# 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.

"""Python decimal arithmetic module"""

__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', 'IEEEContext',

# Limits for the C version for compatibility

'MAX_PREC', 'MAX_EMAX', 'MIN_EMIN', 'MIN_ETINY', 'IEEE_CONTEXT_MAX_BITS',

# 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

IEEE_CONTEXT_MAX_BITS = 512

else:

MAX_PREC = 425000000

MAX_EMAX = 425000000

MIN_EMIN = -425000000

IEEE_CONTEXT_MAX_BITS = 256

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 this 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 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

def IEEEContext(bits, /):

"""

Return a context object initialized to the proper values for one of the

IEEE interchange formats. The argument must be a multiple of 32 and less

than IEEE_CONTEXT_MAX_BITS.

"""

if bits <= 0 or bits > IEEE_CONTEXT_MAX_BITS or bits % 32:

raise ValueError("argument must be a multiple of 32, "

f"with a maximum of {IEEE_CONTEXT_MAX_BITS}")

ctx = Context()

ctx.prec = 9 * (bits//32) - 2

ctx.Emax = 3 * (1 << (bits//16 + 3))

ctx.Emin = 1 - ctx.Emax

ctx.rounding = ROUND_HALF_EVEN

ctx.clamp = 1

ctx.traps = dict.fromkeys(_signals, False)

return ctx

##### 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_number(cls, number):

"""Converts a real number to a decimal number, exactly.

>>> Decimal.from_number(314) # int

Decimal('314')

>>> Decimal.from_number(0.1) # float

Decimal('0.1000000000000000055511151231257827021181583404541015625')

>>> Decimal.from_number(Decimal('3.14')) # another decimal instance

Decimal('3.14')

"""

if isinstance(number, (int, Decimal, float)):

return cls(number)

raise TypeError("Cannot convert %r to Decimal" % number)

@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:

if self.is_nan():

raise ValueError("cannot convert NaN to integer ratio")

else:

raise OverflowError("cannot convert Infinity to integer ratio")

if not self:

return 0, 1

# Find n, d in lowest terms such that abs(self) == n / d;

# we'll deal with the sign later.

n = int(self._int)

if self._exp >= 0:

# self is an integer.

n, d = n * 10**self._exp, 1

else:

# Find d2, d5 such that abs(self) = n / (2**d2 * 5**d5).

d5 = -self._exp

while d5 > 0 and n % 5 == 0:

n //= 5

d5 -= 1

# (n & -n).bit_length() - 1 counts trailing zeros in binary

# representation of n (provided n is nonzero).

d2 = -self._exp

shift2 = min((n & -n).bit_length() - 1, d2)

if shift2:

n >>= shift2

d2 -= shift2

d = 5**d5 << d2

if self._sign:

n = -n

return n, d

def __repr__(self):

"""Represents the number as an instance of Decimal."""

# Invariant: eval(repr(d)) == d

return "Decimal('%s')" % str(self)

def __str__(self, eng=False, context=None):

"""Return string representation of the number in scientific notation.

Captures all of the information in the underlying representation.

"""

sign = ['', '-'][self._sign]

if self._is_special:

if self._exp == 'F':

return sign + 'Infinity'

elif self._exp == 'n':

return sign + 'NaN' + self._int

else: # self._exp == 'N'

return sign + 'sNaN' + self._int

# number of digits of self._int to left of decimal point

leftdigits = self._exp + len(self._int)

# dotplace is number of digits of self._int to the left of the