Ruby: missing/erf.c Source File

Ruby 3.0.5p211 (2022-11-24 revision ba5cf0f7c52d4d35cc6a173c89eda98ceffa2dcf)

erf.c
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1/* erf.c - public domain implementation of error function erf(3m)
2
3reference - Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten
4 (New Algorithm handbook in C language) (Gijyutsu hyouron
5 sha, Tokyo, 1991) p.227 [in Japanese] */
6#include "ruby/missing.h"
7#include <stdio.h>
8#include <math.h>
9
10#ifdef _WIN32
11# include <float.h>
12# if !defined __MINGW32__ || defined __NO_ISOCEXT
13# ifndef isnan
14# define isnan(x) _isnan(x)
15# endif
16# ifndef isinf
17# define isinf(x) (!_finite(x) && !_isnan(x))
18# endif
19# ifndef finite
20# define finite(x) _finite(x)
21# endif
22# endif
23#endif
24
25static double q_gamma(double, double, double);
26
27/* Incomplete gamma function
28 1 / Gamma(a) * Int_0^x exp(-t) t^(a-1) dt */
29static double p_gamma(double a, double x, double loggamma_a)
30{
31 int k;
32 double result, term, previous;
33
34 if (x >= 1 + a) return 1 - q_gamma(a, x, loggamma_a);
35 if (x == 0) return 0;
36 result = term = exp(a * log(x) - x - loggamma_a) / a;
37 for (k = 1; k < 1000; k++) {
38 term *= x / (a + k);
39 previous = result; result += term;
40 if (result == previous) return result;
41 }
42 fprintf(stderr, "erf.c:%d:p_gamma() could not converge.", __LINE__);
43 return result;
44}
45
46/* Incomplete gamma function
47 1 / Gamma(a) * Int_x^inf exp(-t) t^(a-1) dt */
48static double q_gamma(double a, double x, double loggamma_a)
49{
50 int k;
51 double result, w, temp, previous;
52 double la = 1, lb = 1 + x - a; /* Laguerre polynomial */
53
54 if (x < 1 + a) return 1 - p_gamma(a, x, loggamma_a);
55 w = exp(a * log(x) - x - loggamma_a);
56 result = w / lb;
57 for (k = 2; k < 1000; k++) {
58 temp = ((k - 1 - a) * (lb - la) + (k + x) * lb) / k;
59 la = lb; lb = temp;
60 w *= (k - 1 - a) / k;
61 temp = w / (la * lb);
62 previous = result; result += temp;
63 if (result == previous) return result;
64 }
65 fprintf(stderr, "erf.c:%d:q_gamma() could not converge.", __LINE__);
66 return result;
67}
68
69#define LOG_PI_OVER_2 0.572364942924700087071713675675 /* log_e(PI)/2 */
70
71 double erf(double x)
72{
73 if (!finite(x)) {
74 if (isnan(x)) return x; /* erf(NaN) = NaN */
75 return (x>0 ? 1.0 : -1.0); /* erf(+-inf) = +-1.0 */
76 }
77 if (x >= 0) return p_gamma(0.5, x * x, LOG_PI_OVER_2);
78 else return - p_gamma(0.5, x * x, LOG_PI_OVER_2);
79}
80
81 double erfc(double x)
82{
83 if (!finite(x)) {
84 if (isnan(x)) return x; /* erfc(NaN) = NaN */
85 return (x>0 ? 0.0 : 2.0); /* erfc(+-inf) = 0.0, 2.0 */
86 }
87 if (x >= 0) return q_gamma(0.5, x * x, LOG_PI_OVER_2);
88 else return 1 + p_gamma(0.5, x * x, LOG_PI_OVER_2);
89}
erfc
double erfc(double x)
Definition: erf.c:81
LOG_PI_OVER_2
#define LOG_PI_OVER_2
Definition: erf.c:69
erf
double erf(double x)
Definition: erf.c:71
term
const char term
Definition: id.c:37
missing.h
Prototype for *.c in ./missing, and for missing timeval struct.
finite
int finite(double)
Definition: finite.c:6
math.h
Internal header for Math.
log
Definition: gzlog.c:289
isnan
#define isnan(x)
Definition: win32.h:346