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bpo-37798: Add C fastpath for statistics.NormalDist.inv_cdf() (python…
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…GH-15266)
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@corona10 @rhettinger
corona10 authored and rhettinger committed Aug 23, 2019
1 parent 5be6660 commit 0a18ee4
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155 changes: 82 additions & 73 deletions Lib/statistics.py
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Original file line number Diff line number Diff line change
Expand Up @@ -824,6 +824,81 @@ def pstdev(data, mu=None):

## Normal Distribution #####################################################


def _normal_dist_inv_cdf(p, mu, sigma):
# 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.
q = p - 0.5
if fabs(q) <= 0.425:
r = 0.180625 - q * q
# Hash sum: 55.88319_28806_14901_4439
num = (((((((2.50908_09287_30122_6727e+3 * r +
3.34305_75583_58812_8105e+4) * r +
6.72657_70927_00870_0853e+4) * r +
4.59219_53931_54987_1457e+4) * r +
1.37316_93765_50946_1125e+4) * r +
1.97159_09503_06551_4427e+3) * r +
1.33141_66789_17843_7745e+2) * r +
3.38713_28727_96366_6080e+0) * q
den = (((((((5.22649_52788_52854_5610e+3 * r +
2.87290_85735_72194_2674e+4) * r +
3.93078_95800_09271_0610e+4) * r +
2.12137_94301_58659_5867e+4) * r +
5.39419_60214_24751_1077e+3) * r +
6.87187_00749_20579_0830e+2) * r +
4.23133_30701_60091_1252e+1) * r +
1.0)
x = num / den
return mu + (x * sigma)
r = p if q <= 0.0 else 1.0 - p
r = sqrt(-log(r))
if r <= 5.0:
r = r - 1.6
# Hash sum: 49.33206_50330_16102_89036
num = (((((((7.74545_01427_83414_07640e-4 * r +
2.27238_44989_26918_45833e-2) * r +
2.41780_72517_74506_11770e-1) * r +
1.27045_82524_52368_38258e+0) * r +
3.64784_83247_63204_60504e+0) * r +
5.76949_72214_60691_40550e+0) * r +
4.63033_78461_56545_29590e+0) * r +
1.42343_71107_49683_57734e+0)
den = (((((((1.05075_00716_44416_84324e-9 * r +
5.47593_80849_95344_94600e-4) * r +
1.51986_66563_61645_71966e-2) * r +
1.48103_97642_74800_74590e-1) * r +
6.89767_33498_51000_04550e-1) * r +
1.67638_48301_83803_84940e+0) * r +
2.05319_16266_37758_82187e+0) * r +
1.0)
else:
r = r - 5.0
# Hash sum: 47.52583_31754_92896_71629
num = (((((((2.01033_43992_92288_13265e-7 * r +
2.71155_55687_43487_57815e-5) * r +
1.24266_09473_88078_43860e-3) * r +
2.65321_89526_57612_30930e-2) * r +
2.96560_57182_85048_91230e-1) * r +
1.78482_65399_17291_33580e+0) * r +
5.46378_49111_64114_36990e+0) * r +
6.65790_46435_01103_77720e+0)
den = (((((((2.04426_31033_89939_78564e-15 * r +
1.42151_17583_16445_88870e-7) * r +
1.84631_83175_10054_68180e-5) * r +
7.86869_13114_56132_59100e-4) * r +
1.48753_61290_85061_48525e-2) * r +
1.36929_88092_27358_05310e-1) * r +
5.99832_20655_58879_37690e-1) * r +
1.0)
x = num / den
if q < 0.0:
x = -x
return mu + (x * sigma)


class NormalDist:
"Normal distribution of a random variable"
# https://en.wikipedia.org/wiki/Normal_distribution
Expand Down Expand Up @@ -882,79 +957,7 @@ def inv_cdf(self, p):
raise StatisticsError('p must be in the range 0.0 < p < 1.0')
if self._sigma <= 0.0:
raise StatisticsError('cdf() not defined when sigma at or below zero')

# 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.

q = p - 0.5
if fabs(q) <= 0.425:
r = 0.180625 - q * q
# Hash sum: 55.88319_28806_14901_4439
num = (((((((2.50908_09287_30122_6727e+3 * r +
3.34305_75583_58812_8105e+4) * r +
6.72657_70927_00870_0853e+4) * r +
4.59219_53931_54987_1457e+4) * r +
1.37316_93765_50946_1125e+4) * r +
1.97159_09503_06551_4427e+3) * r +
1.33141_66789_17843_7745e+2) * r +
3.38713_28727_96366_6080e+0) * q
den = (((((((5.22649_52788_52854_5610e+3 * r +
2.87290_85735_72194_2674e+4) * r +
3.93078_95800_09271_0610e+4) * r +
2.12137_94301_58659_5867e+4) * r +
5.39419_60214_24751_1077e+3) * r +
6.87187_00749_20579_0830e+2) * r +
4.23133_30701_60091_1252e+1) * r +
1.0)
x = num / den
return self._mu + (x * self._sigma)
r = p if q <= 0.0 else 1.0 - p
r = sqrt(-log(r))
if r <= 5.0:
r = r - 1.6
# Hash sum: 49.33206_50330_16102_89036
num = (((((((7.74545_01427_83414_07640e-4 * r +
2.27238_44989_26918_45833e-2) * r +
2.41780_72517_74506_11770e-1) * r +
1.27045_82524_52368_38258e+0) * r +
3.64784_83247_63204_60504e+0) * r +
5.76949_72214_60691_40550e+0) * r +
4.63033_78461_56545_29590e+0) * r +
1.42343_71107_49683_57734e+0)
den = (((((((1.05075_00716_44416_84324e-9 * r +
5.47593_80849_95344_94600e-4) * r +
1.51986_66563_61645_71966e-2) * r +
1.48103_97642_74800_74590e-1) * r +
6.89767_33498_51000_04550e-1) * r +
1.67638_48301_83803_84940e+0) * r +
2.05319_16266_37758_82187e+0) * r +
1.0)
else:
r = r - 5.0
# Hash sum: 47.52583_31754_92896_71629
num = (((((((2.01033_43992_92288_13265e-7 * r +
2.71155_55687_43487_57815e-5) * r +
1.24266_09473_88078_43860e-3) * r +
2.65321_89526_57612_30930e-2) * r +
2.96560_57182_85048_91230e-1) * r +
1.78482_65399_17291_33580e+0) * r +
5.46378_49111_64114_36990e+0) * r +
6.65790_46435_01103_77720e+0)
den = (((((((2.04426_31033_89939_78564e-15 * r +
1.42151_17583_16445_88870e-7) * r +
1.84631_83175_10054_68180e-5) * r +
7.86869_13114_56132_59100e-4) * r +
1.48753_61290_85061_48525e-2) * r +
1.36929_88092_27358_05310e-1) * r +
5.99832_20655_58879_37690e-1) * r +
1.0)
x = num / den
if q < 0.0:
x = -x
return self._mu + (x * self._sigma)
return _normal_dist_inv_cdf(p, self._mu, self._sigma)

def overlap(self, other):
"""Compute the overlapping coefficient (OVL) between two normal distributions.
Expand Down Expand Up @@ -1078,6 +1081,12 @@ def __hash__(self):
def __repr__(self):
return f'{type(self).__name__}(mu={self._mu!r}, sigma={self._sigma!r})'

# If available, use C implementation
try:
from _statistics import _normal_dist_inv_cdf
except ImportError:
pass


if __name__ == '__main__':

Expand Down
1 change: 1 addition & 0 deletions Misc/NEWS.d/next/Library/2019-08-14-13-51-24.bpo-37798.AmXrik.rst
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@@ -0,0 +1 @@
Add C fastpath for statistics.NormalDist.inv_cdf() Patch by Dong-hee Na
1 change: 1 addition & 0 deletions Modules/Setup
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Original file line number Diff line number Diff line change
Expand Up @@ -182,6 +182,7 @@ _symtable symtablemodule.c
#_heapq _heapqmodule.c # Heap queue algorithm
#_asyncio _asynciomodule.c # Fast asyncio Future
#_json -I$(srcdir)/Include/internal -DPy_BUILD_CORE_BUILTIN _json.c # _json speedups
#_statistics _statisticsmodule.c # statistics accelerator

#unicodedata unicodedata.c # static Unicode character database

Expand Down
122 changes: 122 additions & 0 deletions Modules/_statisticsmodule.c
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Original file line number Diff line number Diff line change
@@ -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;
}
50 changes: 50 additions & 0 deletions Modules/clinic/_statisticsmodule.c.h
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2 changes: 2 additions & 0 deletions PC/config.c
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Original file line number Diff line number Diff line change
Expand Up @@ -23,6 +23,7 @@ extern PyObject* PyInit__sha1(void);
extern PyObject* PyInit__sha256(void);
extern PyObject* PyInit__sha512(void);
extern PyObject* PyInit__sha3(void);
extern PyObject* PyInit__statistics(void);
extern PyObject* PyInit__blake2(void);
extern PyObject* PyInit_time(void);
extern PyObject* PyInit__thread(void);
Expand Down Expand Up @@ -103,6 +104,7 @@ struct _inittab _PyImport_Inittab[] = {
{"_blake2", PyInit__blake2},
{"time", PyInit_time},
{"_thread", PyInit__thread},
{"_statistics", PyInit__statistics},
#ifdef WIN32
{"msvcrt", PyInit_msvcrt},
{"_locale", PyInit__locale},
Expand Down
1 change: 1 addition & 0 deletions PCbuild/pythoncore.vcxproj
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Original file line number Diff line number Diff line change
Expand Up @@ -333,6 +333,7 @@
<ClCompile Include="..\Modules\sha256module.c" />
<ClCompile Include="..\Modules\sha512module.c" />
<ClCompile Include="..\Modules\signalmodule.c" />
<ClCompile Include="..\Modules\_statisticsmodule.c" />
<ClCompile Include="..\Modules\symtablemodule.c" />
<ClCompile Include="..\Modules\_threadmodule.c" />
<ClCompile Include="..\Modules\_tracemalloc.c" />
Expand Down
3 changes: 3 additions & 0 deletions PCbuild/pythoncore.vcxproj.filters
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Original file line number Diff line number Diff line change
Expand Up @@ -611,6 +611,9 @@
<ClCompile Include="..\Modules\_sre.c">
<Filter>Modules</Filter>
</ClCompile>
<ClCompile Include="..\Modules\_statisticsmodule.c">
<Filter>Modules</Filter>
</ClCompile>
<ClCompile Include="..\Modules\_struct.c">
<Filter>Modules</Filter>
</ClCompile>
Expand Down
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