diff options
Diffstat (limited to 'missing')
| -rw-r--r-- | missing/lgamma_r.c | 64 | ||||
| -rw-r--r-- | missing/tgamma.c | 49 |
2 files changed, 113 insertions, 0 deletions
diff --git a/missing/lgamma_r.c b/missing/lgamma_r.c new file mode 100644 index 0000000000..70b6259c6b --- /dev/null +++ b/missing/lgamma_r.c @@ -0,0 +1,64 @@ +/* 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> +#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; + + 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) { + *signp = 1; + return 1.0/0.0; + } + *signp = (fmod(i, 2.0) != 0.0) ? 1 : -1; + s = sin(PI * x); + if (s < 0) s = -s; + return LOG_PI - log(s) - loggamma(1 - x); + } + *signp = 1; + return loggamma(x); +} diff --git a/missing/tgamma.c b/missing/tgamma.c new file mode 100644 index 0000000000..a30108e0b5 --- /dev/null +++ b/missing/tgamma.c @@ -0,0 +1,49 @@ +/* tgamma.c - public domain implementation of error 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 <math.h> +#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) + return PI / (sin(PI * x) * exp(loggamma(1 - x))); + return exp(loggamma(x)); +} + |