1/* lgamma_r.c  - public domain implementation of function lgamma_r(3m)
2
3lgamma_r() is based on gamma().  modified by Tanaka Akira.
4
5reference - 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#include "ruby/missing.h"
12/***********************************************************
13    gamma.c -- Gamma function
14***********************************************************/
15#include <math.h>
16#include <errno.h>
17#define PI      3.14159265358979324  /* $\pi$ */
18#define LOG_2PI 1.83787706640934548  /* $\log 2\pi$ */
19#define LOG_PI  1.14472988584940017  /* $\log_e \pi$ */
20#define N       8
21
22#define B0  1                 /* Bernoulli numbers */
23#define B1  (-1.0 / 2.0)
24#define B2  ( 1.0 / 6.0)
25#define B4  (-1.0 / 30.0)
26#define B6  ( 1.0 / 42.0)
27#define B8  (-1.0 / 30.0)
28#define B10 ( 5.0 / 66.0)
29#define B12 (-691.0 / 2730.0)
30#define B14 ( 7.0 / 6.0)
31#define B16 (-3617.0 / 510.0)
32
33static double
34loggamma(double x)  /* the natural logarithm of the Gamma function. */
35{
36    double v, w;
37
38    if (x == 1.0 || x == 2.0) return 0.0;
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
50
51#ifdef __MINGW_ATTRIB_PURE
52/* get rid of bugs in math.h of mingw */
53#define modf(_X, _Y) __extension__ ({\
54    double intpart_modf_bug = intpart_modf_bug;\
55    double result_modf_bug = modf((_X), &intpart_modf_bug);\
56    *(_Y) = intpart_modf_bug;\
57    result_modf_bug;\
58})
59#endif
60
61/* the natural logarithm of the absolute value of the Gamma function */
62double
63lgamma_r(double x, int *signp)
64{
65    if (x <= 0) {
66        double i, f, s;
67        f = modf(-x, &i);
68        if (f == 0.0) { /* pole error */
69            *signp = 1;
70            errno = ERANGE;
71            return HUGE_VAL;
72        }
73        *signp = (fmod(i, 2.0) != 0.0) ? 1 : -1;
74        s = sin(PI * f);
75        if (s < 0) s = -s;
76        return LOG_PI - log(s) - loggamma(1 - x);
77    }
78    *signp = 1;
79    return loggamma(x);
80}
81