From f3cb68f2e4c3e0c405460f9bb881f5c1db70f535 Mon Sep 17 00:00:00 2001
From: Raymond Hettinger <rhettinger@users.noreply.github.com>
Date: Thu, 15 Aug 2019 20:58:26 -0700
Subject: [PATCH] bpo-37863: Optimize Fraction.__hash__() (#15298)

---
 Lib/fractions.py                              | 24 ++++++++-----------
 .../2019-08-14-20-46-39.bpo-37863.CkXqgX.rst  |  1 +
 2 files changed, 11 insertions(+), 14 deletions(-)
 create mode 100644 Misc/NEWS.d/next/Library/2019-08-14-20-46-39.bpo-37863.CkXqgX.rst

diff --git a/Lib/fractions.py b/Lib/fractions.py
index e774d58e403..c922c38e244 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -556,23 +556,19 @@ class Fraction(numbers.Rational):
     def __hash__(self):
         """hash(self)"""
 
-        # XXX since this method is expensive, consider caching the result
+        # To make sure that the hash of a Fraction agrees with the hash
+        # of a numerically equal integer, float or Decimal instance, we
+        # follow the rules for numeric hashes outlined in the
+        # documentation.  (See library docs, 'Built-in Types').
 
-        # In order to make sure that the hash of a Fraction agrees
-        # with the hash of a numerically equal integer, float or
-        # Decimal instance, we follow the rules for numeric hashes
-        # outlined in the documentation.  (See library docs, 'Built-in
-        # Types').
-
-        # dinv is the inverse of self._denominator modulo the prime
-        # _PyHASH_MODULUS, or 0 if self._denominator is divisible by
-        # _PyHASH_MODULUS.
-        dinv = pow(self._denominator, _PyHASH_MODULUS - 2, _PyHASH_MODULUS)
-        if not dinv:
+        try:
+            dinv = pow(self._denominator, -1, _PyHASH_MODULUS)
+        except ValueError:
+            # ValueError means there is no modular inverse
             hash_ = _PyHASH_INF
         else:
-            hash_ = abs(self._numerator) * dinv % _PyHASH_MODULUS
-        result = hash_ if self >= 0 else -hash_
+            hash_ = hash(abs(self._numerator)) * dinv % _PyHASH_MODULUS
+        result = hash_ if self._numerator >= 0 else -hash_
         return -2 if result == -1 else result
 
     def __eq__(a, b):
diff --git a/Misc/NEWS.d/next/Library/2019-08-14-20-46-39.bpo-37863.CkXqgX.rst b/Misc/NEWS.d/next/Library/2019-08-14-20-46-39.bpo-37863.CkXqgX.rst
new file mode 100644
index 00000000000..90df6e9cb65
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-08-14-20-46-39.bpo-37863.CkXqgX.rst
@@ -0,0 +1 @@
+Optimizations for Fraction.__hash__ suggested by Tim Peters.