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-rw-r--r--test/math/Makefile182
-rw-r--r--test/math/econst.c192
-rw-r--r--test/math/eexp.c154
-rw-r--r--test/math/ehead.h84
-rw-r--r--test/math/elog.c184
-rw-r--r--test/math/eparanoi.c7100
-rw-r--r--test/math/epow.c430
-rw-r--r--test/math/etanh.c104
-rw-r--r--test/math/etodec.c362
-rw-r--r--test/math/ieee.c8238
-rw-r--r--test/math/ieetst.c1700
-rw-r--r--test/math/ieetst.doc264
-rw-r--r--test/math/mconf.h216
-rw-r--r--test/math/mtherr.c192
14 files changed, 9701 insertions, 9701 deletions
diff --git a/test/math/Makefile b/test/math/Makefile
index be7f261de..4d0bc5ee6 100644
--- a/test/math/Makefile
+++ b/test/math/Makefile
@@ -1,91 +1,91 @@
-# Makefile for uClibc
-#
-# Copyright (C) 2000,2001 Erik Andersen <andersen@uclibc.org>
-#
-# 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
-
-
-
-# Unix makefile for ieetst, eparanoi.
-# Set LARGEMEM 1 in qcalc.h for 32-bit memory addresses.
-# Define computer type and/or endianness in mconf.h.
-#
-# Configure eparanoi.c for desired arithmetic test;
-# also define appropriate version of setprec.o, or use a stub that
-# does no FPU setup. To test native arithmetic, eparanoi uses
-# the system libraries only; compile simply by `cc eparanoi.c -lm'.
-#
-
-TESTDIR=../
-include $(TESTDIR)/Rules.mak
-
-
-#CC = gcc
-#CFLAGS= -O
-INCS= mconf.h ehead.h
-OBJS = ieee.o econst.o eexp.o elog.o epow.o etanh.o etodec.o mtherr.o #setprec.o
-TARGETS=ieetst eparanoi
-
-all: $(TARGETS)
-
-ieetst: ieetst.o $(OBJS) drand.o $(INCS)
- $(CC) -o ieetst ieetst.o $(OBJS) drand.o -lc -lm
-
-eparanoi: eparanoi.o $(OBJS) $(INCS)
- $(CC) -o eparanoi eparanoi.o $(OBJS) -lc -lm
-
-#setprec.o: setprec.387
-# as -o setprec.o setprec.387
-
-#setprec.o: setprec.688
-# as -o setprec.o setprec.688
-
-ieee.o: ieee.c $(INCS)
- $(CC) $(CFLAGS) -c ieee.c
-
-econst.o: econst.c $(INCS)
- $(CC) $(CFLAGS) -c econst.c
-
-elog.o: elog.c $(INCS)
- $(CC) $(CFLAGS) -c elog.c
-
-eexp.o: eexp.c $(INCS)
- $(CC) $(CFLAGS) -c eexp.c
-
-etanh.o: etanh.c $(INCS)
- $(CC) $(CFLAGS) -c etanh.c
-
-epow.o: epow.c $(INCS)
- $(CC) $(CFLAGS) -c epow.c
-
-mtherr.o: mtherr.c $(INCS)
- $(CC) $(CFLAGS) -c mtherr.c
-
-ieetst.o: ieetst.c $(INCS)
- $(CC) $(CFLAGS) -c ieetst.c
-
-drand.o: drand.c $(INCS)
- $(CC) $(CFLAGS) -c drand.c
-
-etodec.o: etodec.c $(INCS)
- $(CC) $(CFLAGS) -c etodec.c
-
-eparanoi.o: eparanoi.c $(INCS)
- $(CC) $(CFLAGS) -c eparanoi.c
-
-clean:
- rm -f *.[oa] *~ core $(TARGETS)
-
-
+# Makefile for uClibc
+#
+# Copyright (C) 2000,2001 Erik Andersen <andersen@uclibc.org>
+#
+# 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
+
+
+
+# Unix makefile for ieetst, eparanoi.
+# Set LARGEMEM 1 in qcalc.h for 32-bit memory addresses.
+# Define computer type and/or endianness in mconf.h.
+#
+# Configure eparanoi.c for desired arithmetic test;
+# also define appropriate version of setprec.o, or use a stub that
+# does no FPU setup. To test native arithmetic, eparanoi uses
+# the system libraries only; compile simply by `cc eparanoi.c -lm'.
+#
+
+TESTDIR=../
+include $(TESTDIR)/Rules.mak
+
+
+#CC = gcc
+#CFLAGS= -O
+INCS= mconf.h ehead.h
+OBJS = ieee.o econst.o eexp.o elog.o epow.o etanh.o etodec.o mtherr.o #setprec.o
+TARGETS=ieetst eparanoi
+
+all: $(TARGETS)
+
+ieetst: ieetst.o $(OBJS) drand.o $(INCS)
+ $(CC) -o ieetst ieetst.o $(OBJS) drand.o -lc -lm
+
+eparanoi: eparanoi.o $(OBJS) $(INCS)
+ $(CC) -o eparanoi eparanoi.o $(OBJS) -lc -lm
+
+#setprec.o: setprec.387
+# as -o setprec.o setprec.387
+
+#setprec.o: setprec.688
+# as -o setprec.o setprec.688
+
+ieee.o: ieee.c $(INCS)
+ $(CC) $(CFLAGS) -c ieee.c
+
+econst.o: econst.c $(INCS)
+ $(CC) $(CFLAGS) -c econst.c
+
+elog.o: elog.c $(INCS)
+ $(CC) $(CFLAGS) -c elog.c
+
+eexp.o: eexp.c $(INCS)
+ $(CC) $(CFLAGS) -c eexp.c
+
+etanh.o: etanh.c $(INCS)
+ $(CC) $(CFLAGS) -c etanh.c
+
+epow.o: epow.c $(INCS)
+ $(CC) $(CFLAGS) -c epow.c
+
+mtherr.o: mtherr.c $(INCS)
+ $(CC) $(CFLAGS) -c mtherr.c
+
+ieetst.o: ieetst.c $(INCS)
+ $(CC) $(CFLAGS) -c ieetst.c
+
+drand.o: drand.c $(INCS)
+ $(CC) $(CFLAGS) -c drand.c
+
+etodec.o: etodec.c $(INCS)
+ $(CC) $(CFLAGS) -c etodec.c
+
+eparanoi.o: eparanoi.c $(INCS)
+ $(CC) $(CFLAGS) -c eparanoi.c
+
+clean:
+ rm -f *.[oa] *~ core $(TARGETS)
+
+
diff --git a/test/math/econst.c b/test/math/econst.c
index 21523e568..cfddbe3e2 100644
--- a/test/math/econst.c
+++ b/test/math/econst.c
@@ -1,96 +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[];
-
+/* 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/test/math/eexp.c b/test/math/eexp.c
index dd2a64e1c..14ea9899d 100644
--- a/test/math/eexp.c
+++ b/test/math/eexp.c
@@ -1,77 +1,77 @@
-/* xexp.c */
-/* exponential function check routine */
-/* by Stephen L. Moshier. */
-
-
-#include "ehead.h"
-
-/*
-extern int powinited;
-extern short maxposint[], maxnegint[];
-*/
-
-void eexp( x, y )
-unsigned short *x, *y;
-{
-unsigned short num[NE], den[NE], x2[NE];
-long i;
-unsigned short sign, expchk;
-
-/* range reduction theory: x = i + f, 0<=f<1;
- * e**x = e**i * e**f
- * e**i = 2**(i/log 2).
- * Let i/log2 = i1 + f1, 0<=f1<1.
- * Then e**i = 2**i1 * 2**f1, so
- * e**x = 2**i1 * e**(log 2 * f1) * e**f.
- */
-/*
-if( powinited == 0 )
- initpow();
-*/
-if( ecmp(x, ezero) == 0 )
- {
- emov( eone, y );
- return;
- }
-emov(x, x2);
-expchk = x2[NE-1];
-sign = expchk & 0x8000;
-x2[NE-1] &= 0x7fff;
-
-/* Test for excessively large argument */
-expchk &= 0x7fff;
-if( expchk > (EXONE + 15) )
- {
- eclear( y );
- if( sign == 0 )
- einfin( y );
- return;
- }
-
-eifrac( x2, &i, num ); /* x = i + f */
-
-if( i != 0 )
- {
- ltoe( &i, den ); /* floating point i */
- ediv( elog2, den, den ); /* i/log 2 */
- eifrac( den, &i, den ); /* i/log 2 = i1 + f1 */
- emul( elog2, den, den ); /* log 2 * f1 */
- eadd( den, num, x2 ); /* log 2 * f1 + f */
- }
-
-/*x2[NE-1] -= 1;*/
-eldexp( x2, -1L, x2 ); /* divide by 2 */
-etanh( x2, x2 ); /* tanh( x/2 ) */
-eadd( x2, eone, num ); /* 1 + tanh */
-eneg( x2 );
-eadd( x2, eone, den ); /* 1 - tanh */
-ediv( den, num, y ); /* (1 + tanh)/(1 - tanh) */
-
-/*y[NE-1] += i;*/
-if( sign )
- {
- ediv( y, eone, y );
- i = -i;
- }
-eldexp( y, i, y ); /* multiply by 2**i */
-}
+/* xexp.c */
+/* exponential function check routine */
+/* by Stephen L. Moshier. */
+
+
+#include "ehead.h"
+
+/*
+extern int powinited;
+extern short maxposint[], maxnegint[];
+*/
+
+void eexp( x, y )
+unsigned short *x, *y;
+{
+unsigned short num[NE], den[NE], x2[NE];
+long i;
+unsigned short sign, expchk;
+
+/* range reduction theory: x = i + f, 0<=f<1;
+ * e**x = e**i * e**f
+ * e**i = 2**(i/log 2).
+ * Let i/log2 = i1 + f1, 0<=f1<1.
+ * Then e**i = 2**i1 * 2**f1, so
+ * e**x = 2**i1 * e**(log 2 * f1) * e**f.
+ */
+/*
+if( powinited == 0 )
+ initpow();
+*/
+if( ecmp(x, ezero) == 0 )
+ {
+ emov( eone, y );
+ return;
+ }
+emov(x, x2);
+expchk = x2[NE-1];
+sign = expchk & 0x8000;
+x2[NE-1] &= 0x7fff;
+
+/* Test for excessively large argument */
+expchk &= 0x7fff;
+if( expchk > (EXONE + 15) )
+ {
+ eclear( y );
+ if( sign == 0 )
+ einfin( y );
+ return;
+ }
+
+eifrac( x2, &i, num ); /* x = i + f */
+
+if( i != 0 )
+ {
+ ltoe( &i, den ); /* floating point i */
+ ediv( elog2, den, den ); /* i/log 2 */
+ eifrac( den, &i, den ); /* i/log 2 = i1 + f1 */
+ emul( elog2, den, den ); /* log 2 * f1 */
+ eadd( den, num, x2 ); /* log 2 * f1 + f */
+ }
+
+/*x2[NE-1] -= 1;*/
+eldexp( x2, -1L, x2 ); /* divide by 2 */
+etanh( x2, x2 ); /* tanh( x/2 ) */
+eadd( x2, eone, num ); /* 1 + tanh */
+eneg( x2 );
+eadd( x2, eone, den ); /* 1 - tanh */
+ediv( den, num, y ); /* (1 + tanh)/(1 - tanh) */
+
+/*y[NE-1] += i;*/
+if( sign )
+ {
+ ediv( y, eone, y );
+ i = -i;
+ }
+eldexp( y, i, y ); /* multiply by 2**i */
+}
diff --git a/test/math/ehead.h b/test/math/ehead.h
index 746b60df7..24c95ce05 100644
--- a/test/math/ehead.h
+++ b/test/math/ehead.h
@@ -1,42 +1,42 @@
-
-/* Include file for extended precision arithmetic programs.
- */
-
-/* Number of 16 bit words in external x type format */
-#define NE 6
-
-/* 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();
-void mtherr();
-extern unsigned short ezero[], ehalf[], eone[], etwo[];
-extern unsigned short elog2[], esqrt2[];
-
-
-/* by Stephen L. Moshier. */
+
+/* Include file for extended precision arithmetic programs.
+ */
+
+/* Number of 16 bit words in external x type format */
+#define NE 6
+
+/* 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();
+void mtherr();
+extern unsigned short ezero[], ehalf[], eone[], etwo[];
+extern unsigned short elog2[], esqrt2[];
+
+
+/* by Stephen L. Moshier. */
diff --git a/test/math/elog.c b/test/math/elog.c
index 8afc1e5b4..bc517b197 100644
--- a/test/math/elog.c
+++ b/test/math/elog.c
@@ -1,92 +1,92 @@
-/* xlog.c */
-/* natural logarithm */
-/* by Stephen L. Moshier. */
-
-#include "mconf.h"
-#include "ehead.h"
-
-
-
-void elog( x, y )
-unsigned short *x, *y;
-{
-unsigned short xx[NE], z[NE], a[NE], b[NE], t[NE], qj[NE];
-long ex;
-int fex;
-
-
-if( x[NE-1] & (unsigned short )0x8000 )
- {
- eclear(y);
- mtherr( "elog", DOMAIN );
- return;
- }
-if( ecmp( x, ezero ) == 0 )
- {
- einfin( y );
- eneg(y);
- mtherr( "elog", SING );
- return;
- }
-if( ecmp( x, eone ) == 0 )
- {
- eclear( y );
- return;
- }
-
-/* range reduction: log x = log( 2**ex * m ) = ex * log2 + log m */
-efrexp( x, &fex, xx );
-/*
-emov(x, xx );
-ex = xx[NX-1] & 0x7fff;
-ex -= 0x3ffe;
-xx[NX-1] = 0x3ffe;
-*/
-
-/* Adjust range to 1/sqrt(2), sqrt(2) */
-esqrt2[NE-1] -= 1;
-if( ecmp( xx, esqrt2 ) < 0 )
- {
- fex -= 1;
- emul( xx, etwo, xx );
- }
-esqrt2[NE-1] += 1;
-
-esub( eone, xx, a );
-if( a[NE-1] == 0 )
- {
- eclear( y );
- goto logdon;
- }
-eadd( eone, xx, b );
-ediv( b, a, y ); /* store (x-1)/(x+1) in y */
-
-emul( y, y, z );
-
-emov( eone, a );
-emov( eone, b );
-emov( eone, qj );
-do
- {
- eadd( etwo, qj, qj ); /* 2 * i + 1 */
- emul( z, a, a );
- ediv( qj, a, t );
- eadd( t, b, b );
- }
-while( ((b[NE-1] & 0x7fff) - (t[NE-1] & 0x7fff)) < NBITS );
-
-
-emul( b, y, y );
-emul( y, etwo, y );
-
-logdon:
-
-/* now add log of 2**ex */
-if( fex != 0 )
- {
- ex = fex;
- ltoe( &ex, b );
- emul( elog2, b, b );
- eadd( b, y, y );
- }
-}
+/* xlog.c */
+/* natural logarithm */
+/* by Stephen L. Moshier. */
+
+#include "mconf.h"
+#include "ehead.h"
+
+
+
+void elog( x, y )
+unsigned short *x, *y;
+{
+unsigned short xx[NE], z[NE], a[NE], b[NE], t[NE], qj[NE];
+long ex;
+int fex;
+
+
+if( x[NE-1] & (unsigned short )0x8000 )
+ {
+ eclear(y);
+ mtherr( "elog", DOMAIN );
+ return;
+ }
+if( ecmp( x, ezero ) == 0 )
+ {
+ einfin( y );
+ eneg(y);
+ mtherr( "elog", SING );
+ return;
+ }
+if( ecmp( x, eone ) == 0 )
+ {
+ eclear( y );
+ return;
+ }
+
+/* range reduction: log x = log( 2**ex * m ) = ex * log2 + log m */
+efrexp( x, &fex, xx );
+/*
+emov(x, xx );
+ex = xx[NX-1] & 0x7fff;
+ex -= 0x3ffe;
+xx[NX-1] = 0x3ffe;
+*/
+
+/* Adjust range to 1/sqrt(2), sqrt(2) */
+esqrt2[NE-1] -= 1;
+if( ecmp( xx, esqrt2 ) < 0 )
+ {
+ fex -= 1;
+ emul( xx, etwo, xx );
+ }
+esqrt2[NE-1] += 1;
+
+esub( eone, xx, a );
+if( a[NE-1] == 0 )
+ {
+ eclear( y );
+ goto logdon;
+ }
+eadd( eone, xx, b );
+ediv( b, a, y ); /* store (x-1)/(x+1) in y */
+
+emul( y, y, z );
+
+emov( eone, a );
+emov( eone, b );
+emov( eone, qj );
+do
+ {
+ eadd( etwo, qj, qj ); /* 2 * i + 1 */
+ emul( z, a, a );
+ ediv( qj, a, t );
+ eadd( t, b, b );
+ }
+while( ((b[NE-1] & 0x7fff) - (t[NE-1] & 0x7fff)) < NBITS );
+
+
+emul( b, y, y );
+emul( y, etwo, y );
+
+logdon:
+
+/* now add log of 2**ex */
+if( fex != 0 )
+ {
+ ex = fex;
+ ltoe( &ex, b );
+ emul( elog2, b, b );
+ eadd( b, y, y );
+ }
+}
diff --git a/test/math/eparanoi.c b/test/math/eparanoi.c
index 0e479f9f5..84cab73f8 100644
--- a/test/math/eparanoi.c
+++ b/test/math/eparanoi.c
@@ -1,3550 +1,3550 @@
-/* paranoia.c arithmetic tester
- *
- * This is an implementation of the PARANOIA program. It substitutes
- * subroutine calls for ALL floating point arithmetic operations.
- * This permits you to substitute your own experimental versions of
- * arithmetic routines. It also defeats compiler optimizations,
- * so for native arithmetic you can be pretty sure you are testing
- * the arithmetic and not the compiler.
- *
- * This version of PARANOIA omits the display of division by zero.
- * It also omits the test for extra precise subexpressions, since
- * they cannot occur in this context. Otherwise it includes all the
- * tests of the 27 Jan 86 distribution, plus a few additional tests.
- * Commentary has been reduced to a minimum in order to make the program
- * smaller.
- *
- * The original PARANOIA program, written by W. Kahan, C version
- * by Thos Sumner and David Gay, can be downloaded free from the
- * Internet NETLIB. An MSDOS disk can be obtained for $15 from:
- * Richard Karpinski
- * 6521 Raymond Street
- * Oakland, CA 94609
- *
- * Steve Moshier, 28 Oct 88
- * last rev: 23 May 92
- */
-
-#define DEBUG 0
-
-/* To use the native arithmetic of the computer, define NATIVE
- * to be 1. To use your own supplied arithmetic routines, NATIVE is 0.
- */
-#define NATIVE 0
-
-/* gcc real.c interface */
-#define L128DOUBLE 0
-
-#include <stdio.h>
-
-
-
-
-/* Data structure of floating point number. If NATIVE was
- * selected above, you can define LDOUBLE 1 to test 80-bit long double
- * precision or define it 0 to test 64-bit double precision.
-*/
-#define LDOUBLE 0
-#if NATIVE
-
-#define NE 1
-#if LDOUBLE
-#define FSIZE long double
-#define FLOAT(x) FSIZE x[NE]
-static FSIZE eone[NE] = {1.0L}; /* The constant 1.0 */
-#define ZSQRT sqrtl
-#define ZLOG logl
-#define ZFLOOR floorl
-#define ZPOW powl
-long double sqrtl(), logl(), floorl(), powl();
-#define FSETUP einit
-#else /* not LDOUBLE */
-#define FSIZE double
-#define FLOAT(x) FSIZE x[NE]
-static FSIZE eone[NE] = {1.0}; /* The constant 1.0 */
-#define ZSQRT sqrt
-#define ZLOG log
-#define ZFLOOR floor
-#define ZPOW pow
-double sqrt(), log(), floor(), pow();
-/* Coprocessor initialization,
- * defeat underflow trap or what have you.
- * This is required mainly on i386 and 68K processors.
- */
-#define FSETUP dprec
-#endif /* double, not LDOUBLE */
-
-#else /* not NATIVE */
-
-/* Setup for extended double type.
- * Put NE = 10 for real.c operating with TFmode support (16-byte reals)
- * Put NE = 6 for real.c operating with XFmode support (10- or 12-byte reals)
- * The value of NE must agree with that in ehead.h, if ieee.c is used.
- */
-#define NE 6
-#define FSIZE unsigned short
-#define FLOAT(x) unsigned short x[NE]
-extern unsigned short eone[];
-#define FSETUP einit
-
-/* default for FSETUP */
-/*
-einit()
-{}
-*/
-
-error(s)
-char *s;
-{
-printf( "error: %s\n", s );
-}
-
-#endif /* not NATIVE */
-
-
-
-#if L128DOUBLE
-/* real.c interface */
-
-#undef FSETUP
-#define FSETUP efsetup
-
-FLOAT(enone);
-
-#define ONE enone
-
-/* Use emov to convert from widest type to widest type, ... */
-/*
-#define ENTOE emov
-#define ETOEN emov
-*/
-
-/* ... else choose e24toe, e53toe, etc. */
-#define ENTOE e64toe
-#define ETOEN etoe64
-#define NNBITS 64
-
-#define NIBITS ((NE-1)*16)
-extern int rndprc;
-
-efsetup()
-{
-rndprc = NNBITS;
-ETOEN(eone, enone);
-}
-
-add(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-eadd(aa,bb,cc);
-ETOEN(cc,c);
-}
-
-sub(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-esub(aa,bb,cc);
-ETOEN(cc,c);
-}
-
-mul(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-emul(aa,bb,cc);
-ETOEN(cc,c);
-}
-
-div(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-ediv(aa,bb,cc);
-ETOEN(cc,c);
-}
-
-int cmp(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-unsigned short aa[10], bb[10];
-int c;
-int ecmp();
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-c = ecmp(aa,bb);
-return(c);
-}
-
-mov(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-int i;
-
-for( i=0; i<NE; i++ )
- b[i] = a[i];
-}
-
-
-neg(a)
-FLOAT(a);
-{
-unsigned short aa[10];
-
-ENTOE(a,aa);
-eneg(aa);
-ETOEN(aa,a);
-}
-
-clear(a)
-FLOAT(a);
-{
-int i;
-
-for( i=0; i<NE; i++ )
- a[i] = 0;
-}
-
-FABS(a)
-FLOAT(a);
-{
-unsigned short aa[10];
-
-ENTOE(a,aa);
-eabs(aa);
-ETOEN(aa,a);
-}
-
-FLOOR(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-unsigned short aa[10], bb[10];
-
-ENTOE(a,aa);
-efloor(aa,bb);
-ETOEN(bb,b);
-}
-
-LOG(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-unsigned short aa[10], bb[10];
-int rndsav;
-
-ENTOE(a,aa);
-rndsav = rndprc;
-rndprc = NIBITS;
-elog(aa,bb);
-rndprc = rndsav;
-ETOEN(bb,b);
-}
-
-POW(a,b,c)
-FLOAT(a);
-FLOAT(b);
-FLOAT(c);
-{
-unsigned short aa[10], bb[10], cc[10];
-int rndsav;
-
-ENTOE(a,aa);
-ENTOE(b,bb);
-rndsav = rndprc;
-rndprc = NIBITS;
-epow(aa,bb,cc);
-rndprc = rndsav;
-ETOEN(cc,c);
-}
-
-SQRT(a,b)
-FLOAT(a);
-FLOAT(b);
-{
-unsigned short aa[10], bb[10];
-
-ENTOE(a,aa);
-esqrt(aa,bb);
-ETOEN(bb,b);
-}
-
-FTOL(x,ip,f)
-FLOAT(x);
-long *ip;
-FLOAT(f);
-{
-unsigned short xx[10], ff[10];
-
-ENTOE(x,xx);
-eifrac(xx,ip,ff);
-ETOEN(ff,f);
-}
-
-LTOF(ip,x)
-long *ip;
-FLOAT(x);
-{
-unsigned short xx[10];
-ltoe(ip,xx);
-ETOEN(xx,x);
-}
-
-TOASC(a,b,c)
-FLOAT(a);
-int b;
-char *c;
-{
-unsigned short xx[10];
-
-ENTOE(a,xx);
-etoasc(xx,b,c);
-}
-
-#else /* not L128DOUBLE */
-
-#define ONE eone
-
-/* Note all arguments of operation subroutines are pointers. */
-/* c = b + a */
-#define add(a,b,c) eadd(a,b,c)
-/* c = b - a */
-#define sub(a,b,c) esub(a,b,c)
-/* c = b * a */
-#define mul(a,b,c) emul(a,b,c)
-/* c = b / a */
-#define div(a,b,c) ediv(a,b,c)
-/* 1 if a>b, 0 if a==b, -1 if a<b */
-#define cmp(a,b) ecmp(a,b)
-/* b = a */
-#define mov(a,b) emov(a,b)
-/* a = -a */
-#define neg(a) eneg(a)
-/* a = 0 */
-#define clear(a) eclear(a)
-
-#define FABS(x) eabs(x)
-#define FLOOR(x,y) efloor(x,y)
-#define LOG(x,y) elog(x,y)
-#define POW(x,y,z) epow(x,y,z)
-#define SQRT(x,y) esqrt(x,y)
-
-/* x = &FLOAT input, i = &long integer part, f = &FLOAT fractional part */
-#define FTOL(x,i,f) eifrac(x,i,f)
-
-/* i = &long integer input, x = &FLOAT output */
-#define LTOF(i,x) ltoe(i,x)
-
-/* Convert FLOAT a to decimal ASCII string with b digits */
-#define TOASC(a,b,c) etoasc(a,b,c)
-#endif /* not L128DOUBLE */
-
-
-
-/* The following subroutines are implementations of the above
- * named functions, using the native or default arithmetic.
- */
-#if NATIVE
-eadd(a,b,c)
-FSIZE *a, *b, *c;
-{
-*c = *b + *a;
-}
-
-esub(a,b,c)
-FSIZE *a, *b, *c;
-{
-*c = *b - *a;
-}
-
-emul(a,b,c)
-FSIZE *a, *b, *c;
-{
-*c = (*b) * (*a);
-}
-
-ediv(a,b,c)
-FSIZE *a, *b, *c;
-{
-*c = (*b) / (*a);
-}
-
-
-/* Important note: comparison can be done by subracting
- * or by a compare instruction that may or may not be
- * equivalent to subtracting.
- */
-ecmp(a,b)
-FSIZE *a, *b;
-{
-if( (*a) > (*b) )
- return( 1 );
-if( (*a) < (*b) )
- return( -1 );
-if( (*a) != (*b) )
- goto cmpf;
-if( (*a) == (*b) )
- return( 0 );
-cmpf:
-printf( "Compare fails\n" );
-return(0);
-}
-
-
-emov( a, b )
-FSIZE *a, *b;
-{
-*b = *a;
-}
-
-eneg( a )
-FSIZE *a;
-{
-*a = -(*a);
-}
-
-eclear(a)
-FSIZE *a;
-{
-*a = 0.0;
-}
-
-eabs(x)
-FSIZE *x;
-{
-if( (*x) < 0.0 )
- *x = -(*x);
-}
-
-efloor(x,y)
-FSIZE *x, *y;
-{
-
-*y = (FSIZE )ZFLOOR( *x );
-}
-
-elog(x,y)
-FSIZE *x, *y;
-{
-
-*y = (FSIZE )ZLOG( *x );
-}
-
-epow(x,y,z)
-FSIZE *x, *y, *z;
-{
-
-*z = (FSIZE )ZPOW( *x, *y );
-}
-
-esqrt(x,y)
-FSIZE *x, *y;
-{
-
-*y = (FSIZE )ZSQRT( *x );
-}
-
-
-eifrac(x,i,f)
-FSIZE *x;
-long *i;
-FSIZE *f;
-{
-FSIZE y;
-
-y = (FSIZE )ZFLOOR( *x );
-if( y < 0.0 )
- {
- *f = y - *x;
- *i = -y;
- }
-else
- {
- *f = *x - y;
- *i = y;
- }
-}
-
-
-ltoe(i,x)
-long *i;
-FSIZE *x;
-{
-*x = *i;
-}
-
-
-etoasc(a,str,n)
-FSIZE *a;
-char *str;
-int n;
-{
-double x;
-
-x = (double )(*a);
-sprintf( str, " %.17e ", x );
-}
-
-/* default for FSETUP */
-einit()
-{}
-
-#endif /* NATIVE */
-
-
-
-
-FLOAT(Radix);
-FLOAT(BInvrse);
-FLOAT(RadixD2);
-FLOAT(BMinusU2);
-/*Small floating point constants.*/
-FLOAT(Zero);
-FLOAT(Half);
-FLOAT(One);
-FLOAT(Two);
-FLOAT(Three);
-FLOAT(Four);
-FLOAT(Five);
-FLOAT(Six);
-FLOAT(Eight);
-FLOAT(Nine);
-FLOAT(Ten);
-FLOAT(TwentySeven);
-FLOAT(ThirtyTwo);
-FLOAT(TwoForty);
-FLOAT(MinusOne );
-FLOAT(OneAndHalf);
-
-/*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 */
-FLOAT(AInvrse);
-FLOAT(A1);
-FLOAT(C);
-FLOAT(CInvrse);
-FLOAT(D);
-FLOAT(FourD);
-FLOAT(E0);
-FLOAT(E1);
-FLOAT(Exp2);
-FLOAT(E3);
-FLOAT(MinSqEr);
-FLOAT(SqEr);
-FLOAT(MaxSqEr);
-FLOAT(E9);
-FLOAT(Third);
-FLOAT(F6);
-FLOAT(F9);
-FLOAT(H);
-FLOAT(HInvrse);
-FLOAT(StickyBit);
-FLOAT(J);
-FLOAT(MyZero);
-FLOAT(Precision);
-FLOAT(Q);
-FLOAT(Q9);
-FLOAT(R);
-FLOAT(Random9);
-FLOAT(T);
-FLOAT(Underflow);
-FLOAT(S);
-FLOAT(OneUlp);
-FLOAT(UfThold);
-FLOAT(U1);
-FLOAT(U2);
-FLOAT(V);
-FLOAT(V0);
-FLOAT(V9);
-FLOAT(W);
-FLOAT(X);
-FLOAT(X1);
-FLOAT(X2);
-FLOAT(X8);
-FLOAT(Random1);
-FLOAT(Y);
-FLOAT(YY1);
-FLOAT(Y2);
-FLOAT(Random2);
-FLOAT(Z);
-FLOAT(PseudoZero);
-FLOAT(Z1);
-FLOAT(Z2);
-FLOAT(Z9);
-static FLOAT(t);
-FLOAT(t2);
-FLOAT(Sqarg);
-int ErrCnt[4];
-int fpecount;
-int Milestone;
-int PageNo;
-int I, M, N, N1, stkflg;
-Guard GMult, GDiv, GAddSub;
-Rounding RMult, RDiv, RAddSub, RSqrt;
-int Break, Done, NotMonot, Monot, Anomaly, IEEE;
-int SqRWrng, UfNGrad;
-int k, k2;
-int Indx;
-char ch[8];
-
-long lngint, lng2; /* intermediate for conversion between int and FLOAT */
-
-/* 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 */
-
-
-show( x )
-short x[];
-{
-int i;
-char s[80];
-
-/* Number of 16-bit groups to display */
-#if NATIVE
-#if LDOUBLE
-#define NPRT (sizeof( long double )/2)
-#else
-#define NPRT (sizeof( double )/2)
-#endif
-#else
-#define NPRT NE
-#endif
-
-TOASC( x, s, 70 );
-printf( "%s\n", s );
-for( i=0; i<NPRT; i++ )
- printf( "%04x ", x[i] & 0xffff );
-printf( "\n" );
-}
-
-/* define NOSIGNAL */
-#ifndef NOSIGNAL
-#include <signal.h>
-#endif
-#include <setjmp.h>
-jmp_buf ovfl_buf;
-/*typedef int (*Sig_type)();*/
-typedef void (*Sig_type)();
-Sig_type sigsave;
-
-/* Floating point exception receiver */
-void sigfpe()
-{
-fpecount++;
-printf( "\n* * * FLOATING-POINT ERROR * * *\n" );
-/* reinitialize the floating point unit */
-FSETUP();
-fflush(stdout);
-if( sigsave )
- {
-#ifndef NOSIGNAL
- signal( SIGFPE, sigsave );
-#endif
- sigsave = 0;
- longjmp( ovfl_buf, 1 );
- }
-abort();
-}
-
-
-main()
-{
-
-/* Do coprocessor or other initializations */
-FSETUP();
-
-printf(
- "This version of paranoia omits test for extra precise subexpressions\n" );
-printf( "and includes a few additional tests.\n" );
-
-clear(Zero);
-printf( "0 = " );
-show( Zero );
-mov( ONE, One);
-printf( "1 = " );
-show( One );
-add( One, One, Two );
-printf( "1+1 = " );
-show( Two );
-add( Two, One, Three );
-add( Three, One, Four );
-add( Four, One, Five );
-add( Five, One, Six );
-add( Four, Four, Eight );
-mul( Three, Three, Nine );
-add( Nine, One, Ten );
-mul( Nine, Three, TwentySeven );
-mul( Four, Eight, ThirtyTwo );
-mul( Four, Five, t );
-mul( t, Three, t );
-mul( t, Four, TwoForty );
-mov( One, MinusOne );
-neg( MinusOne );
-div( Two, One, Half );
-add( One, Half, OneAndHalf );
-ErrCnt[Failure] = 0;
-ErrCnt[Serious] = 0;
-ErrCnt[Defect] = 0;
-ErrCnt[Flaw] = 0;
-PageNo = 1;
-#ifndef NOSIGNAL
-signal( SIGFPE, sigfpe );
-#endif
-printf("Program is now RUNNING tests on small integers:\n");
-
-add( Zero, Zero, t );
-if( cmp( t, Zero ) != 0)
- {
- printf( "0+0 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-sub( One, One, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "1-1 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-if( cmp( One, Zero ) <= 0 )
- {
- printf( "1 <= 0\n" );
- ErrCnt[Failure] += 1;
- }
-add( One, One, t );
-if( cmp( t, Two ) != 0 )
- {
- printf( "1+1 != 2\n" );
- ErrCnt[Failure] += 1;
- }
-mov( Zero, Z );
-neg( Z );
-FLOOR( Z, t );
-if( cmp(t,Zero) != 0 )
- {
- ErrCnt[Serious] += 1;
- printf( "FLOOR(-0) should equal 0, is = " );
- show( t );
- }
-if( cmp(Z, Zero) != 0)
- {
- ErrCnt[Failure] += 1;
- printf("Comparison alleges that -0.0 is Non-zero!\n");
- }
-else
- {
- div( TwoForty, One, U1 ); /* U1 = 0.001 */
- mov( One, Radix );
- TstPtUf();
- }
-add( Two, One, t );
-if( cmp( t, Three ) != 0 )
- {
- printf( "2+1 != 3\n" );
- ErrCnt[Failure] += 1;
- }
-add( Three, One, t );
-if( cmp( t, Four ) != 0 )
- {
- printf( "3+1 != 4\n" );
- ErrCnt[Failure] += 1;
- }
-mov( Two, t );
-neg( t );
-mul( Two, t, t );
-add( Four, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "4+2*(-2) != 0\n" );
- ErrCnt[Failure] += 1;
- }
-sub( Three, Four, t );
-sub( One, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "4-3-1 != 0\n" );
- ErrCnt[Failure] += 1;
- }
- sub( One, Zero, t );
-if( cmp( t, MinusOne ) != 0 )
- {
- printf( "-1 != 0-1\n" );
- ErrCnt[Failure] += 1;
- }
-add( One, MinusOne, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "1+(-1) != 0\n" );
- ErrCnt[Failure] += 1;
- }
-mov( One, t );
-FABS( t );
-add( MinusOne, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "-1+abs(1) != 0\n" );
- ErrCnt[Failure] += 1;
- }
-mul( MinusOne, MinusOne, t );
-add( MinusOne, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "-1+(-1)*(-1) != 0\n" );
- ErrCnt[Failure] += 1;
- }
-add( Half, MinusOne, t );
-add( Half, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "1/2 + (-1) + 1/2 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-Milestone = 10;
-mul( Three, Three, t );
-if( cmp( t, Nine ) != 0 )
- {
- printf( "3*3 != 9\n" );
- ErrCnt[Failure] += 1;
- }
-mul( Nine, Three, t );
-if( cmp( t, TwentySeven ) != 0 )
- {
- printf( "3*9 != 27\n" );
- ErrCnt[Failure] += 1;
- }
-add( Four, Four, t );
-if( cmp( t, Eight ) != 0 )
- {
- printf( "4+4 != 8\n" );
- ErrCnt[Failure] += 1;
- }
-mul( Eight, Four, t );
-if( cmp( t, ThirtyTwo ) != 0 )
- {
- printf( "8*4 != 32\n" );
- ErrCnt[Failure] += 1;
- }
-sub( TwentySeven, ThirtyTwo, t );
-sub( Four, t, t );
-sub( One, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "32-27-4-1 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-add( Four, One, t );
-if( cmp( t, Five ) != 0 )
- {
- printf( "4+1 != 5\n" );
- ErrCnt[Failure] += 1;
- }
-mul( Four, Five, t );
-mul( Three, t, t );
-mul( Four, t, t );
-if( cmp( t, TwoForty ) != 0 )
- {
- printf( "4*5*3*4 != 240\n" );
- ErrCnt[Failure] += 1;
- }
-div( Three, TwoForty, t );
-mul( Four, Four, t2 );
-mul( Five, t2, t2 );
-sub( t2, t2, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "240/3 - 4*4*5 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-div( Four, TwoForty, t );
-mul( Five, Three, t2 );
-mul( Four, t2, t2 );
-sub( t2, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "240/4 - 5*3*4 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-div( Five, TwoForty, t );
-mul( Four, Three, t2 );
-mul( Four, t2, t2 );
-sub( t2, t, t );
-if( cmp( t, Zero ) != 0 )
- {
- printf( "240/5 - 4*3*4 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-if(ErrCnt[Failure] == 0)
- {
-printf("-1, 0, 1/2, 1, 2, 3, 4, 5, 9, 27, 32 & 240 are O.K.\n\n");
- }
-printf("Searching for Radix and Precision.\n");
-mov( One, W );
-do
- {
- add( W, W, W );
- add( W, One, Y );
- sub( W, Y, Z );
- sub( One, Z, Y );
- mov( Y, t );
- FABS(t);
- add( MinusOne, t, t );
- k = cmp( t, Zero );
- }
-while( k < 0 );
-/*.. now W is just big enough that |((W+1)-W)-1| >= 1 ...*/
-mov( Zero, Precision );
-mov( One, Y );
-do
- {
- add( W, Y, Radix );
- add( Y, Y, Y );
- sub( W, Radix, Radix );
- k = cmp( Radix, Zero );
- }
-while( k == 0);
-
-if( cmp(Radix, Two) < 0 )
- mov( One, Radix );
-printf("Radix = " );
-show( Radix );
-if( cmp(Radix, One) != 0)
- {
- mov( One, W );
- do
- {
- add( One, Precision, Precision );
- mul( W, Radix, W );
- add( W, One, Y );
- sub( W, Y, t );
- k = cmp( t, One );
- }
- while( k == 0 );
- }
-/* now W == Radix^Precision is barely too big to satisfy (W+1)-W == 1 */
-div( W, One, U1 );
-mul( Radix, U1, U2 );
-printf( "Closest relative separation found is U 1 = " );
-show( U1 );
-printf( "Recalculating radix and precision." );
-
-/*save old values*/
-mov( Radix, E0 );
-mov( U1, E1 );
-mov( U2, E9 );
-mov( Precision, E3 );
-
-div( Three, Four, X );
-sub( One, X, Third );
-sub( Third, Half, F6 );
-add( F6, F6, X );
-sub( Third, X, X );
-FABS( X );
-if( cmp(X, U2) < 0 )
- mov( U2, X );
-
-/*... now X = (unknown no.) ulps of 1+...*/
-do
- {
- mov( X, U2 );
-/* Y = Half * U2 + ThirtyTwo * U2 * U2; */
- mul( ThirtyTwo, U2, t );
- mul( t, U2, t );
- mul( Half, U2, Y );
- add( t, Y, Y );
- add( One, Y, Y );
- sub( One, Y, X );
- k = cmp( U2, X );
- k2 = cmp( X, Zero );
- }
-while ( ! ((k <= 0) || (k2 <= 0)));
-
-/*... now U2 == 1 ulp of 1 + ... */
-div( Three, Two, X );
-sub( Half, X, F6 );
-add( F6, F6, Third );
-sub( Half, Third, X );
-add( F6, X, X );
-FABS( X );
-if( cmp(X, U1) < 0 )
- mov( U1, X );
-
-/*... now X == (unknown no.) ulps of 1 -... */
-do
- {
- mov( X, U1 );
- /* Y = Half * U1 + ThirtyTwo * U1 * U1;*/
- mul( ThirtyTwo, U1, t );
- mul( U1, t, t );
- mul( Half, U1, Y );
- add( t, Y, Y );
- sub( Y, Half, Y );
- add( Half, Y, X );
- sub( X, Half, Y );
- add( Half, Y, X );
- k = cmp( U1, X );
- k2 = cmp( X, Zero );
- } while ( ! ((k <= 0) || (k2 <= 0)));
-/*... now U1 == 1 ulp of 1 - ... */
-if( cmp( U1, E1 ) == 0 )
- printf("confirms closest relative separation U1 .\n");
-else
- {
- printf("gets better closest relative separation U1 = " );
- show( U1 );
- }
-div( U1, One, W );
-sub( U1, Half, F9 );
-add( F9, Half, F9 );
-div( U1, U2, t );
-div( TwoForty, One, t2 );
-add( t2, t, t );
-FLOOR( t, Radix );
-if( cmp(Radix, E0) == 0 )
- printf("Radix confirmed.\n");
-else
- {
- printf("MYSTERY: recalculated Radix = " );
- show( Radix );
- mov( E0, Radix );
- }
-add( Eight, Eight, t );
-if( cmp( Radix, t ) > 0 )
- {
- printf( "Radix is too big: roundoff problems\n" );
- ErrCnt[Defect] += 1;
- }
-k = 1;
-if( cmp( Radix, Two ) == 0 )
- k = 0;
-if( cmp( Radix, Ten ) == 0 )
- k = 0;
-if( cmp( Radix, One ) == 0 )
- k = 0;
-if( k != 0 )
- {
- printf( "Radix is not as good as 2 or 10\n" );
- ErrCnt[Flaw] += 1;
- }
-/*=============================================*/
-Milestone = 20;
-/*=============================================*/
-sub( Half, F9, t );
-if( cmp( t, Half ) >= 0 )
- {
- printf( "(1-U1)-1/2 < 1/2 is FALSE, prog. fails?\n" );
- ErrCnt[Failure] += 1;
- }
-mov( F9, X );
-I = 1;
-sub( Half, X, Y );
-sub( Half, Y, Z );
-if( (cmp( X, One ) == 0) && (cmp( Z, Zero) != 0) )
- {
- printf( "Comparison is fuzzy ,X=1 but X-1/2-1/2 != 0\n" );
- ErrCnt[Failure] += 1;
- }
-add( One, U2, X );
-I = 0;
-/*=============================================*/
-Milestone = 25;
-/*=============================================*/
-/*... BMinusU2 = nextafter(Radix, 0) */
-
-sub( One, Radix, BMinusU2 );
-sub( U2, BMinusU2, t );
-add( One, t, BMinusU2 );
-/* Purify Integers */
-if( cmp(Radix,One) != 0 )
- {
-/*X = - TwoForty * LOG(U1) / LOG(Radix);*/
- LOG( U1, X );
- LOG( Radix, t );
- div( t, X, X );
- mul( TwoForty, X, X );
- neg( X );
-
- add( Half, X, Y );
- FLOOR( Y, Y );
- sub( Y, X, t );
- FABS( t );
- mul( Four, t, t );
- if( cmp( t, One ) < 0 )
- mov( Y, X );
- div( TwoForty, X, Precision );
- add( Half, Precision, Y );
- FLOOR( Y, Y );
- sub( Y, Precision, t );
- FABS( t );
- mul( TwoForty, t, t );
- if( cmp( t, Half ) < 0 )
- mov( Y, Precision );
- }
-FLOOR( Precision, t );
-if( (cmp( Precision, t ) != 0) || (cmp( Radix, One ) == 0) )
- {
- printf("Precision cannot be characterized by an Integer number\n");
- printf("of significant digits but, by itself, this is a minor flaw.\n");
- }
-if( cmp(Radix, One) == 0 )
- printf("logarithmic encoding has precision characterized solely by U1.\n");
-else
- {
- printf("The number of significant digits of the Radix is " );
- show( Precision );
- }
-mul( U2, Nine, t );
-mul( Nine, t, t );
-mul( TwoForty, t, t );
-if( cmp( t, One ) >= 0 )
- {
- printf( "Precision worse than 5 decimal figures\n" );
- ErrCnt[Serious] += 1;
- }
-/*=============================================*/
-Milestone = 30;
-/*=============================================*/
-/* Test for extra-precise subepressions has been deleted. */
-Milestone = 35;
-/*=============================================*/
-if( cmp(Radix,Two) >= 0 )
- {
- mul( Radix, Radix, t );
- div( t, W, X );
- add( X, One, Y );
- sub( X, Y, Z );
- add( Z, U2, T );
- sub( Z, T, X );
- if( cmp( X, U2 ) != 0 )
- {
- printf( "Subtraction is not normalized X=Y,X+Z != Y+Z!\n" );
- ErrCnt[Failure] += 1;
- }
- if( cmp(X,U2) == 0 )
- printf("Subtraction appears to be normalized, as it should be.");
- }
-
-printf("\nChecking for guard digit in *, /, and -.\n");
-mul( F9, One, Y );
-mul( One, F9, Z );
-sub( Half, F9, X );
-sub( Half, Y, Y );
-sub( X, Y, Y );
-sub( Half, Z, Z );
-sub( X, Z, Z );
-add( One, U2, X );
-mul( X, Radix, T );
-mul( Radix, X, R );
-sub( Radix, T, X );
-mul( Radix, U2, t );
-sub( t, X, X );
-sub( Radix, R, T );
-mul( Radix, U2, t );
-sub( t, T, T );
-sub( One, Radix, t );
-mul( t, X, X );
-sub( One, Radix, t );
-mul( t, T, T );
-
-k = cmp(X,Zero);
-k |= cmp(Y,Zero);
-k |= cmp(Z,Zero);
-k |= cmp(T,Zero);
-if( k == 0 )
- GMult = Yes;
-else
- {
- GMult = No;
- ErrCnt[Serious] += 1;
- printf( "* lacks a Guard Digit, so 1*X != X\n" );
- }
-mul( Radix, U2, Z );
-add( One, Z, X );
-add( X, Z, Y );
-mul( X, X, t );
-sub( t, Y, Y );
-FABS( Y );
-sub( U2, Y, Y );
-sub( U2, One, X );
-sub( U2, X, Z );
-mul( X, X, t );
-sub( t, Z, Z );
-FABS( Z );
-sub( U1, Z, Z );
-if( (cmp(Y,Zero) > 0) || (cmp(Z,Zero) > 0) )
- {
- ErrCnt[Failure] += 1;
- printf( "* gets too many final digits wrong.\n" );
- }
-sub( U2, One, Y );
-add( One, U2, X );
-div( Y, One, Z );
-sub( X, Z, Y );
-div( Three, One, X );
-div( Nine, Three, Z );
-sub( Z, X, X );
-div( TwentySeven, Nine, T );
-sub( T, Z, Z );
-k = cmp( X, Zero );
-k |= cmp( Y, Zero );
-k |= cmp( Z, Zero );
-if( k )
- {
- ErrCnt[Defect] += 1;
-printf( "Division lacks a Guard Digit, so error can exceed 1 ulp\n" );
-printf( "or 1/3 and 3/9 and 9/27 may disagree\n" );
- }
-div( One, F9, Y );
-sub( Half, F9, X );
-sub( Half, Y, Y );
-sub( X, Y, Y );
-add( One, U2, X );
-div( One, X, T );
-sub( X, T, X );
-k = cmp( X, Zero );
-k |= cmp( Y, Zero );
-k |= cmp( Z, Zero );
-if( k == 0 )
- GDiv = Yes;
-else
- {
- GDiv = No;
- ErrCnt[Serious] += 1;
- printf( "Division lacks a Guard Digit, so X/1 != X\n" );
- }
-add( One, U2, X );
-div( X, One, X );
-sub( Half, X, Y );
-sub( Half, Y, Y );
-if( cmp(Y,Zero) >= 0 )
- {
- ErrCnt[Serious] += 1;
- printf( "Computed value of 1/1.000..1 >= 1\n" );
- }
-sub( U2, One, X );
-mul( Radix, U2, Y );
-add( One, Y, Y );
-mul( X, Radix, Z );
-mul( Y, Radix, T );
-div( Radix, Z, R );
-div( Radix, T, StickyBit );
-sub( X, R, X );
-sub( Y, StickyBit, Y );
-k = cmp( X, Zero );
-k |= cmp( Y, Zero );
-if( k )
- {
- ErrCnt[Failure] += 1;
- printf( "* and/or / gets too many last digits wrong\n" );
- }
-sub( U1, One, Y );
-sub( F9, One, X );
-sub( Y, One, Y );
-sub( U2, Radix, T );
-sub( BMinusU2, Radix, Z );
-sub( T, Radix, T );
-k = cmp( X, U1 );
-k |= cmp( Y, U1 );
-k |= cmp( Z, U2 );
-k |= cmp( T, U2 );
-if( k == 0 )
- GAddSub = Yes;
-else
- {
- GAddSub = No;
- ErrCnt[Serious] += 1;
- printf( "- lacks Guard Digit, so cancellation is obscured\n" );
- }
-sub( One, F9, t );
-if( (cmp(F9,One) != 0) && (cmp(t,Zero) >= 0) )
- {
- ErrCnt[Serious] += 1;
- printf("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;
-/*=============================================*/
-printf("Checking rounding on multiply, divide and add/subtract.\n");
-RMult = Other;
-RDiv = Other;
-RAddSub = Other;
-div( Two, Radix, RadixD2 );
-mov( Two, A1 );
-Done = False;
-do
- {
- mov( Radix, AInvrse );
- do
- {
- mov( AInvrse, X );
- div( A1, AInvrse, AInvrse );
- FLOOR( AInvrse, t );
- k = cmp( t, AInvrse );
- }
- while( ! (k != 0 ) );
- k = cmp( X, One );
- k2 = cmp( A1, Three );
- Done = (k == 0) || (k2 > 0);
- if(! Done)
- add( Nine, One, A1 );
- }
-while( ! (Done));
-if( cmp(X, One) == 0 )
- mov( Radix, A1 );
-div( A1, One, AInvrse );
-mov( A1, X );
-mov( AInvrse, Y );
-Done = False;
-do
- {
- mul( X, Y, Z );
- sub( Half, Z, Z );
- if( cmp( Z, Half ) != 0 )
- {
- ErrCnt[Failure] += 1;
- printf( "X * (1/X) differs from 1\n" );
- }
- k = cmp( X, Radix );
- Done = (k == 0);
- mov( Radix, X );
- div( X, One, Y );
- }
-while( ! (Done));
-
-add( One, U2, Y2 );
-sub( U2, One, YY1 );
-sub( U2, OneAndHalf, X );
-add( OneAndHalf, U2, Y );
-sub( U2, X, Z );
-mul( Z, Y2, Z );
-mul( Y, YY1, T );
-sub( X, Z, Z );
-sub( X, T, T );
-mul( X, Y2, X );
-add( Y, U2, Y );
-mul( Y, YY1, Y );
-sub( OneAndHalf, X, X );
-sub( OneAndHalf, Y, Y );
-k = cmp( X, Zero );
-k |= cmp( Y, Zero );
-k |= cmp( Z, Zero );
-if( cmp( T, Zero ) > 0 )
- k = 1;
-if( k == 0 )
- {
- add( OneAndHalf, U2, X );
- mul( X, Y2, X );
- sub( U2, OneAndHalf, Y );
- sub( U2, Y, Y );
- add( OneAndHalf, U2, Z );
- add( U2, Z, Z );
- sub( U2, OneAndHalf, T );
- mul( T, YY1, T );
- add( Z, U2, t );
- sub( t, X, X );
- mul( Y, YY1, StickyBit );
- mul( Z, Y2, S );
- sub( Y, T, T );
- sub( Y, U2, Y );
- add( StickyBit, Y, Y );
-/* Z = S - (Z + U2 + U2); */
- add( Z, U2, t );
- add( t, U2, t );
- sub( t, S, Z );
- add( Y2, U2, t );
- mul( t, YY1, StickyBit );
- mul( Y2, YY1, YY1 );
- sub( Y2, StickyBit, StickyBit );
- sub( Half, YY1, YY1 );
- k = cmp( X, Zero );
- k |= cmp( Y, Zero );
- k |= cmp( Z, Zero );
- k |= cmp( T, Zero );
- k |= cmp( StickyBit, Zero );
- k |= cmp( YY1, Half );
- if( k == 0 )
- {
- RMult = Rounded;
- printf("Multiplication appears to round correctly.\n");
- }
- else
- {
- add( X, U2, t );
- k = cmp( t, Zero );
- if( cmp( Y, Zero ) >= 0 )
- k |= 1;
- add( Z, U2, t );
- k |= cmp( t, Zero );
- if( cmp( T, Zero ) >= 0 )
- k |= 1;
- add( StickyBit, U2, t );
- k |= cmp( t, Zero );
- if( cmp(YY1, Half) >= 0 )
- k |= 1;
- if( k == 0 )
- {
- printf("Multiplication appears to chop.\n");
- }
- else
- {
- printf("* is neither chopped nor correctly rounded.\n");
- }
- if( (RMult == Rounded) && (GMult == No) )
- printf("Multiplication has inconsistent result");
- }
- }
-else
- printf("* is neither chopped nor correctly rounded.\n");
-
-/*=============================================*/
-Milestone = 45;
-/*=============================================*/
-add( One, U2, Y2 );
-sub( U2, One, YY1 );
-add( OneAndHalf, U2, Z );
-add( Z, U2, Z );
-div( Y2, Z, X );
-sub( U2, OneAndHalf, T );
-sub( U2, T, T );
-sub( U2, T, Y );
-div( YY1, Y, Y );
-add( Z, U2, Z );
-div( Y2, Z, Z );
-sub( OneAndHalf, X, X );
-sub( T, Y, Y );
-div( YY1, T, T );
-add( OneAndHalf, U2, t );
-sub( t, Z, Z );
-sub( OneAndHalf, U2, t );
-add( t, T, T );
-k = 0;
-if( cmp( X, Zero ) > 0 )
- k = 1;
-if( cmp( Y, Zero ) > 0 )
- k = 1;
-if( cmp( Z, Zero ) > 0 )
- k = 1;
-if( cmp( T, Zero ) > 0 )
- k = 1;
-if( k == 0 )
- {
- div( Y2, OneAndHalf, X );
- sub( U2, OneAndHalf, Y );
- add( U2, OneAndHalf, Z );
- sub( Y, X, X );
- div( YY1, OneAndHalf, T );
- div( YY1, Y, Y );
- add( Z, U2, t );
- sub( t, T, T );
- sub( Z, Y, Y );
- div( Y2, Z, Z );
- add( Y2, U2, YY1 );
- div( Y2, YY1, YY1 );
- sub( OneAndHalf, Z, Z );
- sub( Y2, YY1, Y2 );
- sub( U1, F9, YY1 );
- div( F9, YY1, YY1 );
- k = cmp( X, Zero );
- k |= cmp( Y, Zero );
- k |= cmp( Z, Zero );
- k |= cmp( T, Zero );
- k |= cmp( Y2, Zero );
- sub( Half, YY1, t );
- sub( Half, F9, t2 );
- k |= cmp( t, t2 );
- if( k == 0 )
- {
- RDiv = Rounded;
- printf("Division appears to round correctly.\n");
- if(GDiv == No)
- printf("Division test inconsistent\n");
- }
- else
- {
- k = 0;
- if( cmp( X, Zero ) >= 0 )
- k = 1;
- if( cmp( Y, Zero ) >= 0 )
- k = 1;
- if( cmp( Z, Zero ) >= 0 )
- k = 1;
- if( cmp( T, Zero ) >= 0 )
- k = 1;
- if( cmp( Y, Zero ) >= 0 )
- k = 1;
- sub( Half, YY1, t );
- sub( Half, F9, t2 );
- if( cmp( t, t2 ) >= 0 )
- k = 1;
- if( k == 0 )
- {
- RDiv = Chopped;
- printf("Division appears to chop.\n");
- }
- }
- }
-if(RDiv == Other)
- printf("/ is neither chopped nor correctly rounded.\n");
-div( Radix, One, BInvrse );
-mul( BInvrse, Radix, t );
-sub( Half, t, t );
-if( cmp( t, Half ) != 0 )
- {
- ErrCnt[Failure] += 1;
- printf( "Radix * ( 1 / Radix ) differs from 1\n" );
- }
-
-Milestone = 50;
-/*=============================================*/
-add( F9, U1, t );
-sub( Half, t, t );
-k = cmp( t, Half );
-add( BMinusU2, U2, t );
-sub( One, t, t );
-sub( One, Radix, t2 );
-k |= cmp( t, t2 );
-if( k != 0 )
- {
- ErrCnt[Failure] += 1;
- printf( "Incomplete carry-propagation in Addition\n" );
- }
-mul( U1, U1, X );
-sub( X, One, X );
-sub( U2, One, Y );
-mul( U2, Y, Y );
-add( One, Y, Y );
-sub( Half, F9, Z );
-sub( Half, X, X );
-sub( Z, X, X );
-sub( One, Y, Y );
-if( (cmp(X,Zero) == 0) && (cmp(Y,Zero) == 0) )
- {
- RAddSub = Chopped;
- printf("Add/Subtract appears to be chopped.\n");
- }
-if(GAddSub == Yes)
- {
- add( Half, U2, X );
- mul( X, U2, X );
- sub( U2, Half, Y );
- mul( Y, U2, Y );
- add( One, X, X );
- add( One, Y, Y );
- add( One, U2, t );
- sub( X, t, X );
- sub( Y, One, Y );
- k = cmp(X,Zero);
- if( k )
- printf( "1+U2-[u2(1/2+U2)+1] != 0\n" );
- k2 = cmp(Y,Zero);
- if( k2 )
- printf( "1-[U2(1/2-U2)+1] != 0\n" );
- k |= k2;
- if( k == 0 )
- {
- add( Half, U2, X );
- mul( X, U1, X );
- sub( U2, Half, Y );
- mul( Y, U1, Y );
- sub( X, One, X );
- sub( Y, One, Y );
- sub( X, F9, X );
- sub( Y, One, Y );
- k = cmp(X,Zero);
- if( k )
- printf( "F9-[1-U1(1/2+U2)] != 0\n" );
- k2 = cmp(Y,Zero);
- if( k2 )
- printf( "1-[1-U1(1/2-U2)] != 0\n" );
- k |= k2;
- if( k == 0 )
- {
- RAddSub = Rounded;
- printf("Addition/Subtraction appears to round correctly.\n");
- if(GAddSub == No)
- printf( "Add/Subtract test inconsistent\n");
- }
- 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");
-
-mov( One, S );
-add( One, Half, X );
-mul( Half, X, X );
-add( One, X, X );
-add( One, U2, Y );
-mul( Y, Half, Y );
-sub( Y, X, Z );
-sub( X, Y, T );
-add( Z, T, StickyBit );
-if( cmp(StickyBit, Zero) != 0 )
- {
- mov( Zero, S );
- ErrCnt[Flaw] += 1;
- printf( "(X - Y) + (Y - X) is non zero!\n" );
- }
-mov( Zero, StickyBit );
-FLOOR( RadixD2, t );
-k2 = cmp( t, RadixD2 );
-k = 1;
-if( (GMult == Yes) && (GDiv == Yes) && (GAddSub == Yes)
- && (RMult == Rounded) && (RDiv == Rounded)
- && (RAddSub == Rounded) && (k2 == 0) )
- {
- printf("Checking for sticky bit.\n");
- k = 0;
- add( Half, U1, X );
- mul( X, U2, X );
- mul( Half, U2, Y );
- add( One, Y, Z );
- add( One, X, T );
- sub( One, Z, t );
- sub( One, T, t2 );
- if( cmp(t,Zero) > 0 )
- {
- k = 1;
- printf( "[1+(1/2)U2]-1 > 0\n" );
- }
- if( cmp(t2,U2) < 0 )
- {
- k = 1;
- printf( "[1+U2(1/2+U1)]-1 < U2\n" );
- }
- add( T, Y, Z );
- sub( X, Z, Y );
- sub( T, Z, t );
- sub( T, Y, t2 );
- if( cmp(t,U2) < 0 )
- {
- k = 1;
- printf( "[[1+U2(1/2+U1)]+(1/2)U2]-[1+U2(1/2+U1)] < U2\n" );
- }
- if( cmp(t2,Zero) != 0 )
- {
- k = 1;
- printf( "(1/2)U2-[1+U2(1/2+U1)] != 0\n" );
- }
- add( Half, U1, X );
- mul( X, U1, X );
- mul( Half, U1, Y );
- sub( Y, One, Z );
- sub( X, One, T );
- sub( One, Z, t );
- sub( F9, T, t2 );
- if( cmp(t,Zero) != 0 )
- {
- k = 1;
- printf( "(1-(1/2)U1)-1 != 0\n" );
- }
- if( cmp(t2,Zero) != 0 )
- {
- k = 1;
- printf( "[1-U1(1/2+U1)]-F9 != 0\n" );
- }
- sub( U1, Half, Z );
- mul( Z, U1, Z );
- sub( Z, F9, T );
- sub( Y, F9, Q );
- sub( F9, T, t );
- if( cmp( t, Zero ) != 0 )
- {
- k = 1;
- printf( "[F9-U1(1/2-U1)]-F9 != 0\n" );
- }
- sub( U1, F9, t );
- sub( Q, t, t );
- if( cmp( t, Zero ) != 0 )
- {
- k = 1;
- printf( "(F9-U1)-(F9-(1/2)U1) != 0\n" );
- }
- add( One, U2, Z );
- mul( Z, OneAndHalf, Z );
- add( OneAndHalf, U2, T );
- sub( Z, T, T );
- add( U2, T, T );
- div( Radix, Half, X );
- add( One, X, X );
- mul( Radix, U2, Y );
- add( One, Y, Y );
- mul( X, Y, Z );
- if( cmp( T, Zero ) != 0 )
- {
- k = 1;
- printf( "(3/2+U2)-3/2(1+U2)+U2 != 0\n" );
- }
- mul( Radix, U2, t );
- add( X, t, t );
- sub( Z, t, t );
- if( cmp( t, Zero ) != 0 )
- {
- k = 1;
- printf( "(1+1/2Radix)+Radix*U2-[1+1/(2Radix)][1+Radix*U2] != 0\n" );
- }
- if( cmp(Radix, Two) != 0 )
- {
- add( Two, U2, X );
- div( Two, X, Y );
- sub( One, Y, t );
- if( cmp( t, Zero) != 0 )
- k = 1;
- }
- }
-if( k == 0 )
- {
- printf("Sticky bit apparently used correctly.\n");
- mov( One, StickyBit );
- }
-else
- {
- printf("Sticky bit used incorrectly or not at all.\n");
- }
-
-if( GMult == No || GDiv == No || GAddSub == No ||
- RMult == Other || RDiv == Other || RAddSub == Other)
- {
- ErrCnt[Flaw] += 1;
- printf("lack(s) of guard digits or failure(s) to correctly round or chop\n");
-printf( "(noted above) count as one flaw in the final tally below\n" );
- }
-/*=============================================*/
-Milestone = 60;
-/*=============================================*/
-printf("\n");
-printf("Does Multiplication commute? ");
-printf("Testing on %d random pairs.\n", NoTrials);
-SQRT( Three, Random9 );
-mov( Third, Random1 );
-I = 1;
-do
- {
- Random();
- mov( Random1, X );
- Random();
- mov( Random1, Y );
- mul( Y, X, Z9 );
- mul( X, Y, Z );
- sub( Z9, Z, Z9 );
- I = I + 1;
- }
-while ( ! ((I > NoTrials) || (cmp(Z9,Zero) != 0)));
-if(I == NoTrials)
- {
- div( Three, Half, t );
- add( One, t, Random1 );
- add( U2, U1, t );
- add( t, One, Random2 );
- mul( Random1, Random2, Z );
- mul( Random2, Random1, Y );
-/* Z9 = (One + Half / Three) * ((U2 + U1) + One) - (One + Half /
- * Three) * ((U2 + U1) + One);
- */
- div( Three, Half, t2 );
- add( One, t2, t2 );
- add( U2, U1, t );
- add( t, One, t );
- mul( t2, t, Z9 );
- mul( t2, t, t );
- sub( t, Z9, Z9 );
- }
-if(! ((I == NoTrials) || (cmp(Z9,Zero) == 0)))
- {
- ErrCnt[Defect] += 1;
- printf( "X * Y == Y * X trial fails.\n");
- }
-else
- {
- printf(" No failures found in %d integer pairs.\n", NoTrials);
- }
-/*=============================================*/
-Milestone = 70;
-/*=============================================*/
-sqtest();
-Milestone = 90;
-pow1test();
-
-Milestone = 110;
-
-printf("Seeking Underflow thresholds UfThold and E0.\n");
-mov( U1, D );
-FLOOR( Precision, t );
-if( cmp(Precision, t) != 0 )
- {
- mov( BInvrse, D );
- mov( Precision, X );
- do
- {
- mul( D, BInvrse, D );
- sub( One, X, X );
- }
- while( cmp(X, Zero) > 0 );
- }
-mov( One, Y );
-mov( D, Z );
-/* ... D is power of 1/Radix < 1. */
-sigsave = sigfpe;
-if( setjmp(ovfl_buf) )
- goto under0;
-do
- {
- mov( Y, C );
- mov( Z, Y );
- mul( Y, Y, Z );
- add( Z, Z, t );
- }
-while( (cmp(Y,Z) > 0) && (cmp(t,Z) > 0) );
-
-under0:
-sigsave = 0;
-
-mov( C, Y );
-mul( Y, D, Z );
-sigsave = sigfpe;
-if( setjmp(ovfl_buf) )
- goto under1;
-do
- {
- mov( Y, C );
- mov( Z, Y );
- mul( Y, D, Z );
- add( Z, Z, t );
- }
-while( (cmp(Y,Z) > 0) && (cmp(t,Z) > 0) );
-
-under1:
-sigsave = 0;
-
-if( cmp(Radix,Two) < 0 )
- mov( Two, HInvrse );
-else
- mov( Radix, HInvrse );
-div( HInvrse, One, H );
-/* ... 1/HInvrse == H == Min(1/Radix, 1/2) */
-div( C, One, CInvrse );
-mov( C, E0 );
-mul( E0, H, Z );
-/* ...1/Radix^(BIG Integer) << 1 << CInvrse == 1/C */
-sigsave = sigfpe;
-if( setjmp(ovfl_buf) )
- goto under2;
-do
- {
- mov( E0, Y );
- mov( Z, E0 );
- mul( E0, H, Z );
- add( Z, Z, t );
- }
-while( (cmp(E0,Z) > 0) && (cmp(t,Z) > 0) );
-
-under2:
-sigsave = 0;
-
-mov( E0, UfThold );
-mov( Zero, E1 );
-mov( Zero, Q );
-mov( U2, E9 );
-add( One, E9, S );
-mul( C, S, D );
-if( cmp(D,C) <= 0 )
- {
- mul( Radix, U2, E9 );
- add( One, E9, S );
- mul( C, S, D );
- if( cmp(D, C) <= 0 )
- {
- ErrCnt[Failure] += 1;
- printf( "multiplication gets too many last digits wrong.\n" );
- mov( E0, Underflow );
- mov( Zero, YY1 );
- mov( Z, PseudoZero );
- }
- }
-else
- {
- mov( D, Underflow );
- mul( Underflow, H, PseudoZero );
- mov( Zero, UfThold );
- do
- {
- mov( Underflow, YY1 );
- mov( PseudoZero, Underflow );
- add( E1, E1, t );
- if( cmp(t, E1) <= 0)
- {
- mul( Underflow, HInvrse, Y2 );
- sub( Y2, YY1, E1 );
- FABS( E1 );
- mov( YY1, Q );
- if( (cmp( UfThold, Zero ) == 0)
- && (cmp(YY1, Y2) != 0) )
- mov( YY1, UfThold );
- }
- mul( PseudoZero, H, PseudoZero );
- add( PseudoZero, PseudoZero, t );
- }
- while( (cmp(Underflow, PseudoZero) > 0)
- && (cmp(t, PseudoZero) > 0) );
- }
-/* Comment line 4530 .. 4560 */
-if( cmp(PseudoZero, Zero) != 0 )
- {
- printf("\n");
- mov(PseudoZero, Z );
-/* ... Test PseudoZero for "phoney- zero" violates */
-/* ... PseudoZero < Underflow or PseudoZero < PseudoZero + PseudoZero
- ... */
- if( cmp(PseudoZero, Zero) <= 0 )
- {
- ErrCnt[Failure] += 1;
- printf("Positive expressions can underflow to an\n");
- printf("allegedly negative value\n");
- printf("PseudoZero that prints out as: " );
- show( PseudoZero );
- mov( PseudoZero, X );
- neg( X );
- if( cmp(X, Zero) <= 0 )
- {
- printf("But -PseudoZero, which should be\n");
- printf("positive, isn't; it prints out as " );
- show( X );
- }
- }
- else
- {
- ErrCnt[Flaw] += 1;
- printf( "Underflow can stick at an allegedly positive\n");
- printf("value PseudoZero that prints out as " );
- show( PseudoZero );
- }
-/* TstPtUf();*/
- }
-
-/*=============================================*/
-Milestone = 120;
-/*=============================================*/
-mul( CInvrse, Y, t );
-mul( CInvrse, YY1, t2 );
-if( cmp(t,t2) > 0 )
- {
- mul( H, S, S );
- mov( Underflow, E0 );
- }
-if(! ((cmp(E1,Zero) == 0) || (cmp(E1,E0) == 0)) )
- {
- ErrCnt[Defect] += 1;
- if( cmp(E1,E0) < 0 )
- {
- printf("Products underflow at a higher");
- printf(" threshold than differences.\n");
- if( cmp(PseudoZero,Zero) == 0 )
- mov( E1, E0 );
- }
- else
- {
- printf("Difference underflows at a higher");
- printf(" threshold than products.\n");
- }
- }
-printf("Smallest strictly positive number found is E0 = " );
-show( E0 );
-mov( E0, Z );
-TstPtUf();
-mov( E0, Underflow );
-if(N == 1)
- mov( Y, Underflow );
-I = 4;
-if( cmp(E1,Zero) == 0 )
- I = 3;
-if( cmp( UfThold,Zero) == 0 )
- I = I - 2;
-UfNGrad = True;
-switch(I)
- {
- case 1:
- mov( Underflow, UfThold );
- mul( CInvrse, Q, t );
- mul( CInvrse, Y, t2 );
- mul( t2, S, t2 );
- if( cmp( t, t2 ) != 0 )
- {
- mov( Y, UfThold );
- ErrCnt[Failure] += 1;
- printf( "Either accuracy deteriorates as numbers\n");
- printf("approach a threshold = " );
- show( UfThold );
- printf(" coming down from " );
- show( C );
- printf(" or else multiplication gets too many last digits wrong.\n");
- }
- break;
-
- case 2:
- ErrCnt[Failure] += 1;
- printf( "Underflow confuses Comparison which alleges that\n");
- printf("Q == Y while denying that |Q - Y| == 0; these values\n");
- printf("print out as Q = " );
- show( Q );
- printf( ", Y = " );
- show( Y );
- sub( Y2, Q, t );
- FABS(t);
- printf ("|Q - Y| = " );
- show( t );
- mov( Q, UfThold );
- break;
-
- case 3:
- mov( X, X );
- break;
-
- case 4:
- div( E9, E1, t );
- sub( t, UfThold, t );
- FABS(t);
- if( (cmp(Q,UfThold) == 0) && (cmp(E1,E0) == 0)
- && (cmp(t,E1) <= 0) )
- {
- UfNGrad = False;
- printf("Underflow is gradual; it incurs Absolute Error =\n");
- printf("(roundoff in UfThold) < E0.\n");
- mul( E0, CInvrse, Y );
- add( OneAndHalf, U2, t );
- mul( Y, t, Y );
- add( One, U2, X );
- mul( CInvrse, X, X );
- div( X, Y, t );
- IEEE = (cmp(t,E0) == 0);
- if( IEEE == 0 )
- {
- printf( "((CInvrse E0) (1.5+U2)) / (CInvrse (1+U2)) != E0\n" );
- printf( "CInvrse = " );
- show( CInvrse );
- printf( "E0 = " );
- show( E0 );
- printf( "U2 = " );
- show( U2 );
- printf( "X = " );
- show(X);
- printf( "Y = " );
- show(Y);
- printf( "Y/X = " );
- show(t);
- }
- }
- }
-if(UfNGrad)
- {
- printf("\n");
- div( UfThold, Underflow, R );
- SQRT( R, R );
- if( cmp(R,H) <= 0)
- {
- mul( R, UfThold, Z );
-/* X = Z * (One + R * H * (One + H));*/
- add( One, H, X );
- mul( H, X, X );
- mul( R, X, X );
- add( One, X, X );
- mul( Z, X, X );
- }
- else
- {
- mov( UfThold, Z );
-/*X = Z * (One + H * H * (One + H));*/
- add( One, H, X );
- mul( H, X, X );
- mul( H, X, X );
- add( One, X, X );
- mul( Z, X, X );
- }
- sub( Z, X, t );
-/* if(! ((cmp(X,Z) == 0) || (cmp(t,Zero) != 0)) )*/
- if( (cmp(X,Z) != 0) && (cmp(t,Zero) == 0) )
- {
-/* ErrCnt[Flaw] += 1;*/
- ErrCnt[Serious] += 1;
- printf("X = " );
- show( X );
- printf( "\tis not equal to Z = " );
- show( Z );
-/* sub( Z, X, Z9 );*/
- printf("yet X - Z yields " );
- show( t );
- printf("which compares equal to " );
- show( Zero );
- 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 + " );
- div( Z, X, t );
- sub( Half, t, t );
- sub( Half, t, t );
- show(t);
- }
- }
-printf("The Underflow threshold is " );
-show( UfThold );
-printf( "below which calculation may suffer larger Relative error than" );
-printf( " merely roundoff.\n");
-mul( U1, U1, Y2 );
-mul( Y2, Y2, Y );
-mul( Y, U1, Y2 );
-if( cmp( Y2,UfThold) <= 0 )
- {
- if( cmp(Y,E0) > 0 )
- {
- ErrCnt[Defect] += 1;
- I = 5;
- }
- else
- {
- ErrCnt[Serious] += 1;
- I = 4;
- }
- printf("Range is too narrow; U1^%d Underflows.\n", I);
- }
-Milestone = 130;
-
-/*Y = - FLOOR(Half - TwoForty * LOG(UfThold) / LOG(HInvrse)) / TwoForty;*/
-LOG( UfThold, Y );
-LOG( HInvrse, t );
-div( t, Y, Y );
-mul( TwoForty, Y, Y );
-sub( Y, Half, Y );
-FLOOR( Y, Y );
-div( TwoForty, Y, Y );
-neg(Y);
-sub( One, Y, Y2 ); /* ***** changed from Y2 = Y + Y */
-printf("Since underflow occurs below the threshold\n");
-printf("UfThold = " );
-show( HInvrse );
-printf( "\tto the power " );
-show( Y );
-printf( "only underflow should afflict the expression " );
-show( HInvrse );
-printf( "\tto the power " );
-show( Y2 );
-POW( HInvrse, Y2, V9 );
-printf("Actually calculating yields: " );
-show( V9 );
-add( Radix, Radix, t );
-add( t, E9, t );
-mul( t, UfThold, t );
-if( (cmp(V9,Zero) < 0) || (cmp(V9,t) > 0) )
- {
- ErrCnt[Serious] += 1;
- printf( "this is not between 0 and underflow\n");
- printf(" threshold = " );
- show( UfThold );
- }
-else
- {
- add( One, E9, t );
- mul( UfThold, t, t );
- if( cmp(V9,t) <= 0 )
- printf("This computed value is O.K.\n");
- else
- {
- ErrCnt[Defect] += 1;
- printf( "this is not between 0 and underflow\n");
- printf(" threshold = " );
- show( UfThold );
- }
- }
-
-Milestone = 140;
-
-pow2test();
-
-/*=============================================*/
-Milestone = 160;
-/*=============================================*/
-Pause();
-printf("Searching for Overflow threshold:\n");
-printf("This may generate an error.\n");
-sigsave = sigfpe;
-I = 0;
-mov( CInvrse, Y ); /* a large power of 2 */
-neg(Y);
-mul( HInvrse, Y, V9 ); /* HInvrse = 2 */
-if (setjmp(ovfl_buf))
- goto overflow;
-do
- {
- mov( Y, V );
- mov( V9, Y );
- mul( HInvrse, Y, V9 );
- }
-while( cmp(V9,Y) < 0 ); /* V9 = 2 * Y */
-I = 1;
-
-overflow:
-
-show( HInvrse );
-printf( "\ttimes " );
-show( Y );
-printf( "\tequals " );
-show( V9 );
-
-mov( V9, Z );
-printf("Can `Z = -Y' overflow?\n");
-printf("Trying it on Y = " );
-show(Y);
-mov( Y, V9 );
-neg( V9 );
-mov( V9, V0 );
-sub( Y, V, t );
-add( V, V0, t2 );
-if( cmp(t,t2) == 0 )
- printf("Seems O.K.\n");
-else
- {
- printf("finds a Flaw, -(-Y) differs from Y.\n");
- printf( "V-Y=t:" );
- show(V);
- show(Y);
- show(t);
- printf( "V+V0=t2:" );
- show(V);
- show(V0);
- show(t2);
- ErrCnt[Flaw] += 1;
- }
-if( (cmp(Z, Y) != 0) && (I != 0) )
- {
- ErrCnt[Serious] += 1;
- printf("overflow past " );
- show( Y );
- printf( "\tshrinks to " );
- show( Z );
- printf( "= Y * " );
- show( HInvrse );
- }
-/*Y = V * (HInvrse * U2 - HInvrse);*/
-mul( HInvrse, U2, Y );
-sub( HInvrse, Y, Y );
-mul( V, Y, Y );
-/*Z = Y + ((One - HInvrse) * U2) * V;*/
-sub( HInvrse, One, Z );
-mul( Z, U2, Z );
-mul( Z, V, Z );
-add( Y, Z, Z );
-if( cmp(Z,V0) < 0 )
- mov( Z, Y );
-if( cmp(Y,V0) < 0)
- mov( Y, V );
-sub( V, V0, t );
-if( cmp(t,V0) < 0 )
- mov( V0, V );
-printf("Overflow threshold is V = " );
-show( V );
-if(I)
- {
- printf("Overflow saturates at V0 = " );
- show( V0 );
- }
-else
-printf("There is no saturation value because the system traps on overflow.\n");
-
-mul( V, One, V9 );
-printf("No Overflow should be signaled for V * 1 = " );
-show( V9 );
-div( One, V, V9 );
- printf(" nor for V / 1 = " );
- show( V9 );
- printf("Any overflow signal separating this * from the one\n");
- printf("above is a DEFECT.\n");
-/*=============================================*/
-Milestone = 170;
-/*=============================================*/
-mov( V, t );
-neg( t );
-k = 0;
-if( cmp(t,V) >= 0 )
- k = 1;
-mov( V0, t );
-neg( t );
-if( cmp(t,V0) >= 0 )
- k = 1;
-mov( UfThold, t );
-neg(t);
-if( cmp(t,V) >= 0 )
- k = 1;
-if( cmp(UfThold,V) >= 0 )
- k = 1;
-if( k != 0 )
- {
- ErrCnt[Failure] += 1;
- printf( "Comparisons involving +-");
- show( V );
- show( V0 );
- show( UfThold );
- printf("are confused by Overflow." );
- }
-/*=============================================*/
-Milestone = 175;
-/*=============================================*/
-printf("\n");
-for(Indx = 1; Indx <= 3; ++Indx) {
- switch(Indx)
- {
- case 1: mov(UfThold, Z); break;
- case 2: mov( E0, Z); break;
- case 3: mov(PseudoZero, Z); break;
- }
-if( cmp(Z, Zero) != 0 )
- {
- SQRT( Z, V9 );
- mul( V9, V9, Y );
- mul( Radix, E9, t );
- sub( t, One, t );
- div( t, Y, t );
- add( One, Radix, t2 );
- add( t2, E9, t2 );
- mul( t2, Z, t2 );
- if( (cmp(t,Z) < 0) || (cmp(Y,t2) > 0) )
- {
- if( cmp(V9,U1) > 0 )
- ErrCnt[Serious] += 1;
- else
- ErrCnt[Defect] += 1;
- printf("Comparison alleges that what prints as Z = " );
- show( Z );
- printf(" is too far from sqrt(Z) ^ 2 = " );
- show( Y );
- }
- }
-}
-
-Milestone = 180;
-
-for(Indx = 1; Indx <= 2; ++Indx)
- {
- if(Indx == 1)
- mov( V, Z );
- else
- mov( V0, Z );
- SQRT( Z, V9 );
- mul( Radix, E9, X );
- sub( X, One, X );
- mul( X, V9, X );
- mul( V9, X, V9 );
- mul( Two, Radix, t );
- mul( t, E9, t );
- sub( t, One, t );
- mul( t, Z, t );
- if( (cmp(V9,t) < 0) || (cmp(V9,Z) > 0) )
- {
- mov( V9, Y );
- if( cmp(X,W) < 0 )
- ErrCnt[Serious] += 1;
- else
- ErrCnt[Defect] += 1;
- printf("Comparison alleges that Z = " );
- show( Z );
- printf(" is too far from sqrt(Z) ^ 2 :" );
- show( Y );
- }
- }
-
-Milestone = 190;
-
-Pause();
-mul( UfThold, V, X );
-mul( Radix, Radix, Y );
-mul( X, Y, t );
-if( (cmp(t,One) < 0) || (cmp(X,Y) > 0) )
- {
- mul( X, Y, t );
- div( U1, Y, t2 );
- if( (cmp(t,U1) < 0) || (cmp(X,t2) > 0) )
- {
- ErrCnt[Defect] += 1;
- printf( "Badly " );
- }
- else
- {
- ErrCnt[Flaw] += 1;
- }
- printf(" unbalanced range; UfThold * V = " );
- show( X );
- printf( "\tis too far from 1.\n");
- }
-Milestone = 200;
-
-for(Indx = 1; Indx <= 5; ++Indx)
- {
- mov( F9, X );
- switch(Indx)
- {
- case 2: add( One, U2, X ); break;
- case 3: mov( V, X ); break;
- case 4: mov(UfThold,X); break;
- case 5: mov(Radix,X);
- }
- mov( X, Y );
-
- sigsave = sigfpe;
- if (setjmp(ovfl_buf))
- {
- printf(" X / X traps when X = " );
- show( X );
- }
- else
- {
-/*V9 = (Y / X - Half) - Half;*/
- div( X, Y, t );
- sub( Half, t, t );
- sub( Half, t, V9 );
- if( cmp(V9,Zero) == 0 )
- continue;
- mov( U1, t );
- neg(t);
- if( (cmp(V9,t) == 0) && (Indx < 5) )
- {
- ErrCnt[Flaw] += 1;
- }
- else
- {
- ErrCnt[Serious] += 1;
- }
- printf(" X / X differs from 1 when X = " );
- show( X );
- printf(" instead, X / X - 1/2 - 1/2 = " );
- show( V9 );
- }
- }
-
- 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 {
- k = 0;
- if( cmp( Radix, Two ) == 0 )
- k = 1;
- if( cmp( Radix, Ten ) == 0 )
- k = 1;
- if( (cmp(StickyBit,One) >= 0) && (k == 1) )
- {
- printf("Rounding appears to conform to ");
- printf("the proposed IEEE standard P");
- k = 0;
- k |= cmp( Radix, Two );
- mul( Four, Three, t );
- mul( t, Two, t );
- sub( t, Precision, t );
- sub( TwentySeven, Precision, t2 );
- sub( TwentySeven, t2, t2 );
- add( t2, One, t2 );
- mul( t2, t, t );
- if( (cmp(Radix,Two) == 0)
- && (cmp(t,Zero) == 0) )
- 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");
- }
-
-
-/* Random */
-/* Random computes
- X = (Random1 + Random9)^5
- Random1 = X - FLOOR(X) + 0.000005 * X;
- and returns the new value of Random1
-*/
-
-
-static int randflg = 0;
-FLOAT(C5em6);
-
-Random()
-{
-
-if( randflg == 0 )
- {
- mov( Six, t );
- neg(t);
- POW( Ten, t, t );
- mul( Five, t, C5em6 );
- randflg = 1;
- }
-add( Random1, Random9, t );
-mul( t, t, t2 );
-mul( t2, t2, t2 );
-mul( t, t2, t );
-FLOOR(t, t2 );
-sub( t2, t, t2 );
-mul( t, C5em6, t );
-add( t, t2, Random1 );
-/*return(Random1);*/
-}
-
-/* SqXMinX */
-
-SqXMinX( ErrKind )
-int ErrKind;
-{
-mul( X, BInvrse, t2 );
-sub( t2, X, t );
-/*SqEr = ((SQRT(X * X) - XB) - XA) / OneUlp;*/
-mul( X, X, Sqarg );
-SQRT( Sqarg, SqEr );
-sub( t2, SqEr, SqEr );
-sub( t, SqEr, SqEr );
-div( OneUlp, SqEr, SqEr );
-if( cmp(SqEr,Zero) != 0)
- {
- Showsq( 0 );
- add( J, One, J );
- ErrCnt[ErrKind] += 1;
- printf("sqrt of " );
- mul( X, X, t );
- show( t );
- printf( "minus " );
- show( X );
- printf( "equals " );
- mul( OneUlp, SqEr, t );
- show( t );
- printf("\tinstead of correct value 0 .\n");
- }
-}
-
-/* NewD */
-
-NewD()
-{
-mul( Z1, Q, X );
-/*X = FLOOR(Half - X / Radix) * Radix + X;*/
-div( Radix, X, t );
-sub( t, Half, t );
-FLOOR( t, t );
-mul( t, Radix, t );
-add( t, X, X );
-/*Q = (Q - X * Z) / Radix + X * X * (D / Radix);*/
-mul( X, Z, t );
-sub( t, Q, t );
-div( Radix, t, t );
-div( Radix, D, t2 );
-mul( X, t2, t2 );
-mul( X, t2, t2 );
-add( t, t2, Q );
-/*Z = Z - Two * X * D;*/
-mul( Two, X, t );
-mul( t, D, t );
-sub( t, Z, Z );
-
-if( cmp(Z,Zero) <= 0)
- {
- neg(Z);
- neg(Z1);
- }
-mul( Radix, D, D );
-}
-
-/* SR3750 */
-
-SR3750()
-{
-sub( Radix, X, t );
-sub( Radix, Z2, t2 );
-k = 0;
-if( cmp(t,t2) < 0 )
- k = 1;
-sub( Z2, X, t );
-sub( Z2, W, t2 );
-if( cmp(t,t2) > 0 )
- k = 1;
-/*if (! ((X - Radix < Z2 - Radix) || (X - Z2 > W - Z2))) {*/
-if( k == 0 )
- {
- I = I + 1;
- mul( X, D, X2 );
- mov( X2, Sqarg );
- SQRT( X2, X2 );
-/*Y2 = (X2 - Z2) - (Y - Z2);*/
- sub( Z2, X2, Y2 );
- sub( Z2, Y, t );
- sub( t, Y2, Y2 );
- sub( Half, Y, X2 );
- div( X2, X8, X2 );
- mul( Half, X2, t );
- mul( t, X2, t );
- sub( t, X2, X2 );
-/*SqEr = (Y2 + Half) + (Half - X2);*/
- add( Y2, Half, SqEr );
- sub( X2, Half, t );
- add( t, SqEr, SqEr );
- Showsq( -1 );
- sub( X2, Y2, SqEr );
- Showsq( 1 );
- }
-}
-
-/* IsYeqX */
-
-IsYeqX()
-{
-if( cmp(Y,X) != 0 )
- {
- if (N <= 0)
- {
- if( (cmp(Z,Zero) == 0) && (cmp(Q,Zero) <= 0) )
- printf("WARNING: computing\n");
- else
- {
- ErrCnt[Defect] += 1;
- printf( "computing\n");
- }
- show( Z );
- printf( "\tto the power " );
- show( Q );
- printf("\tyielded " );
- show( Y );
- printf("\twhich compared unequal to correct " );
- show( X );
- sub( X, Y, t );
- printf("\t\tthey differ by " );
- show( t );
- }
- N = N + 1; /* ... count discrepancies. */
- }
-}
-
-/* SR3980 */
-
-SR3980()
-{
-long li;
-
-do
- {
-/*Q = (FLOAT) I;*/
- li = I;
- LTOF( &li, Q );
- POW( Z, Q, Y );
- IsYeqX();
- if(++I > M)
- break;
- mul( Z, X, X );
- }
-while( cmp(X,W) < 0 );
-}
-
-/* PrintIfNPositive */
-
-PrintIfNPositive()
-{
-if(N > 0)
- printf("Similar discrepancies have occurred %d times.\n", N);
-}
-
-
-/* TstPtUf */
-
-TstPtUf()
-{
-N = 0;
-if( cmp(Z,Zero) != 0)
- {
- printf( "Z = " );
- show(Z);
- printf("Since comparison denies Z = 0, evaluating ");
- printf("(Z + Z) / Z should be safe.\n");
- sigsave = sigfpe;
- if (setjmp(ovfl_buf))
- goto very_serious;
- add( Z, Z, Q9 );
- div( Z, Q9, Q9 );
- printf("What the machine gets for (Z + Z) / Z is " );
- show( Q9 );
- sub( Two, Q9, t );
- FABS(t);
- mul( Radix, U2, t2 );
- if( cmp(t,t2) < 0 )
- {
- printf("This is O.K., provided Over/Underflow");
- printf(" has NOT just been signaled.\n");
- }
- else
- {
- if( (cmp(Q9,One) < 0) || (cmp(Q9,Two) > 0) )
- {
-very_serious:
- N = 1;
- ErrCnt [Serious] = ErrCnt [Serious] + 1;
- printf("This is a VERY SERIOUS DEFECT!\n");
- }
- else
- {
- N = 1;
- ErrCnt[Defect] += 1;
- printf("This is a DEFECT!\n");
- }
- }
- mul( Z, One, V9 );
- mov( V9, Random1 );
- mul( One, Z, V9 );
- mov( V9, Random2 );
- div( One, Z, V9 );
- if( (cmp(Z,Random1) == 0) && (cmp(Z,Random2) == 0)
- && (cmp(Z,V9) == 0) )
- {
- if (N > 0)
- Pause();
- }
- else
- {
- N = 1;
- ErrCnt[Defect] += 1;
- printf( "What prints as Z = ");
- show( Z );
- printf( "\tcompares different from " );
- if( cmp(Z,Random1) != 0)
- {
- printf("Z * 1 = " );
- show( Random1 );
- }
- if( (cmp(Z,Random2) != 0)
- || (cmp(Random2,Random1) != 0) )
- {
- printf("1 * Z == " );
- show( Random2 );
- }
- if( cmp(Z,V9) != 0 )
- {
- printf("Z / 1 = " );
- show( V9 );
- }
- if( cmp(Random2,Random1) != 0 )
- {
- ErrCnt[Defect] += 1;
- printf( "Multiplication does not commute!\n");
- printf("\tComparison alleges that 1 * Z = " );
- show(Random2);
- printf("\tdiffers from Z * 1 = " );
- show(Random1);
- }
- Pause();
- }
- }
-}
-
-Pause()
-{
-}
-
-Sign( x, y )
-FSIZE *x, *y;
-{
-
-if( cmp( x, Zero ) < 0 )
- {
- mov( One, y );
- neg( y );
- }
-else
- {
- mov( One, y );
- }
-}
-
-sqtest()
-{
-printf("\nRunning test of square root(x).\n");
-
-RSqrt = Other;
-k = 0;
-SQRT( Zero, t );
-k |= cmp( Zero, t );
-mov( Zero, t );
-neg(t);
-SQRT( t, t2 );
-k |= cmp( t, t2 );
-SQRT( One, t );
-k |= cmp( One, t );
-if( k != 0 )
- {
- ErrCnt[Failure] += 1;
- printf( "Square root of 0.0, -0.0 or 1.0 wrong\n");
- }
-mov( Zero, MinSqEr );
-mov( Zero, MaxSqEr );
-mov( Zero, J );
-mov( Radix, X );
-mov( U2, OneUlp );
-SqXMinX( Serious );
-mov( BInvrse, X );
-mul( BInvrse, U1, OneUlp );
-SqXMinX( Serious );
-mov( U1, X );
-mul( U1, U1, OneUlp );
-SqXMinX( Serious );
-if( cmp(J,Zero) != 0)
- Pause();
-printf("Testing if sqrt(X * X) == X for %d Integers X.\n", NoTrials);
-mov( Zero, J );
-mov( Two, X );
-mov( Radix, Y );
-if( cmp(Radix,One) != 0 )
- {
- lngint = NoTrials;
- LTOF( &lngint, t );
- FTOL( t, &lng2, X );
- if( lngint != lng2 )
- {
- printf( "Integer conversion error\n" );
- exit(1);
- }
- do
- {
- mov( Y, X );
- mul( Radix, Y, Y );
- sub( X, Y, t2 );
- }
- while( ! (cmp(t2,t) >= 0) );
- }
-mul( X, U2, OneUlp );
-I = 1;
-while(I < 10)
- {
- add( X, One, X );
- SqXMinX( Defect );
- if( cmp(J,Zero) > 0 )
- break;
- I = I + 1;
- }
-printf("Test for sqrt monotonicity.\n");
-I = - 1;
-mov( BMinusU2, X );
-mov( Radix, Y );
-mul( Radix, U2, Z );
-add( Radix, Z, Z );
-NotMonot = False;
-Monot = False;
-while( ! (NotMonot || Monot))
- {
- I = I + 1;
- SQRT(X, X);
- SQRT(Y,Q);
- SQRT(Z,Z);
- if( (cmp(X,Q) > 0) || (cmp(Q,Z) > 0) )
- NotMonot = True;
- else
- {
- add( Q, Half, Q );
- FLOOR( Q, Q );
- mul( Q, Q, t );
- if( (I > 0) || (cmp(Radix,t) == 0) )
- Monot = True;
- else if (I > 0)
- {
- if(I > 1)
- Monot = True;
- else
- {
- mul( Y, BInvrse, Y );
- sub( U1, Y, X );
- add( Y, U1, Z );
- }
- }
- else
- {
- mov( Q, Y );
- sub( U2, Y, X );
- add( Y, U2, Z );
- }
- }
- }
-if( Monot )
- printf("sqrt has passed a test for Monotonicity.\n");
-else
- {
- ErrCnt[Defect] += 1;
- printf("sqrt(X) is non-monotonic for X near " );
- show(Y);
- }
-/*=============================================*/
-Milestone = 80;
-/*=============================================*/
-add( MinSqEr, Half, MinSqEr );
-sub( Half, MaxSqEr, MaxSqEr);
-/*Y = (SQRT(One + U2) - One) / U2;*/
-add( One, U2, Sqarg );
-SQRT( Sqarg, Y );
-sub( One, Y, Y );
-div( U2, Y, Y );
-/*SqEr = (Y - One) + U2 / Eight;*/
-sub( One, Y, t );
-div( Eight, U2, SqEr );
-add( t, SqEr, SqEr );
-Showsq( 1 );
-div( Eight, U2, SqEr );
-add( Y, SqEr, SqEr );
-Showsq( -1 );
-/*Y = ((SQRT(F9) - U2) - (One - U2)) / U1;*/
-mov( F9, Sqarg );
-SQRT( Sqarg, Y );
-sub( U2, Y, Y );
-sub( U2, One, t );
-sub( t, Y, Y );
-div( U1, Y, Y );
-div( Eight, U1, SqEr );
-add( Y, SqEr, SqEr );
-Showsq( 1 );
-/*SqEr = (Y + One) + U1 / Eight;*/
-div( Eight, U1, t );
-add( Y, One, SqEr );
-add( SqEr, t, SqEr );
-Showsq( -1 );
-mov( U2, OneUlp );
-mov( OneUlp, X );
-for( Indx = 1; Indx <= 3; ++Indx)
- {
-/*Y = SQRT((X + U1 + X) + F9);*/
- add( X, U1, Y );
- add( Y, X, Y );
- add( Y, F9, Y );
- mov( Y, Sqarg );
- SQRT( Sqarg, Y );
-/*Y = ((Y - U2) - ((One - U2) + X)) / OneUlp;*/
- sub( U2, One, t );
- add( t, X, t );
- sub( U2, Y, Y );
- sub( t, Y, Y );
- div( OneUlp, Y, Y );
-/*Z = ((U1 - X) + F9) * Half * X * X / OneUlp;*/
- sub( X, U1, t );
- add( t, F9, t );
- mul( t, Half, t );
- mul( t, X, t );
- mul( t, X, t );
- div( OneUlp, t, Z );
- add( Y, Half, SqEr );
- add( SqEr, Z, SqEr );
- Showsq( -1 );
- sub( Half, Y, SqEr );
- add( SqEr, Z, SqEr );
- Showsq( 1 );
- if(((Indx == 1) || (Indx == 3)))
- {
-/*X = OneUlp * Sign (X) * FLOOR(Eight / (Nine * SQRT(OneUlp)));*/
- mov( OneUlp, Sqarg );
- SQRT( Sqarg, t );
- mul( Nine, t, t );
- div( t, Eight, t );
- FLOOR( t, t );
- Sign( X, t2 );
- mul( t2, t, t );
- mul( OneUlp, t, X );
- }
- else
- {
- mov( U1, OneUlp );
- mov( OneUlp, X );
- neg( X );
- }
- }
-/*=============================================*/
-Milestone = 85;
-/*=============================================*/
-SqRWrng = False;
-Anomaly = False;
-if( cmp(Radix,One) != 0 )
- {
- printf("Testing whether sqrt is rounded or chopped.\n");
-/*D = FLOOR(Half + POW(Radix, One + Precision - FLOOR(Precision)));*/
- FLOOR( Precision, t2 );
- add( One, Precision, t );
- sub( t2, t, t );
- POW( Radix, t, D );
- add( Half, D, D );
- FLOOR( D, D );
-/* ... == Radix^(1 + fract) if (Precision == Integer + fract. */
- div( Radix, D, X );
- div( A1, D, Y );
- FLOOR( X, t );
- FLOOR( Y, t2 );
- if( (cmp(X,t) != 0) || (cmp(Y,t2) != 0) )
- {
- Anomaly = True;
- printf( "Anomaly 1\n" );
- }
- else
- {
- mov( Zero, X );
- mov( X, Z2 );
- mov( One, Y );
- mov( Y, Y2 );
- sub( One, Radix, Z1 );
- mul( Four, D, FourD );
- do
- {
- if( cmp(Y2,Z2) >0 )
- {
- mov( Radix, Q );
- mov( Y, YY1 );
- do
- {
-/*X1 = FABS(Q + FLOOR(Half - Q / YY1) * YY1);*/
- div( YY1, Q, t );
- sub( t, Half, t );
- FLOOR( t, t );
- mul( t, YY1, t );
- add( Q, t, X1 );
- FABS( X1 );
- mov( YY1, Q );
- mov( X1, YY1 );
- }
- while( ! (cmp(X1,Zero) <= 0) );
- if( cmp(Q,One) <= 0 )
- {
- mov( Y2, Z2 );
- mov( Y, Z );
- }
- }
- add( Y, Two, Y );
- add( X, Eight, X );
- add( Y2, X, Y2 );
- if( cmp(Y2,FourD) >= 0 )
- sub( FourD, Y2, Y2 );
- }
- while( ! (cmp(Y,D) >= 0) );
- sub( Z2, FourD, X8 );
- mul( Z, Z, Q );
- add( X8, Q, Q );
- div( FourD, Q, Q );
- div( Eight, X8, X8 );
- FLOOR( Q, t );
- if( cmp(Q,t) != 0 )
- {
- Anomaly = True;
- printf( "Anomaly 2\n" );
- }
- else
- {
- Break = False;
- do
- {
- mul( Z1, Z, X );
-/*X = X - FLOOR(X / Radix) * Radix;*/
- div( Radix, X, t );
- FLOOR( t, t );
- mul( t, Radix, t );
- sub( t, X, X );
- if( cmp(X,One) == 0 )
- Break = True;
- else
- sub( One, Z1, Z1 );
- }
- while( ! (Break || (cmp(Z1,Zero) <= 0)) );
- if( (cmp(Z1,Zero) <= 0) && (! Break))
- {
- printf( "Anomaly 3\n" );
- Anomaly = True;
- }
- else
- {
- if( cmp(Z1,RadixD2) > 0)
- sub( Radix, Z1, Z1 );
- do
- {
- NewD();
- mul( U2, D, t );
- }
- while( ! (cmp(t,F9) >= 0) );
- mul( D, Radix, t );
- sub( D, t, t );
- sub( D, W, t2 );
- if (cmp(t,t2) != 0 )
- {
- printf( "Anomaly 4\n" );
- Anomaly = True;
- }
- else
- {
- mov( D, Z2 );
- I = 0;
- add( One, Z, t );
- mul( t, Half, t );
- add( D, t, Y );
- add( D, Z, X );
- add( X, Q, X );
- SR3750();
- sub( Z, One, t );
- mul( t, Half, t );
- add( D, t, Y );
- add( Y, D, Y );
- sub( Z, D, X );
- add( X, D, X );
- add( X, Q, t );
- add( t, X, X );
- SR3750();
- NewD();
- sub( Z2, D, t );
- sub( Z2, W, t2 );
- if(cmp(t,t2) != 0 )
- {
- printf( "Anomaly 5\n" );
- Anomaly = True;
- }
- else
- {
-/*Y = (D - Z2) + (Z2 + (One - Z) * Half);*/
- sub( Z, One, t );
- mul( t, Half, t );
- add( Z2, t, t );
- sub( Z2, D, Y );
- add( Y, t, Y );
-/*X = (D - Z2) + (Z2 - Z + Q);*/
- sub( Z, Z2, t );
- add( t, Q, t );
- sub( Z2, D, X );
- add( X, t, X );
- SR3750();
- add( One, Z, Y );
- mul( Y, Half, Y );
- mov( Q, X );
- SR3750();
- if(I == 0)
- {
- printf( "Anomaly 6\n" );
- Anomaly = True;
- }
- }
- }
- }
- }
- }
- if ((I == 0) || Anomaly)
- {
- ErrCnt[Failure] += 1;
- printf( "Anomalous arithmetic with Integer < \n");
- printf("Radix^Precision = " );
- show( W );
- printf(" fails test whether sqrt rounds or chops.\n");
- SqRWrng = True;
- }
- }
-if(! Anomaly)
- {
- if(! ((cmp(MinSqEr,Zero) < 0) || (cmp(MaxSqEr,Zero) > 0))) {
- RSqrt = Rounded;
- printf("Square root appears to be correctly rounded.\n");
- }
- else
- {
- k = 0;
- add( MaxSqEr, U2, t );
- sub( Half, U2, t2 );
- if( cmp(t,t2) > 0 )
- k = 1;
- if( cmp( MinSqEr, Half ) > 0 )
- k = 1;
- add( MinSqEr, Radix, t );
- if( cmp( t, Half ) < 0 )
- k = 1;
- if( k == 1 )
- 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 " );
- sub( Half, MinSqEr, t );
- show( t );
- printf("\tto " );
- add( Half, MaxSqEr, t );
- show( t );
- printf( "ulps.\n" );
- sub( MinSqEr, MaxSqEr, t );
- mul( Radix, Radix, t2 );
- if( cmp( t, t2 ) >= 0 )
- {
- ErrCnt[Serious] += 1;
- printf( "sqrt gets too many last digits wrong\n");
- }
- }
-}
-
-Showsq( arg )
-int arg;
-{
-
-k = 0;
-if( arg <= 0 )
- {
- if( cmp(SqEr,MinSqEr) < 0 )
- {
- k = 1;
- mov( SqEr, MinSqEr );
- }
- }
-if( arg >= 0 )
- {
- if( cmp(SqEr,MaxSqEr) > 0 )
- {
- k = 2;
- mov( SqEr, MaxSqEr );
- }
- }
-#if DEBUG
-if( k != 0 )
- {
- printf( "Square root of " );
- show( arg );
- printf( "\tis in error by " );
- show( SqEr );
- }
-#endif
-}
-
-
-pow1test()
-{
-
-/*=============================================*/
-Milestone = 90;
-/*=============================================*/
-Pause();
-printf("Testing powers Z^i for small Integers Z and i.\n");
-N = 0;
-/* ... test powers of zero. */
-I = 0;
-mov( Zero, Z );
-neg(Z);
-M = 3;
-Break = False;
-do
- {
- mov( One, X );
- SR3980();
- if(I <= 10)
- {
- I = 1023;
- SR3980();
- }
- if( cmp(Z,MinusOne) == 0 )
- Break = True;
- else
- {
- mov( MinusOne, Z );
- PrintIfNPositive();
- N = 0;
-/* .. if(-1)^N is invalid, replace MinusOne by One. */
- I = - 4;
- }
- }
-while( ! Break );
-PrintIfNPositive();
-N1 = N;
-N = 0;
-mov( A1, Z );
-/*M = FLOOR(Two * LOG(W) / LOG(A1));*/
-LOG( W, t );
-mul( Two, t, t );
-FLOOR( t, t );
-LOG( A1, t2 );
-div( t2, t, t );
-FTOL( t, &lngint, t2 );
-M = lngint;
-Break = False;
-do
- {
- mov( Z, X );
- I = 1;
- SR3980();
- if( cmp(Z,AInvrse) == 0 )
- Break = True;
- else
- mov( AInvrse, Z );
- }
-while( ! (Break) );
-/*=============================================*/
-Milestone = 100;
-/*=============================================*/
-/* Powers of Radix have been tested, */
-/* next try a few primes */
-
-M = NoTrials;
-
-mov( Three, Z );
-do
- {
- mov( Z, X );
- I = 1;
- SR3980();
- do
- {
- add( Z, Two, Z );
- div( Three, Z, t );
- FLOOR( t, t );
- mul( Three, t, t );
- }
- while( cmp(t,Z) == 0 );
- mul( Eight, Three, t );
- }
-while( cmp(Z,t) < 0 );
-
-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 discrepancies found.\n");
-if(N > 0)
- Pause();
-else printf("\n");
-}
-
-
-
-pow2test()
-{
-printf("\n");
-/* ...calculate Exp2 == exp(2) == 7.38905 60989 30650 22723 04275-... */
-mov( Zero, X );
-mov( Two, t2 ); /*I = 2;*/
-
-mul( Two, Three, Y );
-mov( Zero, Q );
-N = 0;
-do
- {
- mov( X, Z );
- add( t2, One, t2 ); /*I = I + 1;*/
- add( t2, t2, t );
- div( t, Y, Y ); /*Y = Y / (I + I);*/
- add( Y, Q, R );
- add( Z, R, X );
- sub( X, Z, Q );
- add( Q, R, Q );
- }
-while( cmp(X,Z) > 0 );
-
-/*Z = (OneAndHalf + One / Eight) + X / (OneAndHalf * ThirtyTwo);*/
-div( Eight, One, t );
-add( OneAndHalf, t, Z );
-mul( OneAndHalf, ThirtyTwo, t );
-div( t, X, t );
-add( Z, t, Z );
-mul( Z, Z, X );
-mul( X, X, Exp2 );
-mov( F9, X );
-sub( U1, X, Y );
-printf("Testing X^((X + 1) / (X - 1)) vs. exp(2) = " );
-show( Exp2 );
-printf( "\tas X -> 1.\n" );
-for(I = 1;;)
- {
- sub( BInvrse, X, Z );
-/*Z = (X + One) / (Z - (One - BInvrse));*/
- add( X, One, t2 );
- sub( BInvrse, One, t );
- sub( t, Z, t );
- div( t, t2, Z );
- POW( X, Z, Sqarg );
- sub( Exp2, Sqarg, Q );
- mov( Q, t );
- FABS( t );
- mul( TwoForty, U2, t2 );
- if( cmp( t, t2 ) > 0 )
- {
- N = 1;
- sub( BInvrse, X, V9 );
- sub( BInvrse, One, t );
- sub( t, V9, V9 );
- ErrCnt[Defect] += 1;
- printf( "Calculated " );
- show( Sqarg );
- printf(" for \t(1 + " );
- show( V9 );
- printf( "\tto the power " );
- show( Z );
- printf("\tdiffers from correct value by " );
- show( Q );
- printf("\tThis much error may spoil financial\n");
- printf("\tcalculations involving tiny interest rates.\n");
- break;
- }
- else
- {
- sub( X, Y, Z );
- mul( Z, Two, Z );
- add( Z, Y, Z );
- mov( Y, X );
- mov( Z, Y );
- sub( F9, X, Z );
- mul( Z, Z, Z );
- add( Z, One, Z );
- if( (cmp(Z,One) > 0) && (I < NoTrials) )
- I++;
- else
- {
- if( cmp(X,One) > 0 )
- {
- if(N == 0)
- printf("Accuracy seems adequate.\n");
- break;
- }
- else
- {
- add( One, U2, X );
- add( U2, U2, Y );
- add( X, Y, Y );
- I = 1;
- }
- }
- }
- }
-/*=============================================*/
-Milestone = 150;
-/*=============================================*/
-printf("Testing powers Z^Q at four nearly extreme values.\n");
-N = 0;
-mov( A1, Z );
-/*Q = FLOOR(Half - LOG(C) / LOG(A1));*/
-LOG( C, t );
-LOG( A1, t2 );
-div( t2, t, t );
-sub( t, Half, t );
-FLOOR( t, Q );
-Break = False;
-do
- {
- mov( CInvrse, X );
- POW( Z, Q, Y );
- IsYeqX();
- neg(Q);
- mov( C, X );
- POW( Z, Q, Y );
- IsYeqX();
- if( cmp(Z,One) < 0 )
- Break = True;
- else
- mov( AInvrse, Z );
- }
-while( ! (Break));
-PrintIfNPositive();
-if(N == 0)
- printf(" ... no discrepancies found.\n");
-printf("\n");
-}
+/* paranoia.c arithmetic tester
+ *
+ * This is an implementation of the PARANOIA program. It substitutes
+ * subroutine calls for ALL floating point arithmetic operations.
+ * This permits you to substitute your own experimental versions of
+ * arithmetic routines. It also defeats compiler optimizations,
+ * so for native arithmetic you can be pretty sure you are testing
+ * the arithmetic and not the compiler.
+ *
+ * This version of PARANOIA omits the display of division by zero.
+ * It also omits the test for extra precise subexpressions, since
+ * they cannot occur in this context. Otherwise it includes all the
+ * tests of the 27 Jan 86 distribution, plus a few additional tests.
+ * Commentary has been reduced to a minimum in order to make the program
+ * smaller.
+ *
+ * The original PARANOIA program, written by W. Kahan, C version
+ * by Thos Sumner and David Gay, can be downloaded free from the
+ * Internet NETLIB. An MSDOS disk can be obtained for $15 from:
+ * Richard Karpinski
+ * 6521 Raymond Street
+ * Oakland, CA 94609
+ *
+ * Steve Moshier, 28 Oct 88
+ * last rev: 23 May 92
+ */
+
+#define DEBUG 0
+
+/* To use the native arithmetic of the computer, define NATIVE
+ * to be 1. To use your own supplied arithmetic routines, NATIVE is 0.
+ */
+#define NATIVE 0
+
+/* gcc real.c interface */
+#define L128DOUBLE 0
+
+#include <stdio.h>
+
+
+
+
+/* Data structure of floating point number. If NATIVE was
+ * selected above, you can define LDOUBLE 1 to test 80-bit long double
+ * precision or define it 0 to test 64-bit double precision.
+*/
+#define LDOUBLE 0
+#if NATIVE
+
+#define NE 1
+#if LDOUBLE
+#define FSIZE long double
+#define FLOAT(x) FSIZE x[NE]
+static FSIZE eone[NE] = {1.0L}; /* The constant 1.0 */
+#define ZSQRT sqrtl
+#define ZLOG logl
+#define ZFLOOR floorl
+#define ZPOW powl
+long double sqrtl(), logl(), floorl(), powl();
+#define FSETUP einit
+#else /* not LDOUBLE */
+#define FSIZE double
+#define FLOAT(x) FSIZE x[NE]
+static FSIZE eone[NE] = {1.0}; /* The constant 1.0 */
+#define ZSQRT sqrt
+#define ZLOG log
+#define ZFLOOR floor
+#define ZPOW pow
+double sqrt(), log(), floor(), pow();
+/* Coprocessor initialization,
+ * defeat underflow trap or what have you.
+ * This is required mainly on i386 and 68K processors.
+ */
+#define FSETUP dprec
+#endif /* double, not LDOUBLE */
+
+#else /* not NATIVE */
+
+/* Setup for extended double type.
+ * Put NE = 10 for real.c operating with TFmode support (16-byte reals)
+ * Put NE = 6 for real.c operating with XFmode support (10- or 12-byte reals)
+ * The value of NE must agree with that in ehead.h, if ieee.c is used.
+ */
+#define NE 6
+#define FSIZE unsigned short
+#define FLOAT(x) unsigned short x[NE]
+extern unsigned short eone[];
+#define FSETUP einit
+
+/* default for FSETUP */
+/*
+einit()
+{}
+*/
+
+error(s)
+char *s;
+{
+printf( "error: %s\n", s );
+}
+
+#endif /* not NATIVE */
+
+
+
+#if L128DOUBLE
+/* real.c interface */
+
+#undef FSETUP
+#define FSETUP efsetup
+
+FLOAT(enone);
+
+#define ONE enone
+
+/* Use emov to convert from widest type to widest type, ... */
+/*
+#define ENTOE emov
+#define ETOEN emov
+*/
+
+/* ... else choose e24toe, e53toe, etc. */
+#define ENTOE e64toe
+#define ETOEN etoe64
+#define NNBITS 64
+
+#define NIBITS ((NE-1)*16)
+extern int rndprc;
+
+efsetup()
+{
+rndprc = NNBITS;
+ETOEN(eone, enone);
+}
+
+add(a,b,c)
+FLOAT(a);
+FLOAT(b);
+FLOAT(c);
+{
+unsigned short aa[10], bb[10], cc[10];
+
+ENTOE(a,aa);
+ENTOE(b,bb);
+eadd(aa,bb,cc);
+ETOEN(cc,c);
+}
+
+sub(a,b,c)
+FLOAT(a);
+FLOAT(b);
+FLOAT(c);
+{
+unsigned short aa[10], bb[10], cc[10];
+
+ENTOE(a,aa);
+ENTOE(b,bb);
+esub(aa,bb,cc);
+ETOEN(cc,c);
+}
+
+mul(a,b,c)
+FLOAT(a);
+FLOAT(b);
+FLOAT(c);
+{
+unsigned short aa[10], bb[10], cc[10];
+
+ENTOE(a,aa);
+ENTOE(b,bb);
+emul(aa,bb,cc);
+ETOEN(cc,c);
+}
+
+div(a,b,c)
+FLOAT(a);
+FLOAT(b);
+FLOAT(c);
+{
+unsigned short aa[10], bb[10], cc[10];
+
+ENTOE(a,aa);
+ENTOE(b,bb);
+ediv(aa,bb,cc);
+ETOEN(cc,c);
+}
+
+int cmp(a,b)
+FLOAT(a);
+FLOAT(b);
+{
+unsigned short aa[10], bb[10];
+int c;
+int ecmp();
+
+ENTOE(a,aa);
+ENTOE(b,bb);
+c = ecmp(aa,bb);
+return(c);
+}
+
+mov(a,b)
+FLOAT(a);
+FLOAT(b);
+{
+int i;
+
+for( i=0; i<NE; i++ )
+ b[i] = a[i];
+}
+
+
+neg(a)
+FLOAT(a);
+{
+unsigned short aa[10];
+
+ENTOE(a,aa);
+eneg(aa);
+ETOEN(aa,a);
+}
+
+clear(a)
+FLOAT(a);
+{
+int i;
+
+for( i=0; i<NE; i++ )
+ a[i] = 0;
+}
+
+FABS(a)
+FLOAT(a);
+{
+unsigned short aa[10];
+
+ENTOE(a,aa);
+eabs(aa);
+ETOEN(aa,a);
+}
+
+FLOOR(a,b)
+FLOAT(a);
+FLOAT(b);
+{
+unsigned short aa[10], bb[10];
+
+ENTOE(a,aa);
+efloor(aa,bb);
+ETOEN(bb,b);
+}
+
+LOG(a,b)
+FLOAT(a);
+FLOAT(b);
+{
+unsigned short aa[10], bb[10];
+int rndsav;
+
+ENTOE(a,aa);
+rndsav = rndprc;
+rndprc = NIBITS;
+elog(aa,bb);
+rndprc = rndsav;
+ETOEN(bb,b);
+}
+
+POW(a,b,c)
+FLOAT(a);
+FLOAT(b);
+FLOAT(c);
+{
+unsigned short aa[10], bb[10], cc[10];
+int rndsav;
+
+ENTOE(a,aa);
+ENTOE(b,bb);
+rndsav = rndprc;
+rndprc = NIBITS;
+epow(aa,bb,cc);
+rndprc = rndsav;
+ETOEN(cc,c);
+}
+
+SQRT(a,b)
+FLOAT(a);
+FLOAT(b);
+{
+unsigned short aa[10], bb[10];
+
+ENTOE(a,aa);
+esqrt(aa,bb);
+ETOEN(bb,b);
+}
+
+FTOL(x,ip,f)
+FLOAT(x);
+long *ip;
+FLOAT(f);
+{
+unsigned short xx[10], ff[10];
+
+ENTOE(x,xx);
+eifrac(xx,ip,ff);
+ETOEN(ff,f);
+}
+
+LTOF(ip,x)
+long *ip;
+FLOAT(x);
+{
+unsigned short xx[10];
+ltoe(ip,xx);
+ETOEN(xx,x);
+}
+
+TOASC(a,b,c)
+FLOAT(a);
+int b;
+char *c;
+{
+unsigned short xx[10];
+
+ENTOE(a,xx);
+etoasc(xx,b,c);
+}
+
+#else /* not L128DOUBLE */
+
+#define ONE eone
+
+/* Note all arguments of operation subroutines are pointers. */
+/* c = b + a */
+#define add(a,b,c) eadd(a,b,c)
+/* c = b - a */
+#define sub(a,b,c) esub(a,b,c)
+/* c = b * a */
+#define mul(a,b,c) emul(a,b,c)
+/* c = b / a */
+#define div(a,b,c) ediv(a,b,c)
+/* 1 if a>b, 0 if a==b, -1 if a<b */
+#define cmp(a,b) ecmp(a,b)
+/* b = a */
+#define mov(a,b) emov(a,b)
+/* a = -a */
+#define neg(a) eneg(a)
+/* a = 0 */
+#define clear(a) eclear(a)
+
+#define FABS(x) eabs(x)
+#define FLOOR(x,y) efloor(x,y)
+#define LOG(x,y) elog(x,y)
+#define POW(x,y,z) epow(x,y,z)
+#define SQRT(x,y) esqrt(x,y)
+
+/* x = &FLOAT input, i = &long integer part, f = &FLOAT fractional part */
+#define FTOL(x,i,f) eifrac(x,i,f)
+
+/* i = &long integer input, x = &FLOAT output */
+#define LTOF(i,x) ltoe(i,x)
+
+/* Convert FLOAT a to decimal ASCII string with b digits */
+#define TOASC(a,b,c) etoasc(a,b,c)
+#endif /* not L128DOUBLE */
+
+
+
+/* The following subroutines are implementations of the above
+ * named functions, using the native or default arithmetic.
+ */
+#if NATIVE
+eadd(a,b,c)
+FSIZE *a, *b, *c;
+{
+*c = *b + *a;
+}
+
+esub(a,b,c)
+FSIZE *a, *b, *c;
+{
+*c = *b - *a;
+}
+
+emul(a,b,c)
+FSIZE *a, *b, *c;
+{
+*c = (*b) * (*a);
+}
+
+ediv(a,b,c)
+FSIZE *a, *b, *c;
+{
+*c = (*b) / (*a);
+}
+
+
+/* Important note: comparison can be done by subracting
+ * or by a compare instruction that may or may not be
+ * equivalent to subtracting.
+ */
+ecmp(a,b)
+FSIZE *a, *b;
+{
+if( (*a) > (*b) )
+ return( 1 );
+if( (*a) < (*b) )
+ return( -1 );
+if( (*a) != (*b) )
+ goto cmpf;
+if( (*a) == (*b) )
+ return( 0 );
+cmpf:
+printf( "Compare fails\n" );
+return(0);
+}
+
+
+emov( a, b )
+FSIZE *a, *b;
+{
+*b = *a;
+}
+
+eneg( a )
+FSIZE *a;
+{
+*a = -(*a);
+}
+
+eclear(a)
+FSIZE *a;
+{
+*a = 0.0;
+}
+
+eabs(x)
+FSIZE *x;
+{
+if( (*x) < 0.0 )
+ *x = -(*x);
+}
+
+efloor(x,y)
+FSIZE *x, *y;
+{
+
+*y = (FSIZE )ZFLOOR( *x );
+}
+
+elog(x,y)
+FSIZE *x, *y;
+{
+
+*y = (FSIZE )ZLOG( *x );
+}
+
+epow(x,y,z)
+FSIZE *x, *y, *z;
+{
+
+*z = (FSIZE )ZPOW( *x, *y );
+}
+
+esqrt(x,y)
+FSIZE *x, *y;
+{
+
+*y = (FSIZE )ZSQRT( *x );
+}
+
+
+eifrac(x,i,f)
+FSIZE *x;
+long *i;
+FSIZE *f;
+{
+FSIZE y;
+
+y = (FSIZE )ZFLOOR( *x );
+if( y < 0.0 )
+ {
+ *f = y - *x;
+ *i = -y;
+ }
+else
+ {
+ *f = *x - y;
+ *i = y;
+ }
+}
+
+
+ltoe(i,x)
+long *i;
+FSIZE *x;
+{
+*x = *i;
+}
+
+
+etoasc(a,str,n)
+FSIZE *a;
+char *str;
+int n;
+{
+double x;
+
+x = (double )(*a);
+sprintf( str, " %.17e ", x );
+}
+
+/* default for FSETUP */
+einit()
+{}
+
+#endif /* NATIVE */
+
+
+
+
+FLOAT(Radix);
+FLOAT(BInvrse);
+FLOAT(RadixD2);
+FLOAT(BMinusU2);
+/*Small floating point constants.*/
+FLOAT(Zero);
+FLOAT(Half);
+FLOAT(One);
+FLOAT(Two);
+FLOAT(Three);
+FLOAT(Four);
+FLOAT(Five);
+FLOAT(Six);
+FLOAT(Eight);
+FLOAT(Nine);
+FLOAT(Ten);
+FLOAT(TwentySeven);
+FLOAT(ThirtyTwo);
+FLOAT(TwoForty);
+FLOAT(MinusOne );
+FLOAT(OneAndHalf);
+
+/*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 */
+FLOAT(AInvrse);
+FLOAT(A1);
+FLOAT(C);
+FLOAT(CInvrse);
+FLOAT(D);
+FLOAT(FourD);
+FLOAT(E0);
+FLOAT(E1);
+FLOAT(Exp2);
+FLOAT(E3);
+FLOAT(MinSqEr);
+FLOAT(SqEr);
+FLOAT(MaxSqEr);
+FLOAT(E9);
+FLOAT(Third);
+FLOAT(F6);
+FLOAT(F9);
+FLOAT(H);
+FLOAT(HInvrse);
+FLOAT(StickyBit);
+FLOAT(J);
+FLOAT(MyZero);
+FLOAT(Precision);
+FLOAT(Q);
+FLOAT(Q9);
+FLOAT(R);
+FLOAT(Random9);
+FLOAT(T);
+FLOAT(Underflow);
+FLOAT(S);
+FLOAT(OneUlp);
+FLOAT(UfThold);
+FLOAT(U1);
+FLOAT(U2);
+FLOAT(V);
+FLOAT(V0);
+FLOAT(V9);
+FLOAT(W);
+FLOAT(X);
+FLOAT(X1);
+FLOAT(X2);
+FLOAT(X8);
+FLOAT(Random1);
+FLOAT(Y);
+FLOAT(YY1);
+FLOAT(Y2);
+FLOAT(Random2);
+FLOAT(Z);
+FLOAT(PseudoZero);
+FLOAT(Z1);
+FLOAT(Z2);
+FLOAT(Z9);
+static FLOAT(t);
+FLOAT(t2);
+FLOAT(Sqarg);
+int ErrCnt[4];
+int fpecount;
+int Milestone;
+int PageNo;
+int I, M, N, N1, stkflg;
+Guard GMult, GDiv, GAddSub;
+Rounding RMult, RDiv, RAddSub, RSqrt;
+int Break, Done, NotMonot, Monot, Anomaly, IEEE;
+int SqRWrng, UfNGrad;
+int k, k2;
+int Indx;
+char ch[8];
+
+long lngint, lng2; /* intermediate for conversion between int and FLOAT */
+
+/* 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 */
+
+
+show( x )
+short x[];
+{
+int i;
+char s[80];
+
+/* Number of 16-bit groups to display */
+#if NATIVE
+#if LDOUBLE
+#define NPRT (sizeof( long double )/2)
+#else
+#define NPRT (sizeof( double )/2)
+#endif
+#else
+#define NPRT NE
+#endif
+
+TOASC( x, s, 70 );
+printf( "%s\n", s );
+for( i=0; i<NPRT; i++ )
+ printf( "%04x ", x[i] & 0xffff );
+printf( "\n" );
+}
+
+/* define NOSIGNAL */
+#ifndef NOSIGNAL
+#include <signal.h>
+#endif
+#include <setjmp.h>
+jmp_buf ovfl_buf;
+/*typedef int (*Sig_type)();*/
+typedef void (*Sig_type)();
+Sig_type sigsave;
+
+/* Floating point exception receiver */
+void sigfpe()
+{
+fpecount++;
+printf( "\n* * * FLOATING-POINT ERROR * * *\n" );
+/* reinitialize the floating point unit */
+FSETUP();
+fflush(stdout);
+if( sigsave )
+ {
+#ifndef NOSIGNAL
+ signal( SIGFPE, sigsave );
+#endif
+ sigsave = 0;
+ longjmp( ovfl_buf, 1 );
+ }
+abort();
+}
+
+
+main()
+{
+
+/* Do coprocessor or other initializations */
+FSETUP();
+
+printf(
+ "This version of paranoia omits test for extra precise subexpressions\n" );
+printf( "and includes a few additional tests.\n" );
+
+clear(Zero);
+printf( "0 = " );
+show( Zero );
+mov( ONE, One);
+printf( "1 = " );
+show( One );
+add( One, One, Two );
+printf( "1+1 = " );
+show( Two );
+add( Two, One, Three );
+add( Three, One, Four );
+add( Four, One, Five );
+add( Five, One, Six );
+add( Four, Four, Eight );
+mul( Three, Three, Nine );
+add( Nine, One, Ten );
+mul( Nine, Three, TwentySeven );
+mul( Four, Eight, ThirtyTwo );
+mul( Four, Five, t );
+mul( t, Three, t );
+mul( t, Four, TwoForty );
+mov( One, MinusOne );
+neg( MinusOne );
+div( Two, One, Half );
+add( One, Half, OneAndHalf );
+ErrCnt[Failure] = 0;
+ErrCnt[Serious] = 0;
+ErrCnt[Defect] = 0;
+ErrCnt[Flaw] = 0;
+PageNo = 1;
+#ifndef NOSIGNAL
+signal( SIGFPE, sigfpe );
+#endif
+printf("Program is now RUNNING tests on small integers:\n");
+
+add( Zero, Zero, t );
+if( cmp( t, Zero ) != 0)
+ {
+ printf( "0+0 != 0\n" );
+ ErrCnt[Failure] += 1;
+ }
+sub( One, One, t );
+if( cmp( t, Zero ) != 0 )
+ {
+ printf( "1-1 != 0\n" );
+ ErrCnt[Failure] += 1;
+ }
+if( cmp( One, Zero ) <= 0 )
+ {
+ printf( "1 <= 0\n" );
+ ErrCnt[Failure] += 1;
+ }
+add( One, One, t );
+if( cmp( t, Two ) != 0 )
+ {
+ printf( "1+1 != 2\n" );
+ ErrCnt[Failure] += 1;
+ }
+mov( Zero, Z );
+neg( Z );
+FLOOR( Z, t );
+if( cmp(t,Zero) != 0 )
+ {
+ ErrCnt[Serious] += 1;
+ printf( "FLOOR(-0) should equal 0, is = " );
+ show( t );
+ }
+if( cmp(Z, Zero) != 0)
+ {
+ ErrCnt[Failure] += 1;
+ printf("Comparison alleges that -0.0 is Non-zero!\n");
+ }
+else
+ {
+ div( TwoForty, One, U1 ); /* U1 = 0.001 */
+ mov( One, Radix );
+ TstPtUf();
+ }
+add( Two, One, t );
+if( cmp( t, Three ) != 0 )
+ {
+ printf( "2+1 != 3\n" );
+ ErrCnt[Failure] += 1;
+ }
+add( Three, One, t );
+if( cmp( t, Four ) != 0 )
+ {
+ printf( "3+1 != 4\n" );
+ ErrCnt[Failure] += 1;
+ }
+mov( Two, t );
+neg( t );
+mul( Two, t, t );
+add( Four, t, t );
+if( cmp( t, Zero ) != 0 )
+ {
+ printf( "4+2*(-2) != 0\n" );
+ ErrCnt[Failure] += 1;
+ }
+sub( Three, Four, t );
+sub( One, t, t );
+if( cmp( t, Zero ) != 0 )
+ {
+ printf( "4-3-1 != 0\n" );
+ ErrCnt[Failure] += 1;
+ }
+ sub( One, Zero, t );
+if( cmp( t, MinusOne ) != 0 )
+ {
+ printf( "-1 != 0-1\n" );
+ ErrCnt[Failure] += 1;
+ }
+add( One, MinusOne, t );
+if( cmp( t, Zero ) != 0 )
+ {
+ printf( "1+(-1) != 0\n" );
+ ErrCnt[Failure] += 1;
+ }
+mov( One, t );
+FABS( t );
+add( MinusOne, t, t );
+if( cmp( t, Zero ) != 0 )
+ {
+ printf( "-1+abs(1) != 0\n" );
+ ErrCnt[Failure] += 1;
+ }
+mul( MinusOne, MinusOne, t );
+add( MinusOne, t, t );
+if( cmp( t, Zero ) != 0 )
+ {
+ printf( "-1+(-1)*(-1) != 0\n" );
+ ErrCnt[Failure] += 1;
+ }
+add( Half, MinusOne, t );
+add( Half, t, t );
+if( cmp( t, Zero ) != 0 )
+ {
+ printf( "1/2 + (-1) + 1/2 != 0\n" );
+ ErrCnt[Failure] += 1;
+ }
+Milestone = 10;
+mul( Three, Three, t );
+if( cmp( t, Nine ) != 0 )
+ {
+ printf( "3*3 != 9\n" );
+ ErrCnt[Failure] += 1;
+ }
+mul( Nine, Three, t );
+if( cmp( t, TwentySeven ) != 0 )
+ {
+ printf( "3*9 != 27\n" );
+ ErrCnt[Failure] += 1;
+ }
+add( Four, Four, t );
+if( cmp( t, Eight ) != 0 )
+ {
+ printf( "4+4 != 8\n" );
+ ErrCnt[Failure] += 1;
+ }
+mul( Eight, Four, t );
+if( cmp( t, ThirtyTwo ) != 0 )
+ {
+ printf( "8*4 != 32\n" );
+ ErrCnt[Failure] += 1;
+ }
+sub( TwentySeven, ThirtyTwo, t );
+sub( Four, t, t );
+sub( One, t, t );
+if( cmp( t, Zero ) != 0 )
+ {
+ printf( "32-27-4-1 != 0\n" );
+ ErrCnt[Failure] += 1;
+ }
+add( Four, One, t );
+if( cmp( t, Five ) != 0 )
+ {
+ printf( "4+1 != 5\n" );
+ ErrCnt[Failure] += 1;
+ }
+mul( Four, Five, t );
+mul( Three, t, t );
+mul( Four, t, t );
+if( cmp( t, TwoForty ) != 0 )
+ {
+ printf( "4*5*3*4 != 240\n" );
+ ErrCnt[Failure] += 1;
+ }
+div( Three, TwoForty, t );
+mul( Four, Four, t2 );
+mul( Five, t2, t2 );
+sub( t2, t2, t );
+if( cmp( t, Zero ) != 0 )
+ {
+ printf( "240/3 - 4*4*5 != 0\n" );
+ ErrCnt[Failure] += 1;
+ }
+div( Four, TwoForty, t );
+mul( Five, Three, t2 );
+mul( Four, t2, t2 );
+sub( t2, t, t );
+if( cmp( t, Zero ) != 0 )
+ {
+ printf( "240/4 - 5*3*4 != 0\n" );
+ ErrCnt[Failure] += 1;
+ }
+div( Five, TwoForty, t );
+mul( Four, Three, t2 );
+mul( Four, t2, t2 );
+sub( t2, t, t );
+if( cmp( t, Zero ) != 0 )
+ {
+ printf( "240/5 - 4*3*4 != 0\n" );
+ ErrCnt[Failure] += 1;
+ }
+if(ErrCnt[Failure] == 0)
+ {
+printf("-1, 0, 1/2, 1, 2, 3, 4, 5, 9, 27, 32 & 240 are O.K.\n\n");
+ }
+printf("Searching for Radix and Precision.\n");
+mov( One, W );
+do
+ {
+ add( W, W, W );
+ add( W, One, Y );
+ sub( W, Y, Z );
+ sub( One, Z, Y );
+ mov( Y, t );
+ FABS(t);
+ add( MinusOne, t, t );
+ k = cmp( t, Zero );
+ }
+while( k < 0 );
+/*.. now W is just big enough that |((W+1)-W)-1| >= 1 ...*/
+mov( Zero, Precision );
+mov( One, Y );
+do
+ {
+ add( W, Y, Radix );
+ add( Y, Y, Y );
+ sub( W, Radix, Radix );
+ k = cmp( Radix, Zero );
+ }
+while( k == 0);
+
+if( cmp(Radix, Two) < 0 )
+ mov( One, Radix );
+printf("Radix = " );
+show( Radix );
+if( cmp(Radix, One) != 0)
+ {
+ mov( One, W );
+ do
+ {
+ add( One, Precision, Precision );
+ mul( W, Radix, W );
+ add( W, One, Y );
+ sub( W, Y, t );
+ k = cmp( t, One );
+ }
+ while( k == 0 );
+ }
+/* now W == Radix^Precision is barely too big to satisfy (W+1)-W == 1 */
+div( W, One, U1 );
+mul( Radix, U1, U2 );
+printf( "Closest relative separation found is U 1 = " );
+show( U1 );
+printf( "Recalculating radix and precision." );
+
+/*save old values*/
+mov( Radix, E0 );
+mov( U1, E1 );
+mov( U2, E9 );
+mov( Precision, E3 );
+
+div( Three, Four, X );
+sub( One, X, Third );
+sub( Third, Half, F6 );
+add( F6, F6, X );
+sub( Third, X, X );
+FABS( X );
+if( cmp(X, U2) < 0 )
+ mov( U2, X );
+
+/*... now X = (unknown no.) ulps of 1+...*/
+do
+ {
+ mov( X, U2 );
+/* Y = Half * U2 + ThirtyTwo * U2 * U2; */
+ mul( ThirtyTwo, U2, t );
+ mul( t, U2, t );
+ mul( Half, U2, Y );
+ add( t, Y, Y );
+ add( One, Y, Y );
+ sub( One, Y, X );
+ k = cmp( U2, X );
+ k2 = cmp( X, Zero );
+ }
+while ( ! ((k <= 0) || (k2 <= 0)));
+
+/*... now U2 == 1 ulp of 1 + ... */
+div( Three, Two, X );
+sub( Half, X, F6 );
+add( F6, F6, Third );
+sub( Half, Third, X );
+add( F6, X, X );
+FABS( X );
+if( cmp(X, U1) < 0 )
+ mov( U1, X );
+
+/*... now X == (unknown no.) ulps of 1 -... */
+do
+ {
+ mov( X, U1 );
+ /* Y = Half * U1 + ThirtyTwo * U1 * U1;*/
+ mul( ThirtyTwo, U1, t );
+ mul( U1, t, t );
+ mul( Half, U1, Y );
+ add( t, Y, Y );
+ sub( Y, Half, Y );
+ add( Half, Y, X );
+ sub( X, Half, Y );
+ add( Half, Y, X );
+ k = cmp( U1, X );
+ k2 = cmp( X, Zero );
+ } while ( ! ((k <= 0) || (k2 <= 0)));
+/*... now U1 == 1 ulp of 1 - ... */
+if( cmp( U1, E1 ) == 0 )
+ printf("confirms closest relative separation U1 .\n");
+else
+ {
+ printf("gets better closest relative separation U1 = " );
+ show( U1 );
+ }
+div( U1, One, W );
+sub( U1, Half, F9 );
+add( F9, Half, F9 );
+div( U1, U2, t );
+div( TwoForty, One, t2 );
+add( t2, t, t );
+FLOOR( t, Radix );
+if( cmp(Radix, E0) == 0 )
+ printf("Radix confirmed.\n");
+else
+ {
+ printf("MYSTERY: recalculated Radix = " );
+ show( Radix );
+ mov( E0, Radix );
+ }
+add( Eight, Eight, t );
+if( cmp( Radix, t ) > 0 )
+ {
+ printf( "Radix is too big: roundoff problems\n" );
+ ErrCnt[Defect] += 1;
+ }
+k = 1;
+if( cmp( Radix, Two ) == 0 )
+ k = 0;
+if( cmp( Radix, Ten ) == 0 )
+ k = 0;
+if( cmp( Radix, One ) == 0 )
+ k = 0;
+if( k != 0 )
+ {
+ printf( "Radix is not as good as 2 or 10\n" );
+ ErrCnt[Flaw] += 1;
+ }
+/*=============================================*/
+Milestone = 20;
+/*=============================================*/
+sub( Half, F9, t );
+if( cmp( t, Half ) >= 0 )
+ {
+ printf( "(1-U1)-1/2 < 1/2 is FALSE, prog. fails?\n" );
+ ErrCnt[Failure] += 1;
+ }
+mov( F9, X );
+I = 1;
+sub( Half, X, Y );
+sub( Half, Y, Z );
+if( (cmp( X, One ) == 0) && (cmp( Z, Zero) != 0) )
+ {
+ printf( "Comparison is fuzzy ,X=1 but X-1/2-1/2 != 0\n" );
+ ErrCnt[Failure] += 1;
+ }
+add( One, U2, X );
+I = 0;
+/*=============================================*/
+Milestone = 25;
+/*=============================================*/
+/*... BMinusU2 = nextafter(Radix, 0) */
+
+sub( One, Radix, BMinusU2 );
+sub( U2, BMinusU2, t );
+add( One, t, BMinusU2 );
+/* Purify Integers */
+if( cmp(Radix,One) != 0 )
+ {
+/*X = - TwoForty * LOG(U1) / LOG(Radix);*/
+ LOG( U1, X );
+ LOG( Radix, t );
+ div( t, X, X );
+ mul( TwoForty, X, X );
+ neg( X );
+
+ add( Half, X, Y );
+ FLOOR( Y, Y );
+ sub( Y, X, t );
+ FABS( t );
+ mul( Four, t, t );
+ if( cmp( t, One ) < 0 )
+ mov( Y, X );
+ div( TwoForty, X, Precision );
+ add( Half, Precision, Y );
+ FLOOR( Y, Y );
+ sub( Y, Precision, t );
+ FABS( t );
+ mul( TwoForty, t, t );
+ if( cmp( t, Half ) < 0 )
+ mov( Y, Precision );
+ }
+FLOOR( Precision, t );
+if( (cmp( Precision, t ) != 0) || (cmp( Radix, One ) == 0) )
+ {
+ printf("Precision cannot be characterized by an Integer number\n");
+ printf("of significant digits but, by itself, this is a minor flaw.\n");
+ }
+if( cmp(Radix, One) == 0 )
+ printf("logarithmic encoding has precision characterized solely by U1.\n");
+else
+ {
+ printf("The number of significant digits of the Radix is " );
+ show( Precision );
+ }
+mul( U2, Nine, t );
+mul( Nine, t, t );
+mul( TwoForty, t, t );
+if( cmp( t, One ) >= 0 )
+ {
+ printf( "Precision worse than 5 decimal figures\n" );
+ ErrCnt[Serious] += 1;
+ }
+/*=============================================*/
+Milestone = 30;
+/*=============================================*/
+/* Test for extra-precise subepressions has been deleted. */
+Milestone = 35;
+/*=============================================*/
+if( cmp(Radix,Two) >= 0 )
+ {
+ mul( Radix, Radix, t );
+ div( t, W, X );
+ add( X, One, Y );
+ sub( X, Y, Z );
+ add( Z, U2, T );
+ sub( Z, T, X );
+ if( cmp( X, U2 ) != 0 )
+ {
+ printf( "Subtraction is not normalized X=Y,X+Z != Y+Z!\n" );
+ ErrCnt[Failure] += 1;
+ }
+ if( cmp(X,U2) == 0 )
+ printf("Subtraction appears to be normalized, as it should be.");
+ }
+
+printf("\nChecking for guard digit in *, /, and -.\n");
+mul( F9, One, Y );
+mul( One, F9, Z );
+sub( Half, F9, X );
+sub( Half, Y, Y );
+sub( X, Y, Y );
+sub( Half, Z, Z );
+sub( X, Z, Z );
+add( One, U2, X );
+mul( X, Radix, T );
+mul( Radix, X, R );
+sub( Radix, T, X );
+mul( Radix, U2, t );
+sub( t, X, X );
+sub( Radix, R, T );
+mul( Radix, U2, t );
+sub( t, T, T );
+sub( One, Radix, t );
+mul( t, X, X );
+sub( One, Radix, t );
+mul( t, T, T );
+
+k = cmp(X,Zero);
+k |= cmp(Y,Zero);
+k |= cmp(Z,Zero);
+k |= cmp(T,Zero);
+if( k == 0 )
+ GMult = Yes;
+else
+ {
+ GMult = No;
+ ErrCnt[Serious] += 1;
+ printf( "* lacks a Guard Digit, so 1*X != X\n" );
+ }
+mul( Radix, U2, Z );
+add( One, Z, X );
+add( X, Z, Y );
+mul( X, X, t );
+sub( t, Y, Y );
+FABS( Y );
+sub( U2, Y, Y );
+sub( U2, One, X );
+sub( U2, X, Z );
+mul( X, X, t );
+sub( t, Z, Z );
+FABS( Z );
+sub( U1, Z, Z );
+if( (cmp(Y,Zero) > 0) || (cmp(Z,Zero) > 0) )
+ {
+ ErrCnt[Failure] += 1;
+ printf( "* gets too many final digits wrong.\n" );
+ }
+sub( U2, One, Y );
+add( One, U2, X );
+div( Y, One, Z );
+sub( X, Z, Y );
+div( Three, One, X );
+div( Nine, Three, Z );
+sub( Z, X, X );
+div( TwentySeven, Nine, T );
+sub( T, Z, Z );
+k = cmp( X, Zero );
+k |= cmp( Y, Zero );
+k |= cmp( Z, Zero );
+if( k )
+ {
+ ErrCnt[Defect] += 1;
+printf( "Division lacks a Guard Digit, so error can exceed 1 ulp\n" );
+printf( "or 1/3 and 3/9 and 9/27 may disagree\n" );
+ }
+div( One, F9, Y );
+sub( Half, F9, X );
+sub( Half, Y, Y );
+sub( X, Y, Y );
+add( One, U2, X );
+div( One, X, T );
+sub( X, T, X );
+k = cmp( X, Zero );
+k |= cmp( Y, Zero );
+k |= cmp( Z, Zero );
+if( k == 0 )
+ GDiv = Yes;
+else
+ {
+ GDiv = No;
+ ErrCnt[Serious] += 1;
+ printf( "Division lacks a Guard Digit, so X/1 != X\n" );
+ }
+add( One, U2, X );
+div( X, One, X );
+sub( Half, X, Y );
+sub( Half, Y, Y );
+if( cmp(Y,Zero) >= 0 )
+ {
+ ErrCnt[Serious] += 1;
+ printf( "Computed value of 1/1.000..1 >= 1\n" );
+ }
+sub( U2, One, X );
+mul( Radix, U2, Y );
+add( One, Y, Y );
+mul( X, Radix, Z );
+mul( Y, Radix, T );
+div( Radix, Z, R );
+div( Radix, T, StickyBit );
+sub( X, R, X );
+sub( Y, StickyBit, Y );
+k = cmp( X, Zero );
+k |= cmp( Y, Zero );
+if( k )
+ {
+ ErrCnt[Failure] += 1;
+ printf( "* and/or / gets too many last digits wrong\n" );
+ }
+sub( U1, One, Y );
+sub( F9, One, X );
+sub( Y, One, Y );
+sub( U2, Radix, T );
+sub( BMinusU2, Radix, Z );
+sub( T, Radix, T );
+k = cmp( X, U1 );
+k |= cmp( Y, U1 );
+k |= cmp( Z, U2 );
+k |= cmp( T, U2 );
+if( k == 0 )
+ GAddSub = Yes;
+else
+ {
+ GAddSub = No;
+ ErrCnt[Serious] += 1;
+ printf( "- lacks Guard Digit, so cancellation is obscured\n" );
+ }
+sub( One, F9, t );
+if( (cmp(F9,One) != 0) && (cmp(t,Zero) >= 0) )
+ {
+ ErrCnt[Serious] += 1;
+ printf("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;
+/*=============================================*/
+printf("Checking rounding on multiply, divide and add/subtract.\n");
+RMult = Other;
+RDiv = Other;
+RAddSub = Other;
+div( Two, Radix, RadixD2 );
+mov( Two, A1 );
+Done = False;
+do
+ {
+ mov( Radix, AInvrse );
+ do
+ {
+ mov( AInvrse, X );
+ div( A1, AInvrse, AInvrse );
+ FLOOR( AInvrse, t );
+ k = cmp( t, AInvrse );
+ }
+ while( ! (k != 0 ) );
+ k = cmp( X, One );
+ k2 = cmp( A1, Three );
+ Done = (k == 0) || (k2 > 0);
+ if(! Done)
+ add( Nine, One, A1 );
+ }
+while( ! (Done));
+if( cmp(X, One) == 0 )
+ mov( Radix, A1 );
+div( A1, One, AInvrse );
+mov( A1, X );
+mov( AInvrse, Y );
+Done = False;
+do
+ {
+ mul( X, Y, Z );
+ sub( Half, Z, Z );
+ if( cmp( Z, Half ) != 0 )
+ {
+ ErrCnt[Failure] += 1;
+ printf( "X * (1/X) differs from 1\n" );
+ }
+ k = cmp( X, Radix );
+ Done = (k == 0);
+ mov( Radix, X );
+ div( X, One, Y );
+ }
+while( ! (Done));
+
+add( One, U2, Y2 );
+sub( U2, One, YY1 );
+sub( U2, OneAndHalf, X );
+add( OneAndHalf, U2, Y );
+sub( U2, X, Z );
+mul( Z, Y2, Z );
+mul( Y, YY1, T );
+sub( X, Z, Z );
+sub( X, T, T );
+mul( X, Y2, X );
+add( Y, U2, Y );
+mul( Y, YY1, Y );
+sub( OneAndHalf, X, X );
+sub( OneAndHalf, Y, Y );
+k = cmp( X, Zero );
+k |= cmp( Y, Zero );
+k |= cmp( Z, Zero );
+if( cmp( T, Zero ) > 0 )
+ k = 1;
+if( k == 0 )
+ {
+ add( OneAndHalf, U2, X );
+ mul( X, Y2, X );
+ sub( U2, OneAndHalf, Y );
+ sub( U2, Y, Y );
+ add( OneAndHalf, U2, Z );
+ add( U2, Z, Z );
+ sub( U2, OneAndHalf, T );
+ mul( T, YY1, T );
+ add( Z, U2, t );
+ sub( t, X, X );
+ mul( Y, YY1, StickyBit );
+ mul( Z, Y2, S );
+ sub( Y, T, T );
+ sub( Y, U2, Y );
+ add( StickyBit, Y, Y );
+/* Z = S - (Z + U2 + U2); */
+ add( Z, U2, t );
+ add( t, U2, t );
+ sub( t, S, Z );
+ add( Y2, U2, t );
+ mul( t, YY1, StickyBit );
+ mul( Y2, YY1, YY1 );
+ sub( Y2, StickyBit, StickyBit );
+ sub( Half, YY1, YY1 );
+ k = cmp( X, Zero );
+ k |= cmp( Y, Zero );
+ k |= cmp( Z, Zero );
+ k |= cmp( T, Zero );
+ k |= cmp( StickyBit, Zero );
+ k |= cmp( YY1, Half );
+ if( k == 0 )
+ {
+ RMult = Rounded;
+ printf("Multiplication appears to round correctly.\n");
+ }
+ else
+ {
+ add( X, U2, t );
+ k = cmp( t, Zero );
+ if( cmp( Y, Zero ) >= 0 )
+ k |= 1;
+ add( Z, U2, t );
+ k |= cmp( t, Zero );
+ if( cmp( T, Zero ) >= 0 )
+ k |= 1;
+ add( StickyBit, U2, t );
+ k |= cmp( t, Zero );
+ if( cmp(YY1, Half) >= 0 )
+ k |= 1;
+ if( k == 0 )
+ {
+ printf("Multiplication appears to chop.\n");
+ }
+ else
+ {
+ printf("* is neither chopped nor correctly rounded.\n");
+ }
+ if( (RMult == Rounded) && (GMult == No) )
+ printf("Multiplication has inconsistent result");
+ }
+ }
+else
+ printf("* is neither chopped nor correctly rounded.\n");
+
+/*=============================================*/
+Milestone = 45;
+/*=============================================*/
+add( One, U2, Y2 );
+sub( U2, One, YY1 );
+add( OneAndHalf, U2, Z );
+add( Z, U2, Z );
+div( Y2, Z, X );
+sub( U2, OneAndHalf, T );
+sub( U2, T, T );
+sub( U2, T, Y );
+div( YY1, Y, Y );
+add( Z, U2, Z );
+div( Y2, Z, Z );
+sub( OneAndHalf, X, X );
+sub( T, Y, Y );
+div( YY1, T, T );
+add( OneAndHalf, U2, t );
+sub( t, Z, Z );
+sub( OneAndHalf, U2, t );
+add( t, T, T );
+k = 0;
+if( cmp( X, Zero ) > 0 )
+ k = 1;
+if( cmp( Y, Zero ) > 0 )
+ k = 1;
+if( cmp( Z, Zero ) > 0 )
+ k = 1;
+if( cmp( T, Zero ) > 0 )
+ k = 1;
+if( k == 0 )
+ {
+ div( Y2, OneAndHalf, X );
+ sub( U2, OneAndHalf, Y );
+ add( U2, OneAndHalf, Z );
+ sub( Y, X, X );
+ div( YY1, OneAndHalf, T );
+ div( YY1, Y, Y );
+ add( Z, U2, t );
+ sub( t, T, T );
+ sub( Z, Y, Y );
+ div( Y2, Z, Z );
+ add( Y2, U2, YY1 );
+ div( Y2, YY1, YY1 );
+ sub( OneAndHalf, Z, Z );
+ sub( Y2, YY1, Y2 );
+ sub( U1, F9, YY1 );
+ div( F9, YY1, YY1 );
+ k = cmp( X, Zero );
+ k |= cmp( Y, Zero );
+ k |= cmp( Z, Zero );
+ k |= cmp( T, Zero );
+ k |= cmp( Y2, Zero );
+ sub( Half, YY1, t );
+ sub( Half, F9, t2 );
+ k |= cmp( t, t2 );
+ if( k == 0 )
+ {
+ RDiv = Rounded;
+ printf("Division appears to round correctly.\n");
+ if(GDiv == No)
+ printf("Division test inconsistent\n");
+ }
+ else
+ {
+ k = 0;
+ if( cmp( X, Zero ) >= 0 )
+ k = 1;
+ if( cmp( Y, Zero ) >= 0 )
+ k = 1;
+ if( cmp( Z, Zero ) >= 0 )
+ k = 1;
+ if( cmp( T, Zero ) >= 0 )
+ k = 1;
+ if( cmp( Y, Zero ) >= 0 )
+ k = 1;
+ sub( Half, YY1, t );
+ sub( Half, F9, t2 );
+ if( cmp( t, t2 ) >= 0 )
+ k = 1;
+ if( k == 0 )
+ {
+ RDiv = Chopped;
+ printf("Division appears to chop.\n");
+ }
+ }
+ }
+if(RDiv == Other)
+ printf("/ is neither chopped nor correctly rounded.\n");
+div( Radix, One, BInvrse );
+mul( BInvrse, Radix, t );
+sub( Half, t, t );
+if( cmp( t, Half ) != 0 )
+ {
+ ErrCnt[Failure] += 1;
+ printf( "Radix * ( 1 / Radix ) differs from 1\n" );
+ }
+
+Milestone = 50;
+/*=============================================*/
+add( F9, U1, t );
+sub( Half, t, t );
+k = cmp( t, Half );
+add( BMinusU2, U2, t );
+sub( One, t, t );
+sub( One, Radix, t2 );
+k |= cmp( t, t2 );
+if( k != 0 )
+ {
+ ErrCnt[Failure] += 1;
+ printf( "Incomplete carry-propagation in Addition\n" );
+ }
+mul( U1, U1, X );
+sub( X, One, X );
+sub( U2, One, Y );
+mul( U2, Y, Y );
+add( One, Y, Y );
+sub( Half, F9, Z );
+sub( Half, X, X );
+sub( Z, X, X );
+sub( One, Y, Y );
+if( (cmp(X,Zero) == 0) && (cmp(Y,Zero) == 0) )
+ {
+ RAddSub = Chopped;
+ printf("Add/Subtract appears to be chopped.\n");
+ }
+if(GAddSub == Yes)
+ {
+ add( Half, U2, X );
+ mul( X, U2, X );
+ sub( U2, Half, Y );
+ mul( Y, U2, Y );
+ add( One, X, X );
+ add( One, Y, Y );
+ add( One, U2, t );
+ sub( X, t, X );
+ sub( Y, One, Y );
+ k = cmp(X,Zero);
+ if( k )
+ printf( "1+U2-[u2(1/2+U2)+1] != 0\n" );
+ k2 = cmp(Y,Zero);
+ if( k2 )
+ printf( "1-[U2(1/2-U2)+1] != 0\n" );
+ k |= k2;
+ if( k == 0 )
+ {
+ add( Half, U2, X );
+ mul( X, U1, X );
+ sub( U2, Half, Y );
+ mul( Y, U1, Y );
+ sub( X, One, X );
+ sub( Y, One, Y );
+ sub( X, F9, X );
+ sub( Y, One, Y );
+ k = cmp(X,Zero);
+ if( k )
+ printf( "F9-[1-U1(1/2+U2)] != 0\n" );
+ k2 = cmp(Y,Zero);
+ if( k2 )
+ printf( "1-[1-U1(1/2-U2)] != 0\n" );
+ k |= k2;
+ if( k == 0 )
+ {
+ RAddSub = Rounded;
+ printf("Addition/Subtraction appears to round correctly.\n");
+ if(GAddSub == No)
+ printf( "Add/Subtract test inconsistent\n");
+ }
+ 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");
+
+mov( One, S );
+add( One, Half, X );
+mul( Half, X, X );
+add( One, X, X );
+add( One, U2, Y );
+mul( Y, Half, Y );
+sub( Y, X, Z );
+sub( X, Y, T );
+add( Z, T, StickyBit );
+if( cmp(StickyBit, Zero) != 0 )
+ {
+ mov( Zero, S );
+ ErrCnt[Flaw] += 1;
+ printf( "(X - Y) + (Y - X) is non zero!\n" );
+ }
+mov( Zero, StickyBit );
+FLOOR( RadixD2, t );
+k2 = cmp( t, RadixD2 );
+k = 1;
+if( (GMult == Yes) && (GDiv == Yes) && (GAddSub == Yes)
+ && (RMult == Rounded) && (RDiv == Rounded)
+ && (RAddSub == Rounded) && (k2 == 0) )
+ {
+ printf("Checking for sticky bit.\n");
+ k = 0;
+ add( Half, U1, X );
+ mul( X, U2, X );
+ mul( Half, U2, Y );
+ add( One, Y, Z );
+ add( One, X, T );
+ sub( One, Z, t );
+ sub( One, T, t2 );
+ if( cmp(t,Zero) > 0 )
+ {
+ k = 1;
+ printf( "[1+(1/2)U2]-1 > 0\n" );
+ }
+ if( cmp(t2,U2) < 0 )
+ {
+ k = 1;
+ printf( "[1+U2(1/2+U1)]-1 < U2\n" );
+ }
+ add( T, Y, Z );
+ sub( X, Z, Y );
+ sub( T, Z, t );
+ sub( T, Y, t2 );
+ if( cmp(t,U2) < 0 )
+ {
+ k = 1;
+ printf( "[[1+U2(1/2+U1)]+(1/2)U2]-[1+U2(1/2+U1)] < U2\n" );
+ }
+ if( cmp(t2,Zero) != 0 )
+ {
+ k = 1;
+ printf( "(1/2)U2-[1+U2(1/2+U1)] != 0\n" );
+ }
+ add( Half, U1, X );
+ mul( X, U1, X );
+ mul( Half, U1, Y );
+ sub( Y, One, Z );
+ sub( X, One, T );
+ sub( One, Z, t );
+ sub( F9, T, t2 );
+ if( cmp(t,Zero) != 0 )
+ {
+ k = 1;
+ printf( "(1-(1/2)U1)-1 != 0\n" );
+ }
+ if( cmp(t2,Zero) != 0 )
+ {
+ k = 1;
+ printf( "[1-U1(1/2+U1)]-F9 != 0\n" );
+ }
+ sub( U1, Half, Z );
+ mul( Z, U1, Z );
+ sub( Z, F9, T );
+ sub( Y, F9, Q );
+ sub( F9, T, t );
+ if( cmp( t, Zero ) != 0 )
+ {
+ k = 1;
+ printf( "[F9-U1(1/2-U1)]-F9 != 0\n" );
+ }
+ sub( U1, F9, t );
+ sub( Q, t, t );
+ if( cmp( t, Zero ) != 0 )
+ {
+ k = 1;
+ printf( "(F9-U1)-(F9-(1/2)U1) != 0\n" );
+ }
+ add( One, U2, Z );
+ mul( Z, OneAndHalf, Z );
+ add( OneAndHalf, U2, T );
+ sub( Z, T, T );
+ add( U2, T, T );
+ div( Radix, Half, X );
+ add( One, X, X );
+ mul( Radix, U2, Y );
+ add( One, Y, Y );
+ mul( X, Y, Z );
+ if( cmp( T, Zero ) != 0 )
+ {
+ k = 1;
+ printf( "(3/2+U2)-3/2(1+U2)+U2 != 0\n" );
+ }
+ mul( Radix, U2, t );
+ add( X, t, t );
+ sub( Z, t, t );
+ if( cmp( t, Zero ) != 0 )
+ {
+ k = 1;
+ printf( "(1+1/2Radix)+Radix*U2-[1+1/(2Radix)][1+Radix*U2] != 0\n" );
+ }
+ if( cmp(Radix, Two) != 0 )
+ {
+ add( Two, U2, X );
+ div( Two, X, Y );
+ sub( One, Y, t );
+ if( cmp( t, Zero) != 0 )
+ k = 1;
+ }
+ }
+if( k == 0 )
+ {
+ printf("Sticky bit apparently used correctly.\n");
+ mov( One, StickyBit );
+ }
+else
+ {
+ printf("Sticky bit used incorrectly or not at all.\n");
+ }
+
+if( GMult == No || GDiv == No || GAddSub == No ||
+ RMult == Other || RDiv == Other || RAddSub == Other)
+ {
+ ErrCnt[Flaw] += 1;
+ printf("lack(s) of guard digits or failure(s) to correctly round or chop\n");
+printf( "(noted above) count as one flaw in the final tally below\n" );
+ }
+/*=============================================*/
+Milestone = 60;
+/*=============================================*/
+printf("\n");
+printf("Does Multiplication commute? ");
+printf("Testing on %d random pairs.\n", NoTrials);
+SQRT( Three, Random9 );
+mov( Third, Random1 );
+I = 1;
+do
+ {
+ Random();
+ mov( Random1, X );
+ Random();
+ mov( Random1, Y );
+ mul( Y, X, Z9 );
+ mul( X, Y, Z );
+ sub( Z9, Z, Z9 );
+ I = I + 1;
+ }
+while ( ! ((I > NoTrials) || (cmp(Z9,Zero) != 0)));
+if(I == NoTrials)
+ {
+ div( Three, Half, t );
+ add( One, t, Random1 );
+ add( U2, U1, t );
+ add( t, One, Random2 );
+ mul( Random1, Random2, Z );
+ mul( Random2, Random1, Y );
+/* Z9 = (One + Half / Three) * ((U2 + U1) + One) - (One + Half /
+ * Three) * ((U2 + U1) + One);
+ */
+ div( Three, Half, t2 );
+ add( One, t2, t2 );
+ add( U2, U1, t );
+ add( t, One, t );
+ mul( t2, t, Z9 );
+ mul( t2, t, t );
+ sub( t, Z9, Z9 );
+ }
+if(! ((I == NoTrials) || (cmp(Z9,Zero) == 0)))
+ {
+ ErrCnt[Defect] += 1;
+ printf( "X * Y == Y * X trial fails.\n");
+ }
+else
+ {
+ printf(" No failures found in %d integer pairs.\n", NoTrials);
+ }
+/*=============================================*/
+Milestone = 70;
+/*=============================================*/
+sqtest();
+Milestone = 90;
+pow1test();
+
+Milestone = 110;
+
+printf("Seeking Underflow thresholds UfThold and E0.\n");
+mov( U1, D );
+FLOOR( Precision, t );
+if( cmp(Precision, t) != 0 )
+ {
+ mov( BInvrse, D );
+ mov( Precision, X );
+ do
+ {
+ mul( D, BInvrse, D );
+ sub( One, X, X );
+ }
+ while( cmp(X, Zero) > 0 );
+ }
+mov( One, Y );
+mov( D, Z );
+/* ... D is power of 1/Radix < 1. */
+sigsave = sigfpe;
+if( setjmp(ovfl_buf) )
+ goto under0;
+do
+ {
+ mov( Y, C );
+ mov( Z, Y );
+ mul( Y, Y, Z );
+ add( Z, Z, t );
+ }
+while( (cmp(Y,Z) > 0) && (cmp(t,Z) > 0) );
+
+under0:
+sigsave = 0;
+
+mov( C, Y );
+mul( Y, D, Z );
+sigsave = sigfpe;
+if( setjmp(ovfl_buf) )
+ goto under1;
+do
+ {
+ mov( Y, C );
+ mov( Z, Y );
+ mul( Y, D, Z );
+ add( Z, Z, t );
+ }
+while( (cmp(Y,Z) > 0) && (cmp(t,Z) > 0) );
+
+under1:
+sigsave = 0;
+
+if( cmp(Radix,Two) < 0 )
+ mov( Two, HInvrse );
+else
+ mov( Radix, HInvrse );
+div( HInvrse, One, H );
+/* ... 1/HInvrse == H == Min(1/Radix, 1/2) */
+div( C, One, CInvrse );
+mov( C, E0 );
+mul( E0, H, Z );
+/* ...1/Radix^(BIG Integer) << 1 << CInvrse == 1/C */
+sigsave = sigfpe;
+if( setjmp(ovfl_buf) )
+ goto under2;
+do
+ {
+ mov( E0, Y );
+ mov( Z, E0 );
+ mul( E0, H, Z );
+ add( Z, Z, t );
+ }
+while( (cmp(E0,Z) > 0) && (cmp(t,Z) > 0) );
+
+under2:
+sigsave = 0;
+
+mov( E0, UfThold );
+mov( Zero, E1 );
+mov( Zero, Q );
+mov( U2, E9 );
+add( One, E9, S );
+mul( C, S, D );
+if( cmp(D,C) <= 0 )
+ {
+ mul( Radix, U2, E9 );
+ add( One, E9, S );
+ mul( C, S, D );
+ if( cmp(D, C) <= 0 )
+ {
+ ErrCnt[Failure] += 1;
+ printf( "multiplication gets too many last digits wrong.\n" );
+ mov( E0, Underflow );
+ mov( Zero, YY1 );
+ mov( Z, PseudoZero );
+ }
+ }
+else
+ {
+ mov( D, Underflow );
+ mul( Underflow, H, PseudoZero );
+ mov( Zero, UfThold );
+ do
+ {
+ mov( Underflow, YY1 );
+ mov( PseudoZero, Underflow );
+ add( E1, E1, t );
+ if( cmp(t, E1) <= 0)
+ {
+ mul( Underflow, HInvrse, Y2 );
+ sub( Y2, YY1, E1 );
+ FABS( E1 );
+ mov( YY1, Q );
+ if( (cmp( UfThold, Zero ) == 0)
+ && (cmp(YY1, Y2) != 0) )
+ mov( YY1, UfThold );
+ }
+ mul( PseudoZero, H, PseudoZero );
+ add( PseudoZero, PseudoZero, t );
+ }
+ while( (cmp(Underflow, PseudoZero) > 0)
+ && (cmp(t, PseudoZero) > 0) );
+ }
+/* Comment line 4530 .. 4560 */
+if( cmp(PseudoZero, Zero) != 0 )
+ {
+ printf("\n");
+ mov(PseudoZero, Z );
+/* ... Test PseudoZero for "phoney- zero" violates */
+/* ... PseudoZero < Underflow or PseudoZero < PseudoZero + PseudoZero
+ ... */
+ if( cmp(PseudoZero, Zero) <= 0 )
+ {
+ ErrCnt[Failure] += 1;
+ printf("Positive expressions can underflow to an\n");
+ printf("allegedly negative value\n");
+ printf("PseudoZero that prints out as: " );
+ show( PseudoZero );
+ mov( PseudoZero, X );
+ neg( X );
+ if( cmp(X, Zero) <= 0 )
+ {
+ printf("But -PseudoZero, which should be\n");
+ printf("positive, isn't; it prints out as " );
+ show( X );
+ }
+ }
+ else
+ {
+ ErrCnt[Flaw] += 1;
+ printf( "Underflow can stick at an allegedly positive\n");
+ printf("value PseudoZero that prints out as " );
+ show( PseudoZero );
+ }
+/* TstPtUf();*/
+ }
+
+/*=============================================*/
+Milestone = 120;
+/*=============================================*/
+mul( CInvrse, Y, t );
+mul( CInvrse, YY1, t2 );
+if( cmp(t,t2) > 0 )
+ {
+ mul( H, S, S );
+ mov( Underflow, E0 );
+ }
+if(! ((cmp(E1,Zero) == 0) || (cmp(E1,E0) == 0)) )
+ {
+ ErrCnt[Defect] += 1;
+ if( cmp(E1,E0) < 0 )
+ {
+ printf("Products underflow at a higher");
+ printf(" threshold than differences.\n");
+ if( cmp(PseudoZero,Zero) == 0 )
+ mov( E1, E0 );
+ }
+ else
+ {
+ printf("Difference underflows at a higher");
+ printf(" threshold than products.\n");
+ }
+ }
+printf("Smallest strictly positive number found is E0 = " );
+show( E0 );
+mov( E0, Z );
+TstPtUf();
+mov( E0, Underflow );
+if(N == 1)
+ mov( Y, Underflow );
+I = 4;
+if( cmp(E1,Zero) == 0 )
+ I = 3;
+if( cmp( UfThold,Zero) == 0 )
+ I = I - 2;
+UfNGrad = True;
+switch(I)
+ {
+ case 1:
+ mov( Underflow, UfThold );
+ mul( CInvrse, Q, t );
+ mul( CInvrse, Y, t2 );
+ mul( t2, S, t2 );
+ if( cmp( t, t2 ) != 0 )
+ {
+ mov( Y, UfThold );
+ ErrCnt[Failure] += 1;
+ printf( "Either accuracy deteriorates as numbers\n");
+ printf("approach a threshold = " );
+ show( UfThold );
+ printf(" coming down from " );
+ show( C );
+ printf(" or else multiplication gets too many last digits wrong.\n");
+ }
+ break;
+
+ case 2:
+ ErrCnt[Failure] += 1;
+ printf( "Underflow confuses Comparison which alleges that\n");
+ printf("Q == Y while denying that |Q - Y| == 0; these values\n");
+ printf("print out as Q = " );
+ show( Q );
+ printf( ", Y = " );
+ show( Y );
+ sub( Y2, Q, t );
+ FABS(t);
+ printf ("|Q - Y| = " );
+ show( t );
+ mov( Q, UfThold );
+ break;
+
+ case 3:
+ mov( X, X );
+ break;
+
+ case 4:
+ div( E9, E1, t );
+ sub( t, UfThold, t );
+ FABS(t);
+ if( (cmp(Q,UfThold) == 0) && (cmp(E1,E0) == 0)
+ && (cmp(t,E1) <= 0) )
+ {
+ UfNGrad = False;
+ printf("Underflow is gradual; it incurs Absolute Error =\n");
+ printf("(roundoff in UfThold) < E0.\n");
+ mul( E0, CInvrse, Y );
+ add( OneAndHalf, U2, t );
+ mul( Y, t, Y );
+ add( One, U2, X );
+ mul( CInvrse, X, X );
+ div( X, Y, t );
+ IEEE = (cmp(t,E0) == 0);
+ if( IEEE == 0 )
+ {
+ printf( "((CInvrse E0) (1.5+U2)) / (CInvrse (1+U2)) != E0\n" );
+ printf( "CInvrse = " );
+ show( CInvrse );
+ printf( "E0 = " );
+ show( E0 );
+ printf( "U2 = " );
+ show( U2 );
+ printf( "X = " );
+ show(X);
+ printf( "Y = " );
+ show(Y);
+ printf( "Y/X = " );
+ show(t);
+ }
+ }
+ }
+if(UfNGrad)
+ {
+ printf("\n");
+ div( UfThold, Underflow, R );
+ SQRT( R, R );
+ if( cmp(R,H) <= 0)
+ {
+ mul( R, UfThold, Z );
+/* X = Z * (One + R * H * (One + H));*/
+ add( One, H, X );
+ mul( H, X, X );
+ mul( R, X, X );
+ add( One, X, X );
+ mul( Z, X, X );
+ }
+ else
+ {
+ mov( UfThold, Z );
+/*X = Z * (One + H * H * (One + H));*/
+ add( One, H, X );
+ mul( H, X, X );
+ mul( H, X, X );
+ add( One, X, X );
+ mul( Z, X, X );
+ }
+ sub( Z, X, t );
+/* if(! ((cmp(X,Z) == 0) || (cmp(t,Zero) != 0)) )*/
+ if( (cmp(X,Z) != 0) && (cmp(t,Zero) == 0) )
+ {
+/* ErrCnt[Flaw] += 1;*/
+ ErrCnt[Serious] += 1;
+ printf("X = " );
+ show( X );
+ printf( "\tis not equal to Z = " );
+ show( Z );
+/* sub( Z, X, Z9 );*/
+ printf("yet X - Z yields " );
+ show( t );
+ printf("which compares equal to " );
+ show( Zero );
+ 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 + " );
+ div( Z, X, t );
+ sub( Half, t, t );
+ sub( Half, t, t );
+ show(t);
+ }
+ }
+printf("The Underflow threshold is " );
+show( UfThold );
+printf( "below which calculation may suffer larger Relative error than" );
+printf( " merely roundoff.\n");
+mul( U1, U1, Y2 );
+mul( Y2, Y2, Y );
+mul( Y, U1, Y2 );
+if( cmp( Y2,UfThold) <= 0 )
+ {
+ if( cmp(Y,E0) > 0 )
+ {
+ ErrCnt[Defect] += 1;
+ I = 5;
+ }
+ else
+ {
+ ErrCnt[Serious] += 1;
+ I = 4;
+ }
+ printf("Range is too narrow; U1^%d Underflows.\n", I);
+ }
+Milestone = 130;
+
+/*Y = - FLOOR(Half - TwoForty * LOG(UfThold) / LOG(HInvrse)) / TwoForty;*/
+LOG( UfThold, Y );
+LOG( HInvrse, t );
+div( t, Y, Y );
+mul( TwoForty, Y, Y );
+sub( Y, Half, Y );
+FLOOR( Y, Y );
+div( TwoForty, Y, Y );
+neg(Y);
+sub( One, Y, Y2 ); /* ***** changed from Y2 = Y + Y */
+printf("Since underflow occurs below the threshold\n");
+printf("UfThold = " );
+show( HInvrse );
+printf( "\tto the power " );
+show( Y );
+printf( "only underflow should afflict the expression " );
+show( HInvrse );
+printf( "\tto the power " );
+show( Y2 );
+POW( HInvrse, Y2, V9 );
+printf("Actually calculating yields: " );
+show( V9 );
+add( Radix, Radix, t );
+add( t, E9, t );
+mul( t, UfThold, t );
+if( (cmp(V9,Zero) < 0) || (cmp(V9,t) > 0) )
+ {
+ ErrCnt[Serious] += 1;
+ printf( "this is not between 0 and underflow\n");
+ printf(" threshold = " );
+ show( UfThold );
+ }
+else
+ {
+ add( One, E9, t );
+ mul( UfThold, t, t );
+ if( cmp(V9,t) <= 0 )
+ printf("This computed value is O.K.\n");
+ else
+ {
+ ErrCnt[Defect] += 1;
+ printf( "this is not between 0 and underflow\n");
+ printf(" threshold = " );
+ show( UfThold );
+ }
+ }
+
+Milestone = 140;
+
+pow2test();
+
+/*=============================================*/
+Milestone = 160;
+/*=============================================*/
+Pause();
+printf("Searching for Overflow threshold:\n");
+printf("This may generate an error.\n");
+sigsave = sigfpe;
+I = 0;
+mov( CInvrse, Y ); /* a large power of 2 */
+neg(Y);
+mul( HInvrse, Y, V9 ); /* HInvrse = 2 */
+if (setjmp(ovfl_buf))
+ goto overflow;
+do
+ {
+ mov( Y, V );
+ mov( V9, Y );
+ mul( HInvrse, Y, V9 );
+ }
+while( cmp(V9,Y) < 0 ); /* V9 = 2 * Y */
+I = 1;
+
+overflow:
+
+show( HInvrse );
+printf( "\ttimes " );
+show( Y );
+printf( "\tequals " );
+show( V9 );
+
+mov( V9, Z );
+printf("Can `Z = -Y' overflow?\n");
+printf("Trying it on Y = " );
+show(Y);
+mov( Y, V9 );
+neg( V9 );
+mov( V9, V0 );
+sub( Y, V, t );
+add( V, V0, t2 );
+if( cmp(t,t2) == 0 )
+ printf("Seems O.K.\n");
+else
+ {
+ printf("finds a Flaw, -(-Y) differs from Y.\n");
+ printf( "V-Y=t:" );
+ show(V);
+ show(Y);
+ show(t);
+ printf( "V+V0=t2:" );
+ show(V);
+ show(V0);
+ show(t2);
+ ErrCnt[Flaw] += 1;
+ }
+if( (cmp(Z, Y) != 0) && (I != 0) )
+ {
+ ErrCnt[Serious] += 1;
+ printf("overflow past " );
+ show( Y );
+ printf( "\tshrinks to " );
+ show( Z );
+ printf( "= Y * " );
+ show( HInvrse );
+ }
+/*Y = V * (HInvrse * U2 - HInvrse);*/
+mul( HInvrse, U2, Y );
+sub( HInvrse, Y, Y );
+mul( V, Y, Y );
+/*Z = Y + ((One - HInvrse) * U2) * V;*/
+sub( HInvrse, One, Z );
+mul( Z, U2, Z );
+mul( Z, V, Z );
+add( Y, Z, Z );
+if( cmp(Z,V0) < 0 )
+ mov( Z, Y );
+if( cmp(Y,V0) < 0)
+ mov( Y, V );
+sub( V, V0, t );
+if( cmp(t,V0) < 0 )
+ mov( V0, V );
+printf("Overflow threshold is V = " );
+show( V );
+if(I)
+ {
+ printf("Overflow saturates at V0 = " );
+ show( V0 );
+ }
+else
+printf("There is no saturation value because the system traps on overflow.\n");
+
+mul( V, One, V9 );
+printf("No Overflow should be signaled for V * 1 = " );
+show( V9 );
+div( One, V, V9 );
+ printf(" nor for V / 1 = " );
+ show( V9 );
+ printf("Any overflow signal separating this * from the one\n");
+ printf("above is a DEFECT.\n");
+/*=============================================*/
+Milestone = 170;
+/*=============================================*/
+mov( V, t );
+neg( t );
+k = 0;
+if( cmp(t,V) >= 0 )
+ k = 1;
+mov( V0, t );
+neg( t );
+if( cmp(t,V0) >= 0 )
+ k = 1;
+mov( UfThold, t );
+neg(t);
+if( cmp(t,V) >= 0 )
+ k = 1;
+if( cmp(UfThold,V) >= 0 )
+ k = 1;
+if( k != 0 )
+ {
+ ErrCnt[Failure] += 1;
+ printf( "Comparisons involving +-");
+ show( V );
+ show( V0 );
+ show( UfThold );
+ printf("are confused by Overflow." );
+ }
+/*=============================================*/
+Milestone = 175;
+/*=============================================*/
+printf("\n");
+for(Indx = 1; Indx <= 3; ++Indx) {
+ switch(Indx)
+ {
+ case 1: mov(UfThold, Z); break;
+ case 2: mov( E0, Z); break;
+ case 3: mov(PseudoZero, Z); break;
+ }
+if( cmp(Z, Zero) != 0 )
+ {
+ SQRT( Z, V9 );
+ mul( V9, V9, Y );
+ mul( Radix, E9, t );
+ sub( t, One, t );
+ div( t, Y, t );
+ add( One, Radix, t2 );
+ add( t2, E9, t2 );
+ mul( t2, Z, t2 );
+ if( (cmp(t,Z) < 0) || (cmp(Y,t2) > 0) )
+ {
+ if( cmp(V9,U1) > 0 )
+ ErrCnt[Serious] += 1;
+ else
+ ErrCnt[Defect] += 1;
+ printf("Comparison alleges that what prints as Z = " );
+ show( Z );
+ printf(" is too far from sqrt(Z) ^ 2 = " );
+ show( Y );
+ }
+ }
+}
+
+Milestone = 180;
+
+for(Indx = 1; Indx <= 2; ++Indx)
+ {
+ if(Indx == 1)
+ mov( V, Z );
+ else
+ mov( V0, Z );
+ SQRT( Z, V9 );
+ mul( Radix, E9, X );
+ sub( X, One, X );
+ mul( X, V9, X );
+ mul( V9, X, V9 );
+ mul( Two, Radix, t );
+ mul( t, E9, t );
+ sub( t, One, t );
+ mul( t, Z, t );
+ if( (cmp(V9,t) < 0) || (cmp(V9,Z) > 0) )
+ {
+ mov( V9, Y );
+ if( cmp(X,W) < 0 )
+ ErrCnt[Serious] += 1;
+ else
+ ErrCnt[Defect] += 1;
+ printf("Comparison alleges that Z = " );
+ show( Z );
+ printf(" is too far from sqrt(Z) ^ 2 :" );
+ show( Y );
+ }
+ }
+
+Milestone = 190;
+
+Pause();
+mul( UfThold, V, X );
+mul( Radix, Radix, Y );
+mul( X, Y, t );
+if( (cmp(t,One) < 0) || (cmp(X,Y) > 0) )
+ {
+ mul( X, Y, t );
+ div( U1, Y, t2 );
+ if( (cmp(t,U1) < 0) || (cmp(X,t2) > 0) )
+ {
+ ErrCnt[Defect] += 1;
+ printf( "Badly " );
+ }
+ else
+ {
+ ErrCnt[Flaw] += 1;
+ }
+ printf(" unbalanced range; UfThold * V = " );
+ show( X );
+ printf( "\tis too far from 1.\n");
+ }
+Milestone = 200;
+
+for(Indx = 1; Indx <= 5; ++Indx)
+ {
+ mov( F9, X );
+ switch(Indx)
+ {
+ case 2: add( One, U2, X ); break;
+ case 3: mov( V, X ); break;
+ case 4: mov(UfThold,X); break;
+ case 5: mov(Radix,X);
+ }
+ mov( X, Y );
+
+ sigsave = sigfpe;
+ if (setjmp(ovfl_buf))
+ {
+ printf(" X / X traps when X = " );
+ show( X );
+ }
+ else
+ {
+/*V9 = (Y / X - Half) - Half;*/
+ div( X, Y, t );
+ sub( Half, t, t );
+ sub( Half, t, V9 );
+ if( cmp(V9,Zero) == 0 )
+ continue;
+ mov( U1, t );
+ neg(t);
+ if( (cmp(V9,t) == 0) && (Indx < 5) )
+ {
+ ErrCnt[Flaw] += 1;
+ }
+ else
+ {
+ ErrCnt[Serious] += 1;
+ }
+ printf(" X / X differs from 1 when X = " );
+ show( X );
+ printf(" instead, X / X - 1/2 - 1/2 = " );
+ show( V9 );
+ }
+ }
+
+ 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 {
+ k = 0;
+ if( cmp( Radix, Two ) == 0 )
+ k = 1;
+ if( cmp( Radix, Ten ) == 0 )
+ k = 1;
+ if( (cmp(StickyBit,One) >= 0) && (k == 1) )
+ {
+ printf("Rounding appears to conform to ");
+ printf("the proposed IEEE standard P");
+ k = 0;
+ k |= cmp( Radix, Two );
+ mul( Four, Three, t );
+ mul( t, Two, t );
+ sub( t, Precision, t );
+ sub( TwentySeven, Precision, t2 );
+ sub( TwentySeven, t2, t2 );
+ add( t2, One, t2 );
+ mul( t2, t, t );
+ if( (cmp(Radix,Two) == 0)
+ && (cmp(t,Zero) == 0) )
+ 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");
+ }
+
+
+/* Random */
+/* Random computes
+ X = (Random1 + Random9)^5
+ Random1 = X - FLOOR(X) + 0.000005 * X;
+ and returns the new value of Random1
+*/
+
+
+static int randflg = 0;
+FLOAT(C5em6);
+
+Random()
+{
+
+if( randflg == 0 )
+ {
+ mov( Six, t );
+ neg(t);
+ POW( Ten, t, t );
+ mul( Five, t, C5em6 );
+ randflg = 1;
+ }
+add( Random1, Random9, t );
+mul( t, t, t2 );
+mul( t2, t2, t2 );
+mul( t, t2, t );
+FLOOR(t, t2 );
+sub( t2, t, t2 );
+mul( t, C5em6, t );
+add( t, t2, Random1 );
+/*return(Random1);*/
+}
+
+/* SqXMinX */
+
+SqXMinX( ErrKind )
+int ErrKind;
+{
+mul( X, BInvrse, t2 );
+sub( t2, X, t );
+/*SqEr = ((SQRT(X * X) - XB) - XA) / OneUlp;*/
+mul( X, X, Sqarg );
+SQRT( Sqarg, SqEr );
+sub( t2, SqEr, SqEr );
+sub( t, SqEr, SqEr );
+div( OneUlp, SqEr, SqEr );
+if( cmp(SqEr,Zero) != 0)
+ {
+ Showsq( 0 );
+ add( J, One, J );
+ ErrCnt[ErrKind] += 1;
+ printf("sqrt of " );
+ mul( X, X, t );
+ show( t );
+ printf( "minus " );
+ show( X );
+ printf( "equals " );
+ mul( OneUlp, SqEr, t );
+ show( t );
+ printf("\tinstead of correct value 0 .\n");
+ }
+}
+
+/* NewD */
+
+NewD()
+{
+mul( Z1, Q, X );
+/*X = FLOOR(Half - X / Radix) * Radix + X;*/
+div( Radix, X, t );
+sub( t, Half, t );
+FLOOR( t, t );
+mul( t, Radix, t );
+add( t, X, X );
+/*Q = (Q - X * Z) / Radix + X * X * (D / Radix);*/
+mul( X, Z, t );
+sub( t, Q, t );
+div( Radix, t, t );
+div( Radix, D, t2 );
+mul( X, t2, t2 );
+mul( X, t2, t2 );
+add( t, t2, Q );
+/*Z = Z - Two * X * D;*/
+mul( Two, X, t );
+mul( t, D, t );
+sub( t, Z, Z );
+
+if( cmp(Z,Zero) <= 0)
+ {
+ neg(Z);
+ neg(Z1);
+ }
+mul( Radix, D, D );
+}
+
+/* SR3750 */
+
+SR3750()
+{
+sub( Radix, X, t );
+sub( Radix, Z2, t2 );
+k = 0;
+if( cmp(t,t2) < 0 )
+ k = 1;
+sub( Z2, X, t );
+sub( Z2, W, t2 );
+if( cmp(t,t2) > 0 )
+ k = 1;
+/*if (! ((X - Radix < Z2 - Radix) || (X - Z2 > W - Z2))) {*/
+if( k == 0 )
+ {
+ I = I + 1;
+ mul( X, D, X2 );
+ mov( X2, Sqarg );
+ SQRT( X2, X2 );
+/*Y2 = (X2 - Z2) - (Y - Z2);*/
+ sub( Z2, X2, Y2 );
+ sub( Z2, Y, t );
+ sub( t, Y2, Y2 );
+ sub( Half, Y, X2 );
+ div( X2, X8, X2 );
+ mul( Half, X2, t );
+ mul( t, X2, t );
+ sub( t, X2, X2 );
+/*SqEr = (Y2 + Half) + (Half - X2);*/
+ add( Y2, Half, SqEr );
+ sub( X2, Half, t );
+ add( t, SqEr, SqEr );
+ Showsq( -1 );
+ sub( X2, Y2, SqEr );
+ Showsq( 1 );
+ }
+}
+
+/* IsYeqX */
+
+IsYeqX()
+{
+if( cmp(Y,X) != 0 )
+ {
+ if (N <= 0)
+ {
+ if( (cmp(Z,Zero) == 0) && (cmp(Q,Zero) <= 0) )
+ printf("WARNING: computing\n");
+ else
+ {
+ ErrCnt[Defect] += 1;
+ printf( "computing\n");
+ }
+ show( Z );
+ printf( "\tto the power " );
+ show( Q );
+ printf("\tyielded " );
+ show( Y );
+ printf("\twhich compared unequal to correct " );
+ show( X );
+ sub( X, Y, t );
+ printf("\t\tthey differ by " );
+ show( t );
+ }
+ N = N + 1; /* ... count discrepancies. */
+ }
+}
+
+/* SR3980 */
+
+SR3980()
+{
+long li;
+
+do
+ {
+/*Q = (FLOAT) I;*/
+ li = I;
+ LTOF( &li, Q );
+ POW( Z, Q, Y );
+ IsYeqX();
+ if(++I > M)
+ break;
+ mul( Z, X, X );
+ }
+while( cmp(X,W) < 0 );
+}
+
+/* PrintIfNPositive */
+
+PrintIfNPositive()
+{
+if(N > 0)
+ printf("Similar discrepancies have occurred %d times.\n", N);
+}
+
+
+/* TstPtUf */
+
+TstPtUf()
+{
+N = 0;
+if( cmp(Z,Zero) != 0)
+ {
+ printf( "Z = " );
+ show(Z);
+ printf("Since comparison denies Z = 0, evaluating ");
+ printf("(Z + Z) / Z should be safe.\n");
+ sigsave = sigfpe;
+ if (setjmp(ovfl_buf))
+ goto very_serious;
+ add( Z, Z, Q9 );
+ div( Z, Q9, Q9 );
+ printf("What the machine gets for (Z + Z) / Z is " );
+ show( Q9 );
+ sub( Two, Q9, t );
+ FABS(t);
+ mul( Radix, U2, t2 );
+ if( cmp(t,t2) < 0 )
+ {
+ printf("This is O.K., provided Over/Underflow");
+ printf(" has NOT just been signaled.\n");
+ }
+ else
+ {
+ if( (cmp(Q9,One) < 0) || (cmp(Q9,Two) > 0) )
+ {
+very_serious:
+ N = 1;
+ ErrCnt [Serious] = ErrCnt [Serious] + 1;
+ printf("This is a VERY SERIOUS DEFECT!\n");
+ }
+ else
+ {
+ N = 1;
+ ErrCnt[Defect] += 1;
+ printf("This is a DEFECT!\n");
+ }
+ }
+ mul( Z, One, V9 );
+ mov( V9, Random1 );
+ mul( One, Z, V9 );
+ mov( V9, Random2 );
+ div( One, Z, V9 );
+ if( (cmp(Z,Random1) == 0) && (cmp(Z,Random2) == 0)
+ && (cmp(Z,V9) == 0) )
+ {
+ if (N > 0)
+ Pause();
+ }
+ else
+ {
+ N = 1;
+ ErrCnt[Defect] += 1;
+ printf( "What prints as Z = ");
+ show( Z );
+ printf( "\tcompares different from " );
+ if( cmp(Z,Random1) != 0)
+ {
+ printf("Z * 1 = " );
+ show( Random1 );
+ }
+ if( (cmp(Z,Random2) != 0)
+ || (cmp(Random2,Random1) != 0) )
+ {
+ printf("1 * Z == " );
+ show( Random2 );
+ }
+ if( cmp(Z,V9) != 0 )
+ {
+ printf("Z / 1 = " );
+ show( V9 );
+ }
+ if( cmp(Random2,Random1) != 0 )
+ {
+ ErrCnt[Defect] += 1;
+ printf( "Multiplication does not commute!\n");
+ printf("\tComparison alleges that 1 * Z = " );
+ show(Random2);
+ printf("\tdiffers from Z * 1 = " );
+ show(Random1);
+ }
+ Pause();
+ }
+ }
+}
+
+Pause()
+{
+}
+
+Sign( x, y )
+FSIZE *x, *y;
+{
+
+if( cmp( x, Zero ) < 0 )
+ {
+ mov( One, y );
+ neg( y );
+ }
+else
+ {
+ mov( One, y );
+ }
+}
+
+sqtest()
+{
+printf("\nRunning test of square root(x).\n");
+
+RSqrt = Other;
+k = 0;
+SQRT( Zero, t );
+k |= cmp( Zero, t );
+mov( Zero, t );
+neg(t);
+SQRT( t, t2 );
+k |= cmp( t, t2 );
+SQRT( One, t );
+k |= cmp( One, t );
+if( k != 0 )
+ {
+ ErrCnt[Failure] += 1;
+ printf( "Square root of 0.0, -0.0 or 1.0 wrong\n");
+ }
+mov( Zero, MinSqEr );
+mov( Zero, MaxSqEr );
+mov( Zero, J );
+mov( Radix, X );
+mov( U2, OneUlp );
+SqXMinX( Serious );
+mov( BInvrse, X );
+mul( BInvrse, U1, OneUlp );
+SqXMinX( Serious );
+mov( U1, X );
+mul( U1, U1, OneUlp );
+SqXMinX( Serious );
+if( cmp(J,Zero) != 0)
+ Pause();
+printf("Testing if sqrt(X * X) == X for %d Integers X.\n", NoTrials);
+mov( Zero, J );
+mov( Two, X );
+mov( Radix, Y );
+if( cmp(Radix,One) != 0 )
+ {
+ lngint = NoTrials;
+ LTOF( &lngint, t );
+ FTOL( t, &lng2, X );
+ if( lngint != lng2 )
+ {
+ printf( "Integer conversion error\n" );
+ exit(1);
+ }
+ do
+ {
+ mov( Y, X );
+ mul( Radix, Y, Y );
+ sub( X, Y, t2 );
+ }
+ while( ! (cmp(t2,t) >= 0) );
+ }
+mul( X, U2, OneUlp );
+I = 1;
+while(I < 10)
+ {
+ add( X, One, X );
+ SqXMinX( Defect );
+ if( cmp(J,Zero) > 0 )
+ break;
+ I = I + 1;
+ }
+printf("Test for sqrt monotonicity.\n");
+I = - 1;
+mov( BMinusU2, X );
+mov( Radix, Y );
+mul( Radix, U2, Z );
+add( Radix, Z, Z );
+NotMonot = False;
+Monot = False;
+while( ! (NotMonot || Monot))
+ {
+ I = I + 1;
+ SQRT(X, X);
+ SQRT(Y,Q);
+ SQRT(Z,Z);
+ if( (cmp(X,Q) > 0) || (cmp(Q,Z) > 0) )
+ NotMonot = True;
+ else
+ {
+ add( Q, Half, Q );
+ FLOOR( Q, Q );
+ mul( Q, Q, t );
+ if( (I > 0) || (cmp(Radix,t) == 0) )
+ Monot = True;
+ else if (I > 0)
+ {
+ if(I > 1)
+ Monot = True;
+ else
+ {
+ mul( Y, BInvrse, Y );
+ sub( U1, Y, X );
+ add( Y, U1, Z );
+ }
+ }
+ else
+ {
+ mov( Q, Y );
+ sub( U2, Y, X );
+ add( Y, U2, Z );
+ }
+ }
+ }
+if( Monot )
+ printf("sqrt has passed a test for Monotonicity.\n");
+else
+ {
+ ErrCnt[Defect] += 1;
+ printf("sqrt(X) is non-monotonic for X near " );
+ show(Y);
+ }
+/*=============================================*/
+Milestone = 80;
+/*=============================================*/
+add( MinSqEr, Half, MinSqEr );
+sub( Half, MaxSqEr, MaxSqEr);
+/*Y = (SQRT(One + U2) - One) / U2;*/
+add( One, U2, Sqarg );
+SQRT( Sqarg, Y );
+sub( One, Y, Y );
+div( U2, Y, Y );
+/*SqEr = (Y - One) + U2 / Eight;*/
+sub( One, Y, t );
+div( Eight, U2, SqEr );
+add( t, SqEr, SqEr );
+Showsq( 1 );
+div( Eight, U2, SqEr );
+add( Y, SqEr, SqEr );
+Showsq( -1 );
+/*Y = ((SQRT(F9) - U2) - (One - U2)) / U1;*/
+mov( F9, Sqarg );
+SQRT( Sqarg, Y );
+sub( U2, Y, Y );
+sub( U2, One, t );
+sub( t, Y, Y );
+div( U1, Y, Y );
+div( Eight, U1, SqEr );
+add( Y, SqEr, SqEr );
+Showsq( 1 );
+/*SqEr = (Y + One) + U1 / Eight;*/
+div( Eight, U1, t );
+add( Y, One, SqEr );
+add( SqEr, t, SqEr );
+Showsq( -1 );
+mov( U2, OneUlp );
+mov( OneUlp, X );
+for( Indx = 1; Indx <= 3; ++Indx)
+ {
+/*Y = SQRT((X + U1 + X) + F9);*/
+ add( X, U1, Y );
+ add( Y, X, Y );
+ add( Y, F9, Y );
+ mov( Y, Sqarg );
+ SQRT( Sqarg, Y );
+/*Y = ((Y - U2) - ((One - U2) + X)) / OneUlp;*/
+ sub( U2, One, t );
+ add( t, X, t );
+ sub( U2, Y, Y );
+ sub( t, Y, Y );
+ div( OneUlp, Y, Y );
+/*Z = ((U1 - X) + F9) * Half * X * X / OneUlp;*/
+ sub( X, U1, t );
+ add( t, F9, t );
+ mul( t, Half, t );
+ mul( t, X, t );
+ mul( t, X, t );
+ div( OneUlp, t, Z );
+ add( Y, Half, SqEr );
+ add( SqEr, Z, SqEr );
+ Showsq( -1 );
+ sub( Half, Y, SqEr );
+ add( SqEr, Z, SqEr );
+ Showsq( 1 );
+ if(((Indx == 1) || (Indx == 3)))
+ {
+/*X = OneUlp * Sign (X) * FLOOR(Eight / (Nine * SQRT(OneUlp)));*/
+ mov( OneUlp, Sqarg );
+ SQRT( Sqarg, t );
+ mul( Nine, t, t );
+ div( t, Eight, t );
+ FLOOR( t, t );
+ Sign( X, t2 );
+ mul( t2, t, t );
+ mul( OneUlp, t, X );
+ }
+ else
+ {
+ mov( U1, OneUlp );
+ mov( OneUlp, X );
+ neg( X );
+ }
+ }
+/*=============================================*/
+Milestone = 85;
+/*=============================================*/
+SqRWrng = False;
+Anomaly = False;
+if( cmp(Radix,One) != 0 )
+ {
+ printf("Testing whether sqrt is rounded or chopped.\n");
+/*D = FLOOR(Half + POW(Radix, One + Precision - FLOOR(Precision)));*/
+ FLOOR( Precision, t2 );
+ add( One, Precision, t );
+ sub( t2, t, t );
+ POW( Radix, t, D );
+ add( Half, D, D );
+ FLOOR( D, D );
+/* ... == Radix^(1 + fract) if (Precision == Integer + fract. */
+ div( Radix, D, X );
+ div( A1, D, Y );
+ FLOOR( X, t );
+ FLOOR( Y, t2 );
+ if( (cmp(X,t) != 0) || (cmp(Y,t2) != 0) )
+ {
+ Anomaly = True;
+ printf( "Anomaly 1\n" );
+ }
+ else
+ {
+ mov( Zero, X );
+ mov( X, Z2 );
+ mov( One, Y );
+ mov( Y, Y2 );
+ sub( One, Radix, Z1 );
+ mul( Four, D, FourD );
+ do
+ {
+ if( cmp(Y2,Z2) >0 )
+ {
+ mov( Radix, Q );
+ mov( Y, YY1 );
+ do
+ {
+/*X1 = FABS(Q + FLOOR(Half - Q / YY1) * YY1);*/
+ div( YY1, Q, t );
+ sub( t, Half, t );
+ FLOOR( t, t );
+ mul( t, YY1, t );
+ add( Q, t, X1 );
+ FABS( X1 );
+ mov( YY1, Q );
+ mov( X1, YY1 );
+ }
+ while( ! (cmp(X1,Zero) <= 0) );
+ if( cmp(Q,One) <= 0 )
+ {
+ mov( Y2, Z2 );
+ mov( Y, Z );
+ }
+ }
+ add( Y, Two, Y );
+ add( X, Eight, X );
+ add( Y2, X, Y2 );
+ if( cmp(Y2,FourD) >= 0 )
+ sub( FourD, Y2, Y2 );
+ }
+ while( ! (cmp(Y,D) >= 0) );
+ sub( Z2, FourD, X8 );
+ mul( Z, Z, Q );
+ add( X8, Q, Q );
+ div( FourD, Q, Q );
+ div( Eight, X8, X8 );
+ FLOOR( Q, t );
+ if( cmp(Q,t) != 0 )
+ {
+ Anomaly = True;
+ printf( "Anomaly 2\n" );
+ }
+ else
+ {
+ Break = False;
+ do
+ {
+ mul( Z1, Z, X );
+/*X = X - FLOOR(X / Radix) * Radix;*/
+ div( Radix, X, t );
+ FLOOR( t, t );
+ mul( t, Radix, t );
+ sub( t, X, X );
+ if( cmp(X,One) == 0 )
+ Break = True;
+ else
+ sub( One, Z1, Z1 );
+ }
+ while( ! (Break || (cmp(Z1,Zero) <= 0)) );
+ if( (cmp(Z1,Zero) <= 0) && (! Break))
+ {
+ printf( "Anomaly 3\n" );
+ Anomaly = True;
+ }
+ else
+ {
+ if( cmp(Z1,RadixD2) > 0)
+ sub( Radix, Z1, Z1 );
+ do
+ {
+ NewD();
+ mul( U2, D, t );
+ }
+ while( ! (cmp(t,F9) >= 0) );
+ mul( D, Radix, t );
+ sub( D, t, t );
+ sub( D, W, t2 );
+ if (cmp(t,t2) != 0 )
+ {
+ printf( "Anomaly 4\n" );
+ Anomaly = True;
+ }
+ else
+ {
+ mov( D, Z2 );
+ I = 0;
+ add( One, Z, t );
+ mul( t, Half, t );
+ add( D, t, Y );
+ add( D, Z, X );
+ add( X, Q, X );
+ SR3750();
+ sub( Z, One, t );
+ mul( t, Half, t );
+ add( D, t, Y );
+ add( Y, D, Y );
+ sub( Z, D, X );
+ add( X, D, X );
+ add( X, Q, t );
+ add( t, X, X );
+ SR3750();
+ NewD();
+ sub( Z2, D, t );
+ sub( Z2, W, t2 );
+ if(cmp(t,t2) != 0 )
+ {
+ printf( "Anomaly 5\n" );
+ Anomaly = True;
+ }
+ else
+ {
+/*Y = (D - Z2) + (Z2 + (One - Z) * Half);*/
+ sub( Z, One, t );
+ mul( t, Half, t );
+ add( Z2, t, t );
+ sub( Z2, D, Y );
+ add( Y, t, Y );
+/*X = (D - Z2) + (Z2 - Z + Q);*/
+ sub( Z, Z2, t );
+ add( t, Q, t );
+ sub( Z2, D, X );
+ add( X, t, X );
+ SR3750();
+ add( One, Z, Y );
+ mul( Y, Half, Y );
+ mov( Q, X );
+ SR3750();
+ if(I == 0)
+ {
+ printf( "Anomaly 6\n" );
+ Anomaly = True;
+ }
+ }
+ }
+ }
+ }
+ }
+ if ((I == 0) || Anomaly)
+ {
+ ErrCnt[Failure] += 1;
+ printf( "Anomalous arithmetic with Integer < \n");
+ printf("Radix^Precision = " );
+ show( W );
+ printf(" fails test whether sqrt rounds or chops.\n");
+ SqRWrng = True;
+ }
+ }
+if(! Anomaly)
+ {
+ if(! ((cmp(MinSqEr,Zero) < 0) || (cmp(MaxSqEr,Zero) > 0))) {
+ RSqrt = Rounded;
+ printf("Square root appears to be correctly rounded.\n");
+ }
+ else
+ {
+ k = 0;
+ add( MaxSqEr, U2, t );
+ sub( Half, U2, t2 );
+ if( cmp(t,t2) > 0 )
+ k = 1;
+ if( cmp( MinSqEr, Half ) > 0 )
+ k = 1;
+ add( MinSqEr, Radix, t );
+ if( cmp( t, Half ) < 0 )
+ k = 1;
+ if( k == 1 )
+ 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 " );
+ sub( Half, MinSqEr, t );
+ show( t );
+ printf("\tto " );
+ add( Half, MaxSqEr, t );
+ show( t );
+ printf( "ulps.\n" );
+ sub( MinSqEr, MaxSqEr, t );
+ mul( Radix, Radix, t2 );
+ if( cmp( t, t2 ) >= 0 )
+ {
+ ErrCnt[Serious] += 1;
+ printf( "sqrt gets too many last digits wrong\n");
+ }
+ }
+}
+
+Showsq( arg )
+int arg;
+{
+
+k = 0;
+if( arg <= 0 )
+ {
+ if( cmp(SqEr,MinSqEr) < 0 )
+ {
+ k = 1;
+ mov( SqEr, MinSqEr );
+ }
+ }
+if( arg >= 0 )
+ {
+ if( cmp(SqEr,MaxSqEr) > 0 )
+ {
+ k = 2;
+ mov( SqEr, MaxSqEr );
+ }
+ }
+#if DEBUG
+if( k != 0 )
+ {
+ printf( "Square root of " );
+ show( arg );
+ printf( "\tis in error by " );
+ show( SqEr );
+ }
+#endif
+}
+
+
+pow1test()
+{
+
+/*=============================================*/
+Milestone = 90;
+/*=============================================*/
+Pause();
+printf("Testing powers Z^i for small Integers Z and i.\n");
+N = 0;
+/* ... test powers of zero. */
+I = 0;
+mov( Zero, Z );
+neg(Z);
+M = 3;
+Break = False;
+do
+ {
+ mov( One, X );
+ SR3980();
+ if(I <= 10)
+ {
+ I = 1023;
+ SR3980();
+ }
+ if( cmp(Z,MinusOne) == 0 )
+ Break = True;
+ else
+ {
+ mov( MinusOne, Z );
+ PrintIfNPositive();
+ N = 0;
+/* .. if(-1)^N is invalid, replace MinusOne by One. */
+ I = - 4;
+ }
+ }
+while( ! Break );
+PrintIfNPositive();
+N1 = N;
+N = 0;
+mov( A1, Z );
+/*M = FLOOR(Two * LOG(W) / LOG(A1));*/
+LOG( W, t );
+mul( Two, t, t );
+FLOOR( t, t );
+LOG( A1, t2 );
+div( t2, t, t );
+FTOL( t, &lngint, t2 );
+M = lngint;
+Break = False;
+do
+ {
+ mov( Z, X );
+ I = 1;
+ SR3980();
+ if( cmp(Z,AInvrse) == 0 )
+ Break = True;
+ else
+ mov( AInvrse, Z );
+ }
+while( ! (Break) );
+/*=============================================*/
+Milestone = 100;
+/*=============================================*/
+/* Powers of Radix have been tested, */
+/* next try a few primes */
+
+M = NoTrials;
+
+mov( Three, Z );
+do
+ {
+ mov( Z, X );
+ I = 1;
+ SR3980();
+ do
+ {
+ add( Z, Two, Z );
+ div( Three, Z, t );
+ FLOOR( t, t );
+ mul( Three, t, t );
+ }
+ while( cmp(t,Z) == 0 );
+ mul( Eight, Three, t );
+ }
+while( cmp(Z,t) < 0 );
+
+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 discrepancies found.\n");
+if(N > 0)
+ Pause();
+else printf("\n");
+}
+
+
+
+pow2test()
+{
+printf("\n");
+/* ...calculate Exp2 == exp(2) == 7.38905 60989 30650 22723 04275-... */
+mov( Zero, X );
+mov( Two, t2 ); /*I = 2;*/
+
+mul( Two, Three, Y );
+mov( Zero, Q );
+N = 0;
+do
+ {
+ mov( X, Z );
+ add( t2, One, t2 ); /*I = I + 1;*/
+ add( t2, t2, t );
+ div( t, Y, Y ); /*Y = Y / (I + I);*/
+ add( Y, Q, R );
+ add( Z, R, X );
+ sub( X, Z, Q );
+ add( Q, R, Q );
+ }
+while( cmp(X,Z) > 0 );
+
+/*Z = (OneAndHalf + One / Eight) + X / (OneAndHalf * ThirtyTwo);*/
+div( Eight, One, t );
+add( OneAndHalf, t, Z );
+mul( OneAndHalf, ThirtyTwo, t );
+div( t, X, t );
+add( Z, t, Z );
+mul( Z, Z, X );
+mul( X, X, Exp2 );
+mov( F9, X );
+sub( U1, X, Y );
+printf("Testing X^((X + 1) / (X - 1)) vs. exp(2) = " );
+show( Exp2 );
+printf( "\tas X -> 1.\n" );
+for(I = 1;;)
+ {
+ sub( BInvrse, X, Z );
+/*Z = (X + One) / (Z - (One - BInvrse));*/
+ add( X, One, t2 );
+ sub( BInvrse, One, t );
+ sub( t, Z, t );
+ div( t, t2, Z );
+ POW( X, Z, Sqarg );
+ sub( Exp2, Sqarg, Q );
+ mov( Q, t );
+ FABS( t );
+ mul( TwoForty, U2, t2 );
+ if( cmp( t, t2 ) > 0 )
+ {
+ N = 1;
+ sub( BInvrse, X, V9 );
+ sub( BInvrse, One, t );
+ sub( t, V9, V9 );
+ ErrCnt[Defect] += 1;
+ printf( "Calculated " );
+ show( Sqarg );
+ printf(" for \t(1 + " );
+ show( V9 );
+ printf( "\tto the power " );
+ show( Z );
+ printf("\tdiffers from correct value by " );
+ show( Q );
+ printf("\tThis much error may spoil financial\n");
+ printf("\tcalculations involving tiny interest rates.\n");
+ break;
+ }
+ else
+ {
+ sub( X, Y, Z );
+ mul( Z, Two, Z );
+ add( Z, Y, Z );
+ mov( Y, X );
+ mov( Z, Y );
+ sub( F9, X, Z );
+ mul( Z, Z, Z );
+ add( Z, One, Z );
+ if( (cmp(Z,One) > 0) && (I < NoTrials) )
+ I++;
+ else
+ {
+ if( cmp(X,One) > 0 )
+ {
+ if(N == 0)
+ printf("Accuracy seems adequate.\n");
+ break;
+ }
+ else
+ {
+ add( One, U2, X );
+ add( U2, U2, Y );
+ add( X, Y, Y );
+ I = 1;
+ }
+ }
+ }
+ }
+/*=============================================*/
+Milestone = 150;
+/*=============================================*/
+printf("Testing powers Z^Q at four nearly extreme values.\n");
+N = 0;
+mov( A1, Z );
+/*Q = FLOOR(Half - LOG(C) / LOG(A1));*/
+LOG( C, t );
+LOG( A1, t2 );
+div( t2, t, t );
+sub( t, Half, t );
+FLOOR( t, Q );
+Break = False;
+do
+ {
+ mov( CInvrse, X );
+ POW( Z, Q, Y );
+ IsYeqX();
+ neg(Q);
+ mov( C, X );
+ POW( Z, Q, Y );
+ IsYeqX();
+ if( cmp(Z,One) < 0 )
+ Break = True;
+ else
+ mov( AInvrse, Z );
+ }
+while( ! (Break));
+PrintIfNPositive();
+if(N == 0)
+ printf(" ... no discrepancies found.\n");
+printf("\n");
+}
diff --git a/test/math/epow.c b/test/math/epow.c
index cc4994fe7..d756eaee0 100644
--- a/test/math/epow.c
+++ b/test/math/epow.c
@@ -1,215 +1,215 @@
-/* epow.c */
-/* power function: z = x**y */
-/* by Stephen L. Moshier. */
-
-
-#include "ehead.h"
-#define MAXPOS ((long) (((unsigned long) ~(0L)) >> 1))
-#define MAXNEG (-MAXPOS)
-/* #define MAXNEG (-MAXPOS - 1L) */
-
-extern int rndprc;
-void epowi();
-static void epowr();
-
-
-/* Run-time determination of largest integers */
-
-int powinited = 0;
-unsigned short maxposint[NE], maxnegint[NE];
-
-void initpow()
-{
-long li;
-
-li = MAXPOS;
-ltoe( &li, maxposint );
-li = MAXNEG;
-ltoe( &li, maxnegint );
-powinited = 1;
-}
-
-
-
-
-void epow( x, y, z )
-unsigned short *x, *y, *z;
-{
-unsigned short w[NE];
-int rndsav;
-long li;
-
-if( powinited == 0 )
- initpow();
-
-/* Check for integer power. */
-
-efloor( y, w );
-if( (ecmp(y,w) == 0)
- && (ecmp(maxposint,w) >= 0)
- && (ecmp(w,maxnegint) >= 0) )
- {
- eifrac( y, &li, w );
- epowi( x, y, z );
- return;
- }
-epowr( x, y, z );
-}
-
-
-
-
-/* y is integer valued. */
-
-void epowi( x, y, z )
-unsigned short x[], y[], z[];
-{
-unsigned short w[NE];
-long li, lx;
-unsigned long lu;
-int rndsav;
-unsigned short signx;
-/* unsigned short signy; */
-
-if( powinited == 0 )
- initpow();
-
-rndsav = rndprc;
-
-if( (ecmp(y,maxposint) > 0) || (ecmp(maxnegint,y) > 0) )
- {
- epowr( x, y, z );
- return;
- }
-
-eifrac( y, &li, w );
-if( li < 0 )
- lx = -li;
-else
- lx = li;
-
-/*
-if( (x[NE-1] & (unsigned short )0x7fff) == 0 )
-*/
-
-if( ecmp( x, ezero) == 0 )
- {
- if( li == 0 )
- {
- emov( eone, z );
- return;
- }
- else if( li < 0 )
- {
- einfin( z );
- return;
- }
- else
- {
- eclear( z );
- return;
- }
- }
-
-if( li == 0L )
- {
- emov( eone, z );
- return;
- }
-
-emov( x, w );
-signx = w[NE-1] & (unsigned short )0x8000;
-w[NE-1] &= (unsigned short )0x7fff;
-
-/* Overflow detection */
-/*
-lx = li * (w[NE-1] - 0x3fff);
-if( lx > 16385L )
- {
- einfin( z );
- mtherr( "epowi", OVERFLOW );
- goto done;
- }
-if( lx < -16450L )
- {
- eclear( z );
- return;
- }
-*/
-rndprc = NBITS;
-
-if( li < 0 )
- {
- lu = (unsigned int )( -li );
-/* signy = 0xffff;*/
- ediv( w, eone, w );
- }
-else
- {
- lu = (unsigned int )li;
-/* signy = 0;*/
- }
-
-/* First bit of the power */
-if( lu & 1 )
- {
- emov( w, z );
- }
-else
- {
- emov( eone, z );
- signx = 0;
- }
-
-
-lu >>= 1;
-while( lu != 0L )
- {
- emul( w, w, w ); /* arg to the 2-to-the-kth power */
- if( lu & 1L ) /* if that bit is set, then include in product */
- emul( w, z, z );
- lu >>= 1;
- }
-
-
-done:
-
-if( signx )
- eneg( z ); /* odd power of negative number */
-
-/*
-if( signy )
- {
- if( ecmp( z, ezero ) != 0 )
- {
- ediv( z, eone, z );
- }
- else
- {
- einfin( z );
- printf( "epowi OVERFLOW\n" );
- }
- }
-*/
-rndprc = rndsav;
-emul( eone, z, z );
-}
-
-
-
-/* z = exp( y * log(x) ) */
-
-static void epowr( x, y, z )
-unsigned short *x, *y, *z;
-{
-unsigned short w[NE];
-int rndsav;
-
-rndsav = rndprc;
-rndprc = NBITS;
-elog( x, w );
-emul( y, w, w );
-eexp( w, z );
-rndprc = rndsav;
-emul( eone, z, z );
-}
+/* epow.c */
+/* power function: z = x**y */
+/* by Stephen L. Moshier. */
+
+
+#include "ehead.h"
+#define MAXPOS ((long) (((unsigned long) ~(0L)) >> 1))
+#define MAXNEG (-MAXPOS)
+/* #define MAXNEG (-MAXPOS - 1L) */
+
+extern int rndprc;
+void epowi();
+static void epowr();
+
+
+/* Run-time determination of largest integers */
+
+int powinited = 0;
+unsigned short maxposint[NE], maxnegint[NE];
+
+void initpow()
+{
+long li;
+
+li = MAXPOS;
+ltoe( &li, maxposint );
+li = MAXNEG;
+ltoe( &li, maxnegint );
+powinited = 1;
+}
+
+
+
+
+void epow( x, y, z )
+unsigned short *x, *y, *z;
+{
+unsigned short w[NE];
+int rndsav;
+long li;
+
+if( powinited == 0 )
+ initpow();
+
+/* Check for integer power. */
+
+efloor( y, w );
+if( (ecmp(y,w) == 0)
+ && (ecmp(maxposint,w) >= 0)
+ && (ecmp(w,maxnegint) >= 0) )
+ {
+ eifrac( y, &li, w );
+ epowi( x, y, z );
+ return;
+ }
+epowr( x, y, z );
+}
+
+
+
+
+/* y is integer valued. */
+
+void epowi( x, y, z )
+unsigned short x[], y[], z[];
+{
+unsigned short w[NE];
+long li, lx;
+unsigned long lu;
+int rndsav;
+unsigned short signx;
+/* unsigned short signy; */
+
+if( powinited == 0 )
+ initpow();
+
+rndsav = rndprc;
+
+if( (ecmp(y,maxposint) > 0) || (ecmp(maxnegint,y) > 0) )
+ {
+ epowr( x, y, z );
+ return;
+ }
+
+eifrac( y, &li, w );
+if( li < 0 )
+ lx = -li;
+else
+ lx = li;
+
+/*
+if( (x[NE-1] & (unsigned short )0x7fff) == 0 )
+*/
+
+if( ecmp( x, ezero) == 0 )
+ {
+ if( li == 0 )
+ {
+ emov( eone, z );
+ return;
+ }
+ else if( li < 0 )
+ {
+ einfin( z );
+ return;
+ }
+ else
+ {
+ eclear( z );
+ return;
+ }
+ }
+
+if( li == 0L )
+ {
+ emov( eone, z );
+ return;
+ }
+
+emov( x, w );
+signx = w[NE-1] & (unsigned short )0x8000;
+w[NE-1] &= (unsigned short )0x7fff;
+
+/* Overflow detection */
+/*
+lx = li * (w[NE-1] - 0x3fff);
+if( lx > 16385L )
+ {
+ einfin( z );
+ mtherr( "epowi", OVERFLOW );
+ goto done;
+ }
+if( lx < -16450L )
+ {
+ eclear( z );
+ return;
+ }
+*/
+rndprc = NBITS;
+
+if( li < 0 )
+ {
+ lu = (unsigned int )( -li );
+/* signy = 0xffff;*/
+ ediv( w, eone, w );
+ }
+else
+ {
+ lu = (unsigned int )li;
+/* signy = 0;*/
+ }
+
+/* First bit of the power */
+if( lu & 1 )
+ {
+ emov( w, z );
+ }
+else
+ {
+ emov( eone, z );
+ signx = 0;
+ }
+
+
+lu >>= 1;
+while( lu != 0L )
+ {
+ emul( w, w, w ); /* arg to the 2-to-the-kth power */
+ if( lu & 1L ) /* if that bit is set, then include in product */
+ emul( w, z, z );
+ lu >>= 1;
+ }
+
+
+done:
+
+if( signx )
+ eneg( z ); /* odd power of negative number */
+
+/*
+if( signy )
+ {
+ if( ecmp( z, ezero ) != 0 )
+ {
+ ediv( z, eone, z );
+ }
+ else
+ {
+ einfin( z );
+ printf( "epowi OVERFLOW\n" );
+ }
+ }
+*/
+rndprc = rndsav;
+emul( eone, z, z );
+}
+
+
+
+/* z = exp( y * log(x) ) */
+
+static void epowr( x, y, z )
+unsigned short *x, *y, *z;
+{
+unsigned short w[NE];
+int rndsav;
+
+rndsav = rndprc;
+rndprc = NBITS;
+elog( x, w );
+emul( y, w, w );
+eexp( w, z );
+rndprc = rndsav;
+emul( eone, z, z );
+}
diff --git a/test/math/etanh.c b/test/math/etanh.c
index c74b4700a..8014c6d93 100644
--- a/test/math/etanh.c
+++ b/test/math/etanh.c
@@ -1,52 +1,52 @@
-/* xtanh.c */
-/* hyperbolic tangent check routine */
-/* this subroutine is used by the exponential function routine */
-/* by Stephen L. Moshier. */
-
-
-
-#include "ehead.h"
-
-
-void etanh( x, y )
-unsigned short *x, *y;
-{
-unsigned short e[NE], r[NE], j[NE], xx[NE], m2[NE];
-short i, n;
-long lj;
-
-emov( x, r );
-r[NE-1] &= (unsigned short )0x7fff;
-if( ecmp(r, eone) >= 0 )
- {
-/* tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
- * Note eexp() calls xtanh, but with an argument less than (1 + log 2)/2.
- */
- eexp( r, e );
- ediv( e, eone, r );
- esub( r, e, xx );
- eadd( r, e, j );
- ediv( j, xx, y );
- return;
- }
-
-emov( etwo, m2 );
-eneg( m2 );
-
-n = NBITS/8; /* Number of terms to do in the continued fraction */
-lj = 2 * n + 1;
-ltoe( &lj, j );
-
-emov( j, e );
-emul( x, x, xx );
-
-/* continued fraction */
-for( i=0; i<n; i++)
- {
- ediv( e, xx, r );
- eadd( m2, j, j );
- eadd( r, j, e );
- }
-
-ediv( e, x, y );
-}
+/* xtanh.c */
+/* hyperbolic tangent check routine */
+/* this subroutine is used by the exponential function routine */
+/* by Stephen L. Moshier. */
+
+
+
+#include "ehead.h"
+
+
+void etanh( x, y )
+unsigned short *x, *y;
+{
+unsigned short e[NE], r[NE], j[NE], xx[NE], m2[NE];
+short i, n;
+long lj;
+
+emov( x, r );
+r[NE-1] &= (unsigned short )0x7fff;
+if( ecmp(r, eone) >= 0 )
+ {
+/* tanh(x) = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
+ * Note eexp() calls xtanh, but with an argument less than (1 + log 2)/2.
+ */
+ eexp( r, e );
+ ediv( e, eone, r );
+ esub( r, e, xx );
+ eadd( r, e, j );
+ ediv( j, xx, y );
+ return;
+ }
+
+emov( etwo, m2 );
+eneg( m2 );
+
+n = NBITS/8; /* Number of terms to do in the continued fraction */
+lj = 2 * n + 1;
+ltoe( &lj, j );
+
+emov( j, e );
+emul( x, x, xx );
+
+/* continued fraction */
+for( i=0; i<n; i++)
+ {
+ ediv( e, xx, r );
+ eadd( m2, j, j );
+ eadd( r, j, e );
+ }
+
+ediv( e, x, y );
+}
diff --git a/test/math/etodec.c b/test/math/etodec.c
index 29fee34cd..22545d6fb 100644
--- a/test/math/etodec.c
+++ b/test/math/etodec.c
@@ -1,181 +1,181 @@
-#include "ehead.h"
-void emovi(), emovo(), ecleaz(), eshdn8(), emdnorm();
-void todec();
-/*
-; convert DEC double precision to e type
-; double d;
-; short e[NE];
-; dectoe( &d, e );
-*/
-void dectoe( d, e )
-unsigned short *d;
-unsigned short *e;
-{
-unsigned short y[NI];
-register unsigned short r, *p;
-
-ecleaz(y); /* start with a zero */
-p = y; /* point to our number */
-r = *d; /* get DEC exponent word */
-if( *d & (unsigned int )0x8000 )
- *p = 0xffff; /* fill in our sign */
-++p; /* bump pointer to our exponent word */
-r &= 0x7fff; /* strip the sign bit */
-if( r == 0 ) /* answer = 0 if high order DEC word = 0 */
- goto done;
-
-
-r >>= 7; /* shift exponent word down 7 bits */
-r += EXONE - 0201; /* subtract DEC exponent offset */
- /* add our e type exponent offset */
-*p++ = r; /* to form our exponent */
-
-r = *d++; /* now do the high order mantissa */
-r &= 0177; /* strip off the DEC exponent and sign bits */
-r |= 0200; /* the DEC understood high order mantissa bit */
-*p++ = r; /* put result in our high guard word */
-
-*p++ = *d++; /* fill in the rest of our mantissa */
-*p++ = *d++;
-*p = *d;
-
-eshdn8(y); /* shift our mantissa down 8 bits */
-done:
-emovo( y, e );
-}
-
-
-
-/*
-; convert e type to DEC double precision
-; double d;
-; short e[NE];
-; etodec( e, &d );
-*/
-#if 0
-static unsigned short decbit[NI] = {0,0,0,0,0,0,0200,0};
-void etodec( x, d )
-unsigned short *x, *d;
-{
-unsigned short xi[NI];
-register unsigned short r;
-int i, j;
-
-emovi( x, xi );
-*d = 0;
-if( xi[0] != 0 )
- *d = 0100000;
-r = xi[E];
-if( r < (EXONE - 128) )
- goto zout;
-i = xi[M+4];
-if( (i & 0200) != 0 )
- {
- if( (i & 0377) == 0200 )
- {
- if( (i & 0400) != 0 )
- {
- /* check all less significant bits */
- for( j=M+5; j<NI; j++ )
- {
- if( xi[j] != 0 )
- goto yesrnd;
- }
- }
- goto nornd;
- }
-yesrnd:
- eaddm( decbit, xi );
- r -= enormlz(xi);
- }
-
-nornd:
-
-r -= EXONE;
-r += 0201;
-if( r < 0 )
- {
-zout:
- *d++ = 0;
- *d++ = 0;
- *d++ = 0;
- *d++ = 0;
- return;
- }
-if( r >= 0377 )
- {
- *d++ = 077777;
- *d++ = -1;
- *d++ = -1;
- *d++ = -1;
- return;
- }
-r &= 0377;
-r <<= 7;
-eshup8( xi );
-xi[M] &= 0177;
-r |= xi[M];
-*d++ |= r;
-*d++ = xi[M+1];
-*d++ = xi[M+2];
-*d++ = xi[M+3];
-}
-#else
-
-extern int rndprc;
-
-void etodec( x, d )
-unsigned short *x, *d;
-{
-unsigned short xi[NI];
-long exp;
-int rndsav;
-
-emovi( x, xi );
-exp = (long )xi[E] - (EXONE - 0201); /* adjust exponent for offsets */
-/* round off to nearest or even */
-rndsav = rndprc;
-rndprc = 56;
-emdnorm( xi, 0, 0, exp, 64 );
-rndprc = rndsav;
-todec( xi, d );
-}
-
-void todec( x, y )
-unsigned short *x, *y;
-{
-unsigned short i;
-unsigned short *p;
-
-p = x;
-*y = 0;
-if( *p++ )
- *y = 0100000;
-i = *p++;
-if( i == 0 )
- {
- *y++ = 0;
- *y++ = 0;
- *y++ = 0;
- *y++ = 0;
- return;
- }
-if( i > 0377 )
- {
- *y++ |= 077777;
- *y++ = 0xffff;
- *y++ = 0xffff;
- *y++ = 0xffff;
- return;
- }
-i &= 0377;
-i <<= 7;
-eshup8( x );
-x[M] &= 0177;
-i |= x[M];
-*y++ |= i;
-*y++ = x[M+1];
-*y++ = x[M+2];
-*y++ = x[M+3];
-}
-#endif
+#include "ehead.h"
+void emovi(), emovo(), ecleaz(), eshdn8(), emdnorm();
+void todec();
+/*
+; convert DEC double precision to e type
+; double d;
+; short e[NE];
+; dectoe( &d, e );
+*/
+void dectoe( d, e )
+unsigned short *d;
+unsigned short *e;
+{
+unsigned short y[NI];
+register unsigned short r, *p;
+
+ecleaz(y); /* start with a zero */
+p = y; /* point to our number */
+r = *d; /* get DEC exponent word */
+if( *d & (unsigned int )0x8000 )
+ *p = 0xffff; /* fill in our sign */
+++p; /* bump pointer to our exponent word */
+r &= 0x7fff; /* strip the sign bit */
+if( r == 0 ) /* answer = 0 if high order DEC word = 0 */
+ goto done;
+
+
+r >>= 7; /* shift exponent word down 7 bits */
+r += EXONE - 0201; /* subtract DEC exponent offset */
+ /* add our e type exponent offset */
+*p++ = r; /* to form our exponent */
+
+r = *d++; /* now do the high order mantissa */
+r &= 0177; /* strip off the DEC exponent and sign bits */
+r |= 0200; /* the DEC understood high order mantissa bit */
+*p++ = r; /* put result in our high guard word */
+
+*p++ = *d++; /* fill in the rest of our mantissa */
+*p++ = *d++;
+*p = *d;
+
+eshdn8(y); /* shift our mantissa down 8 bits */
+done:
+emovo( y, e );
+}
+
+
+
+/*
+; convert e type to DEC double precision
+; double d;
+; short e[NE];
+; etodec( e, &d );
+*/
+#if 0
+static unsigned short decbit[NI] = {0,0,0,0,0,0,0200,0};
+void etodec( x, d )
+unsigned short *x, *d;
+{
+unsigned short xi[NI];
+register unsigned short r;
+int i, j;
+
+emovi( x, xi );
+*d = 0;
+if( xi[0] != 0 )
+ *d = 0100000;
+r = xi[E];
+if( r < (EXONE - 128) )
+ goto zout;
+i = xi[M+4];
+if( (i & 0200) != 0 )
+ {
+ if( (i & 0377) == 0200 )
+ {
+ if( (i & 0400) != 0 )
+ {
+ /* check all less significant bits */
+ for( j=M+5; j<NI; j++ )
+ {
+ if( xi[j] != 0 )
+ goto yesrnd;
+ }
+ }
+ goto nornd;
+ }
+yesrnd:
+ eaddm( decbit, xi );
+ r -= enormlz(xi);
+ }
+
+nornd:
+
+r -= EXONE;
+r += 0201;
+if( r < 0 )
+ {
+zout:
+ *d++ = 0;
+ *d++ = 0;
+ *d++ = 0;
+ *d++ = 0;
+ return;
+ }
+if( r >= 0377 )
+ {
+ *d++ = 077777;
+ *d++ = -1;
+ *d++ = -1;
+ *d++ = -1;
+ return;
+ }
+r &= 0377;
+r <<= 7;
+eshup8( xi );
+xi[M] &= 0177;
+r |= xi[M];
+*d++ |= r;
+*d++ = xi[M+1];
+*d++ = xi[M+2];
+*d++ = xi[M+3];
+}
+#else
+
+extern int rndprc;
+
+void etodec( x, d )
+unsigned short *x, *d;
+{
+unsigned short xi[NI];
+long exp;
+int rndsav;
+
+emovi( x, xi );
+exp = (long )xi[E] - (EXONE - 0201); /* adjust exponent for offsets */
+/* round off to nearest or even */
+rndsav = rndprc;
+rndprc = 56;
+emdnorm( xi, 0, 0, exp, 64 );
+rndprc = rndsav;
+todec( xi, d );
+}
+
+void todec( x, y )
+unsigned short *x, *y;
+{
+unsigned short i;
+unsigned short *p;
+
+p = x;
+*y = 0;
+if( *p++ )
+ *y = 0100000;
+i = *p++;
+if( i == 0 )
+ {
+ *y++ = 0;
+ *y++ = 0;
+ *y++ = 0;
+ *y++ = 0;
+ return;
+ }
+if( i > 0377 )
+ {
+ *y++ |= 077777;
+ *y++ = 0xffff;
+ *y++ = 0xffff;
+ *y++ = 0xffff;
+ return;
+ }
+i &= 0377;
+i <<= 7;
+eshup8( x );
+x[M] &= 0177;
+i |= x[M];
+*y++ |= i;
+*y++ = x[M+1];
+*y++ = x[M+2];
+*y++ = x[M+3];
+}
+#endif
diff --git a/test/math/ieee.c b/test/math/ieee.c
index 914d62cbb..17efea01c 100644
--- a/test/math/ieee.c
+++ b/test/math/ieee.c
@@ -1,4119 +1,4119 @@
-/* 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 "\usr\include\stdio.h" */
-#include "ehead.h"
-#include "mconf.h"
-
-/* Change UNK into something else. */
-#ifdef UNK
-#undef UNK
-#define IBMPC 1
-#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;
-
-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();
-
-
-
-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 significance.
- */
-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 * 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.
- */
-#if 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:
-#if 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;
-long lt, lta, ltb;
-
-#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) )
- {
- if( eisneg(a) ^ eisneg(b) )
- *(c+(NE-1)) = 0x8000;
- else
- *(c+(NE-1)) = 0;
- einfin(c);
- return;
- }
-if( eisinf(a) )
- {
- eclear(c);
- return;
- }
-#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);
- return;
- }
-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;
- }
- }
- if( ai[0] == bi[0] )
- *(c+(NE-1)) = 0;
- else
- *(c+(NE-1)) = 0x8000;
- einfin(c);
- mtherr( "ediv", SING );
- return;
- }
-dnzro2:
-
-i = edivm( ai, bi );
-/* calculate exponent */
-lt = ltb - lta + EXONE;
-emdnorm( bi, i, 0, lt, 64 );
-/* set the sign */
-if( ai[0] == bi[0] )
- bi[0] = 0;
-else
- bi[0] = 0Xffff;
-emovo( bi, c );
-}
-
-
-
-/*
-; 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;
-long lt, lta, ltb;
-
-#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) )
- {
- if( eisneg(a) ^ eisneg(b) )
- *(c+(NE-1)) = 0x8000;
- else
- *(c+(NE-1)) = 0;
- einfin(c);
- return;
- }
-#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);
- return;
- }
-mnzer1:
-
-if( bi[E] == 0 )
- {
- for( i=1; i<NI-1; i++ )
- {
- if( bi[i] != 0 )
- {
- ltb -= enormlz( bi );
- goto mnzer2;
- }
- }
- eclear(c);
- return;
- }
-mnzer2:
-
-/* Multiply significands */
-j = emulm( ai, bi );
-/* calculate exponent */
-lt = lta + ltb - (EXONE - 1);
-emdnorm( bi, j, 0, lt, 64 );
-/* calculate sign of product */
-if( ai[0] == bi[0] )
- bi[0] = 0;
-else
- bi[0] = 0xffff;
-emovo( bi, c );
-}
-
-
-
-
-/*
-; 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 denorm, i;
-
-e = pe;
-denorm = 0;
-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 )
-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 );
-}
+/* 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 "\usr\include\stdio.h" */
+#include "ehead.h"
+#include "mconf.h"
+
+/* Change UNK into something else. */
+#ifdef UNK
+#undef UNK
+#define IBMPC 1
+#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;
+
+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();
+
+
+
+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 significance.
+ */
+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 * 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.
+ */
+#if 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:
+#if 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;
+long lt, lta, ltb;
+
+#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) )
+ {
+ if( eisneg(a) ^ eisneg(b) )
+ *(c+(NE-1)) = 0x8000;
+ else
+ *(c+(NE-1)) = 0;
+ einfin(c);
+ return;
+ }
+if( eisinf(a) )
+ {
+ eclear(c);
+ return;
+ }
+#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);
+ return;
+ }
+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;
+ }
+ }
+ if( ai[0] == bi[0] )
+ *(c+(NE-1)) = 0;
+ else
+ *(c+(NE-1)) = 0x8000;
+ einfin(c);
+ mtherr( "ediv", SING );
+ return;
+ }
+dnzro2:
+
+i = edivm( ai, bi );
+/* calculate exponent */
+lt = ltb - lta + EXONE;
+emdnorm( bi, i, 0, lt, 64 );
+/* set the sign */
+if( ai[0] == bi[0] )
+ bi[0] = 0;
+else
+ bi[0] = 0Xffff;
+emovo( bi, c );
+}
+
+
+
+/*
+; 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;
+long lt, lta, ltb;
+
+#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) )
+ {
+ if( eisneg(a) ^ eisneg(b) )
+ *(c+(NE-1)) = 0x8000;
+ else
+ *(c+(NE-1)) = 0;
+ einfin(c);
+ return;
+ }
+#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);
+ return;
+ }
+mnzer1:
+
+if( bi[E] == 0 )
+ {
+ for( i=1; i<NI-1; i++ )
+ {
+ if( bi[i] != 0 )
+ {
+ ltb -= enormlz( bi );
+ goto mnzer2;
+ }
+ }
+ eclear(c);
+ return;
+ }
+mnzer2:
+
+/* Multiply significands */
+j = emulm( ai, bi );
+/* calculate exponent */
+lt = lta + ltb - (EXONE - 1);
+emdnorm( bi, j, 0, lt, 64 );
+/* calculate sign of product */
+if( ai[0] == bi[0] )
+ bi[0] = 0;
+else
+ bi[0] = 0xffff;
+emovo( bi, c );
+}
+
+
+
+
+/*
+; 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 denorm, i;
+
+e = pe;
+denorm = 0;
+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 )
+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/test/math/ieetst.c b/test/math/ieetst.c
index 3c89145e3..8c2453898 100644
--- a/test/math/ieetst.c
+++ b/test/math/ieetst.c
@@ -1,850 +1,850 @@
-/* Floating point to ASCII input and output string test program.
- *
- * Numbers in the native machine data structure are converted
- * to e type, then to and from decimal ASCII strings. Native
- * printf() and scanf() functions are also used to produce
- * and read strings. The resulting e type binary values
- * are compared, with diagnostic printouts of any discrepancies.
- *
- * Steve Moshier, 16 Dec 88
- * last revision: 16 May 92
- */
-
-#include "ehead.h"
-#include "mconf.h"
-
-/* Include tests of 80-bit long double precision: */
-#define LDOUBLE 0
-/* Abort subtest after getting this many errors: */
-#define MAXERR 5
-/* Number of random arguments to try (set as large as you have
- * patience for): */
-#define NRAND 100
-/* Perform internal consistency test: */
-#define CHKINTERNAL 0
-
-static unsigned short fullp[NE], rounded[NE];
-float prec24, sprec24, ssprec24;
-double prec53, sprec53, ssprec53;
-#if LDOUBLE
-long double prec64, sprec64, ssprec64;
-#endif
-
-static unsigned short rprint[NE], rscan[NE];
-static unsigned short q1[NE], q2[NE], q5[NE];
-static unsigned short e1[NE], e2[NE], e3[NE];
-static double d1, d2;
-static int errprint = 0;
-static int errscan = 0;
-static int identerr = 0;
-static int errtot = 0;
-static int count = 0;
-static char str0[80], str1[80], str2[80], str3[80];
-static unsigned short eten[NE], maxm[NE];
-
-int m, n, k2, mprec, SPREC;
-
-char *Ten = "10.0";
-char tformat[10];
-char *format24 = "%.8e";
-#ifdef DEC
-char *format53 = "%.17e";
-#else
-char *format53 = "%.16e";
-#endif
-char *fformat24 = "%e";
-char *fformat53 = "%le";
-char *pct = "%";
-char *quo = "\042";
-#if LDOUBLE
-char *format64 = "%.20Le";
-char *fformat64 = "%Le";
-#endif
-char *format;
-char *fformat;
-char *toomany = "Too many errors; aborting this test.\n";
-
-static int mnrflag;
-static int etrflag;
-void chkit(), printerr(), mnrand(), etrand(), shownoncrit();
-void chkid(), pvec();
-
-main()
-{
-int i, iprec;
-
-printf( "Steve Moshier's printf/scanf tester, version 0.2.\n\n" );
-#ifdef DEC
- /* DEC PDP-11/VAX single precision not yet implemented */
-for( iprec = 1; iprec<2; iprec++ )
-#else
-for( iprec = 0; iprec<3; iprec++ )
-#endif
- {
- errscan = 0;
- identerr = 0;
- errprint = 0;
- eclear( rprint );
- eclear( rscan );
-
-switch( iprec )
- {
- case 0:
- SPREC = 8; /* # digits after the decimal point */
- mprec = 24; /* # bits in the significand */
- m = 9; /* max # decimal digits for correct rounding */
- n = 13; /* max power of ten for correct rounding */
- k2 = -125; /* underflow beyond 2^-k2 */
- format = format24; /* printf format string */
- fformat = fformat24; /* scanf format string */
- mnrflag = 1; /* sets interval for random numbers */
- etrflag = 1;
- printf( "Testing FLOAT precision.\n" );
- break;
-
- case 1:
-#ifdef DEC
- SPREC = 17;
- mprec = 56;
- m = 17;
- n = 27;
- k2 = -125;
- format = format53;
- fformat = fformat53;
- mnrflag = 2;
- etrflag = 1;
- printf( "Testing DEC DOUBLE precision.\n" );
- break;
-#else
- SPREC = 16;
- mprec = 53;
- m = 17;
- n = 27;
- k2 = -1021;
- format = format53;
- fformat = fformat53;
- mnrflag = 2;
- etrflag = 2;
- printf( "Testing DOUBLE precision.\n" );
- break;
-#endif
- case 2:
-#if LDOUBLE
- SPREC = 20;
- mprec = 64;
- m = 20;
- n = 34;
- k2 = -16382;
- format = format64;
- fformat = fformat64;
- mnrflag = 3;
- etrflag = 3;
- printf( "Testing LONG DOUBLE precision.\n" );
- break;
-#else
- goto nodenorm;
-#endif
- }
-
- asctoe( Ten, eten );
-/* 10^m - 1 */
- d2 = m;
- e53toe( &d2, e1 );
- epow( eten, e1, maxm );
- esub( eone, maxm, maxm );
-
-/* test 1 */
- printf( "1. Checking 10^n - 1 for n = %d to %d.\n", -m, m );
- emov( eone, q5 );
- for( count=0; count<=m; count++ )
- {
- esub( eone, q5, fullp );
- chkit( 1 );
- ediv( q5, eone, q2 );
- esub( eone, q2, fullp );
- chkit( 1 );
- emul( eten, q5, q5 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end1;
- }
- }
-end1:
- printerr();
-
-
-/* test 2 */
- printf( "2. Checking powers of 10 from 10^-%d to 10^%d.\n", n, n );
- emov( eone, q5 );
- for( count=0; count<=n; count++ )
- {
- emov( q5, fullp );
- chkit( 2 );
- ediv( q5, eone, fullp );
- chkit( 2 );
- emul( eten, q5, q5 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end2;
- }
- }
-end2:
- printerr();
-
-/* test 3 */
- printf( "3. Checking (10^%d-1)*10^n from n = -%d to %d.\n", m, n, n );
- emov( eone, q5 );
- for( count= -n; count<=n; count++ )
- {
- emul( maxm, q5, fullp );
- chkit( 3 );
- emov( q5, fullp );
- ediv( fullp, eone, fullp );
- emul( maxm, fullp, fullp );
- chkit( 3 );
- emul( eten, q5, q5 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end3;
- }
- }
-end3:
- printerr();
-
-
-
-/* test 4 */
- printf( "4. Checking powers of 2 from 2^-24 to 2^+56.\n" );
- d1 = -24.0;
- e53toe( &d1, q1 );
- epow( etwo, q1, q5 );
-
- for( count = -24; count <= 56; count++ )
- {
- emov( q5, fullp );
- chkit( 4 );
- emul( etwo, q5, q5 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end4;
- }
- }
-end4:
- printerr();
-
-
-/* test 5 */
- printf( "5. Checking 2^n - 1 for n = 0 to %d.\n", mprec );
- emov( eone, q5 );
- for( count=0; count<=mprec; count++ )
- {
- esub( eone, q5, fullp );
- chkit( 5 );
- emul( etwo, q5, q5 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end5;
- }
- }
-end5:
- printerr();
-
-/* test 6 */
- printf( "6. Checking 2^n + 1 for n = 0 to %d.\n", mprec );
- emov( eone, q5 );
- for( count=0; count<=mprec; count++ )
- {
- eadd( eone, q5, fullp );
- chkit( 6 );
- emul( etwo, q5, q5 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end6;
- }
- }
-end6:
- printerr();
-
-/* test 7 */
- printf(
- "7. Checking %d values M * 10^N with random integer M and N,\n",
- NRAND );
- printf(" 1 <= M <= 10^%d - 1 and -%d <= N <= +%d.\n", m, n, n );
- for( i=0; i<NRAND; i++ )
- {
- mnrand( fullp );
- chkit( 7 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end7;
- }
- }
-end7:
- printerr();
-
-/* test 8 */
- printf("8. Checking critical rounding cases.\n" );
- for( i=0; i<20; i++ )
- {
- mnrand( fullp );
- eabs( fullp );
- if( ecmp( fullp, eone ) < 0 )
- ediv( fullp, eone, fullp );
- efloor( fullp, fullp );
- eadd( ehalf, fullp, fullp );
- chkit( 8 );
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto end8;
- }
- }
-end8:
- printerr();
-
-
-
-/* test 9 */
- printf("9. Testing on %d random non-denormal values.\n", NRAND );
- for( i=0; i<NRAND; i++ )
- {
- etrand( fullp );
- chkit( 9 );
- }
- printerr();
- shownoncrit();
-
-/* test 10 */
- printf(
- "Do you want to check denormal numbers in this precision ? (y/n) " );
- gets( str0 );
- if( str0[0] != 'y' )
- goto nodenorm;
-
- printf( "10. Checking denormal numbers.\n" );
-
-/* Form 2^-starting power */
- d1 = k2;
- e53toe( &d1, q1 );
- epow( etwo, q1, e1 );
-
-/* Find 2^-mprec less than starting power */
- d1 = -mprec + 4;
- e53toe( &d1, q1 );
- epow( etwo, q1, e3 );
- emul( e1, e3, e3 );
- emov( e3, e2 );
- ediv( etwo, e2, e2 );
-
- while( ecmp(e1,e2) != 0 )
- {
- eadd( e1, e2, fullp );
- switch( mprec )
- {
-#if LDOUBLE
- case 64:
- etoe64( e1, &sprec64 );
- e64toe( &sprec64, q1 );
- etoe64( fullp, &prec64 );
- e64toe( &prec64, q2 );
- break;
-#endif
-#ifdef DEC
- case 56:
-#endif
- case 53:
- etoe53( e1, &sprec53 );
- e53toe( &sprec53, q1 );
- etoe53( fullp, &prec53 );
- e53toe( &prec53, q2 );
- break;
-
- case 24:
- etoe24( e1, &sprec24 );
- e24toe( &sprec24, q1 );
- etoe24( fullp, &prec24 );
- e24toe( &prec24, q2 );
- break;
- }
- if( ecmp( q2, ezero ) == 0 )
- goto maxden;
- chkit(10);
- if( ecmp(q1,q2) == 0 )
- {
- ediv( etwo, e1, e1 );
- emov( e3, e2 );
- }
- if( errtot >= MAXERR )
- {
- printf( "%s", toomany );
- goto maxden;
- }
- ediv( etwo, e2, e2 );
- }
-maxden:
- printerr();
-nodenorm:
- printf( "\n" );
- } /* loop on precision */
-printf( "End of test.\n" );
-}
-
-#if CHKINTERNAL
-long double xprec64;
-double xprec53;
-float xprec24;
-
-/* Check binary -> printf -> scanf -> binary identity
- * of internal routines
- */
-void chkinternal( ref, tst, string )
-unsigned short ref[], tst[];
-char *string;
-{
-
-if( ecmp(ref,tst) != 0 )
- {
- printf( "internal identity compare error!\n" );
- chkid( ref, tst, string );
- }
-}
-#endif
-
-
-/* Check binary -> printf -> scanf -> binary identity
- */
-void chkid( print, scan, string )
-unsigned short print[], scan[];
-char *string;
-{
-/* Test printf-scanf identity */
-if( ecmp( print, scan ) != 0 )
- {
- pvec( print, NE );
- printf( " ->printf-> %s ->scanf->\n", string );
- pvec( scan, NE );
- printf( " is not an identity.\n" );
- ++identerr;
- }
-}
-
-
-/* Check scanf result
- */
-void chkscan( ref, tst, string )
-unsigned short ref[], tst[];
-char *string;
-{
-/* Test scanf() */
-if( ecmp( ref, tst ) != 0 )
- {
- printf( "scanf(%s) -> ", string );
- pvec( tst, NE );
- printf( "\n should be " );
- pvec( ref, NE );
- printf( ".\n" );
- ++errscan;
- ++errtot;
- }
-}
-
-
-/* Test printf() result
- */
-void chkprint( ref, tst, string )
-unsigned short ref[], tst[];
-char *string;
-{
-if( ecmp(ref, tst) != 0 )
- {
- printf( "printf( ");
- pvec( ref, NE );
- printf( ") -> %s\n", string );
- printf( " = " );
- pvec( tst, NE );
- printf( ".\n" );
- ++errprint;
- ++errtot;
- }
-}
-
-
-/* Print array of n 16-bit shorts
- */
-void pvec( x, n )
-unsigned short x[];
-int n;
-{
-int i;
-
-for( i=0; i<n; i++ )
- {
- printf( "%04x ", x[i] );
- }
-}
-
-/* Measure worst case printf rounding error
- */
-void cmpprint( ref, tst )
-unsigned short ref[], tst[];
-{
-unsigned short e[NE];
-
-if( ecmp( ref, ezero ) != 0 )
- {
- esub( ref, tst, e );
- ediv( ref, e, e );
- eabs( e );
- if( ecmp( e, rprint ) > 0 )
- emov( e, rprint );
- }
-}
-
-/* Measure worst case scanf rounding error
- */
-void cmpscan( ref, tst )
-unsigned short ref[], tst[];
-{
-unsigned short er[NE];
-
-if( ecmp( ref, ezero ) != 0 )
- {
- esub( ref, tst, er );
- ediv( ref, er, er );
- eabs( er );
- if( ecmp( er, rscan ) > 0 )
- emov( er, rscan );
- if( ecmp( er, ehalf ) > 0 )
- {
- etoasc( tst, str1, 21 );
- printf( "Bad error: scanf(%s) = %s !\n", str0, str1 );
- }
- }
-}
-
-/* Check rounded-down decimal string output of printf
- */
-void cmptrunc( ref, tst )
-unsigned short ref[], tst[];
-{
-if( ecmp( ref, tst ) != 0 )
- {
- printf( "printf(%s%s%s, %s) -> %s\n", quo, tformat, quo, str1, str2 );
- printf( "should be %s .\n", str3 );
- errprint += 1;
- }
-}
-
-
-void shownoncrit()
-{
-
-etoasc( rprint, str0, 3 );
-printf( "Maximum relative printf error found = %s .\n", str0 );
-etoasc( rscan, str0, 3 );
-printf( "Maximum relative scanf error found = %s .\n", str0 );
-}
-
-
-
-/* Produce arguments and call comparison subroutines.
- */
-void chkit( testno )
-int testno;
-{
-unsigned short t[NE], u[NE], v[NE];
-int j;
-
-switch( mprec )
- {
-#if LDOUBLE
- case 64:
- etoe64( fullp, &prec64 );
- e64toe( &prec64, rounded );
-#if CHKINTERNAL
- e64toasc( &prec64, str1, SPREC );
- asctoe64( str1, &xprec64 );
- e64toe( &xprec64, t );
- chkinternal( rounded, t, str1 );
-#endif
-/* check printf and scanf */
- sprintf( str2, format, prec64 );
- sscanf( str2, fformat, &sprec64 );
- e64toe( &sprec64, u );
- chkid( rounded, u, str2 );
- asctoe64( str2, &ssprec64 );
- e64toe( &ssprec64, v );
- chkscan( v, u, str2 );
- chkprint( rounded, v, str2 );
- if( testno < 8 )
- break;
-/* rounding error measurement */
- etoasc( fullp, str0, 24 );
- etoe64( fullp, &ssprec64 );
- e64toe( &ssprec64, u );
- sprintf( str2, format, ssprec64 );
- asctoe( str2, t );
- cmpprint( u, t );
- sscanf( str0, fformat, &sprec64 );
- e64toe( &sprec64, t );
- cmpscan( fullp, t );
- if( testno < 8 )
- break;
-/* strings rounded to less than maximum precision */
- e64toasc( &ssprec64, str1, 24 );
- for( j=SPREC-1; j>0; j-- )
- {
- e64toasc( &ssprec64, str3, j );
- asctoe( str3, v );
- sprintf( tformat, "%s.%dLe", pct, j );
- sprintf( str2, tformat, ssprec64 );
- asctoe( str2, t );
- cmptrunc( v, t );
- }
- break;
-#endif
-#ifdef DEC
- case 56:
-#endif
- case 53:
- etoe53( fullp, &prec53 );
- e53toe( &prec53, rounded );
-#if CHKINTERNAL
- e53toasc( &prec53, str1, SPREC );
- asctoe53( str1, &xprec53 );
- e53toe( &xprec53, t );
- chkinternal( rounded, t, str1 );
-#endif
- sprintf( str2, format, prec53 );
- sscanf( str2, fformat, &sprec53 );
- e53toe( &sprec53, u );
- chkid( rounded, u, str2 );
- asctoe53( str2, &ssprec53 );
- e53toe( &ssprec53, v );
- chkscan( v, u, str2 );
- chkprint( rounded, v, str2 );
- if( testno < 8 )
- break;
-/* rounding error measurement */
- etoasc( fullp, str0, 24 );
- etoe53( fullp, &ssprec53 );
- e53toe( &ssprec53, u );
- sprintf( str2, format, ssprec53 );
- asctoe( str2, t );
- cmpprint( u, t );
- sscanf( str0, fformat, &sprec53 );
- e53toe( &sprec53, t );
- cmpscan( fullp, t );
- if( testno < 8 )
- break;
- e53toasc( &ssprec53, str1, 24 );
- for( j=SPREC-1; j>0; j-- )
- {
- e53toasc( &ssprec53, str3, j );
- asctoe( str3, v );
- sprintf( tformat, "%s.%de", pct, j );
- sprintf( str2, tformat, ssprec53 );
- asctoe( str2, t );
- cmptrunc( v, t );
- }
- break;
-
- case 24:
- etoe24( fullp, &prec24 );
- e24toe( &prec24, rounded );
-#if CHKINTERNAL
- e24toasc( &prec24, str1, SPREC );
- asctoe24( str1, &xprec24 );
- e24toe( &xprec24, t );
- chkinternal( rounded, t, str1 );
-#endif
- sprintf( str2, format, prec24 );
- sscanf( str2, fformat, &sprec24 );
- e24toe( &sprec24, u );
- chkid( rounded, u, str2 );
- asctoe24( str2, &ssprec24 );
- e24toe( &ssprec24, v );
- chkscan( v, u, str2 );
- chkprint( rounded, v, str2 );
- if( testno < 8 )
- break;
-/* rounding error measurement */
- etoasc( fullp, str0, 24 );
- etoe24( fullp, &ssprec24 );
- e24toe( &ssprec24, u );
- sprintf( str2, format, ssprec24 );
- asctoe( str2, t );
- cmpprint( u, t );
- sscanf( str0, fformat, &sprec24 );
- e24toe( &sprec24, t );
- cmpscan( fullp, t );
-/*
- if( testno < 8 )
- break;
-*/
- e24toasc( &ssprec24, str1, 24 );
- for( j=SPREC-1; j>0; j-- )
- {
- e24toasc( &ssprec24, str3, j );
- asctoe( str3, v );
- sprintf( tformat, "%s.%de", pct, j );
- sprintf( str2, tformat, ssprec24 );
- asctoe( str2, t );
- cmptrunc( v, t );
- }
- break;
- }
-}
-
-
-void printerr()
-{
-if( (errscan == 0) && (identerr == 0) && (errprint == 0) )
- printf( "No errors found.\n" );
-else
- {
- printf( "%d binary -> decimal errors found.\n", errprint );
- printf( "%d decimal -> binary errors found.\n", errscan );
- }
-errscan = 0; /* reset for next test */
-identerr = 0;
-errprint = 0;
-errtot = 0;
-}
-
-
-/* Random number generator
- * in the range M * 10^N, where 1 <= M <= 10^17 - 1
- * and -27 <= N <= +27. Test values of M are logarithmically distributed
- * random integers; test values of N are uniformly distributed random integers.
- */
-
-static char *fwidth = "1.036163291797320557783096e1"; /* log(sqrt(10^9-1)) */
-static char *dwidth = "1.957197329044938830915E1"; /* log(sqrt(10^17-1)) */
-static char *ldwidth = "2.302585092994045684017491e1"; /* log(sqrt(10^20-1)) */
-
-static char *a13 = "13.0";
-static char *a27 = "27.0";
-static char *a34 = "34.0";
-static char *a10m13 = "1.0e-13";
-static unsigned short LOW[ NE ], WIDTH[NE], e27[NE], e10m13[NE];
-
-
-void mnrand( erand )
-unsigned short erand[];
-{
-unsigned short ea[NE], em[NE], en[NE], ex[NE];
-double x, a;
-
-if( mnrflag )
- {
- if( mnrflag == 3 )
- {
- asctoe( ldwidth, WIDTH );
- asctoe( a34, e27 );
- }
- if( mnrflag == 2 )
- {
- asctoe( dwidth, WIDTH );
- asctoe( a27, e27 );
- }
- if( mnrflag == 1 )
- {
- asctoe( fwidth, WIDTH );
- asctoe( a13, e27 );
- }
- asctoe( a10m13, e10m13 );
- mnrflag = 0;
- }
-drand( &x );
-e53toe( &x, ex ); /* x = WIDTH * ( x - 1.0 ) + LOW; */
-esub( eone, ex, ex );
-emul( WIDTH, ex, ex );
-eexp( ex, ex ); /* x = exp(x); */
-
-drand( &a );
-e53toe( &a, ea );
-emul( ea, ex, ea ); /* a = 1.0e-13 * x * a; */
-emul( e10m13, ea, ea );
-eabs( ea );
-eadd( ea, ex, ex ); /* add fuzz */
-emul( ex, ex, ex ); /* square it, to get range to 10^17 - 1 */
-efloor( ex, em ); /* this is M */
-
-/* Random power of 10 */
-drand( &a );
-e53toe( &a, ex );
-esub( eone, ex, ex ); /* y3 = 54.0 * ( y3 - 1.0 ) + 0.5; */
-emul( e27, ex, ex );
-eadd( ex, ex, ex );
-eadd( ehalf, ex, ex );
-efloor( ex, ex ); /* y3 = floor( y3 ) - 27.0; */
-esub( e27, ex, en ); /* this is N */
-epow( eten, en, ex );
-emul( ex, em, erand );
-}
-
-/* -ln 2^16382 */
-char *ldemin = "-1.1355137111933024058873097E4";
-char *ldewid = "2.2710274223866048117746193E4";
-/* -ln 2^1022 */
-char *demin = "-7.0839641853226410622441123E2";
-char *dewid = "1.4167928370645282124488225E3";
-/* -ln 2^125 */
-char *femin = "-8.6643397569993163677154015E1";
-char *fewid = "1.7328679513998632735430803E2";
-
-void etrand( erand )
-unsigned short erand[];
-{
-unsigned short ea[NE], ex[NE];
-double x, a;
-
-if( etrflag )
- {
- if( etrflag == 3 )
- {
- asctoe( ldemin, LOW );
- asctoe( ldewid, WIDTH );
- asctoe( a34, e27 );
- }
- if( etrflag == 2 )
- {
- asctoe( demin, LOW );
- asctoe( dewid, WIDTH );
- asctoe( a27, e27 );
- }
- if( etrflag == 1 )
- {
- asctoe( femin, LOW );
- asctoe( fewid, WIDTH );
- asctoe( a13, e27 );
- }
- asctoe( a10m13, e10m13 );
- etrflag = 0;
- }
-drand( &x );
-e53toe( &x, ex ); /* x = WIDTH * ( x - 1.0 ) + LOW; */
-esub( eone, ex, ex );
-emul( WIDTH, ex, ex );
-eadd( LOW, ex, ex );
-eexp( ex, ex ); /* x = exp(x); */
-
-/* add fuzz
- */
-drand( &a );
-e53toe( &a, ea );
-emul( ea, ex, ea ); /* a = 1.0e-13 * x * a; */
-emul( e10m13, ea, ea );
-if( ecmp( ex, ezero ) > 0 )
- eneg( ea );
-eadd( ea, ex, erand );
-}
-
+/* Floating point to ASCII input and output string test program.
+ *
+ * Numbers in the native machine data structure are converted
+ * to e type, then to and from decimal ASCII strings. Native
+ * printf() and scanf() functions are also used to produce
+ * and read strings. The resulting e type binary values
+ * are compared, with diagnostic printouts of any discrepancies.
+ *
+ * Steve Moshier, 16 Dec 88
+ * last revision: 16 May 92
+ */
+
+#include "ehead.h"
+#include "mconf.h"
+
+/* Include tests of 80-bit long double precision: */
+#define LDOUBLE 0
+/* Abort subtest after getting this many errors: */
+#define MAXERR 5
+/* Number of random arguments to try (set as large as you have
+ * patience for): */
+#define NRAND 100
+/* Perform internal consistency test: */
+#define CHKINTERNAL 0
+
+static unsigned short fullp[NE], rounded[NE];
+float prec24, sprec24, ssprec24;
+double prec53, sprec53, ssprec53;
+#if LDOUBLE
+long double prec64, sprec64, ssprec64;
+#endif
+
+static unsigned short rprint[NE], rscan[NE];
+static unsigned short q1[NE], q2[NE], q5[NE];
+static unsigned short e1[NE], e2[NE], e3[NE];
+static double d1, d2;
+static int errprint = 0;
+static int errscan = 0;
+static int identerr = 0;
+static int errtot = 0;
+static int count = 0;
+static char str0[80], str1[80], str2[80], str3[80];
+static unsigned short eten[NE], maxm[NE];
+
+int m, n, k2, mprec, SPREC;
+
+char *Ten = "10.0";
+char tformat[10];
+char *format24 = "%.8e";
+#ifdef DEC
+char *format53 = "%.17e";
+#else
+char *format53 = "%.16e";
+#endif
+char *fformat24 = "%e";
+char *fformat53 = "%le";
+char *pct = "%";
+char *quo = "\042";
+#if LDOUBLE
+char *format64 = "%.20Le";
+char *fformat64 = "%Le";
+#endif
+char *format;
+char *fformat;
+char *toomany = "Too many errors; aborting this test.\n";
+
+static int mnrflag;
+static int etrflag;
+void chkit(), printerr(), mnrand(), etrand(), shownoncrit();
+void chkid(), pvec();
+
+main()
+{
+int i, iprec;
+
+printf( "Steve Moshier's printf/scanf tester, version 0.2.\n\n" );
+#ifdef DEC
+ /* DEC PDP-11/VAX single precision not yet implemented */
+for( iprec = 1; iprec<2; iprec++ )
+#else
+for( iprec = 0; iprec<3; iprec++ )
+#endif
+ {
+ errscan = 0;
+ identerr = 0;
+ errprint = 0;
+ eclear( rprint );
+ eclear( rscan );
+
+switch( iprec )
+ {
+ case 0:
+ SPREC = 8; /* # digits after the decimal point */
+ mprec = 24; /* # bits in the significand */
+ m = 9; /* max # decimal digits for correct rounding */
+ n = 13; /* max power of ten for correct rounding */
+ k2 = -125; /* underflow beyond 2^-k2 */
+ format = format24; /* printf format string */
+ fformat = fformat24; /* scanf format string */
+ mnrflag = 1; /* sets interval for random numbers */
+ etrflag = 1;
+ printf( "Testing FLOAT precision.\n" );
+ break;
+
+ case 1:
+#ifdef DEC
+ SPREC = 17;
+ mprec = 56;
+ m = 17;
+ n = 27;
+ k2 = -125;
+ format = format53;
+ fformat = fformat53;
+ mnrflag = 2;
+ etrflag = 1;
+ printf( "Testing DEC DOUBLE precision.\n" );
+ break;
+#else
+ SPREC = 16;
+ mprec = 53;
+ m = 17;
+ n = 27;
+ k2 = -1021;
+ format = format53;
+ fformat = fformat53;
+ mnrflag = 2;
+ etrflag = 2;
+ printf( "Testing DOUBLE precision.\n" );
+ break;
+#endif
+ case 2:
+#if LDOUBLE
+ SPREC = 20;
+ mprec = 64;
+ m = 20;
+ n = 34;
+ k2 = -16382;
+ format = format64;
+ fformat = fformat64;
+ mnrflag = 3;
+ etrflag = 3;
+ printf( "Testing LONG DOUBLE precision.\n" );
+ break;
+#else
+ goto nodenorm;
+#endif
+ }
+
+ asctoe( Ten, eten );
+/* 10^m - 1 */
+ d2 = m;
+ e53toe( &d2, e1 );
+ epow( eten, e1, maxm );
+ esub( eone, maxm, maxm );
+
+/* test 1 */
+ printf( "1. Checking 10^n - 1 for n = %d to %d.\n", -m, m );
+ emov( eone, q5 );
+ for( count=0; count<=m; count++ )
+ {
+ esub( eone, q5, fullp );
+ chkit( 1 );
+ ediv( q5, eone, q2 );
+ esub( eone, q2, fullp );
+ chkit( 1 );
+ emul( eten, q5, q5 );
+ if( errtot >= MAXERR )
+ {
+ printf( "%s", toomany );
+ goto end1;
+ }
+ }
+end1:
+ printerr();
+
+
+/* test 2 */
+ printf( "2. Checking powers of 10 from 10^-%d to 10^%d.\n", n, n );
+ emov( eone, q5 );
+ for( count=0; count<=n; count++ )
+ {
+ emov( q5, fullp );
+ chkit( 2 );
+ ediv( q5, eone, fullp );
+ chkit( 2 );
+ emul( eten, q5, q5 );
+ if( errtot >= MAXERR )
+ {
+ printf( "%s", toomany );
+ goto end2;
+ }
+ }
+end2:
+ printerr();
+
+/* test 3 */
+ printf( "3. Checking (10^%d-1)*10^n from n = -%d to %d.\n", m, n, n );
+ emov( eone, q5 );
+ for( count= -n; count<=n; count++ )
+ {
+ emul( maxm, q5, fullp );
+ chkit( 3 );
+ emov( q5, fullp );
+ ediv( fullp, eone, fullp );
+ emul( maxm, fullp, fullp );
+ chkit( 3 );
+ emul( eten, q5, q5 );
+ if( errtot >= MAXERR )
+ {
+ printf( "%s", toomany );
+ goto end3;
+ }
+ }
+end3:
+ printerr();
+
+
+
+/* test 4 */
+ printf( "4. Checking powers of 2 from 2^-24 to 2^+56.\n" );
+ d1 = -24.0;
+ e53toe( &d1, q1 );
+ epow( etwo, q1, q5 );
+
+ for( count = -24; count <= 56; count++ )
+ {
+ emov( q5, fullp );
+ chkit( 4 );
+ emul( etwo, q5, q5 );
+ if( errtot >= MAXERR )
+ {
+ printf( "%s", toomany );
+ goto end4;
+ }
+ }
+end4:
+ printerr();
+
+
+/* test 5 */
+ printf( "5. Checking 2^n - 1 for n = 0 to %d.\n", mprec );
+ emov( eone, q5 );
+ for( count=0; count<=mprec; count++ )
+ {
+ esub( eone, q5, fullp );
+ chkit( 5 );
+ emul( etwo, q5, q5 );
+ if( errtot >= MAXERR )
+ {
+ printf( "%s", toomany );
+ goto end5;
+ }
+ }
+end5:
+ printerr();
+
+/* test 6 */
+ printf( "6. Checking 2^n + 1 for n = 0 to %d.\n", mprec );
+ emov( eone, q5 );
+ for( count=0; count<=mprec; count++ )
+ {
+ eadd( eone, q5, fullp );
+ chkit( 6 );
+ emul( etwo, q5, q5 );
+ if( errtot >= MAXERR )
+ {
+ printf( "%s", toomany );
+ goto end6;
+ }
+ }
+end6:
+ printerr();
+
+/* test 7 */
+ printf(
+ "7. Checking %d values M * 10^N with random integer M and N,\n",
+ NRAND );
+ printf(" 1 <= M <= 10^%d - 1 and -%d <= N <= +%d.\n", m, n, n );
+ for( i=0; i<NRAND; i++ )
+ {
+ mnrand( fullp );
+ chkit( 7 );
+ if( errtot >= MAXERR )
+ {
+ printf( "%s", toomany );
+ goto end7;
+ }
+ }
+end7:
+ printerr();
+
+/* test 8 */
+ printf("8. Checking critical rounding cases.\n" );
+ for( i=0; i<20; i++ )
+ {
+ mnrand( fullp );
+ eabs( fullp );
+ if( ecmp( fullp, eone ) < 0 )
+ ediv( fullp, eone, fullp );
+ efloor( fullp, fullp );
+ eadd( ehalf, fullp, fullp );
+ chkit( 8 );
+ if( errtot >= MAXERR )
+ {
+ printf( "%s", toomany );
+ goto end8;
+ }
+ }
+end8:
+ printerr();
+
+
+
+/* test 9 */
+ printf("9. Testing on %d random non-denormal values.\n", NRAND );
+ for( i=0; i<NRAND; i++ )
+ {
+ etrand( fullp );
+ chkit( 9 );
+ }
+ printerr();
+ shownoncrit();
+
+/* test 10 */
+ printf(
+ "Do you want to check denormal numbers in this precision ? (y/n) " );
+ gets( str0 );
+ if( str0[0] != 'y' )
+ goto nodenorm;
+
+ printf( "10. Checking denormal numbers.\n" );
+
+/* Form 2^-starting power */
+ d1 = k2;
+ e53toe( &d1, q1 );
+ epow( etwo, q1, e1 );
+
+/* Find 2^-mprec less than starting power */
+ d1 = -mprec + 4;
+ e53toe( &d1, q1 );
+ epow( etwo, q1, e3 );
+ emul( e1, e3, e3 );
+ emov( e3, e2 );
+ ediv( etwo, e2, e2 );
+
+ while( ecmp(e1,e2) != 0 )
+ {
+ eadd( e1, e2, fullp );
+ switch( mprec )
+ {
+#if LDOUBLE
+ case 64:
+ etoe64( e1, &sprec64 );
+ e64toe( &sprec64, q1 );
+ etoe64( fullp, &prec64 );
+ e64toe( &prec64, q2 );
+ break;
+#endif
+#ifdef DEC
+ case 56:
+#endif
+ case 53:
+ etoe53( e1, &sprec53 );
+ e53toe( &sprec53, q1 );
+ etoe53( fullp, &prec53 );
+ e53toe( &prec53, q2 );
+ break;
+
+ case 24:
+ etoe24( e1, &sprec24 );
+ e24toe( &sprec24, q1 );
+ etoe24( fullp, &prec24 );
+ e24toe( &prec24, q2 );
+ break;
+ }
+ if( ecmp( q2, ezero ) == 0 )
+ goto maxden;
+ chkit(10);
+ if( ecmp(q1,q2) == 0 )
+ {
+ ediv( etwo, e1, e1 );
+ emov( e3, e2 );
+ }
+ if( errtot >= MAXERR )
+ {
+ printf( "%s", toomany );
+ goto maxden;
+ }
+ ediv( etwo, e2, e2 );
+ }
+maxden:
+ printerr();
+nodenorm:
+ printf( "\n" );
+ } /* loop on precision */
+printf( "End of test.\n" );
+}
+
+#if CHKINTERNAL
+long double xprec64;
+double xprec53;
+float xprec24;
+
+/* Check binary -> printf -> scanf -> binary identity
+ * of internal routines
+ */
+void chkinternal( ref, tst, string )
+unsigned short ref[], tst[];
+char *string;
+{
+
+if( ecmp(ref,tst) != 0 )
+ {
+ printf( "internal identity compare error!\n" );
+ chkid( ref, tst, string );
+ }
+}
+#endif
+
+
+/* Check binary -> printf -> scanf -> binary identity
+ */
+void chkid( print, scan, string )
+unsigned short print[], scan[];
+char *string;
+{
+/* Test printf-scanf identity */
+if( ecmp( print, scan ) != 0 )
+ {
+ pvec( print, NE );
+ printf( " ->printf-> %s ->scanf->\n", string );
+ pvec( scan, NE );
+ printf( " is not an identity.\n" );
+ ++identerr;
+ }
+}
+
+
+/* Check scanf result
+ */
+void chkscan( ref, tst, string )
+unsigned short ref[], tst[];
+char *string;
+{
+/* Test scanf() */
+if( ecmp( ref, tst ) != 0 )
+ {
+ printf( "scanf(%s) -> ", string );
+ pvec( tst, NE );
+ printf( "\n should be " );
+ pvec( ref, NE );
+ printf( ".\n" );
+ ++errscan;
+ ++errtot;
+ }
+}
+
+
+/* Test printf() result
+ */
+void chkprint( ref, tst, string )
+unsigned short ref[], tst[];
+char *string;
+{
+if( ecmp(ref, tst) != 0 )
+ {
+ printf( "printf( ");
+ pvec( ref, NE );
+ printf( ") -> %s\n", string );
+ printf( " = " );
+ pvec( tst, NE );
+ printf( ".\n" );
+ ++errprint;
+ ++errtot;
+ }
+}
+
+
+/* Print array of n 16-bit shorts
+ */
+void pvec( x, n )
+unsigned short x[];
+int n;
+{
+int i;
+
+for( i=0; i<n; i++ )
+ {
+ printf( "%04x ", x[i] );
+ }
+}
+
+/* Measure worst case printf rounding error
+ */
+void cmpprint( ref, tst )
+unsigned short ref[], tst[];
+{
+unsigned short e[NE];
+
+if( ecmp( ref, ezero ) != 0 )
+ {
+ esub( ref, tst, e );
+ ediv( ref, e, e );
+ eabs( e );
+ if( ecmp( e, rprint ) > 0 )
+ emov( e, rprint );
+ }
+}
+
+/* Measure worst case scanf rounding error
+ */
+void cmpscan( ref, tst )
+unsigned short ref[], tst[];
+{
+unsigned short er[NE];
+
+if( ecmp( ref, ezero ) != 0 )
+ {
+ esub( ref, tst, er );
+ ediv( ref, er, er );
+ eabs( er );
+ if( ecmp( er, rscan ) > 0 )
+ emov( er, rscan );
+ if( ecmp( er, ehalf ) > 0 )
+ {
+ etoasc( tst, str1, 21 );
+ printf( "Bad error: scanf(%s) = %s !\n", str0, str1 );
+ }
+ }
+}
+
+/* Check rounded-down decimal string output of printf
+ */
+void cmptrunc( ref, tst )
+unsigned short ref[], tst[];
+{
+if( ecmp( ref, tst ) != 0 )
+ {
+ printf( "printf(%s%s%s, %s) -> %s\n", quo, tformat, quo, str1, str2 );
+ printf( "should be %s .\n", str3 );
+ errprint += 1;
+ }
+}
+
+
+void shownoncrit()
+{
+
+etoasc( rprint, str0, 3 );
+printf( "Maximum relative printf error found = %s .\n", str0 );
+etoasc( rscan, str0, 3 );
+printf( "Maximum relative scanf error found = %s .\n", str0 );
+}
+
+
+
+/* Produce arguments and call comparison subroutines.
+ */
+void chkit( testno )
+int testno;
+{
+unsigned short t[NE], u[NE], v[NE];
+int j;
+
+switch( mprec )
+ {
+#if LDOUBLE
+ case 64:
+ etoe64( fullp, &prec64 );
+ e64toe( &prec64, rounded );
+#if CHKINTERNAL
+ e64toasc( &prec64, str1, SPREC );
+ asctoe64( str1, &xprec64 );
+ e64toe( &xprec64, t );
+ chkinternal( rounded, t, str1 );
+#endif
+/* check printf and scanf */
+ sprintf( str2, format, prec64 );
+ sscanf( str2, fformat, &sprec64 );
+ e64toe( &sprec64, u );
+ chkid( rounded, u, str2 );
+ asctoe64( str2, &ssprec64 );
+ e64toe( &ssprec64, v );
+ chkscan( v, u, str2 );
+ chkprint( rounded, v, str2 );
+ if( testno < 8 )
+ break;
+/* rounding error measurement */
+ etoasc( fullp, str0, 24 );
+ etoe64( fullp, &ssprec64 );
+ e64toe( &ssprec64, u );
+ sprintf( str2, format, ssprec64 );
+ asctoe( str2, t );
+ cmpprint( u, t );
+ sscanf( str0, fformat, &sprec64 );
+ e64toe( &sprec64, t );
+ cmpscan( fullp, t );
+ if( testno < 8 )
+ break;
+/* strings rounded to less than maximum precision */
+ e64toasc( &ssprec64, str1, 24 );
+ for( j=SPREC-1; j>0; j-- )
+ {
+ e64toasc( &ssprec64, str3, j );
+ asctoe( str3, v );
+ sprintf( tformat, "%s.%dLe", pct, j );
+ sprintf( str2, tformat, ssprec64 );
+ asctoe( str2, t );
+ cmptrunc( v, t );
+ }
+ break;
+#endif
+#ifdef DEC
+ case 56:
+#endif
+ case 53:
+ etoe53( fullp, &prec53 );
+ e53toe( &prec53, rounded );
+#if CHKINTERNAL
+ e53toasc( &prec53, str1, SPREC );
+ asctoe53( str1, &xprec53 );
+ e53toe( &xprec53, t );
+ chkinternal( rounded, t, str1 );
+#endif
+ sprintf( str2, format, prec53 );
+ sscanf( str2, fformat, &sprec53 );
+ e53toe( &sprec53, u );
+ chkid( rounded, u, str2 );
+ asctoe53( str2, &ssprec53 );
+ e53toe( &ssprec53, v );
+ chkscan( v, u, str2 );
+ chkprint( rounded, v, str2 );
+ if( testno < 8 )
+ break;
+/* rounding error measurement */
+ etoasc( fullp, str0, 24 );
+ etoe53( fullp, &ssprec53 );
+ e53toe( &ssprec53, u );
+ sprintf( str2, format, ssprec53 );
+ asctoe( str2, t );
+ cmpprint( u, t );
+ sscanf( str0, fformat, &sprec53 );
+ e53toe( &sprec53, t );
+ cmpscan( fullp, t );
+ if( testno < 8 )
+ break;
+ e53toasc( &ssprec53, str1, 24 );
+ for( j=SPREC-1; j>0; j-- )
+ {
+ e53toasc( &ssprec53, str3, j );
+ asctoe( str3, v );
+ sprintf( tformat, "%s.%de", pct, j );
+ sprintf( str2, tformat, ssprec53 );
+ asctoe( str2, t );
+ cmptrunc( v, t );
+ }
+ break;
+
+ case 24:
+ etoe24( fullp, &prec24 );
+ e24toe( &prec24, rounded );
+#if CHKINTERNAL
+ e24toasc( &prec24, str1, SPREC );
+ asctoe24( str1, &xprec24 );
+ e24toe( &xprec24, t );
+ chkinternal( rounded, t, str1 );
+#endif
+ sprintf( str2, format, prec24 );
+ sscanf( str2, fformat, &sprec24 );
+ e24toe( &sprec24, u );
+ chkid( rounded, u, str2 );
+ asctoe24( str2, &ssprec24 );
+ e24toe( &ssprec24, v );
+ chkscan( v, u, str2 );
+ chkprint( rounded, v, str2 );
+ if( testno < 8 )
+ break;
+/* rounding error measurement */
+ etoasc( fullp, str0, 24 );
+ etoe24( fullp, &ssprec24 );
+ e24toe( &ssprec24, u );
+ sprintf( str2, format, ssprec24 );
+ asctoe( str2, t );
+ cmpprint( u, t );
+ sscanf( str0, fformat, &sprec24 );
+ e24toe( &sprec24, t );
+ cmpscan( fullp, t );
+/*
+ if( testno < 8 )
+ break;
+*/
+ e24toasc( &ssprec24, str1, 24 );
+ for( j=SPREC-1; j>0; j-- )
+ {
+ e24toasc( &ssprec24, str3, j );
+ asctoe( str3, v );
+ sprintf( tformat, "%s.%de", pct, j );
+ sprintf( str2, tformat, ssprec24 );
+ asctoe( str2, t );
+ cmptrunc( v, t );
+ }
+ break;
+ }
+}
+
+
+void printerr()
+{
+if( (errscan == 0) && (identerr == 0) && (errprint == 0) )
+ printf( "No errors found.\n" );
+else
+ {
+ printf( "%d binary -> decimal errors found.\n", errprint );
+ printf( "%d decimal -> binary errors found.\n", errscan );
+ }
+errscan = 0; /* reset for next test */
+identerr = 0;
+errprint = 0;
+errtot = 0;
+}
+
+
+/* Random number generator
+ * in the range M * 10^N, where 1 <= M <= 10^17 - 1
+ * and -27 <= N <= +27. Test values of M are logarithmically distributed
+ * random integers; test values of N are uniformly distributed random integers.
+ */
+
+static char *fwidth = "1.036163291797320557783096e1"; /* log(sqrt(10^9-1)) */
+static char *dwidth = "1.957197329044938830915E1"; /* log(sqrt(10^17-1)) */
+static char *ldwidth = "2.302585092994045684017491e1"; /* log(sqrt(10^20-1)) */
+
+static char *a13 = "13.0";
+static char *a27 = "27.0";
+static char *a34 = "34.0";
+static char *a10m13 = "1.0e-13";
+static unsigned short LOW[ NE ], WIDTH[NE], e27[NE], e10m13[NE];
+
+
+void mnrand( erand )
+unsigned short erand[];
+{
+unsigned short ea[NE], em[NE], en[NE], ex[NE];
+double x, a;
+
+if( mnrflag )
+ {
+ if( mnrflag == 3 )
+ {
+ asctoe( ldwidth, WIDTH );
+ asctoe( a34, e27 );
+ }
+ if( mnrflag == 2 )
+ {
+ asctoe( dwidth, WIDTH );
+ asctoe( a27, e27 );
+ }
+ if( mnrflag == 1 )
+ {
+ asctoe( fwidth, WIDTH );
+ asctoe( a13, e27 );
+ }
+ asctoe( a10m13, e10m13 );
+ mnrflag = 0;
+ }
+drand( &x );
+e53toe( &x, ex ); /* x = WIDTH * ( x - 1.0 ) + LOW; */
+esub( eone, ex, ex );
+emul( WIDTH, ex, ex );
+eexp( ex, ex ); /* x = exp(x); */
+
+drand( &a );
+e53toe( &a, ea );
+emul( ea, ex, ea ); /* a = 1.0e-13 * x * a; */
+emul( e10m13, ea, ea );
+eabs( ea );
+eadd( ea, ex, ex ); /* add fuzz */
+emul( ex, ex, ex ); /* square it, to get range to 10^17 - 1 */
+efloor( ex, em ); /* this is M */
+
+/* Random power of 10 */
+drand( &a );
+e53toe( &a, ex );
+esub( eone, ex, ex ); /* y3 = 54.0 * ( y3 - 1.0 ) + 0.5; */
+emul( e27, ex, ex );
+eadd( ex, ex, ex );
+eadd( ehalf, ex, ex );
+efloor( ex, ex ); /* y3 = floor( y3 ) - 27.0; */
+esub( e27, ex, en ); /* this is N */
+epow( eten, en, ex );
+emul( ex, em, erand );
+}
+
+/* -ln 2^16382 */
+char *ldemin = "-1.1355137111933024058873097E4";
+char *ldewid = "2.2710274223866048117746193E4";
+/* -ln 2^1022 */
+char *demin = "-7.0839641853226410622441123E2";
+char *dewid = "1.4167928370645282124488225E3";
+/* -ln 2^125 */
+char *femin = "-8.6643397569993163677154015E1";
+char *fewid = "1.7328679513998632735430803E2";
+
+void etrand( erand )
+unsigned short erand[];
+{
+unsigned short ea[NE], ex[NE];
+double x, a;
+
+if( etrflag )
+ {
+ if( etrflag == 3 )
+ {
+ asctoe( ldemin, LOW );
+ asctoe( ldewid, WIDTH );
+ asctoe( a34, e27 );
+ }
+ if( etrflag == 2 )
+ {
+ asctoe( demin, LOW );
+ asctoe( dewid, WIDTH );
+ asctoe( a27, e27 );
+ }
+ if( etrflag == 1 )
+ {
+ asctoe( femin, LOW );
+ asctoe( fewid, WIDTH );
+ asctoe( a13, e27 );
+ }
+ asctoe( a10m13, e10m13 );
+ etrflag = 0;
+ }
+drand( &x );
+e53toe( &x, ex ); /* x = WIDTH * ( x - 1.0 ) + LOW; */
+esub( eone, ex, ex );
+emul( WIDTH, ex, ex );
+eadd( LOW, ex, ex );
+eexp( ex, ex ); /* x = exp(x); */
+
+/* add fuzz
+ */
+drand( &a );
+e53toe( &a, ea );
+emul( ea, ex, ea ); /* a = 1.0e-13 * x * a; */
+emul( e10m13, ea, ea );
+if( ecmp( ex, ezero ) > 0 )
+ eneg( ea );
+eadd( ea, ex, erand );
+}
+
diff --git a/test/math/ieetst.doc b/test/math/ieetst.doc
index be2388bcc..bd5134beb 100644
--- a/test/math/ieetst.doc
+++ b/test/math/ieetst.doc
@@ -1,132 +1,132 @@
-
- ieetst, version 0.2
-
- This software tests the numerical accuracy of floating point
-binary <-> decimal string conversion, as done by your C language
-library functions printf() and scanf(), for compliance with the
-IEEE arithmetic standards ANSI/IEEE Std 754-1985 and ANSI/IEEE
-Std 854-1987. The test covers 32-bit float, 64-bit double, and
-80-bit long double precision conversions to and from decimal
-ASCII strings.
-
- The test program checks for proper implementation of the
-following specifications of the standards:
-
- (1) correctly rounded conversions of numbers of the form M *
- 10^N, where M and N are integers such that, in double precision,
- for example, |M| < 10^17, |N| <= 27.
-
- (2) binary -> decimal -> binary conversions to be an identity
- if a sufficiently large number of decimal digits is requested.
-
- (3) correctly rounded decimal outputs of less than the maximum
- number of digits
-
- (4) The maximum observed conversion error of numbers outside the
- domain covered by (1) is reported by the test program; it is
- not supposed to exceed 0.97 ulp.
-
-There are 10 separate tests. Tests 1 through 6 use values near
-2^n and 10^n. Test 7 addresses item (1) above. Test 8 checks
-the rounding of exact half-integer numbers. Test 9 is for item
-(4) above. Test 10 checks denormal numbers. Tests 8 through 10
-address item (3) using printf formats that produce outputs of 1,
-2, 3, ... digits after the decimal point. All tests check, when
-appropriate, that the binary output of scanf is the same as the
-binary input to printf, item (2).
-
-Example error messages:
-
- 0000 0000 0000 1000 8000 3f80 ->printf-> 5.87748296e-39 ->scanf->
- 0000 0000 0000 0000 8000 3f6e is not an identity.
-
- scanf(-9.9999900000000003e-01) -> 0000 4800 085f ef39 ffff bffe
- should be 0000 5000 085f ef39 ffff bffe .
-
- printf("%.14e", 6.13592315154256467968352E-3) -> 6.13592315154257e-03
- should be 6.13592315154256E-3 .
-
-Binary values are displayed as four-digit hex groups in the
-little-endian format of the internal reference arithmetic. The
-least significant 16-bit word is first, the exponent is last.
-
- The design of the test program requires knowing the binary
-data structure of the floating point format under test. For
-configuration, check the .h files carefully. All the programs
-need to be told via mconf.h if the numeric format is
-little-endian (IBMPC) or big-endian (MIEEE). If your system
-supports an 80-bit long double precision data type, define
-LDOUBLE 1 in ieetst.c; otherwise define LDOUBLE 0. A provision
-for DEC PDP-11/VAX numbers is implemented (double precision
-only). Conversions for other data structures can be added by
-analogy to the ifdefs for DEC.
-
- Most of the tests rely on comparison with the results of a
-portable reference arithmetic, contained in the file ieee.c.
-This is configured for an 80-bit significand, to have enough
-precision to satisfy the conversion requirements of IEEE 854 for
-the extended double format of IEEE 754. The reference arithmetic
-includes binary <--> ASCII conversion routines and single <-->
-double <--> extended double conversions. A strictly rounded
-square root function is given in esqrt.c. Additional functions
-are provided by elog.c, eexp.c, etanh.c, epow.c, all of which
-call on ieee.c for their arithmetic. Some of the ANSI C
-functions are supplied in ieee.c; for example, efloor(),
-efrexp(), eldexp(). The functions and the reference arithmetic
-are described further in the book _Methods and Programs for
-Mathematical Functions_ (Prentice-Hall or Simon & Schuster
-International, 1989), by S. L. Moshier.
-
- As an aid in diagnosis, a calculator program, ecalc.c, is
-supplied. It uses ieee.c for its arithmetic. Documentation for
-the calculator's user interface is in the file calc100.doc
-(calc100 is a fuller featured 100-digit version of ecalc). The
-calculator needs to be told by qcalc.h if addresses are 32 bits
-long (define LARGEMEM 1) or 16 bits long (define LARGEMEM 0).
-
- Because the source code of ieee.c is included here, a version
-of W. Kahan's PARANOIA is also provided; this has been heavily
-modified by substituting subroutine calls to ieee.c in place of
-all arithmetic operators. It is important that you use PARANOIA
-to check the arithmetic after any modifications you may make to
-ieee.c.
-
- Several systems have been tested with the initial version of
-ieetst. Sun 4 (SPARC) passes; DEC VMS C has only a small flaw;
-Microsoft flunks; ATT SysVR2 (Motorola) flunks even worse.
-
-
- Files:
-
-calc100.doc calculator documentaton
-descrip.mms part of VAX VMS makefile
-drand.c random number generator
-ecalc.c calculator
-ecalc.opt part of VAX VMS makefile
-econst.c constants for reference arithmetic
-eexp.c reference exponential function
-ehead.h declarations for reference arithmetic routines
-elog.c reference logarithm
-eparanoi.c floating point arithmetic tester
-eparanoi.opt part of VAX VMS makefile
-epow.c reference exponentiation
-esqrt.c reference square root
-etanh.c reference hyperbolic tangent
-etodec.c conversions to and from DEC double precision format
-ieee.c the reference arithmetic
-ieetst.c printf/scanf tester
-ieetst.doc this file
-ieetst.mak Microsoft make file
-ieetst.opt part of VAX VMS makefile
-makefile Unix make file
-mconf.h definitions for arithmetic format
-mtherr.c common error reporter
-qcalc.h definitions for calculator
-
-
-This software may be copied freely.
-
--- Steve Moshier
-
-v0.1 July, 1992
-v0.2 January, 1993
+
+ ieetst, version 0.2
+
+ This software tests the numerical accuracy of floating point
+binary <-> decimal string conversion, as done by your C language
+library functions printf() and scanf(), for compliance with the
+IEEE arithmetic standards ANSI/IEEE Std 754-1985 and ANSI/IEEE
+Std 854-1987. The test covers 32-bit float, 64-bit double, and
+80-bit long double precision conversions to and from decimal
+ASCII strings.
+
+ The test program checks for proper implementation of the
+following specifications of the standards:
+
+ (1) correctly rounded conversions of numbers of the form M *
+ 10^N, where M and N are integers such that, in double precision,
+ for example, |M| < 10^17, |N| <= 27.
+
+ (2) binary -> decimal -> binary conversions to be an identity
+ if a sufficiently large number of decimal digits is requested.
+
+ (3) correctly rounded decimal outputs of less than the maximum
+ number of digits
+
+ (4) The maximum observed conversion error of numbers outside the
+ domain covered by (1) is reported by the test program; it is
+ not supposed to exceed 0.97 ulp.
+
+There are 10 separate tests. Tests 1 through 6 use values near
+2^n and 10^n. Test 7 addresses item (1) above. Test 8 checks
+the rounding of exact half-integer numbers. Test 9 is for item
+(4) above. Test 10 checks denormal numbers. Tests 8 through 10
+address item (3) using printf formats that produce outputs of 1,
+2, 3, ... digits after the decimal point. All tests check, when
+appropriate, that the binary output of scanf is the same as the
+binary input to printf, item (2).
+
+Example error messages:
+
+ 0000 0000 0000 1000 8000 3f80 ->printf-> 5.87748296e-39 ->scanf->
+ 0000 0000 0000 0000 8000 3f6e is not an identity.
+
+ scanf(-9.9999900000000003e-01) -> 0000 4800 085f ef39 ffff bffe
+ should be 0000 5000 085f ef39 ffff bffe .
+
+ printf("%.14e", 6.13592315154256467968352E-3) -> 6.13592315154257e-03
+ should be 6.13592315154256E-3 .
+
+Binary values are displayed as four-digit hex groups in the
+little-endian format of the internal reference arithmetic. The
+least significant 16-bit word is first, the exponent is last.
+
+ The design of the test program requires knowing the binary
+data structure of the floating point format under test. For
+configuration, check the .h files carefully. All the programs
+need to be told via mconf.h if the numeric format is
+little-endian (IBMPC) or big-endian (MIEEE). If your system
+supports an 80-bit long double precision data type, define
+LDOUBLE 1 in ieetst.c; otherwise define LDOUBLE 0. A provision
+for DEC PDP-11/VAX numbers is implemented (double precision
+only). Conversions for other data structures can be added by
+analogy to the ifdefs for DEC.
+
+ Most of the tests rely on comparison with the results of a
+portable reference arithmetic, contained in the file ieee.c.
+This is configured for an 80-bit significand, to have enough
+precision to satisfy the conversion requirements of IEEE 854 for
+the extended double format of IEEE 754. The reference arithmetic
+includes binary <--> ASCII conversion routines and single <-->
+double <--> extended double conversions. A strictly rounded
+square root function is given in esqrt.c. Additional functions
+are provided by elog.c, eexp.c, etanh.c, epow.c, all of which
+call on ieee.c for their arithmetic. Some of the ANSI C
+functions are supplied in ieee.c; for example, efloor(),
+efrexp(), eldexp(). The functions and the reference arithmetic
+are described further in the book _Methods and Programs for
+Mathematical Functions_ (Prentice-Hall or Simon & Schuster
+International, 1989), by S. L. Moshier.
+
+ As an aid in diagnosis, a calculator program, ecalc.c, is
+supplied. It uses ieee.c for its arithmetic. Documentation for
+the calculator's user interface is in the file calc100.doc
+(calc100 is a fuller featured 100-digit version of ecalc). The
+calculator needs to be told by qcalc.h if addresses are 32 bits
+long (define LARGEMEM 1) or 16 bits long (define LARGEMEM 0).
+
+ Because the source code of ieee.c is included here, a version
+of W. Kahan's PARANOIA is also provided; this has been heavily
+modified by substituting subroutine calls to ieee.c in place of
+all arithmetic operators. It is important that you use PARANOIA
+to check the arithmetic after any modifications you may make to
+ieee.c.
+
+ Several systems have been tested with the initial version of
+ieetst. Sun 4 (SPARC) passes; DEC VMS C has only a small flaw;
+Microsoft flunks; ATT SysVR2 (Motorola) flunks even worse.
+
+
+ Files:
+
+calc100.doc calculator documentaton
+descrip.mms part of VAX VMS makefile
+drand.c random number generator
+ecalc.c calculator
+ecalc.opt part of VAX VMS makefile
+econst.c constants for reference arithmetic
+eexp.c reference exponential function
+ehead.h declarations for reference arithmetic routines
+elog.c reference logarithm
+eparanoi.c floating point arithmetic tester
+eparanoi.opt part of VAX VMS makefile
+epow.c reference exponentiation
+esqrt.c reference square root
+etanh.c reference hyperbolic tangent
+etodec.c conversions to and from DEC double precision format
+ieee.c the reference arithmetic
+ieetst.c printf/scanf tester
+ieetst.doc this file
+ieetst.mak Microsoft make file
+ieetst.opt part of VAX VMS makefile
+makefile Unix make file
+mconf.h definitions for arithmetic format
+mtherr.c common error reporter
+qcalc.h definitions for calculator
+
+
+This software may be copied freely.
+
+-- Steve Moshier
+
+v0.1 July, 1992
+v0.2 January, 1993
diff --git a/test/math/mconf.h b/test/math/mconf.h
index cb9c3b50d..faf789b26 100644
--- a/test/math/mconf.h
+++ b/test/math/mconf.h
@@ -1,108 +1,108 @@
-/* mconf.h
- *
- * Common include file for math routines
- *
- *
- *
- * SYNOPSIS:
- *
- * #include "mconf.h"
- *
- *
- *
- * DESCRIPTION:
- *
- * This file contains definitions for error codes that are
- * passed to the common error handling routine mtherr()
- * (which see).
- *
- * 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 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.
- *
- * 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, the symbol UNK is defined.
- *
- * 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.
- *
- */
-
-/*
-Cephes Math Library Release 2.0: April, 1987
-by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-/* 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
-
-/*
-typedef struct
- {
- double r;
- double i;
- }cmplx;
-*/
-
-/* 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 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:
- */
- /*define UNK 1*/
-
-/* Define to ask for infinity support, else undefine. */
-#define INFINITY
-
-/* Define to ask for Not-a-Number support, else undefine. */
-#define NANS
-
-/* Define to support denormal numbers, else undefine. */
-#define DENORMAL
+/* mconf.h
+ *
+ * Common include file for math routines
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * #include "mconf.h"
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * This file contains definitions for error codes that are
+ * passed to the common error handling routine mtherr()
+ * (which see).
+ *
+ * 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 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.
+ *
+ * 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, the symbol UNK is defined.
+ *
+ * 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.
+ *
+ */
+
+/*
+Cephes Math Library Release 2.0: April, 1987
+by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+
+/* 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
+
+/*
+typedef struct
+ {
+ double r;
+ double i;
+ }cmplx;
+*/
+
+/* 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 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:
+ */
+ /*define UNK 1*/
+
+/* Define to ask for infinity support, else undefine. */
+#define INFINITY
+
+/* Define to ask for Not-a-Number support, else undefine. */
+#define NANS
+
+/* Define to support denormal numbers, else undefine. */
+#define DENORMAL
diff --git a/test/math/mtherr.c b/test/math/mtherr.c
index de6d81b94..52e3ec2ad 100644
--- a/test/math/mtherr.c
+++ b/test/math/mtherr.c
@@ -1,96 +1,96 @@
-/* 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 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
-by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include "mconf.h"
-
-/* 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"
-};
-
-
-
-void 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 );
-
-/* 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
- */
-}
+/* 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 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
+by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include "mconf.h"
+
+/* 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"
+};
+
+
+
+void 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 );
+
+/* 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
+ */
+}
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