diff -r ffa851df0825 -r 2fb8b9db1c86 symbian-qemu-0.9.1-12/python-2.6.1/Lib/decimal.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/symbian-qemu-0.9.1-12/python-2.6.1/Lib/decimal.py	Fri Jul 31 15:01:17 2009 +0100
@@ -0,0 +1,5507 @@
+# Copyright (c) 2004 Python Software Foundation.
+# All rights reserved.
+
+# Written by Eric Price <eprice at tjhsst.edu>
+#    and Facundo Batista <facundo at taniquetil.com.ar>
+#    and Raymond Hettinger <python at rcn.com>
+#    and Aahz <aahz at pobox.com>
+#    and Tim Peters
+
+# This module is currently Py2.3 compatible and should be kept that way
+# unless a major compelling advantage arises.  IOW, 2.3 compatibility is
+# strongly preferred, but not guaranteed.
+
+# Also, this module should be kept in sync with the latest updates of
+# the IBM specification as it evolves.  Those updates will be treated
+# as bug fixes (deviation from the spec is a compatibility, usability
+# bug) and will be backported.  At this point the spec is stabilizing
+# and the updates are becoming fewer, smaller, and less significant.
+
+"""
+This is a Py2.3 implementation of decimal floating point arithmetic based on
+the General Decimal Arithmetic Specification:
+
+    www2.hursley.ibm.com/decimal/decarith.html
+
+and IEEE standard 854-1987:
+
+    www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html
+
+Decimal floating point has finite precision with arbitrarily large bounds.
+
+The purpose of this module is to support arithmetic using familiar
+"schoolhouse" rules and to avoid some of the tricky representation
+issues associated with binary floating point.  The package is especially
+useful for financial applications or for contexts where users have
+expectations that are at odds with binary floating point (for instance,
+in binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead
+of the expected Decimal('0.00') returned by decimal floating point).
+
+Here are some examples of using the decimal module:
+
+>>> from decimal import *
+>>> setcontext(ExtendedContext)
+>>> Decimal(0)
+Decimal('0')
+>>> Decimal('1')
+Decimal('1')
+>>> Decimal('-.0123')
+Decimal('-0.0123')
+>>> Decimal(123456)
+Decimal('123456')
+>>> Decimal('123.45e12345678901234567890')
+Decimal('1.2345E+12345678901234567892')
+>>> Decimal('1.33') + Decimal('1.27')
+Decimal('2.60')
+>>> Decimal('12.34') + Decimal('3.87') - Decimal('18.41')
+Decimal('-2.20')
+>>> dig = Decimal(1)
+>>> print dig / Decimal(3)
+0.333333333
+>>> getcontext().prec = 18
+>>> print dig / Decimal(3)
+0.333333333333333333
+>>> print dig.sqrt()
+1
+>>> print Decimal(3).sqrt()
+1.73205080756887729
+>>> print Decimal(3) ** 123
+4.85192780976896427E+58
+>>> inf = Decimal(1) / Decimal(0)
+>>> print inf
+Infinity
+>>> neginf = Decimal(-1) / Decimal(0)
+>>> print neginf
+-Infinity
+>>> print neginf + inf
+NaN
+>>> print neginf * inf
+-Infinity
+>>> print dig / 0
+Infinity
+>>> getcontext().traps[DivisionByZero] = 1
+>>> print dig / 0
+Traceback (most recent call last):
+  ...
+  ...
+  ...
+DivisionByZero: x / 0
+>>> c = Context()
+>>> c.traps[InvalidOperation] = 0
+>>> print c.flags[InvalidOperation]
+0
+>>> c.divide(Decimal(0), Decimal(0))
+Decimal('NaN')
+>>> c.traps[InvalidOperation] = 1
+>>> print c.flags[InvalidOperation]
+1
+>>> c.flags[InvalidOperation] = 0
+>>> print c.flags[InvalidOperation]
+0
+>>> print c.divide(Decimal(0), Decimal(0))
+Traceback (most recent call last):
+  ...
+  ...
+  ...
+InvalidOperation: 0 / 0
+>>> print c.flags[InvalidOperation]
+1
+>>> c.flags[InvalidOperation] = 0
+>>> c.traps[InvalidOperation] = 0
+>>> print c.divide(Decimal(0), Decimal(0))
+NaN
+>>> print c.flags[InvalidOperation]
+1
+>>>
+"""
+
+__all__ = [
+    # Two major classes
+    'Decimal', 'Context',
+
+    # Contexts
+    'DefaultContext', 'BasicContext', 'ExtendedContext',
+
+    # Exceptions
+    'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero',
+    'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow',
+
+    # Constants for use in setting up contexts
+    'ROUND_DOWN', 'ROUND_HALF_UP', 'ROUND_HALF_EVEN', 'ROUND_CEILING',
+    'ROUND_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN', 'ROUND_05UP',
+
+    # Functions for manipulating contexts
+    'setcontext', 'getcontext', 'localcontext'
+]
+
+import copy as _copy
+
+try:
+    from collections import namedtuple as _namedtuple
+    DecimalTuple = _namedtuple('DecimalTuple', 'sign digits exponent')
+except ImportError:
+    DecimalTuple = lambda *args: args
+
+# Rounding
+ROUND_DOWN = 'ROUND_DOWN'
+ROUND_HALF_UP = 'ROUND_HALF_UP'
+ROUND_HALF_EVEN = 'ROUND_HALF_EVEN'
+ROUND_CEILING = 'ROUND_CEILING'
+ROUND_FLOOR = 'ROUND_FLOOR'
+ROUND_UP = 'ROUND_UP'
+ROUND_HALF_DOWN = 'ROUND_HALF_DOWN'
+ROUND_05UP = 'ROUND_05UP'
+
+# Errors
+
+class DecimalException(ArithmeticError):
+    """Base exception class.
+
+    Used exceptions derive from this.
+    If an exception derives from another exception besides this (such as
+    Underflow (Inexact, Rounded, Subnormal) that indicates that it is only
+    called if the others are present.  This isn't actually used for
+    anything, though.
+
+    handle  -- Called when context._raise_error is called and the
+               trap_enabler is set.  First argument is self, second is the
+               context.  More arguments can be given, those being after
+               the explanation in _raise_error (For example,
+               context._raise_error(NewError, '(-x)!', self._sign) would
+               call NewError().handle(context, self._sign).)
+
+    To define a new exception, it should be sufficient to have it derive
+    from DecimalException.
+    """
+    def handle(self, context, *args):
+        pass
+
+
+class Clamped(DecimalException):
+    """Exponent of a 0 changed to fit bounds.
+
+    This occurs and signals clamped if the exponent of a result has been
+    altered in order to fit the constraints of a specific concrete
+    representation.  This may occur when the exponent of a zero result would
+    be outside the bounds of a representation, or when a large normal
+    number would have an encoded exponent that cannot be represented.  In
+    this latter case, the exponent is reduced to fit and the corresponding
+    number of zero digits are appended to the coefficient ("fold-down").
+    """
+
+class InvalidOperation(DecimalException):
+    """An invalid operation was performed.
+
+    Various bad things cause this:
+
+    Something creates a signaling NaN
+    -INF + INF
+    0 * (+-)INF
+    (+-)INF / (+-)INF
+    x % 0
+    (+-)INF % x
+    x._rescale( non-integer )
+    sqrt(-x) , x > 0
+    0 ** 0
+    x ** (non-integer)
+    x ** (+-)INF
+    An operand is invalid
+
+    The result of the operation after these is a quiet positive NaN,
+    except when the cause is a signaling NaN, in which case the result is
+    also a quiet NaN, but with the original sign, and an optional
+    diagnostic information.
+    """
+    def handle(self, context, *args):
+        if args:
+            ans = _dec_from_triple(args[0]._sign, args[0]._int, 'n', True)
+            return ans._fix_nan(context)
+        return NaN
+
+class ConversionSyntax(InvalidOperation):
+    """Trying to convert badly formed string.
+
+    This occurs and signals invalid-operation if an string is being
+    converted to a number and it does not conform to the numeric string
+    syntax.  The result is [0,qNaN].
+    """
+    def handle(self, context, *args):
+        return NaN
+
+class DivisionByZero(DecimalException, ZeroDivisionError):
+    """Division by 0.
+
+    This occurs and signals division-by-zero if division of a finite number
+    by zero was attempted (during a divide-integer or divide operation, or a
+    power operation with negative right-hand operand), and the dividend was
+    not zero.
+
+    The result of the operation is [sign,inf], where sign is the exclusive
+    or of the signs of the operands for divide, or is 1 for an odd power of
+    -0, for power.
+    """
+
+    def handle(self, context, sign, *args):
+        return Infsign[sign]
+
+class DivisionImpossible(InvalidOperation):
+    """Cannot perform the division adequately.
+
+    This occurs and signals invalid-operation if the integer result of a
+    divide-integer or remainder operation had too many digits (would be
+    longer than precision).  The result is [0,qNaN].
+    """
+
+    def handle(self, context, *args):
+        return NaN
+
+class DivisionUndefined(InvalidOperation, ZeroDivisionError):
+    """Undefined result of division.
+
+    This occurs and signals invalid-operation if division by zero was
+    attempted (during a divide-integer, divide, or remainder operation), and
+    the dividend is also zero.  The result is [0,qNaN].
+    """
+
+    def handle(self, context, *args):
+        return NaN
+
+class Inexact(DecimalException):
+    """Had to round, losing information.
+
+    This occurs and signals inexact whenever the result of an operation is
+    not exact (that is, it needed to be rounded and any discarded digits
+    were non-zero), or if an overflow or underflow condition occurs.  The
+    result in all cases is unchanged.
+
+    The inexact signal may be tested (or trapped) to determine if a given
+    operation (or sequence of operations) was inexact.
+    """
+
+class InvalidContext(InvalidOperation):
+    """Invalid context.  Unknown rounding, for example.
+
+    This occurs and signals invalid-operation if an invalid context was
+    detected during an operation.  This can occur if contexts are not checked
+    on creation and either the precision exceeds the capability of the
+    underlying concrete representation or an unknown or unsupported rounding
+    was specified.  These aspects of the context need only be checked when
+    the values are required to be used.  The result is [0,qNaN].
+    """
+
+    def handle(self, context, *args):
+        return NaN
+
+class Rounded(DecimalException):
+    """Number got rounded (not  necessarily changed during rounding).
+
+    This occurs and signals rounded whenever the result of an operation is
+    rounded (that is, some zero or non-zero digits were discarded from the
+    coefficient), or if an overflow or underflow condition occurs.  The
+    result in all cases is unchanged.
+
+    The rounded signal may be tested (or trapped) to determine if a given
+    operation (or sequence of operations) caused a loss of precision.
+    """
+
+class Subnormal(DecimalException):
+    """Exponent < Emin before rounding.
+
+    This occurs and signals subnormal whenever the result of a conversion or
+    operation is subnormal (that is, its adjusted exponent is less than
+    Emin, before any rounding).  The result in all cases is unchanged.
+
+    The subnormal signal may be tested (or trapped) to determine if a given
+    or operation (or sequence of operations) yielded a subnormal result.
+    """
+
+class Overflow(Inexact, Rounded):
+    """Numerical overflow.
+
+    This occurs and signals overflow if the adjusted exponent of a result
+    (from a conversion or from an operation that is not an attempt to divide
+    by zero), after rounding, would be greater than the largest value that
+    can be handled by the implementation (the value Emax).
+
+    The result depends on the rounding mode:
+
+    For round-half-up and round-half-even (and for round-half-down and
+    round-up, if implemented), the result of the operation is [sign,inf],
+    where sign is the sign of the intermediate result.  For round-down, the
+    result is the largest finite number that can be represented in the
+    current precision, with the sign of the intermediate result.  For
+    round-ceiling, the result is the same as for round-down if the sign of
+    the intermediate result is 1, or is [0,inf] otherwise.  For round-floor,
+    the result is the same as for round-down if the sign of the intermediate
+    result is 0, or is [1,inf] otherwise.  In all cases, Inexact and Rounded
+    will also be raised.
+    """
+
+    def handle(self, context, sign, *args):
+        if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN,
+                                ROUND_HALF_DOWN, ROUND_UP):
+            return Infsign[sign]
+        if sign == 0:
+            if context.rounding == ROUND_CEILING:
+                return Infsign[sign]
+            return _dec_from_triple(sign, '9'*context.prec,
+                            context.Emax-context.prec+1)
+        if sign == 1:
+            if context.rounding == ROUND_FLOOR:
+                return Infsign[sign]
+            return _dec_from_triple(sign, '9'*context.prec,
+                             context.Emax-context.prec+1)
+
+
+class Underflow(Inexact, Rounded, Subnormal):
+    """Numerical underflow with result rounded to 0.
+
+    This occurs and signals underflow if a result is inexact and the
+    adjusted exponent of the result would be smaller (more negative) than
+    the smallest value that can be handled by the implementation (the value
+    Emin).  That is, the result is both inexact and subnormal.
+
+    The result after an underflow will be a subnormal number rounded, if
+    necessary, so that its exponent is not less than Etiny.  This may result
+    in 0 with the sign of the intermediate result and an exponent of Etiny.
+
+    In all cases, Inexact, Rounded, and Subnormal will also be raised.
+    """
+
+# List of public traps and flags
+_signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded,
+           Underflow, InvalidOperation, Subnormal]
+
+# Map conditions (per the spec) to signals
+_condition_map = {ConversionSyntax:InvalidOperation,
+                  DivisionImpossible:InvalidOperation,
+                  DivisionUndefined:InvalidOperation,
+                  InvalidContext:InvalidOperation}
+
+##### Context Functions ##################################################
+
+# The getcontext() and setcontext() function manage access to a thread-local
+# current context.  Py2.4 offers direct support for thread locals.  If that
+# is not available, use threading.currentThread() which is slower but will
+# work for older Pythons.  If threads are not part of the build, create a
+# mock threading object with threading.local() returning the module namespace.
+
+try:
+    import threading
+except ImportError:
+    # Python was compiled without threads; create a mock object instead
+    import sys
+    class MockThreading(object):
+        def local(self, sys=sys):
+            return sys.modules[__name__]
+    threading = MockThreading()
+    del sys, MockThreading
+
+try:
+    threading.local
+
+except AttributeError:
+
+    # To fix reloading, force it to create a new context
+    # Old contexts have different exceptions in their dicts, making problems.
+    if hasattr(threading.currentThread(), '__decimal_context__'):
+        del threading.currentThread().__decimal_context__
+
+    def setcontext(context):
+        """Set this thread's context to context."""
+        if context in (DefaultContext, BasicContext, ExtendedContext):
+            context = context.copy()
+            context.clear_flags()
+        threading.currentThread().__decimal_context__ = context
+
+    def getcontext():
+        """Returns this thread's context.
+
+        If this thread does not yet have a context, returns
+        a new context and sets this thread's context.
+        New contexts are copies of DefaultContext.
+        """
+        try:
+            return threading.currentThread().__decimal_context__
+        except AttributeError:
+            context = Context()
+            threading.currentThread().__decimal_context__ = context
+            return context
+
+else:
+
+    local = threading.local()
+    if hasattr(local, '__decimal_context__'):
+        del local.__decimal_context__
+
+    def getcontext(_local=local):
+        """Returns this thread's context.
+
+        If this thread does not yet have a context, returns
+        a new context and sets this thread's context.
+        New contexts are copies of DefaultContext.
+        """
+        try:
+            return _local.__decimal_context__
+        except AttributeError:
+            context = Context()
+            _local.__decimal_context__ = context
+            return context
+
+    def setcontext(context, _local=local):
+        """Set this thread's context to context."""
+        if context in (DefaultContext, BasicContext, ExtendedContext):
+            context = context.copy()
+            context.clear_flags()
+        _local.__decimal_context__ = context
+
+    del threading, local        # Don't contaminate the namespace
+
+def localcontext(ctx=None):
+    """Return a context manager for a copy of the supplied context
+
+    Uses a copy of the current context if no context is specified
+    The returned context manager creates a local decimal context
+    in a with statement:
+        def sin(x):
+             with localcontext() as ctx:
+                 ctx.prec += 2
+                 # Rest of sin calculation algorithm
+                 # uses a precision 2 greater than normal
+             return +s  # Convert result to normal precision
+
+         def sin(x):
+             with localcontext(ExtendedContext):
+                 # Rest of sin calculation algorithm
+                 # uses the Extended Context from the
+                 # General Decimal Arithmetic Specification
+             return +s  # Convert result to normal context
+
+    >>> setcontext(DefaultContext)
+    >>> print getcontext().prec
+    28
+    >>> with localcontext():
+    ...     ctx = getcontext()
+    ...     ctx.prec += 2
+    ...     print ctx.prec
+    ...
+    30
+    >>> with localcontext(ExtendedContext):
+    ...     print getcontext().prec
+    ...
+    9
+    >>> print getcontext().prec
+    28
+    """
+    if ctx is None: ctx = getcontext()
+    return _ContextManager(ctx)
+
+
+##### Decimal class #######################################################
+
+class Decimal(object):
+    """Floating point class for decimal arithmetic."""
+
+    __slots__ = ('_exp','_int','_sign', '_is_special')
+    # Generally, the value of the Decimal instance is given by
+    #  (-1)**_sign * _int * 10**_exp
+    # Special values are signified by _is_special == True
+
+    # We're immutable, so use __new__ not __init__
+    def __new__(cls, value="0", context=None):
+        """Create a decimal point instance.
+
+        >>> Decimal('3.14')              # string input
+        Decimal('3.14')
+        >>> Decimal((0, (3, 1, 4), -2))  # tuple (sign, digit_tuple, exponent)
+        Decimal('3.14')
+        >>> Decimal(314)                 # int or long
+        Decimal('314')
+        >>> Decimal(Decimal(314))        # another decimal instance
+        Decimal('314')
+        >>> Decimal('  3.14  \\n')        # leading and trailing whitespace okay
+        Decimal('3.14')
+        """
+
+        # Note that the coefficient, self._int, is actually stored as
+        # a string rather than as a tuple of digits.  This speeds up
+        # the "digits to integer" and "integer to digits" conversions
+        # that are used in almost every arithmetic operation on
+        # Decimals.  This is an internal detail: the as_tuple function
+        # and the Decimal constructor still deal with tuples of
+        # digits.
+
+        self = object.__new__(cls)
+
+        # From a string
+        # REs insist on real strings, so we can too.
+        if isinstance(value, basestring):
+            m = _parser(value.strip())
+            if m is None:
+                if context is None:
+                    context = getcontext()
+                return context._raise_error(ConversionSyntax,
+                                "Invalid literal for Decimal: %r" % value)
+
+            if m.group('sign') == "-":
+                self._sign = 1
+            else:
+                self._sign = 0
+            intpart = m.group('int')
+            if intpart is not None:
+                # finite number
+                fracpart = m.group('frac')
+                exp = int(m.group('exp') or '0')
+                if fracpart is not None:
+                    self._int = str((intpart+fracpart).lstrip('0') or '0')
+                    self._exp = exp - len(fracpart)
+                else:
+                    self._int = str(intpart.lstrip('0') or '0')
+                    self._exp = exp
+                self._is_special = False
+            else:
+                diag = m.group('diag')
+                if diag is not None:
+                    # NaN
+                    self._int = str(diag.lstrip('0'))
+                    if m.group('signal'):
+                        self._exp = 'N'
+                    else:
+                        self._exp = 'n'
+                else:
+                    # infinity
+                    self._int = '0'
+                    self._exp = 'F'
+                self._is_special = True
+            return self
+
+        # From an integer
+        if isinstance(value, (int,long)):
+            if value >= 0:
+                self._sign = 0
+            else:
+                self._sign = 1
+            self._exp = 0
+            self._int = str(abs(value))
+            self._is_special = False
+            return self
+
+        # From another decimal
+        if isinstance(value, Decimal):
+            self._exp  = value._exp
+            self._sign = value._sign
+            self._int  = value._int
+            self._is_special  = value._is_special
+            return self
+
+        # From an internal working value
+        if isinstance(value, _WorkRep):
+            self._sign = value.sign
+            self._int = str(value.int)
+            self._exp = int(value.exp)
+            self._is_special = False
+            return self
+
+        # tuple/list conversion (possibly from as_tuple())
+        if isinstance(value, (list,tuple)):
+            if len(value) != 3:
+                raise ValueError('Invalid tuple size in creation of Decimal '
+                                 'from list or tuple.  The list or tuple '
+                                 'should have exactly three elements.')
+            # process sign.  The isinstance test rejects floats
+            if not (isinstance(value[0], (int, long)) and value[0] in (0,1)):
+                raise ValueError("Invalid sign.  The first value in the tuple "
+                                 "should be an integer; either 0 for a "
+                                 "positive number or 1 for a negative number.")
+            self._sign = value[0]
+            if value[2] == 'F':
+                # infinity: value[1] is ignored
+                self._int = '0'
+                self._exp = value[2]
+                self._is_special = True
+            else:
+                # process and validate the digits in value[1]
+                digits = []
+                for digit in value[1]:
+                    if isinstance(digit, (int, long)) and 0 <= digit <= 9:
+                        # skip leading zeros
+                        if digits or digit != 0:
+                            digits.append(digit)
+                    else:
+                        raise ValueError("The second value in the tuple must "
+                                         "be composed of integers in the range "
+                                         "0 through 9.")
+                if value[2] in ('n', 'N'):
+                    # NaN: digits form the diagnostic
+                    self._int = ''.join(map(str, digits))
+                    self._exp = value[2]
+                    self._is_special = True
+                elif isinstance(value[2], (int, long)):
+                    # finite number: digits give the coefficient
+                    self._int = ''.join(map(str, digits or [0]))
+                    self._exp = value[2]
+                    self._is_special = False
+                else:
+                    raise ValueError("The third value in the tuple must "
+                                     "be an integer, or one of the "
+                                     "strings 'F', 'n', 'N'.")
+            return self
+
+        if isinstance(value, float):
+            raise TypeError("Cannot convert float to Decimal.  " +
+                            "First convert the float to a string")
+
+        raise TypeError("Cannot convert %r to Decimal" % value)
+
+    def _isnan(self):
+        """Returns whether the number is not actually one.
+
+        0 if a number
+        1 if NaN
+        2 if sNaN
+        """
+        if self._is_special:
+            exp = self._exp
+            if exp == 'n':
+                return 1
+            elif exp == 'N':
+                return 2
+        return 0
+
+    def _isinfinity(self):
+        """Returns whether the number is infinite
+
+        0 if finite or not a number
+        1 if +INF
+        -1 if -INF
+        """
+        if self._exp == 'F':
+            if self._sign:
+                return -1
+            return 1
+        return 0
+
+    def _check_nans(self, other=None, context=None):
+        """Returns whether the number is not actually one.
+
+        if self, other are sNaN, signal
+        if self, other are NaN return nan
+        return 0
+
+        Done before operations.
+        """
+
+        self_is_nan = self._isnan()
+        if other is None:
+            other_is_nan = False
+        else:
+            other_is_nan = other._isnan()
+
+        if self_is_nan or other_is_nan:
+            if context is None:
+                context = getcontext()
+
+            if self_is_nan == 2:
+                return context._raise_error(InvalidOperation, 'sNaN',
+                                        self)
+            if other_is_nan == 2:
+                return context._raise_error(InvalidOperation, 'sNaN',
+                                        other)
+            if self_is_nan:
+                return self._fix_nan(context)
+
+            return other._fix_nan(context)
+        return 0
+
+    def _compare_check_nans(self, other, context):
+        """Version of _check_nans used for the signaling comparisons
+        compare_signal, __le__, __lt__, __ge__, __gt__.
+
+        Signal InvalidOperation if either self or other is a (quiet
+        or signaling) NaN.  Signaling NaNs take precedence over quiet
+        NaNs.
+
+        Return 0 if neither operand is a NaN.
+
+        """
+        if context is None:
+            context = getcontext()
+
+        if self._is_special or other._is_special:
+            if self.is_snan():
+                return context._raise_error(InvalidOperation,
+                                            'comparison involving sNaN',
+                                            self)
+            elif other.is_snan():
+                return context._raise_error(InvalidOperation,
+                                            'comparison involving sNaN',
+                                            other)
+            elif self.is_qnan():
+                return context._raise_error(InvalidOperation,
+                                            'comparison involving NaN',
+                                            self)
+            elif other.is_qnan():
+                return context._raise_error(InvalidOperation,
+                                            'comparison involving NaN',
+                                            other)
+        return 0
+
+    def __nonzero__(self):
+        """Return True if self is nonzero; otherwise return False.
+
+        NaNs and infinities are considered nonzero.
+        """
+        return self._is_special or self._int != '0'
+
+    def _cmp(self, other):
+        """Compare the two non-NaN decimal instances self and other.
+
+        Returns -1 if self < other, 0 if self == other and 1
+        if self > other.  This routine is for internal use only."""
+
+        if self._is_special or other._is_special:
+            return cmp(self._isinfinity(), other._isinfinity())
+
+        # check for zeros;  note that cmp(0, -0) should return 0
+        if not self:
+            if not other:
+                return 0
+            else:
+                return -((-1)**other._sign)
+        if not other:
+            return (-1)**self._sign
+
+        # If different signs, neg one is less
+        if other._sign < self._sign:
+            return -1
+        if self._sign < other._sign:
+            return 1
+
+        self_adjusted = self.adjusted()
+        other_adjusted = other.adjusted()
+        if self_adjusted == other_adjusted:
+            self_padded = self._int + '0'*(self._exp - other._exp)
+            other_padded = other._int + '0'*(other._exp - self._exp)
+            return cmp(self_padded, other_padded) * (-1)**self._sign
+        elif self_adjusted > other_adjusted:
+            return (-1)**self._sign
+        else: # self_adjusted < other_adjusted
+            return -((-1)**self._sign)
+
+    # Note: The Decimal standard doesn't cover rich comparisons for
+    # Decimals.  In particular, the specification is silent on the
+    # subject of what should happen for a comparison involving a NaN.
+    # We take the following approach:
+    #
+    #   == comparisons involving a NaN always return False
+    #   != comparisons involving a NaN always return True
+    #   <, >, <= and >= comparisons involving a (quiet or signaling)
+    #      NaN signal InvalidOperation, and return False if the
+    #      InvalidOperation is not trapped.
+    #
+    # This behavior is designed to conform as closely as possible to
+    # that specified by IEEE 754.
+
+    def __eq__(self, other):
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        if self.is_nan() or other.is_nan():
+            return False
+        return self._cmp(other) == 0
+
+    def __ne__(self, other):
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        if self.is_nan() or other.is_nan():
+            return True
+        return self._cmp(other) != 0
+
+    def __lt__(self, other, context=None):
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        ans = self._compare_check_nans(other, context)
+        if ans:
+            return False
+        return self._cmp(other) < 0
+
+    def __le__(self, other, context=None):
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        ans = self._compare_check_nans(other, context)
+        if ans:
+            return False
+        return self._cmp(other) <= 0
+
+    def __gt__(self, other, context=None):
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        ans = self._compare_check_nans(other, context)
+        if ans:
+            return False
+        return self._cmp(other) > 0
+
+    def __ge__(self, other, context=None):
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        ans = self._compare_check_nans(other, context)
+        if ans:
+            return False
+        return self._cmp(other) >= 0
+
+    def compare(self, other, context=None):
+        """Compares one to another.
+
+        -1 => a < b
+        0  => a = b
+        1  => a > b
+        NaN => one is NaN
+        Like __cmp__, but returns Decimal instances.
+        """
+        other = _convert_other(other, raiseit=True)
+
+        # Compare(NaN, NaN) = NaN
+        if (self._is_special or other and other._is_special):
+            ans = self._check_nans(other, context)
+            if ans:
+                return ans
+
+        return Decimal(self._cmp(other))
+
+    def __hash__(self):
+        """x.__hash__() <==> hash(x)"""
+        # Decimal integers must hash the same as the ints
+        #
+        # The hash of a nonspecial noninteger Decimal must depend only
+        # on the value of that Decimal, and not on its representation.
+        # For example: hash(Decimal('100E-1')) == hash(Decimal('10')).
+        if self._is_special:
+            if self._isnan():
+                raise TypeError('Cannot hash a NaN value.')
+            return hash(str(self))
+        if not self:
+            return 0
+        if self._isinteger():
+            op = _WorkRep(self.to_integral_value())
+            # to make computation feasible for Decimals with large
+            # exponent, we use the fact that hash(n) == hash(m) for
+            # any two nonzero integers n and m such that (i) n and m
+            # have the same sign, and (ii) n is congruent to m modulo
+            # 2**64-1.  So we can replace hash((-1)**s*c*10**e) with
+            # hash((-1)**s*c*pow(10, e, 2**64-1).
+            return hash((-1)**op.sign*op.int*pow(10, op.exp, 2**64-1))
+        # The value of a nonzero nonspecial Decimal instance is
+        # faithfully represented by the triple consisting of its sign,
+        # its adjusted exponent, and its coefficient with trailing
+        # zeros removed.
+        return hash((self._sign,
+                     self._exp+len(self._int),
+                     self._int.rstrip('0')))
+
+    def as_tuple(self):
+        """Represents the number as a triple tuple.
+
+        To show the internals exactly as they are.
+        """
+        return DecimalTuple(self._sign, tuple(map(int, self._int)), self._exp)
+
+    def __repr__(self):
+        """Represents the number as an instance of Decimal."""
+        # Invariant:  eval(repr(d)) == d
+        return "Decimal('%s')" % str(self)
+
+    def __str__(self, eng=False, context=None):
+        """Return string representation of the number in scientific notation.
+
+        Captures all of the information in the underlying representation.
+        """
+
+        sign = ['', '-'][self._sign]
+        if self._is_special:
+            if self._exp == 'F':
+                return sign + 'Infinity'
+            elif self._exp == 'n':
+                return sign + 'NaN' + self._int
+            else: # self._exp == 'N'
+                return sign + 'sNaN' + self._int
+
+        # number of digits of self._int to left of decimal point
+        leftdigits = self._exp + len(self._int)
+
+        # dotplace is number of digits of self._int to the left of the
+        # decimal point in the mantissa of the output string (that is,
+        # after adjusting the exponent)
+        if self._exp <= 0 and leftdigits > -6:
+            # no exponent required
+            dotplace = leftdigits
+        elif not eng:
+            # usual scientific notation: 1 digit on left of the point
+            dotplace = 1
+        elif self._int == '0':
+            # engineering notation, zero
+            dotplace = (leftdigits + 1) % 3 - 1
+        else:
+            # engineering notation, nonzero
+            dotplace = (leftdigits - 1) % 3 + 1
+
+        if dotplace <= 0:
+            intpart = '0'
+            fracpart = '.' + '0'*(-dotplace) + self._int
+        elif dotplace >= len(self._int):
+            intpart = self._int+'0'*(dotplace-len(self._int))
+            fracpart = ''
+        else:
+            intpart = self._int[:dotplace]
+            fracpart = '.' + self._int[dotplace:]
+        if leftdigits == dotplace:
+            exp = ''
+        else:
+            if context is None:
+                context = getcontext()
+            exp = ['e', 'E'][context.capitals] + "%+d" % (leftdigits-dotplace)
+
+        return sign + intpart + fracpart + exp
+
+    def to_eng_string(self, context=None):
+        """Convert to engineering-type string.
+
+        Engineering notation has an exponent which is a multiple of 3, so there
+        are up to 3 digits left of the decimal place.
+
+        Same rules for when in exponential and when as a value as in __str__.
+        """
+        return self.__str__(eng=True, context=context)
+
+    def __neg__(self, context=None):
+        """Returns a copy with the sign switched.
+
+        Rounds, if it has reason.
+        """
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+
+        if not self:
+            # -Decimal('0') is Decimal('0'), not Decimal('-0')
+            ans = self.copy_abs()
+        else:
+            ans = self.copy_negate()
+
+        if context is None:
+            context = getcontext()
+        return ans._fix(context)
+
+    def __pos__(self, context=None):
+        """Returns a copy, unless it is a sNaN.
+
+        Rounds the number (if more then precision digits)
+        """
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+
+        if not self:
+            # + (-0) = 0
+            ans = self.copy_abs()
+        else:
+            ans = Decimal(self)
+
+        if context is None:
+            context = getcontext()
+        return ans._fix(context)
+
+    def __abs__(self, round=True, context=None):
+        """Returns the absolute value of self.
+
+        If the keyword argument 'round' is false, do not round.  The
+        expression self.__abs__(round=False) is equivalent to
+        self.copy_abs().
+        """
+        if not round:
+            return self.copy_abs()
+
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+
+        if self._sign:
+            ans = self.__neg__(context=context)
+        else:
+            ans = self.__pos__(context=context)
+
+        return ans
+
+    def __add__(self, other, context=None):
+        """Returns self + other.
+
+        -INF + INF (or the reverse) cause InvalidOperation errors.
+        """
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if context is None:
+            context = getcontext()
+
+        if self._is_special or other._is_special:
+            ans = self._check_nans(other, context)
+            if ans:
+                return ans
+
+            if self._isinfinity():
+                # If both INF, same sign => same as both, opposite => error.
+                if self._sign != other._sign and other._isinfinity():
+                    return context._raise_error(InvalidOperation, '-INF + INF')
+                return Decimal(self)
+            if other._isinfinity():
+                return Decimal(other)  # Can't both be infinity here
+
+        exp = min(self._exp, other._exp)
+        negativezero = 0
+        if context.rounding == ROUND_FLOOR and self._sign != other._sign:
+            # If the answer is 0, the sign should be negative, in this case.
+            negativezero = 1
+
+        if not self and not other:
+            sign = min(self._sign, other._sign)
+            if negativezero:
+                sign = 1
+            ans = _dec_from_triple(sign, '0', exp)
+            ans = ans._fix(context)
+            return ans
+        if not self:
+            exp = max(exp, other._exp - context.prec-1)
+            ans = other._rescale(exp, context.rounding)
+            ans = ans._fix(context)
+            return ans
+        if not other:
+            exp = max(exp, self._exp - context.prec-1)
+            ans = self._rescale(exp, context.rounding)
+            ans = ans._fix(context)
+            return ans
+
+        op1 = _WorkRep(self)
+        op2 = _WorkRep(other)
+        op1, op2 = _normalize(op1, op2, context.prec)
+
+        result = _WorkRep()
+        if op1.sign != op2.sign:
+            # Equal and opposite
+            if op1.int == op2.int:
+                ans = _dec_from_triple(negativezero, '0', exp)
+                ans = ans._fix(context)
+                return ans
+            if op1.int < op2.int:
+                op1, op2 = op2, op1
+                # OK, now abs(op1) > abs(op2)
+            if op1.sign == 1:
+                result.sign = 1
+                op1.sign, op2.sign = op2.sign, op1.sign
+            else:
+                result.sign = 0
+                # So we know the sign, and op1 > 0.
+        elif op1.sign == 1:
+            result.sign = 1
+            op1.sign, op2.sign = (0, 0)
+        else:
+            result.sign = 0
+        # Now, op1 > abs(op2) > 0
+
+        if op2.sign == 0:
+            result.int = op1.int + op2.int
+        else:
+            result.int = op1.int - op2.int
+
+        result.exp = op1.exp
+        ans = Decimal(result)
+        ans = ans._fix(context)
+        return ans
+
+    __radd__ = __add__
+
+    def __sub__(self, other, context=None):
+        """Return self - other"""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if self._is_special or other._is_special:
+            ans = self._check_nans(other, context=context)
+            if ans:
+                return ans
+
+        # self - other is computed as self + other.copy_negate()
+        return self.__add__(other.copy_negate(), context=context)
+
+    def __rsub__(self, other, context=None):
+        """Return other - self"""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        return other.__sub__(self, context=context)
+
+    def __mul__(self, other, context=None):
+        """Return self * other.
+
+        (+-) INF * 0 (or its reverse) raise InvalidOperation.
+        """
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if context is None:
+            context = getcontext()
+
+        resultsign = self._sign ^ other._sign
+
+        if self._is_special or other._is_special:
+            ans = self._check_nans(other, context)
+            if ans:
+                return ans
+
+            if self._isinfinity():
+                if not other:
+                    return context._raise_error(InvalidOperation, '(+-)INF * 0')
+                return Infsign[resultsign]
+
+            if other._isinfinity():
+                if not self:
+                    return context._raise_error(InvalidOperation, '0 * (+-)INF')
+                return Infsign[resultsign]
+
+        resultexp = self._exp + other._exp
+
+        # Special case for multiplying by zero
+        if not self or not other:
+            ans = _dec_from_triple(resultsign, '0', resultexp)
+            # Fixing in case the exponent is out of bounds
+            ans = ans._fix(context)
+            return ans
+
+        # Special case for multiplying by power of 10
+        if self._int == '1':
+            ans = _dec_from_triple(resultsign, other._int, resultexp)
+            ans = ans._fix(context)
+            return ans
+        if other._int == '1':
+            ans = _dec_from_triple(resultsign, self._int, resultexp)
+            ans = ans._fix(context)
+            return ans
+
+        op1 = _WorkRep(self)
+        op2 = _WorkRep(other)
+
+        ans = _dec_from_triple(resultsign, str(op1.int * op2.int), resultexp)
+        ans = ans._fix(context)
+
+        return ans
+    __rmul__ = __mul__
+
+    def __truediv__(self, other, context=None):
+        """Return self / other."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return NotImplemented
+
+        if context is None:
+            context = getcontext()
+
+        sign = self._sign ^ other._sign
+
+        if self._is_special or other._is_special:
+            ans = self._check_nans(other, context)
+            if ans:
+                return ans
+
+            if self._isinfinity() and other._isinfinity():
+                return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF')
+
+            if self._isinfinity():
+                return Infsign[sign]
+
+            if other._isinfinity():
+                context._raise_error(Clamped, 'Division by infinity')
+                return _dec_from_triple(sign, '0', context.Etiny())
+
+        # Special cases for zeroes
+        if not other:
+            if not self:
+                return context._raise_error(DivisionUndefined, '0 / 0')
+            return context._raise_error(DivisionByZero, 'x / 0', sign)
+
+        if not self:
+            exp = self._exp - other._exp
+            coeff = 0
+        else:
+            # OK, so neither = 0, INF or NaN
+            shift = len(other._int) - len(self._int) + context.prec + 1
+            exp = self._exp - other._exp - shift
+            op1 = _WorkRep(self)
+            op2 = _WorkRep(other)
+            if shift >= 0:
+                coeff, remainder = divmod(op1.int * 10**shift, op2.int)
+            else:
+                coeff, remainder = divmod(op1.int, op2.int * 10**-shift)
+            if remainder:
+                # result is not exact; adjust to ensure correct rounding
+                if coeff % 5 == 0:
+                    coeff += 1
+            else:
+                # result is exact; get as close to ideal exponent as possible
+                ideal_exp = self._exp - other._exp
+                while exp < ideal_exp and coeff % 10 == 0:
+                    coeff //= 10
+                    exp += 1
+
+        ans = _dec_from_triple(sign, str(coeff), exp)
+        return ans._fix(context)
+
+    def _divide(self, other, context):
+        """Return (self // other, self % other), to context.prec precision.
+
+        Assumes that neither self nor other is a NaN, that self is not
+        infinite and that other is nonzero.
+        """
+        sign = self._sign ^ other._sign
+        if other._isinfinity():
+            ideal_exp = self._exp
+        else:
+            ideal_exp = min(self._exp, other._exp)
+
+        expdiff = self.adjusted() - other.adjusted()
+        if not self or other._isinfinity() or expdiff <= -2:
+            return (_dec_from_triple(sign, '0', 0),
+                    self._rescale(ideal_exp, context.rounding))
+        if expdiff <= context.prec:
+            op1 = _WorkRep(self)
+            op2 = _WorkRep(other)
+            if op1.exp >= op2.exp:
+                op1.int *= 10**(op1.exp - op2.exp)
+            else:
+                op2.int *= 10**(op2.exp - op1.exp)
+            q, r = divmod(op1.int, op2.int)
+            if q < 10**context.prec:
+                return (_dec_from_triple(sign, str(q), 0),
+                        _dec_from_triple(self._sign, str(r), ideal_exp))
+
+        # Here the quotient is too large to be representable
+        ans = context._raise_error(DivisionImpossible,
+                                   'quotient too large in //, % or divmod')
+        return ans, ans
+
+    def __rtruediv__(self, other, context=None):
+        """Swaps self/other and returns __truediv__."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        return other.__truediv__(self, context=context)
+
+    __div__ = __truediv__
+    __rdiv__ = __rtruediv__
+
+    def __divmod__(self, other, context=None):
+        """
+        Return (self // other, self % other)
+        """
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if context is None:
+            context = getcontext()
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return (ans, ans)
+
+        sign = self._sign ^ other._sign
+        if self._isinfinity():
+            if other._isinfinity():
+                ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)')
+                return ans, ans
+            else:
+                return (Infsign[sign],
+                        context._raise_error(InvalidOperation, 'INF % x'))
+
+        if not other:
+            if not self:
+                ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)')
+                return ans, ans
+            else:
+                return (context._raise_error(DivisionByZero, 'x // 0', sign),
+                        context._raise_error(InvalidOperation, 'x % 0'))
+
+        quotient, remainder = self._divide(other, context)
+        remainder = remainder._fix(context)
+        return quotient, remainder
+
+    def __rdivmod__(self, other, context=None):
+        """Swaps self/other and returns __divmod__."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        return other.__divmod__(self, context=context)
+
+    def __mod__(self, other, context=None):
+        """
+        self % other
+        """
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if context is None:
+            context = getcontext()
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+
+        if self._isinfinity():
+            return context._raise_error(InvalidOperation, 'INF % x')
+        elif not other:
+            if self:
+                return context._raise_error(InvalidOperation, 'x % 0')
+            else:
+                return context._raise_error(DivisionUndefined, '0 % 0')
+
+        remainder = self._divide(other, context)[1]
+        remainder = remainder._fix(context)
+        return remainder
+
+    def __rmod__(self, other, context=None):
+        """Swaps self/other and returns __mod__."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        return other.__mod__(self, context=context)
+
+    def remainder_near(self, other, context=None):
+        """
+        Remainder nearest to 0-  abs(remainder-near) <= other/2
+        """
+        if context is None:
+            context = getcontext()
+
+        other = _convert_other(other, raiseit=True)
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+
+        # self == +/-infinity -> InvalidOperation
+        if self._isinfinity():
+            return context._raise_error(InvalidOperation,
+                                        'remainder_near(infinity, x)')
+
+        # other == 0 -> either InvalidOperation or DivisionUndefined
+        if not other:
+            if self:
+                return context._raise_error(InvalidOperation,
+                                            'remainder_near(x, 0)')
+            else:
+                return context._raise_error(DivisionUndefined,
+                                            'remainder_near(0, 0)')
+
+        # other = +/-infinity -> remainder = self
+        if other._isinfinity():
+            ans = Decimal(self)
+            return ans._fix(context)
+
+        # self = 0 -> remainder = self, with ideal exponent
+        ideal_exponent = min(self._exp, other._exp)
+        if not self:
+            ans = _dec_from_triple(self._sign, '0', ideal_exponent)
+            return ans._fix(context)
+
+        # catch most cases of large or small quotient
+        expdiff = self.adjusted() - other.adjusted()
+        if expdiff >= context.prec + 1:
+            # expdiff >= prec+1 => abs(self/other) > 10**prec
+            return context._raise_error(DivisionImpossible)
+        if expdiff <= -2:
+            # expdiff <= -2 => abs(self/other) < 0.1
+            ans = self._rescale(ideal_exponent, context.rounding)
+            return ans._fix(context)
+
+        # adjust both arguments to have the same exponent, then divide
+        op1 = _WorkRep(self)
+        op2 = _WorkRep(other)
+        if op1.exp >= op2.exp:
+            op1.int *= 10**(op1.exp - op2.exp)
+        else:
+            op2.int *= 10**(op2.exp - op1.exp)
+        q, r = divmod(op1.int, op2.int)
+        # remainder is r*10**ideal_exponent; other is +/-op2.int *
+        # 10**ideal_exponent.   Apply correction to ensure that
+        # abs(remainder) <= abs(other)/2
+        if 2*r + (q&1) > op2.int:
+            r -= op2.int
+            q += 1
+
+        if q >= 10**context.prec:
+            return context._raise_error(DivisionImpossible)
+
+        # result has same sign as self unless r is negative
+        sign = self._sign
+        if r < 0:
+            sign = 1-sign
+            r = -r
+
+        ans = _dec_from_triple(sign, str(r), ideal_exponent)
+        return ans._fix(context)
+
+    def __floordiv__(self, other, context=None):
+        """self // other"""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if context is None:
+            context = getcontext()
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+
+        if self._isinfinity():
+            if other._isinfinity():
+                return context._raise_error(InvalidOperation, 'INF // INF')
+            else:
+                return Infsign[self._sign ^ other._sign]
+
+        if not other:
+            if self:
+                return context._raise_error(DivisionByZero, 'x // 0',
+                                            self._sign ^ other._sign)
+            else:
+                return context._raise_error(DivisionUndefined, '0 // 0')
+
+        return self._divide(other, context)[0]
+
+    def __rfloordiv__(self, other, context=None):
+        """Swaps self/other and returns __floordiv__."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        return other.__floordiv__(self, context=context)
+
+    def __float__(self):
+        """Float representation."""
+        return float(str(self))
+
+    def __int__(self):
+        """Converts self to an int, truncating if necessary."""
+        if self._is_special:
+            if self._isnan():
+                context = getcontext()
+                return context._raise_error(InvalidContext)
+            elif self._isinfinity():
+                raise OverflowError("Cannot convert infinity to int")
+        s = (-1)**self._sign
+        if self._exp >= 0:
+            return s*int(self._int)*10**self._exp
+        else:
+            return s*int(self._int[:self._exp] or '0')
+
+    __trunc__ = __int__
+
+    @property
+    def real(self):
+        return self
+
+    @property
+    def imag(self):
+        return Decimal(0)
+
+    def conjugate(self):
+        return self
+
+    def __complex__(self):
+        return complex(float(self))
+
+    def __long__(self):
+        """Converts to a long.
+
+        Equivalent to long(int(self))
+        """
+        return long(self.__int__())
+
+    def _fix_nan(self, context):
+        """Decapitate the payload of a NaN to fit the context"""
+        payload = self._int
+
+        # maximum length of payload is precision if _clamp=0,
+        # precision-1 if _clamp=1.
+        max_payload_len = context.prec - context._clamp
+        if len(payload) > max_payload_len:
+            payload = payload[len(payload)-max_payload_len:].lstrip('0')
+            return _dec_from_triple(self._sign, payload, self._exp, True)
+        return Decimal(self)
+
+    def _fix(self, context):
+        """Round if it is necessary to keep self within prec precision.
+
+        Rounds and fixes the exponent.  Does not raise on a sNaN.
+
+        Arguments:
+        self - Decimal instance
+        context - context used.
+        """
+
+        if self._is_special:
+            if self._isnan():
+                # decapitate payload if necessary
+                return self._fix_nan(context)
+            else:
+                # self is +/-Infinity; return unaltered
+                return Decimal(self)
+
+        # if self is zero then exponent should be between Etiny and
+        # Emax if _clamp==0, and between Etiny and Etop if _clamp==1.
+        Etiny = context.Etiny()
+        Etop = context.Etop()
+        if not self:
+            exp_max = [context.Emax, Etop][context._clamp]
+            new_exp = min(max(self._exp, Etiny), exp_max)
+            if new_exp != self._exp:
+                context._raise_error(Clamped)
+                return _dec_from_triple(self._sign, '0', new_exp)
+            else:
+                return Decimal(self)
+
+        # exp_min is the smallest allowable exponent of the result,
+        # equal to max(self.adjusted()-context.prec+1, Etiny)
+        exp_min = len(self._int) + self._exp - context.prec
+        if exp_min > Etop:
+            # overflow: exp_min > Etop iff self.adjusted() > Emax
+            context._raise_error(Inexact)
+            context._raise_error(Rounded)
+            return context._raise_error(Overflow, 'above Emax', self._sign)
+        self_is_subnormal = exp_min < Etiny
+        if self_is_subnormal:
+            context._raise_error(Subnormal)
+            exp_min = Etiny
+
+        # round if self has too many digits
+        if self._exp < exp_min:
+            context._raise_error(Rounded)
+            digits = len(self._int) + self._exp - exp_min
+            if digits < 0:
+                self = _dec_from_triple(self._sign, '1', exp_min-1)
+                digits = 0
+            this_function = getattr(self, self._pick_rounding_function[context.rounding])
+            changed = this_function(digits)
+            coeff = self._int[:digits] or '0'
+            if changed == 1:
+                coeff = str(int(coeff)+1)
+            ans = _dec_from_triple(self._sign, coeff, exp_min)
+
+            if changed:
+                context._raise_error(Inexact)
+                if self_is_subnormal:
+                    context._raise_error(Underflow)
+                    if not ans:
+                        # raise Clamped on underflow to 0
+                        context._raise_error(Clamped)
+                elif len(ans._int) == context.prec+1:
+                    # we get here only if rescaling rounds the
+                    # cofficient up to exactly 10**context.prec
+                    if ans._exp < Etop:
+                        ans = _dec_from_triple(ans._sign,
+                                                   ans._int[:-1], ans._exp+1)
+                    else:
+                        # Inexact and Rounded have already been raised
+                        ans = context._raise_error(Overflow, 'above Emax',
+                                                   self._sign)
+            return ans
+
+        # fold down if _clamp == 1 and self has too few digits
+        if context._clamp == 1 and self._exp > Etop:
+            context._raise_error(Clamped)
+            self_padded = self._int + '0'*(self._exp - Etop)
+            return _dec_from_triple(self._sign, self_padded, Etop)
+
+        # here self was representable to begin with; return unchanged
+        return Decimal(self)
+
+    _pick_rounding_function = {}
+
+    # for each of the rounding functions below:
+    #   self is a finite, nonzero Decimal
+    #   prec is an integer satisfying 0 <= prec < len(self._int)
+    #
+    # each function returns either -1, 0, or 1, as follows:
+    #   1 indicates that self should be rounded up (away from zero)
+    #   0 indicates that self should be truncated, and that all the
+    #     digits to be truncated are zeros (so the value is unchanged)
+    #  -1 indicates that there are nonzero digits to be truncated
+
+    def _round_down(self, prec):
+        """Also known as round-towards-0, truncate."""
+        if _all_zeros(self._int, prec):
+            return 0
+        else:
+            return -1
+
+    def _round_up(self, prec):
+        """Rounds away from 0."""
+        return -self._round_down(prec)
+
+    def _round_half_up(self, prec):
+        """Rounds 5 up (away from 0)"""
+        if self._int[prec] in '56789':
+            return 1
+        elif _all_zeros(self._int, prec):
+            return 0
+        else:
+            return -1
+
+    def _round_half_down(self, prec):
+        """Round 5 down"""
+        if _exact_half(self._int, prec):
+            return -1
+        else:
+            return self._round_half_up(prec)
+
+    def _round_half_even(self, prec):
+        """Round 5 to even, rest to nearest."""
+        if _exact_half(self._int, prec) and \
+                (prec == 0 or self._int[prec-1] in '02468'):
+            return -1
+        else:
+            return self._round_half_up(prec)
+
+    def _round_ceiling(self, prec):
+        """Rounds up (not away from 0 if negative.)"""
+        if self._sign:
+            return self._round_down(prec)
+        else:
+            return -self._round_down(prec)
+
+    def _round_floor(self, prec):
+        """Rounds down (not towards 0 if negative)"""
+        if not self._sign:
+            return self._round_down(prec)
+        else:
+            return -self._round_down(prec)
+
+    def _round_05up(self, prec):
+        """Round down unless digit prec-1 is 0 or 5."""
+        if prec and self._int[prec-1] not in '05':
+            return self._round_down(prec)
+        else:
+            return -self._round_down(prec)
+
+    def fma(self, other, third, context=None):
+        """Fused multiply-add.
+
+        Returns self*other+third with no rounding of the intermediate
+        product self*other.
+
+        self and other are multiplied together, with no rounding of
+        the result.  The third operand is then added to the result,
+        and a single final rounding is performed.
+        """
+
+        other = _convert_other(other, raiseit=True)
+
+        # compute product; raise InvalidOperation if either operand is
+        # a signaling NaN or if the product is zero times infinity.
+        if self._is_special or other._is_special:
+            if context is None:
+                context = getcontext()
+            if self._exp == 'N':
+                return context._raise_error(InvalidOperation, 'sNaN', self)
+            if other._exp == 'N':
+                return context._raise_error(InvalidOperation, 'sNaN', other)
+            if self._exp == 'n':
+                product = self
+            elif other._exp == 'n':
+                product = other
+            elif self._exp == 'F':
+                if not other:
+                    return context._raise_error(InvalidOperation,
+                                                'INF * 0 in fma')
+                product = Infsign[self._sign ^ other._sign]
+            elif other._exp == 'F':
+                if not self:
+                    return context._raise_error(InvalidOperation,
+                                                '0 * INF in fma')
+                product = Infsign[self._sign ^ other._sign]
+        else:
+            product = _dec_from_triple(self._sign ^ other._sign,
+                                       str(int(self._int) * int(other._int)),
+                                       self._exp + other._exp)
+
+        third = _convert_other(third, raiseit=True)
+        return product.__add__(third, context)
+
+    def _power_modulo(self, other, modulo, context=None):
+        """Three argument version of __pow__"""
+
+        # if can't convert other and modulo to Decimal, raise
+        # TypeError; there's no point returning NotImplemented (no
+        # equivalent of __rpow__ for three argument pow)
+        other = _convert_other(other, raiseit=True)
+        modulo = _convert_other(modulo, raiseit=True)
+
+        if context is None:
+            context = getcontext()
+
+        # deal with NaNs: if there are any sNaNs then first one wins,
+        # (i.e. behaviour for NaNs is identical to that of fma)
+        self_is_nan = self._isnan()
+        other_is_nan = other._isnan()
+        modulo_is_nan = modulo._isnan()
+        if self_is_nan or other_is_nan or modulo_is_nan:
+            if self_is_nan == 2:
+                return context._raise_error(InvalidOperation, 'sNaN',
+                                        self)
+            if other_is_nan == 2:
+                return context._raise_error(InvalidOperation, 'sNaN',
+                                        other)
+            if modulo_is_nan == 2:
+                return context._raise_error(InvalidOperation, 'sNaN',
+                                        modulo)
+            if self_is_nan:
+                return self._fix_nan(context)
+            if other_is_nan:
+                return other._fix_nan(context)
+            return modulo._fix_nan(context)
+
+        # check inputs: we apply same restrictions as Python's pow()
+        if not (self._isinteger() and
+                other._isinteger() and
+                modulo._isinteger()):
+            return context._raise_error(InvalidOperation,
+                                        'pow() 3rd argument not allowed '
+                                        'unless all arguments are integers')
+        if other < 0:
+            return context._raise_error(InvalidOperation,
+                                        'pow() 2nd argument cannot be '
+                                        'negative when 3rd argument specified')
+        if not modulo:
+            return context._raise_error(InvalidOperation,
+                                        'pow() 3rd argument cannot be 0')
+
+        # additional restriction for decimal: the modulus must be less
+        # than 10**prec in absolute value
+        if modulo.adjusted() >= context.prec:
+            return context._raise_error(InvalidOperation,
+                                        'insufficient precision: pow() 3rd '
+                                        'argument must not have more than '
+                                        'precision digits')
+
+        # define 0**0 == NaN, for consistency with two-argument pow
+        # (even though it hurts!)
+        if not other and not self:
+            return context._raise_error(InvalidOperation,
+                                        'at least one of pow() 1st argument '
+                                        'and 2nd argument must be nonzero ;'
+                                        '0**0 is not defined')
+
+        # compute sign of result
+        if other._iseven():
+            sign = 0
+        else:
+            sign = self._sign
+
+        # convert modulo to a Python integer, and self and other to
+        # Decimal integers (i.e. force their exponents to be >= 0)
+        modulo = abs(int(modulo))
+        base = _WorkRep(self.to_integral_value())
+        exponent = _WorkRep(other.to_integral_value())
+
+        # compute result using integer pow()
+        base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo
+        for i in xrange(exponent.exp):
+            base = pow(base, 10, modulo)
+        base = pow(base, exponent.int, modulo)
+
+        return _dec_from_triple(sign, str(base), 0)
+
+    def _power_exact(self, other, p):
+        """Attempt to compute self**other exactly.
+
+        Given Decimals self and other and an integer p, attempt to
+        compute an exact result for the power self**other, with p
+        digits of precision.  Return None if self**other is not
+        exactly representable in p digits.
+
+        Assumes that elimination of special cases has already been
+        performed: self and other must both be nonspecial; self must
+        be positive and not numerically equal to 1; other must be
+        nonzero.  For efficiency, other._exp should not be too large,
+        so that 10**abs(other._exp) is a feasible calculation."""
+
+        # In the comments below, we write x for the value of self and
+        # y for the value of other.  Write x = xc*10**xe and y =
+        # yc*10**ye.
+
+        # The main purpose of this method is to identify the *failure*
+        # of x**y to be exactly representable with as little effort as
+        # possible.  So we look for cheap and easy tests that
+        # eliminate the possibility of x**y being exact.  Only if all
+        # these tests are passed do we go on to actually compute x**y.
+
+        # Here's the main idea.  First normalize both x and y.  We
+        # express y as a rational m/n, with m and n relatively prime
+        # and n>0.  Then for x**y to be exactly representable (at
+        # *any* precision), xc must be the nth power of a positive
+        # integer and xe must be divisible by n.  If m is negative
+        # then additionally xc must be a power of either 2 or 5, hence
+        # a power of 2**n or 5**n.
+        #
+        # There's a limit to how small |y| can be: if y=m/n as above
+        # then:
+        #
+        #  (1) if xc != 1 then for the result to be representable we
+        #      need xc**(1/n) >= 2, and hence also xc**|y| >= 2.  So
+        #      if |y| <= 1/nbits(xc) then xc < 2**nbits(xc) <=
+        #      2**(1/|y|), hence xc**|y| < 2 and the result is not
+        #      representable.
+        #
+        #  (2) if xe != 0, |xe|*(1/n) >= 1, so |xe|*|y| >= 1.  Hence if
+        #      |y| < 1/|xe| then the result is not representable.
+        #
+        # Note that since x is not equal to 1, at least one of (1) and
+        # (2) must apply.  Now |y| < 1/nbits(xc) iff |yc|*nbits(xc) <
+        # 10**-ye iff len(str(|yc|*nbits(xc)) <= -ye.
+        #
+        # There's also a limit to how large y can be, at least if it's
+        # positive: the normalized result will have coefficient xc**y,
+        # so if it's representable then xc**y < 10**p, and y <
+        # p/log10(xc).  Hence if y*log10(xc) >= p then the result is
+        # not exactly representable.
+
+        # if len(str(abs(yc*xe)) <= -ye then abs(yc*xe) < 10**-ye,
+        # so |y| < 1/xe and the result is not representable.
+        # Similarly, len(str(abs(yc)*xc_bits)) <= -ye implies |y|
+        # < 1/nbits(xc).
+
+        x = _WorkRep(self)
+        xc, xe = x.int, x.exp
+        while xc % 10 == 0:
+            xc //= 10
+            xe += 1
+
+        y = _WorkRep(other)
+        yc, ye = y.int, y.exp
+        while yc % 10 == 0:
+            yc //= 10
+            ye += 1
+
+        # case where xc == 1: result is 10**(xe*y), with xe*y
+        # required to be an integer
+        if xc == 1:
+            if ye >= 0:
+                exponent = xe*yc*10**ye
+            else:
+                exponent, remainder = divmod(xe*yc, 10**-ye)
+                if remainder:
+                    return None
+            if y.sign == 1:
+                exponent = -exponent
+            # if other is a nonnegative integer, use ideal exponent
+            if other._isinteger() and other._sign == 0:
+                ideal_exponent = self._exp*int(other)
+                zeros = min(exponent-ideal_exponent, p-1)
+            else:
+                zeros = 0
+            return _dec_from_triple(0, '1' + '0'*zeros, exponent-zeros)
+
+        # case where y is negative: xc must be either a power
+        # of 2 or a power of 5.
+        if y.sign == 1:
+            last_digit = xc % 10
+            if last_digit in (2,4,6,8):
+                # quick test for power of 2
+                if xc & -xc != xc:
+                    return None
+                # now xc is a power of 2; e is its exponent
+                e = _nbits(xc)-1
+                # find e*y and xe*y; both must be integers
+                if ye >= 0:
+                    y_as_int = yc*10**ye
+                    e = e*y_as_int
+                    xe = xe*y_as_int
+                else:
+                    ten_pow = 10**-ye
+                    e, remainder = divmod(e*yc, ten_pow)
+                    if remainder:
+                        return None
+                    xe, remainder = divmod(xe*yc, ten_pow)
+                    if remainder:
+                        return None
+
+                if e*65 >= p*93: # 93/65 > log(10)/log(5)
+                    return None
+                xc = 5**e
+
+            elif last_digit == 5:
+                # e >= log_5(xc) if xc is a power of 5; we have
+                # equality all the way up to xc=5**2658
+                e = _nbits(xc)*28//65
+                xc, remainder = divmod(5**e, xc)
+                if remainder:
+                    return None
+                while xc % 5 == 0:
+                    xc //= 5
+                    e -= 1
+                if ye >= 0:
+                    y_as_integer = yc*10**ye
+                    e = e*y_as_integer
+                    xe = xe*y_as_integer
+                else:
+                    ten_pow = 10**-ye
+                    e, remainder = divmod(e*yc, ten_pow)
+                    if remainder:
+                        return None
+                    xe, remainder = divmod(xe*yc, ten_pow)
+                    if remainder:
+                        return None
+                if e*3 >= p*10: # 10/3 > log(10)/log(2)
+                    return None
+                xc = 2**e
+            else:
+                return None
+
+            if xc >= 10**p:
+                return None
+            xe = -e-xe
+            return _dec_from_triple(0, str(xc), xe)
+
+        # now y is positive; find m and n such that y = m/n
+        if ye >= 0:
+            m, n = yc*10**ye, 1
+        else:
+            if xe != 0 and len(str(abs(yc*xe))) <= -ye:
+                return None
+            xc_bits = _nbits(xc)
+            if xc != 1 and len(str(abs(yc)*xc_bits)) <= -ye:
+                return None
+            m, n = yc, 10**(-ye)
+            while m % 2 == n % 2 == 0:
+                m //= 2
+                n //= 2
+            while m % 5 == n % 5 == 0:
+                m //= 5
+                n //= 5
+
+        # compute nth root of xc*10**xe
+        if n > 1:
+            # if 1 < xc < 2**n then xc isn't an nth power
+            if xc != 1 and xc_bits <= n:
+                return None
+
+            xe, rem = divmod(xe, n)
+            if rem != 0:
+                return None
+
+            # compute nth root of xc using Newton's method
+            a = 1L << -(-_nbits(xc)//n) # initial estimate
+            while True:
+                q, r = divmod(xc, a**(n-1))
+                if a <= q:
+                    break
+                else:
+                    a = (a*(n-1) + q)//n
+            if not (a == q and r == 0):
+                return None
+            xc = a
+
+        # now xc*10**xe is the nth root of the original xc*10**xe
+        # compute mth power of xc*10**xe
+
+        # if m > p*100//_log10_lb(xc) then m > p/log10(xc), hence xc**m >
+        # 10**p and the result is not representable.
+        if xc > 1 and m > p*100//_log10_lb(xc):
+            return None
+        xc = xc**m
+        xe *= m
+        if xc > 10**p:
+            return None
+
+        # by this point the result *is* exactly representable
+        # adjust the exponent to get as close as possible to the ideal
+        # exponent, if necessary
+        str_xc = str(xc)
+        if other._isinteger() and other._sign == 0:
+            ideal_exponent = self._exp*int(other)
+            zeros = min(xe-ideal_exponent, p-len(str_xc))
+        else:
+            zeros = 0
+        return _dec_from_triple(0, str_xc+'0'*zeros, xe-zeros)
+
+    def __pow__(self, other, modulo=None, context=None):
+        """Return self ** other [ % modulo].
+
+        With two arguments, compute self**other.
+
+        With three arguments, compute (self**other) % modulo.  For the
+        three argument form, the following restrictions on the
+        arguments hold:
+
+         - all three arguments must be integral
+         - other must be nonnegative
+         - either self or other (or both) must be nonzero
+         - modulo must be nonzero and must have at most p digits,
+           where p is the context precision.
+
+        If any of these restrictions is violated the InvalidOperation
+        flag is raised.
+
+        The result of pow(self, other, modulo) is identical to the
+        result that would be obtained by computing (self**other) %
+        modulo with unbounded precision, but is computed more
+        efficiently.  It is always exact.
+        """
+
+        if modulo is not None:
+            return self._power_modulo(other, modulo, context)
+
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if context is None:
+            context = getcontext()
+
+        # either argument is a NaN => result is NaN
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+
+        # 0**0 = NaN (!), x**0 = 1 for nonzero x (including +/-Infinity)
+        if not other:
+            if not self:
+                return context._raise_error(InvalidOperation, '0 ** 0')
+            else:
+                return Dec_p1
+
+        # result has sign 1 iff self._sign is 1 and other is an odd integer
+        result_sign = 0
+        if self._sign == 1:
+            if other._isinteger():
+                if not other._iseven():
+                    result_sign = 1
+            else:
+                # -ve**noninteger = NaN
+                # (-0)**noninteger = 0**noninteger
+                if self:
+                    return context._raise_error(InvalidOperation,
+                        'x ** y with x negative and y not an integer')
+            # negate self, without doing any unwanted rounding
+            self = self.copy_negate()
+
+        # 0**(+ve or Inf)= 0; 0**(-ve or -Inf) = Infinity
+        if not self:
+            if other._sign == 0:
+                return _dec_from_triple(result_sign, '0', 0)
+            else:
+                return Infsign[result_sign]
+
+        # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0
+        if self._isinfinity():
+            if other._sign == 0:
+                return Infsign[result_sign]
+            else:
+                return _dec_from_triple(result_sign, '0', 0)
+
+        # 1**other = 1, but the choice of exponent and the flags
+        # depend on the exponent of self, and on whether other is a
+        # positive integer, a negative integer, or neither
+        if self == Dec_p1:
+            if other._isinteger():
+                # exp = max(self._exp*max(int(other), 0),
+                # 1-context.prec) but evaluating int(other) directly
+                # is dangerous until we know other is small (other
+                # could be 1e999999999)
+                if other._sign == 1:
+                    multiplier = 0
+                elif other > context.prec:
+                    multiplier = context.prec
+                else:
+                    multiplier = int(other)
+
+                exp = self._exp * multiplier
+                if exp < 1-context.prec:
+                    exp = 1-context.prec
+                    context._raise_error(Rounded)
+            else:
+                context._raise_error(Inexact)
+                context._raise_error(Rounded)
+                exp = 1-context.prec
+
+            return _dec_from_triple(result_sign, '1'+'0'*-exp, exp)
+
+        # compute adjusted exponent of self
+        self_adj = self.adjusted()
+
+        # self ** infinity is infinity if self > 1, 0 if self < 1
+        # self ** -infinity is infinity if self < 1, 0 if self > 1
+        if other._isinfinity():
+            if (other._sign == 0) == (self_adj < 0):
+                return _dec_from_triple(result_sign, '0', 0)
+            else:
+                return Infsign[result_sign]
+
+        # from here on, the result always goes through the call
+        # to _fix at the end of this function.
+        ans = None
+
+        # crude test to catch cases of extreme overflow/underflow.  If
+        # log10(self)*other >= 10**bound and bound >= len(str(Emax))
+        # then 10**bound >= 10**len(str(Emax)) >= Emax+1 and hence
+        # self**other >= 10**(Emax+1), so overflow occurs.  The test
+        # for underflow is similar.
+        bound = self._log10_exp_bound() + other.adjusted()
+        if (self_adj >= 0) == (other._sign == 0):
+            # self > 1 and other +ve, or self < 1 and other -ve
+            # possibility of overflow
+            if bound >= len(str(context.Emax)):
+                ans = _dec_from_triple(result_sign, '1', context.Emax+1)
+        else:
+            # self > 1 and other -ve, or self < 1 and other +ve
+            # possibility of underflow to 0
+            Etiny = context.Etiny()
+            if bound >= len(str(-Etiny)):
+                ans = _dec_from_triple(result_sign, '1', Etiny-1)
+
+        # try for an exact result with precision +1
+        if ans is None:
+            ans = self._power_exact(other, context.prec + 1)
+            if ans is not None and result_sign == 1:
+                ans = _dec_from_triple(1, ans._int, ans._exp)
+
+        # usual case: inexact result, x**y computed directly as exp(y*log(x))
+        if ans is None:
+            p = context.prec
+            x = _WorkRep(self)
+            xc, xe = x.int, x.exp
+            y = _WorkRep(other)
+            yc, ye = y.int, y.exp
+            if y.sign == 1:
+                yc = -yc
+
+            # compute correctly rounded result:  start with precision +3,
+            # then increase precision until result is unambiguously roundable
+            extra = 3
+            while True:
+                coeff, exp = _dpower(xc, xe, yc, ye, p+extra)
+                if coeff % (5*10**(len(str(coeff))-p-1)):
+                    break
+                extra += 3
+
+            ans = _dec_from_triple(result_sign, str(coeff), exp)
+
+        # the specification says that for non-integer other we need to
+        # raise Inexact, even when the result is actually exact.  In
+        # the same way, we need to raise Underflow here if the result
+        # is subnormal.  (The call to _fix will take care of raising
+        # Rounded and Subnormal, as usual.)
+        if not other._isinteger():
+            context._raise_error(Inexact)
+            # pad with zeros up to length context.prec+1 if necessary
+            if len(ans._int) <= context.prec:
+                expdiff = context.prec+1 - len(ans._int)
+                ans = _dec_from_triple(ans._sign, ans._int+'0'*expdiff,
+                                       ans._exp-expdiff)
+            if ans.adjusted() < context.Emin:
+                context._raise_error(Underflow)
+
+        # unlike exp, ln and log10, the power function respects the
+        # rounding mode; no need to use ROUND_HALF_EVEN here
+        ans = ans._fix(context)
+        return ans
+
+    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 context is None:
+            context = getcontext()
+
+        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 _dec_from_triple(dup._sign, '0', 0)
+        exp_max = [context.Emax, context.Etop()][context._clamp]
+        end = len(dup._int)
+        exp = dup._exp
+        while dup._int[end-1] == '0' and exp < exp_max:
+            exp += 1
+            end -= 1
+        return _dec_from_triple(dup._sign, dup._int[:end], exp)
+
+    def quantize(self, exp, rounding=None, context=None, watchexp=True):
+        """Quantize self so its exponent is the same as that of exp.
+
+        Similar to self._rescale(exp._exp) but with error checking.
+        """
+        exp = _convert_other(exp, raiseit=True)
+
+        if context is None:
+            context = getcontext()
+        if rounding is None:
+            rounding = context.rounding
+
+        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 Decimal(self)  # if both are inf, it is OK
+                return context._raise_error(InvalidOperation,
+                                        'quantize with one INF')
+
+        # if we're not watching exponents, do a simple rescale
+        if not watchexp:
+            ans = self._rescale(exp._exp, rounding)
+            # raise Inexact and Rounded where appropriate
+            if ans._exp > self._exp:
+                context._raise_error(Rounded)
+                if ans != self:
+                    context._raise_error(Inexact)
+            return ans
+
+        # exp._exp should be between Etiny and Emax
+        if not (context.Etiny() <= exp._exp <= context.Emax):
+            return context._raise_error(InvalidOperation,
+                   'target exponent out of bounds in quantize')
+
+        if not self:
+            ans = _dec_from_triple(self._sign, '0', exp._exp)
+            return ans._fix(context)
+
+        self_adjusted = self.adjusted()
+        if self_adjusted > context.Emax:
+            return context._raise_error(InvalidOperation,
+                                        'exponent of quantize result too large for current context')
+        if self_adjusted - exp._exp + 1 > context.prec:
+            return context._raise_error(InvalidOperation,
+                                        'quantize result has too many digits for current context')
+
+        ans = self._rescale(exp._exp, rounding)
+        if ans.adjusted() > context.Emax:
+            return context._raise_error(InvalidOperation,
+                                        'exponent of quantize result too large for current context')
+        if len(ans._int) > context.prec:
+            return context._raise_error(InvalidOperation,
+                                        'quantize result has too many digits for current context')
+
+        # raise appropriate flags
+        if ans._exp > self._exp:
+            context._raise_error(Rounded)
+            if ans != self:
+                context._raise_error(Inexact)
+        if ans and ans.adjusted() < context.Emin:
+            context._raise_error(Subnormal)
+
+        # call to fix takes care of any necessary folddown
+        ans = ans._fix(context)
+        return ans
+
+    def same_quantum(self, other):
+        """Return True if self and other have the same exponent; otherwise
+        return False.
+
+        If either operand is a special value, the following rules are used:
+           * return True if both operands are infinities
+           * return True if both operands are NaNs
+           * otherwise, return False.
+        """
+        other = _convert_other(other, raiseit=True)
+        if self._is_special or other._is_special:
+            return (self.is_nan() and other.is_nan() or
+                    self.is_infinite() and other.is_infinite())
+        return self._exp == other._exp
+
+    def _rescale(self, exp, rounding):
+        """Rescale self so that the exponent is exp, either by padding with zeros
+        or by truncating digits, using the given rounding mode.
+
+        Specials are returned without change.  This operation is
+        quiet: it raises no flags, and uses no information from the
+        context.
+
+        exp = exp to scale to (an integer)
+        rounding = rounding mode
+        """
+        if self._is_special:
+            return Decimal(self)
+        if not self:
+            return _dec_from_triple(self._sign, '0', exp)
+
+        if self._exp >= exp:
+            # pad answer with zeros if necessary
+            return _dec_from_triple(self._sign,
+                                        self._int + '0'*(self._exp - exp), exp)
+
+        # too many digits; round and lose data.  If self.adjusted() <
+        # exp-1, replace self by 10**(exp-1) before rounding
+        digits = len(self._int) + self._exp - exp
+        if digits < 0:
+            self = _dec_from_triple(self._sign, '1', exp-1)
+            digits = 0
+        this_function = getattr(self, self._pick_rounding_function[rounding])
+        changed = this_function(digits)
+        coeff = self._int[:digits] or '0'
+        if changed == 1:
+            coeff = str(int(coeff)+1)
+        return _dec_from_triple(self._sign, coeff, exp)
+
+    def _round(self, places, rounding):
+        """Round a nonzero, nonspecial Decimal to a fixed number of
+        significant figures, using the given rounding mode.
+
+        Infinities, NaNs and zeros are returned unaltered.
+
+        This operation is quiet: it raises no flags, and uses no
+        information from the context.
+
+        """
+        if places <= 0:
+            raise ValueError("argument should be at least 1 in _round")
+        if self._is_special or not self:
+            return Decimal(self)
+        ans = self._rescale(self.adjusted()+1-places, rounding)
+        # it can happen that the rescale alters the adjusted exponent;
+        # for example when rounding 99.97 to 3 significant figures.
+        # When this happens we end up with an extra 0 at the end of
+        # the number; a second rescale fixes this.
+        if ans.adjusted() != self.adjusted():
+            ans = ans._rescale(ans.adjusted()+1-places, rounding)
+        return ans
+
+    def to_integral_exact(self, rounding=None, context=None):
+        """Rounds to a nearby integer.
+
+        If no rounding mode is specified, take the rounding mode from
+        the context.  This method raises the Rounded and Inexact flags
+        when appropriate.
+
+        See also: to_integral_value, which does exactly the same as
+        this method except that it doesn't raise Inexact or Rounded.
+        """
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+            return Decimal(self)
+        if self._exp >= 0:
+            return Decimal(self)
+        if not self:
+            return _dec_from_triple(self._sign, '0', 0)
+        if context is None:
+            context = getcontext()
+        if rounding is None:
+            rounding = context.rounding
+        context._raise_error(Rounded)
+        ans = self._rescale(0, rounding)
+        if ans != self:
+            context._raise_error(Inexact)
+        return ans
+
+    def to_integral_value(self, rounding=None, context=None):
+        """Rounds to the nearest integer, without raising inexact, rounded."""
+        if context is None:
+            context = getcontext()
+        if rounding is None:
+            rounding = context.rounding
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+            return Decimal(self)
+        if self._exp >= 0:
+            return Decimal(self)
+        else:
+            return self._rescale(0, rounding)
+
+    # the method name changed, but we provide also the old one, for compatibility
+    to_integral = to_integral_value
+
+    def sqrt(self, context=None):
+        """Return the square root of self."""
+        if context is None:
+            context = getcontext()
+
+        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.  sqrt(-0) = -0
+            ans = _dec_from_triple(self._sign, '0', self._exp // 2)
+            return ans._fix(context)
+
+        if self._sign == 1:
+            return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0')
+
+        # At this point self represents a positive number.  Let p be
+        # the desired precision and express self in the form c*100**e
+        # with c a positive real number and e an integer, c and e
+        # being chosen so that 100**(p-1) <= c < 100**p.  Then the
+        # (exact) square root of self is sqrt(c)*10**e, and 10**(p-1)
+        # <= sqrt(c) < 10**p, so the closest representable Decimal at
+        # precision p is n*10**e where n = round_half_even(sqrt(c)),
+        # the closest integer to sqrt(c) with the even integer chosen
+        # in the case of a tie.
+        #
+        # To ensure correct rounding in all cases, we use the
+        # following trick: we compute the square root to an extra
+        # place (precision p+1 instead of precision p), rounding down.
+        # Then, if the result is inexact and its last digit is 0 or 5,
+        # we increase the last digit to 1 or 6 respectively; if it's
+        # exact we leave the last digit alone.  Now the final round to
+        # p places (or fewer in the case of underflow) will round
+        # correctly and raise the appropriate flags.
+
+        # use an extra digit of precision
+        prec = context.prec+1
+
+        # write argument in the form c*100**e where e = self._exp//2
+        # is the 'ideal' exponent, to be used if the square root is
+        # exactly representable.  l is the number of 'digits' of c in
+        # base 100, so that 100**(l-1) <= c < 100**l.
+        op = _WorkRep(self)
+        e = op.exp >> 1
+        if op.exp & 1:
+            c = op.int * 10
+            l = (len(self._int) >> 1) + 1
+        else:
+            c = op.int
+            l = len(self._int)+1 >> 1
+
+        # rescale so that c has exactly prec base 100 'digits'
+        shift = prec-l
+        if shift >= 0:
+            c *= 100**shift
+            exact = True
+        else:
+            c, remainder = divmod(c, 100**-shift)
+            exact = not remainder
+        e -= shift
+
+        # find n = floor(sqrt(c)) using Newton's method
+        n = 10**prec
+        while True:
+            q = c//n
+            if n <= q:
+                break
+            else:
+                n = n + q >> 1
+        exact = exact and n*n == c
+
+        if exact:
+            # result is exact; rescale to use ideal exponent e
+            if shift >= 0:
+                # assert n % 10**shift == 0
+                n //= 10**shift
+            else:
+                n *= 10**-shift
+            e += shift
+        else:
+            # result is not exact; fix last digit as described above
+            if n % 5 == 0:
+                n += 1
+
+        ans = _dec_from_triple(0, str(n), e)
+
+        # round, and fit to current context
+        context = context._shallow_copy()
+        rounding = context._set_rounding(ROUND_HALF_EVEN)
+        ans = ans._fix(context)
+        context.rounding = rounding
+
+        return ans
+
+    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, raiseit=True)
+
+        if context is None:
+            context = getcontext()
+
+        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._fix_nan(context)
+                if sn == 1 and on != 2:
+                    return other._fix_nan(context)
+                return self._check_nans(other, context)
+
+        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.  This is exactly the ordering used in compare_total.
+            c = self.compare_total(other)
+
+        if c == -1:
+            ans = other
+        else:
+            ans = self
+
+        return ans._fix(context)
+
+    def min(self, other, context=None):
+        """Returns the smaller value.
+
+        Like min(self, other) except if one is not a number, returns
+        NaN (and signals if one is sNaN).  Also rounds.
+        """
+        other = _convert_other(other, raiseit=True)
+
+        if context is None:
+            context = getcontext()
+
+        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._fix_nan(context)
+                if sn == 1 and on != 2:
+                    return other._fix_nan(context)
+                return self._check_nans(other, context)
+
+        c = self._cmp(other)
+        if c == 0:
+            c = self.compare_total(other)
+
+        if c == -1:
+            ans = self
+        else:
+            ans = other
+
+        return ans._fix(context)
+
+    def _isinteger(self):
+        """Returns whether self is an integer"""
+        if self._is_special:
+            return False
+        if self._exp >= 0:
+            return True
+        rest = self._int[self._exp:]
+        return rest == '0'*len(rest)
+
+    def _iseven(self):
+        """Returns True if self is even.  Assumes self is an integer."""
+        if not self or self._exp > 0:
+            return True
+        return self._int[-1+self._exp] in '02468'
+
+    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
+
+    def canonical(self, context=None):
+        """Returns the same Decimal object.
+
+        As we do not have different encodings for the same number, the
+        received object already is in its canonical form.
+        """
+        return self
+
+    def compare_signal(self, other, context=None):
+        """Compares self to the other operand numerically.
+
+        It's pretty much like compare(), but all NaNs signal, with signaling
+        NaNs taking precedence over quiet NaNs.
+        """
+        other = _convert_other(other, raiseit = True)
+        ans = self._compare_check_nans(other, context)
+        if ans:
+            return ans
+        return self.compare(other, context=context)
+
+    def compare_total(self, other):
+        """Compares self to other using the abstract representations.
+
+        This is not like the standard compare, which use their numerical
+        value. Note that a total ordering is defined for all possible abstract
+        representations.
+        """
+        # if one is negative and the other is positive, it's easy
+        if self._sign and not other._sign:
+            return Dec_n1
+        if not self._sign and other._sign:
+            return Dec_p1
+        sign = self._sign
+
+        # let's handle both NaN types
+        self_nan = self._isnan()
+        other_nan = other._isnan()
+        if self_nan or other_nan:
+            if self_nan == other_nan:
+                if self._int < other._int:
+                    if sign:
+                        return Dec_p1
+                    else:
+                        return Dec_n1
+                if self._int > other._int:
+                    if sign:
+                        return Dec_n1
+                    else:
+                        return Dec_p1
+                return Dec_0
+
+            if sign:
+                if self_nan == 1:
+                    return Dec_n1
+                if other_nan == 1:
+                    return Dec_p1
+                if self_nan == 2:
+                    return Dec_n1
+                if other_nan == 2:
+                    return Dec_p1
+            else:
+                if self_nan == 1:
+                    return Dec_p1
+                if other_nan == 1:
+                    return Dec_n1
+                if self_nan == 2:
+                    return Dec_p1
+                if other_nan == 2:
+                    return Dec_n1
+
+        if self < other:
+            return Dec_n1
+        if self > other:
+            return Dec_p1
+
+        if self._exp < other._exp:
+            if sign:
+                return Dec_p1
+            else:
+                return Dec_n1
+        if self._exp > other._exp:
+            if sign:
+                return Dec_n1
+            else:
+                return Dec_p1
+        return Dec_0
+
+
+    def compare_total_mag(self, other):
+        """Compares self to other using abstract repr., ignoring sign.
+
+        Like compare_total, but with operand's sign ignored and assumed to be 0.
+        """
+        s = self.copy_abs()
+        o = other.copy_abs()
+        return s.compare_total(o)
+
+    def copy_abs(self):
+        """Returns a copy with the sign set to 0. """
+        return _dec_from_triple(0, self._int, self._exp, self._is_special)
+
+    def copy_negate(self):
+        """Returns a copy with the sign inverted."""
+        if self._sign:
+            return _dec_from_triple(0, self._int, self._exp, self._is_special)
+        else:
+            return _dec_from_triple(1, self._int, self._exp, self._is_special)
+
+    def copy_sign(self, other):
+        """Returns self with the sign of other."""
+        return _dec_from_triple(other._sign, self._int,
+                                self._exp, self._is_special)
+
+    def exp(self, context=None):
+        """Returns e ** self."""
+
+        if context is None:
+            context = getcontext()
+
+        # exp(NaN) = NaN
+        ans = self._check_nans(context=context)
+        if ans:
+            return ans
+
+        # exp(-Infinity) = 0
+        if self._isinfinity() == -1:
+            return Dec_0
+
+        # exp(0) = 1
+        if not self:
+            return Dec_p1
+
+        # exp(Infinity) = Infinity
+        if self._isinfinity() == 1:
+            return Decimal(self)
+
+        # the result is now guaranteed to be inexact (the true
+        # mathematical result is transcendental). There's no need to
+        # raise Rounded and Inexact here---they'll always be raised as
+        # a result of the call to _fix.
+        p = context.prec
+        adj = self.adjusted()
+
+        # we only need to do any computation for quite a small range
+        # of adjusted exponents---for example, -29 <= adj <= 10 for
+        # the default context.  For smaller exponent the result is
+        # indistinguishable from 1 at the given precision, while for
+        # larger exponent the result either overflows or underflows.
+        if self._sign == 0 and adj > len(str((context.Emax+1)*3)):
+            # overflow
+            ans = _dec_from_triple(0, '1', context.Emax+1)
+        elif self._sign == 1 and adj > len(str((-context.Etiny()+1)*3)):
+            # underflow to 0
+            ans = _dec_from_triple(0, '1', context.Etiny()-1)
+        elif self._sign == 0 and adj < -p:
+            # p+1 digits; final round will raise correct flags
+            ans = _dec_from_triple(0, '1' + '0'*(p-1) + '1', -p)
+        elif self._sign == 1 and adj < -p-1:
+            # p+1 digits; final round will raise correct flags
+            ans = _dec_from_triple(0, '9'*(p+1), -p-1)
+        # general case
+        else:
+            op = _WorkRep(self)
+            c, e = op.int, op.exp
+            if op.sign == 1:
+                c = -c
+
+            # compute correctly rounded result: increase precision by
+            # 3 digits at a time until we get an unambiguously
+            # roundable result
+            extra = 3
+            while True:
+                coeff, exp = _dexp(c, e, p+extra)
+                if coeff % (5*10**(len(str(coeff))-p-1)):
+                    break
+                extra += 3
+
+            ans = _dec_from_triple(0, str(coeff), exp)
+
+        # at this stage, ans should round correctly with *any*
+        # rounding mode, not just with ROUND_HALF_EVEN
+        context = context._shallow_copy()
+        rounding = context._set_rounding(ROUND_HALF_EVEN)
+        ans = ans._fix(context)
+        context.rounding = rounding
+
+        return ans
+
+    def is_canonical(self):
+        """Return True if self is canonical; otherwise return False.
+
+        Currently, the encoding of a Decimal instance is always
+        canonical, so this method returns True for any Decimal.
+        """
+        return True
+
+    def is_finite(self):
+        """Return True if self is finite; otherwise return False.
+
+        A Decimal instance is considered finite if it is neither
+        infinite nor a NaN.
+        """
+        return not self._is_special
+
+    def is_infinite(self):
+        """Return True if self is infinite; otherwise return False."""
+        return self._exp == 'F'
+
+    def is_nan(self):
+        """Return True if self is a qNaN or sNaN; otherwise return False."""
+        return self._exp in ('n', 'N')
+
+    def is_normal(self, context=None):
+        """Return True if self is a normal number; otherwise return False."""
+        if self._is_special or not self:
+            return False
+        if context is None:
+            context = getcontext()
+        return context.Emin <= self.adjusted() <= context.Emax
+
+    def is_qnan(self):
+        """Return True if self is a quiet NaN; otherwise return False."""
+        return self._exp == 'n'
+
+    def is_signed(self):
+        """Return True if self is negative; otherwise return False."""
+        return self._sign == 1
+
+    def is_snan(self):
+        """Return True if self is a signaling NaN; otherwise return False."""
+        return self._exp == 'N'
+
+    def is_subnormal(self, context=None):
+        """Return True if self is subnormal; otherwise return False."""
+        if self._is_special or not self:
+            return False
+        if context is None:
+            context = getcontext()
+        return self.adjusted() < context.Emin
+
+    def is_zero(self):
+        """Return True if self is a zero; otherwise return False."""
+        return not self._is_special and self._int == '0'
+
+    def _ln_exp_bound(self):
+        """Compute a lower bound for the adjusted exponent of self.ln().
+        In other words, compute r such that self.ln() >= 10**r.  Assumes
+        that self is finite and positive and that self != 1.
+        """
+
+        # for 0.1 <= x <= 10 we use the inequalities 1-1/x <= ln(x) <= x-1
+        adj = self._exp + len(self._int) - 1
+        if adj >= 1:
+            # argument >= 10; we use 23/10 = 2.3 as a lower bound for ln(10)
+            return len(str(adj*23//10)) - 1
+        if adj <= -2:
+            # argument <= 0.1
+            return len(str((-1-adj)*23//10)) - 1
+        op = _WorkRep(self)
+        c, e = op.int, op.exp
+        if adj == 0:
+            # 1 < self < 10
+            num = str(c-10**-e)
+            den = str(c)
+            return len(num) - len(den) - (num < den)
+        # adj == -1, 0.1 <= self < 1
+        return e + len(str(10**-e - c)) - 1
+
+
+    def ln(self, context=None):
+        """Returns the natural (base e) logarithm of self."""
+
+        if context is None:
+            context = getcontext()
+
+        # ln(NaN) = NaN
+        ans = self._check_nans(context=context)
+        if ans:
+            return ans
+
+        # ln(0.0) == -Infinity
+        if not self:
+            return negInf
+
+        # ln(Infinity) = Infinity
+        if self._isinfinity() == 1:
+            return Inf
+
+        # ln(1.0) == 0.0
+        if self == Dec_p1:
+            return Dec_0
+
+        # ln(negative) raises InvalidOperation
+        if self._sign == 1:
+            return context._raise_error(InvalidOperation,
+                                        'ln of a negative value')
+
+        # result is irrational, so necessarily inexact
+        op = _WorkRep(self)
+        c, e = op.int, op.exp
+        p = context.prec
+
+        # correctly rounded result: repeatedly increase precision by 3
+        # until we get an unambiguously roundable result
+        places = p - self._ln_exp_bound() + 2 # at least p+3 places
+        while True:
+            coeff = _dlog(c, e, places)
+            # assert len(str(abs(coeff)))-p >= 1
+            if coeff % (5*10**(len(str(abs(coeff)))-p-1)):
+                break
+            places += 3
+        ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places)
+
+        context = context._shallow_copy()
+        rounding = context._set_rounding(ROUND_HALF_EVEN)
+        ans = ans._fix(context)
+        context.rounding = rounding
+        return ans
+
+    def _log10_exp_bound(self):
+        """Compute a lower bound for the adjusted exponent of self.log10().
+        In other words, find r such that self.log10() >= 10**r.
+        Assumes that self is finite and positive and that self != 1.
+        """
+
+        # For x >= 10 or x < 0.1 we only need a bound on the integer
+        # part of log10(self), and this comes directly from the
+        # exponent of x.  For 0.1 <= x <= 10 we use the inequalities
+        # 1-1/x <= log(x) <= x-1. If x > 1 we have |log10(x)| >
+        # (1-1/x)/2.31 > 0.  If x < 1 then |log10(x)| > (1-x)/2.31 > 0
+
+        adj = self._exp + len(self._int) - 1
+        if adj >= 1:
+            # self >= 10
+            return len(str(adj))-1
+        if adj <= -2:
+            # self < 0.1
+            return len(str(-1-adj))-1
+        op = _WorkRep(self)
+        c, e = op.int, op.exp
+        if adj == 0:
+            # 1 < self < 10
+            num = str(c-10**-e)
+            den = str(231*c)
+            return len(num) - len(den) - (num < den) + 2
+        # adj == -1, 0.1 <= self < 1
+        num = str(10**-e-c)
+        return len(num) + e - (num < "231") - 1
+
+    def log10(self, context=None):
+        """Returns the base 10 logarithm of self."""
+
+        if context is None:
+            context = getcontext()
+
+        # log10(NaN) = NaN
+        ans = self._check_nans(context=context)
+        if ans:
+            return ans
+
+        # log10(0.0) == -Infinity
+        if not self:
+            return negInf
+
+        # log10(Infinity) = Infinity
+        if self._isinfinity() == 1:
+            return Inf
+
+        # log10(negative or -Infinity) raises InvalidOperation
+        if self._sign == 1:
+            return context._raise_error(InvalidOperation,
+                                        'log10 of a negative value')
+
+        # log10(10**n) = n
+        if self._int[0] == '1' and self._int[1:] == '0'*(len(self._int) - 1):
+            # answer may need rounding
+            ans = Decimal(self._exp + len(self._int) - 1)
+        else:
+            # result is irrational, so necessarily inexact
+            op = _WorkRep(self)
+            c, e = op.int, op.exp
+            p = context.prec
+
+            # correctly rounded result: repeatedly increase precision
+            # until result is unambiguously roundable
+            places = p-self._log10_exp_bound()+2
+            while True:
+                coeff = _dlog10(c, e, places)
+                # assert len(str(abs(coeff)))-p >= 1
+                if coeff % (5*10**(len(str(abs(coeff)))-p-1)):
+                    break
+                places += 3
+            ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places)
+
+        context = context._shallow_copy()
+        rounding = context._set_rounding(ROUND_HALF_EVEN)
+        ans = ans._fix(context)
+        context.rounding = rounding
+        return ans
+
+    def logb(self, context=None):
+        """ Returns the exponent of the magnitude of self's MSD.
+
+        The result is the integer which is the exponent of the magnitude
+        of the most significant digit of self (as though it were truncated
+        to a single digit while maintaining the value of that digit and
+        without limiting the resulting exponent).
+        """
+        # logb(NaN) = NaN
+        ans = self._check_nans(context=context)
+        if ans:
+            return ans
+
+        if context is None:
+            context = getcontext()
+
+        # logb(+/-Inf) = +Inf
+        if self._isinfinity():
+            return Inf
+
+        # logb(0) = -Inf, DivisionByZero
+        if not self:
+            return context._raise_error(DivisionByZero, 'logb(0)', 1)
+
+        # otherwise, simply return the adjusted exponent of self, as a
+        # Decimal.  Note that no attempt is made to fit the result
+        # into the current context.
+        return Decimal(self.adjusted())
+
+    def _islogical(self):
+        """Return True if self is a logical operand.
+
+        For being logical, it must be a finite number with a sign of 0,
+        an exponent of 0, and a coefficient whose digits must all be
+        either 0 or 1.
+        """
+        if self._sign != 0 or self._exp != 0:
+            return False
+        for dig in self._int:
+            if dig not in '01':
+                return False
+        return True
+
+    def _fill_logical(self, context, opa, opb):
+        dif = context.prec - len(opa)
+        if dif > 0:
+            opa = '0'*dif + opa
+        elif dif < 0:
+            opa = opa[-context.prec:]
+        dif = context.prec - len(opb)
+        if dif > 0:
+            opb = '0'*dif + opb
+        elif dif < 0:
+            opb = opb[-context.prec:]
+        return opa, opb
+
+    def logical_and(self, other, context=None):
+        """Applies an 'and' operation between self and other's digits."""
+        if context is None:
+            context = getcontext()
+        if not self._islogical() or not other._islogical():
+            return context._raise_error(InvalidOperation)
+
+        # fill to context.prec
+        (opa, opb) = self._fill_logical(context, self._int, other._int)
+
+        # make the operation, and clean starting zeroes
+        result = "".join([str(int(a)&int(b)) for a,b in zip(opa,opb)])
+        return _dec_from_triple(0, result.lstrip('0') or '0', 0)
+
+    def logical_invert(self, context=None):
+        """Invert all its digits."""
+        if context is None:
+            context = getcontext()
+        return self.logical_xor(_dec_from_triple(0,'1'*context.prec,0),
+                                context)
+
+    def logical_or(self, other, context=None):
+        """Applies an 'or' operation between self and other's digits."""
+        if context is None:
+            context = getcontext()
+        if not self._islogical() or not other._islogical():
+            return context._raise_error(InvalidOperation)
+
+        # fill to context.prec
+        (opa, opb) = self._fill_logical(context, self._int, other._int)
+
+        # make the operation, and clean starting zeroes
+        result = "".join(str(int(a)|int(b)) for a,b in zip(opa,opb))
+        return _dec_from_triple(0, result.lstrip('0') or '0', 0)
+
+    def logical_xor(self, other, context=None):
+        """Applies an 'xor' operation between self and other's digits."""
+        if context is None:
+            context = getcontext()
+        if not self._islogical() or not other._islogical():
+            return context._raise_error(InvalidOperation)
+
+        # fill to context.prec
+        (opa, opb) = self._fill_logical(context, self._int, other._int)
+
+        # make the operation, and clean starting zeroes
+        result = "".join(str(int(a)^int(b)) for a,b in zip(opa,opb))
+        return _dec_from_triple(0, result.lstrip('0') or '0', 0)
+
+    def max_mag(self, other, context=None):
+        """Compares the values numerically with their sign ignored."""
+        other = _convert_other(other, raiseit=True)
+
+        if context is None:
+            context = getcontext()
+
+        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._fix_nan(context)
+                if sn == 1 and on != 2:
+                    return other._fix_nan(context)
+                return self._check_nans(other, context)
+
+        c = self.copy_abs()._cmp(other.copy_abs())
+        if c == 0:
+            c = self.compare_total(other)
+
+        if c == -1:
+            ans = other
+        else:
+            ans = self
+
+        return ans._fix(context)
+
+    def min_mag(self, other, context=None):
+        """Compares the values numerically with their sign ignored."""
+        other = _convert_other(other, raiseit=True)
+
+        if context is None:
+            context = getcontext()
+
+        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._fix_nan(context)
+                if sn == 1 and on != 2:
+                    return other._fix_nan(context)
+                return self._check_nans(other, context)
+
+        c = self.copy_abs()._cmp(other.copy_abs())
+        if c == 0:
+            c = self.compare_total(other)
+
+        if c == -1:
+            ans = self
+        else:
+            ans = other
+
+        return ans._fix(context)
+
+    def next_minus(self, context=None):
+        """Returns the largest representable number smaller than itself."""
+        if context is None:
+            context = getcontext()
+
+        ans = self._check_nans(context=context)
+        if ans:
+            return ans
+
+        if self._isinfinity() == -1:
+            return negInf
+        if self._isinfinity() == 1:
+            return _dec_from_triple(0, '9'*context.prec, context.Etop())
+
+        context = context.copy()
+        context._set_rounding(ROUND_FLOOR)
+        context._ignore_all_flags()
+        new_self = self._fix(context)
+        if new_self != self:
+            return new_self
+        return self.__sub__(_dec_from_triple(0, '1', context.Etiny()-1),
+                            context)
+
+    def next_plus(self, context=None):
+        """Returns the smallest representable number larger than itself."""
+        if context is None:
+            context = getcontext()
+
+        ans = self._check_nans(context=context)
+        if ans:
+            return ans
+
+        if self._isinfinity() == 1:
+            return Inf
+        if self._isinfinity() == -1:
+            return _dec_from_triple(1, '9'*context.prec, context.Etop())
+
+        context = context.copy()
+        context._set_rounding(ROUND_CEILING)
+        context._ignore_all_flags()
+        new_self = self._fix(context)
+        if new_self != self:
+            return new_self
+        return self.__add__(_dec_from_triple(0, '1', context.Etiny()-1),
+                            context)
+
+    def next_toward(self, other, context=None):
+        """Returns the number closest to self, in the direction towards other.
+
+        The result is the closest representable number to self
+        (excluding self) that is in the direction towards other,
+        unless both have the same value.  If the two operands are
+        numerically equal, then the result is a copy of self with the
+        sign set to be the same as the sign of other.
+        """
+        other = _convert_other(other, raiseit=True)
+
+        if context is None:
+            context = getcontext()
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+
+        comparison = self._cmp(other)
+        if comparison == 0:
+            return self.copy_sign(other)
+
+        if comparison == -1:
+            ans = self.next_plus(context)
+        else: # comparison == 1
+            ans = self.next_minus(context)
+
+        # decide which flags to raise using value of ans
+        if ans._isinfinity():
+            context._raise_error(Overflow,
+                                 'Infinite result from next_toward',
+                                 ans._sign)
+            context._raise_error(Rounded)
+            context._raise_error(Inexact)
+        elif ans.adjusted() < context.Emin:
+            context._raise_error(Underflow)
+            context._raise_error(Subnormal)
+            context._raise_error(Rounded)
+            context._raise_error(Inexact)
+            # if precision == 1 then we don't raise Clamped for a
+            # result 0E-Etiny.
+            if not ans:
+                context._raise_error(Clamped)
+
+        return ans
+
+    def number_class(self, context=None):
+        """Returns an indication of the class of self.
+
+        The class is one of the following strings:
+          sNaN
+          NaN
+          -Infinity
+          -Normal
+          -Subnormal
+          -Zero
+          +Zero
+          +Subnormal
+          +Normal
+          +Infinity
+        """
+        if self.is_snan():
+            return "sNaN"
+        if self.is_qnan():
+            return "NaN"
+        inf = self._isinfinity()
+        if inf == 1:
+            return "+Infinity"
+        if inf == -1:
+            return "-Infinity"
+        if self.is_zero():
+            if self._sign:
+                return "-Zero"
+            else:
+                return "+Zero"
+        if context is None:
+            context = getcontext()
+        if self.is_subnormal(context=context):
+            if self._sign:
+                return "-Subnormal"
+            else:
+                return "+Subnormal"
+        # just a normal, regular, boring number, :)
+        if self._sign:
+            return "-Normal"
+        else:
+            return "+Normal"
+
+    def radix(self):
+        """Just returns 10, as this is Decimal, :)"""
+        return Decimal(10)
+
+    def rotate(self, other, context=None):
+        """Returns a rotated copy of self, value-of-other times."""
+        if context is None:
+            context = getcontext()
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+
+        if other._exp != 0:
+            return context._raise_error(InvalidOperation)
+        if not (-context.prec <= int(other) <= context.prec):
+            return context._raise_error(InvalidOperation)
+
+        if self._isinfinity():
+            return Decimal(self)
+
+        # get values, pad if necessary
+        torot = int(other)
+        rotdig = self._int
+        topad = context.prec - len(rotdig)
+        if topad:
+            rotdig = '0'*topad + rotdig
+
+        # let's rotate!
+        rotated = rotdig[torot:] + rotdig[:torot]
+        return _dec_from_triple(self._sign,
+                                rotated.lstrip('0') or '0', self._exp)
+
+    def scaleb (self, other, context=None):
+        """Returns self operand after adding the second value to its exp."""
+        if context is None:
+            context = getcontext()
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+
+        if other._exp != 0:
+            return context._raise_error(InvalidOperation)
+        liminf = -2 * (context.Emax + context.prec)
+        limsup =  2 * (context.Emax + context.prec)
+        if not (liminf <= int(other) <= limsup):
+            return context._raise_error(InvalidOperation)
+
+        if self._isinfinity():
+            return Decimal(self)
+
+        d = _dec_from_triple(self._sign, self._int, self._exp + int(other))
+        d = d._fix(context)
+        return d
+
+    def shift(self, other, context=None):
+        """Returns a shifted copy of self, value-of-other times."""
+        if context is None:
+            context = getcontext()
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+
+        if other._exp != 0:
+            return context._raise_error(InvalidOperation)
+        if not (-context.prec <= int(other) <= context.prec):
+            return context._raise_error(InvalidOperation)
+
+        if self._isinfinity():
+            return Decimal(self)
+
+        # get values, pad if necessary
+        torot = int(other)
+        if not torot:
+            return Decimal(self)
+        rotdig = self._int
+        topad = context.prec - len(rotdig)
+        if topad:
+            rotdig = '0'*topad + rotdig
+
+        # let's shift!
+        if torot < 0:
+            rotated = rotdig[:torot]
+        else:
+            rotated = rotdig + '0'*torot
+            rotated = rotated[-context.prec:]
+
+        return _dec_from_triple(self._sign,
+                                    rotated.lstrip('0') or '0', self._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))
+
+    # PEP 3101 support.  See also _parse_format_specifier and _format_align
+    def __format__(self, specifier, context=None):
+        """Format a Decimal instance according to the given specifier.
+
+        The specifier should be a standard format specifier, with the
+        form described in PEP 3101.  Formatting types 'e', 'E', 'f',
+        'F', 'g', 'G', and '%' are supported.  If the formatting type
+        is omitted it defaults to 'g' or 'G', depending on the value
+        of context.capitals.
+
+        At this time the 'n' format specifier type (which is supposed
+        to use the current locale) is not supported.
+        """
+
+        # Note: PEP 3101 says that if the type is not present then
+        # there should be at least one digit after the decimal point.
+        # We take the liberty of ignoring this requirement for
+        # Decimal---it's presumably there to make sure that
+        # format(float, '') behaves similarly to str(float).
+        if context is None:
+            context = getcontext()
+
+        spec = _parse_format_specifier(specifier)
+
+        # special values don't care about the type or precision...
+        if self._is_special:
+            return _format_align(str(self), spec)
+
+        # a type of None defaults to 'g' or 'G', depending on context
+        # if type is '%', adjust exponent of self accordingly
+        if spec['type'] is None:
+            spec['type'] = ['g', 'G'][context.capitals]
+        elif spec['type'] == '%':
+            self = _dec_from_triple(self._sign, self._int, self._exp+2)
+
+        # round if necessary, taking rounding mode from the context
+        rounding = context.rounding
+        precision = spec['precision']
+        if precision is not None:
+            if spec['type'] in 'eE':
+                self = self._round(precision+1, rounding)
+            elif spec['type'] in 'gG':
+                if len(self._int) > precision:
+                    self = self._round(precision, rounding)
+            elif spec['type'] in 'fF%':
+                self = self._rescale(-precision, rounding)
+        # special case: zeros with a positive exponent can't be
+        # represented in fixed point; rescale them to 0e0.
+        elif not self and self._exp > 0 and spec['type'] in 'fF%':
+            self = self._rescale(0, rounding)
+
+        # figure out placement of the decimal point
+        leftdigits = self._exp + len(self._int)
+        if spec['type'] in 'fF%':
+            dotplace = leftdigits
+        elif spec['type'] in 'eE':
+            if not self and precision is not None:
+                dotplace = 1 - precision
+            else:
+                dotplace = 1
+        elif spec['type'] in 'gG':
+            if self._exp <= 0 and leftdigits > -6:
+                dotplace = leftdigits
+            else:
+                dotplace = 1
+
+        # figure out main part of numeric string...
+        if dotplace <= 0:
+            num = '0.' + '0'*(-dotplace) + self._int
+        elif dotplace >= len(self._int):
+            # make sure we're not padding a '0' with extra zeros on the right
+            assert dotplace==len(self._int) or self._int != '0'
+            num = self._int + '0'*(dotplace-len(self._int))
+        else:
+            num = self._int[:dotplace] + '.' + self._int[dotplace:]
+
+        # ...then the trailing exponent, or trailing '%'
+        if leftdigits != dotplace or spec['type'] in 'eE':
+            echar = {'E': 'E', 'e': 'e', 'G': 'E', 'g': 'e'}[spec['type']]
+            num = num + "{0}{1:+}".format(echar, leftdigits-dotplace)
+        elif spec['type'] == '%':
+            num = num + '%'
+
+        # add sign
+        if self._sign == 1:
+            num = '-' + num
+        return _format_align(num, spec)
+
+
+def _dec_from_triple(sign, coefficient, exponent, special=False):
+    """Create a decimal instance directly, without any validation,
+    normalization (e.g. removal of leading zeros) or argument
+    conversion.
+
+    This function is for *internal use only*.
+    """
+
+    self = object.__new__(Decimal)
+    self._sign = sign
+    self._int = coefficient
+    self._exp = exponent
+    self._is_special = special
+
+    return self
+
+##### Context class #######################################################
+
+
+# get rounding method function:
+rounding_functions = [name for name in Decimal.__dict__.keys()
+                                    if name.startswith('_round_')]
+for name in rounding_functions:
+    # name is like _round_half_even, goes to the global ROUND_HALF_EVEN value.
+    globalname = name[1:].upper()
+    val = globals()[globalname]
+    Decimal._pick_rounding_function[val] = name
+
+del name, val, globalname, rounding_functions
+
+class _ContextManager(object):
+    """Context manager class to support localcontext().
+
+      Sets a copy of the supplied context in __enter__() and restores
+      the previous decimal context in __exit__()
+    """
+    def __init__(self, new_context):
+        self.new_context = new_context.copy()
+    def __enter__(self):
+        self.saved_context = getcontext()
+        setcontext(self.new_context)
+        return self.new_context
+    def __exit__(self, t, v, tb):
+        setcontext(self.saved_context)
+
+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)
+    traps - If traps[exception] = 1, then the exception is
+                    raised when it is caused.  Otherwise, a value is
+                    substituted in.
+    flags  - When an exception is caused, flags[exception] is set.
+             (Whether or not the trap_enabler is set)
+             Should be reset by user of Decimal instance.
+    Emin -   Minimum exponent
+    Emax -   Maximum exponent
+    capitals -      If 1, 1*10^1 is printed as 1E+1.
+                    If 0, printed as 1e1
+    _clamp - If 1, change exponents if too high (Default 0)
+    """
+
+    def __init__(self, prec=None, rounding=None,
+                 traps=None, flags=None,
+                 Emin=None, Emax=None,
+                 capitals=None, _clamp=0,
+                 _ignored_flags=None):
+        if flags is None:
+            flags = []
+        if _ignored_flags is None:
+            _ignored_flags = []
+        if not isinstance(flags, dict):
+            flags = dict([(s, int(s in flags)) for s in _signals])
+            del s
+        if traps is not None and not isinstance(traps, dict):
+            traps = dict([(s, int(s in traps)) for s in _signals])
+            del s
+        for name, val in locals().items():
+            if val is None:
+                setattr(self, name, _copy.copy(getattr(DefaultContext, name)))
+            else:
+                setattr(self, name, val)
+        del self.self
+
+    def __repr__(self):
+        """Show the current context."""
+        s = []
+        s.append('Context(prec=%(prec)d, rounding=%(rounding)s, '
+                 'Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d'
+                 % vars(self))
+        names = [f.__name__ for f, v in self.flags.items() if v]
+        s.append('flags=[' + ', '.join(names) + ']')
+        names = [t.__name__ for t, v in self.traps.items() if v]
+        s.append('traps=[' + ', '.join(names) + ']')
+        return ', '.join(s) + ')'
+
+    def clear_flags(self):
+        """Reset all flags to zero"""
+        for flag in self.flags:
+            self.flags[flag] = 0
+
+    def _shallow_copy(self):
+        """Returns a shallow copy from self."""
+        nc = Context(self.prec, self.rounding, self.traps,
+                     self.flags, self.Emin, self.Emax,
+                     self.capitals, self._clamp, self._ignored_flags)
+        return nc
+
+    def copy(self):
+        """Returns a deep copy from self."""
+        nc = Context(self.prec, self.rounding, self.traps.copy(),
+                     self.flags.copy(), self.Emin, self.Emax,
+                     self.capitals, self._clamp, self._ignored_flags)
+        return nc
+    __copy__ = copy
+
+    def _raise_error(self, condition, explanation = None, *args):
+        """Handles an error
+
+        If the flag is in _ignored_flags, returns the default response.
+        Otherwise, it sets the flag, then, if the corresponding
+        trap_enabler is set, it reaises the exception.  Otherwise, it returns
+        the default value after setting the flag.
+        """
+        error = _condition_map.get(condition, condition)
+        if error in self._ignored_flags:
+            # Don't touch the flag
+            return error().handle(self, *args)
+
+        self.flags[error] = 1
+        if not self.traps[error]:
+            # The errors define how to handle themselves.
+            return condition().handle(self, *args)
+
+        # Errors should only be risked on copies of the context
+        # self._ignored_flags = []
+        raise error(explanation)
+
+    def _ignore_all_flags(self):
+        """Ignore all flags, if they are raised"""
+        return self._ignore_flags(*_signals)
+
+    def _ignore_flags(self, *flags):
+        """Ignore the flags, if they are raised"""
+        # Do not mutate-- This way, copies of a context leave the original
+        # alone.
+        self._ignored_flags = (self._ignored_flags + list(flags))
+        return list(flags)
+
+    def _regard_flags(self, *flags):
+        """Stop ignoring the flags, if they are raised"""
+        if flags and isinstance(flags[0], (tuple,list)):
+            flags = flags[0]
+        for flag in flags:
+            self._ignored_flags.remove(flag)
+
+    # We inherit object.__hash__, so we must deny this explicitly
+    __hash__ = None
+
+    def Etiny(self):
+        """Returns Etiny (= Emin - prec + 1)"""
+        return int(self.Emin - self.prec + 1)
+
+    def Etop(self):
+        """Returns maximum exponent (= Emax - prec + 1)"""
+        return int(self.Emax - self.prec + 1)
+
+    def _set_rounding(self, type):
+        """Sets the rounding type.
+
+        Sets the rounding type, and returns the current (previous)
+        rounding type.  Often used like:
+
+        context = context.copy()
+        # so you don't change the calling context
+        # if an error occurs in the middle.
+        rounding = context._set_rounding(ROUND_UP)
+        val = self.__sub__(other, context=context)
+        context._set_rounding(rounding)
+
+        This will make it round up for that operation.
+        """
+        rounding = self.rounding
+        self.rounding= type
+        return rounding
+
+    def create_decimal(self, num='0'):
+        """Creates a new Decimal instance but using self as context.
+
+        This method implements the to-number operation of the
+        IBM Decimal specification."""
+
+        if isinstance(num, basestring) and num != num.strip():
+            return self._raise_error(ConversionSyntax,
+                                     "no trailing or leading whitespace is "
+                                     "permitted.")
+
+        d = Decimal(num, context=self)
+        if d._isnan() and len(d._int) > self.prec - self._clamp:
+            return self._raise_error(ConversionSyntax,
+                                     "diagnostic info too long in NaN")
+        return d._fix(self)
+
+    # Methods
+    def abs(self, a):
+        """Returns the absolute value of the operand.
+
+        If the operand is negative, the result is the same as using the minus
+        operation on the operand.  Otherwise, the result is the same as using
+        the plus operation on the operand.
+
+        >>> ExtendedContext.abs(Decimal('2.1'))
+        Decimal('2.1')
+        >>> ExtendedContext.abs(Decimal('-100'))
+        Decimal('100')
+        >>> ExtendedContext.abs(Decimal('101.5'))
+        Decimal('101.5')
+        >>> ExtendedContext.abs(Decimal('-101.5'))
+        Decimal('101.5')
+        """
+        return a.__abs__(context=self)
+
+    def add(self, a, b):
+        """Return the sum of the two operands.
+
+        >>> ExtendedContext.add(Decimal('12'), Decimal('7.00'))
+        Decimal('19.00')
+        >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4'))
+        Decimal('1.02E+4')
+        """
+        return a.__add__(b, context=self)
+
+    def _apply(self, a):
+        return str(a._fix(self))
+
+    def canonical(self, a):
+        """Returns the same Decimal object.
+
+        As we do not have different encodings for the same number, the
+        received object already is in its canonical form.
+
+        >>> ExtendedContext.canonical(Decimal('2.50'))
+        Decimal('2.50')
+        """
+        return a.canonical(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.
+
+        >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3'))
+        Decimal('-1')
+        >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1'))
+        Decimal('0')
+        >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10'))
+        Decimal('0')
+        >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1'))
+        Decimal('1')
+        >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3'))
+        Decimal('1')
+        >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1'))
+        Decimal('-1')
+        """
+        return a.compare(b, context=self)
+
+    def compare_signal(self, a, b):
+        """Compares the values of the two operands numerically.
+
+        It's pretty much like compare(), but all NaNs signal, with signaling
+        NaNs taking precedence over quiet NaNs.
+
+        >>> c = ExtendedContext
+        >>> c.compare_signal(Decimal('2.1'), Decimal('3'))
+        Decimal('-1')
+        >>> c.compare_signal(Decimal('2.1'), Decimal('2.1'))
+        Decimal('0')
+        >>> c.flags[InvalidOperation] = 0
+        >>> print c.flags[InvalidOperation]
+        0
+        >>> c.compare_signal(Decimal('NaN'), Decimal('2.1'))
+        Decimal('NaN')
+        >>> print c.flags[InvalidOperation]
+        1
+        >>> c.flags[InvalidOperation] = 0
+        >>> print c.flags[InvalidOperation]
+        0
+        >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1'))
+        Decimal('NaN')
+        >>> print c.flags[InvalidOperation]
+        1
+        """
+        return a.compare_signal(b, context=self)
+
+    def compare_total(self, a, b):
+        """Compares two operands using their abstract representation.
+
+        This is not like the standard compare, which use their numerical
+        value. Note that a total ordering is defined for all possible abstract
+        representations.
+
+        >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9'))
+        Decimal('-1')
+        >>> ExtendedContext.compare_total(Decimal('-127'),  Decimal('12'))
+        Decimal('-1')
+        >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3'))
+        Decimal('-1')
+        >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30'))
+        Decimal('0')
+        >>> ExtendedContext.compare_total(Decimal('12.3'),  Decimal('12.300'))
+        Decimal('1')
+        >>> ExtendedContext.compare_total(Decimal('12.3'),  Decimal('NaN'))
+        Decimal('-1')
+        """
+        return a.compare_total(b)
+
+    def compare_total_mag(self, a, b):
+        """Compares two operands using their abstract representation ignoring sign.
+
+        Like compare_total, but with operand's sign ignored and assumed to be 0.
+        """
+        return a.compare_total_mag(b)
+
+    def copy_abs(self, a):
+        """Returns a copy of the operand with the sign set to 0.
+
+        >>> ExtendedContext.copy_abs(Decimal('2.1'))
+        Decimal('2.1')
+        >>> ExtendedContext.copy_abs(Decimal('-100'))
+        Decimal('100')
+        """
+        return a.copy_abs()
+
+    def copy_decimal(self, a):
+        """Returns a copy of the decimal objet.
+
+        >>> ExtendedContext.copy_decimal(Decimal('2.1'))
+        Decimal('2.1')
+        >>> ExtendedContext.copy_decimal(Decimal('-1.00'))
+        Decimal('-1.00')
+        """
+        return Decimal(a)
+
+    def copy_negate(self, a):
+        """Returns a copy of the operand with the sign inverted.
+
+        >>> ExtendedContext.copy_negate(Decimal('101.5'))
+        Decimal('-101.5')
+        >>> ExtendedContext.copy_negate(Decimal('-101.5'))
+        Decimal('101.5')
+        """
+        return a.copy_negate()
+
+    def copy_sign(self, a, b):
+        """Copies the second operand's sign to the first one.
+
+        In detail, it returns a copy of the first operand with the sign
+        equal to the sign of the second operand.
+
+        >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33'))
+        Decimal('1.50')
+        >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33'))
+        Decimal('1.50')
+        >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33'))
+        Decimal('-1.50')
+        >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33'))
+        Decimal('-1.50')
+        """
+        return a.copy_sign(b)
+
+    def divide(self, a, b):
+        """Decimal division in a specified context.
+
+        >>> ExtendedContext.divide(Decimal('1'), Decimal('3'))
+        Decimal('0.333333333')
+        >>> ExtendedContext.divide(Decimal('2'), Decimal('3'))
+        Decimal('0.666666667')
+        >>> ExtendedContext.divide(Decimal('5'), Decimal('2'))
+        Decimal('2.5')
+        >>> ExtendedContext.divide(Decimal('1'), Decimal('10'))
+        Decimal('0.1')
+        >>> ExtendedContext.divide(Decimal('12'), Decimal('12'))
+        Decimal('1')
+        >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2'))
+        Decimal('4.00')
+        >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0'))
+        Decimal('1.20')
+        >>> ExtendedContext.divide(Decimal('1000'), Decimal('100'))
+        Decimal('10')
+        >>> ExtendedContext.divide(Decimal('1000'), Decimal('1'))
+        Decimal('1000')
+        >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2'))
+        Decimal('1.20E+6')
+        """
+        return a.__div__(b, context=self)
+
+    def divide_int(self, a, b):
+        """Divides two numbers and returns the integer part of the result.
+
+        >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3'))
+        Decimal('0')
+        >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3'))
+        Decimal('3')
+        >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3'))
+        Decimal('3')
+        """
+        return a.__floordiv__(b, context=self)
+
+    def divmod(self, a, b):
+        return a.__divmod__(b, context=self)
+
+    def exp(self, a):
+        """Returns e ** a.
+
+        >>> c = ExtendedContext.copy()
+        >>> c.Emin = -999
+        >>> c.Emax = 999
+        >>> c.exp(Decimal('-Infinity'))
+        Decimal('0')
+        >>> c.exp(Decimal('-1'))
+        Decimal('0.367879441')
+        >>> c.exp(Decimal('0'))
+        Decimal('1')
+        >>> c.exp(Decimal('1'))
+        Decimal('2.71828183')
+        >>> c.exp(Decimal('0.693147181'))
+        Decimal('2.00000000')
+        >>> c.exp(Decimal('+Infinity'))
+        Decimal('Infinity')
+        """
+        return a.exp(context=self)
+
+    def fma(self, a, b, c):
+        """Returns a multiplied by b, plus c.
+
+        The first two operands are multiplied together, using multiply,
+        the third operand is then added to the result of that
+        multiplication, using add, all with only one final rounding.
+
+        >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7'))
+        Decimal('22')
+        >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7'))
+        Decimal('-8')
+        >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578'))
+        Decimal('1.38435736E+12')
+        """
+        return a.fma(b, c, context=self)
+
+    def is_canonical(self, a):
+        """Return True if the operand is canonical; otherwise return False.
+
+        Currently, the encoding of a Decimal instance is always
+        canonical, so this method returns True for any Decimal.
+
+        >>> ExtendedContext.is_canonical(Decimal('2.50'))
+        True
+        """
+        return a.is_canonical()
+
+    def is_finite(self, a):
+        """Return True if the operand is finite; otherwise return False.
+
+        A Decimal instance is considered finite if it is neither
+        infinite nor a NaN.
+
+        >>> ExtendedContext.is_finite(Decimal('2.50'))
+        True
+        >>> ExtendedContext.is_finite(Decimal('-0.3'))
+        True
+        >>> ExtendedContext.is_finite(Decimal('0'))
+        True
+        >>> ExtendedContext.is_finite(Decimal('Inf'))
+        False
+        >>> ExtendedContext.is_finite(Decimal('NaN'))
+        False
+        """
+        return a.is_finite()
+
+    def is_infinite(self, a):
+        """Return True if the operand is infinite; otherwise return False.
+
+        >>> ExtendedContext.is_infinite(Decimal('2.50'))
+        False
+        >>> ExtendedContext.is_infinite(Decimal('-Inf'))
+        True
+        >>> ExtendedContext.is_infinite(Decimal('NaN'))
+        False
+        """
+        return a.is_infinite()
+
+    def is_nan(self, a):
+        """Return True if the operand is a qNaN or sNaN;
+        otherwise return False.
+
+        >>> ExtendedContext.is_nan(Decimal('2.50'))
+        False
+        >>> ExtendedContext.is_nan(Decimal('NaN'))
+        True
+        >>> ExtendedContext.is_nan(Decimal('-sNaN'))
+        True
+        """
+        return a.is_nan()
+
+    def is_normal(self, a):
+        """Return True if the operand is a normal number;
+        otherwise return False.
+
+        >>> c = ExtendedContext.copy()
+        >>> c.Emin = -999
+        >>> c.Emax = 999
+        >>> c.is_normal(Decimal('2.50'))
+        True
+        >>> c.is_normal(Decimal('0.1E-999'))
+        False
+        >>> c.is_normal(Decimal('0.00'))
+        False
+        >>> c.is_normal(Decimal('-Inf'))
+        False
+        >>> c.is_normal(Decimal('NaN'))
+        False
+        """
+        return a.is_normal(context=self)
+
+    def is_qnan(self, a):
+        """Return True if the operand is a quiet NaN; otherwise return False.
+
+        >>> ExtendedContext.is_qnan(Decimal('2.50'))
+        False
+        >>> ExtendedContext.is_qnan(Decimal('NaN'))
+        True
+        >>> ExtendedContext.is_qnan(Decimal('sNaN'))
+        False
+        """
+        return a.is_qnan()
+
+    def is_signed(self, a):
+        """Return True if the operand is negative; otherwise return False.
+
+        >>> ExtendedContext.is_signed(Decimal('2.50'))
+        False
+        >>> ExtendedContext.is_signed(Decimal('-12'))
+        True
+        >>> ExtendedContext.is_signed(Decimal('-0'))
+        True
+        """
+        return a.is_signed()
+
+    def is_snan(self, a):
+        """Return True if the operand is a signaling NaN;
+        otherwise return False.
+
+        >>> ExtendedContext.is_snan(Decimal('2.50'))
+        False
+        >>> ExtendedContext.is_snan(Decimal('NaN'))
+        False
+        >>> ExtendedContext.is_snan(Decimal('sNaN'))
+        True
+        """
+        return a.is_snan()
+
+    def is_subnormal(self, a):
+        """Return True if the operand is subnormal; otherwise return False.
+
+        >>> c = ExtendedContext.copy()
+        >>> c.Emin = -999
+        >>> c.Emax = 999
+        >>> c.is_subnormal(Decimal('2.50'))
+        False
+        >>> c.is_subnormal(Decimal('0.1E-999'))
+        True
+        >>> c.is_subnormal(Decimal('0.00'))
+        False
+        >>> c.is_subnormal(Decimal('-Inf'))
+        False
+        >>> c.is_subnormal(Decimal('NaN'))
+        False
+        """
+        return a.is_subnormal(context=self)
+
+    def is_zero(self, a):
+        """Return True if the operand is a zero; otherwise return False.
+
+        >>> ExtendedContext.is_zero(Decimal('0'))
+        True
+        >>> ExtendedContext.is_zero(Decimal('2.50'))
+        False
+        >>> ExtendedContext.is_zero(Decimal('-0E+2'))
+        True
+        """
+        return a.is_zero()
+
+    def ln(self, a):
+        """Returns the natural (base e) logarithm of the operand.
+
+        >>> c = ExtendedContext.copy()
+        >>> c.Emin = -999
+        >>> c.Emax = 999
+        >>> c.ln(Decimal('0'))
+        Decimal('-Infinity')
+        >>> c.ln(Decimal('1.000'))
+        Decimal('0')
+        >>> c.ln(Decimal('2.71828183'))
+        Decimal('1.00000000')
+        >>> c.ln(Decimal('10'))
+        Decimal('2.30258509')
+        >>> c.ln(Decimal('+Infinity'))
+        Decimal('Infinity')
+        """
+        return a.ln(context=self)
+
+    def log10(self, a):
+        """Returns the base 10 logarithm of the operand.
+
+        >>> c = ExtendedContext.copy()
+        >>> c.Emin = -999
+        >>> c.Emax = 999
+        >>> c.log10(Decimal('0'))
+        Decimal('-Infinity')
+        >>> c.log10(Decimal('0.001'))
+        Decimal('-3')
+        >>> c.log10(Decimal('1.000'))
+        Decimal('0')
+        >>> c.log10(Decimal('2'))
+        Decimal('0.301029996')
+        >>> c.log10(Decimal('10'))
+        Decimal('1')
+        >>> c.log10(Decimal('70'))
+        Decimal('1.84509804')
+        >>> c.log10(Decimal('+Infinity'))
+        Decimal('Infinity')
+        """
+        return a.log10(context=self)
+
+    def logb(self, a):
+        """ Returns the exponent of the magnitude of the operand's MSD.
+
+        The result is the integer which is the exponent of the magnitude
+        of the most significant digit of the operand (as though the
+        operand were truncated to a single digit while maintaining the
+        value of that digit and without limiting the resulting exponent).
+
+        >>> ExtendedContext.logb(Decimal('250'))
+        Decimal('2')
+        >>> ExtendedContext.logb(Decimal('2.50'))
+        Decimal('0')
+        >>> ExtendedContext.logb(Decimal('0.03'))
+        Decimal('-2')
+        >>> ExtendedContext.logb(Decimal('0'))
+        Decimal('-Infinity')
+        """
+        return a.logb(context=self)
+
+    def logical_and(self, a, b):
+        """Applies the logical operation 'and' between each operand's digits.
+
+        The operands must be both logical numbers.
+
+        >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0'))
+        Decimal('0')
+        >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1'))
+        Decimal('0')
+        >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0'))
+        Decimal('0')
+        >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1'))
+        Decimal('1')
+        >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010'))
+        Decimal('1000')
+        >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10'))
+        Decimal('10')
+        """
+        return a.logical_and(b, context=self)
+
+    def logical_invert(self, a):
+        """Invert all the digits in the operand.
+
+        The operand must be a logical number.
+
+        >>> ExtendedContext.logical_invert(Decimal('0'))
+        Decimal('111111111')
+        >>> ExtendedContext.logical_invert(Decimal('1'))
+        Decimal('111111110')
+        >>> ExtendedContext.logical_invert(Decimal('111111111'))
+        Decimal('0')
+        >>> ExtendedContext.logical_invert(Decimal('101010101'))
+        Decimal('10101010')
+        """
+        return a.logical_invert(context=self)
+
+    def logical_or(self, a, b):
+        """Applies the logical operation 'or' between each operand's digits.
+
+        The operands must be both logical numbers.
+
+        >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0'))
+        Decimal('0')
+        >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1'))
+        Decimal('1')
+        >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0'))
+        Decimal('1')
+        >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1'))
+        Decimal('1')
+        >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010'))
+        Decimal('1110')
+        >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10'))
+        Decimal('1110')
+        """
+        return a.logical_or(b, context=self)
+
+    def logical_xor(self, a, b):
+        """Applies the logical operation 'xor' between each operand's digits.
+
+        The operands must be both logical numbers.
+
+        >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0'))
+        Decimal('0')
+        >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1'))
+        Decimal('1')
+        >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0'))
+        Decimal('1')
+        >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1'))
+        Decimal('0')
+        >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010'))
+        Decimal('110')
+        >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10'))
+        Decimal('1101')
+        """
+        return a.logical_xor(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 though by the compare
+        operation.  If they are numerically equal then the left-hand operand
+        is chosen as the result.  Otherwise the maximum (closer to positive
+        infinity) of the two operands is chosen as the result.
+
+        >>> ExtendedContext.max(Decimal('3'), Decimal('2'))
+        Decimal('3')
+        >>> ExtendedContext.max(Decimal('-10'), Decimal('3'))
+        Decimal('3')
+        >>> ExtendedContext.max(Decimal('1.0'), Decimal('1'))
+        Decimal('1')
+        >>> ExtendedContext.max(Decimal('7'), Decimal('NaN'))
+        Decimal('7')
+        """
+        return a.max(b, context=self)
+
+    def max_mag(self, a, b):
+        """Compares the values numerically with their sign ignored."""
+        return a.max_mag(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 though by the compare
+        operation.  If they are numerically equal then the left-hand operand
+        is chosen as the result.  Otherwise the minimum (closer to negative
+        infinity) of the two operands is chosen as the result.
+
+        >>> ExtendedContext.min(Decimal('3'), Decimal('2'))
+        Decimal('2')
+        >>> ExtendedContext.min(Decimal('-10'), Decimal('3'))
+        Decimal('-10')
+        >>> ExtendedContext.min(Decimal('1.0'), Decimal('1'))
+        Decimal('1.0')
+        >>> ExtendedContext.min(Decimal('7'), Decimal('NaN'))
+        Decimal('7')
+        """
+        return a.min(b, context=self)
+
+    def min_mag(self, a, b):
+        """Compares the values numerically with their sign ignored."""
+        return a.min_mag(b, context=self)
+
+    def minus(self, a):
+        """Minus corresponds to unary prefix minus in Python.
+
+        The operation is evaluated using the same rules as subtract; the
+        operation minus(a) is calculated as subtract('0', a) where the '0'
+        has the same exponent as the operand.
+
+        >>> ExtendedContext.minus(Decimal('1.3'))
+        Decimal('-1.3')
+        >>> ExtendedContext.minus(Decimal('-1.3'))
+        Decimal('1.3')
+        """
+        return a.__neg__(context=self)
+
+    def multiply(self, a, b):
+        """multiply multiplies two operands.
+
+        If either operand is a special value then the general rules apply.
+        Otherwise, the operands are multiplied together ('long multiplication'),
+        resulting in a number which may be as long as the sum of the lengths
+        of the two operands.
+
+        >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3'))
+        Decimal('3.60')
+        >>> ExtendedContext.multiply(Decimal('7'), Decimal('3'))
+        Decimal('21')
+        >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8'))
+        Decimal('0.72')
+        >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0'))
+        Decimal('-0.0')
+        >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321'))
+        Decimal('4.28135971E+11')
+        """
+        return a.__mul__(b, context=self)
+
+    def next_minus(self, a):
+        """Returns the largest representable number smaller than a.
+
+        >>> c = ExtendedContext.copy()
+        >>> c.Emin = -999
+        >>> c.Emax = 999
+        >>> ExtendedContext.next_minus(Decimal('1'))
+        Decimal('0.999999999')
+        >>> c.next_minus(Decimal('1E-1007'))
+        Decimal('0E-1007')
+        >>> ExtendedContext.next_minus(Decimal('-1.00000003'))
+        Decimal('-1.00000004')
+        >>> c.next_minus(Decimal('Infinity'))
+        Decimal('9.99999999E+999')
+        """
+        return a.next_minus(context=self)
+
+    def next_plus(self, a):
+        """Returns the smallest representable number larger than a.
+
+        >>> c = ExtendedContext.copy()
+        >>> c.Emin = -999
+        >>> c.Emax = 999
+        >>> ExtendedContext.next_plus(Decimal('1'))
+        Decimal('1.00000001')
+        >>> c.next_plus(Decimal('-1E-1007'))
+        Decimal('-0E-1007')
+        >>> ExtendedContext.next_plus(Decimal('-1.00000003'))
+        Decimal('-1.00000002')
+        >>> c.next_plus(Decimal('-Infinity'))
+        Decimal('-9.99999999E+999')
+        """
+        return a.next_plus(context=self)
+
+    def next_toward(self, a, b):
+        """Returns the number closest to a, in direction towards b.
+
+        The result is the closest representable number from the first
+        operand (but not the first operand) that is in the direction
+        towards the second operand, unless the operands have the same
+        value.
+
+        >>> c = ExtendedContext.copy()
+        >>> c.Emin = -999
+        >>> c.Emax = 999
+        >>> c.next_toward(Decimal('1'), Decimal('2'))
+        Decimal('1.00000001')
+        >>> c.next_toward(Decimal('-1E-1007'), Decimal('1'))
+        Decimal('-0E-1007')
+        >>> c.next_toward(Decimal('-1.00000003'), Decimal('0'))
+        Decimal('-1.00000002')
+        >>> c.next_toward(Decimal('1'), Decimal('0'))
+        Decimal('0.999999999')
+        >>> c.next_toward(Decimal('1E-1007'), Decimal('-100'))
+        Decimal('0E-1007')
+        >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10'))
+        Decimal('-1.00000004')
+        >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000'))
+        Decimal('-0.00')
+        """
+        return a.next_toward(b, context=self)
+
+    def normalize(self, a):
+        """normalize reduces an operand to its simplest form.
+
+        Essentially a plus operation with all trailing zeros removed from the
+        result.
+
+        >>> ExtendedContext.normalize(Decimal('2.1'))
+        Decimal('2.1')
+        >>> ExtendedContext.normalize(Decimal('-2.0'))
+        Decimal('-2')
+        >>> ExtendedContext.normalize(Decimal('1.200'))
+        Decimal('1.2')
+        >>> ExtendedContext.normalize(Decimal('-120'))
+        Decimal('-1.2E+2')
+        >>> ExtendedContext.normalize(Decimal('120.00'))
+        Decimal('1.2E+2')
+        >>> ExtendedContext.normalize(Decimal('0.00'))
+        Decimal('0')
+        """
+        return a.normalize(context=self)
+
+    def number_class(self, a):
+        """Returns an indication of the class of the operand.
+
+        The class is one of the following strings:
+          -sNaN
+          -NaN
+          -Infinity
+          -Normal
+          -Subnormal
+          -Zero
+          +Zero
+          +Subnormal
+          +Normal
+          +Infinity
+
+        >>> c = Context(ExtendedContext)
+        >>> c.Emin = -999
+        >>> c.Emax = 999
+        >>> c.number_class(Decimal('Infinity'))
+        '+Infinity'
+        >>> c.number_class(Decimal('1E-10'))
+        '+Normal'
+        >>> c.number_class(Decimal('2.50'))
+        '+Normal'
+        >>> c.number_class(Decimal('0.1E-999'))
+        '+Subnormal'
+        >>> c.number_class(Decimal('0'))
+        '+Zero'
+        >>> c.number_class(Decimal('-0'))
+        '-Zero'
+        >>> c.number_class(Decimal('-0.1E-999'))
+        '-Subnormal'
+        >>> c.number_class(Decimal('-1E-10'))
+        '-Normal'
+        >>> c.number_class(Decimal('-2.50'))
+        '-Normal'
+        >>> c.number_class(Decimal('-Infinity'))
+        '-Infinity'
+        >>> c.number_class(Decimal('NaN'))
+        'NaN'
+        >>> c.number_class(Decimal('-NaN'))
+        'NaN'
+        >>> c.number_class(Decimal('sNaN'))
+        'sNaN'
+        """
+        return a.number_class(context=self)
+
+    def plus(self, a):
+        """Plus corresponds to unary prefix plus in Python.
+
+        The operation is evaluated using the same rules as add; the
+        operation plus(a) is calculated as add('0', a) where the '0'
+        has the same exponent as the operand.
+
+        >>> ExtendedContext.plus(Decimal('1.3'))
+        Decimal('1.3')
+        >>> ExtendedContext.plus(Decimal('-1.3'))
+        Decimal('-1.3')
+        """
+        return a.__pos__(context=self)
+
+    def power(self, a, b, modulo=None):
+        """Raises a to the power of b, to modulo if given.
+
+        With two arguments, compute a**b.  If a is negative then b
+        must be integral.  The result will be inexact unless b is
+        integral and the result is finite and can be expressed exactly
+        in 'precision' digits.
+
+        With three arguments, compute (a**b) % modulo.  For the
+        three argument form, the following restrictions on the
+        arguments hold:
+
+         - all three arguments must be integral
+         - b must be nonnegative
+         - at least one of a or b must be nonzero
+         - modulo must be nonzero and have at most 'precision' digits
+
+        The result of pow(a, b, modulo) is identical to the result
+        that would be obtained by computing (a**b) % modulo with
+        unbounded precision, but is computed more efficiently.  It is
+        always exact.
+
+        >>> c = ExtendedContext.copy()
+        >>> c.Emin = -999
+        >>> c.Emax = 999
+        >>> c.power(Decimal('2'), Decimal('3'))
+        Decimal('8')
+        >>> c.power(Decimal('-2'), Decimal('3'))
+        Decimal('-8')
+        >>> c.power(Decimal('2'), Decimal('-3'))
+        Decimal('0.125')
+        >>> c.power(Decimal('1.7'), Decimal('8'))
+        Decimal('69.7575744')
+        >>> c.power(Decimal('10'), Decimal('0.301029996'))
+        Decimal('2.00000000')
+        >>> c.power(Decimal('Infinity'), Decimal('-1'))
+        Decimal('0')
+        >>> c.power(Decimal('Infinity'), Decimal('0'))
+        Decimal('1')
+        >>> c.power(Decimal('Infinity'), Decimal('1'))
+        Decimal('Infinity')
+        >>> c.power(Decimal('-Infinity'), Decimal('-1'))
+        Decimal('-0')
+        >>> c.power(Decimal('-Infinity'), Decimal('0'))
+        Decimal('1')
+        >>> c.power(Decimal('-Infinity'), Decimal('1'))
+        Decimal('-Infinity')
+        >>> c.power(Decimal('-Infinity'), Decimal('2'))
+        Decimal('Infinity')
+        >>> c.power(Decimal('0'), Decimal('0'))
+        Decimal('NaN')
+
+        >>> c.power(Decimal('3'), Decimal('7'), Decimal('16'))
+        Decimal('11')
+        >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16'))
+        Decimal('-11')
+        >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16'))
+        Decimal('1')
+        >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16'))
+        Decimal('11')
+        >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789'))
+        Decimal('11729830')
+        >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729'))
+        Decimal('-0')
+        >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537'))
+        Decimal('1')
+        """
+        return a.__pow__(b, modulo, context=self)
+
+    def quantize(self, a, b):
+        """Returns a value equal to 'a' (rounded), having the exponent of 'b'.
+
+        The coefficient of the result is derived from that of the left-hand
+        operand.  It may be rounded using the current rounding setting (if the
+        exponent is being increased), multiplied by a positive power of ten (if
+        the exponent is being decreased), or is unchanged (if the exponent is
+        already equal to that of the right-hand operand).
+
+        Unlike other operations, if the length of the coefficient after the
+        quantize operation would be greater than precision then an Invalid
+        operation condition is raised.  This guarantees that, unless there is
+        an error condition, the exponent of the result of a quantize is always
+        equal to that of the right-hand operand.
+
+        Also unlike other operations, quantize will never raise Underflow, even
+        if the result is subnormal and inexact.
+
+        >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001'))
+        Decimal('2.170')
+        >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01'))
+        Decimal('2.17')
+        >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1'))
+        Decimal('2.2')
+        >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0'))
+        Decimal('2')
+        >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1'))
+        Decimal('0E+1')
+        >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity'))
+        Decimal('-Infinity')
+        >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity'))
+        Decimal('NaN')
+        >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1'))
+        Decimal('-0')
+        >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5'))
+        Decimal('-0E+5')
+        >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2'))
+        Decimal('NaN')
+        >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2'))
+        Decimal('NaN')
+        >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1'))
+        Decimal('217.0')
+        >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0'))
+        Decimal('217')
+        >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1'))
+        Decimal('2.2E+2')
+        >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2'))
+        Decimal('2E+2')
+        """
+        return a.quantize(b, context=self)
+
+    def radix(self):
+        """Just returns 10, as this is Decimal, :)
+
+        >>> ExtendedContext.radix()
+        Decimal('10')
+        """
+        return Decimal(10)
+
+    def remainder(self, a, b):
+        """Returns the remainder from integer division.
+
+        The result is the residue of the dividend after the operation of
+        calculating integer division as described for divide-integer, rounded
+        to precision digits if necessary.  The sign of the result, if
+        non-zero, is the same as that of the original dividend.
+
+        This operation will fail under the same conditions as integer division
+        (that is, if integer division on the same two operands would fail, the
+        remainder cannot be calculated).
+
+        >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3'))
+        Decimal('2.1')
+        >>> ExtendedContext.remainder(Decimal('10'), Decimal('3'))
+        Decimal('1')
+        >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3'))
+        Decimal('-1')
+        >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1'))
+        Decimal('0.2')
+        >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3'))
+        Decimal('0.1')
+        >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3'))
+        Decimal('1.0')
+        """
+        return a.__mod__(b, context=self)
+
+    def remainder_near(self, a, b):
+        """Returns to be "a - b * n", where n is the integer nearest the exact
+        value of "x / b" (if two integers are equally near then the even one
+        is chosen).  If the result is equal to 0 then its sign will be the
+        sign of a.
+
+        This operation will fail under the same conditions as integer division
+        (that is, if integer division on the same two operands would fail, the
+        remainder cannot be calculated).
+
+        >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3'))
+        Decimal('-0.9')
+        >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6'))
+        Decimal('-2')
+        >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3'))
+        Decimal('1')
+        >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3'))
+        Decimal('-1')
+        >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1'))
+        Decimal('0.2')
+        >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3'))
+        Decimal('0.1')
+        >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3'))
+        Decimal('-0.3')
+        """
+        return a.remainder_near(b, context=self)
+
+    def rotate(self, a, b):
+        """Returns a rotated copy of a, b times.
+
+        The coefficient of the result is a rotated copy of the digits in
+        the coefficient of the first operand.  The number of places of
+        rotation is taken from the absolute value of the second operand,
+        with the rotation being to the left if the second operand is
+        positive or to the right otherwise.
+
+        >>> ExtendedContext.rotate(Decimal('34'), Decimal('8'))
+        Decimal('400000003')
+        >>> ExtendedContext.rotate(Decimal('12'), Decimal('9'))
+        Decimal('12')
+        >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2'))
+        Decimal('891234567')
+        >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0'))
+        Decimal('123456789')
+        >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2'))
+        Decimal('345678912')
+        """
+        return a.rotate(b, context=self)
+
+    def same_quantum(self, a, b):
+        """Returns True if the two operands have the same exponent.
+
+        The result is never affected by either the sign or the coefficient of
+        either operand.
+
+        >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001'))
+        False
+        >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01'))
+        True
+        >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1'))
+        False
+        >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf'))
+        True
+        """
+        return a.same_quantum(b)
+
+    def scaleb (self, a, b):
+        """Returns the first operand after adding the second value its exp.
+
+        >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2'))
+        Decimal('0.0750')
+        >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0'))
+        Decimal('7.50')
+        >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3'))
+        Decimal('7.50E+3')
+        """
+        return a.scaleb (b, context=self)
+
+    def shift(self, a, b):
+        """Returns a shifted copy of a, b times.
+
+        The coefficient of the result is a shifted copy of the digits
+        in the coefficient of the first operand.  The number of places
+        to shift is taken from the absolute value of the second operand,
+        with the shift being to the left if the second operand is
+        positive or to the right otherwise.  Digits shifted into the
+        coefficient are zeros.
+
+        >>> ExtendedContext.shift(Decimal('34'), Decimal('8'))
+        Decimal('400000000')
+        >>> ExtendedContext.shift(Decimal('12'), Decimal('9'))
+        Decimal('0')
+        >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2'))
+        Decimal('1234567')
+        >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0'))
+        Decimal('123456789')
+        >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2'))
+        Decimal('345678900')
+        """
+        return a.shift(b, context=self)
+
+    def sqrt(self, a):
+        """Square root of a non-negative number to context precision.
+
+        If the result must be inexact, it is rounded using the round-half-even
+        algorithm.
+
+        >>> ExtendedContext.sqrt(Decimal('0'))
+        Decimal('0')
+        >>> ExtendedContext.sqrt(Decimal('-0'))
+        Decimal('-0')
+        >>> ExtendedContext.sqrt(Decimal('0.39'))
+        Decimal('0.624499800')
+        >>> ExtendedContext.sqrt(Decimal('100'))
+        Decimal('10')
+        >>> ExtendedContext.sqrt(Decimal('1'))
+        Decimal('1')
+        >>> ExtendedContext.sqrt(Decimal('1.0'))
+        Decimal('1.0')
+        >>> ExtendedContext.sqrt(Decimal('1.00'))
+        Decimal('1.0')
+        >>> ExtendedContext.sqrt(Decimal('7'))
+        Decimal('2.64575131')
+        >>> ExtendedContext.sqrt(Decimal('10'))
+        Decimal('3.16227766')
+        >>> ExtendedContext.prec
+        9
+        """
+        return a.sqrt(context=self)
+
+    def subtract(self, a, b):
+        """Return the difference between the two operands.
+
+        >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07'))
+        Decimal('0.23')
+        >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30'))
+        Decimal('0.00')
+        >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07'))
+        Decimal('-0.77')
+        """
+        return a.__sub__(b, context=self)
+
+    def to_eng_string(self, a):
+        """Converts a number to a string, using scientific notation.
+
+        The operation is not affected by the context.
+        """
+        return a.to_eng_string(context=self)
+
+    def to_sci_string(self, a):
+        """Converts a number to a string, using scientific notation.
+
+        The operation is not affected by the context.
+        """
+        return a.__str__(context=self)
+
+    def to_integral_exact(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; Inexact and Rounded flags
+        are allowed in this operation.  The rounding mode is taken from the
+        context.
+
+        >>> ExtendedContext.to_integral_exact(Decimal('2.1'))
+        Decimal('2')
+        >>> ExtendedContext.to_integral_exact(Decimal('100'))
+        Decimal('100')
+        >>> ExtendedContext.to_integral_exact(Decimal('100.0'))
+        Decimal('100')
+        >>> ExtendedContext.to_integral_exact(Decimal('101.5'))
+        Decimal('102')
+        >>> ExtendedContext.to_integral_exact(Decimal('-101.5'))
+        Decimal('-102')
+        >>> ExtendedContext.to_integral_exact(Decimal('10E+5'))
+        Decimal('1.0E+6')
+        >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77'))
+        Decimal('7.89E+77')
+        >>> ExtendedContext.to_integral_exact(Decimal('-Inf'))
+        Decimal('-Infinity')
+        """
+        return a.to_integral_exact(context=self)
+
+    def to_integral_value(self, a):
+        """Rounds to an integer.
+
+        When the operand has a negative exponent, the result is the same
+        as using the quantize() operation using the given operand as the
+        left-hand-operand, 1E+0 as the right-hand-operand, and the precision
+        of the operand as the precision setting, except that no flags will
+        be set.  The rounding mode is taken from the context.
+
+        >>> ExtendedContext.to_integral_value(Decimal('2.1'))
+        Decimal('2')
+        >>> ExtendedContext.to_integral_value(Decimal('100'))
+        Decimal('100')
+        >>> ExtendedContext.to_integral_value(Decimal('100.0'))
+        Decimal('100')
+        >>> ExtendedContext.to_integral_value(Decimal('101.5'))
+        Decimal('102')
+        >>> ExtendedContext.to_integral_value(Decimal('-101.5'))
+        Decimal('-102')
+        >>> ExtendedContext.to_integral_value(Decimal('10E+5'))
+        Decimal('1.0E+6')
+        >>> ExtendedContext.to_integral_value(Decimal('7.89E+77'))
+        Decimal('7.89E+77')
+        >>> ExtendedContext.to_integral_value(Decimal('-Inf'))
+        Decimal('-Infinity')
+        """
+        return a.to_integral_value(context=self)
+
+    # the method name changed, but we provide also the old one, for compatibility
+    to_integral = to_integral_value
+
+class _WorkRep(object):
+    __slots__ = ('sign','int','exp')
+    # sign: 0 or 1
+    # int:  int or long
+    # exp:  None, int, or string
+
+    def __init__(self, value=None):
+        if value is None:
+            self.sign = None
+            self.int = 0
+            self.exp = None
+        elif isinstance(value, Decimal):
+            self.sign = value._sign
+            self.int = int(value._int)
+            self.exp = value._exp
+        else:
+            # assert isinstance(value, tuple)
+            self.sign = value[0]
+            self.int = value[1]
+            self.exp = value[2]
+
+    def __repr__(self):
+        return "(%r, %r, %r)" % (self.sign, self.int, self.exp)
+
+    __str__ = __repr__
+
+
+
+def _normalize(op1, op2, prec = 0):
+    """Normalizes op1, op2 to have the same exp and length of coefficient.
+
+    Done during addition.
+    """
+    if op1.exp < op2.exp:
+        tmp = op2
+        other = op1
+    else:
+        tmp = op1
+        other = op2
+
+    # Let exp = min(tmp.exp - 1, tmp.adjusted() - precision - 1).
+    # Then adding 10**exp to tmp has the same effect (after rounding)
+    # as adding any positive quantity smaller than 10**exp; similarly
+    # for subtraction.  So if other is smaller than 10**exp we replace
+    # it with 10**exp.  This avoids tmp.exp - other.exp getting too large.
+    tmp_len = len(str(tmp.int))
+    other_len = len(str(other.int))
+    exp = tmp.exp + min(-1, tmp_len - prec - 2)
+    if other_len + other.exp - 1 < exp:
+        other.int = 1
+        other.exp = exp
+
+    tmp.int *= 10 ** (tmp.exp - other.exp)
+    tmp.exp = other.exp
+    return op1, op2
+
+##### Integer arithmetic functions used by ln, log10, exp and __pow__ #####
+
+# This function from Tim Peters was taken from here:
+# http://mail.python.org/pipermail/python-list/1999-July/007758.html
+# The correction being in the function definition is for speed, and
+# the whole function is not resolved with math.log because of avoiding
+# the use of floats.
+def _nbits(n, correction = {
+        '0': 4, '1': 3, '2': 2, '3': 2,
+        '4': 1, '5': 1, '6': 1, '7': 1,
+        '8': 0, '9': 0, 'a': 0, 'b': 0,
+        'c': 0, 'd': 0, 'e': 0, 'f': 0}):
+    """Number of bits in binary representation of the positive integer n,
+    or 0 if n == 0.
+    """
+    if n < 0:
+        raise ValueError("The argument to _nbits should be nonnegative.")
+    hex_n = "%x" % n
+    return 4*len(hex_n) - correction[hex_n[0]]
+
+def _sqrt_nearest(n, a):
+    """Closest integer to the square root of the positive integer n.  a is
+    an initial approximation to the square root.  Any positive integer
+    will do for a, but the closer a is to the square root of n the
+    faster convergence will be.
+
+    """
+    if n <= 0 or a <= 0:
+        raise ValueError("Both arguments to _sqrt_nearest should be positive.")
+
+    b=0
+    while a != b:
+        b, a = a, a--n//a>>1
+    return a
+
+def _rshift_nearest(x, shift):
+    """Given an integer x and a nonnegative integer shift, return closest
+    integer to x / 2**shift; use round-to-even in case of a tie.
+
+    """
+    b, q = 1L << shift, x >> shift
+    return q + (2*(x & (b-1)) + (q&1) > b)
+
+def _div_nearest(a, b):
+    """Closest integer to a/b, a and b positive integers; rounds to even
+    in the case of a tie.
+
+    """
+    q, r = divmod(a, b)
+    return q + (2*r + (q&1) > b)
+
+def _ilog(x, M, L = 8):
+    """Integer approximation to M*log(x/M), with absolute error boundable
+    in terms only of x/M.
+
+    Given positive integers x and M, return an integer approximation to
+    M * log(x/M).  For L = 8 and 0.1 <= x/M <= 10 the difference
+    between the approximation and the exact result is at most 22.  For
+    L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15.  In
+    both cases these are upper bounds on the error; it will usually be
+    much smaller."""
+
+    # The basic algorithm is the following: let log1p be the function
+    # log1p(x) = log(1+x).  Then log(x/M) = log1p((x-M)/M).  We use
+    # the reduction
+    #
+    #    log1p(y) = 2*log1p(y/(1+sqrt(1+y)))
+    #
+    # repeatedly until the argument to log1p is small (< 2**-L in
+    # absolute value).  For small y we can use the Taylor series
+    # expansion
+    #
+    #    log1p(y) ~ y - y**2/2 + y**3/3 - ... - (-y)**T/T
+    #
+    # truncating at T such that y**T is small enough.  The whole
+    # computation is carried out in a form of fixed-point arithmetic,
+    # with a real number z being represented by an integer
+    # approximation to z*M.  To avoid loss of precision, the y below
+    # is actually an integer approximation to 2**R*y*M, where R is the
+    # number of reductions performed so far.
+
+    y = x-M
+    # argument reduction; R = number of reductions performed
+    R = 0
+    while (R <= L and long(abs(y)) << L-R >= M or
+           R > L and abs(y) >> R-L >= M):
+        y = _div_nearest(long(M*y) << 1,
+                         M + _sqrt_nearest(M*(M+_rshift_nearest(y, R)), M))
+        R += 1
+
+    # Taylor series with T terms
+    T = -int(-10*len(str(M))//(3*L))
+    yshift = _rshift_nearest(y, R)
+    w = _div_nearest(M, T)
+    for k in xrange(T-1, 0, -1):
+        w = _div_nearest(M, k) - _div_nearest(yshift*w, M)
+
+    return _div_nearest(w*y, M)
+
+def _dlog10(c, e, p):
+    """Given integers c, e and p with c > 0, p >= 0, compute an integer
+    approximation to 10**p * log10(c*10**e), with an absolute error of
+    at most 1.  Assumes that c*10**e is not exactly 1."""
+
+    # increase precision by 2; compensate for this by dividing
+    # final result by 100
+    p += 2
+
+    # write c*10**e as d*10**f with either:
+    #   f >= 0 and 1 <= d <= 10, or
+    #   f <= 0 and 0.1 <= d <= 1.
+    # Thus for c*10**e close to 1, f = 0
+    l = len(str(c))
+    f = e+l - (e+l >= 1)
+
+    if p > 0:
+        M = 10**p
+        k = e+p-f
+        if k >= 0:
+            c *= 10**k
+        else:
+            c = _div_nearest(c, 10**-k)
+
+        log_d = _ilog(c, M) # error < 5 + 22 = 27
+        log_10 = _log10_digits(p) # error < 1
+        log_d = _div_nearest(log_d*M, log_10)
+        log_tenpower = f*M # exact
+    else:
+        log_d = 0  # error < 2.31
+        log_tenpower = _div_nearest(f, 10**-p) # error < 0.5
+
+    return _div_nearest(log_tenpower+log_d, 100)
+
+def _dlog(c, e, p):
+    """Given integers c, e and p with c > 0, compute an integer
+    approximation to 10**p * log(c*10**e), with an absolute error of
+    at most 1.  Assumes that c*10**e is not exactly 1."""
+
+    # Increase precision by 2. The precision increase is compensated
+    # for at the end with a division by 100.
+    p += 2
+
+    # rewrite c*10**e as d*10**f with either f >= 0 and 1 <= d <= 10,
+    # or f <= 0 and 0.1 <= d <= 1.  Then we can compute 10**p * log(c*10**e)
+    # as 10**p * log(d) + 10**p*f * log(10).
+    l = len(str(c))
+    f = e+l - (e+l >= 1)
+
+    # compute approximation to 10**p*log(d), with error < 27
+    if p > 0:
+        k = e+p-f
+        if k >= 0:
+            c *= 10**k
+        else:
+            c = _div_nearest(c, 10**-k)  # error of <= 0.5 in c
+
+        # _ilog magnifies existing error in c by a factor of at most 10
+        log_d = _ilog(c, 10**p) # error < 5 + 22 = 27
+    else:
+        # p <= 0: just approximate the whole thing by 0; error < 2.31
+        log_d = 0
+
+    # compute approximation to f*10**p*log(10), with error < 11.
+    if f:
+        extra = len(str(abs(f)))-1
+        if p + extra >= 0:
+            # error in f * _log10_digits(p+extra) < |f| * 1 = |f|
+            # after division, error < |f|/10**extra + 0.5 < 10 + 0.5 < 11
+            f_log_ten = _div_nearest(f*_log10_digits(p+extra), 10**extra)
+        else:
+            f_log_ten = 0
+    else:
+        f_log_ten = 0
+
+    # error in sum < 11+27 = 38; error after division < 0.38 + 0.5 < 1
+    return _div_nearest(f_log_ten + log_d, 100)
+
+class _Log10Memoize(object):
+    """Class to compute, store, and allow retrieval of, digits of the
+    constant log(10) = 2.302585....  This constant is needed by
+    Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__."""
+    def __init__(self):
+        self.digits = "23025850929940456840179914546843642076011014886"
+
+    def getdigits(self, p):
+        """Given an integer p >= 0, return floor(10**p)*log(10).
+
+        For example, self.getdigits(3) returns 2302.
+        """
+        # digits are stored as a string, for quick conversion to
+        # integer in the case that we've already computed enough
+        # digits; the stored digits should always be correct
+        # (truncated, not rounded to nearest).
+        if p < 0:
+            raise ValueError("p should be nonnegative")
+
+        if p >= len(self.digits):
+            # compute p+3, p+6, p+9, ... digits; continue until at
+            # least one of the extra digits is nonzero
+            extra = 3
+            while True:
+                # compute p+extra digits, correct to within 1ulp
+                M = 10**(p+extra+2)
+                digits = str(_div_nearest(_ilog(10*M, M), 100))
+                if digits[-extra:] != '0'*extra:
+                    break
+                extra += 3
+            # keep all reliable digits so far; remove trailing zeros
+            # and next nonzero digit
+            self.digits = digits.rstrip('0')[:-1]
+        return int(self.digits[:p+1])
+
+_log10_digits = _Log10Memoize().getdigits
+
+def _iexp(x, M, L=8):
+    """Given integers x and M, M > 0, such that x/M is small in absolute
+    value, compute an integer approximation to M*exp(x/M).  For 0 <=
+    x/M <= 2.4, the absolute error in the result is bounded by 60 (and
+    is usually much smaller)."""
+
+    # Algorithm: to compute exp(z) for a real number z, first divide z
+    # by a suitable power R of 2 so that |z/2**R| < 2**-L.  Then
+    # compute expm1(z/2**R) = exp(z/2**R) - 1 using the usual Taylor
+    # series
+    #
+    #     expm1(x) = x + x**2/2! + x**3/3! + ...
+    #
+    # Now use the identity
+    #
+    #     expm1(2x) = expm1(x)*(expm1(x)+2)
+    #
+    # R times to compute the sequence expm1(z/2**R),
+    # expm1(z/2**(R-1)), ... , exp(z/2), exp(z).
+
+    # Find R such that x/2**R/M <= 2**-L
+    R = _nbits((long(x)<<L)//M)
+
+    # Taylor series.  (2**L)**T > M
+    T = -int(-10*len(str(M))//(3*L))
+    y = _div_nearest(x, T)
+    Mshift = long(M)<<R
+    for i in xrange(T-1, 0, -1):
+        y = _div_nearest(x*(Mshift + y), Mshift * i)
+
+    # Expansion
+    for k in xrange(R-1, -1, -1):
+        Mshift = long(M)<<(k+2)
+        y = _div_nearest(y*(y+Mshift), Mshift)
+
+    return M+y
+
+def _dexp(c, e, p):
+    """Compute an approximation to exp(c*10**e), with p decimal places of
+    precision.
+
+    Returns integers d, f such that:
+
+      10**(p-1) <= d <= 10**p, and
+      (d-1)*10**f < exp(c*10**e) < (d+1)*10**f
+
+    In other words, d*10**f is an approximation to exp(c*10**e) with p
+    digits of precision, and with an error in d of at most 1.  This is
+    almost, but not quite, the same as the error being < 1ulp: when d
+    = 10**(p-1) the error could be up to 10 ulp."""
+
+    # we'll call iexp with M = 10**(p+2), giving p+3 digits of precision
+    p += 2
+
+    # compute log(10) with extra precision = adjusted exponent of c*10**e
+    extra = max(0, e + len(str(c)) - 1)
+    q = p + extra
+
+    # compute quotient c*10**e/(log(10)) = c*10**(e+q)/(log(10)*10**q),
+    # rounding down
+    shift = e+q
+    if shift >= 0:
+        cshift = c*10**shift
+    else:
+        cshift = c//10**-shift
+    quot, rem = divmod(cshift, _log10_digits(q))
+
+    # reduce remainder back to original precision
+    rem = _div_nearest(rem, 10**extra)
+
+    # error in result of _iexp < 120;  error after division < 0.62
+    return _div_nearest(_iexp(rem, 10**p), 1000), quot - p + 3
+
+def _dpower(xc, xe, yc, ye, p):
+    """Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and
+    y = yc*10**ye, compute x**y.  Returns a pair of integers (c, e) such that:
+
+      10**(p-1) <= c <= 10**p, and
+      (c-1)*10**e < x**y < (c+1)*10**e
+
+    in other words, c*10**e is an approximation to x**y with p digits
+    of precision, and with an error in c of at most 1.  (This is
+    almost, but not quite, the same as the error being < 1ulp: when c
+    == 10**(p-1) we can only guarantee error < 10ulp.)
+
+    We assume that: x is positive and not equal to 1, and y is nonzero.
+    """
+
+    # Find b such that 10**(b-1) <= |y| <= 10**b
+    b = len(str(abs(yc))) + ye
+
+    # log(x) = lxc*10**(-p-b-1), to p+b+1 places after the decimal point
+    lxc = _dlog(xc, xe, p+b+1)
+
+    # compute product y*log(x) = yc*lxc*10**(-p-b-1+ye) = pc*10**(-p-1)
+    shift = ye-b
+    if shift >= 0:
+        pc = lxc*yc*10**shift
+    else:
+        pc = _div_nearest(lxc*yc, 10**-shift)
+
+    if pc == 0:
+        # we prefer a result that isn't exactly 1; this makes it
+        # easier to compute a correctly rounded result in __pow__
+        if ((len(str(xc)) + xe >= 1) == (yc > 0)): # if x**y > 1:
+            coeff, exp = 10**(p-1)+1, 1-p
+        else:
+            coeff, exp = 10**p-1, -p
+    else:
+        coeff, exp = _dexp(pc, -(p+1), p+1)
+        coeff = _div_nearest(coeff, 10)
+        exp += 1
+
+    return coeff, exp
+
+def _log10_lb(c, correction = {
+        '1': 100, '2': 70, '3': 53, '4': 40, '5': 31,
+        '6': 23, '7': 16, '8': 10, '9': 5}):
+    """Compute a lower bound for 100*log10(c) for a positive integer c."""
+    if c <= 0:
+        raise ValueError("The argument to _log10_lb should be nonnegative.")
+    str_c = str(c)
+    return 100*len(str_c) - correction[str_c[0]]
+
+##### Helper Functions ####################################################
+
+def _convert_other(other, raiseit=False):
+    """Convert other to Decimal.
+
+    Verifies that it's ok to use in an implicit construction.
+    """
+    if isinstance(other, Decimal):
+        return other
+    if isinstance(other, (int, long)):
+        return Decimal(other)
+    if raiseit:
+        raise TypeError("Unable to convert %s to Decimal" % other)
+    return NotImplemented
+
+##### Setup Specific Contexts ############################################
+
+# The default context prototype used by Context()
+# Is mutable, so that new contexts can have different default values
+
+DefaultContext = Context(
+        prec=28, rounding=ROUND_HALF_EVEN,
+        traps=[DivisionByZero, Overflow, InvalidOperation],
+        flags=[],
+        Emax=999999999,
+        Emin=-999999999,
+        capitals=1
+)
+
+# Pre-made alternate contexts offered by the specification
+# Don't change these; the user should be able to select these
+# contexts and be able to reproduce results from other implementations
+# of the spec.
+
+BasicContext = Context(
+        prec=9, rounding=ROUND_HALF_UP,
+        traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow],
+        flags=[],
+)
+
+ExtendedContext = Context(
+        prec=9, rounding=ROUND_HALF_EVEN,
+        traps=[],
+        flags=[],
+)
+
+
+##### crud for parsing strings #############################################
+#
+# Regular expression used for parsing numeric strings.  Additional
+# comments:
+#
+# 1. Uncomment the two '\s*' lines to allow leading and/or trailing
+# whitespace.  But note that the specification disallows whitespace in
+# a numeric string.
+#
+# 2. For finite numbers (not infinities and NaNs) the body of the
+# number between the optional sign and the optional exponent must have
+# at least one decimal digit, possibly after the decimal point.  The
+# lookahead expression '(?=\d|\.\d)' checks this.
+#
+# As the flag UNICODE is not enabled here, we're explicitly avoiding any
+# other meaning for \d than the numbers [0-9].
+
+import re
+_parser = re.compile(r"""        # A numeric string consists of:
+#    \s*
+    (?P<sign>[-+])?              # an optional sign, followed by either...
+    (
+        (?=[0-9]|\.[0-9])        # ...a number (with at least one digit)
+        (?P<int>[0-9]*)          # having a (possibly empty) integer part
+        (\.(?P<frac>[0-9]*))?    # followed by an optional fractional part
+        (E(?P<exp>[-+]?[0-9]+))? # followed by an optional exponent, or...
+    |
+        Inf(inity)?              # ...an infinity, or...
+    |
+        (?P<signal>s)?           # ...an (optionally signaling)
+        NaN                      # NaN
+        (?P<diag>[0-9]*)         # with (possibly empty) diagnostic info.
+    )
+#    \s*
+    \Z
+""", re.VERBOSE | re.IGNORECASE).match
+
+_all_zeros = re.compile('0*$').match
+_exact_half = re.compile('50*$').match
+
+##### PEP3101 support functions ##############################################
+# The functions parse_format_specifier and format_align have little to do
+# with the Decimal class, and could potentially be reused for other pure
+# Python numeric classes that want to implement __format__
+#
+# A format specifier for Decimal looks like:
+#
+#   [[fill]align][sign][0][minimumwidth][.precision][type]
+#
+
+_parse_format_specifier_regex = re.compile(r"""\A
+(?:
+   (?P<fill>.)?
+   (?P<align>[<>=^])
+)?
+(?P<sign>[-+ ])?
+(?P<zeropad>0)?
+(?P<minimumwidth>(?!0)\d+)?
+(?:\.(?P<precision>0|(?!0)\d+))?
+(?P<type>[eEfFgG%])?
+\Z
+""", re.VERBOSE)
+
+del re
+
+def _parse_format_specifier(format_spec):
+    """Parse and validate a format specifier.
+
+    Turns a standard numeric format specifier into a dict, with the
+    following entries:
+
+      fill: fill character to pad field to minimum width
+      align: alignment type, either '<', '>', '=' or '^'
+      sign: either '+', '-' or ' '
+      minimumwidth: nonnegative integer giving minimum width
+      precision: nonnegative integer giving precision, or None
+      type: one of the characters 'eEfFgG%', or None
+      unicode: either True or False (always True for Python 3.x)
+
+    """
+    m = _parse_format_specifier_regex.match(format_spec)
+    if m is None:
+        raise ValueError("Invalid format specifier: " + format_spec)
+
+    # get the dictionary
+    format_dict = m.groupdict()
+
+    # defaults for fill and alignment
+    fill = format_dict['fill']
+    align = format_dict['align']
+    if format_dict.pop('zeropad') is not None:
+        # in the face of conflict, refuse the temptation to guess
+        if fill is not None and fill != '0':
+            raise ValueError("Fill character conflicts with '0'"
+                             " in format specifier: " + format_spec)
+        if align is not None and align != '=':
+            raise ValueError("Alignment conflicts with '0' in "
+                             "format specifier: " + format_spec)
+        fill = '0'
+        align = '='
+    format_dict['fill'] = fill or ' '
+    format_dict['align'] = align or '<'
+
+    if format_dict['sign'] is None:
+        format_dict['sign'] = '-'
+
+    # turn minimumwidth and precision entries into integers.
+    # minimumwidth defaults to 0; precision remains None if not given
+    format_dict['minimumwidth'] = int(format_dict['minimumwidth'] or '0')
+    if format_dict['precision'] is not None:
+        format_dict['precision'] = int(format_dict['precision'])
+
+    # if format type is 'g' or 'G' then a precision of 0 makes little
+    # sense; convert it to 1.  Same if format type is unspecified.
+    if format_dict['precision'] == 0:
+        if format_dict['type'] in 'gG' or format_dict['type'] is None:
+            format_dict['precision'] = 1
+
+    # record whether return type should be str or unicode
+    format_dict['unicode'] = isinstance(format_spec, unicode)
+
+    return format_dict
+
+def _format_align(body, spec_dict):
+    """Given an unpadded, non-aligned numeric string, add padding and
+    aligment to conform with the given format specifier dictionary (as
+    output from parse_format_specifier).
+
+    It's assumed that if body is negative then it starts with '-'.
+    Any leading sign ('-' or '+') is stripped from the body before
+    applying the alignment and padding rules, and replaced in the
+    appropriate position.
+
+    """
+    # figure out the sign; we only examine the first character, so if
+    # body has leading whitespace the results may be surprising.
+    if len(body) > 0 and body[0] in '-+':
+        sign = body[0]
+        body = body[1:]
+    else:
+        sign = ''
+
+    if sign != '-':
+        if spec_dict['sign'] in ' +':
+            sign = spec_dict['sign']
+        else:
+            sign = ''
+
+    # how much extra space do we have to play with?
+    minimumwidth = spec_dict['minimumwidth']
+    fill = spec_dict['fill']
+    padding = fill*(max(minimumwidth - (len(sign+body)), 0))
+
+    align = spec_dict['align']
+    if align == '<':
+        result = padding + sign + body
+    elif align == '>':
+        result = sign + body + padding
+    elif align == '=':
+        result = sign + padding + body
+    else: #align == '^'
+        half = len(padding)//2
+        result = padding[:half] + sign + body + padding[half:]
+
+    # make sure that result is unicode if necessary
+    if spec_dict['unicode']:
+        result = unicode(result)
+
+    return result
+
+##### Useful Constants (internal use only) ################################
+
+# Reusable defaults
+Inf = Decimal('Inf')
+negInf = Decimal('-Inf')
+NaN = Decimal('NaN')
+Dec_0 = Decimal(0)
+Dec_p1 = Decimal(1)
+Dec_n1 = Decimal(-1)
+
+# Infsign[sign] is infinity w/ that sign
+Infsign = (Inf, negInf)
+
+
+
+if __name__ == '__main__':
+    import doctest, sys
+    doctest.testmod(sys.modules[__name__])