/* lgamma_r.c - public domain implementation of 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/ */ #include "ruby/missing.h" /*********************************************************** 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 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); } #ifdef __MINGW_ATTRIB_PURE /* get rid of bugs in math.h of mingw */ #define modf(_X, _Y) __extension__ ({\ double intpart_modf_bug = intpart_modf_bug;\ double result_modf_bug = modf((_X), &intpart_modf_bug);\ *(_Y) = intpart_modf_bug;\ result_modf_bug;\ }) #endif /* 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 = signbit(x) ? -1 : 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); }