bpo-37798: Add C fastpath for statistics.NormalDist.inv_cdf() (GH-15266) (GH-15441)

(cherry picked from commit 0a18ee4be7ba215f414bef04598e0849504f9f1e)

Co-authored-by: Dong-hee Na <donghee.na92@gmail.com>

1 files changed, 122 insertions, 0 deletions

diff --git a/Modules/_statisticsmodule.c b/Modules/_statisticsmodule.c
new file mode 100644
index 0000000..78ec90a
--- /dev/null
+++ b/Modules/_statisticsmodule.c
@@ -0,0 +1,122 @@
+/* statistics accelerator C extensor: _statistics module. */
+
+#include "Python.h"
+#include "structmember.h"
+#include "clinic/_statisticsmodule.c.h"
+
+/*[clinic input]
+module _statistics
+
+[clinic start generated code]*/
+/*[clinic end generated code: output=da39a3ee5e6b4b0d input=864a6f59b76123b2]*/
+
+
+static PyMethodDef speedups_methods[] = {
+    _STATISTICS__NORMAL_DIST_INV_CDF_METHODDEF
+    {NULL, NULL, 0, NULL}
+};
+
+/*[clinic input]
+_statistics._normal_dist_inv_cdf -> double
+   p: double
+   mu: double
+   sigma: double
+   /
+[clinic start generated code]*/
+
+static double
+_statistics__normal_dist_inv_cdf_impl(PyObject *module, double p, double mu,
+                                      double sigma)
+/*[clinic end generated code: output=02fd19ddaab36602 input=24715a74be15296a]*/
+{
+    double q, num, den, r, x;
+    q = p - 0.5;
+    // Algorithm AS 241: The Percentage Points of the Normal Distribution
+    if(fabs(q) <= 0.425) {
+        r = 0.180625 - q * q;
+        // Hash sum AB: 55.88319 28806 14901 4439
+        num = (((((((2.5090809287301226727e+3 * r +
+                     3.3430575583588128105e+4) * r +
+                     6.7265770927008700853e+4) * r +
+                     4.5921953931549871457e+4) * r +
+                     1.3731693765509461125e+4) * r +
+                     1.9715909503065514427e+3) * r +
+                     1.3314166789178437745e+2) * r +
+                     3.3871328727963666080e+0) * q;
+        den = (((((((5.2264952788528545610e+3 * r +
+                     2.8729085735721942674e+4) * r +
+                     3.9307895800092710610e+4) * r +
+                     2.1213794301586595867e+4) * r +
+                     5.3941960214247511077e+3) * r +
+                     6.8718700749205790830e+2) * r +
+                     4.2313330701600911252e+1) * r +
+                     1.0);
+        x = num / den;
+        return mu + (x * sigma);
+    }
+    r = q <= 0.0? p : 1.0-p;
+    r = sqrt(-log(r));
+    if (r <= 5.0) {
+        r = r - 1.6;
+        // Hash sum CD: 49.33206 50330 16102 89036
+        num = (((((((7.74545014278341407640e-4 * r +
+                     2.27238449892691845833e-2) * r +
+                     2.41780725177450611770e-1) * r +
+                     1.27045825245236838258e+0) * r +
+                     3.64784832476320460504e+0) * r +
+                     5.76949722146069140550e+0) * r +
+                     4.63033784615654529590e+0) * r +
+                     1.42343711074968357734e+0);
+        den = (((((((1.05075007164441684324e-9 * r +
+                     5.47593808499534494600e-4) * r +
+                     1.51986665636164571966e-2) * r +
+                     1.48103976427480074590e-1) * r +
+                     6.89767334985100004550e-1) * r +
+                     1.67638483018380384940e+0) * r +
+                     2.05319162663775882187e+0) * r +
+                     1.0);
+    } else {
+        r -= 5.0;
+        // Hash sum EF: 47.52583 31754 92896 71629
+        num = (((((((2.01033439929228813265e-7 * r +
+                     2.71155556874348757815e-5) * r +
+                     1.24266094738807843860e-3) * r +
+                     2.65321895265761230930e-2) * r +
+                     2.96560571828504891230e-1) * r +
+                     1.78482653991729133580e+0) * r +
+                     5.46378491116411436990e+0) * r +
+                     6.65790464350110377720e+0);
+        den = (((((((2.04426310338993978564e-15 * r +
+                     1.42151175831644588870e-7) * r +
+                     1.84631831751005468180e-5) * r +
+                     7.86869131145613259100e-4) * r +
+                     1.48753612908506148525e-2) * r +
+                     1.36929880922735805310e-1) * r +
+                     5.99832206555887937690e-1) * r +
+                     1.0);
+    }
+    x = num / den;
+    if (q < 0.0) x = -x;
+    return mu + (x * sigma);
+}
+
+static struct PyModuleDef statisticsmodule = {
+        PyModuleDef_HEAD_INIT,
+        "_statistics",
+        _statistics__normal_dist_inv_cdf__doc__,
+        -1,
+        speedups_methods,
+        NULL,
+        NULL,
+        NULL,
+        NULL
+};
+
+
+PyMODINIT_FUNC
+PyInit__statistics(void)
+{
+    PyObject *m = PyModule_Create(&statisticsmodule);
+    if (!m) return NULL;
+    return m;
+}