Correct long standing bugs in the methods for random distributions.

The range of u=random() is [0,1), so log(u) and 1/x can fail.
Fix by setting u=1-random() or by reselecting for a usable value.

Will backport.

1 files changed, 6 insertions, 4 deletions

diff --git a/Lib/random.py b/Lib/random.py
index 03dadf2..4ddac4c 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -282,7 +282,7 @@ class Random(CoreGenerator):
         random = self.random
         while True:
             u1 = random()
-            u2 = random()
+            u2 = 1.0 - random()
             z = NV_MAGICCONST*(u1-0.5)/u2
             zz = z*z/4.0
             if zz <= -_log(u2):
@@ -422,7 +422,9 @@ class Random(CoreGenerator):
 
             while True:
                 u1 = random()
-                u2 = random()
+                if not 1e-7 < u1 < .9999999:
+                    continue
+                u2 = 1.0 - random()
                 v = _log(u1/(1.0-u1))/ainv
                 x = alpha*_exp(v)
                 z = u1*u1*u2
@@ -554,7 +556,7 @@ class Random(CoreGenerator):
         """Pareto distribution.  alpha is the shape parameter."""
         # Jain, pg. 495
 
-        u = self.random()
+        u = 1.0 - self.random()
         return 1.0 / pow(u, 1.0/alpha)
 
 ## -------------------- Weibull --------------------
@@ -567,7 +569,7 @@ class Random(CoreGenerator):
         """
         # Jain, pg. 499; bug fix courtesy Bill Arms
 
-        u = self.random()
+        u = 1.0 - self.random()
         return alpha * pow(-_log(u), 1.0/beta)
 
 ## -------------------- Wichmann-Hill -------------------