newlib/winsup/mingw/mingwex/math/tgamma.c

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/* gamma.c
*
* Gamma function
*
*
*
* SYNOPSIS:
*
* double x, y, __tgamma_r();
* int* sgngam;
* y = __tgamma_r( x, sgngam );
*
* double x, y, tgamma();
* y = tgamma( 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 sgngam.
*
* Arguments |x| <= 34 are reduced by recurrence and the function
* approximated by a rational function of degree 6/7 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
* DEC -34, 34 10000 1.3e-16 2.5e-17
* IEEE -170,-33 20000 2.3e-15 3.3e-16
* IEEE -33, 33 20000 9.4e-16 2.2e-16
* IEEE 33, 171.6 20000 2.3e-15 3.2e-16
*
* Error for arguments outside the test range will be larger
* owing to error amplification by the exponential function.
*
*/
/*
Cephes Math Library Release 2.8: June, 2000
Copyright 1984, 1987, 1989, 1992, 2000 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
#ifdef UNK
static const double P[] = {
1.60119522476751861407E-4,
1.19135147006586384913E-3,
1.04213797561761569935E-2,
4.76367800457137231464E-2,
2.07448227648435975150E-1,
4.94214826801497100753E-1,
9.99999999999999996796E-1
};
static const double Q[] = {
-2.31581873324120129819E-5,
5.39605580493303397842E-4,
-4.45641913851797240494E-3,
1.18139785222060435552E-2,
3.58236398605498653373E-2,
-2.34591795718243348568E-1,
7.14304917030273074085E-2,
1.00000000000000000320E0
};
#define MAXGAM 171.624376956302725
static const double LOGPI = 1.14472988584940017414;
#endif
#ifdef DEC
static const unsigned short P[] = {
0035047,0162701,0146301,0005234,
0035634,0023437,0032065,0176530,
0036452,0137157,0047330,0122574,
0037103,0017310,0143041,0017232,
0037524,0066516,0162563,0164605,
0037775,0004671,0146237,0014222,
0040200,0000000,0000000,0000000
};
static const unsigned short Q[] = {
0134302,0041724,0020006,0116565,
0035415,0072121,0044251,0025634,
0136222,0003447,0035205,0121114,
0036501,0107552,0154335,0104271,
0037022,0135717,0014776,0171471,
0137560,0034324,0165024,0037021,
0037222,0045046,0047151,0161213,
0040200,0000000,0000000,0000000
};
#define MAXGAM 34.84425627277176174
#endif
#ifdef IBMPC
static const uD P[] = {
{ { 0x2153,0x3998,0xfcb8,0x3f24 } },
{ { 0xbfab,0xe686,0x84e3,0x3f53 } },
{ { 0x14b0,0xe9db,0x57cd,0x3f85 } },
{ { 0x23d3,0x18c4,0x63d9,0x3fa8 } },
{ { 0x7d31,0xdcae,0x8da9,0x3fca } },
{ { 0xe312,0x3993,0xa137,0x3fdf } },
{ { 0x0000,0x0000,0x0000,0x3ff0 } }
};
static const uD Q[] = {
{ { 0xd3af,0x8400,0x487a,0xbef8 } },
{ { 0x2573,0x2915,0xae8a,0x3f41 } },
{ { 0xb44a,0xe750,0x40e4,0xbf72 } },
{ { 0xb117,0x5b1b,0x31ed,0x3f88 } },
{ { 0xde67,0xe33f,0x5779,0x3fa2 } },
{ { 0x87c2,0x9d42,0x071a,0xbfce } },
{ { 0x3c51,0xc9cd,0x4944,0x3fb2 } },
{ { 0x0000,0x0000,0x0000,0x3ff0 } }
};
#define MAXGAM 171.624376956302725
#endif
#ifdef MIEEE
static const unsigned short P[] = {
0x3f24,0xfcb8,0x3998,0x2153,
0x3f53,0x84e3,0xe686,0xbfab,
0x3f85,0x57cd,0xe9db,0x14b0,
0x3fa8,0x63d9,0x18c4,0x23d3,
0x3fca,0x8da9,0xdcae,0x7d31,
0x3fdf,0xa137,0x3993,0xe312,
0x3ff0,0x0000,0x0000,0x0000
};
static const unsigned short Q[] = {
0xbef8,0x487a,0x8400,0xd3af,
0x3f41,0xae8a,0x2915,0x2573,
0xbf72,0x40e4,0xe750,0xb44a,
0x3f88,0x31ed,0x5b1b,0xb117,
0x3fa2,0x5779,0xe33f,0xde67,
0xbfce,0x071a,0x9d42,0x87c2,
0x3fb2,0x4944,0xc9cd,0x3c51,
0x3ff0,0x0000,0x0000,0x0000
};
#define MAXGAM 171.624376956302725
#endif
/* Stirling's formula for the gamma function */
#if UNK
static const double STIR[5] = {
7.87311395793093628397E-4,
-2.29549961613378126380E-4,
-2.68132617805781232825E-3,
3.47222221605458667310E-3,
8.33333333333482257126E-2,
};
#define MAXSTIR 143.01608
static const double SQTPI = 2.50662827463100050242E0;
#endif
#if DEC
static const unsigned short STIR[20] = {
0035516,0061622,0144553,0112224,
0135160,0131531,0037460,0165740,
0136057,0134460,0037242,0077270,
0036143,0107070,0156306,0027751,
0037252,0125252,0125252,0146064,
};
#define MAXSTIR 26.77
static const unsigned short SQT[4] = {
0040440,0066230,0177661,0034055,
};
#define SQTPI *(double *)SQT
#endif
#if IBMPC
static const uD STIR[] = {
{ { 0x7293,0x592d,0xcc72,0x3f49 } },
{ { 0x1d7c,0x27e6,0x166b,0xbf2e } },
{ { 0x4fd7,0x07d4,0xf726,0xbf65 } },
{ { 0xc5fd,0x1b98,0x71c7,0x3f6c } },
{ { 0x5986,0x5555,0x5555,0x3fb5 } }
};
#define MAXSTIR 143.01608
static const union
{
unsigned short s[4];
double d;
} sqt = {{0x2706,0x1ff6,0x0d93,0x4004}};
#define SQTPI (sqt.d)
#endif
#if MIEEE
static const unsigned short STIR[20] = {
0x3f49,0xcc72,0x592d,0x7293,
0xbf2e,0x166b,0x27e6,0x1d7c,
0xbf65,0xf726,0x07d4,0x4fd7,
0x3f6c,0x71c7,0x1b98,0xc5fd,
0x3fb5,0x5555,0x5555,0x5986,
};
#define MAXSTIR 143.01608
static const unsigned short SQT[4] = {
0x4004,0x0d93,0x1ff6,0x2706,
};
#define SQTPI *(double *)SQT
#endif
#ifndef __MINGW32__
int sgngam = 0;
extern int sgngam;
extern double MAXLOG, MAXNUM, PI;
#ifdef ANSIPROT
extern double pow ( double, double );
extern double log ( double );
extern double exp ( double );
extern double sin ( double );
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double floor ( double );
extern double fabs ( double );
extern int isnan ( double );
extern int isfinite ( double );
static double stirf ( double );
double lgam ( double );
#else
double pow(), log(), exp(), sin(), polevl(), p1evl(), floor(), fabs();
int isnan(), isfinite();
static double stirf();
double lgam();
#endif
#ifdef INFINITIES
extern double INFINITY;
#endif
#ifdef NANS
extern double NAN;
#endif
#else /* __MINGW32__ */
static double stirf ( double );
#endif
/* Gamma function computed by Stirling's formula.
* The polynomial STIR is valid for 33 <= x <= 172.
*/
static double stirf(x)
double x;
{
double y, w, v;
w = 1.0/x;
w = 1.0 + w * polevl( w, STIR, 4 );
y = exp(x);
if( x > MAXSTIR )
{ /* Avoid overflow in pow() */
v = pow( x, 0.5 * x - 0.25 );
y = v * (v / y);
}
else
{
y = pow( x, x - 0.5 ) / y;
}
y = SQTPI * y * w;
return( y );
}
double __tgamma_r(double x, int* sgngam)
{
double p, q, z;
int i;
*sgngam = 1;
#ifdef NANS
if( isnan(x) )
return(x);
#endif
#ifdef INFINITIES
#ifdef NANS
if( x == INFINITY )
return(x);
if( x == -INFINITY )
return(NAN);
#else
if( !isfinite(x) )
return(x);
#endif
#endif
q = fabs(x);
if( q > 33.0 )
{
if( x < 0.0 )
{
p = floor(q);
if( p == q )
{
gsing:
_SET_ERRNO(EDOM);
mtherr( "tgamma", SING );
#ifdef INFINITIES
return (INFINITY);
#else
return (MAXNUM);
#endif
}
i = p;
if( (i & 1) == 0 )
*sgngam = -1;
z = q - p;
if( z > 0.5 )
{
p += 1.0;
z = q - p;
}
z = q * sin( PI * z );
if( z == 0.0 )
{
_SET_ERRNO(ERANGE);
mtherr( "tgamma", OVERFLOW );
#ifdef INFINITIES
return( *sgngam * INFINITY);
#else
return( *sgngam * MAXNUM);
#endif
}
z = fabs(z);
z = PI/(z * stirf(q) );
}
else
{
z = stirf(x);
}
return( *sgngam * z );
}
z = 1.0;
while( x >= 3.0 )
{
x -= 1.0;
z *= x;
}
while( x < 0.0 )
{
if( x > -1.E-9 )
goto Small;
z /= x;
x += 1.0;
}
while( x < 2.0 )
{
if( x < 1.e-9 )
goto Small;
z /= x;
x += 1.0;
}
if( x == 2.0 )
return(z);
x -= 2.0;
p = polevl( x, P, 6 );
q = polevl( x, Q, 7 );
return( z * p / q );
Small:
if( x == 0.0 )
{
goto gsing;
}
else
return( z/((1.0 + 0.5772156649015329 * x) * x) );
}
/* This is the C99 version */
double tgamma(double x)
{
int local_sgngam=0;
return (__tgamma_r(x, &local_sgngam));
}