diff options
Diffstat (limited to 'winsup/mingw/mingwex/math/tgammal.c')
| -rw-r--r-- | winsup/mingw/mingwex/math/tgammal.c | 501 |
1 files changed, 0 insertions, 501 deletions
diff --git a/winsup/mingw/mingwex/math/tgammal.c b/winsup/mingw/mingwex/math/tgammal.c deleted file mode 100644 index 6db4e3af7..000000000 --- a/winsup/mingw/mingwex/math/tgammal.c +++ /dev/null @@ -1,501 +0,0 @@ -/* gammal.c - * - * Gamma function - * - * - * - * SYNOPSIS: - * - * long double x, y, __tgammal_r(); - * int* sgngaml; - * y = __tgammal_r( x, sgngaml ); - * - * long double x, y, tgammal(); - * y = tgammal( x); * - * - * - * DESCRIPTION: - * - * Returns gamma function of the argument. The result is - * correctly signed. In the reentrant version the sign (+1 or -1) - * is returned in the variable referenced by sgngamf. - * - * Arguments |x| <= 13 are reduced by recurrence and the function - * approximated by a rational function of degree 7/8 in the - * interval (2,3). Large arguments are handled by Stirling's - * formula. Large negative arguments are made positive using - * a reflection formula. - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE -40,+40 10000 3.6e-19 7.9e-20 - * IEEE -1755,+1755 10000 4.8e-18 6.5e-19 - * - * Accuracy for large arguments is dominated by error in powl(). - * - */ - -/* -Copyright 1994 by Stephen L. Moshier -*/ - - -/* - * 26-11-2002 Modified for mingw. - * Danny Smith <dannysmith@users.sourceforge.net> - */ - - -#ifndef __MINGW32__ -#include "mconf.h" -#else -#include "cephes_mconf.h" -#endif - -/* -gamma(x+2) = gamma(x+2) P(x)/Q(x) -0 <= x <= 1 -Relative error -n=7, d=8 -Peak error = 1.83e-20 -Relative error spread = 8.4e-23 -*/ - -#if UNK -static const long double P[8] = { - 4.212760487471622013093E-5L, - 4.542931960608009155600E-4L, - 4.092666828394035500949E-3L, - 2.385363243461108252554E-2L, - 1.113062816019361559013E-1L, - 3.629515436640239168939E-1L, - 8.378004301573126728826E-1L, - 1.000000000000000000009E0L, -}; -static const long double Q[9] = { --1.397148517476170440917E-5L, - 2.346584059160635244282E-4L, --1.237799246653152231188E-3L, --7.955933682494738320586E-4L, - 2.773706565840072979165E-2L, --4.633887671244534213831E-2L, --2.243510905670329164562E-1L, - 4.150160950588455434583E-1L, - 9.999999999999999999908E-1L, -}; -#endif -#if IBMPC -static const unsigned short P[] = { -0x434a,0x3f22,0x2bda,0xb0b2,0x3ff0, XPD -0xf5aa,0xe82f,0x335b,0xee2e,0x3ff3, XPD -0xbe6c,0x3757,0xc717,0x861b,0x3ff7, XPD -0x7f43,0x5196,0xb166,0xc368,0x3ff9, XPD -0x9549,0x8eb5,0x8c3a,0xe3f4,0x3ffb, XPD -0x8d75,0x23af,0xc8e4,0xb9d4,0x3ffd, XPD -0x29cf,0x19b3,0x16c8,0xd67a,0x3ffe, XPD -0x0000,0x0000,0x0000,0x8000,0x3fff, XPD -}; -static const unsigned short Q[] = { -0x5473,0x2de8,0x1268,0xea67,0xbfee, XPD -0x334b,0xc2f0,0xa2dd,0xf60e,0x3ff2, XPD -0xbeed,0x1853,0xa691,0xa23d,0xbff5, XPD -0x296e,0x7cb1,0x5dfd,0xd08f,0xbff4, XPD -0x0417,0x7989,0xd7bc,0xe338,0x3ff9, XPD -0x3295,0x3698,0xd580,0xbdcd,0xbffa, XPD -0x75ef,0x3ab7,0x4ad3,0xe5bc,0xbffc, XPD -0xe458,0x2ec7,0xfd57,0xd47c,0x3ffd, XPD -0x0000,0x0000,0x0000,0x8000,0x3fff, XPD -}; -#endif -#if MIEEE -static const long P[24] = { -0x3ff00000,0xb0b22bda,0x3f22434a, -0x3ff30000,0xee2e335b,0xe82ff5aa, -0x3ff70000,0x861bc717,0x3757be6c, -0x3ff90000,0xc368b166,0x51967f43, -0x3ffb0000,0xe3f48c3a,0x8eb59549, -0x3ffd0000,0xb9d4c8e4,0x23af8d75, -0x3ffe0000,0xd67a16c8,0x19b329cf, -0x3fff0000,0x80000000,0x00000000, -}; -static const long Q[27] = { -0xbfee0000,0xea671268,0x2de85473, -0x3ff20000,0xf60ea2dd,0xc2f0334b, -0xbff50000,0xa23da691,0x1853beed, -0xbff40000,0xd08f5dfd,0x7cb1296e, -0x3ff90000,0xe338d7bc,0x79890417, -0xbffa0000,0xbdcdd580,0x36983295, -0xbffc0000,0xe5bc4ad3,0x3ab775ef, -0x3ffd0000,0xd47cfd57,0x2ec7e458, -0x3fff0000,0x80000000,0x00000000, -}; -#endif -/* -static const long double P[] = { --3.01525602666895735709e0L, --3.25157411956062339893e1L, --2.92929976820724030353e2L, --1.70730828800510297666e3L, --7.96667499622741999770e3L, --2.59780216007146401957e4L, --5.99650230220855581642e4L, --7.15743521530849602425e4L -}; -static const long double Q[] = { - 1.00000000000000000000e0L, --1.67955233807178858919e1L, - 8.85946791747759881659e1L, - 5.69440799097468430177e1L, --1.98526250512761318471e3L, - 3.31667508019495079814e3L, - 1.60577839621734713377e4L, --2.97045081369399940529e4L, --7.15743521530849602412e4L -}; -*/ -#define MAXGAML 1755.455L -/*static const long double LOGPI = 1.14472988584940017414L;*/ - -/* Stirling's formula for the gamma function -gamma(x) = sqrt(2 pi) x^(x-.5) exp(-x) (1 + 1/x P(1/x)) -z(x) = x -13 <= x <= 1024 -Relative error -n=8, d=0 -Peak error = 9.44e-21 -Relative error spread = 8.8e-4 -*/ -#if UNK -static const long double STIR[9] = { - 7.147391378143610789273E-4L, --2.363848809501759061727E-5L, --5.950237554056330156018E-4L, - 6.989332260623193171870E-5L, - 7.840334842744753003862E-4L, --2.294719747873185405699E-4L, --2.681327161876304418288E-3L, - 3.472222222230075327854E-3L, - 8.333333333333331800504E-2L, -}; -#endif -#if IBMPC -static const unsigned short STIR[] = { -0x6ede,0x69f7,0x54e3,0xbb5d,0x3ff4, XPD -0xc395,0x0295,0x4443,0xc64b,0xbfef, XPD -0xba6f,0x7c59,0x5e47,0x9bfb,0xbff4, XPD -0x5704,0x1a39,0xb11d,0x9293,0x3ff1, XPD -0x30b7,0x1a21,0x98b2,0xcd87,0x3ff4, XPD -0xbef3,0x7023,0x6a08,0xf09e,0xbff2, XPD -0x3a1c,0x5ac8,0x3478,0xafb9,0xbff6, XPD -0xc3c9,0x906e,0x38e3,0xe38e,0x3ff6, XPD -0xa1d5,0xaaaa,0xaaaa,0xaaaa,0x3ffb, XPD -}; -#endif -#if MIEEE -static const long STIR[27] = { -0x3ff40000,0xbb5d54e3,0x69f76ede, -0xbfef0000,0xc64b4443,0x0295c395, -0xbff40000,0x9bfb5e47,0x7c59ba6f, -0x3ff10000,0x9293b11d,0x1a395704, -0x3ff40000,0xcd8798b2,0x1a2130b7, -0xbff20000,0xf09e6a08,0x7023bef3, -0xbff60000,0xafb93478,0x5ac83a1c, -0x3ff60000,0xe38e38e3,0x906ec3c9, -0x3ffb0000,0xaaaaaaaa,0xaaaaa1d5, -}; -#endif -#define MAXSTIR 1024.0L -static const long double SQTPI = 2.50662827463100050242E0L; - -/* 1/gamma(x) = z P(z) - * z(x) = 1/x - * 0 < x < 0.03125 - * Peak relative error 4.2e-23 - */ -#if UNK -static const long double S[9] = { --1.193945051381510095614E-3L, - 7.220599478036909672331E-3L, --9.622023360406271645744E-3L, --4.219773360705915470089E-2L, - 1.665386113720805206758E-1L, --4.200263503403344054473E-2L, --6.558780715202540684668E-1L, - 5.772156649015328608253E-1L, - 1.000000000000000000000E0L, -}; -#endif -#if IBMPC -static const unsigned short S[] = { -0xbaeb,0xd6d3,0x25e5,0x9c7e,0xbff5, XPD -0xfe9a,0xceb4,0xc74e,0xec9a,0x3ff7, XPD -0x9225,0xdfef,0xb0e9,0x9da5,0xbff8, XPD -0x10b0,0xec17,0x87dc,0xacd7,0xbffa, XPD -0x6b8d,0x7515,0x1905,0xaa89,0x3ffc, XPD -0xf183,0x126b,0xf47d,0xac0a,0xbffa, XPD -0x7bf6,0x57d1,0xa013,0xa7e7,0xbffe, XPD -0xc7a9,0x7db0,0x67e3,0x93c4,0x3ffe, XPD -0x0000,0x0000,0x0000,0x8000,0x3fff, XPD -}; -#endif -#if MIEEE -static const long S[27] = { -0xbff50000,0x9c7e25e5,0xd6d3baeb, -0x3ff70000,0xec9ac74e,0xceb4fe9a, -0xbff80000,0x9da5b0e9,0xdfef9225, -0xbffa0000,0xacd787dc,0xec1710b0, -0x3ffc0000,0xaa891905,0x75156b8d, -0xbffa0000,0xac0af47d,0x126bf183, -0xbffe0000,0xa7e7a013,0x57d17bf6, -0x3ffe0000,0x93c467e3,0x7db0c7a9, -0x3fff0000,0x80000000,0x00000000, -}; -#endif -/* 1/gamma(-x) = z P(z) - * z(x) = 1/x - * 0 < x < 0.03125 - * Peak relative error 5.16e-23 - * Relative error spread = 2.5e-24 - */ -#if UNK -static const long double SN[9] = { - 1.133374167243894382010E-3L, - 7.220837261893170325704E-3L, - 9.621911155035976733706E-3L, --4.219773343731191721664E-2L, --1.665386113944413519335E-1L, --4.200263503402112910504E-2L, - 6.558780715202536547116E-1L, - 5.772156649015328608727E-1L, --1.000000000000000000000E0L, -}; -#endif -#if IBMPC -static const unsigned short SN[] = { -0x5dd1,0x02de,0xb9f7,0x948d,0x3ff5, XPD -0x989b,0xdd68,0xc5f1,0xec9c,0x3ff7, XPD -0x2ca1,0x18f0,0x386f,0x9da5,0x3ff8, XPD -0x783f,0x41dd,0x87d1,0xacd7,0xbffa, XPD -0x7a5b,0xd76d,0x1905,0xaa89,0xbffc, XPD -0x7f64,0x1234,0xf47d,0xac0a,0xbffa, XPD -0x5e26,0x57d1,0xa013,0xa7e7,0x3ffe, XPD -0xc7aa,0x7db0,0x67e3,0x93c4,0x3ffe, XPD -0x0000,0x0000,0x0000,0x8000,0xbfff, XPD -}; -#endif -#if MIEEE -static const long SN[27] = { -0x3ff50000,0x948db9f7,0x02de5dd1, -0x3ff70000,0xec9cc5f1,0xdd68989b, -0x3ff80000,0x9da5386f,0x18f02ca1, -0xbffa0000,0xacd787d1,0x41dd783f, -0xbffc0000,0xaa891905,0xd76d7a5b, -0xbffa0000,0xac0af47d,0x12347f64, -0x3ffe0000,0xa7e7a013,0x57d15e26, -0x3ffe0000,0x93c467e3,0x7db0c7aa, -0xbfff0000,0x80000000,0x00000000, -}; -#endif - -#ifndef __MINGW32__ -extern long double MAXLOGL, MAXNUML, PIL; -/* #define PIL 3.14159265358979323846L */ -/* #define MAXNUML 1.189731495357231765021263853E4932L */ - -#ifdef ANSIPROT -extern long double fabsl ( long double ); -extern long double lgaml ( long double ); -extern long double logl ( long double ); -extern long double expl ( long double ); -extern long double gammal ( long double ); -extern long double sinl ( long double ); -extern long double floorl ( long double ); -extern long double powl ( long double, long double ); -extern long double polevll ( long double, void *, int ); -extern long double p1evll ( long double, void *, int ); -extern int isnanl ( long double ); -extern int isfinitel ( long double ); -static long double stirf ( long double ); -#else -long double fabsl(), lgaml(), logl(), expl(), gammal(), sinl(); -long double floorl(), powl(), polevll(), p1evll(), isnanl(), isfinitel(); -static long double stirf(); -#endif -#ifdef INFINITIES -extern long double INFINITYL; -#endif -#ifdef NANS -extern long double NANL; -#endif - -#else /* __MINGW32__ */ -static long double stirf ( long double ); -#endif - - -/* Gamma function computed by Stirling's formula. */ - -static long double stirf(x) -long double x; -{ -long double y, w, v; - -w = 1.0L/x; -/* For large x, use rational coefficients from the analytical expansion. */ -if( x > 1024.0L ) - w = (((((6.97281375836585777429E-5L * w - + 7.84039221720066627474E-4L) * w - - 2.29472093621399176955E-4L) * w - - 2.68132716049382716049E-3L) * w - + 3.47222222222222222222E-3L) * w - + 8.33333333333333333333E-2L) * w - + 1.0L; -else - w = 1.0L + w * polevll( w, STIR, 8 ); -y = expl(x); -if( x > MAXSTIR ) - { /* Avoid overflow in pow() */ - v = powl( x, 0.5L * x - 0.25L ); - y = v * (v / y); - } -else - { - y = powl( x, x - 0.5L ) / y; - } -y = SQTPI * y * w; -return( y ); -} - - -long double __tgammal_r(long double x, int* sgngaml) -{ -long double p, q, z; -int i; - -*sgngaml = 1; -#ifdef NANS -if( isnanl(x) ) - return(NANL); -#endif -#ifdef INFINITIES -#ifdef NANS -if( x == INFINITYL ) - return(x); -if( x == -INFINITYL ) - return(NANL); -#else -if( !isfinite(x) ) - return(x); -#endif -#endif -q = fabsl(x); - -if( q > 13.0L ) - { - if( q > MAXGAML ) - goto goverf; - if( x < 0.0L ) - { - p = floorl(q); - if( p == q ) - { -gsing: - _SET_ERRNO(EDOM); - mtherr( "tgammal", SING ); -#ifdef INFINITIES - return (INFINITYL); -#else - return( *sgngaml * MAXNUML); -#endif - } - i = p; - if( (i & 1) == 0 ) - *sgngaml = -1; - z = q - p; - if( z > 0.5L ) - { - p += 1.0L; - z = q - p; - } - z = q * sinl( PIL * z ); - z = fabsl(z) * stirf(q); - if( z <= PIL/MAXNUML ) - { -goverf: - _SET_ERRNO(ERANGE); - mtherr( "tgammal", OVERFLOW ); -#ifdef INFINITIES - return( *sgngaml * INFINITYL); -#else - return( *sgngaml * MAXNUML); -#endif - } - z = PIL/z; - } - else - { - z = stirf(x); - } - return( *sgngaml * z ); - } - -z = 1.0L; -while( x >= 3.0L ) - { - x -= 1.0L; - z *= x; - } - -while( x < -0.03125L ) - { - z /= x; - x += 1.0L; - } - -if( x <= 0.03125L ) - goto Small; - -while( x < 2.0L ) - { - z /= x; - x += 1.0L; - } - -if( x == 2.0L ) - return(z); - -x -= 2.0L; -p = polevll( x, P, 7 ); -q = polevll( x, Q, 8 ); -return( z * p / q ); - -Small: -if( x == 0.0L ) - { - goto gsing; - } -else - { - if( x < 0.0L ) - { - x = -x; - q = z / (x * polevll( x, SN, 8 )); - } - else - q = z / (x * polevll( x, S, 8 )); - } -return q; -} - - -/* This is the C99 version. */ - -long double tgammal(long double x) -{ - int local_sgngaml=0; - return (__tgammal_r(x, &local_sgngaml)); -} - |