266 lines
4.5 KiB
C
266 lines
4.5 KiB
C
/* gammaf.c
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*
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* Gamma function
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*
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*
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*
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* SYNOPSIS:
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*
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* float x, y, __tgammaf_r();
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* int* sgngamf;
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* y = __tgammaf_r( x, sgngamf );
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*
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* float x, y, tgammaf();
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* y = tgammaf( x);
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*
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*
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* DESCRIPTION:
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*
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* Returns gamma function of the argument. The result is
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* correctly signed. In the reentrant version the sign (+1 or -1)
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* is returned in the variable referenced by sgngamf.
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*
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* Arguments between 0 and 10 are reduced by recurrence and the
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* function is approximated by a polynomial function covering
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* the interval (2,3). Large arguments are handled by Stirling's
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* formula. Negative arguments are made positive using
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* a reflection formula.
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE 0,-33 100,000 5.7e-7 1.0e-7
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* IEEE -33,0 100,000 6.1e-7 1.2e-7
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*
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*
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*/
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/*
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Cephes Math Library Release 2.7: July, 1998
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Copyright 1984, 1987, 1989, 1992, 1998 by Stephen L. Moshier
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*/
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/*
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* 26-11-2002 Modified for mingw.
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* Danny Smith <dannysmith@users.sourceforge.net>
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*/
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#ifndef __MINGW32__
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#include "mconf.h"
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#else
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#include "cephes_mconf.h"
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#endif
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/* define MAXGAM 34.84425627277176174 */
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/* Stirling's formula for the gamma function
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* gamma(x) = sqrt(2 pi) x^(x-.5) exp(-x) ( 1 + 1/x P(1/x) )
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* .028 < 1/x < .1
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* relative error < 1.9e-11
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*/
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static const float STIR[] = {
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-2.705194986674176E-003,
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3.473255786154910E-003,
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8.333331788340907E-002,
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};
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static const float MAXSTIR = 26.77;
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static const float SQTPIF = 2.50662827463100050242; /* sqrt( 2 pi ) */
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#ifndef __MINGW32__
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extern float MAXLOGF, MAXNUMF, PIF;
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#ifdef ANSIC
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float expf(float);
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float logf(float);
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float powf( float, float );
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float sinf(float);
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float gammaf(float);
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float floorf(float);
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static float stirf(float);
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float polevlf( float, float *, int );
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float p1evlf( float, float *, int );
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#else
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float expf(), logf(), powf(), sinf(), floorf();
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float polevlf(), p1evlf();
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static float stirf();
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#endif
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#else /* __MINGW32__ */
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static float stirf(float);
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#endif
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/* Gamma function computed by Stirling's formula,
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* sqrt(2 pi) x^(x-.5) exp(-x) (1 + 1/x P(1/x))
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* The polynomial STIR is valid for 33 <= x <= 172.
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*/
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static float stirf( float x )
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{
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float y, w, v;
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w = 1.0/x;
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w = 1.0 + w * polevlf( w, STIR, 2 );
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y = expf( -x );
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if( x > MAXSTIR )
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{ /* Avoid overflow in pow() */
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v = powf( x, 0.5 * x - 0.25 );
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y *= v;
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y *= v;
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}
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else
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{
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y = powf( x, x - 0.5 ) * y;
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}
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y = SQTPIF * y * w;
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return( y );
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}
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/* gamma(x+2), 0 < x < 1 */
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static const float P[] = {
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1.536830450601906E-003,
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5.397581592950993E-003,
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4.130370201859976E-003,
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7.232307985516519E-002,
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8.203960091619193E-002,
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4.117857447645796E-001,
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4.227867745131584E-001,
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9.999999822945073E-001,
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};
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float __tgammaf_r( float x, int* sgngamf)
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{
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float p, q, z, nz;
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int i, direction, negative;
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#ifdef NANS
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if( isnan(x) )
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return(x);
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#endif
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#ifdef INFINITIES
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#ifdef NANS
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if( x == INFINITYF )
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return(x);
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if( x == -INFINITYF )
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return(NANF);
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#else
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if( !isfinite(x) )
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return(x);
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#endif
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#endif
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*sgngamf = 1;
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negative = 0;
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nz = 0.0;
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if( x < 0.0 )
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{
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negative = 1;
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q = -x;
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p = floorf(q);
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if( p == q )
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{
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gsing:
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_SET_ERRNO(EDOM);
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mtherr( "tgammaf", SING );
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#ifdef INFINITIES
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return (INFINITYF);
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#else
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return (MAXNUMF);
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#endif
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}
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i = p;
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if( (i & 1) == 0 )
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*sgngamf = -1;
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nz = q - p;
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if( nz > 0.5 )
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{
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p += 1.0;
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nz = q - p;
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}
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nz = q * sinf( PIF * nz );
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if( nz == 0.0 )
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{
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_SET_ERRNO(ERANGE);
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mtherr( "tgamma", OVERFLOW );
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#ifdef INFINITIES
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return( *sgngamf * INFINITYF);
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#else
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return( *sgngamf * MAXNUMF);
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#endif
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}
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if( nz < 0 )
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nz = -nz;
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x = q;
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}
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if( x >= 10.0 )
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{
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z = stirf(x);
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}
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if( x < 2.0 )
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direction = 1;
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else
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direction = 0;
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z = 1.0;
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while( x >= 3.0 )
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{
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x -= 1.0;
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z *= x;
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}
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/*
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while( x < 0.0 )
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{
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if( x > -1.E-4 )
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goto Small;
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z *=x;
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x += 1.0;
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}
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*/
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while( x < 2.0 )
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{
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if( x < 1.e-4 )
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goto Small;
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z *=x;
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x += 1.0;
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}
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if( direction )
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z = 1.0/z;
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if( x == 2.0 )
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return(z);
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x -= 2.0;
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p = z * polevlf( x, P, 7 );
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gdone:
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if( negative )
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{
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p = *sgngamf * PIF/(nz * p );
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}
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return(p);
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Small:
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if( x == 0.0 )
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{
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goto gsing;
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}
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else
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{
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p = z / ((1.0 + 0.5772156649015329 * x) * x);
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goto gdone;
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}
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}
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/* This is the C99 version */
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float tgammaf(float x)
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{
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int local_sgngamf=0;
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return (__tgammaf_r(x, &local_sgngamf));
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}
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