From 1077fa4d772832f77a677ce7fb7c2d513b959e3f Mon Sep 17 00:00:00 2001 From: Eric Andersen Date: Thu, 10 May 2001 00:40:28 +0000 Subject: uClibc now has a math library. muahahahaha! -Erik --- libm/ldouble/logl.c | 292 ++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 292 insertions(+) create mode 100644 libm/ldouble/logl.c (limited to 'libm/ldouble/logl.c') diff --git a/libm/ldouble/logl.c b/libm/ldouble/logl.c new file mode 100644 index 000000000..d6367eb19 --- /dev/null +++ b/libm/ldouble/logl.c @@ -0,0 +1,292 @@ +/* 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