1 /* tgamma.c - public domain implementation of function tgamma(3m)
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/
9 /***********************************************************
10 gamma.c -- Gamma function
11 ***********************************************************/
12 #include "ruby/internal/config.h"
13 #include "ruby/missing.h"
20 #define PI 3.14159265358979324 /* $\pi$ */
21 #define LOG_2PI 1.83787706640934548 /* $\log 2\pi$ */
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)
36 loggamma(double x
) /* the natural logarithm of the Gamma function. */
41 while (x
< N
) { v
*= 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
);
51 double tgamma(double x
) /* Gamma function */
54 if (x
== 0.0) { /* Pole Error */
56 return 1/x
< 0 ? -HUGE_VAL
: HUGE_VAL
;
59 if (x
< 0) goto domain_error
;
63 static double zero
= 0.0;
66 if (f
== 0.0) { /* Domain Error */
72 sign
= (fmod(i
, 2.0) != 0.0) ? 1 : -1;
73 return sign
* PI
/ (sin(PI
* f
) * exp(loggamma(1 - x
)));
77 return exp(loggamma(x
));
79 x
= lgamma_r(x
, &sign
);