/External.LCA_RESTRICTED/Languages/IronPython/27/Lib/site-packages/win32com/decimal_23.py

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# <win32com>
# This is a clone of Python 2.4's 'decimal' module.  It will only be used when
# 'import decimal' fails - so is likely to be used in Python 2.3.
# </win32com>
# 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

#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 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 False
        return self.__cmp__(other) == 0

    def __ne__(self, other):
        if not isinstance(other, (Decimal, int, long)):
            return True
        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)

        #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._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 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 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)

        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 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 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)
        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)
        return other.__divmod__(self, context=context)

    def __mod__(self, other, context=None):
        """
        self % other
        """
        other = _convert_other(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)
        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 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)
        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]:
              …