diff --git a/Lib/decimal.py b/Lib/decimal.py
index 2b9bc75..3ee078f 100644
--- a/Lib/decimal.py
+++ b/Lib/decimal.py
@@ -29,8 +29,8 @@
 
 Decimal floating point has finite precision with arbitrarily large bounds.
 
-The purpose of the module is to support arithmetic using familiar
-"schoolhouse" rules and to avoid the some of tricky representation
+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,
@@ -128,7 +128,7 @@
 
     # 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_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN', 'ROUND_05UP',
 
     # Functions for manipulating contexts
     'setcontext', 'getcontext', 'localcontext'
@@ -136,7 +136,7 @@
 
 import copy as _copy
 
-#Rounding
+# Rounding
 ROUND_DOWN = 'ROUND_DOWN'
 ROUND_HALF_UP = 'ROUND_HALF_UP'
 ROUND_HALF_EVEN = 'ROUND_HALF_EVEN'
@@ -144,12 +144,9 @@
 ROUND_FLOOR = 'ROUND_FLOOR'
 ROUND_UP = 'ROUND_UP'
 ROUND_HALF_DOWN = 'ROUND_HALF_DOWN'
+ROUND_05UP = 'ROUND_05UP'
 
-#Rounding decision (not part of the public API)
-NEVER_ROUND = 'NEVER_ROUND'    # Round in division (non-divmod), sqrt ONLY
-ALWAYS_ROUND = 'ALWAYS_ROUND'  # Every operation rounds at end.
-
-#Errors
+# Errors
 
 class DecimalException(ArithmeticError):
     """Base exception class.
@@ -179,14 +176,13 @@
 
     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
+    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.
 
@@ -194,8 +190,8 @@
 
     Something creates a signaling NaN
     -INF + INF
-     0 * (+-)INF
-     (+-)INF / (+-)INF
+    0 * (+-)INF
+    (+-)INF / (+-)INF
     x % 0
     (+-)INF % x
     x._rescale( non-integer )
@@ -204,11 +200,16 @@
     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:
-            if args[0] == 1: #sNaN, must drop 's' but keep diagnostics
-                return Decimal( (args[1]._sign, args[1]._int, 'n') )
+            ans = _dec_from_triple(args[0]._sign, args[0]._int, 'n', True)
+            return ans._fix_nan(context)
         return NaN
 
 class ConversionSyntax(InvalidOperation):
@@ -216,11 +217,10 @@
 
     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].
+    syntax.  The result is [0,qNaN].
     """
-
     def handle(self, context, *args):
-        return (0, (0,), 'n') #Passed to something which uses a tuple.
+        return NaN
 
 class DivisionByZero(DecimalException, ZeroDivisionError):
     """Division by 0.
@@ -235,9 +235,7 @@
     -0, for power.
     """
 
-    def handle(self, context, sign, double = None, *args):
-        if double is not None:
-            return (Infsign[sign],)*2
+    def handle(self, context, sign, *args):
         return Infsign[sign]
 
 class DivisionImpossible(InvalidOperation):
@@ -245,23 +243,21 @@
 
     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].
+    longer than precision).  The result is [0,qNaN].
     """
 
     def handle(self, context, *args):
-        return (NaN, NaN)
+        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].
+    the dividend is also zero.  The result is [0,qNaN].
     """
 
-    def handle(self, context, tup=None, *args):
-        if tup is not None:
-            return (NaN, NaN) #for 0 %0, 0 // 0
+    def handle(self, context, *args):
         return NaN
 
 class Inexact(DecimalException):
@@ -269,23 +265,22 @@
 
     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
+    were non-zero), or if an overflow or underflow condition occurs.  The
     result in all cases is unchanged.
 
     The inexact signal may be tested (or trapped) to determine if a given
     operation (or sequence of operations) was inexact.
     """
-    pass
 
 class InvalidContext(InvalidOperation):
     """Invalid context.  Unknown rounding, for example.
 
     This occurs and signals invalid-operation if an invalid context was
-    detected during an operation. This can occur if contexts are not checked
+    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].
+    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):
@@ -296,25 +291,23 @@
 
     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
+    coefficient), or if an overflow or underflow condition occurs.  The
     result in all cases is unchanged.
 
     The rounded signal may be tested (or trapped) to determine if a given
     operation (or sequence of operations) caused a loss of precision.
     """
-    pass
 
 class Subnormal(DecimalException):
     """Exponent < Emin before rounding.
 
     This occurs and signals subnormal whenever the result of a conversion or
     operation is subnormal (that is, its adjusted exponent is less than
-    Emin, before any rounding). The result in all cases is unchanged.
+    Emin, before any rounding).  The result in all cases is unchanged.
 
     The subnormal signal may be tested (or trapped) to determine if a given
     or operation (or sequence of operations) yielded a subnormal result.
     """
-    pass
 
 class Overflow(Inexact, Rounded):
     """Numerical overflow.
@@ -328,30 +321,30 @@
 
     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
+    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
+    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 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
+    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):
+                                ROUND_HALF_DOWN, ROUND_UP):
             return Infsign[sign]
         if sign == 0:
             if context.rounding == ROUND_CEILING:
                 return Infsign[sign]
-            return Decimal((sign, (9,)*context.prec,
-                            context.Emax-context.prec+1))
+            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 Decimal( (sign, (9,)*context.prec,
-                             context.Emax-context.prec+1))
+            return _dec_from_triple(sign, '9'*context.prec,
+                             context.Emax-context.prec+1)
 
 
 class Underflow(Inexact, Rounded, Subnormal):
@@ -360,10 +353,10 @@
     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.
+    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
+    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.
@@ -379,7 +372,7 @@
                   DivisionUndefined:InvalidOperation,
                   InvalidContext:InvalidOperation}
 
-##### Context Functions #######################################
+##### 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
@@ -392,7 +385,7 @@
 except ImportError:
     # Python was compiled without threads; create a mock object instead
     import sys
-    class MockThreading:
+    class MockThreading(object):
         def local(self, sys=sys):
             return sys.modules[__name__]
     threading = MockThreading()
@@ -403,8 +396,8 @@
 
 except AttributeError:
 
-    #To fix reloading, force it to create a new context
-    #Old contexts have different exceptions in their dicts, making problems.
+    # 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__
 
@@ -469,14 +462,14 @@
                  ctx.prec += 2
                  # Rest of sin calculation algorithm
                  # uses a precision 2 greater than normal
-             return +s # Convert result to normal precision
+             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
+             return +s  # Convert result to normal context
 
     """
     # The string below can't be included in the docstring until Python 2.6
@@ -502,7 +495,7 @@
     return _ContextManager(ctx)
 
 
-##### Decimal class ###########################################
+##### Decimal class #######################################################
 
 class Decimal(object):
     """Floating point class for decimal arithmetic."""
@@ -518,7 +511,7 @@
 
         >>> Decimal('3.14')              # string input
         Decimal("3.14")
-        >>> Decimal((0, (3, 1, 4), -2))  # tuple input (sign, digit_tuple, exponent)
+        >>> Decimal((0, (3, 1, 4), -2))  # tuple (sign, digit_tuple, exponent)
         Decimal("3.14")
         >>> Decimal(314)                 # int or long
         Decimal("314")
@@ -526,14 +519,67 @@
         Decimal("314")
         """
 
-        self = object.__new__(cls)
-        self._is_special = False
+        # 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.
 
-        # From an internal working value
-        if isinstance(value, _WorkRep):
-            self._sign = value.sign
-            self._int = tuple(map(int, str(value.int)))
-            self._exp = int(value.exp)
+        self = object.__new__(cls)
+
+        # From a string
+        # REs insist on real strings, so we can too.
+        if isinstance(value, basestring):
+            m = _parser(value)
+            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 = (intpart+fracpart).lstrip('0') or '0'
+                    self._exp = exp - len(fracpart)
+                else:
+                    self._int = 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 = 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
@@ -544,76 +590,63 @@
             self._is_special  = value._is_special
             return self
 
-        # From an integer
-        if isinstance(value, (int,long)):
-            if value >= 0:
-                self._sign = 0
-            else:
-                self._sign = 1
-            self._exp = 0
-            self._int = tuple(map(int, str(abs(value))))
+        # 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 arguments'
-            if value[0] not in (0,1):
-                raise ValueError, 'Invalid sign'
-            for digit in value[1]:
-                if not isinstance(digit, (int,long)) or digit < 0:
-                    raise ValueError, "The second value in the tuple must be composed of non negative integer elements."
-
+                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]
-            self._int  = tuple(value[1])
-            if value[2] in ('F','n','N'):
+            if value[2] == 'F':
+                # infinity: value[1] is ignored
+                self._int = '0'
                 self._exp = value[2]
                 self._is_special = True
             else:
-                self._exp  = int(value[2])
+                # 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")
 
-        # Other argument types may require the context during interpretation
-        if context is None:
-            context = getcontext()
-
-        # From a string
-        # REs insist on real strings, so we can too.
-        if isinstance(value, basestring):
-            if _isinfinity(value):
-                self._exp = 'F'
-                self._int = (0,)
-                self._is_special = True
-                if _isinfinity(value) == 1:
-                    self._sign = 0
-                else:
-                    self._sign = 1
-                return self
-            if _isnan(value):
-                sig, sign, diag = _isnan(value)
-                self._is_special = True
-                if len(diag) > context.prec: #Diagnostic info too long
-                    self._sign, self._int, self._exp = \
-                                context._raise_error(ConversionSyntax)
-                    return self
-                if sig == 1:
-                    self._exp = 'n' #qNaN
-                else: #sig == 2
-                    self._exp = 'N' #sNaN
-                self._sign = sign
-                self._int = tuple(map(int, diag)) #Diagnostic info
-                return self
-            try:
-                self._sign, self._int, self._exp = _string2exact(value)
-            except ValueError:
-                self._is_special = True
-                self._sign, self._int, self._exp = context._raise_error(ConversionSyntax)
-            return self
-
         raise TypeError("Cannot convert %r to Decimal" % value)
 
     def _isnan(self):
@@ -644,7 +677,7 @@
             return 1
         return 0
 
-    def _check_nans(self, other = None, context=None):
+    def _check_nans(self, other=None, context=None):
         """Returns whether the number is not actually one.
 
         if self, other are sNaN, signal
@@ -666,43 +699,47 @@
 
             if self_is_nan == 2:
                 return context._raise_error(InvalidOperation, 'sNaN',
-                                        1, self)
+                                        self)
             if other_is_nan == 2:
                 return context._raise_error(InvalidOperation, 'sNaN',
-                                        1, other)
+                                        other)
             if self_is_nan:
-                return self
+                return self._fix_nan(context)
 
-            return other
+            return other._fix_nan(context)
         return 0
 
     def __nonzero__(self):
-        """Is the number non-zero?
+        """Return True if self is nonzero; otherwise return False.
 
-        0 if self == 0
-        1 if self != 0
+        NaNs and infinities are considered nonzero.
         """
-        if self._is_special:
-            return 1
-        return sum(self._int) != 0
+        return self._is_special or self._int != '0'
 
-    def __cmp__(self, other, context=None):
+    def __cmp__(self, other):
         other = _convert_other(other)
         if other is NotImplemented:
-            return other
+            # Never return NotImplemented
+            return 1
 
         if self._is_special or other._is_special:
-            ans = self._check_nans(other, context)
-            if ans:
-                return 1 # Comparison involving NaN's always reports self > other
+            # check for nans, without raising on a signaling nan
+            if self._isnan() or other._isnan():
+                return 1  # Comparison involving NaN's always reports self > other
 
             # INF = INF
             return cmp(self._isinfinity(), other._isinfinity())
 
-        if not self and not other:
-            return 0 #If both 0, sign comparison isn't certain.
+        # 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 different signs, neg one is less
         if other._sign < self._sign:
             return -1
         if self._sign < other._sign:
@@ -710,35 +747,15 @@
 
         self_adjusted = self.adjusted()
         other_adjusted = other.adjusted()
-        if self_adjusted == other_adjusted and \
-           self._int + (0,)*(self._exp - other._exp) == \
-           other._int + (0,)*(other._exp - self._exp):
-            return 0 #equal, except in precision. ([0]*(-x) = [])
-        elif self_adjusted > other_adjusted and self._int[0] != 0:
+        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
-        elif self_adjusted < other_adjusted and other._int[0] != 0:
+        else: # self_adjusted < other_adjusted
             return -((-1)**self._sign)
 
-        # Need to round, so make sure we have a valid context
-        if context is None:
-            context = getcontext()
-
-        context = context._shallow_copy()
-        rounding = context._set_rounding(ROUND_UP) #round away from 0
-
-        flags = context._ignore_all_flags()
-        res = self.__sub__(other, context=context)
-
-        context._regard_flags(*flags)
-
-        context.rounding = rounding
-
-        if not res:
-            return 0
-        elif res._sign:
-            return -1
-        return 1
-
     def __eq__(self, other):
         if not isinstance(other, (Decimal, int, long)):
             return NotImplemented
@@ -758,126 +775,109 @@
         NaN => one is NaN
         Like __cmp__, but returns Decimal instances.
         """
-        other = _convert_other(other)
-        if other is NotImplemented:
-            return other
+        other = _convert_other(other, raiseit=True)
 
-        #compare(NaN, NaN) = NaN
+        # Compare(NaN, NaN) = NaN
         if (self._is_special or other and other._is_special):
             ans = self._check_nans(other, context)
             if ans:
                 return ans
 
-        return Decimal(self.__cmp__(other, context))
+        return Decimal(self.__cmp__(other))
 
     def __hash__(self):
         """x.__hash__() <==> hash(x)"""
         # Decimal integers must hash the same as the ints
-        # Non-integer decimals are normalized and hashed as strings
-        # Normalization assures that hash(100E-1) == hash(10)
+        #
+        # 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))
-        i = int(self)
-        if self == Decimal(i):
-            return hash(i)
-        assert self.__nonzero__()   # '-0' handled by integer case
-        return hash(str(self.normalize()))
+        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 (self._sign, self._int, self._exp)
+        return (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 = 0, context=None):
+    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._isnan():
-                minus = '-'*self._sign
-                if self._int == (0,):
-                    info = ''
-                else:
-                    info = ''.join(map(str, self._int))
-                if self._isnan() == 2:
-                    return minus + 'sNaN' + info
-                return minus + 'NaN' + info
-            if self._isinfinity():
-                minus = '-'*self._sign
-                return minus + 'Infinity'
+            if self._exp == 'F':
+                return sign + 'Infinity'
+            elif self._exp == 'n':
+                return sign + 'NaN' + self._int
+            else: # self._exp == 'N'
+                return sign + 'sNaN' + self._int
 
-        if context is None:
-            context = getcontext()
+        # number of digits of self._int to left of decimal point
+        leftdigits = self._exp + len(self._int)
 
-        tmp = map(str, self._int)
-        numdigits = len(self._int)
-        leftdigits = self._exp + numdigits
-        if eng and not self: #self = 0eX wants 0[.0[0]]eY, not [[0]0]0eY
-            if self._exp < 0 and self._exp >= -6: #short, no need for e/E
-                s = '-'*self._sign + '0.' + '0'*(abs(self._exp))
-                return s
-            #exp is closest mult. of 3 >= self._exp
-            exp = ((self._exp - 1)// 3 + 1) * 3
-            if exp != self._exp:
-                s = '0.'+'0'*(exp - self._exp)
-            else:
-                s = '0'
-            if exp != 0:
-                if context.capitals:
-                    s += 'E'
-                else:
-                    s += 'e'
-                if exp > 0:
-                    s += '+' #0.0e+3, not 0.0e3
-                s += str(exp)
-            s = '-'*self._sign + s
-            return s
-        if eng:
-            dotplace = (leftdigits-1)%3+1
-            adjexp = leftdigits -1 - (leftdigits-1)%3
-        else:
-            adjexp = leftdigits-1
+        # dotplace 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
-        if self._exp == 0:
-            pass
-        elif self._exp < 0 and adjexp >= 0:
-            tmp.insert(leftdigits, '.')
-        elif self._exp < 0 and adjexp >= -6:
-            tmp[0:0] = ['0'] * int(-leftdigits)
-            tmp.insert(0, '0.')
+        elif self._int == '0':
+            # engineering notation, zero
+            dotplace = (leftdigits + 1) % 3 - 1
         else:
-            if numdigits > dotplace:
-                tmp.insert(dotplace, '.')
-            elif numdigits < dotplace:
-                tmp.extend(['0']*(dotplace-numdigits))
-            if adjexp:
-                if not context.capitals:
-                    tmp.append('e')
-                else:
-                    tmp.append('E')
-                    if adjexp > 0:
-                        tmp.append('+')
-                tmp.append(str(adjexp))
-        if eng:
-            while tmp[0:1] == ['0']:
-                tmp[0:1] = []
-            if len(tmp) == 0 or tmp[0] == '.' or tmp[0].lower() == 'e':
-                tmp[0:0] = ['0']
-        if self._sign:
-            tmp.insert(0, '-')
+            # engineering notation, nonzero
+            dotplace = (leftdigits - 1) % 3 + 1
 
-        return ''.join(tmp)
+        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.
@@ -887,7 +887,7 @@
 
         Same rules for when in exponential and when as a value as in __str__.
         """
-        return self.__str__(eng=1, context=context)
+        return self.__str__(eng=True, context=context)
 
     def __neg__(self, context=None):
         """Returns a copy with the sign switched.
@@ -901,17 +901,13 @@
 
         if not self:
             # -Decimal('0') is Decimal('0'), not Decimal('-0')
-            sign = 0
-        elif self._sign:
-            sign = 0
+            ans = self.copy_abs()
         else:
-            sign = 1
+            ans = self.copy_negate()
 
         if context is None:
             context = getcontext()
-        if context._rounding_decision == ALWAYS_ROUND:
-            return Decimal((sign, self._int, self._exp))._fix(context)
-        return Decimal( (sign, self._int, self._exp))
+        return ans._fix(context)
 
     def __pos__(self, context=None):
         """Returns a copy, unless it is a sNaN.
@@ -923,37 +919,31 @@
             if ans:
                 return ans
 
-        sign = self._sign
         if not self:
             # + (-0) = 0
-            sign = 0
+            ans = self.copy_abs()
+        else:
+            ans = Decimal(self)
 
         if context is None:
             context = getcontext()
+        return ans._fix(context)
 
-        if context._rounding_decision == ALWAYS_ROUND:
-            ans = self._fix(context)
-        else:
-            ans = Decimal(self)
-        ans._sign = sign
-        return ans
-
-    def __abs__(self, round=1, context=None):
+    def __abs__(self, round=True, context=None):
         """Returns the absolute value of self.
 
-        If the second argument is 0, do not round.
+        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 not round:
-            if context is None:
-                context = getcontext()
-            context = context._shallow_copy()
-            context._set_rounding_decision(NEVER_ROUND)
-
         if self._sign:
             ans = self.__neg__(context=context)
         else:
@@ -979,66 +969,63 @@
                 return ans
 
             if self._isinfinity():
-                #If both INF, same sign => same as both, opposite => error.
+                # If both INF, same sign => same as both, opposite => error.
                 if self._sign != other._sign and other._isinfinity():
                     return context._raise_error(InvalidOperation, '-INF + INF')
                 return Decimal(self)
             if other._isinfinity():
-                return Decimal(other)  #Can't both be infinity here
-
-        shouldround = context._rounding_decision == ALWAYS_ROUND
+                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.
+            # If the answer is 0, the sign should be negative, in this case.
             negativezero = 1
 
         if not self and not other:
             sign = min(self._sign, other._sign)
             if negativezero:
                 sign = 1
-            return Decimal( (sign, (0,), exp))
+            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, watchexp=0, context=context)
-            if shouldround:
-                ans = ans._fix(context)
+            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, watchexp=0, context=context)
-            if shouldround:
-                ans = ans._fix(context)
+            ans = self._rescale(exp, context.rounding)
+            ans = ans._fix(context)
             return ans
 
         op1 = _WorkRep(self)
         op2 = _WorkRep(other)
-        op1, op2 = _normalize(op1, op2, shouldround, context.prec)
+        op1, op2 = _normalize(op1, op2, context.prec)
 
         result = _WorkRep()
         if op1.sign != op2.sign:
             # Equal and opposite
             if op1.int == op2.int:
-                if exp < context.Etiny():
-                    exp = context.Etiny()
-                    context._raise_error(Clamped)
-                return Decimal((negativezero, (0,), exp))
+                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)
+                # 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.
+                # 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
+        # Now, op1 > abs(op2) > 0
 
         if op2.sign == 0:
             result.int = op1.int + op2.int
@@ -1047,14 +1034,13 @@
 
         result.exp = op1.exp
         ans = Decimal(result)
-        if shouldround:
-            ans = ans._fix(context)
+        ans = ans._fix(context)
         return ans
 
     __radd__ = __add__
 
     def __sub__(self, other, context=None):
-        """Return self + (-other)"""
+        """Return self - other"""
         other = _convert_other(other)
         if other is NotImplemented:
             return other
@@ -1064,57 +1050,16 @@
             if ans:
                 return ans
 
-        # -Decimal(0) = Decimal(0), which we don't want since
-        # (-0 - 0 = -0 + (-0) = -0, but -0 + 0 = 0.)
-        # so we change the sign directly to a copy
-        tmp = Decimal(other)
-        tmp._sign = 1-tmp._sign
-
-        return self.__add__(tmp, context=context)
+        # 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)"""
+        """Return other - self"""
         other = _convert_other(other)
         if other is NotImplemented:
             return other
 
-        tmp = Decimal(self)
-        tmp._sign = 1 - tmp._sign
-        return other.__add__(tmp, context=context)
-
-    def _increment(self, round=1, context=None):
-        """Special case of add, adding 1eExponent
-
-        Since it is common, (rounding, for example) this adds
-        (sign)*one E self._exp to the number more efficiently than add.
-
-        For example:
-        Decimal('5.624e10')._increment() == Decimal('5.625e10')
-        """
-        if self._is_special:
-            ans = self._check_nans(context=context)
-            if ans:
-                return ans
-
-            return Decimal(self) # Must be infinite, and incrementing makes no difference
-
-        L = list(self._int)
-        L[-1] += 1
-        spot = len(L)-1
-        while L[spot] == 10:
-            L[spot] = 0
-            if spot == 0:
-                L[0:0] = [1]
-                break
-            L[spot-1] += 1
-            spot -= 1
-        ans = Decimal((self._sign, L, self._exp))
-
-        if context is None:
-            context = getcontext()
-        if round and context._rounding_decision == ALWAYS_ROUND:
-            ans = ans._fix(context)
-        return ans
+        return other.__sub__(self, context=context)
 
     def __mul__(self, other, context=None):
         """Return self * other.
@@ -1146,60 +1091,38 @@
                 return Infsign[resultsign]
 
         resultexp = self._exp + other._exp
-        shouldround = context._rounding_decision == ALWAYS_ROUND
 
         # Special case for multiplying by zero
         if not self or not other:
-            ans = Decimal((resultsign, (0,), resultexp))
-            if shouldround:
-                #Fixing in case the exponent is out of bounds
-                ans = ans._fix(context)
+            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 = Decimal((resultsign, other._int, resultexp))
-            if shouldround:
-                ans = ans._fix(context)
+        if self._int == '1':
+            ans = _dec_from_triple(resultsign, other._int, resultexp)
+            ans = ans._fix(context)
             return ans
-        if other._int == (1,):
-            ans = Decimal((resultsign, self._int, resultexp))
-            if shouldround:
-                ans = ans._fix(context)
+        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 = Decimal( (resultsign, map(int, str(op1.int * op2.int)), resultexp))
-        if shouldround:
-            ans = ans._fix(context)
+        ans = _dec_from_triple(resultsign, str(op1.int * op2.int), resultexp)
+        ans = ans._fix(context)
 
         return ans
     __rmul__ = __mul__
 
     def __div__(self, other, context=None):
         """Return self / other."""
-        return self._divide(other, context=context)
-    __truediv__ = __div__
-
-    def _divide(self, other, divmod = 0, context=None):
-        """Return a / b, to context.prec precision.
-
-        divmod:
-        0 => true division
-        1 => (a //b, a%b)
-        2 => a //b
-        3 => a%b
-
-        Actually, if divmod is 2 or 3 a tuple is returned, but errors for
-        computing the other value are not raised.
-        """
         other = _convert_other(other)
         if other is NotImplemented:
-            if divmod in (0, 1):
-                return NotImplemented
-            return (NotImplemented, NotImplemented)
+            return NotImplemented
 
         if context is None:
             context = getcontext()
@@ -1209,145 +1132,85 @@
         if self._is_special or other._is_special:
             ans = self._check_nans(other, context)
             if ans:
-                if divmod:
-                    return (ans, ans)
                 return ans
 
             if self._isinfinity() and other._isinfinity():
-                if divmod:
-                    return (context._raise_error(InvalidOperation,
-                                            '(+-)INF // (+-)INF'),
-                            context._raise_error(InvalidOperation,
-                                            '(+-)INF % (+-)INF'))
                 return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF')
 
             if self._isinfinity():
-                if divmod == 1:
-                    return (Infsign[sign],
-                            context._raise_error(InvalidOperation, 'INF % x'))
-                elif divmod == 2:
-                    return (Infsign[sign], NaN)
-                elif divmod == 3:
-                    return (Infsign[sign],
-                            context._raise_error(InvalidOperation, 'INF % x'))
                 return Infsign[sign]
 
             if other._isinfinity():
-                if divmod:
-                    return (Decimal((sign, (0,), 0)), Decimal(self))
                 context._raise_error(Clamped, 'Division by infinity')
-                return Decimal((sign, (0,), context.Etiny()))
+                return _dec_from_triple(sign, '0', context.Etiny())
 
         # Special cases for zeroes
-        if not self and not other:
-            if divmod:
-                return context._raise_error(DivisionUndefined, '0 / 0', 1)
-            return context._raise_error(DivisionUndefined, '0 / 0')
-
-        if not self:
-            if divmod:
-                otherside = Decimal(self)
-                otherside._exp = min(self._exp, other._exp)
-                return (Decimal((sign, (0,), 0)),  otherside)
-            exp = self._exp - other._exp
-            if exp < context.Etiny():
-                exp = context.Etiny()
-                context._raise_error(Clamped, '0e-x / y')
-            if exp > context.Emax:
-                exp = context.Emax
-                context._raise_error(Clamped, '0e+x / y')
-            return Decimal( (sign, (0,), exp) )
-
         if not other:
-            if divmod:
-                return context._raise_error(DivisionByZero, 'divmod(x,0)',
-                                           sign, 1)
+            if not self:
+                return context._raise_error(DivisionUndefined, '0 / 0')
             return context._raise_error(DivisionByZero, 'x / 0', sign)
 
-        #OK, so neither = 0, INF or NaN
+        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
 
-        shouldround = context._rounding_decision == ALWAYS_ROUND
+        ans = _dec_from_triple(sign, str(coeff), exp)
+        return ans._fix(context)
 
-        #If we're dividing into ints, and self < other, stop.
-        #self.__abs__(0) does not round.
-        if divmod and (self.__abs__(0, context) < other.__abs__(0, context)):
+    __truediv__ = __div__
 
-            if divmod == 1 or divmod == 3:
-                exp = min(self._exp, other._exp)
-                ans2 = self._rescale(exp, context=context, watchexp=0)
-                if shouldround:
-                    ans2 = ans2._fix(context)
-                return (Decimal( (sign, (0,), 0) ),
-                        ans2)
+    def _divide(self, other, context):
+        """Return (self // other, self % other), to context.prec precision.
 
-            elif divmod == 2:
-                #Don't round the mod part, if we don't need it.
-                return (Decimal( (sign, (0,), 0) ), Decimal(self))
+        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)
 
-        op1 = _WorkRep(self)
-        op2 = _WorkRep(other)
-        op1, op2, adjust = _adjust_coefficients(op1, op2)
-        res = _WorkRep( (sign, 0, (op1.exp - op2.exp)) )
-        if divmod and res.exp > context.prec + 1:
-            return context._raise_error(DivisionImpossible)
+        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))
 
-        prec_limit = 10 ** context.prec
-        while 1:
-            while op2.int <= op1.int:
-                res.int += 1
-                op1.int -= op2.int
-            if res.exp == 0 and divmod:
-                if res.int >= prec_limit and shouldround:
-                    return context._raise_error(DivisionImpossible)
-                otherside = Decimal(op1)
-                frozen = context._ignore_all_flags()
-
-                exp = min(self._exp, other._exp)
-                otherside = otherside._rescale(exp, context=context, watchexp=0)
-                context._regard_flags(*frozen)
-                if shouldround:
-                    otherside = otherside._fix(context)
-                return (Decimal(res), otherside)
-
-            if op1.int == 0 and adjust >= 0 and not divmod:
-                break
-            if res.int >= prec_limit and shouldround:
-                if divmod:
-                    return context._raise_error(DivisionImpossible)
-                shouldround=1
-                # Really, the answer is a bit higher, so adding a one to
-                # the end will make sure the rounding is right.
-                if op1.int != 0:
-                    res.int *= 10
-                    res.int += 1
-                    res.exp -= 1
-
-                break
-            res.int *= 10
-            res.exp -= 1
-            adjust += 1
-            op1.int *= 10
-            op1.exp -= 1
-
-            if res.exp == 0 and divmod and op2.int > op1.int:
-                #Solves an error in precision.  Same as a previous block.
-
-                if res.int >= prec_limit and shouldround:
-                    return context._raise_error(DivisionImpossible)
-                otherside = Decimal(op1)
-                frozen = context._ignore_all_flags()
-
-                exp = min(self._exp, other._exp)
-                otherside = otherside._rescale(exp, context=context)
-
-                context._regard_flags(*frozen)
-
-                return (Decimal(res), otherside)
-
-        ans = Decimal(res)
-        if shouldround:
-            ans = ans._fix(context)
-        return ans
+        # Here the quotient is too large to be representable
+        ans = context._raise_error(DivisionImpossible,
+                                   'quotient too large in //, % or divmod')
+        return ans, ans
 
     def __rdiv__(self, other, context=None):
         """Swaps self/other and returns __div__."""
@@ -1359,9 +1222,39 @@
 
     def __divmod__(self, other, context=None):
         """
-        (self // other, self % other)
+        Return (self // other, self % other)
         """
-        return self._divide(other, 1, context)
+        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__."""
@@ -1378,15 +1271,24 @@
         if other is NotImplemented:
             return other
 
-        if self._is_special or other._is_special:
-            ans = self._check_nans(other, context)
-            if ans:
-                return ans
+        if context is None:
+            context = getcontext()
 
-        if self and not other:
-            return context._raise_error(InvalidOperation, 'x % 0')
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
 
-        return self._divide(other, 3, context)[1]
+        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__."""
@@ -1399,84 +1301,104 @@
         """
         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 self._is_special or other._is_special:
-            ans = self._check_nans(other, context)
-            if ans:
-                return ans
-        if self and not other:
-            return context._raise_error(InvalidOperation, 'x % 0')
-
         if context is None:
             context = getcontext()
-        # If DivisionImpossible causes an error, do not leave Rounded/Inexact
-        # ignored in the calling function.
-        context = context._shallow_copy()
-        flags = context._ignore_flags(Rounded, Inexact)
-        #keep DivisionImpossible flags
-        (side, r) = self.__divmod__(other, context=context)
 
-        if r._isnan():
-            context._regard_flags(*flags)
-            return r
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
 
-        context = context._shallow_copy()
-        rounding = context._set_rounding_decision(NEVER_ROUND)
-
-        if other._sign:
-            comparison = other.__div__(Decimal(-2), context=context)
-        else:
-            comparison = other.__div__(Decimal(2), context=context)
-
-        context._set_rounding_decision(rounding)
-        context._regard_flags(*flags)
-
-        s1, s2 = r._sign, comparison._sign
-        r._sign, comparison._sign = 0, 0
-
-        if r < comparison:
-            r._sign, comparison._sign = s1, s2
-            #Get flags now
-            self.__divmod__(other, context=context)
-            return r._fix(context)
-        r._sign, comparison._sign = s1, s2
-
-        rounding = context._set_rounding_decision(NEVER_ROUND)
-
-        (side, r) = self.__divmod__(other, context=context)
-        context._set_rounding_decision(rounding)
-        if r._isnan():
-            return r
-
-        decrease = not side._iseven()
-        rounding = context._set_rounding_decision(NEVER_ROUND)
-        side = side.__abs__(context=context)
-        context._set_rounding_decision(rounding)
-
-        s1, s2 = r._sign, comparison._sign
-        r._sign, comparison._sign = 0, 0
-        if r > comparison or decrease and r == comparison:
-            r._sign, comparison._sign = s1, s2
-            context.prec += 1
-            if len(side.__add__(Decimal(1), context=context)._int) >= context.prec:
-                context.prec -= 1
-                return context._raise_error(DivisionImpossible)[1]
-            context.prec -= 1
-            if self._sign == other._sign:
-                r = r.__sub__(other, context=context)
+        if self._isinfinity():
+            if other._isinfinity():
+                return context._raise_error(InvalidOperation, 'INF // INF')
             else:
-                r = r.__add__(other, context=context)
-        else:
-            r._sign, comparison._sign = s1, s2
+                return Infsign[self._sign ^ other._sign]
 
-        return r._fix(context)
+        if not other:
+            if self:
+                return context._raise_error(DivisionByZero, 'x // 0',
+                                            self._sign ^ other._sign)
+            else:
+                return context._raise_error(DivisionUndefined, '0 // 0')
 
-    def __floordiv__(self, other, context=None):
-        """self // other"""
-        return self._divide(other, 2, context)[0]
+        return self._divide(other, context)[0]
 
     def __rfloordiv__(self, other, context=None):
         """Swaps self/other and returns __floordiv__."""
@@ -1496,15 +1418,12 @@
                 context = getcontext()
                 return context._raise_error(InvalidContext)
             elif self._isinfinity():
-                raise OverflowError, "Cannot convert infinity to long"
+                raise OverflowError("Cannot convert infinity to long")
+        s = (-1)**self._sign
         if self._exp >= 0:
-            s = ''.join(map(str, self._int)) + '0'*self._exp
+            return s*int(self._int)*10**self._exp
         else:
-            s = ''.join(map(str, self._int))[:self._exp]
-        if s == '':
-            s = '0'
-        sign = '-'*self._sign
-        return int(sign + s)
+            return s*int(self._int[:self._exp] or '0')
 
     def __long__(self):
         """Converts to a long.
@@ -1513,6 +1432,18 @@
         """
         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.
 
@@ -1522,301 +1453,673 @@
         self - Decimal instance
         context - context used.
         """
-        if self._is_special:
-            return self
-        if context is None:
-            context = getcontext()
-        prec = context.prec
-        ans = self._fixexponents(context)
-        if len(ans._int) > prec:
-            ans = ans._round(prec, context=context)
-            ans = ans._fixexponents(context)
-        return ans
-
-    def _fixexponents(self, context):
-        """Fix the exponents and return a copy with the exponent in bounds.
-        Only call if known to not be a special value.
-        """
-        folddown = context._clamp
-        Emin = context.Emin
-        ans = self
-        ans_adjusted = ans.adjusted()
-        if ans_adjusted < Emin:
-            Etiny = context.Etiny()
-            if ans._exp < Etiny:
-                if not ans:
-                    ans = Decimal(self)
-                    ans._exp = Etiny
-                    context._raise_error(Clamped)
-                    return ans
-                ans = ans._rescale(Etiny, context=context)
-                #It isn't zero, and exp < Emin => subnormal
-                context._raise_error(Subnormal)
-                if context.flags[Inexact]:
-                    context._raise_error(Underflow)
-            else:
-                if ans:
-                    #Only raise subnormal if non-zero.
-                    context._raise_error(Subnormal)
-        else:
-            Etop = context.Etop()
-            if folddown and ans._exp > Etop:
-                context._raise_error(Clamped)
-                ans = ans._rescale(Etop, context=context)
-            else:
-                Emax = context.Emax
-                if ans_adjusted > Emax:
-                    if not ans:
-                        ans = Decimal(self)
-                        ans._exp = Emax
-                        context._raise_error(Clamped)
-                        return ans
-                    context._raise_error(Inexact)
-                    context._raise_error(Rounded)
-                    return context._raise_error(Overflow, 'above Emax', ans._sign)
-        return ans
-
-    def _round(self, prec=None, rounding=None, context=None):
-        """Returns a rounded version of self.
-
-        You can specify the precision or rounding method.  Otherwise, the
-        context determines it.
-        """
 
         if self._is_special:
-            ans = self._check_nans(context=context)
-            if ans:
-                return ans
-
-            if self._isinfinity():
+            if self._isnan():
+                # decapitate payload if necessary
+                return self._fix_nan(context)
+            else:
+                # self is +/-Infinity; return unaltered
                 return Decimal(self)
 
-        if context is None:
-            context = getcontext()
-
-        if rounding is None:
-            rounding = context.rounding
-        if prec is None:
-            prec = context.prec
-
+        # 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:
-            if prec <= 0:
-                dig = (0,)
-                exp = len(self._int) - prec + self._exp
+            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:
-                dig = (0,) * prec
-                exp = len(self._int) + self._exp - prec
-            ans = Decimal((self._sign, dig, exp))
+                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 ans
+            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
 
-        if prec == 0:
-            temp = Decimal(self)
-            temp._int = (0,)+temp._int
-            prec = 1
-        elif prec < 0:
-            exp = self._exp + len(self._int) - prec - 1
-            temp = Decimal( (self._sign, (0, 1), exp))
-            prec = 1
-        else:
-            temp = Decimal(self)
-
-        numdigits = len(temp._int)
-        if prec == numdigits:
-            return temp
-
-        # See if we need to extend precision
-        expdiff = prec - numdigits
-        if expdiff > 0:
-            tmp = list(temp._int)
-            tmp.extend([0] * expdiff)
-            ans =  Decimal( (temp._sign, tmp, temp._exp - expdiff))
-            return ans
-
-        #OK, but maybe all the lost digits are 0.
-        lostdigits = self._int[expdiff:]
-        if lostdigits == (0,) * len(lostdigits):
-            ans = Decimal( (temp._sign, temp._int[:prec], temp._exp - expdiff))
-            #Rounded, but not Inexact
+        # 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
 
-        # Okay, let's round and lose data
+        # 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)
 
-        this_function = getattr(temp, self._pick_rounding_function[rounding])
-        #Now we've got the rounding function
-
-        if prec != context.prec:
-            context = context._shallow_copy()
-            context.prec = prec
-        ans = this_function(prec, expdiff, context)
-        context._raise_error(Rounded)
-        context._raise_error(Inexact, 'Changed in rounding')
-
-        return ans
+        # here self was representable to begin with; return unchanged
+        return Decimal(self)
 
     _pick_rounding_function = {}
 
-    def _round_down(self, prec, expdiff, context):
+    # 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."""
-        return Decimal( (self._sign, self._int[:prec], self._exp - expdiff) )
+        if _all_zeros(self._int, prec):
+            return 0
+        else:
+            return -1
 
-    def _round_half_up(self, prec, expdiff, context, tmp = None):
-        """Rounds 5 up (away from 0)"""
-
-        if tmp is None:
-            tmp = Decimal( (self._sign,self._int[:prec], self._exp - expdiff))
-        if self._int[prec] >= 5:
-            tmp = tmp._increment(round=0, context=context)
-            if len(tmp._int) > prec:
-                return Decimal( (tmp._sign, tmp._int[:-1], tmp._exp + 1))
-        return tmp
-
-    def _round_half_even(self, prec, expdiff, context):
-        """Round 5 to even, rest to nearest."""
-
-        tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff))
-        half = (self._int[prec] == 5)
-        if half:
-            for digit in self._int[prec+1:]:
-                if digit != 0:
-                    half = 0
-                    break
-        if half:
-            if self._int[prec-1] & 1 == 0:
-                return tmp
-        return self._round_half_up(prec, expdiff, context, tmp)
-
-    def _round_half_down(self, prec, expdiff, context):
-        """Round 5 down"""
-
-        tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff))
-        half = (self._int[prec] == 5)
-        if half:
-            for digit in self._int[prec+1:]:
-                if digit != 0:
-                    half = 0
-                    break
-        if half:
-            return tmp
-        return self._round_half_up(prec, expdiff, context, tmp)
-
-    def _round_up(self, prec, expdiff, context):
+    def _round_up(self, prec):
         """Rounds away from 0."""
-        tmp = Decimal( (self._sign, self._int[:prec], self._exp - expdiff) )
-        for digit in self._int[prec:]:
-            if digit != 0:
-                tmp = tmp._increment(round=1, context=context)
-                if len(tmp._int) > prec:
-                    return Decimal( (tmp._sign, tmp._int[:-1], tmp._exp + 1))
-                else:
-                    return tmp
-        return tmp
+        return -self._round_down(prec)
 
-    def _round_ceiling(self, prec, expdiff, context):
+    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, expdiff, context)
+            return self._round_down(prec)
         else:
-            return self._round_up(prec, expdiff, context)
+            return -self._round_down(prec)
 
-    def _round_floor(self, prec, expdiff, context):
+    def _round_floor(self, prec):
         """Rounds down (not towards 0 if negative)"""
         if not self._sign:
-            return self._round_down(prec, expdiff, context)
+            return self._round_down(prec)
         else:
-            return self._round_up(prec, expdiff, context)
+            return -self._round_down(prec)
 
-    def __pow__(self, n, modulo = None, context=None):
-        """Return self ** n (mod modulo)
+    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)
 
-        If modulo is None (default), don't take it mod modulo.
+    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.
         """
-        n = _convert_other(n)
-        if n is NotImplemented:
-            return n
+
+        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()
 
-        if self._is_special or n._is_special or n.adjusted() > 8:
-            #Because the spot << doesn't work with really big exponents
-            if n._isinfinity() or n.adjusted() > 8:
-                return context._raise_error(InvalidOperation, 'x ** INF')
+        # 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)
 
-            ans = self._check_nans(n, context)
-            if ans:
-                return ans
+        # 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')
 
-        if not n._isinteger():
-            return context._raise_error(InvalidOperation, 'x ** (non-integer)')
+        # 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')
 
-        if not self and not n:
-            return context._raise_error(InvalidOperation, '0 ** 0')
+        # 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')
 
-        if not n:
-            return Decimal(1)
+        # compute sign of result
+        if other._iseven():
+            sign = 0
+        else:
+            sign = self._sign
 
-        if self == Decimal(1):
-            return Decimal(1)
+        # 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())
 
-        sign = self._sign and not n._iseven()
-        n = int(n)
+        # 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 modulo:
-                return context._raise_error(InvalidOperation, 'INF % x')
-            if n > 0:
-                return Infsign[sign]
-            return Decimal( (sign, (0,), 0) )
+            if other._sign == 0:
+                return Infsign[result_sign]
+            else:
+                return _dec_from_triple(result_sign, '0', 0)
 
-        #with ludicrously large exponent, just raise an overflow and return inf.
-        if not modulo and n > 0 and (self._exp + len(self._int) - 1) * n > context.Emax \
-           and self:
+        # 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)
 
-            tmp = Decimal('inf')
-            tmp._sign = sign
-            context._raise_error(Rounded)
+                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)
-            context._raise_error(Overflow, 'Big power', sign)
-            return tmp
+            # 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)
 
-        elength = len(str(abs(n)))
-        firstprec = context.prec
-
-        if not modulo and firstprec + elength + 1 > DefaultContext.Emax:
-            return context._raise_error(Overflow, 'Too much precision.', sign)
-
-        mul = Decimal(self)
-        val = Decimal(1)
-        context = context._shallow_copy()
-        context.prec = firstprec + elength + 1
-        if n < 0:
-            #n is a long now, not Decimal instance
-            n = -n
-            mul = Decimal(1).__div__(mul, context=context)
-
-        spot = 1
-        while spot <= n:
-            spot <<= 1
-
-        spot >>= 1
-        #Spot is the highest power of 2 less than n
-        while spot:
-            val = val.__mul__(val, context=context)
-            if val._isinfinity():
-                val = Infsign[sign]
-                break
-            if spot & n:
-                val = val.__mul__(mul, context=context)
-            if modulo is not None:
-                val = val.__mod__(modulo, context=context)
-            spot >>= 1
-        context.prec = firstprec
-
-        if context._rounding_decision == ALWAYS_ROUND:
-            return val._fix(context)
-        return val
+        # 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__."""
@@ -1828,6 +2131,9 @@
     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:
@@ -1838,20 +2144,27 @@
             return dup
 
         if not dup:
-            return Decimal( (dup._sign, (0,), 0) )
+            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:
+        while dup._int[end-1] == '0' and exp < exp_max:
             exp += 1
             end -= 1
-        return Decimal( (dup._sign, dup._int[:end], exp) )
+        return _dec_from_triple(dup._sign, dup._int[:end], exp)
 
-
-    def quantize(self, exp, rounding=None, context=None, watchexp=1):
+    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:
@@ -1859,101 +2172,156 @@
 
             if exp._isinfinity() or self._isinfinity():
                 if exp._isinfinity() and self._isinfinity():
-                    return self  #if both are inf, it is OK
-                if context is None:
-                    context = getcontext()
+                    return Decimal(self)  # if both are inf, it is OK
                 return context._raise_error(InvalidOperation,
                                         'quantize with one INF')
-        return self._rescale(exp._exp, rounding, context, watchexp)
 
-    def same_quantum(self, other):
-        """Test whether self and other have the same exponent.
-
-        same as self._exp == other._exp, except NaN == sNaN
-        """
-        if self._is_special or other._is_special:
-            if self._isnan() or other._isnan():
-                return self._isnan() and other._isnan() and True
-            if self._isinfinity() or other._isinfinity():
-                return self._isinfinity() and other._isinfinity() and True
-        return self._exp == other._exp
-
-    def _rescale(self, exp, rounding=None, context=None, watchexp=1):
-        """Rescales so that the exponent is exp.
-
-        exp = exp to scale to (an integer)
-        rounding = rounding version
-        watchexp: if set (default) an error is returned if exp is greater
-        than Emax or less than Etiny.
-        """
-        if context is None:
-            context = getcontext()
-
-        if self._is_special:
-            if self._isinfinity():
-                return context._raise_error(InvalidOperation, 'rescale with an INF')
-
-            ans = self._check_nans(context=context)
-            if ans:
-                return ans
-
-        if watchexp and (context.Emax  < exp or context.Etiny() > exp):
-            return context._raise_error(InvalidOperation, 'rescale(a, INF)')
-
-        if not self:
-            ans = Decimal(self)
-            ans._int = (0,)
-            ans._exp = exp
+        # 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
 
-        diff = self._exp - exp
-        digits = len(self._int) + diff
+        # 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 watchexp and digits > context.prec:
-            return context._raise_error(InvalidOperation, 'Rescale > prec')
+        if not self:
+            ans = _dec_from_triple(self._sign, '0', exp._exp)
+            return ans._fix(context)
 
-        tmp = Decimal(self)
-        tmp._int = (0,) + tmp._int
-        digits += 1
+        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')
 
-        if digits < 0:
-            tmp._exp = -digits + tmp._exp
-            tmp._int = (0,1)
-            digits = 1
-        tmp = tmp._round(digits, rounding, context=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')
 
-        if tmp._int[0] == 0 and len(tmp._int) > 1:
-            tmp._int = tmp._int[1:]
-        tmp._exp = exp
-
-        tmp_adjusted = tmp.adjusted()
-        if tmp and tmp_adjusted < context.Emin:
+        # 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)
-        elif tmp and tmp_adjusted > context.Emax:
-            return context._raise_error(InvalidOperation, 'rescale(a, INF)')
-        return tmp
 
-    def to_integral(self, rounding=None, context=None):
-        """Rounds to the nearest integer, without raising inexact, rounded."""
+        # 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 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 self
+            return Decimal(self)
+        if not self:
+            return _dec_from_triple(self._sign, '0', 0)
         if context is None:
             context = getcontext()
-        flags = context._ignore_flags(Rounded, Inexact)
-        ans = self._rescale(0, rounding, context=context)
-        context._regard_flags(flags)
+        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 sqrt(self, context=None):
-        """Return the square root of self.
+    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)
 
-        Uses a converging algorithm (Xn+1 = 0.5*(Xn + self / Xn))
-        Should quadratically approach the right answer.
-        """
+    # 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 self._is_special:
             ans = self._check_nans(context=context)
             if ans:
@@ -1963,16 +2331,9 @@
                 return Decimal(self)
 
         if not self:
-            #exponent = self._exp / 2, using round_down.
-            #if self._exp < 0:
-            #    exp = (self._exp+1) // 2
-            #else:
-            exp = (self._exp) // 2
-            if self._sign == 1:
-                #sqrt(-0) = -0
-                return Decimal( (1, (0,), exp))
-            else:
-                return Decimal( (0, (0,), exp))
+            # exponent = self._exp // 2.  sqrt(-0) = -0
+            ans = _dec_from_triple(self._sign, '0', self._exp // 2)
+            return ans._fix(context)
 
         if context is None:
             context = getcontext()
@@ -1980,216 +2341,988 @@
         if self._sign == 1:
             return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0')
 
-        tmp = Decimal(self)
+        # 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.
 
-        expadd = tmp._exp // 2
-        if tmp._exp & 1:
-            tmp._int += (0,)
-            tmp._exp = 0
+        # 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:
-            tmp._exp = 0
+            c = op.int
+            l = len(self._int)+1 >> 1
 
-        context = context._shallow_copy()
-        flags = context._ignore_all_flags()
-        firstprec = context.prec
-        context.prec = 3
-        if tmp.adjusted() & 1 == 0:
-            ans = Decimal( (0, (8,1,9), tmp.adjusted()  - 2) )
-            ans = ans.__add__(tmp.__mul__(Decimal((0, (2,5,9), -2)),
-                                          context=context), context=context)
-            ans._exp -= 1 + tmp.adjusted() // 2
+        # rescale so that c has exactly prec base 100 'digits'
+        shift = prec-l
+        if shift >= 0:
+            c *= 100**shift
+            exact = True
         else:
-            ans = Decimal( (0, (2,5,9), tmp._exp + len(tmp._int)- 3) )
-            ans = ans.__add__(tmp.__mul__(Decimal((0, (8,1,9), -3)),
-                                          context=context), context=context)
-            ans._exp -= 1 + tmp.adjusted()  // 2
+            c, remainder = divmod(c, 100**-shift)
+            exact = not remainder
+        e -= shift
 
-        #ans is now a linear approximation.
-
-        Emax, Emin = context.Emax, context.Emin
-        context.Emax, context.Emin = DefaultContext.Emax, DefaultContext.Emin
-
-        half = Decimal('0.5')
-
-        maxp = firstprec + 2
-        rounding = context._set_rounding(ROUND_HALF_EVEN)
-        while 1:
-            context.prec = min(2*context.prec - 2, maxp)
-            ans = half.__mul__(ans.__add__(tmp.__div__(ans, context=context),
-                                           context=context), context=context)
-            if context.prec == maxp:
+        # 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
 
-        #round to the answer's precision-- the only error can be 1 ulp.
-        context.prec = firstprec
-        prevexp = ans.adjusted()
-        ans = ans._round(context=context)
-
-        #Now, check if the other last digits are better.
-        context.prec = firstprec + 1
-        # In case we rounded up another digit and we should actually go lower.
-        if prevexp != ans.adjusted():
-            ans._int += (0,)
-            ans._exp -= 1
-
-
-        lower = ans.__sub__(Decimal((0, (5,), ans._exp-1)), context=context)
-        context._set_rounding(ROUND_UP)
-        if lower.__mul__(lower, context=context) > (tmp):
-            ans = ans.__sub__(Decimal((0, (1,), ans._exp)), context=context)
-
+        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:
-            upper = ans.__add__(Decimal((0, (5,), ans._exp-1)),context=context)
-            context._set_rounding(ROUND_DOWN)
-            if upper.__mul__(upper, context=context) < tmp:
-                ans = ans.__add__(Decimal((0, (1,), ans._exp)),context=context)
+            # result is not exact; fix last digit as described above
+            if n % 5 == 0:
+                n += 1
 
-        ans._exp += expadd
+        ans = _dec_from_triple(0, str(n), e)
 
-        context.prec = firstprec
-        context.rounding = rounding
+        # round, and fit to current context
+        context = context._shallow_copy()
+        rounding = context._set_rounding(ROUND_HALF_EVEN)
         ans = ans._fix(context)
+        context.rounding = rounding
 
-        rounding = context._set_rounding_decision(NEVER_ROUND)
-        if not ans.__mul__(ans, context=context) == self:
-            # Only rounded/inexact if here.
-            context._regard_flags(flags)
-            context._raise_error(Rounded)
-            context._raise_error(Inexact)
-        else:
-            #Exact answer, so let's set the exponent right.
-            #if self._exp < 0:
-            #    exp = (self._exp +1)// 2
-            #else:
-            exp = self._exp // 2
-            context.prec += ans._exp - exp
-            ans = ans._rescale(exp, context=context)
-            context.prec = firstprec
-            context._regard_flags(flags)
-        context.Emax, context.Emin = Emax, Emin
-
-        return ans._fix(context)
+        return ans
 
     def max(self, other, context=None):
         """Returns the larger value.
 
-        like max(self, other) except if one is not a number, returns
+        Like max(self, other) except if one is not a number, returns
         NaN (and signals if one is sNaN).  Also rounds.
         """
-        other = _convert_other(other)
-        if other is NotImplemented:
-            return other
+        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
+            # 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
+                    return self._fix_nan(context)
                 if sn == 1 and on != 2:
-                    return other
+                    return other._fix_nan(context)
                 return self._check_nans(other, context)
 
-        ans = self
         c = self.__cmp__(other)
         if c == 0:
-            # if both operands are finite and equal in numerical value
+            # 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
+            # If the signs differ then max returns the operand with the
             # positive sign and min returns the operand with the negative sign
             #
-            # if the signs are the same then the exponent is used to select
-            # the result.
-            if self._sign != other._sign:
-                if self._sign:
-                    ans = other
-            elif self._exp < other._exp and not self._sign:
-                ans = other
-            elif self._exp > other._exp and self._sign:
-                ans = other
-        elif c == -1:
-            ans = other
+            # If 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 context is None:
-            context = getcontext()
-        if context._rounding_decision == ALWAYS_ROUND:
-            return ans._fix(context)
-        return ans
+        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
+        Like min(self, other) except if one is not a number, returns
         NaN (and signals if one is sNaN).  Also rounds.
         """
-        other = _convert_other(other)
-        if other is NotImplemented:
-            return other
+        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
+            # 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
+                    return self._fix_nan(context)
                 if sn == 1 and on != 2:
-                    return other
+                    return other._fix_nan(context)
                 return self._check_nans(other, context)
 
-        ans = self
         c = self.__cmp__(other)
         if c == 0:
-            # if both operands are finite and equal in numerical value
-            # then an ordering is applied:
-            #
-            # if the signs differ then max returns the operand with the
-            # positive sign and min returns the operand with the negative sign
-            #
-            # if the signs are the same then the exponent is used to select
-            # the result.
-            if self._sign != other._sign:
-                if other._sign:
-                    ans = other
-            elif self._exp > other._exp and not self._sign:
-                ans = other
-            elif self._exp < other._exp and self._sign:
-                ans = other
-        elif c == 1:
+            c = self.compare_total(other)
+
+        if c == -1:
+            ans = self
+        else:
             ans = other
 
-        if context is None:
-            context = getcontext()
-        if context._rounding_decision == ALWAYS_ROUND:
-            return ans._fix(context)
-        return ans
+        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)
+        return rest == '0'*len(rest)
 
     def _iseven(self):
-        """Returns 1 if self is even.  Assumes self is an integer."""
-        if self._exp > 0:
-            return 1
-        return self._int[-1+self._exp] & 1 == 0
+        """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
+        # If NaN or Infinity, self._exp is string
         except TypeError:
             return 0
 
-    # support for pickling, copy, and deepcopy
+    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.
+        """
+        if context is None:
+            context = getcontext()
+
+        self_is_nan = self._isnan()
+        other_is_nan = other._isnan()
+        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 context._raise_error(InvalidOperation, 'NaN in compare_signal',
+                                        self)
+        if other_is_nan:
+            return context._raise_error(InvalidOperation, 'NaN in compare_signal',
+                                        other)
+        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 numbers 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),))
 
@@ -2203,13 +3336,30 @@
             return self     # My components are also immutable
         return self.__class__(str(self))
 
-##### Context class ###########################################
+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_')]
+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.
+    # 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
@@ -2236,8 +3386,7 @@
 
     Contains:
     prec - precision (for use in rounding, division, square roots..)
-    rounding - rounding type. (how you round)
-    _rounding_decision - ALWAYS_ROUND, NEVER_ROUND -- do you round?
+    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.
@@ -2253,7 +3402,6 @@
 
     def __init__(self, prec=None, rounding=None,
                  traps=None, flags=None,
-                 _rounding_decision=None,
                  Emin=None, Emax=None,
                  capitals=None, _clamp=0,
                  _ignored_flags=None):
@@ -2277,9 +3425,13 @@
     def __repr__(self):
         """Show the current context."""
         s = []
-        s.append('Context(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d' % vars(self))
-        s.append('flags=[' + ', '.join([f.__name__ for f, v in self.flags.items() if v]) + ']')
-        s.append('traps=[' + ', '.join([t.__name__ for t, v in self.traps.items() if v]) + ']')
+        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):
@@ -2289,16 +3441,16 @@
 
     def _shallow_copy(self):
         """Returns a shallow copy from self."""
-        nc = Context(self.prec, self.rounding, self.traps, self.flags,
-                         self._rounding_decision, self.Emin, self.Emax,
-                         self.capitals, self._clamp, self._ignored_flags)
+        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._rounding_decision, self.Emin, self.Emax,
-                         self.capitals, self._clamp, self._ignored_flags)
+        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
 
@@ -2312,16 +3464,16 @@
         """
         error = _condition_map.get(condition, condition)
         if error in self._ignored_flags:
-            #Don't touch the flag
+            # 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.
+            # 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 = []
+        # self._ignored_flags = []
         raise error, explanation
 
     def _ignore_all_flags(self):
@@ -2345,7 +3497,7 @@
     def __hash__(self):
         """A Context cannot be hashed."""
         # We inherit object.__hash__, so we must deny this explicitly
-        raise TypeError, "Cannot hash a Context."
+        raise TypeError("Cannot hash a Context.")
 
     def Etiny(self):
         """Returns Etiny (= Emin - prec + 1)"""
@@ -2355,27 +3507,6 @@
         """Returns maximum exponent (= Emax - prec + 1)"""
         return int(self.Emax - self.prec + 1)
 
-    def _set_rounding_decision(self, type):
-        """Sets the rounding decision.
-
-        Sets the rounding decision, and returns the current (previous)
-        rounding decision.  Often used like:
-
-        context = context._shallow_copy()
-        # That so you don't change the calling context
-        # if an error occurs in the middle (say DivisionImpossible is raised).
-
-        rounding = context._set_rounding_decision(NEVER_ROUND)
-        instance = instance / Decimal(2)
-        context._set_rounding_decision(rounding)
-
-        This will make it not round for that operation.
-        """
-
-        rounding = self._rounding_decision
-        self._rounding_decision = type
-        return rounding
-
     def _set_rounding(self, type):
         """Sets the rounding type.
 
@@ -2398,14 +3529,17 @@
     def create_decimal(self, num='0'):
         """Creates a new Decimal instance but using self as context."""
         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
+    # 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
+        operation on the operand.  Otherwise, the result is the same as using
         the plus operation on the operand.
 
         >>> ExtendedContext.abs(Decimal('2.1'))
@@ -2432,6 +3566,17 @@
     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.
 
@@ -2461,6 +3606,110 @@
         """
         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.
 
@@ -2502,13 +3751,330 @@
     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 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
+        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'))
@@ -2522,13 +4088,17 @@
         """
         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 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
+        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'))
@@ -2542,6 +4112,10 @@
         """
         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.
 
@@ -2577,6 +4151,68 @@
         """
         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.
 
@@ -2598,6 +4234,53 @@
         """
         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.
 
@@ -2615,65 +4298,85 @@
     def power(self, a, b, modulo=None):
         """Raises a to the power of b, to modulo if given.
 
-        The right-hand operand must be a whole number whose integer part (after
-        any exponent has been applied) has no more than 9 digits and whose
-        fractional part (if any) is all zeros before any rounding. The operand
-        may be positive, negative, or zero; if negative, the absolute value of
-        the power is used, and the left-hand operand is inverted (divided into
-        1) before use.
+        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.
 
-        If the increased precision needed for the intermediate calculations
-        exceeds the capabilities of the implementation then an Invalid operation
-        condition is raised.
+        With three arguments, compute (a**b) % modulo.  For the
+        three argument form, the following restrictions on the
+        arguments hold:
 
-        If, when raising to a negative power, an underflow occurs during the
-        division into 1, the operation is not halted at that point but
-        continues.
+         - 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
 
-        >>> ExtendedContext.power(Decimal('2'), Decimal('3'))
+        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")
-        >>> ExtendedContext.power(Decimal('2'), Decimal('-3'))
+        >>> c.power(Decimal('-2'), Decimal('3'))
+        Decimal("-8")
+        >>> c.power(Decimal('2'), Decimal('-3'))
         Decimal("0.125")
-        >>> ExtendedContext.power(Decimal('1.7'), Decimal('8'))
+        >>> c.power(Decimal('1.7'), Decimal('8'))
         Decimal("69.7575744")
-        >>> ExtendedContext.power(Decimal('Infinity'), Decimal('-2'))
+        >>> c.power(Decimal('10'), Decimal('0.301029996'))
+        Decimal("2.00000000")
+        >>> c.power(Decimal('Infinity'), Decimal('-1'))
         Decimal("0")
-        >>> ExtendedContext.power(Decimal('Infinity'), Decimal('-1'))
-        Decimal("0")
-        >>> ExtendedContext.power(Decimal('Infinity'), Decimal('0'))
+        >>> c.power(Decimal('Infinity'), Decimal('0'))
         Decimal("1")
-        >>> ExtendedContext.power(Decimal('Infinity'), Decimal('1'))
+        >>> c.power(Decimal('Infinity'), Decimal('1'))
         Decimal("Infinity")
-        >>> ExtendedContext.power(Decimal('Infinity'), Decimal('2'))
-        Decimal("Infinity")
-        >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-2'))
-        Decimal("0")
-        >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('-1'))
+        >>> c.power(Decimal('-Infinity'), Decimal('-1'))
         Decimal("-0")
-        >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('0'))
+        >>> c.power(Decimal('-Infinity'), Decimal('0'))
         Decimal("1")
-        >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('1'))
+        >>> c.power(Decimal('-Infinity'), Decimal('1'))
         Decimal("-Infinity")
-        >>> ExtendedContext.power(Decimal('-Infinity'), Decimal('2'))
+        >>> c.power(Decimal('-Infinity'), Decimal('2'))
         Decimal("Infinity")
-        >>> ExtendedContext.power(Decimal('0'), Decimal('0'))
+        >>> 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) and having the exponent of '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
+        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
+        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
@@ -2712,13 +4415,21 @@
         """
         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.
+        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
@@ -2742,7 +4453,7 @@
     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
+        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
@@ -2766,6 +4477,28 @@
         """
         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.
 
@@ -2783,8 +4516,43 @@
         """
         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):
-        """Returns the square root of a non-negative number to context precision.
+        """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.
@@ -2838,33 +4606,65 @@
         """
         return a.__str__(context=self)
 
-    def to_integral(self, a):
+    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.
+        be set.  The rounding mode is taken from the context.
 
-        >>> ExtendedContext.to_integral(Decimal('2.1'))
+        >>> ExtendedContext.to_integral_value(Decimal('2.1'))
         Decimal("2")
-        >>> ExtendedContext.to_integral(Decimal('100'))
+        >>> ExtendedContext.to_integral_value(Decimal('100'))
         Decimal("100")
-        >>> ExtendedContext.to_integral(Decimal('100.0'))
+        >>> ExtendedContext.to_integral_value(Decimal('100.0'))
         Decimal("100")
-        >>> ExtendedContext.to_integral(Decimal('101.5'))
+        >>> ExtendedContext.to_integral_value(Decimal('101.5'))
         Decimal("102")
-        >>> ExtendedContext.to_integral(Decimal('-101.5'))
+        >>> ExtendedContext.to_integral_value(Decimal('-101.5'))
         Decimal("-102")
-        >>> ExtendedContext.to_integral(Decimal('10E+5'))
+        >>> ExtendedContext.to_integral_value(Decimal('10E+5'))
         Decimal("1.0E+6")
-        >>> ExtendedContext.to_integral(Decimal('7.89E+77'))
+        >>> ExtendedContext.to_integral_value(Decimal('7.89E+77'))
         Decimal("7.89E+77")
-        >>> ExtendedContext.to_integral(Decimal('-Inf'))
+        >>> ExtendedContext.to_integral_value(Decimal('-Inf'))
         Decimal("-Infinity")
         """
-        return a.to_integral(context=self)
+        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')
@@ -2879,10 +4679,7 @@
             self.exp = None
         elif isinstance(value, Decimal):
             self.sign = value._sign
-            cum = 0
-            for digit  in value._int:
-                cum = cum * 10 + digit
-            self.int = cum
+            self.int = int(value._int)
             self.exp = value._exp
         else:
             # assert isinstance(value, tuple)
@@ -2897,70 +4694,375 @@
 
 
 
-def _normalize(op1, op2, shouldround = 0, prec = 0):
+def _normalize(op1, op2, prec = 0):
     """Normalizes op1, op2 to have the same exp and length of coefficient.
 
     Done during addition.
     """
-    # Yes, the exponent is a long, but the difference between exponents
-    # must be an int-- otherwise you'd get a big memory problem.
-    numdigits = int(op1.exp - op2.exp)
-    if numdigits < 0:
-        numdigits = -numdigits
+    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
 
-    if shouldround and numdigits > prec + 1:
-        # Big difference in exponents - check the adjusted exponents
-        tmp_len = len(str(tmp.int))
-        other_len = len(str(other.int))
-        if numdigits > (other_len + prec + 1 - tmp_len):
-            # If the difference in adjusted exps is > prec+1, we know
-            # other is insignificant, so might as well put a 1 after the precision.
-            # (since this is only for addition.)  Also stops use of massive longs.
-
-            extend = prec + 2 - tmp_len
-            if extend <= 0:
-                extend = 1
-            tmp.int *= 10 ** extend
-            tmp.exp -= extend
-            other.int = 1
-            other.exp = tmp.exp
-            return op1, op2
-
-    tmp.int *= 10 ** numdigits
-    tmp.exp -= numdigits
+    tmp.int *= 10 ** (tmp.exp - other.exp)
+    tmp.exp = other.exp
     return op1, op2
 
-def _adjust_coefficients(op1, op2):
-    """Adjust op1, op2 so that op2.int * 10 > op1.int >= op2.int.
+##### Integer arithmetic functions used by ln, log10, exp and __pow__ #####
 
-    Returns the adjusted op1, op2 as well as the change in op1.exp-op2.exp.
-
-    Used on _WorkRep instances during division.
+# 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.
     """
-    adjust = 0
-    #If op1 is smaller, make it larger
-    while op2.int > op1.int:
-        op1.int *= 10
-        op1.exp -= 1
-        adjust += 1
+    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]]
 
-    #If op2 is too small, make it larger
-    while op1.int >= (10 * op2.int):
-        op2.int *= 10
-        op2.exp -= 1
-        adjust -= 1
+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.
 
-    return op1, op2, adjust
+    """
+    if n <= 0 or a <= 0:
+        raise ValueError("Both arguments to _sqrt_nearest should be positive.")
 
-##### Helper Functions ########################################
+    b=0
+    while a != b:
+        b, a = a, a--n//a>>1
+    return a
 
-def _convert_other(other):
+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.
@@ -2969,56 +5071,11 @@
         return other
     if isinstance(other, (int, long)):
         return Decimal(other)
+    if raiseit:
+        raise TypeError("Unable to convert %s to Decimal" % other)
     return NotImplemented
 
-_infinity_map = {
-    'inf' : 1,
-    'infinity' : 1,
-    '+inf' : 1,
-    '+infinity' : 1,
-    '-inf' : -1,
-    '-infinity' : -1
-}
-
-def _isinfinity(num):
-    """Determines whether a string or float is infinity.
-
-    +1 for negative infinity; 0 for finite ; +1 for positive infinity
-    """
-    num = str(num).lower()
-    return _infinity_map.get(num, 0)
-
-def _isnan(num):
-    """Determines whether a string or float is NaN
-
-    (1, sign, diagnostic info as string) => NaN
-    (2, sign, diagnostic info as string) => sNaN
-    0 => not a NaN
-    """
-    num = str(num).lower()
-    if not num:
-        return 0
-
-    #get the sign, get rid of trailing [+-]
-    sign = 0
-    if num[0] == '+':
-        num = num[1:]
-    elif num[0] == '-':  #elif avoids '+-nan'
-        num = num[1:]
-        sign = 1
-
-    if num.startswith('nan'):
-        if len(num) > 3 and not num[3:].isdigit(): #diagnostic info
-            return 0
-        return (1, sign, num[3:].lstrip('0'))
-    if num.startswith('snan'):
-        if len(num) > 4 and not num[4:].isdigit():
-            return 0
-        return (2, sign, num[4:].lstrip('0'))
-    return 0
-
-
-##### Setup Specific Contexts ################################
+##### Setup Specific Contexts ############################################
 
 # The default context prototype used by Context()
 # Is mutable, so that new contexts can have different default values
@@ -3027,7 +5084,6 @@
         prec=28, rounding=ROUND_HALF_EVEN,
         traps=[DivisionByZero, Overflow, InvalidOperation],
         flags=[],
-        _rounding_decision=ALWAYS_ROUND,
         Emax=999999999,
         Emin=-999999999,
         capitals=1
@@ -3051,85 +5107,62 @@
 )
 
 
-##### Useful Constants (internal use only) ####################
-
-#Reusable defaults
-Inf = Decimal('Inf')
-negInf = Decimal('-Inf')
-
-#Infsign[sign] is infinity w/ that sign
-Infsign = (Inf, negInf)
-
-NaN = Decimal('NaN')
-
-
-##### crud for parsing strings #################################
+##### crud for parsing strings #############################################
 import re
 
-# There's an optional sign at the start, and an optional exponent
-# at the end.  The exponent has an optional sign and at least one
-# digit.  In between, must have either at least one digit followed
-# by an optional fraction, or a decimal point followed by at least
-# one digit.  Yuck.
+# 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].
 
-_parser = re.compile(r"""
+import re
+_parser = re.compile(r"""     # A numeric string consists of:
 #    \s*
-    (?P<sign>[-+])?
+    (?P<sign>[-+])?           # an optional sign, followed by either...
     (
-        (?P<int>\d+) (\. (?P<frac>\d*))?
+        (?=\d|\.\d)           # ...a number (with at least one digit)
+        (?P<int>\d*)          # consisting of a (possibly empty) integer part
+        (\.(?P<frac>\d*))?    # followed by an optional fractional part
+        (E(?P<exp>[-+]?\d+))? # followed by an optional exponent, or...
     |
-        \. (?P<onlyfrac>\d+)
+        Inf(inity)?           # ...an infinity, or...
+    |
+        (?P<signal>s)?        # ...an (optionally signaling)
+        NaN                   # NaN
+        (?P<diag>\d*)         # with (possibly empty) diagnostic information.
     )
-    ([eE](?P<exp>[-+]? \d+))?
 #    \s*
     $
-""", re.VERBOSE).match #Uncomment the \s* to allow leading or trailing spaces.
+""", re.VERBOSE | re.IGNORECASE).match
 
+_all_zeros = re.compile('0*$').match
+_exact_half = re.compile('50*$').match
 del re
 
-# return sign, n, p s.t. float string value == -1**sign * n * 10**p exactly
 
-def _string2exact(s):
-    m = _parser(s)
-    if m is None:
-        raise ValueError("invalid literal for Decimal: %r" % s)
+##### Useful Constants (internal use only) ################################
 
-    if m.group('sign') == "-":
-        sign = 1
-    else:
-        sign = 0
+# Reusable defaults
+Inf = Decimal('Inf')
+negInf = Decimal('-Inf')
+NaN = Decimal('NaN')
+Dec_0 = Decimal(0)
+Dec_p1 = Decimal(1)
+Dec_n1 = Decimal(-1)
 
-    exp = m.group('exp')
-    if exp is None:
-        exp = 0
-    else:
-        exp = int(exp)
+# Infsign[sign] is infinity w/ that sign
+Infsign = (Inf, negInf)
 
-    intpart = m.group('int')
-    if intpart is None:
-        intpart = ""
-        fracpart = m.group('onlyfrac')
-    else:
-        fracpart = m.group('frac')
-        if fracpart is None:
-            fracpart = ""
-
-    exp -= len(fracpart)
-
-    mantissa = intpart + fracpart
-    tmp = map(int, mantissa)
-    backup = tmp
-    while tmp and tmp[0] == 0:
-        del tmp[0]
-
-    # It's a zero
-    if not tmp:
-        if backup:
-            return (sign, tuple(backup), exp)
-        return (sign, (0,), exp)
-    mantissa = tuple(tmp)
-
-    return (sign, mantissa, exp)
 
 
 if __name__ == '__main__':