Issue #6431: Fix Fraction comparisons to return NotImplemented when

the Fraction type doesn't know how to handle the comparison without
loss of accuracy.  Also, make sure that comparisons between Fractions
and float infinities or nans do the right thing.

Lib/fractions.py

@@ -501,54 +501,56 @@ class Fraction(numbers.Rational):
         if isinstance(b, numbers.Complex) and b.imag == 0:
             b = b.real
         if isinstance(b, float):
+            if math.isnan(b) or math.isinf(b):
+                # comparisons with an infinity or nan should behave in
+                # the same way for any finite a, so treat a as zero.
+                return 0.0 == b
+            else:
                 return a == a.from_float(b)
         else:
-            # XXX: If b.__eq__ is implemented like this method, it may
-            # give the wrong answer after float(a) changes a's
-            # value. Better ways of doing this are welcome.
-            return float(a) == b
+            # Since a doesn't know how to compare with b, let's give b
+            # a chance to compare itself with a.
+            return NotImplemented
 
-    def _subtractAndCompareToZero(a, b, op):
-        """Helper function for comparison operators.
+    def _richcmp(self, other, op):
+        """Helper for comparison operators, for internal use only.
 
-        Subtracts b from a, exactly if possible, and compares the
-        result with 0 using op, in such a way that the comparison
-        won't recurse. If the difference raises a TypeError, returns
-        NotImplemented instead.
+        Implement comparison between a Rational instance `self`, and
+        either another Rational instance or a float `other`.  If
+        `other` is not a Rational instance or a float, return
+        NotImplemented. `op` should be one of the six standard
+        comparison operators.
 
         """
-        if isinstance(b, numbers.Complex) and b.imag == 0:
-            b = b.real
-        if isinstance(b, float):
-            b = a.from_float(b)
-        try:
-            # XXX: If b <: Real but not <: Rational, this is likely
-            # to fall back to a float. If the actual values differ by
-            # less than MIN_FLOAT, this could falsely call them equal,
-            # which would make <= inconsistent with ==. Better ways of
-            # doing this are welcome.
-            diff = a - b
-        except TypeError:
+        # convert other to a Rational instance where reasonable.
+        if isinstance(other, numbers.Rational):
+            return op(self._numerator * other.denominator,
+                      self._denominator * other.numerator)
+        if isinstance(other, numbers.Complex) and other.imag == 0:
+            other = other.real
+        if isinstance(other, float):
+            if math.isnan(other) or math.isinf(other):
+                return op(0.0, other)
+            else:
+                return op(self, self.from_float(other))
+        else:
             return NotImplemented
-        if isinstance(diff, numbers.Rational):
-            return op(diff.numerator, 0)
-        return op(diff, 0)
 
     def __lt__(a, b):
         """a < b"""
-        return a._subtractAndCompareToZero(b, operator.lt)
+        return a._richcmp(b, operator.lt)
 
     def __gt__(a, b):
         """a > b"""
-        return a._subtractAndCompareToZero(b, operator.gt)
+        return a._richcmp(b, operator.gt)
 
     def __le__(a, b):
         """a <= b"""
-        return a._subtractAndCompareToZero(b, operator.le)
+        return a._richcmp(b, operator.le)
 
     def __ge__(a, b):
         """a >= b"""
-        return a._subtractAndCompareToZero(b, operator.ge)
+        return a._richcmp(b, operator.ge)
 
     def __bool__(a):
         """a != 0"""

Lib/test/test_fractions.py

@@ -3,6 +3,7 @@
 from decimal import Decimal
 from test.support import run_unittest
 import math
+import numbers
 import operator
 import fractions
 import unittest
@@ -11,6 +12,69 @@ from pickle import dumps, loads
 F = fractions.Fraction
 gcd = fractions.gcd
 
+class DummyFloat(object):
+    """Dummy float class for testing comparisons with Fractions"""
+
+    def __init__(self, value):
+        if not isinstance(value, float):
+            raise TypeError("DummyFloat can only be initialized from float")
+        self.value = value
+
+    def _richcmp(self, other, op):
+        if isinstance(other, numbers.Rational):
+            return op(F.from_float(self.value), other)
+        elif isinstance(other, DummyFloat):
+            return op(self.value, other.value)
+        else:
+            return NotImplemented
+
+    def __eq__(self, other): return self._richcmp(other, operator.eq)
+    def __le__(self, other): return self._richcmp(other, operator.le)
+    def __lt__(self, other): return self._richcmp(other, operator.lt)
+    def __ge__(self, other): return self._richcmp(other, operator.ge)
+    def __gt__(self, other): return self._richcmp(other, operator.gt)
+
+    # shouldn't be calling __float__ at all when doing comparisons
+    def __float__(self):
+        assert False, "__float__ should not be invoked for comparisons"
+
+    # same goes for subtraction
+    def __sub__(self, other):
+        assert False, "__sub__ should not be invoked for comparisons"
+    __rsub__ = __sub__
+
+
+class DummyRational(object):
+    """Test comparison of Fraction with a naive rational implementation."""
+
+    def __init__(self, num, den):
+        g = gcd(num, den)
+        self.num = num // g
+        self.den = den // g
+
+    def __eq__(self, other):
+        if isinstance(other, fractions.Fraction):
+            return (self.num == other._numerator and
+                    self.den == other._denominator)
+        else:
+            return NotImplemented
+
+    def __lt__(self, other):
+        return(self.num * other._denominator < self.den * other._numerator)
+
+    def __gt__(self, other):
+        return(self.num * other._denominator > self.den * other._numerator)
+
+    def __le__(self, other):
+        return(self.num * other._denominator <= self.den * other._numerator)
+
+    def __ge__(self, other):
+        return(self.num * other._denominator >= self.den * other._numerator)
+
+    # this class is for testing comparisons; conversion to float
+    # should never be used for a comparison, since it loses accuracy
+    def __float__(self):
+        assert False, "__float__ should not be invoked"
 
 class GcdTest(unittest.TestCase):
 
@@ -324,6 +388,50 @@ class FractionTest(unittest.TestCase):
         self.assertFalse(F(1, 2) != F(1, 2))
         self.assertTrue(F(1, 2) != F(1, 3))
 
+    def testComparisonsDummyRational(self):
+        self.assertTrue(F(1, 2) == DummyRational(1, 2))
+        self.assertTrue(DummyRational(1, 2) == F(1, 2))
+        self.assertFalse(F(1, 2) == DummyRational(3, 4))
+        self.assertFalse(DummyRational(3, 4) == F(1, 2))
+
+        self.assertTrue(F(1, 2) < DummyRational(3, 4))
+        self.assertFalse(F(1, 2) < DummyRational(1, 2))
+        self.assertFalse(F(1, 2) < DummyRational(1, 7))
+        self.assertFalse(F(1, 2) > DummyRational(3, 4))
+        self.assertFalse(F(1, 2) > DummyRational(1, 2))
+        self.assertTrue(F(1, 2) > DummyRational(1, 7))
+        self.assertTrue(F(1, 2) <= DummyRational(3, 4))
+        self.assertTrue(F(1, 2) <= DummyRational(1, 2))
+        self.assertFalse(F(1, 2) <= DummyRational(1, 7))
+        self.assertFalse(F(1, 2) >= DummyRational(3, 4))
+        self.assertTrue(F(1, 2) >= DummyRational(1, 2))
+        self.assertTrue(F(1, 2) >= DummyRational(1, 7))
+
+        self.assertTrue(DummyRational(1, 2) < F(3, 4))
+        self.assertFalse(DummyRational(1, 2) < F(1, 2))
+        self.assertFalse(DummyRational(1, 2) < F(1, 7))
+        self.assertFalse(DummyRational(1, 2) > F(3, 4))
+        self.assertFalse(DummyRational(1, 2) > F(1, 2))
+        self.assertTrue(DummyRational(1, 2) > F(1, 7))
+        self.assertTrue(DummyRational(1, 2) <= F(3, 4))
+        self.assertTrue(DummyRational(1, 2) <= F(1, 2))
+        self.assertFalse(DummyRational(1, 2) <= F(1, 7))
+        self.assertFalse(DummyRational(1, 2) >= F(3, 4))
+        self.assertTrue(DummyRational(1, 2) >= F(1, 2))
+        self.assertTrue(DummyRational(1, 2) >= F(1, 7))
+
+    def testComparisonsDummyFloat(self):
+        x = DummyFloat(1./3.)
+        y = F(1, 3)
+        self.assertTrue(x != y)
+        self.assertTrue(x < y or x > y)
+        self.assertFalse(x == y)
+        self.assertFalse(x <= y and x >= y)
+        self.assertTrue(y != x)
+        self.assertTrue(y < x or y > x)
+        self.assertFalse(y == x)
+        self.assertFalse(y <= x and y >= x)
+
     def testMixedLess(self):
         self.assertTrue(2 < F(5, 2))
         self.assertFalse(2 < F(4, 2))
@@ -335,6 +443,13 @@ class FractionTest(unittest.TestCase):
         self.assertTrue(0.4 < F(1, 2))
         self.assertFalse(0.5 < F(1, 2))
 
+        self.assertFalse(float('inf') < F(1, 2))
+        self.assertTrue(float('-inf') < F(0, 10))
+        self.assertFalse(float('nan') < F(-3, 7))
+        self.assertTrue(F(1, 2) < float('inf'))
+        self.assertFalse(F(17, 12) < float('-inf'))
+        self.assertFalse(F(144, -89) < float('nan'))
+
     def testMixedLessEqual(self):
         self.assertTrue(0.5 <= F(1, 2))
         self.assertFalse(0.6 <= F(1, 2))
@@ -345,6 +460,13 @@ class FractionTest(unittest.TestCase):
         self.assertTrue(F(4, 2) <= 2)
         self.assertFalse(F(5, 2) <= 2)
 
+        self.assertFalse(float('inf') <= F(1, 2))
+        self.assertTrue(float('-inf') <= F(0, 10))
+        self.assertFalse(float('nan') <= F(-3, 7))
+        self.assertTrue(F(1, 2) <= float('inf'))
+        self.assertFalse(F(17, 12) <= float('-inf'))
+        self.assertFalse(F(144, -89) <= float('nan'))
+
     def testBigFloatComparisons(self):
         # Because 10**23 can't be represented exactly as a float:
         self.assertFalse(F(10**23) == float(10**23))
@@ -369,6 +491,10 @@ class FractionTest(unittest.TestCase):
         self.assertFalse(2 == F(3, 2))
         self.assertTrue(F(4, 2) == 2)
         self.assertFalse(F(5, 2) == 2)
+        self.assertFalse(F(5, 2) == float('nan'))
+        self.assertFalse(float('nan') == F(3, 7))
+        self.assertFalse(F(5, 2) == float('inf'))
+        self.assertFalse(float('-inf') == F(2, 5))
 
     def testStringification(self):
         self.assertEquals("Fraction(7, 3)", repr(F(7, 3)))

Misc/NEWS

@@ -40,6 +40,10 @@ C-API
 Library
 -------
 
+- Issue #6431: Make Fraction type return NotImplemented when it doesn't
+  know how to handle a comparison without loss of precision.  Also add
+  correct handling of infinities and nans for comparisons with float.
+
 - Issue #6415: Fixed warnings.warn sagfault on bad formatted string.
 
 - Issue #6358: The exit status of a command started with os.popen() was