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-rw-r--r--missing/erf.c91
1 files changed, 91 insertions, 0 deletions
diff --git a/missing/erf.c b/missing/erf.c
new file mode 100644
index 00000000000..e30a90051e5
--- /dev/null
+++ b/missing/erf.c
@@ -0,0 +1,91 @@
+/* erf.c
+reference - Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten
+ (New Algorithm handbook in C language) (Gijyutsu hyouron
+ sha, Tokyo, 1991) p.227 [in Japanese] */
+#include <stdio.h>
+#include <math.h>
+
+#ifdef _WIN32
+# include <float.h>
+# if !defined __MINGW32__ || defined __NO_ISOCEXT
+# ifndef isnan
+# define isnan(x) _isnan(x)
+# endif
+# ifndef isinf
+# define isinf(x) (!_finite(x) && !_isnan(x))
+# endif
+# ifndef finite
+# define finite(x) _finite(x)
+# endif
+# endif
+#endif
+
+static double q_gamma(double, double, double);
+
+/* Incomplete gamma function
+ 1 / Gamma(a) * Int_0^x exp(-t) t^(a-1) dt */
+static double p_gamma(a, x, loggamma_a)
+ double a, x, loggamma_a;
+{
+ int k;
+ double result, term, previous;
+
+ if (x >= 1 + a) return 1 - q_gamma(a, x, loggamma_a);
+ if (x == 0) return 0;
+ result = term = exp(a * log(x) - x - loggamma_a) / a;
+ for (k = 1; k < 1000; k++) {
+ term *= x / (a + k);
+ previous = result; result += term;
+ if (result == previous) return result;
+ }
+ fprintf(stderr, "erf.c:%d:p_gamma() could not converge.", __LINE__);
+ return result;
+}
+
+/* Incomplete gamma function
+ 1 / Gamma(a) * Int_x^inf exp(-t) t^(a-1) dt */
+static double q_gamma(a, x, loggamma_a)
+ double a, x, loggamma_a;
+{
+ int k;
+ double result, w, temp, previous;
+ double la = 1, lb = 1 + x - a; /* Laguerre polynomial */
+
+ if (x < 1 + a) return 1 - p_gamma(a, x, loggamma_a);
+ w = exp(a * log(x) - x - loggamma_a);
+ result = w / lb;
+ for (k = 2; k < 1000; k++) {
+ temp = ((k - 1 - a) * (lb - la) + (k + x) * lb) / k;
+ la = lb; lb = temp;
+ w *= (k - 1 - a) / k;
+ temp = w / (la * lb);
+ previous = result; result += temp;
+ if (result == previous) return result;
+ }
+ fprintf(stderr, "erf.c:%d:q_gamma() could not converge.", __LINE__);
+ return result;
+}
+
+#define LOG_PI_OVER_2 0.572364942924700087071713675675 /* log_e(PI)/2 */
+
+double erf(x)
+ double x;
+{
+ if (!finite(x)) {
+ if (isnan(x)) return x; /* erf(NaN) = NaN */
+ return (x>0 ? 1.0 : -1.0); /* erf(+-inf) = +-1.0 */
+ }
+ if (x >= 0) return p_gamma(0.5, x * x, LOG_PI_OVER_2);
+ else return - p_gamma(0.5, x * x, LOG_PI_OVER_2);
+}
+
+double erfc(x)
+ double x;
+{
+ if (!finite(x)) {
+ if (isnan(x)) return x; /* erfc(NaN) = NaN */
+ return (x>0 ? 0.0 : 2.0); /* erfc(+-inf) = 0.0, 2.0 */
+ }
+ if (x >= 0) return q_gamma(0.5, x * x, LOG_PI_OVER_2);
+ else return 1 + p_gamma(0.5, x * x, LOG_PI_OVER_2);
+}