From 1077fa4d772832f77a677ce7fb7c2d513b959e3f Mon Sep 17 00:00:00 2001
From: Eric Andersen <andersen@codepoet.org>
Date: Thu, 10 May 2001 00:40:28 +0000
Subject: uClibc now has a math library.  muahahahaha!  -Erik

---
 libm/ldouble/expl.c | 183 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 183 insertions(+)
 create mode 100644 libm/ldouble/expl.c

(limited to 'libm/ldouble/expl.c')

diff --git a/libm/ldouble/expl.c b/libm/ldouble/expl.c
new file mode 100644
index 000000000..524246987
--- /dev/null
+++ b/libm/ldouble/expl.c
@@ -0,0 +1,183 @@
+/*							expl.c
+ *
+ *	Exponential function, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, expl();
+ *
+ * y = expl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns e (2.71828...) raised to the x power.
+ *
+ * Range reduction is accomplished by separating the argument
+ * into an integer k and fraction f such that
+ *
+ *     x    k  f
+ *    e  = 2  e.
+ *
+ * A Pade' form of degree 2/3 is used to approximate exp(f) - 1
+ * in the basic range [-0.5 ln 2, 0.5 ln 2].
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      +-10000     50000       1.12e-19    2.81e-20
+ *
+ *
+ * Error amplification in the exponential function can be
+ * a serious matter.  The error propagation involves
+ * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
+ * which shows that a 1 lsb error in representing X produces
+ * a relative error of X times 1 lsb in the function.
+ * While the routine gives an accurate result for arguments
+ * that are exactly represented by a long double precision
+ * computer number, the result contains amplified roundoff
+ * error for large arguments not exactly represented.
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition      value returned
+ * exp underflow    x < MINLOG         0.0
+ * exp overflow     x > MAXLOG         MAXNUM
+ *
+ */
+
+/*
+Cephes Math Library Release 2.7:  May, 1998
+Copyright 1984, 1990, 1998 by Stephen L. Moshier
+*/
+
+
+/*	Exponential function	*/
+
+#include <math.h>
+
+#ifdef UNK
+static long double P[3] = {
+ 1.2617719307481059087798E-4L,
+ 3.0299440770744196129956E-2L,
+ 9.9999999999999999991025E-1L,
+};
+static long double Q[4] = {
+ 3.0019850513866445504159E-6L,
+ 2.5244834034968410419224E-3L,
+ 2.2726554820815502876593E-1L,
+ 2.0000000000000000000897E0L,
+};
+static long double C1 = 6.9314575195312500000000E-1L;
+static long double C2 = 1.4286068203094172321215E-6L;
+#endif
+
+#ifdef DEC
+not supported in long double precision
+#endif
+
+#ifdef IBMPC
+static short P[] = {
+0x424e,0x225f,0x6eaf,0x844e,0x3ff2, XPD
+0xf39e,0x5163,0x8866,0xf836,0x3ff9, XPD
+0xfffe,0xffff,0xffff,0xffff,0x3ffe, XPD
+};
+static short Q[] = {
+0xff1e,0xb2fc,0xb5e1,0xc975,0x3fec, XPD
+0xff3e,0x45b5,0xcda8,0xa571,0x3ff6, XPD
+0x9ee1,0x3f03,0x4cc4,0xe8b8,0x3ffc, XPD
+0x0000,0x0000,0x0000,0x8000,0x4000, XPD
+};
+static short sc1[] = {0x0000,0x0000,0x0000,0xb172,0x3ffe, XPD};
+#define C1 (*(long double *)sc1)
+static short sc2[] = {0x4f1e,0xcd5e,0x8e7b,0xbfbe,0x3feb, XPD};
+#define C2 (*(long double *)sc2)
+#endif
+
+#ifdef MIEEE
+static long P[9] = {
+0x3ff20000,0x844e6eaf,0x225f424e,
+0x3ff90000,0xf8368866,0x5163f39e,
+0x3ffe0000,0xffffffff,0xfffffffe,
+};
+static long Q[12] = {
+0x3fec0000,0xc975b5e1,0xb2fcff1e,
+0x3ff60000,0xa571cda8,0x45b5ff3e,
+0x3ffc0000,0xe8b84cc4,0x3f039ee1,
+0x40000000,0x80000000,0x00000000,
+};
+static long sc1[] = {0x3ffe0000,0xb1720000,0x00000000};
+#define C1 (*(long double *)sc1)
+static long sc2[] = {0x3feb0000,0xbfbe8e7b,0xcd5e4f1e};
+#define C2 (*(long double *)sc2)
+#endif
+
+extern long double LOG2EL, MAXLOGL, MINLOGL, MAXNUML;
+#ifdef ANSIPROT
+extern long double polevll ( long double, void *, int );
+extern long double floorl ( long double );
+extern long double ldexpl ( long double, int );
+extern int isnanl ( long double );
+#else
+long double polevll(), floorl(), ldexpl(), isnanl();
+#endif
+#ifdef INFINITIES
+extern long double INFINITYL;
+#endif
+
+long double expl(x)
+long double x;
+{
+long double px, xx;
+int n;
+
+#ifdef NANS
+if( isnanl(x) )
+	return(x);
+#endif
+if( x > MAXLOGL)
+	{
+#ifdef INFINITIES
+	return( INFINITYL );
+#else
+	mtherr( "expl", OVERFLOW );
+	return( MAXNUML );
+#endif
+	}
+
+if( x < MINLOGL )
+	{
+#ifndef INFINITIES
+	mtherr( "expl", UNDERFLOW );
+#endif
+	return(0.0L);
+	}
+
+/* Express e**x = e**g 2**n
+ *   = e**g e**( n loge(2) )
+ *   = e**( g + n loge(2) )
+ */
+px = floorl( LOG2EL * x + 0.5L ); /* floor() truncates toward -infinity. */
+n = px;
+x -= px * C1;
+x -= px * C2;
+
+
+/* rational approximation for exponential
+ * of the fractional part:
+ * e**x =  1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
+ */
+xx = x * x;
+px = x * polevll( xx, P, 2 );
+x =  px/( polevll( xx, Q, 3 ) - px );
+x = 1.0L + ldexpl( x, 1 );
+
+x = ldexpl( x, n );
+return(x);
+}
-- 
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