Raymond Hettinger | 6fee0f8 | 2019-08-26 11:25:58 -0700 | [diff] [blame] | 1 | /* statistics accelerator C extension: _statistics module. */ |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 2 | |
| 3 | #include "Python.h" |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 4 | #include "clinic/_statisticsmodule.c.h" |
| 5 | |
| 6 | /*[clinic input] |
| 7 | module _statistics |
| 8 | |
| 9 | [clinic start generated code]*/ |
| 10 | /*[clinic end generated code: output=da39a3ee5e6b4b0d input=864a6f59b76123b2]*/ |
| 11 | |
Raymond Hettinger | 6fee0f8 | 2019-08-26 11:25:58 -0700 | [diff] [blame] | 12 | /* |
| 13 | * There is no closed-form solution to the inverse CDF for the normal |
| 14 | * distribution, so we use a rational approximation instead: |
| 15 | * Wichura, M.J. (1988). "Algorithm AS241: The Percentage Points of the |
| 16 | * Normal Distribution". Applied Statistics. Blackwell Publishing. 37 |
| 17 | * (3): 477–484. doi:10.2307/2347330. JSTOR 2347330. |
| 18 | */ |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 19 | |
| 20 | /*[clinic input] |
| 21 | _statistics._normal_dist_inv_cdf -> double |
| 22 | p: double |
| 23 | mu: double |
| 24 | sigma: double |
| 25 | / |
| 26 | [clinic start generated code]*/ |
| 27 | |
| 28 | static double |
| 29 | _statistics__normal_dist_inv_cdf_impl(PyObject *module, double p, double mu, |
| 30 | double sigma) |
| 31 | /*[clinic end generated code: output=02fd19ddaab36602 input=24715a74be15296a]*/ |
| 32 | { |
| 33 | double q, num, den, r, x; |
Raymond Hettinger | 6e27a0d | 2019-09-15 09:36:38 -0700 | [diff] [blame] | 34 | if (p <= 0.0 || p >= 1.0 || sigma <= 0.0) { |
| 35 | goto error; |
| 36 | } |
| 37 | |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 38 | q = p - 0.5; |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 39 | if(fabs(q) <= 0.425) { |
| 40 | r = 0.180625 - q * q; |
Raymond Hettinger | 6fee0f8 | 2019-08-26 11:25:58 -0700 | [diff] [blame] | 41 | // Hash sum-55.8831928806149014439 |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 42 | num = (((((((2.5090809287301226727e+3 * r + |
| 43 | 3.3430575583588128105e+4) * r + |
| 44 | 6.7265770927008700853e+4) * r + |
| 45 | 4.5921953931549871457e+4) * r + |
| 46 | 1.3731693765509461125e+4) * r + |
| 47 | 1.9715909503065514427e+3) * r + |
| 48 | 1.3314166789178437745e+2) * r + |
| 49 | 3.3871328727963666080e+0) * q; |
| 50 | den = (((((((5.2264952788528545610e+3 * r + |
| 51 | 2.8729085735721942674e+4) * r + |
| 52 | 3.9307895800092710610e+4) * r + |
| 53 | 2.1213794301586595867e+4) * r + |
| 54 | 5.3941960214247511077e+3) * r + |
| 55 | 6.8718700749205790830e+2) * r + |
| 56 | 4.2313330701600911252e+1) * r + |
| 57 | 1.0); |
Raymond Hettinger | 6e27a0d | 2019-09-15 09:36:38 -0700 | [diff] [blame] | 58 | if (den == 0.0) { |
| 59 | goto error; |
| 60 | } |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 61 | x = num / den; |
| 62 | return mu + (x * sigma); |
| 63 | } |
Raymond Hettinger | 6fee0f8 | 2019-08-26 11:25:58 -0700 | [diff] [blame] | 64 | r = (q <= 0.0) ? p : (1.0 - p); |
Raymond Hettinger | 6e27a0d | 2019-09-15 09:36:38 -0700 | [diff] [blame] | 65 | if (r <= 0.0 || r >= 1.0) { |
| 66 | goto error; |
| 67 | } |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 68 | r = sqrt(-log(r)); |
| 69 | if (r <= 5.0) { |
| 70 | r = r - 1.6; |
Raymond Hettinger | 6fee0f8 | 2019-08-26 11:25:58 -0700 | [diff] [blame] | 71 | // Hash sum-49.33206503301610289036 |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 72 | num = (((((((7.74545014278341407640e-4 * r + |
| 73 | 2.27238449892691845833e-2) * r + |
| 74 | 2.41780725177450611770e-1) * r + |
| 75 | 1.27045825245236838258e+0) * r + |
| 76 | 3.64784832476320460504e+0) * r + |
| 77 | 5.76949722146069140550e+0) * r + |
| 78 | 4.63033784615654529590e+0) * r + |
| 79 | 1.42343711074968357734e+0); |
| 80 | den = (((((((1.05075007164441684324e-9 * r + |
| 81 | 5.47593808499534494600e-4) * r + |
| 82 | 1.51986665636164571966e-2) * r + |
| 83 | 1.48103976427480074590e-1) * r + |
| 84 | 6.89767334985100004550e-1) * r + |
| 85 | 1.67638483018380384940e+0) * r + |
| 86 | 2.05319162663775882187e+0) * r + |
| 87 | 1.0); |
| 88 | } else { |
| 89 | r -= 5.0; |
Raymond Hettinger | 6fee0f8 | 2019-08-26 11:25:58 -0700 | [diff] [blame] | 90 | // Hash sum-47.52583317549289671629 |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 91 | num = (((((((2.01033439929228813265e-7 * r + |
| 92 | 2.71155556874348757815e-5) * r + |
| 93 | 1.24266094738807843860e-3) * r + |
| 94 | 2.65321895265761230930e-2) * r + |
| 95 | 2.96560571828504891230e-1) * r + |
| 96 | 1.78482653991729133580e+0) * r + |
| 97 | 5.46378491116411436990e+0) * r + |
| 98 | 6.65790464350110377720e+0); |
| 99 | den = (((((((2.04426310338993978564e-15 * r + |
| 100 | 1.42151175831644588870e-7) * r + |
| 101 | 1.84631831751005468180e-5) * r + |
| 102 | 7.86869131145613259100e-4) * r + |
| 103 | 1.48753612908506148525e-2) * r + |
| 104 | 1.36929880922735805310e-1) * r + |
| 105 | 5.99832206555887937690e-1) * r + |
| 106 | 1.0); |
| 107 | } |
Raymond Hettinger | 6e27a0d | 2019-09-15 09:36:38 -0700 | [diff] [blame] | 108 | if (den == 0.0) { |
| 109 | goto error; |
| 110 | } |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 111 | x = num / den; |
Raymond Hettinger | 6fee0f8 | 2019-08-26 11:25:58 -0700 | [diff] [blame] | 112 | if (q < 0.0) { |
| 113 | x = -x; |
| 114 | } |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 115 | return mu + (x * sigma); |
Raymond Hettinger | 6e27a0d | 2019-09-15 09:36:38 -0700 | [diff] [blame] | 116 | |
| 117 | error: |
| 118 | PyErr_SetString(PyExc_ValueError, "inv_cdf undefined for these parameters"); |
| 119 | return -1.0; |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 120 | } |
| 121 | |
Raymond Hettinger | 6fee0f8 | 2019-08-26 11:25:58 -0700 | [diff] [blame] | 122 | |
| 123 | static PyMethodDef statistics_methods[] = { |
| 124 | _STATISTICS__NORMAL_DIST_INV_CDF_METHODDEF |
| 125 | {NULL, NULL, 0, NULL} |
| 126 | }; |
| 127 | |
Dong-hee Na | 0cf832a | 2019-09-03 18:21:45 +0900 | [diff] [blame] | 128 | PyDoc_STRVAR(statistics_doc, |
| 129 | "Accelerators for the statistics module.\n"); |
| 130 | |
Dong-hee Na | 356c878 | 2020-03-17 00:10:21 +0900 | [diff] [blame] | 131 | static struct PyModuleDef_Slot _statisticsmodule_slots[] = { |
| 132 | {0, NULL} |
| 133 | }; |
| 134 | |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 135 | static struct PyModuleDef statisticsmodule = { |
| 136 | PyModuleDef_HEAD_INIT, |
| 137 | "_statistics", |
Dong-hee Na | 0cf832a | 2019-09-03 18:21:45 +0900 | [diff] [blame] | 138 | statistics_doc, |
Dong-hee Na | 356c878 | 2020-03-17 00:10:21 +0900 | [diff] [blame] | 139 | 0, |
Raymond Hettinger | 6fee0f8 | 2019-08-26 11:25:58 -0700 | [diff] [blame] | 140 | statistics_methods, |
Dong-hee Na | 356c878 | 2020-03-17 00:10:21 +0900 | [diff] [blame] | 141 | _statisticsmodule_slots, |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 142 | NULL, |
| 143 | NULL, |
| 144 | NULL |
| 145 | }; |
| 146 | |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 147 | PyMODINIT_FUNC |
| 148 | PyInit__statistics(void) |
| 149 | { |
Dong-hee Na | 356c878 | 2020-03-17 00:10:21 +0900 | [diff] [blame] | 150 | return PyModuleDef_Init(&statisticsmodule); |
Dong-hee Na | 0a18ee4 | 2019-08-24 07:20:30 +0900 | [diff] [blame] | 151 | } |