missing/tgamma.c

   1 /* tgamma.c  - public domain implementation of function tgamma(3m)
   2
   3 reference - Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten
   4             (New Algorithm handbook in C language) (Gijyutsu hyouron
   5             sha, Tokyo, 1991) [in Japanese]
   6             http://oku.edu.mie-u.ac.jp/~okumura/algo/
   7 */
   8
   9 /***********************************************************
  10     gamma.c -- Gamma function
  11 ***********************************************************/
  12 #include "ruby/internal/config.h"
  13 #include "ruby/missing.h"
  14 #include <math.h>
  15 #include <errno.h>
  16
  17 #ifndef HAVE_LGAMMA_R
  18
  19 #include <errno.h>
  20 #define PI      3.14159265358979324  /* $\pi$ */
  21 #define LOG_2PI 1.83787706640934548  /* $\log 2\pi$ */
  22 #define N       8
  23
  24 #define B0  1                 /* Bernoulli numbers */
  25 #define B1  (-1.0 / 2.0)
  26 #define B2  ( 1.0 / 6.0)
  27 #define B4  (-1.0 / 30.0)
  28 #define B6  ( 1.0 / 42.0)
  29 #define B8  (-1.0 / 30.0)
  30 #define B10 ( 5.0 / 66.0)
  31 #define B12 (-691.0 / 2730.0)
  32 #define B14 ( 7.0 / 6.0)
  33 #define B16 (-3617.0 / 510.0)
  34
  35 static double
  36 loggamma(double x)  /* the natural logarithm of the Gamma function. */
  37 {
  38     double v, w;
  39
  40     v = 1;
  41     while (x < N) {  v *= x;  x++;  }
  42     w = 1 / (x * x);
  43     return ((((((((B16 / (16 * 15))  * w + (B14 / (14 * 13))) * w
  44                 + (B12 / (12 * 11))) * w + (B10 / (10 *  9))) * w
  45                 + (B8  / ( 8 *  7))) * w + (B6  / ( 6 *  5))) * w
  46                 + (B4  / ( 4 *  3))) * w + (B2  / ( 2 *  1))) / x
  47                 + 0.5 * LOG_2PI - log(v) - x + (x - 0.5) * log(x);
  48 }
  49 #endif
  50
  51 double tgamma(double x)  /* Gamma function */
  52 {
  53     int sign;
  54     if (x == 0.0) { /* Pole Error */
  55         errno = ERANGE;
  56         return 1/x < 0 ? -HUGE_VAL : HUGE_VAL;
  57     }
  58     if (isinf(x)) {
  59         if (x < 0) goto domain_error;
  60         return x;
  61     }
  62     if (x < 0) {
  63         static double zero = 0.0;
  64         double i, f;
  65         f = modf(-x, &i);
  66         if (f == 0.0) { /* Domain Error */
  67           domain_error:
  68             errno = EDOM;
  69             return zero/zero;
  70         }
  71 #ifndef HAVE_LGAMMA_R
  72         sign = (fmod(i, 2.0) != 0.0) ? 1 : -1;
  73         return sign * PI / (sin(PI * f) * exp(loggamma(1 - x)));
  74 #endif
  75     }
  76 #ifndef HAVE_LGAMMA_R
  77     return exp(loggamma(x));
  78 #else
  79     x = lgamma_r(x, &sign);
  80     return sign * exp(x);
  81 #endif
  82 }