Issue #8188: Introduce a new scheme for computing hashes of numbers
(instances of int, float, complex, decimal.Decimal and
fractions.Fraction) that makes it easy to maintain the invariant that
hash(x) == hash(y) whenever x and y have equal value.
diff --git a/Lib/decimal.py b/Lib/decimal.py
index cc71cd8..29ce398 100644
--- a/Lib/decimal.py
+++ b/Lib/decimal.py
@@ -862,7 +862,7 @@
# that specified by IEEE 754.
def __eq__(self, other, context=None):
- other = _convert_other(other, allow_float=True)
+ other = _convert_other(other, allow_float = True)
if other is NotImplemented:
return other
if self._check_nans(other, context):
@@ -870,7 +870,7 @@
return self._cmp(other) == 0
def __ne__(self, other, context=None):
- other = _convert_other(other, allow_float=True)
+ other = _convert_other(other, allow_float = True)
if other is NotImplemented:
return other
if self._check_nans(other, context):
@@ -879,7 +879,7 @@
def __lt__(self, other, context=None):
- other = _convert_other(other, allow_float=True)
+ other = _convert_other(other, allow_float = True)
if other is NotImplemented:
return other
ans = self._compare_check_nans(other, context)
@@ -888,7 +888,7 @@
return self._cmp(other) < 0
def __le__(self, other, context=None):
- other = _convert_other(other, allow_float=True)
+ other = _convert_other(other, allow_float = True)
if other is NotImplemented:
return other
ans = self._compare_check_nans(other, context)
@@ -897,7 +897,7 @@
return self._cmp(other) <= 0
def __gt__(self, other, context=None):
- other = _convert_other(other, allow_float=True)
+ other = _convert_other(other, allow_float = True)
if other is NotImplemented:
return other
ans = self._compare_check_nans(other, context)
@@ -906,7 +906,7 @@
return self._cmp(other) > 0
def __ge__(self, other, context=None):
- other = _convert_other(other, allow_float=True)
+ other = _convert_other(other, allow_float = True)
if other is NotImplemented:
return other
ans = self._compare_check_nans(other, context)
@@ -935,55 +935,28 @@
def __hash__(self):
"""x.__hash__() <==> hash(x)"""
- # Decimal integers must hash the same as the ints
- #
- # The hash of a nonspecial noninteger Decimal must depend only
- # on the value of that Decimal, and not on its representation.
- # For example: hash(Decimal('100E-1')) == hash(Decimal('10')).
- # Equality comparisons involving signaling nans can raise an
- # exception; since equality checks are implicitly and
- # unpredictably used when checking set and dict membership, we
- # prevent signaling nans from being used as set elements or
- # dict keys by making __hash__ raise an exception.
+ # In order to make sure that the hash of a Decimal instance
+ # agrees with the hash of a numerically equal integer, float
+ # or Fraction, we follow the rules for numeric hashes outlined
+ # in the documentation. (See library docs, 'Built-in Types').
if self._is_special:
if self.is_snan():
raise TypeError('Cannot hash a signaling NaN value.')
elif self.is_nan():
- # 0 to match hash(float('nan'))
- return 0
+ return _PyHASH_NAN
else:
- # values chosen to match hash(float('inf')) and
- # hash(float('-inf')).
if self._sign:
- return -271828
+ return -_PyHASH_INF
else:
- return 314159
+ return _PyHASH_INF
- # In Python 2.7, we're allowing comparisons (but not
- # arithmetic operations) between floats and Decimals; so if
- # a Decimal instance is exactly representable as a float then
- # its hash should match that of the float.
- self_as_float = float(self)
- if Decimal.from_float(self_as_float) == self:
- return hash(self_as_float)
-
- if self._isinteger():
- op = _WorkRep(self.to_integral_value())
- # to make computation feasible for Decimals with large
- # exponent, we use the fact that hash(n) == hash(m) for
- # any two nonzero integers n and m such that (i) n and m
- # have the same sign, and (ii) n is congruent to m modulo
- # 2**64-1. So we can replace hash((-1)**s*c*10**e) with
- # hash((-1)**s*c*pow(10, e, 2**64-1).
- return hash((-1)**op.sign*op.int*pow(10, op.exp, 2**64-1))
- # The value of a nonzero nonspecial Decimal instance is
- # faithfully represented by the triple consisting of its sign,
- # its adjusted exponent, and its coefficient with trailing
- # zeros removed.
- return hash((self._sign,
- self._exp+len(self._int),
- self._int.rstrip('0')))
+ if self._exp >= 0:
+ exp_hash = pow(10, self._exp, _PyHASH_MODULUS)
+ else:
+ exp_hash = pow(_PyHASH_10INV, -self._exp, _PyHASH_MODULUS)
+ hash_ = int(self._int) * exp_hash % _PyHASH_MODULUS
+ return hash_ if self >= 0 else -hash_
def as_tuple(self):
"""Represents the number as a triple tuple.
@@ -6218,6 +6191,17 @@
# _SignedInfinity[sign] is infinity w/ that sign
_SignedInfinity = (_Infinity, _NegativeInfinity)
+# Constants related to the hash implementation; hash(x) is based
+# on the reduction of x modulo _PyHASH_MODULUS
+import sys
+_PyHASH_MODULUS = sys.hash_info.modulus
+# hash values to use for positive and negative infinities, and nans
+_PyHASH_INF = sys.hash_info.inf
+_PyHASH_NAN = sys.hash_info.nan
+del sys
+
+# _PyHASH_10INV is the inverse of 10 modulo the prime _PyHASH_MODULUS
+_PyHASH_10INV = pow(10, _PyHASH_MODULUS - 2, _PyHASH_MODULUS)
if __name__ == '__main__':