mirror of
https://github.com/KolibriOS/kolibrios.git
synced 2024-12-17 20:32:35 +03:00
417 lines
9.8 KiB
C
417 lines
9.8 KiB
C
/* lgaml()
|
|
*
|
|
* Natural logarithm of gamma function
|
|
*
|
|
*
|
|
*
|
|
* SYNOPSIS:
|
|
*
|
|
* long double x, y, __lgammal_r();
|
|
* int* sgngaml;
|
|
* y = __lgammal_r( x, sgngaml );
|
|
*
|
|
* long double x, y, lgammal();
|
|
* y = lgammal( x);
|
|
*
|
|
*
|
|
*
|
|
* DESCRIPTION:
|
|
*
|
|
* Returns the base e (2.718...) logarithm of the absolute
|
|
* value of the gamma function of the argument. In the reentrant
|
|
* version, the sign (+1 or -1) of the gamma function is returned
|
|
* in the variable referenced by sgngaml.
|
|
*
|
|
* For arguments greater than 33, the logarithm of the gamma
|
|
* function is approximated by the logarithmic version of
|
|
* Stirling's formula using a polynomial approximation of
|
|
* degree 4. Arguments between -33 and +33 are reduced by
|
|
* recurrence to the interval [2,3] of a rational approximation.
|
|
* The cosecant reflection formula is employed for arguments
|
|
* less than -33.
|
|
*
|
|
* Arguments greater than MAXLGML (10^4928) return MAXNUML.
|
|
*
|
|
*
|
|
*
|
|
* ACCURACY:
|
|
*
|
|
*
|
|
* arithmetic domain # trials peak rms
|
|
* IEEE -40, 40 100000 2.2e-19 4.6e-20
|
|
* IEEE 10^-2000,10^+2000 20000 1.6e-19 3.3e-20
|
|
* The error criterion was relative when the function magnitude
|
|
* was greater than one but absolute when it was less than one.
|
|
*
|
|
*/
|
|
|
|
/*
|
|
* Copyright 1994 by Stephen L. Moshier
|
|
*/
|
|
|
|
/*
|
|
* 26-11-2002 Modified for mingw.
|
|
* Danny Smith <dannysmith@users.sourceforge.net>
|
|
*/
|
|
|
|
#ifndef __MINGW32__
|
|
#include "mconf.h"
|
|
#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 );
|
|
#else
|
|
long double fabsl(), lgaml(), logl(), expl(), gammal(), sinl();
|
|
long double floorl(), powl(), polevll(), p1evll(), isnanl(), isfinitel();
|
|
#endif
|
|
#ifdef INFINITIES
|
|
extern long double INFINITYL;
|
|
#endif
|
|
#ifdef NANS
|
|
extern long double NANL;
|
|
#endif
|
|
#else /* __MINGW32__ */
|
|
#include "cephes_mconf.h"
|
|
#endif /* __MINGW32__ */
|
|
|
|
#if UNK
|
|
static 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 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
|
|
|
|
#if UNK
|
|
static 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 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 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
|
|
|
|
|
|
/* A[]: Stirling's formula expansion of log gamma
|
|
* B[], C[]: log gamma function between 2 and 3
|
|
*/
|
|
|
|
|
|
/* log gamma(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x A(1/x^2)
|
|
* x >= 8
|
|
* Peak relative error 1.51e-21
|
|
* Relative spread of error peaks 5.67e-21
|
|
*/
|
|
#if UNK
|
|
static long double A[7] = {
|
|
4.885026142432270781165E-3L,
|
|
-1.880801938119376907179E-3L,
|
|
8.412723297322498080632E-4L,
|
|
-5.952345851765688514613E-4L,
|
|
7.936507795855070755671E-4L,
|
|
-2.777777777750349603440E-3L,
|
|
8.333333333333331447505E-2L,
|
|
};
|
|
#endif
|
|
#if IBMPC
|
|
static const unsigned short A[] = {
|
|
0xd984,0xcc08,0x91c2,0xa012,0x3ff7, XPD
|
|
0x3d91,0x0304,0x3da1,0xf685,0xbff5, XPD
|
|
0x3bdc,0xaad1,0xd492,0xdc88,0x3ff4, XPD
|
|
0x8b20,0x9fce,0x844e,0x9c09,0xbff4, XPD
|
|
0xf8f2,0x30e5,0x0092,0xd00d,0x3ff4, XPD
|
|
0x4d88,0x03a8,0x60b6,0xb60b,0xbff6, XPD
|
|
0x9fcc,0xaaaa,0xaaaa,0xaaaa,0x3ffb, XPD
|
|
};
|
|
#endif
|
|
#if MIEEE
|
|
static long A[21] = {
|
|
0x3ff70000,0xa01291c2,0xcc08d984,
|
|
0xbff50000,0xf6853da1,0x03043d91,
|
|
0x3ff40000,0xdc88d492,0xaad13bdc,
|
|
0xbff40000,0x9c09844e,0x9fce8b20,
|
|
0x3ff40000,0xd00d0092,0x30e5f8f2,
|
|
0xbff60000,0xb60b60b6,0x03a84d88,
|
|
0x3ffb0000,0xaaaaaaaa,0xaaaa9fcc,
|
|
};
|
|
#endif
|
|
|
|
/* log gamma(x+2) = x B(x)/C(x)
|
|
* 0 <= x <= 1
|
|
* Peak relative error 7.16e-22
|
|
* Relative spread of error peaks 4.78e-20
|
|
*/
|
|
#if UNK
|
|
static long double B[7] = {
|
|
-2.163690827643812857640E3L,
|
|
-8.723871522843511459790E4L,
|
|
-1.104326814691464261197E6L,
|
|
-6.111225012005214299996E6L,
|
|
-1.625568062543700591014E7L,
|
|
-2.003937418103815175475E7L,
|
|
-8.875666783650703802159E6L,
|
|
};
|
|
static long double C[7] = {
|
|
/* 1.000000000000000000000E0L,*/
|
|
-5.139481484435370143617E2L,
|
|
-3.403570840534304670537E4L,
|
|
-6.227441164066219501697E5L,
|
|
-4.814940379411882186630E6L,
|
|
-1.785433287045078156959E7L,
|
|
-3.138646407656182662088E7L,
|
|
-2.099336717757895876142E7L,
|
|
};
|
|
#endif
|
|
#if IBMPC
|
|
static const unsigned short B[] = {
|
|
0x9557,0x4995,0x0da1,0x873b,0xc00a, XPD
|
|
0xfe44,0x9af8,0x5b8c,0xaa63,0xc00f, XPD
|
|
0x5aa8,0x7cf5,0x3684,0x86ce,0xc013, XPD
|
|
0x259a,0x258c,0xf206,0xba7f,0xc015, XPD
|
|
0xbe18,0x1ca3,0xc0a0,0xf80a,0xc016, XPD
|
|
0x168f,0x2c42,0x6717,0x98e3,0xc017, XPD
|
|
0x2051,0x9d55,0x92c8,0x876e,0xc016, XPD
|
|
};
|
|
static const unsigned short C[] = {
|
|
/*0x0000,0x0000,0x0000,0x8000,0x3fff, XPD*/
|
|
0xaa77,0xcf2f,0xae76,0x807c,0xc008, XPD
|
|
0xb280,0x0d74,0xb55a,0x84f3,0xc00e, XPD
|
|
0xa505,0xcd30,0x81dc,0x9809,0xc012, XPD
|
|
0x3369,0x4246,0xb8c2,0x92f0,0xc015, XPD
|
|
0x63cf,0x6aee,0xbe6f,0x8837,0xc017, XPD
|
|
0x26bb,0xccc7,0xb009,0xef75,0xc017, XPD
|
|
0x462b,0xbae8,0xab96,0xa02a,0xc017, XPD
|
|
};
|
|
#endif
|
|
#if MIEEE
|
|
static long B[21] = {
|
|
0xc00a0000,0x873b0da1,0x49959557,
|
|
0xc00f0000,0xaa635b8c,0x9af8fe44,
|
|
0xc0130000,0x86ce3684,0x7cf55aa8,
|
|
0xc0150000,0xba7ff206,0x258c259a,
|
|
0xc0160000,0xf80ac0a0,0x1ca3be18,
|
|
0xc0170000,0x98e36717,0x2c42168f,
|
|
0xc0160000,0x876e92c8,0x9d552051,
|
|
};
|
|
static long C[21] = {
|
|
/*0x3fff0000,0x80000000,0x00000000,*/
|
|
0xc0080000,0x807cae76,0xcf2faa77,
|
|
0xc00e0000,0x84f3b55a,0x0d74b280,
|
|
0xc0120000,0x980981dc,0xcd30a505,
|
|
0xc0150000,0x92f0b8c2,0x42463369,
|
|
0xc0170000,0x8837be6f,0x6aee63cf,
|
|
0xc0170000,0xef75b009,0xccc726bb,
|
|
0xc0170000,0xa02aab96,0xbae8462b,
|
|
};
|
|
#endif
|
|
|
|
/* log( sqrt( 2*pi ) ) */
|
|
static const long double LS2PI = 0.91893853320467274178L;
|
|
#define MAXLGM 1.04848146839019521116e+4928L
|
|
|
|
|
|
/* Logarithm of gamma function */
|
|
/* Reentrant version */
|
|
|
|
long double __lgammal_r(long double x, int* sgngaml)
|
|
{
|
|
long double p, q, w, z, f, nx;
|
|
int i;
|
|
|
|
*sgngaml = 1;
|
|
#ifdef NANS
|
|
if( isnanl(x) )
|
|
return(NANL);
|
|
#endif
|
|
#ifdef INFINITIES
|
|
if( !isfinitel(x) )
|
|
return(INFINITYL);
|
|
#endif
|
|
if( x < -34.0L )
|
|
{
|
|
q = -x;
|
|
w = __lgammal_r(q, sgngaml); /* note this modifies sgngam! */
|
|
p = floorl(q);
|
|
if( p == q )
|
|
{
|
|
lgsing:
|
|
_SET_ERRNO(EDOM);
|
|
mtherr( "lgammal", SING );
|
|
#ifdef INFINITIES
|
|
return (INFINITYL);
|
|
#else
|
|
return (MAXNUML);
|
|
#endif
|
|
}
|
|
i = p;
|
|
if( (i & 1) == 0 )
|
|
*sgngaml = -1;
|
|
else
|
|
*sgngaml = 1;
|
|
z = q - p;
|
|
if( z > 0.5L )
|
|
{
|
|
p += 1.0L;
|
|
z = p - q;
|
|
}
|
|
z = q * sinl( PIL * z );
|
|
if( z == 0.0L )
|
|
goto lgsing;
|
|
/* z = LOGPI - logl( z ) - w; */
|
|
z = logl( PIL/z ) - w;
|
|
return( z );
|
|
}
|
|
|
|
if( x < 13.0L )
|
|
{
|
|
z = 1.0L;
|
|
nx = floorl( x + 0.5L );
|
|
f = x - nx;
|
|
while( x >= 3.0L )
|
|
{
|
|
nx -= 1.0L;
|
|
x = nx + f;
|
|
z *= x;
|
|
}
|
|
while( x < 2.0L )
|
|
{
|
|
if( fabsl(x) <= 0.03125 )
|
|
goto lsmall;
|
|
z /= nx + f;
|
|
nx += 1.0L;
|
|
x = nx + f;
|
|
}
|
|
if( z < 0.0L )
|
|
{
|
|
*sgngaml = -1;
|
|
z = -z;
|
|
}
|
|
else
|
|
*sgngaml = 1;
|
|
if( x == 2.0L )
|
|
return( logl(z) );
|
|
x = (nx - 2.0L) + f;
|
|
p = x * polevll( x, B, 6 ) / p1evll( x, C, 7);
|
|
return( logl(z) + p );
|
|
}
|
|
|
|
if( x > MAXLGM )
|
|
{
|
|
_SET_ERRNO(ERANGE);
|
|
mtherr( "lgammal", OVERFLOW );
|
|
#ifdef INFINITIES
|
|
return( *sgngaml * INFINITYL );
|
|
#else
|
|
return( *sgngaml * MAXNUML );
|
|
#endif
|
|
}
|
|
|
|
q = ( x - 0.5L ) * logl(x) - x + LS2PI;
|
|
if( x > 1.0e10L )
|
|
return(q);
|
|
p = 1.0L/(x*x);
|
|
q += polevll( p, A, 6 ) / x;
|
|
return( q );
|
|
|
|
|
|
lsmall:
|
|
if( x == 0.0L )
|
|
goto lgsing;
|
|
if( x < 0.0L )
|
|
{
|
|
x = -x;
|
|
q = z / (x * polevll( x, SN, 8 ));
|
|
}
|
|
else
|
|
q = z / (x * polevll( x, S, 8 ));
|
|
if( q < 0.0L )
|
|
{
|
|
*sgngaml = -1;
|
|
q = -q;
|
|
}
|
|
else
|
|
*sgngaml = 1;
|
|
q = logl( q );
|
|
return(q);
|
|
}
|
|
|
|
/* This is the C99 version */
|
|
|
|
long double lgammal(long double x)
|
|
{
|
|
int local_sgngaml=0;
|
|
return (__lgammal_r(x, &local_sgngaml));
|
|
}
|