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authorEric Andersen <andersen@codepoet.org>2001-11-22 14:04:29 +0000
committerEric Andersen <andersen@codepoet.org>2001-11-22 14:04:29 +0000
commit7ce331c01ce6eb7b3f5c715a38a24359da9c6ee2 (patch)
tree3a7e8476e868ae15f4da1b7ce26b2db6f434468c /libm/ldouble/expl.c
parentc117dd5fb183afb1a4790a6f6110d88704be6bf8 (diff)
Totally rework the math library, this time based on the MacOs X
math library (which is itself based on the math lib from FreeBSD). -Erik
Diffstat (limited to 'libm/ldouble/expl.c')
-rw-r--r--libm/ldouble/expl.c183
1 files changed, 0 insertions, 183 deletions
diff --git a/libm/ldouble/expl.c b/libm/ldouble/expl.c
deleted file mode 100644
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--- a/libm/ldouble/expl.c
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@@ -1,183 +0,0 @@
-/* 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);
-}