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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 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92  /* tgamma.c - public domain implementation of function tgamma(3m) 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 "ruby/config.h" #include #include #ifdef HAVE_LGAMMA_R double tgamma(double x) { int sign; double d; if (x == 0.0) { /* Pole Error */ errno = ERANGE; return 1/x < 0 ? -HUGE_VAL : HUGE_VAL; } if (x < 0) { static double zero = 0.0; double i, f; f = modf(-x, &i); if (f == 0.0) { /* Domain Error */ errno = EDOM; return zero/zero; } } d = lgamma_r(x, &sign); return sign * exp(d); } #else #include #define PI 3.14159265358979324 /* $\pi$ */ #define LOG_2PI 1.83787706640934548 /* $\log 2\pi$ */ #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; 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); } double tgamma(double x) /* Gamma function */ { if (x == 0.0) { /* Pole Error */ errno = ERANGE; return 1/x < 0 ? -HUGE_VAL : HUGE_VAL; } if (x < 0) { int sign; static double zero = 0.0; double i, f; f = modf(-x, &i); if (f == 0.0) { /* Domain Error */ errno = EDOM; return zero/zero; } sign = (fmod(i, 2.0) != 0.0) ? 1 : -1; return sign * PI / (sin(PI * f) * exp(loggamma(1 - x))); } return exp(loggamma(x)); } #endif