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Minor edit: Move comments closer to the code they describe #136477

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Jul 9, 2025
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Minor edit: Move comments closer to the code they describe #136477

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11 changes: 6 additions & 5 deletions Lib/random.py
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Original file line number Diff line number Diff line change
Expand Up @@ -844,8 +844,8 @@ def binomialvariate(self, n=1, p=0.5):
# BTRS: Transformed rejection with squeeze method by Wolfgang Hörmann
# https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.47.8407&rep=rep1&type=pdf
assert n*p >= 10.0 and p <= 0.5
setup_complete = False

setup_complete = False
spq = _sqrt(n * p * (1.0 - p)) # Standard deviation of the distribution
b = 1.15 + 2.53 * spq
a = -0.0873 + 0.0248 * b + 0.01 * p
Expand All @@ -860,22 +860,23 @@ def binomialvariate(self, n=1, p=0.5):
k = _floor((2.0 * a / us + b) * u + c)
if k < 0 or k > n:
continue
v = random()

# The early-out "squeeze" test substantially reduces
# the number of acceptance condition evaluations.
v = random()
if us >= 0.07 and v <= vr:
return k

# Acceptance-rejection test.
# Note, the original paper erroneously omits the call to log(v)
# when comparing to the log of the rescaled binomial distribution.
if not setup_complete:
alpha = (2.83 + 5.1 / b) * spq
lpq = _log(p / (1.0 - p))
m = _floor((n + 1) * p) # Mode of the distribution
h = _lgamma(m + 1) + _lgamma(n - m + 1)
setup_complete = True # Only needs to be done once

# Acceptance-rejection test.
# Note, the original paper erroneously omits the call to log(v)
# when comparing to the log of the rescaled binomial distribution.
v *= alpha / (a / (us * us) + b)
if _log(v) <= h - _lgamma(k + 1) - _lgamma(n - k + 1) + (k - m) * lpq:
return k
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