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