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# Copyright (c) 2004 Python Software Foundation.
# All rights reserved.
# 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>
# 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', module='decimal')
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, context, *args):
return _NaN
class DivisionByZero(DecimalException, ZeroDivisionError):
"""Division by 0.
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
not zero.
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
-0, for power.
"""
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):
return _NaN
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):
return _NaN
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):
return _NaN
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):
"""Numerical overflow.
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
will also be raised.
"""
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 sign == 0:
if context.rounding == ROUND_CEILING:
return _SignedInfinity[sign]
return _dec_from_triple(sign, '9'*context.prec,
context.Emax-context.prec+1)
if sign == 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
10BC8
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.
"""
class FloatOperation(DecimalException, TypeError):
"""Enable stricter semantics for mixing floats and Decimals.
If the signal is not trapped (default), mixing floats and Decimals is
permitted in the Decimal() constructor, context.create_decimal() and
all comparison operators. Both conversion and comparisons are exact.
Any occurrence of a mixed operation is silently recorded by setting
FloatOperation in the context flags. Explicit conversions with
Decimal.from_float() or context.create_decimal_from_float() do not
set the flag.
Otherwise (the signal is trapped), only equality comparisons and explicit
conversions are silent. All other mixed operations raise FloatOperation.
"""
# List of public traps and flags
_signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded,
Underflow, InvalidOperation, Subnormal, FloatOperation]
# Map conditions (per the spec) to signals
_condition_map = {ConversionSyntax:InvalidOperation,
DivisionImpossible:InvalidOperation,
DivisionUndefined:InvalidOperation,
InvalidContext:InvalidOperation}
# Valid rounding modes
_rounding_modes = (ROUND_DOWN, ROUND_HALF_UP, ROUND_HALF_EVEN, ROUND_CEILING,
ROUND_FLOOR, ROUND_UP, ROUND_HALF_DOWN, ROUND_05UP)
##### Context Functions ##################################################
# The getcontext() and setcontext() function manage access to a thread-local
# current context.
import contextvars
_current_context_var = contextvars.ContextVar('decimal_context')
_context_attributes = frozenset(
['prec', 'Emin', 'Emax', 'capitals', 'clamp', 'rounding', 'flags', 'traps']
)
def getcontext():
"""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.
"""
try:
return _current_context_var.get()
except LookupError:
context = Context()
_current_context_var.set(context)
return context
def setcontext(context):
"""Set this thread's context to context."""
if context in (DefaultContext, BasicContext, ExtendedContext):
context = context.copy()
context.clear_flags()
_current_context_var.set(context)
del contextvars # Don't contaminate the namespace
def localcontext(ctx=None, **kwargs):
"""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
in a with statement:
def sin(x):
with localcontext() as ctx:
ctx.prec += 2
# Rest of sin calculation algorithm
# uses a precision 2 greater than normal
return +s # Convert result to normal precision
def sin(x):
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)
28
>>> with localcontext():
... ctx = getcontext()
... ctx.prec += 2
... print(ctx.prec)
...
30
>>> with localcontext(ExtendedContext):
... print(getcontext().prec)
...
9
>>> print(getcontext().prec)
28
"""
if ctx is None:
ctx = getcontext()
ctx_manager = _ContextManager(ctx)
for key, value in kwargs.items():
if key not in _context_attributes:
raise TypeError(f"'{key}' is an invalid keyword argument for this function")
setattr(ctx_manager.new_context, key, value)
return ctx_manager
##### Decimal class #######################################################
# Do not subclass Decimal from numbers.Real and do not register it as such
# (because Decimals are not interoperable with floats). See the notes in
# numbers.py for more detail.
class Decimal(object):
"""Floating point class for decimal arithmetic."""
__slots__ = ('_exp','_int','_sign', '_is_special')
# Generally, the value of the Decimal instance is given by
# (-1)**_sign * _int * 10**_exp
# Special values are signified by _is_special == True
# We're immutable, so use __new__ not __init__
def __new__(cls, value="0", context=None):
"""Create a decimal point instance.
>>> Decimal('3.14') # string input
Decimal('3.14')
>>> Decimal((0, (3, 1, 4), -2)) # tuple (sign, digit_tuple, exponent)
Decimal('3.14')
>>> Decimal(314) # int
Decimal('314')
>>> Decimal(Decimal(314)) # another decimal instance
Decimal('314')
>>> Decimal(' 3.14 \\n') # leading and trailing whitespace okay
Decimal('3.14')
"""
# Note that the coefficient, self._int, is actually stored as
# a string rather than as a tuple of digits. This speeds up
# the "digits to integer" and "integer to digits" conversions
# that are used in almost every arithmetic operation on
# Decimals. This is an internal detail: the as_tuple function
# and the Decimal constructor still deal with tuples of
# digits.
self = object.__new__(cls)
# From a string
# REs insist on real strings, so we can too.
if isinstance(value, str):
m = _parser(value.strip().replace("_", ""))
if m is None:
if context is None:
context = getcontext()
return context._raise_error(ConversionSyntax,
"Invalid literal for Decimal: %r" % value)
if m.group('sign') == "-":
self._sign = 1
else:
self._sign = 0
intpart = m.group('int')
if intpart is not None:
# finite number
fracpart = m.group('frac') or ''
exp = int(m.group('exp') or '0')
self._int = str(int(intpart+fracpart))
self._exp = exp - len(fracpart)
self._is_special = False
else:
diag = m.group('diag')
if diag is not None:
# NaN
self._int = str(int(diag or '0')).lstrip('0')
if m.group('signal'):
self._exp = 'N'
else:
self._exp = 'n'
else:
# infinity
self._int = '0'
self._exp = 'F'
self._is_special = True
return self
# From an integer
if isinstance(value, int):
if value >= 0:
self._sign = 0
else:
self._sign = 1
self._exp = 0
self._int = str(abs(value))
self._is_special = False
return self
# From another decimal
if isinstance(value, Decimal):
self._exp = value._exp
self._sign = value._sign
self._int = value._int
self._is_special = value._is_special
return self
# From an internal working value
if isinstance(value, _WorkRep):
self._sign = value.sign
self._int = str(value.int)
self._exp = int(value.exp)
self._is_special = False
return self
# tuple/list conversion (possibly from as_tuple())
if isinstance(value, (list,tuple)):
if len(value) != 3:
raise ValueError('Invalid tuple size in creation of Decimal '
'from list or tuple. The list or tuple '
'should have exactly three elements.')
# process sign. The isinstance test rejects floats
if not (isinstance(value[0], int) and value[0] in (0,1)):
raise ValueError("Invalid sign. The first value in the tuple "
"should be an integer; either 0 for a "
"positive number or 1 for a negative number.")
self._sign = value[0]
if value[2] == 'F':
# infinity: value[1] is ignored
self._int = '0'
self._exp = value[2]
self._is_special = True
else:
# process and validate the digits in value[1]
digits = []
for digit in value[1]:
if isinstance(digit, int) and 0 <= digit <= 9:
# skip leading zeros
if digits or digit != 0:
digits.append(digit)
else:
raise ValueError("The second value in the tuple must "
"be composed of integers in the range "
"0 through 9.")
if value[2] in ('n', 'N'):
# NaN: digits form the diagnostic
self._int = ''.join(map(str, digits))
self._exp = value[2]
self._is_special = True
elif isinstance(value[2], int):
# finite number: digits give the coefficient
self._int = ''.join(map(str, digits or [0]))
self._exp = value[2]
self._is_special = False
else:
raise ValueError("The third value in the tuple must "
"be an integer, or one of the "
"strings 'F', 'n', 'N'.")
return self
if isinstance(value, float):
if context is None:
context = getcontext()
context._raise_error(FloatOperation,
"strict semantics for mixing floats and Decimals are "
"enabled")
value = Decimal.from_float(value)
self._exp = value._exp
self._sign = value._sign
self._int = value._int
self._is_special = value._is_special
return self
raise TypeError("Cannot convert %r to Decimal" % value)
@classmethod
def from_float(cls, f):
"""Converts a float to a decimal number, exactly.
Note that Decimal.from_float(0.1) is not the same as Decimal('0.1').
Since 0.1 is not exactly representable in binary floating point, the
value is stored as the nearest representable value which is
0x1.999999999999ap-4. The exact equivalent of the value in decimal
is 0.1000000000000000055511151231257827021181583404541015625.
>>> Decimal.from_float(0.1)
Decimal('0.1000000000000000055511151231257827021181583404541015625')
>>> Decimal.from_float(float('nan'))
Decimal('NaN')
>>> Decimal.from_float(float('inf'))
Decimal('Infinity')
>>> Decimal.from_float(-float('inf'))
Decimal('-Infinity')
>>> Decimal.from_float(-0.0)
Decimal('-0')
"""
if isinstance(f, int): # handle integer inputs
sign = 0 if f >= 0 else 1
k = 0
coeff = str(abs(f))
elif isinstance(f, float):
if _math.isinf(f) or _math.isnan(f):
return cls(repr(f))
if _math.copysign(1.0, f) == 1.0:
sign = 0
else:
sign = 1
n, d = abs(f).as_integer_ratio()
k = d.bit_length() - 1
coeff = str(n*5**k)
else:
raise TypeError("argument must be int or float.")
result = _dec_from_triple(sign, coeff, -k)
if cls is Decimal:
return result
else:
return cls(result)
def _isnan(self):
"""Returns whether the number is not actually one.
0 if a number
1 if NaN
2 if sNaN
"""
if self._is_special:
exp = self._exp
if exp == 'n':
return 1
elif exp == 'N':
return 2
return 0
def _isinfinity(self):
"""Returns whether the number is infinite
0 if finite or not a number
1 if +INF
-1 if -INF
"""
if self._exp == 'F':
if self._sign:
return -1
return 1
return 0
def _check_nans(self, other=None, context=None):
"""Returns whether the number is not actually one.
if self, other are sNaN, signal
if self, other are NaN return nan
return 0
Done before operations.
"""
self_is_nan = self._isnan()
if other is None:
other_is_nan = False
else:
other_is_nan = other._isnan()
if self_is_nan or other_is_nan:
if context is None:
context = getcontext()
if self_is_nan == 2:
return context._raise_error(InvalidOperation, 'sNaN',
self)
if other_is_nan == 2:
return context._raise_error(InvalidOperation, 'sNaN',
other)
if self_is_nan:
return self._fix_nan(context)
return other._fix_nan(context)
return 0
def _compare_check_nans(self, other, context):
"""Version of _check_nans used for the signaling comparisons
compare_signal, __le__, __lt__, __ge__, __gt__.
Signal InvalidOperation if either self or other is a (quiet
or signaling) NaN. Signaling NaNs take precedence over quiet
NaNs.
Return 0 if neither operand is a NaN.
"""
if context is None:
context = getcontext()
if self._is_special or other._is_special:
if self.is_snan():
return context._raise_error(InvalidOperation,
'comparison involving sNaN',
self)
elif other.is_snan():
return context._raise_error(InvalidOperation,
'comparison involving sNaN',
other)
elif self.is_qnan():
return context._raise_error(InvalidOperation,
'comparison involving NaN',
self)
elif other.is_qnan():
return context._raise_error(InvalidOperation,
'comparison involving NaN',
other)
return 0
def __bool__(self):
"""Return True if self is nonzero; otherwise return False.
NaNs and infinities are considered nonzero.
"""
return self._is_special or self._int != '0'
def _cmp(self, other):
"""Compare the two non-NaN decimal instances self and other.
Returns -1 if self < other, 0 if self == other and 1
if self > other. This routine is for internal use only."""
if self._is_special or other._is_special:
self_inf = self._isinfinity()
other_inf = other._isinfinity()
if self_inf == other_inf:
return 0
elif self_inf < other_inf:
return -1
else:
return 1
# check for zeros; Decimal('0') == Decimal('-0')
if not self:
if not other:
return 0
else:
return -((-1)**other._sign)
if not other:
return (-1)**self._sign
# If different signs, neg one is less
if other._sign < self._sign:
return -1
if self._sign < other._sign:
return 1
self_adjusted = self.adjusted()
other_adjusted = other.adjusted()
if self_adjusted == other_adjusted:
self_padded = self._int + '0'*(self._exp - other._exp)
other_padded = other._int + '0'*(other._exp - self._exp)
if self_padded == other_padded:
return 0
elif self_padded < other_padded:
return -(-1)**self._sign
else:
return (-1)**self._sign
elif self_adjusted > other_adjusted:
return (-1)**self._sign
else: # self_adjusted < other_adjusted
return -((-1)**self._sign)
# Note: The Decimal standard doesn't cover rich comparisons for
# Decimals. In particular, the specification is silent on the
# subject of what should happen for a comparison involving a NaN.
# We take the following approach:
#
# == comparisons involving a quiet NaN always return False
# != comparisons involving a quiet NaN always return True
# == or != comparisons involving a signaling NaN signal
# InvalidOperation, and return False or True as above if the
# InvalidOperation is not trapped.
# <, >, <= and >= comparisons involving a (quiet or signaling)
# NaN signal InvalidOperation, and return False if the
# InvalidOperation is not trapped.
#
# This behavior is designed to conform as closely as possible to
# that specified by IEEE 754.
def __eq__(self, other, context=None):
self, other = _convert_for_comparison(self, other, equality_op=True)
if other is NotImplemented:
return other
if self._check_nans(other, context):
return False
return self._cmp(other) == 0
def __lt__(self, other, context=None):
self, other = _convert_for_comparison(self, other)
if other is NotImplemented:
return other
ans = self._compare_check_nans(other, context)
if ans:
return False
return self._cmp(other) < 0
def __le__(self, other, context=None):
self, other = _convert_for_comparison(self, other)
if other is NotImplemented:
return other
ans = self._compare_check_nans(other, context)
if ans:
return False
return self._cmp(other) <= 0
def __gt__(self, other, context=None):
self, other = _convert_for_comparison(self, other)
if other is NotImplemented:
return other
ans = self._compare_check_nans(other, context)
if ans:
return False
return self._cmp(other) > 0
def __ge__(self, other, context=None):
self, other = _convert_for_comparison(self, other)
if other is NotImplemented:
return other
ans = self._compare_check_nans(other, context)
if ans:
return False
return self._cmp(other) >= 0
def compare(self, other, context=None):
"""Compare self to other. Return a decimal value:
a or b is a NaN ==> Decimal('NaN')
a < b ==> Decimal('-1')
a == b ==> Decimal('0')
a > b ==> Decimal('1')
"""
other = _convert_other(other, raiseit=True)
# Compare(NaN, NaN) = NaN
if (self._is_special or other and other._is_special):
ans = self._check_nans(other, context)
if ans:
return ans
return Decimal(self._cmp(other))
def __hash__(self):
"""x.__hash__() <==> hash(x)"""
# In order to make sure that the hash of a Decimal instance
# agrees with the hash of a numerically equal integer, float
# or Fraction, we follow the rules for numeric hashes outlined
# in the documentation. (See library docs, 'Built-in Types').
if self._is_special:
if self.is_snan():
raise TypeError('Cannot hash a signaling NaN value.')
elif self.is_nan():
return object.__hash__(self)
else:
if self._sign:
return -_PyHASH_INF
else:
return _PyHASH_INF
if self._exp >= 0:
exp_hash = pow(10, self._exp, _PyHASH_MODULUS)
else:
exp_hash = pow(_PyHASH_10INV, -self._exp, _PyHASH_MODULUS)
hash_ = int(self._int) * exp_hash % _PyHASH_MODULUS
ans = hash_ if self >= 0 else -hash_
return -2 if ans == -1 else ans
def as_tuple(self):
"""Represents the number as a triple tuple.
To show the internals exactly as they are.
"""
return DecimalTuple(self._sign, tuple(map(int, self._int)), self._exp)
def as_integer_ratio(self):
"""Express a finite Decimal instance in the form n / d.
Returns a pair (n, d) of integers. When called on an infinity
or NaN, raises OverflowError or ValueError respectively.
>>> Decimal('3.14').as_integer_ratio()
(157, 50)
>>> Decimal('-123e5').as_integer_ratio()
(-12300000, 1)
>>> Decimal('0.00').as_integer_ratio()
(0, 1)
"""
if self._is_special: