1/* statistics accelerator C extension: _statistics module. */
2
3#include "Python.h"
4#include "clinic/_statisticsmodule.c.h"
5
6/*[clinic input]
7module _statistics
8
9[clinic start generated code]*/
10/*[clinic end generated code: output=da39a3ee5e6b4b0d input=864a6f59b76123b2]*/
11
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 */
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
28static 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;
34    if (p <= 0.0 || p >= 1.0 || sigma <= 0.0) {
35        goto error;
36    }
37
38    q = p - 0.5;
39    if(fabs(q) <= 0.425) {
40        r = 0.180625 - q * q;
41        // Hash sum-55.8831928806149014439
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);
58        if (den == 0.0) {
59            goto error;
60        }
61        x = num / den;
62        return mu + (x * sigma);
63    }
64    r = (q <= 0.0) ? p : (1.0 - p);
65    if (r <= 0.0 || r >= 1.0) {
66        goto error;
67    }
68    r = sqrt(-log(r));
69    if (r <= 5.0) {
70        r = r - 1.6;
71        // Hash sum-49.33206503301610289036
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;
90        // Hash sum-47.52583317549289671629
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    }
108    if (den == 0.0) {
109        goto error;
110    }
111    x = num / den;
112    if (q < 0.0) {
113        x = -x;
114    }
115    return mu + (x * sigma);
116
117  error:
118    PyErr_SetString(PyExc_ValueError, "inv_cdf undefined for these parameters");
119    return -1.0;
120}
121
122
123static PyMethodDef statistics_methods[] = {
124    _STATISTICS__NORMAL_DIST_INV_CDF_METHODDEF
125    {NULL, NULL, 0, NULL}
126};
127
128PyDoc_STRVAR(statistics_doc,
129"Accelerators for the statistics module.\n");
130
131static struct PyModuleDef_Slot _statisticsmodule_slots[] = {
132    {0, NULL}
133};
134
135static struct PyModuleDef statisticsmodule = {
136        PyModuleDef_HEAD_INIT,
137        "_statistics",
138        statistics_doc,
139        0,
140        statistics_methods,
141        _statisticsmodule_slots,
142        NULL,
143        NULL,
144        NULL
145};
146
147PyMODINIT_FUNC
148PyInit__statistics(void)
149{
150    return PyModuleDef_Init(&statisticsmodule);
151}
152