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68 lines
2 KiB
C
68 lines
2 KiB
C
/* lgamma_r.c - public domain implementation of function lgamma_r(3m)
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lgamma_r() is based on gamma(). modified by Tanaka Akira.
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reference - Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten
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(New Algorithm handbook in C language) (Gijyutsu hyouron
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sha, Tokyo, 1991) [in Japanese]
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http://oku.edu.mie-u.ac.jp/~okumura/algo/
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*/
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/***********************************************************
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gamma.c -- Gamma function
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***********************************************************/
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#include <math.h>
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#include <errno.h>
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#define PI 3.14159265358979324 /* $\pi$ */
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#define LOG_2PI 1.83787706640934548 /* $\log 2\pi$ */
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#define LOG_PI 1.14472988584940017 /* $\log_e \pi$ */
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#define N 8
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#define B0 1 /* Bernoulli numbers */
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#define B1 (-1.0 / 2.0)
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#define B2 ( 1.0 / 6.0)
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#define B4 (-1.0 / 30.0)
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#define B6 ( 1.0 / 42.0)
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#define B8 (-1.0 / 30.0)
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#define B10 ( 5.0 / 66.0)
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#define B12 (-691.0 / 2730.0)
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#define B14 ( 7.0 / 6.0)
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#define B16 (-3617.0 / 510.0)
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static double
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loggamma(double x) /* the natural logarithm of the Gamma function. */
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{
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double v, w;
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if (x == 1.0 || x == 2.0) return 0.0;
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v = 1;
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while (x < N) { v *= x; x++; }
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w = 1 / (x * x);
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return ((((((((B16 / (16 * 15)) * w + (B14 / (14 * 13))) * w
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+ (B12 / (12 * 11))) * w + (B10 / (10 * 9))) * w
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+ (B8 / ( 8 * 7))) * w + (B6 / ( 6 * 5))) * w
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+ (B4 / ( 4 * 3))) * w + (B2 / ( 2 * 1))) / x
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+ 0.5 * LOG_2PI - log(v) - x + (x - 0.5) * log(x);
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}
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/* the natural logarithm of the absolute value of the Gamma function */
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double
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lgamma_r(double x, int *signp)
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{
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if (x <= 0) {
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double i, f, s;
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f = modf(-x, &i);
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if (f == 0.0) { /* pole error */
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*signp = 1;
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errno = ERANGE;
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return HUGE_VAL;
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}
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*signp = (fmod(i, 2.0) != 0.0) ? 1 : -1;
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s = sin(PI * f);
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if (s < 0) s = -s;
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return LOG_PI - log(s) - loggamma(1 - x);
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}
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*signp = 1;
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return loggamma(x);
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}
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