[Python-checkins] bpo-37798: Add C fastpath for statistics.NormalDist.inv_cdf() (GH-15266) (GH-15441)
Raymond Hettinger
webhook-mailer at python.org
Fri Aug 23 18:39:31 EDT 2019
https://github.com/python/cpython/commit/5779c536321e1405b4c17654a85b8f9221be765e
commit: 5779c536321e1405b4c17654a85b8f9221be765e
branch: 3.8
author: Miss Islington (bot) <31488909+miss-islington at users.noreply.github.com>
committer: Raymond Hettinger <rhettinger at users.noreply.github.com>
date: 2019-08-23T15:39:27-07:00
summary:
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 at gmail.com>
files:
A Misc/NEWS.d/next/Library/2019-08-14-13-51-24.bpo-37798.AmXrik.rst
A Modules/_statisticsmodule.c
A Modules/clinic/_statisticsmodule.c.h
M Lib/statistics.py
M Modules/Setup
M PC/config.c
M PCbuild/pythoncore.vcxproj
M PCbuild/pythoncore.vcxproj.filters
M setup.py
diff --git a/Lib/statistics.py b/Lib/statistics.py
index 77291dd62cb9..c7d6568145e0 100644
--- a/Lib/statistics.py
+++ b/Lib/statistics.py
@@ -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
@@ -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.
@@ -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__':
diff --git a/Misc/NEWS.d/next/Library/2019-08-14-13-51-24.bpo-37798.AmXrik.rst b/Misc/NEWS.d/next/Library/2019-08-14-13-51-24.bpo-37798.AmXrik.rst
new file mode 100644
index 000000000000..620f0ecdf41a
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-08-14-13-51-24.bpo-37798.AmXrik.rst
@@ -0,0 +1 @@
+Add C fastpath for statistics.NormalDist.inv_cdf() Patch by Dong-hee Na
diff --git a/Modules/Setup b/Modules/Setup
index ed5ee6c5033b..983fa014ecb2 100644
--- a/Modules/Setup
+++ b/Modules/Setup
@@ -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
diff --git a/Modules/_statisticsmodule.c b/Modules/_statisticsmodule.c
new file mode 100644
index 000000000000..78ec90a66b0f
--- /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;
+}
diff --git a/Modules/clinic/_statisticsmodule.c.h b/Modules/clinic/_statisticsmodule.c.h
new file mode 100644
index 000000000000..f5a2e4678f30
--- /dev/null
+++ b/Modules/clinic/_statisticsmodule.c.h
@@ -0,0 +1,50 @@
+/*[clinic input]
+preserve
+[clinic start generated code]*/
+
+PyDoc_STRVAR(_statistics__normal_dist_inv_cdf__doc__,
+"_normal_dist_inv_cdf($module, p, mu, sigma, /)\n"
+"--\n"
+"\n");
+
+#define _STATISTICS__NORMAL_DIST_INV_CDF_METHODDEF \
+ {"_normal_dist_inv_cdf", (PyCFunction)(void(*)(void))_statistics__normal_dist_inv_cdf, METH_FASTCALL, _statistics__normal_dist_inv_cdf__doc__},
+
+static double
+_statistics__normal_dist_inv_cdf_impl(PyObject *module, double p, double mu,
+ double sigma);
+
+static PyObject *
+_statistics__normal_dist_inv_cdf(PyObject *module, PyObject *const *args, Py_ssize_t nargs)
+{
+ PyObject *return_value = NULL;
+ double p;
+ double mu;
+ double sigma;
+ double _return_value;
+
+ if (!_PyArg_CheckPositional("_normal_dist_inv_cdf", nargs, 3, 3)) {
+ goto exit;
+ }
+ p = PyFloat_AsDouble(args[0]);
+ if (PyErr_Occurred()) {
+ goto exit;
+ }
+ mu = PyFloat_AsDouble(args[1]);
+ if (PyErr_Occurred()) {
+ goto exit;
+ }
+ sigma = PyFloat_AsDouble(args[2]);
+ if (PyErr_Occurred()) {
+ goto exit;
+ }
+ _return_value = _statistics__normal_dist_inv_cdf_impl(module, p, mu, sigma);
+ if ((_return_value == -1.0) && PyErr_Occurred()) {
+ goto exit;
+ }
+ return_value = PyFloat_FromDouble(_return_value);
+
+exit:
+ return return_value;
+}
+/*[clinic end generated code: output=ba6af124acd34732 input=a9049054013a1b77]*/
diff --git a/PC/config.c b/PC/config.c
index 6f34962bd72d..8eaeb31c9b93 100644
--- a/PC/config.c
+++ b/PC/config.c
@@ -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);
@@ -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},
diff --git a/PCbuild/pythoncore.vcxproj b/PCbuild/pythoncore.vcxproj
index 09a63c04eab8..13c3b594e443 100644
--- a/PCbuild/pythoncore.vcxproj
+++ b/PCbuild/pythoncore.vcxproj
@@ -331,6 +331,7 @@
<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" />
diff --git a/PCbuild/pythoncore.vcxproj.filters b/PCbuild/pythoncore.vcxproj.filters
index 63ab88b4a01d..ebab11930183 100644
--- a/PCbuild/pythoncore.vcxproj.filters
+++ b/PCbuild/pythoncore.vcxproj.filters
@@ -605,6 +605,9 @@
<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>
diff --git a/setup.py b/setup.py
index 6cbbec9e1212..be2ac0b01d00 100644
--- a/setup.py
+++ b/setup.py
@@ -784,6 +784,8 @@ def detect_simple_extensions(self):
self.add(Extension("_abc", ["_abc.c"]))
# _queue module
self.add(Extension("_queue", ["_queuemodule.c"]))
+ # _statistics module
+ self.add(Extension("_statistics", ["_statisticsmodule.c"]))
# Modules with some UNIX dependencies -- on by default:
# (If you have a really backward UNIX, select and socket may not be
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