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/* 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 <math.h>
#include <errno.h>
#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 double
loggamma(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 */
double
lgamma_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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