Move Decimal from the sandbox into production.

1 files changed, 3085 insertions, 0 deletions

diff --git a/Lib/decimal.py b/Lib/decimal.py
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+++ b/Lib/decimal.py
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+# 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
+
+
+# Todo:
+#    Add deepcopy and pickle support for contexts
+#    Consider having a SimpleDecimal subclass implementing X3.274 semantics
+#    Improve the Context API
+#         Especially with respect to setting flags and traps
+#         Consider adding a clear_flags() method to Context
+#    Provide a clean way of attaching monetary format representations
+#    Review all exposed constants for utility vs. namespace clutter
+
+
+"""
+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
+
+IEEE standard 854-1987:
+
+    www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html
+
+and ANSI standard X3.274-1996:
+
+    www.rexxla.org/Standards/ansi.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 *
+>>> 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().trap_enablers[DivisionByZero] = 1
+>>> print dig / 0
+Traceback (most recent call last):
+  ...
+  ...
+  ...
+DivisionByZero: x / 0
+>>> c = Context()
+>>> c.trap_enablers[DivisionUndefined] = 0
+>>> print c.flags[DivisionUndefined]
+0
+>>> c.divide(Decimal(0), Decimal(0))
+Decimal("NaN")
+>>> c.trap_enablers[DivisionUndefined] = 1
+>>> print c.flags[DivisionUndefined]
+1
+>>> c.flags[DivisionUndefined] = 0
+>>> print c.flags[DivisionUndefined]
+0
+>>> print c.divide(Decimal(0), Decimal(0))
+Traceback (most recent call last):
+  ...
+  ...
+  ...
+DivisionUndefined: 0 / 0
+>>> print c.flags[DivisionUndefined]
+1
+>>> c.flags[DivisionUndefined] = 0
+>>> c.trap_enablers[DivisionUndefined] = False
+>>> print c.divide(Decimal(0), Decimal(0))
+NaN
+>>> print c.flags[DivisionUndefined]
+1
+>>>
+"""
+
+__all__ = [
+    # Two major classes
+    'Decimal', 'Context',
+
+    # Contexts
+    'DefaultContext', 'BasicDefaultContext', 'ExtendedDefaultContext',
+
+    # Exceptions
+    'DecimalException', 'Clamped', 'InvalidOperation', 'ConversionSyntax',
+    'DivisionByZero', 'DivisionImpossible', 'DivisionUndefined',
+    'Inexact', 'InvalidContext', 'Rounded', 'Subnormal', 'Overflow',
+    'Underflow',
+
+    # Module parameters
+    'SINGLE_PRECISION', 'DEFAULT_MAX_EXPONENT', 'DEFAULT_MIN_EXPONENT',
+
+    # Constants for use in setting up contexts
+    'ROUND_DOWN', 'ROUND_HALF_UP', 'ROUND_HALF_EVEN', 'ROUND_CEILING',
+    'ROUND_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN',
+    'NEVER_ROUND', 'ALWAYS_ROUND',
+    'ExceptionList',    # <-- Used for building trap/flag dictionaries
+
+    # Functions for manipulating contexts
+    'setcontext', 'getcontext',
+
+    # Functions for working with decimals
+    'isinfinity', 'isnan',
+]
+
+import threading
+import copy
+import math
+import operator
+xor = operator.xor
+
+#Precision
+SINGLE_PRECISION = 9
+
+#Exponent Range
+DEFAULT_MAX_EXPONENT = 999999999
+DEFAULT_MIN_EXPONENT = -999999999
+
+#Rounding
+ROUND_DOWN = 'down'
+ROUND_HALF_UP = 'half_up'
+ROUND_HALF_EVEN = 'half_even'
+ROUND_CEILING = 'ceiling'
+ROUND_FLOOR = 'floor'
+ROUND_UP = 'up'
+ROUND_HALF_DOWN = 'half_down'
+
+#Rounding decision
+NEVER_ROUND = 'never'    # Round in division (non-divmod), sqrt ONLY
+ALWAYS_ROUND = 'always'  # Every operation rounds at end.
+
+#Errors
+
+class DecimalException(ArithmeticError):
+    """Base exception class, defines default things.
+
+    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.
+
+    Attributes:
+
+    default -- If the context is basic, the trap_enablers are set to
+               this by default.  Extended contexts start out with them set
+               to 0, regardless.
+
+    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.
+    """
+    default = 1
+    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.
+    """
+    default = 0
+
+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.
+    """
+    default = 0
+
+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.
+    """
+
+
+def _filterfunc(obj):
+    """Returns true if a subclass of DecimalException"""
+    try:
+        return issubclass(obj, DecimalException)
+    except TypeError:
+        return False
+
+#ExceptionList holds the exceptions
+ExceptionList = filter(_filterfunc, globals().values())
+
+del _filterfunc
+
+
+##### Context Functions #######################################
+
+#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."""
+    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
+
+
+##### Decimal class ###########################################
+
+class Decimal(object):
+    """Floating point class for decimal arithmetic."""
+
+    __slots__ = ('_exp','_int','_sign')
+
+    def __init__(self, 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")
+        """
+        if context is None:
+            context = getcontext()
+
+        if isinstance(value, (int,long)):
+            value = str(value)
+
+        # String?
+        # REs insist on real strings, so we can too.
+        if isinstance(value, basestring):
+            if isinfinity(value):
+                self._exp = 'F'
+                self._int = (0,)
+                sign = isinfinity(value)
+                if sign == 1:
+                    self._sign = 0
+                else:
+                    self._sign = 1
+                return
+            if isnan(value):
+                sig, sign, diag = isnan(value)
+                if len(diag) > context.prec: #Diagnostic info too long
+                    self._sign, self._int, self._exp = \
+                                context._raise_error(ConversionSyntax)
+                    return
+                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._convertString(value, context)
+            return
+
+        # 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]
+            else:
+                self._exp  = int(value[2])
+            return
+
+        # Turn an intermediate value back to Decimal()
+        if isinstance(value, _WorkRep):
+            if value.sign == 1:
+                self._sign = 0
+            else:
+                self._sign = 1
+            self._int = tuple(value.int)
+            self._exp = int(value.exp)
+            return
+
+        if isinstance(value, Decimal):
+          self._exp  = value._exp
+          self._sign = value._sign
+          self._int  = value._int
+          return
+
+        raise TypeError("Can't convert %r" % value)
+
+    def _convert_other(self, 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)):
+            other = Decimal(other)
+            return other
+
+        raise TypeError, "You can interact Decimal only with int, long or Decimal data types."
+
+    def _isnan(self):
+        """Returns whether the number is not actually one.
+
+        0 if a number
+        1 if NaN
+        2 if sNaN
+        """
+        if self._exp == 'n':
+            return 1
+        elif self._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.
+        """
+        if context is None:
+            context = getcontext()
+
+        if self._isnan() == 2:
+            return context._raise_error(InvalidOperation, 'sNaN',
+                                       1, self)
+        if other is not None and other._isnan() == 2:
+            return context._raise_error(InvalidOperation, 'sNaN',
+                                       1, other)
+        if self._isnan():
+            return self
+        if other is not None and other._isnan():
+            return other
+        return 0
+
+    def _convertString(self, value, context=None):
+        """Changes self's value to that in a string.
+
+        A bad string causes a ConversionSyntax error.
+        """
+        if context is None:
+            context = getcontext()
+        try:
+            self._sign, self._int, self._exp = _string2exact(value)
+        except ValueError:
+            self._sign, self._int, self._exp = context._raise_error(ConversionSyntax)
+        return
+
+    def __nonzero__(self):
+        """Is the number non-zero?
+
+        0 if self == 0
+        1 if self != 0
+        """
+        if isinstance(self._exp, str):
+            return 1
+        return self._int != (0,)*len(self._int)
+
+    def __cmp__(self, other, context=None):
+        if context is None:
+            context = getcontext()
+        other = self._convert_other(other)
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return 1
+
+        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
+
+        # INF = INF
+        if self._isinfinity() and other._isinfinity():
+            return 0
+        if self._isinfinity():
+            return (-1)**self._sign
+        if other._isinfinity():
+            return -((-1)**other._sign)
+
+        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)
+
+        context = context.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 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.
+        """
+        if context is None:
+            context = getcontext()
+        other = self._convert_other(other)
+
+        #compare(NaN, NaN) = NaN
+        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)
+        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__.
+        """
+        if context is None:
+            context = getcontext()
+        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 context is None:
+            context = getcontext()
+        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._rounding_decision == ALWAYS_ROUND:
+            return Decimal((sign, self._int, self._exp))._fix(context=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 context is None:
+            context = getcontext()
+        ans = self._check_nans(context=context)
+        if ans:
+            return ans
+
+        sign = self._sign
+        if not self:
+            # + (-0) = 0
+            sign = 0
+
+        if context._rounding_decision == ALWAYS_ROUND:
+            ans = self._fix(context=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 context is None:
+            context = getcontext()
+        ans = self._check_nans(context=context)
+        if ans:
+            return ans
+
+        if not round:
+            context = context.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.
+        """
+        if context is None:
+            context = getcontext()
+        other = self._convert_other(other)
+
+        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:
+            if exp < other._exp - context.prec-1:
+                exp = other._exp - context.prec-1
+            ans = other._rescale(exp, watchexp=0, context=context)
+            if shouldround:
+                ans = ans._fix(context=context)
+            return ans
+        if not other:
+            if exp < self._exp - context.prec-1:
+                exp = self._exp - context.prec-1
+            ans = self._rescale(exp, watchexp=0, context=context)
+            if shouldround:
+                ans = ans._fix(context=context)
+            return ans
+
+        op1 = _WorkRep(self)
+        op2 = _WorkRep(other)
+        op1, op2 = _normalize(op1, op2, shouldround, context.prec)
+
+        result = _WorkRep()
+
+        if op1.sign != op2.sign:
+            diff = cmp(abs(op1), abs(op2))
+            # Equal and opposite
+            if diff == 0:
+                if exp < context.Etiny():
+                    exp = context.Etiny()
+                    context._raise_error(Clamped)
+                return Decimal((negativezero, (0,), exp))
+            if diff < 0:
+                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 = 1
+                #So we know the sign, and op1 > 0.
+        elif op1.sign == -1:
+            result.sign = -1
+            op1.sign, op2.sign = (1, 1)
+        else:
+            result.sign = 1
+        #Now, op1 > abs(op2) > 0
+
+        op1.int.reverse()
+        op2.int.reverse()
+
+        if op2.sign == 1:
+            result.int = resultint = map(operator.add, op1.int, op2.int)
+            carry = 0
+            for i in xrange(len(op1.int)):
+                tmp = resultint[i] + carry
+                carry = 0
+                if tmp > 9:
+                    carry = 1
+                    tmp -= 10
+                resultint[i] = tmp
+            if carry:
+                resultint.append(1)
+        else:
+            result.int = resultint = map(operator.sub, op1.int, op2.int)
+            loan = 0
+            for i in xrange(len(op1.int)):
+                tmp = resultint[i] - loan
+                loan = 0
+                if tmp < 0:
+                    loan = 1
+                    tmp += 10
+                resultint[i] = tmp
+            assert not loan
+
+        while resultint[-1] == 0:
+            resultint.pop()
+        resultint.reverse()
+
+        result.exp = op1.exp
+        ans = Decimal(result)
+        if shouldround:
+            ans = ans._fix(context=context)
+        return ans
+
+    __radd__ = __add__
+
+    def __sub__(self, other, context=None):
+        """Return self + (-other)"""
+        if context is None:
+            context = getcontext()
+        other = self._convert_other(other)
+
+        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)"""
+        if context is None:
+            context = getcontext()
+        other = self._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 context is None:
+            context = getcontext()
+        ans = self._check_nans(context=context)
+        if ans:
+            return ans
+
+        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 round and context._rounding_decision == ALWAYS_ROUND:
+            ans = ans._fix(context=context)
+        return ans
+
+    def __mul__(self, other, context=None):
+        """Return self * other.
+
+        (+-) INF * 0 (or its reverse) raise InvalidOperation.
+        """
+        if context is None:
+            context = getcontext()
+        other = self._convert_other(other)
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+
+        resultsign = xor(self._sign, other._sign)
+        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=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=context)
+            return ans
+        if other._int == (1,):
+            ans = Decimal((resultsign, self._int, resultexp))
+            if shouldround:
+                ans = ans._fix(context=context)
+            return ans
+
+        op1 = list(self._int)
+        op2 = list(other._int)
+        op1.reverse()
+        op2.reverse()
+        # Minimize Decimal additions
+        if len(op2) > len(op1):
+            op1, op2 = op2, op1
+
+        _divmod = divmod
+        accumulator = [0]*(len(self._int) + len(other._int))
+        for i in xrange(len(op2)):
+            if op2[i] == 0:
+                continue
+            mult = op2[i]
+            carry = 0
+            for j in xrange(len(op1)):
+                carry, accumulator[i+j] = _divmod( mult * op1[j] + carry
+                                                  + accumulator[i+j], 10)
+
+            if carry:
+                accumulator[i + j + 1] += carry
+        while not accumulator[-1]:
+            accumulator.pop()
+        accumulator.reverse()
+
+        ans = Decimal( (resultsign, accumulator, resultexp))
+        if shouldround:
+            ans = ans._fix(context=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.
+        """
+        if context is None:
+            context = getcontext()
+        other = self._convert_other(other)
+
+        ans = self._check_nans(other, context)
+        if ans:
+            if divmod:
+                return (ans, ans)
+            else:
+                return ans
+
+        sign = xor(self._sign, other._sign)
+        if not self and not other:
+            if divmod:
+                return context._raise_error(DivisionUndefined, '0 / 0', 1)
+            return context._raise_error(DivisionUndefined, '0 / 0')
+        if self._isinfinity() and other._isinfinity():
+            if not divmod:
+                return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF')
+            else:
+                return (context._raise_error(InvalidOperation,
+                                         '(+-)INF // (+-)INF'),
+                        context._raise_error(InvalidOperation,
+                                         '(+-)INF % (+-)INF'))
+
+        if not divmod:
+            if other._isinfinity():
+                context._raise_error(Clamped, 'Division by infinity')
+                return Decimal((sign, (0,), context.Etiny()))
+            if self._isinfinity():
+                return Infsign[sign]
+            #These two have different precision.
+            if not self:
+                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:
+                return context._raise_error(DivisionByZero, 'x / 0', sign)
+        if divmod:
+            if other._isinfinity():
+                return (Decimal((sign, (0,), 0)), Decimal(self))
+            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'))
+            if not self:
+                otherside = Decimal(self)
+                otherside._exp = min(self._exp, other._exp)
+                return (Decimal((sign, (0,), 0)),  otherside)
+
+            if not other:
+                return context._raise_error(DivisionByZero, 'divmod(x,0)',
+                                           sign, 1)
+
+        #OK, so neither = 0, INF
+
+        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=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))
+
+        if sign:
+            sign = -1
+        else:
+            sign = 1
+        adjust = 0
+        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)
+
+        ans = None
+        while 1:
+            while( (len(op2.int) < len(op1.int) and op1.int[0]) or
+                   (len(op2.int) == len(op1.int) and op2.int <= op1.int)):
+                   #Meaning, while op2.int < op1.int, when normalized.
+                res._increment()
+                op1.subtract(op2.int)
+            if res.exp == 0 and divmod:
+                if len(res.int) > context.prec 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=context)
+                return (Decimal(res), otherside)
+
+            if op1.int == [0]*len(op1.int) and adjust >= 0 and not divmod:
+                break
+            if (len(res.int) > context.prec) 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]*len(op1.int):
+                    res.int.append(1)
+                    res.exp -= 1
+
+                break
+            res.exp -= 1
+            adjust += 1
+            res.int.append(0)
+            op1.int.append(0)
+            op1.exp -= 1
+
+            if res.exp == 0 and divmod and (len(op2.int) > len(op1.int) or
+                                            (len(op2.int) == len(op1.int) and
+                                             op2.int > op1.int)):
+                #Solves an error in precision.  Same as a previous block.
+
+                if len(res.int) > context.prec 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=context)
+        return ans
+
+    def __rdiv__(self, other, context=None):
+        """Swaps self/other and returns __div__."""
+        other = self._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 = self._convert_other(other)
+        return other.__divmod__(self, context=context)
+
+    def __mod__(self, other, context=None):
+        """
+        self % other
+        """
+        if context is None:
+            context = getcontext()
+        other = self._convert_other(other)
+
+        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 = self._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
+        """
+        if context is None:
+            context = getcontext()
+        other = self._convert_other(other)
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+        if self and not other:
+            return context._raise_error(InvalidOperation, 'x % 0')
+
+        # If DivisionImpossible causes an error, do not leave Rounded/Inexact
+        # ignored in the calling function.
+        context = context.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.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=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=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 = self._convert_other(other)
+        return other.__floordiv__(self, context=context)
+
+    def __float__(self):
+        """Float representation."""
+        return float(str(self))
+
+    def __int__(self):
+        """Converts self to a int, truncating if necessary."""
+        # XXX This should be implemented in terms of tested
+        # functions in the standard
+        if self._isnan():
+            context = getcontext()
+            return context._raise_error(InvalidContext)
+        elif self._isinfinity():
+            raise OverflowError, "Cannot convert infinity to long"
+        if not self:
+            return 0
+        sign = '-'*self._sign
+        if self._exp >= 0:
+            s = sign + ''.join(map(str, self._int)) + '0'*self._exp
+            return int(s)
+        s = sign + ''.join(map(str, self._int))[:self._exp]
+        return int(s)
+        tmp = list(self._int)
+        tmp.reverse()
+        val = 0
+        while tmp:
+            val *= 10
+            val += tmp.pop()
+        return int(((-1) ** self._sign) * val * 10.**int(self._exp))
+
+    def __long__(self):
+        """Converts to a long.
+
+        Equivalent to long(int(self))
+        """
+        return long(self.__int__())
+
+    def _fix(self, prec=None, rounding=None, folddown=None, context=None):
+        """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
+        prec - precision to which  to round.  By default, the context decides.
+        rounding - Rounding method.  By default, the context decides.
+        folddown - Fold down high elements, by default context._clamp
+        context - context used.
+        """
+        if self._isinfinity() or self._isnan():
+            return self
+        if context is None:
+            context = getcontext()
+        if prec is None:
+            prec = context.prec
+        ans = Decimal(self)
+        ans = ans._fixexponents(prec, rounding, folddown=folddown,
+                               context=context)
+        if len(ans._int) > prec:
+            ans = ans._round(prec, rounding, context=context)
+        ans = ans._fixexponents(prec, rounding, folddown=folddown,
+                               context=context)
+        return ans
+
+    def _fixexponents(self, prec=None, rounding=None, folddown=None,
+                     context=None):
+        """Fix the exponents and return a copy with the exponent in bounds."""
+        if self._isinfinity():
+            return self
+        if context is None:
+            context = getcontext()
+        if prec is None:
+            prec = context.prec
+        if folddown is None:
+            folddown = context._clamp
+        Emin, Emax = context.Emin, context.Emax
+        Etop = context.Etop()
+        ans = Decimal(self)
+        if ans.adjusted() < Emin:
+            Etiny = context.Etiny()
+            if ans._exp < Etiny:
+                if not ans:
+                    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)
+        elif folddown and ans._exp > Etop:
+            context._raise_error(Clamped)
+            ans = ans._rescale(Etop, context=context)
+        elif ans.adjusted() > Emax:
+            if not ans:
+                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 context is None:
+            context = getcontext()
+        ans = self._check_nans(context=context)
+        if ans:
+            return ans
+
+        if self._isinfinity():
+            return Decimal(self)
+
+        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.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] %2 == 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.
+        """
+        if context is None:
+            context = getcontext()
+        n = self._convert_other(n)
+
+        #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._isinfinity() and 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 > DEFAULT_MAX_EXPONENT:
+            return context._raise_error(Overflow, 'Too much precision.', sign)
+
+        mul = Decimal(self)
+        val = Decimal(1)
+        context = context.copy()
+        context.prec = firstprec + elength + 1
+        rounding = context.rounding
+        if n < 0:
+            #n is a long now, not Decimal instance
+            n = -n
+            mul = Decimal(1).__div__(mul, context=context)
+
+        shouldround = context._rounding_decision == ALWAYS_ROUND
+
+        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 shouldround:
+            return val._fix(context=context)
+        return val
+
+    def __rpow__(self, other, context=None):
+        """Swaps self/other and returns __pow__."""
+        other = self._convert_other(other)
+        return other.__pow__(self, context=context)
+
+    def normalize(self, context=None):
+        """Normalize- strip trailing 0s, change anything equal to 0 to 0e0"""
+        if context is None:
+            context = getcontext()
+
+        ans = self._check_nans(context=context)
+        if ans:
+            return ans
+
+        dup = self._fix(context=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 context is None:
+            context = getcontext()
+
+        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
+            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._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._isinfinity():
+            return context._raise_error(InvalidOperation, 'rescale with an INF')
+
+        ans = self._check_nans(context=context)
+        if ans:
+            return ans
+
+        out = 0
+
+        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
+
+        prevexact = context.flags[Inexact]
+        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
+
+        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 context is None:
+            context = getcontext()
+        ans = self._check_nans(context=context)
+        if ans:
+            return ans
+        if self._exp >= 0:
+            return self
+        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 context is None:
+            context = getcontext()
+
+        ans = self._check_nans(context=context)
+        if ans:
+            return ans
+
+        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 self._sign == 1:
+            return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0')
+
+        if self._isinfinity():
+            return Decimal(self)
+
+        tmp = Decimal(self)
+
+        expadd = tmp._exp / 2
+        if tmp._exp % 2 == 1:
+            tmp._int += (0,)
+            tmp._exp = 0
+        else:
+            tmp._exp = 0
+
+        context = context.copy()
+        flags = context._ignore_all_flags()
+        firstprec = context.prec
+        context.prec = 3
+        if tmp.adjusted() % 2 == 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 = DEFAULT_MAX_EXPONENT, DEFAULT_MIN_EXPONENT
+
+
+        half = Decimal('0.5')
+
+        count = 1
+        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=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=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.
+        """
+        if context is None:
+            context = getcontext()
+        other = self._convert_other(other)
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+
+        ans = self
+        if self < other:
+            ans = other
+        shouldround = context._rounding_decision == ALWAYS_ROUND
+        if shouldround:
+            ans = ans._fix(context=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.
+        """
+        if context is None:
+            context = getcontext()
+        other = self._convert_other(other)
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+
+        ans = self
+
+        if self > other:
+            ans = other
+
+        if context._rounding_decision == ALWAYS_ROUND:
+            ans = ans._fix(context=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] % 2 == 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
+
+    #properties to immutability-near feature
+    def _get_sign(self):
+        return self._sign
+    def _get_int(self):
+        return self._int
+    def _get_exp(self):
+        return self._exp
+    sign = property(_get_sign)
+    int = property(_get_int)
+    exp = property(_get_exp)
+
+    # 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))
+
+
+# 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
+
+DefaultLock = threading.Lock()
+
+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?
+    trap_enablers - If trap_enablers[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 (defaults to -999999999)
+    Emax -   Maximum exponent (defaults to 999999999)
+    capitals -      If 1, 1*10^1 is printed as 1E+1.
+                    If 0, printed as 1e1
+                    (Defaults to 1)
+    clamp - If 1, change exponents if too high (Default 0)
+    """
+    def __init__(self, prec=None, rounding=None,
+                 trap_enablers=None, flags=None,
+                 _rounding_decision=None,
+                 Emin=DEFAULT_MIN_EXPONENT, Emax=DEFAULT_MAX_EXPONENT,
+                 capitals=1, _clamp=0,
+                 _ignored_flags=[]):
+        DefaultLock.acquire()
+        for name, val in locals().items():
+            if val is None:
+                setattr(self, name, copy.copy(getattr(DefaultContext, name)))
+            else:
+                setattr(self, name, val)
+        DefaultLock.release()
+        del self.self
+
+    def copy(self):
+        """Returns a copy from self."""
+        nc = Context(self.prec, self.rounding, self.trap_enablers, self.flags,
+                         self._rounding_decision, self.Emin, self.Emax,
+                         self.capitals, self._clamp, self._ignored_flags)
+        return nc
+    __copy__ = copy
+
+    def _raise_error(self, error, 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.
+        """
+        if error in self._ignored_flags:
+            #Don't touch the flag
+            return error().handle(self, *args)
+
+        self.flags[error] += 1
+        if not self.trap_enablers[error]:
+            #The errors define how to handle themselves.
+            return error().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(*ExceptionList)
+
+    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 Etiny(self):
+        """Returns Etiny (= Emin - prec + 1)"""
+        return int(self.Emin - self.prec + 1)
+
+    def Etop(self):
+        """Returns maximum exponent (= Emin - 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.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):
+        """Creates a new Decimal instance but using self as context."""
+        d = Decimal(num, context=self)
+        return d._fix(context=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.
+
+        >>> DefaultContext.abs(Decimal('2.1'))
+        Decimal("2.1")
+        >>> DefaultContext.abs(Decimal('-100'))
+        Decimal("100")
+        >>> DefaultContext.abs(Decimal('101.5'))
+        Decimal("101.5")
+        >>> DefaultContext.abs(Decimal('-101.5'))
+        Decimal("101.5")
+        """
+        return a.__abs__(context=self)
+
+    def add(self, a, b):
+        """Return the sum of the two operands.
+
+        >>> DefaultContext.add(Decimal('12'), Decimal('7.00'))
+        Decimal("19.00")
+        >>> DefaultContext.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(context=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.
+
+        >>> DefaultContext.compare(Decimal('2.1'), Decimal('3'))
+        Decimal("-1")
+        >>> DefaultContext.compare(Decimal('2.1'), Decimal('2.1'))
+        Decimal("0")
+        >>> DefaultContext.compare(Decimal('2.1'), Decimal('2.10'))
+        Decimal("0")
+        >>> DefaultContext.compare(Decimal('3'), Decimal('2.1'))
+        Decimal("1")
+        >>> DefaultContext.compare(Decimal('2.1'), Decimal('-3'))
+        Decimal("1")
+        >>> DefaultContext.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.
+
+        >>> DefaultContext.divide(Decimal('1'), Decimal('3'))
+        Decimal("0.333333333")
+        >>> DefaultContext.divide(Decimal('2'), Decimal('3'))
+        Decimal("0.666666667")
+        >>> DefaultContext.divide(Decimal('5'), Decimal('2'))
+        Decimal("2.5")
+        >>> DefaultContext.divide(Decimal('1'), Decimal('10'))
+        Decimal("0.1")
+        >>> DefaultContext.divide(Decimal('12'), Decimal('12'))
+        Decimal("1")
+        >>> DefaultContext.divide(Decimal('8.00'), Decimal('2'))
+        Decimal("4.00")
+        >>> DefaultContext.divide(Decimal('2.400'), Decimal('2.0'))
+        Decimal("1.20")
+        >>> DefaultContext.divide(Decimal('1000'), Decimal('100'))
+        Decimal("10")
+        >>> DefaultContext.divide(Decimal('1000'), Decimal('1'))
+        Decimal("1000")
+        >>> DefaultContext.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.
+
+        >>> DefaultContext.divide_int(Decimal('2'), Decimal('3'))
+        Decimal("0")
+        >>> DefaultContext.divide_int(Decimal('10'), Decimal('3'))
+        Decimal("3")
+        >>> DefaultContext.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.
+
+        >>> DefaultContext.max(Decimal('3'), Decimal('2'))
+        Decimal("3")
+        >>> DefaultContext.max(Decimal('-10'), Decimal('3'))
+        Decimal("3")
+        >>> DefaultContext.max(Decimal('1.0'), Decimal('1'))
+        Decimal("1.0")
+        """
+        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.
+
+        >>> DefaultContext.min(Decimal('3'), Decimal('2'))
+        Decimal("2")
+        >>> DefaultContext.min(Decimal('-10'), Decimal('3'))
+        Decimal("-10")
+        >>> DefaultContext.min(Decimal('1.0'), Decimal('1'))
+        Decimal("1.0")
+        """
+        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.
+
+        >>> DefaultContext.minus(Decimal('1.3'))
+        Decimal("-1.3")
+        >>> DefaultContext.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.
+
+        >>> DefaultContext.multiply(Decimal('1.20'), Decimal('3'))
+        Decimal("3.60")
+        >>> DefaultContext.multiply(Decimal('7'), Decimal('3'))
+        Decimal("21")
+        >>> DefaultContext.multiply(Decimal('0.9'), Decimal('0.8'))
+        Decimal("0.72")
+        >>> DefaultContext.multiply(Decimal('0.9'), Decimal('-0'))
+        Decimal("-0.0")
+        >>> DefaultContext.multiply(Decimal('654321'), Decimal('654321'))
+        Decimal("4.28135971E+11")
+        """
+        return a.__mul__(b, context=self)
+
+    def normalize(self, a):
+        """normalize reduces its operand to its simplest form.
+
+        Essentially a plus operation with all trailing zeros removed from the
+        result.
+
+        >>> DefaultContext.normalize(Decimal('2.1'))
+        Decimal("2.1")
+        >>> DefaultContext.normalize(Decimal('-2.0'))
+        Decimal("-2")
+        >>> DefaultContext.normalize(Decimal('1.200'))
+        Decimal("1.2")
+        >>> DefaultContext.normalize(Decimal('-120'))
+        Decimal("-1.2E+2")
+        >>> DefaultContext.normalize(Decimal('120.00'))
+        Decimal("1.2E+2")
+        >>> DefaultContext.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.
+
+        >>> DefaultContext.plus(Decimal('1.3'))
+        Decimal("1.3")
+        >>> DefaultContext.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.
+
+        >>> DefaultContext.power(Decimal('2'), Decimal('3'))
+        Decimal("8")
+        >>> DefaultContext.power(Decimal('2'), Decimal('-3'))
+        Decimal("0.125")
+        >>> DefaultContext.power(Decimal('1.7'), Decimal('8'))
+        Decimal("69.7575744")
+        >>> DefaultContext.power(Decimal('Infinity'), Decimal('-2'))
+        Decimal("0")
+        >>> DefaultContext.power(Decimal('Infinity'), Decimal('-1'))
+        Decimal("0")
+        >>> DefaultContext.power(Decimal('Infinity'), Decimal('0'))
+        Decimal("1")
+        >>> DefaultContext.power(Decimal('Infinity'), Decimal('1'))
+        Decimal("Infinity")
+        >>> DefaultContext.power(Decimal('Infinity'), Decimal('2'))
+        Decimal("Infinity")
+        >>> DefaultContext.power(Decimal('-Infinity'), Decimal('-2'))
+        Decimal("0")
+        >>> DefaultContext.power(Decimal('-Infinity'), Decimal('-1'))
+        Decimal("-0")
+        >>> DefaultContext.power(Decimal('-Infinity'), Decimal('0'))
+        Decimal("1")
+        >>> DefaultContext.power(Decimal('-Infinity'), Decimal('1'))
+        Decimal("-Infinity")
+        >>> DefaultContext.power(Decimal('-Infinity'), Decimal('2'))
+        Decimal("Infinity")
+        >>> DefaultContext.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.
+
+        >>> DefaultContext.quantize(Decimal('2.17'), Decimal('0.001'))
+        Decimal("2.170")
+        >>> DefaultContext.quantize(Decimal('2.17'), Decimal('0.01'))
+        Decimal("2.17")
+        >>> DefaultContext.quantize(Decimal('2.17'), Decimal('0.1'))
+        Decimal("2.2")
+        >>> DefaultContext.quantize(Decimal('2.17'), Decimal('1e+0'))
+        Decimal("2")
+        >>> DefaultContext.quantize(Decimal('2.17'), Decimal('1e+1'))
+        Decimal("0E+1")
+        >>> DefaultContext.quantize(Decimal('-Inf'), Decimal('Infinity'))
+        Decimal("-Infinity")
+        >>> DefaultContext.quantize(Decimal('2'), Decimal('Infinity'))
+        Decimal("NaN")
+        >>> DefaultContext.quantize(Decimal('-0.1'), Decimal('1'))
+        Decimal("-0")
+        >>> DefaultContext.quantize(Decimal('-0'), Decimal('1e+5'))
+        Decimal("-0E+5")
+        >>> DefaultContext.quantize(Decimal('+35236450.6'), Decimal('1e-2'))
+        Decimal("NaN")
+        >>> DefaultContext.quantize(Decimal('-35236450.6'), Decimal('1e-2'))
+        Decimal("NaN")
+        >>> DefaultContext.quantize(Decimal('217'), Decimal('1e-1'))
+        Decimal("217.0")
+        >>> DefaultContext.quantize(Decimal('217'), Decimal('1e-0'))
+        Decimal("217")
+        >>> DefaultContext.quantize(Decimal('217'), Decimal('1e+1'))
+        Decimal("2.2E+2")
+        >>> DefaultContext.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).
+
+        >>> DefaultContext.remainder(Decimal('2.1'), Decimal('3'))
+        Decimal("2.1")
+        >>> DefaultContext.remainder(Decimal('10'), Decimal('3'))
+        Decimal("1")
+        >>> DefaultContext.remainder(Decimal('-10'), Decimal('3'))
+        Decimal("-1")
+        >>> DefaultContext.remainder(Decimal('10.2'), Decimal('1'))
+        Decimal("0.2")
+        >>> DefaultContext.remainder(Decimal('10'), Decimal('0.3'))
+        Decimal("0.1")
+        >>> DefaultContext.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).
+
+        >>> DefaultContext.remainder_near(Decimal('2.1'), Decimal('3'))
+        Decimal("-0.9")
+        >>> DefaultContext.remainder_near(Decimal('10'), Decimal('6'))
+        Decimal("-2")
+        >>> DefaultContext.remainder_near(Decimal('10'), Decimal('3'))
+        Decimal("1")
+        >>> DefaultContext.remainder_near(Decimal('-10'), Decimal('3'))
+        Decimal("-1")
+        >>> DefaultContext.remainder_near(Decimal('10.2'), Decimal('1'))
+        Decimal("0.2")
+        >>> DefaultContext.remainder_near(Decimal('10'), Decimal('0.3'))
+        Decimal("0.1")
+        >>> DefaultContext.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.
+
+        >>> DefaultContext.same_quantum(Decimal('2.17'), Decimal('0.001'))
+        False
+        >>> DefaultContext.same_quantum(Decimal('2.17'), Decimal('0.01'))
+        True
+        >>> DefaultContext.same_quantum(Decimal('2.17'), Decimal('1'))
+        False
+        >>> DefaultContext.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.
+
+        >>> DefaultContext.sqrt(Decimal('0'))
+        Decimal("0")
+        >>> DefaultContext.sqrt(Decimal('-0'))
+        Decimal("-0")
+        >>> DefaultContext.sqrt(Decimal('0.39'))
+        Decimal("0.624499800")
+        >>> DefaultContext.sqrt(Decimal('100'))
+        Decimal("10")
+        >>> DefaultContext.sqrt(Decimal('1'))
+        Decimal("1")
+        >>> DefaultContext.sqrt(Decimal('1.0'))
+        Decimal("1.0")
+        >>> DefaultContext.sqrt(Decimal('1.00'))
+        Decimal("1.0")
+        >>> DefaultContext.sqrt(Decimal('7'))
+        Decimal("2.64575131")
+        >>> DefaultContext.sqrt(Decimal('10'))
+        Decimal("3.16227766")
+        """
+        return a.sqrt(context=self)
+
+    def subtract(self, a, b):
+        """Return the sum of the two operands.
+
+        >>> DefaultContext.subtract(Decimal('1.3'), Decimal('1.07'))
+        Decimal("0.23")
+        >>> DefaultContext.subtract(Decimal('1.3'), Decimal('1.30'))
+        Decimal("0.00")
+        >>> DefaultContext.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.
+
+        >>> DefaultContext.to_integral(Decimal('2.1'))
+        Decimal("2")
+        >>> DefaultContext.to_integral(Decimal('100'))
+        Decimal("100")
+        >>> DefaultContext.to_integral(Decimal('100.0'))
+        Decimal("100")
+        >>> DefaultContext.to_integral(Decimal('101.5'))
+        Decimal("102")
+        >>> DefaultContext.to_integral(Decimal('-101.5'))
+        Decimal("-102")
+        >>> DefaultContext.to_integral(Decimal('10E+5'))
+        Decimal("1.0E+6")
+        >>> DefaultContext.to_integral(Decimal('7.89E+77'))
+        Decimal("7.89E+77")
+        >>> DefaultContext.to_integral(Decimal('-Inf'))
+        Decimal("-Infinity")
+        """
+        return a.to_integral(context=self)
+
+class _WorkRep(object):
+    __slots__ = ('sign','int','exp')
+    # sign: -1 None 1
+    # int:  list
+    # exp:  None, int, or string
+
+    def __init__(self, value=None):
+        if value is None:
+            self.sign = None
+            self.int = []
+            self.exp = None
+        if isinstance(value, Decimal):
+            if value._sign:
+                self.sign = -1
+            else:
+                self.sign = 1
+            self.int = list(value._int)
+            self.exp = value._exp
+        if 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 __neg__(self):
+        if self.sign == 1:
+            return _WorkRep( (-1, self.int, self.exp) )
+        else:
+            return _WorkRep( (1, self.int, self.exp) )
+
+    def __abs__(self):
+        if self.sign == -1:
+            return -self
+        else:
+            return self
+
+    def __cmp__(self, other):
+        if self.exp != other.exp:
+            raise ValueError("Operands not normalized: %r, %r" % (self, other))
+        if self.sign != other.sign:
+            if self.sign == -1:
+                return -1
+            else:
+                return 1
+        if self.sign == -1:
+            direction = -1
+        else:
+            direction = 1
+        int1 = self.int
+        int2 = other.int
+        if len(int1) > len(int2):
+            return direction * 1
+        if len(int1) < len(int2):
+            return direction * -1
+        for i in xrange(len(int1)):
+            if int1[i] > int2[i]:
+                return direction * 1
+            if int1[i] < int2[i]:
+                return direction * -1
+        return 0
+
+    def _increment(self):
+        curspot = len(self.int) - 1
+        self.int[curspot]+= 1
+        while (self.int[curspot] >= 10):
+            self.int[curspot] -= 10
+            if curspot == 0:
+                self.int[0:0] = [1]
+                break
+            self.int[curspot-1] += 1
+            curspot -= 1
+
+    def subtract(self, alist):
+        """Subtract a list from the current int (in place).
+
+        It is assured that (len(list) = len(self.int) and list < self.int) or
+        len(list) = len(self.int)-1
+        (i.e. that int(join(list)) < int(join(self.int)))
+        """
+
+        selfint = self.int
+        selfint.reverse()
+        alist.reverse()
+
+        carry = 0
+        for x in xrange(len(alist)):
+            selfint[x] -= alist[x] + carry
+            if selfint[x] < 0:
+                carry = 1
+                selfint[x] += 10
+            else:
+              carry = 0
+        if carry:
+            selfint[x+1] -= 1
+        last = len(selfint)-1
+        while len(selfint) > 1 and selfint[last] == 0:
+            last -= 1
+            if last == 0:
+                break
+        selfint[last+1:]=[]
+        selfint.reverse()
+        alist.reverse()
+        return
+
+
+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 > len(other.int) + prec + 1 -len(tmp.int):
+        # 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 MemoryErrors.
+
+        extend = prec + 2 -len(tmp.int)
+        if extend <= 0:
+            extend = 1
+        tmp.int.extend([0]*extend)
+        tmp.exp -= extend
+        other.int[:] = [0]*(len(tmp.int)-1)+[1]
+        other.exp = tmp.exp
+        return op1, op2
+
+    tmp.int.extend([0] * numdigits)
+    tmp.exp = tmp.exp - numdigits
+    numdigits = len(op1.int) - len(op2.int)
+    # numdigits != 0 => They have the same exponent, but not the same length
+    # of the coefficient.
+    if numdigits < 0:
+        numdigits = -numdigits
+        tmp = op1
+    else:
+        tmp = op2
+    tmp.int[0:0] = [0] * numdigits
+    return op1, op2
+
+def _adjust_coefficients(op1, op2):
+    """Adjust op1, op2 so that op2.int+[0] > 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, get it to same size
+    if len(op2.int) > len(op1.int):
+        diff = len(op2.int) - len(op1.int)
+        op1.int.extend([0]*diff)
+        op1.exp -= diff
+        adjust = diff
+
+    #Same length, wrong order
+    if len(op1.int) == len(op2.int) and op1.int < op2.int:
+        op1.int.append(0)
+        op1.exp -= 1
+        adjust+= 1
+        return op1, op2, adjust
+
+    if len(op1.int) > len(op2.int) + 1:
+        diff = len(op1.int) - len(op2.int) - 1
+        op2.int.extend([0]*diff)
+        op2.exp -= diff
+        adjust -= diff
+
+    if len(op1.int) == len(op2.int)+1 and op1.int > op2.int:
+
+        op2.int.append(0)
+        op2.exp -= 1
+        adjust -= 1
+    return op1, op2, adjust
+
+##### Helper Functions ########################################
+
+_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 positive 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 ################################
+
+def _zero_exceptions():
+    "Helper function mapping all exceptions to zero."
+    d = {}
+    for exception in ExceptionList:
+        d[exception] = 0
+    return d
+
+# The default context prototype used by Context()
+# Is mutable, so than new contexts can have different default values
+
+DefaultContext = Context(
+        prec=SINGLE_PRECISION, rounding=ROUND_HALF_EVEN,
+        trap_enablers=_zero_exceptions(),
+        flags=_zero_exceptions(),
+        _rounding_decision=ALWAYS_ROUND,
+)
+
+# 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.
+
+_basic_traps = _zero_exceptions()
+_basic_traps.update({Inexact:1, Rounded:1, Subnormal:1})
+
+BasicDefaultContext = Context(
+        prec=9, rounding=ROUND_HALF_UP,
+        trap_enablers=_basic_traps,
+        flags=_zero_exceptions(),
+        _rounding_decision=ALWAYS_ROUND,
+)
+
+ExtendedDefaultContext = Context(
+        prec=SINGLE_PRECISION, rounding=ROUND_HALF_EVEN,
+        trap_enablers=_zero_exceptions(),
+        flags=_zero_exceptions(),
+        _rounding_decision=ALWAYS_ROUND,
+)
+
+
+##### 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__])