Issue #17141: random.vonmisesvariate() no more hangs for large kappas.

1 files changed, 6 insertions, 8 deletions

diff --git a/Lib/random.py b/Lib/random.py
index 0e67ddbe6a..b2e9ae1b84 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -432,22 +432,20 @@ class Random(_random.Random):
         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)
-            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:
             theta = (mu + _acos(f)) % TWOPI