| 1 | /* erf.c |
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| 2 | reference - Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten |
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| 3 | (New Algorithm handbook in C language) (Gijyutsu hyouron |
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| 4 | sha, Tokyo, 1991) p.227 [in Japanese] */ |
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| 5 | #include <stdio.h> |
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| 6 | #include <math.h> |
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| 7 | |
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| 8 | #ifdef _MSC_VER |
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| 9 | |
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| 10 | |
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| 11 | #ifdef _WIN32 |
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| 12 | # include <float.h> |
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| 13 | # if !defined __MINGW32__ || defined __NO_ISOCEXT |
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| 14 | # ifndef isnan |
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| 15 | # define isnan(x) _isnan(x) |
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| 16 | # endif |
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| 17 | # ifndef isinf |
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| 18 | # define isinf(x) (!_finite(x) && !_isnan(x)) |
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| 19 | # endif |
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| 20 | # ifndef finite |
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| 21 | # define finite(x) _finite(x) |
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| 22 | # endif |
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| 23 | # endif |
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| 24 | #endif |
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| 25 | |
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| 26 | static double q_gamma(double, double, double); |
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| 27 | |
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| 28 | /* Incomplete gamma function |
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| 29 | 1 / Gamma(a) * Int_0^x exp(-t) t^(a-1) dt */ |
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| 30 | static double p_gamma(a, x, loggamma_a) |
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| 31 | double a, x, loggamma_a; |
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| 32 | { |
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| 33 | int k; |
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| 34 | double result, term, previous; |
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| 35 | |
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| 36 | if (x >= 1 + a) return 1 - q_gamma(a, x, loggamma_a); |
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| 37 | if (x == 0) return 0; |
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| 38 | result = term = exp(a * log(x) - x - loggamma_a) / a; |
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| 39 | for (k = 1; k < 1000; k++) { |
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| 40 | term *= x / (a + k); |
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| 41 | previous = result; result += term; |
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| 42 | if (result == previous) return result; |
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| 43 | } |
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| 44 | fprintf(stderr, "erf.c:%d:p_gamma() could not converge.", __LINE__); |
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| 45 | return result; |
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| 46 | } |
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| 47 | |
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| 48 | /* Incomplete gamma function |
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| 49 | 1 / Gamma(a) * Int_x^inf exp(-t) t^(a-1) dt */ |
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| 50 | static double q_gamma(a, x, loggamma_a) |
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| 51 | double a, x, loggamma_a; |
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| 52 | { |
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| 53 | int k; |
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| 54 | double result, w, temp, previous; |
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| 55 | double la = 1, lb = 1 + x - a; /* Laguerre polynomial */ |
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| 56 | |
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| 57 | if (x < 1 + a) return 1 - p_gamma(a, x, loggamma_a); |
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| 58 | w = exp(a * log(x) - x - loggamma_a); |
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| 59 | result = w / lb; |
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| 60 | for (k = 2; k < 1000; k++) { |
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| 61 | temp = ((k - 1 - a) * (lb - la) + (k + x) * lb) / k; |
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| 62 | la = lb; lb = temp; |
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| 63 | w *= (k - 1 - a) / k; |
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| 64 | temp = w / (la * lb); |
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| 65 | previous = result; result += temp; |
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| 66 | if (result == previous) return result; |
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| 67 | } |
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| 68 | fprintf(stderr, "erf.c:%d:q_gamma() could not converge.", __LINE__); |
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| 69 | return result; |
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| 70 | } |
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| 71 | |
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| 72 | #define LOG_PI_OVER_2 0.572364942924700087071713675675 /* log_e(PI)/2 */ |
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| 73 | |
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| 74 | double erf(x) |
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| 75 | double x; |
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| 76 | { |
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| 77 | if (!finite(x)) { |
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| 78 | if (isnan(x)) return x; /* erf(NaN) = NaN */ |
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| 79 | return (x>0 ? 1.0 : -1.0); /* erf(+-inf) = +-1.0 */ |
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| 80 | } |
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| 81 | if (x >= 0) return p_gamma(0.5, x * x, LOG_PI_OVER_2); |
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| 82 | else return - p_gamma(0.5, x * x, LOG_PI_OVER_2); |
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| 83 | } |
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| 84 | |
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| 85 | double erfc(x) |
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| 86 | double x; |
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| 87 | { |
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| 88 | if (!finite(x)) { |
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| 89 | if (isnan(x)) return x; /* erfc(NaN) = NaN */ |
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| 90 | return (x>0 ? 0.0 : 2.0); /* erfc(+-inf) = 0.0, 2.0 */ |
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| 91 | } |
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| 92 | if (x >= 0) return q_gamma(0.5, x * x, LOG_PI_OVER_2); |
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| 93 | else return 1 + p_gamma(0.5, x * x, LOG_PI_OVER_2); |
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| 94 | } |
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| 95 | |
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| 96 | #endif |
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