# Copyright (c) 2004 Python Software Foundation.
# Written by Eric Price <eprice at tjhsst.edu>
# and Facundo Batista <facundo at taniquetil.com.ar>
# and Raymond Hettinger <python at rcn.com>
# and Aahz <aahz at pobox.com>
# This module is currently Py2.3 compatible and should be kept that way
# unless a major compelling advantage arises. IOW, 2.3 compatibility is
# strongly preferred, but not guaranteed.
# Also, 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 a Py2.3 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 the expected Decimal('0.00') returned by decimal floating point).
Here are some examples of using the decimal module:
>>> from decimal import *
>>> setcontext(ExtendedContext)
>>> Decimal('123.45e12345678901234567890')
Decimal('1.2345E+12345678901234567892')
>>> Decimal('1.33') + Decimal('1.27')
>>> Decimal('12.34') + Decimal('3.87') - Decimal('18.41')
>>> print dig / Decimal(3)
>>> getcontext().prec = 18
>>> print dig / Decimal(3)
>>> print Decimal(3).sqrt()
>>> print Decimal(3) ** 123
>>> inf = Decimal(1) / Decimal(0)
>>> neginf = Decimal(-1) / Decimal(0)
>>> getcontext().traps[DivisionByZero] = 1
Traceback (most recent call last):
>>> c.traps[InvalidOperation] = 0
>>> print c.flags[InvalidOperation]
>>> c.divide(Decimal(0), Decimal(0))
>>> c.traps[InvalidOperation] = 1
>>> print c.flags[InvalidOperation]
>>> c.flags[InvalidOperation] = 0
>>> print c.flags[InvalidOperation]
>>> print c.divide(Decimal(0), Decimal(0))
Traceback (most recent call last):
>>> print c.flags[InvalidOperation]
>>> c.flags[InvalidOperation] = 0
>>> c.traps[InvalidOperation] = 0
>>> print c.divide(Decimal(0), Decimal(0))
>>> print c.flags[InvalidOperation]
'DefaultContext', 'BasicContext', 'ExtendedContext',
'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero',
'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow',
# 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'
__version__ = '1.70' # Highest version of the spec this complies with
import numbers as _numbers
from collections import namedtuple as _namedtuple
DecimalTuple = _namedtuple('DecimalTuple', 'sign digits exponent')
DecimalTuple = lambda *args: args
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_HALF_DOWN = 'ROUND_HALF_DOWN'
ROUND_05UP = 'ROUND_05UP'
class DecimalException(ArithmeticError):
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
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
def handle(self, context, *args):
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
x._rescale( non-integer )
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
def handle(self, context, *args):
ans = _dec_from_triple(args[0]._sign, args[0]._int, 'n', True)
return ans._fix_nan(context)
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, context, *args):
class DivisionByZero(DecimalException, ZeroDivisionError):
This occurs and signals division-by-zero if division of a finite number
by zero was attempted (during a divide-integer or divide operation, or a
power operation with negative right-hand operand), and the dividend was
The result of the operation is [sign,inf], where sign is the exclusive
or of the signs of the operands for divide, or is 1 for an odd power of
def handle(self, context, sign, *args):
return _SignedInfinity[sign]
class DivisionImpossible(InvalidOperation):
"""Cannot perform the division adequately.
This occurs and signals invalid-operation if the integer result of a
divide-integer or remainder operation had too many digits (would be
longer than precision). The result is [0,qNaN].
def handle(self, context, *args):
class DivisionUndefined(InvalidOperation, ZeroDivisionError):
"""Undefined result of division.
This occurs and signals invalid-operation if division by zero was
attempted (during a divide-integer, divide, or remainder operation), and
the dividend is also zero. The result is [0,qNaN].
def handle(self, context, *args):
class Inexact(DecimalException):
"""Had to round, losing information.
This occurs and signals inexact whenever the result of an operation is
not exact (that is, it needed to be rounded and any discarded digits
were non-zero), or if an overflow or underflow condition occurs. The
result in all cases is unchanged.
The inexact signal may be tested (or trapped) to determine if a given
operation (or sequence of operations) was inexact.
class InvalidContext(InvalidOperation):
"""Invalid context. Unknown rounding, for example.
This occurs and signals invalid-operation if an invalid context was
detected during an operation. This can occur if contexts are not checked
on creation and either the precision exceeds the capability of the
underlying concrete representation or an unknown or unsupported rounding
was specified. These aspects of the context need only be checked when
the values are required to be used. The result is [0,qNaN].
def handle(self, context, *args):
class Rounded(DecimalException):
"""Number got rounded (not necessarily changed during rounding).
This occurs and signals rounded whenever the result of an operation is
rounded (that is, some zero or non-zero digits were discarded from the
coefficient), or if an overflow or underflow condition occurs. The
result in all cases is unchanged.
The rounded signal may be tested (or trapped) to determine if a given
operation (or sequence of operations) caused a loss of precision.
class Subnormal(DecimalException):
"""Exponent < Emin before rounding.
This occurs and signals subnormal whenever the result of a conversion or
operation is subnormal (that is, its adjusted exponent is less than
Emin, before any rounding). The result in all cases is unchanged.
The subnormal signal may be tested (or trapped) to determine if a given
or operation (or sequence of operations) yielded a subnormal result.
class Overflow(Inexact, Rounded):
This occurs and signals overflow if the adjusted exponent of a result
(from a conversion or from an operation that is not an attempt to divide
by zero), after rounding, would be greater than the largest value that
can be handled by the implementation (the value Emax).
The result depends on the rounding mode:
For round-half-up and round-half-even (and for round-half-down and
round-up, if implemented), the result of the operation is [sign,inf],
where sign is the sign of the intermediate result. For round-down, the
result is the largest finite number that can be represented in the
current precision, with the sign of the intermediate result. For
round-ceiling, the result is the same as for round-down if the sign of
the intermediate result is 1, or is [0,inf] otherwise. For round-floor,
the result is the same as for round-down if the sign of the intermediate
result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded
def handle(self, context, sign, *args):
if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN,
ROUND_HALF_DOWN, ROUND_UP):
return _SignedInfinity[sign]
if context.rounding == ROUND_CEILING:
return _SignedInfinity[sign]
return _dec_from_triple(sign, '9'*context.prec,
context.Emax-context.prec+1)
if context.rounding == ROUND_FLOOR:
return _SignedInfinity[sign]
return _dec_from_triple(sign, '9'*context.prec,
context.Emax-context.prec+1)
class Underflow(Inexact, Rounded, Subnormal):
"""Numerical underflow with result rounded to 0.
This occurs and signals underflow if a result is inexact and the
adjusted exponent of the result would be smaller (more negative) than
the smallest value that can be handled by the implementation (the value
Emin). That is, the result is both inexact and subnormal.
The result after an underflow will be a subnormal number rounded, if
necessary, so that its exponent is not less than Etiny. This may result
in 0 with the sign of the intermediate result and an exponent of Etiny.
In all cases, Inexact, Rounded, and Subnormal will also be raised.
# List of public traps and flags
_signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded,
Underflow, InvalidOperation, Subnormal]
# Map conditions (per the spec) to signals
_condition_map = {ConversionSyntax:InvalidOperation,
DivisionImpossible:InvalidOperation,
DivisionUndefined:InvalidOperation,
InvalidContext:InvalidOperation}
##### Context Functions ##################################################
# The getcontext() and setcontext() function manage access to a thread-local
# current context. Py2.4 offers direct support for thread locals. If that
# is not available, use threading.currentThread() which is slower but will
# work for older Pythons. If threads are not part of the build, create a
# mock threading object with threading.local() returning the module namespace.
# Python was compiled without threads; create a mock object instead
class MockThreading(object):
def local(self, sys=sys):
return sys.modules[__name__]
threading = MockThreading()
# To fix reloading, force it to create a new context
# Old contexts have different exceptions in their dicts, making problems.
if hasattr(threading.currentThread(), '__decimal_context__'):
del threading.currentThread().__decimal_context__
"""Set this thread's context to context."""
if context in (DefaultContext, BasicContext, ExtendedContext):
threading.currentThread().__decimal_context__ = context
"""Returns this thread's context.
If this thread does not yet have a context, returns
a new context and sets this thread's context.
New contexts are copies of DefaultContext.
return threading.currentThread().__decimal_context__
threading.currentThread().__decimal_context__ = context
local = threading.local()
if hasattr(local, '__decimal_context__'):
del local.__decimal_context__
def getcontext(_local=local):
"""Returns this thread's context.
If this thread does not yet have a context, returns
a new context and sets this thread's context.
New contexts are copies of DefaultContext.
return _local.__decimal_context__
_local.__decimal_context__ = context
def setcontext(context, _local=local):
"""Set this thread's context to context."""
if context in (DefaultContext, BasicContext, ExtendedContext):
_local.__decimal_context__ = context
del threading, local # Don't contaminate the namespace
def localcontext(ctx=None):
"""Return a context manager for a copy of the supplied context
Uses a copy of the current context if no context is specified
The returned context manager creates a local decimal context
with localcontext() as ctx:
# Rest of sin calculation algorithm
# uses a precision 2 greater than normal
return +s # Convert result to normal precision
with localcontext(ExtendedContext):
# Rest of sin calculation algorithm
# uses the Extended Context from the
# General Decimal Arithmetic Specification
return +s # Convert result to normal context
>>> setcontext(DefaultContext)
>>> print getcontext().prec
>>> with localcontext(ExtendedContext):
... print getcontext().prec
>>> print getcontext().prec
if ctx is None: ctx = getcontext()
return _ContextManager(ctx)
It is recommended that you Edit text format, this type of Fix handles quite a lot in one request
