mingw-w64-crt/math/tgamma.c

/**
 * This file has no copyright assigned and is placed in the Public Domain.
 * This file is part of the mingw-w64 runtime package.
 * No warranty is given; refer to the file DISCLAIMER.PD within this package.
 */
#include "cephes_mconf.h"

#ifdef UNK
static const uD P[7] = {
  { { 1.60119522476751861407E-4 } },
  { { 1.19135147006586384913E-3 } },
  { { 1.04213797561761569935E-2 } },
  { { 4.76367800457137231464E-2 } },
  { { 2.07448227648435975150E-1 } },
  { { 4.94214826801497100753E-1 } },
  { { 9.99999999999999996796E-1 } }
};
static const uD Q[8] = {
  { { -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 IBMPC
static const uD P[7] = {
  { { 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[8] = {
  { { 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 uD P[7] = {
  { { 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[8] = {
  { { 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 uD 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 IBMPC
static const uD STIR[5] = {
  { { 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 uD STIR[5] = {
  { { 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 uD SQT = {
  { { 0x4004,0x0d93,0x1ff6,0x2706 } }
};
#define SQTPI SQT.d
#endif

static double stirf (double);

/* Gamma function computed by Stirling's formula.
 * The polynomial STIR is valid for 33 <= x <= 172.
 */
static double stirf(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 __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
	if (x == 0.0)
		return copysign(HUGE_VAL, x);

	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 NANS
				return (NAN);
#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));
}