/* statistics accelerator C extension: _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]*/

/*
 * There is no closed-form solution to the inverse CDF for the normal
 * distribution, so we use a rational approximation instead:
 * Wichura, M.J. (1988). "Algorithm AS241: The Percentage Points of the
 * Normal Distribution".  Applied Statistics. Blackwell Publishing. 37
 * (3): 477–484. doi:10.2307/2347330. JSTOR 2347330.
 */

/*[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-55.8831928806149014439
        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-49.33206503301610289036
        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-47.52583317549289671629
        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 PyMethodDef statistics_methods[] = {
    _STATISTICS__NORMAL_DIST_INV_CDF_METHODDEF
    {NULL, NULL, 0, NULL}
};

PyDoc_STRVAR(statistics_doc,
"Accelerators for the statistics module.\n");

static struct PyModuleDef statisticsmodule = {
        PyModuleDef_HEAD_INIT,
        "_statistics",
        statistics_doc,
        -1,
        statistics_methods,
        NULL,
        NULL,
        NULL,
        NULL
};

PyMODINIT_FUNC
PyInit__statistics(void)
{
    PyObject *m = PyModule_Create(&statisticsmodule);
    if (!m) return NULL;
    return m;
}