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/* tgamma.c - public domain implementation of function tgamma(3m)
reference - Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten
(New Algorithm handbook in C language) (Gijyutsu hyouron
sha, Tokyo, 1991) [in Japanese]
http://oku.edu.mie-u.ac.jp/~okumura/algo/
*/
/***********************************************************
gamma.c -- Gamma function
***********************************************************/
#include "ruby/config.h"
#include <math.h>
#include <errno.h>
#ifdef HAVE_LGAMMA_R
double tgamma(double x)
{
int sign;
double d;
if (x == 0.0) { /* Pole Error */
errno = ERANGE;
return 1/x < 0 ? -HUGE_VAL : HUGE_VAL;
}
if (x < 0) {
static double zero = 0.0;
double i, f;
f = modf(-x, &i);
if (f == 0.0) { /* Domain Error */
errno = EDOM;
return zero/zero;
}
}
d = lgamma_r(x, &sign);
return sign * exp(d);
}
#else
#include <errno.h>
#define PI 3.14159265358979324 /* $\pi$ */
#define LOG_2PI 1.83787706640934548 /* $\log 2\pi$ */
#define N 8
#define B0 1 /* Bernoulli numbers */
#define B1 (-1.0 / 2.0)
#define B2 ( 1.0 / 6.0)
#define B4 (-1.0 / 30.0)
#define B6 ( 1.0 / 42.0)
#define B8 (-1.0 / 30.0)
#define B10 ( 5.0 / 66.0)
#define B12 (-691.0 / 2730.0)
#define B14 ( 7.0 / 6.0)
#define B16 (-3617.0 / 510.0)
static double
loggamma(double x) /* the natural logarithm of the Gamma function. */
{
double v, w;
v = 1;
while (x < N) { v *= x; x++; }
w = 1 / (x * x);
return ((((((((B16 / (16 * 15)) * w + (B14 / (14 * 13))) * w
+ (B12 / (12 * 11))) * w + (B10 / (10 * 9))) * w
+ (B8 / ( 8 * 7))) * w + (B6 / ( 6 * 5))) * w
+ (B4 / ( 4 * 3))) * w + (B2 / ( 2 * 1))) / x
+ 0.5 * LOG_2PI - log(v) - x + (x - 0.5) * log(x);
}
double tgamma(double x) /* Gamma function */
{
if (x == 0.0) { /* Pole Error */
errno = ERANGE;
return 1/x < 0 ? -HUGE_VAL : HUGE_VAL;
}
if (x < 0) {
int sign;
static double zero = 0.0;
double i, f;
f = modf(-x, &i);
if (f == 0.0) { /* Domain Error */
errno = EDOM;
return zero/zero;
}
sign = (fmod(i, 2.0) != 0.0) ? 1 : -1;
return sign * PI / (sin(PI * f) * exp(loggamma(1 - x)));
}
return exp(loggamma(x));
}
#endif
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