1  /* statistics accelerator C extension: _statistics module. */
       2  
       3  #include "Python.h"
       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  
      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  
      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;
      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  
     123  static PyMethodDef statistics_methods[] = {
     124      _STATISTICS__NORMAL_DIST_INV_CDF_METHODDEF
     125      {NULL, NULL, 0, NULL}
     126  };
     127  
     128  PyDoc_STRVAR(statistics_doc,
     129  "Accelerators for the statistics module.\n");
     130  
     131  static struct PyModuleDef_Slot _statisticsmodule_slots[] = {
     132      {0, NULL}
     133  };
     134  
     135  static 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  
     147  PyMODINIT_FUNC
     148  PyInit__statistics(void)
     149  {
     150      return PyModuleDef_Init(&statisticsmodule);
     151  }