Menu
▾
▴
jython-checkins
|
From: <le...@us...> - 2008-07-15 16:14:37
|
Revision: 4939
http://jython.svn.sourceforge.net/jython/?rev=4939&view=rev
Author: leosoto
Date: 2008-07-15 09:13:50 -0700 (Tue, 15 Jul 2008)
Log Message:
-----------
decimal.py from http://svn.python.org/projects/python/branches/release25-maint/Lib/decimal.py@64967
Added Paths:
-----------
branches/asm/Lib/decimal.py
Added: branches/asm/Lib/decimal.py
===================================================================
--- branches/asm/Lib/decimal.py (rev 0)
+++ branches/asm/Lib/decimal.py 2008-07-15 16:13:50 UTC (rev 4939)
@@ -0,0 +1,5164 @@
+# 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 is currently Py2.3 compatible and should be kept that way
+# unless a major compelling advantage arises. IOW, 2.3 compatibility is
+# strongly preferred, but not guaranteed.
+
+# Also, this module should be kept in sync with the latest updates of
+# the IBM specification as it evolves. Those updates will be treated
+# as bug fixes (deviation from the spec is a compatibility, usability
+# bug) and will be backported. At this point the spec is stabilizing
+# and the updates are becoming fewer, smaller, and less significant.
+
+"""
+This is a Py2.3 implementation of decimal floating point arithmetic based on
+the General Decimal Arithmetic Specification:
+
+ www2.hursley.ibm.com/decimal/decarith.html
+
+and IEEE standard 854-1987:
+
+ www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html
+
+Decimal floating point has finite precision with arbitrarily large bounds.
+
+The purpose of this module is to support arithmetic using familiar
+"schoolhouse" rules and to avoid some of the tricky representation
+issues associated with binary floating point. The package is especially
+useful for financial applications or for contexts where users have
+expectations that are at odds with binary floating point (for instance,
+in binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead
+of the expected Decimal("0.00") returned by decimal floating point).
+
+Here are some examples of using the decimal module:
+
+>>> from decimal import *
+>>> setcontext(ExtendedContext)
+>>> Decimal(0)
+Decimal("0")
+>>> Decimal("1")
+Decimal("1")
+>>> Decimal("-.0123")
+Decimal("-0.0123")
+>>> Decimal(123456)
+Decimal("123456")
+>>> Decimal("123.45e12345678901234567890")
+Decimal("1.2345E+12345678901234567892")
+>>> 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):
+ ...
+ ...
+ ...
+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):
+ ...
+ ...
+ ...
+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',
+
+ # Contexts
+ 'DefaultContext', 'BasicContext', 'ExtendedContext',
+
+ # Exceptions
+ 'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero',
+ 'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow',
+
+ # Constants for use in setting up contexts
+ 'ROUND_DOWN', 'ROUND_HALF_UP', 'ROUND_HALF_EVEN', 'ROUND_CEILING',
+ 'ROUND_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN', 'ROUND_05UP',
+
+ # Functions for manipulating contexts
+ 'setcontext', 'getcontext', 'localcontext'
+]
+
+import copy as _copy
+
+# 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'
+
+# 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 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 Infsign[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 Infsign[sign]
+ if sign == 0:
+ if context.rounding == ROUND_CEILING:
+ return Infsign[sign]
+ return _dec_from_triple(sign, '9'*context.prec,
+ context.Emax-context.prec+1)
+ if sign == 1:
+ if context.rounding == ROUND_FLOOR:
+ return Infsign[sign]
+ return _dec_from_triple(sign, '9'*context.prec,
+ context.Emax-context.prec+1)
+
+
+class Underflow(Inexact, Rounded, Subnormal):
+ """Numerical underflow with result rounded to 0.
+
+ This occurs and signals underflow if a result is inexact and the
+ adjusted exponent of the result would be smaller (more negative) than
+ the smallest value that can be handled by the implementation (the value
+ Emin). That is, the result is both inexact and subnormal.
+
+ The result after an underflow will be a subnormal number rounded, if
+ necessary, so that its exponent is not less than Etiny. This may result
+ in 0 with the sign of the intermediate result and an exponent of Etiny.
+
+ In all cases, Inexact, Rounded, and Subnormal will also be raised.
+ """
+
+# List of public traps and flags
+_signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded,
+ Underflow, InvalidOperation, Subnormal]
+
+# Map conditions (per the spec) to signals
+_condition_map = {ConversionSyntax:InvalidOperation,
+ DivisionImpossible:InvalidOperation,
+ DivisionUndefined:InvalidOperation,
+ InvalidContext:InvalidOperation}
+
+##### Context Functions ##################################################
+
+# The getcontext() and setcontext() function manage access to a thread-local
+# current context. Py2.4 offers direct support for thread locals. If that
+# is not available, use threading.currentThread() which is slower but will
+# work for older Pythons. If threads are not part of the build, create a
+# mock threading object with threading.local() returning the module namespace.
+
+try:
+ import threading
+except ImportError:
+ # Python was compiled without threads; create a mock object instead
+ import sys
+ class MockThreading(object):
+ def local(self, sys=sys):
+ return sys.modules[__name__]
+ threading = MockThreading()
+ del sys, 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.currentThread(), '__decimal_context__'):
+ del threading.currentThread().__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.currentThread().__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.currentThread().__decimal_context__
+ except AttributeError:
+ context = Context()
+ threading.currentThread().__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
+
+ """
+ # The string below can't be included in the docstring until Python 2.6
+ # as the doctest module doesn't understand __future__ statements
+ """
+ >>> from __future__ import with_statement
+ >>> 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 #######################################################
+
+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 or long
+ Decimal("314")
+ >>> Decimal(Decimal(314)) # another decimal instance
+ Decimal("314")
+ """
+
+ # 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, basestring):
+ m = _parser(value)
+ 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')
+ exp = int(m.group('exp') or '0')
+ if fracpart is not None:
+ self._int = str((intpart+fracpart).lstrip('0') or '0')
+ self._exp = exp - len(fracpart)
+ else:
+ self._int = str(intpart.lstrip('0') or '0')
+ self._exp = exp
+ self._is_special = False
+ else:
+ diag = m.group('diag')
+ if diag is not None:
+ # NaN
+ self._int = str(diag.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,long)):
+ 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, long)) 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, long)) 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, long)):
+ # 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):
+ raise TypeError("Cannot convert float to Decimal. " +
+ "First convert the float to a string")
+
+ raise TypeError("Cannot convert %r to Decimal" % value)
+
+ 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 __nonzero__(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):
+ other = _convert_other(other)
+ if other is NotImplemented:
+ # Never return NotImplemented
+ return 1
+
+ if self._is_special or other._is_special:
+ # check for nans, without raising on a signaling nan
+ if self._isnan() or other._isnan():
+ return 1 # Comparison involving NaN's always reports self > other
+
+ # INF = INF
+ return cmp(self._isinfinity(), other._isinfinity())
+
+ # check for zeros; note that cmp(0, -0) should return 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)
+ return cmp(self_padded, other_padded) * (-1)**self._sign
+ elif self_adjusted > other_adjusted:
+ return (-1)**self._sign
+ else: # self_adjusted < other_adjusted
+ return -((-1)**self._sign)
+
+ def __eq__(self, other):
+ if not isinstance(other, (Decimal, int, long)):
+ return NotImplemented
+ return self.__cmp__(other) == 0
+
+ def __ne__(self, other):
+ if not isinstance(other, (Decimal, int, long)):
+ return NotImplemented
+ 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)"""
+ # Decimal integers must hash the same as the ints
+ #
+ # The hash of a nonspecial noninteger Decimal must depend only
+ # on the value of that Decimal, and not on its representation.
+ # For example: hash(Decimal("100E-1")) == hash(Decimal("10")).
+ if self._is_special:
+ if self._isnan():
+ raise TypeError('Cannot hash a NaN value.')
+ return hash(str(self))
+ if not self:
+ return 0
+ if self._isinteger():
+ op = _WorkRep(self.to_integral_value())
+ return hash((-1)**op.sign*op.int*10**op.exp)
+ # The value of a nonzero nonspecial Decimal instance is
+ # faithfully represented by the triple consisting of its sign,
+ # its adjusted exponent, and its coefficient with trailing
+ # zeros removed.
+ return hash((self._sign,
+ self._exp+len(self._int),
+ self._int.rstrip('0')))
+
+ def as_tuple(self):
+ """Represents the number as a triple tuple.
+
+ To show the internals exactly as they are.
+ """
+ return (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 not self:
+ # -Decimal('0') is Decimal('0'), not Decimal('-0')
+ ans = self.copy_abs()
+ else:
+ ans = self.copy_negate()
+
+ if context is None:
+ context = getcontext()
+ 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 not self:
+ # + (-0) = 0
+ ans = self.copy_abs()
+ else:
+ ans = Decimal(self)
+
+ if context is None:
+ context = getcontext()
+ 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 Infsign[resultsign]
+
+ if other._isinfinity():
+ if not self:
+ return context._raise_error(InvalidOperation, '0 * (+-)INF')
+ return Infsign[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 __div__(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 Infsign[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)
+
+ __truediv__ = __div__
+
+ 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 __rdiv__(self, other, context=None):
+ """Swaps self/other and returns __div__."""
+ other = _convert_other(other)
+ if other is NotImplemented:
+ return other
+ return other.__div__(self, context=context)
+ __rtruediv__ = __rdiv__
+
+ 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 (Infsign[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 Infsign[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."""
+ return float(str(self))
+
+ def __int__(self):
+ """Converts self to an int, truncating if necessary."""
+ if self._is_special:
+ if self._isnan():
+ context = getcontext()
+ return context._raise_error(InvalidContext)
+ elif self._isinfinity():
+ raise OverflowError("Cannot convert infinity to long")
+ 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')
+
+ def __long__(self):
+ """Converts to a long.
+
+ Equivalent to long(int(self))
+ """
+ return long(self.__int__())
+
+ 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
+ context._raise_error(Inexact)
+ context._raise_error(Rounded)
+ return context._raise_error(Overflow, 'above Emax', self._sign)
+ self_is_subnormal = exp_min < Etiny
+ if self_is_subnormal:
+ context._raise_error(Subnormal)
+ exp_min = Etiny
+
+ # round if self has too many digits
+ if self._exp < exp_min:
+ context._raise_error(Rounded)
+ digits = len(self._int) + self._exp - exp_min
+ if digits < 0:
+ self = _dec_from_triple(self._sign, '1', exp_min-1)
+ digits = 0
+ this_function = getattr(self, self._pick_rounding_function[context.rounding])
+ changed = this_function(digits)
+ coeff = self._int[:digits] or '0'
+ if changed == 1:
+ coeff = str(int(coeff)+1)
+ ans = _dec_from_triple(self._sign, coeff, exp_min)
+
+ if changed:
+ context._raise_error(Inexact)
+ if self_is_subnormal:
+ context._raise_error(Underflow)
+ if not ans:
+ # raise Clamped on underflow to 0
+ context._raise_error(Clamped)
+ elif len(ans._int) == context.prec+1:
+ # we get here only if rescaling rounds the
+ # cofficient up to exactly 10**context.prec
+ if ans._exp < Etop:
+ ans = _dec_from_triple(ans._sign,
+ ans._int[:-1], ans._exp+1)
+ else:
+ # Inexact and Rounded have already been raised
+ ans = context._raise_error(Overflow, 'above Emax',
+ self._sign)
+ return ans
+
+ # 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)
+
+ _pick_rounding_function = {}
+
+ # 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)
+
+ 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)
+
+ # 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 = Infsign[self._sign ^ other._sign]
+ elif other._exp == 'F':
+ if not self:
+ return context._raise_error(InvalidOperation,
+ '0 * INF in fma')
+ product = Infsign[self._sign ^ other._sign]
+ else:
+ product = _dec_from_triple(self._sign ^ other._sign,
+ str(int(self._int) * int(other._int)),
+ self._exp + other._exp)
+
+ third = _convert_other(third, raiseit=True)
+ return product.__add__(third, context)
+
+ def _power_modulo(self, other, modulo, context=None):
+ """Three argument version of __pow__"""
+
+ # if can't convert other and modulo to Decimal, raise
+ # TypeError; there's no point returning NotImplemented (no
+ # equivalent of __rpow__ for three argument pow)
+ other = _convert_other(other, raiseit=True)
+ modulo = _convert_other(modulo, raiseit=True)
+
+ 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_n...
[truncated message content] |
|
From: <le...@us...> - 2008-07-15 16:24:46
|
Revision: 4940
http://jython.svn.sourceforge.net/jython/?rev=4940&view=rev
Author: leosoto
Date: 2008-07-15 09:24:18 -0700 (Tue, 15 Jul 2008)
Log Message:
-----------
Implemented decimal.Decimal.__tojava__ to convert decimal instances to java BigDecimal when python -> java conversion is requested
Modified Paths:
--------------
branches/asm/Lib/decimal.py
Modified: branches/asm/Lib/decimal.py
===================================================================
--- branches/asm/Lib/decimal.py 2008-07-15 16:13:50 UTC (rev 4939)
+++ branches/asm/Lib/decimal.py 2008-07-15 16:24:18 UTC (rev 4940)
@@ -3330,6 +3330,15 @@
return self # My components are also immutable
return self.__class__(str(self))
+ # support for Jython __tojava__:
+ def __tojava__(self, java_class):
+ from java.lang import Object
+ from java.math import BigDecimal
+ from org.python.core import Py
+ if java_class not in (BigDecimal, Object):
+ return Py.NoConversion
+ return BigDecimal(str(self))
+
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
This was sent by the SourceForge.net collaborative development platform, the world's largest Open Source development site.
|
×
Want the latest updates on software, tech news, and AI?
Get latest updates about software, tech news, and AI from SourceForge directly in your inbox once a month.
Thanks for helping keep SourceForge clean.
X