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Diffstat (limited to 'libm/ldouble/log10l.c')
-rw-r--r-- | libm/ldouble/log10l.c | 319 |
1 files changed, 0 insertions, 319 deletions
diff --git a/libm/ldouble/log10l.c b/libm/ldouble/log10l.c deleted file mode 100644 index fa13ff3a2..000000000 --- a/libm/ldouble/log10l.c +++ /dev/null @@ -1,319 +0,0 @@ -/* log10l.c - * - * Common logarithm, long double precision - * - * - * - * SYNOPSIS: - * - * long double x, y, log10l(); - * - * y = log10l( x ); - * - * - * - * DESCRIPTION: - * - * Returns the base 10 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 30000 9.0e-20 2.6e-20 - * IEEE exp(+-10000) 30000 6.0e-20 2.3e-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 MINLOG - * log domain: x < 0; returns MINLOG - */ - -/* -Cephes Math Library Release 2.2: January, 1991 -Copyright 1984, 1991 by Stephen L. Moshier -Direct inquiries to 30 Frost Street, Cambridge, MA 02140 -*/ - -#include <math.h> -static char fname[] = {"log10l"}; - -/* 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 = 6.2e-22 - */ -#ifdef UNK -static long double P[] = { - 4.9962495940332550844739E-1L, - 1.0767376367209449010438E1L, - 7.7671073698359539859595E1L, - 2.5620629828144409632571E2L, - 4.2401812743503691187826E2L, - 3.4258224542413922935104E2L, - 1.0747524399916215149070E2L, -}; -static long double Q[] = { -/* 1.0000000000000000000000E0,*/ - 2.3479774160285863271658E1L, - 1.9444210022760132894510E2L, - 7.7952888181207260646090E2L, - 1.6911722418503949084863E3L, - 2.0307734695595183428202E3L, - 1.2695660352705325274404E3L, - 3.2242573199748645407652E2L, -}; -#endif - -#ifdef IBMPC -static short P[] = { -0xfe72,0xce22,0xd7b9,0xffce,0x3ffd, XPD -0xb778,0x0e34,0x2c71,0xac47,0x4002, XPD -0xea8b,0xc751,0x96f8,0x9b57,0x4005, XPD -0xfeaf,0x6a02,0x67fb,0x801a,0x4007, XPD -0x6b5a,0xf252,0x51ff,0xd402,0x4007, XPD -0x39ce,0x9f76,0x8704,0xab4a,0x4007, XPD -0x1b39,0x740b,0x532e,0xd6f3,0x4005, XPD -}; -static short Q[] = { -/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/ -0x2f3a,0xbf26,0x93d5,0xbbd6,0x4003, XPD -0x13c8,0x031a,0x2d7b,0xc271,0x4006, XPD -0x449d,0x1993,0xd933,0xc2e1,0x4008, XPD -0x5b65,0x574e,0x8301,0xd365,0x4009, XPD -0xa65d,0x3bd2,0xc043,0xfdd8,0x4009, XPD -0x3b21,0xffea,0x1cf5,0x9eb2,0x4009, XPD -0x545c,0xd708,0x7e62,0xa136,0x4007, XPD -}; -#endif - -#ifdef MIEEE -static long P[] = { -0x3ffd0000,0xffced7b9,0xce22fe72, -0x40020000,0xac472c71,0x0e34b778, -0x40050000,0x9b5796f8,0xc751ea8b, -0x40070000,0x801a67fb,0x6a02feaf, -0x40070000,0xd40251ff,0xf2526b5a, -0x40070000,0xab4a8704,0x9f7639ce, -0x40050000,0xd6f3532e,0x740b1b39, -}; -static long Q[] = { -/*0x3fff0000,0x80000000,0x00000000,*/ -0x40030000,0xbbd693d5,0xbf262f3a, -0x40060000,0xc2712d7b,0x031a13c8, -0x40080000,0xc2e1d933,0x1993449d, -0x40090000,0xd3658301,0x574e5b65, -0x40090000,0xfdd8c043,0x3bd2a65d, -0x40090000,0x9eb21cf5,0xffea3b21, -0x40070000,0xa1367e62,0xd708545c, -}; -#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, -}; -/* log10(2) */ -#define L102A 0.3125L -#define L102B -1.1470004336018804786261e-2L -/* log10(e) */ -#define L10EA 0.5L -#define L10EB -6.5705518096748172348871e-2L -#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 LG102A[] = {0x0000,0x0000,0x0000,0xa000,0x3ffd, XPD}; -#define L102A *(long double *)LG102A -static short LG102B[] = {0x0cee,0x8601,0xaf60,0xbbec,0xbff8, XPD}; -#define L102B *(long double *)LG102B -static short LG10EA[] = {0x0000,0x0000,0x0000,0x8000,0x3ffe, XPD}; -#define L10EA *(long double *)LG10EA -static short LG10EB[] = {0x39ab,0x235e,0x9d5b,0x8690,0xbffb, XPD}; -#define L10EB *(long double *)LG10EB -#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 LG102A[] = {0x3ffd0000,0xa0000000,0x00000000}; -#define L102A *(long double *)LG102A -static long LG102B[] = {0xbff80000,0xbbecaf60,0x86010cee}; -#define L102B *(long double *)LG102B -static long LG10EA[] = {0x3ffe0000,0x80000000,0x00000000}; -#define L10EA *(long double *)LG10EA -static long LG10EB[] = {0xbffb0000,0x86909d5b,0x235e39ab}; -#define L10EB *(long double *)LG10EB -#endif - - -#define SQRTH 0.70710678118654752440L -#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 log10l(x) -long double x; -{ -long double y; -VOLATILE long double z; -int e; - -#ifdef NANS -if( isnanl(x) ) - return(x); -#endif -/* Test for domain */ -if( x <= 0.0L ) - { - if( x == 0.0L ) - { - mtherr( fname, SING ); -#ifdef INFINITIES - return(-INFINITYL); -#else - return( -4.9314733889673399399914e3L ); -#endif - } - else - { - mtherr( fname, DOMAIN ); -#ifdef NANS - return(NANL); -#else - return( -4.9314733889673399399914e3L ); -#endif - } - } -#ifdef INFINITIES -if( x == INFINITYL ) - return(INFINITYL); -#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; -y = x * ( z * polevll( z, R, 3 ) / p1evll( z, S, 3 ) ); -goto done; -} - - -/* 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, 7 ) ); -y = y - ldexpl( z, -1 ); /* -0.5x^2 + ... */ - -done: - -/* Multiply log of fraction by log10(e) - * and base 2 exponent by log10(2). - * - * ***CAUTION*** - * - * This sequence of operations is critical and it may - * be horribly defeated by some compiler optimizers. - */ -z = y * (L10EB); -z += x * (L10EB); -z += e * (L102B); -z += y * (L10EA); -z += x * (L10EA); -z += e * (L102A); - -return( z ); -} |