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/log2l.c | 302 +++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 302 insertions(+) create mode 100644 libm/ldouble/log2l.c (limited to 'libm/ldouble/log2l.c') diff --git a/libm/ldouble/log2l.c b/libm/ldouble/log2l.c new file mode 100644 index 000000000..220b881ae --- /dev/null +++ b/libm/ldouble/log2l.c @@ -0,0 +1,302 @@ +/* log2l.c + * + * Base 2 logarithm, long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, log2l(); + * + * y = log2l( x ); + * + * + * + * DESCRIPTION: + * + * Returns the base 2 logarithm of x. + * + * The argument is separated into its exponent and fractional + * parts. If the exponent is between -1 and +1, the (natural) + * 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 9.8e-20 2.7e-20 + * IEEE exp(+-10000) 70000 5.4e-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 -INFINITYL + * log domain: x < 0; returns NANL + */ + +/* +Cephes Math Library Release 2.8: May, 1998 +Copyright 1984, 1991, 1998 by Stephen L. Moshier +*/ + +#include + +/* Coefficients for ln(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, +}; +/* log2(e) - 1 */ +#define LOG2EA 4.4269504088896340735992e-1L +#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 LG2EA[] = {0xc2ef,0x705f,0xeca5,0xe2a8,0x3ffd, XPD}; +#define LOG2EA *(long double *)LG2EA +#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 LG2EA[] = {0x3ffd0000,0xe2a8eca5,0x705fc2ef}; +#define LOG2EA *(long double *)LG2EA +#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(); +extern int isnanl (); +#endif +#ifdef INFINITIES +extern long double INFINITYL; +#endif +#ifdef NANS +extern long double NANL; +#endif + +long double log2l(x) +long double x; +{ +VOLATILE long double z; +long double y; +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( "log2l", SING ); + return( -16384.0L ); +#endif + } + else + { +#ifdef NANS + return( NANL ); +#else + mtherr( "log2l", DOMAIN ); + return( -16384.0L ); +#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 log2(e) + * and base 2 exponent by 1 + * + * ***CAUTION*** + * + * This sequence of operations is critical and it may + * be horribly defeated by some compiler optimizers. + */ +z = y * LOG2EA; +z += x * LOG2EA; +z += y; +z += x; +z += e; +return( z ); +} + -- cgit v1.2.3