;
+struct varent indtbl[] = {
+{"t", VAR | IND, &vs[21]},
+{"u", VAR | IND, &vs[20]},
+{"v", VAR | IND, &vs[19]},
+{"w", VAR | IND, &vs[18]},
+{"x", VAR | IND, &vs[10]},
+{"y", VAR | IND, &vs[11]},
+{"z", VAR | IND, &vs[12]},
+{"pi", VAR | IND, &PIL},
+{"\0", ILLEG, 0}
+};
+
+/* the symbol table of constants: */
+
+#define NCONST 10
+struct varent contbl[NCONST] = {
+{"C",CONST,&vs[0]},
+{"C",CONST,&vs[1]},
+{"C",CONST,&vs[2]},
+{"C",CONST,&vs[3]},
+{"C",CONST,&vs[4]},
+{"C",CONST,&vs[5]},
+{"C",CONST,&vs[6]},
+{"C",CONST,&vs[7]},
+{"C",CONST,&vs[8]},
+{"\0",CONST,&vs[9]}
+};
+
+/* the symbol table of string variables: */
+
+static char strngs[160] = {0};
+
+#define NSTRNG 5
+struct strent strtbl[NSTRNG] = {
+{0, VAR | STRING, 0},
+{0, VAR | STRING, 0},
+{0, VAR | STRING, 0},
+{0, VAR | STRING, 0},
+{"\0",ILLEG,0},
+};
+
+
+/* Help messages */
+#if INTHELP
+static char *intmsg[] = {
+"?",
+"Unkown symbol",
+"Expression ends in illegal operator",
+"Precede ( by operator",
+")( is illegal",
+"Unmatched )",
+"Missing )",
+"Illegal left hand side",
+"Missing symbol",
+"Must assign to a variable",
+"Divide by zero",
+"Missing symbol",
+"Missing operator",
+"Precede quantity by operator",
+"Quantity preceded by )",
+"Function syntax",
+"Too many function args",
+"No more temps",
+"Arg list"
+};
+#endif
+
+/* the symbol table of functions: */
+#if SALONE
+long double hex(), cmdh(), cmdhlp();
+long double cmddm(), cmdtm(), cmdem();
+long double take(), mxit(), exit(), bits(), csys();
+long double cmddig(), prhlst(), abmac();
+long double ifrac(), xcmpl();
+long double floorl(), logl(), powl(), sqrtl(), tanhl(), expl();
+long double ellpel(), ellpkl(), incbetl(), incbil();
+long double stdtrl(), stdtril(), zstdtrl(), zstdtril();
+long double sinl(), cosl(), tanl(), asinl(), acosl(), atanl(), atan2l();
+long double tanhl(), atanhl();
+#ifdef NANS
+int isnanl(), isfinitel(), signbitl();
+long double zisnan(), zisfinite(), zsignbit();
+#endif
+
+struct funent funtbl[] = {
+{"h", OPR | FUNC, cmdh},
+{"help", OPR | FUNC, cmdhlp},
+{"hex", OPR | FUNC, hex},
+/*"view", OPR | FUNC, view,*/
+{"exp", OPR | FUNC, expl},
+{"floor", OPR | FUNC, floorl},
+{"log", OPR | FUNC, logl},
+{"pow", OPR | FUNC, powl},
+{"sqrt", OPR | FUNC, sqrtl},
+{"tanh", OPR | FUNC, tanhl},
+{"sin", OPR | FUNC, sinl},
+{"cos", OPR | FUNC, cosl},
+{"tan", OPR | FUNC, tanl},
+{"asin", OPR | FUNC, asinl},
+{"acos", OPR | FUNC, acosl},
+{"atan", OPR | FUNC, atanl},
+{"atantwo", OPR | FUNC, atan2l},
+{"tanh", OPR | FUNC, tanhl},
+{"atanh", OPR | FUNC, atanhl},
+{"ellpe", OPR | FUNC, ellpel},
+{"ellpk", OPR | FUNC, ellpkl},
+{"incbet", OPR | FUNC, incbetl},
+{"incbi", OPR | FUNC, incbil},
+{"stdtr", OPR | FUNC, zstdtrl},
+{"stdtri", OPR | FUNC, zstdtril},
+{"ifrac", OPR | FUNC, ifrac},
+{"cmp", OPR | FUNC, xcmpl},
+#ifdef NANS
+{"isnan", OPR | FUNC, zisnan},
+{"isfinite", OPR | FUNC, zisfinite},
+{"signbit", OPR | FUNC, zsignbit},
+#endif
+{"bits", OPR | FUNC, bits},
+{"digits", OPR | FUNC, cmddig},
+{"dm", OPR | FUNC, cmddm},
+{"tm", OPR | FUNC, cmdtm},
+{"em", OPR | FUNC, cmdem},
+{"take", OPR | FUNC | COMMAN, take},
+{"system", OPR | FUNC | COMMAN, csys},
+{"exit", OPR | FUNC, mxit},
+/*
+"remain", OPR | FUNC, eremain,
+*/
+{"\0", OPR | FUNC, 0}
+};
+
+/* the symbol table of key words */
+struct funent keytbl[] = {
+{"\0", ILLEG, 0}
+};
+#endif
+
+void zgets(), init();
+
+/* Number of decimals to display */
+#define DEFDIS 70
+static int ndigits = DEFDIS;
+
+/* Menu stack */
+struct funent *menstk[5] = {&funtbl[0], NULL, NULL, NULL, NULL};
+int menptr = 0;
+
+/* Take file stack */
+FILE *takstk[10] = {0};
+int takptr = -1;
+
+/* size of the expression scan list: */
+#define NSCAN 20
+
+/* previous token, saved for syntax checking: */
+struct symbol *lastok = 0;
+
+/* variables used by parser: */
+static char str[128] = {0};
+int uposs = 0; /* possible unary operator */
+static long double qnc;
+char lc[40] = { '\n' }; /* ASCII string of token symbol */
+static char line[LINLEN] = { '\n','\0' }; /* input command line */
+static char maclin[LINLEN] = { '\n','\0' }; /* macro command */
+char *interl = line; /* pointer into line */
+extern char *interl;
+static int maccnt = 0; /* number of times to execute macro command */
+static int comptr = 0; /* comma stack pointer */
+static long double comstk[5]; /* comma argument stack */
+static int narptr = 0; /* pointer to number of args */
+static int narstk[5] = {0}; /* stack of number of function args */
+
+/* main() */
+
+/* Entire program starts here */
+
+int main()
+{
+
+/* the scan table: */
+
+/* array of pointers to symbols which have been parsed: */
+struct symbol *ascsym[NSCAN];
+
+/* current place in ascsym: */
+register struct symbol **as;
+
+/* array of attributes of operators parsed: */
+int ascopr[NSCAN];
+
+/* current place in ascopr: */
+register int *ao;
+
+#if LARGEMEM
+/* array of precedence levels of operators: */
+long asclev[NSCAN];
+/* current place in asclev: */
+long *al;
+long symval; /* value of symbol just parsed */
+#else
+int asclev[NSCAN];
+int *al;
+int symval;
+#endif
+
+long double acc; /* the accumulator, for arithmetic */
+int accflg; /* flags accumulator in use */
+long double val; /* value to be combined into accumulator */
+register struct symbol *psym; /* pointer to symbol just parsed */
+struct varent *pvar; /* pointer to an indirect variable symbol */
+struct funent *pfun; /* pointer to a function symbol */
+struct strent *pstr; /* pointer to a string symbol */
+int att; /* attributes of symbol just parsed */
+int i; /* counter */
+int offset; /* parenthesis level */
+int lhsflg; /* kluge to detect illegal assignments */
+struct symbol *parser(); /* parser returns pointer to symbol */
+int errcod; /* for syntax error printout */
+
+
+/* Perform general initialization */
+
+init();
+
+menstk[0] = &funtbl[0];
+menptr = 0;
+cmdhlp(); /* print out list of symbols */
+
+
+/* Return here to get next command line to execute */
+getcmd:
+
+/* initialize registers and mutable symbols */
+
+accflg = 0; /* Accumulator not in use */
+acc = 0.0L; /* Clear the accumulator */
+offset = 0; /* Parenthesis level zero */
+comptr = 0; /* Start of comma stack */
+narptr = -1; /* Start of function arg counter stack */
+
+psym = (struct symbol *)&contbl[0];
+for( i=0; i<NCONST; i++ )
+ {
+ psym->attrib = CONST; /* clearing the busy bit */
+ ++psym;
+ }
+psym = (struct symbol *)&temp[0];
+for( i=0; i<NTEMP; i++ )
+ {
+ psym->attrib = VAR | TEMP; /* clearing the busy bit */
+ ++psym;
+ }
+
+pstr = &strtbl[0];
+for( i=0; i<NSTRNG; i++ )
+ {
+ pstr->spel = &strngs[ 40*i ];
+ pstr->attrib = STRING | VAR;
+ pstr->string = &strngs[ 40*i ];
+ ++pstr;
+ }
+
+/* List of scanned symbols is empty: */
+as = &ascsym[0];
+*as = 0;
+--as;
+/* First item in scan list is Beginning of Line operator */
+ao = &ascopr[0];
+*ao = oprtbl[0].attrib & 0xf; /* BOL */
+/* value of first item: */
+al = &asclev[0];
+*al = oprtbl[0].sym;
+
+lhsflg = 0; /* illegal left hand side flag */
+psym = &oprtbl[0]; /* pointer to current token */
+
+/* get next token from input string */
+
+gettok:
+lastok = psym; /* last token = current token */
+psym = parser(); /* get a new current token */
+/*printf( "%s attrib %7o value %7o\n", psym->spel, psym->attrib & 0xffff,
+ psym->sym );*/
+
+/* Examine attributes of the symbol returned by the parser */
+att = psym->attrib;
+if( att == ILLEG )
+ {
+ errcod = 1;
+ goto synerr;
+ }
+
+/* Push functions onto scan list without analyzing further */
+if( att & FUNC )
+ {
+ /* A command is a function whose argument is
+ * a pointer to the rest of the input line.
+ * A second argument is also passed: the address
+ * of the last token parsed.
+ */
+ if( att & COMMAN )
+ {
+ pfun = (struct funent *)psym;
+ ( *(pfun->fun))( interl, lastok );
+ abmac(); /* scrub the input line */
+ goto getcmd; /* and ask for more input */
+ }
+ ++narptr; /* offset to number of args */
+ narstk[narptr] = 0;
+ i = lastok->attrib & 0xffff; /* attrib=short, i=int */
+ if( ((i & OPR) == 0)
+ || (i == (OPR | RPAREN))
+ || (i == (OPR | FUNC)) )
+ {
+ errcod = 15;
+ goto synerr;
+ }
+
+ ++lhsflg;
+ ++as;
+ *as = psym;
+ ++ao;
+ *ao = FUNC;
+ ++al;
+ *al = offset + UMINUS;
+ goto gettok;
+ }
+
+/* deal with operators */
+if( att & OPR )
+ {
+ att &= 0xf;
+ /* expression cannot end with an operator other than
+ * (, ), BOL, or a function
+ */
+ if( (att == RPAREN) || (att == EOL) || (att == EOE))
+ {
+ i = lastok->attrib & 0xffff; /* attrib=short, i=int */
+ if( (i & OPR)
+ && (i != (OPR | RPAREN))
+ && (i != (OPR | LPAREN))
+ && (i != (OPR | FUNC))
+ && (i != (OPR | BOL)) )
+ {
+ errcod = 2;
+ goto synerr;
+ }
+ }
+ ++lhsflg; /* any operator but ( and = is not a legal lhs */
+
+/* operator processing, continued */
+
+ switch( att )
+ {
+ case EOE:
+ lhsflg = 0;
+ break;
+ case LPAREN:
+ /* ( must be preceded by an operator of some sort. */
+ if( ((lastok->attrib & OPR) == 0) )
+ {
+ errcod = 3;
+ goto synerr;
+ }
+ /* also, a preceding ) is illegal */
+ if( (unsigned short )lastok->attrib == (OPR|RPAREN))
+ {
+ errcod = 4;
+ goto synerr;
+ }
+ /* Begin looking for illegal left hand sides: */
+ lhsflg = 0;
+ offset += RPAREN; /* new parenthesis level */
+ goto gettok;
+ case RPAREN:
+ offset -= RPAREN; /* parenthesis level */
+ if( offset < 0 )
+ {
+ errcod = 5; /* parenthesis error */
+ goto synerr;
+ }
+ goto gettok;
+ case EOL:
+ if( offset != 0 )
+ {
+ errcod = 6; /* parenthesis error */
+ goto synerr;
+ }
+ break;
+ case EQU:
+ if( --lhsflg ) /* was incremented before switch{} */
+ {
+ errcod = 7;
+ goto synerr;
+ }
+ case UMINUS:
+ case COMP:
+ goto pshopr; /* evaluate right to left */
+ default: ;
+ }
+
+
+/* evaluate expression whenever precedence is not increasing */
+
+symval = psym->sym + offset;
+
+while( symval <= *al )
+ {
+ /* if just starting, must fill accumulator with last
+ * thing on the line
+ */
+ if( (accflg == 0) && (as >= ascsym) && (((*as)->attrib & FUNC) == 0 ))
+ {
+ pvar = (struct varent *)*as;
+/*
+ if( pvar->attrib & STRING )
+ strcpy( (char *)&acc, (char *)pvar->value );
+ else
+*/
+ acc = *pvar->value;
+ --as;
+ accflg = 1;
+ }
+
+/* handle beginning of line type cases, where the symbol
+ * list ascsym[] may be empty.
+ */
+ switch( *ao )
+ {
+ case BOL:
+/* printf( "%.16e\n", (double )acc ); */
+#if NE == 6
+ e64toasc( &acc, str, 100 );
+#else
+ e113toasc( &acc, str, 100 );
+#endif
+ printf( "%s\n", str );
+ goto getcmd; /* all finished */
+ case UMINUS:
+ acc = -acc;
+ goto nochg;
+/*
+ case COMP:
+ acc = ~acc;
+ goto nochg;
+*/
+ default: ;
+ }
+/* Now it is illegal for symbol list to be empty,
+ * because we are going to need a symbol below.
+ */
+ if( as < &ascsym[0] )
+ {
+ errcod = 8;
+ goto synerr;
+ }
+/* get attributes and value of current symbol */
+ att = (*as)->attrib;
+ pvar = (struct varent *)*as;
+ if( att & FUNC )
+ val = 0.0L;
+ else
+ {
+/*
+ if( att & STRING )
+ strcpy( (char *)&val, (char *)pvar->value );
+ else
+*/
+ val = *pvar->value;
+ }
+
+/* Expression evaluation, continued. */
+
+ switch( *ao )
+ {
+ case FUNC:
+ pfun = (struct funent *)*as;
+ /* Call the function with appropriate number of args */
+ i = narstk[ narptr ];
+ --narptr;
+ switch(i)
+ {
+ case 0:
+ acc = ( *(pfun->fun) )(acc);
+ break;
+ case 1:
+ acc = ( *(pfun->fun) )(acc, comstk[comptr-1]);
+ break;
+ case 2:
+ acc = ( *(pfun->fun) )(acc, comstk[comptr-2],
+ comstk[comptr-1]);
+ break;
+ case 3:
+ acc = ( *(pfun->fun) )(acc, comstk[comptr-3],
+ comstk[comptr-2], comstk[comptr-1]);
+ break;
+ default:
+ errcod = 16;
+ goto synerr;
+ }
+ comptr -= i;
+ accflg = 1; /* in case at end of line */
+ break;
+ case EQU:
+ if( ( att & TEMP) || ((att & VAR) == 0) || (att & STRING) )
+ {
+ errcod = 9;
+ goto synerr; /* can only assign to a variable */
+ }
+ pvar = (struct varent *)*as;
+ *pvar->value = acc;
+ break;
+ case PLUS:
+ acc = acc + val; break;
+ case MINUS:
+ acc = val - acc; break;
+ case MULT:
+ acc = acc * val; break;
+ case DIV:
+ if( acc == 0.0L )
+ {
+/*
+divzer:
+*/
+ errcod = 10;
+ goto synerr;
+ }
+ acc = val / acc; break;
+/*
+ case MOD:
+ if( acc == 0 )
+ goto divzer;
+ acc = val % acc; break;
+ case LOR:
+ acc |= val; break;
+ case LXOR:
+ acc ^= val; break;
+ case LAND:
+ acc &= val; break;
+*/
+ case EOE:
+ if( narptr < 0 )
+ {
+ errcod = 18;
+ goto synerr;
+ }
+ narstk[narptr] += 1;
+ comstk[comptr++] = acc;
+/* printf( "\ncomptr: %d narptr: %d %d\n", comptr, narptr, acc );*/
+ acc = val;
+ break;
+ }
+
+
+/* expression evaluation, continued */
+
+/* Pop evaluated tokens from scan list: */
+ /* make temporary variable not busy */
+ if( att & TEMP )
+ (*as)->attrib &= ~BUSY;
+ if( as < &ascsym[0] ) /* can this happen? */
+ {
+ errcod = 11;
+ goto synerr;
+ }
+ --as;
+nochg:
+ --ao;
+ --al;
+ if( ao < &ascopr[0] ) /* can this happen? */
+ {
+ errcod = 12;
+ goto synerr;
+ }
+/* If precedence level will now increase, then */
+/* save accumulator in a temporary location */
+ if( symval > *al )
+ {
+ /* find a free temp location */
+ pvar = &temp[0];
+ for( i=0; i<NTEMP; i++ )
+ {
+ if( (pvar->attrib & BUSY) == 0)
+ goto temfnd;
+ ++pvar;
+ }
+ errcod = 17;
+ printf( "no more temps\n" );
+ pvar = &temp[0];
+ goto synerr;
+
+ temfnd:
+ pvar->attrib |= BUSY;
+ *pvar->value = acc;
+ /*printf( "temp %d\n", acc );*/
+ accflg = 0;
+ ++as; /* push the temp onto the scan list */
+ *as = (struct symbol *)pvar;
+ }
+ } /* End of evaluation loop */
+
+
+/* Push operator onto scan list when precedence increases */
+
+pshopr:
+ ++ao;
+ *ao = psym->attrib & 0xf;
+ ++al;
+ *al = psym->sym + offset;
+ goto gettok;
+ } /* end of OPR processing */
+
+
+/* Token was not an operator. Push symbol onto scan list. */
+if( (lastok->attrib & OPR) == 0 )
+ {
+ errcod = 13;
+ goto synerr; /* quantities must be preceded by an operator */
+ }
+if( (unsigned short )lastok->attrib == (OPR | RPAREN) ) /* ...but not by ) */
+ {
+ errcod = 14;
+ goto synerr;
+ }
+++as;
+*as = psym;
+goto gettok;
+
+synerr:
+
+#if INTHELP
+printf( "%s ", intmsg[errcod] );
+#endif
+printf( " error %d\n", errcod );
+abmac(); /* flush the command line */
+goto getcmd;
+} /* end of program */
+
+/* parser() */
+
+/* Get token from input string and identify it. */
+
+
+static char number[128];
+
+struct symbol *parser( )
+{
+register struct symbol *psym;
+register char *pline;
+struct varent *pvar;
+struct strent *pstr;
+char *cp, *plc, *pn;
+long lnc;
+int i;
+long double tem;
+
+/* reference for old Whitesmiths compiler: */
+/*
+ *extern FILE *stdout;
+ */
+
+pline = interl; /* get current location in command string */
+
+
+/* If at beginning of string, must ask for more input */
+if( pline == line )
+ {
+
+ if( maccnt > 0 )
+ {
+ --maccnt;
+ cp = maclin;
+ plc = pline;
+ while( (*plc++ = *cp++) != 0 )
+ ;
+ goto mstart;
+ }
+ if( takptr < 0 )
+ { /* no take file active: prompt keyboard input */
+ printf("* ");
+ }
+/* Various ways of typing in a command line. */
+
+/*
+ * Old Whitesmiths call to print "*" immediately
+ * use RT11 .GTLIN to get command string
+ * from command file or terminal
+ */
+
+/*
+ * fflush(stdout);
+ * gtlin(line);
+ */
+
+
+ zgets( line, TRUE ); /* keyboard input for other systems: */
+
+
+mstart:
+ uposs = 1; /* unary operators possible at start of line */
+ }
+
+ignore:
+/* Skip over spaces */
+while( *pline == ' ' )
+ ++pline;
+
+/* unary minus after operator */
+if( uposs && (*pline == '-') )
+ {
+ psym = &oprtbl[2]; /* UMINUS */
+ ++pline;
+ goto pdon3;
+ }
+ /* COMP */
+/*
+if( uposs && (*pline == '~') )
+ {
+ psym = &oprtbl[3];
+ ++pline;
+ goto pdon3;
+ }
+*/
+if( uposs && (*pline == '+') ) /* ignore leading plus sign */
+ {
+ ++pline;
+ goto ignore;
+ }
+
+/* end of null terminated input */
+if( (*pline == '\n') || (*pline == '\0') || (*pline == '\r') )
+ {
+ pline = line;
+ goto endlin;
+ }
+if( *pline == ';' )
+ {
+ ++pline;
+endlin:
+ psym = &oprtbl[1]; /* EOL */
+ goto pdon2;
+ }
+
+
+/* parser() */
+
+
+/* Test for numeric input */
+if( (ISDIGIT(*pline)) || (*pline == '.') )
+ {
+ lnc = 0; /* initialize numeric input to zero */
+ qnc = 0.0L;
+ if( *pline == '0' )
+ { /* leading "0" may mean octal or hex radix */
+ ++pline;
+ if( *pline == '.' )
+ goto decimal; /* 0.ddd */
+ /* leading "0x" means hexadecimal radix */
+ if( (*pline == 'x') || (*pline == 'X') )
+ {
+ ++pline;
+ while( ISXDIGIT(*pline) )
+ {
+ i = *pline++ & 0xff;
+ if( i >= 'a' )
+ i -= 047;
+ if( i >= 'A' )
+ i -= 07;
+ i -= 060;
+ lnc = (lnc << 4) + i;
+ qnc = lnc;
+ }
+ goto numdon;
+ }
+ else
+ {
+ while( ISOCTAL( *pline ) )
+ {
+ i = ((*pline++) & 0xff) - 060;
+ lnc = (lnc << 3) + i;
+ qnc = lnc;
+ }
+ goto numdon;
+ }
+ }
+ else
+ {
+ /* no leading "0" means decimal radix */
+/******/
+decimal:
+ pn = number;
+ while( (ISDIGIT(*pline)) || (*pline == '.') )
+ *pn++ = *pline++;
+/* get possible exponent field */
+ if( (*pline == 'e') || (*pline == 'E') )
+ *pn++ = *pline++;
+ else
+ goto numcvt;
+ if( (*pline == '-') || (*pline == '+') )
+ *pn++ = *pline++;
+ while( ISDIGIT(*pline) )
+ *pn++ = *pline++;
+numcvt:
+ *pn++ = ' ';
+ *pn++ = 0;
+#if NE == 6
+ asctoe64( number, &qnc );
+#else
+ asctoe113( number, &qnc );
+#endif
+/* sscanf( number, "%le", &nc ); */
+ }
+/* output the number */
+numdon:
+ /* search the symbol table of constants */
+ pvar = &contbl[0];
+ for( i=0; i<NCONST; i++ )
+ {
+ if( (pvar->attrib & BUSY) == 0 )
+ goto confnd;
+ tem = *pvar->value;
+ if( tem == qnc )
+ {
+ psym = (struct symbol *)pvar;
+ goto pdon2;
+ }
+ ++pvar;
+ }
+ printf( "no room for constant\n" );
+ psym = (struct symbol *)&contbl[0];
+ goto pdon2;
+
+confnd:
+ pvar->spel= contbl[0].spel;
+ pvar->attrib = CONST | BUSY;
+ *pvar->value = qnc;
+ psym = (struct symbol *)pvar;
+ goto pdon2;
+ }
+
+/* check for operators */
+psym = &oprtbl[3];
+for( i=0; i<NOPR; i++ )
+ {
+ if( *pline == *(psym->spel) )
+ goto pdon1;
+ ++psym;
+ }
+
+/* if quoted, it is a string variable */
+if( *pline == '"' )
+ {
+ /* find an empty slot for the string */
+ pstr = strtbl; /* string table */
+ for( i=0; i<NSTRNG-1; i++ )
+ {
+ if( (pstr->attrib & BUSY) == 0 )
+ goto fndstr;
+ ++pstr;
+ }
+ printf( "No room for string\n" );
+ pstr->attrib |= ILLEG;
+ psym = (struct symbol *)pstr;
+ goto pdon0;
+
+fndstr:
+ pstr->attrib |= BUSY;
+ plc = pstr->string;
+ ++pline;
+ for( i=0; i<39; i++ )
+ {
+ *plc++ = *pline;
+ if( (*pline == '\n') || (*pline == '\0') || (*pline == '\r') )
+ {
+illstr:
+ pstr = &strtbl[NSTRNG-1];
+ pstr->attrib |= ILLEG;
+ printf( "Missing string terminator\n" );
+ psym = (struct symbol *)pstr;
+ goto pdon0;
+ }
+ if( *pline++ == '"' )
+ goto finstr;
+ }
+
+ goto illstr; /* no terminator found */
+
+finstr:
+ --plc;
+ *plc = '\0';
+ psym = (struct symbol *)pstr;
+ goto pdon2;
+ }
+/* If none of the above, search function and symbol tables: */
+
+/* copy character string to array lc[] */
+plc = &lc[0];
+while( ISALPHA(*pline) )
+ {
+ /* convert to lower case characters */
+ if( ISUPPER( *pline ) )
+ *pline += 040;
+ *plc++ = *pline++;
+ }
+*plc = 0; /* Null terminate the output string */
+
+/* parser() */
+
+psym = (struct symbol *)menstk[menptr]; /* function table */
+plc = &lc[0];
+cp = psym->spel;
+do
+ {
+ if( strcmp( plc, cp ) == 0 )
+ goto pdon3; /* following unary minus is possible */
+ ++psym;
+ cp = psym->spel;
+ }
+while( *cp != '\0' );
+
+psym = (struct symbol *)&indtbl[0]; /* indirect symbol table */
+plc = &lc[0];
+cp = psym->spel;
+do
+ {
+ if( strcmp( plc, cp ) == 0 )
+ goto pdon2;
+ ++psym;
+ cp = psym->spel;
+ }
+while( *cp != '\0' );
+
+pdon0:
+pline = line; /* scrub line if illegal symbol */
+goto pdon2;
+
+pdon1:
+++pline;
+if( (psym->attrib & 0xf) == RPAREN )
+pdon2: uposs = 0;
+else
+pdon3: uposs = 1;
+
+interl = pline;
+return( psym );
+} /* end of parser */
+
+/* exit from current menu */
+
+long double cmdex()
+{
+
+if( menptr == 0 )
+ {
+ printf( "Main menu is active.\n" );
+ }
+else
+ --menptr;
+
+cmdh();
+return(0.0L);
+}
+
+
+/* gets() */
+
+void zgets( gline, echo )
+char *gline;
+int echo;
+{
+register char *pline;
+register int i;
+
+
+scrub:
+pline = gline;
+getsl:
+ if( (pline - gline) >= LINLEN )
+ {
+ printf( "\nLine too long\n *" );
+ goto scrub;
+ }
+ if( takptr < 0 )
+ { /* get character from keyboard */
+/*
+if DECPDP
+ gtlin( gline );
+ return(0);
+else
+*/
+ *pline = getchar();
+/*endif*/
+ }
+ else
+ { /* get a character from take file */
+ i = fgetc( takstk[takptr] );
+ if( i == -1 )
+ { /* end of take file */
+ if( takptr >= 0 )
+ { /* close file and bump take stack */
+ fclose( takstk[takptr] );
+ takptr -= 1;
+ }
+ if( takptr < 0 ) /* no more take files: */
+ printf( "*" ); /* prompt keyboard input */
+ goto scrub; /* start a new input line */
+ }
+ *pline = i;
+ }
+
+ *pline &= 0x7f;
+ /* xon or xoff characters need filtering out. */
+ if ( *pline == XON || *pline == XOFF )
+ goto getsl;
+
+ /* control U or control C */
+ if( (*pline == 025) || (*pline == 03) )
+ {
+ printf( "\n" );
+ goto scrub;
+ }
+
+ /* Backspace or rubout */
+ if( (*pline == 010) || (*pline == 0177) )
+ {
+ pline -= 1;
+ if( pline >= gline )
+ {
+ if ( echo )
+ printf( "\010\040\010" );
+ goto getsl;
+ }
+ else
+ goto scrub;
+ }
+ if ( echo )
+ printf( "%c", *pline );
+ if( (*pline != '\n') && (*pline != '\r') )
+ {
+ ++pline;
+ goto getsl;
+ }
+ *pline = 0;
+ if ( echo )
+ printf( "%c", '\n' ); /* \r already echoed */
+}
+
+
+/* help function */
+long double cmdhlp()
+{
+
+printf( "%s", idterp );
+printf( "\nFunctions:\n" );
+prhlst( &funtbl[0] );
+printf( "\nVariables:\n" );
+prhlst( &indtbl[0] );
+printf( "\nOperators:\n" );
+prhlst( &oprtbl[2] );
+printf("\n");
+return(0.0L);
+}
+
+
+long double cmdh()
+{
+
+prhlst( menstk[menptr] );
+printf( "\n" );
+return(0.0L);
+}
+
+/* print keyword spellings */
+
+long double prhlst(ps)
+register struct symbol *ps;
+{
+register int j, k;
+int m;
+
+j = 0;
+while( *(ps->spel) != '\0' )
+ {
+ k = strlen( ps->spel ) - 1;
+/* size of a tab field is 2**3 chars */
+ m = ((k >> 3) + 1) << 3;
+ j += m;
+ if( j > 72 )
+ {
+ printf( "\n" );
+ j = m;
+ }
+ printf( "%s\t", ps->spel );
+ ++ps;
+ }
+return(0.0L);
+}
+
+
+#if SALONE
+void init(){}
+#endif
+
+
+/* macro commands */
+
+/* define macro */
+long double cmddm()
+{
+
+zgets( maclin, TRUE );
+return(0.0L);
+}
+
+/* type (i.e., display) macro */
+long double cmdtm()
+{
+
+printf( "%s\n", maclin );
+return(0.0L);
+}
+
+/* execute macro # times */
+long double cmdem( arg )
+long double arg;
+{
+long double f;
+long n;
+long double floorl();
+
+f = floorl(arg);
+n = f;
+if( n <= 0 )
+ n = 1;
+maccnt = n;
+return(0.0L);
+}
+
+
+/* open a take file */
+
+long double take( fname )
+char *fname;
+{
+FILE *f;
+
+while( *fname == ' ' )
+ fname += 1;
+f = fopen( fname, "r" );
+
+if( f == 0 )
+ {
+ printf( "Can't open take file %s\n", fname );
+ takptr = -1; /* terminate all take file input */
+ return(0.0L);
+ }
+takptr += 1;
+takstk[ takptr ] = f;
+printf( "Running %s\n", fname );
+return(0.0L);
+}
+
+
+/* abort macro execution */
+long double abmac()
+{
+
+maccnt = 0;
+interl = line;
+return(0.0L);
+}
+
+
+/* display integer part in hex, octal, and decimal
+ */
+long double hex(qx)
+long double qx;
+{
+long double f;
+long z;
+long double floorl();
+
+f = floorl(qx);
+z = f;
+printf( "0%lo 0x%lx %ld.\n", z, z, z );
+return(qx);
+}
+
+#define NASC 16
+
+long double bits( x )
+long double x;
+{
+int i, j;
+unsigned short dd[4], ee[10];
+char strx[40];
+unsigned short *p;
+
+p = (unsigned short *) &x;
+for( i=0; i<NE; i++ )
+ ee[i] = *p++;
+
+j = 0;
+for( i=0; i<NE; i++ )
+ {
+ printf( "0x%04x,", ee[i] & 0xffff );
+ if( ++j > 7 )
+ {
+ j = 0;
+ printf( "\n" );
+ }
+ }
+printf( "\n" );
+
+/* double conversions
+ */
+*((double *)dd) = x;
+printf( "double: " );
+for( i=0; i<4; i++ )
+ printf( "0x%04x,", dd[i] & 0xffff );
+printf( "\n" );
+
+#if 1
+printf( "double -> long double: " );
+*(long double *)ee = *(double *)dd;
+for( i=0; i<6; i++ )
+ printf( "0x%04x,", ee[i] & 0xffff );
+printf( "\n" );
+e53toasc( dd, strx, NASC );
+printf( "e53toasc: %s\n", strx );
+printf( "Native printf: %.17e\n", *(double *)dd );
+
+/* float conversions
+ */
+*((float *)dd) = x;
+printf( "float: " );
+for( i=0; i<2; i++ )
+ printf( "0x%04x,", dd[i] & 0xffff );
+printf( "\n" );
+e24toe( dd, ee );
+printf( "e24toe: " );
+for( i=0; i<NE; i++ )
+ printf( "0x%04x,", ee[i] & 0xffff );
+printf( "\n" );
+e24toasc( dd, strx, NASC );
+printf( "e24toasc: %s\n", strx );
+/* printf( "Native printf: %.16e\n", (double) *(float *)dd ); */
+
+#ifdef DEC
+printf( "etodec: " );
+etodec( x, dd );
+for( i=0; i<4; i++ )
+ printf( "0x%04x,", dd[i] & 0xffff );
+printf( "\n" );
+printf( "dectoe: " );
+dectoe( dd, ee );
+for( i=0; i<NE; i++ )
+ printf( "0x%04x,", ee[i] & 0xffff );
+printf( "\n" );
+printf( "DEC printf: %.16e\n", *(double *)dd );
+#endif
+#endif /* 0 */
+return(x);
+}
+
+
+/* Exit to monitor. */
+long double mxit()
+{
+
+exit(0);
+return(0.0L);
+}
+
+
+long double cmddig( x )
+long double x;
+{
+long double f;
+long lx;
+
+f = floorl(x);
+lx = f;
+ndigits = lx;
+if( ndigits <= 0 )
+ ndigits = DEFDIS;
+return(f);
+}
+
+
+long double csys(x)
+char *x;
+{
+void system();
+
+system( x+1 );
+cmdh();
+return(0.0L);
+}
+
+
+long double ifrac(x)
+long double x;
+{
+unsigned long lx;
+long double y, z;
+
+z = floorl(x);
+lx = z;
+y = x - z;
+printf( " int = %lx\n", lx );
+return(y);
+}
+
+long double xcmpl(x,y)
+long double x,y;
+{
+long double ans;
+char str[40];
+
+#if NE == 6
+ e64toasc( &x, str, 100 );
+ printf( "x = %s\n", str );
+ e64toasc( &y, str, 100 );
+ printf( "y = %s\n", str );
+#else
+ e113toasc( &x, str, 100 );
+ printf( "x = %s\n", str );
+ e113toasc( &y, str, 100 );
+ printf( "y = %s\n", str );
+#endif
+
+ans = -2.0;
+if( x == y )
+ {
+ printf( "x == y " );
+ ans = 0.0;
+ }
+if( x < y )
+ {
+ printf( "x < y" );
+ ans = -1.0;
+ }
+if( x > y )
+ {
+ printf( "x > y" );
+ ans = 1.0;
+ }
+return( ans );
+}
+
+long double zstdtrl(k,t)
+long double k, t;
+{
+int ki;
+long double y;
+ki = k;
+y = stdtrl(ki,t);
+return(y);
+}
+
+long double zstdtril(k,t)
+long double k, t;
+{
+int ki;
+long double y;
+ki = k;
+y = stdtril(ki,t);
+return(y);
+}
+
+#ifdef NANS
+long double zisnan(x)
+long double x;
+{
+ long double y;
+ int k;
+ k = isnanl(x);
+ y = k;
+ return(y);
+}
+long double zisfinite(x)
+long double x;
+{
+ long double y;
+ int k;
+ k = isfinitel(x);
+ y = k;
+ return(y);
+}
+long double zsignbit(x)
+long double x;
+{
+ long double y;
+ int k;
+ k = signbitl(x);
+ y = k;
+ return(y);
+}
+#endif
diff --git a/libm/ldouble/lcalc.h b/libm/ldouble/lcalc.h
new file mode 100644
index 000000000..7be51d79e
--- /dev/null
+++ b/libm/ldouble/lcalc.h
@@ -0,0 +1,79 @@
+/* calc.h
+ * include file for calc.c
+ */
+
+/* 32 bit memory addresses: */
+#ifndef LARGEMEM
+#define LARGEMEM 1
+#endif
+
+/* data structure of symbol table */
+struct symbol
+ {
+ char *spel;
+ short attrib;
+#if LARGEMEM
+ long sym;
+#else
+ short sym;
+#endif
+ };
+
+struct funent
+ {
+ char *spel;
+ short attrib;
+ long double (*fun )();
+ };
+
+struct varent
+ {
+ char *spel;
+ short attrib;
+ long double *value;
+ };
+
+struct strent
+ {
+ char *spel;
+ short attrib;
+ char *string;
+ };
+
+
+/* general symbol attributes: */
+#define OPR 0x8000
+#define VAR 0x4000
+#define CONST 0x2000
+#define FUNC 0x1000
+#define ILLEG 0x800
+#define BUSY 0x400
+#define TEMP 0x200
+#define STRING 0x100
+#define COMMAN 0x80
+#define IND 0x1
+
+/* attributes of operators (ordered by precedence): */
+#define BOL 1
+#define EOL 2
+/* end of expression (comma): */
+#define EOE 3
+#define EQU 4
+#define PLUS 5
+#define MINUS 6
+#define MULT 7
+#define DIV 8
+#define UMINUS 9
+#define LPAREN 10
+#define RPAREN 11
+#define COMP 12
+#define MOD 13
+#define LAND 14
+#define LOR 15
+#define LXOR 16
+
+
+extern struct funent funtbl[];
+/*extern struct symbol symtbl[];*/
+extern struct varent indtbl[];
+
diff --git a/libm/ldouble/ldrand.c b/libm/ldouble/ldrand.c
new file mode 100644
index 000000000..892b465df
--- /dev/null
+++ b/libm/ldouble/ldrand.c
@@ -0,0 +1,175 @@
+/* ldrand.c
+ *
+ * Pseudorandom number generator
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double y;
+ * int ldrand();
+ *
+ * ldrand( &y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Yields a random number 1.0 <= y < 2.0.
+ *
+ * The three-generator congruential algorithm by Brian
+ * Wichmann and David Hill (BYTE magazine, March, 1987,
+ * pp 127-8) is used.
+ *
+ * Versions invoked by the different arithmetic compile
+ * time options IBMPC, and MIEEE, produce the same sequences.
+ *
+ */
+
+
+
+#include <math.h>
+#ifdef ANSIPROT
+int ranwh ( void );
+#else
+int ranwh();
+#endif
+#ifdef UNK
+#undef UNK
+#if BIGENDIAN
+#define MIEEE
+#else
+#define IBMPC
+#endif
+#endif
+
+/* Three-generator random number algorithm
+ * of Brian Wichmann and David Hill
+ * BYTE magazine, March, 1987 pp 127-8
+ *
+ * The period, given by them, is (p-1)(q-1)(r-1)/4 = 6.95e12.
+ */
+
+static int sx = 1;
+static int sy = 10000;
+static int sz = 3000;
+
+static union {
+ long double d;
+ unsigned short s[8];
+} unkans;
+
+/* This function implements the three
+ * congruential generators.
+ */
+
+int ranwh()
+{
+int r, s;
+
+/* sx = sx * 171 mod 30269 */
+r = sx/177;
+s = sx - 177 * r;
+sx = 171 * s - 2 * r;
+if( sx < 0 )
+ sx += 30269;
+
+
+/* sy = sy * 172 mod 30307 */
+r = sy/176;
+s = sy - 176 * r;
+sy = 172 * s - 35 * r;
+if( sy < 0 )
+ sy += 30307;
+
+/* sz = 170 * sz mod 30323 */
+r = sz/178;
+s = sz - 178 * r;
+sz = 170 * s - 63 * r;
+if( sz < 0 )
+ sz += 30323;
+/* The results are in static sx, sy, sz. */
+return 0;
+}
+
+/* ldrand.c
+ *
+ * Random double precision floating point number between 1 and 2.
+ *
+ * C callable:
+ * drand( &x );
+ */
+
+int ldrand( a )
+long double *a;
+{
+unsigned short r;
+
+/* This algorithm of Wichmann and Hill computes a floating point
+ * result:
+ */
+ranwh();
+unkans.d = sx/30269.0L + sy/30307.0L + sz/30323.0L;
+r = unkans.d;
+unkans.d -= r;
+unkans.d += 1.0L;
+
+if( sizeof(long double) == 16 )
+ {
+#ifdef MIEEE
+ ranwh();
+ r = sx * sy + sz;
+ unkans.s[7] = r;
+ ranwh();
+ r = sx * sy + sz;
+ unkans.s[6] = r;
+ ranwh();
+ r = sx * sy + sz;
+ unkans.s[5] = r;
+ ranwh();
+ r = sx * sy + sz;
+ unkans.s[4] = r;
+ ranwh();
+ r = sx * sy + sz;
+ unkans.s[3] = r;
+#endif
+#ifdef IBMPC
+ ranwh();
+ r = sx * sy + sz;
+ unkans.s[0] = r;
+ ranwh();
+ r = sx * sy + sz;
+ unkans.s[1] = r;
+ ranwh();
+ r = sx * sy + sz;
+ unkans.s[2] = r;
+ ranwh();
+ r = sx * sy + sz;
+ unkans.s[3] = r;
+ ranwh();
+ r = sx * sy + sz;
+ unkans.s[4] = r;
+#endif
+ }
+else
+ {
+#ifdef MIEEE
+ ranwh();
+ r = sx * sy + sz;
+ unkans.s[5] = r;
+ ranwh();
+ r = sx * sy + sz;
+ unkans.s[4] = r;
+#endif
+#ifdef IBMPC
+ ranwh();
+ r = sx * sy + sz;
+ unkans.s[0] = r;
+ ranwh();
+ r = sx * sy + sz;
+ unkans.s[1] = r;
+#endif
+ }
+*a = unkans.d;
+return 0;
+}
diff --git a/libm/ldouble/log10l.c b/libm/ldouble/log10l.c
new file mode 100644
index 000000000..fa13ff3a2
--- /dev/null
+++ b/libm/ldouble/log10l.c
@@ -0,0 +1,319 @@
+/* log10l.c
+ *
+ * Common logarithm, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, log10l();
+ *
+ * y = log10l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base 10 logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the logarithm
+ * of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting z = 2(x-1)/x+1),
+ *
+ * log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 30000 9.0e-20 2.6e-20
+ * IEEE exp(+-10000) 30000 6.0e-20 2.3e-20
+ *
+ * In the tests over the interval exp(+-10000), the logarithms
+ * of the random arguments were uniformly distributed over
+ * [-10000, +10000].
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity: x = 0; returns MINLOG
+ * log domain: x < 0; returns MINLOG
+ */
+
+/*
+Cephes Math Library Release 2.2: January, 1991
+Copyright 1984, 1991 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+static char fname[] = {"log10l"};
+
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 6.2e-22
+ */
+#ifdef UNK
+static long double P[] = {
+ 4.9962495940332550844739E-1L,
+ 1.0767376367209449010438E1L,
+ 7.7671073698359539859595E1L,
+ 2.5620629828144409632571E2L,
+ 4.2401812743503691187826E2L,
+ 3.4258224542413922935104E2L,
+ 1.0747524399916215149070E2L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0,*/
+ 2.3479774160285863271658E1L,
+ 1.9444210022760132894510E2L,
+ 7.7952888181207260646090E2L,
+ 1.6911722418503949084863E3L,
+ 2.0307734695595183428202E3L,
+ 1.2695660352705325274404E3L,
+ 3.2242573199748645407652E2L,
+};
+#endif
+
+#ifdef IBMPC
+static short P[] = {
+0xfe72,0xce22,0xd7b9,0xffce,0x3ffd, XPD
+0xb778,0x0e34,0x2c71,0xac47,0x4002, XPD
+0xea8b,0xc751,0x96f8,0x9b57,0x4005, XPD
+0xfeaf,0x6a02,0x67fb,0x801a,0x4007, XPD
+0x6b5a,0xf252,0x51ff,0xd402,0x4007, XPD
+0x39ce,0x9f76,0x8704,0xab4a,0x4007, XPD
+0x1b39,0x740b,0x532e,0xd6f3,0x4005, XPD
+};
+static short Q[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0x2f3a,0xbf26,0x93d5,0xbbd6,0x4003, XPD
+0x13c8,0x031a,0x2d7b,0xc271,0x4006, XPD
+0x449d,0x1993,0xd933,0xc2e1,0x4008, XPD
+0x5b65,0x574e,0x8301,0xd365,0x4009, XPD
+0xa65d,0x3bd2,0xc043,0xfdd8,0x4009, XPD
+0x3b21,0xffea,0x1cf5,0x9eb2,0x4009, XPD
+0x545c,0xd708,0x7e62,0xa136,0x4007, XPD
+};
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0x3ffd0000,0xffced7b9,0xce22fe72,
+0x40020000,0xac472c71,0x0e34b778,
+0x40050000,0x9b5796f8,0xc751ea8b,
+0x40070000,0x801a67fb,0x6a02feaf,
+0x40070000,0xd40251ff,0xf2526b5a,
+0x40070000,0xab4a8704,0x9f7639ce,
+0x40050000,0xd6f3532e,0x740b1b39,
+};
+static long Q[] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x40030000,0xbbd693d5,0xbf262f3a,
+0x40060000,0xc2712d7b,0x031a13c8,
+0x40080000,0xc2e1d933,0x1993449d,
+0x40090000,0xd3658301,0x574e5b65,
+0x40090000,0xfdd8c043,0x3bd2a65d,
+0x40090000,0x9eb21cf5,0xffea3b21,
+0x40070000,0xa1367e62,0xd708545c,
+};
+#endif
+
+/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
+ * where z = 2(x-1)/(x+1)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 6.16e-22
+ */
+
+#ifdef UNK
+static long double R[4] = {
+ 1.9757429581415468984296E-3L,
+-7.1990767473014147232598E-1L,
+ 1.0777257190312272158094E1L,
+-3.5717684488096787370998E1L,
+};
+static long double S[4] = {
+/* 1.00000000000000000000E0L,*/
+-2.6201045551331104417768E1L,
+ 1.9361891836232102174846E2L,
+-4.2861221385716144629696E2L,
+};
+/* log10(2) */
+#define L102A 0.3125L
+#define L102B -1.1470004336018804786261e-2L
+/* log10(e) */
+#define L10EA 0.5L
+#define L10EB -6.5705518096748172348871e-2L
+#endif
+#ifdef IBMPC
+static short R[] = {
+0x6ef4,0xf922,0x7763,0x817b,0x3ff6, XPD
+0x15fd,0x1af9,0xde8f,0xb84b,0xbffe, XPD
+0x8b96,0x4f8d,0xa53c,0xac6f,0x4002, XPD
+0x8932,0xb4e3,0xe8ae,0x8ede,0xc004, XPD
+};
+static short S[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0x7ce4,0x1fc9,0xbdc5,0xd19b,0xc003, XPD
+0x0af3,0x0d10,0x716f,0xc19e,0x4006, XPD
+0x4d7d,0x0f55,0x5d06,0xd64e,0xc007, XPD
+};
+static short LG102A[] = {0x0000,0x0000,0x0000,0xa000,0x3ffd, XPD};
+#define L102A *(long double *)LG102A
+static short LG102B[] = {0x0cee,0x8601,0xaf60,0xbbec,0xbff8, XPD};
+#define L102B *(long double *)LG102B
+static short LG10EA[] = {0x0000,0x0000,0x0000,0x8000,0x3ffe, XPD};
+#define L10EA *(long double *)LG10EA
+static short LG10EB[] = {0x39ab,0x235e,0x9d5b,0x8690,0xbffb, XPD};
+#define L10EB *(long double *)LG10EB
+#endif
+
+#ifdef MIEEE
+static long R[12] = {
+0x3ff60000,0x817b7763,0xf9226ef4,
+0xbffe0000,0xb84bde8f,0x1af915fd,
+0x40020000,0xac6fa53c,0x4f8d8b96,
+0xc0040000,0x8edee8ae,0xb4e38932,
+};
+static long S[9] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0xc0030000,0xd19bbdc5,0x1fc97ce4,
+0x40060000,0xc19e716f,0x0d100af3,
+0xc0070000,0xd64e5d06,0x0f554d7d,
+};
+static long LG102A[] = {0x3ffd0000,0xa0000000,0x00000000};
+#define L102A *(long double *)LG102A
+static long LG102B[] = {0xbff80000,0xbbecaf60,0x86010cee};
+#define L102B *(long double *)LG102B
+static long LG10EA[] = {0x3ffe0000,0x80000000,0x00000000};
+#define L10EA *(long double *)LG10EA
+static long LG10EB[] = {0xbffb0000,0x86909d5b,0x235e39ab};
+#define L10EB *(long double *)LG10EB
+#endif
+
+
+#define SQRTH 0.70710678118654752440L
+#ifdef ANSIPROT
+extern long double frexpl ( long double, int * );
+extern long double ldexpl ( long double, int );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern int isnanl ( long double );
+#else
+long double frexpl(), ldexpl(), polevll(), p1evll(), isnanl();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+#ifdef NANS
+extern long double NANL;
+#endif
+
+long double log10l(x)
+long double x;
+{
+long double y;
+VOLATILE long double z;
+int e;
+
+#ifdef NANS
+if( isnanl(x) )
+ return(x);
+#endif
+/* Test for domain */
+if( x <= 0.0L )
+ {
+ if( x == 0.0L )
+ {
+ mtherr( fname, SING );
+#ifdef INFINITIES
+ return(-INFINITYL);
+#else
+ return( -4.9314733889673399399914e3L );
+#endif
+ }
+ else
+ {
+ mtherr( fname, DOMAIN );
+#ifdef NANS
+ return(NANL);
+#else
+ return( -4.9314733889673399399914e3L );
+#endif
+ }
+ }
+#ifdef INFINITIES
+if( x == INFINITYL )
+ return(INFINITYL);
+#endif
+/* separate mantissa from exponent */
+
+/* Note, frexp is used so that denormal numbers
+ * will be handled properly.
+ */
+x = frexpl( x, &e );
+
+
+/* logarithm using log(x) = z + z**3 P(z)/Q(z),
+ * where z = 2(x-1)/x+1)
+ */
+if( (e > 2) || (e < -2) )
+{
+if( x < SQRTH )
+ { /* 2( 2x-1 )/( 2x+1 ) */
+ e -= 1;
+ z = x - 0.5L;
+ y = 0.5L * z + 0.5L;
+ }
+else
+ { /* 2 (x-1)/(x+1) */
+ z = x - 0.5L;
+ z -= 0.5L;
+ y = 0.5L * x + 0.5L;
+ }
+x = z / y;
+z = x*x;
+y = x * ( z * polevll( z, R, 3 ) / p1evll( z, S, 3 ) );
+goto done;
+}
+
+
+/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+
+if( x < SQRTH )
+ {
+ e -= 1;
+ x = ldexpl( x, 1 ) - 1.0L; /* 2x - 1 */
+ }
+else
+ {
+ x = x - 1.0L;
+ }
+z = x*x;
+y = x * ( z * polevll( x, P, 6 ) / p1evll( x, Q, 7 ) );
+y = y - ldexpl( z, -1 ); /* -0.5x^2 + ... */
+
+done:
+
+/* Multiply log of fraction by log10(e)
+ * and base 2 exponent by log10(2).
+ *
+ * ***CAUTION***
+ *
+ * This sequence of operations is critical and it may
+ * be horribly defeated by some compiler optimizers.
+ */
+z = y * (L10EB);
+z += x * (L10EB);
+z += e * (L102B);
+z += y * (L10EA);
+z += x * (L10EA);
+z += e * (L102A);
+
+return( z );
+}
diff --git a/libm/ldouble/log2l.c b/libm/ldouble/log2l.c
new file mode 100644
index 000000000..220b881ae
--- /dev/null
+++ b/libm/ldouble/log2l.c
@@ -0,0 +1,302 @@
+/* log2l.c
+ *
+ * Base 2 logarithm, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, log2l();
+ *
+ * y = log2l( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base 2 logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the (natural)
+ * logarithm of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting z = 2(x-1)/x+1),
+ *
+ * log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 30000 9.8e-20 2.7e-20
+ * IEEE exp(+-10000) 70000 5.4e-20 2.3e-20
+ *
+ * In the tests over the interval exp(+-10000), the logarithms
+ * of the random arguments were uniformly distributed over
+ * [-10000, +10000].
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity: x = 0; returns -INFINITYL
+ * log domain: x < 0; returns NANL
+ */
+
+/*
+Cephes Math Library Release 2.8: May, 1998
+Copyright 1984, 1991, 1998 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 6.2e-22
+ */
+#ifdef UNK
+static long double P[] = {
+ 4.9962495940332550844739E-1L,
+ 1.0767376367209449010438E1L,
+ 7.7671073698359539859595E1L,
+ 2.5620629828144409632571E2L,
+ 4.2401812743503691187826E2L,
+ 3.4258224542413922935104E2L,
+ 1.0747524399916215149070E2L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0,*/
+ 2.3479774160285863271658E1L,
+ 1.9444210022760132894510E2L,
+ 7.7952888181207260646090E2L,
+ 1.6911722418503949084863E3L,
+ 2.0307734695595183428202E3L,
+ 1.2695660352705325274404E3L,
+ 3.2242573199748645407652E2L,
+};
+#endif
+
+#ifdef IBMPC
+static short P[] = {
+0xfe72,0xce22,0xd7b9,0xffce,0x3ffd, XPD
+0xb778,0x0e34,0x2c71,0xac47,0x4002, XPD
+0xea8b,0xc751,0x96f8,0x9b57,0x4005, XPD
+0xfeaf,0x6a02,0x67fb,0x801a,0x4007, XPD
+0x6b5a,0xf252,0x51ff,0xd402,0x4007, XPD
+0x39ce,0x9f76,0x8704,0xab4a,0x4007, XPD
+0x1b39,0x740b,0x532e,0xd6f3,0x4005, XPD
+};
+static short Q[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0x2f3a,0xbf26,0x93d5,0xbbd6,0x4003, XPD
+0x13c8,0x031a,0x2d7b,0xc271,0x4006, XPD
+0x449d,0x1993,0xd933,0xc2e1,0x4008, XPD
+0x5b65,0x574e,0x8301,0xd365,0x4009, XPD
+0xa65d,0x3bd2,0xc043,0xfdd8,0x4009, XPD
+0x3b21,0xffea,0x1cf5,0x9eb2,0x4009, XPD
+0x545c,0xd708,0x7e62,0xa136,0x4007, XPD
+};
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0x3ffd0000,0xffced7b9,0xce22fe72,
+0x40020000,0xac472c71,0x0e34b778,
+0x40050000,0x9b5796f8,0xc751ea8b,
+0x40070000,0x801a67fb,0x6a02feaf,
+0x40070000,0xd40251ff,0xf2526b5a,
+0x40070000,0xab4a8704,0x9f7639ce,
+0x40050000,0xd6f3532e,0x740b1b39,
+};
+static long Q[] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x40030000,0xbbd693d5,0xbf262f3a,
+0x40060000,0xc2712d7b,0x031a13c8,
+0x40080000,0xc2e1d933,0x1993449d,
+0x40090000,0xd3658301,0x574e5b65,
+0x40090000,0xfdd8c043,0x3bd2a65d,
+0x40090000,0x9eb21cf5,0xffea3b21,
+0x40070000,0xa1367e62,0xd708545c,
+};
+#endif
+
+/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
+ * where z = 2(x-1)/(x+1)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 6.16e-22
+ */
+#ifdef UNK
+static long double R[4] = {
+ 1.9757429581415468984296E-3L,
+-7.1990767473014147232598E-1L,
+ 1.0777257190312272158094E1L,
+-3.5717684488096787370998E1L,
+};
+static long double S[4] = {
+/* 1.00000000000000000000E0L,*/
+-2.6201045551331104417768E1L,
+ 1.9361891836232102174846E2L,
+-4.2861221385716144629696E2L,
+};
+/* log2(e) - 1 */
+#define LOG2EA 4.4269504088896340735992e-1L
+#endif
+#ifdef IBMPC
+static short R[] = {
+0x6ef4,0xf922,0x7763,0x817b,0x3ff6, XPD
+0x15fd,0x1af9,0xde8f,0xb84b,0xbffe, XPD
+0x8b96,0x4f8d,0xa53c,0xac6f,0x4002, XPD
+0x8932,0xb4e3,0xe8ae,0x8ede,0xc004, XPD
+};
+static short S[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0x7ce4,0x1fc9,0xbdc5,0xd19b,0xc003, XPD
+0x0af3,0x0d10,0x716f,0xc19e,0x4006, XPD
+0x4d7d,0x0f55,0x5d06,0xd64e,0xc007, XPD
+};
+static short LG2EA[] = {0xc2ef,0x705f,0xeca5,0xe2a8,0x3ffd, XPD};
+#define LOG2EA *(long double *)LG2EA
+#endif
+
+#ifdef MIEEE
+static long R[12] = {
+0x3ff60000,0x817b7763,0xf9226ef4,
+0xbffe0000,0xb84bde8f,0x1af915fd,
+0x40020000,0xac6fa53c,0x4f8d8b96,
+0xc0040000,0x8edee8ae,0xb4e38932,
+};
+static long S[9] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0xc0030000,0xd19bbdc5,0x1fc97ce4,
+0x40060000,0xc19e716f,0x0d100af3,
+0xc0070000,0xd64e5d06,0x0f554d7d,
+};
+static long LG2EA[] = {0x3ffd0000,0xe2a8eca5,0x705fc2ef};
+#define LOG2EA *(long double *)LG2EA
+#endif
+
+
+#define SQRTH 0.70710678118654752440L
+extern long double MINLOGL;
+#ifdef ANSIPROT
+extern long double frexpl ( long double, int * );
+extern long double ldexpl ( long double, int );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern int isnanl ( long double );
+#else
+long double frexpl(), ldexpl(), polevll(), p1evll();
+extern int isnanl ();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+#ifdef NANS
+extern long double NANL;
+#endif
+
+long double log2l(x)
+long double x;
+{
+VOLATILE long double z;
+long double y;
+int e;
+
+#ifdef NANS
+if( isnanl(x) )
+ return(x);
+#endif
+#ifdef INFINITIES
+if( x == INFINITYL )
+ return(x);
+#endif
+/* Test for domain */
+if( x <= 0.0L )
+ {
+ if( x == 0.0L )
+ {
+#ifdef INFINITIES
+ return( -INFINITYL );
+#else
+ mtherr( "log2l", SING );
+ return( -16384.0L );
+#endif
+ }
+ else
+ {
+#ifdef NANS
+ return( NANL );
+#else
+ mtherr( "log2l", DOMAIN );
+ return( -16384.0L );
+#endif
+ }
+ }
+
+/* separate mantissa from exponent */
+
+/* Note, frexp is used so that denormal numbers
+ * will be handled properly.
+ */
+x = frexpl( x, &e );
+
+
+/* logarithm using log(x) = z + z**3 P(z)/Q(z),
+ * where z = 2(x-1)/x+1)
+ */
+if( (e > 2) || (e < -2) )
+{
+if( x < SQRTH )
+ { /* 2( 2x-1 )/( 2x+1 ) */
+ e -= 1;
+ z = x - 0.5L;
+ y = 0.5L * z + 0.5L;
+ }
+else
+ { /* 2 (x-1)/(x+1) */
+ z = x - 0.5L;
+ z -= 0.5L;
+ y = 0.5L * x + 0.5L;
+ }
+x = z / y;
+z = x*x;
+y = x * ( z * polevll( z, R, 3 ) / p1evll( z, S, 3 ) );
+goto done;
+}
+
+
+/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+
+if( x < SQRTH )
+ {
+ e -= 1;
+ x = ldexpl( x, 1 ) - 1.0L; /* 2x - 1 */
+ }
+else
+ {
+ x = x - 1.0L;
+ }
+z = x*x;
+y = x * ( z * polevll( x, P, 6 ) / p1evll( x, Q, 7 ) );
+y = y - ldexpl( z, -1 ); /* -0.5x^2 + ... */
+
+done:
+
+/* Multiply log of fraction by log2(e)
+ * and base 2 exponent by 1
+ *
+ * ***CAUTION***
+ *
+ * This sequence of operations is critical and it may
+ * be horribly defeated by some compiler optimizers.
+ */
+z = y * LOG2EA;
+z += x * LOG2EA;
+z += y;
+z += x;
+z += e;
+return( z );
+}
+
diff --git a/libm/ldouble/logl.c b/libm/ldouble/logl.c
new file mode 100644
index 000000000..d6367eb19
--- /dev/null
+++ b/libm/ldouble/logl.c
@@ -0,0 +1,292 @@
+/* logl.c
+ *
+ * Natural logarithm, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, logl();
+ *
+ * y = logl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of x.
+ *
+ * The argument is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the logarithm
+ * of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
+ *
+ * Otherwise, setting z = 2(x-1)/x+1),
+ *
+ * log(x) = z + z**3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2.0 150000 8.71e-20 2.75e-20
+ * IEEE exp(+-10000) 100000 5.39e-20 2.34e-20
+ *
+ * In the tests over the interval exp(+-10000), the logarithms
+ * of the random arguments were uniformly distributed over
+ * [-10000, +10000].
+ *
+ * ERROR MESSAGES:
+ *
+ * log singularity: x = 0; returns -INFINITYL
+ * log domain: x < 0; returns NANL
+ */
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright 1984, 1990, 1998 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 2.32e-20
+ */
+#ifdef UNK
+static long double P[] = {
+ 4.5270000862445199635215E-5L,
+ 4.9854102823193375972212E-1L,
+ 6.5787325942061044846969E0L,
+ 2.9911919328553073277375E1L,
+ 6.0949667980987787057556E1L,
+ 5.7112963590585538103336E1L,
+ 2.0039553499201281259648E1L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0,*/
+ 1.5062909083469192043167E1L,
+ 8.3047565967967209469434E1L,
+ 2.2176239823732856465394E2L,
+ 3.0909872225312059774938E2L,
+ 2.1642788614495947685003E2L,
+ 6.0118660497603843919306E1L,
+};
+#endif
+
+#ifdef IBMPC
+static short P[] = {
+0x51b9,0x9cae,0x4b15,0xbde0,0x3ff0, XPD
+0x19cf,0xf0d4,0xc507,0xff40,0x3ffd, XPD
+0x9942,0xa7d2,0xfa37,0xd284,0x4001, XPD
+0x4add,0x65ce,0x9c5c,0xef4b,0x4003, XPD
+0x8445,0x619a,0x75c3,0xf3cc,0x4004, XPD
+0x81ab,0x3cd0,0xacba,0xe473,0x4004, XPD
+0x4cbf,0xcc18,0x016c,0xa051,0x4003, XPD
+};
+static short Q[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0xb8b7,0x81f1,0xacf4,0xf101,0x4002, XPD
+0xbc31,0x09a4,0x5a91,0xa618,0x4005, XPD
+0xaeec,0xe7da,0x2c87,0xddc3,0x4006, XPD
+0x2bde,0x4845,0xa2ee,0x9a8c,0x4007, XPD
+0x3120,0x4703,0x89f2,0xd86d,0x4006, XPD
+0x7347,0x3224,0x8223,0xf079,0x4004, XPD
+};
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0x3ff00000,0xbde04b15,0x9cae51b9,
+0x3ffd0000,0xff40c507,0xf0d419cf,
+0x40010000,0xd284fa37,0xa7d29942,
+0x40030000,0xef4b9c5c,0x65ce4add,
+0x40040000,0xf3cc75c3,0x619a8445,
+0x40040000,0xe473acba,0x3cd081ab,
+0x40030000,0xa051016c,0xcc184cbf,
+};
+static long Q[] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x40020000,0xf101acf4,0x81f1b8b7,
+0x40050000,0xa6185a91,0x09a4bc31,
+0x40060000,0xddc32c87,0xe7daaeec,
+0x40070000,0x9a8ca2ee,0x48452bde,
+0x40060000,0xd86d89f2,0x47033120,
+0x40040000,0xf0798223,0x32247347,
+};
+#endif
+
+/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
+ * where z = 2(x-1)/(x+1)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 6.16e-22
+ */
+
+#ifdef UNK
+static long double R[4] = {
+ 1.9757429581415468984296E-3L,
+-7.1990767473014147232598E-1L,
+ 1.0777257190312272158094E1L,
+-3.5717684488096787370998E1L,
+};
+static long double S[4] = {
+/* 1.00000000000000000000E0L,*/
+-2.6201045551331104417768E1L,
+ 1.9361891836232102174846E2L,
+-4.2861221385716144629696E2L,
+};
+static long double C1 = 6.9314575195312500000000E-1L;
+static long double C2 = 1.4286068203094172321215E-6L;
+#endif
+#ifdef IBMPC
+static short R[] = {
+0x6ef4,0xf922,0x7763,0x817b,0x3ff6, XPD
+0x15fd,0x1af9,0xde8f,0xb84b,0xbffe, XPD
+0x8b96,0x4f8d,0xa53c,0xac6f,0x4002, XPD
+0x8932,0xb4e3,0xe8ae,0x8ede,0xc004, XPD
+};
+static short S[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0x7ce4,0x1fc9,0xbdc5,0xd19b,0xc003, XPD
+0x0af3,0x0d10,0x716f,0xc19e,0x4006, XPD
+0x4d7d,0x0f55,0x5d06,0xd64e,0xc007, XPD
+};
+static short sc1[] = {0x0000,0x0000,0x0000,0xb172,0x3ffe, XPD};
+#define C1 (*(long double *)sc1)
+static short sc2[] = {0x4f1e,0xcd5e,0x8e7b,0xbfbe,0x3feb, XPD};
+#define C2 (*(long double *)sc2)
+#endif
+#ifdef MIEEE
+static long R[12] = {
+0x3ff60000,0x817b7763,0xf9226ef4,
+0xbffe0000,0xb84bde8f,0x1af915fd,
+0x40020000,0xac6fa53c,0x4f8d8b96,
+0xc0040000,0x8edee8ae,0xb4e38932,
+};
+static long S[9] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0xc0030000,0xd19bbdc5,0x1fc97ce4,
+0x40060000,0xc19e716f,0x0d100af3,
+0xc0070000,0xd64e5d06,0x0f554d7d,
+};
+static long sc1[] = {0x3ffe0000,0xb1720000,0x00000000};
+#define C1 (*(long double *)sc1)
+static long sc2[] = {0x3feb0000,0xbfbe8e7b,0xcd5e4f1e};
+#define C2 (*(long double *)sc2)
+#endif
+
+
+#define SQRTH 0.70710678118654752440L
+extern long double MINLOGL;
+#ifdef ANSIPROT
+extern long double frexpl ( long double, int * );
+extern long double ldexpl ( long double, int );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern int isnanl ( long double );
+#else
+long double frexpl(), ldexpl(), polevll(), p1evll(), isnanl();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+#ifdef NANS
+extern long double NANL;
+#endif
+
+long double logl(x)
+long double x;
+{
+long double y, z;
+int e;
+
+#ifdef NANS
+if( isnanl(x) )
+ return(x);
+#endif
+#ifdef INFINITIES
+if( x == INFINITYL )
+ return(x);
+#endif
+/* Test for domain */
+if( x <= 0.0L )
+ {
+ if( x == 0.0L )
+ {
+#ifdef INFINITIES
+ return( -INFINITYL );
+#else
+ mtherr( "logl", SING );
+ return( MINLOGL );
+#endif
+ }
+ else
+ {
+#ifdef NANS
+ return( NANL );
+#else
+ mtherr( "logl", DOMAIN );
+ return( MINLOGL );
+#endif
+ }
+ }
+
+/* separate mantissa from exponent */
+
+/* Note, frexp is used so that denormal numbers
+ * will be handled properly.
+ */
+x = frexpl( x, &e );
+
+/* logarithm using log(x) = z + z**3 P(z)/Q(z),
+ * where z = 2(x-1)/x+1)
+ */
+if( (e > 2) || (e < -2) )
+{
+if( x < SQRTH )
+ { /* 2( 2x-1 )/( 2x+1 ) */
+ e -= 1;
+ z = x - 0.5L;
+ y = 0.5L * z + 0.5L;
+ }
+else
+ { /* 2 (x-1)/(x+1) */
+ z = x - 0.5L;
+ z -= 0.5L;
+ y = 0.5L * x + 0.5L;
+ }
+x = z / y;
+z = x*x;
+z = x * ( z * polevll( z, R, 3 ) / p1evll( z, S, 3 ) );
+z = z + e * C2;
+z = z + x;
+z = z + e * C1;
+return( z );
+}
+
+
+/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
+
+if( x < SQRTH )
+ {
+ e -= 1;
+ x = ldexpl( x, 1 ) - 1.0L; /* 2x - 1 */
+ }
+else
+ {
+ x = x - 1.0L;
+ }
+z = x*x;
+y = x * ( z * polevll( x, P, 6 ) / p1evll( x, Q, 6 ) );
+y = y + e * C2;
+z = y - ldexpl( z, -1 ); /* y - 0.5 * z */
+/* Note, the sum of above terms does not exceed x/4,
+ * so it contributes at most about 1/4 lsb to the error.
+ */
+z = z + x;
+z = z + e * C1; /* This sum has an error of 1/2 lsb. */
+return( z );
+}
diff --git a/libm/ldouble/lparanoi.c b/libm/ldouble/lparanoi.c
new file mode 100644
index 000000000..eb8fd25c7
--- /dev/null
+++ b/libm/ldouble/lparanoi.c
@@ -0,0 +1,2348 @@
+/* A C version of Kahan's Floating Point Test "Paranoia"
+
+ Thos Sumner, UCSF, Feb. 1985
+ David Gay, BTL, Jan. 1986
+
+ This is a rewrite from the Pascal version by
+
+ B. A. Wichmann, 18 Jan. 1985
+
+ (and does NOT exhibit good C programming style).
+
+(C) Apr 19 1983 in BASIC version by:
+ Professor W. M. Kahan,
+ 567 Evans Hall
+ Electrical Engineering & Computer Science Dept.
+ University of California
+ Berkeley, California 94720
+ USA
+
+converted to Pascal by:
+ B. A. Wichmann
+ National Physical Laboratory
+ Teddington Middx
+ TW11 OLW
+ UK
+
+converted to C by:
+
+ David M. Gay and Thos Sumner
+ AT&T Bell Labs Computer Center, Rm. U-76
+ 600 Mountainn Avenue University of California
+ Murray Hill, NJ 07974 San Francisco, CA 94143
+ USA USA
+
+with simultaneous corrections to the Pascal source (reflected
+in the Pascal source available over netlib).
+
+Reports of results on various systems from all the versions
+of Paranoia are being collected by Richard Karpinski at the
+same address as Thos Sumner. This includes sample outputs,
+bug reports, and criticisms.
+
+You may copy this program freely if you acknowledge its source.
+Comments on the Pascal version to NPL, please.
+
+
+The C version catches signals from floating-point exceptions.
+If signal(SIGFPE,...) is unavailable in your environment, you may
+#define NOSIGNAL to comment out the invocations of signal.
+
+This source file is too big for some C compilers, but may be split
+into pieces. Comments containing "SPLIT" suggest convenient places
+for this splitting. At the end of these comments is an "ed script"
+(for the UNIX(tm) editor ed) that will do this splitting.
+
+By #defining Single when you compile this source, you may obtain
+a single-precision C version of Paranoia.
+
+
+The following is from the introductory commentary from Wichmann's work:
+
+The BASIC program of Kahan is written in Microsoft BASIC using many
+facilities which have no exact analogy in Pascal. The Pascal
+version below cannot therefore be exactly the same. Rather than be
+a minimal transcription of the BASIC program, the Pascal coding
+follows the conventional style of block-structured languages. Hence
+the Pascal version could be useful in producing versions in other
+structured languages.
+
+Rather than use identifiers of minimal length (which therefore have
+little mnemonic significance), the Pascal version uses meaningful
+identifiers as follows [Note: A few changes have been made for C]:
+
+
+BASIC C BASIC C BASIC C
+
+ A J S StickyBit
+ A1 AInverse J0 NoErrors T
+ B Radix [Failure] T0 Underflow
+ B1 BInverse J1 NoErrors T2 ThirtyTwo
+ B2 RadixD2 [SeriousDefect] T5 OneAndHalf
+ B9 BMinusU2 J2 NoErrors T7 TwentySeven
+ C [Defect] T8 TwoForty
+ C1 CInverse J3 NoErrors U OneUlp
+ D [Flaw] U0 UnderflowThreshold
+ D4 FourD K PageNo U1
+ E0 L Milestone U2
+ E1 M V
+ E2 Exp2 N V0
+ E3 N1 V8
+ E5 MinSqEr O Zero V9
+ E6 SqEr O1 One W
+ E7 MaxSqEr O2 Two X
+ E8 O3 Three X1
+ E9 O4 Four X8
+ F1 MinusOne O5 Five X9 Random1
+ F2 Half O8 Eight Y
+ F3 Third O9 Nine Y1
+ F6 P Precision Y2
+ F9 Q Y9 Random2
+ G1 GMult Q8 Z
+ G2 GDiv Q9 Z0 PseudoZero
+ G3 GAddSub R Z1
+ H R1 RMult Z2
+ H1 HInverse R2 RDiv Z9
+ I R3 RAddSub
+ IO NoTrials R4 RSqrt
+ I3 IEEE R9 Random9
+
+ SqRWrng
+
+All the variables in BASIC are true variables and in consequence,
+the program is more difficult to follow since the "constants" must
+be determined (the glossary is very helpful). The Pascal version
+uses Real constants, but checks are added to ensure that the values
+are correctly converted by the compiler.
+
+The major textual change to the Pascal version apart from the
+identifiersis that named procedures are used, inserting parameters
+wherehelpful. New procedures are also introduced. The
+correspondence is as follows:
+
+
+BASIC Pascal
+lines
+
+ 90- 140 Pause
+ 170- 250 Instructions
+ 380- 460 Heading
+ 480- 670 Characteristics
+ 690- 870 History
+2940-2950 Random
+3710-3740 NewD
+4040-4080 DoesYequalX
+4090-4110 PrintIfNPositive
+4640-4850 TestPartialUnderflow
+
+=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=
+
+Below is an "ed script" that splits para.c into 10 files
+of the form part[1-8].c, subs.c, and msgs.c, plus a header
+file, paranoia.h, that these files require.
+r paranoia.c
+$
+?SPLIT
++,$w msgs.c
+.,$d
+?SPLIT
+.d
++d
+-,$w subs.c
+-,$d
+?part8
++d
+?include
+.,$w part8.c
+.,$d
+-d
+?part7
++d
+?include
+.,$w part7.c
+.,$d
+-d
+?part6
++d
+?include
+.,$w part6.c
+.,$d
+-d
+?part5
++d
+?include
+.,$w part5.c
+.,$d
+-d
+?part4
++d
+?include
+.,$w part4.c
+.,$d
+-d
+?part3
++d
+?include
+.,$w part3.c
+.,$d
+-d
+?part2
++d
+?include
+.,$w part2.c
+.,$d
+?SPLIT
+.d
+1,/^#include/-1d
+1,$w part1.c
+/Computed constants/,$d
+1,$s/^int/extern &/
+1,$s/^FLOAT/extern &/
+1,$s! = .*!;!
+/^Guard/,/^Round/s/^/extern /
+/^jmp_buf/s/^/extern /
+/^Sig_type/s/^/extern /
+a
+extern int sigfpe();
+.
+w paranoia.h
+q
+
+*/
+
+#include <stdio.h>
+#ifndef NOSIGNAL
+#include <signal.h>
+#endif
+#include <setjmp.h>
+
+#define Ldouble
+/*#define Single*/
+
+#ifdef Single
+#define NPRT 2
+extern double fabs(), floor(), log(), pow(), sqrt();
+#define FLOAT float
+#define FABS(x) (float)fabs((double)(x))
+#define FLOOR(x) (float)floor((double)(x))
+#define LOG(x) (float)log((double)(x))
+#define POW(x,y) (float)pow((double)(x),(double)(y))
+#define SQRT(x) (float)sqrt((double)(x))
+#define FSETUP sprec
+/*sprec() { }*/
+#else
+#ifdef Ldouble
+#define NPRT 6
+extern long double fabsl(), floorl(), logl(), powl(), sqrtl();
+#define FLOAT long double
+#define FABS(x) fabsl(x)
+#define FLOOR(x) floorl(x)
+#define LOG(x) logl(x)
+#define POW(x,y) powl(x,y)
+#define SQRT(x) sqrtl(x)
+#define FSETUP ldprec
+#else
+#define NPRT 4
+extern double fabs(), floor(), log(), pow(), sqrt();
+#define FLOAT double
+#define FABS(x) fabs(x)
+#define FLOOR(x) floor(x)
+#define LOG(x) log(x)
+#define POW(x,y) pow(x,y)
+#define SQRT(x) sqrt(x)
+/*double __sqrtdf2();
+#define SQRT(x) __sqrtdf2(x)
+*/
+#define FSETUP dprec
+/* dprec() { } */
+#endif
+#endif
+
+jmp_buf ovfl_buf;
+typedef int (*Sig_type)();
+Sig_type sigsave;
+
+#define KEYBOARD 0
+
+FLOAT Radix, BInvrse, RadixD2, BMinusU2;
+FLOAT Sign(), Random();
+
+/*Small floating point constants.*/
+FLOAT Zero = 0.0;
+FLOAT Half = 0.5;
+FLOAT One = 1.0;
+FLOAT Two = 2.0;
+FLOAT Three = 3.0;
+FLOAT Four = 4.0;
+FLOAT Five = 5.0;
+FLOAT Eight = 8.0;
+FLOAT Nine = 9.0;
+FLOAT TwentySeven = 27.0;
+FLOAT ThirtyTwo = 32.0;
+FLOAT TwoForty = 240.0;
+FLOAT MinusOne = -1.0;
+FLOAT OneAndHalf = 1.5;
+/*Integer constants*/
+int NoTrials = 20; /*Number of tests for commutativity. */
+#define False 0
+#define True 1
+
+/* Definitions for declared types
+ Guard == (Yes, No);
+ Rounding == (Chopped, Rounded, Other);
+ Message == packed array [1..40] of char;
+ Class == (Flaw, Defect, Serious, Failure);
+ */
+#define Yes 1
+#define No 0
+#define Chopped 2
+#define Rounded 1
+#define Other 0
+#define Flaw 3
+#define Defect 2
+#define Serious 1
+#define Failure 0
+typedef int Guard, Rounding, Class;
+typedef char Message;
+
+/* Declarations of Variables */
+int Indx;
+char ch[8];
+FLOAT AInvrse, A1;
+FLOAT C, CInvrse;
+FLOAT D, FourD;
+static FLOAT E0, E1, Exp2, E3, MinSqEr;
+FLOAT SqEr, MaxSqEr, E9;
+FLOAT Third;
+FLOAT F6, F9;
+FLOAT H, HInvrse;
+int I;
+FLOAT StickyBit, J;
+FLOAT MyZero;
+FLOAT Precision;
+FLOAT Q, Q9;
+FLOAT R, Random9;
+FLOAT T, Underflow, S;
+FLOAT OneUlp, UfThold, U1, U2;
+FLOAT V, V0, V9;
+FLOAT W;
+FLOAT X, X1, X2, X8, Random1;
+static FLOAT Y, Y1, Y2, Random2;
+FLOAT Z, PseudoZero, Z1, Z2, Z9;
+int ErrCnt[4];
+int fpecount;
+int Milestone;
+int PageNo;
+int M, N, N1;
+Guard GMult, GDiv, GAddSub;
+Rounding RMult, RDiv, RAddSub, RSqrt;
+int Break, Done, NotMonot, Monot, Anomaly, IEEE,
+ SqRWrng, UfNGrad;
+/* Computed constants. */
+/*U1 gap below 1.0, i.e, 1.0-U1 is next number below 1.0 */
+/*U2 gap above 1.0, i.e, 1.0+U2 is next number above 1.0 */
+
+/* floating point exception receiver */
+sigfpe()
+{
+ fpecount++;
+ printf("\n* * * FLOATING-POINT ERROR * * *\n");
+ fflush(stdout);
+ if (sigsave) {
+#ifndef NOSIGNAL
+ signal(SIGFPE, sigsave);
+#endif
+ sigsave = 0;
+ longjmp(ovfl_buf, 1);
+ }
+ abort();
+}
+
+
+FLOAT Ptemp;
+
+pnum( x )
+FLOAT *x;
+{
+char str[30];
+double d;
+unsigned short *p;
+int i;
+
+p = (unsigned short *)x;
+for( i=0; i<NPRT; i++ )
+ printf( "%04x ", *p++ & 0xffff );
+#ifdef Ldouble
+e64toasc( x, str, 20 );
+#else
+#ifdef Single
+e24toasc( x, str, 20 );
+#else
+e53toasc( x, str, 20 );
+#endif
+#endif
+printf( " = %s\n", str );
+/*
+d = *x;
+printf( " = %.16e\n", d );
+*/
+}
+
+
+
+main()
+{
+/* noexcept(); */
+ FSETUP();
+ /* First two assignments use integer right-hand sides. */
+ Zero = 0;
+ One = 1;
+ Two = One + One;
+ Three = Two + One;
+ Four = Three + One;
+ Five = Four + One;
+ Eight = Four + Four;
+ Nine = Three * Three;
+ TwentySeven = Nine * Three;
+ ThirtyTwo = Four * Eight;
+ TwoForty = Four * Five * Three * Four;
+ MinusOne = -One;
+ Half = One / Two;
+ OneAndHalf = One + Half;
+ ErrCnt[Failure] = 0;
+ ErrCnt[Serious] = 0;
+ ErrCnt[Defect] = 0;
+ ErrCnt[Flaw] = 0;
+ PageNo = 1;
+ /*=============================================*/
+ Milestone = 0;
+ /*=============================================*/
+#ifndef NOSIGNAL
+ signal(SIGFPE, sigfpe);
+#endif
+ Instructions();
+ Pause();
+ Heading();
+ Pause();
+ Characteristics();
+ Pause();
+ History();
+ Pause();
+ /*=============================================*/
+ Milestone = 7;
+ /*=============================================*/
+ printf("Program is now RUNNING tests on small integers:\n");
+
+ TstCond (Failure, (Zero + Zero == Zero) && (One - One == Zero)
+ && (One > Zero) && (One + One == Two),
+ "0+0 != 0, 1-1 != 0, 1 <= 0, or 1+1 != 2");
+ Z = - Zero;
+ if (Z == 0.0) {
+ U1 = 0.001;
+ Radix = 1;
+ TstPtUf();
+ }
+ else {
+ ErrCnt[Failure] = ErrCnt[Failure] + 1;
+ printf("Comparison alleges that -0.0 is Non-zero!\n");
+ }
+ TstCond (Failure, (Three == Two + One) && (Four == Three + One)
+ && (Four + Two * (- Two) == Zero)
+ && (Four - Three - One == Zero),
+ "3 != 2+1, 4 != 3+1, 4+2*(-2) != 0, or 4-3-1 != 0");
+ TstCond (Failure, (MinusOne == (0 - One))
+ && (MinusOne + One == Zero ) && (One + MinusOne == Zero)
+ && (MinusOne + FABS(One) == Zero)
+ && (MinusOne + MinusOne * MinusOne == Zero),
+ "-1+1 != 0, (-1)+abs(1) != 0, or -1+(-1)*(-1) != 0");
+ TstCond (Failure, Half + MinusOne + Half == Zero,
+ "1/2 + (-1) + 1/2 != 0");
+ /*=============================================*/
+ /*SPLIT
+ part2();
+ part3();
+ part4();
+ part5();
+ part6();
+ part7();
+ part8();
+ }
+#include "paranoia.h"
+part2(){
+*/
+ Milestone = 10;
+ /*=============================================*/
+ TstCond (Failure, (Nine == Three * Three)
+ && (TwentySeven == Nine * Three) && (Eight == Four + Four)
+ && (ThirtyTwo == Eight * Four)
+ && (ThirtyTwo - TwentySeven - Four - One == Zero),
+ "9 != 3*3, 27 != 9*3, 32 != 8*4, or 32-27-4-1 != 0");
+ TstCond (Failure, (Five == Four + One) &&
+ (TwoForty == Four * Five * Three * Four)
+ && (TwoForty / Three - Four * Four * Five == Zero)
+ && ( TwoForty / Four - Five * Three * Four == Zero)
+ && ( TwoForty / Five - Four * Three * Four == Zero),
+ "5 != 4+1, 240/3 != 80, 240/4 != 60, or 240/5 != 48");
+ if (ErrCnt[Failure] == 0) {
+ printf("-1, 0, 1/2, 1, 2, 3, 4, 5, 9, 27, 32 & 240 are O.K.\n");
+ printf("\n");
+ }
+ printf("Searching for Radix and Precision.\n");
+ W = One;
+ do {
+ W = W + W;
+ Y = W + One;
+ Z = Y - W;
+ Y = Z - One;
+ } while (MinusOne + FABS(Y) < Zero);
+ /*.. now W is just big enough that |((W+1)-W)-1| >= 1 ...*/
+ Precision = Zero;
+ Y = One;
+ do {
+ Radix = W + Y;
+ Y = Y + Y;
+ Radix = Radix - W;
+ } while ( Radix == Zero);
+ if (Radix < Two) Radix = One;
+ printf("Radix = " );
+ pnum( &Radix );
+ if (Radix != 1) {
+ W = One;
+ do {
+ Precision = Precision + One;
+ W = W * Radix;
+ Y = W + One;
+ } while ((Y - W) == One);
+ }
+ /*... now W == Radix^Precision is barely too big to satisfy (W+1)-W == 1
+ ...*/
+ U1 = One / W;
+ U2 = Radix * U1;
+ printf("Closest relative separation found is U1 = " );
+ pnum( &U1 );
+ printf("U2 = ");
+ pnum( &U2 );
+ printf("Recalculating radix and precision.");
+
+ /*save old values*/
+ E0 = Radix;
+ E1 = U1;
+ E9 = U2;
+ E3 = Precision;
+
+ X = Four / Three;
+ Third = X - One;
+ F6 = Half - Third;
+ X = F6 + F6;
+ X = FABS(X - Third);
+ if (X < U2) X = U2;
+
+ /*... now X = (unknown no.) ulps of 1+...*/
+ do {
+ U2 = X;
+ Y = Half * U2 + ThirtyTwo * U2 * U2;
+ Y = One + Y;
+ X = Y - One;
+ } while ( ! ((U2 <= X) || (X <= Zero)));
+
+ /*... now U2 == 1 ulp of 1 + ... */
+ X = Two / Three;
+ F6 = X - Half;
+ Third = F6 + F6;
+ X = Third - Half;
+ X = FABS(X + F6);
+ if (X < U1) X = U1;
+
+ /*... now X == (unknown no.) ulps of 1 -... */
+ do {
+ U1 = X;
+ Y = Half * U1 + ThirtyTwo * U1 * U1;
+ Y = Half - Y;
+ X = Half + Y;
+ Y = Half - X;
+ X = Half + Y;
+ } while ( ! ((U1 <= X) || (X <= Zero)));
+ /*... now U1 == 1 ulp of 1 - ... */
+ if (U1 == E1) printf("confirms closest relative separation U1 .\n");
+ else
+ {
+ printf("gets better closest relative separation U1 = " );
+ pnum( &U1 );
+ }
+ W = One / U1;
+ F9 = (Half - U1) + Half;
+ Radix = FLOOR(0.01 + U2 / U1);
+ if (Radix == E0) printf("Radix confirmed.\n");
+ else
+ {
+ printf("MYSTERY: recalculated Radix = " );
+ pnum( &Radix );
+ }
+ TstCond (Defect, Radix <= Eight + Eight,
+ "Radix is too big: roundoff problems");
+ TstCond (Flaw, (Radix == Two) || (Radix == 10)
+ || (Radix == One), "Radix is not as good as 2 or 10");
+ /*=============================================*/
+ Milestone = 20;
+ /*=============================================*/
+ TstCond (Failure, F9 - Half < Half,
+ "(1-U1)-1/2 < 1/2 is FALSE, prog. fails?");
+ X = F9;
+ I = 1;
+ Y = X - Half;
+ Z = Y - Half;
+ TstCond (Failure, (X != One)
+ || (Z == Zero), "Comparison is fuzzy,X=1 but X-1/2-1/2 != 0");
+ X = One + U2;
+ I = 0;
+ /*=============================================*/
+ Milestone = 25;
+ /*=============================================*/
+ /*... BMinusU2 = nextafter(Radix, 0) */
+ BMinusU2 = Radix - One;
+ BMinusU2 = (BMinusU2 - U2) + One;
+ /* Purify Integers */
+ if (Radix != One) {
+ X = - TwoForty * LOG(U1) / LOG(Radix);
+ Y = FLOOR(Half + X);
+ if (FABS(X - Y) * Four < One) X = Y;
+ Precision = X / TwoForty;
+ Y = FLOOR(Half + Precision);
+ if (FABS(Precision - Y) * TwoForty < Half) Precision = Y;
+ }
+ if ((Precision != FLOOR(Precision)) || (Radix == One)) {
+ printf("Precision cannot be characterized by an Integer number\n");
+ printf("of significant digits but, by itself, this is a minor flaw.\n");
+ }
+ if (Radix == One)
+ printf("logarithmic encoding has precision characterized solely by U1.\n");
+ else
+ {
+ printf("The number of significant digits of the Radix is " );
+ pnum( &Precision );
+ }
+ TstCond (Serious, U2 * Nine * Nine * TwoForty < One,
+ "Precision worse than 5 decimal figures ");
+ /*=============================================*/
+ Milestone = 30;
+ /*=============================================*/
+ /* Test for extra-precise subepressions */
+ X = FABS(((Four / Three - One) - One / Four) * Three - One / Four);
+ do {
+ Z2 = X;
+ X = (One + (Half * Z2 + ThirtyTwo * Z2 * Z2)) - One;
+ } while ( ! ((Z2 <= X) || (X <= Zero)));
+ X = Y = Z = FABS((Three / Four - Two / Three) * Three - One / Four);
+ do {
+ Z1 = Z;
+ Z = (One / Two - ((One / Two - (Half * Z1 + ThirtyTwo * Z1 * Z1))
+ + One / Two)) + One / Two;
+ } while ( ! ((Z1 <= Z) || (Z <= Zero)));
+ do {
+ do {
+ Y1 = Y;
+ Y = (Half - ((Half - (Half * Y1 + ThirtyTwo * Y1 * Y1)) + Half
+ )) + Half;
+ } while ( ! ((Y1 <= Y) || (Y <= Zero)));
+ X1 = X;
+ X = ((Half * X1 + ThirtyTwo * X1 * X1) - F9) + F9;
+ } while ( ! ((X1 <= X) || (X <= Zero)));
+ if ((X1 != Y1) || (X1 != Z1)) {
+ BadCond(Serious, "Disagreements among the values X1, Y1, Z1,\n");
+ printf("respectively " );
+ pnum( &X1 );
+ pnum( &Y1 );
+ pnum( &Z1 );
+ printf("are symptoms of inconsistencies introduced\n");
+ printf("by extra-precise evaluation of arithmetic subexpressions.\n");
+ notify("Possibly some part of this");
+ if ((X1 == U1) || (Y1 == U1) || (Z1 == U1)) printf(
+ "That feature is not tested further by this program.\n") ;
+ }
+ else {
+ if ((Z1 != U1) || (Z2 != U2)) {
+ if ((Z1 >= U1) || (Z2 >= U2)) {
+ BadCond(Failure, "");
+ notify("Precision");
+ printf("\tU1 = " );
+ pnum( &U1 );
+ printf( "Z1 - U1 = " );
+ Ptemp = Z1-U1;
+ pnum( &Ptemp );
+ printf("\tU2 = " );
+ pnum( &U2 );
+ Ptemp = Z2-U2;
+ printf( "Z2 - U2 = " );
+ pnum( &Ptemp );
+ }
+ else {
+ if ((Z1 <= Zero) || (Z2 <= Zero)) {
+ printf("Because of unusual Radix = ");
+ pnum( &Radix );
+ printf(", or exact rational arithmetic a result\n");
+ printf("Z1 = " );
+ pnum( &Z1 );
+ printf( "or Z2 = " );
+ pnum( &Z2 );
+ notify("of an\nextra-precision");
+ }
+ if (Z1 != Z2 || Z1 > Zero) {
+ X = Z1 / U1;
+ Y = Z2 / U2;
+ if (Y > X) X = Y;
+ Q = - LOG(X);
+ printf("Some subexpressions appear to be calculated extra\n");
+ printf("precisely with about" );
+ Ptemp = Q / LOG(Radix);
+ pnum( &Ptemp );
+ printf( "extra B-digits, i.e.\n" );
+ Ptemp = Q / LOG(10.);
+ printf("roughly " );
+ pnum( &Ptemp );
+ printf( "extra significant decimals.\n");
+ }
+ printf("That feature is not tested further by this program.\n");
+ }
+ }
+ }
+ Pause();
+ /*=============================================*/
+ /*SPLIT
+ }
+#include "paranoia.h"
+part3(){
+*/
+ Milestone = 35;
+ /*=============================================*/
+ if (Radix >= Two) {
+ X = W / (Radix * Radix);
+ Y = X + One;
+ Z = Y - X;
+ T = Z + U2;
+ X = T - Z;
+ TstCond (Failure, X == U2,
+ "Subtraction is not normalized X=Y,X+Z != Y+Z!");
+ if (X == U2) printf(
+ "Subtraction appears to be normalized, as it should be.");
+ }
+ printf("\nChecking for guard digit in *, /, and -.\n");
+ Y = F9 * One;
+ Z = One * F9;
+ X = F9 - Half;
+ Y = (Y - Half) - X;
+ Z = (Z - Half) - X;
+ X = One + U2;
+ T = X * Radix;
+ R = Radix * X;
+ X = T - Radix;
+ X = X - Radix * U2;
+ T = R - Radix;
+ T = T - Radix * U2;
+ X = X * (Radix - One);
+ T = T * (Radix - One);
+ if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)) GMult = Yes;
+ else {
+ GMult = No;
+ TstCond (Serious, False,
+ "* lacks a Guard Digit, so 1*X != X");
+ }
+ Z = Radix * U2;
+ X = One + Z;
+ Y = FABS((X + Z) - X * X) - U2;
+ X = One - U2;
+ Z = FABS((X - U2) - X * X) - U1;
+ TstCond (Failure, (Y <= Zero)
+ && (Z <= Zero), "* gets too many final digits wrong.\n");
+ Y = One - U2;
+ X = One + U2;
+ Z = One / Y;
+ Y = Z - X;
+ X = One / Three;
+ Z = Three / Nine;
+ X = X - Z;
+ T = Nine / TwentySeven;
+ Z = Z - T;
+ TstCond(Defect, X == Zero && Y == Zero && Z == Zero,
+ "Division lacks a Guard Digit, so error can exceed 1 ulp\n\
+or 1/3 and 3/9 and 9/27 may disagree");
+ Y = F9 / One;
+ X = F9 - Half;
+ Y = (Y - Half) - X;
+ X = One + U2;
+ T = X / One;
+ X = T - X;
+ if ((X == Zero) && (Y == Zero) && (Z == Zero)) GDiv = Yes;
+ else {
+ GDiv = No;
+ TstCond (Serious, False,
+ "Division lacks a Guard Digit, so X/1 != X");
+ }
+ X = One / (One + U2);
+ Y = X - Half - Half;
+ TstCond (Serious, Y < Zero,
+ "Computed value of 1/1.000..1 >= 1");
+ X = One - U2;
+ Y = One + Radix * U2;
+ Z = X * Radix;
+ T = Y * Radix;
+ R = Z / Radix;
+ StickyBit = T / Radix;
+ X = R - X;
+ Y = StickyBit - Y;
+ TstCond (Failure, X == Zero && Y == Zero,
+ "* and/or / gets too many last digits wrong");
+ Y = One - U1;
+ X = One - F9;
+ Y = One - Y;
+ T = Radix - U2;
+ Z = Radix - BMinusU2;
+ T = Radix - T;
+ if ((X == U1) && (Y == U1) && (Z == U2) && (T == U2)) GAddSub = Yes;
+ else {
+ GAddSub = No;
+ TstCond (Serious, False,
+ "- lacks Guard Digit, so cancellation is obscured");
+ }
+ if (F9 != One && F9 - One >= Zero) {
+ BadCond(Serious, "comparison alleges (1-U1) < 1 although\n");
+ printf(" subtration yields (1-U1) - 1 = 0 , thereby vitiating\n");
+ printf(" such precautions against division by zero as\n");
+ printf(" ... if (X == 1.0) {.....} else {.../(X-1.0)...}\n");
+ }
+ if (GMult == Yes && GDiv == Yes && GAddSub == Yes) printf(
+ " *, /, and - appear to have guard digits, as they should.\n");
+ /*=============================================*/
+ Milestone = 40;
+ /*=============================================*/
+ Pause();
+ printf("Checking rounding on multiply, divide and add/subtract.\n");
+ RMult = Other;
+ RDiv = Other;
+ RAddSub = Other;
+ RadixD2 = Radix / Two;
+ A1 = Two;
+ Done = False;
+ do {
+ AInvrse = Radix;
+ do {
+ X = AInvrse;
+ AInvrse = AInvrse / A1;
+ } while ( ! (FLOOR(AInvrse) != AInvrse));
+ Done = (X == One) || (A1 > Three);
+ if (! Done) A1 = Nine + One;
+ } while ( ! (Done));
+ if (X == One) A1 = Radix;
+ AInvrse = One / A1;
+ X = A1;
+ Y = AInvrse;
+ Done = False;
+ do {
+ Z = X * Y - Half;
+ TstCond (Failure, Z == Half,
+ "X * (1/X) differs from 1");
+ Done = X == Radix;
+ X = Radix;
+ Y = One / X;
+ } while ( ! (Done));
+ Y2 = One + U2;
+ Y1 = One - U2;
+ X = OneAndHalf - U2;
+ Y = OneAndHalf + U2;
+ Z = (X - U2) * Y2;
+ T = Y * Y1;
+ Z = Z - X;
+ T = T - X;
+ X = X * Y2;
+ Y = (Y + U2) * Y1;
+ X = X - OneAndHalf;
+ Y = Y - OneAndHalf;
+ if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T <= Zero)) {
+ printf("Y2 = ");
+ pnum( &Y2 );
+ printf("Y1 = ");
+ pnum( &Y1 );
+ printf("U2 = ");
+ pnum( &U2 );
+ X = (OneAndHalf + U2) * Y2;
+ Y = OneAndHalf - U2 - U2;
+ Z = OneAndHalf + U2 + U2;
+ T = (OneAndHalf - U2) * Y1;
+ X = X - (Z + U2);
+ StickyBit = Y * Y1;
+ S = Z * Y2;
+ T = T - Y;
+ Y = (U2 - Y) + StickyBit;
+ Z = S - (Z + U2 + U2);
+ StickyBit = (Y2 + U2) * Y1;
+ Y1 = Y2 * Y1;
+ StickyBit = StickyBit - Y2;
+ Y1 = Y1 - Half;
+ if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)
+ && ( StickyBit == Zero) && (Y1 == Half)) {
+ RMult = Rounded;
+ printf("Multiplication appears to round correctly.\n");
+ }
+ else if ((X + U2 == Zero) && (Y < Zero) && (Z + U2 == Zero)
+ && (T < Zero) && (StickyBit + U2 == Zero)
+ && (Y1 < Half)) {
+ RMult = Chopped;
+ printf("Multiplication appears to chop.\n");
+ }
+ else printf("* is neither chopped nor correctly rounded.\n");
+ if ((RMult == Rounded) && (GMult == No)) notify("Multiplication");
+ }
+ else printf("* is neither chopped nor correctly rounded.\n");
+ /*=============================================*/
+ Milestone = 45;
+ /*=============================================*/
+ Y2 = One + U2;
+ Y1 = One - U2;
+ Z = OneAndHalf + U2 + U2;
+ X = Z / Y2;
+ T = OneAndHalf - U2 - U2;
+ Y = (T - U2) / Y1;
+ Z = (Z + U2) / Y2;
+ X = X - OneAndHalf;
+ Y = Y - T;
+ T = T / Y1;
+ Z = Z - (OneAndHalf + U2);
+ T = (U2 - OneAndHalf) + T;
+ if (! ((X > Zero) || (Y > Zero) || (Z > Zero) || (T > Zero))) {
+ X = OneAndHalf / Y2;
+ Y = OneAndHalf - U2;
+ Z = OneAndHalf + U2;
+ X = X - Y;
+ T = OneAndHalf / Y1;
+ Y = Y / Y1;
+ T = T - (Z + U2);
+ Y = Y - Z;
+ Z = Z / Y2;
+ Y1 = (Y2 + U2) / Y2;
+ Z = Z - OneAndHalf;
+ Y2 = Y1 - Y2;
+ Y1 = (F9 - U1) / F9;
+ if ((X == Zero) && (Y == Zero) && (Z == Zero) && (T == Zero)
+ && (Y2 == Zero) && (Y2 == Zero)
+ && (Y1 - Half == F9 - Half )) {
+ RDiv = Rounded;
+ printf("Division appears to round correctly.\n");
+ if (GDiv == No) notify("Division");
+ }
+ else if ((X < Zero) && (Y < Zero) && (Z < Zero) && (T < Zero)
+ && (Y2 < Zero) && (Y1 - Half < F9 - Half)) {
+ RDiv = Chopped;
+ printf("Division appears to chop.\n");
+ }
+ }
+ if (RDiv == Other) printf("/ is neither chopped nor correctly rounded.\n");
+ BInvrse = One / Radix;
+ TstCond (Failure, (BInvrse * Radix - Half == Half),
+ "Radix * ( 1 / Radix ) differs from 1");
+ /*=============================================*/
+ /*SPLIT
+ }
+#include "paranoia.h"
+part4(){
+*/
+ Milestone = 50;
+ /*=============================================*/
+ TstCond (Failure, ((F9 + U1) - Half == Half)
+ && ((BMinusU2 + U2 ) - One == Radix - One),
+ "Incomplete carry-propagation in Addition");
+ X = One - U1 * U1;
+ Y = One + U2 * (One - U2);
+ Z = F9 - Half;
+ X = (X - Half) - Z;
+ Y = Y - One;
+ if ((X == Zero) && (Y == Zero)) {
+ RAddSub = Chopped;
+ printf("Add/Subtract appears to be chopped.\n");
+ }
+ if (GAddSub == Yes) {
+ X = (Half + U2) * U2;
+ Y = (Half - U2) * U2;
+ X = One + X;
+ Y = One + Y;
+ X = (One + U2) - X;
+ Y = One - Y;
+ if ((X == Zero) && (Y == Zero)) {
+ X = (Half + U2) * U1;
+ Y = (Half - U2) * U1;
+ X = One - X;
+ Y = One - Y;
+ X = F9 - X;
+ Y = One - Y;
+ if ((X == Zero) && (Y == Zero)) {
+ RAddSub = Rounded;
+ printf("Addition/Subtraction appears to round correctly.\n");
+ if (GAddSub == No) notify("Add/Subtract");
+ }
+ else printf("Addition/Subtraction neither rounds nor chops.\n");
+ }
+ else printf("Addition/Subtraction neither rounds nor chops.\n");
+ }
+ else printf("Addition/Subtraction neither rounds nor chops.\n");
+ S = One;
+ X = One + Half * (One + Half);
+ Y = (One + U2) * Half;
+ Z = X - Y;
+ T = Y - X;
+ StickyBit = Z + T;
+ if (StickyBit != Zero) {
+ S = Zero;
+ BadCond(Flaw, "(X - Y) + (Y - X) is non zero!\n");
+ }
+ StickyBit = Zero;
+ if ((GMult == Yes) && (GDiv == Yes) && (GAddSub == Yes)
+ && (RMult == Rounded) && (RDiv == Rounded)
+ && (RAddSub == Rounded) && (FLOOR(RadixD2) == RadixD2)) {
+ printf("Checking for sticky bit.\n");
+ X = (Half + U1) * U2;
+ Y = Half * U2;
+ Z = One + Y;
+ T = One + X;
+ if ((Z - One <= Zero) && (T - One >= U2)) {
+ Z = T + Y;
+ Y = Z - X;
+ if ((Z - T >= U2) && (Y - T == Zero)) {
+ X = (Half + U1) * U1;
+ Y = Half * U1;
+ Z = One - Y;
+ T = One - X;
+ if ((Z - One == Zero) && (T - F9 == Zero)) {
+ Z = (Half - U1) * U1;
+ T = F9 - Z;
+ Q = F9 - Y;
+ if ((T - F9 == Zero) && (F9 - U1 - Q == Zero)) {
+ Z = (One + U2) * OneAndHalf;
+ T = (OneAndHalf + U2) - Z + U2;
+ X = One + Half / Radix;
+ Y = One + Radix * U2;
+ Z = X * Y;
+ if (T == Zero && X + Radix * U2 - Z == Zero) {
+ if (Radix != Two) {
+ X = Two + U2;
+ Y = X / Two;
+ if ((Y - One == Zero)) StickyBit = S;
+ }
+ else StickyBit = S;
+ }
+ }
+ }
+ }
+ }
+ }
+ if (StickyBit == One) printf("Sticky bit apparently used correctly.\n");
+ else printf("Sticky bit used incorrectly or not at all.\n");
+ TstCond (Flaw, !(GMult == No || GDiv == No || GAddSub == No ||
+ RMult == Other || RDiv == Other || RAddSub == Other),
+ "lack(s) of guard digits or failure(s) to correctly round or chop\n\
+(noted above) count as one flaw in the final tally below");
+ /*=============================================*/
+ Milestone = 60;
+ /*=============================================*/
+ printf("\n");
+ printf("Does Multiplication commute? ");
+ printf("Testing on %d random pairs.\n", NoTrials);
+ Ptemp = 3.0;
+ Random9 = SQRT(Ptemp);
+ Random1 = Third;
+ I = 1;
+ do {
+ X = Random();
+ Y = Random();
+ Z9 = Y * X;
+ Z = X * Y;
+ Z9 = Z - Z9;
+ I = I + 1;
+ } while ( ! ((I > NoTrials) || (Z9 != Zero)));
+ if (I == NoTrials) {
+ Random1 = One + Half / Three;
+ Random2 = (U2 + U1) + One;
+ Z = Random1 * Random2;
+ Y = Random2 * Random1;
+ Z9 = (One + Half / Three) * ((U2 + U1) + One) - (One + Half /
+ Three) * ((U2 + U1) + One);
+ }
+ if (! ((I == NoTrials) || (Z9 == Zero)))
+ BadCond(Defect, "X * Y == Y * X trial fails.\n");
+ else printf(" No failures found in %d integer pairs.\n", NoTrials);
+ /*=============================================*/
+ Milestone = 70;
+ /*=============================================*/
+ printf("\nRunning test of square root(x).\n");
+ TstCond (Failure, (Zero == SQRT(Zero))
+ && (- Zero == SQRT(- Zero))
+ && (One == SQRT(One)), "Square root of 0.0, -0.0 or 1.0 wrong");
+ MinSqEr = Zero;
+ MaxSqEr = Zero;
+ J = Zero;
+ X = Radix;
+ OneUlp = U2;
+ SqXMinX (Serious);
+ X = BInvrse;
+ OneUlp = BInvrse * U1;
+ SqXMinX (Serious);
+ X = U1;
+ OneUlp = U1 * U1;
+ SqXMinX (Serious);
+ if (J != Zero) Pause();
+ printf("Testing if sqrt(X * X) == X for %d Integers X.\n", NoTrials);
+ J = Zero;
+ X = Two;
+ Y = Radix;
+ if ((Radix != One)) do {
+ X = Y;
+ Y = Radix * Y;
+ } while ( ! ((Y - X >= NoTrials)));
+ OneUlp = X * U2;
+ I = 1;
+ while (I < 10) {
+ X = X + One;
+ SqXMinX (Defect);
+ if (J > Zero) break;
+ I = I + 1;
+ }
+ printf("Test for sqrt monotonicity.\n");
+ I = - 1;
+ X = BMinusU2;
+ Y = Radix;
+ Z = Radix + Radix * U2;
+ NotMonot = False;
+ Monot = False;
+ while ( ! (NotMonot || Monot)) {
+ I = I + 1;
+ X = SQRT(X);
+ Q = SQRT(Y);
+ Z = SQRT(Z);
+ if ((X > Q) || (Q > Z)) NotMonot = True;
+ else {
+ Q = FLOOR(Q + Half);
+ if ((I > 0) || (Radix == Q * Q)) Monot = True;
+ else if (I > 0) {
+ if (I > 1) Monot = True;
+ else {
+ Y = Y * BInvrse;
+ X = Y - U1;
+ Z = Y + U1;
+ }
+ }
+ else {
+ Y = Q;
+ X = Y - U2;
+ Z = Y + U2;
+ }
+ }
+ }
+ if (Monot) printf("sqrt has passed a test for Monotonicity.\n");
+ else {
+ BadCond(Defect, "");
+ printf("sqrt(X) is non-monotonic for X near " );
+ pnum( &Y );
+ }
+ /*=============================================*/
+ /*SPLIT
+ }
+#include "paranoia.h"
+part5(){
+*/
+ Milestone = 80;
+ /*=============================================*/
+ MinSqEr = MinSqEr + Half;
+ MaxSqEr = MaxSqEr - Half;
+ Y = (SQRT(One + U2) - One) / U2;
+ SqEr = (Y - One) + U2 / Eight;
+ if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+ SqEr = Y + U2 / Eight;
+ if (SqEr < MinSqEr) MinSqEr = SqEr;
+ Y = ((SQRT(F9) - U2) - (One - U2)) / U1;
+ SqEr = Y + U1 / Eight;
+ if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+ SqEr = (Y + One) + U1 / Eight;
+ if (SqEr < MinSqEr) MinSqEr = SqEr;
+ OneUlp = U2;
+ X = OneUlp;
+ for( Indx = 1; Indx <= 3; ++Indx) {
+ Y = SQRT((X + U1 + X) + F9);
+ Y = ((Y - U2) - ((One - U2) + X)) / OneUlp;
+ Z = ((U1 - X) + F9) * Half * X * X / OneUlp;
+ SqEr = (Y + Half) + Z;
+ if (SqEr < MinSqEr) MinSqEr = SqEr;
+ SqEr = (Y - Half) + Z;
+ if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+ if (((Indx == 1) || (Indx == 3)))
+ X = OneUlp * Sign (X) * FLOOR(Eight / (Nine * SQRT(OneUlp)));
+ else {
+ OneUlp = U1;
+ X = - OneUlp;
+ }
+ }
+ /*=============================================*/
+ Milestone = 85;
+ /*=============================================*/
+ SqRWrng = False;
+ Anomaly = False;
+ if (Radix != One) {
+ printf("Testing whether sqrt is rounded or chopped.\n");
+ D = FLOOR(Half + POW(Radix, One + Precision - FLOOR(Precision)));
+ /* ... == Radix^(1 + fract) if (Precision == Integer + fract. */
+ X = D / Radix;
+ Y = D / A1;
+ if ((X != FLOOR(X)) || (Y != FLOOR(Y))) {
+ Anomaly = True;
+ }
+ else {
+ X = Zero;
+ Z2 = X;
+ Y = One;
+ Y2 = Y;
+ Z1 = Radix - One;
+ FourD = Four * D;
+ do {
+ if (Y2 > Z2) {
+ Q = Radix;
+ Y1 = Y;
+ do {
+ X1 = FABS(Q + FLOOR(Half - Q / Y1) * Y1);
+ Q = Y1;
+ Y1 = X1;
+ } while ( ! (X1 <= Zero));
+ if (Q <= One) {
+ Z2 = Y2;
+ Z = Y;
+ }
+ }
+ Y = Y + Two;
+ X = X + Eight;
+ Y2 = Y2 + X;
+ if (Y2 >= FourD) Y2 = Y2 - FourD;
+ } while ( ! (Y >= D));
+ X8 = FourD - Z2;
+ Q = (X8 + Z * Z) / FourD;
+ X8 = X8 / Eight;
+ if (Q != FLOOR(Q)) Anomaly = True;
+ else {
+ Break = False;
+ do {
+ X = Z1 * Z;
+ X = X - FLOOR(X / Radix) * Radix;
+ if (X == One)
+ Break = True;
+ else
+ Z1 = Z1 - One;
+ } while ( ! (Break || (Z1 <= Zero)));
+ if ((Z1 <= Zero) && (! Break)) Anomaly = True;
+ else {
+ if (Z1 > RadixD2) Z1 = Z1 - Radix;
+ do {
+ NewD();
+ } while ( ! (U2 * D >= F9));
+ if (D * Radix - D != W - D) Anomaly = True;
+ else {
+ Z2 = D;
+ I = 0;
+ Y = D + (One + Z) * Half;
+ X = D + Z + Q;
+ SR3750();
+ Y = D + (One - Z) * Half + D;
+ X = D - Z + D;
+ X = X + Q + X;
+ SR3750();
+ NewD();
+ if (D - Z2 != W - Z2) Anomaly = True;
+ else {
+ Y = (D - Z2) + (Z2 + (One - Z) * Half);
+ X = (D - Z2) + (Z2 - Z + Q);
+ SR3750();
+ Y = (One + Z) * Half;
+ X = Q;
+ SR3750();
+ if (I == 0) Anomaly = True;
+ }
+ }
+ }
+ }
+ }
+ if ((I == 0) || Anomaly) {
+ BadCond(Failure, "Anomalous arithmetic with Integer < ");
+ printf("Radix^Precision = " );
+ pnum( &W );
+ printf(" fails test whether sqrt rounds or chops.\n");
+ SqRWrng = True;
+ }
+ }
+ if (! Anomaly) {
+ if (! ((MinSqEr < Zero) || (MaxSqEr > Zero))) {
+ RSqrt = Rounded;
+ printf("Square root appears to be correctly rounded.\n");
+ }
+ else {
+ if ((MaxSqEr + U2 > U2 - Half) || (MinSqEr > Half)
+ || (MinSqEr + Radix < Half)) SqRWrng = True;
+ else {
+ RSqrt = Chopped;
+ printf("Square root appears to be chopped.\n");
+ }
+ }
+ }
+ if (SqRWrng) {
+ printf("Square root is neither chopped nor correctly rounded.\n");
+ printf("Observed errors run from " );
+ Ptemp = MinSqEr - Half;
+ pnum( &Ptemp );
+ printf("to %.7e ulps.\n");
+ Ptemp = Half + MaxSqEr;
+ pnum( &Ptemp );
+ TstCond (Serious, MaxSqEr - MinSqEr < Radix * Radix,
+ "sqrt gets too many last digits wrong");
+ }
+ /*=============================================*/
+ Milestone = 90;
+ /*=============================================*/
+ Pause();
+ printf("Testing powers Z^i for small Integers Z and i.\n");
+ N = 0;
+ /* ... test powers of zero. */
+ I = 0;
+ Z = -Zero;
+ M = 3.0;
+ Break = False;
+ do {
+ X = One;
+ SR3980();
+ if (I <= 10) {
+ I = 1023;
+ SR3980();
+ }
+ if (Z == MinusOne) Break = True;
+ else {
+ Z = MinusOne;
+ PrintIfNPositive();
+ N = 0;
+ /* .. if(-1)^N is invalid, replace MinusOne by One. */
+ I = - 4;
+ }
+ } while ( ! Break);
+ PrintIfNPositive();
+ N1 = N;
+ N = 0;
+ Z = A1;
+ M = FLOOR(Two * LOG(W) / LOG(A1));
+ Break = False;
+ do {
+ X = Z;
+ I = 1;
+ SR3980();
+ if (Z == AInvrse) Break = True;
+ else Z = AInvrse;
+ } while ( ! (Break));
+ /*=============================================*/
+ Milestone = 100;
+ /*=============================================*/
+ /* Powers of Radix have been tested, */
+ /* next try a few primes */
+ M = NoTrials;
+ Z = Three;
+ do {
+ X = Z;
+ I = 1;
+ SR3980();
+ do {
+ Z = Z + Two;
+ } while ( Three * FLOOR(Z / Three) == Z );
+ } while ( Z < Eight * Three );
+ if (N > 0) {
+ printf("Errors like this may invalidate financial calculations\n");
+ printf("\tinvolving interest rates.\n");
+ }
+ PrintIfNPositive();
+ N += N1;
+ if (N == 0) printf("... no discrepancis found.\n");
+ if (N > 0) Pause();
+ else printf("\n");
+ /*=============================================*/
+ /*SPLIT
+ }
+#include "paranoia.h"
+part6(){
+*/
+ Milestone = 110;
+ /*=============================================*/
+ printf("Seeking Underflow thresholds UfThold and E0.\n");
+ D = U1;
+ if (Precision != FLOOR(Precision)) {
+ D = BInvrse;
+ X = Precision;
+ do {
+ D = D * BInvrse;
+ X = X - One;
+ } while ( X > Zero);
+ }
+ Y = One;
+ Z = D;
+ /* ... D is power of 1/Radix < 1. */
+ do {
+ C = Y;
+ Y = Z;
+ Z = Y * Y;
+ } while ((Y > Z) && (Z + Z > Z));
+ Y = C;
+ Z = Y * D;
+ do {
+ C = Y;
+ Y = Z;
+ Z = Y * D;
+ } while ((Y > Z) && (Z + Z > Z));
+ if (Radix < Two) HInvrse = Two;
+ else HInvrse = Radix;
+ H = One / HInvrse;
+ /* ... 1/HInvrse == H == Min(1/Radix, 1/2) */
+ CInvrse = One / C;
+ E0 = C;
+ Z = E0 * H;
+ /* ...1/Radix^(BIG Integer) << 1 << CInvrse == 1/C */
+ do {
+ Y = E0;
+ E0 = Z;
+ Z = E0 * H;
+ } while ((E0 > Z) && (Z + Z > Z));
+ UfThold = E0;
+ E1 = Zero;
+ Q = Zero;
+ E9 = U2;
+ S = One + E9;
+ D = C * S;
+ if (D <= C) {
+ E9 = Radix * U2;
+ S = One + E9;
+ D = C * S;
+ if (D <= C) {
+ BadCond(Failure, "multiplication gets too many last digits wrong.\n");
+ Underflow = E0;
+ Y1 = Zero;
+ PseudoZero = Z;
+ Pause();
+ }
+ }
+ else {
+ Underflow = D;
+ PseudoZero = Underflow * H;
+ UfThold = Zero;
+ do {
+ Y1 = Underflow;
+ Underflow = PseudoZero;
+ if (E1 + E1 <= E1) {
+ Y2 = Underflow * HInvrse;
+ E1 = FABS(Y1 - Y2);
+ Q = Y1;
+ if ((UfThold == Zero) && (Y1 != Y2)) UfThold = Y1;
+ }
+ PseudoZero = PseudoZero * H;
+ } while ((Underflow > PseudoZero)
+ && (PseudoZero + PseudoZero > PseudoZero));
+ }
+ /* Comment line 4530 .. 4560 */
+ if (PseudoZero != Zero) {
+ printf("\n");
+ Z = PseudoZero;
+ /* ... Test PseudoZero for "phoney- zero" violates */
+ /* ... PseudoZero < Underflow or PseudoZero < PseudoZero + PseudoZero
+ ... */
+ if (PseudoZero <= Zero) {
+ BadCond(Failure, "Positive expressions can underflow to an\n");
+ printf("allegedly negative value\n");
+ printf("PseudoZero that prints out as: " );
+ pnum( &PseudoZero );
+ X = - PseudoZero;
+ if (X <= Zero) {
+ printf("But -PseudoZero, which should be\n");
+ printf("positive, isn't; it prints out as " );
+ pnum( &X );
+ }
+ }
+ else {
+ BadCond(Flaw, "Underflow can stick at an allegedly positive\n");
+ printf("value PseudoZero that prints out as ");
+ pnum( &PseudoZero );
+ }
+ TstPtUf();
+ }
+ /*=============================================*/
+ Milestone = 120;
+ /*=============================================*/
+ if (CInvrse * Y > CInvrse * Y1) {
+ S = H * S;
+ E0 = Underflow;
+ }
+ if (! ((E1 == Zero) || (E1 == E0))) {
+ BadCond(Defect, "");
+ if (E1 < E0) {
+ printf("Products underflow at a higher");
+ printf(" threshold than differences.\n");
+ if (PseudoZero == Zero)
+ E0 = E1;
+ }
+ else {
+ printf("Difference underflows at a higher");
+ printf(" threshold than products.\n");
+ }
+ }
+ printf("Smallest strictly positive number found is E0 = ");
+ Pause();
+ pnum( &E0 );
+ Z = E0;
+ TstPtUf();
+ Underflow = E0;
+ if (N == 1) Underflow = Y;
+ I = 4;
+ if (E1 == Zero) I = 3;
+ if (UfThold == Zero) I = I - 2;
+ UfNGrad = True;
+ switch (I) {
+ case 1:
+ UfThold = Underflow;
+ if ((CInvrse * Q) != ((CInvrse * Y) * S)) {
+ UfThold = Y;
+ BadCond(Failure, "Either accuracy deteriorates as numbers\n");
+ printf("approach a threshold = ");
+ pnum( &UfThold );
+ printf(" coming down from " );
+ pnum( &C );
+ printf(" or else multiplication gets too many last digits wrong.\n");
+ }
+ Pause();
+ break;
+
+ case 2:
+ BadCond(Failure, "Underflow confuses Comparison which alleges that\n");
+ printf("Q == Y while denying that |Q - Y| == 0; these values\n");
+ printf("print out as Q = " );
+ pnum( &Q );
+ printf( "Y = " );
+ pnum( &Y );
+ printf ("|Q - Y| = " );
+ Ptemp = FABS(Q - Y2);
+ pnum( &Ptemp );
+ UfThold = Q;
+ break;
+
+ case 3:
+ X = X;
+ break;
+
+ case 4:
+ if ((Q == UfThold) && (E1 == E0)
+ && (FABS( UfThold - E1 / E9) <= E1)) {
+ UfNGrad = False;
+ printf("Underflow is gradual; it incurs Absolute Error =\n");
+ printf("(roundoff in UfThold) < E0.\n");
+ Y = E0 * CInvrse;
+ Y = Y * (OneAndHalf + U2);
+ X = CInvrse * (One + U2);
+ Y = Y / X;
+ IEEE = (Y == E0);
+ }
+ }
+ if (UfNGrad) {
+ printf("\n");
+ R = SQRT(Underflow / UfThold);
+ if (R <= H) {
+ Z = R * UfThold;
+ X = Z * (One + R * H * (One + H));
+ }
+ else {
+ Z = UfThold;
+ X = Z * (One + H * H * (One + H));
+ }
+ if (! ((X == Z) || (X - Z != Zero))) {
+ BadCond(Flaw, "");
+ printf("X = " );
+ pnum( &X );
+ printf( "is not equal to Z = ");
+ pnum( &Z );
+ Z9 = X - Z;
+ printf("yet X - Z yields " );
+ pnum( &Z9 );
+ printf(" Should this NOT signal Underflow, ");
+ printf("this is a SERIOUS DEFECT\nthat causes ");
+ printf("confusion when innocent statements like\n");;
+ printf(" if (X == Z) ... else");
+ printf(" ... (f(X) - f(Z)) / (X - Z) ...\n");
+ printf("encounter Division by Zero although actually\n");
+ printf("X / Z = 1 + ");
+ Ptemp = (X / Z - Half) - Half;
+ pnum( &Ptemp );
+ }
+ }
+ printf("The Underflow threshold is ");
+ pnum( &UfThold );
+ printf("below which calculation may suffer larger Relative error than ");
+ printf("merely roundoff.\n");
+ Y2 = U1 * U1;
+ Y = Y2 * Y2;
+ Y2 = Y * U1;
+ if (Y2 <= UfThold) {
+ if (Y > E0) {
+ BadCond(Defect, "");
+ I = 5;
+ }
+ else {
+ BadCond(Serious, "");
+ I = 4;
+ }
+ printf("Range is too narrow; U1^%d Underflows.\n", I);
+ }
+ /*=============================================*/
+ /*SPLIT
+ }
+#include "paranoia.h"
+part7(){
+*/
+ Milestone = 130;
+ /*=============================================*/
+ Y = - FLOOR(Half - TwoForty * LOG(UfThold) / LOG(HInvrse)) / TwoForty;
+ Y2 = Y - One;
+ printf("Since underflow occurs below the threshold\n");
+ printf("UfThold = ");
+ pnum( &HInvrse );
+ printf( ") ^ (Y=" );
+ pnum( &Y );
+ printf( ")\nonly underflow " );
+ printf("should afflict the expression HInvrse^(Y+1).\n");
+ pnum( &HInvrse );
+ pnum( &Y2 );
+ V9 = POW(HInvrse, Y2);
+ printf("actually calculating yields: ");
+ pnum( &V9 );
+ if (! ((V9 >= Zero) && (V9 <= (Radix + Radix + E9) * UfThold))) {
+ BadCond(Serious, "this is not between 0 and underflow\n");
+ printf(" threshold = ");
+ pnum( &UfThold );
+ }
+ else if (! (V9 > UfThold * (One + E9)))
+ printf("This computed value is O.K.\n");
+ else {
+ BadCond(Defect, "this is not between 0 and underflow\n");
+ printf(" threshold = ");
+ pnum( &UfThold);
+ }
+ /*=============================================*/
+ Milestone = 140;
+ /*=============================================*/
+ printf("\n");
+ /* ...calculate Exp2 == exp(2) == 7.389056099... */
+ X = Zero;
+ I = 2;
+ Y = Two * Three;
+ Q = Zero;
+ N = 0;
+ do {
+ Z = X;
+ I = I + 1;
+ Y = Y / (I + I);
+ R = Y + Q;
+ X = Z + R;
+ Q = (Z - X) + R;
+ } while(X > Z);
+ Z = (OneAndHalf + One / Eight) + X / (OneAndHalf * ThirtyTwo);
+ X = Z * Z;
+ Exp2 = X * X;
+ X = F9;
+ Y = X - U1;
+ printf("Testing X^((X + 1) / (X - 1)) vs. exp(2) = ");
+ pnum( &Exp2 );
+ printf( "as X -> 1.\n");
+ for(I = 1;;) {
+ Z = X - BInvrse;
+ Z = (X + One) / (Z - (One - BInvrse));
+ Q = POW(X, Z) - Exp2;
+ if (FABS(Q) > TwoForty * U2) {
+ N = 1;
+ V9 = (X - BInvrse) - (One - BInvrse);
+ BadCond(Defect, "Calculated");
+ Ptemp = POW(X,Z);
+ pnum(&Ptemp);
+ printf("for (1 + (" );
+ pnum( &V9 );
+ printf( ") ^ (" );
+ pnum( &Z );
+ printf(") differs from correct value by ");
+ pnum( &Q );
+ printf("\tThis much error may spoil financial\n");
+ printf("\tcalculations involving tiny interest rates.\n");
+ break;
+ }
+ else {
+ Z = (Y - X) * Two + Y;
+ X = Y;
+ Y = Z;
+ Z = One + (X - F9)*(X - F9);
+ if (Z > One && I < NoTrials) I++;
+ else {
+ if (X > One) {
+ if (N == 0)
+ printf("Accuracy seems adequate.\n");
+ break;
+ }
+ else {
+ X = One + U2;
+ Y = U2 + U2;
+ Y += X;
+ I = 1;
+ }
+ }
+ }
+ }
+ /*=============================================*/
+ Milestone = 150;
+ /*=============================================*/
+ printf("Testing powers Z^Q at four nearly extreme values.\n");
+ N = 0;
+ Z = A1;
+ Q = FLOOR(Half - LOG(C) / LOG(A1));
+ Break = False;
+ do {
+ X = CInvrse;
+ Y = POW(Z, Q);
+ IsYeqX();
+ Q = - Q;
+ X = C;
+ Y = POW(Z, Q);
+ IsYeqX();
+ if (Z < One) Break = True;
+ else Z = AInvrse;
+ } while ( ! (Break));
+ PrintIfNPositive();
+ if (N == 0) printf(" ... no discrepancies found.\n");
+ printf("\n");
+
+ /*=============================================*/
+ Milestone = 160;
+ /*=============================================*/
+ Pause();
+ printf("Searching for Overflow threshold:\n");
+ printf("This may generate an error.\n");
+ sigsave = sigfpe;
+ I = 0;
+ Y = - CInvrse;
+ V9 = HInvrse * Y;
+ if (setjmp(ovfl_buf)) goto overflow;
+ do {
+ V = Y;
+ Y = V9;
+ V9 = HInvrse * Y;
+ } while(V9 < Y);
+ I = 1;
+overflow:
+ Z = V9;
+ printf("Can `Z = -Y' overflow?\n");
+ printf("Trying it on Y = " );
+ pnum( &Y );
+ V9 = - Y;
+ V0 = V9;
+ if (V - Y == V + V0) printf("Seems O.K.\n");
+ else {
+ printf("finds a ");
+ BadCond(Flaw, "-(-Y) differs from Y.\n");
+ }
+#if 0
+/* this doesn't handle infinity. */
+ if (Z != Y) {
+ BadCond(Serious, "");
+ printf("overflow past " );
+ pnum( &Y );
+ printf( "shrinks to " );
+ pnum( &Z );
+ }
+#endif
+ Y = V * (HInvrse * U2 - HInvrse);
+ Z = Y + ((One - HInvrse) * U2) * V;
+ if (Z < V0) Y = Z;
+ if (Y < V0) V = Y;
+ if (V0 - V < V0) V = V0;
+ printf("Overflow threshold is V = " );
+ pnum( &V );
+ if (I)
+ {
+ printf("Overflow saturates at V0 = " );
+ pnum( &V0 );
+ }
+ else printf("There is no saturation value because the system traps on overflow.\n");
+ V9 = V * One;
+ printf("No Overflow should be signaled for V * 1 = " );
+ pnum( &V9 );
+ V9 = V / One;
+ printf(" nor for V / 1 = " );
+ pnum( &V9 );
+ printf("Any overflow signal separating this * from the one\n");
+ printf("above is a DEFECT.\n");
+ /*=============================================*/
+ Milestone = 170;
+ /*=============================================*/
+ if (!(-V < V && -V0 < V0 && -UfThold < V && UfThold < V)) {
+ BadCond(Failure, "Comparisons involving ");
+ printf("+-" );
+ pnum( &V );
+ printf( ", +- " );
+ pnum( &V0 );
+ printf( "and +- " );
+ pnum( &UfThold );
+ printf( "are confused by Overflow." );
+ }
+ /*=============================================*/
+ Milestone = 175;
+ /*=============================================*/
+ printf("\n");
+ for(Indx = 1; Indx <= 3; ++Indx) {
+ switch (Indx) {
+ case 1: Z = UfThold; break;
+ case 2: Z = E0; break;
+ case 3: Z = PseudoZero; break;
+ }
+ if (Z != Zero) {
+ V9 = SQRT(Z);
+ Y = V9 * V9;
+ if (Y / (One - Radix * E9) < Z
+ || Y > (One + Radix + E9) * Z) {
+ if (V9 > U1) BadCond(Serious, "");
+ else BadCond(Defect, "");
+ printf("Comparison alleges that what prints as Z =" );
+ pnum( &Z );
+ printf(" is too far from sqrt(Z) ^ 2 = ");
+ pnum( &Y );
+ }
+ }
+ }
+ /*=============================================*/
+ Milestone = 180;
+ /*=============================================*/
+ for(Indx = 1; Indx <= 2; ++Indx) {
+ if (Indx == 1) Z = V;
+ else Z = V0;
+ V9 = SQRT(Z);
+ X = (One - Radix * E9) * V9;
+ V9 = V9 * X;
+ if (((V9 < (One - Two * Radix * E9) * Z) || (V9 > Z))) {
+ Y = V9;
+ if (X < W) BadCond(Serious, "");
+ else BadCond(Defect, "");
+ printf("Comparison alleges that Z = ");
+ pnum( &Z );
+ printf(" is too far from sqrt(Z) ^ 2 " );
+ pnum( &Y );
+ }
+ }
+ /*=============================================*/
+ /*SPLIT
+ }
+#include "paranoia.h"
+part8(){
+*/
+ Milestone = 190;
+ /*=============================================*/
+ Pause();
+ X = UfThold * V;
+ Y = Radix * Radix;
+ if (X*Y < One || X > Y) {
+ if (X * Y < U1 || X > Y/U1) BadCond(Defect, "Badly");
+ else BadCond(Flaw, "");
+
+ printf(" unbalanced range; UfThold * V = " );
+ pnum( &X );
+ printf( "is too far from 1.\n");
+ }
+ /*=============================================*/
+ Milestone = 200;
+ /*=============================================*/
+ for (Indx = 1; Indx <= 5; ++Indx) {
+ X = F9;
+ switch (Indx) {
+ case 2: X = One + U2; break;
+ case 3: X = V; break;
+ case 4: X = UfThold; break;
+ case 5: X = Radix;
+ }
+ Y = X;
+ sigsave = sigfpe;
+ if (setjmp(ovfl_buf))
+ {
+ printf(" X / X traps when X = ");
+ pnum( &X );
+ }
+ else {
+ V9 = (Y / X - Half) - Half;
+ if (V9 == Zero) continue;
+ if (V9 == - U1 && Indx < 5) BadCond(Flaw, "");
+ else BadCond(Serious, "");
+ printf(" X / X differs from 1 when X =");
+ pnum( &X );
+ printf(" instead, X / X - 1/2 - 1/2 = ");
+ pnum( &V9 );
+ }
+ }
+ /*=============================================*/
+ Milestone = 210;
+ /*=============================================*/
+ MyZero = Zero;
+ printf("\n");
+ printf("What message and/or values does Division by Zero produce?\n") ;
+#ifndef NOPAUSE
+ printf("This can interupt your program. You can ");
+ printf("skip this part if you wish.\n");
+ printf("Do you wish to compute 1 / 0? ");
+ fflush(stdout);
+ read (KEYBOARD, ch, 8);
+ if ((ch[0] == 'Y') || (ch[0] == 'y')) {
+#endif
+ sigsave = sigfpe;
+ printf(" Trying to compute 1 / 0 produces ...");
+ if (!setjmp(ovfl_buf))
+ {
+ Ptemp = One / MyZero;
+ pnum( &Ptemp );
+ }
+#ifndef NOPAUSE
+ }
+ else printf("O.K.\n");
+ printf("\nDo you wish to compute 0 / 0? ");
+ fflush(stdout);
+ read (KEYBOARD, ch, 80);
+ if ((ch[0] == 'Y') || (ch[0] == 'y')) {
+#endif
+ sigsave = sigfpe;
+ printf("\n Trying to compute 0 / 0 produces ...");
+ if (!setjmp(ovfl_buf))
+ {
+ Ptemp = Zero / MyZero;
+ pnum( &Ptemp );
+ }
+#ifndef NOPAUSE
+ }
+ else printf("O.K.\n");
+#endif
+ /*=============================================*/
+ Milestone = 220;
+ /*=============================================*/
+ Pause();
+ printf("\n");
+ {
+ static char *msg[] = {
+ "FAILUREs encountered =",
+ "SERIOUS DEFECTs discovered =",
+ "DEFECTs discovered =",
+ "FLAWs discovered =" };
+ int i;
+ for(i = 0; i < 4; i++) if (ErrCnt[i])
+ printf("The number of %-29s %d.\n",
+ msg[i], ErrCnt[i]);
+ }
+ printf("\n");
+ if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[Defect]
+ + ErrCnt[Flaw]) > 0) {
+ if ((ErrCnt[Failure] + ErrCnt[Serious] + ErrCnt[
+ Defect] == 0) && (ErrCnt[Flaw] > 0)) {
+ printf("The arithmetic diagnosed seems ");
+ printf("satisfactory though flawed.\n");
+ }
+ if ((ErrCnt[Failure] + ErrCnt[Serious] == 0)
+ && ( ErrCnt[Defect] > 0)) {
+ printf("The arithmetic diagnosed may be acceptable\n");
+ printf("despite inconvenient Defects.\n");
+ }
+ if ((ErrCnt[Failure] + ErrCnt[Serious]) > 0) {
+ printf("The arithmetic diagnosed has ");
+ printf("unacceptable serious defects.\n");
+ }
+ if (ErrCnt[Failure] > 0) {
+ printf("Fatal FAILURE may have spoiled this");
+ printf(" program's subsequent diagnoses.\n");
+ }
+ }
+ else {
+ printf("No failures, defects nor flaws have been discovered.\n");
+ if (! ((RMult == Rounded) && (RDiv == Rounded)
+ && (RAddSub == Rounded) && (RSqrt == Rounded)))
+ printf("The arithmetic diagnosed seems satisfactory.\n");
+ else {
+ if (StickyBit >= One &&
+ (Radix - Two) * (Radix - Nine - One) == Zero) {
+ printf("Rounding appears to conform to ");
+ printf("the proposed IEEE standard P");
+ if ((Radix == Two) &&
+ ((Precision - Four * Three * Two) *
+ ( Precision - TwentySeven -
+ TwentySeven + One) == Zero))
+ printf("754");
+ else printf("854");
+ if (IEEE) printf(".\n");
+ else {
+ printf(",\nexcept for possibly Double Rounding");
+ printf(" during Gradual Underflow.\n");
+ }
+ }
+ printf("The arithmetic diagnosed appears to be excellent!\n");
+ }
+ }
+ if (fpecount)
+ printf("\nA total of %d floating point exceptions were registered.\n",
+ fpecount);
+ printf("END OF TEST.\n");
+ }
+
+/*SPLIT subs.c
+#include "paranoia.h"
+*/
+
+/* Sign */
+
+FLOAT Sign (X)
+FLOAT X;
+{ return X >= 0. ? 1.0 : -1.0; }
+
+/* Pause */
+
+Pause()
+{
+ char ch[8];
+
+#ifndef NOPAUSE
+ printf("\nTo continue, press RETURN");
+ fflush(stdout);
+ read(KEYBOARD, ch, 8);
+#endif
+ printf("\nDiagnosis resumes after milestone Number %d", Milestone);
+ printf(" Page: %d\n\n", PageNo);
+ ++Milestone;
+ ++PageNo;
+ }
+
+ /* TstCond */
+
+TstCond (K, Valid, T)
+int K, Valid;
+char *T;
+{ if (! Valid) { BadCond(K,T); printf(".\n"); } }
+
+BadCond(K, T)
+int K;
+char *T;
+{
+ static char *msg[] = { "FAILURE", "SERIOUS DEFECT", "DEFECT", "FLAW" };
+
+ ErrCnt [K] = ErrCnt [K] + 1;
+ printf("%s: %s", msg[K], T);
+ }
+
+/* Random */
+/* Random computes
+ X = (Random1 + Random9)^5
+ Random1 = X - FLOOR(X) + 0.000005 * X;
+ and returns the new value of Random1
+*/
+
+FLOAT Random()
+{
+ FLOAT X, Y;
+
+ X = Random1 + Random9;
+ Y = X * X;
+ Y = Y * Y;
+ X = X * Y;
+ Y = X - FLOOR(X);
+ Random1 = Y + X * 0.000005;
+ return(Random1);
+ }
+
+/* SqXMinX */
+
+SqXMinX (ErrKind)
+int ErrKind;
+{
+ FLOAT XA, XB;
+
+ XB = X * BInvrse;
+ XA = X - XB;
+ SqEr = ((SQRT(X * X) - XB) - XA) / OneUlp;
+ if (SqEr != Zero) {
+ if (SqEr < MinSqEr) MinSqEr = SqEr;
+ if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+ J = J + 1.0;
+ BadCond(ErrKind, "\n");
+ printf("sqrt( ");
+ Ptemp = X * X;
+ pnum( &Ptemp );
+ printf( ") - " );
+ pnum( &X );
+ printf(" = " );
+ Ptemp = OneUlp * SqEr;
+ pnum( &Ptemp );
+ printf("\tinstead of correct value 0 .\n");
+ }
+ }
+
+/* NewD */
+
+NewD()
+{
+ X = Z1 * Q;
+ X = FLOOR(Half - X / Radix) * Radix + X;
+ Q = (Q - X * Z) / Radix + X * X * (D / Radix);
+ Z = Z - Two * X * D;
+ if (Z <= Zero) {
+ Z = - Z;
+ Z1 = - Z1;
+ }
+ D = Radix * D;
+ }
+
+/* SR3750 */
+
+SR3750()
+{
+ if (! ((X - Radix < Z2 - Radix) || (X - Z2 > W - Z2))) {
+ I = I + 1;
+ X2 = SQRT(X * D);
+ Y2 = (X2 - Z2) - (Y - Z2);
+ X2 = X8 / (Y - Half);
+ X2 = X2 - Half * X2 * X2;
+ SqEr = (Y2 + Half) + (Half - X2);
+ if (SqEr < MinSqEr) MinSqEr = SqEr;
+ SqEr = Y2 - X2;
+ if (SqEr > MaxSqEr) MaxSqEr = SqEr;
+ }
+ }
+
+/* IsYeqX */
+
+IsYeqX()
+{
+ if (Y != X) {
+ if (N <= 0) {
+ if (Z == Zero && Q <= Zero)
+ printf("WARNING: computing\n");
+ else BadCond(Defect, "computing\n");
+ printf("\t(");
+ pnum( &Z );
+ printf( ") ^ (" );
+ pnum( &Q );
+ printf("\tyielded " );
+ pnum( &Y );
+ printf("\twhich compared unequal to correct " );
+ pnum( &X );
+ printf("\t\tthey differ by " );
+ Ptemp = Y - X;
+ pnum( &Ptemp );
+ }
+ N = N + 1; /* ... count discrepancies. */
+ }
+ }
+
+/* SR3980 */
+
+SR3980()
+{
+ do {
+ Q = (FLOAT) I;
+ Y = POW(Z, Q);
+ IsYeqX();
+ if (++I > M) break;
+ X = Z * X;
+ } while ( X < W );
+ }
+
+/* PrintIfNPositive */
+
+PrintIfNPositive()
+{
+ if (N > 0) printf("Similar discrepancies have occurred %d times.\n", N);
+ }
+
+/* TstPtUf */
+
+TstPtUf()
+{
+ N = 0;
+ if (Z != Zero) {
+ printf("Since comparison denies Z = 0, evaluating ");
+ printf("(Z + Z) / Z should be safe.\n");
+ sigsave = sigfpe;
+ if (setjmp(ovfl_buf)) goto very_serious;
+ Q9 = (Z + Z) / Z;
+ printf("What the machine gets for (Z + Z) / Z is " );
+ pnum( &Q9 );
+ if (FABS(Q9 - Two) < Radix * U2) {
+ printf("This is O.K., provided Over/Underflow");
+ printf(" has NOT just been signaled.\n");
+ }
+ else {
+ if ((Q9 < One) || (Q9 > Two)) {
+very_serious:
+ N = 1;
+ ErrCnt [Serious] = ErrCnt [Serious] + 1;
+ printf("This is a VERY SERIOUS DEFECT!\n");
+ }
+ else {
+ N = 1;
+ ErrCnt [Defect] = ErrCnt [Defect] + 1;
+ printf("This is a DEFECT!\n");
+ }
+ }
+ V9 = Z * One;
+ Random1 = V9;
+ V9 = One * Z;
+ Random2 = V9;
+ V9 = Z / One;
+ if ((Z == Random1) && (Z == Random2) && (Z == V9)) {
+ if (N > 0) Pause();
+ }
+ else {
+ N = 1;
+ BadCond(Defect, "What prints as Z = ");
+ pnum( &Z );
+ printf("\tcompares different from ");
+ if (Z != Random1)
+ {
+ printf("Z * 1 = " );
+ pnum( &Random1 );
+ }
+ if (! ((Z == Random2)
+ || (Random2 == Random1)))
+ {
+ printf("1 * Z == " );
+ pnum( &Random2 );
+ }
+ if (! (Z == V9))
+ {
+ printf("Z / 1 = ");
+ pnum( &V9 );
+ }
+ if (Random2 != Random1) {
+ ErrCnt [Defect] = ErrCnt [Defect] + 1;
+ BadCond(Defect, "Multiplication does not commute!\n");
+ printf("\tComparison alleges that 1 * Z = ");
+ pnum( &Random2 );
+ printf("\tdiffers from Z * 1 = ");
+ pnum( &Random1 );
+ }
+ Pause();
+ }
+ }
+ }
+
+notify(s)
+char *s;
+{
+ printf("%s test appears to be inconsistent...\n", s);
+ printf(" PLEASE NOTIFY KARPINKSI!\n");
+ }
+
+/*SPLIT msgs.c */
+
+/* Instructions */
+
+msglist(s)
+char **s;
+{ while(*s) printf("%s\n", *s++); }
+
+Instructions()
+{
+ static char *instr[] = {
+ "Lest this program stop prematurely, i.e. before displaying\n",
+ " `END OF TEST',\n",
+ "try to persuade the computer NOT to terminate execution when an",
+ "error like Over/Underflow or Division by Zero occurs, but rather",
+ "to persevere with a surrogate value after, perhaps, displaying some",
+ "warning. If persuasion avails naught, don't despair but run this",
+ "program anyway to see how many milestones it passes, and then",
+ "amend it to make further progress.\n",
+ "Answer questions with Y, y, N or n (unless otherwise indicated).\n",
+ 0};
+
+ msglist(instr);
+ }
+
+/* Heading */
+
+Heading()
+{
+ static char *head[] = {
+ "Users are invited to help debug and augment this program so it will",
+ "cope with unanticipated and newly uncovered arithmetic pathologies.\n",
+ "Please send suggestions and interesting results to",
+ "\tRichard Karpinski",
+ "\tComputer Center U-76",
+ "\tUniversity of California",
+ "\tSan Francisco, CA 94143-0704, USA\n",
+ "In doing so, please include the following information:",
+#ifdef Single
+ "\tPrecision:\tsingle;",
+#else
+ "\tPrecision:\tdouble;",
+#endif
+ "\tVersion:\t27 January 1986;",
+ "\tComputer:\n",
+ "\tCompiler:\n",
+ "\tOptimization level:\n",
+ "\tOther relevant compiler options:",
+ 0};
+
+ msglist(head);
+ }
+
+/* Characteristics */
+
+Characteristics()
+{
+ static char *chars[] = {
+ "Running this program should reveal these characteristics:",
+ " Radix = 1, 2, 4, 8, 10, 16, 100, 256 ...",
+ " Precision = number of significant digits carried.",
+ " U2 = Radix/Radix^Precision = One Ulp",
+ "\t(OneUlpnit in the Last Place) of 1.000xxx .",
+ " U1 = 1/Radix^Precision = One Ulp of numbers a little less than 1.0 .",
+ " Adequacy of guard digits for Mult., Div. and Subt.",
+ " Whether arithmetic is chopped, correctly rounded, or something else",
+ "\tfor Mult., Div., Add/Subt. and Sqrt.",
+ " Whether a Sticky Bit used correctly for rounding.",
+ " UnderflowThreshold = an underflow threshold.",
+ " E0 and PseudoZero tell whether underflow is abrupt, gradual, or fuzzy.",
+ " V = an overflow threshold, roughly.",
+ " V0 tells, roughly, whether Infinity is represented.",
+ " Comparisions are checked for consistency with subtraction",
+ "\tand for contamination with pseudo-zeros.",
+ " Sqrt is tested. Y^X is not tested.",
+ " Extra-precise subexpressions are revealed but NOT YET tested.",
+ " Decimal-Binary conversion is NOT YET tested for accuracy.",
+ 0};
+
+ msglist(chars);
+ }
+
+History()
+
+{ /* History */
+ /* Converted from Brian Wichmann's Pascal version to C by Thos Sumner,
+ with further massaging by David M. Gay. */
+
+ static char *hist[] = {
+ "The program attempts to discriminate among",
+ " FLAWs, like lack of a sticky bit,",
+ " Serious DEFECTs, like lack of a guard digit, and",
+ " FAILUREs, like 2+2 == 5 .",
+ "Failures may confound subsequent diagnoses.\n",
+ "The diagnostic capabilities of this program go beyond an earlier",
+ "program called `MACHAR', which can be found at the end of the",
+ "book `Software Manual for the Elementary Functions' (1980) by",
+ "W. J. Cody and W. Waite. Although both programs try to discover",
+ "the Radix, Precision and range (over/underflow thresholds)",
+ "of the arithmetic, this program tries to cope with a wider variety",
+ "of pathologies, and to say how well the arithmetic is implemented.",
+ "\nThe program is based upon a conventional radix representation for",
+ "floating-point numbers, but also allows logarithmic encoding",
+ "as used by certain early WANG machines.\n",
+ "BASIC version of this program (C) 1983 by Prof. W. M. Kahan;",
+ "see source comments for more history.",
+ 0};
+
+ msglist(hist);
+ }
diff --git a/libm/ldouble/monotl.c b/libm/ldouble/monotl.c
new file mode 100644
index 000000000..86b85eca1
--- /dev/null
+++ b/libm/ldouble/monotl.c
@@ -0,0 +1,307 @@
+
+/* monot.c
+ Floating point function test vectors.
+
+ Arguments and function values are synthesized for NPTS points in
+ the vicinity of each given tabulated test point. The points are
+ chosen to be near and on either side of the likely function algorithm
+ domain boundaries. Since the function programs change their methods
+ at these points, major coding errors or monotonicity failures might be
+ detected.
+
+ August, 1998
+ S. L. Moshier */
+
+
+#include <stdio.h>
+
+/* Avoid including math.h. */
+long double frexpl (long double, int *);
+long double ldexpl (long double, int);
+
+/* Number of test points to generate on each side of tabulated point. */
+#define NPTS 100
+
+/* Functions of one variable. */
+long double expl (long double);
+long double logl (long double);
+long double sinl (long double);
+long double cosl (long double);
+long double tanl (long double);
+long double atanl (long double);
+long double asinl (long double);
+long double acosl (long double);
+long double sinhl (long double);
+long double coshl (long double);
+long double tanhl (long double);
+long double asinhl (long double);
+long double acoshl (long double);
+long double atanhl (long double);
+long double gammal (long double);
+long double fabsl (long double);
+long double floorl (long double);
+
+struct oneargument
+ {
+ char *name; /* Name of the function. */
+ long double (*func) (long double);
+ long double arg1; /* Function argument, assumed exact. */
+ long double answer1; /* Exact, close to function value. */
+ long double answer2; /* answer1 + answer2 has extended precision. */
+ long double derivative; /* dy/dx evaluated at x = arg1. */
+ int thresh; /* Error report threshold. 2 = 1 ULP approx. */
+ };
+
+/* Add this to error threshold test[i].thresh. */
+#define OKERROR 2
+
+/* Unit of relative error in test[i].thresh. */
+static long double MACHEPL = 5.42101086242752217003726400434970855712890625E-20L;
+
+/* extern double MACHEP; */
+
+
+struct oneargument test1[] =
+{
+ {"exp", expl, 1.0L, 2.7182769775390625L,
+ 4.85091998273536028747e-6L, 2.71828182845904523536L, 1},
+ {"exp", expl, -1.0L, 3.678741455078125e-1L,
+ 5.29566362982159552377e-6L, 3.678794411714423215955e-1L, 1},
+ {"exp", expl, 0.5L, 1.648712158203125L,
+ 9.1124970031468486507878e-6L, 1.64872127070012814684865L, 1},
+ {"exp", expl, -0.5L, 6.065216064453125e-1L,
+ 9.0532673209236037995e-6L, 6.0653065971263342360e-1L, 1},
+ {"exp", expl, 2.0L, 7.3890533447265625L,
+ 2.75420408772723042746e-6L, 7.38905609893065022723L, 1},
+ {"exp", expl, -2.0L, 1.353302001953125e-1L,
+ 5.08304130019189399949e-6L, 1.3533528323661269189e-1L, 1},
+ {"log", logl, 1.41421356237309492343L, 3.465728759765625e-1L,
+ 7.1430341006605745676897e-7L, 7.0710678118654758708668e-1L, 1},
+ {"log", logl, 7.07106781186547461715e-1L, -3.46588134765625e-1L,
+ 1.45444856522566402246e-5L, 1.41421356237309517417L, 1},
+ {"sin", sinl, 7.85398163397448278999e-1L, 7.0709228515625e-1L,
+ 1.4496030297502751942956e-5L, 7.071067811865475460497e-1L, 1},
+ {"sin", sinl, -7.85398163397448501044e-1L, -7.071075439453125e-1L,
+ 7.62758764840238811175e-7L, 7.07106781186547389040e-1L, 1},
+ {"sin", sinl, 1.570796326794896558L, 9.999847412109375e-1L,
+ 1.52587890625e-5L, 6.12323399573676588613e-17L, 1},
+ {"sin", sinl, -1.57079632679489678004L, -1.0L,
+ 1.29302922820150306903e-32L, -1.60812264967663649223e-16L, 1},
+ {"sin", sinl, 4.712388980384689674L, -1.0L,
+ 1.68722975549458979398e-32L, -1.83697019872102976584e-16L, 1},
+ {"sin", sinl, -4.71238898038468989604L, 9.999847412109375e-1L,
+ 1.52587890625e-5L, 3.83475850529283315008e-17L, 1},
+ {"cos", cosl, 3.92699081698724139500E-1L, 9.23873901367187500000E-1L,
+ 5.63114409926198633370E-6L, -3.82683432365089757586E-1L, 1},
+ {"cos", cosl, 7.85398163397448278999E-1L, 7.07092285156250000000E-1L,
+ 1.44960302975460497458E-5L, -7.07106781186547502752E-1L, 1},
+ {"cos", cosl, 1.17809724509617241850E0L, 3.82675170898437500000E-1L,
+ 8.26146665231415693919E-6L, -9.23879532511286738554E-1L, 1},
+ {"cos", cosl, 1.96349540849362069750E0L, -3.82690429687500000000E-1L,
+ 6.99732241029898567203E-6L, -9.23879532511286785419E-1L, 1},
+ {"cos", cosl, 2.35619449019234483700E0L, -7.07107543945312500000E-1L,
+ 7.62758765040545859856E-7L, -7.07106781186547589348E-1L, 1},
+ {"cos", cosl, 2.74889357189106897650E0L, -9.23889160156250000000E-1L,
+ 9.62764496328487887036E-6L, -3.82683432365089870728E-1L, 1},
+ {"cos", cosl, 3.14159265358979311600E0L, -1.00000000000000000000E0L,
+ 7.49879891330928797323E-33L, -1.22464679914735317723E-16L, 1},
+ {"tan", tanl, 7.85398163397448278999E-1L, 9.999847412109375e-1L,
+ 1.52587890624387676600E-5L, 1.99999999999999987754E0L, 1},
+ {"tan", tanl, 1.17809724509617241850E0L, 2.41419982910156250000E0L,
+ 1.37332715322352112604E-5L, 6.82842712474618858345E0L, 1},
+ {"tan", tanl, 1.96349540849362069750E0L, -2.41421508789062500000E0L,
+ 1.52551752942854759743E-6L, 6.82842712474619262118E0L, 1},
+ {"tan", tanl, 2.35619449019234483700E0L, -1.00001525878906250000E0L,
+ 1.52587890623163029801E-5L, 2.00000000000000036739E0L, 1},
+ {"tan", tanl, 2.74889357189106897650E0L, -4.14215087890625000000E-1L,
+ 1.52551752982565655126E-6L, 1.17157287525381000640E0L, 1},
+ {"atan", atanl, 4.14213562373094923430E-1L, 3.92684936523437500000E-1L,
+ 1.41451752865477964149E-5L, 8.53553390593273837869E-1L, 1},
+ {"atan", atanl, 1.0L, 7.85385131835937500000E-1L,
+ 1.30315615108096156608E-5L, 0.5L, 1},
+ {"atan", atanl, 2.41421356237309492343E0L, 1.17808532714843750000E0L,
+ 1.19179477349460632350E-5L, 1.46446609406726250782E-1L, 1},
+ {"atan", atanl, -2.41421356237309514547E0L, -1.17810058593750000000E0L,
+ 3.34084132752141908545E-6L, 1.46446609406726227789E-1L, 1},
+ {"atan", atanl, -1.0L, -7.85400390625000000000E-1L,
+ 2.22722755169038433915E-6L, 0.5L, 1},
+ {"atan", atanl, -4.14213562373095145475E-1L, -3.92700195312500000000E-1L,
+ 1.11361377576267665972E-6L, 8.53553390593273703853E-1L, 1},
+ {"asin", asinl, 3.82683432365089615246E-1L, 3.92684936523437500000E-1L,
+ 1.41451752864854321970E-5L, 1.08239220029239389286E0L, 1},
+ {"asin", asinl, 0.5L, 5.23590087890625000000E-1L,
+ 8.68770767387307710723E-6L, 1.15470053837925152902E0L, 1},
+ {"asin", asinl, 7.07106781186547461715E-1L, 7.85385131835937500000E-1L,
+ 1.30315615107209645016E-5L, 1.41421356237309492343E0L, 1},
+ {"asin", asinl, 9.23879532511286738483E-1L, 1.17808532714843750000E0L,
+ 1.19179477349183147612E-5L, 2.61312592975275276483E0L, 1},
+ {"asin", asinl, -0.5L, -5.23605346679687500000E-1L,
+ 6.57108138862692289277E-6L, 1.15470053837925152902E0L, 1},
+ {"acos", acosl, 1.95090322016128192573E-1L, 1.37443542480468750000E0L,
+ 1.13611408471185777914E-5L, -1.01959115820831832232E0L, 1},
+ {"acos", acosl, 3.82683432365089615246E-1L, 1.17808532714843750000E0L,
+ 1.19179477351337991247E-5L, -1.08239220029239389286E0L, 1},
+ {"acos", acosl, 0.5L, 1.04719543457031250000E0L,
+ 2.11662628524615421446E-6L, -1.15470053837925152902E0L, 1},
+ {"acos", acosl, 7.07106781186547461715E-1L, 7.85385131835937500000E-1L,
+ 1.30315615108982668201E-5L, -1.41421356237309492343E0L, 1},
+ {"acos", acosl, 9.23879532511286738483E-1L, 3.92684936523437500000E-1L,
+ 1.41451752867009165605E-5L, -2.61312592975275276483E0L, 1},
+ {"acos", acosl, 9.80785280403230430579E-1L, 1.96334838867187500000E-1L,
+ 1.47019821746724723933E-5L, -5.12583089548300990774E0L, 1},
+ {"acos", acosl, -0.5L, 2.09439086914062500000E0L,
+ 4.23325257049230842892E-6L, -1.15470053837925152902E0L, 1},
+ {"sinh", sinhl, 1.0L, 1.17518615722656250000E0L,
+ 1.50364172389568823819E-5L, 1.54308063481524377848E0L, 1},
+ {"sinh", sinhl, 7.09089565712818057364E2L, 4.49423283712885057274E307L,
+ 4.25947714184369757620E208L, 4.49423283712885057274E307L, 1},
+ {"sinh", sinhl, 2.22044604925031308085E-16L, 0.00000000000000000000E0L,
+ 2.22044604925031308085E-16L, 1.00000000000000000000E0L, 1},
+ {"cosh", coshl, 7.09089565712818057364E2L, 4.49423283712885057274E307L,
+ 4.25947714184369757620E208L, 4.49423283712885057274E307L, 1},
+ {"cosh", coshl, 1.0L, 1.54307556152343750000E0L,
+ 5.07329180627847790562E-6L, 1.17520119364380145688E0L, 1},
+ {"cosh", coshl, 0.5L, 1.12762451171875000000E0L,
+ 1.45348763078522622516E-6L, 5.21095305493747361622E-1L, 1},
+ {"tanh", tanhl, 0.5L, 4.62112426757812500000E-1L,
+ 4.73050219725850231848E-6L, 7.86447732965927410150E-1L, 1},
+ {"tanh", tanhl, 5.49306144334054780032E-1L, 4.99984741210937500000E-1L,
+ 1.52587890624507506378E-5L, 7.50000000000000049249E-1L, 1},
+ {"tanh", tanhl, 0.625L, 5.54595947265625000000E-1L,
+ 3.77508375729399903910E-6L, 6.92419147969988069631E-1L, 1},
+ {"asinh", asinhl, 0.5L, 4.81201171875000000000E-1L,
+ 1.06531846034474977589E-5L, 8.94427190999915878564E-1L, 1},
+ {"asinh", asinhl, 1.0L, 8.81362915039062500000E-1L,
+ 1.06719804805252326093E-5L, 7.07106781186547524401E-1L, 1},
+ {"asinh", asinhl, 2.0L, 1.44363403320312500000E0L,
+ 1.44197568534249327674E-6L, 4.47213595499957939282E-1L, 1},
+ {"acosh", acoshl, 2.0L, 1.31695556640625000000E0L,
+ 2.33051856670862504635E-6L, 5.77350269189625764509E-1L, 1},
+ {"acosh", acoshl, 1.5L, 9.62417602539062500000E-1L,
+ 6.04758014439499551783E-6L, 8.94427190999915878564E-1L, 1},
+ {"acosh", acoshl, 1.03125L, 2.49343872070312500000E-1L,
+ 9.62177257298785143908E-6L, 3.96911150685467059809E0L, 1},
+ {"atanh", atanhl, 0.5L, 5.49301147460937500000E-1L,
+ 4.99687311734569762262E-6L, 1.33333333333333333333E0L, 1},
+#if 0
+ {"gamma", gammal, 1.0L, 1.0L,
+ 0.0L, -5.772156649015328606e-1L, 1},
+ {"gamma", gammal, 2.0L, 1.0L,
+ 0.0L, 4.2278433509846713939e-1L, 1},
+ {"gamma", gammal, 3.0L, 2.0L,
+ 0.0L, 1.845568670196934279L, 1},
+ {"gamma", gammal, 4.0L, 6.0L,
+ 0.0L, 7.536706010590802836L, 1},
+#endif
+ {"null", NULL, 0.0L, 0.0L, 0.0L, 1},
+};
+
+/* These take care of extra-precise floating point register problems. */
+volatile long double volat1;
+volatile long double volat2;
+
+
+/* Return the next nearest floating point value to X
+ in the direction of UPDOWN (+1 or -1).
+ (Fails if X is denormalized.) */
+
+long double
+nextval (x, updown)
+ long double x;
+ int updown;
+{
+ long double m;
+ int i;
+
+ volat1 = x;
+ m = 0.25L * MACHEPL * volat1 * updown;
+ volat2 = volat1 + m;
+ if (volat2 != volat1)
+ printf ("successor failed\n");
+
+ for (i = 2; i < 10; i++)
+ {
+ volat2 = volat1 + i * m;
+ if (volat1 != volat2)
+ return volat2;
+ }
+
+ printf ("nextval failed\n");
+ return volat1;
+}
+
+
+
+
+int
+main ()
+{
+ long double (*fun1) (long double);
+ int i, j, errs, tests;
+ long double x, x0, y, dy, err;
+
+ errs = 0;
+ tests = 0;
+ i = 0;
+
+ for (;;)
+ {
+ fun1 = test1[i].func;
+ if (fun1 == NULL)
+ break;
+ volat1 = test1[i].arg1;
+ x0 = volat1;
+ x = volat1;
+ for (j = 0; j <= NPTS; j++)
+ {
+ volat1 = x - x0;
+ dy = volat1 * test1[i].derivative;
+ dy = test1[i].answer2 + dy;
+ volat1 = test1[i].answer1 + dy;
+ volat2 = (*(fun1)) (x);
+ if (volat2 != volat1)
+ {
+ /* Report difference between program result
+ and extended precision function value. */
+ err = volat2 - test1[i].answer1;
+ err = err - dy;
+ err = err / volat1;
+ if (fabsl (err) > ((OKERROR + test1[i].thresh) * MACHEPL))
+ {
+ printf ("%d %s(%.19Le) = %.19Le, rel err = %.3Le\n",
+ j, test1[i].name, x, volat2, err);
+ errs += 1;
+ }
+ }
+ x = nextval (x, 1);
+ tests += 1;
+ }
+
+ x = x0;
+ x = nextval (x, -1);
+ for (j = 1; j < NPTS; j++)
+ {
+ volat1 = x - x0;
+ dy = volat1 * test1[i].derivative;
+ dy = test1[i].answer2 + dy;
+ volat1 = test1[i].answer1 + dy;
+ volat2 = (*(fun1)) (x);
+ if (volat2 != volat1)
+ {
+ err = volat2 - test1[i].answer1;
+ err = err - dy;
+ err = err / volat1;
+ if (fabsl (err) > ((OKERROR + test1[i].thresh) * MACHEPL))
+ {
+ printf ("%d %s(%.19Le) = %.19Le, rel err = %.3Le\n",
+ j, test1[i].name, x, volat2, err);
+ errs += 1;
+ }
+ }
+ x = nextval (x, -1);
+ tests += 1;
+ }
+ i += 1;
+ }
+ printf ("%d errors in %d tests\n", errs, tests);
+}
diff --git a/libm/ldouble/mtherr.c b/libm/ldouble/mtherr.c
new file mode 100644
index 000000000..17d0485d2
--- /dev/null
+++ b/libm/ldouble/mtherr.c
@@ -0,0 +1,102 @@
+/* mtherr.c
+ *
+ * Library common error handling routine
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * char *fctnam;
+ * int code;
+ * int mtherr();
+ *
+ * mtherr( fctnam, code );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This routine may be called to report one of the following
+ * error conditions (in the include file mconf.h).
+ *
+ * Mnemonic Value Significance
+ *
+ * DOMAIN 1 argument domain error
+ * SING 2 function singularity
+ * OVERFLOW 3 overflow range error
+ * UNDERFLOW 4 underflow range error
+ * TLOSS 5 total loss of precision
+ * PLOSS 6 partial loss of precision
+ * EDOM 33 Unix domain error code
+ * ERANGE 34 Unix range error code
+ *
+ * The default version of the file prints the function name,
+ * passed to it by the pointer fctnam, followed by the
+ * error condition. The display is directed to the standard
+ * output device. The routine then returns to the calling
+ * program. Users may wish to modify the program to abort by
+ * calling exit() under severe error conditions such as domain
+ * errors.
+ *
+ * Since all error conditions pass control to this function,
+ * the display may be easily changed, eliminated, or directed
+ * to an error logging device.
+ *
+ * SEE ALSO:
+ *
+ * mconf.h
+ *
+ */
+
+/*
+Cephes Math Library Release 2.0: April, 1987
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <stdio.h>
+#include <math.h>
+
+int merror = 0;
+
+/* Notice: the order of appearance of the following
+ * messages is bound to the error codes defined
+ * in mconf.h.
+ */
+static char *ermsg[7] = {
+"unknown", /* error code 0 */
+"domain", /* error code 1 */
+"singularity", /* et seq. */
+"overflow",
+"underflow",
+"total loss of precision",
+"partial loss of precision"
+};
+
+
+int mtherr( name, code )
+char *name;
+int code;
+{
+
+/* Display string passed by calling program,
+ * which is supposed to be the name of the
+ * function in which the error occurred:
+ */
+printf( "\n%s ", name );
+
+/* Set global error message word */
+merror = code;
+
+/* Display error message defined
+ * by the code argument.
+ */
+if( (code <= 0) || (code >= 7) )
+ code = 0;
+printf( "%s error\n", ermsg[code] );
+
+/* Return to calling
+ * program
+ */
+return( 0 );
+}
diff --git a/libm/ldouble/mtstl.c b/libm/ldouble/mtstl.c
new file mode 100644
index 000000000..0cd6eed16
--- /dev/null
+++ b/libm/ldouble/mtstl.c
@@ -0,0 +1,521 @@
+/* mtst.c
+ Consistency tests for math functions.
+
+ With NTRIALS=10000, the following are typical results for
+ an alleged IEEE long double precision arithmetic:
+
+Consistency test of math functions.
+Max and rms errors for 10000 random arguments.
+A = absolute error criterion (but relative if >1):
+Otherwise, estimate is of relative error
+x = cbrt( cube(x) ): max = 7.65E-20 rms = 4.39E-21
+x = atan( tan(x) ): max = 2.01E-19 rms = 3.96E-20
+x = sin( asin(x) ): max = 2.15E-19 rms = 3.00E-20
+x = sqrt( square(x) ): max = 0.00E+00 rms = 0.00E+00
+x = log( exp(x) ): max = 5.42E-20 A rms = 1.87E-21 A
+x = log2( exp2(x) ): max = 1.08E-19 A rms = 3.37E-21 A
+x = log10( exp10(x) ): max = 2.71E-20 A rms = 6.76E-22 A
+x = acosh( cosh(x) ): max = 3.13E-18 A rms = 3.21E-20 A
+x = pow( pow(x,a),1/a ): max = 1.25E-17 rms = 1.70E-19
+x = tanh( atanh(x) ): max = 1.08E-19 rms = 1.16E-20
+x = asinh( sinh(x) ): max = 1.03E-19 rms = 2.94E-21
+x = cos( acos(x) ): max = 1.63E-19 A rms = 4.37E-20 A
+lgam(x) = log(gamma(x)): max = 2.31E-19 A rms = 5.93E-20 A
+x = ndtri( ndtr(x) ): max = 5.07E-17 rms = 7.03E-19
+Legendre ellpk, ellpe: max = 7.59E-19 A rms = 1.72E-19 A
+Absolute error and only 2000 trials:
+Wronksian of Yn, Jn: max = 6.40E-18 A rms = 1.49E-19 A
+Relative error and only 100 trials:
+x = stdtri(stdtr(k,x) ): max = 6.73E-19 rms = 2.46E-19
+*/
+
+/*
+Cephes Math Library Release 2.3: November, 1995
+Copyright 1984, 1987, 1988, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+/* C9X spells lgam lgamma. */
+#define GLIBC2 0
+
+#define NTRIALS 10000
+#define WTRIALS (NTRIALS/5)
+#define STRTST 0
+
+/* Note, fabsl may be an intrinsic function. */
+#ifdef ANSIPROT
+extern long double fabsl ( long double );
+extern long double sqrtl ( long double );
+extern long double cbrtl ( long double );
+extern long double expl ( long double );
+extern long double logl ( long double );
+extern long double tanl ( long double );
+extern long double atanl ( long double );
+extern long double sinl ( long double );
+extern long double asinl ( long double );
+extern long double cosl ( long double );
+extern long double acosl ( long double );
+extern long double powl ( long double, long double );
+extern long double tanhl ( long double );
+extern long double atanhl ( long double );
+extern long double sinhl ( long double );
+extern long double asinhl ( long double );
+extern long double coshl ( long double );
+extern long double acoshl ( long double );
+extern long double exp2l ( long double );
+extern long double log2l ( long double );
+extern long double exp10l ( long double );
+extern long double log10l ( long double );
+extern long double gammal ( long double );
+extern long double lgaml ( long double );
+extern long double jnl ( int, long double );
+extern long double ynl ( int, long double );
+extern long double ndtrl ( long double );
+extern long double ndtril ( long double );
+extern long double stdtrl ( int, long double );
+extern long double stdtril ( int, long double );
+extern long double ellpel ( long double );
+extern long double ellpkl ( long double );
+extern void exit (int);
+#else
+long double fabsl(), sqrtl();
+long double cbrtl(), expl(), logl(), tanl(), atanl();
+long double sinl(), asinl(), cosl(), acosl(), powl();
+long double tanhl(), atanhl(), sinhl(), asinhl(), coshl(), acoshl();
+long double exp2l(), log2l(), exp10l(), log10l();
+long double gammal(), lgaml(), jnl(), ynl(), ndtrl(), ndtril();
+long double stdtrl(), stdtril(), ellpel(), ellpkl();
+void exit ();
+#endif
+extern int merror;
+#if GLIBC2
+long double lgammal(long double);
+#endif
+/*
+NYI:
+double iv(), kn();
+*/
+
+/* Provide inverses for square root and cube root: */
+long double squarel(x)
+long double x;
+{
+return( x * x );
+}
+
+long double cubel(x)
+long double x;
+{
+return( x * x * x );
+}
+
+/* lookup table for each function */
+struct fundef
+ {
+ char *nam1; /* the function */
+ long double (*name )();
+ char *nam2; /* its inverse */
+ long double (*inv )();
+ int nargs; /* number of function arguments */
+ int tstyp; /* type code of the function */
+ long ctrl; /* relative error flag */
+ long double arg1w; /* width of domain for 1st arg */
+ long double arg1l; /* lower bound domain 1st arg */
+ long arg1f; /* flags, e.g. integer arg */
+ long double arg2w; /* same info for args 2, 3, 4 */
+ long double arg2l;
+ long arg2f;
+/*
+ double arg3w;
+ double arg3l;
+ long arg3f;
+ double arg4w;
+ double arg4l;
+ long arg4f;
+*/
+ };
+
+
+/* fundef.ctrl bits: */
+#define RELERR 1
+#define EXPSCAL 4
+
+/* fundef.tstyp test types: */
+#define POWER 1
+#define ELLIP 2
+#define GAMMA 3
+#define WRONK1 4
+#define WRONK2 5
+#define WRONK3 6
+#define STDTR 7
+
+/* fundef.argNf argument flag bits: */
+#define INT 2
+
+extern long double MINLOGL;
+extern long double MAXLOGL;
+extern long double PIL;
+extern long double PIO2L;
+/*
+define MINLOG -170.0
+define MAXLOG +170.0
+define PI 3.14159265358979323846
+define PIO2 1.570796326794896619
+*/
+
+#define NTESTS 17
+struct fundef defs[NTESTS] = {
+{" cube", cubel, " cbrt", cbrtl, 1, 0, 1, 2000.0L, -1000.0L, 0,
+0.0, 0.0, 0},
+{" tan", tanl, " atan", atanl, 1, 0, 1, 0.0L, 0.0L, 0,
+0.0, 0.0, 0},
+{" asin", asinl, " sin", sinl, 1, 0, 1, 2.0L, -1.0L, 0,
+0.0, 0.0, 0},
+{"square", squarel, " sqrt", sqrtl, 1, 0, 1, 170.0L, -85.0L, EXPSCAL,
+0.0, 0.0, 0},
+{" exp", expl, " log", logl, 1, 0, 0, 340.0L, -170.0L, 0,
+0.0, 0.0, 0},
+{" exp2", exp2l, " log2", log2l, 1, 0, 0, 340.0L, -170.0L, 0,
+0.0, 0.0, 0},
+{" exp10", exp10l, " log10", log10l, 1, 0, 0, 340.0L, -170.0L, 0,
+0.0, 0.0, 0},
+{" cosh", coshl, " acosh", acoshl, 1, 0, 0, 340.0L, 0.0L, 0,
+0.0, 0.0, 0},
+{"pow", powl, "pow", powl, 2, POWER, 1, 25.0L, 0.0L, 0,
+50.0, -25.0, 0},
+{" atanh", atanhl, " tanh", tanhl, 1, 0, 1, 2.0L, -1.0L, 0,
+0.0, 0.0, 0},
+{" sinh", sinhl, " asinh", asinhl, 1, 0, 1, 340.0L, 0.0L, 0,
+0.0, 0.0, 0},
+{" acos", acosl, " cos", cosl, 1, 0, 0, 2.0L, -1.0L, 0,
+0.0, 0.0, 0},
+#if GLIBC2
+ /*
+{ "gamma", gammal, "lgammal", lgammal, 1, GAMMA, 0, 34.0, 0.0, 0,
+0.0, 0.0, 0},
+*/
+#else
+{ "gamma", gammal, "lgam", lgaml, 1, GAMMA, 0, 34.0, 0.0, 0,
+0.0, 0.0, 0},
+{ " ndtr", ndtrl, " ndtri", ndtril, 1, 0, 1, 10.0L, -10.0L, 0,
+0.0, 0.0, 0},
+{" ellpe", ellpel, " ellpk", ellpkl, 1, ELLIP, 0, 1.0L, 0.0L, 0,
+0.0, 0.0, 0},
+{ "stdtr", stdtrl, "stdtri", stdtril, 2, STDTR, 1, 4.0L, -2.0L, 0,
+30.0, 1.0, INT},
+{ " Jn", jnl, " Yn", ynl, 2, WRONK1, 0, 30.0, 0.1, 0,
+40.0, -20.0, INT},
+#endif
+};
+
+static char *headrs[] = {
+"x = %s( %s(x) ): ",
+"x = %s( %s(x,a),1/a ): ", /* power */
+"Legendre %s, %s: ", /* ellip */
+"%s(x) = log(%s(x)): ", /* gamma */
+"Wronksian of %s, %s: ", /* wronk1 */
+"Wronksian of %s, %s: ", /* wronk2 */
+"Wronksian of %s, %s: ", /* wronk3 */
+"x = %s(%s(k,x) ): ", /* stdtr */
+};
+
+static long double y1 = 0.0;
+static long double y2 = 0.0;
+static long double y3 = 0.0;
+static long double y4 = 0.0;
+static long double a = 0.0;
+static long double x = 0.0;
+static long double y = 0.0;
+static long double z = 0.0;
+static long double e = 0.0;
+static long double max = 0.0;
+static long double rmsa = 0.0;
+static long double rms = 0.0;
+static long double ave = 0.0;
+static double da, db, dc, dd;
+
+int ldrand();
+int printf();
+
+int
+main()
+{
+long double (*fun )();
+long double (*ifun )();
+struct fundef *d;
+int i, k, itst;
+int m, ntr;
+
+ntr = NTRIALS;
+printf( "Consistency test of math functions.\n" );
+printf( "Max and rms errors for %d random arguments.\n",
+ ntr );
+printf( "A = absolute error criterion (but relative if >1):\n" );
+printf( "Otherwise, estimate is of relative error\n" );
+
+/* Initialize machine dependent parameters to test near the
+ * largest an smallest possible arguments. To compare different
+ * machines, use the same test intervals for all systems.
+ */
+defs[1].arg1w = PIL;
+defs[1].arg1l = -PIL/2.0;
+/*
+defs[3].arg1w = MAXLOGL;
+defs[3].arg1l = -MAXLOGL/2.0;
+defs[4].arg1w = 2.0*MAXLOGL;
+defs[4].arg1l = -MAXLOGL;
+defs[6].arg1w = 2.0*MAXLOGL;
+defs[6].arg1l = -MAXLOGL;
+defs[7].arg1w = MAXLOGL;
+defs[7].arg1l = 0.0;
+*/
+
+/* Outer loop, on the test number: */
+
+for( itst=STRTST; itst<NTESTS; itst++ )
+{
+d = &defs[itst];
+m = 0;
+max = 0.0L;
+rmsa = 0.0L;
+ave = 0.0L;
+fun = d->name;
+ifun = d->inv;
+
+/* Smaller number of trials for Wronksians
+ * (put them at end of list)
+ */
+if( d->tstyp == WRONK1 )
+ {
+ ntr = WTRIALS;
+ printf( "Absolute error and only %d trials:\n", ntr );
+ }
+else if( d->tstyp == STDTR )
+ {
+ ntr = NTRIALS/100;
+ printf( "Relative error and only %d trials:\n", ntr );
+ }
+/*
+y1 = d->arg1l;
+y2 = d->arg1w;
+da = y1;
+db = y2;
+printf( "arg1l = %.4e, arg1w = %.4e\n", da, db );
+*/
+printf( headrs[d->tstyp], d->nam2, d->nam1 );
+
+for( i=0; i<ntr; i++ )
+{
+m++;
+k = 0;
+/* make random number(s) in desired range(s) */
+switch( d->nargs )
+{
+
+default:
+goto illegn;
+
+case 2:
+ldrand( &a );
+a = d->arg2w * ( a - 1.0L ) + d->arg2l;
+if( d->arg2f & EXPSCAL )
+ {
+ a = expl(a);
+ ldrand( &y2 );
+ a -= 1.0e-13L * a * (y2 - 1.0L);
+ }
+if( d->arg2f & INT )
+ {
+ k = a + 0.25L;
+ a = k;
+ }
+
+case 1:
+ldrand( &x );
+y1 = d->arg1l;
+y2 = d->arg1w;
+x = y2 * ( x - 1.0L ) + y1;
+if( x < y1 )
+ x = y1;
+y1 += y2;
+if( x > y1 )
+ x = y1;
+if( d->arg1f & EXPSCAL )
+ {
+ x = expl(x);
+ ldrand( &y2 );
+ x += 1.0e-13L * x * (y2 - 1.0L);
+ }
+}
+
+/* compute function under test */
+switch( d->nargs )
+ {
+ case 1:
+ switch( d->tstyp )
+ {
+ case ELLIP:
+ y1 = ( *(fun) )(x);
+ y2 = ( *(fun) )(1.0L-x);
+ y3 = ( *(ifun) )(x);
+ y4 = ( *(ifun) )(1.0L-x);
+ break;
+#if 1
+ case GAMMA:
+ y = lgaml(x);
+ x = logl( gammal(x) );
+ break;
+#endif
+ default:
+ z = ( *(fun) )(x);
+ y = ( *(ifun) )(z);
+ }
+/*
+if( merror )
+ {
+ printf( "error: x = %.15e, z = %.15e, y = %.15e\n",
+ (double )x, (double )z, (double )y );
+ }
+*/
+ break;
+
+ case 2:
+ if( d->arg2f & INT )
+ {
+ switch( d->tstyp )
+ {
+ case WRONK1:
+ y1 = (*fun)( k, x ); /* jn */
+ y2 = (*fun)( k+1, x );
+ y3 = (*ifun)( k, x ); /* yn */
+ y4 = (*ifun)( k+1, x );
+ break;
+
+ case WRONK2:
+ y1 = (*fun)( a, x ); /* iv */
+ y2 = (*fun)( a+1.0L, x );
+ y3 = (*ifun)( k, x ); /* kn */
+ y4 = (*ifun)( k+1, x );
+ break;
+
+ default:
+ z = (*fun)( k, x );
+ y = (*ifun)( k, z );
+ }
+ }
+ else
+ {
+ if( d->tstyp == POWER )
+ {
+ z = (*fun)( x, a );
+ y = (*ifun)( z, 1.0L/a );
+ }
+ else
+ {
+ z = (*fun)( a, x );
+ y = (*ifun)( a, z );
+ }
+ }
+ break;
+
+
+ default:
+illegn:
+ printf( "Illegal nargs= %d", d->nargs );
+ exit(1);
+ }
+
+switch( d->tstyp )
+ {
+ case WRONK1:
+ /* Jn, Yn */
+/* e = (y2*y3 - y1*y4) - 2.0L/(PIL*x);*/
+ e = x*(y2*y3 - y1*y4) - 2.0L/PIL;
+ break;
+
+ case WRONK2:
+/* In, Kn */
+/* e = (y2*y3 + y1*y4) - 1.0L/x; */
+ e = x*(y2*y3 + y1*y4) - 1.0L;
+ break;
+
+ case ELLIP:
+ e = (y1-y3)*y4 + y3*y2 - PIO2L;
+ break;
+
+ default:
+ e = y - x;
+ break;
+ }
+
+if( d->ctrl & RELERR )
+ {
+ if( x != 0.0L )
+ e /= x;
+ else
+ printf( "warning, x == 0\n" );
+ }
+else
+ {
+ if( fabsl(x) > 1.0L )
+ e /= x;
+ }
+
+ave += e;
+/* absolute value of error */
+if( e < 0 )
+ e = -e;
+
+/* peak detect the error */
+if( e > max )
+ {
+ max = e;
+
+ if( e > 1.0e-10L )
+ {
+da = x;
+db = z;
+dc = y;
+dd = max;
+ printf("x %.6E z %.6E y %.6E max %.4E\n",
+ da, db, dc, dd );
+/*
+ if( d->tstyp >= WRONK1 )
+ {
+ printf( "y1 %.4E y2 %.4E y3 %.4E y4 %.4E k %d x %.4E\n",
+ (double )y1, (double )y2, (double )y3,
+ (double )y4, k, (double )x );
+ }
+*/
+ }
+
+/*
+ printf("%.8E %.8E %.4E %6ld \n", x, y, max, n);
+ printf("%d %.8E %.8E %.4E %6ld \n", k, x, y, max, n);
+ printf("%.6E %.6E %.6E %.4E %6ld \n", a, x, y, max, n);
+ printf("%.6E %.6E %.6E %.6E %.4E %6ld \n", a, b, x, y, max, n);
+ printf("%.4E %.4E %.4E %.4E %.4E %.4E %6ld \n",
+ a, b, c, x, y, max, n);
+*/
+ }
+
+/* accumulate rms error */
+e *= 1.0e16L; /* adjust range */
+rmsa += e * e; /* accumulate the square of the error */
+}
+
+/* report after NTRIALS trials */
+rms = 1.0e-16L * sqrtl( rmsa/m );
+da = max;
+db = rms;
+if(d->ctrl & RELERR)
+ printf(" max = %.2E rms = %.2E\n", da, db );
+else
+ printf(" max = %.2E A rms = %.2E A\n", da, db );
+} /* loop on itst */
+
+exit (0);
+return 0;
+}
+
diff --git a/libm/ldouble/nantst.c b/libm/ldouble/nantst.c
new file mode 100644
index 000000000..855a43b5a
--- /dev/null
+++ b/libm/ldouble/nantst.c
@@ -0,0 +1,61 @@
+#include <stdio.h>
+long double inf = 1.0f/0.0f;
+long double nnn = 1.0f/0.0f - 1.0f/0.0f;
+long double fin = 1.0f;
+long double neg = -1.0f;
+long double nn2;
+
+int isnanl(), isfinitel(), signbitl();
+void abort (void);
+void exit (int);
+
+void pvalue (char *str, long double x)
+{
+union
+ {
+ long double f;
+ unsigned int i[3];
+ }u;
+int k;
+
+printf("%s ", str);
+u.f = x;
+for (k = 0; k < 3; k++)
+ printf("%08x ", u.i[k]);
+printf ("\n");
+}
+
+
+int
+main()
+{
+
+if (!isnanl(nnn))
+ abort();
+pvalue("nnn", nnn);
+pvalue("inf", inf);
+nn2 = inf - inf;
+pvalue("inf - inf", nn2);
+if (isnanl(fin))
+ abort();
+if (isnanl(inf))
+ abort();
+if (!isfinitel(fin))
+ abort();
+if (isfinitel(nnn))
+ abort();
+if (isfinitel(inf))
+ abort();
+if (!signbitl(neg))
+ abort();
+if (signbitl(fin))
+ abort();
+if (signbitl(inf))
+ abort();
+/*
+if (signbitf(nnn))
+ abort();
+ */
+exit (0);
+return 0;
+}
diff --git a/libm/ldouble/nbdtrl.c b/libm/ldouble/nbdtrl.c
new file mode 100644
index 000000000..91593f544
--- /dev/null
+++ b/libm/ldouble/nbdtrl.c
@@ -0,0 +1,197 @@
+/* nbdtrl.c
+ *
+ * Negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, nbdtrl();
+ *
+ * y = nbdtrl( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms 0 through k of the negative
+ * binomial distribution:
+ *
+ * k
+ * -- ( n+j-1 ) n j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=0
+ *
+ * In a sequence of Bernoulli trials, this is the probability
+ * that k or fewer failures precede the nth success.
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (k,n,p) with k and n between 1 and 10,000
+ * and p between 0 and 1.
+ *
+ * arithmetic domain # trials peak rms
+ * Absolute error:
+ * IEEE 0,10000 10000 9.8e-15 2.1e-16
+ *
+ */
+ /* nbdtrcl.c
+ *
+ * Complemented negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, nbdtrcl();
+ *
+ * y = nbdtrcl( k, n, p );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the negative
+ * binomial distribution:
+ *
+ * inf
+ * -- ( n+j-1 ) n j
+ * > ( ) p (1-p)
+ * -- ( j )
+ * j=k+1
+ *
+ * The terms are not computed individually; instead the incomplete
+ * beta integral is employed, according to the formula
+ *
+ * y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p ).
+ *
+ * The arguments must be positive, with p ranging from 0 to 1.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See incbetl.c.
+ *
+ */
+ /* nbdtril
+ *
+ * Functional inverse of negative binomial distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k, n;
+ * long double p, y, nbdtril();
+ *
+ * p = nbdtril( k, n, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the argument p such that nbdtr(k,n,p) is equal to y.
+ *
+ * ACCURACY:
+ *
+ * Tested at random points (a,b,y), with y between 0 and 1.
+ *
+ * a,b Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,100
+ * See also incbil.c.
+ */
+
+/*
+Cephes Math Library Release 2.3: January,1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double incbetl ( long double, long double, long double );
+extern long double powl ( long double, long double );
+extern long double incbil ( long double, long double, long double );
+#else
+long double incbetl(), powl(), incbil();
+#endif
+
+long double nbdtrcl( k, n, p )
+int k, n;
+long double p;
+{
+long double dk, dn;
+
+if( (p < 0.0L) || (p > 1.0L) )
+ goto domerr;
+if( k < 0 )
+ {
+domerr:
+ mtherr( "nbdtrl", DOMAIN );
+ return( 0.0L );
+ }
+dn = n;
+if( k == 0 )
+ return( 1.0L - powl( p, dn ) );
+
+dk = k+1;
+return( incbetl( dk, dn, 1.0L - p ) );
+}
+
+
+
+long double nbdtrl( k, n, p )
+int k, n;
+long double p;
+{
+long double dk, dn;
+
+if( (p < 0.0L) || (p > 1.0L) )
+ goto domerr;
+if( k < 0 )
+ {
+domerr:
+ mtherr( "nbdtrl", DOMAIN );
+ return( 0.0L );
+ }
+dn = n;
+if( k == 0 )
+ return( powl( p, dn ) );
+
+dk = k+1;
+return( incbetl( dn, dk, p ) );
+}
+
+
+long double nbdtril( k, n, p )
+int k, n;
+long double p;
+{
+long double dk, dn, w;
+
+if( (p < 0.0L) || (p > 1.0L) )
+ goto domerr;
+if( k < 0 )
+ {
+domerr:
+ mtherr( "nbdtrl", DOMAIN );
+ return( 0.0L );
+ }
+dk = k+1;
+dn = n;
+w = incbil( dn, dk, p );
+return( w );
+}
diff --git a/libm/ldouble/ndtril.c b/libm/ldouble/ndtril.c
new file mode 100644
index 000000000..b1a15cedf
--- /dev/null
+++ b/libm/ldouble/ndtril.c
@@ -0,0 +1,416 @@
+/* ndtril.c
+ *
+ * Inverse of Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, ndtril();
+ *
+ * x = ndtril( y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the argument, x, for which the area under the
+ * Gaussian probability density function (integrated from
+ * minus infinity to x) is equal to y.
+ *
+ *
+ * For small arguments 0 < y < exp(-2), the program computes
+ * z = sqrt( -2 log(y) ); then the approximation is
+ * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z) .
+ * For larger arguments, x/sqrt(2 pi) = w + w^3 R(w^2)/S(w^2)) ,
+ * where w = y - 0.5 .
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * Arguments uniformly distributed:
+ * IEEE 0, 1 5000 7.8e-19 9.9e-20
+ * Arguments exponentially distributed:
+ * IEEE exp(-11355),-1 30000 1.7e-19 4.3e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ndtril domain x <= 0 -MAXNUML
+ * ndtril domain x >= 1 MAXNUML
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.3: January, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+extern long double MAXNUML;
+
+/* ndtri(y+0.5)/sqrt(2 pi) = y + y^3 R(y^2)
+ 0 <= y <= 3/8
+ Peak relative error 6.8e-21. */
+#if UNK
+/* sqrt(2pi) */
+static long double s2pi = 2.506628274631000502416E0L;
+static long double P0[8] = {
+ 8.779679420055069160496E-3L,
+-7.649544967784380691785E-1L,
+ 2.971493676711545292135E0L,
+-4.144980036933753828858E0L,
+ 2.765359913000830285937E0L,
+-9.570456817794268907847E-1L,
+ 1.659219375097958322098E-1L,
+-1.140013969885358273307E-2L,
+};
+static long double Q0[7] = {
+/* 1.000000000000000000000E0L, */
+-5.303846964603721860329E0L,
+ 9.908875375256718220854E0L,
+-9.031318655459381388888E0L,
+ 4.496118508523213950686E0L,
+-1.250016921424819972516E0L,
+ 1.823840725000038842075E-1L,
+-1.088633151006419263153E-2L,
+};
+#endif
+#if IBMPC
+static unsigned short s2p[] = {
+0x2cb3,0xb138,0x98ff,0xa06c,0x4000, XPD
+};
+#define s2pi *(long double *)s2p
+static short P0[] = {
+0xb006,0x9fc1,0xa4fe,0x8fd8,0x3ff8, XPD
+0x6f8a,0x976e,0x0ed2,0xc3d4,0xbffe, XPD
+0xf1f1,0x6fcc,0xf3d0,0xbe2c,0x4000, XPD
+0xccfb,0xa681,0xad2c,0x84a3,0xc001, XPD
+0x9a0d,0x0082,0xa825,0xb0fb,0x4000, XPD
+0x13d1,0x054a,0xf220,0xf500,0xbffe, XPD
+0xcee9,0x2c92,0x70bd,0xa9e7,0x3ffc, XPD
+0x5fee,0x4a42,0xa6cb,0xbac7,0xbff8, XPD
+};
+static short Q0[] = {
+/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
+0x841e,0xfec7,0x1d44,0xa9b9,0xc001, XPD
+0x97e6,0xcde0,0xc0e7,0x9e8a,0x4002, XPD
+0x66f9,0x8f3e,0x47fd,0x9080,0xc002, XPD
+0x212f,0x2185,0x33ec,0x8fe0,0x4001, XPD
+0x8e73,0x7bac,0x8df2,0xa000,0xbfff, XPD
+0xc143,0xcb94,0xe3ea,0xbac2,0x3ffc, XPD
+0x25d9,0xc8f3,0x9573,0xb25c,0xbff8, XPD
+};
+#endif
+#if MIEEE
+static unsigned long s2p[] = {
+0x40000000,0xa06c98ff,0xb1382cb3,
+};
+#define s2pi *(long double *)s2p
+static long P0[24] = {
+0x3ff80000,0x8fd8a4fe,0x9fc1b006,
+0xbffe0000,0xc3d40ed2,0x976e6f8a,
+0x40000000,0xbe2cf3d0,0x6fccf1f1,
+0xc0010000,0x84a3ad2c,0xa681ccfb,
+0x40000000,0xb0fba825,0x00829a0d,
+0xbffe0000,0xf500f220,0x054a13d1,
+0x3ffc0000,0xa9e770bd,0x2c92cee9,
+0xbff80000,0xbac7a6cb,0x4a425fee,
+};
+static long Q0[21] = {
+/* 0x3fff0000,0x80000000,0x00000000, */
+0xc0010000,0xa9b91d44,0xfec7841e,
+0x40020000,0x9e8ac0e7,0xcde097e6,
+0xc0020000,0x908047fd,0x8f3e66f9,
+0x40010000,0x8fe033ec,0x2185212f,
+0xbfff0000,0xa0008df2,0x7bac8e73,
+0x3ffc0000,0xbac2e3ea,0xcb94c143,
+0xbff80000,0xb25c9573,0xc8f325d9,
+};
+#endif
+
+/* Approximation for interval z = sqrt(-2 log y ) between 2 and 8
+ */
+/* ndtri(p) = z - ln(z)/z - 1/z P1(1/z)/Q1(1/z)
+ z = sqrt(-2 ln(p))
+ 2 <= z <= 8, i.e., y between exp(-2) = .135 and exp(-32) = 1.27e-14.
+ Peak relative error 5.3e-21 */
+#if UNK
+static long double P1[10] = {
+ 4.302849750435552180717E0L,
+ 4.360209451837096682600E1L,
+ 9.454613328844768318162E1L,
+ 9.336735653151873871756E1L,
+ 5.305046472191852391737E1L,
+ 1.775851836288460008093E1L,
+ 3.640308340137013109859E0L,
+ 3.691354900171224122390E-1L,
+ 1.403530274998072987187E-2L,
+ 1.377145111380960566197E-4L,
+};
+static long double Q1[9] = {
+/* 1.000000000000000000000E0L, */
+ 2.001425109170530136741E1L,
+ 7.079893963891488254284E1L,
+ 8.033277265194672063478E1L,
+ 5.034715121553662712917E1L,
+ 1.779820137342627204153E1L,
+ 3.845554944954699547539E0L,
+ 3.993627390181238962857E-1L,
+ 1.526870689522191191380E-2L,
+ 1.498700676286675466900E-4L,
+};
+#endif
+#if IBMPC
+static short P1[] = {
+0x6105,0xb71e,0xf1f5,0x89b0,0x4001, XPD
+0x461d,0x2604,0x8b77,0xae68,0x4004, XPD
+0x8b33,0x4a47,0x9ec8,0xbd17,0x4005, XPD
+0xa0b2,0xc1b0,0x1627,0xbabc,0x4005, XPD
+0x9901,0x28f7,0xad06,0xd433,0x4004, XPD
+0xddcb,0x5009,0x7213,0x8e11,0x4003, XPD
+0x2432,0x0fa6,0xcfd5,0xe8fa,0x4000, XPD
+0x3e24,0xd53c,0x53b2,0xbcff,0x3ffd, XPD
+0x4058,0x3d75,0x5393,0xe5f4,0x3ff8, XPD
+0x1789,0xf50a,0x7524,0x9067,0x3ff2, XPD
+};
+static short Q1[] = {
+/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
+0xd901,0x2673,0x2fad,0xa01d,0x4003, XPD
+0x24f5,0xc93c,0x0e9d,0x8d99,0x4005, XPD
+0x8cda,0x523a,0x612d,0xa0aa,0x4005, XPD
+0x602c,0xb5fc,0x7b9b,0xc963,0x4004, XPD
+0xac72,0xd3e7,0xb766,0x8e62,0x4003, XPD
+0x048e,0xe34c,0x927c,0xf61d,0x4000, XPD
+0x6d88,0xa5cc,0x45de,0xcc79,0x3ffd, XPD
+0xe6d1,0x199a,0x9931,0xfa29,0x3ff8, XPD
+0x4c7d,0x3675,0x70a0,0x9d26,0x3ff2, XPD
+};
+#endif
+#if MIEEE
+static long P1[30] = {
+0x40010000,0x89b0f1f5,0xb71e6105,
+0x40040000,0xae688b77,0x2604461d,
+0x40050000,0xbd179ec8,0x4a478b33,
+0x40050000,0xbabc1627,0xc1b0a0b2,
+0x40040000,0xd433ad06,0x28f79901,
+0x40030000,0x8e117213,0x5009ddcb,
+0x40000000,0xe8facfd5,0x0fa62432,
+0x3ffd0000,0xbcff53b2,0xd53c3e24,
+0x3ff80000,0xe5f45393,0x3d754058,
+0x3ff20000,0x90677524,0xf50a1789,
+};
+static long Q1[27] = {
+/* 0x3fff0000,0x80000000,0x00000000, */
+0x40030000,0xa01d2fad,0x2673d901,
+0x40050000,0x8d990e9d,0xc93c24f5,
+0x40050000,0xa0aa612d,0x523a8cda,
+0x40040000,0xc9637b9b,0xb5fc602c,
+0x40030000,0x8e62b766,0xd3e7ac72,
+0x40000000,0xf61d927c,0xe34c048e,
+0x3ffd0000,0xcc7945de,0xa5cc6d88,
+0x3ff80000,0xfa299931,0x199ae6d1,
+0x3ff20000,0x9d2670a0,0x36754c7d,
+};
+#endif
+
+/* ndtri(x) = z - ln(z)/z - 1/z P2(1/z)/Q2(1/z)
+ z = sqrt(-2 ln(y))
+ 8 <= z <= 32
+ i.e., y between exp(-32) = 1.27e-14 and exp(-512) = 4.38e-223
+ Peak relative error 1.0e-21 */
+#if UNK
+static long double P2[8] = {
+ 3.244525725312906932464E0L,
+ 6.856256488128415760904E0L,
+ 3.765479340423144482796E0L,
+ 1.240893301734538935324E0L,
+ 1.740282292791367834724E-1L,
+ 9.082834200993107441750E-3L,
+ 1.617870121822776093899E-4L,
+ 7.377405643054504178605E-7L,
+};
+static long double Q2[7] = {
+/* 1.000000000000000000000E0L, */
+ 6.021509481727510630722E0L,
+ 3.528463857156936773982E0L,
+ 1.289185315656302878699E0L,
+ 1.874290142615703609510E-1L,
+ 9.867655920899636109122E-3L,
+ 1.760452434084258930442E-4L,
+ 8.028288500688538331773E-7L,
+};
+#endif
+#if IBMPC
+static short P2[] = {
+0xafb1,0x4ff9,0x4f3a,0xcfa6,0x4000, XPD
+0xbd81,0xaffa,0x7401,0xdb66,0x4001, XPD
+0x3a32,0x3863,0x9d0f,0xf0fd,0x4000, XPD
+0x300e,0x633d,0x977a,0x9ed5,0x3fff, XPD
+0xea3a,0x56b6,0x74c5,0xb234,0x3ffc, XPD
+0x38c6,0x49d2,0x2af6,0x94d0,0x3ff8, XPD
+0xc85d,0xe17d,0x5ed1,0xa9a5,0x3ff2, XPD
+0x536c,0x808b,0x2542,0xc609,0x3fea, XPD
+};
+static short Q2[] = {
+/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
+0xaabd,0x125a,0x34a7,0xc0b0,0x4001, XPD
+0x0ded,0xe6da,0x5a11,0xe1d2,0x4000, XPD
+0xc742,0x9d16,0x0640,0xa504,0x3fff, XPD
+0xea1e,0x4cc2,0x643a,0xbfed,0x3ffc, XPD
+0x7a9b,0xfaff,0xf2dd,0xa1ab,0x3ff8, XPD
+0xfd90,0x4688,0xc902,0xb898,0x3ff2, XPD
+0xf003,0x032a,0xfa7e,0xd781,0x3fea, XPD
+};
+#endif
+#if MIEEE
+static long P2[24] = {
+0x40000000,0xcfa64f3a,0x4ff9afb1,
+0x40010000,0xdb667401,0xaffabd81,
+0x40000000,0xf0fd9d0f,0x38633a32,
+0x3fff0000,0x9ed5977a,0x633d300e,
+0x3ffc0000,0xb23474c5,0x56b6ea3a,
+0x3ff80000,0x94d02af6,0x49d238c6,
+0x3ff20000,0xa9a55ed1,0xe17dc85d,
+0x3fea0000,0xc6092542,0x808b536c,
+};
+static long Q2[21] = {
+/* 0x3fff0000,0x80000000,0x00000000, */
+0x40010000,0xc0b034a7,0x125aaabd,
+0x40000000,0xe1d25a11,0xe6da0ded,
+0x3fff0000,0xa5040640,0x9d16c742,
+0x3ffc0000,0xbfed643a,0x4cc2ea1e,
+0x3ff80000,0xa1abf2dd,0xfaff7a9b,
+0x3ff20000,0xb898c902,0x4688fd90,
+0x3fea0000,0xd781fa7e,0x032af003,
+};
+#endif
+
+/* ndtri(x) = z - ln(z)/z - 1/z P3(1/z)/Q3(1/z)
+ 32 < z < 2048/13
+ Peak relative error 1.4e-20 */
+#if UNK
+static long double P3[8] = {
+ 2.020331091302772535752E0L,
+ 2.133020661587413053144E0L,
+ 2.114822217898707063183E-1L,
+-6.500909615246067985872E-3L,
+-7.279315200737344309241E-4L,
+-1.275404675610280787619E-5L,
+-6.433966387613344714022E-8L,
+-7.772828380948163386917E-11L,
+};
+static long double Q3[7] = {
+/* 1.000000000000000000000E0L, */
+ 2.278210997153449199574E0L,
+ 2.345321838870438196534E-1L,
+-6.916708899719964982855E-3L,
+-7.908542088737858288849E-4L,
+-1.387652389480217178984E-5L,
+-7.001476867559193780666E-8L,
+-8.458494263787680376729E-11L,
+};
+#endif
+#if IBMPC
+static short P3[] = {
+0x87b2,0x0f31,0x1ac7,0x814d,0x4000, XPD
+0x491c,0xcd74,0x6917,0x8883,0x4000, XPD
+0x935e,0x1776,0xcba9,0xd88e,0x3ffc, XPD
+0xbafd,0x8abb,0x9518,0xd505,0xbff7, XPD
+0xc87e,0x2ed3,0xa84a,0xbed2,0xbff4, XPD
+0x0094,0xa402,0x36b5,0xd5fa,0xbfee, XPD
+0xbc53,0x0fc3,0x1ab2,0x8a2b,0xbfe7, XPD
+0x30b4,0x71c0,0x223d,0xaaed,0xbfdd, XPD
+};
+static short Q3[] = {
+/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
+0xdfc1,0x8a57,0x357f,0x91ce,0x4000, XPD
+0xcc4f,0x9e03,0x346e,0xf029,0x3ffc, XPD
+0x38b1,0x9788,0x8f42,0xe2a5,0xbff7, XPD
+0xb281,0x2117,0x53da,0xcf51,0xbff4, XPD
+0xf2ab,0x1d42,0x3760,0xe8cf,0xbfee, XPD
+0x741b,0xf14f,0x06b0,0x965b,0xbfe7, XPD
+0x37c2,0xa91f,0x16ea,0xba01,0xbfdd, XPD
+};
+#endif
+#if MIEEE
+static long P3[24] = {
+0x40000000,0x814d1ac7,0x0f3187b2,
+0x40000000,0x88836917,0xcd74491c,
+0x3ffc0000,0xd88ecba9,0x1776935e,
+0xbff70000,0xd5059518,0x8abbbafd,
+0xbff40000,0xbed2a84a,0x2ed3c87e,
+0xbfee0000,0xd5fa36b5,0xa4020094,
+0xbfe70000,0x8a2b1ab2,0x0fc3bc53,
+0xbfdd0000,0xaaed223d,0x71c030b4,
+};
+static long Q3[21] = {
+/* 0x3fff0000,0x80000000,0x00000000, */
+0x40000000,0x91ce357f,0x8a57dfc1,
+0x3ffc0000,0xf029346e,0x9e03cc4f,
+0xbff70000,0xe2a58f42,0x978838b1,
+0xbff40000,0xcf5153da,0x2117b281,
+0xbfee0000,0xe8cf3760,0x1d42f2ab,
+0xbfe70000,0x965b06b0,0xf14f741b,
+0xbfdd0000,0xba0116ea,0xa91f37c2,
+};
+#endif
+#ifdef ANSIPROT
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern long double logl ( long double );
+extern long double sqrtl ( long double );
+#else
+long double polevll(), p1evll(), logl(), sqrtl();
+#endif
+
+long double ndtril(y0)
+long double y0;
+{
+long double x, y, z, y2, x0, x1;
+int code;
+
+if( y0 <= 0.0L )
+ {
+ mtherr( "ndtril", DOMAIN );
+ return( -MAXNUML );
+ }
+if( y0 >= 1.0L )
+ {
+ mtherr( "ndtri", DOMAIN );
+ return( MAXNUML );
+ }
+code = 1;
+y = y0;
+if( y > (1.0L - 0.13533528323661269189L) ) /* 0.135... = exp(-2) */
+ {
+ y = 1.0L - y;
+ code = 0;
+ }
+
+if( y > 0.13533528323661269189L )
+ {
+ y = y - 0.5L;
+ y2 = y * y;
+ x = y + y * (y2 * polevll( y2, P0, 7 )/p1evll( y2, Q0, 7 ));
+ x = x * s2pi;
+ return(x);
+ }
+
+x = sqrtl( -2.0L * logl(y) );
+x0 = x - logl(x)/x;
+z = 1.0L/x;
+if( x < 8.0L )
+ x1 = z * polevll( z, P1, 9 )/p1evll( z, Q1, 9 );
+else if( x < 32.0L )
+ x1 = z * polevll( z, P2, 7 )/p1evll( z, Q2, 7 );
+else
+ x1 = z * polevll( z, P3, 7 )/p1evll( z, Q3, 7 );
+x = x0 - x1;
+if( code != 0 )
+ x = -x;
+return( x );
+}
diff --git a/libm/ldouble/ndtrl.c b/libm/ldouble/ndtrl.c
new file mode 100644
index 000000000..2c53314a5
--- /dev/null
+++ b/libm/ldouble/ndtrl.c
@@ -0,0 +1,473 @@
+/* ndtrl.c
+ *
+ * Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, ndtrl();
+ *
+ * y = ndtrl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the area under the Gaussian probability density
+ * function, integrated from minus infinity to x:
+ *
+ * x
+ * -
+ * 1 | | 2
+ * ndtr(x) = --------- | exp( - t /2 ) dt
+ * sqrt(2pi) | |
+ * -
+ * -inf.
+ *
+ * = ( 1 + erf(z) ) / 2
+ * = erfc(z) / 2
+ *
+ * where z = x/sqrt(2). Computation is via the functions
+ * erf and erfc.
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -13,0 30000 1.6e-17 2.9e-18
+ * IEEE -150.7,0 2000 1.6e-15 3.8e-16
+ * Accuracy is limited by error amplification in computing exp(-x^2).
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * erfcl underflow x^2 / 2 > MAXLOGL 0.0
+ *
+ */
+ /* erfl.c
+ *
+ * Error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, erfl();
+ *
+ * y = erfl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The integral is
+ *
+ * x
+ * -
+ * 2 | | 2
+ * erf(x) = -------- | exp( - t ) dt.
+ * sqrt(pi) | |
+ * -
+ * 0
+ *
+ * The magnitude of x is limited to about 106.56 for IEEE
+ * arithmetic; 1 or -1 is returned outside this range.
+ *
+ * For 0 <= |x| < 1, erf(x) = x * P6(x^2)/Q6(x^2); otherwise
+ * erf(x) = 1 - erfc(x).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,1 50000 2.0e-19 5.7e-20
+ *
+ */
+ /* erfcl.c
+ *
+ * Complementary error function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, erfcl();
+ *
+ * y = erfcl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ *
+ * 1 - erf(x) =
+ *
+ * inf.
+ * -
+ * 2 | | 2
+ * erfc(x) = -------- | exp( - t ) dt
+ * sqrt(pi) | |
+ * -
+ * x
+ *
+ *
+ * For small x, erfc(x) = 1 - erf(x); otherwise rational
+ * approximations are computed.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,13 20000 7.0e-18 1.8e-18
+ * IEEE 0,106.56 10000 4.4e-16 1.2e-16
+ * Accuracy is limited by error amplification in computing exp(-x^2).
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * erfcl underflow x^2 > MAXLOGL 0.0
+ *
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.3: January, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+extern long double MAXLOGL;
+static long double SQRTHL = 7.071067811865475244008e-1L;
+
+/* erfc(x) = exp(-x^2) P(1/x)/Q(1/x)
+ 1/8 <= 1/x <= 1
+ Peak relative error 5.8e-21 */
+#if UNK
+static long double P[10] = {
+ 1.130609921802431462353E9L,
+ 2.290171954844785638925E9L,
+ 2.295563412811856278515E9L,
+ 1.448651275892911637208E9L,
+ 6.234814405521647580919E8L,
+ 1.870095071120436715930E8L,
+ 3.833161455208142870198E7L,
+ 4.964439504376477951135E6L,
+ 3.198859502299390825278E5L,
+-9.085943037416544232472E-6L,
+};
+static long double Q[10] = {
+/* 1.000000000000000000000E0L, */
+ 1.130609910594093747762E9L,
+ 3.565928696567031388910E9L,
+ 5.188672873106859049556E9L,
+ 4.588018188918609726890E9L,
+ 2.729005809811924550999E9L,
+ 1.138778654945478547049E9L,
+ 3.358653716579278063988E8L,
+ 6.822450775590265689648E7L,
+ 8.799239977351261077610E6L,
+ 5.669830829076399819566E5L,
+};
+#endif
+#if IBMPC
+static short P[] = {
+0x4bf0,0x9ad8,0x7a03,0x86c7,0x401d, XPD
+0xdf23,0xd843,0x4032,0x8881,0x401e, XPD
+0xd025,0xcfd5,0x8494,0x88d3,0x401e, XPD
+0xb6d0,0xc92b,0x5417,0xacb1,0x401d, XPD
+0xada8,0x356a,0x4982,0x94a6,0x401c, XPD
+0x4e13,0xcaee,0x9e31,0xb258,0x401a, XPD
+0x5840,0x554d,0x37a3,0x9239,0x4018, XPD
+0x3b58,0x3da2,0xaf02,0x9780,0x4015, XPD
+0x0144,0x489e,0xbe68,0x9c31,0x4011, XPD
+0x333b,0xd9e6,0xd404,0x986f,0xbfee, XPD
+};
+static short Q[] = {
+/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
+0x0e43,0x302d,0x79ed,0x86c7,0x401d, XPD
+0xf817,0x9128,0xc0f8,0xd48b,0x401e, XPD
+0x8eae,0x8dad,0x6eb4,0x9aa2,0x401f, XPD
+0x00e7,0x7595,0xcd06,0x88bb,0x401f, XPD
+0x4991,0xcfda,0x52f1,0xa2a9,0x401e, XPD
+0xc39d,0xe415,0xc43d,0x87c0,0x401d, XPD
+0xa75d,0x436f,0x30dd,0xa027,0x401b, XPD
+0xc4cb,0x305a,0xbf78,0x8220,0x4019, XPD
+0x3708,0x33b1,0x07fa,0x8644,0x4016, XPD
+0x24fa,0x96f6,0x7153,0x8a6c,0x4012, XPD
+};
+#endif
+#if MIEEE
+static long P[30] = {
+0x401d0000,0x86c77a03,0x9ad84bf0,
+0x401e0000,0x88814032,0xd843df23,
+0x401e0000,0x88d38494,0xcfd5d025,
+0x401d0000,0xacb15417,0xc92bb6d0,
+0x401c0000,0x94a64982,0x356aada8,
+0x401a0000,0xb2589e31,0xcaee4e13,
+0x40180000,0x923937a3,0x554d5840,
+0x40150000,0x9780af02,0x3da23b58,
+0x40110000,0x9c31be68,0x489e0144,
+0xbfee0000,0x986fd404,0xd9e6333b,
+};
+static long Q[30] = {
+/* 0x3fff0000,0x80000000,0x00000000, */
+0x401d0000,0x86c779ed,0x302d0e43,
+0x401e0000,0xd48bc0f8,0x9128f817,
+0x401f0000,0x9aa26eb4,0x8dad8eae,
+0x401f0000,0x88bbcd06,0x759500e7,
+0x401e0000,0xa2a952f1,0xcfda4991,
+0x401d0000,0x87c0c43d,0xe415c39d,
+0x401b0000,0xa02730dd,0x436fa75d,
+0x40190000,0x8220bf78,0x305ac4cb,
+0x40160000,0x864407fa,0x33b13708,
+0x40120000,0x8a6c7153,0x96f624fa,
+};
+#endif
+
+/* erfc(x) = exp(-x^2) 1/x R(1/x^2) / S(1/x^2)
+ 1/128 <= 1/x < 1/8
+ Peak relative error 1.9e-21 */
+#if UNK
+static long double R[5] = {
+ 3.621349282255624026891E0L,
+ 7.173690522797138522298E0L,
+ 3.445028155383625172464E0L,
+ 5.537445669807799246891E-1L,
+ 2.697535671015506686136E-2L,
+};
+static long double S[5] = {
+/* 1.000000000000000000000E0L, */
+ 1.072884067182663823072E1L,
+ 1.533713447609627196926E1L,
+ 6.572990478128949439509E0L,
+ 1.005392977603322982436E0L,
+ 4.781257488046430019872E-2L,
+};
+#endif
+#if IBMPC
+static short R[] = {
+0x260a,0xab95,0x2fc7,0xe7c4,0x4000, XPD
+0x4761,0x613e,0xdf6d,0xe58e,0x4001, XPD
+0x0615,0x4b00,0x575f,0xdc7b,0x4000, XPD
+0x521d,0x8527,0x3435,0x8dc2,0x3ffe, XPD
+0x22cf,0xc711,0x6c5b,0xdcfb,0x3ff9, XPD
+};
+static short S[] = {
+/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
+0x5de6,0x17d7,0x54d6,0xaba9,0x4002, XPD
+0x55d5,0xd300,0xe71e,0xf564,0x4002, XPD
+0xb611,0x8f76,0xf020,0xd255,0x4001, XPD
+0x3684,0x3798,0xb793,0x80b0,0x3fff, XPD
+0xf5af,0x2fb2,0x1e57,0xc3d7,0x3ffa, XPD
+};
+#endif
+#if MIEEE
+static long R[15] = {
+0x40000000,0xe7c42fc7,0xab95260a,
+0x40010000,0xe58edf6d,0x613e4761,
+0x40000000,0xdc7b575f,0x4b000615,
+0x3ffe0000,0x8dc23435,0x8527521d,
+0x3ff90000,0xdcfb6c5b,0xc71122cf,
+};
+static long S[15] = {
+/* 0x3fff0000,0x80000000,0x00000000, */
+0x40020000,0xaba954d6,0x17d75de6,
+0x40020000,0xf564e71e,0xd30055d5,
+0x40010000,0xd255f020,0x8f76b611,
+0x3fff0000,0x80b0b793,0x37983684,
+0x3ffa0000,0xc3d71e57,0x2fb2f5af,
+};
+#endif
+
+/* erf(x) = x P(x^2)/Q(x^2)
+ 0 <= x <= 1
+ Peak relative error 7.6e-23 */
+#if UNK
+static long double T[7] = {
+ 1.097496774521124996496E-1L,
+ 5.402980370004774841217E0L,
+ 2.871822526820825849235E2L,
+ 2.677472796799053019985E3L,
+ 4.825977363071025440855E4L,
+ 1.549905740900882313773E5L,
+ 1.104385395713178565288E6L,
+};
+static long double U[6] = {
+/* 1.000000000000000000000E0L, */
+ 4.525777638142203713736E1L,
+ 9.715333124857259246107E2L,
+ 1.245905812306219011252E4L,
+ 9.942956272177178491525E4L,
+ 4.636021778692893773576E5L,
+ 9.787360737578177599571E5L,
+};
+#endif
+#if IBMPC
+static short T[] = {
+0xfd7a,0x3a1a,0x705b,0xe0c4,0x3ffb, XPD
+0x3128,0xc337,0x3716,0xace5,0x4001, XPD
+0x9517,0x4e93,0x540e,0x8f97,0x4007, XPD
+0x6118,0x6059,0x9093,0xa757,0x400a, XPD
+0xb954,0xa987,0xc60c,0xbc83,0x400e, XPD
+0x7a56,0xe45a,0xa4bd,0x975b,0x4010, XPD
+0xc446,0x6bab,0x0b2a,0x86d0,0x4013, XPD
+};
+static short U[] = {
+/* 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD */
+0x3453,0x1f8e,0xf688,0xb507,0x4004, XPD
+0x71ac,0xb12f,0x21ca,0xf2e2,0x4008, XPD
+0xffe8,0x9cac,0x3b84,0xc2ac,0x400c, XPD
+0x481d,0x445b,0xc807,0xc232,0x400f, XPD
+0x9ad5,0x1aef,0x45b1,0xe25e,0x4011, XPD
+0x71a7,0x1cad,0x012e,0xeef3,0x4012, XPD
+};
+#endif
+#if MIEEE
+static long T[21] = {
+0x3ffb0000,0xe0c4705b,0x3a1afd7a,
+0x40010000,0xace53716,0xc3373128,
+0x40070000,0x8f97540e,0x4e939517,
+0x400a0000,0xa7579093,0x60596118,
+0x400e0000,0xbc83c60c,0xa987b954,
+0x40100000,0x975ba4bd,0xe45a7a56,
+0x40130000,0x86d00b2a,0x6babc446,
+};
+static long U[18] = {
+/* 0x3fff0000,0x80000000,0x00000000, */
+0x40040000,0xb507f688,0x1f8e3453,
+0x40080000,0xf2e221ca,0xb12f71ac,
+0x400c0000,0xc2ac3b84,0x9cacffe8,
+0x400f0000,0xc232c807,0x445b481d,
+0x40110000,0xe25e45b1,0x1aef9ad5,
+0x40120000,0xeef3012e,0x1cad71a7,
+};
+#endif
+#ifdef ANSIPROT
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern long double expl ( long double );
+extern long double logl ( long double );
+extern long double erfl ( long double );
+extern long double erfcl ( long double );
+extern long double fabsl ( long double );
+#else
+long double polevll(), p1evll(), expl(), logl(), erfl(), erfcl(), fabsl();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+
+long double ndtrl(a)
+long double a;
+{
+long double x, y, z;
+
+x = a * SQRTHL;
+z = fabsl(x);
+
+if( z < SQRTHL )
+ y = 0.5L + 0.5L * erfl(x);
+
+else
+ {
+ y = 0.5L * erfcl(z);
+
+ if( x > 0.0L )
+ y = 1.0L - y;
+ }
+
+return(y);
+}
+
+
+long double erfcl(a)
+long double a;
+{
+long double p,q,x,y,z;
+
+#ifdef INFINITIES
+if( a == INFINITYL )
+ return(0.0L);
+if( a == -INFINITYL )
+ return(2.0L);
+#endif
+if( a < 0.0L )
+ x = -a;
+else
+ x = a;
+
+if( x < 1.0L )
+ return( 1.0L - erfl(a) );
+
+z = -a * a;
+
+if( z < -MAXLOGL )
+ {
+under:
+ mtherr( "erfcl", UNDERFLOW );
+ if( a < 0 )
+ return( 2.0L );
+ else
+ return( 0.0L );
+ }
+
+z = expl(z);
+y = 1.0L/x;
+
+if( x < 8.0L )
+ {
+ p = polevll( y, P, 9 );
+ q = p1evll( y, Q, 10 );
+ }
+else
+ {
+ q = y * y;
+ p = y * polevll( q, R, 4 );
+ q = p1evll( q, S, 5 );
+ }
+y = (z * p)/q;
+
+if( a < 0.0L )
+ y = 2.0L - y;
+
+if( y == 0.0L )
+ goto under;
+
+return(y);
+}
+
+
+
+long double erfl(x)
+long double x;
+{
+long double y, z;
+
+#if MINUSZERO
+if( x == 0.0L )
+ return(x);
+#endif
+#ifdef INFINITIES
+if( x == -INFINITYL )
+ return(-1.0L);
+if( x == INFINITYL )
+ return(1.0L);
+#endif
+if( fabsl(x) > 1.0L )
+ return( 1.0L - erfcl(x) );
+
+z = x * x;
+y = x * polevll( z, T, 6 ) / p1evll( z, U, 6 );
+return( y );
+}
diff --git a/libm/ldouble/pdtrl.c b/libm/ldouble/pdtrl.c
new file mode 100644
index 000000000..861b1d9ae
--- /dev/null
+++ b/libm/ldouble/pdtrl.c
@@ -0,0 +1,184 @@
+/* pdtrl.c
+ *
+ * Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * long double m, y, pdtrl();
+ *
+ * y = pdtrl( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the first k terms of the Poisson
+ * distribution:
+ *
+ * k j
+ * -- -m m
+ * > e --
+ * -- j!
+ * j=0
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the relation
+ *
+ * y = pdtr( k, m ) = igamc( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igamc().
+ *
+ */
+ /* pdtrcl()
+ *
+ * Complemented poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * long double m, y, pdtrcl();
+ *
+ * y = pdtrcl( k, m );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the sum of the terms k+1 to infinity of the Poisson
+ * distribution:
+ *
+ * inf. j
+ * -- -m m
+ * > e --
+ * -- j!
+ * j=k+1
+ *
+ * The terms are not summed directly; instead the incomplete
+ * gamma integral is employed, according to the formula
+ *
+ * y = pdtrc( k, m ) = igam( k+1, m ).
+ *
+ * The arguments must both be positive.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igam.c.
+ *
+ */
+ /* pdtril()
+ *
+ * Inverse Poisson distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int k;
+ * long double m, y, pdtrl();
+ *
+ * m = pdtril( k, y );
+ *
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Finds the Poisson variable x such that the integral
+ * from 0 to x of the Poisson density is equal to the
+ * given probability y.
+ *
+ * This is accomplished using the inverse gamma integral
+ * function and the relation
+ *
+ * m = igami( k+1, y ).
+ *
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * See igami.c.
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * pdtri domain y < 0 or y >= 1 0.0
+ * k < 0
+ *
+ */
+
+/*
+Cephes Math Library Release 2.3: March, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+#ifdef ANSIPROT
+extern long double igaml ( long double, long double );
+extern long double igamcl ( long double, long double );
+extern long double igamil ( long double, long double );
+#else
+long double igaml(), igamcl(), igamil();
+#endif
+
+long double pdtrcl( k, m )
+int k;
+long double m;
+{
+long double v;
+
+if( (k < 0) || (m <= 0.0L) )
+ {
+ mtherr( "pdtrcl", DOMAIN );
+ return( 0.0L );
+ }
+v = k+1;
+return( igaml( v, m ) );
+}
+
+
+
+long double pdtrl( k, m )
+int k;
+long double m;
+{
+long double v;
+
+if( (k < 0) || (m <= 0.0L) )
+ {
+ mtherr( "pdtrl", DOMAIN );
+ return( 0.0L );
+ }
+v = k+1;
+return( igamcl( v, m ) );
+}
+
+
+long double pdtril( k, y )
+int k;
+long double y;
+{
+long double v;
+
+if( (k < 0) || (y < 0.0L) || (y >= 1.0L) )
+ {
+ mtherr( "pdtril", DOMAIN );
+ return( 0.0L );
+ }
+v = k+1;
+v = igamil( v, y );
+return( v );
+}
diff --git a/libm/ldouble/polevll.c b/libm/ldouble/polevll.c
new file mode 100644
index 000000000..ce37c6d9d
--- /dev/null
+++ b/libm/ldouble/polevll.c
@@ -0,0 +1,182 @@
+/* polevll.c
+ * p1evll.c
+ *
+ * Evaluate polynomial
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * int N;
+ * long double x, y, coef[N+1], polevl[];
+ *
+ * y = polevll( x, coef, N );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Evaluates polynomial of degree N:
+ *
+ * 2 N
+ * y = C + C x + C x +...+ C x
+ * 0 1 2 N
+ *
+ * Coefficients are stored in reverse order:
+ *
+ * coef[0] = C , ..., coef[N] = C .
+ * N 0
+ *
+ * The function p1evll() assumes that coef[N] = 1.0 and is
+ * omitted from the array. Its calling arguments are
+ * otherwise the same as polevll().
+ *
+ * This module also contains the following globally declared constants:
+ * MAXNUML = 1.189731495357231765021263853E4932L;
+ * MACHEPL = 5.42101086242752217003726400434970855712890625E-20L;
+ * MAXLOGL = 1.1356523406294143949492E4L;
+ * MINLOGL = -1.1355137111933024058873E4L;
+ * LOGE2L = 6.9314718055994530941723E-1L;
+ * LOG2EL = 1.4426950408889634073599E0L;
+ * PIL = 3.1415926535897932384626L;
+ * PIO2L = 1.5707963267948966192313L;
+ * PIO4L = 7.8539816339744830961566E-1L;
+ *
+ * SPEED:
+ *
+ * In the interest of speed, there are no checks for out
+ * of bounds arithmetic. This routine is used by most of
+ * the functions in the library. Depending on available
+ * equipment features, the user may wish to rewrite the
+ * program in microcode or assembly language.
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.2: July, 1992
+Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+#include <math.h>
+
+#if UNK
+/* almost 2^16384 */
+long double MAXNUML = 1.189731495357231765021263853E4932L;
+/* 2^-64 */
+long double MACHEPL = 5.42101086242752217003726400434970855712890625E-20L;
+/* log( MAXNUML ) */
+long double MAXLOGL = 1.1356523406294143949492E4L;
+#ifdef DENORMAL
+/* log(smallest denormal number = 2^-16446) */
+long double MINLOGL = -1.13994985314888605586758E4L;
+#else
+/* log( underflow threshold = 2^(-16382) ) */
+long double MINLOGL = -1.1355137111933024058873E4L;
+#endif
+long double LOGE2L = 6.9314718055994530941723E-1L;
+long double LOG2EL = 1.4426950408889634073599E0L;
+long double PIL = 3.1415926535897932384626L;
+long double PIO2L = 1.5707963267948966192313L;
+long double PIO4L = 7.8539816339744830961566E-1L;
+#ifdef INFINITIES
+long double NANL = 0.0L / 0.0L;
+long double INFINITYL = 1.0L / 0.0L;
+#else
+long double INFINITYL = 1.189731495357231765021263853E4932L;
+long double NANL = 0.0L;
+#endif
+#endif
+#if IBMPC
+short MAXNUML[] = {0xffff,0xffff,0xffff,0xffff,0x7ffe, XPD};
+short MAXLOGL[] = {0x79ab,0xd1cf,0x17f7,0xb172,0x400c, XPD};
+#ifdef INFINITIES
+short INFINITYL[] = {0,0,0,0x8000,0x7fff, XPD};
+short NANL[] = {0,0,0,0xc000,0x7fff, XPD};
+#else
+short INFINITYL[] = {0xffff,0xffff,0xffff,0xffff,0x7ffe, XPD};
+long double NANL = 0.0L;
+#endif
+#ifdef DENORMAL
+short MINLOGL[] = {0xbaaa,0x09e2,0xfe7f,0xb21d,0xc00c, XPD};
+#else
+short MINLOGL[] = {0xeb2f,0x1210,0x8c67,0xb16c,0xc00c, XPD};
+#endif
+short MACHEPL[] = {0x0000,0x0000,0x0000,0x8000,0x3fbf, XPD};
+short LOGE2L[] = {0x79ac,0xd1cf,0x17f7,0xb172,0x3ffe, XPD};
+short LOG2EL[] = {0xf0bc,0x5c17,0x3b29,0xb8aa,0x3fff, XPD};
+short PIL[] = {0xc235,0x2168,0xdaa2,0xc90f,0x4000, XPD};
+short PIO2L[] = {0xc235,0x2168,0xdaa2,0xc90f,0x3fff, XPD};
+short PIO4L[] = {0xc235,0x2168,0xdaa2,0xc90f,0x3ffe, XPD};
+#endif
+#if MIEEE
+long MAXNUML[] = {0x7ffe0000,0xffffffff,0xffffffff};
+long MAXLOGL[] = {0x400c0000,0xb17217f7,0xd1cf79ab};
+#ifdef INFINITIES
+long INFINITY[] = {0x7fff0000,0x80000000,0x00000000};
+long NANL[] = {0x7fff0000,0xffffffff,0xffffffff};
+#else
+long INFINITYL[] = {0x7ffe0000,0xffffffff,0xffffffff};
+long double NANL = 0.0L;
+#endif
+#ifdef DENORMAL
+long MINLOGL[] = {0xc00c0000,0xb21dfe7f,0x09e2baaa};
+#else
+long MINLOGL[] = {0xc00c0000,0xb16c8c67,0x1210eb2f};
+#endif
+long MACHEPL[] = {0x3fbf0000,0x80000000,0x00000000};
+long LOGE2L[] = {0x3ffe0000,0xb17217f7,0xd1cf79ac};
+long LOG2EL[] = {0x3fff0000,0xb8aa3b29,0x5c17f0bc};
+long PIL[] = {0x40000000,0xc90fdaa2,0x2168c235};
+long PIO2L[] = {0x3fff0000,0xc90fdaa2,0x2168c235};
+long PIO4L[] = {0x3ffe0000,0xc90fdaa2,0x2168c235};
+#endif
+
+#ifdef MINUSZERO
+long double NEGZEROL = -0.0L;
+#else
+long double NEGZEROL = 0.0L;
+#endif
+
+/* Polynomial evaluator:
+ * P[0] x^n + P[1] x^(n-1) + ... + P[n]
+ */
+long double polevll( x, p, n )
+long double x;
+void *p;
+int n;
+{
+register long double y;
+register long double *P = (long double *)p;
+
+y = *P++;
+do
+ {
+ y = y * x + *P++;
+ }
+while( --n );
+return(y);
+}
+
+
+
+/* Polynomial evaluator:
+ * x^n + P[0] x^(n-1) + P[1] x^(n-2) + ... + P[n]
+ */
+long double p1evll( x, p, n )
+long double x;
+void *p;
+int n;
+{
+register long double y;
+register long double *P = (long double *)p;
+
+n -= 1;
+y = x + *P++;
+do
+ {
+ y = y * x + *P++;
+ }
+while( --n );
+return( y );
+}
diff --git a/libm/ldouble/powil.c b/libm/ldouble/powil.c
new file mode 100644
index 000000000..d36c7854e
--- /dev/null
+++ b/libm/ldouble/powil.c
@@ -0,0 +1,164 @@
+/* powil.c
+ *
+ * Real raised to integer power, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, powil();
+ * int n;
+ *
+ * y = powil( x, n );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns argument x raised to the nth power.
+ * The routine efficiently decomposes n as a sum of powers of
+ * two. The desired power is a product of two-to-the-kth
+ * powers of x. Thus to compute the 32767 power of x requires
+ * 28 multiplications instead of 32767 multiplications.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error:
+ * arithmetic x domain n domain # trials peak rms
+ * IEEE .001,1000 -1022,1023 50000 4.3e-17 7.8e-18
+ * IEEE 1,2 -1022,1023 20000 3.9e-17 7.6e-18
+ * IEEE .99,1.01 0,8700 10000 3.6e-16 7.2e-17
+ *
+ * Returns MAXNUM on overflow, zero on underflow.
+ *
+ */
+
+/* powil.c */
+
+/*
+Cephes Math Library Release 2.2: December, 1990
+Copyright 1984, 1990 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+extern long double MAXNUML, MAXLOGL, MINLOGL;
+extern long double LOGE2L;
+#ifdef ANSIPROT
+extern long double frexpl ( long double, int * );
+#else
+long double frexpl();
+#endif
+
+long double powil( x, nn )
+long double x;
+int nn;
+{
+long double w, y;
+long double s;
+int n, e, sign, asign, lx;
+
+if( x == 0.0L )
+ {
+ if( nn == 0 )
+ return( 1.0L );
+ else if( nn < 0 )
+ return( MAXNUML );
+ else
+ return( 0.0L );
+ }
+
+if( nn == 0 )
+ return( 1.0L );
+
+
+if( x < 0.0L )
+ {
+ asign = -1;
+ x = -x;
+ }
+else
+ asign = 0;
+
+
+if( nn < 0 )
+ {
+ sign = -1;
+ n = -nn;
+ }
+else
+ {
+ sign = 1;
+ n = nn;
+ }
+
+/* Overflow detection */
+
+/* Calculate approximate logarithm of answer */
+s = x;
+s = frexpl( s, &lx );
+e = (lx - 1)*n;
+if( (e == 0) || (e > 64) || (e < -64) )
+ {
+ s = (s - 7.0710678118654752e-1L) / (s + 7.0710678118654752e-1L);
+ s = (2.9142135623730950L * s - 0.5L + lx) * nn * LOGE2L;
+ }
+else
+ {
+ s = LOGE2L * e;
+ }
+
+if( s > MAXLOGL )
+ {
+ mtherr( "powil", OVERFLOW );
+ y = MAXNUML;
+ goto done;
+ }
+
+if( s < MINLOGL )
+ {
+ mtherr( "powil", UNDERFLOW );
+ return(0.0L);
+ }
+/* Handle tiny denormal answer, but with less accuracy
+ * since roundoff error in 1.0/x will be amplified.
+ * The precise demarcation should be the gradual underflow threshold.
+ */
+if( s < (-MAXLOGL+2.0L) )
+ {
+ x = 1.0L/x;
+ sign = -sign;
+ }
+
+/* First bit of the power */
+if( n & 1 )
+ y = x;
+
+else
+ {
+ y = 1.0L;
+ asign = 0;
+ }
+
+w = x;
+n >>= 1;
+while( n )
+ {
+ w = w * w; /* arg to the 2-to-the-kth power */
+ if( n & 1 ) /* if that bit is set, then include in product */
+ y *= w;
+ n >>= 1;
+ }
+
+
+done:
+
+if( asign )
+ y = -y; /* odd power of negative number */
+if( sign < 0 )
+ y = 1.0L/y;
+return(y);
+}
diff --git a/libm/ldouble/powl.c b/libm/ldouble/powl.c
new file mode 100644
index 000000000..bad380696
--- /dev/null
+++ b/libm/ldouble/powl.c
@@ -0,0 +1,739 @@
+/* powl.c
+ *
+ * Power function, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, z, powl();
+ *
+ * z = powl( x, y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes x raised to the yth power. Analytically,
+ *
+ * x**y = exp( y log(x) ).
+ *
+ * Following Cody and Waite, this program uses a lookup table
+ * of 2**-i/32 and pseudo extended precision arithmetic to
+ * obtain several extra bits of accuracy in both the logarithm
+ * and the exponential.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * The relative error of pow(x,y) can be estimated
+ * by y dl ln(2), where dl is the absolute error of
+ * the internally computed base 2 logarithm. At the ends
+ * of the approximation interval the logarithm equal 1/32
+ * and its relative error is about 1 lsb = 1.1e-19. Hence
+ * the predicted relative error in the result is 2.3e-21 y .
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ *
+ * IEEE +-1000 40000 2.8e-18 3.7e-19
+ * .001 < x < 1000, with log(x) uniformly distributed.
+ * -1000 < y < 1000, y uniformly distributed.
+ *
+ * IEEE 0,8700 60000 6.5e-18 1.0e-18
+ * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * pow overflow x**y > MAXNUM INFINITY
+ * pow underflow x**y < 1/MAXNUM 0.0
+ * pow domain x<0 and y noninteger 0.0
+ *
+ */
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright 1984, 1991, 1998 by Stephen L. Moshier
+*/
+
+
+#include <math.h>
+
+static char fname[] = {"powl"};
+
+/* Table size */
+#define NXT 32
+/* log2(Table size) */
+#define LNXT 5
+
+#ifdef UNK
+/* log(1+x) = x - .5x^2 + x^3 * P(z)/Q(z)
+ * on the domain 2^(-1/32) - 1 <= x <= 2^(1/32) - 1
+ */
+static long double P[] = {
+ 8.3319510773868690346226E-4L,
+ 4.9000050881978028599627E-1L,
+ 1.7500123722550302671919E0L,
+ 1.4000100839971580279335E0L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0L,*/
+ 5.2500282295834889175431E0L,
+ 8.4000598057587009834666E0L,
+ 4.2000302519914740834728E0L,
+};
+/* A[i] = 2^(-i/32), rounded to IEEE long double precision.
+ * If i is even, A[i] + B[i/2] gives additional accuracy.
+ */
+static long double A[33] = {
+ 1.0000000000000000000000E0L,
+ 9.7857206208770013448287E-1L,
+ 9.5760328069857364691013E-1L,
+ 9.3708381705514995065011E-1L,
+ 9.1700404320467123175367E-1L,
+ 8.9735453750155359320742E-1L,
+ 8.7812608018664974155474E-1L,
+ 8.5930964906123895780165E-1L,
+ 8.4089641525371454301892E-1L,
+ 8.2287773907698242225554E-1L,
+ 8.0524516597462715409607E-1L,
+ 7.8799042255394324325455E-1L,
+ 7.7110541270397041179298E-1L,
+ 7.5458221379671136985669E-1L,
+ 7.3841307296974965571198E-1L,
+ 7.2259040348852331001267E-1L,
+ 7.0710678118654752438189E-1L,
+ 6.9195494098191597746178E-1L,
+ 6.7712777346844636413344E-1L,
+ 6.6261832157987064729696E-1L,
+ 6.4841977732550483296079E-1L,
+ 6.3452547859586661129850E-1L,
+ 6.2092890603674202431705E-1L,
+ 6.0762367999023443907803E-1L,
+ 5.9460355750136053334378E-1L,
+ 5.8186242938878875689693E-1L,
+ 5.6939431737834582684856E-1L,
+ 5.5719337129794626814472E-1L,
+ 5.4525386633262882960438E-1L,
+ 5.3357020033841180906486E-1L,
+ 5.2213689121370692017331E-1L,
+ 5.1094857432705833910408E-1L,
+ 5.0000000000000000000000E-1L,
+};
+static long double B[17] = {
+ 0.0000000000000000000000E0L,
+ 2.6176170809902549338711E-20L,
+-1.0126791927256478897086E-20L,
+ 1.3438228172316276937655E-21L,
+ 1.2207982955417546912101E-20L,
+-6.3084814358060867200133E-21L,
+ 1.3164426894366316434230E-20L,
+-1.8527916071632873716786E-20L,
+ 1.8950325588932570796551E-20L,
+ 1.5564775779538780478155E-20L,
+ 6.0859793637556860974380E-21L,
+-2.0208749253662532228949E-20L,
+ 1.4966292219224761844552E-20L,
+ 3.3540909728056476875639E-21L,
+-8.6987564101742849540743E-22L,
+-1.2327176863327626135542E-20L,
+ 0.0000000000000000000000E0L,
+};
+
+/* 2^x = 1 + x P(x),
+ * on the interval -1/32 <= x <= 0
+ */
+static long double R[] = {
+ 1.5089970579127659901157E-5L,
+ 1.5402715328927013076125E-4L,
+ 1.3333556028915671091390E-3L,
+ 9.6181291046036762031786E-3L,
+ 5.5504108664798463044015E-2L,
+ 2.4022650695910062854352E-1L,
+ 6.9314718055994530931447E-1L,
+};
+
+#define douba(k) A[k]
+#define doubb(k) B[k]
+#define MEXP (NXT*16384.0L)
+/* The following if denormal numbers are supported, else -MEXP: */
+#ifdef DENORMAL
+#define MNEXP (-NXT*(16384.0L+64.0L))
+#else
+#define MNEXP (-NXT*16384.0L)
+#endif
+/* log2(e) - 1 */
+#define LOG2EA 0.44269504088896340735992L
+#endif
+
+
+#ifdef IBMPC
+static short P[] = {
+0xb804,0xa8b7,0xc6f4,0xda6a,0x3ff4, XPD
+0x7de9,0xcf02,0x58c0,0xfae1,0x3ffd, XPD
+0x405a,0x3722,0x67c9,0xe000,0x3fff, XPD
+0xcd99,0x6b43,0x87ca,0xb333,0x3fff, XPD
+};
+static short Q[] = {
+/* 0x0000,0x0000,0x0000,0x8000,0x3fff, */
+0x6307,0xa469,0x3b33,0xa800,0x4001, XPD
+0xfec2,0x62d7,0xa51c,0x8666,0x4002, XPD
+0xda32,0xd072,0xa5d7,0x8666,0x4001, XPD
+};
+static short A[] = {
+0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
+0x033a,0x722a,0xb2db,0xfa83,0x3ffe, XPD
+0xcc2c,0x2486,0x7d15,0xf525,0x3ffe, XPD
+0xf5cb,0xdcda,0xb99b,0xefe4,0x3ffe, XPD
+0x392f,0xdd24,0xc6e7,0xeac0,0x3ffe, XPD
+0x48a8,0x7c83,0x06e7,0xe5b9,0x3ffe, XPD
+0xe111,0x2a94,0xdeec,0xe0cc,0x3ffe, XPD
+0x3755,0xdaf2,0xb797,0xdbfb,0x3ffe, XPD
+0x6af4,0xd69d,0xfcca,0xd744,0x3ffe, XPD
+0xe45a,0xf12a,0x1d91,0xd2a8,0x3ffe, XPD
+0x80e4,0x1f84,0x8c15,0xce24,0x3ffe, XPD
+0x27a3,0x6e2f,0xbd86,0xc9b9,0x3ffe, XPD
+0xdadd,0x5506,0x2a11,0xc567,0x3ffe, XPD
+0x9456,0x6670,0x4cca,0xc12c,0x3ffe, XPD
+0x36bf,0x580c,0xa39f,0xbd08,0x3ffe, XPD
+0x9ee9,0x62fb,0xaf47,0xb8fb,0x3ffe, XPD
+0x6484,0xf9de,0xf333,0xb504,0x3ffe, XPD
+0x2590,0xd2ac,0xf581,0xb123,0x3ffe, XPD
+0x4ac6,0x42a1,0x3eea,0xad58,0x3ffe, XPD
+0x0ef8,0xea7c,0x5ab4,0xa9a1,0x3ffe, XPD
+0x38ea,0xb151,0xd6a9,0xa5fe,0x3ffe, XPD
+0x6819,0x0c49,0x4303,0xa270,0x3ffe, XPD
+0x11ae,0x91a1,0x3260,0x9ef5,0x3ffe, XPD
+0x5539,0xd54e,0x39b9,0x9b8d,0x3ffe, XPD
+0xa96f,0x8db8,0xf051,0x9837,0x3ffe, XPD
+0x0961,0xfef7,0xefa8,0x94f4,0x3ffe, XPD
+0xc336,0xab11,0xd373,0x91c3,0x3ffe, XPD
+0x53c0,0x45cd,0x398b,0x8ea4,0x3ffe, XPD
+0xd6e7,0xea8b,0xc1e3,0x8b95,0x3ffe, XPD
+0x8527,0x92da,0x0e80,0x8898,0x3ffe, XPD
+0x7b15,0xcc48,0xc367,0x85aa,0x3ffe, XPD
+0xa1d7,0xac2b,0x8698,0x82cd,0x3ffe, XPD
+0x0000,0x0000,0x0000,0x8000,0x3ffe, XPD
+};
+static short B[] = {
+0x0000,0x0000,0x0000,0x0000,0x0000, XPD
+0x1f87,0xdb30,0x18f5,0xf73a,0x3fbd, XPD
+0xac15,0x3e46,0x2932,0xbf4a,0xbfbc, XPD
+0x7944,0xba66,0xa091,0xcb12,0x3fb9, XPD
+0xff78,0x40b4,0x2ee6,0xe69a,0x3fbc, XPD
+0xc895,0x5069,0xe383,0xee53,0xbfbb, XPD
+0x7cde,0x9376,0x4325,0xf8ab,0x3fbc, XPD
+0xa10c,0x25e0,0xc093,0xaefd,0xbfbd, XPD
+0x7d3e,0xea95,0x1366,0xb2fb,0x3fbd, XPD
+0x5d89,0xeb34,0x5191,0x9301,0x3fbd, XPD
+0x80d9,0xb883,0xfb10,0xe5eb,0x3fbb, XPD
+0x045d,0x288c,0xc1ec,0xbedd,0xbfbd, XPD
+0xeded,0x5c85,0x4630,0x8d5a,0x3fbd, XPD
+0x9d82,0xe5ac,0x8e0a,0xfd6d,0x3fba, XPD
+0x6dfd,0xeb58,0xaf14,0x8373,0xbfb9, XPD
+0xf938,0x7aac,0x91cf,0xe8da,0xbfbc, XPD
+0x0000,0x0000,0x0000,0x0000,0x0000, XPD
+};
+static short R[] = {
+0xa69b,0x530e,0xee1d,0xfd2a,0x3fee, XPD
+0xc746,0x8e7e,0x5960,0xa182,0x3ff2, XPD
+0x63b6,0xadda,0xfd6a,0xaec3,0x3ff5, XPD
+0xc104,0xfd99,0x5b7c,0x9d95,0x3ff8, XPD
+0xe05e,0x249d,0x46b8,0xe358,0x3ffa, XPD
+0x5d1d,0x162c,0xeffc,0xf5fd,0x3ffc, XPD
+0x79aa,0xd1cf,0x17f7,0xb172,0x3ffe, XPD
+};
+
+/* 10 byte sizes versus 12 byte */
+#define douba(k) (*(long double *)(&A[(sizeof( long double )/2)*(k)]))
+#define doubb(k) (*(long double *)(&B[(sizeof( long double )/2)*(k)]))
+#define MEXP (NXT*16384.0L)
+#ifdef DENORMAL
+#define MNEXP (-NXT*(16384.0L+64.0L))
+#else
+#define MNEXP (-NXT*16384.0L)
+#endif
+static short L[] = {0xc2ef,0x705f,0xeca5,0xe2a8,0x3ffd, XPD};
+#define LOG2EA (*(long double *)(&L[0]))
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0x3ff40000,0xda6ac6f4,0xa8b7b804,
+0x3ffd0000,0xfae158c0,0xcf027de9,
+0x3fff0000,0xe00067c9,0x3722405a,
+0x3fff0000,0xb33387ca,0x6b43cd99,
+};
+static long Q[] = {
+/* 0x3fff0000,0x80000000,0x00000000, */
+0x40010000,0xa8003b33,0xa4696307,
+0x40020000,0x8666a51c,0x62d7fec2,
+0x40010000,0x8666a5d7,0xd072da32,
+};
+static long A[] = {
+0x3fff0000,0x80000000,0x00000000,
+0x3ffe0000,0xfa83b2db,0x722a033a,
+0x3ffe0000,0xf5257d15,0x2486cc2c,
+0x3ffe0000,0xefe4b99b,0xdcdaf5cb,
+0x3ffe0000,0xeac0c6e7,0xdd24392f,
+0x3ffe0000,0xe5b906e7,0x7c8348a8,
+0x3ffe0000,0xe0ccdeec,0x2a94e111,
+0x3ffe0000,0xdbfbb797,0xdaf23755,
+0x3ffe0000,0xd744fcca,0xd69d6af4,
+0x3ffe0000,0xd2a81d91,0xf12ae45a,
+0x3ffe0000,0xce248c15,0x1f8480e4,
+0x3ffe0000,0xc9b9bd86,0x6e2f27a3,
+0x3ffe0000,0xc5672a11,0x5506dadd,
+0x3ffe0000,0xc12c4cca,0x66709456,
+0x3ffe0000,0xbd08a39f,0x580c36bf,
+0x3ffe0000,0xb8fbaf47,0x62fb9ee9,
+0x3ffe0000,0xb504f333,0xf9de6484,
+0x3ffe0000,0xb123f581,0xd2ac2590,
+0x3ffe0000,0xad583eea,0x42a14ac6,
+0x3ffe0000,0xa9a15ab4,0xea7c0ef8,
+0x3ffe0000,0xa5fed6a9,0xb15138ea,
+0x3ffe0000,0xa2704303,0x0c496819,
+0x3ffe0000,0x9ef53260,0x91a111ae,
+0x3ffe0000,0x9b8d39b9,0xd54e5539,
+0x3ffe0000,0x9837f051,0x8db8a96f,
+0x3ffe0000,0x94f4efa8,0xfef70961,
+0x3ffe0000,0x91c3d373,0xab11c336,
+0x3ffe0000,0x8ea4398b,0x45cd53c0,
+0x3ffe0000,0x8b95c1e3,0xea8bd6e7,
+0x3ffe0000,0x88980e80,0x92da8527,
+0x3ffe0000,0x85aac367,0xcc487b15,
+0x3ffe0000,0x82cd8698,0xac2ba1d7,
+0x3ffe0000,0x80000000,0x00000000,
+};
+static long B[51] = {
+0x00000000,0x00000000,0x00000000,
+0x3fbd0000,0xf73a18f5,0xdb301f87,
+0xbfbc0000,0xbf4a2932,0x3e46ac15,
+0x3fb90000,0xcb12a091,0xba667944,
+0x3fbc0000,0xe69a2ee6,0x40b4ff78,
+0xbfbb0000,0xee53e383,0x5069c895,
+0x3fbc0000,0xf8ab4325,0x93767cde,
+0xbfbd0000,0xaefdc093,0x25e0a10c,
+0x3fbd0000,0xb2fb1366,0xea957d3e,
+0x3fbd0000,0x93015191,0xeb345d89,
+0x3fbb0000,0xe5ebfb10,0xb88380d9,
+0xbfbd0000,0xbeddc1ec,0x288c045d,
+0x3fbd0000,0x8d5a4630,0x5c85eded,
+0x3fba0000,0xfd6d8e0a,0xe5ac9d82,
+0xbfb90000,0x8373af14,0xeb586dfd,
+0xbfbc0000,0xe8da91cf,0x7aacf938,
+0x00000000,0x00000000,0x00000000,
+};
+static long R[] = {
+0x3fee0000,0xfd2aee1d,0x530ea69b,
+0x3ff20000,0xa1825960,0x8e7ec746,
+0x3ff50000,0xaec3fd6a,0xadda63b6,
+0x3ff80000,0x9d955b7c,0xfd99c104,
+0x3ffa0000,0xe35846b8,0x249de05e,
+0x3ffc0000,0xf5fdeffc,0x162c5d1d,
+0x3ffe0000,0xb17217f7,0xd1cf79aa,
+};
+
+#define douba(k) (*(long double *)&A[3*(k)])
+#define doubb(k) (*(long double *)&B[3*(k)])
+#define MEXP (NXT*16384.0L)
+#ifdef DENORMAL
+#define MNEXP (-NXT*(16384.0L+64.0L))
+#else
+#define MNEXP (-NXT*16382.0L)
+#endif
+static long L[3] = {0x3ffd0000,0xe2a8eca5,0x705fc2ef};
+#define LOG2EA (*(long double *)(&L[0]))
+#endif
+
+
+#define F W
+#define Fa Wa
+#define Fb Wb
+#define G W
+#define Ga Wa
+#define Gb u
+#define H W
+#define Ha Wb
+#define Hb Wb
+
+extern long double MAXNUML;
+static VOLATILE long double z;
+static long double w, W, Wa, Wb, ya, yb, u;
+#ifdef ANSIPROT
+extern long double floorl ( long double );
+extern long double fabsl ( long double );
+extern long double frexpl ( long double, int * );
+extern long double ldexpl ( long double, int );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern long double powil ( long double, int );
+extern int isnanl ( long double );
+extern int isfinitel ( long double );
+static long double reducl( long double );
+extern int signbitl ( long double );
+#else
+long double floorl(), fabsl(), frexpl(), ldexpl();
+long double polevll(), p1evll(), powil();
+static long double reducl();
+int isnanl(), isfinitel(), signbitl();
+#endif
+
+#ifdef INFINITIES
+extern long double INFINITYL;
+#else
+#define INFINITYL MAXNUML
+#endif
+
+#ifdef NANS
+extern long double NANL;
+#endif
+#ifdef MINUSZERO
+extern long double NEGZEROL;
+#endif
+
+long double powl( x, y )
+long double x, y;
+{
+/* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */
+int i, nflg, iyflg, yoddint;
+long e;
+
+if( y == 0.0L )
+ return( 1.0L );
+
+#ifdef NANS
+if( isnanl(x) )
+ return( x );
+if( isnanl(y) )
+ return( y );
+#endif
+
+if( y == 1.0L )
+ return( x );
+
+#ifdef INFINITIES
+if( !isfinitel(y) && (x == -1.0L || x == 1.0L) )
+ {
+ mtherr( "powl", DOMAIN );
+#ifdef NANS
+ return( NANL );
+#else
+ return( INFINITYL );
+#endif
+ }
+#endif
+
+if( x == 1.0L )
+ return( 1.0L );
+
+if( y >= MAXNUML )
+ {
+#ifdef INFINITIES
+ if( x > 1.0L )
+ return( INFINITYL );
+#else
+ if( x > 1.0L )
+ return( MAXNUML );
+#endif
+ if( x > 0.0L && x < 1.0L )
+ return( 0.0L );
+#ifdef INFINITIES
+ if( x < -1.0L )
+ return( INFINITYL );
+#else
+ if( x < -1.0L )
+ return( MAXNUML );
+#endif
+ if( x > -1.0L && x < 0.0L )
+ return( 0.0L );
+ }
+if( y <= -MAXNUML )
+ {
+ if( x > 1.0L )
+ return( 0.0L );
+#ifdef INFINITIES
+ if( x > 0.0L && x < 1.0L )
+ return( INFINITYL );
+#else
+ if( x > 0.0L && x < 1.0L )
+ return( MAXNUML );
+#endif
+ if( x < -1.0L )
+ return( 0.0L );
+#ifdef INFINITIES
+ if( x > -1.0L && x < 0.0L )
+ return( INFINITYL );
+#else
+ if( x > -1.0L && x < 0.0L )
+ return( MAXNUML );
+#endif
+ }
+if( x >= MAXNUML )
+ {
+#if INFINITIES
+ if( y > 0.0L )
+ return( INFINITYL );
+#else
+ if( y > 0.0L )
+ return( MAXNUML );
+#endif
+ return( 0.0L );
+ }
+
+w = floorl(y);
+/* Set iyflg to 1 if y is an integer. */
+iyflg = 0;
+if( w == y )
+ iyflg = 1;
+
+/* Test for odd integer y. */
+yoddint = 0;
+if( iyflg )
+ {
+ ya = fabsl(y);
+ ya = floorl(0.5L * ya);
+ yb = 0.5L * fabsl(w);
+ if( ya != yb )
+ yoddint = 1;
+ }
+
+if( x <= -MAXNUML )
+ {
+ if( y > 0.0L )
+ {
+#ifdef INFINITIES
+ if( yoddint )
+ return( -INFINITYL );
+ return( INFINITYL );
+#else
+ if( yoddint )
+ return( -MAXNUML );
+ return( MAXNUML );
+#endif
+ }
+ if( y < 0.0L )
+ {
+#ifdef MINUSZERO
+ if( yoddint )
+ return( NEGZEROL );
+#endif
+ return( 0.0 );
+ }
+ }
+
+
+nflg = 0; /* flag = 1 if x<0 raised to integer power */
+if( x <= 0.0L )
+ {
+ if( x == 0.0L )
+ {
+ if( y < 0.0 )
+ {
+#ifdef MINUSZERO
+ if( signbitl(x) && yoddint )
+ return( -INFINITYL );
+#endif
+#ifdef INFINITIES
+ return( INFINITYL );
+#else
+ return( MAXNUML );
+#endif
+ }
+ if( y > 0.0 )
+ {
+#ifdef MINUSZERO
+ if( signbitl(x) && yoddint )
+ return( NEGZEROL );
+#endif
+ return( 0.0 );
+ }
+ if( y == 0.0L )
+ return( 1.0L ); /* 0**0 */
+ else
+ return( 0.0L ); /* 0**y */
+ }
+ else
+ {
+ if( iyflg == 0 )
+ { /* noninteger power of negative number */
+ mtherr( fname, DOMAIN );
+#ifdef NANS
+ return(NANL);
+#else
+ return(0.0L);
+#endif
+ }
+ nflg = 1;
+ }
+ }
+
+/* Integer power of an integer. */
+
+if( iyflg )
+ {
+ i = w;
+ w = floorl(x);
+ if( (w == x) && (fabsl(y) < 32768.0) )
+ {
+ w = powil( x, (int) y );
+ return( w );
+ }
+ }
+
+
+if( nflg )
+ x = fabsl(x);
+
+/* separate significand from exponent */
+x = frexpl( x, &i );
+e = i;
+
+/* find significand in antilog table A[] */
+i = 1;
+if( x <= douba(17) )
+ i = 17;
+if( x <= douba(i+8) )
+ i += 8;
+if( x <= douba(i+4) )
+ i += 4;
+if( x <= douba(i+2) )
+ i += 2;
+if( x >= douba(1) )
+ i = -1;
+i += 1;
+
+
+/* Find (x - A[i])/A[i]
+ * in order to compute log(x/A[i]):
+ *
+ * log(x) = log( a x/a ) = log(a) + log(x/a)
+ *
+ * log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a
+ */
+x -= douba(i);
+x -= doubb(i/2);
+x /= douba(i);
+
+
+/* rational approximation for log(1+v):
+ *
+ * log(1+v) = v - v**2/2 + v**3 P(v) / Q(v)
+ */
+z = x*x;
+w = x * ( z * polevll( x, P, 3 ) / p1evll( x, Q, 3 ) );
+w = w - ldexpl( z, -1 ); /* w - 0.5 * z */
+
+/* Convert to base 2 logarithm:
+ * multiply by log2(e) = 1 + LOG2EA
+ */
+z = LOG2EA * w;
+z += w;
+z += LOG2EA * x;
+z += x;
+
+/* Compute exponent term of the base 2 logarithm. */
+w = -i;
+w = ldexpl( w, -LNXT ); /* divide by NXT */
+w += e;
+/* Now base 2 log of x is w + z. */
+
+/* Multiply base 2 log by y, in extended precision. */
+
+/* separate y into large part ya
+ * and small part yb less than 1/NXT
+ */
+ya = reducl(y);
+yb = y - ya;
+
+/* (w+z)(ya+yb)
+ * = w*ya + w*yb + z*y
+ */
+F = z * y + w * yb;
+Fa = reducl(F);
+Fb = F - Fa;
+
+G = Fa + w * ya;
+Ga = reducl(G);
+Gb = G - Ga;
+
+H = Fb + Gb;
+Ha = reducl(H);
+w = ldexpl( Ga+Ha, LNXT );
+
+/* Test the power of 2 for overflow */
+if( w > MEXP )
+ {
+/* printf( "w = %.4Le ", w ); */
+ mtherr( fname, OVERFLOW );
+ return( MAXNUML );
+ }
+
+if( w < MNEXP )
+ {
+/* printf( "w = %.4Le ", w ); */
+ mtherr( fname, UNDERFLOW );
+ return( 0.0L );
+ }
+
+e = w;
+Hb = H - Ha;
+
+if( Hb > 0.0L )
+ {
+ e += 1;
+ Hb -= (1.0L/NXT); /*0.0625L;*/
+ }
+
+/* Now the product y * log2(x) = Hb + e/NXT.
+ *
+ * Compute base 2 exponential of Hb,
+ * where -0.0625 <= Hb <= 0.
+ */
+z = Hb * polevll( Hb, R, 6 ); /* z = 2**Hb - 1 */
+
+/* Express e/NXT as an integer plus a negative number of (1/NXT)ths.
+ * Find lookup table entry for the fractional power of 2.
+ */
+if( e < 0 )
+ i = 0;
+else
+ i = 1;
+i = e/NXT + i;
+e = NXT*i - e;
+w = douba( e );
+z = w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */
+z = z + w;
+z = ldexpl( z, i ); /* multiply by integer power of 2 */
+
+if( nflg )
+ {
+/* For negative x,
+ * find out if the integer exponent
+ * is odd or even.
+ */
+ w = ldexpl( y, -1 );
+ w = floorl(w);
+ w = ldexpl( w, 1 );
+ if( w != y )
+ z = -z; /* odd exponent */
+ }
+
+return( z );
+}
+
+
+/* Find a multiple of 1/NXT that is within 1/NXT of x. */
+static long double reducl(x)
+long double x;
+{
+long double t;
+
+t = ldexpl( x, LNXT );
+t = floorl( t );
+t = ldexpl( t, -LNXT );
+return(t);
+}
diff --git a/libm/ldouble/sinhl.c b/libm/ldouble/sinhl.c
new file mode 100644
index 000000000..0533a1c7a
--- /dev/null
+++ b/libm/ldouble/sinhl.c
@@ -0,0 +1,150 @@
+/* sinhl.c
+ *
+ * Hyperbolic sine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, sinhl();
+ *
+ * y = sinhl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic sine of argument in the range MINLOGL to
+ * MAXLOGL.
+ *
+ * The range is partitioned into two segments. If |x| <= 1, a
+ * rational function of the form x + x**3 P(x)/Q(x) is employed.
+ * Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -2,2 10000 1.5e-19 3.9e-20
+ * IEEE +-10000 30000 1.1e-19 2.8e-20
+ *
+ */
+
+/*
+Cephes Math Library Release 2.7: January, 1998
+Copyright 1984, 1991, 1998 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static long double P[] = {
+ 1.7550769032975377032681E-6L,
+ 4.1680702175874268714539E-4L,
+ 3.0993532520425419002409E-2L,
+ 9.9999999999999999998002E-1L,
+};
+static long double Q[] = {
+ 1.7453965448620151484660E-8L,
+-5.9116673682651952419571E-6L,
+ 1.0599252315677389339530E-3L,
+-1.1403880487744749056675E-1L,
+ 6.0000000000000000000200E0L,
+};
+#endif
+
+#ifdef IBMPC
+static short P[] = {
+0xec6a,0xd942,0xfbb3,0xeb8f,0x3feb, XPD
+0x365e,0xb30a,0xe437,0xda86,0x3ff3, XPD
+0x8890,0x01f6,0x2612,0xfde6,0x3ff9, XPD
+0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
+};
+static short Q[] = {
+0x4edd,0x4c21,0xad09,0x95ed,0x3fe5, XPD
+0x4376,0x9b70,0xd605,0xc65c,0xbfed, XPD
+0xc8ad,0x5d21,0x3069,0x8aed,0x3ff5, XPD
+0x9c32,0x6374,0x2d4b,0xe98d,0xbffb, XPD
+0x0000,0x0000,0x0000,0xc000,0x4001, XPD
+};
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0x3feb0000,0xeb8ffbb3,0xd942ec6a,
+0x3ff30000,0xda86e437,0xb30a365e,
+0x3ff90000,0xfde62612,0x01f68890,
+0x3fff0000,0x80000000,0x00000000,
+};
+static long Q[] = {
+0x3fe50000,0x95edad09,0x4c214edd,
+0xbfed0000,0xc65cd605,0x9b704376,
+0x3ff50000,0x8aed3069,0x5d21c8ad,
+0xbffb0000,0xe98d2d4b,0x63749c32,
+0x40010000,0xc0000000,0x00000000,
+};
+#endif
+
+extern long double MAXNUML, MAXLOGL, MINLOGL, LOGE2L;
+#ifdef ANSIPROT
+extern long double fabsl ( long double );
+extern long double expl ( long double );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+#else
+long double fabsl(), expl(), polevll(), p1evll();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+#ifdef NANS
+extern long double NANL;
+#endif
+
+long double sinhl(x)
+long double x;
+{
+long double a;
+
+#ifdef MINUSZERO
+if( x == 0.0 )
+ return(x);
+#endif
+a = fabsl(x);
+if( (x > (MAXLOGL + LOGE2L)) || (x > -(MINLOGL-LOGE2L) ) )
+ {
+ mtherr( "sinhl", DOMAIN );
+#ifdef INFINITIES
+ if( x > 0.0L )
+ return( INFINITYL );
+ else
+ return( -INFINITYL );
+#else
+ if( x > 0.0L )
+ return( MAXNUML );
+ else
+ return( -MAXNUML );
+#endif
+ }
+if( a > 1.0L )
+ {
+ if( a >= (MAXLOGL - LOGE2L) )
+ {
+ a = expl(0.5L*a);
+ a = (0.5L * a) * a;
+ if( x < 0.0L )
+ a = -a;
+ return(a);
+ }
+ a = expl(a);
+ a = 0.5L*a - (0.5L/a);
+ if( x < 0.0L )
+ a = -a;
+ return(a);
+ }
+
+a *= a;
+return( x + x * a * (polevll(a,P,3)/polevll(a,Q,4)) );
+}
diff --git a/libm/ldouble/sinl.c b/libm/ldouble/sinl.c
new file mode 100644
index 000000000..dc7d739f9
--- /dev/null
+++ b/libm/ldouble/sinl.c
@@ -0,0 +1,342 @@
+/* sinl.c
+ *
+ * Circular sine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, sinl();
+ *
+ * y = sinl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of pi/4. The reduction
+ * error is nearly eliminated by contriving an extended precision
+ * modular arithmetic.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the sine is approximated by the Cody
+ * and Waite polynomial form
+ * x + x**3 P(x**2) .
+ * Between pi/4 and pi/2 the cosine is represented as
+ * 1 - .5 x**2 + x**4 Q(x**2) .
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-5.5e11 200,000 1.2e-19 2.9e-20
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sin total loss x > 2**39 0.0
+ *
+ * Loss of precision occurs for x > 2**39 = 5.49755813888e11.
+ * The routine as implemented flags a TLOSS error for
+ * x > 2**39 and returns 0.0.
+ */
+ /* cosl.c
+ *
+ * Circular cosine, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, cosl();
+ *
+ * y = cosl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Range reduction is into intervals of pi/4. The reduction
+ * error is nearly eliminated by contriving an extended precision
+ * modular arithmetic.
+ *
+ * Two polynomial approximating functions are employed.
+ * Between 0 and pi/4 the cosine is approximated by
+ * 1 - .5 x**2 + x**4 Q(x**2) .
+ * Between pi/4 and pi/2 the sine is represented by the Cody
+ * and Waite polynomial form
+ * x + x**3 P(x**2) .
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-5.5e11 50000 1.2e-19 2.9e-20
+ */
+
+/* sin.c */
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright 1985, 1990, 1998 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static long double sincof[7] = {
+-7.5785404094842805756289E-13L,
+ 1.6058363167320443249231E-10L,
+-2.5052104881870868784055E-8L,
+ 2.7557319214064922217861E-6L,
+-1.9841269841254799668344E-4L,
+ 8.3333333333333225058715E-3L,
+-1.6666666666666666640255E-1L,
+};
+static long double coscof[7] = {
+ 4.7377507964246204691685E-14L,
+-1.1470284843425359765671E-11L,
+ 2.0876754287081521758361E-9L,
+-2.7557319214999787979814E-7L,
+ 2.4801587301570552304991E-5L,
+-1.3888888888888872993737E-3L,
+ 4.1666666666666666609054E-2L,
+};
+static long double DP1 = 7.853981554508209228515625E-1L;
+static long double DP2 = 7.946627356147928367136046290398E-9L;
+static long double DP3 = 3.061616997868382943065164830688E-17L;
+#endif
+
+#ifdef IBMPC
+static short sincof[] = {
+0x4e27,0xe1d6,0x2389,0xd551,0xbfd6, XPD
+0x64d7,0xe706,0x4623,0xb090,0x3fde, XPD
+0x01b1,0xbf34,0x2946,0xd732,0xbfe5, XPD
+0xc8f7,0x9845,0x1d29,0xb8ef,0x3fec, XPD
+0x6514,0x0c53,0x00d0,0xd00d,0xbff2, XPD
+0x569a,0x8888,0x8888,0x8888,0x3ff8, XPD
+0xaa97,0xaaaa,0xaaaa,0xaaaa,0xbffc, XPD
+};
+static short coscof[] = {
+0x7436,0x6f99,0x8c3a,0xd55e,0x3fd2, XPD
+0x2f37,0x58f4,0x920f,0xc9c9,0xbfda, XPD
+0x5350,0x659e,0xc648,0x8f76,0x3fe2, XPD
+0x4d2b,0xf5c6,0x7dba,0x93f2,0xbfe9, XPD
+0x53ed,0x0c66,0x00d0,0xd00d,0x3fef, XPD
+0x7b67,0x0b60,0x60b6,0xb60b,0xbff5, XPD
+0xaa9a,0xaaaa,0xaaaa,0xaaaa,0x3ffa, XPD
+};
+static short P1[] = {0x0000,0x0000,0xda80,0xc90f,0x3ffe, XPD};
+static short P2[] = {0x0000,0x0000,0xa300,0x8885,0x3fe4, XPD};
+static short P3[] = {0x3707,0xa2e0,0x3198,0x8d31,0x3fc8, XPD};
+#define DP1 *(long double *)P1
+#define DP2 *(long double *)P2
+#define DP3 *(long double *)P3
+#endif
+
+#ifdef MIEEE
+static long sincof[] = {
+0xbfd60000,0xd5512389,0xe1d64e27,
+0x3fde0000,0xb0904623,0xe70664d7,
+0xbfe50000,0xd7322946,0xbf3401b1,
+0x3fec0000,0xb8ef1d29,0x9845c8f7,
+0xbff20000,0xd00d00d0,0x0c536514,
+0x3ff80000,0x88888888,0x8888569a,
+0xbffc0000,0xaaaaaaaa,0xaaaaaa97,
+};
+static long coscof[] = {
+0x3fd20000,0xd55e8c3a,0x6f997436,
+0xbfda0000,0xc9c9920f,0x58f42f37,
+0x3fe20000,0x8f76c648,0x659e5350,
+0xbfe90000,0x93f27dba,0xf5c64d2b,
+0x3fef0000,0xd00d00d0,0x0c6653ed,
+0xbff50000,0xb60b60b6,0x0b607b67,
+0x3ffa0000,0xaaaaaaaa,0xaaaaaa9a,
+};
+static long P1[] = {0x3ffe0000,0xc90fda80,0x00000000};
+static long P2[] = {0x3fe40000,0x8885a300,0x00000000};
+static long P3[] = {0x3fc80000,0x8d313198,0xa2e03707};
+#define DP1 *(long double *)P1
+#define DP2 *(long double *)P2
+#define DP3 *(long double *)P3
+#endif
+
+static long double lossth = 5.49755813888e11L; /* 2^39 */
+extern long double PIO4L;
+#ifdef ANSIPROT
+extern long double polevll ( long double, void *, int );
+extern long double floorl ( long double );
+extern long double ldexpl ( long double, int );
+extern int isnanl ( long double );
+extern int isfinitel ( long double );
+#else
+long double polevll(), floorl(), ldexpl(), isnanl(), isfinitel();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+#ifdef NANS
+extern long double NANL;
+#endif
+
+long double sinl(x)
+long double x;
+{
+long double y, z, zz;
+int j, sign;
+
+#ifdef NANS
+if( isnanl(x) )
+ return(x);
+#endif
+#ifdef MINUSZERO
+if( x == 0.0L )
+ return(x);
+#endif
+#ifdef NANS
+if( !isfinitel(x) )
+ {
+ mtherr( "sinl", DOMAIN );
+#ifdef NANS
+ return(NANL);
+#else
+ return(0.0L);
+#endif
+ }
+#endif
+/* make argument positive but save the sign */
+sign = 1;
+if( x < 0 )
+ {
+ x = -x;
+ sign = -1;
+ }
+
+if( x > lossth )
+ {
+ mtherr( "sinl", TLOSS );
+ return(0.0L);
+ }
+
+y = floorl( x/PIO4L ); /* integer part of x/PIO4 */
+
+/* strip high bits of integer part to prevent integer overflow */
+z = ldexpl( y, -4 );
+z = floorl(z); /* integer part of y/8 */
+z = y - ldexpl( z, 4 ); /* y - 16 * (y/16) */
+
+j = z; /* convert to integer for tests on the phase angle */
+/* map zeros to origin */
+if( j & 1 )
+ {
+ j += 1;
+ y += 1.0L;
+ }
+j = j & 07; /* octant modulo 360 degrees */
+/* reflect in x axis */
+if( j > 3)
+ {
+ sign = -sign;
+ j -= 4;
+ }
+
+/* Extended precision modular arithmetic */
+z = ((x - y * DP1) - y * DP2) - y * DP3;
+
+zz = z * z;
+if( (j==1) || (j==2) )
+ {
+ y = 1.0L - ldexpl(zz,-1) + zz * zz * polevll( zz, coscof, 6 );
+ }
+else
+ {
+ y = z + z * (zz * polevll( zz, sincof, 6 ));
+ }
+
+if(sign < 0)
+ y = -y;
+
+return(y);
+}
+
+
+
+
+
+long double cosl(x)
+long double x;
+{
+long double y, z, zz;
+long i;
+int j, sign;
+
+
+#ifdef NANS
+if( isnanl(x) )
+ return(x);
+#endif
+#ifdef INFINITIES
+if( !isfinitel(x) )
+ {
+ mtherr( "cosl", DOMAIN );
+#ifdef NANS
+ return(NANL);
+#else
+ return(0.0L);
+#endif
+ }
+#endif
+
+/* make argument positive */
+sign = 1;
+if( x < 0 )
+ x = -x;
+
+if( x > lossth )
+ {
+ mtherr( "cosl", TLOSS );
+ return(0.0L);
+ }
+
+y = floorl( x/PIO4L );
+z = ldexpl( y, -4 );
+z = floorl(z); /* integer part of y/8 */
+z = y - ldexpl( z, 4 ); /* y - 16 * (y/16) */
+
+/* integer and fractional part modulo one octant */
+i = z;
+if( i & 1 ) /* map zeros to origin */
+ {
+ i += 1;
+ y += 1.0L;
+ }
+j = i & 07;
+if( j > 3)
+ {
+ j -=4;
+ sign = -sign;
+ }
+
+if( j > 1 )
+ sign = -sign;
+
+/* Extended precision modular arithmetic */
+z = ((x - y * DP1) - y * DP2) - y * DP3;
+
+zz = z * z;
+if( (j==1) || (j==2) )
+ {
+ y = z + z * (zz * polevll( zz, sincof, 6 ));
+ }
+else
+ {
+ y = 1.0L - ldexpl(zz,-1) + zz * zz * polevll( zz, coscof, 6 );
+ }
+
+if(sign < 0)
+ y = -y;
+
+return(y);
+}
diff --git a/libm/ldouble/sqrtl.c b/libm/ldouble/sqrtl.c
new file mode 100644
index 000000000..a3b17175f
--- /dev/null
+++ b/libm/ldouble/sqrtl.c
@@ -0,0 +1,172 @@
+/* sqrtl.c
+ *
+ * Square root, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, sqrtl();
+ *
+ * y = sqrtl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the square root of x.
+ *
+ * Range reduction involves isolating the power of two of the
+ * argument and using a polynomial approximation to obtain
+ * a rough value for the square root. Then Heron's iteration
+ * is used three times to converge to an accurate value.
+ *
+ * Note, some arithmetic coprocessors such as the 8087 and
+ * 68881 produce correctly rounded square roots, which this
+ * routine will not.
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,10 30000 8.1e-20 3.1e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * sqrt domain x < 0 0.0
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: December, 1990
+Copyright 1984, 1990 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+#include <math.h>
+
+#define SQRT2 1.4142135623730950488017E0L
+#ifdef ANSIPROT
+extern long double frexpl ( long double, int * );
+extern long double ldexpl ( long double, int );
+#else
+long double frexpl(), ldexpl();
+#endif
+
+long double sqrtl(x)
+long double x;
+{
+int e;
+long double z, w;
+#ifndef UNK
+short *q;
+#endif
+
+if( x <= 0.0 )
+ {
+ if( x < 0.0 )
+ mtherr( "sqrtl", DOMAIN );
+ return( 0.0 );
+ }
+w = x;
+/* separate exponent and significand */
+#ifdef UNK
+z = frexpl( x, &e );
+#endif
+
+/* Note, frexp and ldexp are used in order to
+ * handle denormal numbers properly.
+ */
+#ifdef IBMPC
+z = frexpl( x, &e );
+q = (short *)&x; /* point to the exponent word */
+q += 4;
+/*
+e = ((*q >> 4) & 0x0fff) - 0x3fe;
+*q &= 0x000f;
+*q |= 0x3fe0;
+z = x;
+*/
+#endif
+#ifdef MIEEE
+z = frexpl( x, &e );
+q = (short *)&x;
+/*
+e = ((*q >> 4) & 0x0fff) - 0x3fe;
+*q &= 0x000f;
+*q |= 0x3fe0;
+z = x;
+*/
+#endif
+
+/* approximate square root of number between 0.5 and 1
+ * relative error of linear approximation = 7.47e-3
+ */
+/*
+x = 0.4173075996388649989089L + 0.59016206709064458299663L * z;
+*/
+
+/* quadratic approximation, relative error 6.45e-4 */
+x = ( -0.20440583154734771959904L * z
+ + 0.89019407351052789754347L) * z
+ + 0.31356706742295303132394L;
+
+/* adjust for odd powers of 2 */
+if( (e & 1) != 0 )
+ x *= SQRT2;
+
+/* re-insert exponent */
+#ifdef UNK
+x = ldexpl( x, (e >> 1) );
+#endif
+#ifdef IBMPC
+x = ldexpl( x, (e >> 1) );
+/*
+*q += ((e >>1) & 0x7ff) << 4;
+*q &= 077777;
+*/
+#endif
+#ifdef MIEEE
+x = ldexpl( x, (e >> 1) );
+/*
+*q += ((e >>1) & 0x7ff) << 4;
+*q &= 077777;
+*/
+#endif
+
+/* Newton iterations: */
+#ifdef UNK
+x += w/x;
+x = ldexpl( x, -1 ); /* divide by 2 */
+x += w/x;
+x = ldexpl( x, -1 );
+x += w/x;
+x = ldexpl( x, -1 );
+#endif
+
+/* Note, assume the square root cannot be denormal,
+ * so it is safe to use integer exponent operations here.
+ */
+#ifdef IBMPC
+x += w/x;
+*q -= 1;
+x += w/x;
+*q -= 1;
+x += w/x;
+*q -= 1;
+#endif
+#ifdef MIEEE
+x += w/x;
+*q -= 1;
+x += w/x;
+*q -= 1;
+x += w/x;
+*q -= 1;
+#endif
+
+return(x);
+}
diff --git a/libm/ldouble/stdtrl.c b/libm/ldouble/stdtrl.c
new file mode 100644
index 000000000..4218d4133
--- /dev/null
+++ b/libm/ldouble/stdtrl.c
@@ -0,0 +1,225 @@
+/* stdtrl.c
+ *
+ * Student's t distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double p, t, stdtrl();
+ * int k;
+ *
+ * p = stdtrl( k, t );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the integral from minus infinity to t of the Student
+ * t distribution with integer k > 0 degrees of freedom:
+ *
+ * t
+ * -
+ * | |
+ * - | 2 -(k+1)/2
+ * | ( (k+1)/2 ) | ( x )
+ * ---------------------- | ( 1 + --- ) dx
+ * - | ( k )
+ * sqrt( k pi ) | ( k/2 ) |
+ * | |
+ * -
+ * -inf.
+ *
+ * Relation to incomplete beta integral:
+ *
+ * 1 - stdtr(k,t) = 0.5 * incbet( k/2, 1/2, z )
+ * where
+ * z = k/(k + t**2).
+ *
+ * For t < -1.6, this is the method of computation. For higher t,
+ * a direct method is derived from integration by parts.
+ * Since the function is symmetric about t=0, the area under the
+ * right tail of the density is found by calling the function
+ * with -t instead of t.
+ *
+ * ACCURACY:
+ *
+ * Tested at random 1 <= k <= 100. The "domain" refers to t.
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -100,-1.6 10000 5.7e-18 9.8e-19
+ * IEEE -1.6,100 10000 3.8e-18 1.0e-19
+ */
+
+/* stdtril.c
+ *
+ * Functional inverse of Student's t distribution
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double p, t, stdtril();
+ * int k;
+ *
+ * t = stdtril( k, p );
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Given probability p, finds the argument t such that stdtrl(k,t)
+ * is equal to p.
+ *
+ * ACCURACY:
+ *
+ * Tested at random 1 <= k <= 100. The "domain" refers to p:
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,1 3500 4.2e-17 4.1e-18
+ */
+
+
+/*
+Cephes Math Library Release 2.3: January, 1995
+Copyright 1984, 1995 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+extern long double PIL, MACHEPL, MAXNUML;
+#ifdef ANSIPROT
+extern long double sqrtl ( long double );
+extern long double atanl ( long double );
+extern long double incbetl ( long double, long double, long double );
+extern long double incbil ( long double, long double, long double );
+extern long double fabsl ( long double );
+#else
+long double sqrtl(), atanl(), incbetl(), incbil(), fabsl();
+#endif
+
+long double stdtrl( k, t )
+int k;
+long double t;
+{
+long double x, rk, z, f, tz, p, xsqk;
+int j;
+
+if( k <= 0 )
+ {
+ mtherr( "stdtrl", DOMAIN );
+ return(0.0L);
+ }
+
+if( t == 0.0L )
+ return( 0.5L );
+
+if( t < -1.6L )
+ {
+ rk = k;
+ z = rk / (rk + t * t);
+ p = 0.5L * incbetl( 0.5L*rk, 0.5L, z );
+ return( p );
+ }
+
+/* compute integral from -t to + t */
+
+if( t < 0.0L )
+ x = -t;
+else
+ x = t;
+
+rk = k; /* degrees of freedom */
+z = 1.0L + ( x * x )/rk;
+
+/* test if k is odd or even */
+if( (k & 1) != 0)
+ {
+
+ /* computation for odd k */
+
+ xsqk = x/sqrtl(rk);
+ p = atanl( xsqk );
+ if( k > 1 )
+ {
+ f = 1.0L;
+ tz = 1.0L;
+ j = 3;
+ while( (j<=(k-2)) && ( (tz/f) > MACHEPL ) )
+ {
+ tz *= (j-1)/( z * j );
+ f += tz;
+ j += 2;
+ }
+ p += f * xsqk/z;
+ }
+ p *= 2.0L/PIL;
+ }
+
+
+else
+ {
+
+ /* computation for even k */
+
+ f = 1.0L;
+ tz = 1.0L;
+ j = 2;
+
+ while( ( j <= (k-2) ) && ( (tz/f) > MACHEPL ) )
+ {
+ tz *= (j - 1)/( z * j );
+ f += tz;
+ j += 2;
+ }
+ p = f * x/sqrtl(z*rk);
+ }
+
+/* common exit */
+
+
+if( t < 0.0L )
+ p = -p; /* note destruction of relative accuracy */
+
+ p = 0.5L + 0.5L * p;
+return(p);
+}
+
+
+long double stdtril( k, p )
+int k;
+long double p;
+{
+long double t, rk, z;
+int rflg;
+
+if( k <= 0 || p <= 0.0L || p >= 1.0L )
+ {
+ mtherr( "stdtril", DOMAIN );
+ return(0.0L);
+ }
+
+rk = k;
+
+if( p > 0.25L && p < 0.75L )
+ {
+ if( p == 0.5L )
+ return( 0.0L );
+ z = 1.0L - 2.0L * p;
+ z = incbil( 0.5L, 0.5L*rk, fabsl(z) );
+ t = sqrtl( rk*z/(1.0L-z) );
+ if( p < 0.5L )
+ t = -t;
+ return( t );
+ }
+rflg = -1;
+if( p >= 0.5L)
+ {
+ p = 1.0L - p;
+ rflg = 1;
+ }
+z = incbil( 0.5L*rk, 0.5L, 2.0L*p );
+
+if( MAXNUML * z < rk )
+ return(rflg* MAXNUML);
+t = sqrtl( rk/z - rk );
+return( rflg * t );
+}
diff --git a/libm/ldouble/tanhl.c b/libm/ldouble/tanhl.c
new file mode 100644
index 000000000..42c7133c3
--- /dev/null
+++ b/libm/ldouble/tanhl.c
@@ -0,0 +1,129 @@
+/* tanhl.c
+ *
+ * Hyperbolic tangent, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, tanhl();
+ *
+ * y = tanhl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns hyperbolic tangent of argument in the range MINLOGL to
+ * MAXLOGL.
+ *
+ * A rational function is used for |x| < 0.625. The form
+ * x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
+ * Otherwise,
+ * tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -2,2 30000 1.3e-19 2.4e-20
+ *
+ */
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright 1984, 1987, 1989, 1998 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static long double P[] = {
+-6.8473739392677100872869E-5L,
+-9.5658283111794641589011E-1L,
+-8.4053568599672284488465E1L,
+-1.3080425704712825945553E3L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0L,*/
+ 9.6259501838840336946872E1L,
+ 1.8218117903645559060232E3L,
+ 3.9241277114138477845780E3L,
+};
+#endif
+
+#ifdef IBMPC
+static short P[] = {
+0xd2a4,0x1b0c,0x8f15,0x8f99,0xbff1, XPD
+0x5959,0x9111,0x9cc7,0xf4e2,0xbffe, XPD
+0xb576,0xef5e,0x6d57,0xa81b,0xc005, XPD
+0xe3be,0xbfbd,0x5cbc,0xa381,0xc009, XPD
+};
+static short Q[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0x687f,0xce24,0xdd6c,0xc084,0x4005, XPD
+0x3793,0xc95f,0xfa2f,0xe3b9,0x4009, XPD
+0xd5a2,0x1f9c,0x0b1b,0xf542,0x400a, XPD
+};
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0xbff10000,0x8f998f15,0x1b0cd2a4,
+0xbffe0000,0xf4e29cc7,0x91115959,
+0xc0050000,0xa81b6d57,0xef5eb576,
+0xc0090000,0xa3815cbc,0xbfbde3be,
+};
+static long Q[] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x40050000,0xc084dd6c,0xce24687f,
+0x40090000,0xe3b9fa2f,0xc95f3793,
+0x400a0000,0xf5420b1b,0x1f9cd5a2,
+};
+#endif
+
+extern long double MAXLOGL;
+#ifdef ANSIPROT
+extern long double fabsl ( long double );
+extern long double expl ( long double );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+#else
+long double fabsl(), expl(), polevll(), p1evll();
+#endif
+
+long double tanhl(x)
+long double x;
+{
+long double s, z;
+
+#ifdef MINUSZERO
+if( x == 0.0L )
+ return(x);
+#endif
+z = fabsl(x);
+if( z > 0.5L * MAXLOGL )
+ {
+ if( x > 0 )
+ return( 1.0L );
+ else
+ return( -1.0L );
+ }
+if( z >= 0.625L )
+ {
+ s = expl(2.0*z);
+ z = 1.0L - 2.0/(s + 1.0L);
+ if( x < 0 )
+ z = -z;
+ }
+else
+ {
+ s = x * x;
+ z = polevll( s, P, 3 )/p1evll(s, Q, 3);
+ z = x * s * z;
+ z = x + z;
+ }
+return( z );
+}
diff --git a/libm/ldouble/tanl.c b/libm/ldouble/tanl.c
new file mode 100644
index 000000000..e546dd664
--- /dev/null
+++ b/libm/ldouble/tanl.c
@@ -0,0 +1,279 @@
+/* tanl.c
+ *
+ * Circular tangent, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, tanl();
+ *
+ * y = tanl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular tangent of the radian argument x.
+ *
+ * Range reduction is modulo pi/4. A rational function
+ * x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-1.07e9 30000 1.9e-19 4.8e-20
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * tan total loss x > 2^39 0.0
+ *
+ */
+ /* cotl.c
+ *
+ * Circular cotangent, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, cotl();
+ *
+ * y = cotl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the circular cotangent of the radian argument x.
+ *
+ * Range reduction is modulo pi/4. A rational function
+ * x + x**3 P(x**2)/Q(x**2)
+ * is employed in the basic interval [0, pi/4].
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE +-1.07e9 30000 1.9e-19 5.1e-20
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * cot total loss x > 2^39 0.0
+ * cot singularity x = 0 INFINITYL
+ *
+ */
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright 1984, 1990, 1998 by Stephen L. Moshier
+*/
+
+#include <math.h>
+
+#ifdef UNK
+static long double P[] = {
+-1.3093693918138377764608E4L,
+ 1.1535166483858741613983E6L,
+-1.7956525197648487798769E7L,
+};
+static long double Q[] = {
+/* 1.0000000000000000000000E0L,*/
+ 1.3681296347069295467845E4L,
+-1.3208923444021096744731E6L,
+ 2.5008380182335791583922E7L,
+-5.3869575592945462988123E7L,
+};
+static long double DP1 = 7.853981554508209228515625E-1L;
+static long double DP2 = 7.946627356147928367136046290398E-9L;
+static long double DP3 = 3.061616997868382943065164830688E-17L;
+#endif
+
+
+#ifdef IBMPC
+static short P[] = {
+0xbc1c,0x79f9,0xc692,0xcc96,0xc00c, XPD
+0xe5b1,0xe4ee,0x652f,0x8ccf,0x4013, XPD
+0xaf9a,0x4c8b,0x5699,0x88ff,0xc017, XPD
+};
+static short Q[] = {
+/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
+0x8ed4,0x9b2b,0x2f75,0xd5c5,0x400c, XPD
+0xadcd,0x55e4,0xe2c1,0xa13d,0xc013, XPD
+0x7adf,0x56c7,0x7e17,0xbecc,0x4017, XPD
+0x86f6,0xf2d1,0x01e5,0xcd7f,0xc018, XPD
+};
+static short P1[] = {0x0000,0x0000,0xda80,0xc90f,0x3ffe, XPD};
+static short P2[] = {0x0000,0x0000,0xa300,0x8885,0x3fe4, XPD};
+static short P3[] = {0x3707,0xa2e0,0x3198,0x8d31,0x3fc8, XPD};
+#define DP1 *(long double *)P1
+#define DP2 *(long double *)P2
+#define DP3 *(long double *)P3
+#endif
+
+#ifdef MIEEE
+static long P[] = {
+0xc00c0000,0xcc96c692,0x79f9bc1c,
+0x40130000,0x8ccf652f,0xe4eee5b1,
+0xc0170000,0x88ff5699,0x4c8baf9a,
+};
+static long Q[] = {
+/*0x3fff0000,0x80000000,0x00000000,*/
+0x400c0000,0xd5c52f75,0x9b2b8ed4,
+0xc0130000,0xa13de2c1,0x55e4adcd,
+0x40170000,0xbecc7e17,0x56c77adf,
+0xc0180000,0xcd7f01e5,0xf2d186f6,
+};
+static long P1[] = {0x3ffe0000,0xc90fda80,0x00000000};
+static long P2[] = {0x3fe40000,0x8885a300,0x00000000};
+static long P3[] = {0x3fc80000,0x8d313198,0xa2e03707};
+#define DP1 *(long double *)P1
+#define DP2 *(long double *)P2
+#define DP3 *(long double *)P3
+#endif
+
+static long double lossth = 5.49755813888e11L; /* 2^39 */
+extern long double PIO4L;
+extern long double MAXNUML;
+
+#ifdef ANSIPROT
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+extern long double floorl ( long double );
+extern long double ldexpl ( long double, int );
+extern int isnanl ( long double );
+extern int isfinitel ( long double );
+static long double tancotl( long double, int );
+#else
+long double polevll(), p1evll(), floorl(), ldexpl(), isnanl(), isfinitel();
+static long double tancotl();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+#ifdef NANS
+extern long double NANL;
+#endif
+
+long double tanl(x)
+long double x;
+{
+
+#ifdef NANS
+if( isnanl(x) )
+ return(x);
+#endif
+#ifdef MINUSZERO
+if( x == 0.0L )
+ return(x);
+#endif
+#ifdef NANS
+if( !isfinitel(x) )
+ {
+ mtherr( "tanl", DOMAIN );
+ return(NANL);
+ }
+#endif
+return( tancotl(x,0) );
+}
+
+
+long double cotl(x)
+long double x;
+{
+
+if( x == 0.0L )
+ {
+ mtherr( "cotl", SING );
+#ifdef INFINITIES
+ return( INFINITYL );
+#else
+ return( MAXNUML );
+#endif
+ }
+return( tancotl(x,1) );
+}
+
+
+static long double tancotl( xx, cotflg )
+long double xx;
+int cotflg;
+{
+long double x, y, z, zz;
+int j, sign;
+
+/* make argument positive but save the sign */
+if( xx < 0.0L )
+ {
+ x = -xx;
+ sign = -1;
+ }
+else
+ {
+ x = xx;
+ sign = 1;
+ }
+
+if( x > lossth )
+ {
+ if( cotflg )
+ mtherr( "cotl", TLOSS );
+ else
+ mtherr( "tanl", TLOSS );
+ return(0.0L);
+ }
+
+/* compute x mod PIO4 */
+y = floorl( x/PIO4L );
+
+/* strip high bits of integer part */
+z = ldexpl( y, -4 );
+z = floorl(z); /* integer part of y/16 */
+z = y - ldexpl( z, 4 ); /* y - 16 * (y/16) */
+
+/* integer and fractional part modulo one octant */
+j = z;
+
+/* map zeros and singularities to origin */
+if( j & 1 )
+ {
+ j += 1;
+ y += 1.0L;
+ }
+
+z = ((x - y * DP1) - y * DP2) - y * DP3;
+
+zz = z * z;
+
+if( zz > 1.0e-20L )
+ y = z + z * (zz * polevll( zz, P, 2 )/p1evll(zz, Q, 4));
+else
+ y = z;
+
+if( j & 2 )
+ {
+ if( cotflg )
+ y = -y;
+ else
+ y = -1.0L/y;
+ }
+else
+ {
+ if( cotflg )
+ y = 1.0L/y;
+ }
+
+if( sign < 0 )
+ y = -y;
+
+return( y );
+}
diff --git a/libm/ldouble/testvect.c b/libm/ldouble/testvect.c
new file mode 100644
index 000000000..1c3ffcb91
--- /dev/null
+++ b/libm/ldouble/testvect.c
@@ -0,0 +1,497 @@
+
+/* Test vectors for math functions.
+ See C9X section F.9.
+
+ On some systems it may be necessary to modify the default exception
+ settings of the floating point arithmetic unit. */
+
+/*
+Cephes Math Library Release 2.7: May, 1998
+Copyright 1998 by Stephen L. Moshier
+*/
+
+#include <stdio.h>
+int isfinitel (long double);
+
+/* Some compilers will not accept these expressions. */
+
+#define ZINF 1
+#define ZMINF 2
+#define ZNANL 3
+#define ZPIL 4
+#define ZPIO2L 4
+
+extern long double INFINITYL, NANL, NEGZEROL;
+long double MINFL;
+extern long double PIL, PIO2L, PIO4L, MACHEPL;
+long double MPIL;
+long double MPIO2L;
+long double MPIO4L;
+long double THPIO4L = 2.35619449019234492884698L;
+long double MTHPIO4L = -2.35619449019234492884698L;
+long double SQRT2L = 1.414213562373095048802E0L;
+long double SQRTHL = 7.071067811865475244008E-1L;
+long double ZEROL = 0.0L;
+long double HALFL = 0.5L;
+long double MHALFL = -0.5L;
+long double ONEL = 1.0L;
+long double MONEL = -1.0L;
+long double TWOL = 2.0L;
+long double MTWOL = -2.0L;
+long double THREEL = 3.0L;
+long double MTHREEL = -3.0L;
+
+/* Functions of one variable. */
+long double logl (long double);
+long double expl (long double);
+long double atanl (long double);
+long double sinl (long double);
+long double cosl (long double);
+long double tanl (long double);
+long double acosl (long double);
+long double asinl (long double);
+long double acoshl (long double);
+long double asinhl (long double);
+long double atanhl (long double);
+long double sinhl (long double);
+long double coshl (long double);
+long double tanhl (long double);
+long double exp2l (long double);
+long double expm1l (long double);
+long double log10l (long double);
+long double log1pl (long double);
+long double log2l (long double);
+long double fabsl (long double);
+long double erfl (long double);
+long double erfcl (long double);
+long double gammal (long double);
+long double lgaml (long double);
+long double floorl (long double);
+long double ceill (long double);
+long double cbrtl (long double);
+
+struct oneargument
+ {
+ char *name; /* Name of the function. */
+ long double (*func) (long double);
+ long double *arg1;
+ long double *answer;
+ int thresh; /* Error report threshold. */
+ };
+
+#if 0
+ {"sinl", sinl, 32767.L, 1.8750655394138942394239E-1L, 0},
+ {"cosl", cosl, 32767.L, 9.8226335176928229845654E-1L, 0},
+ {"tanl", tanl, 32767.L, 1.9089234430221485740826E-1L, 0},
+ {"sinl", sinl, 8388607.L, 9.9234509376961249835628E-1L, 0},
+ {"cosl", cosl, 8388607.L, -1.2349580912475928183718E-1L, 0},
+ {"tanl", tanl, 8388607.L, -8.0354556223613614748329E0L, 0},
+ {"sinl", sinl, 2147483647.L, -7.2491655514455639054829E-1L, 0},
+ {"cosl", cosl, 2147483647.L, -6.8883669187794383467976E-1L, 0},
+ {"tanl", tanl, 2147483647.L, 1.0523779637351339136698E0L, 0},
+ {"sinl", sinl, PIO4L, 7.0710678118654752440084E-1L, 0},
+ {"cosl", cosl, PIO2L, -2.50827880633416613471e-20L, 0},
+#endif
+
+struct oneargument test1[] =
+{
+ {"atanl", atanl, &ONEL, &PIO4L, 0},
+ {"sinl", sinl, &PIO2L, &ONEL, 0},
+ {"cosl", cosl, &PIO4L, &SQRTHL, 0},
+ {"acosl", acosl, &NANL, &NANL, 0},
+ {"acosl", acosl, &ONEL, &ZEROL, 0},
+ {"acosl", acosl, &TWOL, &NANL, 0},
+ {"acosl", acosl, &MTWOL, &NANL, 0},
+ {"asinl", asinl, &NANL, &NANL, 0},
+ {"asinl", asinl, &ZEROL, &ZEROL, 0},
+ {"asinl", asinl, &NEGZEROL, &NEGZEROL, 0},
+ {"asinl", asinl, &TWOL, &NANL, 0},
+ {"asinl", asinl, &MTWOL, &NANL, 0},
+ {"atanl", atanl, &NANL, &NANL, 0},
+ {"atanl", atanl, &ZEROL, &ZEROL, 0},
+ {"atanl", atanl, &NEGZEROL, &NEGZEROL, 0},
+ {"atanl", atanl, &INFINITYL, &PIO2L, 0},
+ {"atanl", atanl, &MINFL, &MPIO2L, 0},
+ {"cosl", cosl, &NANL, &NANL, 0},
+ {"cosl", cosl, &ZEROL, &ONEL, 0},
+ {"cosl", cosl, &NEGZEROL, &ONEL, 0},
+ {"cosl", cosl, &INFINITYL, &NANL, 0},
+ {"cosl", cosl, &MINFL, &NANL, 0},
+ {"sinl", sinl, &NANL, &NANL, 0},
+ {"sinl", sinl, &NEGZEROL, &NEGZEROL, 0},
+ {"sinl", sinl, &ZEROL, &ZEROL, 0},
+ {"sinl", sinl, &INFINITYL, &NANL, 0},
+ {"sinl", sinl, &MINFL, &NANL, 0},
+ {"tanl", tanl, &NANL, &NANL, 0},
+ {"tanl", tanl, &ZEROL, &ZEROL, 0},
+ {"tanl", tanl, &NEGZEROL, &NEGZEROL, 0},
+ {"tanl", tanl, &INFINITYL, &NANL, 0},
+ {"tanl", tanl, &MINFL, &NANL, 0},
+ {"acoshl", acoshl, &NANL, &NANL, 0},
+ {"acoshl", acoshl, &ONEL, &ZEROL, 0},
+ {"acoshl", acoshl, &INFINITYL, &INFINITYL, 0},
+ {"acoshl", acoshl, &HALFL, &NANL, 0},
+ {"acoshl", acoshl, &MONEL, &NANL, 0},
+ {"asinhl", asinhl, &NANL, &NANL, 0},
+ {"asinhl", asinhl, &ZEROL, &ZEROL, 0},
+ {"asinhl", asinhl, &NEGZEROL, &NEGZEROL, 0},
+ {"asinhl", asinhl, &INFINITYL, &INFINITYL, 0},
+ {"asinhl", asinhl, &MINFL, &MINFL, 0},
+ {"atanhl", atanhl, &NANL, &NANL, 0},
+ {"atanhl", atanhl, &ZEROL, &ZEROL, 0},
+ {"atanhl", atanhl, &NEGZEROL, &NEGZEROL, 0},
+ {"atanhl", atanhl, &ONEL, &INFINITYL, 0},
+ {"atanhl", atanhl, &MONEL, &MINFL, 0},
+ {"atanhl", atanhl, &TWOL, &NANL, 0},
+ {"atanhl", atanhl, &MTWOL, &NANL, 0},
+ {"coshl", coshl, &NANL, &NANL, 0},
+ {"coshl", coshl, &ZEROL, &ONEL, 0},
+ {"coshl", coshl, &NEGZEROL, &ONEL, 0},
+ {"coshl", coshl, &INFINITYL, &INFINITYL, 0},
+ {"coshl", coshl, &MINFL, &INFINITYL, 0},
+ {"sinhl", sinhl, &NANL, &NANL, 0},
+ {"sinhl", sinhl, &ZEROL, &ZEROL, 0},
+ {"sinhl", sinhl, &NEGZEROL, &NEGZEROL, 0},
+ {"sinhl", sinhl, &INFINITYL, &INFINITYL, 0},
+ {"sinhl", sinhl, &MINFL, &MINFL, 0},
+ {"tanhl", tanhl, &NANL, &NANL, 0},
+ {"tanhl", tanhl, &ZEROL, &ZEROL, 0},
+ {"tanhl", tanhl, &NEGZEROL, &NEGZEROL, 0},
+ {"tanhl", tanhl, &INFINITYL, &ONEL, 0},
+ {"tanhl", tanhl, &MINFL, &MONEL, 0},
+ {"expl", expl, &NANL, &NANL, 0},
+ {"expl", expl, &ZEROL, &ONEL, 0},
+ {"expl", expl, &NEGZEROL, &ONEL, 0},
+ {"expl", expl, &INFINITYL, &INFINITYL, 0},
+ {"expl", expl, &MINFL, &ZEROL, 0},
+ {"exp2l", exp2l, &NANL, &NANL, 0},
+ {"exp2l", exp2l, &ZEROL, &ONEL, 0},
+ {"exp2l", exp2l, &NEGZEROL, &ONEL, 0},
+ {"exp2l", exp2l, &INFINITYL, &INFINITYL, 0},
+ {"exp2l", exp2l, &MINFL, &ZEROL, 0},
+ {"expm1l", expm1l, &NANL, &NANL, 0},
+ {"expm1l", expm1l, &ZEROL, &ZEROL, 0},
+ {"expm1l", expm1l, &NEGZEROL, &NEGZEROL, 0},
+ {"expm1l", expm1l, &INFINITYL, &INFINITYL, 0},
+ {"expm1l", expm1l, &MINFL, &MONEL, 0},
+ {"logl", logl, &NANL, &NANL, 0},
+ {"logl", logl, &ZEROL, &MINFL, 0},
+ {"logl", logl, &NEGZEROL, &MINFL, 0},
+ {"logl", logl, &ONEL, &ZEROL, 0},
+ {"logl", logl, &MONEL, &NANL, 0},
+ {"logl", logl, &INFINITYL, &INFINITYL, 0},
+ {"log10l", log10l, &NANL, &NANL, 0},
+ {"log10l", log10l, &ZEROL, &MINFL, 0},
+ {"log10l", log10l, &NEGZEROL, &MINFL, 0},
+ {"log10l", log10l, &ONEL, &ZEROL, 0},
+ {"log10l", log10l, &MONEL, &NANL, 0},
+ {"log10l", log10l, &INFINITYL, &INFINITYL, 0},
+ {"log1pl", log1pl, &NANL, &NANL, 0},
+ {"log1pl", log1pl, &ZEROL, &ZEROL, 0},
+ {"log1pl", log1pl, &NEGZEROL, &NEGZEROL, 0},
+ {"log1pl", log1pl, &MONEL, &MINFL, 0},
+ {"log1pl", log1pl, &MTWOL, &NANL, 0},
+ {"log1pl", log1pl, &INFINITYL, &INFINITYL, 0},
+ {"log2l", log2l, &NANL, &NANL, 0},
+ {"log2l", log2l, &ZEROL, &MINFL, 0},
+ {"log2l", log2l, &NEGZEROL, &MINFL, 0},
+ {"log2l", log2l, &MONEL, &NANL, 0},
+ {"log2l", log2l, &INFINITYL, &INFINITYL, 0},
+ /* {"fabsl", fabsl, &NANL, &NANL, 0}, */
+ {"fabsl", fabsl, &ONEL, &ONEL, 0},
+ {"fabsl", fabsl, &MONEL, &ONEL, 0},
+ {"fabsl", fabsl, &ZEROL, &ZEROL, 0},
+ {"fabsl", fabsl, &NEGZEROL, &ZEROL, 0},
+ {"fabsl", fabsl, &INFINITYL, &INFINITYL, 0},
+ {"fabsl", fabsl, &MINFL, &INFINITYL, 0},
+ {"cbrtl", cbrtl, &NANL, &NANL, 0},
+ {"cbrtl", cbrtl, &ZEROL, &ZEROL, 0},
+ {"cbrtl", cbrtl, &NEGZEROL, &NEGZEROL, 0},
+ {"cbrtl", cbrtl, &INFINITYL, &INFINITYL, 0},
+ {"cbrtl", cbrtl, &MINFL, &MINFL, 0},
+ {"erfl", erfl, &NANL, &NANL, 0},
+ {"erfl", erfl, &ZEROL, &ZEROL, 0},
+ {"erfl", erfl, &NEGZEROL, &NEGZEROL, 0},
+ {"erfl", erfl, &INFINITYL, &ONEL, 0},
+ {"erfl", erfl, &MINFL, &MONEL, 0},
+ {"erfcl", erfcl, &NANL, &NANL, 0},
+ {"erfcl", erfcl, &INFINITYL, &ZEROL, 0},
+ {"erfcl", erfcl, &MINFL, &TWOL, 0},
+ {"gammal", gammal, &NANL, &NANL, 0},
+ {"gammal", gammal, &INFINITYL, &INFINITYL, 0},
+ {"gammal", gammal, &MONEL, &NANL, 0},
+ {"gammal", gammal, &ZEROL, &NANL, 0},
+ {"gammal", gammal, &MINFL, &NANL, 0},
+ {"lgaml", lgaml, &NANL, &NANL, 0},
+ {"lgaml", lgaml, &INFINITYL, &INFINITYL, 0},
+ {"lgaml", lgaml, &MONEL, &INFINITYL, 0},
+ {"lgaml", lgaml, &ZEROL, &INFINITYL, 0},
+ {"lgaml", lgaml, &MINFL, &INFINITYL, 0},
+ {"ceill", ceill, &NANL, &NANL, 0},
+ {"ceill", ceill, &ZEROL, &ZEROL, 0},
+ {"ceill", ceill, &NEGZEROL, &NEGZEROL, 0},
+ {"ceill", ceill, &INFINITYL, &INFINITYL, 0},
+ {"ceill", ceill, &MINFL, &MINFL, 0},
+ {"floorl", floorl, &NANL, &NANL, 0},
+ {"floorl", floorl, &ZEROL, &ZEROL, 0},
+ {"floorl", floorl, &NEGZEROL, &NEGZEROL, 0},
+ {"floorl", floorl, &INFINITYL, &INFINITYL, 0},
+ {"floorl", floorl, &MINFL, &MINFL, 0},
+ {"null", NULL, &ZEROL, &ZEROL, 0},
+};
+
+/* Functions of two variables. */
+long double atan2l (long double, long double);
+long double powl (long double, long double);
+
+struct twoarguments
+ {
+ char *name; /* Name of the function. */
+ long double (*func) (long double, long double);
+ long double *arg1;
+ long double *arg2;
+ long double *answer;
+ int thresh;
+ };
+
+struct twoarguments test2[] =
+{
+ {"atan2l", atan2l, &ZEROL, &ONEL, &ZEROL, 0},
+ {"atan2l", atan2l, &NEGZEROL, &ONEL,&NEGZEROL, 0},
+ {"atan2l", atan2l, &ZEROL, &ZEROL, &ZEROL, 0},
+ {"atan2l", atan2l, &NEGZEROL, &ZEROL, &NEGZEROL, 0},
+ {"atan2l", atan2l, &ZEROL, &MONEL, &PIL, 0},
+ {"atan2l", atan2l, &NEGZEROL, &MONEL, &MPIL, 0},
+ {"atan2l", atan2l, &ZEROL, &NEGZEROL, &PIL, 0},
+ {"atan2l", atan2l, &NEGZEROL, &NEGZEROL, &MPIL, 0},
+ {"atan2l", atan2l, &ONEL, &ZEROL, &PIO2L, 0},
+ {"atan2l", atan2l, &ONEL, &NEGZEROL, &PIO2L, 0},
+ {"atan2l", atan2l, &MONEL, &ZEROL, &MPIO2L, 0},
+ {"atan2l", atan2l, &MONEL, &NEGZEROL, &MPIO2L, 0},
+ {"atan2l", atan2l, &ONEL, &INFINITYL, &ZEROL, 0},
+ {"atan2l", atan2l, &MONEL, &INFINITYL, &NEGZEROL, 0},
+ {"atan2l", atan2l, &INFINITYL, &ONEL, &PIO2L, 0},
+ {"atan2l", atan2l, &INFINITYL, &MONEL, &PIO2L, 0},
+ {"atan2l", atan2l, &MINFL, &ONEL, &MPIO2L, 0},
+ {"atan2l", atan2l, &MINFL, &MONEL, &MPIO2L, 0},
+ {"atan2l", atan2l, &ONEL, &MINFL, &PIL, 0},
+ {"atan2l", atan2l, &MONEL, &MINFL, &MPIL, 0},
+ {"atan2l", atan2l, &INFINITYL, &INFINITYL, &PIO4L, 0},
+ {"atan2l", atan2l, &MINFL, &INFINITYL, &MPIO4L, 0},
+ {"atan2l", atan2l, &INFINITYL, &MINFL, &THPIO4L, 0},
+ {"atan2l", atan2l, &MINFL, &MINFL, &MTHPIO4L, 0},
+ {"atan2l", atan2l, &ONEL, &ONEL, &PIO4L, 0},
+ {"atan2l", atan2l, &NANL, &ONEL, &NANL, 0},
+ {"atan2l", atan2l, &ONEL, &NANL, &NANL, 0},
+ {"atan2l", atan2l, &NANL, &NANL, &NANL, 0},
+ {"powl", powl, &ONEL, &ZEROL, &ONEL, 0},
+ {"powl", powl, &ONEL, &NEGZEROL, &ONEL, 0},
+ {"powl", powl, &MONEL, &ZEROL, &ONEL, 0},
+ {"powl", powl, &MONEL, &NEGZEROL, &ONEL, 0},
+ {"powl", powl, &INFINITYL, &ZEROL, &ONEL, 0},
+ {"powl", powl, &INFINITYL, &NEGZEROL, &ONEL, 0},
+ {"powl", powl, &NANL, &ZEROL, &ONEL, 0},
+ {"powl", powl, &NANL, &NEGZEROL, &ONEL, 0},
+ {"powl", powl, &TWOL, &INFINITYL, &INFINITYL, 0},
+ {"powl", powl, &MTWOL, &INFINITYL, &INFINITYL, 0},
+ {"powl", powl, &HALFL, &INFINITYL, &ZEROL, 0},
+ {"powl", powl, &MHALFL, &INFINITYL, &ZEROL, 0},
+ {"powl", powl, &TWOL, &MINFL, &ZEROL, 0},
+ {"powl", powl, &MTWOL, &MINFL, &ZEROL, 0},
+ {"powl", powl, &HALFL, &MINFL, &INFINITYL, 0},
+ {"powl", powl, &MHALFL, &MINFL, &INFINITYL, 0},
+ {"powl", powl, &INFINITYL, &HALFL, &INFINITYL, 0},
+ {"powl", powl, &INFINITYL, &TWOL, &INFINITYL, 0},
+ {"powl", powl, &INFINITYL, &MHALFL, &ZEROL, 0},
+ {"powl", powl, &INFINITYL, &MTWOL, &ZEROL, 0},
+ {"powl", powl, &MINFL, &THREEL, &MINFL, 0},
+ {"powl", powl, &MINFL, &TWOL, &INFINITYL, 0},
+ {"powl", powl, &MINFL, &MTHREEL, &NEGZEROL, 0},
+ {"powl", powl, &MINFL, &MTWOL, &ZEROL, 0},
+ {"powl", powl, &NANL, &ONEL, &NANL, 0},
+ {"powl", powl, &ONEL, &NANL, &NANL, 0},
+ {"powl", powl, &NANL, &NANL, &NANL, 0},
+ {"powl", powl, &ONEL, &INFINITYL, &NANL, 0},
+ {"powl", powl, &MONEL, &INFINITYL, &NANL, 0},
+ {"powl", powl, &ONEL, &MINFL, &NANL, 0},
+ {"powl", powl, &MONEL, &MINFL, &NANL, 0},
+ {"powl", powl, &MTWOL, &HALFL, &NANL, 0},
+ {"powl", powl, &ZEROL, &MTHREEL, &INFINITYL, 0},
+ {"powl", powl, &NEGZEROL, &MTHREEL, &MINFL, 0},
+ {"powl", powl, &ZEROL, &MHALFL, &INFINITYL, 0},
+ {"powl", powl, &NEGZEROL, &MHALFL, &INFINITYL, 0},
+ {"powl", powl, &ZEROL, &THREEL, &ZEROL, 0},
+ {"powl", powl, &NEGZEROL, &THREEL, &NEGZEROL, 0},
+ {"powl", powl, &ZEROL, &HALFL, &ZEROL, 0},
+ {"powl", powl, &NEGZEROL, &HALFL, &ZEROL, 0},
+ {"null", NULL, &ZEROL, &ZEROL, &ZEROL, 0},
+};
+
+/* Integer functions of one variable. */
+
+int isnanl (long double);
+int signbitl (long double);
+
+struct intans
+ {
+ char *name; /* Name of the function. */
+ int (*func) (long double);
+ long double *arg1;
+ int ianswer;
+ };
+
+struct intans test3[] =
+{
+ {"isfinitel", isfinitel, &ZEROL, 1},
+ {"isfinitel", isfinitel, &INFINITYL, 0},
+ {"isfinitel", isfinitel, &MINFL, 0},
+ {"isnanl", isnanl, &NANL, 1},
+ {"isnanl", isnanl, &INFINITYL, 0},
+ {"isnanl", isnanl, &ZEROL, 0},
+ {"isnanl", isnanl, &NEGZEROL, 0},
+ {"signbitl", signbitl, &NEGZEROL, 1},
+ {"signbitl", signbitl, &MONEL, 1},
+ {"signbitl", signbitl, &ZEROL, 0},
+ {"signbitl", signbitl, &ONEL, 0},
+ {"signbitl", signbitl, &MINFL, 1},
+ {"signbitl", signbitl, &INFINITYL, 0},
+ {"null", NULL, &ZEROL, 0},
+};
+
+static volatile long double x1;
+static volatile long double x2;
+static volatile long double y;
+static volatile long double answer;
+
+int
+main ()
+{
+ int i, nerrors, k, ianswer, ntests;
+ long double (*fun1) (long double);
+ long double (*fun2) (long double, long double);
+ int (*fun3) (long double);
+ long double e;
+ union
+ {
+ long double d;
+ char c[12];
+ } u, v;
+
+ /* This masks off fpu exceptions on i386. */
+ /* setfpu(0x137f); */
+ nerrors = 0;
+ ntests = 0;
+ MINFL = -INFINITYL;
+ MPIL = -PIL;
+ MPIO2L = -PIO2L;
+ MPIO4L = -PIO4L;
+ i = 0;
+ for (;;)
+ {
+ fun1 = test1[i].func;
+ if (fun1 == NULL)
+ break;
+ x1 = *(test1[i].arg1);
+ y = (*(fun1)) (x1);
+ answer = *(test1[i].answer);
+ if (test1[i].thresh == 0)
+ {
+ v.d = answer;
+ u.d = y;
+ if (memcmp(u.c, v.c, 10) != 0)
+ {
+ /* O.K. if both are NaNs of some sort. */
+ if (isnanl(v.d) && isnanl(u.d))
+ goto nxttest1;
+ goto wrongone;
+ }
+ else
+ goto nxttest1;
+ }
+ if (y != answer)
+ {
+ e = y - answer;
+ if (answer != 0.0L)
+ e = e / answer;
+ if (e < 0)
+ e = -e;
+ if (e > test1[i].thresh * MACHEPL)
+ {
+wrongone:
+ printf ("%s (%.20Le) = %.20Le\n should be %.20Le\n",
+ test1[i].name, x1, y, answer);
+ nerrors += 1;
+ }
+ }
+nxttest1:
+ ntests += 1;
+ i += 1;
+ }
+
+ i = 0;
+ for (;;)
+ {
+ fun2 = test2[i].func;
+ if (fun2 == NULL)
+ break;
+ x1 = *(test2[i].arg1);
+ x2 = *(test2[i].arg2);
+ y = (*(fun2)) (x1, x2);
+ answer = *(test2[i].answer);
+ if (test2[i].thresh == 0)
+ {
+ v.d = answer;
+ u.d = y;
+ if (memcmp(u.c, v.c, 10) != 0)
+ {
+ /* O.K. if both are NaNs of some sort. */
+ if (isnanl(v.d) && isnanl(u.d))
+ goto nxttest2;
+ goto wrongtwo;
+ }
+ else
+ goto nxttest2;
+ }
+ if (y != answer)
+ {
+ e = y - answer;
+ if (answer != 0.0L)
+ e = e / answer;
+ if (e < 0)
+ e = -e;
+ if (e > test2[i].thresh * MACHEPL)
+ {
+wrongtwo:
+ printf ("%s (%.20Le, %.20Le) = %.20Le\n should be %.20Le\n",
+ test2[i].name, x1, x2, y, answer);
+ nerrors += 1;
+ }
+ }
+nxttest2:
+ ntests += 1;
+ i += 1;
+ }
+
+
+ i = 0;
+ for (;;)
+ {
+ fun3 = test3[i].func;
+ if (fun3 == NULL)
+ break;
+ x1 = *(test3[i].arg1);
+ k = (*(fun3)) (x1);
+ ianswer = test3[i].ianswer;
+ if (k != ianswer)
+ {
+ printf ("%s (%.20Le) = %d\n should be. %d\n",
+ test3[i].name, x1, k, ianswer);
+ nerrors += 1;
+ }
+ ntests += 1;
+ i += 1;
+ }
+
+ printf ("testvect: %d errors in %d tests\n", nerrors, ntests);
+ exit (0);
+}
diff --git a/libm/ldouble/unityl.c b/libm/ldouble/unityl.c
new file mode 100644
index 000000000..10670ce3a
--- /dev/null
+++ b/libm/ldouble/unityl.c
@@ -0,0 +1,128 @@
+/* unityl.c
+ *
+ * Relative error approximations for function arguments near
+ * unity.
+ *
+ * log1p(x) = log(1+x)
+ * expm1(x) = exp(x) - 1
+ * cosm1(x) = cos(x) - 1
+ *
+ */
+
+
+/* log1p(x) = log(1 + x)
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0.5, 2 30000 1.4e-19 4.1e-20
+ *
+ */
+
+#include <math.h>
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 2.32e-20
+ */
+static long double LP[] = {
+ 4.5270000862445199635215E-5L,
+ 4.9854102823193375972212E-1L,
+ 6.5787325942061044846969E0L,
+ 2.9911919328553073277375E1L,
+ 6.0949667980987787057556E1L,
+ 5.7112963590585538103336E1L,
+ 2.0039553499201281259648E1L,
+};
+static long double LQ[] = {
+/* 1.0000000000000000000000E0L,*/
+ 1.5062909083469192043167E1L,
+ 8.3047565967967209469434E1L,
+ 2.2176239823732856465394E2L,
+ 3.0909872225312059774938E2L,
+ 2.1642788614495947685003E2L,
+ 6.0118660497603843919306E1L,
+};
+
+#define SQRTH 0.70710678118654752440L
+#define SQRT2 1.41421356237309504880L
+#ifdef ANSIPROT
+extern long double logl ( long double );
+extern long double expl ( long double );
+extern long double cosl ( long double );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double, void *, int );
+#else
+long double logl(), expl(), cosl(), polevll(), p1evll();
+#endif
+
+long double log1pl(x)
+long double x;
+{
+long double z;
+
+z = 1.0L + x;
+if( (z < SQRTH) || (z > SQRT2) )
+ return( logl(z) );
+z = x*x;
+z = -0.5L * z + x * ( z * polevll( x, LP, 6 ) / p1evll( x, LQ, 6 ) );
+return (x + z);
+}
+
+
+
+/* expm1(x) = exp(x) - 1 */
+
+/* e^x = 1 + 2x P(x^2)/( Q(x^2) - P(x^2) )
+ * -0.5 <= x <= 0.5
+ */
+
+static long double EP[3] = {
+ 1.2617719307481059087798E-4L,
+ 3.0299440770744196129956E-2L,
+ 9.9999999999999999991025E-1L,
+};
+static long double EQ[4] = {
+ 3.0019850513866445504159E-6L,
+ 2.5244834034968410419224E-3L,
+ 2.2726554820815502876593E-1L,
+ 2.0000000000000000000897E0L,
+};
+
+long double expm1l(x)
+long double x;
+{
+long double r, xx;
+
+if( (x < -0.5L) || (x > 0.5L) )
+ return( expl(x) - 1.0L );
+xx = x * x;
+r = x * polevll( xx, EP, 2 );
+r = r/( polevll( xx, EQ, 3 ) - r );
+return (r + r);
+}
+
+
+
+/* cosm1(x) = cos(x) - 1 */
+
+static long double coscof[7] = {
+ 4.7377507964246204691685E-14L,
+-1.1470284843425359765671E-11L,
+ 2.0876754287081521758361E-9L,
+-2.7557319214999787979814E-7L,
+ 2.4801587301570552304991E-5L,
+-1.3888888888888872993737E-3L,
+ 4.1666666666666666609054E-2L,
+};
+
+extern long double PIO4L;
+
+long double cosm1l(x)
+long double x;
+{
+long double xx;
+
+if( (x < -PIO4L) || (x > PIO4L) )
+ return( cosl(x) - 1.0L );
+xx = x * x;
+xx = -0.5L*xx + xx * xx * polevll( xx, coscof, 6 );
+return xx;
+}
diff --git a/libm/ldouble/wronkl.c b/libm/ldouble/wronkl.c
new file mode 100644
index 000000000..bec958f01
--- /dev/null
+++ b/libm/ldouble/wronkl.c
@@ -0,0 +1,67 @@
+/* Wronksian test for Bessel functions. */
+
+long double jnl (), ynl (), floorl ();
+#define PI 3.14159265358979323846L
+
+long double y, Jn, Jnp1, Jmn, Jmnp1, Yn, Ynp1;
+long double w1, w2, err1, max1, err2, max2;
+void wronk ();
+
+main ()
+{
+ long double x, delta;
+ int n, i, j;
+
+ max1 = 0.0L;
+ max2 = 0.0L;
+ delta = 0.6 / PI;
+ for (n = -30; n <= 30; n++)
+ {
+ x = -30.0;
+ while (x < 30.0)
+ {
+ wronk (n, x);
+ x += delta;
+ }
+ delta += .00123456;
+ }
+}
+
+void
+wronk (n, x)
+ int n;
+ long double x;
+{
+
+ Jnp1 = jnl (n + 1, x);
+ Jmn = jnl (-n, x);
+ Jn = jnl (n, x);
+ Jmnp1 = jnl (-(n + 1), x);
+ /* This should be trivially zero. */
+ err1 = Jnp1 * Jmn + Jn * Jmnp1;
+ if (err1 < 0.0)
+ err1 = -err1;
+ if (err1 > max1)
+ {
+ max1 = err1;
+ printf ("1 %3d %.5Le %.3Le\n", n, x, max1);
+ }
+ if (x < 0.0)
+ {
+ x = -x;
+ Jn = jnl (n, x);
+ Jnp1 = jnl (n + 1, x);
+ }
+ Yn = ynl (n, x);
+ Ynp1 = ynl (n + 1, x);
+ /* The Wronksian. */
+ w1 = Jnp1 * Yn - Jn * Ynp1;
+ /* What the Wronksian should be. */
+ w2 = 2.0 / (PI * x);
+ err2 = w1 - w2;
+ if (err2 > max2)
+ {
+ max2 = err2;
+ printf ("2 %3d %.5Le %.3Le\n", n, x, max2);
+ }
+}
diff --git a/libm/ldouble/ynl.c b/libm/ldouble/ynl.c
new file mode 100644
index 000000000..444792850
--- /dev/null
+++ b/libm/ldouble/ynl.c
@@ -0,0 +1,113 @@
+/* ynl.c
+ *
+ * Bessel function of second kind of integer order
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, ynl();
+ * int n;
+ *
+ * y = ynl( n, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns Bessel function of order n, where n is a
+ * (possibly negative) integer.
+ *
+ * The function is evaluated by forward recurrence on
+ * n, starting with values computed by the routines
+ * y0l() and y1l().
+ *
+ * If n = 0 or 1 the routine for y0l or y1l is called
+ * directly.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Absolute error, except relative error when y > 1.
+ * x >= 0, -30 <= n <= +30.
+ * arithmetic domain # trials peak rms
+ * IEEE -30, 30 10000 1.3e-18 1.8e-19
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ * message condition value returned
+ * ynl singularity x = 0 MAXNUML
+ * ynl overflow MAXNUML
+ *
+ * Spot checked against tables for x, n between 0 and 100.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.1: December, 1988
+Copyright 1984, 1987 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+extern long double MAXNUML;
+#ifdef ANSIPROT
+extern long double y0l ( long double );
+extern long double y1l ( long double );
+#else
+long double y0l(), y1l();
+#endif
+
+long double ynl( n, x )
+int n;
+long double x;
+{
+long double an, anm1, anm2, r;
+int k, sign;
+
+if( n < 0 )
+ {
+ n = -n;
+ if( (n & 1) == 0 ) /* -1**n */
+ sign = 1;
+ else
+ sign = -1;
+ }
+else
+ sign = 1;
+
+
+if( n == 0 )
+ return( sign * y0l(x) );
+if( n == 1 )
+ return( sign * y1l(x) );
+
+/* test for overflow */
+if( x <= 0.0L )
+ {
+ mtherr( "ynl", SING );
+ return( -MAXNUML );
+ }
+
+/* forward recurrence on n */
+
+anm2 = y0l(x);
+anm1 = y1l(x);
+k = 1;
+r = 2 * k;
+do
+ {
+ an = r * anm1 / x - anm2;
+ anm2 = anm1;
+ anm1 = an;
+ r += 2.0L;
+ ++k;
+ }
+while( k < n );
+
+
+return( sign * an );
+}