--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/app/django/utils/_decimal.py Fri Jul 18 18:22:23 2008 +0000
@@ -0,0 +1,3079 @@
+# 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 the module is to support arithmetic using familiar
+"schoolhouse" rules and to avoid the some of 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',
+
+ # Functions for manipulating contexts
+ 'setcontext', 'getcontext'
+]
+
+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'
+
+#Rounding decision (not part of the public API)
+NEVER_ROUND = 'NEVER_ROUND' # Round in division (non-divmod), sqrt ONLY
+ALWAYS_ROUND = 'ALWAYS_ROUND' # Every operation rounds at end.
+
+#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
+ """
+ def handle(self, context, *args):
+ if args:
+ if args[0] == 1: #sNaN, must drop 's' but keep diagnostics
+ return Decimal( (args[1]._sign, args[1]._int, 'n') )
+ 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 (0, (0,), 'n') #Passed to something which uses a tuple.
+
+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, double = None, *args):
+ if double is not None:
+ return (Infsign[sign],)*2
+ 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, 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, tup=None, *args):
+ if tup is not None:
+ return (NaN, NaN) #for 0 %0, 0 // 0
+ 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.
+ """
+ pass
+
+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.
+ """
+ pass
+
+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.
+ """
+ pass
+
+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 Decimal((sign, (9,)*context.prec,
+ context.Emax-context.prec+1))
+ if sign == 1:
+ if context.rounding == ROUND_FLOOR:
+ return Infsign[sign]
+ return Decimal( (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:
+ 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
+
+
+##### 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 input (sign, digit_tuple, exponent)
+ Decimal("3.14")
+ >>> Decimal(314) # int or long
+ Decimal("314")
+ >>> Decimal(Decimal(314)) # another decimal instance
+ Decimal("314")
+ """
+
+ self = object.__new__(cls)
+ self._is_special = False
+
+ # From an internal working value
+ if isinstance(value, _WorkRep):
+ self._sign = value.sign
+ self._int = tuple(map(int, str(value.int)))
+ self._exp = int(value.exp)
+ 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 integer
+ if isinstance(value, (int,long)):
+ if value >= 0:
+ self._sign = 0
+ else:
+ self._sign = 1
+ self._exp = 0
+ self._int = tuple(map(int, str(abs(value))))
+ return self
+
+ # tuple/list conversion (possibly from as_tuple())
+ if isinstance(value, (list,tuple)):
+ if len(value) != 3:
+ raise ValueError, 'Invalid arguments'
+ if value[0] not in (0,1):
+ raise ValueError, 'Invalid sign'
+ for digit in value[1]:
+ if not isinstance(digit, (int,long)) or digit < 0:
+ raise ValueError, "The second value in the tuple must be composed of non negative integer elements."
+
+ self._sign = value[0]
+ self._int = tuple(value[1])
+ if value[2] in ('F','n','N'):
+ self._exp = value[2]
+ self._is_special = True
+ else:
+ self._exp = int(value[2])
+ return self
+
+ if isinstance(value, float):
+ raise TypeError("Cannot convert float to Decimal. " +
+ "First convert the float to a string")
+
+ # Other argument types may require the context during interpretation
+ if context is None:
+ context = getcontext()
+
+ # From a string
+ # REs insist on real strings, so we can too.
+ if isinstance(value, basestring):
+ if _isinfinity(value):
+ self._exp = 'F'
+ self._int = (0,)
+ self._is_special = True
+ if _isinfinity(value) == 1:
+ self._sign = 0
+ else:
+ self._sign = 1
+ return self
+ if _isnan(value):
+ sig, sign, diag = _isnan(value)
+ self._is_special = True
+ if len(diag) > context.prec: #Diagnostic info too long
+ self._sign, self._int, self._exp = \
+ context._raise_error(ConversionSyntax)
+ return self
+ if sig == 1:
+ self._exp = 'n' #qNaN
+ else: #sig == 2
+ self._exp = 'N' #sNaN
+ self._sign = sign
+ self._int = tuple(map(int, diag)) #Diagnostic info
+ return self
+ try:
+ self._sign, self._int, self._exp = _string2exact(value)
+ except ValueError:
+ self._is_special = True
+ self._sign, self._int, self._exp = context._raise_error(ConversionSyntax)
+ return self
+
+ 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',
+ 1, self)
+ if other_is_nan == 2:
+ return context._raise_error(InvalidOperation, 'sNaN',
+ 1, other)
+ if self_is_nan:
+ return self
+
+ return other
+ return 0
+
+ def __nonzero__(self):
+ """Is the number non-zero?
+
+ 0 if self == 0
+ 1 if self != 0
+ """
+ if self._is_special:
+ return 1
+ return sum(self._int) != 0
+
+ def __cmp__(self, other, context=None):
+ other = _convert_other(other)
+ if other is NotImplemented:
+ return other
+
+ if self._is_special or other._is_special:
+ ans = self._check_nans(other, context)
+ if ans:
+ return 1 # Comparison involving NaN's always reports self > other
+
+ # INF = INF
+ return cmp(self._isinfinity(), other._isinfinity())
+
+ if not self and not other:
+ return 0 #If both 0, sign comparison isn't certain.
+
+ #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 and \
+ self._int + (0,)*(self._exp - other._exp) == \
+ other._int + (0,)*(other._exp - self._exp):
+ return 0 #equal, except in precision. ([0]*(-x) = [])
+ elif self_adjusted > other_adjusted and self._int[0] != 0:
+ return (-1)**self._sign
+ elif self_adjusted < other_adjusted and other._int[0] != 0:
+ return -((-1)**self._sign)
+
+ # Need to round, so make sure we have a valid context
+ if context is None:
+ context = getcontext()
+
+ context = context._shallow_copy()
+ rounding = context._set_rounding(ROUND_UP) #round away from 0
+
+ flags = context._ignore_all_flags()
+ res = self.__sub__(other, context=context)
+
+ context._regard_flags(*flags)
+
+ context.rounding = rounding
+
+ if not res:
+ return 0
+ elif res._sign:
+ return -1
+ return 1
+
+ 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)
+ if other is NotImplemented:
+ return other
+
+ #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, context))
+
+ def __hash__(self):
+ """x.__hash__() <==> hash(x)"""
+ # Decimal integers must hash the same as the ints
+ # Non-integer decimals are normalized and hashed as strings
+ # Normalization assures that hast(100E-1) == hash(10)
+ if self._is_special:
+ if self._isnan():
+ raise TypeError('Cannot hash a NaN value.')
+ return hash(str(self))
+ i = int(self)
+ if self == Decimal(i):
+ return hash(i)
+ assert self.__nonzero__() # '-0' handled by integer case
+ return hash(str(self.normalize()))
+
+ def as_tuple(self):
+ """Represents the number as a triple tuple.
+
+ To show the internals exactly as they are.
+ """
+ return (self._sign, 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 = 0, context=None):
+ """Return string representation of the number in scientific notation.
+
+ Captures all of the information in the underlying representation.
+ """
+
+ if self._is_special:
+ if self._isnan():
+ minus = '-'*self._sign
+ if self._int == (0,):
+ info = ''
+ else:
+ info = ''.join(map(str, self._int))
+ if self._isnan() == 2:
+ return minus + 'sNaN' + info
+ return minus + 'NaN' + info
+ if self._isinfinity():
+ minus = '-'*self._sign
+ return minus + 'Infinity'
+
+ if context is None:
+ context = getcontext()
+
+ tmp = map(str, self._int)
+ numdigits = len(self._int)
+ leftdigits = self._exp + numdigits
+ if eng and not self: #self = 0eX wants 0[.0[0]]eY, not [[0]0]0eY
+ if self._exp < 0 and self._exp >= -6: #short, no need for e/E
+ s = '-'*self._sign + '0.' + '0'*(abs(self._exp))
+ return s
+ #exp is closest mult. of 3 >= self._exp
+ exp = ((self._exp - 1)// 3 + 1) * 3
+ if exp != self._exp:
+ s = '0.'+'0'*(exp - self._exp)
+ else:
+ s = '0'
+ if exp != 0:
+ if context.capitals:
+ s += 'E'
+ else:
+ s += 'e'
+ if exp > 0:
+ s += '+' #0.0e+3, not 0.0e3
+ s += str(exp)
+ s = '-'*self._sign + s
+ return s
+ if eng:
+ dotplace = (leftdigits-1)%3+1
+ adjexp = leftdigits -1 - (leftdigits-1)%3
+ else:
+ adjexp = leftdigits-1
+ dotplace = 1
+ if self._exp == 0:
+ pass
+ elif self._exp < 0 and adjexp >= 0:
+ tmp.insert(leftdigits, '.')
+ elif self._exp < 0 and adjexp >= -6:
+ tmp[0:0] = ['0'] * int(-leftdigits)
+ tmp.insert(0, '0.')
+ else:
+ if numdigits > dotplace:
+ tmp.insert(dotplace, '.')
+ elif numdigits < dotplace:
+ tmp.extend(['0']*(dotplace-numdigits))
+ if adjexp:
+ if not context.capitals:
+ tmp.append('e')
+ else:
+ tmp.append('E')
+ if adjexp > 0:
+ tmp.append('+')
+ tmp.append(str(adjexp))
+ if eng:
+ while tmp[0:1] == ['0']:
+ tmp[0:1] = []
+ if len(tmp) == 0 or tmp[0] == '.' or tmp[0].lower() == 'e':
+ tmp[0:0] = ['0']
+ if self._sign:
+ tmp.insert(0, '-')
+
+ return ''.join(tmp)
+
+ 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=1, 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')
+ sign = 0
+ elif self._sign:
+ sign = 0
+ else:
+ sign = 1
+
+ if context is None:
+ context = getcontext()
+ if context._rounding_decision == ALWAYS_ROUND:
+ return Decimal((sign, self._int, self._exp))._fix(context)
+ return Decimal( (sign, self._int, self._exp))
+
+ 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
+
+ sign = self._sign
+ if not self:
+ # + (-0) = 0
+ sign = 0
+
+ if context is None:
+ context = getcontext()
+
+ if context._rounding_decision == ALWAYS_ROUND:
+ ans = self._fix(context)
+ else:
+ ans = Decimal(self)
+ ans._sign = sign
+ return ans
+
+ def __abs__(self, round=1, context=None):
+ """Returns the absolute value of self.
+
+ If the second argument is 0, do not round.
+ """
+ if self._is_special:
+ ans = self._check_nans(context=context)
+ if ans:
+ return ans
+
+ if not round:
+ if context is None:
+ context = getcontext()
+ context = context._shallow_copy()
+ context._set_rounding_decision(NEVER_ROUND)
+
+ 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
+
+ shouldround = context._rounding_decision == ALWAYS_ROUND
+
+ 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
+ return Decimal( (sign, (0,), exp))
+ if not self:
+ exp = max(exp, other._exp - context.prec-1)
+ ans = other._rescale(exp, watchexp=0, context=context)
+ if shouldround:
+ ans = ans._fix(context)
+ return ans
+ if not other:
+ exp = max(exp, self._exp - context.prec-1)
+ ans = self._rescale(exp, watchexp=0, context=context)
+ if shouldround:
+ ans = ans._fix(context)
+ return ans
+
+ op1 = _WorkRep(self)
+ op2 = _WorkRep(other)
+ op1, op2 = _normalize(op1, op2, shouldround, context.prec)
+
+ result = _WorkRep()
+ if op1.sign != op2.sign:
+ # Equal and opposite
+ if op1.int == op2.int:
+ if exp < context.Etiny():
+ exp = context.Etiny()
+ context._raise_error(Clamped)
+ return Decimal((negativezero, (0,), exp))
+ 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)
+ if shouldround:
+ 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
+
+ # -Decimal(0) = Decimal(0), which we don't want since
+ # (-0 - 0 = -0 + (-0) = -0, but -0 + 0 = 0.)
+ # so we change the sign directly to a copy
+ tmp = Decimal(other)
+ tmp._sign = 1-tmp._sign
+
+ return self.__add__(tmp, context=context)
+
+ def __rsub__(self, other, context=None):
+ """Return other + (-self)"""
+ other = _convert_other(other)
+ if other is NotImplemented:
+ return other
+
+ tmp = Decimal(self)
+ tmp._sign = 1 - tmp._sign
+ return other.__add__(tmp, context=context)
+
+ def _increment(self, round=1, context=None):
+ """Special case of add, adding 1eExponent
+
+ Since it is common, (rounding, for example) this adds
+ (sign)*one E self._exp to the number more efficiently than add.
+
+ For example:
+ Decimal('5.624e10')._increment() == Decimal('5.625e10')
+ """
+ if self._is_special:
+ ans = self._check_nans(context=context)
+ if ans:
+ return ans
+
+ return Decimal(self) # Must be infinite, and incrementing makes no difference
+
+ L = list(self._int)
+ L[-1] += 1
+ spot = len(L)-1
+ while L[spot] == 10:
+ L[spot] = 0
+ if spot == 0:
+ L[0:0] = [1]
+ break
+ L[spot-1] += 1
+ spot -= 1
+ ans = Decimal((self._sign, L, self._exp))
+
+ if context is None:
+ context = getcontext()
+ if round and context._rounding_decision == ALWAYS_ROUND:
+ ans = ans._fix(context)
+ return ans
+
+ 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
+ shouldround = context._rounding_decision == ALWAYS_ROUND
+
+ # Special case for multiplying by zero
+ if not self or not other:
+ ans = Decimal((resultsign, (0,), resultexp))
+ if shouldround:
+ #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 = Decimal((resultsign, other._int, resultexp))
+ if shouldround:
+ ans = ans._fix(context)
+ return ans
+ if other._int == (1,):
+ ans = Decimal((resultsign, self._int, resultexp))
+ if shouldround:
+ ans = ans._fix(context)
+ return ans
+
+ op1 = _WorkRep(self)
+ op2 = _WorkRep(other)
+
+ ans = Decimal( (resultsign, map(int, str(op1.int * op2.int)), resultexp))
+ if shouldround:
+ ans = ans._fix(context)
+
+ return ans
+ __rmul__ = __mul__
+
+ def __div__(self, other, context=None):
+ """Return self / other."""
+ return self._divide(other, context=context)
+ __truediv__ = __div__
+
+ def _divide(self, other, divmod = 0, context=None):
+ """Return a / b, to context.prec precision.
+
+ divmod:
+ 0 => true division
+ 1 => (a //b, a%b)
+ 2 => a //b
+ 3 => a%b
+
+ Actually, if divmod is 2 or 3 a tuple is returned, but errors for
+ computing the other value are not raised.
+ """
+ other = _convert_other(other)
+ if other is NotImplemented:
+ if divmod in (0, 1):
+ return NotImplemented
+ return (NotImplemented, 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:
+ if divmod:
+ return (ans, ans)
+ return ans
+
+ if self._isinfinity() and other._isinfinity():
+ if divmod:
+ return (context._raise_error(InvalidOperation,
+ '(+-)INF // (+-)INF'),
+ context._raise_error(InvalidOperation,
+ '(+-)INF % (+-)INF'))
+ return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF')
+
+ if self._isinfinity():
+ if divmod == 1:
+ return (Infsign[sign],
+ context._raise_error(InvalidOperation, 'INF % x'))
+ elif divmod == 2:
+ return (Infsign[sign], NaN)
+ elif divmod == 3:
+ return (Infsign[sign],
+ context._raise_error(InvalidOperation, 'INF % x'))
+ return Infsign[sign]
+
+ if other._isinfinity():
+ if divmod:
+ return (Decimal((sign, (0,), 0)), Decimal(self))
+ context._raise_error(Clamped, 'Division by infinity')
+ return Decimal((sign, (0,), context.Etiny()))
+
+ # Special cases for zeroes
+ if not self and not other:
+ if divmod:
+ return context._raise_error(DivisionUndefined, '0 / 0', 1)
+ return context._raise_error(DivisionUndefined, '0 / 0')
+
+ if not self:
+ if divmod:
+ otherside = Decimal(self)
+ otherside._exp = min(self._exp, other._exp)
+ return (Decimal((sign, (0,), 0)), otherside)
+ exp = self._exp - other._exp
+ if exp < context.Etiny():
+ exp = context.Etiny()
+ context._raise_error(Clamped, '0e-x / y')
+ if exp > context.Emax:
+ exp = context.Emax
+ context._raise_error(Clamped, '0e+x / y')
+ return Decimal( (sign, (0,), exp) )
+
+ if not other:
+ if divmod:
+ return context._raise_error(DivisionByZero, 'divmod(x,0)',
+ sign, 1)
+ return context._raise_error(DivisionByZero, 'x / 0', sign)
+
+ #OK, so neither = 0, INF or NaN
+
+ shouldround = context._rounding_decision == ALWAYS_ROUND
+
+ #If we're dividing into ints, and self < other, stop.
+ #self.__abs__(0) does not round.
+ if divmod and (self.__abs__(0, context) < other.__abs__(0, context)):
+
+ if divmod == 1 or divmod == 3:
+ exp = min(self._exp, other._exp)
+ ans2 = self._rescale(exp, context=context, watchexp=0)
+ if shouldround:
+ ans2 = ans2._fix(context)
+ return (Decimal( (sign, (0,), 0) ),
+ ans2)
+
+ elif divmod == 2:
+ #Don't round the mod part, if we don't need it.
+ return (Decimal( (sign, (0,), 0) ), Decimal(self))
+
+ op1 = _WorkRep(self)
+ op2 = _WorkRep(other)
+ op1, op2, adjust = _adjust_coefficients(op1, op2)
+ res = _WorkRep( (sign, 0, (op1.exp - op2.exp)) )
+ if divmod and res.exp > context.prec + 1:
+ return context._raise_error(DivisionImpossible)
+
+ prec_limit = 10 ** context.prec
+ while 1:
+ while op2.int <= op1.int:
+ res.int += 1
+ op1.int -= op2.int
+ if res.exp == 0 and divmod:
+ if res.int >= prec_limit and shouldround:
+ return context._raise_error(DivisionImpossible)
+ otherside = Decimal(op1)
+ frozen = context._ignore_all_flags()
+
+ exp = min(self._exp, other._exp)
+ otherside = otherside._rescale(exp, context=context, watchexp=0)
+ context._regard_flags(*frozen)
+ if shouldround:
+ otherside = otherside._fix(context)
+ return (Decimal(res), otherside)
+
+ if op1.int == 0 and adjust >= 0 and not divmod:
+ break
+ if res.int >= prec_limit and shouldround:
+ if divmod:
+ return context._raise_error(DivisionImpossible)
+ shouldround=1
+ # Really, the answer is a bit higher, so adding a one to
+ # the end will make sure the rounding is right.
+ if op1.int != 0:
+ res.int *= 10
+ res.int += 1
+ res.exp -= 1
+
+ break
+ res.int *= 10
+ res.exp -= 1
+ adjust += 1
+ op1.int *= 10
+ op1.exp -= 1
+
+ if res.exp == 0 and divmod and op2.int > op1.int:
+ #Solves an error in precision. Same as a previous block.
+
+ if res.int >= prec_limit and shouldround:
+ return context._raise_error(DivisionImpossible)
+ otherside = Decimal(op1)
+ frozen = context._ignore_all_flags()
+
+ exp = min(self._exp, other._exp)
+ otherside = otherside._rescale(exp, context=context)
+
+ context._regard_flags(*frozen)
+
+ return (Decimal(res), otherside)
+
+ ans = Decimal(res)
+ if shouldround:
+ ans = ans._fix(context)
+ return 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):
+ """
+ (self // other, self % other)
+ """
+ return self._divide(other, 1, context)
+
+ 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 self._is_special or other._is_special:
+ ans = self._check_nans(other, context)
+ if ans:
+ return ans
+
+ if self and not other:
+ return context._raise_error(InvalidOperation, 'x % 0')
+
+ return self._divide(other, 3, context)[1]
+
+ 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
+ """
+ other = _convert_other(other)
+ if other is NotImplemented:
+ return other
+
+ if self._is_special or other._is_special:
+ ans = self._check_nans(other, context)
+ if ans:
+ return ans
+ if self and not other:
+ return context._raise_error(InvalidOperation, 'x % 0')
+
+ if context is None:
+ context = getcontext()
+ # If DivisionImpossible causes an error, do not leave Rounded/Inexact
+ # ignored in the calling function.
+ context = context._shallow_copy()
+ flags = context._ignore_flags(Rounded, Inexact)
+ #keep DivisionImpossible flags
+ (side, r) = self.__divmod__(other, context=context)
+
+ if r._isnan():
+ context._regard_flags(*flags)
+ return r
+
+ context = context._shallow_copy()
+ rounding = context._set_rounding_decision(NEVER_ROUND)
+
+ if other._sign:
+ comparison = other.__div__(Decimal(-2), context=context)
+ else:
+ comparison = other.__div__(Decimal(2), context=context)
+
+ context._set_rounding_decision(rounding)
+ context._regard_flags(*flags)
+
+ s1, s2 = r._sign, comparison._sign
+ r._sign, comparison._sign = 0, 0
+
+ if r < comparison:
+ r._sign, comparison._sign = s1, s2
+ #Get flags now
+ self.__divmod__(other, context=context)
+ return r._fix(context)
+ r._sign, comparison._sign = s1, s2
+
+ rounding = context._set_rounding_decision(NEVER_ROUND)
+
+ (side, r) = self.__divmod__(other, context=context)
+ context._set_rounding_decision(rounding)
+ if r._isnan():
+ return r
+
+ decrease = not side._iseven()
+ rounding = context._set_rounding_decision(NEVER_ROUND)
+ side = side.__abs__(context=context)
+ context._set_rounding_decision(rounding)
+
+ s1, s2 = r._sign, comparison._sign
+ r._sign, comparison._sign = 0, 0
+ if r > comparison or decrease and r == comparison:
+ r._sign, comparison._sign = s1, s2
+ context.prec += 1
+ if len(side.__add__(Decimal(1), context=context)._int) >= context.prec:
+ context.prec -= 1
+ return context._raise_error(DivisionImpossible)[1]
+ context.prec -= 1
+ if self._sign == other._sign:
+ r = r.__sub__(other, context=context)
+ else:
+ r = r.__add__(other, context=context)
+ else:
+ r._sign, comparison._sign = s1, s2
+
+ return r._fix(context)
+
+ def __floordiv__(self, other, context=None):
+ """self // other"""
+ return self._divide(other, 2, 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"
+ if self._exp >= 0:
+ s = ''.join(map(str, self._int)) + '0'*self._exp
+ else:
+ s = ''.join(map(str, self._int))[:self._exp]
+ if s == '':
+ s = '0'
+ sign = '-'*self._sign
+ return int(sign + s)
+
+ def __long__(self):
+ """Converts to a long.
+
+ Equivalent to long(int(self))
+ """
+ return long(self.__int__())
+
+ 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:
+ return self
+ if context is None:
+ context = getcontext()
+ prec = context.prec
+ ans = self._fixexponents(context)
+ if len(ans._int) > prec:
+ ans = ans._round(prec, context=context)
+ ans = ans._fixexponents(context)
+ return ans
+
+ def _fixexponents(self, context):
+ """Fix the exponents and return a copy with the exponent in bounds.
+ Only call if known to not be a special value.
+ """
+ folddown = context._clamp
+ Emin = context.Emin
+ ans = self
+ ans_adjusted = ans.adjusted()
+ if ans_adjusted < Emin:
+ Etiny = context.Etiny()
+ if ans._exp < Etiny:
+ if not ans:
+ ans = Decimal(self)
+ ans._exp = Etiny
+ context._raise_error(Clamped)
+ return ans
+ ans = ans._rescale(Etiny, context=context)
+ #It isn't zero, and exp < Emin => subnormal
+ context._raise_error(Subnormal)
+ if context.flags[Inexact]:
+ context._raise_error(Underflow)
+ else:
+ if ans:
+ #Only raise subnormal if non-zero.
+ context._raise_error(Subnormal)
+ else:
+ Etop = context.Etop()
+ if folddown and ans._exp > Etop:
+ context._raise_error(Clamped)
+ ans = ans._rescale(Etop, context=context)
+ else:
+ Emax = context.Emax
+ if ans_adjusted > Emax:
+ if not ans:
+ ans = Decimal(self)
+ ans._exp = Emax
+ context._raise_error(Clamped)
+ return ans
+ context._raise_error(Inexact)
+ context._raise_error(Rounded)
+ return context._raise_error(Overflow, 'above Emax', ans._sign)
+ return ans
+
+ def _round(self, prec=None, rounding=None, context=None):
+ """Returns a rounded version of self.
+
+ You can specify the precision or rounding method. Otherwise, the
+ context determines it.
+ """
+
+ if self._is_special:
+ ans = self._check_nans(context=context)
+ if ans:
+ return ans
+
+ if self._isinfinity():
+ return Decimal(self)
+
+ if context is None:
+ context = getcontext()
+
+ if rounding is None:
+ rounding = context.rounding
+ if prec is None:
+ prec = context.prec
+
+ if not self:
+ if prec <= 0:
+ dig = (0,)
+ exp = len(self._int) - prec + self._exp
+ else:
+ dig = (0,) * prec
+ exp = len(self._int) + self._exp - prec
+ ans = Decimal((self._sign, dig, exp))
+ context._raise_error(Rounded)
+ return ans
+
+ if prec == 0:
+ temp = Decimal(self)
+ temp._int = (0,)+temp._int
+ prec = 1
+ elif prec < 0:
+ exp = self._exp + len(self._int) - prec - 1
+ temp = Decimal( (self._sign, (0, 1), exp))
+ prec = 1
+ else:
+ temp = Decimal(self)
+
+ numdigits = len(temp._int)
+ if prec == numdigits:
+ return temp
+
+ # See if we need to extend precision
+ expdiff = prec - numdigits
+ if expdiff > 0:
+ tmp = list(temp._int)
+ tmp.extend([0] * expdiff)
+ ans = Decimal( (temp._sign, tmp, temp._exp - expdiff))
+ return ans
+
+ #OK, but maybe all the lost digits are 0.
+ lostdigits = self._int[expdiff:]
+ if lostdigits == (0,) * len(lostdigits):
+ ans = Decimal( (temp._sign, temp._int[:prec], temp._exp - expdiff))
+ #Rounded, but not Inexact
+ context._raise_error(Rounded)
+ return ans
+
+ # Okay, let's round and lose data
+
+ this_function = getattr(temp, self._pick_rounding_function[rounding])
+ #Now we've got the rounding function
+
+ if prec != context.prec:
+ context = context._shallow_copy()
+ context.prec = prec
+ ans = this_function(prec, expdiff, context)
+ context._raise_error(Rounded)
+ context._raise_error(Inexact, 'Changed in rounding')
+
+ return ans
+
+ _pick_rounding_function = {}
+
+ def _round_down(self, prec, expdiff, context):
+ """Also known as round-towards-0, truncate."""
+ return Decimal( (self._sign, self._int[:prec], self._exp - expdiff) )
+
+ def _round_half_up(self, prec, expdiff, context, tmp = None):
+ """Rounds 5 up (away from 0)"""
+
+ if tmp is None:
+ tmp = Decimal( (self._sign,self._int[:prec], self._exp - expdiff))
+ if self._int[prec] >= 5:
+ tmp = tmp._increment(round=0, context=context)
+ if len(tmp._int) > prec:
+ return Decimal( (tmp._sign, tmp._int[:-1], tmp._exp + 1))
+ return tmp
+
+ def _round_half_even(self, prec, expdiff, context):
+ """Round 5 to even, rest to nearest."""
+
+ tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff))
+ half = (self._int[prec] == 5)
+ if half:
+ for digit in self._int[prec+1:]:
+ if digit != 0:
+ half = 0
+ break
+ if half:
+ if self._int[prec-1] & 1 == 0:
+ return tmp
+ return self._round_half_up(prec, expdiff, context, tmp)
+
+ def _round_half_down(self, prec, expdiff, context):
+ """Round 5 down"""
+
+ tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff))
+ half = (self._int[prec] == 5)
+ if half:
+ for digit in self._int[prec+1:]:
+ if digit != 0:
+ half = 0
+ break
+ if half:
+ return tmp
+ return self._round_half_up(prec, expdiff, context, tmp)
+
+ def _round_up(self, prec, expdiff, context):
+ """Rounds away from 0."""
+ tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff) )
+ for digit in self._int[prec:]:
+ if digit != 0:
+ tmp = tmp._increment(round=1, context=context)
+ if len(tmp._int) > prec:
+ return Decimal( (tmp._sign, tmp._int[:-1], tmp._exp + 1))
+ else:
+ return tmp
+ return tmp
+
+ def _round_ceiling(self, prec, expdiff, context):
+ """Rounds up (not away from 0 if negative.)"""
+ if self._sign:
+ return self._round_down(prec, expdiff, context)
+ else:
+ return self._round_up(prec, expdiff, context)
+
+ def _round_floor(self, prec, expdiff, context):
+ """Rounds down (not towards 0 if negative)"""
+ if not self._sign:
+ return self._round_down(prec, expdiff, context)
+ else:
+ return self._round_up(prec, expdiff, context)
+
+ def __pow__(self, n, modulo = None, context=None):
+ """Return self ** n (mod modulo)
+
+ If modulo is None (default), don't take it mod modulo.
+ """
+ n = _convert_other(n)
+ if n is NotImplemented:
+ return n
+
+ if context is None:
+ context = getcontext()
+
+ if self._is_special or n._is_special or n.adjusted() > 8:
+ #Because the spot << doesn't work with really big exponents
+ if n._isinfinity() or n.adjusted() > 8:
+ return context._raise_error(InvalidOperation, 'x ** INF')
+
+ ans = self._check_nans(n, context)
+ if ans:
+ return ans
+
+ if not n._isinteger():
+ return context._raise_error(InvalidOperation, 'x ** (non-integer)')
+
+ if not self and not n:
+ return context._raise_error(InvalidOperation, '0 ** 0')
+
+ if not n:
+ return Decimal(1)
+
+ if self == Decimal(1):
+ return Decimal(1)
+
+ sign = self._sign and not n._iseven()
+ n = int(n)
+
+ if self._isinfinity():
+ if modulo:
+ return context._raise_error(InvalidOperation, 'INF % x')
+ if n > 0:
+ return Infsign[sign]
+ return Decimal( (sign, (0,), 0) )
+
+ #with ludicrously large exponent, just raise an overflow and return inf.
+ if not modulo and n > 0 and (self._exp + len(self._int) - 1) * n > context.Emax \
+ and self:
+
+ tmp = Decimal('inf')
+ tmp._sign = sign
+ context._raise_error(Rounded)
+ context._raise_error(Inexact)
+ context._raise_error(Overflow, 'Big power', sign)
+ return tmp
+
+ elength = len(str(abs(n)))
+ firstprec = context.prec
+
+ if not modulo and firstprec + elength + 1 > DefaultContext.Emax:
+ return context._raise_error(Overflow, 'Too much precision.', sign)
+
+ mul = Decimal(self)
+ val = Decimal(1)
+ context = context._shallow_copy()
+ context.prec = firstprec + elength + 1
+ if n < 0:
+ #n is a long now, not Decimal instance
+ n = -n
+ mul = Decimal(1).__div__(mul, context=context)
+
+ spot = 1
+ while spot <= n:
+ spot <<= 1
+
+ spot >>= 1
+ #Spot is the highest power of 2 less than n
+ while spot:
+ val = val.__mul__(val, context=context)
+ if val._isinfinity():
+ val = Infsign[sign]
+ break
+ if spot & n:
+ val = val.__mul__(mul, context=context)
+ if modulo is not None:
+ val = val.__mod__(modulo, context=context)
+ spot >>= 1
+ context.prec = firstprec
+
+ if context._rounding_decision == ALWAYS_ROUND:
+ return val._fix(context)
+ return val
+
+ 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 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 Decimal( (dup._sign, (0,), 0) )
+ end = len(dup._int)
+ exp = dup._exp
+ while dup._int[end-1] == 0:
+ exp += 1
+ end -= 1
+ return Decimal( (dup._sign, dup._int[:end], exp) )
+
+
+ def quantize(self, exp, rounding=None, context=None, watchexp=1):
+ """Quantize self so its exponent is the same as that of exp.
+
+ Similar to self._rescale(exp._exp) but with error checking.
+ """
+ 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 self #if both are inf, it is OK
+ if context is None:
+ context = getcontext()
+ return context._raise_error(InvalidOperation,
+ 'quantize with one INF')
+ return self._rescale(exp._exp, rounding, context, watchexp)
+
+ def same_quantum(self, other):
+ """Test whether self and other have the same exponent.
+
+ same as self._exp == other._exp, except NaN == sNaN
+ """
+ if self._is_special or other._is_special:
+ if self._isnan() or other._isnan():
+ return self._isnan() and other._isnan() and True
+ if self._isinfinity() or other._isinfinity():
+ return self._isinfinity() and other._isinfinity() and True
+ return self._exp == other._exp
+
+ def _rescale(self, exp, rounding=None, context=None, watchexp=1):
+ """Rescales so that the exponent is exp.
+
+ exp = exp to scale to (an integer)
+ rounding = rounding version
+ watchexp: if set (default) an error is returned if exp is greater
+ than Emax or less than Etiny.
+ """
+ if context is None:
+ context = getcontext()
+
+ if self._is_special:
+ if self._isinfinity():
+ return context._raise_error(InvalidOperation, 'rescale with an INF')
+
+ ans = self._check_nans(context=context)
+ if ans:
+ return ans
+
+ if watchexp and (context.Emax < exp or context.Etiny() > exp):
+ return context._raise_error(InvalidOperation, 'rescale(a, INF)')
+
+ if not self:
+ ans = Decimal(self)
+ ans._int = (0,)
+ ans._exp = exp
+ return ans
+
+ diff = self._exp - exp
+ digits = len(self._int) + diff
+
+ if watchexp and digits > context.prec:
+ return context._raise_error(InvalidOperation, 'Rescale > prec')
+
+ tmp = Decimal(self)
+ tmp._int = (0,) + tmp._int
+ digits += 1
+
+ if digits < 0:
+ tmp._exp = -digits + tmp._exp
+ tmp._int = (0,1)
+ digits = 1
+ tmp = tmp._round(digits, rounding, context=context)
+
+ if tmp._int[0] == 0 and len(tmp._int) > 1:
+ tmp._int = tmp._int[1:]
+ tmp._exp = exp
+
+ tmp_adjusted = tmp.adjusted()
+ if tmp and tmp_adjusted < context.Emin:
+ context._raise_error(Subnormal)
+ elif tmp and tmp_adjusted > context.Emax:
+ return context._raise_error(InvalidOperation, 'rescale(a, INF)')
+ return tmp
+
+ def to_integral(self, rounding=None, context=None):
+ """Rounds to the nearest integer, without raising inexact, rounded."""
+ if self._is_special:
+ ans = self._check_nans(context=context)
+ if ans:
+ return ans
+ if self._exp >= 0:
+ return self
+ if context is None:
+ context = getcontext()
+ flags = context._ignore_flags(Rounded, Inexact)
+ ans = self._rescale(0, rounding, context=context)
+ context._regard_flags(flags)
+ return ans
+
+ def sqrt(self, context=None):
+ """Return the square root of self.
+
+ Uses a converging algorithm (Xn+1 = 0.5*(Xn + self / Xn))
+ Should quadratically approach the right answer.
+ """
+ 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, using round_down.
+ #if self._exp < 0:
+ # exp = (self._exp+1) // 2
+ #else:
+ exp = (self._exp) // 2
+ if self._sign == 1:
+ #sqrt(-0) = -0
+ return Decimal( (1, (0,), exp))
+ else:
+ return Decimal( (0, (0,), exp))
+
+ if context is None:
+ context = getcontext()
+
+ if self._sign == 1:
+ return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0')
+
+ tmp = Decimal(self)
+
+ expadd = tmp._exp // 2
+ if tmp._exp & 1:
+ tmp._int += (0,)
+ tmp._exp = 0
+ else:
+ tmp._exp = 0
+
+ context = context._shallow_copy()
+ flags = context._ignore_all_flags()
+ firstprec = context.prec
+ context.prec = 3
+ if tmp.adjusted() & 1 == 0:
+ ans = Decimal( (0, (8,1,9), tmp.adjusted() - 2) )
+ ans = ans.__add__(tmp.__mul__(Decimal((0, (2,5,9), -2)),
+ context=context), context=context)
+ ans._exp -= 1 + tmp.adjusted() // 2
+ else:
+ ans = Decimal( (0, (2,5,9), tmp._exp + len(tmp._int)- 3) )
+ ans = ans.__add__(tmp.__mul__(Decimal((0, (8,1,9), -3)),
+ context=context), context=context)
+ ans._exp -= 1 + tmp.adjusted() // 2
+
+ #ans is now a linear approximation.
+
+ Emax, Emin = context.Emax, context.Emin
+ context.Emax, context.Emin = DefaultContext.Emax, DefaultContext.Emin
+
+ half = Decimal('0.5')
+
+ maxp = firstprec + 2
+ rounding = context._set_rounding(ROUND_HALF_EVEN)
+ while 1:
+ context.prec = min(2*context.prec - 2, maxp)
+ ans = half.__mul__(ans.__add__(tmp.__div__(ans, context=context),
+ context=context), context=context)
+ if context.prec == maxp:
+ break
+
+ #round to the answer's precision-- the only error can be 1 ulp.
+ context.prec = firstprec
+ prevexp = ans.adjusted()
+ ans = ans._round(context=context)
+
+ #Now, check if the other last digits are better.
+ context.prec = firstprec + 1
+ # In case we rounded up another digit and we should actually go lower.
+ if prevexp != ans.adjusted():
+ ans._int += (0,)
+ ans._exp -= 1
+
+
+ lower = ans.__sub__(Decimal((0, (5,), ans._exp-1)), context=context)
+ context._set_rounding(ROUND_UP)
+ if lower.__mul__(lower, context=context) > (tmp):
+ ans = ans.__sub__(Decimal((0, (1,), ans._exp)), context=context)
+
+ else:
+ upper = ans.__add__(Decimal((0, (5,), ans._exp-1)),context=context)
+ context._set_rounding(ROUND_DOWN)
+ if upper.__mul__(upper, context=context) < tmp:
+ ans = ans.__add__(Decimal((0, (1,), ans._exp)),context=context)
+
+ ans._exp += expadd
+
+ context.prec = firstprec
+ context.rounding = rounding
+ ans = ans._fix(context)
+
+ rounding = context._set_rounding_decision(NEVER_ROUND)
+ if not ans.__mul__(ans, context=context) == self:
+ # Only rounded/inexact if here.
+ context._regard_flags(flags)
+ context._raise_error(Rounded)
+ context._raise_error(Inexact)
+ else:
+ #Exact answer, so let's set the exponent right.
+ #if self._exp < 0:
+ # exp = (self._exp +1)// 2
+ #else:
+ exp = self._exp // 2
+ context.prec += ans._exp - exp
+ ans = ans._rescale(exp, context=context)
+ context.prec = firstprec
+ context._regard_flags(flags)
+ context.Emax, context.Emin = Emax, Emin
+
+ return ans._fix(context)
+
+ 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)
+ if other is NotImplemented:
+ return other
+
+ 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 != 2:
+ return self
+ if sn == 1 and on != 2:
+ return other
+ return self._check_nans(other, context)
+
+ ans = self
+ 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.
+ if self._sign != other._sign:
+ if self._sign:
+ ans = other
+ elif self._exp < other._exp and not self._sign:
+ ans = other
+ elif self._exp > other._exp and self._sign:
+ ans = other
+ elif c == -1:
+ ans = other
+
+ if context is None:
+ context = getcontext()
+ if context._rounding_decision == ALWAYS_ROUND:
+ return ans._fix(context)
+ return ans
+
+ 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)
+ if other is NotImplemented:
+ return other
+
+ 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 != 2:
+ return self
+ if sn == 1 and on != 2:
+ return other
+ return self._check_nans(other, context)
+
+ ans = self
+ 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.
+ if self._sign != other._sign:
+ if other._sign:
+ ans = other
+ elif self._exp > other._exp and not self._sign:
+ ans = other
+ elif self._exp < other._exp and self._sign:
+ ans = other
+ elif c == 1:
+ ans = other
+
+ if context is None:
+ context = getcontext()
+ if context._rounding_decision == ALWAYS_ROUND:
+ return ans._fix(context)
+ return ans
+
+ def _isinteger(self):
+ """Returns whether self is an integer"""
+ if self._exp >= 0:
+ return True
+ rest = self._int[self._exp:]
+ return rest == (0,)*len(rest)
+
+ def _iseven(self):
+ """Returns 1 if self is even. Assumes self is an integer."""
+ if self._exp > 0:
+ return 1
+ return self._int[-1+self._exp] & 1 == 0
+
+ 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
+
+ # support for pickling, copy, and deepcopy
+ def __reduce__(self):
+ return (self.__class__, (str(self),))
+
+ def __copy__(self):
+ if type(self) == Decimal:
+ return self # I'm immutable; therefore I am my own clone
+ return self.__class__(str(self))
+
+ def __deepcopy__(self, memo):
+ if type(self) == Decimal:
+ return self # My components are also immutable
+ return self.__class__(str(self))
+
+##### Context class ###########################################
+
+
+# get rounding method function:
+rounding_functions = [name for name in Decimal.__dict__.keys() if name.startswith('_round_')]
+for name in rounding_functions:
+ #name is like _round_half_even, goes to the global ROUND_HALF_EVEN value.
+ globalname = name[1:].upper()
+ val = globals()[globalname]
+ Decimal._pick_rounding_function[val] = name
+
+del name, val, globalname, rounding_functions
+
+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)
+ _rounding_decision - ALWAYS_ROUND, NEVER_ROUND -- do 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 incremented.
+ (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,
+ traps=None, flags=None,
+ _rounding_decision=None,
+ Emin=None, Emax=None,
+ capitals=None, _clamp=0,
+ _ignored_flags=None):
+ if flags is None:
+ flags = []
+ if _ignored_flags is None:
+ _ignored_flags = []
+ if not isinstance(flags, dict):
+ flags = dict([(s,s in flags) for s in _signals])
+ del s
+ if traps is not None and not isinstance(traps, dict):
+ traps = dict([(s,s in traps) for s in _signals])
+ del s
+ for name, val in locals().items():
+ if val is None:
+ setattr(self, name, _copy.copy(getattr(DefaultContext, name)))
+ else:
+ setattr(self, name, val)
+ del self.self
+
+ 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' % vars(self))
+ s.append('flags=[' + ', '.join([f.__name__ for f, v in self.flags.items() if v]) + ']')
+ s.append('traps=[' + ', '.join([t.__name__ for t, v in self.traps.items() if v]) + ']')
+ return ', '.join(s) + ')'
+
+ def clear_flags(self):
+ """Reset all flags to zero"""
+ for flag in self.flags:
+ self.flags[flag] = 0
+
+ def _shallow_copy(self):
+ """Returns a shallow copy from self."""
+ nc = Context(self.prec, self.rounding, self.traps, self.flags,
+ self._rounding_decision, self.Emin, self.Emax,
+ self.capitals, self._clamp, self._ignored_flags)
+ return nc
+
+ def copy(self):
+ """Returns a deep copy from self."""
+ nc = Context(self.prec, self.rounding, self.traps.copy(), self.flags.copy(),
+ self._rounding_decision, self.Emin, self.Emax,
+ self.capitals, self._clamp, 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 increments the flag, then, if the corresponding
+ trap_enabler is set, it reaises the exception. Otherwise, it returns
+ the default value after incrementing 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)
+
+ def __hash__(self):
+ """A Context cannot be hashed."""
+ # We inherit object.__hash__, so we must deny this explicitly
+ raise TypeError, "Cannot hash a Context."
+
+ 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_decision(self, type):
+ """Sets the rounding decision.
+
+ Sets the rounding decision, and returns the current (previous)
+ rounding decision. Often used like:
+
+ context = context._shallow_copy()
+ # That so you don't change the calling context
+ # if an error occurs in the middle (say DivisionImpossible is raised).
+
+ rounding = context._set_rounding_decision(NEVER_ROUND)
+ instance = instance / Decimal(2)
+ context._set_rounding_decision(rounding)
+
+ This will make it not round for that operation.
+ """
+
+ rounding = self._rounding_decision
+ self._rounding_decision = type
+ return rounding
+
+ 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."""
+ d = Decimal(num, context=self)
+ return d._fix(self)
+
+ #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")
+ """
+ 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")
+ """
+ return a.__add__(b, context=self)
+
+ def _apply(self, a):
+ return str(a._fix(self))
+
+ 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")
+ """
+ return a.compare(b, context=self)
+
+ 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")
+ """
+ return a.__div__(b, context=self)
+
+ 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")
+ """
+ return a.__floordiv__(b, context=self)
+
+ def divmod(self, a, b):
+ return a.__divmod__(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 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")
+ """
+ return a.max(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 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")
+ """
+ return a.min(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")
+ """
+ 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")
+ """
+ return a.__mul__(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")
+ """
+ return a.normalize(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")
+ """
+ return a.__pos__(context=self)
+
+ def power(self, a, b, modulo=None):
+ """Raises a to the power of b, to modulo if given.
+
+ The right-hand operand must be a whole number whose integer part (after
+ any exponent has been applied) has no more than 9 digits and whose
+ fractional part (if any) is all zeros before any rounding. The operand
+ may be positive, negative, or zero; if negative, the absolute value of
+ the power is used, and the left-hand operand is inverted (divided into
+ 1) before use.
+
+ If the increased precision needed for the intermediate calculations
+ exceeds the capabilities of the implementation then an Invalid operation
+ condition is raised.
+
+ If, when raising to a negative power, an underflow occurs during the
+ division into 1, the operation is not halted at that point but
+ continues.
+
+ >>> ExtendedContext.power(Decimal('2'), Decimal('3'))
+ Decimal("8")
+ >>> ExtendedContext.power(Decimal('2'), Decimal('-3'))
+ Decimal("0.125")
+ >>> ExtendedContext.power(Decimal('1.7'), Decimal('8'))
+ Decimal("69.7575744")
+ >>> ExtendedContext.power(Decimal('Infinity'), Decimal('-2'))
+ Decimal("0")
+ >>> ExtendedContext.power(Decimal('Infinity'), Decimal('-1'))
+ Decimal("0")
+ >>> ExtendedContext.power(Decimal('Infinity'), Decimal('0'))
+ Decimal("1")
+ >>> ExtendedContext.power(Decimal('Infinity'), Decimal('1'))
+ Decimal("Infinity")
+ >>> ExtendedContext.power(Decimal('Infinity'), Decimal('2'))
+ Decimal("Infinity")
+ >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-2'))
+ Decimal("0")
+ >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-1'))
+ Decimal("-0")
+ >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('0'))
+ Decimal("1")
+ >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('1'))
+ Decimal("-Infinity")
+ >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('2'))
+ Decimal("Infinity")
+ >>> ExtendedContext.power(Decimal('0'), Decimal('0'))
+ Decimal("NaN")
+ """
+ return a.__pow__(b, modulo, context=self)
+
+ def quantize(self, a, b):
+ """Returns a value equal to 'a' (rounded) and 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")
+ """
+ return a.quantize(b, context=self)
+
+ 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")
+ """
+ return a.__mod__(b, context=self)
+
+ 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")
+ """
+ return a.remainder_near(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
+ """
+ return a.same_quantum(b)
+
+ def sqrt(self, a):
+ """Returns the 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.prec
+ 9
+ """
+ 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")
+ """
+ return a.__sub__(b, context=self)
+
+ def to_eng_string(self, a):
+ """Converts a number to a string, using scientific notation.
+
+ The operation is not affected by the context.
+ """
+ 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.
+ """
+ return a.__str__(context=self)
+
+ def to_integral(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(Decimal('2.1'))
+ Decimal("2")
+ >>> ExtendedContext.to_integral(Decimal('100'))
+ Decimal("100")
+ >>> ExtendedContext.to_integral(Decimal('100.0'))
+ Decimal("100")
+ >>> ExtendedContext.to_integral(Decimal('101.5'))
+ Decimal("102")
+ >>> ExtendedContext.to_integral(Decimal('-101.5'))
+ Decimal("-102")
+ >>> ExtendedContext.to_integral(Decimal('10E+5'))
+ Decimal("1.0E+6")
+ >>> ExtendedContext.to_integral(Decimal('7.89E+77'))
+ Decimal("7.89E+77")
+ >>> ExtendedContext.to_integral(Decimal('-Inf'))
+ Decimal("-Infinity")
+ """
+ return a.to_integral(context=self)
+
+class _WorkRep(object):
+ __slots__ = ('sign','int','exp')
+ # sign: 0 or 1
+ # int: int or long
+ # 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
+ cum = 0
+ for digit in value._int:
+ cum = cum * 10 + digit
+ self.int = cum
+ 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, shouldround = 0, prec = 0):
+ """Normalizes op1, op2 to have the same exp and length of coefficient.
+
+ Done during addition.
+ """
+ # Yes, the exponent is a long, but the difference between exponents
+ # must be an int-- otherwise you'd get a big memory problem.
+ numdigits = int(op1.exp - op2.exp)
+ if numdigits < 0:
+ numdigits = -numdigits
+ tmp = op2
+ other = op1
+ else:
+ tmp = op1
+ other = op2
+
+
+ if shouldround and numdigits > prec + 1:
+ # Big difference in exponents - check the adjusted exponents
+ tmp_len = len(str(tmp.int))
+ other_len = len(str(other.int))
+ if numdigits > (other_len + prec + 1 - tmp_len):
+ # If the difference in adjusted exps is > prec+1, we know
+ # other is insignificant, so might as well put a 1 after the precision.
+ # (since this is only for addition.) Also stops use of massive longs.
+
+ extend = prec + 2 - tmp_len
+ if extend <= 0:
+ extend = 1
+ tmp.int *= 10 ** extend
+ tmp.exp -= extend
+ other.int = 1
+ other.exp = tmp.exp
+ return op1, op2
+
+ tmp.int *= 10 ** numdigits
+ tmp.exp -= numdigits
+ return op1, op2
+
+def _adjust_coefficients(op1, op2):
+ """Adjust op1, op2 so that op2.int * 10 > op1.int >= op2.int.
+
+ Returns the adjusted op1, op2 as well as the change in op1.exp-op2.exp.
+
+ Used on _WorkRep instances during division.
+ """
+ adjust = 0
+ #If op1 is smaller, make it larger
+ while op2.int > op1.int:
+ op1.int *= 10
+ op1.exp -= 1
+ adjust += 1
+
+ #If op2 is too small, make it larger
+ while op1.int >= (10 * op2.int):
+ op2.int *= 10
+ op2.exp -= 1
+ adjust -= 1
+
+ return op1, op2, adjust
+
+##### Helper Functions ########################################
+
+def _convert_other(other):
+ """Convert other to Decimal.
+
+ Verifies that it's ok to use in an implicit construction.
+ """
+ if isinstance(other, Decimal):
+ return other
+ if isinstance(other, (int, long)):
+ return Decimal(other)
+ return NotImplemented
+
+_infinity_map = {
+ 'inf' : 1,
+ 'infinity' : 1,
+ '+inf' : 1,
+ '+infinity' : 1,
+ '-inf' : -1,
+ '-infinity' : -1
+}
+
+def _isinfinity(num):
+ """Determines whether a string or float is infinity.
+
+ +1 for negative infinity; 0 for finite ; +1 for positive infinity
+ """
+ num = str(num).lower()
+ return _infinity_map.get(num, 0)
+
+def _isnan(num):
+ """Determines whether a string or float is NaN
+
+ (1, sign, diagnostic info as string) => NaN
+ (2, sign, diagnostic info as string) => sNaN
+ 0 => not a NaN
+ """
+ num = str(num).lower()
+ if not num:
+ return 0
+
+ #get the sign, get rid of trailing [+-]
+ sign = 0
+ if num[0] == '+':
+ num = num[1:]
+ elif num[0] == '-': #elif avoids '+-nan'
+ num = num[1:]
+ sign = 1
+
+ if num.startswith('nan'):
+ if len(num) > 3 and not num[3:].isdigit(): #diagnostic info
+ return 0
+ return (1, sign, num[3:].lstrip('0'))
+ if num.startswith('snan'):
+ if len(num) > 4 and not num[4:].isdigit():
+ return 0
+ return (2, sign, num[4:].lstrip('0'))
+ return 0
+
+
+##### 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=[],
+ _rounding_decision=ALWAYS_ROUND,
+ Emax=999999999,
+ Emin=-999999999,
+ capitals=1
+)
+
+# 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=[],
+)
+
+
+##### Useful Constants (internal use only) ####################
+
+#Reusable defaults
+Inf = Decimal('Inf')
+negInf = Decimal('-Inf')
+
+#Infsign[sign] is infinity w/ that sign
+Infsign = (Inf, negInf)
+
+NaN = Decimal('NaN')
+
+
+##### crud for parsing strings #################################
+import re
+
+# There's an optional sign at the start, and an optional exponent
+# at the end. The exponent has an optional sign and at least one
+# digit. In between, must have either at least one digit followed
+# by an optional fraction, or a decimal point followed by at least
+# one digit. Yuck.
+
+_parser = re.compile(r"""
+# \s*
+ (?P<sign>[-+])?
+ (
+ (?P<int>\d+) (\. (?P<frac>\d*))?
+ |
+ \. (?P<onlyfrac>\d+)
+ )
+ ([eE](?P<exp>[-+]? \d+))?
+# \s*
+ $
+""", re.VERBOSE).match #Uncomment the \s* to allow leading or trailing spaces.
+
+del re
+
+# return sign, n, p s.t. float string value == -1**sign * n * 10**p exactly
+
+def _string2exact(s):
+ m = _parser(s)
+ if m is None:
+ raise ValueError("invalid literal for Decimal: %r" % s)
+
+ if m.group('sign') == "-":
+ sign = 1
+ else:
+ sign = 0
+
+ exp = m.group('exp')
+ if exp is None:
+ exp = 0
+ else:
+ exp = int(exp)
+
+ intpart = m.group('int')
+ if intpart is None:
+ intpart = ""
+ fracpart = m.group('onlyfrac')
+ else:
+ fracpart = m.group('frac')
+ if fracpart is None:
+ fracpart = ""
+
+ exp -= len(fracpart)
+
+ mantissa = intpart + fracpart
+ tmp = map(int, mantissa)
+ backup = tmp
+ while tmp and tmp[0] == 0:
+ del tmp[0]
+
+ # It's a zero
+ if not tmp:
+ if backup:
+ return (sign, tuple(backup), exp)
+ return (sign, (0,), exp)
+ mantissa = tuple(tmp)
+
+ return (sign, mantissa, exp)
+
+
+if __name__ == '__main__':
+ import doctest, sys
+ doctest.testmod(sys.modules[__name__])