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Diffstat (limited to 'libm/ldouble/expl.c')
| -rw-r--r-- | libm/ldouble/expl.c | 183 |
1 files changed, 0 insertions, 183 deletions
diff --git a/libm/ldouble/expl.c b/libm/ldouble/expl.c deleted file mode 100644 index 524246987..000000000 --- a/libm/ldouble/expl.c +++ /dev/null @@ -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); -} |