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Speed up of the various division operations (remainder, divide,
divideint and divmod). Thanks Mark Dickinson.
This commit is contained in:
Facundo Batista
parent
745e48dffa
commit
cce8df2f67
1 changed files with 139 additions and 161 deletions
300
Lib/decimal.py
300
Lib/decimal.py
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@ -244,9 +244,7 @@ class DivisionByZero(DecimalException, ZeroDivisionError):
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-0, for power.
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"""
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def handle(self, context, sign, double = None, *args):
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if double is not None:
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return (Infsign[sign],)*2
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def handle(self, context, sign, *args):
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return Infsign[sign]
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class DivisionImpossible(InvalidOperation):
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@ -258,7 +256,7 @@ class DivisionImpossible(InvalidOperation):
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"""
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def handle(self, context, *args):
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return (NaN, NaN)
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return NaN
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class DivisionUndefined(InvalidOperation, ZeroDivisionError):
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"""Undefined result of division.
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@ -268,9 +266,7 @@ class DivisionUndefined(InvalidOperation, ZeroDivisionError):
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the dividend is also zero. The result is [0,qNaN].
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"""
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def handle(self, context, tup=None, *args):
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if tup is not None:
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return (NaN, NaN) # for 0 %0, 0 // 0
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def handle(self, context, *args):
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return NaN
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class Inexact(DecimalException):
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@ -1151,157 +1147,97 @@ def __mul__(self, other, context=None):
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def __div__(self, other, context=None):
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"""Return self / other."""
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return self._divide(other, context=context)
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__truediv__ = __div__
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def _divide(self, other, divmod = 0, context=None):
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"""Return a / b, to context.prec precision.
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divmod:
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0 => true division
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1 => (a //b, a%b)
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2 => a //b
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3 => a%b
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Actually, if divmod is 2 or 3 a tuple is returned, but errors for
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computing the other value are not raised.
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"""
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other = _convert_other(other)
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if other is NotImplemented:
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if divmod in (0, 1):
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return NotImplemented
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return (NotImplemented, NotImplemented)
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return NotImplemented
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if context is None:
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context = getcontext()
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shouldround = context._rounding_decision == ALWAYS_ROUND
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sign = self._sign ^ other._sign
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if self._is_special or other._is_special:
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ans = self._check_nans(other, context)
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if ans:
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if divmod:
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return (ans, ans)
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return ans
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if self._isinfinity() and other._isinfinity():
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if divmod:
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reloco = (context._raise_error(InvalidOperation,
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'(+-)INF // (+-)INF'),
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context._raise_error(InvalidOperation,
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'(+-)INF % (+-)INF'))
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return reloco
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return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF')
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if self._isinfinity():
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if divmod == 1:
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return (Infsign[sign],
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context._raise_error(InvalidOperation, 'INF % x'))
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elif divmod == 2:
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return (Infsign[sign], NaN)
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elif divmod == 3:
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return (Infsign[sign],
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context._raise_error(InvalidOperation, 'INF % x'))
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return Infsign[sign]
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if other._isinfinity():
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if divmod:
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otherside = Decimal(self)
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if shouldround and (divmod == 1 or divmod == 3):
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otherside = otherside._fix(context)
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return (Decimal((sign, (0,), 0)), otherside)
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context._raise_error(Clamped, 'Division by infinity')
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return Decimal((sign, (0,), context.Etiny()))
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# Special cases for zeroes
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if not self and not other:
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if divmod:
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return context._raise_error(DivisionUndefined, '0 / 0', 1)
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return context._raise_error(DivisionUndefined, '0 / 0')
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if not self:
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if divmod:
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otherside = Decimal((self._sign, (0,), min(self._exp, other._exp)))
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if shouldround and (divmod == 1 or divmod == 3):
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otherside = otherside._fix(context)
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return (Decimal((sign, (0,), 0)), otherside)
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exp = self._exp - other._exp
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ans = Decimal((sign, (0,), exp))
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ans = ans._fix(context)
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return ans
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if not other:
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if divmod:
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return context._raise_error(DivisionByZero, 'divmod(x,0)',
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sign, 1)
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if not self:
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return context._raise_error(DivisionUndefined, '0 / 0')
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return context._raise_error(DivisionByZero, 'x / 0', sign)
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# OK, so neither = 0, INF or NaN
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if not self:
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exp = self._exp - other._exp
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coeff = 0
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else:
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# OK, so neither = 0, INF or NaN
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shift = len(other._int) - len(self._int) + context.prec + 1
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exp = self._exp - other._exp - shift
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op1 = _WorkRep(self)
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op2 = _WorkRep(other)
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if shift >= 0:
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coeff, remainder = divmod(op1.int * 10**shift, op2.int)
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else:
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coeff, remainder = divmod(op1.int, op2.int * 10**-shift)
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if remainder:
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# result is not exact; adjust to ensure correct rounding
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if coeff % 5 == 0:
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coeff += 1
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else:
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# result is exact; get as close to ideal exponent as possible
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ideal_exp = self._exp - other._exp
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while exp < ideal_exp and coeff % 10 == 0:
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coeff //= 10
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exp += 1
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# If we're dividing into ints, and self < other, stop.
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# self.__abs__(0) does not round.
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if divmod and (self.__abs__(0, context) < other.__abs__(0, context)):
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ans = Decimal((sign, map(int, str(coeff)), exp))
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return ans._fix(context)
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if divmod == 1 or divmod == 3:
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exp = min(self._exp, other._exp)
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ans2 = self._rescale(exp, context.rounding)
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if shouldround:
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ans2 = ans2._fix(context)
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return (Decimal( (sign, (0,), 0) ),
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ans2)
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__truediv__ = __div__
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elif divmod == 2:
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# Don't round the mod part, if we don't need it.
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return (Decimal( (sign, (0,), 0) ), Decimal(self))
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def _divide(self, other, context):
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"""Return (self // other, self % other), to context.prec precision.
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op1 = _WorkRep(self)
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op2 = _WorkRep(other)
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op1, op2, adjust = _adjust_coefficients(op1, op2)
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res = _WorkRep( (sign, 0, (op1.exp - op2.exp)) )
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if divmod and res.exp > context.prec + 1:
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return context._raise_error(DivisionImpossible)
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Assumes that neither self nor other is a NaN, that self is not
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infinite and that other is nonzero.
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"""
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sign = self._sign ^ other._sign
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if other._isinfinity():
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ideal_exp = self._exp
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else:
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ideal_exp = min(self._exp, other._exp)
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prec_limit = 10 ** context.prec
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while 1:
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while op2.int <= op1.int:
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res.int += 1
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op1.int -= op2.int
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if res.exp == 0 and divmod:
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if res.int >= prec_limit and shouldround:
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return context._raise_error(DivisionImpossible)
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otherside = Decimal(op1)
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exp = min(self._exp, other._exp)
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otherside = otherside._rescale(exp, context.rounding)
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if shouldround and (divmod == 1 or divmod == 3):
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otherside = otherside._fix(context)
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return (Decimal(res), otherside)
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expdiff = self.adjusted() - other.adjusted()
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if not self or other._isinfinity() or expdiff <= -2:
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return (Decimal((sign, (0,), 0)),
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self._rescale(ideal_exp, context.rounding))
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if expdiff <= context.prec:
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op1 = _WorkRep(self)
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op2 = _WorkRep(other)
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if op1.exp >= op2.exp:
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op1.int *= 10**(op1.exp - op2.exp)
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else:
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op2.int *= 10**(op2.exp - op1.exp)
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q, r = divmod(op1.int, op2.int)
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if q < 10**context.prec:
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return (Decimal((sign, map(int, str(q)), 0)),
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Decimal((self._sign, map(int, str(r)), ideal_exp)))
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if op1.int == 0 and adjust >= 0 and not divmod:
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break
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if res.int >= prec_limit and shouldround:
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if divmod:
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return context._raise_error(DivisionImpossible)
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shouldround=1
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# Really, the answer is a bit higher, so adding a one to
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# the end will make sure the rounding is right.
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if op1.int != 0:
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res.int *= 10
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res.int += 1
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res.exp -= 1
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break
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res.int *= 10
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res.exp -= 1
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adjust += 1
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op1.int *= 10
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op1.exp -= 1
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ans = Decimal(res)
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if shouldround:
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ans = ans._fix(context)
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return ans
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# Here the quotient is too large to be representable
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ans = context._raise_error(DivisionImpossible,
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'quotient too large in //, % or divmod')
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return ans, ans
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def __rdiv__(self, other, context=None):
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"""Swaps self/other and returns __div__."""
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@ -1313,9 +1249,40 @@ def __rdiv__(self, other, context=None):
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def __divmod__(self, other, context=None):
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"""
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(self // other, self % other)
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Return (self // other, self % other)
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"""
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return self._divide(other, 1, context)
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other = _convert_other(other)
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if other is NotImplemented:
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return other
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if context is None:
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context = getcontext()
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ans = self._check_nans(other, context)
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if ans:
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return (ans, ans)
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sign = self._sign ^ other._sign
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if self._isinfinity():
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if other._isinfinity():
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ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)')
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return ans, ans
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else:
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return (Infsign[sign],
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context._raise_error(InvalidOperation, 'INF % x'))
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if not other:
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if not self:
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ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)')
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return ans, ans
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else:
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return (context._raise_error(DivisionByZero, 'x // 0', sign),
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context._raise_error(InvalidOperation, 'x % 0'))
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quotient, remainder = self._divide(other, context)
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if context._rounding_decision == ALWAYS_ROUND:
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remainder = remainder._fix(context)
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return quotient, remainder
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def __rdivmod__(self, other, context=None):
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"""Swaps self/other and returns __divmod__."""
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@ -1332,15 +1299,25 @@ def __mod__(self, other, context=None):
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if other is NotImplemented:
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return other
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if self._is_special or other._is_special:
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ans = self._check_nans(other, context)
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if ans:
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return ans
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if context is None:
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context = getcontext()
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if self and not other:
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return context._raise_error(InvalidOperation, 'x % 0')
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ans = self._check_nans(other, context)
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if ans:
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return ans
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return self._divide(other, 3, context)[1]
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if self._isinfinity():
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return context._raise_error(InvalidOperation, 'INF % x')
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elif not other:
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if self:
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return context._raise_error(InvalidOperation, 'x % 0')
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else:
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return context._raise_error(DivisionUndefined, '0 % 0')
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remainder = self._divide(other, context)[1]
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if context._rounding_decision == ALWAYS_ROUND:
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remainder = remainder._fix(context)
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return remainder
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def __rmod__(self, other, context=None):
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"""Swaps self/other and returns __mod__."""
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@ -1391,7 +1368,7 @@ def remainder_near(self, other, context=None):
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expdiff = self.adjusted() - other.adjusted()
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if expdiff >= context.prec + 1:
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# expdiff >= prec+1 => abs(self/other) > 10**prec
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return context._raise_error(DivisionImpossible)[0]
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return context._raise_error(DivisionImpossible)
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if expdiff <= -2:
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# expdiff <= -2 => abs(self/other) < 0.1
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ans = self._rescale(ideal_exponent, context.rounding)
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@ -1413,7 +1390,7 @@ def remainder_near(self, other, context=None):
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q += 1
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if q >= 10**context.prec:
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return context._raise_error(DivisionImpossible)[0]
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return context._raise_error(DivisionImpossible)
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# result has same sign as self unless r is negative
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sign = self._sign
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@ -1426,7 +1403,31 @@ def remainder_near(self, other, context=None):
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def __floordiv__(self, other, context=None):
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"""self // other"""
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return self._divide(other, 2, context)[0]
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other = _convert_other(other)
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if other is NotImplemented:
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return other
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if context is None:
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context = getcontext()
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ans = self._check_nans(other, context)
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if ans:
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return ans
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if self._isinfinity():
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if other._isinfinity():
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return context._raise_error(InvalidOperation, 'INF // INF')
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else:
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return Infsign[self._sign ^ other._sign]
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if not other:
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if self:
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return context._raise_error(DivisionByZero, 'x // 0',
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self._sign ^ other._sign)
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else:
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return context._raise_error(DivisionUndefined, '0 // 0')
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return self._divide(other, context)[0]
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def __rfloordiv__(self, other, context=None):
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"""Swaps self/other and returns __floordiv__."""
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@ -2979,7 +2980,7 @@ def logb(self, context=None):
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# logb(0) = -Inf, DivisionByZero
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if not self:
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return context._raise_error(DivisionByZero, 'logb(0)', -1)
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return context._raise_error(DivisionByZero, 'logb(0)', 1)
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# otherwise, simply return the adjusted exponent of self, as a
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# Decimal. Note that no attempt is made to fit the result
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@ -4793,29 +4794,6 @@ def _normalize(op1, op2, shouldround = 0, prec = 0):
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tmp.exp = other.exp
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return op1, op2
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def _adjust_coefficients(op1, op2):
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"""Adjust op1, op2 so that op2.int * 10 > op1.int >= op2.int.
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Returns the adjusted op1, op2 as well as the change in op1.exp-op2.exp.
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Used on _WorkRep instances during division.
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"""
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adjust = 0
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# If op1 is smaller, make it larger
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while op2.int > op1.int:
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op1.int *= 10
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op1.exp -= 1
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adjust += 1
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# If op2 is too small, make it larger
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while op1.int >= (10 * op2.int):
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op2.int *= 10
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op2.exp -= 1
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adjust -= 1
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return op1, op2, adjust
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##### Integer arithmetic functions used by ln, log10, exp and __pow__ #####
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# This function from Tim Peters was taken from here:
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