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Commit cce8df2f authored by Facundo Batista's avatar Facundo Batista
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Speed up of the various division operations (remainder, divide, 

divideint and divmod). Thanks Mark Dickinson.
parent 745e48df
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Showing with 139 additions and 161 deletions
Lib/decimal.py
View file @ cce8df2f
...@@ -244,9 +244,7 @@ class DivisionByZero(DecimalException, ZeroDivisionError): ...@@ -244,9 +244,7 @@ class DivisionByZero(DecimalException, ZeroDivisionError):
-0, for power. -0, for power.
""" """
def handle(self, context, sign, double = None, *args): def handle(self, context, sign, *args):
if double is not None:
return (Infsign[sign],)*2
return Infsign[sign] return Infsign[sign]
class DivisionImpossible(InvalidOperation): class DivisionImpossible(InvalidOperation):
...@@ -258,7 +256,7 @@ class DivisionImpossible(InvalidOperation): ...@@ -258,7 +256,7 @@ class DivisionImpossible(InvalidOperation):
""" """
def handle(self, context, *args): def handle(self, context, *args):
return (NaN, NaN) return NaN
class DivisionUndefined(InvalidOperation, ZeroDivisionError): class DivisionUndefined(InvalidOperation, ZeroDivisionError):
"""Undefined result of division. """Undefined result of division.
...@@ -268,9 +266,7 @@ class DivisionUndefined(InvalidOperation, ZeroDivisionError): ...@@ -268,9 +266,7 @@ class DivisionUndefined(InvalidOperation, ZeroDivisionError):
the dividend is also zero. The result is [0,qNaN]. the dividend is also zero. The result is [0,qNaN].
""" """
def handle(self, context, tup=None, *args): def handle(self, context, *args):
if tup is not None:
return (NaN, NaN) # for 0 %0, 0 // 0
return NaN return NaN
class Inexact(DecimalException): class Inexact(DecimalException):
...@@ -1151,157 +1147,97 @@ class Decimal(object): ...@@ -1151,157 +1147,97 @@ class Decimal(object):
def __div__(self, other, context=None): def __div__(self, other, context=None):
"""Return self / other.""" """Return self / other."""
return self._divide(other, context=context)
__truediv__ = __div__
def _divide(self, other, divmod = 0, context=None):
"""Return a / b, to context.prec precision.
divmod:
0 => true division
1 => (a //b, a%b)
2 => a //b
3 => a%b
Actually, if divmod is 2 or 3 a tuple is returned, but errors for
computing the other value are not raised.
"""
other = _convert_other(other) other = _convert_other(other)
if other is NotImplemented: if other is NotImplemented:
if divmod in (0, 1): return NotImplemented
return NotImplemented
return (NotImplemented, NotImplemented)
if context is None: if context is None:
context = getcontext() context = getcontext()
shouldround = context._rounding_decision == ALWAYS_ROUND
sign = self._sign ^ other._sign sign = self._sign ^ other._sign
if self._is_special or other._is_special: if self._is_special or other._is_special:
ans = self._check_nans(other, context) ans = self._check_nans(other, context)
if ans: if ans:
if divmod:
return (ans, ans)
return ans return ans
if self._isinfinity() and other._isinfinity(): if self._isinfinity() and other._isinfinity():
if divmod:
reloco = (context._raise_error(InvalidOperation,
'(+-)INF // (+-)INF'),
context._raise_error(InvalidOperation,
'(+-)INF % (+-)INF'))
return reloco
return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF') return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF')
if self._isinfinity(): if self._isinfinity():
if divmod == 1:
return (Infsign[sign],
context._raise_error(InvalidOperation, 'INF % x'))
elif divmod == 2:
return (Infsign[sign], NaN)
elif divmod == 3:
return (Infsign[sign],
context._raise_error(InvalidOperation, 'INF % x'))
return Infsign[sign] return Infsign[sign]
if other._isinfinity(): if other._isinfinity():
if divmod:
otherside = Decimal(self)
if shouldround and (divmod == 1 or divmod == 3):
otherside = otherside._fix(context)
return (Decimal((sign, (0,), 0)), otherside)
context._raise_error(Clamped, 'Division by infinity') context._raise_error(Clamped, 'Division by infinity')
return Decimal((sign, (0,), context.Etiny())) return Decimal((sign, (0,), context.Etiny()))
# Special cases for zeroes # Special cases for zeroes
if not self and not other:
if divmod:
return context._raise_error(DivisionUndefined, '0 / 0', 1)
return context._raise_error(DivisionUndefined, '0 / 0')
if not self:
if divmod:
otherside = Decimal((self._sign, (0,), min(self._exp, other._exp)))
if shouldround and (divmod == 1 or divmod == 3):
otherside = otherside._fix(context)
return (Decimal((sign, (0,), 0)), otherside)
exp = self._exp - other._exp
ans = Decimal((sign, (0,), exp))
ans = ans._fix(context)
return ans
if not other: if not other:
if divmod: if not self:
return context._raise_error(DivisionByZero, 'divmod(x,0)', return context._raise_error(DivisionUndefined, '0 / 0')
sign, 1)
return context._raise_error(DivisionByZero, 'x / 0', sign) return context._raise_error(DivisionByZero, 'x / 0', sign)
# OK, so neither = 0, INF or NaN if not self:
exp = self._exp - other._exp
# If we're dividing into ints, and self < other, stop. coeff = 0
# self.__abs__(0) does not round. else:
if divmod and (self.__abs__(0, context) < other.__abs__(0, context)): # OK, so neither = 0, INF or NaN
shift = len(other._int) - len(self._int) + context.prec + 1
exp = self._exp - other._exp - shift
op1 = _WorkRep(self)
op2 = _WorkRep(other)
if shift >= 0:
coeff, remainder = divmod(op1.int * 10**shift, op2.int)
else:
coeff, remainder = divmod(op1.int, op2.int * 10**-shift)
if remainder:
# result is not exact; adjust to ensure correct rounding
if coeff % 5 == 0:
coeff += 1
else:
# result is exact; get as close to ideal exponent as possible
ideal_exp = self._exp - other._exp
while exp < ideal_exp and coeff % 10 == 0:
coeff //= 10
exp += 1
if divmod == 1 or divmod == 3: ans = Decimal((sign, map(int, str(coeff)), exp))
exp = min(self._exp, other._exp) return ans._fix(context)
ans2 = self._rescale(exp, context.rounding)
if shouldround:
ans2 = ans2._fix(context)
return (Decimal( (sign, (0,), 0) ),
ans2)
elif divmod == 2: __truediv__ = __div__
# Don't round the mod part, if we don't need it.
return (Decimal( (sign, (0,), 0) ), Decimal(self))
op1 = _WorkRep(self) def _divide(self, other, context):
op2 = _WorkRep(other) """Return (self // other, self % other), to context.prec precision.
op1, op2, adjust = _adjust_coefficients(op1, op2)
res = _WorkRep( (sign, 0, (op1.exp - op2.exp)) )
if divmod and res.exp > context.prec + 1:
return context._raise_error(DivisionImpossible)
prec_limit = 10 ** context.prec Assumes that neither self nor other is a NaN, that self is not
while 1: infinite and that other is nonzero.
while op2.int <= op1.int: """
res.int += 1 sign = self._sign ^ other._sign
op1.int -= op2.int if other._isinfinity():
if res.exp == 0 and divmod: ideal_exp = self._exp
if res.int >= prec_limit and shouldround: else:
return context._raise_error(DivisionImpossible) ideal_exp = min(self._exp, other._exp)
otherside = Decimal(op1)
exp = min(self._exp, other._exp)
otherside = otherside._rescale(exp, context.rounding)
if shouldround and (divmod == 1 or divmod == 3):
otherside = otherside._fix(context)
return (Decimal(res), otherside)
if op1.int == 0 and adjust >= 0 and not divmod:
break
if res.int >= prec_limit and shouldround:
if divmod:
return context._raise_error(DivisionImpossible)
shouldround=1
# Really, the answer is a bit higher, so adding a one to
# the end will make sure the rounding is right.
if op1.int != 0:
res.int *= 10
res.int += 1
res.exp -= 1
break expdiff = self.adjusted() - other.adjusted()
res.int *= 10 if not self or other._isinfinity() or expdiff <= -2:
res.exp -= 1 return (Decimal((sign, (0,), 0)),
adjust += 1 self._rescale(ideal_exp, context.rounding))
op1.int *= 10 if expdiff <= context.prec:
op1.exp -= 1 op1 = _WorkRep(self)
op2 = _WorkRep(other)
if op1.exp >= op2.exp:
op1.int *= 10**(op1.exp - op2.exp)
else:
op2.int *= 10**(op2.exp - op1.exp)
q, r = divmod(op1.int, op2.int)
if q < 10**context.prec:
return (Decimal((sign, map(int, str(q)), 0)),
Decimal((self._sign, map(int, str(r)), ideal_exp)))
ans = Decimal(res) # Here the quotient is too large to be representable
if shouldround: ans = context._raise_error(DivisionImpossible,
ans = ans._fix(context) 'quotient too large in //, % or divmod')
return ans return ans, ans
def __rdiv__(self, other, context=None): def __rdiv__(self, other, context=None):
"""Swaps self/other and returns __div__.""" """Swaps self/other and returns __div__."""
...@@ -1313,9 +1249,40 @@ class Decimal(object): ...@@ -1313,9 +1249,40 @@ class Decimal(object):
def __divmod__(self, other, context=None): def __divmod__(self, other, context=None):
""" """
(self // other, self % other) Return (self // other, self % other)
""" """
return self._divide(other, 1, context) other = _convert_other(other)
if other is NotImplemented:
return other
if context is None:
context = getcontext()
ans = self._check_nans(other, context)
if ans:
return (ans, ans)
sign = self._sign ^ other._sign
if self._isinfinity():
if other._isinfinity():
ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)')
return ans, ans
else:
return (Infsign[sign],
context._raise_error(InvalidOperation, 'INF % x'))
if not other:
if not self:
ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)')
return ans, ans
else:
return (context._raise_error(DivisionByZero, 'x // 0', sign),
context._raise_error(InvalidOperation, 'x % 0'))
quotient, remainder = self._divide(other, context)
if context._rounding_decision == ALWAYS_ROUND:
remainder = remainder._fix(context)
return quotient, remainder
def __rdivmod__(self, other, context=None): def __rdivmod__(self, other, context=None):
"""Swaps self/other and returns __divmod__.""" """Swaps self/other and returns __divmod__."""
...@@ -1332,15 +1299,25 @@ class Decimal(object): ...@@ -1332,15 +1299,25 @@ class Decimal(object):
if other is NotImplemented: if other is NotImplemented:
return other return other
if self._is_special or other._is_special: if context is None:
ans = self._check_nans(other, context) context = getcontext()
if ans:
return ans
if self and not other: ans = self._check_nans(other, context)
return context._raise_error(InvalidOperation, 'x % 0') if ans:
return ans
return self._divide(other, 3, context)[1] if self._isinfinity():
return context._raise_error(InvalidOperation, 'INF % x')
elif not other:
if self:
return context._raise_error(InvalidOperation, 'x % 0')
else:
return context._raise_error(DivisionUndefined, '0 % 0')
remainder = self._divide(other, context)[1]
if context._rounding_decision == ALWAYS_ROUND:
remainder = remainder._fix(context)
return remainder
def __rmod__(self, other, context=None): def __rmod__(self, other, context=None):
"""Swaps self/other and returns __mod__.""" """Swaps self/other and returns __mod__."""
...@@ -1391,7 +1368,7 @@ class Decimal(object): ...@@ -1391,7 +1368,7 @@ class Decimal(object):
expdiff = self.adjusted() - other.adjusted() expdiff = self.adjusted() - other.adjusted()
if expdiff >= context.prec + 1: if expdiff >= context.prec + 1:
# expdiff >= prec+1 => abs(self/other) > 10**prec # expdiff >= prec+1 => abs(self/other) > 10**prec
return context._raise_error(DivisionImpossible)[0] return context._raise_error(DivisionImpossible)
if expdiff <= -2: if expdiff <= -2:
# expdiff <= -2 => abs(self/other) < 0.1 # expdiff <= -2 => abs(self/other) < 0.1
ans = self._rescale(ideal_exponent, context.rounding) ans = self._rescale(ideal_exponent, context.rounding)
...@@ -1413,7 +1390,7 @@ class Decimal(object): ...@@ -1413,7 +1390,7 @@ class Decimal(object):
q += 1 q += 1
if q >= 10**context.prec: if q >= 10**context.prec:
return context._raise_error(DivisionImpossible)[0] return context._raise_error(DivisionImpossible)
# result has same sign as self unless r is negative # result has same sign as self unless r is negative
sign = self._sign sign = self._sign
...@@ -1426,7 +1403,31 @@ class Decimal(object): ...@@ -1426,7 +1403,31 @@ class Decimal(object):
def __floordiv__(self, other, context=None): def __floordiv__(self, other, context=None):
"""self // other""" """self // other"""
return self._divide(other, 2, context)[0] other = _convert_other(other)
if other is NotImplemented:
return other
if context is None:
context = getcontext()
ans = self._check_nans(other, context)
if ans:
return ans
if self._isinfinity():
if other._isinfinity():
return context._raise_error(InvalidOperation, 'INF // INF')
else:
return Infsign[self._sign ^ other._sign]
if not other:
if self:
return context._raise_error(DivisionByZero, 'x // 0',
self._sign ^ other._sign)
else:
return context._raise_error(DivisionUndefined, '0 // 0')
return self._divide(other, context)[0]
def __rfloordiv__(self, other, context=None): def __rfloordiv__(self, other, context=None):
"""Swaps self/other and returns __floordiv__.""" """Swaps self/other and returns __floordiv__."""
...@@ -2979,7 +2980,7 @@ class Decimal(object): ...@@ -2979,7 +2980,7 @@ class Decimal(object):
# logb(0) = -Inf, DivisionByZero # logb(0) = -Inf, DivisionByZero
if not self: if not self:
return context._raise_error(DivisionByZero, 'logb(0)', -1) return context._raise_error(DivisionByZero, 'logb(0)', 1)
# otherwise, simply return the adjusted exponent of self, as a # otherwise, simply return the adjusted exponent of self, as a
# Decimal. Note that no attempt is made to fit the result # Decimal. Note that no attempt is made to fit the result
...@@ -4793,29 +4794,6 @@ def _normalize(op1, op2, shouldround = 0, prec = 0): ...@@ -4793,29 +4794,6 @@ def _normalize(op1, op2, shouldround = 0, prec = 0):
tmp.exp = other.exp tmp.exp = other.exp
return op1, op2 return op1, op2
def _adjust_coefficients(op1, op2):
"""Adjust op1, op2 so that op2.int * 10 > op1.int >= op2.int.
Returns the adjusted op1, op2 as well as the change in op1.exp-op2.exp.
Used on _WorkRep instances during division.
"""
adjust = 0
# If op1 is smaller, make it larger
while op2.int > op1.int:
op1.int *= 10
op1.exp -= 1
adjust += 1
# If op2 is too small, make it larger
while op1.int >= (10 * op2.int):
op2.int *= 10
op2.exp -= 1
adjust -= 1
return op1, op2, adjust
##### Integer arithmetic functions used by ln, log10, exp and __pow__ ##### ##### Integer arithmetic functions used by ln, log10, exp and __pow__ #####
# This function from Tim Peters was taken from here: # This function from Tim Peters was taken from here:
......
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