[Python-checkins] cpython: Issue #19232: Speed up decimal import. Additionally, since _decimal is
stefan.krah
python-checkins at python.org
Wed Sep 10 18:01:22 CEST 2014
http://hg.python.org/cpython/rev/8bf51cf94405
changeset: 92382:8bf51cf94405
user: Stefan Krah <skrah at bytereef.org>
date: Wed Sep 10 17:58:15 2014 +0200
summary:
Issue #19232: Speed up decimal import. Additionally, since _decimal is
self-contained, this change facilitates maintenance and the Python version
can be easily imported for experimentation.
files:
Lib/decimal.py | 17 +-
Lib/decimal.py | 6406 +---------------
Lib/test/test_decimal.py | 4 +-
Modules/_decimal/tests/deccheck.py | 7 +-
4 files changed, 14 insertions(+), 6420 deletions(-)
diff --git a/Lib/decimal.py b/Lib/_pydecimal.py
copy from Lib/decimal.py
copy to Lib/_pydecimal.py
--- a/Lib/decimal.py
+++ b/Lib/_pydecimal.py
@@ -144,6 +144,7 @@
'HAVE_THREADS'
]
+__name__ = 'decimal' # For pickling
__version__ = '1.70' # Highest version of the spec this complies with
# See http://speleotrove.com/decimal/
__libmpdec_version__ = "2.4.1" # compatible libmpdec version
@@ -6386,19 +6387,3 @@
# _PyHASH_10INV is the inverse of 10 modulo the prime _PyHASH_MODULUS
_PyHASH_10INV = pow(10, _PyHASH_MODULUS - 2, _PyHASH_MODULUS)
del sys
-
-try:
- import _decimal
-except ImportError:
- pass
-else:
- s1 = set(dir())
- s2 = set(dir(_decimal))
- for name in s1 - s2:
- del globals()[name]
- del s1, s2, name
- from _decimal import *
-
-if __name__ == '__main__':
- import doctest, decimal
- doctest.testmod(decimal)
diff --git a/Lib/decimal.py b/Lib/decimal.py
--- a/Lib/decimal.py
+++ b/Lib/decimal.py
@@ -1,6404 +1,14 @@
-# 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
- 'HAVE_THREADS'
-]
-
-__version__ = '1.70' # Highest version of the spec this complies with
- # See http://speleotrove.com/decimal/
-__libmpdec_version__ = "2.4.1" # 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')
+ from _decimal import *
+ from _decimal import __doc__
+ from _decimal import __version__
+ from _decimal import __libmpdec_version__
except ImportError:
- DecimalTuple = lambda *args: args
+ from _pydecimal import *
+ from _pydecimal import __doc__
+ from _pydecimal import __version__
+ from _pydecimal import __libmpdec_version__
-# 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
-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 an 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. Py2.4 offers direct support for thread locals. If that
-# is not available, use threading.current_thread() 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.
-
-try:
- import threading
-except ImportError:
- # Python was compiled without threads; create a mock object instead
- class MockThreading(object):
- def local(self, sys=sys):
- return sys.modules[__name__]
- threading = MockThreading()
- del MockThreading
-
-try:
- threading.local
-
-except AttributeError:
-
- # To fix reloading, force it to create a new context
- # Old contexts have different exceptions in their dicts, making problems.
- if hasattr(threading.current_thread(), '__decimal_context__'):
- del threading.current_thread().__decimal_context__
-
- def setcontext(context):
- """Set this thread's context to context."""
- if context in (DefaultContext, BasicContext, ExtendedContext):
- context = context.copy()
- context.clear_flags()
- threading.current_thread().__decimal_context__ = context
-
- 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 threading.current_thread().__decimal_context__
- except AttributeError:
- context = Context()
- threading.current_thread().__decimal_context__ = context
- return context
-
-else:
-
- 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.
- """
- try:
- return _local.__decimal_context__
- except AttributeError:
- context = Context()
- _local.__decimal_context__ = context
- return context
-
- def setcontext(context, _local=local):
- """Set this thread's context to context."""
- if context in (DefaultContext, BasicContext, ExtendedContext):
- context = context.copy()
- context.clear_flags()
- _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
- 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()
- return _ContextManager(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())
- 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
- return cls(f)
- if not isinstance(f, float):
- raise TypeError("argument must be int or 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
- result = _dec_from_triple(sign, str(n*5**k), -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 __ne__(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 True
- 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):
- """Compares one to another.
-
- -1 => a < b
- 0 => a = b
- 1 => a > b
- NaN => one is NaN
- Like __cmp__, but returns Decimal instances.
- """
- 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 _PyHASH_NAN
- 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 __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
- # decimal point in the mantissa of the output string (that is,
- # after adjusting the exponent)
- if self._exp <= 0 and leftdigits > -6:
- # no exponent required
- dotplace = leftdigits
- elif not eng:
- # usual scientific notation: 1 digit on left of the point
- dotplace = 1
- elif self._int == '0':
- # engineering notation, zero
- dotplace = (leftdigits + 1) % 3 - 1
- else:
- # engineering notation, nonzero
- dotplace = (leftdigits - 1) % 3 + 1
-
- if dotplace <= 0:
- intpart = '0'
- fracpart = '.' + '0'*(-dotplace) + self._int
- elif dotplace >= len(self._int):
- intpart = self._int+'0'*(dotplace-len(self._int))
- fracpart = ''
- else:
- intpart = self._int[:dotplace]
- fracpart = '.' + self._int[dotplace:]
- if leftdigits == dotplace:
- exp = ''
- else:
- if context is None:
- context = getcontext()
- exp = ['e', 'E'][context.capitals] + "%+d" % (leftdigits-dotplace)
-
- return sign + intpart + fracpart + exp
-
- def to_eng_string(self, context=None):
- """Convert to engineering-type string.
-
- Engineering notation has an exponent which is a multiple of 3, so there
- are up to 3 digits left of the decimal place.
-
- Same rules for when in exponential and when as a value as in __str__.
- """
- return self.__str__(eng=True, context=context)
-
- def __neg__(self, context=None):
- """Returns a copy with the sign switched.
-
- Rounds, if it has reason.
- """
- if self._is_special:
- ans = self._check_nans(context=context)
- if ans:
- return ans
-
- if context is None:
- context = getcontext()
-
- if not self and context.rounding != ROUND_FLOOR:
- # -Decimal('0') is Decimal('0'), not Decimal('-0'), except
- # in ROUND_FLOOR rounding mode.
- ans = self.copy_abs()
- else:
- ans = self.copy_negate()
-
- return ans._fix(context)
-
- def __pos__(self, context=None):
- """Returns a copy, unless it is a sNaN.
-
- Rounds the number (if more then precision digits)
- """
- if self._is_special:
- ans = self._check_nans(context=context)
- if ans:
- return ans
-
- if context is None:
- context = getcontext()
-
- if not self and context.rounding != ROUND_FLOOR:
- # + (-0) = 0, except in ROUND_FLOOR rounding mode.
- ans = self.copy_abs()
- else:
- ans = Decimal(self)
-
- return ans._fix(context)
-
- def __abs__(self, round=True, context=None):
- """Returns the absolute value of self.
-
- If the keyword argument 'round' is false, do not round. The
- expression self.__abs__(round=False) is equivalent to
- self.copy_abs().
- """
- if not round:
- return self.copy_abs()
-
- if self._is_special:
- ans = self._check_nans(context=context)
- if ans:
- return ans
-
- if self._sign:
- ans = self.__neg__(context=context)
- else:
- ans = self.__pos__(context=context)
-
- return ans
-
- def __add__(self, other, context=None):
- """Returns self + other.
-
- -INF + INF (or the reverse) cause InvalidOperation errors.
- """
- other = _convert_other(other)
- if other is NotImplemented:
- return other
-
- if context is None:
- context = getcontext()
-
- if self._is_special or other._is_special:
- ans = self._check_nans(other, context)
- if ans:
- return ans
-
- if self._isinfinity():
- # If both INF, same sign => same as both, opposite => error.
- if self._sign != other._sign and other._isinfinity():
- return context._raise_error(InvalidOperation, '-INF + INF')
- return Decimal(self)
- if other._isinfinity():
- return Decimal(other) # Can't both be infinity here
-
- exp = min(self._exp, other._exp)
- negativezero = 0
- if context.rounding == ROUND_FLOOR and self._sign != other._sign:
- # If the answer is 0, the sign should be negative, in this case.
- negativezero = 1
-
- if not self and not other:
- sign = min(self._sign, other._sign)
- if negativezero:
- sign = 1
- ans = _dec_from_triple(sign, '0', exp)
- ans = ans._fix(context)
- return ans
- if not self:
- exp = max(exp, other._exp - context.prec-1)
- ans = other._rescale(exp, context.rounding)
- ans = ans._fix(context)
- return ans
- if not other:
- exp = max(exp, self._exp - context.prec-1)
- ans = self._rescale(exp, context.rounding)
- ans = ans._fix(context)
- return ans
-
- op1 = _WorkRep(self)
- op2 = _WorkRep(other)
- op1, op2 = _normalize(op1, op2, context.prec)
-
- result = _WorkRep()
- if op1.sign != op2.sign:
- # Equal and opposite
- if op1.int == op2.int:
- ans = _dec_from_triple(negativezero, '0', exp)
- ans = ans._fix(context)
- return ans
- if op1.int < op2.int:
- op1, op2 = op2, op1
- # OK, now abs(op1) > abs(op2)
- if op1.sign == 1:
- result.sign = 1
- op1.sign, op2.sign = op2.sign, op1.sign
- else:
- result.sign = 0
- # So we know the sign, and op1 > 0.
- elif op1.sign == 1:
- result.sign = 1
- op1.sign, op2.sign = (0, 0)
- else:
- result.sign = 0
- # Now, op1 > abs(op2) > 0
-
- if op2.sign == 0:
- result.int = op1.int + op2.int
- else:
- result.int = op1.int - op2.int
-
- result.exp = op1.exp
- ans = Decimal(result)
- ans = ans._fix(context)
- return ans
-
- __radd__ = __add__
-
- def __sub__(self, other, context=None):
- """Return self - other"""
- other = _convert_other(other)
- if other is NotImplemented:
- return other
-
- if self._is_special or other._is_special:
- ans = self._check_nans(other, context=context)
- if ans:
- return ans
-
- # self - other is computed as self + other.copy_negate()
- return self.__add__(other.copy_negate(), context=context)
-
- def __rsub__(self, other, context=None):
- """Return other - self"""
- other = _convert_other(other)
- if other is NotImplemented:
- return other
-
- return other.__sub__(self, context=context)
-
- def __mul__(self, other, context=None):
- """Return self * other.
-
- (+-) INF * 0 (or its reverse) raise InvalidOperation.
- """
- other = _convert_other(other)
- if other is NotImplemented:
- return other
-
- if context is None:
- context = getcontext()
-
- resultsign = self._sign ^ other._sign
-
- if self._is_special or other._is_special:
- ans = self._check_nans(other, context)
- if ans:
- return ans
-
- if self._isinfinity():
- if not other:
- return context._raise_error(InvalidOperation, '(+-)INF * 0')
- return _SignedInfinity[resultsign]
-
- if other._isinfinity():
- if not self:
- return context._raise_error(InvalidOperation, '0 * (+-)INF')
- return _SignedInfinity[resultsign]
-
- resultexp = self._exp + other._exp
-
- # Special case for multiplying by zero
- if not self or not other:
- ans = _dec_from_triple(resultsign, '0', resultexp)
- # Fixing in case the exponent is out of bounds
- ans = ans._fix(context)
- return ans
-
- # Special case for multiplying by power of 10
- if self._int == '1':
- ans = _dec_from_triple(resultsign, other._int, resultexp)
- ans = ans._fix(context)
- return ans
- if other._int == '1':
- ans = _dec_from_triple(resultsign, self._int, resultexp)
- ans = ans._fix(context)
- return ans
-
- op1 = _WorkRep(self)
- op2 = _WorkRep(other)
-
- ans = _dec_from_triple(resultsign, str(op1.int * op2.int), resultexp)
- ans = ans._fix(context)
-
- return ans
- __rmul__ = __mul__
-
- def __truediv__(self, other, context=None):
- """Return self / other."""
- other = _convert_other(other)
- if other is NotImplemented:
- return NotImplemented
-
- if context is None:
- context = getcontext()
-
- sign = self._sign ^ other._sign
-
- if self._is_special or other._is_special:
- ans = self._check_nans(other, context)
- if ans:
- return ans
-
- if self._isinfinity() and other._isinfinity():
- return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF')
-
- if self._isinfinity():
- return _SignedInfinity[sign]
-
- if other._isinfinity():
- context._raise_error(Clamped, 'Division by infinity')
- return _dec_from_triple(sign, '0', context.Etiny())
-
- # Special cases for zeroes
- if not other:
- if not self:
- return context._raise_error(DivisionUndefined, '0 / 0')
- return context._raise_error(DivisionByZero, 'x / 0', sign)
-
- if not self:
- exp = self._exp - other._exp
- coeff = 0
- else:
- # OK, so neither = 0, INF or NaN
- shift = len(other._int) - len(self._int) + context.prec + 1
- exp = self._exp - other._exp - shift
- op1 = _WorkRep(self)
- op2 = _WorkRep(other)
- if shift >= 0:
- coeff, remainder = divmod(op1.int * 10**shift, op2.int)
- else:
- coeff, remainder = divmod(op1.int, op2.int * 10**-shift)
- if remainder:
- # result is not exact; adjust to ensure correct rounding
- if coeff % 5 == 0:
- coeff += 1
- else:
- # result is exact; get as close to ideal exponent as possible
- ideal_exp = self._exp - other._exp
- while exp < ideal_exp and coeff % 10 == 0:
- coeff //= 10
- exp += 1
-
- ans = _dec_from_triple(sign, str(coeff), exp)
- return ans._fix(context)
-
- def _divide(self, other, context):
- """Return (self // other, self % other), to context.prec precision.
-
- Assumes that neither self nor other is a NaN, that self is not
- infinite and that other is nonzero.
- """
- sign = self._sign ^ other._sign
- if other._isinfinity():
- ideal_exp = self._exp
- else:
- ideal_exp = min(self._exp, other._exp)
-
- expdiff = self.adjusted() - other.adjusted()
- if not self or other._isinfinity() or expdiff <= -2:
- return (_dec_from_triple(sign, '0', 0),
- self._rescale(ideal_exp, context.rounding))
- if expdiff <= context.prec:
- op1 = _WorkRep(self)
- op2 = _WorkRep(other)
- if op1.exp >= op2.exp:
- op1.int *= 10**(op1.exp - op2.exp)
- else:
- op2.int *= 10**(op2.exp - op1.exp)
- q, r = divmod(op1.int, op2.int)
- if q < 10**context.prec:
- return (_dec_from_triple(sign, str(q), 0),
- _dec_from_triple(self._sign, str(r), ideal_exp))
-
- # Here the quotient is too large to be representable
- ans = context._raise_error(DivisionImpossible,
- 'quotient too large in //, % or divmod')
- return ans, ans
-
- def __rtruediv__(self, other, context=None):
- """Swaps self/other and returns __truediv__."""
- other = _convert_other(other)
- if other is NotImplemented:
- return other
- return other.__truediv__(self, context=context)
-
- def __divmod__(self, other, context=None):
- """
- Return (self // other, self % other)
- """
- other = _convert_other(other)
- if other is NotImplemented:
- return other
-
- if context is None:
- context = getcontext()
-
- ans = self._check_nans(other, context)
- if ans:
- return (ans, ans)
-
- sign = self._sign ^ other._sign
- if self._isinfinity():
- if other._isinfinity():
- ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)')
- return ans, ans
- else:
- return (_SignedInfinity[sign],
- context._raise_error(InvalidOperation, 'INF % x'))
-
- if not other:
- if not self:
- ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)')
- return ans, ans
- else:
- return (context._raise_error(DivisionByZero, 'x // 0', sign),
- context._raise_error(InvalidOperation, 'x % 0'))
-
- quotient, remainder = self._divide(other, context)
- remainder = remainder._fix(context)
- return quotient, remainder
-
- def __rdivmod__(self, other, context=None):
- """Swaps self/other and returns __divmod__."""
- other = _convert_other(other)
- if other is NotImplemented:
- return other
- return other.__divmod__(self, context=context)
-
- def __mod__(self, other, context=None):
- """
- self % other
- """
- other = _convert_other(other)
- if other is NotImplemented:
- return other
-
- if context is None:
- context = getcontext()
-
- ans = self._check_nans(other, context)
- if ans:
- return ans
-
- if self._isinfinity():
- return context._raise_error(InvalidOperation, 'INF % x')
- elif not other:
- if self:
- return context._raise_error(InvalidOperation, 'x % 0')
- else:
- return context._raise_error(DivisionUndefined, '0 % 0')
-
- remainder = self._divide(other, context)[1]
- remainder = remainder._fix(context)
- return remainder
-
- def __rmod__(self, other, context=None):
- """Swaps self/other and returns __mod__."""
- other = _convert_other(other)
- if other is NotImplemented:
- return other
- return other.__mod__(self, context=context)
-
- def remainder_near(self, other, context=None):
- """
- Remainder nearest to 0- abs(remainder-near) <= other/2
- """
- if context is None:
- context = getcontext()
-
- other = _convert_other(other, raiseit=True)
-
- ans = self._check_nans(other, context)
- if ans:
- return ans
-
- # self == +/-infinity -> InvalidOperation
- if self._isinfinity():
- return context._raise_error(InvalidOperation,
- 'remainder_near(infinity, x)')
-
- # other == 0 -> either InvalidOperation or DivisionUndefined
- if not other:
- if self:
- return context._raise_error(InvalidOperation,
- 'remainder_near(x, 0)')
- else:
- return context._raise_error(DivisionUndefined,
- 'remainder_near(0, 0)')
-
- # other = +/-infinity -> remainder = self
- if other._isinfinity():
- ans = Decimal(self)
- return ans._fix(context)
-
- # self = 0 -> remainder = self, with ideal exponent
- ideal_exponent = min(self._exp, other._exp)
- if not self:
- ans = _dec_from_triple(self._sign, '0', ideal_exponent)
- return ans._fix(context)
-
- # catch most cases of large or small quotient
- expdiff = self.adjusted() - other.adjusted()
- if expdiff >= context.prec + 1:
- # expdiff >= prec+1 => abs(self/other) > 10**prec
- return context._raise_error(DivisionImpossible)
- if expdiff <= -2:
- # expdiff <= -2 => abs(self/other) < 0.1
- ans = self._rescale(ideal_exponent, context.rounding)
- return ans._fix(context)
-
- # adjust both arguments to have the same exponent, then divide
- op1 = _WorkRep(self)
- op2 = _WorkRep(other)
- if op1.exp >= op2.exp:
- op1.int *= 10**(op1.exp - op2.exp)
- else:
- op2.int *= 10**(op2.exp - op1.exp)
- q, r = divmod(op1.int, op2.int)
- # remainder is r*10**ideal_exponent; other is +/-op2.int *
- # 10**ideal_exponent. Apply correction to ensure that
- # abs(remainder) <= abs(other)/2
- if 2*r + (q&1) > op2.int:
- r -= op2.int
- q += 1
-
- if q >= 10**context.prec:
- return context._raise_error(DivisionImpossible)
-
- # result has same sign as self unless r is negative
- sign = self._sign
- if r < 0:
- sign = 1-sign
- r = -r
-
- ans = _dec_from_triple(sign, str(r), ideal_exponent)
- return ans._fix(context)
-
- def __floordiv__(self, other, context=None):
- """self // other"""
- other = _convert_other(other)
- if other is NotImplemented:
- return other
-
- if context is None:
- context = getcontext()
-
- ans = self._check_nans(other, context)
- if ans:
- return ans
-
- if self._isinfinity():
- if other._isinfinity():
- return context._raise_error(InvalidOperation, 'INF // INF')
- else:
- return _SignedInfinity[self._sign ^ other._sign]
-
- if not other:
- if self:
- return context._raise_error(DivisionByZero, 'x // 0',
- self._sign ^ other._sign)
- else:
- return context._raise_error(DivisionUndefined, '0 // 0')
-
- return self._divide(other, context)[0]
-
- def __rfloordiv__(self, other, context=None):
- """Swaps self/other and returns __floordiv__."""
- other = _convert_other(other)
- if other is NotImplemented:
- return other
- return other.__floordiv__(self, context=context)
-
- def __float__(self):
- """Float representation."""
- if self._isnan():
- if self.is_snan():
- raise ValueError("Cannot convert signaling NaN to float")
- s = "-nan" if self._sign else "nan"
- else:
- s = str(self)
- return float(s)
-
- def __int__(self):
- """Converts self to an int, truncating if necessary."""
- if self._is_special:
- if self._isnan():
- raise ValueError("Cannot convert NaN to integer")
- elif self._isinfinity():
- raise OverflowError("Cannot convert infinity to integer")
- s = (-1)**self._sign
- if self._exp >= 0:
- return s*int(self._int)*10**self._exp
- else:
- return s*int(self._int[:self._exp] or '0')
-
- __trunc__ = __int__
-
- def real(self):
- return self
- real = property(real)
-
- def imag(self):
- return Decimal(0)
- imag = property(imag)
-
- def conjugate(self):
- return self
-
- def __complex__(self):
- return complex(float(self))
-
- def _fix_nan(self, context):
- """Decapitate the payload of a NaN to fit the context"""
- payload = self._int
-
- # maximum length of payload is precision if clamp=0,
- # precision-1 if clamp=1.
- max_payload_len = context.prec - context.clamp
- if len(payload) > max_payload_len:
- payload = payload[len(payload)-max_payload_len:].lstrip('0')
- return _dec_from_triple(self._sign, payload, self._exp, True)
- return Decimal(self)
-
- def _fix(self, context):
- """Round if it is necessary to keep self within prec precision.
-
- Rounds and fixes the exponent. Does not raise on a sNaN.
-
- Arguments:
- self - Decimal instance
- context - context used.
- """
-
- if self._is_special:
- if self._isnan():
- # decapitate payload if necessary
- return self._fix_nan(context)
- else:
- # self is +/-Infinity; return unaltered
- return Decimal(self)
-
- # if self is zero then exponent should be between Etiny and
- # Emax if clamp==0, and between Etiny and Etop if clamp==1.
- Etiny = context.Etiny()
- Etop = context.Etop()
- if not self:
- exp_max = [context.Emax, Etop][context.clamp]
- new_exp = min(max(self._exp, Etiny), exp_max)
- if new_exp != self._exp:
- context._raise_error(Clamped)
- return _dec_from_triple(self._sign, '0', new_exp)
- else:
- return Decimal(self)
-
- # exp_min is the smallest allowable exponent of the result,
- # equal to max(self.adjusted()-context.prec+1, Etiny)
- exp_min = len(self._int) + self._exp - context.prec
- if exp_min > Etop:
- # overflow: exp_min > Etop iff self.adjusted() > Emax
- ans = context._raise_error(Overflow, 'above Emax', self._sign)
- context._raise_error(Inexact)
- context._raise_error(Rounded)
- return ans
-
- self_is_subnormal = exp_min < Etiny
- if self_is_subnormal:
- exp_min = Etiny
-
- # round if self has too many digits
- if self._exp < exp_min:
- digits = len(self._int) + self._exp - exp_min
- if digits < 0:
- self = _dec_from_triple(self._sign, '1', exp_min-1)
- digits = 0
- rounding_method = self._pick_rounding_function[context.rounding]
- changed = rounding_method(self, digits)
- coeff = self._int[:digits] or '0'
- if changed > 0:
- coeff = str(int(coeff)+1)
- if len(coeff) > context.prec:
- coeff = coeff[:-1]
- exp_min += 1
-
- # check whether the rounding pushed the exponent out of range
- if exp_min > Etop:
- ans = context._raise_error(Overflow, 'above Emax', self._sign)
- else:
- ans = _dec_from_triple(self._sign, coeff, exp_min)
-
- # raise the appropriate signals, taking care to respect
- # the precedence described in the specification
- if changed and self_is_subnormal:
- context._raise_error(Underflow)
- if self_is_subnormal:
- context._raise_error(Subnormal)
- if changed:
- context._raise_error(Inexact)
- context._raise_error(Rounded)
- if not ans:
- # raise Clamped on underflow to 0
- context._raise_error(Clamped)
- return ans
-
- if self_is_subnormal:
- context._raise_error(Subnormal)
-
- # fold down if clamp == 1 and self has too few digits
- if context.clamp == 1 and self._exp > Etop:
- context._raise_error(Clamped)
- self_padded = self._int + '0'*(self._exp - Etop)
- return _dec_from_triple(self._sign, self_padded, Etop)
-
- # here self was representable to begin with; return unchanged
- return Decimal(self)
-
- # for each of the rounding functions below:
- # self is a finite, nonzero Decimal
- # prec is an integer satisfying 0 <= prec < len(self._int)
- #
- # each function returns either -1, 0, or 1, as follows:
- # 1 indicates that self should be rounded up (away from zero)
- # 0 indicates that self should be truncated, and that all the
- # digits to be truncated are zeros (so the value is unchanged)
- # -1 indicates that there are nonzero digits to be truncated
-
- def _round_down(self, prec):
- """Also known as round-towards-0, truncate."""
- if _all_zeros(self._int, prec):
- return 0
- else:
- return -1
-
- def _round_up(self, prec):
- """Rounds away from 0."""
- return -self._round_down(prec)
-
- def _round_half_up(self, prec):
- """Rounds 5 up (away from 0)"""
- if self._int[prec] in '56789':
- return 1
- elif _all_zeros(self._int, prec):
- return 0
- else:
- return -1
-
- def _round_half_down(self, prec):
- """Round 5 down"""
- if _exact_half(self._int, prec):
- return -1
- else:
- return self._round_half_up(prec)
-
- def _round_half_even(self, prec):
- """Round 5 to even, rest to nearest."""
- if _exact_half(self._int, prec) and \
- (prec == 0 or self._int[prec-1] in '02468'):
- return -1
- else:
- return self._round_half_up(prec)
-
- def _round_ceiling(self, prec):
- """Rounds up (not away from 0 if negative.)"""
- if self._sign:
- return self._round_down(prec)
- else:
- return -self._round_down(prec)
-
- def _round_floor(self, prec):
- """Rounds down (not towards 0 if negative)"""
- if not self._sign:
- return self._round_down(prec)
- else:
- return -self._round_down(prec)
-
- def _round_05up(self, prec):
- """Round down unless digit prec-1 is 0 or 5."""
- if prec and self._int[prec-1] not in '05':
- return self._round_down(prec)
- else:
- return -self._round_down(prec)
-
- _pick_rounding_function = dict(
- ROUND_DOWN = _round_down,
- ROUND_UP = _round_up,
- ROUND_HALF_UP = _round_half_up,
- ROUND_HALF_DOWN = _round_half_down,
- ROUND_HALF_EVEN = _round_half_even,
- ROUND_CEILING = _round_ceiling,
- ROUND_FLOOR = _round_floor,
- ROUND_05UP = _round_05up,
- )
-
- def __round__(self, n=None):
- """Round self to the nearest integer, or to a given precision.
-
- If only one argument is supplied, round a finite Decimal
- instance self to the nearest integer. If self is infinite or
- a NaN then a Python exception is raised. If self is finite
- and lies exactly halfway between two integers then it is
- rounded to the integer with even last digit.
-
- >>> round(Decimal('123.456'))
- 123
- >>> round(Decimal('-456.789'))
- -457
- >>> round(Decimal('-3.0'))
- -3
- >>> round(Decimal('2.5'))
- 2
- >>> round(Decimal('3.5'))
- 4
- >>> round(Decimal('Inf'))
- Traceback (most recent call last):
- ...
- OverflowError: cannot round an infinity
- >>> round(Decimal('NaN'))
- Traceback (most recent call last):
- ...
- ValueError: cannot round a NaN
-
- If a second argument n is supplied, self is rounded to n
- decimal places using the rounding mode for the current
- context.
-
- For an integer n, round(self, -n) is exactly equivalent to
- self.quantize(Decimal('1En')).
-
- >>> round(Decimal('123.456'), 0)
- Decimal('123')
- >>> round(Decimal('123.456'), 2)
- Decimal('123.46')
- >>> round(Decimal('123.456'), -2)
- Decimal('1E+2')
- >>> round(Decimal('-Infinity'), 37)
- Decimal('NaN')
- >>> round(Decimal('sNaN123'), 0)
- Decimal('NaN123')
-
- """
- if n is not None:
- # two-argument form: use the equivalent quantize call
- if not isinstance(n, int):
- raise TypeError('Second argument to round should be integral')
- exp = _dec_from_triple(0, '1', -n)
- return self.quantize(exp)
-
- # one-argument form
- if self._is_special:
- if self.is_nan():
- raise ValueError("cannot round a NaN")
- else:
- raise OverflowError("cannot round an infinity")
- return int(self._rescale(0, ROUND_HALF_EVEN))
-
- def __floor__(self):
- """Return the floor of self, as an integer.
-
- For a finite Decimal instance self, return the greatest
- integer n such that n <= self. If self is infinite or a NaN
- then a Python exception is raised.
-
- """
- if self._is_special:
- if self.is_nan():
- raise ValueError("cannot round a NaN")
- else:
- raise OverflowError("cannot round an infinity")
- return int(self._rescale(0, ROUND_FLOOR))
-
- def __ceil__(self):
- """Return the ceiling of self, as an integer.
-
- For a finite Decimal instance self, return the least integer n
- such that n >= self. If self is infinite or a NaN then a
- Python exception is raised.
-
- """
- if self._is_special:
- if self.is_nan():
- raise ValueError("cannot round a NaN")
- else:
- raise OverflowError("cannot round an infinity")
- return int(self._rescale(0, ROUND_CEILING))
-
- def fma(self, other, third, context=None):
- """Fused multiply-add.
-
- Returns self*other+third with no rounding of the intermediate
- product self*other.
-
- self and other are multiplied together, with no rounding of
- the result. The third operand is then added to the result,
- and a single final rounding is performed.
- """
-
- other = _convert_other(other, raiseit=True)
- third = _convert_other(third, raiseit=True)
-
- # compute product; raise InvalidOperation if either operand is
- # a signaling NaN or if the product is zero times infinity.
- if self._is_special or other._is_special:
- if context is None:
- context = getcontext()
- if self._exp == 'N':
- return context._raise_error(InvalidOperation, 'sNaN', self)
- if other._exp == 'N':
- return context._raise_error(InvalidOperation, 'sNaN', other)
- if self._exp == 'n':
- product = self
- elif other._exp == 'n':
- product = other
- elif self._exp == 'F':
- if not other:
- return context._raise_error(InvalidOperation,
- 'INF * 0 in fma')
- product = _SignedInfinity[self._sign ^ other._sign]
- elif other._exp == 'F':
- if not self:
- return context._raise_error(InvalidOperation,
- '0 * INF in fma')
- product = _SignedInfinity[self._sign ^ other._sign]
- else:
- product = _dec_from_triple(self._sign ^ other._sign,
- str(int(self._int) * int(other._int)),
- self._exp + other._exp)
-
- return product.__add__(third, context)
-
- def _power_modulo(self, other, modulo, context=None):
- """Three argument version of __pow__"""
-
- other = _convert_other(other)
- if other is NotImplemented:
- return other
- modulo = _convert_other(modulo)
- if modulo is NotImplemented:
- return modulo
-
- if context is None:
- context = getcontext()
-
- # deal with NaNs: if there are any sNaNs then first one wins,
- # (i.e. behaviour for NaNs is identical to that of fma)
- self_is_nan = self._isnan()
- other_is_nan = other._isnan()
- modulo_is_nan = modulo._isnan()
- if self_is_nan or other_is_nan or modulo_is_nan:
- 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 modulo_is_nan == 2:
- return context._raise_error(InvalidOperation, 'sNaN',
- modulo)
- if self_is_nan:
- return self._fix_nan(context)
- if other_is_nan:
- return other._fix_nan(context)
- return modulo._fix_nan(context)
-
- # check inputs: we apply same restrictions as Python's pow()
- if not (self._isinteger() and
- other._isinteger() and
- modulo._isinteger()):
- return context._raise_error(InvalidOperation,
- 'pow() 3rd argument not allowed '
- 'unless all arguments are integers')
- if other < 0:
- return context._raise_error(InvalidOperation,
- 'pow() 2nd argument cannot be '
- 'negative when 3rd argument specified')
- if not modulo:
- return context._raise_error(InvalidOperation,
- 'pow() 3rd argument cannot be 0')
-
- # additional restriction for decimal: the modulus must be less
- # than 10**prec in absolute value
- if modulo.adjusted() >= context.prec:
- return context._raise_error(InvalidOperation,
- 'insufficient precision: pow() 3rd '
- 'argument must not have more than '
- 'precision digits')
-
- # define 0**0 == NaN, for consistency with two-argument pow
- # (even though it hurts!)
- if not other and not self:
- return context._raise_error(InvalidOperation,
- 'at least one of pow() 1st argument '
- 'and 2nd argument must be nonzero ;'
- '0**0 is not defined')
-
- # compute sign of result
- if other._iseven():
- sign = 0
- else:
- sign = self._sign
-
- # convert modulo to a Python integer, and self and other to
- # Decimal integers (i.e. force their exponents to be >= 0)
- modulo = abs(int(modulo))
- base = _WorkRep(self.to_integral_value())
- exponent = _WorkRep(other.to_integral_value())
-
- # compute result using integer pow()
- base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo
- for i in range(exponent.exp):
- base = pow(base, 10, modulo)
- base = pow(base, exponent.int, modulo)
-
- return _dec_from_triple(sign, str(base), 0)
-
- def _power_exact(self, other, p):
- """Attempt to compute self**other exactly.
-
- Given Decimals self and other and an integer p, attempt to
- compute an exact result for the power self**other, with p
- digits of precision. Return None if self**other is not
- exactly representable in p digits.
-
- Assumes that elimination of special cases has already been
- performed: self and other must both be nonspecial; self must
- be positive and not numerically equal to 1; other must be
- nonzero. For efficiency, other._exp should not be too large,
- so that 10**abs(other._exp) is a feasible calculation."""
-
- # In the comments below, we write x for the value of self and y for the
- # value of other. Write x = xc*10**xe and abs(y) = yc*10**ye, with xc
- # and yc positive integers not divisible by 10.
-
- # The main purpose of this method is to identify the *failure*
- # of x**y to be exactly representable with as little effort as
- # possible. So we look for cheap and easy tests that
- # eliminate the possibility of x**y being exact. Only if all
- # these tests are passed do we go on to actually compute x**y.
-
- # Here's the main idea. Express y as a rational number m/n, with m and
- # n relatively prime and n>0. Then for x**y to be exactly
- # representable (at *any* precision), xc must be the nth power of a
- # positive integer and xe must be divisible by n. If y is negative
- # then additionally xc must be a power of either 2 or 5, hence a power
- # of 2**n or 5**n.
- #
- # There's a limit to how small |y| can be: if y=m/n as above
- # then:
- #
- # (1) if xc != 1 then for the result to be representable we
- # need xc**(1/n) >= 2, and hence also xc**|y| >= 2. So
- # if |y| <= 1/nbits(xc) then xc < 2**nbits(xc) <=
- # 2**(1/|y|), hence xc**|y| < 2 and the result is not
- # representable.
- #
- # (2) if xe != 0, |xe|*(1/n) >= 1, so |xe|*|y| >= 1. Hence if
- # |y| < 1/|xe| then the result is not representable.
- #
- # Note that since x is not equal to 1, at least one of (1) and
- # (2) must apply. Now |y| < 1/nbits(xc) iff |yc|*nbits(xc) <
- # 10**-ye iff len(str(|yc|*nbits(xc)) <= -ye.
- #
- # There's also a limit to how large y can be, at least if it's
- # positive: the normalized result will have coefficient xc**y,
- # so if it's representable then xc**y < 10**p, and y <
- # p/log10(xc). Hence if y*log10(xc) >= p then the result is
- # not exactly representable.
-
- # if len(str(abs(yc*xe)) <= -ye then abs(yc*xe) < 10**-ye,
- # so |y| < 1/xe and the result is not representable.
- # Similarly, len(str(abs(yc)*xc_bits)) <= -ye implies |y|
- # < 1/nbits(xc).
-
- x = _WorkRep(self)
- xc, xe = x.int, x.exp
- while xc % 10 == 0:
- xc //= 10
- xe += 1
-
- y = _WorkRep(other)
- yc, ye = y.int, y.exp
- while yc % 10 == 0:
- yc //= 10
- ye += 1
-
- # case where xc == 1: result is 10**(xe*y), with xe*y
- # required to be an integer
- if xc == 1:
- xe *= yc
- # result is now 10**(xe * 10**ye); xe * 10**ye must be integral
- while xe % 10 == 0:
- xe //= 10
- ye += 1
- if ye < 0:
- return None
- exponent = xe * 10**ye
- if y.sign == 1:
- exponent = -exponent
- # if other is a nonnegative integer, use ideal exponent
- if other._isinteger() and other._sign == 0:
- ideal_exponent = self._exp*int(other)
- zeros = min(exponent-ideal_exponent, p-1)
- else:
- zeros = 0
- return _dec_from_triple(0, '1' + '0'*zeros, exponent-zeros)
-
- # case where y is negative: xc must be either a power
- # of 2 or a power of 5.
- if y.sign == 1:
- last_digit = xc % 10
- if last_digit in (2,4,6,8):
- # quick test for power of 2
- if xc & -xc != xc:
- return None
- # now xc is a power of 2; e is its exponent
- e = _nbits(xc)-1
-
- # We now have:
- #
- # x = 2**e * 10**xe, e > 0, and y < 0.
- #
- # The exact result is:
- #
- # x**y = 5**(-e*y) * 10**(e*y + xe*y)
- #
- # provided that both e*y and xe*y are integers. Note that if
- # 5**(-e*y) >= 10**p, then the result can't be expressed
- # exactly with p digits of precision.
- #
- # Using the above, we can guard against large values of ye.
- # 93/65 is an upper bound for log(10)/log(5), so if
- #
- # ye >= len(str(93*p//65))
- #
- # then
- #
- # -e*y >= -y >= 10**ye > 93*p/65 > p*log(10)/log(5),
- #
- # so 5**(-e*y) >= 10**p, and the coefficient of the result
- # can't be expressed in p digits.
-
- # emax >= largest e such that 5**e < 10**p.
- emax = p*93//65
- if ye >= len(str(emax)):
- return None
-
- # Find -e*y and -xe*y; both must be integers
- e = _decimal_lshift_exact(e * yc, ye)
- xe = _decimal_lshift_exact(xe * yc, ye)
- if e is None or xe is None:
- return None
-
- if e > emax:
- return None
- xc = 5**e
-
- elif last_digit == 5:
- # e >= log_5(xc) if xc is a power of 5; we have
- # equality all the way up to xc=5**2658
- e = _nbits(xc)*28//65
- xc, remainder = divmod(5**e, xc)
- if remainder:
- return None
- while xc % 5 == 0:
- xc //= 5
- e -= 1
-
- # Guard against large values of ye, using the same logic as in
- # the 'xc is a power of 2' branch. 10/3 is an upper bound for
- # log(10)/log(2).
- emax = p*10//3
- if ye >= len(str(emax)):
- return None
-
- e = _decimal_lshift_exact(e * yc, ye)
- xe = _decimal_lshift_exact(xe * yc, ye)
- if e is None or xe is None:
- return None
-
- if e > emax:
- return None
- xc = 2**e
- else:
- return None
-
- if xc >= 10**p:
- return None
- xe = -e-xe
- return _dec_from_triple(0, str(xc), xe)
-
- # now y is positive; find m and n such that y = m/n
- if ye >= 0:
- m, n = yc*10**ye, 1
- else:
- if xe != 0 and len(str(abs(yc*xe))) <= -ye:
- return None
- xc_bits = _nbits(xc)
- if xc != 1 and len(str(abs(yc)*xc_bits)) <= -ye:
- return None
- m, n = yc, 10**(-ye)
- while m % 2 == n % 2 == 0:
- m //= 2
- n //= 2
- while m % 5 == n % 5 == 0:
- m //= 5
- n //= 5
-
- # compute nth root of xc*10**xe
- if n > 1:
- # if 1 < xc < 2**n then xc isn't an nth power
- if xc != 1 and xc_bits <= n:
- return None
-
- xe, rem = divmod(xe, n)
- if rem != 0:
- return None
-
- # compute nth root of xc using Newton's method
- a = 1 << -(-_nbits(xc)//n) # initial estimate
- while True:
- q, r = divmod(xc, a**(n-1))
- if a <= q:
- break
- else:
- a = (a*(n-1) + q)//n
- if not (a == q and r == 0):
- return None
- xc = a
-
- # now xc*10**xe is the nth root of the original xc*10**xe
- # compute mth power of xc*10**xe
-
- # if m > p*100//_log10_lb(xc) then m > p/log10(xc), hence xc**m >
- # 10**p and the result is not representable.
- if xc > 1 and m > p*100//_log10_lb(xc):
- return None
- xc = xc**m
- xe *= m
- if xc > 10**p:
- return None
-
- # by this point the result *is* exactly representable
- # adjust the exponent to get as close as possible to the ideal
- # exponent, if necessary
- str_xc = str(xc)
- if other._isinteger() and other._sign == 0:
- ideal_exponent = self._exp*int(other)
- zeros = min(xe-ideal_exponent, p-len(str_xc))
- else:
- zeros = 0
- return _dec_from_triple(0, str_xc+'0'*zeros, xe-zeros)
-
- def __pow__(self, other, modulo=None, context=None):
- """Return self ** other [ % modulo].
-
- With two arguments, compute self**other.
-
- With three arguments, compute (self**other) % modulo. For the
- three argument form, the following restrictions on the
- arguments hold:
-
- - all three arguments must be integral
- - other must be nonnegative
- - either self or other (or both) must be nonzero
- - modulo must be nonzero and must have at most p digits,
- where p is the context precision.
-
- If any of these restrictions is violated the InvalidOperation
- flag is raised.
-
- The result of pow(self, other, modulo) is identical to the
- result that would be obtained by computing (self**other) %
- modulo with unbounded precision, but is computed more
- efficiently. It is always exact.
- """
-
- if modulo is not None:
- return self._power_modulo(other, modulo, context)
-
- other = _convert_other(other)
- if other is NotImplemented:
- return other
-
- if context is None:
- context = getcontext()
-
- # either argument is a NaN => result is NaN
- ans = self._check_nans(other, context)
- if ans:
- return ans
-
- # 0**0 = NaN (!), x**0 = 1 for nonzero x (including +/-Infinity)
- if not other:
- if not self:
- return context._raise_error(InvalidOperation, '0 ** 0')
- else:
- return _One
-
- # result has sign 1 iff self._sign is 1 and other is an odd integer
- result_sign = 0
- if self._sign == 1:
- if other._isinteger():
- if not other._iseven():
- result_sign = 1
- else:
- # -ve**noninteger = NaN
- # (-0)**noninteger = 0**noninteger
- if self:
- return context._raise_error(InvalidOperation,
- 'x ** y with x negative and y not an integer')
- # negate self, without doing any unwanted rounding
- self = self.copy_negate()
-
- # 0**(+ve or Inf)= 0; 0**(-ve or -Inf) = Infinity
- if not self:
- if other._sign == 0:
- return _dec_from_triple(result_sign, '0', 0)
- else:
- return _SignedInfinity[result_sign]
-
- # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0
- if self._isinfinity():
- if other._sign == 0:
- return _SignedInfinity[result_sign]
- else:
- return _dec_from_triple(result_sign, '0', 0)
-
- # 1**other = 1, but the choice of exponent and the flags
- # depend on the exponent of self, and on whether other is a
- # positive integer, a negative integer, or neither
- if self == _One:
- if other._isinteger():
- # exp = max(self._exp*max(int(other), 0),
- # 1-context.prec) but evaluating int(other) directly
- # is dangerous until we know other is small (other
- # could be 1e999999999)
- if other._sign == 1:
- multiplier = 0
- elif other > context.prec:
- multiplier = context.prec
- else:
- multiplier = int(other)
-
- exp = self._exp * multiplier
- if exp < 1-context.prec:
- exp = 1-context.prec
- context._raise_error(Rounded)
- else:
- context._raise_error(Inexact)
- context._raise_error(Rounded)
- exp = 1-context.prec
-
- return _dec_from_triple(result_sign, '1'+'0'*-exp, exp)
-
- # compute adjusted exponent of self
- self_adj = self.adjusted()
-
- # self ** infinity is infinity if self > 1, 0 if self < 1
- # self ** -infinity is infinity if self < 1, 0 if self > 1
- if other._isinfinity():
- if (other._sign == 0) == (self_adj < 0):
- return _dec_from_triple(result_sign, '0', 0)
- else:
- return _SignedInfinity[result_sign]
-
- # from here on, the result always goes through the call
- # to _fix at the end of this function.
- ans = None
- exact = False
-
- # crude test to catch cases of extreme overflow/underflow. If
- # log10(self)*other >= 10**bound and bound >= len(str(Emax))
- # then 10**bound >= 10**len(str(Emax)) >= Emax+1 and hence
- # self**other >= 10**(Emax+1), so overflow occurs. The test
- # for underflow is similar.
- bound = self._log10_exp_bound() + other.adjusted()
- if (self_adj >= 0) == (other._sign == 0):
- # self > 1 and other +ve, or self < 1 and other -ve
- # possibility of overflow
- if bound >= len(str(context.Emax)):
- ans = _dec_from_triple(result_sign, '1', context.Emax+1)
- else:
- # self > 1 and other -ve, or self < 1 and other +ve
- # possibility of underflow to 0
- Etiny = context.Etiny()
- if bound >= len(str(-Etiny)):
- ans = _dec_from_triple(result_sign, '1', Etiny-1)
-
- # try for an exact result with precision +1
- if ans is None:
- ans = self._power_exact(other, context.prec + 1)
- if ans is not None:
- if result_sign == 1:
- ans = _dec_from_triple(1, ans._int, ans._exp)
- exact = True
-
- # usual case: inexact result, x**y computed directly as exp(y*log(x))
- if ans is None:
- p = context.prec
- x = _WorkRep(self)
- xc, xe = x.int, x.exp
- y = _WorkRep(other)
- yc, ye = y.int, y.exp
- if y.sign == 1:
- yc = -yc
-
- # compute correctly rounded result: start with precision +3,
- # then increase precision until result is unambiguously roundable
- extra = 3
- while True:
- coeff, exp = _dpower(xc, xe, yc, ye, p+extra)
- if coeff % (5*10**(len(str(coeff))-p-1)):
- break
- extra += 3
-
- ans = _dec_from_triple(result_sign, str(coeff), exp)
-
- # unlike exp, ln and log10, the power function respects the
- # rounding mode; no need to switch to ROUND_HALF_EVEN here
-
- # There's a difficulty here when 'other' is not an integer and
- # the result is exact. In this case, the specification
- # requires that the Inexact flag be raised (in spite of
- # exactness), but since the result is exact _fix won't do this
- # for us. (Correspondingly, the Underflow signal should also
- # be raised for subnormal results.) We can't directly raise
- # these signals either before or after calling _fix, since
- # that would violate the precedence for signals. So we wrap
- # the ._fix call in a temporary context, and reraise
- # afterwards.
- if exact and not other._isinteger():
- # pad with zeros up to length context.prec+1 if necessary; this
- # ensures that the Rounded signal will be raised.
- if len(ans._int) <= context.prec:
- expdiff = context.prec + 1 - len(ans._int)
- ans = _dec_from_triple(ans._sign, ans._int+'0'*expdiff,
- ans._exp-expdiff)
-
- # create a copy of the current context, with cleared flags/traps
- newcontext = context.copy()
- newcontext.clear_flags()
- for exception in _signals:
- newcontext.traps[exception] = 0
-
- # round in the new context
- ans = ans._fix(newcontext)
-
- # raise Inexact, and if necessary, Underflow
- newcontext._raise_error(Inexact)
- if newcontext.flags[Subnormal]:
- newcontext._raise_error(Underflow)
-
- # propagate signals to the original context; _fix could
- # have raised any of Overflow, Underflow, Subnormal,
- # Inexact, Rounded, Clamped. Overflow needs the correct
- # arguments. Note that the order of the exceptions is
- # important here.
- if newcontext.flags[Overflow]:
- context._raise_error(Overflow, 'above Emax', ans._sign)
- for exception in Underflow, Subnormal, Inexact, Rounded, Clamped:
- if newcontext.flags[exception]:
- context._raise_error(exception)
-
- else:
- ans = ans._fix(context)
-
- return ans
-
- def __rpow__(self, other, context=None):
- """Swaps self/other and returns __pow__."""
- other = _convert_other(other)
- if other is NotImplemented:
- return other
- return other.__pow__(self, context=context)
-
- def normalize(self, context=None):
- """Normalize- strip trailing 0s, change anything equal to 0 to 0e0"""
-
- if context is None:
- context = getcontext()
-
- if self._is_special:
- ans = self._check_nans(context=context)
- if ans:
- return ans
-
- dup = self._fix(context)
- if dup._isinfinity():
- return dup
-
- if not dup:
- return _dec_from_triple(dup._sign, '0', 0)
- exp_max = [context.Emax, context.Etop()][context.clamp]
- end = len(dup._int)
- exp = dup._exp
- while dup._int[end-1] == '0' and exp < exp_max:
- exp += 1
- end -= 1
- return _dec_from_triple(dup._sign, dup._int[:end], exp)
-
- def quantize(self, exp, rounding=None, context=None):
- """Quantize self so its exponent is the same as that of exp.
-
- Similar to self._rescale(exp._exp) but with error checking.
- """
- exp = _convert_other(exp, raiseit=True)
-
- if context is None:
- context = getcontext()
- if rounding is None:
- rounding = context.rounding
-
- if self._is_special or exp._is_special:
- ans = self._check_nans(exp, context)
- if ans:
- return ans
-
- if exp._isinfinity() or self._isinfinity():
- if exp._isinfinity() and self._isinfinity():
- return Decimal(self) # if both are inf, it is OK
- return context._raise_error(InvalidOperation,
- 'quantize with one INF')
-
- # exp._exp should be between Etiny and Emax
- if not (context.Etiny() <= exp._exp <= context.Emax):
- return context._raise_error(InvalidOperation,
- 'target exponent out of bounds in quantize')
-
- if not self:
- ans = _dec_from_triple(self._sign, '0', exp._exp)
- return ans._fix(context)
-
- self_adjusted = self.adjusted()
- if self_adjusted > context.Emax:
- return context._raise_error(InvalidOperation,
- 'exponent of quantize result too large for current context')
- if self_adjusted - exp._exp + 1 > context.prec:
- return context._raise_error(InvalidOperation,
- 'quantize result has too many digits for current context')
-
- ans = self._rescale(exp._exp, rounding)
- if ans.adjusted() > context.Emax:
- return context._raise_error(InvalidOperation,
- 'exponent of quantize result too large for current context')
- if len(ans._int) > context.prec:
- return context._raise_error(InvalidOperation,
- 'quantize result has too many digits for current context')
-
- # raise appropriate flags
- if ans and ans.adjusted() < context.Emin:
- context._raise_error(Subnormal)
- if ans._exp > self._exp:
- if ans != self:
- context._raise_error(Inexact)
- context._raise_error(Rounded)
-
- # call to fix takes care of any necessary folddown, and
- # signals Clamped if necessary
- ans = ans._fix(context)
- return ans
-
- def same_quantum(self, other, context=None):
- """Return True if self and other have the same exponent; otherwise
- return False.
-
- If either operand is a special value, the following rules are used:
- * return True if both operands are infinities
- * return True if both operands are NaNs
- * otherwise, return False.
- """
- other = _convert_other(other, raiseit=True)
- if self._is_special or other._is_special:
- return (self.is_nan() and other.is_nan() or
- self.is_infinite() and other.is_infinite())
- return self._exp == other._exp
-
- def _rescale(self, exp, rounding):
- """Rescale self so that the exponent is exp, either by padding with zeros
- or by truncating digits, using the given rounding mode.
-
- Specials are returned without change. This operation is
- quiet: it raises no flags, and uses no information from the
- context.
-
- exp = exp to scale to (an integer)
- rounding = rounding mode
- """
- if self._is_special:
- return Decimal(self)
- if not self:
- return _dec_from_triple(self._sign, '0', exp)
-
- if self._exp >= exp:
- # pad answer with zeros if necessary
- return _dec_from_triple(self._sign,
- self._int + '0'*(self._exp - exp), exp)
-
- # too many digits; round and lose data. If self.adjusted() <
- # exp-1, replace self by 10**(exp-1) before rounding
- digits = len(self._int) + self._exp - exp
- if digits < 0:
- self = _dec_from_triple(self._sign, '1', exp-1)
- digits = 0
- this_function = self._pick_rounding_function[rounding]
- changed = this_function(self, digits)
- coeff = self._int[:digits] or '0'
- if changed == 1:
- coeff = str(int(coeff)+1)
- return _dec_from_triple(self._sign, coeff, exp)
-
- def _round(self, places, rounding):
- """Round a nonzero, nonspecial Decimal to a fixed number of
- significant figures, using the given rounding mode.
-
- Infinities, NaNs and zeros are returned unaltered.
-
- This operation is quiet: it raises no flags, and uses no
- information from the context.
-
- """
- if places <= 0:
- raise ValueError("argument should be at least 1 in _round")
- if self._is_special or not self:
- return Decimal(self)
- ans = self._rescale(self.adjusted()+1-places, rounding)
- # it can happen that the rescale alters the adjusted exponent;
- # for example when rounding 99.97 to 3 significant figures.
- # When this happens we end up with an extra 0 at the end of
- # the number; a second rescale fixes this.
- if ans.adjusted() != self.adjusted():
- ans = ans._rescale(ans.adjusted()+1-places, rounding)
- return ans
-
- 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_value(self, rounding=None, context=None):
- """Rounds to the nearest integer, without raising inexact, rounded."""
- if context is None:
- context = getcontext()
- if rounding is None:
- rounding = context.rounding
- if self._is_special:
- ans = self._check_nans(context=context)
- if ans:
- return ans
- return Decimal(self)
- if self._exp >= 0:
- return Decimal(self)
- else:
- return self._rescale(0, rounding)
-
- # the method name changed, but we provide also the old one, for compatibility
- to_integral = to_integral_value
-
- def sqrt(self, context=None):
- """Return the square root of self."""
- if context is None:
- context = getcontext()
-
- if self._is_special:
- ans = self._check_nans(context=context)
- if ans:
- return ans
-
- if self._isinfinity() and self._sign == 0:
- return Decimal(self)
-
- if not self:
- # exponent = self._exp // 2. sqrt(-0) = -0
- ans = _dec_from_triple(self._sign, '0', self._exp // 2)
- return ans._fix(context)
-
- if self._sign == 1:
- return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0')
-
- # At this point self represents a positive number. Let p be
- # the desired precision and express self in the form c*100**e
- # with c a positive real number and e an integer, c and e
- # being chosen so that 100**(p-1) <= c < 100**p. Then the
- # (exact) square root of self is sqrt(c)*10**e, and 10**(p-1)
- # <= sqrt(c) < 10**p, so the closest representable Decimal at
- # precision p is n*10**e where n = round_half_even(sqrt(c)),
- # the closest integer to sqrt(c) with the even integer chosen
- # in the case of a tie.
- #
- # To ensure correct rounding in all cases, we use the
- # following trick: we compute the square root to an extra
- # place (precision p+1 instead of precision p), rounding down.
- # Then, if the result is inexact and its last digit is 0 or 5,
- # we increase the last digit to 1 or 6 respectively; if it's
- # exact we leave the last digit alone. Now the final round to
- # p places (or fewer in the case of underflow) will round
- # correctly and raise the appropriate flags.
-
- # use an extra digit of precision
- prec = context.prec+1
-
- # write argument in the form c*100**e where e = self._exp//2
- # is the 'ideal' exponent, to be used if the square root is
- # exactly representable. l is the number of 'digits' of c in
- # base 100, so that 100**(l-1) <= c < 100**l.
- op = _WorkRep(self)
- e = op.exp >> 1
- if op.exp & 1:
- c = op.int * 10
- l = (len(self._int) >> 1) + 1
- else:
- c = op.int
- l = len(self._int)+1 >> 1
-
- # rescale so that c has exactly prec base 100 'digits'
- shift = prec-l
- if shift >= 0:
- c *= 100**shift
- exact = True
- else:
- c, remainder = divmod(c, 100**-shift)
- exact = not remainder
- e -= shift
-
- # find n = floor(sqrt(c)) using Newton's method
- n = 10**prec
- while True:
- q = c//n
- if n <= q:
- break
- else:
- n = n + q >> 1
- exact = exact and n*n == c
-
- if exact:
- # result is exact; rescale to use ideal exponent e
- if shift >= 0:
- # assert n % 10**shift == 0
- n //= 10**shift
- else:
- n *= 10**-shift
- e += shift
- else:
- # result is not exact; fix last digit as described above
- if n % 5 == 0:
- n += 1
-
- ans = _dec_from_triple(0, str(n), e)
-
- # round, and fit to current context
- context = context._shallow_copy()
- rounding = context._set_rounding(ROUND_HALF_EVEN)
- ans = ans._fix(context)
- context.rounding = rounding
-
- return ans
-
- def max(self, other, context=None):
- """Returns the larger value.
-
- Like max(self, other) except if one is not a number, returns
- NaN (and signals if one is sNaN). Also rounds.
- """
- other = _convert_other(other, raiseit=True)
-
- if context is None:
- context = getcontext()
-
- if self._is_special or other._is_special:
- # If one operand is a quiet NaN and the other is number, then the
- # number is always returned
- sn = self._isnan()
- on = other._isnan()
- if sn or on:
- if on == 1 and sn == 0:
- return self._fix(context)
- if sn == 1 and on == 0:
- return other._fix(context)
- return self._check_nans(other, context)
-
- c = self._cmp(other)
- if c == 0:
- # If both operands are finite and equal in numerical value
- # then an ordering is applied:
- #
- # If the signs differ then max returns the operand with the
- # positive sign and min returns the operand with the negative sign
- #
- # If the signs are the same then the exponent is used to select
- # the result. This is exactly the ordering used in compare_total.
- c = self.compare_total(other)
-
- if c == -1:
- ans = other
- else:
- ans = self
-
- return ans._fix(context)
-
- def min(self, other, context=None):
- """Returns the smaller value.
-
- Like min(self, other) except if one is not a number, returns
- NaN (and signals if one is sNaN). Also rounds.
- """
- other = _convert_other(other, raiseit=True)
-
- if context is None:
- context = getcontext()
-
- if self._is_special or other._is_special:
- # If one operand is a quiet NaN and the other is number, then the
- # number is always returned
- sn = self._isnan()
- on = other._isnan()
- if sn or on:
- if on == 1 and sn == 0:
- return self._fix(context)
- if sn == 1 and on == 0:
- return other._fix(context)
- return self._check_nans(other, context)
-
- c = self._cmp(other)
- if c == 0:
- c = self.compare_total(other)
-
- if c == -1:
- ans = self
- else:
- ans = other
-
- return ans._fix(context)
-
- def _isinteger(self):
- """Returns whether self is an integer"""
- if self._is_special:
- return False
- if self._exp >= 0:
- return True
- rest = self._int[self._exp:]
- return rest == '0'*len(rest)
-
- def _iseven(self):
- """Returns True if self is even. Assumes self is an integer."""
- if not self or self._exp > 0:
- return True
- return self._int[-1+self._exp] in '02468'
-
- def adjusted(self):
- """Return the adjusted exponent of self"""
- try:
- return self._exp + len(self._int) - 1
- # If NaN or Infinity, self._exp is string
- except TypeError:
- return 0
-
- def canonical(self):
- """Returns the same Decimal object.
-
- As we do not have different encodings for the same number, the
- received object already is in its canonical form.
- """
- return self
-
- def compare_signal(self, other, context=None):
- """Compares self to the other operand numerically.
-
- It's pretty much like compare(), but all NaNs signal, with signaling
- NaNs taking precedence over quiet NaNs.
- """
- other = _convert_other(other, raiseit = True)
- ans = self._compare_check_nans(other, context)
- if ans:
- return ans
- return self.compare(other, context=context)
-
- def compare_total(self, other, context=None):
- """Compares self to other using the abstract representations.
-
- This is not like the standard compare, which use their numerical
- value. Note that a total ordering is defined for all possible abstract
- representations.
- """
- other = _convert_other(other, raiseit=True)
-
- # if one is negative and the other is positive, it's easy
- if self._sign and not other._sign:
- return _NegativeOne
- if not self._sign and other._sign:
- return _One
- sign = self._sign
-
- # let's handle both NaN types
- self_nan = self._isnan()
- other_nan = other._isnan()
- if self_nan or other_nan:
- if self_nan == other_nan:
- # compare payloads as though they're integers
- self_key = len(self._int), self._int
- other_key = len(other._int), other._int
- if self_key < other_key:
- if sign:
- return _One
- else:
- return _NegativeOne
- if self_key > other_key:
- if sign:
- return _NegativeOne
- else:
- return _One
- return _Zero
-
- if sign:
- if self_nan == 1:
- return _NegativeOne
- if other_nan == 1:
- return _One
- if self_nan == 2:
- return _NegativeOne
- if other_nan == 2:
- return _One
- else:
- if self_nan == 1:
- return _One
- if other_nan == 1:
- return _NegativeOne
- if self_nan == 2:
- return _One
- if other_nan == 2:
- return _NegativeOne
-
- if self < other:
- return _NegativeOne
- if self > other:
- return _One
-
- if self._exp < other._exp:
- if sign:
- return _One
- else:
- return _NegativeOne
- if self._exp > other._exp:
- if sign:
- return _NegativeOne
- else:
- return _One
- return _Zero
-
-
- def compare_total_mag(self, other, context=None):
- """Compares self to other using abstract repr., ignoring sign.
-
- Like compare_total, but with operand's sign ignored and assumed to be 0.
- """
- other = _convert_other(other, raiseit=True)
-
- s = self.copy_abs()
- o = other.copy_abs()
- return s.compare_total(o)
-
- def copy_abs(self):
- """Returns a copy with the sign set to 0. """
- return _dec_from_triple(0, self._int, self._exp, self._is_special)
-
- def copy_negate(self):
- """Returns a copy with the sign inverted."""
- if self._sign:
- return _dec_from_triple(0, self._int, self._exp, self._is_special)
- else:
- return _dec_from_triple(1, self._int, self._exp, self._is_special)
-
- def copy_sign(self, other, context=None):
- """Returns self with the sign of other."""
- other = _convert_other(other, raiseit=True)
- return _dec_from_triple(other._sign, self._int,
- self._exp, self._is_special)
-
- def exp(self, context=None):
- """Returns e ** self."""
-
- if context is None:
- context = getcontext()
-
- # exp(NaN) = NaN
- ans = self._check_nans(context=context)
- if ans:
- return ans
-
- # exp(-Infinity) = 0
- if self._isinfinity() == -1:
- return _Zero
-
- # exp(0) = 1
- if not self:
- return _One
-
- # exp(Infinity) = Infinity
- if self._isinfinity() == 1:
- return Decimal(self)
-
- # the result is now guaranteed to be inexact (the true
- # mathematical result is transcendental). There's no need to
- # raise Rounded and Inexact here---they'll always be raised as
- # a result of the call to _fix.
- p = context.prec
- adj = self.adjusted()
-
- # we only need to do any computation for quite a small range
- # of adjusted exponents---for example, -29 <= adj <= 10 for
- # the default context. For smaller exponent the result is
- # indistinguishable from 1 at the given precision, while for
- # larger exponent the result either overflows or underflows.
- if self._sign == 0 and adj > len(str((context.Emax+1)*3)):
- # overflow
- ans = _dec_from_triple(0, '1', context.Emax+1)
- elif self._sign == 1 and adj > len(str((-context.Etiny()+1)*3)):
- # underflow to 0
- ans = _dec_from_triple(0, '1', context.Etiny()-1)
- elif self._sign == 0 and adj < -p:
- # p+1 digits; final round will raise correct flags
- ans = _dec_from_triple(0, '1' + '0'*(p-1) + '1', -p)
- elif self._sign == 1 and adj < -p-1:
- # p+1 digits; final round will raise correct flags
- ans = _dec_from_triple(0, '9'*(p+1), -p-1)
- # general case
- else:
- op = _WorkRep(self)
- c, e = op.int, op.exp
- if op.sign == 1:
- c = -c
-
- # compute correctly rounded result: increase precision by
- # 3 digits at a time until we get an unambiguously
- # roundable result
- extra = 3
- while True:
- coeff, exp = _dexp(c, e, p+extra)
- if coeff % (5*10**(len(str(coeff))-p-1)):
- break
- extra += 3
-
- ans = _dec_from_triple(0, str(coeff), exp)
-
- # at this stage, ans should round correctly with *any*
- # rounding mode, not just with ROUND_HALF_EVEN
- context = context._shallow_copy()
- rounding = context._set_rounding(ROUND_HALF_EVEN)
- ans = ans._fix(context)
- context.rounding = rounding
-
- return ans
-
- def is_canonical(self):
- """Return True if self is canonical; otherwise return False.
-
- Currently, the encoding of a Decimal instance is always
- canonical, so this method returns True for any Decimal.
- """
- return True
-
- def is_finite(self):
- """Return True if self is finite; otherwise return False.
-
- A Decimal instance is considered finite if it is neither
- infinite nor a NaN.
- """
- return not self._is_special
-
- def is_infinite(self):
- """Return True if self is infinite; otherwise return False."""
- return self._exp == 'F'
-
- def is_nan(self):
- """Return True if self is a qNaN or sNaN; otherwise return False."""
- return self._exp in ('n', 'N')
-
- def is_normal(self, context=None):
- """Return True if self is a normal number; otherwise return False."""
- if self._is_special or not self:
- return False
- if context is None:
- context = getcontext()
- return context.Emin <= self.adjusted()
-
- def is_qnan(self):
- """Return True if self is a quiet NaN; otherwise return False."""
- return self._exp == 'n'
-
- def is_signed(self):
- """Return True if self is negative; otherwise return False."""
- return self._sign == 1
-
- def is_snan(self):
- """Return True if self is a signaling NaN; otherwise return False."""
- return self._exp == 'N'
-
- def is_subnormal(self, context=None):
- """Return True if self is subnormal; otherwise return False."""
- if self._is_special or not self:
- return False
- if context is None:
- context = getcontext()
- return self.adjusted() < context.Emin
-
- def is_zero(self):
- """Return True if self is a zero; otherwise return False."""
- return not self._is_special and self._int == '0'
-
- def _ln_exp_bound(self):
- """Compute a lower bound for the adjusted exponent of self.ln().
- In other words, compute r such that self.ln() >= 10**r. Assumes
- that self is finite and positive and that self != 1.
- """
-
- # for 0.1 <= x <= 10 we use the inequalities 1-1/x <= ln(x) <= x-1
- adj = self._exp + len(self._int) - 1
- if adj >= 1:
- # argument >= 10; we use 23/10 = 2.3 as a lower bound for ln(10)
- return len(str(adj*23//10)) - 1
- if adj <= -2:
- # argument <= 0.1
- return len(str((-1-adj)*23//10)) - 1
- op = _WorkRep(self)
- c, e = op.int, op.exp
- if adj == 0:
- # 1 < self < 10
- num = str(c-10**-e)
- den = str(c)
- return len(num) - len(den) - (num < den)
- # adj == -1, 0.1 <= self < 1
- return e + len(str(10**-e - c)) - 1
-
-
- def ln(self, context=None):
- """Returns the natural (base e) logarithm of self."""
-
- if context is None:
- context = getcontext()
-
- # ln(NaN) = NaN
- ans = self._check_nans(context=context)
- if ans:
- return ans
-
- # ln(0.0) == -Infinity
- if not self:
- return _NegativeInfinity
-
- # ln(Infinity) = Infinity
- if self._isinfinity() == 1:
- return _Infinity
-
- # ln(1.0) == 0.0
- if self == _One:
- return _Zero
-
- # ln(negative) raises InvalidOperation
- if self._sign == 1:
- return context._raise_error(InvalidOperation,
- 'ln of a negative value')
-
- # result is irrational, so necessarily inexact
- op = _WorkRep(self)
- c, e = op.int, op.exp
- p = context.prec
-
- # correctly rounded result: repeatedly increase precision by 3
- # until we get an unambiguously roundable result
- places = p - self._ln_exp_bound() + 2 # at least p+3 places
- while True:
- coeff = _dlog(c, e, places)
- # assert len(str(abs(coeff)))-p >= 1
- if coeff % (5*10**(len(str(abs(coeff)))-p-1)):
- break
- places += 3
- ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places)
-
- context = context._shallow_copy()
- rounding = context._set_rounding(ROUND_HALF_EVEN)
- ans = ans._fix(context)
- context.rounding = rounding
- return ans
-
- def _log10_exp_bound(self):
- """Compute a lower bound for the adjusted exponent of self.log10().
- In other words, find r such that self.log10() >= 10**r.
- Assumes that self is finite and positive and that self != 1.
- """
-
- # For x >= 10 or x < 0.1 we only need a bound on the integer
- # part of log10(self), and this comes directly from the
- # exponent of x. For 0.1 <= x <= 10 we use the inequalities
- # 1-1/x <= log(x) <= x-1. If x > 1 we have |log10(x)| >
- # (1-1/x)/2.31 > 0. If x < 1 then |log10(x)| > (1-x)/2.31 > 0
-
- adj = self._exp + len(self._int) - 1
- if adj >= 1:
- # self >= 10
- return len(str(adj))-1
- if adj <= -2:
- # self < 0.1
- return len(str(-1-adj))-1
- op = _WorkRep(self)
- c, e = op.int, op.exp
- if adj == 0:
- # 1 < self < 10
- num = str(c-10**-e)
- den = str(231*c)
- return len(num) - len(den) - (num < den) + 2
- # adj == -1, 0.1 <= self < 1
- num = str(10**-e-c)
- return len(num) + e - (num < "231") - 1
-
- def log10(self, context=None):
- """Returns the base 10 logarithm of self."""
-
- if context is None:
- context = getcontext()
-
- # log10(NaN) = NaN
- ans = self._check_nans(context=context)
- if ans:
- return ans
-
- # log10(0.0) == -Infinity
- if not self:
- return _NegativeInfinity
-
- # log10(Infinity) = Infinity
- if self._isinfinity() == 1:
- return _Infinity
-
- # log10(negative or -Infinity) raises InvalidOperation
- if self._sign == 1:
- return context._raise_error(InvalidOperation,
- 'log10 of a negative value')
-
- # log10(10**n) = n
- if self._int[0] == '1' and self._int[1:] == '0'*(len(self._int) - 1):
- # answer may need rounding
- ans = Decimal(self._exp + len(self._int) - 1)
- else:
- # result is irrational, so necessarily inexact
- op = _WorkRep(self)
- c, e = op.int, op.exp
- p = context.prec
-
- # correctly rounded result: repeatedly increase precision
- # until result is unambiguously roundable
- places = p-self._log10_exp_bound()+2
- while True:
- coeff = _dlog10(c, e, places)
- # assert len(str(abs(coeff)))-p >= 1
- if coeff % (5*10**(len(str(abs(coeff)))-p-1)):
- break
- places += 3
- ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places)
-
- context = context._shallow_copy()
- rounding = context._set_rounding(ROUND_HALF_EVEN)
- ans = ans._fix(context)
- context.rounding = rounding
- return ans
-
- def logb(self, context=None):
- """ Returns the exponent of the magnitude of self's MSD.
-
- The result is the integer which is the exponent of the magnitude
- of the most significant digit of self (as though it were truncated
- to a single digit while maintaining the value of that digit and
- without limiting the resulting exponent).
- """
- # logb(NaN) = NaN
- ans = self._check_nans(context=context)
- if ans:
- return ans
-
- if context is None:
- context = getcontext()
-
- # logb(+/-Inf) = +Inf
- if self._isinfinity():
- return _Infinity
-
- # logb(0) = -Inf, DivisionByZero
- if not self:
- return context._raise_error(DivisionByZero, 'logb(0)', 1)
-
- # otherwise, simply return the adjusted exponent of self, as a
- # Decimal. Note that no attempt is made to fit the result
- # into the current context.
- ans = Decimal(self.adjusted())
- return ans._fix(context)
-
- def _islogical(self):
- """Return True if self is a logical operand.
-
- For being logical, it must be a finite number with a sign of 0,
- an exponent of 0, and a coefficient whose digits must all be
- either 0 or 1.
- """
- if self._sign != 0 or self._exp != 0:
- return False
- for dig in self._int:
- if dig not in '01':
- return False
- return True
-
- def _fill_logical(self, context, opa, opb):
- dif = context.prec - len(opa)
- if dif > 0:
- opa = '0'*dif + opa
- elif dif < 0:
- opa = opa[-context.prec:]
- dif = context.prec - len(opb)
- if dif > 0:
- opb = '0'*dif + opb
- elif dif < 0:
- opb = opb[-context.prec:]
- return opa, opb
-
- def logical_and(self, other, context=None):
- """Applies an 'and' operation between self and other's digits."""
- if context is None:
- context = getcontext()
-
- other = _convert_other(other, raiseit=True)
-
- if not self._islogical() or not other._islogical():
- return context._raise_error(InvalidOperation)
-
- # fill to context.prec
- (opa, opb) = self._fill_logical(context, self._int, other._int)
-
- # make the operation, and clean starting zeroes
- result = "".join([str(int(a)&int(b)) for a,b in zip(opa,opb)])
- return _dec_from_triple(0, result.lstrip('0') or '0', 0)
-
- def logical_invert(self, context=None):
- """Invert all its digits."""
- if context is None:
- context = getcontext()
- return self.logical_xor(_dec_from_triple(0,'1'*context.prec,0),
- context)
-
- def logical_or(self, other, context=None):
- """Applies an 'or' operation between self and other's digits."""
- if context is None:
- context = getcontext()
-
- other = _convert_other(other, raiseit=True)
-
- if not self._islogical() or not other._islogical():
- return context._raise_error(InvalidOperation)
-
- # fill to context.prec
- (opa, opb) = self._fill_logical(context, self._int, other._int)
-
- # make the operation, and clean starting zeroes
- result = "".join([str(int(a)|int(b)) for a,b in zip(opa,opb)])
- return _dec_from_triple(0, result.lstrip('0') or '0', 0)
-
- def logical_xor(self, other, context=None):
- """Applies an 'xor' operation between self and other's digits."""
- if context is None:
- context = getcontext()
-
- other = _convert_other(other, raiseit=True)
-
- if not self._islogical() or not other._islogical():
- return context._raise_error(InvalidOperation)
-
- # fill to context.prec
- (opa, opb) = self._fill_logical(context, self._int, other._int)
-
- # make the operation, and clean starting zeroes
- result = "".join([str(int(a)^int(b)) for a,b in zip(opa,opb)])
- return _dec_from_triple(0, result.lstrip('0') or '0', 0)
-
- def max_mag(self, other, context=None):
- """Compares the values numerically with their sign ignored."""
- other = _convert_other(other, raiseit=True)
-
- if context is None:
- context = getcontext()
-
- if self._is_special or other._is_special:
- # If one operand is a quiet NaN and the other is number, then the
- # number is always returned
- sn = self._isnan()
- on = other._isnan()
- if sn or on:
- if on == 1 and sn == 0:
- return self._fix(context)
- if sn == 1 and on == 0:
- return other._fix(context)
- return self._check_nans(other, context)
-
- c = self.copy_abs()._cmp(other.copy_abs())
- if c == 0:
- c = self.compare_total(other)
-
- if c == -1:
- ans = other
- else:
- ans = self
-
- return ans._fix(context)
-
- def min_mag(self, other, context=None):
- """Compares the values numerically with their sign ignored."""
- other = _convert_other(other, raiseit=True)
-
- if context is None:
- context = getcontext()
-
- if self._is_special or other._is_special:
- # If one operand is a quiet NaN and the other is number, then the
- # number is always returned
- sn = self._isnan()
- on = other._isnan()
- if sn or on:
- if on == 1 and sn == 0:
- return self._fix(context)
- if sn == 1 and on == 0:
- return other._fix(context)
- return self._check_nans(other, context)
-
- c = self.copy_abs()._cmp(other.copy_abs())
- if c == 0:
- c = self.compare_total(other)
-
- if c == -1:
- ans = self
- else:
- ans = other
-
- return ans._fix(context)
-
- def next_minus(self, context=None):
- """Returns the largest representable number smaller than itself."""
- if context is None:
- context = getcontext()
-
- ans = self._check_nans(context=context)
- if ans:
- return ans
-
- if self._isinfinity() == -1:
- return _NegativeInfinity
- if self._isinfinity() == 1:
- return _dec_from_triple(0, '9'*context.prec, context.Etop())
-
- context = context.copy()
- context._set_rounding(ROUND_FLOOR)
- context._ignore_all_flags()
- new_self = self._fix(context)
- if new_self != self:
- return new_self
- return self.__sub__(_dec_from_triple(0, '1', context.Etiny()-1),
- context)
-
- def next_plus(self, context=None):
- """Returns the smallest representable number larger than itself."""
- if context is None:
- context = getcontext()
-
- ans = self._check_nans(context=context)
- if ans:
- return ans
-
- if self._isinfinity() == 1:
- return _Infinity
- if self._isinfinity() == -1:
- return _dec_from_triple(1, '9'*context.prec, context.Etop())
-
- context = context.copy()
- context._set_rounding(ROUND_CEILING)
- context._ignore_all_flags()
- new_self = self._fix(context)
- if new_self != self:
- return new_self
- return self.__add__(_dec_from_triple(0, '1', context.Etiny()-1),
- context)
-
- 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 number_class(self, context=None):
- """Returns an indication of the class of self.
-
- The class is one of the following strings:
- sNaN
- NaN
- -Infinity
- -Normal
- -Subnormal
- -Zero
- +Zero
- +Subnormal
- +Normal
- +Infinity
- """
- if self.is_snan():
- return "sNaN"
- if self.is_qnan():
- return "NaN"
- inf = self._isinfinity()
- if inf == 1:
- return "+Infinity"
- if inf == -1:
- return "-Infinity"
- if self.is_zero():
- if self._sign:
- return "-Zero"
- else:
- return "+Zero"
- if context is None:
- context = getcontext()
- if self.is_subnormal(context=context):
- if self._sign:
- return "-Subnormal"
- else:
- return "+Subnormal"
- # just a normal, regular, boring number, :)
- if self._sign:
- return "-Normal"
- else:
- return "+Normal"
-
- def radix(self):
- """Just returns 10, as this is Decimal, :)"""
- return Decimal(10)
-
- def rotate(self, other, context=None):
- """Returns a rotated copy of self, value-of-other times."""
- if context is None:
- context = getcontext()
-
- other = _convert_other(other, raiseit=True)
-
- ans = self._check_nans(other, context)
- if ans:
- return ans
-
- if other._exp != 0:
- return context._raise_error(InvalidOperation)
- if not (-context.prec <= int(other) <= context.prec):
- return context._raise_error(InvalidOperation)
-
- if self._isinfinity():
- return Decimal(self)
-
- # get values, pad if necessary
- torot = int(other)
- rotdig = self._int
- topad = context.prec - len(rotdig)
- if topad > 0:
- rotdig = '0'*topad + rotdig
- elif topad < 0:
- rotdig = rotdig[-topad:]
-
- # let's rotate!
- rotated = rotdig[torot:] + rotdig[:torot]
- return _dec_from_triple(self._sign,
- rotated.lstrip('0') or '0', self._exp)
-
- def scaleb(self, other, context=None):
- """Returns self operand after adding the second value to its exp."""
- if context is None:
- context = getcontext()
-
- other = _convert_other(other, raiseit=True)
-
- ans = self._check_nans(other, context)
- if ans:
- return ans
-
- if other._exp != 0:
- return context._raise_error(InvalidOperation)
- liminf = -2 * (context.Emax + context.prec)
- limsup = 2 * (context.Emax + context.prec)
- if not (liminf <= int(other) <= limsup):
- return context._raise_error(InvalidOperation)
-
- if self._isinfinity():
- return Decimal(self)
-
- d = _dec_from_triple(self._sign, self._int, self._exp + int(other))
- d = d._fix(context)
- return d
-
- def shift(self, other, context=None):
- """Returns a shifted copy of self, value-of-other times."""
- if context is None:
- context = getcontext()
-
- other = _convert_other(other, raiseit=True)
-
- ans = self._check_nans(other, context)
- if ans:
- return ans
-
- if other._exp != 0:
- return context._raise_error(InvalidOperation)
- if not (-context.prec <= int(other) <= context.prec):
- return context._raise_error(InvalidOperation)
-
- if self._isinfinity():
- return Decimal(self)
-
- # get values, pad if necessary
- torot = int(other)
- rotdig = self._int
- topad = context.prec - len(rotdig)
- if topad > 0:
- rotdig = '0'*topad + rotdig
- elif topad < 0:
- rotdig = rotdig[-topad:]
-
- # let's shift!
- if torot < 0:
- shifted = rotdig[:torot]
- else:
- shifted = rotdig + '0'*torot
- shifted = shifted[-context.prec:]
-
- return _dec_from_triple(self._sign,
- shifted.lstrip('0') or '0', self._exp)
-
- # Support for pickling, copy, and deepcopy
- def __reduce__(self):
- return (self.__class__, (str(self),))
-
- def __copy__(self):
- if type(self) is Decimal:
- return self # I'm immutable; therefore I am my own clone
- return self.__class__(str(self))
-
- def __deepcopy__(self, memo):
- if type(self) is Decimal:
- return self # My components are also immutable
- return self.__class__(str(self))
-
- # PEP 3101 support. the _localeconv keyword argument should be
- # considered private: it's provided for ease of testing only.
- def __format__(self, specifier, context=None, _localeconv=None):
- """Format a Decimal instance according to the given specifier.
-
- The specifier should be a standard format specifier, with the
- form described in PEP 3101. Formatting types 'e', 'E', 'f',
- 'F', 'g', 'G', 'n' and '%' are supported. If the formatting
- type is omitted it defaults to 'g' or 'G', depending on the
- value of context.capitals.
- """
-
- # Note: PEP 3101 says that if the type is not present then
- # there should be at least one digit after the decimal point.
- # We take the liberty of ignoring this requirement for
- # Decimal---it's presumably there to make sure that
- # format(float, '') behaves similarly to str(float).
- if context is None:
- context = getcontext()
-
- spec = _parse_format_specifier(specifier, _localeconv=_localeconv)
-
- # special values don't care about the type or precision
- if self._is_special:
- sign = _format_sign(self._sign, spec)
- body = str(self.copy_abs())
- if spec['type'] == '%':
- body += '%'
- return _format_align(sign, body, spec)
-
- # a type of None defaults to 'g' or 'G', depending on context
- if spec['type'] is None:
- spec['type'] = ['g', 'G'][context.capitals]
-
- # if type is '%', adjust exponent of self accordingly
- if spec['type'] == '%':
- self = _dec_from_triple(self._sign, self._int, self._exp+2)
-
- # round if necessary, taking rounding mode from the context
- rounding = context.rounding
- precision = spec['precision']
- if precision is not None:
- if spec['type'] in 'eE':
- self = self._round(precision+1, rounding)
- elif spec['type'] in 'fF%':
- self = self._rescale(-precision, rounding)
- elif spec['type'] in 'gG' and len(self._int) > precision:
- self = self._round(precision, rounding)
- # special case: zeros with a positive exponent can't be
- # represented in fixed point; rescale them to 0e0.
- if not self and self._exp > 0 and spec['type'] in 'fF%':
- self = self._rescale(0, rounding)
-
- # figure out placement of the decimal point
- leftdigits = self._exp + len(self._int)
- if spec['type'] in 'eE':
- if not self and precision is not None:
- dotplace = 1 - precision
- else:
- dotplace = 1
- elif spec['type'] in 'fF%':
- dotplace = leftdigits
- elif spec['type'] in 'gG':
- if self._exp <= 0 and leftdigits > -6:
- dotplace = leftdigits
- else:
- dotplace = 1
-
- # find digits before and after decimal point, and get exponent
- if dotplace < 0:
- intpart = '0'
- fracpart = '0'*(-dotplace) + self._int
- elif dotplace > len(self._int):
- intpart = self._int + '0'*(dotplace-len(self._int))
- fracpart = ''
- else:
- intpart = self._int[:dotplace] or '0'
- fracpart = self._int[dotplace:]
- exp = leftdigits-dotplace
-
- # done with the decimal-specific stuff; hand over the rest
- # of the formatting to the _format_number function
- return _format_number(self._sign, intpart, fracpart, exp, spec)
-
-def _dec_from_triple(sign, coefficient, exponent, special=False):
- """Create a decimal instance directly, without any validation,
- normalization (e.g. removal of leading zeros) or argument
- conversion.
-
- This function is for *internal use only*.
- """
-
- self = object.__new__(Decimal)
- self._sign = sign
- self._int = coefficient
- self._exp = exponent
- self._is_special = special
-
- return self
-
-# Register Decimal as a kind of Number (an abstract base class).
-# However, do not register it as Real (because Decimals are not
-# interoperable with floats).
-_numbers.Number.register(Decimal)
-
-
-##### Context class #######################################################
-
-class _ContextManager(object):
- """Context manager class to support localcontext().
-
- Sets a copy of the supplied context in __enter__() and restores
- the previous decimal context in __exit__()
- """
- def __init__(self, new_context):
- self.new_context = new_context.copy()
- def __enter__(self):
- self.saved_context = getcontext()
- setcontext(self.new_context)
- return self.new_context
- def __exit__(self, t, v, tb):
- setcontext(self.saved_context)
-
-class Context(object):
- """Contains the context for a Decimal instance.
-
- Contains:
- prec - precision (for use in rounding, division, square roots..)
- rounding - rounding type (how you round)
- traps - If traps[exception] = 1, then the exception is
- raised when it is caused. Otherwise, a value is
- substituted in.
- flags - When an exception is caused, flags[exception] is set.
- (Whether or not the trap_enabler is set)
- Should be reset by user of Decimal instance.
- Emin - Minimum exponent
- Emax - Maximum exponent
- capitals - If 1, 1*10^1 is printed as 1E+1.
- If 0, printed as 1e1
- clamp - If 1, change exponents if too high (Default 0)
- """
-
- def __init__(self, prec=None, rounding=None, Emin=None, Emax=None,
- capitals=None, clamp=None, flags=None, traps=None,
- _ignored_flags=None):
- # Set defaults; for everything except flags and _ignored_flags,
- # inherit from DefaultContext.
- try:
- dc = DefaultContext
- except NameError:
- pass
-
- self.prec = prec if prec is not None else dc.prec
- self.rounding = rounding if rounding is not None else dc.rounding
- self.Emin = Emin if Emin is not None else dc.Emin
- self.Emax = Emax if Emax is not None else dc.Emax
- self.capitals = capitals if capitals is not None else dc.capitals
- self.clamp = clamp if clamp is not None else dc.clamp
-
- if _ignored_flags is None:
- self._ignored_flags = []
- else:
- self._ignored_flags = _ignored_flags
-
- if traps is None:
- self.traps = dc.traps.copy()
- elif not isinstance(traps, dict):
- self.traps = dict((s, int(s in traps)) for s in _signals + traps)
- else:
- self.traps = traps
-
- if flags is None:
- self.flags = dict.fromkeys(_signals, 0)
- elif not isinstance(flags, dict):
- self.flags = dict((s, int(s in flags)) for s in _signals + flags)
- else:
- self.flags = flags
-
- def _set_integer_check(self, name, value, vmin, vmax):
- if not isinstance(value, int):
- raise TypeError("%s must be an integer" % name)
- if vmin == '-inf':
- if value > vmax:
- raise ValueError("%s must be in [%s, %d]. got: %s" % (name, vmin, vmax, value))
- elif vmax == 'inf':
- if value < vmin:
- raise ValueError("%s must be in [%d, %s]. got: %s" % (name, vmin, vmax, value))
- else:
- if value < vmin or value > vmax:
- raise ValueError("%s must be in [%d, %d]. got %s" % (name, vmin, vmax, value))
- return object.__setattr__(self, name, value)
-
- def _set_signal_dict(self, name, d):
- if not isinstance(d, dict):
- raise TypeError("%s must be a signal dict" % d)
- for key in d:
- if not key in _signals:
- raise KeyError("%s is not a valid signal dict" % d)
- for key in _signals:
- if not key in d:
- raise KeyError("%s is not a valid signal dict" % d)
- return object.__setattr__(self, name, d)
-
- def __setattr__(self, name, value):
- if name == 'prec':
- return self._set_integer_check(name, value, 1, 'inf')
- elif name == 'Emin':
- return self._set_integer_check(name, value, '-inf', 0)
- elif name == 'Emax':
- return self._set_integer_check(name, value, 0, 'inf')
- elif name == 'capitals':
- return self._set_integer_check(name, value, 0, 1)
- elif name == 'clamp':
- return self._set_integer_check(name, value, 0, 1)
- elif name == 'rounding':
- if not value in _rounding_modes:
- # raise TypeError even for strings to have consistency
- # among various implementations.
- raise TypeError("%s: invalid rounding mode" % value)
- return object.__setattr__(self, name, value)
- elif name == 'flags' or name == 'traps':
- return self._set_signal_dict(name, value)
- elif name == '_ignored_flags':
- return object.__setattr__(self, name, value)
- else:
- raise AttributeError(
- "'decimal.Context' object has no attribute '%s'" % name)
-
- def __delattr__(self, name):
- raise AttributeError("%s cannot be deleted" % name)
-
- # Support for pickling, copy, and deepcopy
- def __reduce__(self):
- flags = [sig for sig, v in self.flags.items() if v]
- traps = [sig for sig, v in self.traps.items() if v]
- return (self.__class__,
- (self.prec, self.rounding, self.Emin, self.Emax,
- self.capitals, self.clamp, flags, traps))
-
- def __repr__(self):
- """Show the current context."""
- s = []
- s.append('Context(prec=%(prec)d, rounding=%(rounding)s, '
- 'Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d, '
- 'clamp=%(clamp)d'
- % vars(self))
- names = [f.__name__ for f, v in self.flags.items() if v]
- s.append('flags=[' + ', '.join(names) + ']')
- names = [t.__name__ for t, v in self.traps.items() if v]
- s.append('traps=[' + ', '.join(names) + ']')
- return ', '.join(s) + ')'
-
- def clear_flags(self):
- """Reset all flags to zero"""
- for flag in self.flags:
- self.flags[flag] = 0
-
- def clear_traps(self):
- """Reset all traps to zero"""
- for flag in self.traps:
- self.traps[flag] = 0
-
- def _shallow_copy(self):
- """Returns a shallow copy from self."""
- nc = Context(self.prec, self.rounding, self.Emin, self.Emax,
- self.capitals, self.clamp, self.flags, self.traps,
- self._ignored_flags)
- return nc
-
- def copy(self):
- """Returns a deep copy from self."""
- nc = Context(self.prec, self.rounding, self.Emin, self.Emax,
- self.capitals, self.clamp,
- self.flags.copy(), self.traps.copy(),
- self._ignored_flags)
- return nc
- __copy__ = copy
-
- def _raise_error(self, condition, explanation = None, *args):
- """Handles an error
-
- If the flag is in _ignored_flags, returns the default response.
- Otherwise, it sets the flag, then, if the corresponding
- trap_enabler is set, it reraises the exception. Otherwise, it returns
- the default value after setting the flag.
- """
- error = _condition_map.get(condition, condition)
- if error in self._ignored_flags:
- # Don't touch the flag
- return error().handle(self, *args)
-
- self.flags[error] = 1
- if not self.traps[error]:
- # The errors define how to handle themselves.
- return condition().handle(self, *args)
-
- # Errors should only be risked on copies of the context
- # self._ignored_flags = []
- raise error(explanation)
-
- def _ignore_all_flags(self):
- """Ignore all flags, if they are raised"""
- return self._ignore_flags(*_signals)
-
- def _ignore_flags(self, *flags):
- """Ignore the flags, if they are raised"""
- # Do not mutate-- This way, copies of a context leave the original
- # alone.
- self._ignored_flags = (self._ignored_flags + list(flags))
- return list(flags)
-
- def _regard_flags(self, *flags):
- """Stop ignoring the flags, if they are raised"""
- if flags and isinstance(flags[0], (tuple,list)):
- flags = flags[0]
- for flag in flags:
- self._ignored_flags.remove(flag)
-
- # We inherit object.__hash__, so we must deny this explicitly
- __hash__ = None
-
- def Etiny(self):
- """Returns Etiny (= Emin - prec + 1)"""
- return int(self.Emin - self.prec + 1)
-
- def Etop(self):
- """Returns maximum exponent (= Emax - prec + 1)"""
- return int(self.Emax - self.prec + 1)
-
- def _set_rounding(self, type):
- """Sets the rounding type.
-
- Sets the rounding type, and returns the current (previous)
- rounding type. Often used like:
-
- context = context.copy()
- # so you don't change the calling context
- # if an error occurs in the middle.
- rounding = context._set_rounding(ROUND_UP)
- val = self.__sub__(other, context=context)
- context._set_rounding(rounding)
-
- This will make it round up for that operation.
- """
- rounding = self.rounding
- self.rounding= type
- return rounding
-
- def create_decimal(self, num='0'):
- """Creates a new Decimal instance but using self as context.
-
- This method implements the to-number operation of the
- IBM Decimal specification."""
-
- if isinstance(num, str) and num != num.strip():
- return self._raise_error(ConversionSyntax,
- "no trailing or leading whitespace is "
- "permitted.")
-
- d = Decimal(num, context=self)
- if d._isnan() and len(d._int) > self.prec - self.clamp:
- return self._raise_error(ConversionSyntax,
- "diagnostic info too long in NaN")
- return d._fix(self)
-
- 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 abs(self, a):
- """Returns the absolute value of the operand.
-
- If the operand is negative, the result is the same as using the minus
- operation on the operand. Otherwise, the result is the same as using
- the plus operation on the operand.
-
- >>> ExtendedContext.abs(Decimal('2.1'))
- Decimal('2.1')
- >>> ExtendedContext.abs(Decimal('-100'))
- Decimal('100')
- >>> ExtendedContext.abs(Decimal('101.5'))
- Decimal('101.5')
- >>> ExtendedContext.abs(Decimal('-101.5'))
- Decimal('101.5')
- >>> ExtendedContext.abs(-1)
- Decimal('1')
- """
- a = _convert_other(a, raiseit=True)
- return a.__abs__(context=self)
-
- def add(self, a, b):
- """Return the sum of the two operands.
-
- >>> ExtendedContext.add(Decimal('12'), Decimal('7.00'))
- Decimal('19.00')
- >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4'))
- Decimal('1.02E+4')
- >>> ExtendedContext.add(1, Decimal(2))
- Decimal('3')
- >>> ExtendedContext.add(Decimal(8), 5)
- Decimal('13')
- >>> ExtendedContext.add(5, 5)
- Decimal('10')
- """
- a = _convert_other(a, raiseit=True)
- r = a.__add__(b, context=self)
- if r is NotImplemented:
- raise TypeError("Unable to convert %s to Decimal" % b)
- else:
- return r
-
- def _apply(self, a):
- return str(a._fix(self))
-
- def canonical(self, a):
- """Returns the same Decimal object.
-
- As we do not have different encodings for the same number, the
- received object already is in its canonical form.
-
- >>> ExtendedContext.canonical(Decimal('2.50'))
- Decimal('2.50')
- """
- if not isinstance(a, Decimal):
- raise TypeError("canonical requires a Decimal as an argument.")
- return a.canonical()
-
- def compare(self, a, b):
- """Compares values numerically.
-
- If the signs of the operands differ, a value representing each operand
- ('-1' if the operand is less than zero, '0' if the operand is zero or
- negative zero, or '1' if the operand is greater than zero) is used in
- place of that operand for the comparison instead of the actual
- operand.
-
- The comparison is then effected by subtracting the second operand from
- the first and then returning a value according to the result of the
- subtraction: '-1' if the result is less than zero, '0' if the result is
- zero or negative zero, or '1' if the result is greater than zero.
-
- >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3'))
- Decimal('-1')
- >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1'))
- Decimal('0')
- >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10'))
- Decimal('0')
- >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1'))
- Decimal('1')
- >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3'))
- Decimal('1')
- >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1'))
- Decimal('-1')
- >>> ExtendedContext.compare(1, 2)
- Decimal('-1')
- >>> ExtendedContext.compare(Decimal(1), 2)
- Decimal('-1')
- >>> ExtendedContext.compare(1, Decimal(2))
- Decimal('-1')
- """
- a = _convert_other(a, raiseit=True)
- return a.compare(b, context=self)
-
- def compare_signal(self, a, b):
- """Compares the values of the two operands numerically.
-
- It's pretty much like compare(), but all NaNs signal, with signaling
- NaNs taking precedence over quiet NaNs.
-
- >>> c = ExtendedContext
- >>> c.compare_signal(Decimal('2.1'), Decimal('3'))
- Decimal('-1')
- >>> c.compare_signal(Decimal('2.1'), Decimal('2.1'))
- Decimal('0')
- >>> c.flags[InvalidOperation] = 0
- >>> print(c.flags[InvalidOperation])
- 0
- >>> c.compare_signal(Decimal('NaN'), Decimal('2.1'))
- Decimal('NaN')
- >>> print(c.flags[InvalidOperation])
- 1
- >>> c.flags[InvalidOperation] = 0
- >>> print(c.flags[InvalidOperation])
- 0
- >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1'))
- Decimal('NaN')
- >>> print(c.flags[InvalidOperation])
- 1
- >>> c.compare_signal(-1, 2)
- Decimal('-1')
- >>> c.compare_signal(Decimal(-1), 2)
- Decimal('-1')
- >>> c.compare_signal(-1, Decimal(2))
- Decimal('-1')
- """
- a = _convert_other(a, raiseit=True)
- return a.compare_signal(b, context=self)
-
- def compare_total(self, a, b):
- """Compares two operands using their abstract representation.
-
- This is not like the standard compare, which use their numerical
- value. Note that a total ordering is defined for all possible abstract
- representations.
-
- >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9'))
- Decimal('-1')
- >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12'))
- Decimal('-1')
- >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3'))
- Decimal('-1')
- >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30'))
- Decimal('0')
- >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300'))
- Decimal('1')
- >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN'))
- Decimal('-1')
- >>> ExtendedContext.compare_total(1, 2)
- Decimal('-1')
- >>> ExtendedContext.compare_total(Decimal(1), 2)
- Decimal('-1')
- >>> ExtendedContext.compare_total(1, Decimal(2))
- Decimal('-1')
- """
- a = _convert_other(a, raiseit=True)
- return a.compare_total(b)
-
- def compare_total_mag(self, a, b):
- """Compares two operands using their abstract representation ignoring sign.
-
- Like compare_total, but with operand's sign ignored and assumed to be 0.
- """
- a = _convert_other(a, raiseit=True)
- return a.compare_total_mag(b)
-
- def copy_abs(self, a):
- """Returns a copy of the operand with the sign set to 0.
-
- >>> ExtendedContext.copy_abs(Decimal('2.1'))
- Decimal('2.1')
- >>> ExtendedContext.copy_abs(Decimal('-100'))
- Decimal('100')
- >>> ExtendedContext.copy_abs(-1)
- Decimal('1')
- """
- a = _convert_other(a, raiseit=True)
- return a.copy_abs()
-
- def copy_decimal(self, a):
- """Returns a copy of the decimal object.
-
- >>> ExtendedContext.copy_decimal(Decimal('2.1'))
- Decimal('2.1')
- >>> ExtendedContext.copy_decimal(Decimal('-1.00'))
- Decimal('-1.00')
- >>> ExtendedContext.copy_decimal(1)
- Decimal('1')
- """
- a = _convert_other(a, raiseit=True)
- return Decimal(a)
-
- def copy_negate(self, a):
- """Returns a copy of the operand with the sign inverted.
-
- >>> ExtendedContext.copy_negate(Decimal('101.5'))
- Decimal('-101.5')
- >>> ExtendedContext.copy_negate(Decimal('-101.5'))
- Decimal('101.5')
- >>> ExtendedContext.copy_negate(1)
- Decimal('-1')
- """
- a = _convert_other(a, raiseit=True)
- return a.copy_negate()
-
- def copy_sign(self, a, b):
- """Copies the second operand's sign to the first one.
-
- In detail, it returns a copy of the first operand with the sign
- equal to the sign of the second operand.
-
- >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33'))
- Decimal('1.50')
- >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33'))
- Decimal('1.50')
- >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33'))
- Decimal('-1.50')
- >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33'))
- Decimal('-1.50')
- >>> ExtendedContext.copy_sign(1, -2)
- Decimal('-1')
- >>> ExtendedContext.copy_sign(Decimal(1), -2)
- Decimal('-1')
- >>> ExtendedContext.copy_sign(1, Decimal(-2))
- Decimal('-1')
- """
- a = _convert_other(a, raiseit=True)
- return a.copy_sign(b)
-
- def divide(self, a, b):
- """Decimal division in a specified context.
-
- >>> ExtendedContext.divide(Decimal('1'), Decimal('3'))
- Decimal('0.333333333')
- >>> ExtendedContext.divide(Decimal('2'), Decimal('3'))
- Decimal('0.666666667')
- >>> ExtendedContext.divide(Decimal('5'), Decimal('2'))
- Decimal('2.5')
- >>> ExtendedContext.divide(Decimal('1'), Decimal('10'))
- Decimal('0.1')
- >>> ExtendedContext.divide(Decimal('12'), Decimal('12'))
- Decimal('1')
- >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2'))
- Decimal('4.00')
- >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0'))
- Decimal('1.20')
- >>> ExtendedContext.divide(Decimal('1000'), Decimal('100'))
- Decimal('10')
- >>> ExtendedContext.divide(Decimal('1000'), Decimal('1'))
- Decimal('1000')
- >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2'))
- Decimal('1.20E+6')
- >>> ExtendedContext.divide(5, 5)
- Decimal('1')
- >>> ExtendedContext.divide(Decimal(5), 5)
- Decimal('1')
- >>> ExtendedContext.divide(5, Decimal(5))
- Decimal('1')
- """
- a = _convert_other(a, raiseit=True)
- r = a.__truediv__(b, context=self)
- if r is NotImplemented:
- raise TypeError("Unable to convert %s to Decimal" % b)
- else:
- return r
-
- def divide_int(self, a, b):
- """Divides two numbers and returns the integer part of the result.
-
- >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3'))
- Decimal('0')
- >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3'))
- Decimal('3')
- >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3'))
- Decimal('3')
- >>> ExtendedContext.divide_int(10, 3)
- Decimal('3')
- >>> ExtendedContext.divide_int(Decimal(10), 3)
- Decimal('3')
- >>> ExtendedContext.divide_int(10, Decimal(3))
- Decimal('3')
- """
- a = _convert_other(a, raiseit=True)
- r = a.__floordiv__(b, context=self)
- if r is NotImplemented:
- raise TypeError("Unable to convert %s to Decimal" % b)
- else:
- return r
-
- def divmod(self, a, b):
- """Return (a // b, a % b).
-
- >>> ExtendedContext.divmod(Decimal(8), Decimal(3))
- (Decimal('2'), Decimal('2'))
- >>> ExtendedContext.divmod(Decimal(8), Decimal(4))
- (Decimal('2'), Decimal('0'))
- >>> ExtendedContext.divmod(8, 4)
- (Decimal('2'), Decimal('0'))
- >>> ExtendedContext.divmod(Decimal(8), 4)
- (Decimal('2'), Decimal('0'))
- >>> ExtendedContext.divmod(8, Decimal(4))
- (Decimal('2'), Decimal('0'))
- """
- a = _convert_other(a, raiseit=True)
- r = a.__divmod__(b, context=self)
- if r is NotImplemented:
- raise TypeError("Unable to convert %s to Decimal" % b)
- else:
- return r
-
- def exp(self, a):
- """Returns e ** a.
-
- >>> c = ExtendedContext.copy()
- >>> c.Emin = -999
- >>> c.Emax = 999
- >>> c.exp(Decimal('-Infinity'))
- Decimal('0')
- >>> c.exp(Decimal('-1'))
- Decimal('0.367879441')
- >>> c.exp(Decimal('0'))
- Decimal('1')
- >>> c.exp(Decimal('1'))
- Decimal('2.71828183')
- >>> c.exp(Decimal('0.693147181'))
- Decimal('2.00000000')
- >>> c.exp(Decimal('+Infinity'))
- Decimal('Infinity')
- >>> c.exp(10)
- Decimal('22026.4658')
- """
- a =_convert_other(a, raiseit=True)
- return a.exp(context=self)
-
- def fma(self, a, b, c):
- """Returns a multiplied by b, plus c.
-
- The first two operands are multiplied together, using multiply,
- the third operand is then added to the result of that
- multiplication, using add, all with only one final rounding.
-
- >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7'))
- Decimal('22')
- >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7'))
- Decimal('-8')
- >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578'))
- Decimal('1.38435736E+12')
- >>> ExtendedContext.fma(1, 3, 4)
- Decimal('7')
- >>> ExtendedContext.fma(1, Decimal(3), 4)
- Decimal('7')
- >>> ExtendedContext.fma(1, 3, Decimal(4))
- Decimal('7')
- """
- a = _convert_other(a, raiseit=True)
- return a.fma(b, c, context=self)
-
- def is_canonical(self, a):
- """Return True if the operand is canonical; otherwise return False.
-
- Currently, the encoding of a Decimal instance is always
- canonical, so this method returns True for any Decimal.
-
- >>> ExtendedContext.is_canonical(Decimal('2.50'))
- True
- """
- if not isinstance(a, Decimal):
- raise TypeError("is_canonical requires a Decimal as an argument.")
- return a.is_canonical()
-
- def is_finite(self, a):
- """Return True if the operand is finite; otherwise return False.
-
- A Decimal instance is considered finite if it is neither
- infinite nor a NaN.
-
- >>> ExtendedContext.is_finite(Decimal('2.50'))
- True
- >>> ExtendedContext.is_finite(Decimal('-0.3'))
- True
- >>> ExtendedContext.is_finite(Decimal('0'))
- True
- >>> ExtendedContext.is_finite(Decimal('Inf'))
- False
- >>> ExtendedContext.is_finite(Decimal('NaN'))
- False
- >>> ExtendedContext.is_finite(1)
- True
- """
- a = _convert_other(a, raiseit=True)
- return a.is_finite()
-
- def is_infinite(self, a):
- """Return True if the operand is infinite; otherwise return False.
-
- >>> ExtendedContext.is_infinite(Decimal('2.50'))
- False
- >>> ExtendedContext.is_infinite(Decimal('-Inf'))
- True
- >>> ExtendedContext.is_infinite(Decimal('NaN'))
- False
- >>> ExtendedContext.is_infinite(1)
- False
- """
- a = _convert_other(a, raiseit=True)
- return a.is_infinite()
-
- def is_nan(self, a):
- """Return True if the operand is a qNaN or sNaN;
- otherwise return False.
-
- >>> ExtendedContext.is_nan(Decimal('2.50'))
- False
- >>> ExtendedContext.is_nan(Decimal('NaN'))
- True
- >>> ExtendedContext.is_nan(Decimal('-sNaN'))
- True
- >>> ExtendedContext.is_nan(1)
- False
- """
- a = _convert_other(a, raiseit=True)
- return a.is_nan()
-
- def is_normal(self, a):
- """Return True if the operand is a normal number;
- otherwise return False.
-
- >>> c = ExtendedContext.copy()
- >>> c.Emin = -999
- >>> c.Emax = 999
- >>> c.is_normal(Decimal('2.50'))
- True
- >>> c.is_normal(Decimal('0.1E-999'))
- False
- >>> c.is_normal(Decimal('0.00'))
- False
- >>> c.is_normal(Decimal('-Inf'))
- False
- >>> c.is_normal(Decimal('NaN'))
- False
- >>> c.is_normal(1)
- True
- """
- a = _convert_other(a, raiseit=True)
- return a.is_normal(context=self)
-
- def is_qnan(self, a):
- """Return True if the operand is a quiet NaN; otherwise return False.
-
- >>> ExtendedContext.is_qnan(Decimal('2.50'))
- False
- >>> ExtendedContext.is_qnan(Decimal('NaN'))
- True
- >>> ExtendedContext.is_qnan(Decimal('sNaN'))
- False
- >>> ExtendedContext.is_qnan(1)
- False
- """
- a = _convert_other(a, raiseit=True)
- return a.is_qnan()
-
- def is_signed(self, a):
- """Return True if the operand is negative; otherwise return False.
-
- >>> ExtendedContext.is_signed(Decimal('2.50'))
- False
- >>> ExtendedContext.is_signed(Decimal('-12'))
- True
- >>> ExtendedContext.is_signed(Decimal('-0'))
- True
- >>> ExtendedContext.is_signed(8)
- False
- >>> ExtendedContext.is_signed(-8)
- True
- """
- a = _convert_other(a, raiseit=True)
- return a.is_signed()
-
- def is_snan(self, a):
- """Return True if the operand is a signaling NaN;
- otherwise return False.
-
- >>> ExtendedContext.is_snan(Decimal('2.50'))
- False
- >>> ExtendedContext.is_snan(Decimal('NaN'))
- False
- >>> ExtendedContext.is_snan(Decimal('sNaN'))
- True
- >>> ExtendedContext.is_snan(1)
- False
- """
- a = _convert_other(a, raiseit=True)
- return a.is_snan()
-
- def is_subnormal(self, a):
- """Return True if the operand is subnormal; otherwise return False.
-
- >>> c = ExtendedContext.copy()
- >>> c.Emin = -999
- >>> c.Emax = 999
- >>> c.is_subnormal(Decimal('2.50'))
- False
- >>> c.is_subnormal(Decimal('0.1E-999'))
- True
- >>> c.is_subnormal(Decimal('0.00'))
- False
- >>> c.is_subnormal(Decimal('-Inf'))
- False
- >>> c.is_subnormal(Decimal('NaN'))
- False
- >>> c.is_subnormal(1)
- False
- """
- a = _convert_other(a, raiseit=True)
- return a.is_subnormal(context=self)
-
- def is_zero(self, a):
- """Return True if the operand is a zero; otherwise return False.
-
- >>> ExtendedContext.is_zero(Decimal('0'))
- True
- >>> ExtendedContext.is_zero(Decimal('2.50'))
- False
- >>> ExtendedContext.is_zero(Decimal('-0E+2'))
- True
- >>> ExtendedContext.is_zero(1)
- False
- >>> ExtendedContext.is_zero(0)
- True
- """
- a = _convert_other(a, raiseit=True)
- return a.is_zero()
-
- def ln(self, a):
- """Returns the natural (base e) logarithm of the operand.
-
- >>> c = ExtendedContext.copy()
- >>> c.Emin = -999
- >>> c.Emax = 999
- >>> c.ln(Decimal('0'))
- Decimal('-Infinity')
- >>> c.ln(Decimal('1.000'))
- Decimal('0')
- >>> c.ln(Decimal('2.71828183'))
- Decimal('1.00000000')
- >>> c.ln(Decimal('10'))
- Decimal('2.30258509')
- >>> c.ln(Decimal('+Infinity'))
- Decimal('Infinity')
- >>> c.ln(1)
- Decimal('0')
- """
- a = _convert_other(a, raiseit=True)
- return a.ln(context=self)
-
- def log10(self, a):
- """Returns the base 10 logarithm of the operand.
-
- >>> c = ExtendedContext.copy()
- >>> c.Emin = -999
- >>> c.Emax = 999
- >>> c.log10(Decimal('0'))
- Decimal('-Infinity')
- >>> c.log10(Decimal('0.001'))
- Decimal('-3')
- >>> c.log10(Decimal('1.000'))
- Decimal('0')
- >>> c.log10(Decimal('2'))
- Decimal('0.301029996')
- >>> c.log10(Decimal('10'))
- Decimal('1')
- >>> c.log10(Decimal('70'))
- Decimal('1.84509804')
- >>> c.log10(Decimal('+Infinity'))
- Decimal('Infinity')
- >>> c.log10(0)
- Decimal('-Infinity')
- >>> c.log10(1)
- Decimal('0')
- """
- a = _convert_other(a, raiseit=True)
- return a.log10(context=self)
-
- def logb(self, a):
- """ Returns the exponent of the magnitude of the operand's MSD.
-
- The result is the integer which is the exponent of the magnitude
- of the most significant digit of the operand (as though the
- operand were truncated to a single digit while maintaining the
- value of that digit and without limiting the resulting exponent).
-
- >>> ExtendedContext.logb(Decimal('250'))
- Decimal('2')
- >>> ExtendedContext.logb(Decimal('2.50'))
- Decimal('0')
- >>> ExtendedContext.logb(Decimal('0.03'))
- Decimal('-2')
- >>> ExtendedContext.logb(Decimal('0'))
- Decimal('-Infinity')
- >>> ExtendedContext.logb(1)
- Decimal('0')
- >>> ExtendedContext.logb(10)
- Decimal('1')
- >>> ExtendedContext.logb(100)
- Decimal('2')
- """
- a = _convert_other(a, raiseit=True)
- return a.logb(context=self)
-
- def logical_and(self, a, b):
- """Applies the logical operation 'and' between each operand's digits.
-
- The operands must be both logical numbers.
-
- >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0'))
- Decimal('0')
- >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1'))
- Decimal('0')
- >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0'))
- Decimal('0')
- >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1'))
- Decimal('1')
- >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010'))
- Decimal('1000')
- >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10'))
- Decimal('10')
- >>> ExtendedContext.logical_and(110, 1101)
- Decimal('100')
- >>> ExtendedContext.logical_and(Decimal(110), 1101)
- Decimal('100')
- >>> ExtendedContext.logical_and(110, Decimal(1101))
- Decimal('100')
- """
- a = _convert_other(a, raiseit=True)
- return a.logical_and(b, context=self)
-
- def logical_invert(self, a):
- """Invert all the digits in the operand.
-
- The operand must be a logical number.
-
- >>> ExtendedContext.logical_invert(Decimal('0'))
- Decimal('111111111')
- >>> ExtendedContext.logical_invert(Decimal('1'))
- Decimal('111111110')
- >>> ExtendedContext.logical_invert(Decimal('111111111'))
- Decimal('0')
- >>> ExtendedContext.logical_invert(Decimal('101010101'))
- Decimal('10101010')
- >>> ExtendedContext.logical_invert(1101)
- Decimal('111110010')
- """
- a = _convert_other(a, raiseit=True)
- return a.logical_invert(context=self)
-
- def logical_or(self, a, b):
- """Applies the logical operation 'or' between each operand's digits.
-
- The operands must be both logical numbers.
-
- >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0'))
- Decimal('0')
- >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1'))
- Decimal('1')
- >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0'))
- Decimal('1')
- >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1'))
- Decimal('1')
- >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010'))
- Decimal('1110')
- >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10'))
- Decimal('1110')
- >>> ExtendedContext.logical_or(110, 1101)
- Decimal('1111')
- >>> ExtendedContext.logical_or(Decimal(110), 1101)
- Decimal('1111')
- >>> ExtendedContext.logical_or(110, Decimal(1101))
- Decimal('1111')
- """
- a = _convert_other(a, raiseit=True)
- return a.logical_or(b, context=self)
-
- def logical_xor(self, a, b):
- """Applies the logical operation 'xor' between each operand's digits.
-
- The operands must be both logical numbers.
-
- >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0'))
- Decimal('0')
- >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1'))
- Decimal('1')
- >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0'))
- Decimal('1')
- >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1'))
- Decimal('0')
- >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010'))
- Decimal('110')
- >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10'))
- Decimal('1101')
- >>> ExtendedContext.logical_xor(110, 1101)
- Decimal('1011')
- >>> ExtendedContext.logical_xor(Decimal(110), 1101)
- Decimal('1011')
- >>> ExtendedContext.logical_xor(110, Decimal(1101))
- Decimal('1011')
- """
- a = _convert_other(a, raiseit=True)
- return a.logical_xor(b, context=self)
-
- def max(self, a, b):
- """max compares two values numerically and returns the maximum.
-
- If either operand is a NaN then the general rules apply.
- Otherwise, the operands are compared as though by the compare
- operation. If they are numerically equal then the left-hand operand
- is chosen as the result. Otherwise the maximum (closer to positive
- infinity) of the two operands is chosen as the result.
-
- >>> ExtendedContext.max(Decimal('3'), Decimal('2'))
- Decimal('3')
- >>> ExtendedContext.max(Decimal('-10'), Decimal('3'))
- Decimal('3')
- >>> ExtendedContext.max(Decimal('1.0'), Decimal('1'))
- Decimal('1')
- >>> ExtendedContext.max(Decimal('7'), Decimal('NaN'))
- Decimal('7')
- >>> ExtendedContext.max(1, 2)
- Decimal('2')
- >>> ExtendedContext.max(Decimal(1), 2)
- Decimal('2')
- >>> ExtendedContext.max(1, Decimal(2))
- Decimal('2')
- """
- a = _convert_other(a, raiseit=True)
- return a.max(b, context=self)
-
- def max_mag(self, a, b):
- """Compares the values numerically with their sign ignored.
-
- >>> ExtendedContext.max_mag(Decimal('7'), Decimal('NaN'))
- Decimal('7')
- >>> ExtendedContext.max_mag(Decimal('7'), Decimal('-10'))
- Decimal('-10')
- >>> ExtendedContext.max_mag(1, -2)
- Decimal('-2')
- >>> ExtendedContext.max_mag(Decimal(1), -2)
- Decimal('-2')
- >>> ExtendedContext.max_mag(1, Decimal(-2))
- Decimal('-2')
- """
- a = _convert_other(a, raiseit=True)
- return a.max_mag(b, context=self)
-
- def min(self, a, b):
- """min compares two values numerically and returns the minimum.
-
- If either operand is a NaN then the general rules apply.
- Otherwise, the operands are compared as though by the compare
- operation. If they are numerically equal then the left-hand operand
- is chosen as the result. Otherwise the minimum (closer to negative
- infinity) of the two operands is chosen as the result.
-
- >>> ExtendedContext.min(Decimal('3'), Decimal('2'))
- Decimal('2')
- >>> ExtendedContext.min(Decimal('-10'), Decimal('3'))
- Decimal('-10')
- >>> ExtendedContext.min(Decimal('1.0'), Decimal('1'))
- Decimal('1.0')
- >>> ExtendedContext.min(Decimal('7'), Decimal('NaN'))
- Decimal('7')
- >>> ExtendedContext.min(1, 2)
- Decimal('1')
- >>> ExtendedContext.min(Decimal(1), 2)
- Decimal('1')
- >>> ExtendedContext.min(1, Decimal(29))
- Decimal('1')
- """
- a = _convert_other(a, raiseit=True)
- return a.min(b, context=self)
-
- def min_mag(self, a, b):
- """Compares the values numerically with their sign ignored.
-
- >>> ExtendedContext.min_mag(Decimal('3'), Decimal('-2'))
- Decimal('-2')
- >>> ExtendedContext.min_mag(Decimal('-3'), Decimal('NaN'))
- Decimal('-3')
- >>> ExtendedContext.min_mag(1, -2)
- Decimal('1')
- >>> ExtendedContext.min_mag(Decimal(1), -2)
- Decimal('1')
- >>> ExtendedContext.min_mag(1, Decimal(-2))
- Decimal('1')
- """
- a = _convert_other(a, raiseit=True)
- return a.min_mag(b, context=self)
-
- def minus(self, a):
- """Minus corresponds to unary prefix minus in Python.
-
- The operation is evaluated using the same rules as subtract; the
- operation minus(a) is calculated as subtract('0', a) where the '0'
- has the same exponent as the operand.
-
- >>> ExtendedContext.minus(Decimal('1.3'))
- Decimal('-1.3')
- >>> ExtendedContext.minus(Decimal('-1.3'))
- Decimal('1.3')
- >>> ExtendedContext.minus(1)
- Decimal('-1')
- """
- a = _convert_other(a, raiseit=True)
- return a.__neg__(context=self)
-
- def multiply(self, a, b):
- """multiply multiplies two operands.
-
- If either operand is a special value then the general rules apply.
- Otherwise, the operands are multiplied together
- ('long multiplication'), resulting in a number which may be as long as
- the sum of the lengths of the two operands.
-
- >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3'))
- Decimal('3.60')
- >>> ExtendedContext.multiply(Decimal('7'), Decimal('3'))
- Decimal('21')
- >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8'))
- Decimal('0.72')
- >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0'))
- Decimal('-0.0')
- >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321'))
- Decimal('4.28135971E+11')
- >>> ExtendedContext.multiply(7, 7)
- Decimal('49')
- >>> ExtendedContext.multiply(Decimal(7), 7)
- Decimal('49')
- >>> ExtendedContext.multiply(7, Decimal(7))
- Decimal('49')
- """
- a = _convert_other(a, raiseit=True)
- r = a.__mul__(b, context=self)
- if r is NotImplemented:
- raise TypeError("Unable to convert %s to Decimal" % b)
- else:
- return r
-
- def next_minus(self, a):
- """Returns the largest representable number smaller than a.
-
- >>> c = ExtendedContext.copy()
- >>> c.Emin = -999
- >>> c.Emax = 999
- >>> ExtendedContext.next_minus(Decimal('1'))
- Decimal('0.999999999')
- >>> c.next_minus(Decimal('1E-1007'))
- Decimal('0E-1007')
- >>> ExtendedContext.next_minus(Decimal('-1.00000003'))
- Decimal('-1.00000004')
- >>> c.next_minus(Decimal('Infinity'))
- Decimal('9.99999999E+999')
- >>> c.next_minus(1)
- Decimal('0.999999999')
- """
- a = _convert_other(a, raiseit=True)
- return a.next_minus(context=self)
-
- def next_plus(self, a):
- """Returns the smallest representable number larger than a.
-
- >>> c = ExtendedContext.copy()
- >>> c.Emin = -999
- >>> c.Emax = 999
- >>> ExtendedContext.next_plus(Decimal('1'))
- Decimal('1.00000001')
- >>> c.next_plus(Decimal('-1E-1007'))
- Decimal('-0E-1007')
- >>> ExtendedContext.next_plus(Decimal('-1.00000003'))
- Decimal('-1.00000002')
- >>> c.next_plus(Decimal('-Infinity'))
- Decimal('-9.99999999E+999')
- >>> c.next_plus(1)
- Decimal('1.00000001')
- """
- a = _convert_other(a, raiseit=True)
- return a.next_plus(context=self)
-
- def next_toward(self, a, b):
- """Returns the number closest to a, in direction towards b.
-
- The result is the closest representable number from the first
- operand (but not the first operand) that is in the direction
- towards the second operand, unless the operands have the same
- value.
-
- >>> c = ExtendedContext.copy()
- >>> c.Emin = -999
- >>> c.Emax = 999
- >>> c.next_toward(Decimal('1'), Decimal('2'))
- Decimal('1.00000001')
- >>> c.next_toward(Decimal('-1E-1007'), Decimal('1'))
- Decimal('-0E-1007')
- >>> c.next_toward(Decimal('-1.00000003'), Decimal('0'))
- Decimal('-1.00000002')
- >>> c.next_toward(Decimal('1'), Decimal('0'))
- Decimal('0.999999999')
- >>> c.next_toward(Decimal('1E-1007'), Decimal('-100'))
- Decimal('0E-1007')
- >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10'))
- Decimal('-1.00000004')
- >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000'))
- Decimal('-0.00')
- >>> c.next_toward(0, 1)
- Decimal('1E-1007')
- >>> c.next_toward(Decimal(0), 1)
- Decimal('1E-1007')
- >>> c.next_toward(0, Decimal(1))
- Decimal('1E-1007')
- """
- a = _convert_other(a, raiseit=True)
- return a.next_toward(b, context=self)
-
- def normalize(self, a):
- """normalize reduces an operand to its simplest form.
-
- Essentially a plus operation with all trailing zeros removed from the
- result.
-
- >>> ExtendedContext.normalize(Decimal('2.1'))
- Decimal('2.1')
- >>> ExtendedContext.normalize(Decimal('-2.0'))
- Decimal('-2')
- >>> ExtendedContext.normalize(Decimal('1.200'))
- Decimal('1.2')
- >>> ExtendedContext.normalize(Decimal('-120'))
- Decimal('-1.2E+2')
- >>> ExtendedContext.normalize(Decimal('120.00'))
- Decimal('1.2E+2')
- >>> ExtendedContext.normalize(Decimal('0.00'))
- Decimal('0')
- >>> ExtendedContext.normalize(6)
- Decimal('6')
- """
- a = _convert_other(a, raiseit=True)
- return a.normalize(context=self)
-
- def number_class(self, a):
- """Returns an indication of the class of the operand.
-
- The class is one of the following strings:
- -sNaN
- -NaN
- -Infinity
- -Normal
- -Subnormal
- -Zero
- +Zero
- +Subnormal
- +Normal
- +Infinity
-
- >>> c = ExtendedContext.copy()
- >>> c.Emin = -999
- >>> c.Emax = 999
- >>> c.number_class(Decimal('Infinity'))
- '+Infinity'
- >>> c.number_class(Decimal('1E-10'))
- '+Normal'
- >>> c.number_class(Decimal('2.50'))
- '+Normal'
- >>> c.number_class(Decimal('0.1E-999'))
- '+Subnormal'
- >>> c.number_class(Decimal('0'))
- '+Zero'
- >>> c.number_class(Decimal('-0'))
- '-Zero'
- >>> c.number_class(Decimal('-0.1E-999'))
- '-Subnormal'
- >>> c.number_class(Decimal('-1E-10'))
- '-Normal'
- >>> c.number_class(Decimal('-2.50'))
- '-Normal'
- >>> c.number_class(Decimal('-Infinity'))
- '-Infinity'
- >>> c.number_class(Decimal('NaN'))
- 'NaN'
- >>> c.number_class(Decimal('-NaN'))
- 'NaN'
- >>> c.number_class(Decimal('sNaN'))
- 'sNaN'
- >>> c.number_class(123)
- '+Normal'
- """
- a = _convert_other(a, raiseit=True)
- return a.number_class(context=self)
-
- def plus(self, a):
- """Plus corresponds to unary prefix plus in Python.
-
- The operation is evaluated using the same rules as add; the
- operation plus(a) is calculated as add('0', a) where the '0'
- has the same exponent as the operand.
-
- >>> ExtendedContext.plus(Decimal('1.3'))
- Decimal('1.3')
- >>> ExtendedContext.plus(Decimal('-1.3'))
- Decimal('-1.3')
- >>> ExtendedContext.plus(-1)
- Decimal('-1')
- """
- a = _convert_other(a, raiseit=True)
- return a.__pos__(context=self)
-
- def power(self, a, b, modulo=None):
- """Raises a to the power of b, to modulo if given.
-
- With two arguments, compute a**b. If a is negative then b
- must be integral. The result will be inexact unless b is
- integral and the result is finite and can be expressed exactly
- in 'precision' digits.
-
- With three arguments, compute (a**b) % modulo. For the
- three argument form, the following restrictions on the
- arguments hold:
-
- - all three arguments must be integral
- - b must be nonnegative
- - at least one of a or b must be nonzero
- - modulo must be nonzero and have at most 'precision' digits
-
- The result of pow(a, b, modulo) is identical to the result
- that would be obtained by computing (a**b) % modulo with
- unbounded precision, but is computed more efficiently. It is
- always exact.
-
- >>> c = ExtendedContext.copy()
- >>> c.Emin = -999
- >>> c.Emax = 999
- >>> c.power(Decimal('2'), Decimal('3'))
- Decimal('8')
- >>> c.power(Decimal('-2'), Decimal('3'))
- Decimal('-8')
- >>> c.power(Decimal('2'), Decimal('-3'))
- Decimal('0.125')
- >>> c.power(Decimal('1.7'), Decimal('8'))
- Decimal('69.7575744')
- >>> c.power(Decimal('10'), Decimal('0.301029996'))
- Decimal('2.00000000')
- >>> c.power(Decimal('Infinity'), Decimal('-1'))
- Decimal('0')
- >>> c.power(Decimal('Infinity'), Decimal('0'))
- Decimal('1')
- >>> c.power(Decimal('Infinity'), Decimal('1'))
- Decimal('Infinity')
- >>> c.power(Decimal('-Infinity'), Decimal('-1'))
- Decimal('-0')
- >>> c.power(Decimal('-Infinity'), Decimal('0'))
- Decimal('1')
- >>> c.power(Decimal('-Infinity'), Decimal('1'))
- Decimal('-Infinity')
- >>> c.power(Decimal('-Infinity'), Decimal('2'))
- Decimal('Infinity')
- >>> c.power(Decimal('0'), Decimal('0'))
- Decimal('NaN')
-
- >>> c.power(Decimal('3'), Decimal('7'), Decimal('16'))
- Decimal('11')
- >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16'))
- Decimal('-11')
- >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16'))
- Decimal('1')
- >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16'))
- Decimal('11')
- >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789'))
- Decimal('11729830')
- >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729'))
- Decimal('-0')
- >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537'))
- Decimal('1')
- >>> ExtendedContext.power(7, 7)
- Decimal('823543')
- >>> ExtendedContext.power(Decimal(7), 7)
- Decimal('823543')
- >>> ExtendedContext.power(7, Decimal(7), 2)
- Decimal('1')
- """
- a = _convert_other(a, raiseit=True)
- r = a.__pow__(b, modulo, context=self)
- if r is NotImplemented:
- raise TypeError("Unable to convert %s to Decimal" % b)
- else:
- return r
-
- def quantize(self, a, b):
- """Returns a value equal to 'a' (rounded), having the exponent of 'b'.
-
- The coefficient of the result is derived from that of the left-hand
- operand. It may be rounded using the current rounding setting (if the
- exponent is being increased), multiplied by a positive power of ten (if
- the exponent is being decreased), or is unchanged (if the exponent is
- already equal to that of the right-hand operand).
-
- Unlike other operations, if the length of the coefficient after the
- quantize operation would be greater than precision then an Invalid
- operation condition is raised. This guarantees that, unless there is
- an error condition, the exponent of the result of a quantize is always
- equal to that of the right-hand operand.
-
- Also unlike other operations, quantize will never raise Underflow, even
- if the result is subnormal and inexact.
-
- >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001'))
- Decimal('2.170')
- >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01'))
- Decimal('2.17')
- >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1'))
- Decimal('2.2')
- >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0'))
- Decimal('2')
- >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1'))
- Decimal('0E+1')
- >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity'))
- Decimal('-Infinity')
- >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity'))
- Decimal('NaN')
- >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1'))
- Decimal('-0')
- >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5'))
- Decimal('-0E+5')
- >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2'))
- Decimal('NaN')
- >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2'))
- Decimal('NaN')
- >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1'))
- Decimal('217.0')
- >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0'))
- Decimal('217')
- >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1'))
- Decimal('2.2E+2')
- >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2'))
- Decimal('2E+2')
- >>> ExtendedContext.quantize(1, 2)
- Decimal('1')
- >>> ExtendedContext.quantize(Decimal(1), 2)
- Decimal('1')
- >>> ExtendedContext.quantize(1, Decimal(2))
- Decimal('1')
- """
- a = _convert_other(a, raiseit=True)
- return a.quantize(b, context=self)
-
- def radix(self):
- """Just returns 10, as this is Decimal, :)
-
- >>> ExtendedContext.radix()
- Decimal('10')
- """
- return Decimal(10)
-
- def remainder(self, a, b):
- """Returns the remainder from integer division.
-
- The result is the residue of the dividend after the operation of
- calculating integer division as described for divide-integer, rounded
- to precision digits if necessary. The sign of the result, if
- non-zero, is the same as that of the original dividend.
-
- This operation will fail under the same conditions as integer division
- (that is, if integer division on the same two operands would fail, the
- remainder cannot be calculated).
-
- >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3'))
- Decimal('2.1')
- >>> ExtendedContext.remainder(Decimal('10'), Decimal('3'))
- Decimal('1')
- >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3'))
- Decimal('-1')
- >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1'))
- Decimal('0.2')
- >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3'))
- Decimal('0.1')
- >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3'))
- Decimal('1.0')
- >>> ExtendedContext.remainder(22, 6)
- Decimal('4')
- >>> ExtendedContext.remainder(Decimal(22), 6)
- Decimal('4')
- >>> ExtendedContext.remainder(22, Decimal(6))
- Decimal('4')
- """
- a = _convert_other(a, raiseit=True)
- r = a.__mod__(b, context=self)
- if r is NotImplemented:
- raise TypeError("Unable to convert %s to Decimal" % b)
- else:
- return r
-
- def remainder_near(self, a, b):
- """Returns to be "a - b * n", where n is the integer nearest the exact
- value of "x / b" (if two integers are equally near then the even one
- is chosen). If the result is equal to 0 then its sign will be the
- sign of a.
-
- This operation will fail under the same conditions as integer division
- (that is, if integer division on the same two operands would fail, the
- remainder cannot be calculated).
-
- >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3'))
- Decimal('-0.9')
- >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6'))
- Decimal('-2')
- >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3'))
- Decimal('1')
- >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3'))
- Decimal('-1')
- >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1'))
- Decimal('0.2')
- >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3'))
- Decimal('0.1')
- >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3'))
- Decimal('-0.3')
- >>> ExtendedContext.remainder_near(3, 11)
- Decimal('3')
- >>> ExtendedContext.remainder_near(Decimal(3), 11)
- Decimal('3')
- >>> ExtendedContext.remainder_near(3, Decimal(11))
- Decimal('3')
- """
- a = _convert_other(a, raiseit=True)
- return a.remainder_near(b, context=self)
-
- def rotate(self, a, b):
- """Returns a rotated copy of a, b times.
-
- The coefficient of the result is a rotated copy of the digits in
- the coefficient of the first operand. The number of places of
- rotation is taken from the absolute value of the second operand,
- with the rotation being to the left if the second operand is
- positive or to the right otherwise.
-
- >>> ExtendedContext.rotate(Decimal('34'), Decimal('8'))
- Decimal('400000003')
- >>> ExtendedContext.rotate(Decimal('12'), Decimal('9'))
- Decimal('12')
- >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2'))
- Decimal('891234567')
- >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0'))
- Decimal('123456789')
- >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2'))
- Decimal('345678912')
- >>> ExtendedContext.rotate(1333333, 1)
- Decimal('13333330')
- >>> ExtendedContext.rotate(Decimal(1333333), 1)
- Decimal('13333330')
- >>> ExtendedContext.rotate(1333333, Decimal(1))
- Decimal('13333330')
- """
- a = _convert_other(a, raiseit=True)
- return a.rotate(b, context=self)
-
- def same_quantum(self, a, b):
- """Returns True if the two operands have the same exponent.
-
- The result is never affected by either the sign or the coefficient of
- either operand.
-
- >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001'))
- False
- >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01'))
- True
- >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1'))
- False
- >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf'))
- True
- >>> ExtendedContext.same_quantum(10000, -1)
- True
- >>> ExtendedContext.same_quantum(Decimal(10000), -1)
- True
- >>> ExtendedContext.same_quantum(10000, Decimal(-1))
- True
- """
- a = _convert_other(a, raiseit=True)
- return a.same_quantum(b)
-
- def scaleb (self, a, b):
- """Returns the first operand after adding the second value its exp.
-
- >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2'))
- Decimal('0.0750')
- >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0'))
- Decimal('7.50')
- >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3'))
- Decimal('7.50E+3')
- >>> ExtendedContext.scaleb(1, 4)
- Decimal('1E+4')
- >>> ExtendedContext.scaleb(Decimal(1), 4)
- Decimal('1E+4')
- >>> ExtendedContext.scaleb(1, Decimal(4))
- Decimal('1E+4')
- """
- a = _convert_other(a, raiseit=True)
- return a.scaleb(b, context=self)
-
- def shift(self, a, b):
- """Returns a shifted copy of a, b times.
-
- The coefficient of the result is a shifted copy of the digits
- in the coefficient of the first operand. The number of places
- to shift is taken from the absolute value of the second operand,
- with the shift being to the left if the second operand is
- positive or to the right otherwise. Digits shifted into the
- coefficient are zeros.
-
- >>> ExtendedContext.shift(Decimal('34'), Decimal('8'))
- Decimal('400000000')
- >>> ExtendedContext.shift(Decimal('12'), Decimal('9'))
- Decimal('0')
- >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2'))
- Decimal('1234567')
- >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0'))
- Decimal('123456789')
- >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2'))
- Decimal('345678900')
- >>> ExtendedContext.shift(88888888, 2)
- Decimal('888888800')
- >>> ExtendedContext.shift(Decimal(88888888), 2)
- Decimal('888888800')
- >>> ExtendedContext.shift(88888888, Decimal(2))
- Decimal('888888800')
- """
- a = _convert_other(a, raiseit=True)
- return a.shift(b, context=self)
-
- def sqrt(self, a):
- """Square root of a non-negative number to context precision.
-
- If the result must be inexact, it is rounded using the round-half-even
- algorithm.
-
- >>> ExtendedContext.sqrt(Decimal('0'))
- Decimal('0')
- >>> ExtendedContext.sqrt(Decimal('-0'))
- Decimal('-0')
- >>> ExtendedContext.sqrt(Decimal('0.39'))
- Decimal('0.624499800')
- >>> ExtendedContext.sqrt(Decimal('100'))
- Decimal('10')
- >>> ExtendedContext.sqrt(Decimal('1'))
- Decimal('1')
- >>> ExtendedContext.sqrt(Decimal('1.0'))
- Decimal('1.0')
- >>> ExtendedContext.sqrt(Decimal('1.00'))
- Decimal('1.0')
- >>> ExtendedContext.sqrt(Decimal('7'))
- Decimal('2.64575131')
- >>> ExtendedContext.sqrt(Decimal('10'))
- Decimal('3.16227766')
- >>> ExtendedContext.sqrt(2)
- Decimal('1.41421356')
- >>> ExtendedContext.prec
- 9
- """
- a = _convert_other(a, raiseit=True)
- return a.sqrt(context=self)
-
- def subtract(self, a, b):
- """Return the difference between the two operands.
-
- >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07'))
- Decimal('0.23')
- >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30'))
- Decimal('0.00')
- >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07'))
- Decimal('-0.77')
- >>> ExtendedContext.subtract(8, 5)
- Decimal('3')
- >>> ExtendedContext.subtract(Decimal(8), 5)
- Decimal('3')
- >>> ExtendedContext.subtract(8, Decimal(5))
- Decimal('3')
- """
- a = _convert_other(a, raiseit=True)
- r = a.__sub__(b, context=self)
- if r is NotImplemented:
- raise TypeError("Unable to convert %s to Decimal" % b)
- else:
- return r
-
- def to_eng_string(self, a):
- """Converts a number to a string, using scientific notation.
-
- The operation is not affected by the context.
- """
- a = _convert_other(a, raiseit=True)
- return a.to_eng_string(context=self)
-
- def to_sci_string(self, a):
- """Converts a number to a string, using scientific notation.
-
- The operation is not affected by the context.
- """
- a = _convert_other(a, raiseit=True)
- return a.__str__(context=self)
-
- 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_value(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, except that no flags will
- be set. The rounding mode is taken from the context.
-
- >>> ExtendedContext.to_integral_value(Decimal('2.1'))
- Decimal('2')
- >>> ExtendedContext.to_integral_value(Decimal('100'))
- Decimal('100')
- >>> ExtendedContext.to_integral_value(Decimal('100.0'))
- Decimal('100')
- >>> ExtendedContext.to_integral_value(Decimal('101.5'))
- Decimal('102')
- >>> ExtendedContext.to_integral_value(Decimal('-101.5'))
- Decimal('-102')
- >>> ExtendedContext.to_integral_value(Decimal('10E+5'))
- Decimal('1.0E+6')
- >>> ExtendedContext.to_integral_value(Decimal('7.89E+77'))
- Decimal('7.89E+77')
- >>> ExtendedContext.to_integral_value(Decimal('-Inf'))
- Decimal('-Infinity')
- """
- a = _convert_other(a, raiseit=True)
- return a.to_integral_value(context=self)
-
- # the method name changed, but we provide also the old one, for compatibility
- to_integral = to_integral_value
-
-class _WorkRep(object):
- __slots__ = ('sign','int','exp')
- # sign: 0 or 1
- # int: int
- # exp: None, int, or string
-
- def __init__(self, value=None):
- if value is None:
- self.sign = None
- self.int = 0
- self.exp = None
- elif isinstance(value, Decimal):
- self.sign = value._sign
- self.int = int(value._int)
- self.exp = value._exp
- else:
- # assert isinstance(value, tuple)
- self.sign = value[0]
- self.int = value[1]
- self.exp = value[2]
-
- def __repr__(self):
- return "(%r, %r, %r)" % (self.sign, self.int, self.exp)
-
- __str__ = __repr__
-
-
-
-def _normalize(op1, op2, prec = 0):
- """Normalizes op1, op2 to have the same exp and length of coefficient.
-
- Done during addition.
- """
- if op1.exp < op2.exp:
- tmp = op2
- other = op1
- else:
- tmp = op1
- other = op2
-
- # Let exp = min(tmp.exp - 1, tmp.adjusted() - precision - 1).
- # Then adding 10**exp to tmp has the same effect (after rounding)
- # as adding any positive quantity smaller than 10**exp; similarly
- # for subtraction. So if other is smaller than 10**exp we replace
- # it with 10**exp. This avoids tmp.exp - other.exp getting too large.
- tmp_len = len(str(tmp.int))
- other_len = len(str(other.int))
- exp = tmp.exp + min(-1, tmp_len - prec - 2)
- if other_len + other.exp - 1 < exp:
- other.int = 1
- other.exp = exp
-
- tmp.int *= 10 ** (tmp.exp - other.exp)
- tmp.exp = other.exp
- return op1, op2
-
-##### Integer arithmetic functions used by ln, log10, exp and __pow__ #####
-
-_nbits = int.bit_length
-
-def _decimal_lshift_exact(n, e):
- """ Given integers n and e, return n * 10**e if it's an integer, else None.
-
- The computation is designed to avoid computing large powers of 10
- unnecessarily.
-
- >>> _decimal_lshift_exact(3, 4)
- 30000
- >>> _decimal_lshift_exact(300, -999999999) # returns None
-
- """
- if n == 0:
- return 0
- elif e >= 0:
- return n * 10**e
- else:
- # val_n = largest power of 10 dividing n.
- str_n = str(abs(n))
- val_n = len(str_n) - len(str_n.rstrip('0'))
- return None if val_n < -e else n // 10**-e
-
-def _sqrt_nearest(n, a):
- """Closest integer to the square root of the positive integer n. a is
- an initial approximation to the square root. Any positive integer
- will do for a, but the closer a is to the square root of n the
- faster convergence will be.
-
- """
- if n <= 0 or a <= 0:
- raise ValueError("Both arguments to _sqrt_nearest should be positive.")
-
- b=0
- while a != b:
- b, a = a, a--n//a>>1
- return a
-
-def _rshift_nearest(x, shift):
- """Given an integer x and a nonnegative integer shift, return closest
- integer to x / 2**shift; use round-to-even in case of a tie.
-
- """
- b, q = 1 << shift, x >> shift
- return q + (2*(x & (b-1)) + (q&1) > b)
-
-def _div_nearest(a, b):
- """Closest integer to a/b, a and b positive integers; rounds to even
- in the case of a tie.
-
- """
- q, r = divmod(a, b)
- return q + (2*r + (q&1) > b)
-
-def _ilog(x, M, L = 8):
- """Integer approximation to M*log(x/M), with absolute error boundable
- in terms only of x/M.
-
- Given positive integers x and M, return an integer approximation to
- M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference
- between the approximation and the exact result is at most 22. For
- L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In
- both cases these are upper bounds on the error; it will usually be
- much smaller."""
-
- # The basic algorithm is the following: let log1p be the function
- # log1p(x) = log(1+x). Then log(x/M) = log1p((x-M)/M). We use
- # the reduction
- #
- # log1p(y) = 2*log1p(y/(1+sqrt(1+y)))
- #
- # repeatedly until the argument to log1p is small (< 2**-L in
- # absolute value). For small y we can use the Taylor series
- # expansion
- #
- # log1p(y) ~ y - y**2/2 + y**3/3 - ... - (-y)**T/T
- #
- # truncating at T such that y**T is small enough. The whole
- # computation is carried out in a form of fixed-point arithmetic,
- # with a real number z being represented by an integer
- # approximation to z*M. To avoid loss of precision, the y below
- # is actually an integer approximation to 2**R*y*M, where R is the
- # number of reductions performed so far.
-
- y = x-M
- # argument reduction; R = number of reductions performed
- R = 0
- while (R <= L and abs(y) << L-R >= M or
- R > L and abs(y) >> R-L >= M):
- y = _div_nearest((M*y) << 1,
- M + _sqrt_nearest(M*(M+_rshift_nearest(y, R)), M))
- R += 1
-
- # Taylor series with T terms
- T = -int(-10*len(str(M))//(3*L))
- yshift = _rshift_nearest(y, R)
- w = _div_nearest(M, T)
- for k in range(T-1, 0, -1):
- w = _div_nearest(M, k) - _div_nearest(yshift*w, M)
-
- return _div_nearest(w*y, M)
-
-def _dlog10(c, e, p):
- """Given integers c, e and p with c > 0, p >= 0, compute an integer
- approximation to 10**p * log10(c*10**e), with an absolute error of
- at most 1. Assumes that c*10**e is not exactly 1."""
-
- # increase precision by 2; compensate for this by dividing
- # final result by 100
- p += 2
-
- # write c*10**e as d*10**f with either:
- # f >= 0 and 1 <= d <= 10, or
- # f <= 0 and 0.1 <= d <= 1.
- # Thus for c*10**e close to 1, f = 0
- l = len(str(c))
- f = e+l - (e+l >= 1)
-
- if p > 0:
- M = 10**p
- k = e+p-f
- if k >= 0:
- c *= 10**k
- else:
- c = _div_nearest(c, 10**-k)
-
- log_d = _ilog(c, M) # error < 5 + 22 = 27
- log_10 = _log10_digits(p) # error < 1
- log_d = _div_nearest(log_d*M, log_10)
- log_tenpower = f*M # exact
- else:
- log_d = 0 # error < 2.31
- log_tenpower = _div_nearest(f, 10**-p) # error < 0.5
-
- return _div_nearest(log_tenpower+log_d, 100)
-
-def _dlog(c, e, p):
- """Given integers c, e and p with c > 0, compute an integer
- approximation to 10**p * log(c*10**e), with an absolute error of
- at most 1. Assumes that c*10**e is not exactly 1."""
-
- # Increase precision by 2. The precision increase is compensated
- # for at the end with a division by 100.
- p += 2
-
- # rewrite c*10**e as d*10**f with either f >= 0 and 1 <= d <= 10,
- # or f <= 0 and 0.1 <= d <= 1. Then we can compute 10**p * log(c*10**e)
- # as 10**p * log(d) + 10**p*f * log(10).
- l = len(str(c))
- f = e+l - (e+l >= 1)
-
- # compute approximation to 10**p*log(d), with error < 27
- if p > 0:
- k = e+p-f
- if k >= 0:
- c *= 10**k
- else:
- c = _div_nearest(c, 10**-k) # error of <= 0.5 in c
-
- # _ilog magnifies existing error in c by a factor of at most 10
- log_d = _ilog(c, 10**p) # error < 5 + 22 = 27
- else:
- # p <= 0: just approximate the whole thing by 0; error < 2.31
- log_d = 0
-
- # compute approximation to f*10**p*log(10), with error < 11.
- if f:
- extra = len(str(abs(f)))-1
- if p + extra >= 0:
- # error in f * _log10_digits(p+extra) < |f| * 1 = |f|
- # after division, error < |f|/10**extra + 0.5 < 10 + 0.5 < 11
- f_log_ten = _div_nearest(f*_log10_digits(p+extra), 10**extra)
- else:
- f_log_ten = 0
- else:
- f_log_ten = 0
-
- # error in sum < 11+27 = 38; error after division < 0.38 + 0.5 < 1
- return _div_nearest(f_log_ten + log_d, 100)
-
-class _Log10Memoize(object):
- """Class to compute, store, and allow retrieval of, digits of the
- constant log(10) = 2.302585.... This constant is needed by
- Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__."""
- def __init__(self):
- self.digits = "23025850929940456840179914546843642076011014886"
-
- def getdigits(self, p):
- """Given an integer p >= 0, return floor(10**p)*log(10).
-
- For example, self.getdigits(3) returns 2302.
- """
- # digits are stored as a string, for quick conversion to
- # integer in the case that we've already computed enough
- # digits; the stored digits should always be correct
- # (truncated, not rounded to nearest).
- if p < 0:
- raise ValueError("p should be nonnegative")
-
- if p >= len(self.digits):
- # compute p+3, p+6, p+9, ... digits; continue until at
- # least one of the extra digits is nonzero
- extra = 3
- while True:
- # compute p+extra digits, correct to within 1ulp
- M = 10**(p+extra+2)
- digits = str(_div_nearest(_ilog(10*M, M), 100))
- if digits[-extra:] != '0'*extra:
- break
- extra += 3
- # keep all reliable digits so far; remove trailing zeros
- # and next nonzero digit
- self.digits = digits.rstrip('0')[:-1]
- return int(self.digits[:p+1])
-
-_log10_digits = _Log10Memoize().getdigits
-
-def _iexp(x, M, L=8):
- """Given integers x and M, M > 0, such that x/M is small in absolute
- value, compute an integer approximation to M*exp(x/M). For 0 <=
- x/M <= 2.4, the absolute error in the result is bounded by 60 (and
- is usually much smaller)."""
-
- # Algorithm: to compute exp(z) for a real number z, first divide z
- # by a suitable power R of 2 so that |z/2**R| < 2**-L. Then
- # compute expm1(z/2**R) = exp(z/2**R) - 1 using the usual Taylor
- # series
- #
- # expm1(x) = x + x**2/2! + x**3/3! + ...
- #
- # Now use the identity
- #
- # expm1(2x) = expm1(x)*(expm1(x)+2)
- #
- # R times to compute the sequence expm1(z/2**R),
- # expm1(z/2**(R-1)), ... , exp(z/2), exp(z).
-
- # Find R such that x/2**R/M <= 2**-L
- R = _nbits((x<<L)//M)
-
- # Taylor series. (2**L)**T > M
- T = -int(-10*len(str(M))//(3*L))
- y = _div_nearest(x, T)
- Mshift = M<<R
- for i in range(T-1, 0, -1):
- y = _div_nearest(x*(Mshift + y), Mshift * i)
-
- # Expansion
- for k in range(R-1, -1, -1):
- Mshift = M<<(k+2)
- y = _div_nearest(y*(y+Mshift), Mshift)
-
- return M+y
-
-def _dexp(c, e, p):
- """Compute an approximation to exp(c*10**e), with p decimal places of
- precision.
-
- Returns integers d, f such that:
-
- 10**(p-1) <= d <= 10**p, and
- (d-1)*10**f < exp(c*10**e) < (d+1)*10**f
-
- In other words, d*10**f is an approximation to exp(c*10**e) with p
- digits of precision, and with an error in d of at most 1. This is
- almost, but not quite, the same as the error being < 1ulp: when d
- = 10**(p-1) the error could be up to 10 ulp."""
-
- # we'll call iexp with M = 10**(p+2), giving p+3 digits of precision
- p += 2
-
- # compute log(10) with extra precision = adjusted exponent of c*10**e
- extra = max(0, e + len(str(c)) - 1)
- q = p + extra
-
- # compute quotient c*10**e/(log(10)) = c*10**(e+q)/(log(10)*10**q),
- # rounding down
- shift = e+q
- if shift >= 0:
- cshift = c*10**shift
- else:
- cshift = c//10**-shift
- quot, rem = divmod(cshift, _log10_digits(q))
-
- # reduce remainder back to original precision
- rem = _div_nearest(rem, 10**extra)
-
- # error in result of _iexp < 120; error after division < 0.62
- return _div_nearest(_iexp(rem, 10**p), 1000), quot - p + 3
-
-def _dpower(xc, xe, yc, ye, p):
- """Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and
- y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that:
-
- 10**(p-1) <= c <= 10**p, and
- (c-1)*10**e < x**y < (c+1)*10**e
-
- in other words, c*10**e is an approximation to x**y with p digits
- of precision, and with an error in c of at most 1. (This is
- almost, but not quite, the same as the error being < 1ulp: when c
- == 10**(p-1) we can only guarantee error < 10ulp.)
-
- We assume that: x is positive and not equal to 1, and y is nonzero.
- """
-
- # Find b such that 10**(b-1) <= |y| <= 10**b
- b = len(str(abs(yc))) + ye
-
- # log(x) = lxc*10**(-p-b-1), to p+b+1 places after the decimal point
- lxc = _dlog(xc, xe, p+b+1)
-
- # compute product y*log(x) = yc*lxc*10**(-p-b-1+ye) = pc*10**(-p-1)
- shift = ye-b
- if shift >= 0:
- pc = lxc*yc*10**shift
- else:
- pc = _div_nearest(lxc*yc, 10**-shift)
-
- if pc == 0:
- # we prefer a result that isn't exactly 1; this makes it
- # easier to compute a correctly rounded result in __pow__
- if ((len(str(xc)) + xe >= 1) == (yc > 0)): # if x**y > 1:
- coeff, exp = 10**(p-1)+1, 1-p
- else:
- coeff, exp = 10**p-1, -p
- else:
- coeff, exp = _dexp(pc, -(p+1), p+1)
- coeff = _div_nearest(coeff, 10)
- exp += 1
-
- return coeff, exp
-
-def _log10_lb(c, correction = {
- '1': 100, '2': 70, '3': 53, '4': 40, '5': 31,
- '6': 23, '7': 16, '8': 10, '9': 5}):
- """Compute a lower bound for 100*log10(c) for a positive integer c."""
- if c <= 0:
- raise ValueError("The argument to _log10_lb should be nonnegative.")
- str_c = str(c)
- return 100*len(str_c) - correction[str_c[0]]
-
-##### Helper Functions ####################################################
-
-def _convert_other(other, raiseit=False, allow_float=False):
- """Convert other to Decimal.
-
- Verifies that it's ok to use in an implicit construction.
- If allow_float is true, allow conversion from float; this
- is used in the comparison methods (__eq__ and friends).
-
- """
- if isinstance(other, Decimal):
- return other
- if isinstance(other, int):
- return Decimal(other)
- if allow_float and isinstance(other, float):
- return Decimal.from_float(other)
-
- if raiseit:
- raise TypeError("Unable to convert %s to Decimal" % other)
- return NotImplemented
-
-def _convert_for_comparison(self, other, equality_op=False):
- """Given a Decimal instance self and a Python object other, return
- a pair (s, o) of Decimal instances such that "s op o" is
- equivalent to "self op other" for any of the 6 comparison
- operators "op".
-
- """
- if isinstance(other, Decimal):
- return self, other
-
- # Comparison with a Rational instance (also includes integers):
- # self op n/d <=> self*d op n (for n and d integers, d positive).
- # A NaN or infinity can be left unchanged without affecting the
- # comparison result.
- if isinstance(other, _numbers.Rational):
- if not self._is_special:
- self = _dec_from_triple(self._sign,
- str(int(self._int) * other.denominator),
- self._exp)
- return self, Decimal(other.numerator)
-
- # Comparisons with float and complex types. == and != comparisons
- # with complex numbers should succeed, returning either True or False
- # as appropriate. Other comparisons return NotImplemented.
- if equality_op and isinstance(other, _numbers.Complex) and other.imag == 0:
- other = other.real
- if isinstance(other, float):
- context = getcontext()
- if equality_op:
- context.flags[FloatOperation] = 1
- else:
- context._raise_error(FloatOperation,
- "strict semantics for mixing floats and Decimals are enabled")
- return self, Decimal.from_float(other)
- return NotImplemented, NotImplemented
-
-
-##### Setup Specific Contexts ############################################
-
-# The default context prototype used by Context()
-# Is mutable, so that new contexts can have different default values
-
-DefaultContext = Context(
- prec=28, rounding=ROUND_HALF_EVEN,
- traps=[DivisionByZero, Overflow, InvalidOperation],
- flags=[],
- Emax=999999,
- Emin=-999999,
- capitals=1,
- clamp=0
-)
-
-# Pre-made alternate contexts offered by the specification
-# Don't change these; the user should be able to select these
-# contexts and be able to reproduce results from other implementations
-# of the spec.
-
-BasicContext = Context(
- prec=9, rounding=ROUND_HALF_UP,
- traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow],
- flags=[],
-)
-
-ExtendedContext = Context(
- prec=9, rounding=ROUND_HALF_EVEN,
- traps=[],
- flags=[],
-)
-
-
-##### crud for parsing strings #############################################
-#
-# Regular expression used for parsing numeric strings. Additional
-# comments:
-#
-# 1. Uncomment the two '\s*' lines to allow leading and/or trailing
-# whitespace. But note that the specification disallows whitespace in
-# a numeric string.
-#
-# 2. For finite numbers (not infinities and NaNs) the body of the
-# number between the optional sign and the optional exponent must have
-# at least one decimal digit, possibly after the decimal point. The
-# lookahead expression '(?=\d|\.\d)' checks this.
-
-import re
-_parser = re.compile(r""" # A numeric string consists of:
-# \s*
- (?P<sign>[-+])? # an optional sign, followed by either...
- (
- (?=\d|\.\d) # ...a number (with at least one digit)
- (?P<int>\d*) # having a (possibly empty) integer part
- (\.(?P<frac>\d*))? # followed by an optional fractional part
- (E(?P<exp>[-+]?\d+))? # followed by an optional exponent, or...
- |
- Inf(inity)? # ...an infinity, or...
- |
- (?P<signal>s)? # ...an (optionally signaling)
- NaN # NaN
- (?P<diag>\d*) # with (possibly empty) diagnostic info.
- )
-# \s*
- \Z
-""", re.VERBOSE | re.IGNORECASE).match
-
-_all_zeros = re.compile('0*$').match
-_exact_half = re.compile('50*$').match
-
-##### PEP3101 support functions ##############################################
-# The functions in this section have little to do with the Decimal
-# class, and could potentially be reused or adapted for other pure
-# Python numeric classes that want to implement __format__
-#
-# A format specifier for Decimal looks like:
-#
-# [[fill]align][sign][#][0][minimumwidth][,][.precision][type]
-
-_parse_format_specifier_regex = re.compile(r"""\A
-(?:
- (?P<fill>.)?
- (?P<align>[<>=^])
-)?
-(?P<sign>[-+ ])?
-(?P<alt>\#)?
-(?P<zeropad>0)?
-(?P<minimumwidth>(?!0)\d+)?
-(?P<thousands_sep>,)?
-(?:\.(?P<precision>0|(?!0)\d+))?
-(?P<type>[eEfFgGn%])?
-\Z
-""", re.VERBOSE|re.DOTALL)
-
-del re
-
-# The locale module is only needed for the 'n' format specifier. The
-# rest of the PEP 3101 code functions quite happily without it, so we
-# don't care too much if locale isn't present.
-try:
- import locale as _locale
-except ImportError:
- pass
-
-def _parse_format_specifier(format_spec, _localeconv=None):
- """Parse and validate a format specifier.
-
- Turns a standard numeric format specifier into a dict, with the
- following entries:
-
- fill: fill character to pad field to minimum width
- align: alignment type, either '<', '>', '=' or '^'
- sign: either '+', '-' or ' '
- minimumwidth: nonnegative integer giving minimum width
- zeropad: boolean, indicating whether to pad with zeros
- thousands_sep: string to use as thousands separator, or ''
- grouping: grouping for thousands separators, in format
- used by localeconv
- decimal_point: string to use for decimal point
- precision: nonnegative integer giving precision, or None
- type: one of the characters 'eEfFgG%', or None
-
- """
- m = _parse_format_specifier_regex.match(format_spec)
- if m is None:
- raise ValueError("Invalid format specifier: " + format_spec)
-
- # get the dictionary
- format_dict = m.groupdict()
-
- # zeropad; defaults for fill and alignment. If zero padding
- # is requested, the fill and align fields should be absent.
- fill = format_dict['fill']
- align = format_dict['align']
- format_dict['zeropad'] = (format_dict['zeropad'] is not None)
- if format_dict['zeropad']:
- if fill is not None:
- raise ValueError("Fill character conflicts with '0'"
- " in format specifier: " + format_spec)
- if align is not None:
- raise ValueError("Alignment conflicts with '0' in "
- "format specifier: " + format_spec)
- format_dict['fill'] = fill or ' '
- # PEP 3101 originally specified that the default alignment should
- # be left; it was later agreed that right-aligned makes more sense
- # for numeric types. See http://bugs.python.org/issue6857.
- format_dict['align'] = align or '>'
-
- # default sign handling: '-' for negative, '' for positive
- if format_dict['sign'] is None:
- format_dict['sign'] = '-'
-
- # minimumwidth defaults to 0; precision remains None if not given
- format_dict['minimumwidth'] = int(format_dict['minimumwidth'] or '0')
- if format_dict['precision'] is not None:
- format_dict['precision'] = int(format_dict['precision'])
-
- # if format type is 'g' or 'G' then a precision of 0 makes little
- # sense; convert it to 1. Same if format type is unspecified.
- if format_dict['precision'] == 0:
- if format_dict['type'] is None or format_dict['type'] in 'gGn':
- format_dict['precision'] = 1
-
- # determine thousands separator, grouping, and decimal separator, and
- # add appropriate entries to format_dict
- if format_dict['type'] == 'n':
- # apart from separators, 'n' behaves just like 'g'
- format_dict['type'] = 'g'
- if _localeconv is None:
- _localeconv = _locale.localeconv()
- if format_dict['thousands_sep'] is not None:
- raise ValueError("Explicit thousands separator conflicts with "
- "'n' type in format specifier: " + format_spec)
- format_dict['thousands_sep'] = _localeconv['thousands_sep']
- format_dict['grouping'] = _localeconv['grouping']
- format_dict['decimal_point'] = _localeconv['decimal_point']
- else:
- if format_dict['thousands_sep'] is None:
- format_dict['thousands_sep'] = ''
- format_dict['grouping'] = [3, 0]
- format_dict['decimal_point'] = '.'
-
- return format_dict
-
-def _format_align(sign, body, spec):
- """Given an unpadded, non-aligned numeric string 'body' and sign
- string 'sign', add padding and alignment conforming to the given
- format specifier dictionary 'spec' (as produced by
- parse_format_specifier).
-
- """
- # how much extra space do we have to play with?
- minimumwidth = spec['minimumwidth']
- fill = spec['fill']
- padding = fill*(minimumwidth - len(sign) - len(body))
-
- align = spec['align']
- if align == '<':
- result = sign + body + padding
- elif align == '>':
- result = padding + sign + body
- elif align == '=':
- result = sign + padding + body
- elif align == '^':
- half = len(padding)//2
- result = padding[:half] + sign + body + padding[half:]
- else:
- raise ValueError('Unrecognised alignment field')
-
- return result
-
-def _group_lengths(grouping):
- """Convert a localeconv-style grouping into a (possibly infinite)
- iterable of integers representing group lengths.
-
- """
- # The result from localeconv()['grouping'], and the input to this
- # function, should be a list of integers in one of the
- # following three forms:
- #
- # (1) an empty list, or
- # (2) nonempty list of positive integers + [0]
- # (3) list of positive integers + [locale.CHAR_MAX], or
-
- from itertools import chain, repeat
- if not grouping:
- return []
- elif grouping[-1] == 0 and len(grouping) >= 2:
- return chain(grouping[:-1], repeat(grouping[-2]))
- elif grouping[-1] == _locale.CHAR_MAX:
- return grouping[:-1]
- else:
- raise ValueError('unrecognised format for grouping')
-
-def _insert_thousands_sep(digits, spec, min_width=1):
- """Insert thousands separators into a digit string.
-
- spec is a dictionary whose keys should include 'thousands_sep' and
- 'grouping'; typically it's the result of parsing the format
- specifier using _parse_format_specifier.
-
- The min_width keyword argument gives the minimum length of the
- result, which will be padded on the left with zeros if necessary.
-
- If necessary, the zero padding adds an extra '0' on the left to
- avoid a leading thousands separator. For example, inserting
- commas every three digits in '123456', with min_width=8, gives
- '0,123,456', even though that has length 9.
-
- """
-
- sep = spec['thousands_sep']
- grouping = spec['grouping']
-
- groups = []
- for l in _group_lengths(grouping):
- if l <= 0:
- raise ValueError("group length should be positive")
- # max(..., 1) forces at least 1 digit to the left of a separator
- l = min(max(len(digits), min_width, 1), l)
- groups.append('0'*(l - len(digits)) + digits[-l:])
- digits = digits[:-l]
- min_width -= l
- if not digits and min_width <= 0:
- break
- min_width -= len(sep)
- else:
- l = max(len(digits), min_width, 1)
- groups.append('0'*(l - len(digits)) + digits[-l:])
- return sep.join(reversed(groups))
-
-def _format_sign(is_negative, spec):
- """Determine sign character."""
-
- if is_negative:
- return '-'
- elif spec['sign'] in ' +':
- return spec['sign']
- else:
- return ''
-
-def _format_number(is_negative, intpart, fracpart, exp, spec):
- """Format a number, given the following data:
-
- is_negative: true if the number is negative, else false
- intpart: string of digits that must appear before the decimal point
- fracpart: string of digits that must come after the point
- exp: exponent, as an integer
- spec: dictionary resulting from parsing the format specifier
-
- This function uses the information in spec to:
- insert separators (decimal separator and thousands separators)
- format the sign
- format the exponent
- add trailing '%' for the '%' type
- zero-pad if necessary
- fill and align if necessary
- """
-
- sign = _format_sign(is_negative, spec)
-
- if fracpart or spec['alt']:
- fracpart = spec['decimal_point'] + fracpart
-
- if exp != 0 or spec['type'] in 'eE':
- echar = {'E': 'E', 'e': 'e', 'G': 'E', 'g': 'e'}[spec['type']]
- fracpart += "{0}{1:+}".format(echar, exp)
- if spec['type'] == '%':
- fracpart += '%'
-
- if spec['zeropad']:
- min_width = spec['minimumwidth'] - len(fracpart) - len(sign)
- else:
- min_width = 0
- intpart = _insert_thousands_sep(intpart, spec, min_width)
-
- return _format_align(sign, intpart+fracpart, spec)
-
-
-##### Useful Constants (internal use only) ################################
-
-# Reusable defaults
-_Infinity = Decimal('Inf')
-_NegativeInfinity = Decimal('-Inf')
-_NaN = Decimal('NaN')
-_Zero = Decimal(0)
-_One = Decimal(1)
-_NegativeOne = Decimal(-1)
-
-# _SignedInfinity[sign] is infinity w/ that sign
-_SignedInfinity = (_Infinity, _NegativeInfinity)
-
-# Constants related to the hash implementation; hash(x) is based
-# on the reduction of x modulo _PyHASH_MODULUS
-_PyHASH_MODULUS = sys.hash_info.modulus
-# hash values to use for positive and negative infinities, and nans
-_PyHASH_INF = sys.hash_info.inf
-_PyHASH_NAN = sys.hash_info.nan
-
-# _PyHASH_10INV is the inverse of 10 modulo the prime _PyHASH_MODULUS
-_PyHASH_10INV = pow(10, _PyHASH_MODULUS - 2, _PyHASH_MODULUS)
-del sys
-
-try:
- import _decimal
-except ImportError:
- pass
-else:
- s1 = set(dir())
- s2 = set(dir(_decimal))
- for name in s1 - s2:
- del globals()[name]
- del s1, s2, name
- from _decimal import *
-
-if __name__ == '__main__':
- import doctest, decimal
- doctest.testmod(decimal)
diff --git a/Lib/test/test_decimal.py b/Lib/test/test_decimal.py
--- a/Lib/test/test_decimal.py
+++ b/Lib/test/test_decimal.py
@@ -4173,9 +4173,7 @@
self.assertEqual(C.__version__, P.__version__)
self.assertEqual(C.__libmpdec_version__, P.__libmpdec_version__)
- x = dir(C)
- y = [s for s in dir(P) if '__' in s or not s.startswith('_')]
- self.assertEqual(set(x) - set(y), set())
+ self.assertEqual(dir(C), dir(P))
def test_context_attributes(self):
diff --git a/Modules/_decimal/tests/deccheck.py b/Modules/_decimal/tests/deccheck.py
--- a/Modules/_decimal/tests/deccheck.py
+++ b/Modules/_decimal/tests/deccheck.py
@@ -36,6 +36,7 @@
from randdec import randfloat, all_unary, all_binary, all_ternary
from randdec import unary_optarg, binary_optarg, ternary_optarg
from formathelper import rand_format, rand_locale
+from _pydecimal import _dec_from_triple
C = import_fresh_module('decimal', fresh=['_decimal'])
P = import_fresh_module('decimal', blocked=['_decimal'])
@@ -370,7 +371,7 @@
return abs(a - b)
def standard_ulp(self, dec, prec):
- return P._dec_from_triple(0, '1', dec._exp+len(dec._int)-prec)
+ return _dec_from_triple(0, '1', dec._exp+len(dec._int)-prec)
def rounding_direction(self, x, mode):
"""Determine the effective direction of the rounding when
@@ -401,10 +402,10 @@
# Convert infinities to the largest representable number + 1.
x = exact
if exact.is_infinite():
- x = P._dec_from_triple(exact._sign, '10', context.p.Emax)
+ x = _dec_from_triple(exact._sign, '10', context.p.Emax)
y = rounded
if rounded.is_infinite():
- y = P._dec_from_triple(rounded._sign, '10', context.p.Emax)
+ y = _dec_from_triple(rounded._sign, '10', context.p.Emax)
# err = (rounded - exact) / ulp(rounded)
self.maxctx.prec = p * 2
--
Repository URL: http://hg.python.org/cpython
More information about the Python-checkins
mailing list