From 7ce331c01ce6eb7b3f5c715a38a24359da9c6ee2 Mon Sep 17 00:00:00 2001 From: Eric Andersen Date: Thu, 22 Nov 2001 14:04:29 +0000 Subject: 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 --- libm/ldouble/logl.c | 292 ---------------------------------------------------- 1 file changed, 292 deletions(-) delete mode 100644 libm/ldouble/logl.c (limited to 'libm/ldouble/logl.c') diff --git a/libm/ldouble/logl.c b/libm/ldouble/logl.c deleted file mode 100644 index d6367eb19..000000000 --- a/libm/ldouble/logl.c +++ /dev/null @@ -1,292 +0,0 @@ -/* logl.c - * - * Natural logarithm, long double precision - * - * - * - * SYNOPSIS: - * - * long double x, y, logl(); - * - * y = logl( x ); - * - * - * - * DESCRIPTION: - * - * Returns the base e (2.718...) logarithm of x. - * - * The argument is separated into its exponent and fractional - * parts. If the exponent is between -1 and +1, the logarithm - * of the fraction is approximated by - * - * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x). - * - * Otherwise, setting z = 2(x-1)/x+1), - * - * log(x) = z + z**3 P(z)/Q(z). - * - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 0.5, 2.0 150000 8.71e-20 2.75e-20 - * IEEE exp(+-10000) 100000 5.39e-20 2.34e-20 - * - * In the tests over the interval exp(+-10000), the logarithms - * of the random arguments were uniformly distributed over - * [-10000, +10000]. - * - * ERROR MESSAGES: - * - * log singularity: x = 0; returns -INFINITYL - * log domain: x < 0; returns NANL - */ - -/* -Cephes Math Library Release 2.7: May, 1998 -Copyright 1984, 1990, 1998 by Stephen L. Moshier -*/ - -#include - -/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x) - * 1/sqrt(2) <= x < sqrt(2) - * Theoretical peak relative error = 2.32e-20 - */ -#ifdef UNK -static long double P[] = { - 4.5270000862445199635215E-5L, - 4.9854102823193375972212E-1L, - 6.5787325942061044846969E0L, - 2.9911919328553073277375E1L, - 6.0949667980987787057556E1L, - 5.7112963590585538103336E1L, - 2.0039553499201281259648E1L, -}; -static long double Q[] = { -/* 1.0000000000000000000000E0,*/ - 1.5062909083469192043167E1L, - 8.3047565967967209469434E1L, - 2.2176239823732856465394E2L, - 3.0909872225312059774938E2L, - 2.1642788614495947685003E2L, - 6.0118660497603843919306E1L, -}; -#endif - -#ifdef IBMPC -static short P[] = { -0x51b9,0x9cae,0x4b15,0xbde0,0x3ff0, XPD -0x19cf,0xf0d4,0xc507,0xff40,0x3ffd, XPD -0x9942,0xa7d2,0xfa37,0xd284,0x4001, XPD -0x4add,0x65ce,0x9c5c,0xef4b,0x4003, XPD -0x8445,0x619a,0x75c3,0xf3cc,0x4004, XPD -0x81ab,0x3cd0,0xacba,0xe473,0x4004, XPD -0x4cbf,0xcc18,0x016c,0xa051,0x4003, XPD -}; -static short Q[] = { -/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/ -0xb8b7,0x81f1,0xacf4,0xf101,0x4002, XPD -0xbc31,0x09a4,0x5a91,0xa618,0x4005, XPD -0xaeec,0xe7da,0x2c87,0xddc3,0x4006, XPD -0x2bde,0x4845,0xa2ee,0x9a8c,0x4007, XPD -0x3120,0x4703,0x89f2,0xd86d,0x4006, XPD -0x7347,0x3224,0x8223,0xf079,0x4004, XPD -}; -#endif - -#ifdef MIEEE -static long P[] = { -0x3ff00000,0xbde04b15,0x9cae51b9, -0x3ffd0000,0xff40c507,0xf0d419cf, -0x40010000,0xd284fa37,0xa7d29942, -0x40030000,0xef4b9c5c,0x65ce4add, -0x40040000,0xf3cc75c3,0x619a8445, -0x40040000,0xe473acba,0x3cd081ab, -0x40030000,0xa051016c,0xcc184cbf, -}; -static long Q[] = { -/*0x3fff0000,0x80000000,0x00000000,*/ -0x40020000,0xf101acf4,0x81f1b8b7, -0x40050000,0xa6185a91,0x09a4bc31, -0x40060000,0xddc32c87,0xe7daaeec, -0x40070000,0x9a8ca2ee,0x48452bde, -0x40060000,0xd86d89f2,0x47033120, -0x40040000,0xf0798223,0x32247347, -}; -#endif - -/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), - * where z = 2(x-1)/(x+1) - * 1/sqrt(2) <= x < sqrt(2) - * Theoretical peak relative error = 6.16e-22 - */ - -#ifdef UNK -static long double R[4] = { - 1.9757429581415468984296E-3L, --7.1990767473014147232598E-1L, - 1.0777257190312272158094E1L, --3.5717684488096787370998E1L, -}; -static long double S[4] = { -/* 1.00000000000000000000E0L,*/ --2.6201045551331104417768E1L, - 1.9361891836232102174846E2L, --4.2861221385716144629696E2L, -}; -static long double C1 = 6.9314575195312500000000E-1L; -static long double C2 = 1.4286068203094172321215E-6L; -#endif -#ifdef IBMPC -static short R[] = { -0x6ef4,0xf922,0x7763,0x817b,0x3ff6, XPD -0x15fd,0x1af9,0xde8f,0xb84b,0xbffe, XPD -0x8b96,0x4f8d,0xa53c,0xac6f,0x4002, XPD -0x8932,0xb4e3,0xe8ae,0x8ede,0xc004, XPD -}; -static short S[] = { -/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/ -0x7ce4,0x1fc9,0xbdc5,0xd19b,0xc003, XPD -0x0af3,0x0d10,0x716f,0xc19e,0x4006, XPD -0x4d7d,0x0f55,0x5d06,0xd64e,0xc007, XPD -}; -static short sc1[] = {0x0000,0x0000,0x0000,0xb172,0x3ffe, XPD}; -#define C1 (*(long double *)sc1) -static short sc2[] = {0x4f1e,0xcd5e,0x8e7b,0xbfbe,0x3feb, XPD}; -#define C2 (*(long double *)sc2) -#endif -#ifdef MIEEE -static long R[12] = { -0x3ff60000,0x817b7763,0xf9226ef4, -0xbffe0000,0xb84bde8f,0x1af915fd, -0x40020000,0xac6fa53c,0x4f8d8b96, -0xc0040000,0x8edee8ae,0xb4e38932, -}; -static long S[9] = { -/*0x3fff0000,0x80000000,0x00000000,*/ -0xc0030000,0xd19bbdc5,0x1fc97ce4, -0x40060000,0xc19e716f,0x0d100af3, -0xc0070000,0xd64e5d06,0x0f554d7d, -}; -static long sc1[] = {0x3ffe0000,0xb1720000,0x00000000}; -#define C1 (*(long double *)sc1) -static long sc2[] = {0x3feb0000,0xbfbe8e7b,0xcd5e4f1e}; -#define C2 (*(long double *)sc2) -#endif - - -#define SQRTH 0.70710678118654752440L -extern long double MINLOGL; -#ifdef ANSIPROT -extern long double frexpl ( long double, int * ); -extern long double ldexpl ( long double, int ); -extern long double polevll ( long double, void *, int ); -extern long double p1evll ( long double, void *, int ); -extern int isnanl ( long double ); -#else -long double frexpl(), ldexpl(), polevll(), p1evll(), isnanl(); -#endif -#ifdef INFINITIES -extern long double INFINITYL; -#endif -#ifdef NANS -extern long double NANL; -#endif - -long double logl(x) -long double x; -{ -long double y, z; -int e; - -#ifdef NANS -if( isnanl(x) ) - return(x); -#endif -#ifdef INFINITIES -if( x == INFINITYL ) - return(x); -#endif -/* Test for domain */ -if( x <= 0.0L ) - { - if( x == 0.0L ) - { -#ifdef INFINITIES - return( -INFINITYL ); -#else - mtherr( "logl", SING ); - return( MINLOGL ); -#endif - } - else - { -#ifdef NANS - return( NANL ); -#else - mtherr( "logl", DOMAIN ); - return( MINLOGL ); -#endif - } - } - -/* separate mantissa from exponent */ - -/* Note, frexp is used so that denormal numbers - * will be handled properly. - */ -x = frexpl( x, &e ); - -/* logarithm using log(x) = z + z**3 P(z)/Q(z), - * where z = 2(x-1)/x+1) - */ -if( (e > 2) || (e < -2) ) -{ -if( x < SQRTH ) - { /* 2( 2x-1 )/( 2x+1 ) */ - e -= 1; - z = x - 0.5L; - y = 0.5L * z + 0.5L; - } -else - { /* 2 (x-1)/(x+1) */ - z = x - 0.5L; - z -= 0.5L; - y = 0.5L * x + 0.5L; - } -x = z / y; -z = x*x; -z = x * ( z * polevll( z, R, 3 ) / p1evll( z, S, 3 ) ); -z = z + e * C2; -z = z + x; -z = z + e * C1; -return( z ); -} - - -/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ - -if( x < SQRTH ) - { - e -= 1; - x = ldexpl( x, 1 ) - 1.0L; /* 2x - 1 */ - } -else - { - x = x - 1.0L; - } -z = x*x; -y = x * ( z * polevll( x, P, 6 ) / p1evll( x, Q, 6 ) ); -y = y + e * C2; -z = y - ldexpl( z, -1 ); /* y - 0.5 * z */ -/* Note, the sum of above terms does not exceed x/4, - * so it contributes at most about 1/4 lsb to the error. - */ -z = z + x; -z = z + e * C1; /* This sum has an error of 1/2 lsb. */ -return( z ); -} -- cgit v1.2.3