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Issue #8188: Introduce a new scheme for computing hashes of numbers

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(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.
This commit is contained in:
Mark Dickinson 2010-05-23 13:33:13 +00:00
parent 03721133a6
commit dc787d2055
14 changed files with 566 additions and 137 deletions
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39
Objects/longobject.c
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@ -2571,18 +2571,37 @@ long_hash(PyLongObject *v)
sign = -1;
i = -(i);
}
/* The following loop produces a C unsigned long x such that x is
congruent to the absolute value of v modulo ULONG_MAX. The
resulting x is nonzero if and only if v is. */
while (--i >= 0) {
/* Force a native long #-bits (32 or 64) circular shift */
x = (x >> (8*SIZEOF_LONG-PyLong_SHIFT)) | (x << PyLong_SHIFT);
/* Here x is a quantity in the range [0, _PyHASH_MODULUS); we
want to compute x * 2**PyLong_SHIFT + v->ob_digit[i] modulo
_PyHASH_MODULUS.
The computation of x * 2**PyLong_SHIFT % _PyHASH_MODULUS
amounts to a rotation of the bits of x. To see this, write
x * 2**PyLong_SHIFT = y * 2**_PyHASH_BITS + z
where y = x >> (_PyHASH_BITS - PyLong_SHIFT) gives the top
PyLong_SHIFT bits of x (those that are shifted out of the
original _PyHASH_BITS bits, and z = (x << PyLong_SHIFT) &
_PyHASH_MODULUS gives the bottom _PyHASH_BITS - PyLong_SHIFT
bits of x, shifted up. Then since 2**_PyHASH_BITS is
congruent to 1 modulo _PyHASH_MODULUS, y*2**_PyHASH_BITS is
congruent to y modulo _PyHASH_MODULUS. So
x * 2**PyLong_SHIFT = y + z (mod _PyHASH_MODULUS).
The right-hand side is just the result of rotating the
_PyHASH_BITS bits of x left by PyLong_SHIFT places; since
not all _PyHASH_BITS bits of x are 1s, the same is true
after rotation, so 0 <= y+z < _PyHASH_MODULUS and y + z is
the reduction of x*2**PyLong_SHIFT modulo
_PyHASH_MODULUS. */
x = ((x << PyLong_SHIFT) & _PyHASH_MODULUS) |
(x >> (_PyHASH_BITS - PyLong_SHIFT));
x += v->ob_digit[i];
/* If the addition above overflowed we compensate by
incrementing. This preserves the value modulo
ULONG_MAX. */
if (x < v->ob_digit[i])
x++;
if (x >= _PyHASH_MODULUS)
x -= _PyHASH_MODULUS;
}
x = x * sign;
if (x == (unsigned long)-1)