From 5c3270939c09e4c8e80fd26449b718a998701912 Mon Sep 17 00:00:00 2001
From: Raymond Hettinger <rhettinger@users.noreply.github.com>
Date: Sat, 1 Aug 2020 01:18:26 -0700
Subject: [PATCH] bpo-41421: Algebraic simplification for
 random.paretovariate() (GH-21695)

---
 Lib/random.py                                                  | 2 +-
 .../next/Library/2020-08-01-00-51-15.bpo-41421.dHKRVB.rst      | 3 +++
 2 files changed, 4 insertions(+), 1 deletion(-)
 create mode 100644 Misc/NEWS.d/next/Library/2020-08-01-00-51-15.bpo-41421.dHKRVB.rst

diff --git a/Lib/random.py b/Lib/random.py
index a6454f520df..37f71110403 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -749,7 +749,7 @@ class Random(_random.Random):
         # Jain, pg. 495
 
         u = 1.0 - self.random()
-        return 1.0 / u ** (1.0 / alpha)
+        return u ** (-1.0 / alpha)
 
     def weibullvariate(self, alpha, beta):
         """Weibull distribution.
diff --git a/Misc/NEWS.d/next/Library/2020-08-01-00-51-15.bpo-41421.dHKRVB.rst b/Misc/NEWS.d/next/Library/2020-08-01-00-51-15.bpo-41421.dHKRVB.rst
new file mode 100644
index 00000000000..cf291c60d8a
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-08-01-00-51-15.bpo-41421.dHKRVB.rst
@@ -0,0 +1,3 @@
+Make an algebraic simplification to random.paretovariate().  It now is
+slightly less subject to round-off error and is slightly faster. Inputs that
+used to cause ZeroDivisionError now cause an OverflowError instead.