# Copyright (c) 2004 Python Software Foundation.
# All rights reserved.
# Written by Eric Price
# and Facundo Batista
# and Raymond Hettinger
# and Aahz
# and Tim Peters
# This module should be kept in sync with the latest updates of the
# IBM specification as it evolves. Those updates will be treated
# as bug fixes (deviation from the spec is a compatibility, usability
# bug) and will be backported. At this point the spec is stabilizing
# and the updates are becoming fewer, smaller, and less significant.
"""
This is an implementation of decimal floating point arithmetic based on
the General Decimal Arithmetic Specification:
http://speleotrove.com/decimal/decarith.html
and IEEE standard 854-1987:
http://en.wikipedia.org/wiki/IEEE_854-1987
Decimal floating point has finite precision with arbitrarily large bounds.
The purpose of this module is to support arithmetic using familiar
"schoolhouse" rules and to avoid some of the tricky representation
issues associated with binary floating point. The package is especially
useful for financial applications or for contexts where users have
expectations that are at odds with binary floating point (for instance,
in binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead
of 0.0; Decimal('1.00') % Decimal('0.1') returns the expected
Decimal('0.00')).
Here are some examples of using the decimal module:
>>> from decimal import *
>>> setcontext(ExtendedContext)
>>> Decimal(0)
Decimal('0')
>>> Decimal('1')
Decimal('1')
>>> Decimal('-.0123')
Decimal('-0.0123')
>>> Decimal(123456)
Decimal('123456')
>>> Decimal('123.45e12345678')
Decimal('1.2345E+12345680')
>>> Decimal('1.33') + Decimal('1.27')
Decimal('2.60')
>>> Decimal('12.34') + Decimal('3.87') - Decimal('18.41')
Decimal('-2.20')
>>> dig = Decimal(1)
>>> print(dig / Decimal(3))
0.333333333
>>> getcontext().prec = 18
>>> print(dig / Decimal(3))
0.333333333333333333
>>> print(dig.sqrt())
1
>>> print(Decimal(3).sqrt())
1.73205080756887729
>>> print(Decimal(3) ** 123)
4.85192780976896427E+58
>>> inf = Decimal(1) / Decimal(0)
>>> print(inf)
Infinity
>>> neginf = Decimal(-1) / Decimal(0)
>>> print(neginf)
-Infinity
>>> print(neginf + inf)
NaN
>>> print(neginf * inf)
-Infinity
>>> print(dig / 0)
Infinity
>>> getcontext().traps[DivisionByZero] = 1
>>> print(dig / 0)
Traceback (most recent call last):
...
...
...
decimal.DivisionByZero: x / 0
>>> c = Context()
>>> c.traps[InvalidOperation] = 0
>>> print(c.flags[InvalidOperation])
0
>>> c.divide(Decimal(0), Decimal(0))
Decimal('NaN')
>>> c.traps[InvalidOperation] = 1
>>> print(c.flags[InvalidOperation])
1
>>> c.flags[InvalidOperation] = 0
>>> print(c.flags[InvalidOperation])
0
>>> print(c.divide(Decimal(0), Decimal(0)))
Traceback (most recent call last):
...
...
...
decimal.InvalidOperation: 0 / 0
>>> print(c.flags[InvalidOperation])
1
>>> c.flags[InvalidOperation] = 0
>>> c.traps[InvalidOperation] = 0
>>> print(c.divide(Decimal(0), Decimal(0)))
NaN
>>> print(c.flags[InvalidOperation])
1
>>>
"""
__all__ = [
# Two major classes
'Decimal', 'Context',
# Named tuple representation
'DecimalTuple',
# Contexts
'DefaultContext', 'BasicContext', 'ExtendedContext',
# Exceptions
'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero',
'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow',
'FloatOperation',
# Exceptional conditions that trigger InvalidOperation
'DivisionImpossible', 'InvalidContext', 'ConversionSyntax', 'DivisionUndefined',
# Constants for use in setting up contexts
'ROUND_DOWN', 'ROUND_HALF_UP', 'ROUND_HALF_EVEN', 'ROUND_CEILING',
'ROUND_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN', 'ROUND_05UP',
# Functions for manipulating contexts
'setcontext', 'getcontext', 'localcontext',
# Limits for the C version for compatibility
'MAX_PREC', 'MAX_EMAX', 'MIN_EMIN', 'MIN_ETINY',
# C version: compile time choice that enables the thread local context (deprecated, now always true)
'HAVE_THREADS',
# C version: compile time choice that enables the coroutine local context
'HAVE_CONTEXTVAR'
]
__xname__ = __name__ # sys.modules lookup (--without-threads)
__name__ = 'decimal' # For pickling
__version__ = '1.70' # Highest version of the spec this complies with
# See http://speleotrove.com/decimal/
__libmpdec_version__ = "2.4.2" # compatible libmpdec version
import math as _math
import numbers as _numbers
import sys
try:
from collections import namedtuple as _namedtuple
DecimalTuple = _namedtuple('DecimalTuple', 'sign digits exponent')
except ImportError:
DecimalTuple = lambda *args: args
# Rounding
ROUND_DOWN = 'ROUND_DOWN'
ROUND_HALF_UP = 'ROUND_HALF_UP'
ROUND_HALF_EVEN = 'ROUND_HALF_EVEN'
ROUND_CEILING = 'ROUND_CEILING'
ROUND_FLOOR = 'ROUND_FLOOR'
ROUND_UP = 'ROUND_UP'
ROUND_HALF_DOWN = 'ROUND_HALF_DOWN'
ROUND_05UP = 'ROUND_05UP'
# Compatibility with the C version
HAVE_THREADS = True
HAVE_CONTEXTVAR = True
if sys.maxsize == 2**63-1:
MAX_PREC = 999999999999999999
MAX_EMAX = 999999999999999999
MIN_EMIN = -999999999999999999
else:
MAX_PREC = 425000000
MAX_EMAX = 425000000
MIN_EMIN = -425000000
MIN_ETINY = MIN_EMIN - (MAX_PREC-1)
# Errors
class DecimalException(ArithmeticError):
"""Base exception class.
Used exceptions derive from this.
If an exception derives from another exception besides this (such as
Underflow (Inexact, Rounded, Subnormal) that indicates that it is only
called if the others are present. This isn't actually used for
anything, though.
handle -- Called when context._raise_error is called and the
trap_enabler is not set. First argument is self, second is the
context. More arguments can be given, those being after
the explanation in _raise_error (For example,
context._raise_error(NewError, '(-x)!', self._sign) would
call NewError().handle(context, self._sign).)
To define a new exception, it should be sufficient to have it derive
from DecimalException.
"""
def handle(self, context, *args):
pass
class Clamped(DecimalException):
"""Exponent of a 0 changed to fit bounds.
This occurs and signals clamped if the exponent of a result has been
altered in order to fit the constraints of a specific concrete
representation. This may occur when the exponent of a zero result would
be outside the bounds of a representation, or when a large normal
number would have an encoded exponent that cannot be represented. In
this latter case, the exponent is reduced to fit and the corresponding
number of zero digits are appended to the coefficient ("fold-down").
"""
class InvalidOperation(DecimalException):
"""An invalid operation was performed.
Various bad things cause this:
Something creates a signaling NaN
-INF + INF
0 * (+-)INF
(+-)INF / (+-)INF
x % 0
(+-)INF % x
x._rescale( non-integer )
sqrt(-x) , x > 0
0 ** 0
x ** (non-integer)
x ** (+-)INF
An operand is invalid
The result of the operation after these is a quiet positive NaN,
except when the cause is a signaling NaN, in which case the result is
also a quiet NaN, but with the original sign, and an optional
diagnostic information.
"""
def handle(self, context, *args):
if args:
ans = _dec_from_triple(args[0]._sign, args[0]._int, 'n', True)
return ans._fix_nan(context)
return _NaN
class ConversionSyntax(InvalidOperation):
"""Trying to convert badly formed string.
This occurs and signals invalid-operation if a string is being
converted to a number and it does not conform to the numeric string
syntax. The result is [0,qNaN].
"""
def handle(self,