def dsum(iterable):
"Full precision summation using Decimal objects for intermediate values"
# Transform (exactly) a float to m * 2 ** e where m and e are integers.
# Convert (mant, exp) to a Decimal and add to the cumulative sum.
# If the precision is too small for exact conversion and addition,
# then retry with a larger precision.
total = Decimal(0)
for x in iterable:
mant, exp = frexp(x)
mant, exp = int(mant * 2.0 ** 53), exp-53
while True:
try:
total += mant * Decimal(2) ** exp
break
except Inexact:
getcontext().prec += 1
return float(total)
python类Inexact()的实例源码
def create_decimal_from_float(self, f):
"""Creates a new Decimal instance from a float but rounding using self
as the context.
>>> context = Context(prec=5, rounding=ROUND_DOWN)
>>> context.create_decimal_from_float(3.1415926535897932)
Decimal('3.1415')
>>> context = Context(prec=5, traps=[Inexact])
>>> context.create_decimal_from_float(3.1415926535897932)
Traceback (most recent call last):
...
decimal.Inexact: None
"""
d = Decimal.from_float(f) # An exact conversion
return d._fix(self) # Apply the context rounding
# Methods
def create_decimal_from_float(self, f):
"""Creates a new Decimal instance from a float but rounding using self
as the context.
>>> context = Context(prec=5, rounding=ROUND_DOWN)
>>> context.create_decimal_from_float(3.1415926535897932)
Decimal('3.1415')
>>> context = Context(prec=5, traps=[Inexact])
>>> context.create_decimal_from_float(3.1415926535897932)
Traceback (most recent call last):
...
decimal.Inexact: None
"""
d = Decimal.from_float(f) # An exact conversion
return d._fix(self) # Apply the context rounding
# Methods
def create_decimal_from_float(self, f):
"""Creates a new Decimal instance from a float but rounding using self
as the context.
>>> context = Context(prec=5, rounding=ROUND_DOWN)
>>> context.create_decimal_from_float(3.1415926535897932)
Decimal('3.1415')
>>> context = Context(prec=5, traps=[Inexact])
>>> context.create_decimal_from_float(3.1415926535897932)
Traceback (most recent call last):
...
decimal.Inexact: None
"""
d = Decimal.from_float(f) # An exact conversion
return d._fix(self) # Apply the context rounding
# Methods
def create_decimal_from_float(self, f):
"""Creates a new Decimal instance from a float but rounding using self
as the context.
>>> context = Context(prec=5, rounding=ROUND_DOWN)
>>> context.create_decimal_from_float(3.1415926535897932)
Decimal('3.1415')
>>> context = Context(prec=5, traps=[Inexact])
>>> context.create_decimal_from_float(3.1415926535897932)
Traceback (most recent call last):
...
decimal.Inexact: None
"""
d = Decimal.from_float(f) # An exact conversion
return d._fix(self) # Apply the context rounding
# Methods
def float_to_decimal(f):
"""
Convert a floating point number to a Decimal with
no loss of information. Intended for Python 2.6 where
casting float to Decimal does not work.
"""
n, d = f.as_integer_ratio()
numerator, denominator = Decimal(n), Decimal(d)
ctx = Context(prec=60)
result = ctx.divide(numerator, denominator)
while ctx.flags[Inexact]:
ctx.flags[Inexact] = False
ctx.prec *= 2
result = ctx.divide(numerator, denominator)
return result
def to_integral_exact(self, rounding=None, context=None):
"""Rounds to a nearby integer.
If no rounding mode is specified, take the rounding mode from
the context. This method raises the Rounded and Inexact flags
when appropriate.
See also: to_integral_value, which does exactly the same as
this method except that it doesn't raise Inexact or Rounded.
"""
if self._is_special:
ans = self._check_nans(context=context)
if ans:
return ans
return Decimal(self)
if self._exp >= 0:
return Decimal(self)
if not self:
return _dec_from_triple(self._sign, '0', 0)
if context is None:
context = getcontext()
if rounding is None:
rounding = context.rounding
ans = self._rescale(0, rounding)
if ans != self:
context._raise_error(Inexact)
context._raise_error(Rounded)
return ans
def to_integral_exact(self, a):
"""Rounds to an integer.
When the operand has a negative exponent, the result is the same
as using the quantize() operation using the given operand as the
left-hand-operand, 1E+0 as the right-hand-operand, and the precision
of the operand as the precision setting; Inexact and Rounded flags
are allowed in this operation. The rounding mode is taken from the
context.
>>> ExtendedContext.to_integral_exact(Decimal('2.1'))
Decimal('2')
>>> ExtendedContext.to_integral_exact(Decimal('100'))
Decimal('100')
>>> ExtendedContext.to_integral_exact(Decimal('100.0'))
Decimal('100')
>>> ExtendedContext.to_integral_exact(Decimal('101.5'))
Decimal('102')
>>> ExtendedContext.to_integral_exact(Decimal('-101.5'))
Decimal('-102')
>>> ExtendedContext.to_integral_exact(Decimal('10E+5'))
Decimal('1.0E+6')
>>> ExtendedContext.to_integral_exact(Decimal('7.89E+77'))
Decimal('7.89E+77')
>>> ExtendedContext.to_integral_exact(Decimal('-Inf'))
Decimal('-Infinity')
"""
a = _convert_other(a, raiseit=True)
return a.to_integral_exact(context=self)
def to_integral_exact(self, rounding=None, context=None):
"""Rounds to a nearby integer.
If no rounding mode is specified, take the rounding mode from
the context. This method raises the Rounded and Inexact flags
when appropriate.
See also: to_integral_value, which does exactly the same as
this method except that it doesn't raise Inexact or Rounded.
"""
if self._is_special:
ans = self._check_nans(context=context)
if ans:
return ans
return Decimal(self)
if self._exp >= 0:
return Decimal(self)
if not self:
return _dec_from_triple(self._sign, '0', 0)
if context is None:
context = getcontext()
if rounding is None:
rounding = context.rounding
ans = self._rescale(0, rounding)
if ans != self:
context._raise_error(Inexact)
context._raise_error(Rounded)
return ans
def to_integral_exact(self, a):
"""Rounds to an integer.
When the operand has a negative exponent, the result is the same
as using the quantize() operation using the given operand as the
left-hand-operand, 1E+0 as the right-hand-operand, and the precision
of the operand as the precision setting; Inexact and Rounded flags
are allowed in this operation. The rounding mode is taken from the
context.
>>> ExtendedContext.to_integral_exact(Decimal('2.1'))
Decimal('2')
>>> ExtendedContext.to_integral_exact(Decimal('100'))
Decimal('100')
>>> ExtendedContext.to_integral_exact(Decimal('100.0'))
Decimal('100')
>>> ExtendedContext.to_integral_exact(Decimal('101.5'))
Decimal('102')
>>> ExtendedContext.to_integral_exact(Decimal('-101.5'))
Decimal('-102')
>>> ExtendedContext.to_integral_exact(Decimal('10E+5'))
Decimal('1.0E+6')
>>> ExtendedContext.to_integral_exact(Decimal('7.89E+77'))
Decimal('7.89E+77')
>>> ExtendedContext.to_integral_exact(Decimal('-Inf'))
Decimal('-Infinity')
"""
a = _convert_other(a, raiseit=True)
return a.to_integral_exact(context=self)
def to_integral_exact(self, rounding=None, context=None):
"""Rounds to a nearby integer.
If no rounding mode is specified, take the rounding mode from
the context. This method raises the Rounded and Inexact flags
when appropriate.
See also: to_integral_value, which does exactly the same as
this method except that it doesn't raise Inexact or Rounded.
"""
if self._is_special:
ans = self._check_nans(context=context)
if ans:
return ans
return Decimal(self)
if self._exp >= 0:
return Decimal(self)
if not self:
return _dec_from_triple(self._sign, '0', 0)
if context is None:
context = getcontext()
if rounding is None:
rounding = context.rounding
ans = self._rescale(0, rounding)
if ans != self:
context._raise_error(Inexact)
context._raise_error(Rounded)
return ans
def to_integral_exact(self, a):
"""Rounds to an integer.
When the operand has a negative exponent, the result is the same
as using the quantize() operation using the given operand as the
left-hand-operand, 1E+0 as the right-hand-operand, and the precision
of the operand as the precision setting; Inexact and Rounded flags
are allowed in this operation. The rounding mode is taken from the
context.
>>> ExtendedContext.to_integral_exact(Decimal('2.1'))
Decimal('2')
>>> ExtendedContext.to_integral_exact(Decimal('100'))
Decimal('100')
>>> ExtendedContext.to_integral_exact(Decimal('100.0'))
Decimal('100')
>>> ExtendedContext.to_integral_exact(Decimal('101.5'))
Decimal('102')
>>> ExtendedContext.to_integral_exact(Decimal('-101.5'))
Decimal('-102')
>>> ExtendedContext.to_integral_exact(Decimal('10E+5'))
Decimal('1.0E+6')
>>> ExtendedContext.to_integral_exact(Decimal('7.89E+77'))
Decimal('7.89E+77')
>>> ExtendedContext.to_integral_exact(Decimal('-Inf'))
Decimal('-Infinity')
"""
a = _convert_other(a, raiseit=True)
return a.to_integral_exact(context=self)
def float_to_decimal(f):
"""Convert a floating point number to a Decimal with no loss of information.
See: http://docs.python.org/release/2.6.7/library/decimal.html#decimal-faq
"""
n, d = f.as_integer_ratio()
numerator, denominator = Decimal(n), Decimal(d)
ctx = Context(prec=60)
result = ctx.divide(numerator, denominator)
while ctx.flags[Inexact]:
ctx.flags[Inexact] = False
ctx.prec *= 2
result = ctx.divide(numerator, denominator)
return result
def to_integral_exact(self, rounding=None, context=None):
"""Rounds to a nearby integer.
If no rounding mode is specified, take the rounding mode from
the context. This method raises the Rounded and Inexact flags
when appropriate.
See also: to_integral_value, which does exactly the same as
this method except that it doesn't raise Inexact or Rounded.
"""
if self._is_special:
ans = self._check_nans(context=context)
if ans:
return ans
return Decimal(self)
if self._exp >= 0:
return Decimal(self)
if not self:
return _dec_from_triple(self._sign, '0', 0)
if context is None:
context = getcontext()
if rounding is None:
rounding = context.rounding
ans = self._rescale(0, rounding)
if ans != self:
context._raise_error(Inexact)
context._raise_error(Rounded)
return ans
def to_integral_exact(self, a):
"""Rounds to an integer.
When the operand has a negative exponent, the result is the same
as using the quantize() operation using the given operand as the
left-hand-operand, 1E+0 as the right-hand-operand, and the precision
of the operand as the precision setting; Inexact and Rounded flags
are allowed in this operation. The rounding mode is taken from the
context.
>>> ExtendedContext.to_integral_exact(Decimal('2.1'))
Decimal('2')
>>> ExtendedContext.to_integral_exact(Decimal('100'))
Decimal('100')
>>> ExtendedContext.to_integral_exact(Decimal('100.0'))
Decimal('100')
>>> ExtendedContext.to_integral_exact(Decimal('101.5'))
Decimal('102')
>>> ExtendedContext.to_integral_exact(Decimal('-101.5'))
Decimal('-102')
>>> ExtendedContext.to_integral_exact(Decimal('10E+5'))
Decimal('1.0E+6')
>>> ExtendedContext.to_integral_exact(Decimal('7.89E+77'))
Decimal('7.89E+77')
>>> ExtendedContext.to_integral_exact(Decimal('-Inf'))
Decimal('-Infinity')
"""
a = _convert_other(a, raiseit=True)
return a.to_integral_exact(context=self)
def next_toward(self, other, context=None):
"""Returns the number closest to self, in the direction towards other.
The result is the closest representable number to self
(excluding self) that is in the direction towards other,
unless both have the same value. If the two operands are
numerically equal, then the result is a copy of self with the
sign set to be the same as the sign of other.
"""
other = _convert_other(other, raiseit=True)
if context is None:
context = getcontext()
ans = self._check_nans(other, context)
if ans:
return ans
comparison = self._cmp(other)
if comparison == 0:
return self.copy_sign(other)
if comparison == -1:
ans = self.next_plus(context)
else: # comparison == 1
ans = self.next_minus(context)
# decide which flags to raise using value of ans
if ans._isinfinity():
context._raise_error(Overflow,
'Infinite result from next_toward',
ans._sign)
context._raise_error(Inexact)
context._raise_error(Rounded)
elif ans.adjusted() < context.Emin:
context._raise_error(Underflow)
context._raise_error(Subnormal)
context._raise_error(Inexact)
context._raise_error(Rounded)
# if precision == 1 then we don't raise Clamped for a
# result 0E-Etiny.
if not ans:
context._raise_error(Clamped)
return ans
def next_toward(self, other, context=None):
"""Returns the number closest to self, in the direction towards other.
The result is the closest representable number to self
(excluding self) that is in the direction towards other,
unless both have the same value. If the two operands are
numerically equal, then the result is a copy of self with the
sign set to be the same as the sign of other.
"""
other = _convert_other(other, raiseit=True)
if context is None:
context = getcontext()
ans = self._check_nans(other, context)
if ans:
return ans
comparison = self._cmp(other)
if comparison == 0:
return self.copy_sign(other)
if comparison == -1:
ans = self.next_plus(context)
else: # comparison == 1
ans = self.next_minus(context)
# decide which flags to raise using value of ans
if ans._isinfinity():
context._raise_error(Overflow,
'Infinite result from next_toward',
ans._sign)
context._raise_error(Inexact)
context._raise_error(Rounded)
elif ans.adjusted() < context.Emin:
context._raise_error(Underflow)
context._raise_error(Subnormal)
context._raise_error(Inexact)
context._raise_error(Rounded)
# if precision == 1 then we don't raise Clamped for a
# result 0E-Etiny.
if not ans:
context._raise_error(Clamped)
return ans
def next_toward(self, other, context=None):
"""Returns the number closest to self, in the direction towards other.
The result is the closest representable number to self
(excluding self) that is in the direction towards other,
unless both have the same value. If the two operands are
numerically equal, then the result is a copy of self with the
sign set to be the same as the sign of other.
"""
other = _convert_other(other, raiseit=True)
if context is None:
context = getcontext()
ans = self._check_nans(other, context)
if ans:
return ans
comparison = self._cmp(other)
if comparison == 0:
return self.copy_sign(other)
if comparison == -1:
ans = self.next_plus(context)
else: # comparison == 1
ans = self.next_minus(context)
# decide which flags to raise using value of ans
if ans._isinfinity():
context._raise_error(Overflow,
'Infinite result from next_toward',
ans._sign)
context._raise_error(Inexact)
context._raise_error(Rounded)
elif ans.adjusted() < context.Emin:
context._raise_error(Underflow)
context._raise_error(Subnormal)
context._raise_error(Inexact)
context._raise_error(Rounded)
# if precision == 1 then we don't raise Clamped for a
# result 0E-Etiny.
if not ans:
context._raise_error(Clamped)
return ans
def next_toward(self, other, context=None):
"""Returns the number closest to self, in the direction towards other.
The result is the closest representable number to self
(excluding self) that is in the direction towards other,
unless both have the same value. If the two operands are
numerically equal, then the result is a copy of self with the
sign set to be the same as the sign of other.
"""
other = _convert_other(other, raiseit=True)
if context is None:
context = getcontext()
ans = self._check_nans(other, context)
if ans:
return ans
comparison = self._cmp(other)
if comparison == 0:
return self.copy_sign(other)
if comparison == -1:
ans = self.next_plus(context)
else: # comparison == 1
ans = self.next_minus(context)
# decide which flags to raise using value of ans
if ans._isinfinity():
context._raise_error(Overflow,
'Infinite result from next_toward',
ans._sign)
context._raise_error(Inexact)
context._raise_error(Rounded)
elif ans.adjusted() < context.Emin:
context._raise_error(Underflow)
context._raise_error(Subnormal)
context._raise_error(Inexact)
context._raise_error(Rounded)
# if precision == 1 then we don't raise Clamped for a
# result 0E-Etiny.
if not ans:
context._raise_error(Clamped)
return ans
