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