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This is an implementation of decimal floating point arithmetic based on
the General Decimal Arithmetic Specification:

    http://speleotrove.com/decimal/decarith.html

and IEEE standard 854-1987:

    http://en.wikipedia.org/wiki/IEEE_854-1987

Decimal floating point has finite precision with arbitrarily large bounds.

The purpose of this module is to support arithmetic using familiar
"schoolhouse" rules and to avoid some of the tricky representation
issues associated with binary floating point.  The package is especially
useful for financial applications or for contexts where users have
expectations that are at odds with binary floating point (for instance,
in binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead
of 0.0; Decimal('1.00') % Decimal('0.1') returns the expected
Decimal('0.00')).

Here are some examples of using the decimal module:

>>> from decimal import *
>>> setcontext(ExtendedContext)
>>> Decimal(0)
Decimal('0')
>>> Decimal('1')
Decimal('1')
>>> Decimal('-.0123')
Decimal('-0.0123')
>>> Decimal(123456)
Decimal('123456')
>>> Decimal('123.45e12345678')
Decimal('1.2345E+12345680')
>>> Decimal('1.33') + Decimal('1.27')
Decimal('2.60')
>>> Decimal('12.34') + Decimal('3.87') - Decimal('18.41')
Decimal('-2.20')
>>> dig = Decimal(1)
>>> print(dig / Decimal(3))
0.333333333
>>> getcontext().prec = 18
>>> print(dig / Decimal(3))
0.333333333333333333
>>> print(dig.sqrt())
1
>>> print(Decimal(3).sqrt())
1.73205080756887729
>>> print(Decimal(3) ** 123)
4.85192780976896427E+58
>>> inf = Decimal(1) / Decimal(0)
>>> print(inf)
Infinity
>>> neginf = Decimal(-1) / Decimal(0)
>>> print(neginf)
-Infinity
>>> print(neginf + inf)
NaN
>>> print(neginf * inf)
-Infinity
>>> print(dig / 0)
Infinity
>>> getcontext().traps[DivisionByZero] = 1
>>> print(dig / 0)
Traceback (most recent call last):
  ...
  ...
  ...
decimal.DivisionByZero: x / 0
>>> c = Context()
>>> c.traps[InvalidOperation] = 0
>>> print(c.flags[InvalidOperation])
0
>>> c.divide(Decimal(0), Decimal(0))
Decimal('NaN')
>>> c.traps[InvalidOperation] = 1
>>> print(c.flags[InvalidOperation])
1
>>> c.flags[InvalidOperation] = 0
>>> print(c.flags[InvalidOperation])
0
>>> print(c.divide(Decimal(0), Decimal(0)))
Traceback (most recent call last):
  ...
  ...
  ...
decimal.InvalidOperation: 0 / 0
>>> print(c.flags[InvalidOperation])
1
>>> c.flags[InvalidOperation] = 0
>>> c.traps[InvalidOperation] = 0
>>> print(c.divide(Decimal(0), Decimal(0)))
NaN
>>> print(c.flags[InvalidOperation])
1
>>>
ÚDecimalÚContextÚDecimalTupleÚDefaultContextÚBasicContextÚExtendedContextÚDecimalExceptionÚClampedÚInvalidOperationÚDivisionByZeroÚInexactÚRoundedÚ	SubnormalÚOverflowÚ	UnderflowÚFloatOperationÚDivisionImpossibleÚInvalidContextÚConversionSyntaxÚDivisionUndefinedÚ
ROUND_DOWNÚ
ROUND_HALF_UPÚROUND_HALF_EVENÚ
ROUND_CEILINGÚROUND_FLOORÚROUND_UPÚROUND_HALF_DOWNÚ
ROUND_05UPÚ
setcontextÚ
getcontextÚlocalcontextÚMAX_PRECÚMAX_EMAXÚMIN_EMINÚ	MIN_ETINYÚHAVE_THREADSÚdecimalz1.70z2.4.2éN)Ú
namedtuplezsign digits exponentcGs|S)N©)Úargsr(r(ú"/usr/lib64/python3.6/_pydecimal.pyÚ<lambda>¡sr+Téé?élÿÇNÎZoi@üTc@seZdZdZdd„ZdS)ra1Base 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.
    cGsdS)Nr()ÚselfÚcontextr)r(r(r*ÚhandleÏszDecimalException.handleN)Ú__name__Ú
__module__Ú__qualname__Ú__doc__r1r(r(r(r*r¼sc@seZdZdZdS)ra)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").
    N)r2r3r4r5r(r(r(r*rÓs
c@seZdZdZdd„ZdS)r	a0An 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.
    cGs,|r(t|dj|djddƒ}|j|ƒStS)Nr&ÚnT)Ú_dec_from_tripleÚ_signÚ_intÚ_fix_nanÚ_NaN)r/r0r)Úansr(r(r*r1ös
zInvalidOperation.handleN)r2r3r4r5r1r(r(r(r*r	ßsc@seZdZdZdd„ZdS)rzÜTrying 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].
    cGstS)N)r;)r/r0r)r(r(r*r1szConversionSyntax.handleN)r2r3r4r5r1r(r(r(r*rüsc@seZdZdZdd„ZdS)r
a²Division 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.
    cGst|S)N)Ú_SignedInfinity)r/r0Úsignr)r(r(r*r1szDivisionByZero.handleN)r2r3r4r5r1r(r(r(r*r
sc@seZdZdZdd„ZdS)rzóCannot 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].
    cGstS)N)r;)r/r0r)r(r(r*r1szDivisionImpossible.handleN)r2r3r4r5r1r(r(r(r*rsc@seZdZdZdd„ZdS)rzîUndefined 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].
    cGstS)N)r;)r/r0r)r(r(r*r1)szDivisionUndefined.handleN)r2r3r4r5r1r(r(r(r*r!sc@seZdZdZdS)raHad 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.
    N)r2r3r4r5r(r(r(r*r,s
c@seZdZdZdd„ZdS)raìInvalid 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].
    cGstS)N)r;)r/r0r)r(r(r*r1CszInvalidContext.handleN)r2r3r4r5r1r(r(r(r*r8s	c@seZdZdZdS)raÙNumber 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.
    N)r2r3r4r5r(r(r(r*rFs
c@seZdZdZdS)r
a˜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.
    N)r2r3r4r5r(r(r(r*r
Rs	c@seZdZdZdd„ZdS)raNumerical 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.
    cGsŽ|jttttfkrt|S|dkrR|jtkr4t|St|d|j|j	|jdƒS|dkrŠ|jt
krlt|St|d|j|j	|jdƒSdS)Nr&Ú9r.)Úroundingrrrrr=rr7ÚprecÚEmaxr)r/r0r>r)r(r(r*r1ss


zOverflow.handleN)r2r3r4r5r1r(r(r(r*r]sc@seZdZdZdS)raxNumerical 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.
    N)r2r3r4r5r(r(r(r*rƒs
c@seZdZdZdS)raœEnable 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.
    N)r2r3r4r5r(r(r(r*r’s
c@seZdZefdd„ZdS)Ú
MockThreadingcCs
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tjƒjStk
r.tƒ}|tjƒ_|SXdS)zÍReturns this thread's context.

        If this thread does not yet have a context, returns
        a new context and sets this thread's context.
        New contexts are copies of DefaultContext.
        N)rKrLrHÚAttributeErrorr)r0r(r(r*rÒs

cCs,y|jStk
r&tƒ}||_|SXdS)zÍReturns this thread's context.

        If this thread does not yet have a context, returns
        a new context and sets this thread's context.
        New contexts are copies of DefaultContext.
        N)rHrMr)Ú_localr0r(r(r*ræscCs(|tttfkr|jƒ}|jƒ||_dS)z%Set this thread's context to context.N)rrrrIrJrH)r0rNr(r(r*rôscCs|dkrtƒ}t|ƒS)abReturn a context manager for a copy of the supplied context

    Uses a copy of the current context if no context is specified
    The returned context manager creates a local decimal context
    in a with statement:
        def sin(x):
             with localcontext() as ctx:
                 ctx.prec += 2
                 # Rest of sin calculation algorithm
                 # uses a precision 2 greater than normal
             return +s  # Convert result to normal precision

         def sin(x):
             with localcontext(ExtendedContext):
                 # Rest of sin calculation algorithm
                 # uses the Extended Context from the
                 # General Decimal Arithmetic Specification
             return +s  # Convert result to normal context

    >>> setcontext(DefaultContext)
    >>> print(getcontext().prec)
    28
    >>> with localcontext():
    ...     ctx = getcontext()
    ...     ctx.prec += 2
    ...     print(ctx.prec)
    ...
    30
    >>> with localcontext(ExtendedContext):
    ...     print(getcontext().prec)
    ...
    9
    >>> print(getcontext().prec)
    28
    N)rÚ_ContextManager)Zctxr(r(r*rýs$c
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dNdO„Z*ddPdQ„Z+ddRdS„Z,dTdU„Z-dVdW„Z.e.Z/dXdY„Z0e1e0ƒZ0dZd[„Z2e1e2ƒZ2d\d]„Z3d^d_„Z4d`da„Z5dbdc„Z6ddde„Z7dfdg„Z8dhdi„Z9djdk„Z:dldm„Z;dndo„Z<dpdq„Z=drds„Z>e?e7e8e9e:e;e<e=e>dtZ@ddudv„ZAdwdx„ZBdydz„ZCdd{d|„ZDdd}d~„ZEdd€„ZFddd‚„ZGddƒd„„ZHdd…d†„ZIdd‡dˆ„ZJdd‰dŠ„ZKd‹dŒ„ZLddŽ„ZMddd„ZNdd‘d’„ZOeOZPdd“d”„ZQdd•d–„ZRdd—d˜„ZSd™dš„ZTd›dœ„ZUddž„ZVdŸd „ZWdd¡d¢„ZXdd£d¤„ZYdd¥d¦„ZZd§d¨„Z[d©dª„Z\d d«d¬„Z]d!dd®„Z^d¯d°„Z_d±d²„Z`d³d´„Zadµd¶„Zbd"d·d¸„Zcd¹dº„Zdd»d¼„Zed½d¾„Zfd#d¿dÀ„ZgdÁdÂ„ZhdÃdÄ„Zid$dÅdÆ„ZjdÇdÈ„Zkd%dÉdÊ„Zld&dËdÌ„ZmdÍdÎ„ZndÏdÐ„Zod'dÑdÒ„Zpd(dÓdÔ„Zqd)dÕdÖ„Zrd*d×dØ„Zsd+dÙdÚ„Ztd,dÛdÜ„Zud-dÝdÞ„Zvd.dßdà„Zwd/dádâ„Zxd0dãdä„Zydådæ„Zzd1dçdè„Z{d2dédê„Z|d3dëdì„Z}dídî„Z~dïdð„Zdñdò„Z€d4dódô„ZdS(5rz,Floating point class for decimal arithmetic.Ú_expr9r8Ú_is_specialÚ0NcCsŒtj|ƒ}t|tƒr$t|jƒjddƒƒ}|dkrP|dkr@tƒ}|jt	d|ƒS|j
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|_
|j|_|St d|ƒ‚dS)aêCreate 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')
        Ú_ÚNzInvalid literal for Decimal: %rr>ú-r.r&ÚintZfracÚexprRFÚdiagÚsignalÚNr6ÚFTéztInvalid tuple size in creation of Decimal from list or tuple.  The list or tuple should have exactly three elements.z|Invalid sign.  The first value in the tuple should be an integer; either 0 for a positive number or 1 for a negative number.r,é	zTThe second value in the tuple must be composed of integers in the range 0 through 9.zUThe third value in the tuple must be an integer, or one of the strings 'F', 'n', 'N'.z;strict semantics for mixing floats and Decimals are enabledzCannot convert %r to Decimal)r&r.)r6rZ)!ÚobjectÚ__new__Ú
isinstanceÚstrÚ_parserÚstripÚreplacerÚ_raise_errorrÚgroupr8rVr9ÚlenrPrQÚlstripÚabsrÚ_WorkRepr>rWÚlistÚtupleÚ
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zDecimal.__new__cCs¬t|tƒr||ƒSt|tƒs$tdƒ‚tj|ƒs8tj|ƒrD|t|ƒƒStjd|ƒdkrZd}nd}t	|ƒj
ƒ\}}|jƒd}t|t
|d|ƒ|ƒ}|tkr |S||ƒSdS)a.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')

        zargument must be int or float.gð?r&r.éN)r`rVrqrsÚ_mathZisinfZisnanÚreprZcopysignriÚas_integer_ratioÚ
bit_lengthr7rar)rtÚfr>r6ÚdÚkÚresultr(r(r*rrÊs

zDecimal.from_floatcCs(|jr$|j}|dkrdS|dkr$dSdS)zrReturns whether the number is not actually one.

        0 if a number
        1 if NaN
        2 if sNaN
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zDecimal._isinfinitycCs||jƒ}|dkrd}n|jƒ}|s&|rx|dkr4tƒ}|dkrJ|jtd|ƒS|dkr`|jtd|ƒS|rn|j|ƒS|j|ƒSdS)z½Returns whether the number is not actually one.

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ƒƒS)aÊRound self to the nearest integer, or to a given precision.

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        >>> 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'))
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        ValueError: cannot round a NaN

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        >>> round(Decimal('123.456'), 0)
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        >>> round(Decimal('123.456'), -2)
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zContext.__init__cCs”t|tƒstd|ƒ‚|dkr<||kr†td||||fƒ‚nJ|dkrb||kr†td||||fƒ‚n$||ksr||kr†td||||fƒ‚tj|||ƒS)Nz%s must be an integerz-infz%s must be in [%s, %d]. got: %srcz%s must be in [%d, %s]. got: %sz%s must be in [%d, %d]. got %s)r`rVrsrmr^Ú__setattr__)r/ÚnameruZvminZvmaxr(r(r*Ú_set_integer_checkys
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zContext._set_signal_dictcCsä|dkr|j||ddƒS|dkr0|j||ddƒS|dkrH|j||ddƒS|dkr`|j||ddƒS|d	krx|j||ddƒS|d
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kr¾|j||ƒS|dkrÔtj|||ƒStd|ƒ‚dS)NrAr.rcr$z-infr&rBr±rår@z%s: invalid rounding moderrrz.'decimal.Context' object has no attribute '%s')r”Ú_rounding_modesrsr^r’r—rM)r/r“rur(r(r*r’’s(zContext.__setattr__cCstd|ƒ‚dS)Nz%s cannot be deleted)rM)r/r“r(r(r*Ú__delattr__«szContext.__delattr__c	CsNdd„|jjƒDƒ}dd„|jjƒDƒ}|j|j|j|j|j|j|j	||ffS)NcSsg|]\}}|r|‘qSr(r()rTÚsigr‹r(r(r*rV°sz&Context.__reduce__.<locals>.<listcomp>cSsg|]\}}|r|‘qSr(r()rTršr‹r(r(r*rV±s)
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zContext.__reduce__cCs|g}|jdt|ƒƒdd„|jjƒDƒ}|jddj|ƒdƒdd„|jjƒDƒ}|jddj|ƒdƒdj|ƒd	S)
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Cs.t|j|j|j|j|j|j|j|j|j	ƒ	}|S)z!Returns a shallow copy from self.)
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zContext.copycGsZtj||ƒ}||jkr(|ƒj|f|žŽSd|j|<|j|sN|ƒj|f|žŽS||ƒ‚dS)a#Handles an error

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        Decimal('3.1415')
        >>> context = Context(prec=5, traps=[Inexact])
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z!Context.create_decimal_from_floatcCst|dd}|j|dS)a[Returns the absolute value of the operand.

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        >>> 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')
        T)rœ)r0)rr½)r/rr(r(r*riFszContext.abscCs8t|dd}|j||d}|tkr0td|ƒ‚n|SdS)a«Return the sum of the two operands.

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        >>> 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')
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        Decimal('10')
        T)rœ)r0zUnable to convert %s to DecimalN)rrÃr–rs)r/rrUrÑr(r(r*Úadd[s
zContext.addcCst|j|ƒƒS)N)rar¹)r/rr(r(r*Ú_applypszContext._applycCst|tƒstdƒ‚|jƒS)zûReturns the same Decimal object.

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        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')
        T)rœ)r0)rrž)r/rrUr(r(r*rž€s!zContext.comparecCst|dd}|j||dS)aCompares 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')
        T)rœ)r0)rr5)r/rrUr(r(r*r5¤s zContext.compare_signalcCst|dd}|j|ƒS)a+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')
        T)rœ)rr0)r/rrUr(r(r*r0ÇszContext.compare_totalcCst|dd}|j|ƒS)z£Compares two operands using their abstract representation ignoring sign.

        Like compare_total, but with operand's sign ignored and assumed to be 0.
        T)rœ)rr9)r/rrUr(r(r*r9äszContext.compare_total_magcCst|dd}|jƒS)aReturns 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')
        T)rœ)rr·)r/rr(r(r*r·ìs
zContext.copy_abscCst|dd}t|ƒS)aReturns 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')
        T)rœ)rr)r/rr(r(r*Úcopy_decimalùs
zContext.copy_decimalcCst|dd}|jƒS)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')
        T)rœ)rr¸)r/rr(r(r*r¸s
zContext.copy_negatecCst|dd}|j|ƒS)aCopies 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')
        T)rœ)rr:)r/rrUr(r(r*r:szContext.copy_signcCs8t|dd}|j||d}|tkr0td|ƒ‚n|SdS)aˆDecimal 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')
        T)rœ)r0zUnable to convert %s to DecimalN)rrÎr–rs)r/rrUrÑr(r(r*Údivide+s
zContext.dividecCs8t|dd}|j||d}|tkr0td|ƒ‚n|SdS)a/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')
        T)rœ)r0zUnable to convert %s to DecimalN)rrÚr–rs)r/rrUrÑr(r(r*Ú
divide_intPs
zContext.divide_intcCs8t|dd}|j||d}|tkr0td|ƒ‚n|SdS)aÝReturn (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'))
        T)rœ)r0zUnable to convert %s to DecimalN)rrÔr–rs)r/rrUrÑr(r(r*rÉgs
zContext.divmodcCst|dd}|j|dS)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')
        T)rœ)r0)rrW)r/rr(r(r*rW|szContext.expcCst|dd}|j|||dS)aReturns 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')
        T)rœ)r0)rrú)r/rrUr-r(r(r*rú”szContext.fmacCst|tƒstdƒ‚|jƒS)aReturn 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
        z/is_canonical requires a Decimal as an argument.)r`rrsr=)r/rr(r(r*r=«s	
zContext.is_canonicalcCst|dd}|jƒS)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
        T)rœ)rr>)r/rr(r(r*r>¸szContext.is_finitecCst|dd}|jƒS)aUReturn 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
        T)rœ)rr%)r/rr(r(r*r%ÎszContext.is_infinitecCst|dd}|jƒS)aOReturn 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
        T)rœ)rr¡)r/rr(r(r*r¡Ýs
zContext.is_nancCst|dd}|j|dS)aïReturn 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
        T)rœ)r0)rr?)r/rr(r(r*r?íszContext.is_normalcCst|dd}|jƒS)aHReturn 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
        T)rœ)rr)r/rr(r(r*rszContext.is_qnancCst|dd}|jƒS)aReturn 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
        T)rœ)rr@)r/rr(r(r*r@szContext.is_signedcCst|dd}|jƒS)aTReturn 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
        T)rœ)rrŒ)r/rr(r(r*rŒ$s
zContext.is_snancCst|dd}|j|dS)aôReturn 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
        T)rœ)r0)rrA)r/rr(r(r*rA4szContext.is_subnormalcCst|dd}|jƒS)auReturn 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
        T)rœ)rrB)r/rr(r(r*rBJszContext.is_zerocCst|dd}|j|dS)aþReturns 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')
        T)rœ)r0)rrJ)r/rr(r(r*rJ[sz
Context.lncCst|dd}|j|dS)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')
        T)rœ)r0)rrM)r/rr(r(r*rMqsz
Context.log10cCst|dd}|j|dS)a4 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')
        T)rœ)r0)rrN)r/rr(r(r*rNszContext.logbcCst|dd}|j||dS)a”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')
        T)rœ)r0)rrX)r/rrUr(r(r*rX§szContext.logical_andcCst|dd}|j|dS)aInvert 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')
        T)rœ)r0)rrZ)r/rr(r(r*rZÂszContext.logical_invertcCst|dd}|j||dS)aApplies 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')
        T)rœ)r0)rr[)r/rrUr(r(r*r[ÕszContext.logical_orcCst|dd}|j||dS)a˜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')
        T)rœ)r0)rrY)r/rrUr(r(r*rYðszContext.logical_xorcCst|dd}|j||dS)a³max 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')
        T)rœ)r0)rr¾)r/rrUr(r(r*r¾szContext.maxcCst|dd}|j||dS)aÇCompares 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')
        T)rœ)r0)rr\)r/rrUr(r(r*r\&szContext.max_magcCst|dd}|j||dS)a¸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')
        T)rœ)r0)rrª)r/rrUr(r(r*rª7szContext.mincCst|dd}|j||dS)aÄCompares 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')
        T)rœ)r0)rr])r/rrUr(r(r*r]RszContext.min_magcCst|dd}|j|dS)aÎMinus 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')
        T)rœ)r0)rrº)r/rr(r(r*Úminuscsz
Context.minuscCs8t|dd}|j||d}|tkr0td|ƒ‚n|SdS)aàmultiply 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')
        T)rœ)r0zUnable to convert %s to DecimalN)rrÇr–rs)r/rrUrÑr(r(r*Úmultiplyts
zContext.multiplycCst|dd}|j|dS)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')
        T)rœ)r0)rr`)r/rr(r(r*r`”szContext.next_minuscCst|dd}|j|dS)aReturns 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')
        T)rœ)r0)rra)r/rr(r(r*ra¨szContext.next_pluscCst|dd}|j||dS)a´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')
        T)rœ)r0)rrb)r/rrUr(r(r*rb¼s zContext.next_towardcCst|dd}|j|dS)a³normalize 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')
        T)rœ)r0)rr#)r/rr(r(r*r#ßszContext.normalizecCst|dd}|j|dS)aâReturns 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'
        T)rœ)r0)rrd)r/rr(r(r*rd÷s/zContext.number_classcCst|dd}|j|dS)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')
        T)rœ)r0)rr»)r/rr(r(r*Úplus)szContext.pluscCs:t|dd}|j|||d}|tkr2td|ƒ‚n|SdS)aRaises 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')
        T)rœ)r0zUnable to convert %s to DecimalN)rrr–rs)r/rrUrÿrÑr(r(r*Úpower:s
Iz
Context.powercCst|dd}|j||dS)a
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')
        T)rœ)r0)rrõ)r/rrUr(r(r*rõŠs7zContext.quantizecCstdƒS)zkJust returns 10, as this is Decimal, :)

        >>> ExtendedContext.radix()
        Decimal('10')
        rŸ)r)r/r(r(r*reÄsz
Context.radixcCs8t|dd}|j||d}|tkr0td|ƒ‚n|SdS)aReturns 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')
        T)rœ)r0zUnable to convert %s to DecimalN)rrÖr–rs)r/rrUrÑr(r(r*rÌÌs
zContext.remaindercCst|dd}|j||dS)aGReturns 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')
        T)rœ)r0)rrÙ)r/rrUr(r(r*rÙòszContext.remainder_nearcCst|dd}|j||dS)aNReturns 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')
        T)rœ)r0)rri)r/rrUr(r(r*riszContext.rotatecCst|dd}|j|ƒS)aÝReturns 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
        T)rœ)rr&)r/rrUr(r(r*r&1szContext.same_quantumcCst|dd}|j||dS)a3Returns 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')
        T)rœ)r0)rrj)r/rrUr(r(r*rjIszContext.scalebcCst|dd}|j||dS)a{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')
        T)rœ)r0)rrË)r/rrUr(r(r*rË\sz
Context.shiftcCst|dd}|j|dS)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
        T)rœ)r0)rr/)r/rr(r(r*r/zszContext.sqrtcCs8t|dd}|j||d}|tkr0td|ƒ‚n|SdS)a&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')
        T)rœ)r0zUnable to convert %s to DecimalN)rrÄr–rs)r/rrUrÑr(r(r*Úsubtractšs
zContext.subtractcCst|dd}|j|dS)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'

        T)rœ)r0)rr¶)r/rr(r(r*r¶±szContext.to_eng_stringcCst|dd}|j|dS)zyConverts a number to a string, using scientific notation.

        The operation is not affected by the context.
        T)rœ)r0)rrµ)r/rr(r(r*Ú
to_sci_stringÍszContext.to_sci_stringcCst|dd}|j|dS)akRounds 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')
        T)rœ)r0)rr))r/rr(r(r*r)ÕszContext.to_integral_exactcCst|dd}|j|dS)aLRounds 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')
        T)rœ)r0)rrý)r/rr(r(r*rýószContext.to_integral_value)	NNNNNNNNN)N)rR)N)Xr2r3r4r5r‡r”r—r’r™rlr«rJr¡r*rIrnrer^r¦r¨r§rÈrær+r©rªrir«r¬r4ržr5r0r9r·rr¸r:r®r¯rÉrWrúr=r>r%r¡r?rr@rŒrArBrJrMrNrXrZr[rYr¾r\rªr]r°r±r`rarbr#rdr²r³rõrerÌrÙrir&rjrËr/r´r¶rµr)rýr…r(r(r(r*rBs®
"



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 #2
P:&" c@s&eZdZd	Zd
dd„Zdd„ZeZdS)rjr>rVrWNcCsf|dkrd|_d|_d|_nFt|tƒrD|j|_t|jƒ|_|j|_n|d|_|d|_|d|_dS)Nr&r.r,)r>rVrWr`rr8r9rP)r/rur(r(r*r‡s



z_WorkRep.__init__cCsd|j|j|jfS)Nz(%r, %r, %r))r>rVrW)r/r(r(r*r«(sz_WorkRep.__repr__)r>rVrW)N)r2r3r4r~r‡r«rµr(r(r(r*rjs
rjcCsš|j|jkr|}|}n|}|}tt|jƒƒ}tt|jƒƒ}|jtd||dƒ}||jd|krpd|_||_|jd|j|j9_|j|_||fS)zcNormalizes op1, op2 to have the same exp and length of coefficient.

    Done during addition.
    r.r,rŸr…)rWrgrarVrª)rÁrÂrAZtmprˆZtmp_lenZ	other_lenrWr(r(r*rÀ/srÀcCsb|dkrdS|dkr |d|Stt|ƒƒ}t|ƒt|jdƒƒ}||krPdS|d|SdS)a Given integers n and e, return n * 10**e if it's an integer, else None.

    The computation is designed to avoid computing large powers of 10
    unnecessarily.

    >>> _decimal_lshift_exact(3, 4)
    30000
    >>> _decimal_lshift_exact(300, -999999999)  # returns None

    r&rŸrRN)rarirgÚrstrip)r6r¯Zstr_nZval_nr(r(r*rOsrcCsF|dks|dkrtdƒ‚d}x$||kr@||||d?}}qW|S)zóClosest integer to the square root of the positive integer n.  a is
    an initial approximation to the square root.  Any positive integer
    will do for a, but the closer a is to the square root of n the
    faster convergence will be.

    r&z3Both arguments to _sqrt_nearest should be positive.r.)rm)r6rrUr(r(r*Ú
_sqrt_nearestds
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    In other words, d*10**f is an approximation to exp(c*10**e) with p
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      (c-1)*10**e < x**y < (c+1)*10**e

    in other words, c*10**e is an approximation to x**y with p digits
    of precision, and with an error in c of at most 1.  (This is
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      sign: either '+', '-' or ' '
      minimumwidth: nonnegative integer giving minimum width
      zeropad: boolean, indicating whether to pad with zeros
      thousands_sep: string to use as thousands separator, or ''
      grouping: grouping for thousands separators, in format
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      decimal_point: string to use for decimal point
      precision: nonnegative integer giving precision, or None
      type: one of the characters 'eEfFgG%', or None

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    If necessary, the zero padding adds an extra '0' on the left to
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    fracpart: string of digits that must come after the point
    exp: exponent, as an integer
    spec: dictionary resulting from parsing the format specifier

    This function uses the information in spec to:
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      format the sign
      format the exponent
      add trailing '%' for the '%' type
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