https://github.com/python/cpython/commit/d22213434af5223d34628f8796f4ec697e5449bc
commit: d22213434af5223d34628f8796f4ec697e5449bc
branch: main
author: Raymond Hettinger <[email protected]>
committer: rhettinger <[email protected]>
date: 2026-09-13T10:32:53-05:00
summary:
Minor accuracy improvements in statistics (gh-157380)
files:
M Lib/statistics.py
diff --git a/Lib/statistics.py b/Lib/statistics.py
index 758b5b58848fb9..eee3e6eb94e990 100644
--- a/Lib/statistics.py
+++ b/Lib/statistics.py
@@ -138,14 +138,15 @@
from decimal import Decimal
from itertools import compress, count, groupby, repeat
from bisect import bisect_left, bisect_right
-from math import hypot, sqrt, fabs, exp, erfc, tau, log, fsum, sumprod
-from math import isfinite, isinf, pi, cos, sin, tan, cosh, asin, atan, acos
+from math import hypot, sqrt, fabs, exp, erfc, log, fsum, sumprod
+from math import isfinite, isinf, pi, sin, cosh
+from math import sinpi, cospi, tanpi, asinpi, acospi, atanpi
from functools import reduce
from operator import itemgetter
from collections import Counter, namedtuple, defaultdict
_SQRT2 = sqrt(2.0)
-_SQRT2PI = sqrt(tau)
+_SQRT2PI = float.fromhex('0x1.40d931ff62706p+1') # Correctly rounded
sqrt(2*pi)
_random = random
## Exceptions ##############################################################
@@ -820,8 +821,8 @@ def deco(builder):
@register('normal', 'gauss')
def normal_kernel():
- sqrt2pi = sqrt(2 * pi)
- neg_sqrt2 = -sqrt(2)
+ sqrt2pi = _SQRT2PI
+ neg_sqrt2 = -_SQRT2
pdf = lambda t: exp(-1/2 * t * t) / sqrt2pi
cdf = lambda t: 1/2 * erfc(t / neg_sqrt2)
invcdf = lambda t: _normal_dist_inv_cdf(t, 0.0, 1.0)
@@ -840,12 +841,10 @@ def logistic_kernel():
@register('sigmoid')
def sigmoid_kernel():
# (2/pi) / (exp(t) + exp(-t))
- c1 = 1 / pi
- c2 = 2 / pi
- c3 = pi / 2
- pdf = lambda t: c1 / cosh(t)
- cdf = lambda t: c2 * atan(exp(t))
- invcdf = lambda p: log(tan(p * c3))
+ recip_pi = 1 / pi
+ pdf = lambda t: recip_pi / cosh(t)
+ cdf = lambda t: 2.0 * atanpi(exp(t))
+ invcdf = lambda p: log(tanpi(p * 0.5))
support = None
return pdf, cdf, invcdf, support
@@ -869,7 +868,7 @@ def triangular_kernel():
def parabolic_kernel():
pdf = lambda t: 3/4 * (1.0 - t * t)
cdf = lambda t: sumprod((-1/4, 3/4, 1/2), (t**3, t, 1.0))
- invcdf = lambda p: 2.0 * cos((acos(2.0*p - 1.0) + pi) / 3.0)
+ invcdf = lambda p: 2.0 * cospi((acospi(2.0 * p - 1.0) + 1.0) / 3.0)
support = 1.0
return pdf, cdf, invcdf, support
@@ -906,7 +905,7 @@ def _triweight_invcdf_estimate(p):
sign, p = (1.0, p) if p <= 1/2 else (-1.0, 1.0 - p)
x = (2.0 * p) ** 0.3400218741872791 - 1.0
if 0.00001 < p < 0.499:
- x -= 0.033 * sin(1.07 * tau * (p - 0.035))
+ x -= 0.033 * sinpi(2.14 * (p - 0.035))
return x * sign
@register('triweight')
@@ -921,10 +920,9 @@ def triweight_kernel():
@register('cosine')
def cosine_kernel():
c1 = pi / 4
- c2 = pi / 2
- pdf = lambda t: c1 * cos(c2 * t)
- cdf = lambda t: 1/2 * sin(c2 * t) + 1/2
- invcdf = lambda p: 2.0 * asin(2.0 * p - 1.0) / pi
+ pdf = lambda t: c1 * cospi(0.5 * t)
+ cdf = lambda t: 1/2 * sinpi(0.5 * t) + 1/2
+ invcdf = lambda p: 2.0 * asinpi(2.0 * p - 1.0)
support = 1.0
return pdf, cdf, invcdf, support
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