Fixed a bug in the gauss() function. The bug was reported by Mike
Miller, who complained that its kurtosis was bad, and then fixed by
Lambert Meertens (author of the original algorithm) who discovered
that the mathematical analysis leading to his solution was wrong, and
provided a corrected version. Mike then tested the fix and reported
that the kurtosis was now good.
diff --git a/Lib/random.py b/Lib/random.py
index ebab1f8..49921cb 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -182,12 +182,13 @@
# When x and y are two variables from [0, 1), uniformly
# distributed, then
#
- # cos(2*pi*x)*log(1-y)
- # sin(2*pi*x)*log(1-y)
+ # cos(2*pi*x)*sqrt(-2*log(1-y))
+ # sin(2*pi*x)*sqrt(-2*log(1-y))
#
# are two *independent* variables with normal distribution
# (mu = 0, sigma = 1).
# (Lambert Meertens)
+ # (corrected version; bug discovered by Mike Miller, fixed by LM)
global gauss_next
@@ -196,9 +197,9 @@
gauss_next = None
else:
x2pi = random() * TWOPI
- log1_y = log(1.0 - random())
- z = cos(x2pi) * log1_y
- gauss_next = sin(x2pi) * log1_y
+ g2rad = sqrt(-2.0 * log(1.0 - random()))
+ z = cos(x2pi) * g2rad
+ gauss_next = sin(x2pi) * g2rad
return mu + z*sigma