missing/lgamma_r.c

   1 /* lgamma_r.c  - public domain implementation of function lgamma_r(3m)
   2
   3 lgamma_r() is based on gamma().  modified by Tanaka Akira.
   4
   5 reference - Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten
   6             (New Algorithm handbook in C language) (Gijyutsu hyouron
   7             sha, Tokyo, 1991) [in Japanese]
   8             http://oku.edu.mie-u.ac.jp/~okumura/algo/
   9 */
  10
  11 /***********************************************************
  12     gamma.c -- Gamma function
  13 ***********************************************************/
  14 #include <math.h>
  15 #include <errno.h>
  16 #define PI      3.14159265358979324  /* $\pi$ */
  17 #define LOG_2PI 1.83787706640934548  /* $\log 2\pi$ */
  18 #define LOG_PI  1.14472988584940017  /* $\log_e \pi$ */
  19 #define N       8
  20
  21 #define B0  1                 /* Bernoulli numbers */
  22 #define B1  (-1.0 / 2.0)
  23 #define B2  ( 1.0 / 6.0)
  24 #define B4  (-1.0 / 30.0)
  25 #define B6  ( 1.0 / 42.0)
  26 #define B8  (-1.0 / 30.0)
  27 #define B10 ( 5.0 / 66.0)
  28 #define B12 (-691.0 / 2730.0)
  29 #define B14 ( 7.0 / 6.0)
  30 #define B16 (-3617.0 / 510.0)
  31
  32 static double
  33 loggamma(double x)  /* the natural logarithm of the Gamma function. */
  34 {
  35     double v, w;
  36
  37     if (x == 1.0 || x == 2.0) return 0.0;
  38
  39     v = 1;
  40     while (x < N) {  v *= x;  x++;  }
  41     w = 1 / (x * x);
  42     return ((((((((B16 / (16 * 15))  * w + (B14 / (14 * 13))) * w
  43                 + (B12 / (12 * 11))) * w + (B10 / (10 *  9))) * w
  44                 + (B8  / ( 8 *  7))) * w + (B6  / ( 6 *  5))) * w
  45                 + (B4  / ( 4 *  3))) * w + (B2  / ( 2 *  1))) / x
  46                 + 0.5 * LOG_2PI - log(v) - x + (x - 0.5) * log(x);
  47 }
  48
  49 /* the natural logarithm of the absolute value of the Gamma function */
  50 double
  51 lgamma_r(double x, int *signp)
  52 {
  53     if (x <= 0) {
  54         double i, f, s;
  55         f = modf(-x, &i);
  56         if (f == 0.0) { /* pole error */
  57             *signp = 1;
  58             errno = ERANGE;
  59             return HUGE_VAL;
  60         }
  61         *signp = (fmod(i, 2.0) != 0.0) ? 1 : -1;
  62         s = sin(PI * f);
  63         if (s < 0) s = -s;
  64         return LOG_PI - log(s) - loggamma(1 - x);
  65     }
  66     *signp = 1;
  67     return loggamma(x);
  68 }