Merge branch 'master' of gitlab.com:python-on-guile/python-on-guile

4 files changed, 5954 insertions, 9 deletions

diff --git a/modules/language/python/module/cmath.scm b/modules/language/python/module/cmath.scm
new file mode 100644
index 0000000..b02be2d
--- /dev/null
+++ b/modules/language/python/module/cmath.scm
@@ -0,0 +1,63 @@
+(define-module (language python module cmath)
+  #:export (polar rect exp log log10 sqrt pi e tau inf nan infj nanj isclose
+		  isnan isinf isfinite sin cos tan asin acos atan
+		  sinh cosh tanh asinh acosh atanh))
+
+(define (polar x)
+  (list (magnitude x) (angle x)))
+
+(define (rect r phi)
+  (make-polar r phi))
+
+;; pow log
+
+(define exp   (@ (guile) exp))
+(define log   (@ (guile) log))
+(define log10 (@ (guile) log10))
+(define sqrt  (@ (guile) sqrt))
+
+;; trig
+(define sin   (@ (guile) sin))
+(define cos   (@ (guile) cos))
+(define tan   (@ (guile) tan))
+(define asin  (@ (guile) asin))
+(define acos  (@ (guile) acos))
+(define atan  (@ (guile) atan))
+
+;; hyp
+(define sinh   (@ (guile) sinh))
+(define cosh   (@ (guile) cosh))
+(define tanh   (@ (guile) tanh))
+(define asinh  (@ (guile) asinh))
+(define acosh  (@ (guile) acosh))
+(define atanh  (@ (guile) atanh))
+
+;; classification
+(define isfinite1 (@ (language python module math) isfinite))
+
+(define (isfinite x)
+  (and (isfinite1 (real-part x))
+       (isfinite1 (imag-part x))))
+
+(define (isinf x)
+  (or (inf? (real-part x))
+      (inf? (imag-part x))))
+
+(define (isnan x)
+  (or (nan? (real-part x))
+      (nan? (imag-part x))))
+
+(define* (isclose a b #:key (rel_tol 1e-9) (abs_tol 0.0))
+  (define e-abs (magnitude (- a b)))
+  (if (< e-abs (max (* rel_tol (max (magnitude a) (magnitude b))) abs_tol))
+      #t
+      #f))
+ 
+(define pi  (@ (language python module math) pi))
+(define e   (@ (language python module math) e))
+(define tau (@ (language python module math) tau))
+(define inf (@ (language python module math) inf))
+(define nan (@ (language python module math) nan))
+(define infj (make-rectangular 0 inf))
+(define nanj (make-rectangular 0 nan))
+
diff --git a/modules/language/python/module/decimal.scm b/modules/language/python/module/decimal.scm
new file mode 100644
index 0000000..55a6675
--- /dev/null
+++ b/modules/language/python/module/decimal.scm
@@ -0,0 +1,5627 @@
+(define-module (language python module decimal)
+  #:use-module ((language python module collections) #:select (namedtuple))
+  #:export ())
+
+(define __name__   "decimal")
+(define __xname__  __name__)
+(define __version__ "1.70")
+;; Highest version of the spec this complies with
+;; See http://speleotrove.com/decimal/
+
+
+(define DecimalTuple (namedtuple "DecimalTuple" "sign digits exponent"))
+
+;; Rounding
+(define ROUND_DOWN      'ROUND_DOWN)
+(define ROUND_HALF_UP   'ROUND_HALF_UP)
+(define ROUND_HALF_EVEN 'ROUND_HALF_EVEN)
+(define ROUND_CEILING   'ROUND_CEILING)
+(define ROUND_FLOOR     'ROUND_FLOOR)
+(define ROUND_UP        'ROUND_UP)
+(define ROUND_HALF_DOWN 'ROUND_HALF_DOWN)
+(define ROUND_05UP      'ROUND_05UP)
+
+;; Compatibility with the C version
+(define MAX_PREC 425000000)
+(define MAX_EMAX 425000000)
+(define MIN_EMIN -425000000)
+
+(if (= sys:maxsize  (- (ash 1 63) 1))
+    (begin
+      (set! MAX_PREC 999999999999999999)
+      (set! MAX_EMAX 999999999999999999)
+      (set! MIN_EMIN -999999999999999999)))
+
+(define MIN_ETINY  (- MIN_EMIN (- MAX_PREC 1)))
+
+;; Context
+(define (cx-prec     x) (vector-ref x 0))
+(define (cx-emax     x) (vector-ref x 1))
+(define (cx-raise    x) (vector-ref x 2))
+(define (cx-error    x) (vector-ref x 3))
+(define (cx-capitals x) (vector-ref x 4))
+(define (cx-rounding x) (vector-ref x 5))
+;; Errors
+
+(define-python-class DecimalException (ArithmeticError)
+    "Base exception class.
+
+    Used exceptions derive from this.
+    If an exception derives from another exception besides this (such as
+    Underflow (Inexact, Rounded, Subnormal) that indicates that it is only
+    called if the others are present.  This isn't actually used for
+    anything, though.
+
+    handle  -- Called when context._raise_error is called and the
+               trap_enabler is not set.  First argument is self, second is the
+               context.  More arguments can be given, those being after
+               the explanation in _raise_error (For example,
+               context._raise_error(NewError, '(-x)!', self._sign) would
+               call NewError().handle(context, self._sign).)
+
+    To define a new exception, it should be sufficient to have it derive
+    from DecimalException.
+    "
+    
+    (define handle
+      (lambda (self context . args)
+        (values))))
+
+
+(define-python-class Clamped (DecimalException)
+    """Exponent of a 0 changed to fit bounds.
+
+    This occurs and signals clamped if the exponent of a result has been
+    altered in order to fit the constraints of a specific concrete
+    representation.  This may occur when the exponent of a zero result would
+    be outside the bounds of a representation, or when a large normal
+    number would have an encoded exponent that cannot be represented.  In
+    this latter case, the exponent is reduced to fit and the corresponding
+    number of zero digits are appended to the coefficient ("fold-down").
+    """)
+
+(define-python-class InvalidOperation (DecimalException)
+    "An invalid operation was performed.
+
+    Various bad things cause this:
+
+    Something creates a signaling NaN
+    -INF + INF
+    0 * (+-)INF
+    (+-)INF / (+-)INF
+    x % 0
+    (+-)INF % x
+    x._rescale( non-integer )
+    sqrt(-x) , x > 0
+    0 ** 0
+    x ** (non-integer)
+    x ** (+-)INF
+    An operand is invalid
+
+    The result of the operation after these is a quiet positive NaN,
+    except when the cause is a signaling NaN, in which case the result is
+    also a quiet NaN, but with the original sign, and an optional
+    diagnostic information.
+    "
+    (define handle
+      (lambda (self context . args)
+        (if (bool args)
+	    (let ((ans  (_dec_from_triple
+			 (ref (car args) '_sign)
+			 (ref (car args) '_int)
+			 "n" #t)))
+	      ((ref ans '_fix_nan) context))
+	    _NaN))))
+
+(define-python-class ConversionSyntax (InvalidOperation)
+    "Trying to convert badly formed string.
+
+    This occurs and signals invalid-operation if a string is being
+    converted to a number and it does not conform to the numeric string
+    syntax.  The result is [0,qNaN].
+    "
+    (define handle
+      (lambda x _NaN)))
+
+(define-python-class DivisionByZero (DecimalException ZeroDivisionError)
+    "Division by 0.
+
+    This occurs and signals division-by-zero if division of a finite number
+    by zero was attempted (during a divide-integer or divide operation, or a
+    power operation with negative right-hand operand), and the dividend was
+    not zero.
+
+    The result of the operation is [sign,inf], where sign is the exclusive
+    or of the signs of the operands for divide, or is 1 for an odd power of
+    -0, for power.
+    "
+
+    (define handle
+      (lambda (self context sign . args)
+        (pylist-ref _SignedInfinity sign))))
+
+(define-python-class DivisionImpossible (InvalidOperation)
+    "Cannot perform the division adequately.
+
+    This occurs and signals invalid-operation if the integer result of a
+    divide-integer or remainder operation had too many digits (would be
+    longer than precision).  The result is [0,qNaN].
+    "
+
+    (define handle
+      (lambda x _NaN)))
+
+(define-python-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].
+    "
+
+    (define handle
+      (lambda x _NaN)))
+
+(define-python-class Inexact (DecimalException)
+    "Had to round, losing information.
+
+    This occurs and signals inexact whenever the result of an operation is
+    not exact (that is, it needed to be rounded and any discarded digits
+    were non-zero), or if an overflow or underflow condition occurs.  The
+    result in all cases is unchanged.
+
+    The inexact signal may be tested (or trapped) to determine if a given
+    operation (or sequence of operations) was inexact.
+    ")
+
+(define-python-class InvalidContext (InvalidOperation)
+    "Invalid context.  Unknown rounding, for example.
+
+    This occurs and signals invalid-operation if an invalid context was
+    detected during an operation.  This can occur if contexts are not checked
+    on creation and either the precision exceeds the capability of the
+    underlying concrete representation or an unknown or unsupported rounding
+    was specified.  These aspects of the context need only be checked when
+    the values are required to be used.  The result is [0,qNaN].
+    "
+
+    (define handle
+      (lambda x _NaN)))
+
+(define-python-class Rounded (DecimalException)
+    "Number got rounded (not  necessarily changed during rounding).
+
+    This occurs and signals rounded whenever the result of an operation is
+    rounded (that is, some zero or non-zero digits were discarded from the
+    coefficient), or if an overflow or underflow condition occurs.  The
+    result in all cases is unchanged.
+
+    The rounded signal may be tested (or trapped) to determine if a given
+    operation (or sequence of operations) caused a loss of precision.
+    ")
+
+(define-python-class Subnormal (DecimalException)
+    "Exponent < Emin before rounding.
+
+    This occurs and signals subnormal whenever the result of a conversion or
+    operation is subnormal (that is, its adjusted exponent is less than
+    Emin, before any rounding).  The result in all cases is unchanged.
+
+    The subnormal signal may be tested (or trapped) to determine if a given
+    or operation (or sequence of operations) yielded a subnormal result.
+    ")
+
+(define-python-class Overflow (Inexact Rounded)
+    "Numerical overflow.
+
+    This occurs and signals overflow if the adjusted exponent of a result
+    (from a conversion or from an operation that is not an attempt to divide
+    by zero), after rounding, would be greater than the largest value that
+    can be handled by the implementation (the value Emax).
+
+    The result depends on the rounding mode:
+
+    For round-half-up and round-half-even (and for round-half-down and
+    round-up, if implemented), the result of the operation is [sign,inf],
+    where sign is the sign of the intermediate result.  For round-down, the
+    result is the largest finite number that can be represented in the
+    current precision, with the sign of the intermediate result.  For
+    round-ceiling, the result is the same as for round-down if the sign of
+    the intermediate result is 1, or is [0,inf] otherwise.  For round-floor,
+    the result is the same as for round-down if the sign of the intermediate
+    result is 0, or is [1,inf] otherwise.  In all cases, Inexact and Rounded
+    will also be raised.
+    "
+
+    (define handle
+      (let ((l (list ROUND_HALF_UP ROUND_HALF_EVEN
+		     ROUND_HALF_DOWN ROUND_U)))
+	(lambda (self context sign . args)
+	  (let/ec ret
+	    (if (memq (ref context 'rounding) l)
+		(ret (pylist-ref _SignedInfinity sign)))
+            
+	    (if (= sign 0)
+		(if (eq? (ref context 'rounding) ROUND_CEILING)
+		    (ret (pylist-ref _SignedInfinity sign))
+		    (ret (_dec_from_triple
+			  sign
+			  (* "9" (cx-prec context))
+			  (+ (- (cx-emax context) (cx-prec context)) 1)))))
+
+	    (if (= sign 1)
+		(if (eq? (ref context 'rounding) ROUND_FLOOR)
+		    (ret (pylist-ref _SignedInfinity sign))
+		    (ret (_dec_from_triple
+			  sign
+			  (* "9" (cx-prec context))
+			  (+ (- (cx-emax context) (cx-prec context)) 1))))))))))
+
+
+(define-python-class Underflow (Inexact Rounded Subnormal)
+    "Numerical underflow with result rounded to 0.
+
+    This occurs and signals underflow if a result is inexact and the
+    adjusted exponent of the result would be smaller (more negative) than
+    the smallest value that can be handled by the implementation (the value
+    Emin).  That is, the result is both inexact and subnormal.
+
+    The result after an underflow will be a subnormal number rounded, if
+    necessary, so that its exponent is not less than Etiny.  This may result
+    in 0 with the sign of the intermediate result and an exponent of Etiny.
+
+    In all cases, Inexact, Rounded, and Subnormal will also be raised.
+    ")
+
+(define-python-class FloatOperation (DecimalException TypeError)
+    """Enable stricter semantics for mixing floats and Decimals.
+
+    If the signal is not trapped (default), mixing floats and Decimals is
+    permitted in the Decimal() constructor, context.create_decimal() and
+    all comparison operators. Both conversion and comparisons are exact.
+    Any occurrence of a mixed operation is silently recorded by setting
+    FloatOperation in the context flags.  Explicit conversions with
+    Decimal.from_float() or context.create_decimal_from_float() do not
+    set the flag.
+
+    Otherwise (the signal is trapped), only equality comparisons and explicit
+    conversions are silent. All other mixed operations raise FloatOperation.
+    """)
+
+;; List of public traps and flags
+(define _signals
+  (vector Clamped DivisionByZero Inexact Overflow Rounded,
+            Underflow InvalidOperation Subnormal FloatOperation))
+
+;; Map conditions (per the spec) to signals
+(define _condition_map
+  `((,ConversionSyntax   . ,InvalidOperation)
+    (,DivisionImpossible . ,InvalidOperation)
+    (,DivisionUndefined  . ,InvalidOperation)
+    (,InvalidContext     . ,InvalidOperation)))
+
+;; Valid rounding modes
+(define _rounding_modes
+  (list ROUND_DOWN ROUND_HALF_UP ROUND_HALF_EVEN ROUND_CEILING,
+	ROUND_FLOOR ROUND_UP ROUND_HALF_DOWN ROUND_05UP))
+
+;; ##### Context Functions ##################################################
+
+;; The getcontext() and setcontext() function manage access to a thread-local
+;; current context.
+(define *context* (make-fluid #f))
+(define (getcontext)
+  (fluid-ref *context*))
+(define (setcontext context)
+  (fluid-set! *context* context))
+
+;; ##### Decimal class #######################################################
+
+;; Do not subclass Decimal from numbers.Real and do not register it as such
+;; (because Decimals are not interoperable with floats).  See the notes in
+;; numbers.py for more detail.
+
+(define _dec_from_triple
+  (lam (sign coefficient exponent (= special #f))
+    "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*.
+    "
+    (Decimal sign coeficient exponent special)))
+
+(def _mk (self  (= value "0") (= context None))
+       "Create a decimal point instance.
+
+        >>> Decimal('3.14')              # string input
+        Decimal('3.14')
+        >>> Decimal((0, (3, 1, 4), -2))  # tuple (sign, digit_tuple, exponent)
+        Decimal('3.14')
+        >>> Decimal(314)                 # int
+        Decimal('314')
+        >>> Decimal(Decimal(314))        # another decimal instance
+        Decimal('314')
+        >>> Decimal('  3.14  \\n')        # leading and trailing whitespace okay
+        Decimal('3.14')
+        "
+
+        ;; Note that the coefficient, self._int, is actually stored as
+        ;; a string rather than as a tuple of digits.  This speeds up
+        ;; the "digits to integer" and "integer to digits" conversions
+        ;; that are used in almost every arithmetic operation on
+        ;; Decimals.  This is an internal detail: the as_tuple function
+        ;; and the Decimal constructor still deal with tuples of
+        ;; digits.
+
+        ;; From a string
+        ;; REs insist on real strings, so we can too.
+        (cond
+	 ((isinstance value str)
+	    (let ((m (parser (scm-str str))))
+	      (if (not m)
+                (let ((context (if (eq? context None)
+				   (getcontext)
+				   context)))
+		  ((cx-raise context)
+		   ConversionSyntax
+		   (+ "Invalid literal for Decimal: " value))))
+
+	      (let ((sign     (get-parsed-sign m))
+		    (intpart  (get-parsed-int  m))
+		    (fracpart (get-parsed-frac m))
+		    (exp      (get-parsed-exp  m))
+		    (diag     (get-parsed-diag m))
+		    (signal   (get-parsed-sig  m)))
+		
+		(set self 'sign sign)
+		
+		(if (not (eq? intpart None))
+		    (begin
+		      (set self '_int (str (int (+ intpart fracpart))))
+		      (set self '_exp (- exp (len fracpart)))
+		      (set self '_is_special False))
+		    (begin
+		      (if (not (eq? diag None))
+			  (begin
+			    ;; NaN
+			    (set self '_int
+				 (py-lstrip (str (int (if (bool diag)
+							  diag
+							  "0")))
+					    "0"))
+			    (if signal
+				(set self '_exp "N")
+				(set self '_exp "n")))
+			  (begin
+			    ;; infinity
+			    (set self '_int "0")
+			    (set self '_exp "F")))
+		      (set self '_is_special #t))))))
+	 
+	;; From an integer	   
+        ((isinstance value int)
+	 (if (>= value 0)
+	     (set self '_sign 0)
+	     (set self '_sign 1))
+	 (set self '_exp 0)
+         (set self '_int (str (abs value)))
+	 (set self '_is_special #f))
+	
+        ;; From another decimal
+        ((isinstance value Decimal)
+            (set self '_exp        (ref value '_exp       ))
+            (set self '_sign       (ref value '_sign      ))
+            (set self '_int        (ref value '_int       ))
+            (set self '_is_special (ref value '_is_special)))
+
+        ;; From an internal working value
+        ((isinstance value _WorkRep)
+	 (set self '_exp        (int (ref value '_exp)))
+	 (set self '_sign       (ref value '_sign))
+	 (set self '_int        (str (ref value 'int)))
+	 (set self '_is_special #f))
+
+        ;; tuple/list conversion (possibly from as_tuple())
+        ((isinstance value (list list tuple))
+            (if (not (= (len value) 3))
+                (raise (ValueError
+			(+ "Invalid tuple size in creation of Decimal "
+			   "from list or tuple.  The list or tuple "
+			   "should have exactly three elements."))))
+	    ;; # process sign.  The isinstance test rejects floats
+	    (let ((v0 (pylist-ref value 0))
+		  (v1 (pylist-ref value 1))
+		  (v2 (pylist-ref value 2)))
+	      (if (not (and (isinstance v0 int)
+			    (or (= v0 0) (= v0 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."))))
+	      (set self '_sign v0)
+            (if (eq? v2 'F)
+		(begin
+		  (set self '_int "0")
+		  (set self '_exp v2)
+		  (set self 'is_special #t))
+		(let ((digits (py-list)))
+		  ;; process and validate the digits in value[1]
+		  (for ((digit : v1)) ()
+		       (if (and (isinstance digit int)
+				(<= 0 digit)
+				(<= digit 9))
+			   ;; skip leading zeros
+			   (if (or (bool digits) (> digit 0))
+			       (pylist-append digits digit))
+			   (raise (ValueError
+				   (+ "The second value in the tuple must "
+				      "be composed of integers in the range "
+				      "0 through 9.")))))
+		  
+		  (cond
+		   ((or (eq? v2 'n) (eq? v2 'N))
+		    (begin
+		      ;; NaN: digits form the diagnostic
+		      (set self '_int  (py-join "" (map str digits)))
+		      (set self '_exp  v2)
+			(set self '_is_special #t)))
+		   ((isinstance v2  int)
+		    ;; finite number: digits give the coefficient
+		    (set self '_int (py-join "" (map str digits)))
+		    (set self '_exp v2)
+		    (set self '_is_special #f))
+		   (else
+		    (raise (ValueError
+			    (+ "The third value in the tuple must "
+			       "be an integer, or one of the "
+			       "strings 'F', 'n', 'N'.")))))))))
+
+	((isinstance value float)
+	 (let ((context (if (eq? context None)
+			    (getcontext)
+			    context)))
+	   ((cx-error context)
+	    FloatOperation,
+	    (+ "strict semantics for mixing floats and Decimals are "
+	       "enabled"))
+	   
+	   (__init__ self ((ref Decimal 'from_float) value))))
+
+	(else
+	 (raise (TypeError
+		 (format #f "Cannot convert %r to Decimal" value))))))
+
+(define-inlinable (divmod x y)
+  (values (quotient x y) (modulo x y)))
+
+(define-syntax twix
+  (syntax-rules (let)
+    ((_ a) a)
+    ((_ (let (a ...)) . l)
+     (a ... (twix - l)))
+    ((_ (a it code ...) . l)
+     (aif it a (begin code ...) (twix - l)))))
+
+(define-syntax-rule (norm-op op)
+  (begin
+    (set! op ((ref self '_convert_other) op))
+    (if (eq? op NotImplemented)
+	other
+	#f)))
+
+(define-syntax-rule (get-context context code)
+  (let ((context (if (eq? context None)
+		     (getcontext)
+		     context)))
+    code))
+
+(define-syntax-rule (un-special self context)
+  (if ((ref self '_is_special))
+      (let ((ans ((ref self '_check_nans) #:context context)))
+	(if (bool ans)
+	    (ret ans)
+	    #f))
+      #f))
+
+(define-syntax-rule (bin-special o1 o2 context)
+  (if (or (ref o1  '_is_special)
+	  (ref o2  '_is_special))
+      (or (un-special o1 context) (un-special o2 context))))
+
+(define-syntax-rule (add-special self other context)
+  (or (bin-special self other context)
+      (if ((ref self '_isinfinity))
+	  ;; If both INF, same sign =>
+	  ;; same as both, opposite => error.
+	  (if (and (not (= (ref self '_sign) (ref other '_sign)))
+		   ((ref other '_isinfinity)))
+	      ((cx-error context) InvalidOperation "-INF + INF")
+	      (Decimal self))	      
+	  (if ((ref other '_isinfinity))
+	      (ret (Decimal other)) ; Can't both be infinity here
+	      #f))))
+
+(define-syntax-rule (mul-special self other context)
+  (if (or (ref self '_is_special) (ref other '_is_special))
+      (twix
+       ((bin-special self other context) it it)
+	       
+       ((if ((ref self '_isinfinity))
+	    (if (not (bool other))
+		((cx-error context) InvalidOperation "(+-)INF * 0")
+		(pylist-ref _SignedInfinity resultsign))
+	    #f) it it)
+
+       (if ((ref other '_isinfinity))
+	   (if (not (bool self))
+	       ((cx-error context) InvalidOperation "(+-)INF * 0")
+	       (pylist-ref _SignedInfinity resultsign))
+	   #f))
+      #f))
+
+  (define-syntax-rule (div-special self other context)
+    (if (or (ref self '_is_special) (ref other '_is_special))
+	(twix
+	 ((bin-special self other context) it it)
+	       
+	 ((and ((ref self '_isinfinity)) ((ref other '_isinfinity))) it
+	  ((cx-error context) InvalidOperation "(+-)INF/(+-)INF"))
+
+	 (((ref self '_isinfinity)) it
+          (pylist-ref _SignedInfinity sign))
+
+	 (((ref other '_isinfinity)) it
+	  ((cx-error context) Clamped "Division by infinity")
+	  (_dec_from_triple sign  "0", (cx-etiny context))))))
+        
+
+(define-python-class Decimal (object)
+    "Floating point class for decimal arithmetic."
+    
+    
+    ;; Generally, the value of the Decimal instance is given by
+    ;;  (-1)**_sign * _int * 10**_exp
+    ;; Special values are signified by _is_special == True
+
+    (define __init__
+      (case-lambda
+       ((self sign coefficient exponent special)
+	(set self '_sign       sign)
+	(set self '_int        coefficient)
+	(set self '_exp        exponent)
+	(set self '_is_special special))
+       
+       ((self)
+	(_mk self))
+       ((self a)
+	(_mk self a))
+       ((self a b)
+	(_mk self a b))))
+
+    (define from_float
+      (classmethod
+       (lambda (cls f)
+        "Converts a float to a decimal number, exactly.
+
+        Note that Decimal.from_float(0.1) is not the same as Decimal('0.1').
+        Since 0.1 is not exactly representable in binary floating point, the
+        value is stored as the nearest representable value which is
+        0x1.999999999999ap-4.  The exact equivalent of the value in decimal
+        is 0.1000000000000000055511151231257827021181583404541015625.
+
+        >>> Decimal.from_float(0.1)
+        Decimal('0.1000000000000000055511151231257827021181583404541015625')
+        >>> Decimal.from_float(float('nan'))
+        Decimal('NaN')
+        >>> Decimal.from_float(float('inf'))
+        Decimal('Infinity')
+        >>> Decimal.from_float(-float('inf'))
+        Decimal('-Infinity')
+        >>> Decimal.from_float(-0.0)
+        Decimal('-0')
+
+        "
+        (cond
+	 ((isinstance f  int)                ; handle integer inputs
+	  (cls f))
+	 ((not (isinstance f float))
+	  (raise (TypeError "argument must be int or float.")))
+	 ((or (inf? f) (nan? f))
+	  (cls (cond
+		((nan? f)         "")
+		((eq? f (inf))    "")
+		(eq? f (- (inf))) "")))
+	 (else
+	  (let* ((sign (if (>= f 0) 0 1))
+		 (me   (frexp f))
+		 (m    (car  me))
+		 (e    (cadr me))
+		 (res  (_dec_from_triple sign, str(m) e)))
+	    (if (eq? cls Decimal)
+		res
+		(cls res))))))))
+    
+    (define _isnan
+      (lambda (self)
+        "Returns whether the number is not actually one.
+
+        0 if a number
+        1 if NaN
+        2 if sNaN
+        "
+        (if (ref self '_is_special)
+            (let ((exp (ref self '_exp)))
+	      (cond
+	       ((eq? exp 'n) 1)
+	       ((eq? exp 'N) 2)
+	       (else         0)))
+	    0)))
+    
+    (define _isinfinity
+      (lambda (self)
+        "Returns whether the number is infinite
+
+        0 if finite or not a number
+        1 if +INF
+        -1 if -INF
+        "
+        (if (eq? (ref self '_exp) 'F)
+            (if (eq? (ref self '_sign) 1)
+                -1
+		1)
+	    0)))
+    
+    (define _check_nans
+      (lam (self (= other None) (= context None))
+        "Returns whether the number is not actually one.
+
+        if self, other are sNaN, signal
+        if self, other are NaN return nan
+        return 0
+
+        Done before operations.
+        "
+
+        (let ((self_is_nan ((ref self '_isnan)))
+	      (other_is_nan
+	       (if (eq? other None)
+		   #f
+		   ((ref other '_isnan)))))
+	  
+	  (if (or self_is_nan other_is_nan)
+	      (let ((context (if (eq? context None)
+				 (getcontext)
+				 context)))
+		(cond
+		 ((eq? self_is_nan 2)
+		  ((cx-error context) InvalidOperation "sNaN" self))
+		 ((eq? other_is_nan 2)
+		  ((cx-error context) InvalidOperation "sNaN" other))
+		 (self_is_nan
+		  ((ref self '_fix_nan) context))
+		 (else
+		  ((ref other '_fix_nan) context))))
+	      0))))
+		 
+
+    (define _compare_check_nans
+      (lambda (self other context)
+        "Version of _check_nans used for the signaling comparisons
+        compare_signal, __le__, __lt__, __ge__, __gt__.
+
+        Signal InvalidOperation if either self or other is a (quiet
+        or signaling) NaN.  Signaling NaNs take precedence over quiet
+        NaNs.
+
+        Return 0 if neither operand is a NaN.
+
+        "
+        (let ((context (if (eq? context None)
+			   (getcontext)
+			   context)))
+
+	  (if (or (ref self  '_is_special)
+		  (ref other '_is_special))
+	      (cond
+	       (((ref self 'is_snan))
+		((cx-error context)
+		 InvalidOperation
+		 "comparison involving sNaN" self))
+
+ 	       (((ref other 'is_snan))
+		((cx-error context)
+		 InvalidOperation
+		 "comparison involving sNaN" other))
+		
+	       (((ref self 'is_qnan))
+		((cx-error context)
+		 InvalidOperation
+		 "comparison involving NaN" self))
+
+ 	       (((ref other 'is_qnan))
+		((cx-error context)
+		 InvalidOperation
+		 "comparison involving NaN" other))
+	       
+	       (else 0))
+	      0))))
+
+    (define __bool__
+      (lambda (self)
+        "Return True if self is nonzero; otherwise return False.
+
+        NaNs and infinities are considered nonzero.
+        "
+        (or (ref self '_is_special) (not (equal (ref self '_int) "0")))))
+
+    (define _cmp
+      (lambda (self other)
+        "Compare the two non-NaN decimal instances self and other.
+
+        Returns -1 if self < other, 0 if self == other and 1
+        if self > other.  This routine is for internal use only."
+
+	(let ((self_sign  (ref self  '_sign))
+	      (other_sign (ref other '_sign)))
+	  (cond
+	   ((or (ref self '_is_special) (ref other '_is_special))
+	    (let ((self_inf  ((ref self  '_isinfinity)))
+		  (other_inf ((ref other '_isinfinity))))
+	      (cond
+	       ((eq? self_inf other_inf) 0)
+	       ((< self_inf other_inf)  -1)
+	       (else                     1)))
+	    
+	    ;; check for zeros;  Decimal('0') == Decimal('-0')
+	    ((not (bool self))
+	     (if (not (bool other))
+		 0
+		 (let ((s (ref other '_sign)))
+		   (if (= s 0)
+		       -1
+		       1))))
+	    ((not (bool other))
+	     (let ((s (ref self '_sign)))
+	       (if (= s 0)
+		   1
+		   -1)))
+	  
+	    ((< other_sign self_sign)
+	     -1)
+	    ((< self_sign other_sign)
+	     1)
+
+	    (else
+	     (let ((self_adjusted  ((ref self  'adjusted)))
+		   (other_adjusted ((ref other 'adjusted)))
+		   (self_exp       (ref self  '_exp))
+		   (other_exp      (ref other '_exp)))
+	       (cond
+		((= self_adjusted other_adjusted)
+		 (let ((self_padded  (+ (ref self '_int)
+					(* "0" (- self_exp  other_exp))))
+		       (other_padded (+ (ref other '_int)
+					(* "0" (- other_exp  self_exp)))))
+		   (cond
+		    ((equal? self_padded other_padded)
+		     0)
+		    ((< self_padded other_padded)
+		     (if (= self_sign 0)
+			 -1
+			 1))
+		    (else
+		     (if (= self_sign 0)
+			 1
+			 -1)))))
+		((> self_adjusted other_adjusted)
+		 (if (= self_sign 0)
+		     1
+		     -1))
+		(else
+		 (if (= self_sign 0)
+		     -1
+		     1))))))))))
+    
+    ;; Note: The Decimal standard doesn't cover rich comparisons for
+    ;; Decimals.  In particular, the specification is silent on the
+    ;; subject of what should happen for a comparison involving a NaN.
+    ;; We take the following approach:
+    ;;
+    ;;   == comparisons involving a quiet NaN always return False
+    ;;   != comparisons involving a quiet NaN always return True
+    ;;   == or != comparisons involving a signaling NaN signal
+    ;;      InvalidOperation, and return False or True as above if the
+    ;;      InvalidOperation is not trapped.
+    ;;   <, >, <= and >= comparisons involving a (quiet or signaling)
+    ;;      NaN signal InvalidOperation, and return False if the
+    ;;      InvalidOperation is not trapped.
+    ;;
+    ;; This behavior is designed to conform as closely as possible to
+    ;; that specified by IEEE 754.
+    
+    (define __eq__
+      (lam (self other (= context None))
+	   (let ((so    (_convert_for_comparisonc self other #:equality_op #t))
+		 (self  (car  so))
+		 (other (cadr so)))
+	     
+	     (cond
+	      ((eq? other NotImplemented)
+	       other)
+	      ((bool ((ref self '_check_nans) other context))
+	       #f)
+	      (else (= ((ref self '_cmp) other) 0))))))
+
+    (define _xlt
+      (lambda (<)
+	(lam (self other (= context None))
+	     (let ((so (_convert_for_comparisonc self other #:equality_op #t))
+		   (self  (car  so))
+		   (other (cadr so)))
+	     
+	       (cond
+		((eq? other NotImplemented)
+		 other)
+		((bool ((ref self '_compare_check_nans) other context))
+		 #f)
+		(else (< ((ref self '_cmp) other) 0)))))))
+      
+    (define __lt__ (_xlt < ))
+    (define __le__ (_xlt <=))
+    (define __gt__ (_xlt > ))
+    (define __ge__ (_xlt >=))
+
+    (define compare
+      (lam (self other (= context None))
+        "Compare self to other.  Return a decimal value:
+
+        a or b is a NaN ==> Decimal('NaN')
+        a < b           ==> Decimal('-1')
+        a == b          ==> Decimal('0')
+        a > b           ==> Decimal('1')
+        "
+        (let ((other (_convert_other other #:raiseit #t)))
+	  ;; Compare(NaN, NaN) = NaN
+	  (if (or (ref self '_is_special)
+		  (and (bool other)
+		       (ref other '_is_special)))
+	      (aif it ((ref self '_check_nans) other context)
+		   it
+		   (Decimal ((ref self '_cmp) other)))))))
+
+    (define __hash__
+      (lambda (self)
+	"x.__hash__() <==> hash(x)"
+
+        ;; In order to make sure that the hash of a Decimal instance
+        ;; agrees with the hash of a numerically equal integer, float
+        ;; or Fraction, we follow the rules for numeric hashes outlined
+        ;; in the documentation.  (See library docs, 'Built-in Types').
+        (cond
+	 ((ref self '_is_special)
+	  (cond
+	   (((ref self 'is_snan))
+	    (raise (TypeError "Cannot hash a signaling NaN value.")))
+	   (((ref self 'is_snan))
+	    (hash (nan)))
+	   ((= 1 (ref self '_sign))
+	    (hash (- (inf))))
+	   (else
+	    (hash (inf)))))
+	    
+	 (else
+	  (let* ((exp (ref self '_exp))
+		 (exp_hash
+		  (if (>= exp 0)
+		      (expt 10            exp _   pyhash-N)
+		      (expt _PyHASH_10INV (- exp) pyhash-N)))
+		 
+		 (hash_
+		  (modulus (* (int (ref self '_int)) exp_hash)
+			   pyhash-N))
+
+		 (ans
+		  (if (>= self 0) hash_ (- hash_))))
+	    (if (= ans -1) -2 ans))))))
+    
+    (define as_tuple
+      (lambda (self)
+        "Represents the number as a triple tuple.
+
+        To show the internals exactly as they are.
+        "
+	(DecimalTuple self._sign
+		      (tuple (map int (ref self '_int)))
+		      (ref self '_exp))))
+
+    (define as_integer_ratio
+      (lambda (self)
+        "Express a finite Decimal instance in the form n / d.
+
+        Returns a pair (n, d) of integers.  When called on an infinity
+        or NaN, raises OverflowError or ValueError respectively.
+
+        >>> Decimal('3.14').as_integer_ratio()
+        (157, 50)
+        >>> Decimal('-123e5').as_integer_ratio()
+        (-12300000, 1)
+        >>> Decimal('0.00').as_integer_ratio()
+        (0, 1)
+        "
+        (if (ref self '_is_special)
+            (if ((ref self 'is_nan))
+                (raise (ValueError
+			"cannot convert NaN to integer ratio"))
+                (raise (OverflowError
+			"cannot convert Infinity to integer ratio"))))
+
+        (if (not (bool self))
+            (values 0 1)
+	    (let ((s (ref self '_sign))
+		  (n (int (ref self '_int)))
+		  (e (ref self '_exp))
+		  (x
+		   (* n (if (> exp 0)
+			    (expt 10 exo)
+			    (/ 1 (expt 10 (- expt)))))))
+	      (values (numerator x)
+		      (denomerator x))))))
+    
+    (define __repr__
+      (lambda (self)
+        "Represents the number as an instance of Decimal."
+        ;# Invariant:  eval(repr(d)) == d
+        (format #f "Decimal('~a')" (str self))))
+
+    (define __str__
+      (lam (self  (= eng #f) (= context None))
+        "Return string representation of the number in scientific notation.
+
+        Captures all of the information in the underlying representation.
+        "
+	(let* ((sign         (if (= (reg self '_sign) 0) "" "-"))
+	       (exp          (ref self '_exp))
+	       (i            (ref self '_int))
+	       (leftdigits   (+ exp (len i)))
+	       (dotplace     #f)
+	       (intpart      #f)
+	       (fracpart     #f)
+	       (exppart      #f))
+	  
+	  (cond
+	   ((ref self '_is_special)
+            (cond
+	     ((eq? (ref self '_exp) 'F)
+	      (+ sign "Infinity"))
+	     ((eq? (ref self '_exp) 'n)
+	      (+ sign  "NaN" (ref self '_int)))
+	     (else ; self._exp == 'N'
+	      (+ sign  "sNaN" (ref self '_int)))))
+	   (else
+	    ;; 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)
+	    (cond
+	     ((and (<= exp 0) (> leftdigits  -6))
+	      ;; no exponent required
+	      (set! dotplace leftdigits))
+	     
+	     ((not eng)
+	      ;; usual scientific notation: 1 digit on left of the point
+	      (set! dotplace 1))
+	     
+	     ((equal? i "0")
+	      ;; engineering notation, zero
+	      (set! dotplace (- (modulo (+ leftdigits 1) 3) 1)))
+	     (else
+	      ;; engineering notation, nonzero
+	      (set! dotplace (- (modulo (+ leftdigits 1) 3) 1))))
+
+	    (cond
+	     ((<= dotplace 0)
+	      (set! intpart "0")
+	      (set! fracpart (+ "." + (* "0" (- dotplace)) + i)))
+	     ((>= dotplace (len i))
+	      (set! intpart (+ i (* "0" (- dotplace (len i)))))
+	      (set! fracpart ""))
+	     (else
+	      (set! intpart (pylist-slice i None dotplace None))
+	      (set! fracpart (+ '.' (pylist-slice i dotplace None None)))))
+
+	    
+	    (cond
+	     ((= leftdigits dotplace)
+	      (set! exp ""))
+	     (else
+	      (let ((context (if (eq? context None)
+				 (getcontext)
+				 context)))
+		(set! exp
+		      (+ (pylist-ref (lise "e" "E") (cx-capitals context))
+			 (format #f "%@d" (- leftdigits dotplace)))))))
+	    (+ sign intpart fracpart exp))))))
+    
+    (define to_eng_string
+      (lam (self (= context None))
+        "Convert to a string, using engineering notation if an exponent is needed.
+        Engineering notation has an exponent which is a multiple of 3.  This
+        can leave up to 3 digits to the left of the decimal place and may
+        require the addition of either one or two trailing zeros.
+        "
+        ((ref self '__str__) #:eng #t #:contect context)))
+
+    (define __neg__
+      (lam (self (= contextNone))
+        "Returns a copy with the sign switched.
+
+        Rounds, if it has reason.
+        "
+	(twix 
+	  ((un-special self context) it it)
+	  (let* ((context (if (eq? context None)
+			      (getcontext)
+			      context))
+		 (ans     (if (and (not (bool self))
+				   (not (eq? (cx-rounding context)
+					     ROUND_FLOOR)))
+			      ;; -Decimal('0') is Decimal('0'),
+			      ;; not Decimal('-0'), except
+			      ;; in ROUND_FLOOR rounding mode.
+			      ((ref self 'copy_abs))
+			      ((ref self 'copy_negate)))))
+
+	    ((ref ans '_fix) context)))))
+    
+    (define __pos__
+      (lam (self (= context None))
+        "Returns a copy, unless it is a sNaN.
+
+        Rounds the number (if more than precision digits)
+        "
+	(twix
+	 ((un-special self context) it it)
+	 
+	 (let* ((context (if (eq? context None)
+			     (getcontext)
+			     context))
+		(ans     (if (and (not (bool self))
+				  (not (eq? (cx-rounding context)
+					    ROUND_FLOOR)))
+			     ;; -Decimal('0') is Decimal('0'),
+			     ;; not Decimal('-0'), except
+			     ;; in ROUND_FLOOR rounding mode.
+			     ((ref self 'copy_abs))
+			     (Decimal self))))
+
+	   ((ref ans '_fix) context)))))
+
+    (define __abs__
+      (lam (self  (= round #t) (= context None))
+	"Returns the absolute value of self.
+
+        If the keyword argument 'round' is false, do not round.  The
+        expression self.__abs__(round=False) is equivalent to
+        self.copy_abs().
+        "
+	(twix
+	 ((not (bool round))
+	  ((ref self 'copy_abs)))
+
+	 ((un-special self context) it it)
+
+	 (if (= (ref self '_sign) 1)
+	     ((ref self '__neg__) #:context context)
+	     ((ref self '__pos__) #:context context)))))
+    
+    (define __add__
+      (lam (self other (= context None))
+        "Returns self + other.
+
+        -INF + INF (or the reverse) cause InvalidOperation errors.
+        "
+	(twix
+	 ((norm-op other) it it)
+	 
+	 (let (get-context context))
+	 
+	 ((add-special o1 o2 context) it it)
+	 		 
+	 (let (let* ((negativezero 0)
+		     (self_sign    (ref self  '_sign))
+		     (other_sign   (ref other '_sign))
+		     (self_exp     (ref self  '_sign))
+		     (other_exp    (ref other '_sign))
+		     (prec         (cx-prec context))
+		     (exp          (min self_exp other_exp))		    
+		     (sign         #f)
+		     (ans          #f))
+	  
+		(if (and (eq? (cx-rounding context) ROUND_FLOOR)
+			 (not (= self_sign other_sign)))
+		    ;; If the answer is 0, the sign should be negative,
+		    ;; in this case.
+		    (set! negativezero 1))))
+
+	 ((if (and (not (bool self)) (not (bool other)))
+	      (begin
+		(set! sign (min self_sign other_sign))
+		(if (= negativezero 1)
+		    (set! sign 1))
+		(set! ans (_dec_from_triple sign "0" exp))
+		(set! ans ((ref ans '_fix) context))
+		ans)
+	      #f) it it)
+
+	 ((if (not (bool self))
+	      (begin
+		(set! exp (max exp (- other_exp prec 1)))
+		(set! ans ((ref other '_rescale) exp
+			   (cx-rounding rounding)))
+		(set! ans ((ref ans '_fix) context))
+		ans)
+	      #f) it it)
+
+	 ((if (not (bool other))
+	      (begin
+		(set! exp (max exp (- self_exp prec 1)))
+		(set! ans ((ref self '_rescale) exp
+			   (cx-rounding rounding)))
+		(set! ans ((ref ans '_fix) context))
+		ans)
+	      #f) it it)
+		
+		
+	 (let (let* ((op1    (_WorkRep self))
+		     (op2    (_WorkRep other))
+		     (ab     (_normalize op1 op2 prec))
+		     (op1    (car  ab))
+		     (op2    (cadr ab))
+		     (result (_WorkRep)))))
+
+	 ((cond
+	   ((not (= (ref op1 'sign) (ref op2 'sign)))
+	    ;; Equal and opposite
+	    (twix
+	     ((= op1_i op2_i) it
+	      (set! ans (_dec_from_triple negativezero "0" exp))
+	      (set! ans ((ref ans '_fix) context))
+	      ans)
+		    
+	     (begin
+	       (if (< op1_i op2_i)
+		   (let ((t op1))
+		     (set! op1 op2)
+		     (set! op2 t)))
+		    
+	       (if (= (ref op1 'sign) 1)			
+		   (let ((t (ref op1 'sign)))
+		     (set result 'sign 1)
+		     (set op1 'sign (ref op2 'sign))
+		     (set op2 'sign t))
+		   (set result 'sign 0))
+	       #f)))
+	   ((= (ref op1 'sign) 1)
+	    (set result 'sign 1)
+	    #f)
+	   
+	   (begin
+	     (set result 'sign 0)
+	     #f)) it it)
+
+	 (begin
+	   (if (= (ref op2 'sign) 0)
+	       (set result 'int (+ (ref op1 'int) (ref op2 'int)))
+	       (set result 'int (- (ref op1 'int) (ref op2 'int))))
+
+	   (set result 'exp (ref op1 'exp))
+	   (set! ans (Decimal result))
+	   ((ref ans '_fix) context)))))
+
+    (define __radd__ __add__)
+
+    (define __sub__
+      (lam (self other (= context None))
+	"Return self - other"
+	(twix
+	 ((norm-op other)            it it)
+	 ((bin-special o1 o2 context) it it)
+	 ((ref self '__add__)
+	  ((ref other 'copy_negate)) #:context context))))
+
+    (define  __rsub__
+      (lam (self other (= context None))
+        "Return other - self"
+    	(twix
+	 ((norm-op other) it it)
+	 ((ref 'other '__sub__) self  #:context context))))
+
+    (define __mul__
+      (lam (self other (= context None))
+        "Return self * other.
+
+        (+-) INF * 0 (or its reverse) raise InvalidOperation.
+        "
+	(twix
+	 ((norm-op other) it it)	 
+	 (let (get-context context))
+	 
+	 (let (let ((resultsign (logxor (ref self  '_sign)
+					(ref other '_sign))))))
+
+	 ((mul-special o1 o2 context) it it)
+
+	 (let (let ((resultexp (+ (ref self '_exp) (ref other '_exp))))))
+
+	 ;; Special case for multiplying by zero
+	 ((or (not (bool self)) (not (bool other)))
+	  (let ((ans (_dec_from_triple resultsign "0" resultexp)))
+	    ((ref and '_fix) context)))
+	 
+	 ;; Special case for multiplying by power of 10
+	 ((equal? (ref self '_int) "1")
+	  (let ((ans (_dec_from_triple resultsign (ref other '_int) resultexp)))
+	    ((ref and '_fix) context)))
+
+	 ((equal? (ref other '_int) "1")
+	  (let ((ans (_dec_from_triple resultsign (ref self '_int) resultexp)))
+	    ((ref and '_fix) context)))
+
+	 (let* ((op1 (_WorkRep self))
+		(op2 (_WorkRep other))
+		(ans (_dec_from_triple resultsign
+				       (str (* (ref op1 ') (ref op2 'int)))
+				       resultexp)))
+	   ((ref and '_fix) context)))))
+
+    (define __rmul__ __mul__)
+
+    (define __truediv__
+      (lam (self other (= context None))
+	"Return self / other."
+	(twix
+	 ((norm-op other) it it)	 
+	 (let (get-context context))
+   
+	 (let (let ((sign (logxor (ref self  '_sign)
+				  (ref other '_sign))))))
+
+	 ((div-special o1 o2 context) it it)	 
+
+	 ;; Special cases for zeroes
+        ((if (not (bool other))
+	     (if (not (bool self))
+                 ((cx-error context) DivisionUndefined "0 / 0")
+		 ((cx-error context) DivisionByZero    "x / 0" sign))
+	     #f) it it)
+
+	(let ((exp    #f)
+	      (coeff  #f)
+	      (nself  (len (ref self '_int)))
+	      (nother (len (ref other '_int))))
+	  (if (not (bool self))
+	      (begin
+		(set! exp   (- (ref self '_exp) (ref other '_exp)))
+		(set! coeff 0))
+	      ;; OK, so neither = 0, INF or NaN
+	      (let ((shift (+ nother (- nself) prec 1))
+		    (op1   (_WorkRep self))
+		    (op2   (_WorkRep other)))
+		(set! exp (- (ref self '_exp) (ref other '_exp) shift))
+		(call-with-values
+		    (lambda ()
+		      (if (>= shift 0)
+			  (divmod (* (ref op1 'int) (expt 10 shift))
+				  (ref op2 'int))
+			  (divmod (ref op1 'int)
+				  (* (ref op2 'int) (expt 10 shift)))))
+		  (lambda (coeff- remainder)
+		    (set! coeff
+			  (if (not (= remainder 0))
+			      ;; result is not exact adjust to ensure
+			      ;; correct rounding
+			      (if (= (modulus coeff- 5) 0)
+				  (+ coeff- 1)
+				  coeff)
+			      (let (ideal_exp (- (ref self '_exp)
+						 (ref other '_exp)))
+				(let lp ((coeff- coeff-) (exp- exp))
+				  (if (and (< exp- indeal_exp)
+					   (= (modulo coeff 10) 0))
+				      (lp (/ coeff 10) (+ exp- 1))
+				      (begin
+					(set exp exp-)
+					coeff))))))))))
+			      
+			    
+	  (let ((ans (_dec_from_triple sign, (str coeff) exp)))
+	    ((ref ans '_fix) context))))))
+
+    def _divide(self, other, context):
+        """Return (self // other, self % other), to context.prec precision.
+
+        Assumes that neither self nor other is a NaN, that self is not
+        infinite and that other is nonzero.
+        """
+        sign = self._sign ^ other._sign
+        if other._isinfinity():
+            ideal_exp = self._exp
+        else:
+            ideal_exp = min(self._exp, other._exp)
+
+        expdiff = self.adjusted() - other.adjusted()
+        if not self or other._isinfinity() or expdiff <= -2:
+            return (_dec_from_triple(sign, '0', 0),
+                    self._rescale(ideal_exp, context.rounding))
+        if expdiff <= context.prec:
+            op1 = _WorkRep(self)
+            op2 = _WorkRep(other)
+            if op1.exp >= op2.exp:
+                op1.int *= 10**(op1.exp - op2.exp)
+            else:
+                op2.int *= 10**(op2.exp - op1.exp)
+            q, r = divmod(op1.int, op2.int)
+            if q < 10**context.prec:
+                return (_dec_from_triple(sign, str(q), 0),
+                        _dec_from_triple(self._sign, str(r), ideal_exp))
+
+        # Here the quotient is too large to be representable
+        ans = context._raise_error(DivisionImpossible,
+                                   'quotient too large in //, % or divmod')
+        return ans, ans
+
+    def __rtruediv__(self, other, context=None):
+        """Swaps self/other and returns __truediv__."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        return other.__truediv__(self, context=context)
+
+    def __divmod__(self, other, context=None):
+        """
+        Return (self // other, self % other)
+        """
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if context is None:
+            context = getcontext()
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return (ans, ans)
+
+        sign = self._sign ^ other._sign
+        if self._isinfinity():
+            if other._isinfinity():
+                ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)')
+                return ans, ans
+            else:
+                return (_SignedInfinity[sign],
+                        context._raise_error(InvalidOperation, 'INF % x'))
+
+        if not other:
+            if not self:
+                ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)')
+                return ans, ans
+            else:
+                return (context._raise_error(DivisionByZero, 'x // 0', sign),
+                        context._raise_error(InvalidOperation, 'x % 0'))
+
+        quotient, remainder = self._divide(other, context)
+        remainder = remainder._fix(context)
+        return quotient, remainder
+
+    def __rdivmod__(self, other, context=None):
+        """Swaps self/other and returns __divmod__."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        return other.__divmod__(self, context=context)
+
+    def __mod__(self, other, context=None):
+        """
+        self % other
+        """
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if context is None:
+            context = getcontext()
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+
+        if self._isinfinity():
+            return context._raise_error(InvalidOperation, 'INF % x')
+        elif not other:
+            if self:
+                return context._raise_error(InvalidOperation, 'x % 0')
+            else:
+                return context._raise_error(DivisionUndefined, '0 % 0')
+
+        remainder = self._divide(other, context)[1]
+        remainder = remainder._fix(context)
+        return remainder
+
+    def __rmod__(self, other, context=None):
+        """Swaps self/other and returns __mod__."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        return other.__mod__(self, context=context)
+
+    def remainder_near(self, other, context=None):
+        """
+        Remainder nearest to 0-  abs(remainder-near) <= other/2
+        """
+        if context is None:
+            context = getcontext()
+
+        other = _convert_other(other, raiseit=True)
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+
+        # self == +/-infinity -> InvalidOperation
+        if self._isinfinity():
+            return context._raise_error(InvalidOperation,
+                                        'remainder_near(infinity, x)')
+
+        # other == 0 -> either InvalidOperation or DivisionUndefined
+        if not other:
+            if self:
+                return context._raise_error(InvalidOperation,
+                                            'remainder_near(x, 0)')
+            else:
+                return context._raise_error(DivisionUndefined,
+                                            'remainder_near(0, 0)')
+
+        # other = +/-infinity -> remainder = self
+        if other._isinfinity():
+            ans = Decimal(self)
+            return ans._fix(context)
+
+        # self = 0 -> remainder = self, with ideal exponent
+        ideal_exponent = min(self._exp, other._exp)
+        if not self:
+            ans = _dec_from_triple(self._sign, '0', ideal_exponent)
+            return ans._fix(context)
+
+        # catch most cases of large or small quotient
+        expdiff = self.adjusted() - other.adjusted()
+        if expdiff >= context.prec + 1:
+            # expdiff >= prec+1 => abs(self/other) > 10**prec
+            return context._raise_error(DivisionImpossible)
+        if expdiff <= -2:
+            # expdiff <= -2 => abs(self/other) < 0.1
+            ans = self._rescale(ideal_exponent, context.rounding)
+            return ans._fix(context)
+
+        # adjust both arguments to have the same exponent, then divide
+        op1 = _WorkRep(self)
+        op2 = _WorkRep(other)
+        if op1.exp >= op2.exp:
+            op1.int *= 10**(op1.exp - op2.exp)
+        else:
+            op2.int *= 10**(op2.exp - op1.exp)
+        q, r = divmod(op1.int, op2.int)
+        # remainder is r*10**ideal_exponent; other is +/-op2.int *
+        # 10**ideal_exponent.   Apply correction to ensure that
+        # abs(remainder) <= abs(other)/2
+        if 2*r + (q&1) > op2.int:
+            r -= op2.int
+            q += 1
+
+        if q >= 10**context.prec:
+            return context._raise_error(DivisionImpossible)
+
+        # result has same sign as self unless r is negative
+        sign = self._sign
+        if r < 0:
+            sign = 1-sign
+            r = -r
+
+        ans = _dec_from_triple(sign, str(r), ideal_exponent)
+        return ans._fix(context)
+
+    def __floordiv__(self, other, context=None):
+        """self // other"""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+
+        if context is None:
+            context = getcontext()
+
+        ans = self._check_nans(other, context)
+        if ans:
+            return ans
+
+        if self._isinfinity():
+            if other._isinfinity():
+                return context._raise_error(InvalidOperation, 'INF // INF')
+            else:
+                return _SignedInfinity[self._sign ^ other._sign]
+
+        if not other:
+            if self:
+                return context._raise_error(DivisionByZero, 'x // 0',
+                                            self._sign ^ other._sign)
+            else:
+                return context._raise_error(DivisionUndefined, '0 // 0')
+
+        return self._divide(other, context)[0]
+
+    def __rfloordiv__(self, other, context=None):
+        """Swaps self/other and returns __floordiv__."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        return other.__floordiv__(self, context=context)
+
+    def __float__(self):
+        """Float representation."""
+        if self._isnan():
+            if self.is_snan():
+                raise ValueError("Cannot convert signaling NaN to float")
+            s = "-nan" if self._sign else "nan"
+        else:
+            s = str(self)
+        return float(s)
+
+    def __int__(self):
+        """Converts self to an int, truncating if necessary."""
+        if self._is_special:
+            if self._isnan():
+	        raise ValueError("Cannot convert NaN to integer")
+            elif self._isinfinity():
+                raise OverflowError("Cannot convert infinity to integer")
+        s = (-1)**self._sign
+        if self._exp >= 0:
+            return s*int(self._int)*10**self._exp
+        else:
+            return s*int(self._int[:self._exp] or '0')
+
+    __trunc__ = __int__
+
+    def real(self):
+        return self
+    real = property(real)
+
+    def imag(self):
+        return Decimal(0)
+    imag = property(imag)
+
+    def conjugate(self):
+        return self
+
+    def __complex__(self):
+        return complex(float(self))
+
+    def _fix_nan(self, context):
+        """Decapitate the payload of a NaN to fit the context"""
+        payload = self._int
+
+        # maximum length of payload is precision if clamp=0,
+        # precision-1 if clamp=1.
+        max_payload_len = context.prec - context.clamp
+        if len(payload) > max_payload_len:
+            payload = payload[len(payload)-max_payload_len:].lstrip('0')
+            return _dec_from_triple(self._sign, payload, self._exp, True)
+        return Decimal(self)
+
+    def _fix(self, context):
+        """Round if it is necessary to keep self within prec precision.
+
+        Rounds and fixes the exponent.  Does not raise on a sNaN.
+
+        Arguments:
+        self - Decimal instance
+        context - context used.
+        """
+
+        if self._is_special:
+            if self._isnan():
+                # decapitate payload if necessary
+                return self._fix_nan(context)
+            else:
+                # self is +/-Infinity; return unaltered
+                return Decimal(self)
+
+        # if self is zero then exponent should be between Etiny and
+        # Emax if clamp==0, and between Etiny and Etop if clamp==1.
+        Etiny = context.Etiny()
+        Etop = context.Etop()
+        if not self:
+            exp_max = [context.Emax, Etop][context.clamp]
+            new_exp = min(max(self._exp, Etiny), exp_max)
+            if new_exp != self._exp:
+                context._raise_error(Clamped)
+                return _dec_from_triple(self._sign, '0', new_exp)
+            else:
+                return Decimal(self)
+
+        # exp_min is the smallest allowable exponent of the result,
+        # equal to max(self.adjusted()-context.prec+1, Etiny)
+        exp_min = len(self._int) + self._exp - context.prec
+        if exp_min > Etop:
+            # overflow: exp_min > Etop iff self.adjusted() > Emax
+            ans = context._raise_error(Overflow, 'above Emax', self._sign)
+            context._raise_error(Inexact)
+            context._raise_error(Rounded)
+            return ans
+
+        self_is_subnormal = exp_min < Etiny
+        if self_is_subnormal:
+            exp_min = Etiny
+
+        # round if self has too many digits
+        if self._exp < exp_min:
+            digits = len(self._int) + self._exp - exp_min
+            if digits < 0:
+                self = _dec_from_triple(self._sign, '1', exp_min-1)
+                digits = 0
+            rounding_method = self._pick_rounding_function[context.rounding]
+            changed = rounding_method(self, digits)
+            coeff = self._int[:digits] or '0'
+            if changed > 0:
+                coeff = str(int(coeff)+1)
+                if len(coeff) > context.prec:
+                    coeff = coeff[:-1]
+                    exp_min += 1
+
+            # check whether the rounding pushed the exponent out of range
+            if exp_min > Etop:
+                ans = context._raise_error(Overflow, 'above Emax', self._sign)
+            else:
+                ans = _dec_from_triple(self._sign, coeff, exp_min)
+
+            # raise the appropriate signals, taking care to respect
+            # the precedence described in the specification
+            if changed and self_is_subnormal:
+                context._raise_error(Underflow)
+            if self_is_subnormal:
+                context._raise_error(Subnormal)
+            if changed:
+                context._raise_error(Inexact)
+            context._raise_error(Rounded)
+            if not ans:
+                # raise Clamped on underflow to 0
+                context._raise_error(Clamped)
+            return ans
+
+        if self_is_subnormal:
+            context._raise_error(Subnormal)
+
+        # fold down if clamp == 1 and self has too few digits
+        if context.clamp == 1 and self._exp > Etop:
+            context._raise_error(Clamped)
+            self_padded = self._int + '0'*(self._exp - Etop)
+            return _dec_from_triple(self._sign, self_padded, Etop)
+
+        # here self was representable to begin with; return unchanged
+        return Decimal(self)
+
+    # for each of the rounding functions below:
+    #   self is a finite, nonzero Decimal
+    #   prec is an integer satisfying 0 <= prec < len(self._int)
+    #
+    # each function returns either -1, 0, or 1, as follows:
+    #   1 indicates that self should be rounded up (away from zero)
+    #   0 indicates that self should be truncated, and that all the
+    #     digits to be truncated are zeros (so the value is unchanged)
+    #  -1 indicates that there are nonzero digits to be truncated
+
+    def _round_down(self, prec):
+        """Also known as round-towards-0, truncate."""
+        if _all_zeros(self._int, prec):
+            return 0
+        else:
+            return -1
+
+    def _round_up(self, prec):
+        """Rounds away from 0."""
+        return -self._round_down(prec)
+
+    def _round_half_up(self, prec):
+        """Rounds 5 up (away from 0)"""
+        if self._int[prec] in '56789':
+            return 1
+        elif _all_zeros(self._int, prec):
+            return 0
+        else:
+            return -1
+
+    def _round_half_down(self, prec):
+        """Round 5 down"""
+        if _exact_half(self._int, prec):
+            return -1
+        else:
+            return self._round_half_up(prec)
+
+    def _round_half_even(self, prec):
+        """Round 5 to even, rest to nearest."""
+        if _exact_half(self._int, prec) and \
+                (prec == 0 or self._int[prec-1] in '02468'):
+            return -1
+        else:
+            return self._round_half_up(prec)
+
+    def _round_ceiling(self, prec):
+        """Rounds up (not away from 0 if negative.)"""
+        if self._sign:
+            return self._round_down(prec)
+        else:
+            return -self._round_down(prec)
+
+    def _round_floor(self, prec):
+        """Rounds down (not towards 0 if negative)"""
+        if not self._sign:
+            return self._round_down(prec)
+        else:
+            return -self._round_down(prec)
+
+    def _round_05up(self, prec):
+        """Round down unless digit prec-1 is 0 or 5."""
+        if prec and self._int[prec-1] not in '05':
+            return self._round_down(prec)
+        else:
+            return -self._round_down(prec)
+
+    _pick_rounding_function = dict(
+        ROUND_DOWN = _round_down,
+        ROUND_UP = _round_up,
+        ROUND_HALF_UP = _round_half_up,
+        ROUND_HALF_DOWN = _round_half_down,
+        ROUND_HALF_EVEN = _round_half_even,
+        ROUND_CEILING = _round_ceiling,
+        ROUND_FLOOR = _round_floor,
+        ROUND_05UP = _round_05up,
+    )
+
+    def __round__(self, n=None):
+        """Round self to the nearest integer, or to a given precision.
+
+        If only one argument is supplied, round a finite Decimal
+        instance self to the nearest integer.  If self is infinite or
+        a NaN then a Python exception is raised.  If self is finite
+        and lies exactly halfway between two integers then it is
+        rounded to the integer with even last digit.
+
+        >>> round(Decimal('123.456'))
+        123
+        >>> round(Decimal('-456.789'))
+        -457
+        >>> round(Decimal('-3.0'))
+        -3
+        >>> round(Decimal('2.5'))
+        2
+        >>> round(Decimal('3.5'))
+        4
+        >>> round(Decimal('Inf'))
+        Traceback (most recent call last):
+          ...
+        OverflowError: cannot round an infinity
+        >>> round(Decimal('NaN'))
+        Traceback (most recent call last):
+          ...
+        ValueError: cannot round a NaN
+
+        If a second argument n is supplied, self is rounded to n
+        decimal places using the rounding mode for the current
+        context.
+
+        For an integer n, round(self, -n) is exactly equivalent to
+        self.quantize(Decimal('1En')).
+
+        >>> round(Decimal('123.456'), 0)
+        Decimal('123')
+        >>> round(Decimal('123.456'), 2)
+        Decimal('123.46')
+        >>> round(Decimal('123.456'), -2)
+        Decimal('1E+2')
+        >>> round(Decimal('-Infinity'), 37)
+        Decimal('NaN')
+        >>> round(Decimal('sNaN123'), 0)
+        Decimal('NaN123')
+
+        """
+        if n is not None:
+            # two-argument form: use the equivalent quantize call
+            if not isinstance(n, int):
+                raise TypeError('Second argument to round should be integral')
+            exp = _dec_from_triple(0, '1', -n)
+            return self.quantize(exp)
+
+        # one-argument form
+        if self._is_special:
+            if self.is_nan():
+                raise ValueError("cannot round a NaN")
+            else:
+                raise OverflowError("cannot round an infinity")
+        return int(self._rescale(0, ROUND_HALF_EVEN))
+
+    def __floor__(self):
+        """Return the floor of self, as an integer.
+
+        For a finite Decimal instance self, return the greatest
+        integer n such that n <= self.  If self is infinite or a NaN
+        then a Python exception is raised.
+
+        """
+        if self._is_special:
+            if self.is_nan():
+                raise ValueError("cannot round a NaN")
+            else:
+                raise OverflowError("cannot round an infinity")
+        return int(self._rescale(0, ROUND_FLOOR))
+
+    def __ceil__(self):
+        """Return the ceiling of self, as an integer.
+
+        For a finite Decimal instance self, return the least integer n
+        such that n >= self.  If self is infinite or a NaN then a
+        Python exception is raised.
+
+        """
+        if self._is_special:
+            if self.is_nan():
+                raise ValueError("cannot round a NaN")
+            else:
+                raise OverflowError("cannot round an infinity")
+        return int(self._rescale(0, ROUND_CEILING))
+
+    def fma(self, other, third, context=None):
+        """Fused multiply-add.
+
+        Returns self*other+third with no rounding of the intermediate
+        product self*other.
+
+        self and other are multiplied together, with no rounding of
+        the result.  The third operand is then added to the result,
+        and a single final rounding is performed.
+        """
+
+        other = _convert_other(other, raiseit=True)
+        third = _convert_other(third, 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 = _SignedInfinity[self._sign ^ other._sign]
+            elif other._exp == 'F':
+                if not self:
+                    return context._raise_error(InvalidOperation,
+                                                '0 * INF in fma')
+                product = _SignedInfinity[self._sign ^ other._sign]
+        else:
+            product = _dec_from_triple(self._sign ^ other._sign,
+                                       str(int(self._int) * int(other._int)),
+                                       self._exp + other._exp)
+
+        return product.__add__(third, context)
+
+    def _power_modulo(self, other, modulo, context=None):
+        """Three argument version of __pow__"""
+
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        modulo = _convert_other(modulo)
+        if modulo is NotImplemented:
+            return modulo
+
+        if context is None:
+            context = getcontext()
+
+        # deal with NaNs: if there are any sNaNs then first one wins,
+        # (i.e. behaviour for NaNs is identical to that of fma)
+        self_is_nan = self._isnan()
+        other_is_nan = other._isnan()
+        modulo_is_nan = modulo._isnan()
+        if self_is_nan or other_is_nan or modulo_is_nan:
+            if self_is_nan == 2:
+                return context._raise_error(InvalidOperation, 'sNaN',
+                                        self)
+            if other_is_nan == 2:
+                return context._raise_error(InvalidOperation, 'sNaN',
+                                        other)
+            if modulo_is_nan == 2:
+                return context._raise_error(InvalidOperation, 'sNaN',
+                                        modulo)
+            if self_is_nan:
+                return self._fix_nan(context)
+            if other_is_nan:
+                return other._fix_nan(context)
+            return modulo._fix_nan(context)
+
+        # check inputs: we apply same restrictions as Python's pow()
+        if not (self._isinteger() and
+                other._isinteger() and
+                modulo._isinteger()):
+            return context._raise_error(InvalidOperation,
+                                        'pow() 3rd argument not allowed '
+                                        'unless all arguments are integers')
+        if other < 0:
+            return context._raise_error(InvalidOperation,
+                                        'pow() 2nd argument cannot be '
+                                        'negative when 3rd argument specified')
+        if not modulo:
+            return context._raise_error(InvalidOperation,
+                                        'pow() 3rd argument cannot be 0')
+
+        # additional restriction for decimal: the modulus must be less
+        # than 10**prec in absolute value
+        if modulo.adjusted() >= context.prec:
+            return context._raise_error(InvalidOperation,
+                                        'insufficient precision: pow() 3rd '
+                                        'argument must not have more than '
+                                        'precision digits')
+
+        # define 0**0 == NaN, for consistency with two-argument pow
+        # (even though it hurts!)
+        if not other and not self:
+            return context._raise_error(InvalidOperation,
+                                        'at least one of pow() 1st argument '
+                                        'and 2nd argument must be nonzero ;'
+                                        '0**0 is not defined')
+
+        # compute sign of result
+        if other._iseven():
+            sign = 0
+        else:
+            sign = self._sign
+
+        # convert modulo to a Python integer, and self and other to
+        # Decimal integers (i.e. force their exponents to be >= 0)
+        modulo = abs(int(modulo))
+        base = _WorkRep(self.to_integral_value())
+        exponent = _WorkRep(other.to_integral_value())
+
+        # compute result using integer pow()
+        base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo
+        for i in range(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 abs(y) = yc*10**ye, with xc
+        # and yc positive integers not divisible by 10.
+
+        # 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.  Express y as a rational number 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 y 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:
+            xe *= yc
+            # result is now 10**(xe * 10**ye);  xe * 10**ye must be integral
+            while xe % 10 == 0:
+                xe //= 10
+                ye += 1
+            if ye < 0:
+                return None
+            exponent = xe * 10**ye
+            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
+
+                # We now have:
+                #
+                #   x = 2**e * 10**xe, e > 0, and y < 0.
+                #
+                # The exact result is:
+                #
+                #   x**y = 5**(-e*y) * 10**(e*y + xe*y)
+                #
+                # provided that both e*y and xe*y are integers.  Note that if
+                # 5**(-e*y) >= 10**p, then the result can't be expressed
+                # exactly with p digits of precision.
+                #
+                # Using the above, we can guard against large values of ye.
+                # 93/65 is an upper bound for log(10)/log(5), so if
+                #
+                #   ye >= len(str(93*p//65))
+                #
+                # then
+                #
+                #   -e*y >= -y >= 10**ye > 93*p/65 > p*log(10)/log(5),
+                #
+                # so 5**(-e*y) >= 10**p, and the coefficient of the result
+                # can't be expressed in p digits.
+
+                # emax >= largest e such that 5**e < 10**p.
+                emax = p*93//65
+                if ye >= len(str(emax)):
+                    return None
+
+                # Find -e*y and -xe*y; both must be integers
+                e = _decimal_lshift_exact(e * yc, ye)
+                xe = _decimal_lshift_exact(xe * yc, ye)
+                if e is None or xe is None:
+                    return None
+
+                if e > emax:
+                    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
+
+                # Guard against large values of ye, using the same logic as in
+                # the 'xc is a power of 2' branch.  10/3 is an upper bound for
+                # log(10)/log(2).
+                emax = p*10//3
+                if ye >= len(str(emax)):
+                    return None
+
+                e = _decimal_lshift_exact(e * yc, ye)
+                xe = _decimal_lshift_exact(xe * yc, ye)
+                if e is None or xe is None:
+                    return None
+
+                if e > emax:
+                    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 = 1 << -(-_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 _One
+
+        # 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 _SignedInfinity[result_sign]
+
+        # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0
+        if self._isinfinity():
+            if other._sign == 0:
+                return _SignedInfinity[result_sign]
+            else:
+                return _dec_from_triple(result_sign, '0', 0)
+
+        # 1**other = 1, but the choice of exponent and the flags
+        # depend on the exponent of self, and on whether other is a
+        # positive integer, a negative integer, or neither
+        if self == _One:
+            if other._isinteger():
+                # exp = max(self._exp*max(int(other), 0),
+                # 1-context.prec) but evaluating int(other) directly
+                # is dangerous until we know other is small (other
+                # could be 1e999999999)
+                if other._sign == 1:
+                    multiplier = 0
+                elif other > context.prec:
+                    multiplier = context.prec
+                else:
+                    multiplier = int(other)
+
+                exp = self._exp * multiplier
+                if exp < 1-context.prec:
+                    exp = 1-context.prec
+                    context._raise_error(Rounded)
+            else:
+                context._raise_error(Inexact)
+                context._raise_error(Rounded)
+                exp = 1-context.prec
+
+            return _dec_from_triple(result_sign, '1'+'0'*-exp, exp)
+
+        # compute adjusted exponent of self
+        self_adj = self.adjusted()
+
+        # self ** infinity is infinity if self > 1, 0 if self < 1
+        # self ** -infinity is infinity if self < 1, 0 if self > 1
+        if other._isinfinity():
+            if (other._sign == 0) == (self_adj < 0):
+                return _dec_from_triple(result_sign, '0', 0)
+            else:
+                return _SignedInfinity[result_sign]
+
+        # from here on, the result always goes through the call
+        # to _fix at the end of this function.
+        ans = None
+        exact = False
+
+        # 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:
+                if result_sign == 1:
+                    ans = _dec_from_triple(1, ans._int, ans._exp)
+                exact = True
+
+        # 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)
+
+        # unlike exp, ln and log10, the power function respects the
+        # rounding mode; no need to switch to ROUND_HALF_EVEN here
+
+        # There's a difficulty here when 'other' is not an integer and
+        # the result is exact.  In this case, the specification
+        # requires that the Inexact flag be raised (in spite of
+        # exactness), but since the result is exact _fix won't do this
+        # for us.  (Correspondingly, the Underflow signal should also
+        # be raised for subnormal results.)  We can't directly raise
+        # these signals either before or after calling _fix, since
+        # that would violate the precedence for signals.  So we wrap
+        # the ._fix call in a temporary context, and reraise
+        # afterwards.
+        if exact and not other._isinteger():
+            # pad with zeros up to length context.prec+1 if necessary; this
+            # ensures that the Rounded signal will be raised.
+            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)
+
+            # create a copy of the current context, with cleared flags/traps
+            newcontext = context.copy()
+            newcontext.clear_flags()
+            for exception in _signals:
+                newcontext.traps[exception] = 0
+
+            # round in the new context
+            ans = ans._fix(newcontext)
+
+            # raise Inexact, and if necessary, Underflow
+            newcontext._raise_error(Inexact)
+            if newcontext.flags[Subnormal]:
+                newcontext._raise_error(Underflow)
+
+            # propagate signals to the original context; _fix could
+            # have raised any of Overflow, Underflow, Subnormal,
+            # Inexact, Rounded, Clamped.  Overflow needs the correct
+            # arguments.  Note that the order of the exceptions is
+            # important here.
+            if newcontext.flags[Overflow]:
+                context._raise_error(Overflow, 'above Emax', ans._sign)
+            for exception in Underflow, Subnormal, Inexact, Rounded, Clamped:
+                if newcontext.flags[exception]:
+                    context._raise_error(exception)
+
+        else:
+            ans = ans._fix(context)
+
+        return ans
+
+    def __rpow__(self, other, context=None):
+        """Swaps self/other and returns __pow__."""
+        other = _convert_other(other)
+        if other is NotImplemented:
+            return other
+        return other.__pow__(self, context=context)
+
+    def normalize(self, context=None):
+        """Normalize- strip trailing 0s, change anything equal to 0 to 0e0"""
+
+        if context is None:
+            context = getcontext()
+
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+
+        dup = self._fix(context)
+        if dup._isinfinity():
+            return dup
+
+        if not dup:
+            return _dec_from_triple(dup._sign, '0', 0)
+        exp_max = [context.Emax, context.Etop()][context.clamp]
+        end = len(dup._int)
+        exp = dup._exp
+        while dup._int[end-1] == '0' and exp < exp_max:
+            exp += 1
+            end -= 1
+        return _dec_from_triple(dup._sign, dup._int[:end], exp)
+
+    def quantize(self, exp, rounding=None, context=None):
+        """Quantize self so its exponent is the same as that of exp.
+
+        Similar to self._rescale(exp._exp) but with error checking.
+        """
+        exp = _convert_other(exp, raiseit=True)
+
+        if context is None:
+            context = getcontext()
+        if rounding is None:
+            rounding = context.rounding
+
+        if self._is_special or exp._is_special:
+            ans = self._check_nans(exp, context)
+            if ans:
+                return ans
+
+            if exp._isinfinity() or self._isinfinity():
+                if exp._isinfinity() and self._isinfinity():
+                    return Decimal(self)  # if both are inf, it is OK
+                return context._raise_error(InvalidOperation,
+                                        'quantize with one INF')
+
+        # exp._exp should be between Etiny and Emax
+        if not (context.Etiny() <= exp._exp <= context.Emax):
+            return context._raise_error(InvalidOperation,
+                   'target exponent out of bounds in quantize')
+
+        if not self:
+            ans = _dec_from_triple(self._sign, '0', exp._exp)
+            return ans._fix(context)
+
+        self_adjusted = self.adjusted()
+        if self_adjusted > context.Emax:
+            return context._raise_error(InvalidOperation,
+                                        'exponent of quantize result too large for current context')
+        if self_adjusted - exp._exp + 1 > context.prec:
+            return context._raise_error(InvalidOperation,
+                                        'quantize result has too many digits for current context')
+
+        ans = self._rescale(exp._exp, rounding)
+        if ans.adjusted() > context.Emax:
+            return context._raise_error(InvalidOperation,
+                                        'exponent of quantize result too large for current context')
+        if len(ans._int) > context.prec:
+            return context._raise_error(InvalidOperation,
+                                        'quantize result has too many digits for current context')
+
+        # raise appropriate flags
+        if ans and ans.adjusted() < context.Emin:
+            context._raise_error(Subnormal)
+        if ans._exp > self._exp:
+            if ans != self:
+                context._raise_error(Inexact)
+            context._raise_error(Rounded)
+
+        # call to fix takes care of any necessary folddown, and
+        # signals Clamped if necessary
+        ans = ans._fix(context)
+        return ans
+
+    def same_quantum(self, other, context=None):
+        """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 = self._pick_rounding_function[rounding]
+        changed = this_function(self, digits)
+        coeff = self._int[:digits] or '0'
+        if changed == 1:
+            coeff = str(int(coeff)+1)
+        return _dec_from_triple(self._sign, coeff, exp)
+
+    def _round(self, places, rounding):
+        """Round a nonzero, nonspecial Decimal to a fixed number of
+        significant figures, using the given rounding mode.
+
+        Infinities, NaNs and zeros are returned unaltered.
+
+        This operation is quiet: it raises no flags, and uses no
+        information from the context.
+
+        """
+        if places <= 0:
+            raise ValueError("argument should be at least 1 in _round")
+        if self._is_special or not self:
+            return Decimal(self)
+        ans = self._rescale(self.adjusted()+1-places, rounding)
+        # it can happen that the rescale alters the adjusted exponent;
+        # for example when rounding 99.97 to 3 significant figures.
+        # When this happens we end up with an extra 0 at the end of
+        # the number; a second rescale fixes this.
+        if ans.adjusted() != self.adjusted():
+            ans = ans._rescale(ans.adjusted()+1-places, rounding)
+        return ans
+
+    def to_integral_exact(self, rounding=None, context=None):
+        """Rounds to a nearby integer.
+
+        If no rounding mode is specified, take the rounding mode from
+        the context.  This method raises the Rounded and Inexact flags
+        when appropriate.
+
+        See also: to_integral_value, which does exactly the same as
+        this method except that it doesn't raise Inexact or Rounded.
+        """
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+            return Decimal(self)
+        if self._exp >= 0:
+            return Decimal(self)
+        if not self:
+            return _dec_from_triple(self._sign, '0', 0)
+        if context is None:
+            context = getcontext()
+        if rounding is None:
+            rounding = context.rounding
+        ans = self._rescale(0, rounding)
+        if ans != self:
+            context._raise_error(Inexact)
+        context._raise_error(Rounded)
+        return ans
+
+    def to_integral_value(self, rounding=None, context=None):
+        """Rounds to the nearest integer, without raising inexact, rounded."""
+        if context is None:
+            context = getcontext()
+        if rounding is None:
+            rounding = context.rounding
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+            return Decimal(self)
+        if self._exp >= 0:
+            return Decimal(self)
+        else:
+            return self._rescale(0, rounding)
+
+    # the method name changed, but we provide also the old one, for compatibility
+    to_integral = to_integral_value
+
+    def sqrt(self, context=None):
+        """Return the square root of self."""
+        if context is None:
+            context = getcontext()
+
+        if self._is_special:
+            ans = self._check_nans(context=context)
+            if ans:
+                return ans
+
+            if self._isinfinity() and self._sign == 0:
+                return Decimal(self)
+
+        if not self:
+            # exponent = self._exp // 2.  sqrt(-0) = -0
+            ans = _dec_from_triple(self._sign, '0', self._exp // 2)
+            return ans._fix(context)
+
+        if self._sign == 1:
+            return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0')
+
+        # At this point self represents a positive number.  Let p be
+        # the desired precision and express self in the form c*100**e
+        # with c a positive real number and e an integer, c and e
+        # being chosen so that 100**(p-1) <= c < 100**p.  Then the
+        # (exact) square root of self is sqrt(c)*10**e, and 10**(p-1)
+        # <= sqrt(c) < 10**p, so the closest representable Decimal at
+        # precision p is n*10**e where n = round_half_even(sqrt(c)),
+        # the closest integer to sqrt(c) with the even integer chosen
+        # in the case of a tie.
+        #
+        # To ensure correct rounding in all cases, we use the
+        # following trick: we compute the square root to an extra
+        # place (precision p+1 instead of precision p), rounding down.
+        # Then, if the result is inexact and its last digit is 0 or 5,
+        # we increase the last digit to 1 or 6 respectively; if it's
+        # exact we leave the last digit alone.  Now the final round to
+        # p places (or fewer in the case of underflow) will round
+        # correctly and raise the appropriate flags.
+
+        # use an extra digit of precision
+        prec = context.prec+1
+
+        # write argument in the form c*100**e where e = self._exp//2
+        # is the 'ideal' exponent, to be used if the square root is
+        # exactly representable.  l is the number of 'digits' of c in
+        # base 100, so that 100**(l-1) <= c < 100**l.
+        op = _WorkRep(self)
+        e = op.exp >> 1
+        if op.exp & 1:
+            c = op.int * 10
+            l = (len(self._int) >> 1) + 1
+        else:
+            c = op.int
+            l = len(self._int)+1 >> 1
+
+        # rescale so that c has exactly prec base 100 'digits'
+        shift = prec-l
+        if shift >= 0:
+            c *= 100**shift
+            exact = True
+        else:
+            c, remainder = divmod(c, 100**-shift)
+            exact = not remainder
+        e -= shift
+
+        # find n = floor(sqrt(c)) using Newton's method
+        n = 10**prec
+        while True:
+            q = c//n
+            if n <= q:
+                break
+            else:
+                n = n + q >> 1
+        exact = exact and n*n == c
+
+        if exact:
+            # result is exact; rescale to use ideal exponent e
+            if shift >= 0:
+                # assert n % 10**shift == 0
+                n //= 10**shift
+            else:
+                n *= 10**-shift
+            e += shift
+        else:
+            # result is not exact; fix last digit as described above
+            if n % 5 == 0:
+                n += 1
+
+        ans = _dec_from_triple(0, str(n), e)
+
+        # round, and fit to current context
+        context = context._shallow_copy()
+        rounding = context._set_rounding(ROUND_HALF_EVEN)
+        ans = ans._fix(context)
+        context.rounding = rounding
+
+        return ans
+
+    def max(self, other, context=None):
+        """Returns the larger value.
+
+        Like max(self, other) except if one is not a number, returns
+        NaN (and signals if one is sNaN).  Also rounds.
+        """
+        other = _convert_other(other, raiseit=True)
+
+        if context is None:
+            context = getcontext()
+
+        if self._is_special or other._is_special:
+            # If one operand is a quiet NaN and the other is number, then the
+            # number is always returned
+            sn = self._isnan()
+            on = other._isnan()
+            if sn or on:
+                if on == 1 and sn == 0:
+                    return self._fix(context)
+                if sn == 1 and on == 0:
+                    return other._fix(context)
+                return self._check_nans(other, context)
+
+        c = self._cmp(other)
+        if c == 0:
+            # If both operands are finite and equal in numerical value
+            # then an ordering is applied:
+            #
+            # If the signs differ then max returns the operand with the
+            # positive sign and min returns the operand with the negative sign
+            #
+            # If the signs are the same then the exponent is used to select
+            # the result.  This is exactly the ordering used in compare_total.
+            c = self.compare_total(other)
+
+        if c == -1:
+            ans = other
+        else:
+            ans = self
+
+        return ans._fix(context)
+
+    def min(self, other, context=None):
+        """Returns the smaller value.
+
+        Like min(self, other) except if one is not a number, returns
+        NaN (and signals if one is sNaN).  Also rounds.
+        """
+        other = _convert_other(other, raiseit=True)
+
+        if context is None:
+            context = getcontext()
+
+        if self._is_special or other._is_special:
+            # If one operand is a quiet NaN and the other is number, then the
+            # number is always returned
+            sn = self._isnan()
+            on = other._isnan()
+            if sn or on:
+                if on == 1 and sn == 0:
+                    return self._fix(context)
+                if sn == 1 and on == 0:
+                    return other._fix(context)
+                return self._check_nans(other, context)
+
+        c = self._cmp(other)
+        if c == 0:
+            c = self.compare_total(other)
+
+        if c == -1:
+            ans = self
+        else:
+            ans = other
+
+        return ans._fix(context)
+
+    def _isinteger(self):
+        """Returns whether self is an integer"""
+        if self._is_special:
+            return False
+        if self._exp >= 0:
+            return True
+        rest = self._int[self._exp:]
+        return rest == '0'*len(rest)
+
+    def _iseven(self):
+        """Returns True if self is even.  Assumes self is an integer."""
+        if not self or self._exp > 0:
+            return True
+        return self._int[-1+self._exp] in '02468'
+
+    def adjusted(self):
+        """Return the adjusted exponent of self"""
+        try:
+            return self._exp + len(self._int) - 1
+        # If NaN or Infinity, self._exp is string
+        except TypeError:
+            return 0
+
+    def canonical(self):
+        """Returns the same Decimal object.
+
+        As we do not have different encodings for the same number, the
+        received object already is in its canonical form.
+        """
+        return self
+
+    def compare_signal(self, other, context=None):
+        """Compares self to the other operand numerically.
+
+        It's pretty much like compare(), but all NaNs signal, with signaling
+        NaNs taking precedence over quiet NaNs.
+        """
+        other = _convert_other(other, raiseit = True)
+        ans = self._compare_check_nans(other, context)
+        if ans:
+            return ans
+        return self.compare(other, context=context)
+
+    def compare_total(self, other, context=None):
+        """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.
+        """
+        other = _convert_other(other, raiseit=True)
+
+        # if one is negative and the other is positive, it's easy
+        if self._sign and not other._sign:
+            return _NegativeOne
+        if not self._sign and other._sign:
+            return _One
+        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:
+                # compare payloads as though they're integers
+                self_key = len(self._int), self._int
+                other_key = len(other._int), other._int
+                if self_key < other_key:
+                    if sign:
+                        return _One
+                    else:
+                        return _NegativeOne
+                if self_key > other_key:
+                    if sign:
+                        return _NegativeOne
+                    else:
+                        return _One
+                return _Zero
+
+            if sign:
+                if self_nan == 1:
+                    return _NegativeOne
+                if other_nan == 1:
+                    return _One
+                if self_nan == 2:
+                    return _NegativeOne
+                if other_nan == 2:
+                    return _One
+            else:
+                if self_nan == 1:
+                    return _One
+                if other_nan == 1:
+                    return _NegativeOne
+                if self_nan == 2:
+                    return _One
+                if other_nan == 2:
+                    return _NegativeOne
+
+        if self < other:
+            return _NegativeOne
+        if self > other:
+            return _One
+
+        if self._exp < other._exp:
+            if sign:
+                return _One
+            else:
+                return _NegativeOne
+        if self._exp > other._exp:
+            if sign:
+                return _NegativeOne
+            else:
+                return _One
+        return _Zero
+
+
+    def compare_total_mag(self, other, context=None):
+        """Compares self to other using abstract repr., ignoring sign.
+
+        Like compare_total, but with operand's sign ignored and assumed to be 0.
+        """
+        other = _convert_other(other, raiseit=True)
+
+        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, context=None):
+        """Returns self with the sign of other."""
+        other = _convert_other(other, raiseit=True)
+        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 _Zero
+
+        # exp(0) = 1
+        if not self:
+            return _One
+
+        # 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()
+
+    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 _NegativeInfinity
+
+        # ln(Infinity) = Infinity
+        if self._isinfinity() == 1:
+            return _Infinity
+
+        # ln(1.0) == 0.0
+        if self == _One:
+            return _Zero
+
+        # 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 _NegativeInfinity
+
+        # log10(Infinity) = Infinity
+        if self._isinfinity() == 1:
+            return _Infinity
+
+        # 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 _Infinity
+
+        # 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.
+        ans = Decimal(self.adjusted())
+        return ans._fix(context)
+
+    def _islogical(self):
+        """Return True if self is a logical operand.
+
+        For being logical, it must be a finite number with a sign of 0,
+        an exponent of 0, and a coefficient whose digits must all be
+        either 0 or 1.
+        """
+        if self._sign != 0 or self._exp != 0:
+            return False
+        for dig in self._int:
+            if dig not in '01':
+                return False
+        return True
+
+    def _fill_logical(self, context, opa, opb):
+        dif = context.prec - len(opa)
+        if dif > 0:
+            opa = '0'*dif + opa
+        elif dif < 0:
+            opa = opa[-context.prec:]
+        dif = context.prec - len(opb)
+        if dif > 0:
+            opb = '0'*dif + opb
+        elif dif < 0:
+            opb = opb[-context.prec:]
+        return opa, opb
+
+    def logical_and(self, other, context=None):
+        """Applies an 'and' operation between self and other's digits."""
+        if context is None:
+            context = getcontext()
+
+        other = _convert_other(other, raiseit=True)
+
+        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()
+
+        other = _convert_other(other, raiseit=True)
+
+        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()
+
+        other = _convert_other(other, raiseit=True)
+
+        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 == 0:
+                    return self._fix(context)
+                if sn == 1 and on == 0:
+                    return other._fix(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 == 0:
+                    return self._fix(context)
+                if sn == 1 and on == 0:
+                    return other._fix(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 _NegativeInfinity
+        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 _Infinity
+        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(Inexact)
+            context._raise_error(Rounded)
+        elif ans.adjusted() < context.Emin:
+            context._raise_error(Underflow)
+            context._raise_error(Subnormal)
+            context._raise_error(Inexact)
+            context._raise_error(Rounded)
+            # 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()
+
+        other = _convert_other(other, raiseit=True)
+
+        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 > 0:
+            rotdig = '0'*topad + rotdig
+        elif topad < 0:
+            rotdig = rotdig[-topad:]
+
+        # 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()
+
+        other = _convert_other(other, raiseit=True)
+
+        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()
+
+        other = _convert_other(other, raiseit=True)
+
+        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 > 0:
+            rotdig = '0'*topad + rotdig
+        elif topad < 0:
+            rotdig = rotdig[-topad:]
+
+        # let's shift!
+        if torot < 0:
+            shifted = rotdig[:torot]
+        else:
+            shifted = rotdig + '0'*torot
+            shifted = shifted[-context.prec:]
+
+        return _dec_from_triple(self._sign,
+                                    shifted.lstrip('0') or '0', self._exp)
+
+    # Support for pickling, copy, and deepcopy
+    def __reduce__(self):
+        return (self.__class__, (str(self),))
+
+    def __copy__(self):
+        if type(self) is Decimal:
+            return self     # I'm immutable; therefore I am my own clone
+        return self.__class__(str(self))
+
+    def __deepcopy__(self, memo):
+        if type(self) is Decimal:
+            return self     # My components are also immutable
+        return self.__class__(str(self))
+
+    # PEP 3101 support.  the _localeconv keyword argument should be
+    # considered private: it's provided for ease of testing only.
+    def __format__(self, specifier, context=None, _localeconv=None):
+        """Format a Decimal instance according to the given specifier.
+
+        The specifier should be a standard format specifier, with the
+        form described in PEP 3101.  Formatting types 'e', 'E', 'f',
+        'F', 'g', 'G', 'n' and '%' are supported.  If the formatting
+        type is omitted it defaults to 'g' or 'G', depending on the
+        value of context.capitals.
+        """
+
+        # Note: PEP 3101 says that if the type is not present then
+        # there should be at least one digit after the decimal point.
+        # We take the liberty of ignoring this requirement for
+        # Decimal---it's presumably there to make sure that
+        # format(float, '') behaves similarly to str(float).
+        if context is None:
+            context = getcontext()
+
+        spec = _parse_format_specifier(specifier, _localeconv=_localeconv)
+
+        # special values don't care about the type or precision
+        if self._is_special:
+            sign = _format_sign(self._sign, spec)
+            body = str(self.copy_abs())
+            if spec['type'] == '%':
+                body += '%'
+            return _format_align(sign, body, spec)
+
+        # a type of None defaults to 'g' or 'G', depending on context
+        if spec['type'] is None:
+            spec['type'] = ['g', 'G'][context.capitals]
+
+        # if type is '%', adjust exponent of self accordingly
+        if spec['type'] == '%':
+            self = _dec_from_triple(self._sign, self._int, self._exp+2)
+
+        # round if necessary, taking rounding mode from the context
+        rounding = context.rounding
+        precision = spec['precision']
+        if precision is not None:
+            if spec['type'] in 'eE':
+                self = self._round(precision+1, rounding)
+            elif spec['type'] in 'fF%':
+                self = self._rescale(-precision, rounding)
+            elif spec['type'] in 'gG' and len(self._int) > precision:
+                self = self._round(precision, rounding)
+        # special case: zeros with a positive exponent can't be
+        # represented in fixed point; rescale them to 0e0.
+        if not self and self._exp > 0 and spec['type'] in 'fF%':
+            self = self._rescale(0, rounding)
+
+        # figure out placement of the decimal point
+        leftdigits = self._exp + len(self._int)
+        if spec['type'] in 'eE':
+            if not self and precision is not None:
+                dotplace = 1 - precision
+            else:
+                dotplace = 1
+        elif spec['type'] in 'fF%':
+            dotplace = leftdigits
+        elif spec['type'] in 'gG':
+            if self._exp <= 0 and leftdigits > -6:
+                dotplace = leftdigits
+            else:
+                dotplace = 1
+
+        # find digits before and after decimal point, and get exponent
+        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] or '0'
+            fracpart = self._int[dotplace:]
+        exp = leftdigits-dotplace
+
+        # done with the decimal-specific stuff;  hand over the rest
+        # of the formatting to the _format_number function
+        return _format_number(self._sign, intpart, fracpart, exp, spec)
+
+def _dec_from_triple(sign, coefficient, exponent, special=False):
+    """Create a decimal instance directly, without any validation,
+    normalization (e.g. removal of leading zeros) or argument
+    conversion.
+
+    This function is for *internal use only*.
+    """
+
+    self = object.__new__(Decimal)
+    self._sign = sign
+    self._int = coefficient
+    self._exp = exponent
+    self._is_special = special
+
+    return self
+
+# Register Decimal as a kind of Number (an abstract base class).
+# However, do not register it as Real (because Decimals are not
+# interoperable with floats).
+_numbers.Number.register(Decimal)
+
+
+##### Context class #######################################################
+
+class _ContextManager(object):
+    """Context manager class to support localcontext().
+
+      Sets a copy of the supplied context in __enter__() and restores
+      the previous decimal context in __exit__()
+    """
+    def __init__(self, new_context):
+        self.new_context = new_context.copy()
+    def __enter__(self):
+        self.saved_context = getcontext()
+        setcontext(self.new_context)
+        return self.new_context
+    def __exit__(self, t, v, tb):
+        setcontext(self.saved_context)
+
+class Context(object):
+    """Contains the context for a Decimal instance.
+
+    Contains:
+    prec - precision (for use in rounding, division, square roots..)
+    rounding - rounding type (how you round)
+    traps - If traps[exception] = 1, then the exception is
+                    raised when it is caused.  Otherwise, a value is
+                    substituted in.
+    flags  - When an exception is caused, flags[exception] is set.
+             (Whether or not the trap_enabler is set)
+             Should be reset by user of Decimal instance.
+    Emin -   Minimum exponent
+    Emax -   Maximum exponent
+    capitals -      If 1, 1*10^1 is printed as 1E+1.
+                    If 0, printed as 1e1
+    clamp -  If 1, change exponents if too high (Default 0)
+    """
+
+    def __init__(self, prec=None, rounding=None, Emin=None, Emax=None,
+                       capitals=None, clamp=None, flags=None, traps=None,
+                       _ignored_flags=None):
+        # Set defaults; for everything except flags and _ignored_flags,
+        # inherit from DefaultContext.
+        try:
+            dc = DefaultContext
+        except NameError:
+            pass
+
+        self.prec = prec if prec is not None else dc.prec
+        self.rounding = rounding if rounding is not None else dc.rounding
+        self.Emin = Emin if Emin is not None else dc.Emin
+        self.Emax = Emax if Emax is not None else dc.Emax
+        self.capitals = capitals if capitals is not None else dc.capitals
+        self.clamp = clamp if clamp is not None else dc.clamp
+
+        if _ignored_flags is None:
+            self._ignored_flags = []
+        else:
+            self._ignored_flags = _ignored_flags
+
+        if traps is None:
+            self.traps = dc.traps.copy()
+        elif not isinstance(traps, dict):
+            self.traps = dict((s, int(s in traps)) for s in _signals + traps)
+        else:
+            self.traps = traps
+
+        if flags is None:
+            self.flags = dict.fromkeys(_signals, 0)
+        elif not isinstance(flags, dict):
+            self.flags = dict((s, int(s in flags)) for s in _signals + flags)
+        else:
+            self.flags = flags
+
+    def _set_integer_check(self, name, value, vmin, vmax):
+        if not isinstance(value, int):
+            raise TypeError("%s must be an integer" % name)
+        if vmin == '-inf':
+            if value > vmax:
+                raise ValueError("%s must be in [%s, %d]. got: %s" % (name, vmin, vmax, value))
+        elif vmax == 'inf':
+            if value < vmin:
+                raise ValueError("%s must be in [%d, %s]. got: %s" % (name, vmin, vmax, value))
+        else:
+            if value < vmin or value > vmax:
+                raise ValueError("%s must be in [%d, %d]. got %s" % (name, vmin, vmax, value))
+        return object.__setattr__(self, name, value)
+
+    def _set_signal_dict(self, name, d):
+        if not isinstance(d, dict):
+            raise TypeError("%s must be a signal dict" % d)
+        for key in d:
+            if not key in _signals:
+                raise KeyError("%s is not a valid signal dict" % d)
+        for key in _signals:
+            if not key in d:
+                raise KeyError("%s is not a valid signal dict" % d)
+        return object.__setattr__(self, name, d)
+
+    def __setattr__(self, name, value):
+        if name == 'prec':
+            return self._set_integer_check(name, value, 1, 'inf')
+        elif name == 'Emin':
+            return self._set_integer_check(name, value, '-inf', 0)
+        elif name == 'Emax':
+            return self._set_integer_check(name, value, 0, 'inf')
+        elif name == 'capitals':
+            return self._set_integer_check(name, value, 0, 1)
+        elif name == 'clamp':
+            return self._set_integer_check(name, value, 0, 1)
+        elif name == 'rounding':
+            if not value in _rounding_modes:
+                # raise TypeError even for strings to have consistency
+                # among various implementations.
+                raise TypeError("%s: invalid rounding mode" % value)
+            return object.__setattr__(self, name, value)
+        elif name == 'flags' or name == 'traps':
+            return self._set_signal_dict(name, value)
+        elif name == '_ignored_flags':
+            return object.__setattr__(self, name, value)
+        else:
+            raise AttributeError(
+                "'decimal.Context' object has no attribute '%s'" % name)
+
+    def __delattr__(self, name):
+        raise AttributeError("%s cannot be deleted" % name)
+
+    # Support for pickling, copy, and deepcopy
+    def __reduce__(self):
+        flags = [sig for sig, v in self.flags.items() if v]
+        traps = [sig for sig, v in self.traps.items() if v]
+        return (self.__class__,
+                (self.prec, self.rounding, self.Emin, self.Emax,
+                 self.capitals, self.clamp, flags, traps))
+
+    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, '
+                 'clamp=%(clamp)d'
+                 % vars(self))
+        names = [f.__name__ for f, v in self.flags.items() if v]
+        s.append('flags=[' + ', '.join(names) + ']')
+        names = [t.__name__ for t, v in self.traps.items() if v]
+        s.append('traps=[' + ', '.join(names) + ']')
+        return ', '.join(s) + ')'
+
+    def clear_flags(self):
+        """Reset all flags to zero"""
+        for flag in self.flags:
+            self.flags[flag] = 0
+
+    def clear_traps(self):
+        """Reset all traps to zero"""
+        for flag in self.traps:
+            self.traps[flag] = 0
+
+    def _shallow_copy(self):
+        """Returns a shallow copy from self."""
+        nc = Context(self.prec, self.rounding, self.Emin, self.Emax,
+                     self.capitals, self.clamp, self.flags, self.traps,
+                     self._ignored_flags)
+        return nc
+
+    def copy(self):
+        """Returns a deep copy from self."""
+        nc = Context(self.prec, self.rounding, self.Emin, self.Emax,
+                     self.capitals, self.clamp,
+                     self.flags.copy(), self.traps.copy(),
+                     self._ignored_flags)
+        return nc
+    __copy__ = copy
+
+    def _raise_error(self, condition, explanation = None, *args):
+        """Handles an error
+
+        If the flag is in _ignored_flags, returns the default response.
+        Otherwise, it sets the flag, then, if the corresponding
+        trap_enabler is set, it reraises the exception.  Otherwise, it returns
+        the default value after setting the flag.
+        """
+        error = _condition_map.get(condition, condition)
+        if error in self._ignored_flags:
+            # Don't touch the flag
+            return error().handle(self, *args)
+
+        self.flags[error] = 1
+        if not self.traps[error]:
+            # The errors define how to handle themselves.
+            return condition().handle(self, *args)
+
+        # Errors should only be risked on copies of the context
+        # self._ignored_flags = []
+        raise error(explanation)
+
+    def _ignore_all_flags(self):
+        """Ignore all flags, if they are raised"""
+        return self._ignore_flags(*_signals)
+
+    def _ignore_flags(self, *flags):
+        """Ignore the flags, if they are raised"""
+        # Do not mutate-- This way, copies of a context leave the original
+        # alone.
+        self._ignored_flags = (self._ignored_flags + list(flags))
+        return list(flags)
+
+    def _regard_flags(self, *flags):
+        """Stop ignoring the flags, if they are raised"""
+        if flags and isinstance(flags[0], (tuple,list)):
+            flags = flags[0]
+        for flag in flags:
+            self._ignored_flags.remove(flag)
+
+    # We inherit object.__hash__, so we must deny this explicitly
+    __hash__ = None
+
+    def Etiny(self):
+        """Returns Etiny (= Emin - prec + 1)"""
+        return int(self.Emin - self.prec + 1)
+
+    def Etop(self):
+        """Returns maximum exponent (= Emax - prec + 1)"""
+        return int(self.Emax - self.prec + 1)
+
+    def _set_rounding(self, type):
+        """Sets the rounding type.
+
+        Sets the rounding type, and returns the current (previous)
+        rounding type.  Often used like:
+
+        context = context.copy()
+        # so you don't change the calling context
+        # if an error occurs in the middle.
+        rounding = context._set_rounding(ROUND_UP)
+        val = self.__sub__(other, context=context)
+        context._set_rounding(rounding)
+
+        This will make it round up for that operation.
+        """
+        rounding = self.rounding
+        self.rounding = type
+        return rounding
+
+    def create_decimal(self, num='0'):
+        """Creates a new Decimal instance but using self as context.
+
+        This method implements the to-number operation of the
+        IBM Decimal specification."""
+
+        if isinstance(num, str) and (num != num.strip() or '_' in num):
+            return self._raise_error(ConversionSyntax,
+                                     "trailing or leading whitespace and "
+                                     "underscores are not permitted.")
+
+        d = Decimal(num, context=self)
+        if d._isnan() and len(d._int) > self.prec - self.clamp:
+            return self._raise_error(ConversionSyntax,
+                                     "diagnostic info too long in NaN")
+        return d._fix(self)
+
+    def create_decimal_from_float(self, f):
+        """Creates a new Decimal instance from a float but rounding using self
+        as the context.
+
+        >>> context = Context(prec=5, rounding=ROUND_DOWN)
+        >>> context.create_decimal_from_float(3.1415926535897932)
+        Decimal('3.1415')
+        >>> context = Context(prec=5, traps=[Inexact])
+        >>> context.create_decimal_from_float(3.1415926535897932)
+        Traceback (most recent call last):
+            ...
+        decimal.Inexact: None
+
+        """
+        d = Decimal.from_float(f)       # An exact conversion
+        return d._fix(self)             # Apply the context rounding
+
+    # Methods
+    def abs(self, a):
+        """Returns the absolute value of the operand.
+
+        If the operand is negative, the result is the same as using the minus
+        operation on the operand.  Otherwise, the result is the same as using
+        the plus operation on the operand.
+
+        >>> ExtendedContext.abs(Decimal('2.1'))
+        Decimal('2.1')
+        >>> ExtendedContext.abs(Decimal('-100'))
+        Decimal('100')
+        >>> ExtendedContext.abs(Decimal('101.5'))
+        Decimal('101.5')
+        >>> ExtendedContext.abs(Decimal('-101.5'))
+        Decimal('101.5')
+        >>> ExtendedContext.abs(-1)
+        Decimal('1')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.__abs__(context=self)
+
+    def add(self, a, b):
+        """Return the sum of the two operands.
+
+        >>> ExtendedContext.add(Decimal('12'), Decimal('7.00'))
+        Decimal('19.00')
+        >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4'))
+        Decimal('1.02E+4')
+        >>> ExtendedContext.add(1, Decimal(2))
+        Decimal('3')
+        >>> ExtendedContext.add(Decimal(8), 5)
+        Decimal('13')
+        >>> ExtendedContext.add(5, 5)
+        Decimal('10')
+        """
+        a = _convert_other(a, raiseit=True)
+        r = a.__add__(b, context=self)
+        if r is NotImplemented:
+            raise TypeError("Unable to convert %s to Decimal" % b)
+        else:
+            return r
+
+    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')
+        """
+        if not isinstance(a, Decimal):
+            raise TypeError("canonical requires a Decimal as an argument.")
+        return a.canonical()
+
+    def compare(self, a, b):
+        """Compares values numerically.
+
+        If the signs of the operands differ, a value representing each operand
+        ('-1' if the operand is less than zero, '0' if the operand is zero or
+        negative zero, or '1' if the operand is greater than zero) is used in
+        place of that operand for the comparison instead of the actual
+        operand.
+
+        The comparison is then effected by subtracting the second operand from
+        the first and then returning a value according to the result of the
+        subtraction: '-1' if the result is less than zero, '0' if the result is
+        zero or negative zero, or '1' if the result is greater than zero.
+
+        >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3'))
+        Decimal('-1')
+        >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1'))
+        Decimal('0')
+        >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10'))
+        Decimal('0')
+        >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1'))
+        Decimal('1')
+        >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3'))
+        Decimal('1')
+        >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1'))
+        Decimal('-1')
+        >>> ExtendedContext.compare(1, 2)
+        Decimal('-1')
+        >>> ExtendedContext.compare(Decimal(1), 2)
+        Decimal('-1')
+        >>> ExtendedContext.compare(1, Decimal(2))
+        Decimal('-1')
+        """
+        a = _convert_other(a, raiseit=True)
+        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
+        >>> c.compare_signal(-1, 2)
+        Decimal('-1')
+        >>> c.compare_signal(Decimal(-1), 2)
+        Decimal('-1')
+        >>> c.compare_signal(-1, Decimal(2))
+        Decimal('-1')
+        """
+        a = _convert_other(a, raiseit=True)
+        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')
+        >>> ExtendedContext.compare_total(1, 2)
+        Decimal('-1')
+        >>> ExtendedContext.compare_total(Decimal(1), 2)
+        Decimal('-1')
+        >>> ExtendedContext.compare_total(1, Decimal(2))
+        Decimal('-1')
+        """
+        a = _convert_other(a, raiseit=True)
+        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.
+        """
+        a = _convert_other(a, raiseit=True)
+        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')
+        >>> ExtendedContext.copy_abs(-1)
+        Decimal('1')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.copy_abs()
+
+    def copy_decimal(self, a):
+        """Returns a copy of the decimal object.
+
+        >>> ExtendedContext.copy_decimal(Decimal('2.1'))
+        Decimal('2.1')
+        >>> ExtendedContext.copy_decimal(Decimal('-1.00'))
+        Decimal('-1.00')
+        >>> ExtendedContext.copy_decimal(1)
+        Decimal('1')
+        """
+        a = _convert_other(a, raiseit=True)
+        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')
+        >>> ExtendedContext.copy_negate(1)
+        Decimal('-1')
+        """
+        a = _convert_other(a, raiseit=True)
+        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')
+        >>> ExtendedContext.copy_sign(1, -2)
+        Decimal('-1')
+        >>> ExtendedContext.copy_sign(Decimal(1), -2)
+        Decimal('-1')
+        >>> ExtendedContext.copy_sign(1, Decimal(-2))
+        Decimal('-1')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.copy_sign(b)
+
+    def divide(self, a, b):
+        """Decimal division in a specified context.
+
+        >>> ExtendedContext.divide(Decimal('1'), Decimal('3'))
+        Decimal('0.333333333')
+        >>> ExtendedContext.divide(Decimal('2'), Decimal('3'))
+        Decimal('0.666666667')
+        >>> ExtendedContext.divide(Decimal('5'), Decimal('2'))
+        Decimal('2.5')
+        >>> ExtendedContext.divide(Decimal('1'), Decimal('10'))
+        Decimal('0.1')
+        >>> ExtendedContext.divide(Decimal('12'), Decimal('12'))
+        Decimal('1')
+        >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2'))
+        Decimal('4.00')
+        >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0'))
+        Decimal('1.20')
+        >>> ExtendedContext.divide(Decimal('1000'), Decimal('100'))
+        Decimal('10')
+        >>> ExtendedContext.divide(Decimal('1000'), Decimal('1'))
+        Decimal('1000')
+        >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2'))
+        Decimal('1.20E+6')
+        >>> ExtendedContext.divide(5, 5)
+        Decimal('1')
+        >>> ExtendedContext.divide(Decimal(5), 5)
+        Decimal('1')
+        >>> ExtendedContext.divide(5, Decimal(5))
+        Decimal('1')
+        """
+        a = _convert_other(a, raiseit=True)
+        r = a.__truediv__(b, context=self)
+        if r is NotImplemented:
+            raise TypeError("Unable to convert %s to Decimal" % b)
+        else:
+            return r
+
+    def divide_int(self, a, b):
+        """Divides two numbers and returns the integer part of the result.
+
+        >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3'))
+        Decimal('0')
+        >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3'))
+        Decimal('3')
+        >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3'))
+        Decimal('3')
+        >>> ExtendedContext.divide_int(10, 3)
+        Decimal('3')
+        >>> ExtendedContext.divide_int(Decimal(10), 3)
+        Decimal('3')
+        >>> ExtendedContext.divide_int(10, Decimal(3))
+        Decimal('3')
+        """
+        a = _convert_other(a, raiseit=True)
+        r = a.__floordiv__(b, context=self)
+        if r is NotImplemented:
+            raise TypeError("Unable to convert %s to Decimal" % b)
+        else:
+            return r
+
+    def divmod(self, a, b):
+        """Return (a // b, a % b).
+
+        >>> ExtendedContext.divmod(Decimal(8), Decimal(3))
+        (Decimal('2'), Decimal('2'))
+        >>> ExtendedContext.divmod(Decimal(8), Decimal(4))
+        (Decimal('2'), Decimal('0'))
+        >>> ExtendedContext.divmod(8, 4)
+        (Decimal('2'), Decimal('0'))
+        >>> ExtendedContext.divmod(Decimal(8), 4)
+        (Decimal('2'), Decimal('0'))
+        >>> ExtendedContext.divmod(8, Decimal(4))
+        (Decimal('2'), Decimal('0'))
+        """
+        a = _convert_other(a, raiseit=True)
+        r = a.__divmod__(b, context=self)
+        if r is NotImplemented:
+            raise TypeError("Unable to convert %s to Decimal" % b)
+        else:
+            return r
+
+    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')
+        >>> c.exp(10)
+        Decimal('22026.4658')
+        """
+        a =_convert_other(a, raiseit=True)
+        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')
+        >>> ExtendedContext.fma(1, 3, 4)
+        Decimal('7')
+        >>> ExtendedContext.fma(1, Decimal(3), 4)
+        Decimal('7')
+        >>> ExtendedContext.fma(1, 3, Decimal(4))
+        Decimal('7')
+        """
+        a = _convert_other(a, raiseit=True)
+        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
+        """
+        if not isinstance(a, Decimal):
+            raise TypeError("is_canonical requires a Decimal as an argument.")
+        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
+        >>> ExtendedContext.is_finite(1)
+        True
+        """
+        a = _convert_other(a, raiseit=True)
+        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
+        >>> ExtendedContext.is_infinite(1)
+        False
+        """
+        a = _convert_other(a, raiseit=True)
+        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
+        >>> ExtendedContext.is_nan(1)
+        False
+        """
+        a = _convert_other(a, raiseit=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
+        >>> c.is_normal(1)
+        True
+        """
+        a = _convert_other(a, raiseit=True)
+        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
+        >>> ExtendedContext.is_qnan(1)
+        False
+        """
+        a = _convert_other(a, raiseit=True)
+        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
+        >>> ExtendedContext.is_signed(8)
+        False
+        >>> ExtendedContext.is_signed(-8)
+        True
+        """
+        a = _convert_other(a, raiseit=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
+        >>> ExtendedContext.is_snan(1)
+        False
+        """
+        a = _convert_other(a, raiseit=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
+        >>> c.is_subnormal(1)
+        False
+        """
+        a = _convert_other(a, raiseit=True)
+        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
+        >>> ExtendedContext.is_zero(1)
+        False
+        >>> ExtendedContext.is_zero(0)
+        True
+        """
+        a = _convert_other(a, raiseit=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')
+        >>> c.ln(1)
+        Decimal('0')
+        """
+        a = _convert_other(a, raiseit=True)
+        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')
+        >>> c.log10(0)
+        Decimal('-Infinity')
+        >>> c.log10(1)
+        Decimal('0')
+        """
+        a = _convert_other(a, raiseit=True)
+        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')
+        >>> ExtendedContext.logb(1)
+        Decimal('0')
+        >>> ExtendedContext.logb(10)
+        Decimal('1')
+        >>> ExtendedContext.logb(100)
+        Decimal('2')
+        """
+        a = _convert_other(a, raiseit=True)
+        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')
+        >>> ExtendedContext.logical_and(110, 1101)
+        Decimal('100')
+        >>> ExtendedContext.logical_and(Decimal(110), 1101)
+        Decimal('100')
+        >>> ExtendedContext.logical_and(110, Decimal(1101))
+        Decimal('100')
+        """
+        a = _convert_other(a, raiseit=True)
+        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')
+        >>> ExtendedContext.logical_invert(1101)
+        Decimal('111110010')
+        """
+        a = _convert_other(a, raiseit=True)
+        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')
+        >>> ExtendedContext.logical_or(110, 1101)
+        Decimal('1111')
+        >>> ExtendedContext.logical_or(Decimal(110), 1101)
+        Decimal('1111')
+        >>> ExtendedContext.logical_or(110, Decimal(1101))
+        Decimal('1111')
+        """
+        a = _convert_other(a, raiseit=True)
+        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')
+        >>> ExtendedContext.logical_xor(110, 1101)
+        Decimal('1011')
+        >>> ExtendedContext.logical_xor(Decimal(110), 1101)
+        Decimal('1011')
+        >>> ExtendedContext.logical_xor(110, Decimal(1101))
+        Decimal('1011')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.logical_xor(b, context=self)
+
+    def max(self, a, b):
+        """max compares two values numerically and returns the maximum.
+
+        If either operand is a NaN then the general rules apply.
+        Otherwise, the operands are compared as though by the compare
+        operation.  If they are numerically equal then the left-hand operand
+        is chosen as the result.  Otherwise the maximum (closer to positive
+        infinity) of the two operands is chosen as the result.
+
+        >>> ExtendedContext.max(Decimal('3'), Decimal('2'))
+        Decimal('3')
+        >>> ExtendedContext.max(Decimal('-10'), Decimal('3'))
+        Decimal('3')
+        >>> ExtendedContext.max(Decimal('1.0'), Decimal('1'))
+        Decimal('1')
+        >>> ExtendedContext.max(Decimal('7'), Decimal('NaN'))
+        Decimal('7')
+        >>> ExtendedContext.max(1, 2)
+        Decimal('2')
+        >>> ExtendedContext.max(Decimal(1), 2)
+        Decimal('2')
+        >>> ExtendedContext.max(1, Decimal(2))
+        Decimal('2')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.max(b, context=self)
+
+    def max_mag(self, a, b):
+        """Compares the values numerically with their sign ignored.
+
+        >>> ExtendedContext.max_mag(Decimal('7'), Decimal('NaN'))
+        Decimal('7')
+        >>> ExtendedContext.max_mag(Decimal('7'), Decimal('-10'))
+        Decimal('-10')
+        >>> ExtendedContext.max_mag(1, -2)
+        Decimal('-2')
+        >>> ExtendedContext.max_mag(Decimal(1), -2)
+        Decimal('-2')
+        >>> ExtendedContext.max_mag(1, Decimal(-2))
+        Decimal('-2')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.max_mag(b, context=self)
+
+    def min(self, a, b):
+        """min compares two values numerically and returns the minimum.
+
+        If either operand is a NaN then the general rules apply.
+        Otherwise, the operands are compared as though by the compare
+        operation.  If they are numerically equal then the left-hand operand
+        is chosen as the result.  Otherwise the minimum (closer to negative
+        infinity) of the two operands is chosen as the result.
+
+        >>> ExtendedContext.min(Decimal('3'), Decimal('2'))
+        Decimal('2')
+        >>> ExtendedContext.min(Decimal('-10'), Decimal('3'))
+        Decimal('-10')
+        >>> ExtendedContext.min(Decimal('1.0'), Decimal('1'))
+        Decimal('1.0')
+        >>> ExtendedContext.min(Decimal('7'), Decimal('NaN'))
+        Decimal('7')
+        >>> ExtendedContext.min(1, 2)
+        Decimal('1')
+        >>> ExtendedContext.min(Decimal(1), 2)
+        Decimal('1')
+        >>> ExtendedContext.min(1, Decimal(29))
+        Decimal('1')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.min(b, context=self)
+
+    def min_mag(self, a, b):
+        """Compares the values numerically with their sign ignored.
+
+        >>> ExtendedContext.min_mag(Decimal('3'), Decimal('-2'))
+        Decimal('-2')
+        >>> ExtendedContext.min_mag(Decimal('-3'), Decimal('NaN'))
+        Decimal('-3')
+        >>> ExtendedContext.min_mag(1, -2)
+        Decimal('1')
+        >>> ExtendedContext.min_mag(Decimal(1), -2)
+        Decimal('1')
+        >>> ExtendedContext.min_mag(1, Decimal(-2))
+        Decimal('1')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.min_mag(b, context=self)
+
+    def minus(self, a):
+        """Minus corresponds to unary prefix minus in Python.
+
+        The operation is evaluated using the same rules as subtract; the
+        operation minus(a) is calculated as subtract('0', a) where the '0'
+        has the same exponent as the operand.
+
+        >>> ExtendedContext.minus(Decimal('1.3'))
+        Decimal('-1.3')
+        >>> ExtendedContext.minus(Decimal('-1.3'))
+        Decimal('1.3')
+        >>> ExtendedContext.minus(1)
+        Decimal('-1')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.__neg__(context=self)
+
+    def multiply(self, a, b):
+        """multiply multiplies two operands.
+
+        If either operand is a special value then the general rules apply.
+        Otherwise, the operands are multiplied together
+        ('long multiplication'), resulting in a number which may be as long as
+        the sum of the lengths of the two operands.
+
+        >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3'))
+        Decimal('3.60')
+        >>> ExtendedContext.multiply(Decimal('7'), Decimal('3'))
+        Decimal('21')
+        >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8'))
+        Decimal('0.72')
+        >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0'))
+        Decimal('-0.0')
+        >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321'))
+        Decimal('4.28135971E+11')
+        >>> ExtendedContext.multiply(7, 7)
+        Decimal('49')
+        >>> ExtendedContext.multiply(Decimal(7), 7)
+        Decimal('49')
+        >>> ExtendedContext.multiply(7, Decimal(7))
+        Decimal('49')
+        """
+        a = _convert_other(a, raiseit=True)
+        r = a.__mul__(b, context=self)
+        if r is NotImplemented:
+            raise TypeError("Unable to convert %s to Decimal" % b)
+        else:
+            return r
+
+    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')
+        >>> c.next_minus(1)
+        Decimal('0.999999999')
+        """
+        a = _convert_other(a, raiseit=True)
+        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')
+        >>> c.next_plus(1)
+        Decimal('1.00000001')
+        """
+        a = _convert_other(a, raiseit=True)
+        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')
+        >>> c.next_toward(0, 1)
+        Decimal('1E-1007')
+        >>> c.next_toward(Decimal(0), 1)
+        Decimal('1E-1007')
+        >>> c.next_toward(0, Decimal(1))
+        Decimal('1E-1007')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.next_toward(b, context=self)
+
+    def normalize(self, a):
+        """normalize reduces an operand to its simplest form.
+
+        Essentially a plus operation with all trailing zeros removed from the
+        result.
+
+        >>> ExtendedContext.normalize(Decimal('2.1'))
+        Decimal('2.1')
+        >>> ExtendedContext.normalize(Decimal('-2.0'))
+        Decimal('-2')
+        >>> ExtendedContext.normalize(Decimal('1.200'))
+        Decimal('1.2')
+        >>> ExtendedContext.normalize(Decimal('-120'))
+        Decimal('-1.2E+2')
+        >>> ExtendedContext.normalize(Decimal('120.00'))
+        Decimal('1.2E+2')
+        >>> ExtendedContext.normalize(Decimal('0.00'))
+        Decimal('0')
+        >>> ExtendedContext.normalize(6)
+        Decimal('6')
+        """
+        a = _convert_other(a, raiseit=True)
+        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 = ExtendedContext.copy()
+        >>> 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'
+        >>> c.number_class(123)
+        '+Normal'
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.number_class(context=self)
+
+    def plus(self, a):
+        """Plus corresponds to unary prefix plus in Python.
+
+        The operation is evaluated using the same rules as add; the
+        operation plus(a) is calculated as add('0', a) where the '0'
+        has the same exponent as the operand.
+
+        >>> ExtendedContext.plus(Decimal('1.3'))
+        Decimal('1.3')
+        >>> ExtendedContext.plus(Decimal('-1.3'))
+        Decimal('-1.3')
+        >>> ExtendedContext.plus(-1)
+        Decimal('-1')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.__pos__(context=self)
+
+    def power(self, a, b, modulo=None):
+        """Raises a to the power of b, to modulo if given.
+
+        With two arguments, compute a**b.  If a is negative then b
+        must be integral.  The result will be inexact unless b is
+        integral and the result is finite and can be expressed exactly
+        in 'precision' digits.
+
+        With three arguments, compute (a**b) % modulo.  For the
+        three argument form, the following restrictions on the
+        arguments hold:
+
+         - all three arguments must be integral
+         - b must be nonnegative
+         - at least one of a or b must be nonzero
+         - modulo must be nonzero and have at most 'precision' digits
+
+        The result of pow(a, b, modulo) is identical to the result
+        that would be obtained by computing (a**b) % modulo with
+        unbounded precision, but is computed more efficiently.  It is
+        always exact.
+
+        >>> c = ExtendedContext.copy()
+        >>> c.Emin = -999
+        >>> c.Emax = 999
+        >>> c.power(Decimal('2'), Decimal('3'))
+        Decimal('8')
+        >>> c.power(Decimal('-2'), Decimal('3'))
+        Decimal('-8')
+        >>> c.power(Decimal('2'), Decimal('-3'))
+        Decimal('0.125')
+        >>> c.power(Decimal('1.7'), Decimal('8'))
+        Decimal('69.7575744')
+        >>> c.power(Decimal('10'), Decimal('0.301029996'))
+        Decimal('2.00000000')
+        >>> c.power(Decimal('Infinity'), Decimal('-1'))
+        Decimal('0')
+        >>> c.power(Decimal('Infinity'), Decimal('0'))
+        Decimal('1')
+        >>> c.power(Decimal('Infinity'), Decimal('1'))
+        Decimal('Infinity')
+        >>> c.power(Decimal('-Infinity'), Decimal('-1'))
+        Decimal('-0')
+        >>> c.power(Decimal('-Infinity'), Decimal('0'))
+        Decimal('1')
+        >>> c.power(Decimal('-Infinity'), Decimal('1'))
+        Decimal('-Infinity')
+        >>> c.power(Decimal('-Infinity'), Decimal('2'))
+        Decimal('Infinity')
+        >>> c.power(Decimal('0'), Decimal('0'))
+        Decimal('NaN')
+
+        >>> c.power(Decimal('3'), Decimal('7'), Decimal('16'))
+        Decimal('11')
+        >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16'))
+        Decimal('-11')
+        >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16'))
+        Decimal('1')
+        >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16'))
+        Decimal('11')
+        >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789'))
+        Decimal('11729830')
+        >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729'))
+        Decimal('-0')
+        >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537'))
+        Decimal('1')
+        >>> ExtendedContext.power(7, 7)
+        Decimal('823543')
+        >>> ExtendedContext.power(Decimal(7), 7)
+        Decimal('823543')
+        >>> ExtendedContext.power(7, Decimal(7), 2)
+        Decimal('1')
+        """
+        a = _convert_other(a, raiseit=True)
+        r = a.__pow__(b, modulo, context=self)
+        if r is NotImplemented:
+            raise TypeError("Unable to convert %s to Decimal" % b)
+        else:
+            return r
+
+    def quantize(self, a, b):
+        """Returns a value equal to 'a' (rounded), having the exponent of 'b'.
+
+        The coefficient of the result is derived from that of the left-hand
+        operand.  It may be rounded using the current rounding setting (if the
+        exponent is being increased), multiplied by a positive power of ten (if
+        the exponent is being decreased), or is unchanged (if the exponent is
+        already equal to that of the right-hand operand).
+
+        Unlike other operations, if the length of the coefficient after the
+        quantize operation would be greater than precision then an Invalid
+        operation condition is raised.  This guarantees that, unless there is
+        an error condition, the exponent of the result of a quantize is always
+        equal to that of the right-hand operand.
+
+        Also unlike other operations, quantize will never raise Underflow, even
+        if the result is subnormal and inexact.
+
+        >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001'))
+        Decimal('2.170')
+        >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01'))
+        Decimal('2.17')
+        >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1'))
+        Decimal('2.2')
+        >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0'))
+        Decimal('2')
+        >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1'))
+        Decimal('0E+1')
+        >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity'))
+        Decimal('-Infinity')
+        >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity'))
+        Decimal('NaN')
+        >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1'))
+        Decimal('-0')
+        >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5'))
+        Decimal('-0E+5')
+        >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2'))
+        Decimal('NaN')
+        >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2'))
+        Decimal('NaN')
+        >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1'))
+        Decimal('217.0')
+        >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0'))
+        Decimal('217')
+        >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1'))
+        Decimal('2.2E+2')
+        >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2'))
+        Decimal('2E+2')
+        >>> ExtendedContext.quantize(1, 2)
+        Decimal('1')
+        >>> ExtendedContext.quantize(Decimal(1), 2)
+        Decimal('1')
+        >>> ExtendedContext.quantize(1, Decimal(2))
+        Decimal('1')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.quantize(b, context=self)
+
+    def radix(self):
+        """Just returns 10, as this is Decimal, :)
+
+        >>> ExtendedContext.radix()
+        Decimal('10')
+        """
+        return Decimal(10)
+
+    def remainder(self, a, b):
+        """Returns the remainder from integer division.
+
+        The result is the residue of the dividend after the operation of
+        calculating integer division as described for divide-integer, rounded
+        to precision digits if necessary.  The sign of the result, if
+        non-zero, is the same as that of the original dividend.
+
+        This operation will fail under the same conditions as integer division
+        (that is, if integer division on the same two operands would fail, the
+        remainder cannot be calculated).
+
+        >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3'))
+        Decimal('2.1')
+        >>> ExtendedContext.remainder(Decimal('10'), Decimal('3'))
+        Decimal('1')
+        >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3'))
+        Decimal('-1')
+        >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1'))
+        Decimal('0.2')
+        >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3'))
+        Decimal('0.1')
+        >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3'))
+        Decimal('1.0')
+        >>> ExtendedContext.remainder(22, 6)
+        Decimal('4')
+        >>> ExtendedContext.remainder(Decimal(22), 6)
+        Decimal('4')
+        >>> ExtendedContext.remainder(22, Decimal(6))
+        Decimal('4')
+        """
+        a = _convert_other(a, raiseit=True)
+        r = a.__mod__(b, context=self)
+        if r is NotImplemented:
+            raise TypeError("Unable to convert %s to Decimal" % b)
+        else:
+            return r
+
+    def remainder_near(self, a, b):
+        """Returns to be "a - b * n", where n is the integer nearest the exact
+        value of "x / b" (if two integers are equally near then the even one
+        is chosen).  If the result is equal to 0 then its sign will be the
+        sign of a.
+
+        This operation will fail under the same conditions as integer division
+        (that is, if integer division on the same two operands would fail, the
+        remainder cannot be calculated).
+
+        >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3'))
+        Decimal('-0.9')
+        >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6'))
+        Decimal('-2')
+        >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3'))
+        Decimal('1')
+        >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3'))
+        Decimal('-1')
+        >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1'))
+        Decimal('0.2')
+        >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3'))
+        Decimal('0.1')
+        >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3'))
+        Decimal('-0.3')
+        >>> ExtendedContext.remainder_near(3, 11)
+        Decimal('3')
+        >>> ExtendedContext.remainder_near(Decimal(3), 11)
+        Decimal('3')
+        >>> ExtendedContext.remainder_near(3, Decimal(11))
+        Decimal('3')
+        """
+        a = _convert_other(a, raiseit=True)
+        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')
+        >>> ExtendedContext.rotate(1333333, 1)
+        Decimal('13333330')
+        >>> ExtendedContext.rotate(Decimal(1333333), 1)
+        Decimal('13333330')
+        >>> ExtendedContext.rotate(1333333, Decimal(1))
+        Decimal('13333330')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.rotate(b, context=self)
+
+    def same_quantum(self, a, b):
+        """Returns True if the two operands have the same exponent.
+
+        The result is never affected by either the sign or the coefficient of
+        either operand.
+
+        >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001'))
+        False
+        >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01'))
+        True
+        >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1'))
+        False
+        >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf'))
+        True
+        >>> ExtendedContext.same_quantum(10000, -1)
+        True
+        >>> ExtendedContext.same_quantum(Decimal(10000), -1)
+        True
+        >>> ExtendedContext.same_quantum(10000, Decimal(-1))
+        True
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.same_quantum(b)
+
+    def scaleb (self, a, b):
+        """Returns the first operand after adding the second value its exp.
+
+        >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2'))
+        Decimal('0.0750')
+        >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0'))
+        Decimal('7.50')
+        >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3'))
+        Decimal('7.50E+3')
+        >>> ExtendedContext.scaleb(1, 4)
+        Decimal('1E+4')
+        >>> ExtendedContext.scaleb(Decimal(1), 4)
+        Decimal('1E+4')
+        >>> ExtendedContext.scaleb(1, Decimal(4))
+        Decimal('1E+4')
+        """
+        a = _convert_other(a, raiseit=True)
+        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')
+        >>> ExtendedContext.shift(88888888, 2)
+        Decimal('888888800')
+        >>> ExtendedContext.shift(Decimal(88888888), 2)
+        Decimal('888888800')
+        >>> ExtendedContext.shift(88888888, Decimal(2))
+        Decimal('888888800')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.shift(b, context=self)
+
+    def sqrt(self, a):
+        """Square root of a non-negative number to context precision.
+
+        If the result must be inexact, it is rounded using the round-half-even
+        algorithm.
+
+        >>> ExtendedContext.sqrt(Decimal('0'))
+        Decimal('0')
+        >>> ExtendedContext.sqrt(Decimal('-0'))
+        Decimal('-0')
+        >>> ExtendedContext.sqrt(Decimal('0.39'))
+        Decimal('0.624499800')
+        >>> ExtendedContext.sqrt(Decimal('100'))
+        Decimal('10')
+        >>> ExtendedContext.sqrt(Decimal('1'))
+        Decimal('1')
+        >>> ExtendedContext.sqrt(Decimal('1.0'))
+        Decimal('1.0')
+        >>> ExtendedContext.sqrt(Decimal('1.00'))
+        Decimal('1.0')
+        >>> ExtendedContext.sqrt(Decimal('7'))
+        Decimal('2.64575131')
+        >>> ExtendedContext.sqrt(Decimal('10'))
+        Decimal('3.16227766')
+        >>> ExtendedContext.sqrt(2)
+        Decimal('1.41421356')
+        >>> ExtendedContext.prec
+        9
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.sqrt(context=self)
+
+    def subtract(self, a, b):
+        """Return the difference between the two operands.
+
+        >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07'))
+        Decimal('0.23')
+        >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30'))
+        Decimal('0.00')
+        >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07'))
+        Decimal('-0.77')
+        >>> ExtendedContext.subtract(8, 5)
+        Decimal('3')
+        >>> ExtendedContext.subtract(Decimal(8), 5)
+        Decimal('3')
+        >>> ExtendedContext.subtract(8, Decimal(5))
+        Decimal('3')
+        """
+        a = _convert_other(a, raiseit=True)
+        r = a.__sub__(b, context=self)
+        if r is NotImplemented:
+            raise TypeError("Unable to convert %s to Decimal" % b)
+        else:
+            return r
+
+    def to_eng_string(self, a):
+        """Convert to a string, using engineering notation if an exponent is needed.
+
+        Engineering notation has an exponent which is a multiple of 3.  This
+        can leave up to 3 digits to the left of the decimal place and may
+        require the addition of either one or two trailing zeros.
+
+        The operation is not affected by the context.
+
+        >>> ExtendedContext.to_eng_string(Decimal('123E+1'))
+        '1.23E+3'
+        >>> ExtendedContext.to_eng_string(Decimal('123E+3'))
+        '123E+3'
+        >>> ExtendedContext.to_eng_string(Decimal('123E-10'))
+        '12.3E-9'
+        >>> ExtendedContext.to_eng_string(Decimal('-123E-12'))
+        '-123E-12'
+        >>> ExtendedContext.to_eng_string(Decimal('7E-7'))
+        '700E-9'
+        >>> ExtendedContext.to_eng_string(Decimal('7E+1'))
+        '70'
+        >>> ExtendedContext.to_eng_string(Decimal('0E+1'))
+        '0.00E+3'
+
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.to_eng_string(context=self)
+
+    def to_sci_string(self, a):
+        """Converts a number to a string, using scientific notation.
+
+        The operation is not affected by the context.
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.__str__(context=self)
+
+    def to_integral_exact(self, a):
+        """Rounds to an integer.
+
+        When the operand has a negative exponent, the result is the same
+        as using the quantize() operation using the given operand as the
+        left-hand-operand, 1E+0 as the right-hand-operand, and the precision
+        of the operand as the precision setting; Inexact and Rounded flags
+        are allowed in this operation.  The rounding mode is taken from the
+        context.
+
+        >>> ExtendedContext.to_integral_exact(Decimal('2.1'))
+        Decimal('2')
+        >>> ExtendedContext.to_integral_exact(Decimal('100'))
+        Decimal('100')
+        >>> ExtendedContext.to_integral_exact(Decimal('100.0'))
+        Decimal('100')
+        >>> ExtendedContext.to_integral_exact(Decimal('101.5'))
+        Decimal('102')
+        >>> ExtendedContext.to_integral_exact(Decimal('-101.5'))
+        Decimal('-102')
+        >>> ExtendedContext.to_integral_exact(Decimal('10E+5'))
+        Decimal('1.0E+6')
+        >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77'))
+        Decimal('7.89E+77')
+        >>> ExtendedContext.to_integral_exact(Decimal('-Inf'))
+        Decimal('-Infinity')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.to_integral_exact(context=self)
+
+    def to_integral_value(self, a):
+        """Rounds to an integer.
+
+        When the operand has a negative exponent, the result is the same
+        as using the quantize() operation using the given operand as the
+        left-hand-operand, 1E+0 as the right-hand-operand, and the precision
+        of the operand as the precision setting, except that no flags will
+        be set.  The rounding mode is taken from the context.
+
+        >>> ExtendedContext.to_integral_value(Decimal('2.1'))
+        Decimal('2')
+        >>> ExtendedContext.to_integral_value(Decimal('100'))
+        Decimal('100')
+        >>> ExtendedContext.to_integral_value(Decimal('100.0'))
+        Decimal('100')
+        >>> ExtendedContext.to_integral_value(Decimal('101.5'))
+        Decimal('102')
+        >>> ExtendedContext.to_integral_value(Decimal('-101.5'))
+        Decimal('-102')
+        >>> ExtendedContext.to_integral_value(Decimal('10E+5'))
+        Decimal('1.0E+6')
+        >>> ExtendedContext.to_integral_value(Decimal('7.89E+77'))
+        Decimal('7.89E+77')
+        >>> ExtendedContext.to_integral_value(Decimal('-Inf'))
+        Decimal('-Infinity')
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.to_integral_value(context=self)
+
+    # the method name changed, but we provide also the old one, for compatibility
+    to_integral = to_integral_value
+
+class _WorkRep(object):
+    __slots__ = ('sign','int','exp')
+    # sign: 0 or 1
+    # int:  int
+    # exp:  None, int, or string
+
+    def __init__(self, value=None):
+        if value is None:
+            self.sign = None
+            self.int = 0
+            self.exp = None
+        elif isinstance(value, Decimal):
+            self.sign = value._sign
+            self.int = int(value._int)
+            self.exp = value._exp
+        else:
+            # assert isinstance(value, tuple)
+            self.sign = value[0]
+            self.int = value[1]
+            self.exp = value[2]
+
+    def __repr__(self):
+        return "(%r, %r, %r)" % (self.sign, self.int, self.exp)
+
+    __str__ = __repr__
+
+
+
+def _normalize(op1, op2, prec = 0):
+    """Normalizes op1, op2 to have the same exp and length of coefficient.
+
+    Done during addition.
+    """
+    if op1.exp < op2.exp:
+        tmp = op2
+        other = op1
+    else:
+        tmp = op1
+        other = op2
+
+    # Let exp = min(tmp.exp - 1, tmp.adjusted() - precision - 1).
+    # Then adding 10**exp to tmp has the same effect (after rounding)
+    # as adding any positive quantity smaller than 10**exp; similarly
+    # for subtraction.  So if other is smaller than 10**exp we replace
+    # it with 10**exp.  This avoids tmp.exp - other.exp getting too large.
+    tmp_len = len(str(tmp.int))
+    other_len = len(str(other.int))
+    exp = tmp.exp + min(-1, tmp_len - prec - 2)
+    if other_len + other.exp - 1 < exp:
+        other.int = 1
+        other.exp = exp
+
+    tmp.int *= 10 ** (tmp.exp - other.exp)
+    tmp.exp = other.exp
+    return op1, op2
+
+
diff --git a/modules/language/python/module/math.scm b/modules/language/python/module/math.scm
new file mode 100644
index 0000000..ef137aa
--- /dev/null
+++ b/modules/language/python/module/math.scm
@@ -0,0 +1,196 @@
+(define-module (language python module math)
+  #:use-module (language python for)
+  #:use-module (language python try)
+  #:use-module (language python exceptions)
+  #:use-module (language python number)
+  #:use-module (system foreign)
+  #:use-module (rnrs bytevectors)
+  
+  #:export (ceil copysign fabs factorial floor fmod frexp fsum gcd isclose
+		 isfinite isinf isnan modf trunc exp expm1 log log1p log2 log10
+		 pow sqrt acos asin atan cos sin tan atan2 hypot pi
+		 degrees radians acosh asinh atanh cosh sinh tanh
+		 erf erfc gamma lgamma e tau inf nan))
+
+(define (real! s x)
+  (if (= (imag-part x) 0)
+      (real-part x)
+      (raise ValueError "real math fkn result in complex number" s)))
+
+(define ceil
+  (lambda (x)
+    ((@ (guile) inexac->exact)
+     ((@ (guile) ceiling)
+      x))))
+  
+(define (copysign x y)
+  (let ((x ((@ (guile) abs) x)))
+    (if (< y 0) (- x) x)))
+
+(define (fabs x) ((@ (guile) abs) x))
+
+(define (factorial x)
+  (if (not (and (number? x) (integer? x)))
+      (raise ValueError "Not an integer"))
+  (if (< x 0)
+      (raise ValueError "Negative integer"))
+
+  (let lp ((x x))
+    (if (= x 0)
+	1
+	(* x (lp (- x 1))))))
+
+(define (floor x)
+  ((@ (guile) inexac->exact)
+   ((@ (guile) floor)
+    x)))
+
+(define (fmod x y) ((@ (guile) truncate-remainder) x y))
+
+(define frexp
+  (let ((f (pointer->procedure double
+                               (dynamic-func "frexp" (dynamic-link))
+                               (list double '*))))
+    (lambda (x)
+      (let* ((v  (make-bytevector 4))
+	     (vp (bytevector->pointer v)))
+	(list (f x) (bytevector-s32-ref v 0 (native-endianness)))))))
+
+(define (fsum it)
+  (for ((x : it)) ((s 0))
+       (+ s x)
+       #:final s))
+       
+
+(define gcd (@ (guile) gcd))
+
+(define* (isclose a b #:key (rel_tol 1e-9) (abs_tol 0.0))
+  (define e-abs (abs (- a b)))
+  (if (< e-abs (max (* rel_tol (max (abs a) (abs b))) abs_tol))
+      #t
+      #f))
+
+(define (isfinite x)
+  (if (or (inf? x) (nan? x))
+      #f
+      #t))
+
+(define isinf inf?)
+(define isnan nan?)
+
+(define (ldexp x i) (* x ((@ (guile) expt) 2 i)))
+
+(define (modf x)
+  (let* ((x1 (floor x))
+	 (x2 (- x x1)))
+    (values x2 x1)))
+
+(define trunc py-trunc)
+
+;; Power and logarithms
+(define (exp x) (real! 'exp ((@ (guile) exp)) x))
+
+(define expm1
+  (let ((f (pointer->procedure double
+                               (dynamic-func "expm1" (dynamic-link))
+                               (list double))))
+    (lambda (x) (f x))))
+
+(define (log x) (real! 'log ((@ (guile) log)) x))
+
+(define log1p
+  (let ((f (pointer->procedure double
+                               (dynamic-func "log1p" (dynamic-link))
+                               (list double))))
+
+    (lambda (x) (f x))))
+
+(define log2
+  (let ((f (pointer->procedure double
+                               (dynamic-func "log2" (dynamic-link))
+                               (list double))))
+    (lambda (x) (f x))))
+
+(define (log10 x) (real! 'log10 (@ (guile) log10)))
+
+(define (pow x y) (real! 'pow ((@ (guile) expt) x y)))
+
+(define (sqrt x) (real! 'sqrt (@ (guile) sqrt)))
+
+;; Trigs
+(define (acos x) (real! 'acos ((@ (guile) acos) x)))
+(define (asin x) (real! 'asin ((@ (guile) asin) x)))
+(define (atan x) (real! 'atan ((@ (guile) atan) x)))
+(define (cos  x) (real! 'cos ( (@ (guile) cos) x)))
+(define (sin  x) (real! 'sin ( (@ (guile) sin) x)))
+(define (tan  x) (real! 'tan ( (@ (guile) tan) x)))
+
+(define atan2
+  (let ((f (pointer->procedure double
+                               (dynamic-func "atan2" (dynamic-link))
+                               (list double double))))
+    (lambda (x y) (f x y))))
+
+(define hypot
+  (let ((f (pointer->procedure double
+                               (dynamic-func "hypot" (dynamic-link))
+                               (list double double))))
+
+    (lambda (x y) (f x y))))
+
+
+;; angular conversion
+(define pi (* 4 (atan 1)))
+
+(define degrees
+  (let ((f (/ 360 (* 2 pi))))
+    (lambda (x) (* f x))))
+
+(define radians
+  (let ((f (/ (* 2 pi) 360)))
+    (lambda (x) (* f x))))
+
+;; Hyperbolic funcitons
+(define (acosh x) (real! 'acosh ((@ (guile) acosh) x)))
+(define (asinh x) (real! 'asinh ((@ (guile) asinh) x)))
+(define (atanh x) (real! 'atanh ((@ (guile) atanh) x)))
+(define (cosh  x) (real! 'cosh ( (@ (guile) cosh) x)))
+(define (sinh  x) (real! 'sinh ( (@ (guile) sinh) x)))
+(define (tanh  x) (real! 'tanh ( (@ (guile) tanh) x)))
+
+
+;; Special functions
+(define erf
+  (let ((f (pointer->procedure double
+                               (dynamic-func "erf" (dynamic-link))
+                               (list double))))
+    (lambda (x) (f x))))
+
+(define erfc
+  (let ((f (pointer->procedure double
+                               (dynamic-func "erfc" (dynamic-link))
+                               (list double))))
+    (lambda (x) (f x))))
+
+(define gamma
+  (let ((f (pointer->procedure double
+                               (dynamic-func "tgamma" (dynamic-link))
+                               (list double))))
+
+    (lambda (x)
+      (if (integer? x)
+	  (factorial (- x 1)) 
+	  (f x)))))
+
+(define lgamma
+  (let ((f (pointer->procedure double
+                               (dynamic-func "lgamma" (dynamic-link))
+                               (list double))))
+    (lambda (x)
+      (f x))))
+
+;; constants
+(define e   (exp 1))
+(define tau (* 2 pi))
+(define inf ((@ (guile) inf)))
+(define nan ((@ (guile) nan)))
diff --git a/modules/language/python/module/python.scm b/modules/language/python/module/python.scm
index 96b0aa7..3398dbb 100644
--- a/modules/language/python/module/python.scm
+++ b/modules/language/python/module/python.scm
@@ -126,15 +126,74 @@
 	   #t
 	   (is-a? (ref sub '__goops__) (ref cls '__goops__)))))
 
-(define-method (isinstance x y) #f)
+(define-method (isinstance x y)
+  (if (null? y)
+      #f
+      (if (pair? y)
+	  (or (isinstance x (car y))
+	      (isinstance x (cdr y)))
+	  (is-a? x y))))
+
+(define-method (isinstance (i <integer>) y)
+  (if (issubclass y int)
+      #t
+      (if (pair? y)
+	  (or (isinstance i (car y))
+	      (isinstance i (cdr y)))
+	  (is-a? i y))))
+
+(define-method (isinstance (i <real>) y)
+  (if (issubclass y float)
+      #t
+      (if (pair? y)
+	  (or (isinstance i (car y))
+	      (isinstance i (cdr y)))
+	  (is-a? i y))))
+
+(define-method (isinstance (i <pair>) y)
+  (if (issubclass y tuple)
+      #t
+      (if (pair? y)
+	  (or (isinstance i (car y))
+	      (isinstance i (cdr y)))
+	  (is-a? i y))))
+
+(define-method (isinstance (i <string>) y)
+  (if (issubclass y str)
+      #t
+      (if (pair? y)
+	  (or (isinstance i (car y))
+	      (isinstance i (cdr y)))
+	  (is-a? i y))))
+
+(define-method (isinstance (i <bytevector>) y)
+  (if (issubclass y bytes)
+      #t
+      (if (pair? y)
+	  (or (isinstance i (car y))
+	      (isinstance i (cdr y)))
+	  (is-a? i y))))
+
+
+(define-method (isinstance o (cl <p>))
+  (cond
+   ((eq? cl py-list)
+    (is-a? o <py-list>))
+   (else #f)))
+  
 (define-method (isinstance (o <p>) (cl <p>))
-  (aif it (ref cl '__instancecheck__)
-       (it o)
-       (if (pair? cl)
-           (or
-            (isinstance o (car cl))
-            (isinstance o (cdr cl)))
-           (is-a? o (ref cl '__goops__)))))
+  (cond
+   ((ref cl '__instancecheck__) =>
+    (lambda (it)
+      (it o)))
+   ((pair? cl)
+    (or
+     (isinstance o (car cl))
+     (isinstance o (cdr cl))))
+   (else
+    (is-a? o (ref cl '__goops__)))))
+	       
+	       
 
 (define iter
   (case-lambda
@@ -177,7 +236,7 @@
 (define (id x) (object-address x))
 
 (define (input str)
-  (format #t str)
+  ((@ (guile) format) #t str)
   (readline))
 
 (define (idx x) x)