newlib-cygwin/winsup/mingw/mingwex/math/tgammaf.c

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/* gammaf.c
*
* Gamma function
*
*
*
* SYNOPSIS:
*
* float x, y, __tgammaf_r();
* int* sgngamf;
* y = __tgammaf_r( x, sgngamf );
*
* float x, y, tgammaf();
* y = tgammaf( 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 between 0 and 10 are reduced by recurrence and the
* function is approximated by a polynomial function covering
* the interval (2,3). Large arguments are handled by Stirling's
* formula. Negative arguments are made positive using
* a reflection formula.
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,-33 100,000 5.7e-7 1.0e-7
* IEEE -33,0 100,000 6.1e-7 1.2e-7
*
*
*/
/*
Cephes Math Library Release 2.7: July, 1998
Copyright 1984, 1987, 1989, 1992, 1998 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
/* define MAXGAM 34.84425627277176174 */
/* Stirling's formula for the gamma function
* gamma(x) = sqrt(2 pi) x^(x-.5) exp(-x) ( 1 + 1/x P(1/x) )
* .028 < 1/x < .1
* relative error < 1.9e-11
*/
static const float STIR[] = {
-2.705194986674176E-003,
3.473255786154910E-003,
8.333331788340907E-002,
};
static const float MAXSTIR = 26.77;
static const float SQTPIF = 2.50662827463100050242; /* sqrt( 2 pi ) */
#ifndef __MINGW32__
extern float MAXLOGF, MAXNUMF, PIF;
#ifdef ANSIC
float expf(float);
float logf(float);
float powf( float, float );
float sinf(float);
float gammaf(float);
float floorf(float);
static float stirf(float);
float polevlf( float, float *, int );
float p1evlf( float, float *, int );
#else
float expf(), logf(), powf(), sinf(), floorf();
float polevlf(), p1evlf();
static float stirf();
#endif
#else /* __MINGW32__ */
static float stirf(float);
#endif
/* Gamma function computed by Stirling's formula,
* sqrt(2 pi) x^(x-.5) exp(-x) (1 + 1/x P(1/x))
* The polynomial STIR is valid for 33 <= x <= 172.
*/
static float stirf( float x )
{
float y, w, v;
w = 1.0/x;
w = 1.0 + w * polevlf( w, STIR, 2 );
y = expf( -x );
if( x > MAXSTIR )
{ /* Avoid overflow in pow() */
v = powf( x, 0.5 * x - 0.25 );
y *= v;
y *= v;
}
else
{
y = powf( x, x - 0.5 ) * y;
}
y = SQTPIF * y * w;
return( y );
}
/* gamma(x+2), 0 < x < 1 */
static const float P[] = {
1.536830450601906E-003,
5.397581592950993E-003,
4.130370201859976E-003,
7.232307985516519E-002,
8.203960091619193E-002,
4.117857447645796E-001,
4.227867745131584E-001,
9.999999822945073E-001,
};
float __tgammaf_r( float x, int* sgngamf)
{
float p, q, z, nz;
int i, direction, negative;
#ifdef NANS
if( isnan(x) )
return(x);
#endif
#ifdef INFINITIES
#ifdef NANS
if( x == INFINITYF )
return(x);
if( x == -INFINITYF )
return(NANF);
#else
if( !isfinite(x) )
return(x);
#endif
#endif
*sgngamf = 1;
negative = 0;
nz = 0.0;
if( x < 0.0 )
{
negative = 1;
q = -x;
p = floorf(q);
if( p == q )
{
gsing:
_SET_ERRNO(EDOM);
mtherr( "tgammaf", SING );
#ifdef INFINITIES
return (INFINITYF);
#else
return (MAXNUMF);
#endif
}
i = p;
if( (i & 1) == 0 )
*sgngamf = -1;
nz = q - p;
if( nz > 0.5 )
{
p += 1.0;
nz = q - p;
}
nz = q * sinf( PIF * nz );
if( nz == 0.0 )
{
_SET_ERRNO(ERANGE);
mtherr( "tgamma", OVERFLOW );
#ifdef INFINITIES
return( *sgngamf * INFINITYF);
#else
return( *sgngamf * MAXNUMF);
#endif
}
if( nz < 0 )
nz = -nz;
x = q;
}
if( x >= 10.0 )
{
z = stirf(x);
}
if( x < 2.0 )
direction = 1;
else
direction = 0;
z = 1.0;
while( x >= 3.0 )
{
x -= 1.0;
z *= x;
}
/*
while( x < 0.0 )
{
if( x > -1.E-4 )
goto Small;
z *=x;
x += 1.0;
}
*/
while( x < 2.0 )
{
if( x < 1.e-4 )
goto Small;
z *=x;
x += 1.0;
}
if( direction )
z = 1.0/z;
if( x == 2.0 )
return(z);
x -= 2.0;
p = z * polevlf( x, P, 7 );
gdone:
if( negative )
{
p = *sgngamf * PIF/(nz * p );
}
return(p);
Small:
if( x == 0.0 )
{
goto gsing;
}
else
{
p = z / ((1.0 + 0.5772156649015329 * x) * x);
goto gdone;
}
}
/* This is the C99 version */
float tgammaf(float x)
{
int local_sgngamf=0;
return (__tgammaf_r(x, &local_sgngamf));
}