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clach04 committed 490c45b

Decimal support back port.

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File lib-python/compat/decimal.py

+# Copyright (c) 2004 Python Software Foundation.
+# All rights reserved.
+
+# Written by Eric Price <eprice at tjhsst.edu>
+#    and Facundo Batista <facundo at taniquetil.com.ar>
+#    and Raymond Hettinger <python at rcn.com>
+#    and Aahz <aahz at pobox.com>
+#    and Tim Peters
+
+# This module is currently Py2.3 compatible and should be kept that way
+# unless a major compelling advantage arises.  IOW, 2.3 compatibility is
+# strongly preferred, but not guaranteed.
+
+# Also, this module should be kept in sync with the latest updates of
+# the IBM specification as it evolves.  Those updates will be treated
+# as bug fixes (deviation from the spec is a compatibility, usability
+# bug) and will be backported.  At this point the spec is stabilizing
+# and the updates are becoming fewer, smaller, and less significant.
+
+"""
+This is a Py2.3 implementation of decimal floating point arithmetic based on
+the General Decimal Arithmetic Specification:
+
+    www2.hursley.ibm.com/decimal/decarith.html
+
+and IEEE standard 854-1987:
+
+    www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html
+
+Decimal floating point has finite precision with arbitrarily large bounds.
+
+The purpose of the module is to support arithmetic using familiar
+"schoolhouse" rules and to avoid the some of tricky representation
+issues associated with binary floating point.  The package is especially
+useful for financial applications or for contexts where users have
+expectations that are at odds with binary floating point (for instance,
+in binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead
+of the expected Decimal("0.00") returned by decimal floating point).
+
+Here are some examples of using the decimal module:
+
+>>> from decimal import *
+>>> setcontext(ExtendedContext)
+>>> Decimal(0)
+Decimal("0")
+>>> Decimal("1")
+Decimal("1")
+>>> Decimal("-.0123")
+Decimal("-0.0123")
+>>> Decimal(123456)
+Decimal("123456")
+>>> Decimal("123.45e12345678901234567890")
+Decimal("1.2345E+12345678901234567892")
+>>> Decimal("1.33") + Decimal("1.27")
+Decimal("2.60")
+>>> Decimal("12.34") + Decimal("3.87") - Decimal("18.41")
+Decimal("-2.20")
+>>> dig = Decimal(1)
+>>> print dig / Decimal(3)
+0.333333333
+>>> getcontext().prec = 18
+>>> print dig / Decimal(3)
+0.333333333333333333
+>>> print dig.sqrt()
+1
+>>> print Decimal(3).sqrt()
+1.73205080756887729
+>>> print Decimal(3) ** 123
+4.85192780976896427E+58
+>>> inf = Decimal(1) / Decimal(0)
+>>> print inf
+Infinity
+>>> neginf = Decimal(-1) / Decimal(0)
+>>> print neginf
+-Infinity
+>>> print neginf + inf
+NaN
+>>> print neginf * inf
+-Infinity
+>>> print dig / 0
+Infinity
+>>> getcontext().traps[DivisionByZero] = 1
+>>> print dig / 0
+Traceback (most recent call last):
+  ...
+  ...
+  ...
+DivisionByZero: x / 0
+>>> c = Context()
+>>> c.traps[InvalidOperation] = 0
+>>> print c.flags[InvalidOperation]
+0
+>>> c.divide(Decimal(0), Decimal(0))
+Decimal("NaN")
+>>> c.traps[InvalidOperation] = 1
+>>> print c.flags[InvalidOperation]
+1
+>>> c.flags[InvalidOperation] = 0
+>>> print c.flags[InvalidOperation]
+0
+>>> print c.divide(Decimal(0), Decimal(0))
+Traceback (most recent call last):
+  ...
+  ...
+  ...
+InvalidOperation: 0 / 0
+>>> print c.flags[InvalidOperation]
+1
+>>> c.flags[InvalidOperation] = 0
+>>> c.traps[InvalidOperation] = 0
+>>> print c.divide(Decimal(0), Decimal(0))
+NaN
+>>> print c.flags[InvalidOperation]
+1
+>>>
+"""
+
+__all__ = [
+    # Two major classes
+    'Decimal', 'Context',
+
+    # Contexts
+    'DefaultContext', 'BasicContext', 'ExtendedContext',
+
+    # Exceptions
+    'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero',
+    'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow',
+
+    # Constants for use in setting up contexts
+    'ROUND_DOWN', 'ROUND_HALF_UP', 'ROUND_HALF_EVEN', 'ROUND_CEILING',
+    'ROUND_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN',
+
+    # Functions for manipulating contexts
+    'setcontext', 'getcontext'
+]
+
+import copy as _copy
+
+try:
+    basestring
+except NameError:
+    # probably Python 2.2 or earlier
+    basestring = (str, unicode)
+
+#Rounding
+ROUND_DOWN = 'ROUND_DOWN'
+ROUND_HALF_UP = 'ROUND_HALF_UP'
+ROUND_HALF_EVEN = 'ROUND_HALF_EVEN'
+ROUND_CEILING = 'ROUND_CEILING'
+ROUND_FLOOR = 'ROUND_FLOOR'
+ROUND_UP = 'ROUND_UP'
+ROUND_HALF_DOWN = 'ROUND_HALF_DOWN'
+
+#Rounding decision (not part of the public API)
+NEVER_ROUND = 'NEVER_ROUND'    # Round in division (non-divmod), sqrt ONLY
+ALWAYS_ROUND = 'ALWAYS_ROUND'  # Every operation rounds at end.
+
+#Errors
+
+class DecimalException(ArithmeticError):
+    """Base exception class.
+
+    Used exceptions derive from this.
+    If an exception derives from another exception besides this (such as
+    Underflow (Inexact, Rounded, Subnormal) that indicates that it is only
+    called if the others are present.  This isn't actually used for
+    anything, though.
+
+    handle  -- Called when context._raise_error is called and the
+               trap_enabler is set.  First argument is self, second is the
+               context.  More arguments can be given, those being after
+               the explanation in _raise_error (For example,
+               context._raise_error(NewError, '(-x)!', self._sign) would
+               call NewError().handle(context, self._sign).)
+
+    To define a new exception, it should be sufficient to have it derive
+    from DecimalException.
+    """
+    def handle(self, context, *args):
+        pass
+
+
+class Clamped(DecimalException):
+    """Exponent of a 0 changed to fit bounds.
+
+    This occurs and signals clamped if the exponent of a result has been
+    altered in order to fit the constraints of a specific concrete
+    representation. This may occur when the exponent of a zero result would
+    be outside the bounds of a representation, or  when a large normal
+    number would have an encoded exponent that cannot be represented. In
+    this latter case, the exponent is reduced to fit and the corresponding
+    number of zero digits are appended to the coefficient ("fold-down").
+    """
+
+
+class InvalidOperation(DecimalException):
+    """An invalid operation was performed.
+
+    Various bad things cause this:
+
+    Something creates a signaling NaN
+    -INF + INF
+     0 * (+-)INF
+     (+-)INF / (+-)INF
+    x % 0
+    (+-)INF % x
+    x._rescale( non-integer )
+    sqrt(-x) , x > 0
+    0 ** 0
+    x ** (non-integer)
+    x ** (+-)INF
+    An operand is invalid
+    """
+    def handle(self, context, *args):
+        if args:
+            if args[0] == 1: #sNaN, must drop 's' but keep diagnostics
+                return Decimal( (args[1]._sign, args[1]._int, 'n') )
+        return NaN
+
+class ConversionSyntax(InvalidOperation):
+    """Trying to convert badly formed string.
+
+    This occurs and signals invalid-operation if an string is being
+    converted to a number and it does not conform to the numeric string
+    syntax. The result is [0,qNaN].
+    """
+
+    def handle(self, context, *args):
+        return (0, (0,), 'n') #Passed to something which uses a tuple.
+
+class DivisionByZero(DecimalException, ZeroDivisionError):
+    """Division by 0.
+
+    This occurs and signals division-by-zero if division of a finite number
+    by zero was attempted (during a divide-integer or divide operation, or a
+    power operation with negative right-hand operand), and the dividend was
+    not zero.
+
+    The result of the operation is [sign,inf], where sign is the exclusive
+    or of the signs of the operands for divide, or is 1 for an odd power of
+    -0, for power.
+    """
+
+    def handle(self, context, sign, double = None, *args):
+        if double is not None:
+            return (Infsign[sign],)*2
+        return Infsign[sign]
+
+class DivisionImpossible(InvalidOperation):
+    """Cannot perform the division adequately.
+
+    This occurs and signals invalid-operation if the integer result of a
+    divide-integer or remainder operation had too many digits (would be
+    longer than precision). The result is [0,qNaN].
+    """
+
+    def handle(self, context, *args):
+        return (NaN, NaN)
+
+class DivisionUndefined(InvalidOperation, ZeroDivisionError):
+    """Undefined result of division.
+
+    This occurs and signals invalid-operation if division by zero was
+    attempted (during a divide-integer, divide, or remainder operation), and
+    the dividend is also zero. The result is [0,qNaN].
+    """
+
+    def handle(self, context, tup=None, *args):
+        if tup is not None:
+            return (NaN, NaN) #for 0 %0, 0 // 0
+        return NaN
+
+class Inexact(DecimalException):
+    """Had to round, losing information.
+
+    This occurs and signals inexact whenever the result of an operation is
+    not exact (that is, it needed to be rounded and any discarded digits
+    were non-zero), or if an overflow or underflow condition occurs. The
+    result in all cases is unchanged.
+
+    The inexact signal may be tested (or trapped) to determine if a given
+    operation (or sequence of operations) was inexact.
+    """
+    pass
+
+class InvalidContext(InvalidOperation):
+    """Invalid context.  Unknown rounding, for example.
+
+    This occurs and signals invalid-operation if an invalid context was
+    detected during an operation. This can occur if contexts are not checked
+    on creation and either the precision exceeds the capability of the
+    underlying concrete representation or an unknown or unsupported rounding
+    was specified. These aspects of the context need only be checked when
+    the values are required to be used. The result is [0,qNaN].
+    """
+
+    def handle(self, context, *args):
+        return NaN
+
+class Rounded(DecimalException):
+    """Number got rounded (not  necessarily changed during rounding).
+
+    This occurs and signals rounded whenever the result of an operation is
+    rounded (that is, some zero or non-zero digits were discarded from the
+    coefficient), or if an overflow or underflow condition occurs. The
+    result in all cases is unchanged.
+
+    The rounded signal may be tested (or trapped) to determine if a given
+    operation (or sequence of operations) caused a loss of precision.
+    """
+    pass
+
+class Subnormal(DecimalException):
+    """Exponent < Emin before rounding.
+
+    This occurs and signals subnormal whenever the result of a conversion or
+    operation is subnormal (that is, its adjusted exponent is less than
+    Emin, before any rounding). The result in all cases is unchanged.
+
+    The subnormal signal may be tested (or trapped) to determine if a given
+    or operation (or sequence of operations) yielded a subnormal result.
+    """
+    pass
+
+class Overflow(Inexact, Rounded):
+    """Numerical overflow.
+
+    This occurs and signals overflow if the adjusted exponent of a result
+    (from a conversion or from an operation that is not an attempt to divide
+    by zero), after rounding, would be greater than the largest value that
+    can be handled by the implementation (the value Emax).
+
+    The result depends on the rounding mode:
+
+    For round-half-up and round-half-even (and for round-half-down and
+    round-up, if implemented), the result of the operation is [sign,inf],
+    where sign is the sign of the intermediate result. For round-down, the
+    result is the largest finite number that can be represented in the
+    current precision, with the sign of the intermediate result. For
+    round-ceiling, the result is the same as for round-down if the sign of
+    the intermediate result is 1, or is [0,inf] otherwise. For round-floor,
+    the result is the same as for round-down if the sign of the intermediate
+    result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded
+    will also be raised.
+   """
+
+    def handle(self, context, sign, *args):
+        if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN,
+                                     ROUND_HALF_DOWN, ROUND_UP):
+            return Infsign[sign]
+        if sign == 0:
+            if context.rounding == ROUND_CEILING:
+                return Infsign[sign]
+            return Decimal((sign, (9,)*context.prec,
+                            context.Emax-context.prec+1))
+        if sign == 1:
+            if context.rounding == ROUND_FLOOR:
+                return Infsign[sign]
+            return Decimal( (sign, (9,)*context.prec,
+                             context.Emax-context.prec+1))
+
+
+class Underflow(Inexact, Rounded, Subnormal):
+    """Numerical underflow with result rounded to 0.
+
+    This occurs and signals underflow if a result is inexact and the
+    adjusted exponent of the result would be smaller (more negative) than
+    the smallest value that can be handled by the implementation (the value
+    Emin). That is, the result is both inexact and subnormal.
+
+    The result after an underflow will be a subnormal number rounded, if
+    necessary, so that its exponent is not less than Etiny. This may result
+    in 0 with the sign of the intermediate result and an exponent of Etiny.
+
+    In all cases, Inexact, Rounded, and Subnormal will also be raised.
+    """
+
+# List of public traps and flags
+_signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded,
+           Underflow, InvalidOperation, Subnormal]
+
+# Map conditions (per the spec) to signals
+_condition_map = {ConversionSyntax:InvalidOperation,
+                  DivisionImpossible:InvalidOperation,
+                  DivisionUndefined:InvalidOperation,
+                  InvalidContext:InvalidOperation}
+
+##### Context Functions #######################################
+
+# The getcontext() and setcontext() function manage access to a thread-local
+# current context.  Py2.4 offers direct support for thread locals.  If that
+# is not available, use threading.currentThread() which is slower but will
+# work for older Pythons.  If threads are not part of the build, create a
+# mock threading object with threading.local() returning the module namespace.
+
+try:
+    import threading
+except ImportError:
+    # Python was compiled without threads; create a mock object instead
+    import sys
+    class MockThreading:
+        def local(self, sys=sys):
+            return sys.modules[__name__]
+    threading = MockThreading()
+    del sys, MockThreading
+
+try:
+    threading.local
+
+except AttributeError:
+
+    #To fix reloading, force it to create a new context
+    #Old contexts have different exceptions in their dicts, making problems.
+    if hasattr(threading.currentThread(), '__decimal_context__'):
+        del threading.currentThread().__decimal_context__
+
+    def setcontext(context):
+        """Set this thread's context to context."""
+        if context in (DefaultContext, BasicContext, ExtendedContext):
+            context = context.copy()
+            context.clear_flags()
+        threading.currentThread().__decimal_context__ = context
+
+    def getcontext():
+        """Returns this thread's context.
+
+        If this thread does not yet have a context, returns
+        a new context and sets this thread's context.
+        New contexts are copies of DefaultContext.
+        """
+        try:
+            return threading.currentThread().__decimal_context__
+        except AttributeError:
+            context = Context()
+            threading.currentThread().__decimal_context__ = context
+            return context
+
+else:
+
+    local = threading.local()
+    if hasattr(local, '__decimal_context__'):
+        del local.__decimal_context__
+
+    def getcontext(_local=local):
+        """Returns this thread's context.
+
+        If this thread does not yet have a context, returns
+        a new context and sets this thread's context.
+        New contexts are copies of DefaultContext.
+        """
+        try:
+            return _local.__decimal_context__
+        except AttributeError:
+            context = Context()
+            _local.__decimal_context__ = context
+            return context
+
+    def setcontext(context, _local=local):
+        """Set this thread's context to context."""
+        if context in (DefaultContext, BasicContext, ExtendedContext):
+            context = context.copy()
+            context.clear_flags()
+        _local.__decimal_context__ = context
+
+    del threading, local        # Don't contaminate the namespace
+
+
+##### Decimal class ###########################################
+
+class Decimal(object):
+    """Floating point class for decimal arithmetic."""
+
+    __slots__ = ('_exp','_int','_sign', '_is_special')
+    # Generally, the value of the Decimal instance is given by
+    #  (-1)**_sign * _int * 10**_exp
+    # Special values are signified by _is_special == True
+
+    # We're immutable, so use __new__ not __init__
+    def __new__(cls, value="0", context=None):
+        """Create a decimal point instance.
+
+        >>> Decimal('3.14')              # string input
+        Decimal("3.14")
+        >>> Decimal((0, (3, 1, 4), -2))  # tuple input (sign, digit_tuple, exponent)
+        Decimal("3.14")
+        >>> Decimal(314)                 # int or long
+        Decimal("314")
+        >>> Decimal(Decimal(314))        # another decimal instance
+        Decimal("314")
+        """
+
+        self = object.__new__(cls)
+        self._is_special = False
+
+        # From an internal working value
+        if isinstance(value, _WorkRep):
+            self._sign = value.sign
+            self._int = tuple(map(int, str(value.int)))
+            self._exp = int(value.exp)
+            return self
+
+        # From another decimal
+        if isinstance(value, Decimal):
+            self._exp  = value._exp
+            self._sign = value._sign
+            self._int  = value._int
+            self._is_special  = value._is_special
+            return self
+
+        # From an integer
+        if isinstance(value, (int,long)):
+            if value >= 0:
+                self._sign = 0
+            else:
+                self._sign = 1
+            self._exp = 0
+            self._int = tuple(map(int, str(abs(value))))
+            return self
+
+        # tuple/list conversion (possibly from as_tuple())
+        if isinstance(value, (list,tuple)):
+            if len(value) != 3:
+                raise ValueError, 'Invalid arguments'
+            if value[0] not in (0,1):
+                raise ValueError, 'Invalid sign'
+            for digit in value[1]:
+                if not isinstance(digit, (int,long)) or digit < 0:
+                    raise ValueError, "The second value in the tuple must be composed of non negative integer elements."
+
+            self._sign = value[0]
+            self._int  = tuple(value[1])
+            if value[2] in ('F','n','N'):
+                self._exp = value[2]
+                self._is_special = True
+            else:
+                self._exp  = int(value[2])
+            return self
+
+        if isinstance(value, float):
+            raise TypeError("Cannot convert float to Decimal.  " +
+                            "First convert the float to a string")
+
+        # Other argument types may require the context during interpretation
+        if context is None:
+            context = getcontext()
+
+        # From a string
+        # REs insist on real strings, so we can too.
+        if isinstance(value, basestring):
+            if _isinfinity(value):
+                self._exp = 'F'
+                self._int = (0,)
+                self._is_special = True
+                if _isinfinity(value) == 1:
+                    self._sign = 0
+                else:
+                    self._sign = 1
+                return self
+            if _isnan(value):
+                sig, sign, diag = _isnan(value)
+                self._is_special = True
+                if len(diag) > context.prec: #Diagnostic info too long
+                    self._sign, self._int, self._exp = \
+                                context._raise_error(ConversionSyntax)
+                    return self
+                if sig == 1:
+                    self._exp = 'n' #qNaN
+                else: #sig == 2
+                    self._exp = 'N' #sNaN
+                self._sign = sign
+                self._int = tuple(map(int, diag)) #Diagnostic info
+                return self
+            try:
+                self._sign, self._int, self._exp = _string2exact(value)
+            except ValueError:
+                self._is_special = True
+                self._sign, self._int, self._exp = context._raise_error(ConversionSyntax)
+            return self
+
+        raise TypeError("Cannot convert %r to Decimal" % value)
+
+    def _isnan(self):
+        """Returns whether the number is not actually one.
+
+        0 if a number
+        1 if NaN
+        2 if sNaN
+        """
+        if self._is_special:
+            exp = self._exp
+            if exp == 'n':
+                return 1
+            elif exp == 'N':
+                return 2
+        return 0
+
+    def _isinfinity(self):
+        """Returns whether the number is infinite
+
+        0 if finite or not a number
+        1 if +INF
+        -1 if -INF
+        """
+        if self._exp == 'F':
+            if self._sign:
+                return -1
+            return 1
+        return 0
+
+    def _check_nans(self, other = None, context=None):
+        """Returns whether the number is not actually one.
+
+        if self, other are sNaN, signal
+        if self, other are NaN return nan
+        return 0
+
+        Done before operations.
+        """
+
+        self_is_nan = self._isnan()
+        if other is None:
+            other_is_nan = False
+        else:
+            other_is_nan = other._isnan()
+
+        if self_is_nan or other_is_nan:
+            if context is None:
+                context = getcontext()
+
+            if self_is_nan == 2:
+                return context._raise_error(InvalidOperation, 'sNaN',
+                                        1, self)
+            if other_is_nan == 2:
+                return context._raise_error(InvalidOperation, 'sNaN',
+                                        1, other)
+            if self_is_nan:
+                return self
+
+            return other
+        return 0
+
+    def __nonzero__(self):
+        """Is the number non-zero?
+
+        0 if self == 0
+        1 if self != 0
+        """
+        if self._is_special:
+            return 1
+        return sum(self._int) != 0
+
+    def __cmp__(self, other, context=None):
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if self._is_special or other._is_special:
+            ans = self._check_nans(other, context)
+            if ans:
+                return 1 # Comparison involving NaN's always reports self > other
+
+            # INF = INF
+            return cmp(self._isinfinity(), other._isinfinity())
+
+        if not self and not other:
+            return 0 #If both 0, sign comparison isn't certain.
+
+        #If different signs, neg one is less
+        if other._sign < self._sign:
+            return -1
+        if self._sign < other._sign:
+            return 1
+
+        self_adjusted = self.adjusted()
+        other_adjusted = other.adjusted()
+        if self_adjusted == other_adjusted and \
+           self._int + (0,)*(self._exp - other._exp) == \
+           other._int + (0,)*(other._exp - self._exp):
+            return 0 #equal, except in precision. ([0]*(-x) = [])
+        elif self_adjusted > other_adjusted and self._int[0] != 0:
+            return (-1)**self._sign
+        elif self_adjusted < other_adjusted and other._int[0] != 0:
+            return -((-1)**self._sign)
+
+        # Need to round, so make sure we have a valid context
+        if context is None:
+            context = getcontext()
+
+        context = context._shallow_copy()
+        rounding = context._set_rounding(ROUND_UP) #round away from 0
+
+        flags = context._ignore_all_flags()
+        res = self.__sub__(other, context=context)
+
+        context._regard_flags(*flags)
+
+        context.rounding = rounding
+
+        if not res:
+            return 0
+        elif res._sign:
+            return -1
+        return 1
+
+    def __eq__(self, other):
+        if not isinstance(other, (Decimal, int, long)):
+            return NotImplemented
+        return self.__cmp__(other) == 0
+
+    def __ne__(self, other):
+        if not isinstance(other, (Decimal, int, long)):
+            return NotImplemented
+        return self.__cmp__(other) != 0
+
+    def compare(self, other, context=None):
+        """Compares one to another.
+
+        -1 => a < b
+        0  => a = b
+        1  => a > b
+        NaN => one is NaN
+        Like __cmp__, but returns Decimal instances.
+        """
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        #compare(NaN, NaN) = NaN
+        if (self._is_special or other and other._is_special):
+            ans = self._check_nans(other, context)
+            if ans:
+                return ans
+
+        return Decimal(self.__cmp__(other, context))
+
+    def __hash__(self):
+        """x.__hash__() <==> hash(x)"""
+        # Decimal integers must hash the same as the ints
+        # Non-integer decimals are normalized and hashed as strings
+        # Normalization assures that hast(100E-1) == hash(10)
+        if self._is_special:
+            if self._isnan():
+                raise TypeError('Cannot hash a NaN value.')
+            return hash(str(self))
+        i = int(self)
+        if self == Decimal(i):
+            return hash(i)
+        assert self.__nonzero__()   # '-0' handled by integer case
+        return hash(str(self.normalize()))
+
+    def as_tuple(self):
+        """Represents the number as a triple tuple.
+
+        To show the internals exactly as they are.
+        """
+        return (self._sign, self._int, self._exp)
+
+    def __repr__(self):
+        """Represents the number as an instance of Decimal."""
+        # Invariant:  eval(repr(d)) == d
+        return 'Decimal("%s")' % str(self)
+
+    def __str__(self, eng = 0, context=None):
+        """Return string representation of the number in scientific notation.
+
+        Captures all of the information in the underlying representation.
+        """
+
+        if self._is_special:
+            if self._isnan():
+                minus = '-'*self._sign
+                if self._int == (0,):
+                    info = ''
+                else:
+                    info = ''.join(map(str, self._int))
+                if self._isnan() == 2:
+                    return minus + 'sNaN' + info
+                return minus + 'NaN' + info
+            if self._isinfinity():
+                minus = '-'*self._sign
+                return minus + 'Infinity'
+
+        if context is None:
+            context = getcontext()
+
+        tmp = map(str, self._int)
+        numdigits = len(self._int)
+        leftdigits = self._exp + numdigits
+        if eng and not self: #self = 0eX wants 0[.0[0]]eY, not [[0]0]0eY
+            if self._exp < 0 and self._exp >= -6: #short, no need for e/E
+                s = '-'*self._sign + '0.' + '0'*(abs(self._exp))
+                return s
+            #exp is closest mult. of 3 >= self._exp
+            exp = ((self._exp - 1)// 3 + 1) * 3
+            if exp != self._exp:
+                s = '0.'+'0'*(exp - self._exp)
+            else:
+                s = '0'
+            if exp != 0:
+                if context.capitals:
+                    s += 'E'
+                else:
+                    s += 'e'
+                if exp > 0:
+                    s += '+' #0.0e+3, not 0.0e3
+                s += str(exp)
+            s = '-'*self._sign + s
+            return s
+        if eng:
+            dotplace = (leftdigits-1)%3+1
+            adjexp = leftdigits -1 - (leftdigits-1)%3
+        else:
+            adjexp = leftdigits-1
+            dotplace = 1
+        if self._exp == 0:
+            pass
+        elif self._exp < 0 and adjexp >= 0:
+            tmp.insert(leftdigits, '.')
+        elif self._exp < 0 and adjexp >= -6:
+            tmp[0:0] = ['0'] * int(-leftdigits)
+            tmp.insert(0, '0.')
+        else:
+            if numdigits > dotplace:
+                tmp.insert(dotplace, '.')
+            elif numdigits < dotplace:
+                tmp.extend(['0']*(dotplace-numdigits))
+            if adjexp:
+                if not context.capitals:
+                    tmp.append('e')
+                else:
+                    tmp.append('E')
+                    if adjexp > 0:
+                        tmp.append('+')
+                tmp.append(str(adjexp))
+        if eng:
+            while tmp[0:1] == ['0']:
+                tmp[0:1] = []
+            if len(tmp) == 0 or tmp[0] == '.' or tmp[0].lower() == 'e':
+                tmp[0:0] = ['0']
+        if self._sign:
+            tmp.insert(0, '-')
+
+        return ''.join(tmp)
+
+    def to_eng_string(self, context=None):
+        """Convert to engineering-type string.
+
+        Engineering notation has an exponent which is a multiple of 3, so there
+        are up to 3 digits left of the decimal place.
+
+        Same rules for when in exponential and when as a value as in __str__.
+        """
+        return self.__str__(eng=1, context=context)
+
+    def __neg__(self, context=None):
+        """Returns a copy with the sign switched.
+
+        Rounds, if it has reason.
+        """
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+
+        if not self:
+            # -Decimal('0') is Decimal('0'), not Decimal('-0')
+            sign = 0
+        elif self._sign:
+            sign = 0
+        else:
+            sign = 1
+
+        if context is None:
+            context = getcontext()
+        if context._rounding_decision == ALWAYS_ROUND:
+            return Decimal((sign, self._int, self._exp))._fix(context)
+        return Decimal( (sign, self._int, self._exp))
+
+    def __pos__(self, context=None):
+        """Returns a copy, unless it is a sNaN.
+
+        Rounds the number (if more then precision digits)
+        """
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+
+        sign = self._sign
+        if not self:
+            # + (-0) = 0
+            sign = 0
+
+        if context is None:
+            context = getcontext()
+
+        if context._rounding_decision == ALWAYS_ROUND:
+            ans = self._fix(context)
+        else:
+            ans = Decimal(self)
+        ans._sign = sign
+        return ans
+
+    def __abs__(self, round=1, context=None):
+        """Returns the absolute value of self.
+
+        If the second argument is 0, do not round.
+        """
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+
+        if not round:
+            if context is None:
+                context = getcontext()
+            context = context._shallow_copy()
+            context._set_rounding_decision(NEVER_ROUND)
+
+        if self._sign:
+            ans = self.__neg__(context=context)
+        else:
+            ans = self.__pos__(context=context)
+
+        return ans
+
+    def __add__(self, other, context=None):
+        """Returns self + other.
+
+        -INF + INF (or the reverse) cause InvalidOperation errors.
+        """
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if context is None:
+            context = getcontext()
+
+        if self._is_special or other._is_special:
+            ans = self._check_nans(other, context)
+            if ans:
+                return ans
+
+            if self._isinfinity():
+                #If both INF, same sign => same as both, opposite => error.
+                if self._sign != other._sign and other._isinfinity():
+                    return context._raise_error(InvalidOperation, '-INF + INF')
+                return Decimal(self)
+            if other._isinfinity():
+                return Decimal(other)  #Can't both be infinity here
+
+        shouldround = context._rounding_decision == ALWAYS_ROUND
+
+        exp = min(self._exp, other._exp)
+        negativezero = 0
+        if context.rounding == ROUND_FLOOR and self._sign != other._sign:
+            #If the answer is 0, the sign should be negative, in this case.
+            negativezero = 1
+
+        if not self and not other:
+            sign = min(self._sign, other._sign)
+            if negativezero:
+                sign = 1
+            return Decimal( (sign, (0,), exp))
+        if not self:
+            exp = max(exp, other._exp - context.prec-1)
+            ans = other._rescale(exp, watchexp=0, context=context)
+            if shouldround:
+                ans = ans._fix(context)
+            return ans
+        if not other:
+            exp = max(exp, self._exp - context.prec-1)
+            ans = self._rescale(exp, watchexp=0, context=context)
+            if shouldround:
+                ans = ans._fix(context)
+            return ans
+
+        op1 = _WorkRep(self)
+        op2 = _WorkRep(other)
+        op1, op2 = _normalize(op1, op2, shouldround, context.prec)
+
+        result = _WorkRep()
+        if op1.sign != op2.sign:
+            # Equal and opposite
+            if op1.int == op2.int:
+                if exp < context.Etiny():
+                    exp = context.Etiny()
+                    context._raise_error(Clamped)
+                return Decimal((negativezero, (0,), exp))
+            if op1.int < op2.int:
+                op1, op2 = op2, op1
+                #OK, now abs(op1) > abs(op2)
+            if op1.sign == 1:
+                result.sign = 1
+                op1.sign, op2.sign = op2.sign, op1.sign
+            else:
+                result.sign = 0
+                #So we know the sign, and op1 > 0.
+        elif op1.sign == 1:
+            result.sign = 1
+            op1.sign, op2.sign = (0, 0)
+        else:
+            result.sign = 0
+        #Now, op1 > abs(op2) > 0
+
+        if op2.sign == 0:
+            result.int = op1.int + op2.int
+        else:
+            result.int = op1.int - op2.int
+
+        result.exp = op1.exp
+        ans = Decimal(result)
+        if shouldround:
+            ans = ans._fix(context)
+        return ans
+
+    __radd__ = __add__
+
+    def __sub__(self, other, context=None):
+        """Return self + (-other)"""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if self._is_special or other._is_special:
+            ans = self._check_nans(other, context=context)
+            if ans:
+                return ans
+
+        # -Decimal(0) = Decimal(0), which we don't want since
+        # (-0 - 0 = -0 + (-0) = -0, but -0 + 0 = 0.)
+        # so we change the sign directly to a copy
+        tmp = Decimal(other)
+        tmp._sign = 1-tmp._sign
+
+        return self.__add__(tmp, context=context)
+
+    def __rsub__(self, other, context=None):
+        """Return other + (-self)"""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        tmp = Decimal(self)
+        tmp._sign = 1 - tmp._sign
+        return other.__add__(tmp, context=context)
+
+    def _increment(self, round=1, context=None):
+        """Special case of add, adding 1eExponent
+
+        Since it is common, (rounding, for example) this adds
+        (sign)*one E self._exp to the number more efficiently than add.
+
+        For example:
+        Decimal('5.624e10')._increment() == Decimal('5.625e10')
+        """
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+
+            return Decimal(self) # Must be infinite, and incrementing makes no difference
+
+        L = list(self._int)
+        L[-1] += 1
+        spot = len(L)-1
+        while L[spot] == 10:
+            L[spot] = 0
+            if spot == 0:
+                L[0:0] = [1]
+                break
+            L[spot-1] += 1
+            spot -= 1
+        ans = Decimal((self._sign, L, self._exp))
+
+        if context is None:
+            context = getcontext()
+        if round and context._rounding_decision == ALWAYS_ROUND:
+            ans = ans._fix(context)
+        return ans
+
+    def __mul__(self, other, context=None):
+        """Return self * other.
+
+        (+-) INF * 0 (or its reverse) raise InvalidOperation.
+        """
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if context is None:
+            context = getcontext()
+
+        resultsign = self._sign ^ other._sign
+
+        if self._is_special or other._is_special:
+            ans = self._check_nans(other, context)
+            if ans:
+                return ans
+
+            if self._isinfinity():
+                if not other:
+                    return context._raise_error(InvalidOperation, '(+-)INF * 0')
+                return Infsign[resultsign]
+
+            if other._isinfinity():
+                if not self:
+                    return context._raise_error(InvalidOperation, '0 * (+-)INF')
+                return Infsign[resultsign]
+
+        resultexp = self._exp + other._exp
+        shouldround = context._rounding_decision == ALWAYS_ROUND
+
+        # Special case for multiplying by zero
+        if not self or not other:
+            ans = Decimal((resultsign, (0,), resultexp))
+            if shouldround:
+                #Fixing in case the exponent is out of bounds
+                ans = ans._fix(context)
+            return ans
+
+        # Special case for multiplying by power of 10
+        if self._int == (1,):
+            ans = Decimal((resultsign, other._int, resultexp))
+            if shouldround:
+                ans = ans._fix(context)
+            return ans
+        if other._int == (1,):
+            ans = Decimal((resultsign, self._int, resultexp))
+            if shouldround:
+                ans = ans._fix(context)
+            return ans
+
+        op1 = _WorkRep(self)
+        op2 = _WorkRep(other)
+
+        ans = Decimal( (resultsign, map(int, str(op1.int * op2.int)), resultexp))
+        if shouldround:
+            ans = ans._fix(context)
+
+        return ans
+    __rmul__ = __mul__
+
+    def __div__(self, other, context=None):
+        """Return self / other."""
+        return self._divide(other, context=context)
+    __truediv__ = __div__
+
+    def _divide(self, other, divmod = 0, context=None):
+        """Return a / b, to context.prec precision.
+
+        divmod:
+        0 => true division
+        1 => (a //b, a%b)
+        2 => a //b
+        3 => a%b
+
+        Actually, if divmod is 2 or 3 a tuple is returned, but errors for
+        computing the other value are not raised.
+        """
+        other = _convert_other(other)
+        if other is NotImplemented:
+            if divmod in (0, 1):
+                return NotImplemented
+            return (NotImplemented, NotImplemented)
+
+        if context is None:
+            context = getcontext()
+
+        sign = self._sign ^ other._sign
+
+        if self._is_special or other._is_special:
+            ans = self._check_nans(other, context)
+            if ans:
+                if divmod:
+                    return (ans, ans)
+                return ans
+
+            if self._isinfinity() and other._isinfinity():
+                if divmod:
+                    return (context._raise_error(InvalidOperation,
+                                            '(+-)INF // (+-)INF'),
+                            context._raise_error(InvalidOperation,
+                                            '(+-)INF % (+-)INF'))
+                return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF')
+
+            if self._isinfinity():
+                if divmod == 1:
+                    return (Infsign[sign],
+                            context._raise_error(InvalidOperation, 'INF % x'))
+                elif divmod == 2:
+                    return (Infsign[sign], NaN)
+                elif divmod == 3:
+                    return (Infsign[sign],
+                            context._raise_error(InvalidOperation, 'INF % x'))
+                return Infsign[sign]
+
+            if other._isinfinity():
+                if divmod:
+                    return (Decimal((sign, (0,), 0)), Decimal(self))
+                context._raise_error(Clamped, 'Division by infinity')
+                return Decimal((sign, (0,), context.Etiny()))
+
+        # Special cases for zeroes
+        if not self and not other:
+            if divmod:
+                return context._raise_error(DivisionUndefined, '0 / 0', 1)
+            return context._raise_error(DivisionUndefined, '0 / 0')
+
+        if not self:
+            if divmod:
+                otherside = Decimal(self)
+                otherside._exp = min(self._exp, other._exp)
+                return (Decimal((sign, (0,), 0)),  otherside)
+            exp = self._exp - other._exp
+            if exp < context.Etiny():
+                exp = context.Etiny()
+                context._raise_error(Clamped, '0e-x / y')
+            if exp > context.Emax:
+                exp = context.Emax
+                context._raise_error(Clamped, '0e+x / y')
+            return Decimal( (sign, (0,), exp) )
+
+        if not other:
+            if divmod:
+                return context._raise_error(DivisionByZero, 'divmod(x,0)',
+                                           sign, 1)
+            return context._raise_error(DivisionByZero, 'x / 0', sign)
+
+        #OK, so neither = 0, INF or NaN
+
+        shouldround = context._rounding_decision == ALWAYS_ROUND
+
+        #If we're dividing into ints, and self < other, stop.
+        #self.__abs__(0) does not round.
+        if divmod and (self.__abs__(0, context) < other.__abs__(0, context)):
+
+            if divmod == 1 or divmod == 3:
+                exp = min(self._exp, other._exp)
+                ans2 = self._rescale(exp, context=context, watchexp=0)
+                if shouldround:
+                    ans2 = ans2._fix(context)
+                return (Decimal( (sign, (0,), 0) ),
+                        ans2)
+
+            elif divmod == 2:
+                #Don't round the mod part, if we don't need it.
+                return (Decimal( (sign, (0,), 0) ), Decimal(self))
+
+        op1 = _WorkRep(self)
+        op2 = _WorkRep(other)
+        op1, op2, adjust = _adjust_coefficients(op1, op2)
+        res = _WorkRep( (sign, 0, (op1.exp - op2.exp)) )
+        if divmod and res.exp > context.prec + 1:
+            return context._raise_error(DivisionImpossible)
+
+        prec_limit = 10 ** context.prec
+        while 1:
+            while op2.int <= op1.int:
+                res.int += 1
+                op1.int -= op2.int
+            if res.exp == 0 and divmod:
+                if res.int >= prec_limit and shouldround:
+                    return context._raise_error(DivisionImpossible)
+                otherside = Decimal(op1)
+                frozen = context._ignore_all_flags()
+
+                exp = min(self._exp, other._exp)
+                otherside = otherside._rescale(exp, context=context, watchexp=0)
+                context._regard_flags(*frozen)
+                if shouldround:
+                    otherside = otherside._fix(context)
+                return (Decimal(res), otherside)
+
+            if op1.int == 0 and adjust >= 0 and not divmod:
+                break
+            if res.int >= prec_limit and shouldround:
+                if divmod:
+                    return context._raise_error(DivisionImpossible)
+                shouldround=1
+                # Really, the answer is a bit higher, so adding a one to
+                # the end will make sure the rounding is right.
+                if op1.int != 0:
+                    res.int *= 10
+                    res.int += 1
+                    res.exp -= 1
+
+                break
+            res.int *= 10
+            res.exp -= 1
+            adjust += 1
+            op1.int *= 10
+            op1.exp -= 1
+
+            if res.exp == 0 and divmod and op2.int > op1.int:
+                #Solves an error in precision.  Same as a previous block.
+
+                if res.int >= prec_limit and shouldround:
+                    return context._raise_error(DivisionImpossible)
+                otherside = Decimal(op1)
+                frozen = context._ignore_all_flags()
+
+                exp = min(self._exp, other._exp)
+                otherside = otherside._rescale(exp, context=context)
+
+                context._regard_flags(*frozen)
+
+                return (Decimal(res), otherside)
+
+        ans = Decimal(res)
+        if shouldround:
+            ans = ans._fix(context)
+        return ans
+
+    def __rdiv__(self, other, context=None):
+        """Swaps self/other and returns __div__."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        return other.__div__(self, context=context)
+    __rtruediv__ = __rdiv__
+
+    def __divmod__(self, other, context=None):
+        """
+        (self // other, self % other)
+        """
+        return self._divide(other, 1, context)
+
+    def __rdivmod__(self, other, context=None):
+        """Swaps self/other and returns __divmod__."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        return other.__divmod__(self, context=context)
+
+    def __mod__(self, other, context=None):
+        """
+        self % other
+        """
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if self._is_special or other._is_special:
+            ans = self._check_nans(other, context)
+            if ans:
+                return ans
+
+        if self and not other:
+            return context._raise_error(InvalidOperation, 'x % 0')
+
+        return self._divide(other, 3, context)[1]
+
+    def __rmod__(self, other, context=None):
+        """Swaps self/other and returns __mod__."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        return other.__mod__(self, context=context)
+
+    def remainder_near(self, other, context=None):
+        """
+        Remainder nearest to 0-  abs(remainder-near) <= other/2
+        """
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if self._is_special or other._is_special:
+            ans = self._check_nans(other, context)
+            if ans:
+                return ans
+        if self and not other:
+            return context._raise_error(InvalidOperation, 'x % 0')
+
+        if context is None:
+            context = getcontext()
+        # If DivisionImpossible causes an error, do not leave Rounded/Inexact
+        # ignored in the calling function.
+        context = context._shallow_copy()
+        flags = context._ignore_flags(Rounded, Inexact)
+        #keep DivisionImpossible flags
+        (side, r) = self.__divmod__(other, context=context)
+
+        if r._isnan():
+            context._regard_flags(*flags)
+            return r
+
+        context = context._shallow_copy()
+        rounding = context._set_rounding_decision(NEVER_ROUND)
+
+        if other._sign:
+            comparison = other.__div__(Decimal(-2), context=context)
+        else:
+            comparison = other.__div__(Decimal(2), context=context)
+
+        context._set_rounding_decision(rounding)
+        context._regard_flags(*flags)
+
+        s1, s2 = r._sign, comparison._sign
+        r._sign, comparison._sign = 0, 0
+
+        if r < comparison:
+            r._sign, comparison._sign = s1, s2
+            #Get flags now
+            self.__divmod__(other, context=context)
+            return r._fix(context)
+        r._sign, comparison._sign = s1, s2
+
+        rounding = context._set_rounding_decision(NEVER_ROUND)
+
+        (side, r) = self.__divmod__(other, context=context)
+        context._set_rounding_decision(rounding)
+        if r._isnan():
+            return r
+
+        decrease = not side._iseven()
+        rounding = context._set_rounding_decision(NEVER_ROUND)
+        side = side.__abs__(context=context)
+        context._set_rounding_decision(rounding)
+
+        s1, s2 = r._sign, comparison._sign
+        r._sign, comparison._sign = 0, 0
+        if r > comparison or decrease and r == comparison:
+            r._sign, comparison._sign = s1, s2
+            context.prec += 1
+            if len(side.__add__(Decimal(1), context=context)._int) >= context.prec:
+                context.prec -= 1
+                return context._raise_error(DivisionImpossible)[1]
+            context.prec -= 1
+            if self._sign == other._sign:
+                r = r.__sub__(other, context=context)
+            else:
+                r = r.__add__(other, context=context)
+        else:
+            r._sign, comparison._sign = s1, s2
+
+        return r._fix(context)
+
+    def __floordiv__(self, other, context=None):
+        """self // other"""
+        return self._divide(other, 2, context)[0]
+
+    def __rfloordiv__(self, other, context=None):
+        """Swaps self/other and returns __floordiv__."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        return other.__floordiv__(self, context=context)
+
+    def __float__(self):
+        """Float representation."""
+        return float(str(self))
+
+    def __int__(self):
+        """Converts self to an int, truncating if necessary."""
+        if self._is_special:
+            if self._isnan():
+                context = getcontext()
+                return context._raise_error(InvalidContext)
+            elif self._isinfinity():
+                raise OverflowError, "Cannot convert infinity to long"
+        if self._exp >= 0:
+            s = ''.join(map(str, self._int)) + '0'*self._exp
+        else:
+            s = ''.join(map(str, self._int))[:self._exp]
+        if s == '':
+            s = '0'
+        sign = '-'*self._sign
+        return int(sign + s)
+
+    def __long__(self):
+        """Converts to a long.
+
+        Equivalent to long(int(self))
+        """
+        return long(self.__int__())
+
+    def _fix(self, context):
+        """Round if it is necessary to keep self within prec precision.
+
+        Rounds and fixes the exponent.  Does not raise on a sNaN.
+
+        Arguments:
+        self - Decimal instance
+        context - context used.
+        """
+        if self._is_special:
+            return self
+        if context is None:
+            context = getcontext()
+        prec = context.prec
+        ans = self._fixexponents(context)
+        if len(ans._int) > prec:
+            ans = ans._round(prec, context=context)
+            ans = ans._fixexponents(context)
+        return ans
+
+    def _fixexponents(self, context):
+        """Fix the exponents and return a copy with the exponent in bounds.
+        Only call if known to not be a special value.
+        """
+        folddown = context._clamp
+        Emin = context.Emin
+        ans = self
+        ans_adjusted = ans.adjusted()
+        if ans_adjusted < Emin:
+            Etiny = context.Etiny()
+            if ans._exp < Etiny:
+                if not ans:
+                    ans = Decimal(self)
+                    ans._exp = Etiny
+                    context._raise_error(Clamped)
+                    return ans
+                ans = ans._rescale(Etiny, context=context)
+                #It isn't zero, and exp < Emin => subnormal
+                context._raise_error(Subnormal)
+                if context.flags[Inexact]:
+                    context._raise_error(Underflow)
+            else:
+                if ans:
+                    #Only raise subnormal if non-zero.
+                    context._raise_error(Subnormal)
+        else:
+            Etop = context.Etop()
+            if folddown and ans._exp > Etop:
+                context._raise_error(Clamped)
+                ans = ans._rescale(Etop, context=context)
+            else:
+                Emax = context.Emax
+                if ans_adjusted > Emax:
+                    if not ans:
+                        ans = Decimal(self)
+                        ans._exp = Emax
+                        context._raise_error(Clamped)
+                        return ans
+                    context._raise_error(Inexact)
+                    context._raise_error(Rounded)
+                    return context._raise_error(Overflow, 'above Emax', ans._sign)
+        return ans
+
+    def _round(self, prec=None, rounding=None, context=None):
+        """Returns a rounded version of self.
+
+        You can specify the precision or rounding method.  Otherwise, the
+        context determines it.
+        """
+
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+
+            if self._isinfinity():
+                return Decimal(self)
+
+        if context is None:
+            context = getcontext()
+
+        if rounding is None:
+            rounding = context.rounding
+        if prec is None:
+            prec = context.prec
+
+        if not self:
+            if prec <= 0:
+                dig = (0,)
+                exp = len(self._int) - prec + self._exp
+            else:
+                dig = (0,) * prec
+                exp = len(self._int) + self._exp - prec
+            ans = Decimal((self._sign, dig, exp))
+            context._raise_error(Rounded)
+            return ans
+
+        if prec == 0:
+            temp = Decimal(self)
+            temp._int = (0,)+temp._int
+            prec = 1
+        elif prec < 0:
+            exp = self._exp + len(self._int) - prec - 1
+            temp = Decimal( (self._sign, (0, 1), exp))
+            prec = 1
+        else:
+            temp = Decimal(self)
+
+        numdigits = len(temp._int)
+        if prec == numdigits:
+            return temp
+
+        # See if we need to extend precision
+        expdiff = prec - numdigits
+        if expdiff > 0:
+            tmp = list(temp._int)
+            tmp.extend([0] * expdiff)
+            ans =  Decimal( (temp._sign, tmp, temp._exp - expdiff))
+            return ans
+
+        #OK, but maybe all the lost digits are 0.
+        lostdigits = self._int[expdiff:]
+        if lostdigits == (0,) * len(lostdigits):
+            ans = Decimal( (temp._sign, temp._int[:prec], temp._exp - expdiff))
+            #Rounded, but not Inexact
+            context._raise_error(Rounded)
+            return ans
+
+        # Okay, let's round and lose data
+
+        this_function = getattr(temp, self._pick_rounding_function[rounding])
+        #Now we've got the rounding function
+
+        if prec != context.prec:
+            context = context._shallow_copy()
+            context.prec = prec
+        ans = this_function(prec, expdiff, context)
+        context._raise_error(Rounded)
+        context._raise_error(Inexact, 'Changed in rounding')
+
+        return ans
+
+    _pick_rounding_function = {}
+
+    def _round_down(self, prec, expdiff, context):
+        """Also known as round-towards-0, truncate."""
+        return Decimal( (self._sign, self._int[:prec], self._exp - expdiff) )
+
+    def _round_half_up(self, prec, expdiff, context, tmp = None):
+        """Rounds 5 up (away from 0)"""
+
+        if tmp is None:
+            tmp = Decimal( (self._sign,self._int[:prec], self._exp - expdiff))
+        if self._int[prec] >= 5:
+            tmp = tmp._increment(round=0, context=context)
+            if len(tmp._int) > prec:
+                return Decimal( (tmp._sign, tmp._int[:-1], tmp._exp + 1))
+        return tmp
+
+    def _round_half_even(self, prec, expdiff, context):
+        """Round 5 to even, rest to nearest."""
+
+        tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff))
+        half = (self._int[prec] == 5)
+        if half:
+            for digit in self._int[prec+1:]:
+                if digit != 0:
+                    half = 0
+                    break
+        if half:
+            if self._int[prec-1] & 1 == 0:
+                return tmp
+        return self._round_half_up(prec, expdiff, context, tmp)
+
+    def _round_half_down(self, prec, expdiff, context):
+        """Round 5 down"""
+
+        tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff))
+        half = (self._int[prec] == 5)
+        if half:
+            for digit in self._int[prec+1:]:
+                if digit != 0:
+                    half = 0
+                    break
+        if half:
+            return tmp
+        return self._round_half_up(prec, expdiff, context, tmp)
+
+    def _round_up(self, prec, expdiff, context):
+        """Rounds away from 0."""
+        tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff) )
+        for digit in self._int[prec:]:
+            if digit != 0:
+                tmp = tmp._increment(round=1, context=context)
+                if len(tmp._int) > prec:
+                    return Decimal( (tmp._sign, tmp._int[:-1], tmp._exp + 1))
+                else:
+                    return tmp
+        return tmp
+
+    def _round_ceiling(self, prec, expdiff, context):
+        """Rounds up (not away from 0 if negative.)"""
+        if self._sign:
+            return self._round_down(prec, expdiff, context)
+        else:
+            return self._round_up(prec, expdiff, context)
+
+    def _round_floor(self, prec, expdiff, context):
+        """Rounds down (not towards 0 if negative)"""
+        if not self._sign:
+            return self._round_down(prec, expdiff, context)
+        else:
+            return self._round_up(prec, expdiff, context)
+
+    def __pow__(self, n, modulo = None, context=None):
+        """Return self ** n (mod modulo)
+
+        If modulo is None (default), don't take it mod modulo.
+        """
+        n = _convert_other(n)
+        if n is NotImplemented:
+            return n
+
+        if context is None:
+            context = getcontext()
+
+        if self._is_special or n._is_special or n.adjusted() > 8:
+            #Because the spot << doesn't work with really big exponents
+            if n._isinfinity() or n.adjusted() > 8:
+                return context._raise_error(InvalidOperation, 'x ** INF')
+
+            ans = self._check_nans(n, context)
+            if ans:
+                return ans
+
+        if not n._isinteger():
+            return context._raise_error(InvalidOperation, 'x ** (non-integer)')
+
+        if not self and not n:
+            return context._raise_error(InvalidOperation, '0 ** 0')
+
+        if not n:
+            return Decimal(1)
+
+        if self == Decimal(1):
+            return Decimal(1)
+
+        sign = self._sign and not n._iseven()
+        n = int(n)
+
+        if self._isinfinity():
+            if modulo:
+                return context._raise_error(InvalidOperation, 'INF % x')
+            if n > 0:
+                return Infsign[sign]
+            return Decimal( (sign, (0,), 0) )
+
+        #with ludicrously large exponent, just raise an overflow and return inf.
+        if not modulo and n > 0 and (self._exp + len(self._int) - 1) * n > context.Emax \
+           and self:
+
+            tmp = Decimal('inf')
+            tmp._sign = sign
+            context._raise_error(Rounded)
+            context._raise_error(Inexact)
+            context._raise_error(Overflow, 'Big power', sign)
+            return tmp
+
+        elength = len(str(abs(n)))
+        firstprec = context.prec
+
+        if not modulo and firstprec + elength + 1 > DefaultContext.Emax:
+            return context._raise_error(Overflow, 'Too much precision.', sign)
+
+        mul = Decimal(self)
+        val = Decimal(1)
+        context = context._shallow_copy()
+        context.prec = firstprec + elength + 1
+        if n < 0:
+            #n is a long now, not Decimal instance
+            n = -n
+            mul = Decimal(1).__div__(mul, context=context)
+
+        spot = 1
+        while spot <= n:
+            spot <<= 1
+
+        spot >>= 1
+        #Spot is the highest power of 2 less than n
+        while spot:
+            val = val.__mul__(val, context=context)
+            if val._isinfinity():
+                val = Infsign[sign]
+                break
+            if spot & n:
+                val = val.__mul__(mul, context=context)
+            if modulo is not None:
+                val = val.__mod__(modulo, context=context)
+            spot >>= 1
+        context.prec = firstprec
+
+        if context._rounding_decision == ALWAYS_ROUND:
+            return val._fix(context)
+        return val
+
+    def __rpow__(self, other, context=None):
+        """Swaps self/other and returns __pow__."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        return other.__pow__(self, context=context)
+
+    def normalize(self, context=None):
+        """Normalize- strip trailing 0s, change anything equal to 0 to 0e0"""
+
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+
+        dup = self._fix(context)
+        if dup._isinfinity():
+            return dup
+
+        if not dup:
+            return Decimal( (dup._sign, (0,), 0) )
+        end = len(dup._int)
+        exp = dup._exp
+        while dup._int[end-1] == 0:
+            exp += 1
+            end -= 1
+        return Decimal( (dup._sign, dup._int[:end], exp) )
+
+
+    def quantize(self, exp, rounding=None, context=None, watchexp=1):
+        """Quantize self so its exponent is the same as that of exp.
+
+        Similar to self._rescale(exp._exp) but with error checking.
+        """
+        if self._is_special or exp._is_special:
+            ans = self._check_nans(exp, context)
+            if ans:
+                return ans
+
+            if exp._isinfinity() or self._isinfinity():
+                if exp._isinfinity() and self._isinfinity():
+                    return self  #if both are inf, it is OK
+                if context is None:
+                    context = getcontext()
+                return context._raise_error(InvalidOperation,
+                                        'quantize with one INF')
+        return self._rescale(exp._exp, rounding, context, watchexp)
+
+    def same_quantum(self, other):
+        """Test whether self and other have the same exponent.
+
+        same as self._exp == other._exp, except NaN == sNaN
+        """
+        if self._is_special or other._is_special:
+            if self._isnan() or other._isnan():
+                return self._isnan() and other._isnan() and True
+            if self._isinfinity() or other._isinfinity():
+                return self._isinfinity() and other._isinfinity() and True
+        return self._exp == other._exp
+
+    def _rescale(self, exp, rounding=None, context=None, watchexp=1):
+        """Rescales so that the exponent is exp.
+
+        exp = exp to scale to (an integer)
+        rounding = rounding version
+        watchexp: if set (default) an error is returned if exp is greater
+        than Emax or less than Etiny.
+        """
+        if context is None:
+            context = getcontext()
+
+        if self._is_special:
+            if self._isinfinity():
+                return context._raise_error(InvalidOperation, 'rescale with an INF')
+
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+
+        if watchexp and (context.Emax  < exp or context.Etiny() > exp):
+            return context._raise_error(InvalidOperation, 'rescale(a, INF)')
+
+        if not self:
+            ans = Decimal(self)
+            ans._int = (0,)
+            ans._exp = exp
+            return ans
+
+        diff = self._exp - exp
+        digits = len(self._int) + diff
+
+        if watchexp and digits > context.prec:
+            return context._raise_error(InvalidOperation, 'Rescale > prec')
+
+        tmp = Decimal(self)
+        tmp._int = (0,) + tmp._int
+        digits += 1
+
+        if digits < 0:
+            tmp._exp = -digits + tmp._exp
+            tmp._int = (0,1)
+            digits = 1
+        tmp = tmp._round(digits, rounding, context=context)
+
+        if tmp._int[0] == 0 and len(tmp._int) > 1:
+            tmp._int = tmp._int[1:]
+        tmp._exp = exp
+
+        tmp_adjusted = tmp.adjusted()
+        if tmp and tmp_adjusted < context.Emin:
+            context._raise_error(Subnormal)
+        elif tmp and tmp_adjusted > context.Emax:
+            return context._raise_error(InvalidOperation, 'rescale(a, INF)')
+        return tmp
+
+    def to_integral(self, rounding=None, context=None):
+        """Rounds to the nearest integer, without raising inexact, rounded."""
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+        if self._exp >= 0:
+            return self
+        if context is None:
+            context = getcontext()
+        flags = context._ignore_flags(Rounded, Inexact)
+        ans = self._rescale(0, rounding, context=context)
+        context._regard_flags(flags)
+        return ans
+
+    def sqrt(self, context=None):
+        """Return the square root of self.
+
+        Uses a converging algorithm (Xn+1 = 0.5*(Xn + self / Xn))
+        Should quadratically approach the right answer.
+        """
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+
+            if self._isinfinity() and self._sign == 0:
+                return Decimal(self)
+
+        if not self:
+            #exponent = self._exp / 2, using round_down.
+            #if self._exp < 0:
+            #    exp = (self._exp+1) // 2
+            #else:
+            exp = (self._exp) // 2
+            if self._sign == 1:
+                #sqrt(-0) = -0
+                return Decimal( (1, (0,), exp))
+            else:
+                return Decimal( (0, (0,), exp))
+
+        if context is None:
+            context = getcontext()
+
+        if self._sign == 1:
+            return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0')
+
+        tmp = Decimal(self)
+
+        expadd = tmp._exp // 2
+        if tmp._exp & 1:
+            tmp._int += (0,)
+            tmp._exp = 0
+        else:
+            tmp._exp = 0
+
+        context = context._shallow_copy()
+        flags = context._ignore_all_flags()
+        firstprec = context.prec
+        context.prec = 3
+        if tmp.adjusted() & 1 == 0:
+            ans = Decimal( (0, (8,1,9), tmp.adjusted()  - 2) )
+            ans = ans.__add__(tmp.__mul__(Decimal((0, (2,5,9), -2)),
+                                          context=context), context=context)
+            ans._exp -= 1 + tmp.adjusted() // 2
+        else:
+            ans = Decimal( (0, (2,5,9), tmp._exp + len(tmp._int)- 3) )
+            ans = ans.__add__(tmp.__mul__(Decimal((0, (8,1,9), -3)),
+                                          context=context), context=context)
+            ans._exp -= 1 + tmp.adjusted()  // 2
+
+        #ans is now a linear approximation.
+
+        Emax, Emin = context.Emax, context.Emin
+        context.Emax, context.Emin = DefaultContext.Emax, DefaultContext.Emin
+
+        half = Decimal('0.5')
+
+        maxp = firstprec + 2
+        rounding = context._set_rounding(ROUND_HALF_EVEN)
+        while 1:
+            context.prec = min(2*context.prec - 2, maxp)
+            ans = half.__mul__(ans.__add__(tmp.__div__(ans, context=context),
+                                           context=context), context=context)
+            if context.prec == maxp:
+                break
+
+        #round to the answer's precision-- the only error can be 1 ulp.
+        context.prec = firstprec
+        prevexp = ans.adjusted()
+        ans = ans._round(context=context)
+
+        #Now, check if the other last digits are better.
+        context.prec = firstprec + 1
+        # In case we rounded up another digit and we should actually go lower.
+        if prevexp != ans.adjusted():
+            ans._int += (0,)
+            ans._exp -= 1
+
+
+        lower = ans.__sub__(Decimal((0, (5,), ans._exp-1)), context=context)
+        context._set_rounding(ROUND_UP)
+        if lower.__mul__(lower, context=context) > (tmp):
+            ans = ans.__sub__(Decimal((0, (1,), ans._exp)), context=context)
+
+        else:
+            upper = ans.__add__(Decimal((0, (5,), ans._exp-1)),context=context)
+            context._set_rounding(ROUND_DOWN)
+            if upper.__mul__(upper, context=context) < tmp:
+                ans = ans.__add__(Decimal((0, (1,), ans._exp)),context=context)
+
+        ans._exp += expadd
+
+        context.prec = firstprec
+        context.rounding = rounding
+        ans = ans._fix(context)
+
+        rounding = context._set_rounding_decision(NEVER_ROUND)
+        if not ans.__mul__(ans, context=context) == self:
+            # Only rounded/inexact if here.
+            context._regard_flags(flags)
+            context._raise_error(Rounded)
+            context._raise_error(Inexact)
+        else:
+            #Exact answer, so let's set the exponent right.
+            #if self._exp < 0:
+            #    exp = (self._exp +1)// 2
+            #else:
+            exp = self._exp // 2
+            context.prec += ans._exp - exp
+            ans = ans._rescale(exp, context=context)
+            context.prec = firstprec
+            context._regard_flags(flags)
+        context.Emax, context.Emin = Emax, Emin
+
+        return ans._fix(context)
+
+    def max(self, other, context=None):
+        """Returns the larger value.
+
+        like max(self, other) except if one is not a number, returns
+        NaN (and signals if one is sNaN).  Also rounds.
+        """
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if self._is_special or other._is_special:
+            # if one operand is a quiet NaN and the other is number, then the
+            # number is always returned
+            sn = self._isnan()
+            on = other._isnan()
+            if sn or on:
+                if on == 1 and sn != 2:
+                    return self
+                if sn == 1 and on != 2:
+                    return other
+                return self._check_nans(other, context)
+
+        ans = self
+        c = self.__cmp__(other)
+        if c == 0:
+            # if both operands are finite and equal in numerical value
+            # then an ordering is applied:
+            #
+            # if the signs differ then max returns the operand with the
+            # positive sign and min returns the operand with the negative sign
+            #
+            # if the signs are the same then the exponent is used to select
+            # the result.
+            if self._sign != other._sign:
+                if self._sign:
+                    ans = other
+            elif self._exp < other._exp and not self._sign:
+                ans = other
+            elif self._exp > other._exp and self._sign:
+                ans = other
+        elif c == -1:
+            ans = other
+
+        if context is None:
+            context = getcontext()
+        if context._rounding_decision == ALWAYS_ROUND:
+            return ans._fix(context)
+        return ans
+
+    def min(self, other, context=None):
+        """Returns the smaller value.
+
+        like min(self, other) except if one is not a number, returns