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):
-            return a == a.from_float(b)
+            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"""