From 3c286e2e0d2aa17b5a90d671280a95ba5cd6521c Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Sat, 5 Apr 2014 09:29:00 +0100
Subject: [PATCH] Issue #21136: Avoid unnecessary normalization in Fractions
 resulting from power and other operations.

---
 Lib/fractions.py           | 23 ++++++++++++++---------
 Lib/test/test_fractions.py |  3 ++-
 Misc/NEWS                  |  3 +++
 3 files changed, 19 insertions(+), 10 deletions(-)

diff --git a/Lib/fractions.py b/Lib/fractions.py
index 79e83ff2c00..43f146f9391 100644
--- a/Lib/fractions.py
+++ b/Lib/fractions.py
@@ -70,7 +70,7 @@ class Fraction(numbers.Rational):
     __slots__ = ('_numerator', '_denominator')
 
     # We're immutable, so use __new__ not __init__
-    def __new__(cls, numerator=0, denominator=None):
+    def __new__(cls, numerator=0, denominator=None, _normalize=True):
         """Constructs a Rational.
 
         Takes a string like '3/2' or '1.5', another Rational instance, a
@@ -165,9 +165,12 @@ class Fraction(numbers.Rational):
 
         if denominator == 0:
             raise ZeroDivisionError('Fraction(%s, 0)' % numerator)
-        g = gcd(numerator, denominator)
-        self._numerator = numerator // g
-        self._denominator = denominator // g
+        if _normalize:
+            g = gcd(numerator, denominator)
+            numerator //= g
+            denominator //= g
+        self._numerator = numerator
+        self._denominator = denominator
         return self
 
     @classmethod
@@ -453,10 +456,12 @@ class Fraction(numbers.Rational):
                 power = b.numerator
                 if power >= 0:
                     return Fraction(a._numerator ** power,
-                                    a._denominator ** power)
+                                    a._denominator ** power,
+                                    _normalize=False)
                 else:
                     return Fraction(a._denominator ** -power,
-                                    a._numerator ** -power)
+                                    a._numerator ** -power,
+                                    _normalize=False)
             else:
                 # A fractional power will generally produce an
                 # irrational number.
@@ -480,15 +485,15 @@ class Fraction(numbers.Rational):
 
     def __pos__(a):
         """+a: Coerces a subclass instance to Fraction"""
-        return Fraction(a._numerator, a._denominator)
+        return Fraction(a._numerator, a._denominator, _normalize=False)
 
     def __neg__(a):
         """-a"""
-        return Fraction(-a._numerator, a._denominator)
+        return Fraction(-a._numerator, a._denominator, _normalize=False)
 
     def __abs__(a):
         """abs(a)"""
-        return Fraction(abs(a._numerator), a._denominator)
+        return Fraction(abs(a._numerator), a._denominator, _normalize=False)
 
     def __trunc__(a):
         """trunc(a)"""
diff --git a/Lib/test/test_fractions.py b/Lib/test/test_fractions.py
index 33365322b94..e86d5cee6e7 100644
--- a/Lib/test/test_fractions.py
+++ b/Lib/test/test_fractions.py
@@ -330,7 +330,6 @@ class FractionTest(unittest.TestCase):
         self.assertTypedEquals(F(-2, 10), round(F(-15, 100), 1))
         self.assertTypedEquals(F(-2, 10), round(F(-25, 100), 1))
 
-
     def testArithmetic(self):
         self.assertEqual(F(1, 2), F(1, 10) + F(2, 5))
         self.assertEqual(F(-3, 10), F(1, 10) - F(2, 5))
@@ -402,6 +401,8 @@ class FractionTest(unittest.TestCase):
         self.assertTypedEquals(2.0 , 4 ** F(1, 2))
         self.assertTypedEquals(0.25, 2.0 ** F(-2, 1))
         self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** F(1, 10))
+        self.assertRaises(ZeroDivisionError, operator.pow,
+                          F(0, 1), -2)
 
     def testMixingWithDecimal(self):
         # Decimal refuses mixed arithmetic (but not mixed comparisons)
diff --git a/Misc/NEWS b/Misc/NEWS
index d01f375a6ce..3bc36a9b5b1 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -29,6 +29,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #21136: Avoid unnecessary normalization of Fractions resulting from
+  power and other operations.  Patch by Raymond Hettinger.
+
 - Issue #17621: Introduce importlib.util.LazyLoader.
 
 - Issue #21076: signal module constants were turned into enums.