diff -r b79df3e8a9a0 Lib/random.py
--- a/Lib/random.py	Thu Feb 07 00:50:02 2013 -0800
+++ b/Lib/random.py	Thu Feb 07 13:37:31 2013 +0200
@@ -432,24 +432,22 @@
         if kappa <= 1e-6:
             return TWOPI * random()
 
-        a = 1.0 + _sqrt(1.0 + 4.0 * kappa * kappa)
-        b = (a - _sqrt(2.0 * a))/(2.0 * kappa)
-        r = (1.0 + b * b)/(2.0 * b)
+        s = 0.5 / kappa
+        r = s + _sqrt(1.0 + s * s)
 
         while 1:
             u1 = random()
+            z = _cos(_pi * u1)
 
-            z = _cos(_pi * u1)
-            f = (1.0 + r * z)/(r + z)
-            c = kappa * (r - f)
-
+            d = z / (r + z)
             u2 = random()
-
-            if u2 < c * (2.0 - c) or u2 <= c * _exp(1.0 - c):
+            if u2 < 1.0 - d * d or u2 <= (1.0 - d) * _exp(d):
                 break
 
+        q = 1.0 / r
+        f = (q + z) / (1.0 + q * z)
         u3 = random()
-        if u3 > 0.5:
+        if u3 >= 0.5:
             theta = (mu % TWOPI) + _acos(f)
         else:
             theta = (mu % TWOPI) - _acos(f)