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e"`&ne"d2ДZ(e"d3ДZ'[["e)d4ДZ*de fd5ДГYZ+e,d6ДZ-gZ.e+i/i0ГD]!Z1e1i2d7Гoe.e1nq>[.Z3x8e3D]0Z1e1d8i4ГZ5e6Гe5Z7e1e+i8e7<qoW[1[7[5[3d9e fd:ДГYZ9de fd;ДГYZ:d<e fd=ДГYZ;d>d?ДZ<hd@dA<dBdC<dDdE<dDdF<d8dG<d8dH<d8dI<d8dJ<d>dK<d>dL<d>dM<d>dN<d>dO<d>dP<d>dQ<d>dR<dSДZ=dTДZ>dUДZ?dVДZ@dWdXДZAdYДZBdZДZCd[e fd\ДГYZDeDГiEZFdWd]ДZGd^ДZHd_ДZIhd`dC<dadE<dbdF<dcdG<dddH<dedI<dfdJ<dgdK<dhdL<diДZJe,djДZKe:dkdldmedneeegdogdpdqdrdsdtd8ГZLe:dkdudmedneeeeegdogГZMe:dkdudmedngdogГZNddkOZOddkOZOeOiPdveOiQeOiRBГiSZTeOiPdwГiSZUeOiPdxГiSZV[Oe+dyГZWe+dzГZXe+d{ГZYe+d>ГZZe+d8ГZ[e+dГZ\eWeXfZ]e^d|jo0ddk_Z_ddkZe_i`eiae^ГndS(}s╔	
This is a Py2.3 implementation of decimal floating point arithmetic based on
the General Decimal Arithmetic Specification:

    www2.hursley.ibm.com/decimal/decarith.html

and IEEE standard 854-1987:

    www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html

Decimal floating point has finite precision with arbitrarily large bounds.

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

Here are some examples of using the decimal module:

>>> from decimal import *
>>> setcontext(ExtendedContext)
>>> Decimal(0)
Decimal("0")
>>> Decimal("1")
Decimal("1")
>>> Decimal("-.0123")
Decimal("-0.0123")
>>> Decimal(123456)
Decimal("123456")
>>> Decimal("123.45e12345678901234567890")
Decimal("1.2345E+12345678901234567892")
>>> Decimal("1.33") + Decimal("1.27")
Decimal("2.60")
>>> Decimal("12.34") + Decimal("3.87") - Decimal("18.41")
Decimal("-2.20")
>>> dig = Decimal(1)
>>> print dig / Decimal(3)
0.333333333
>>> getcontext().prec = 18
>>> print dig / Decimal(3)
0.333333333333333333
>>> print dig.sqrt()
1
>>> print Decimal(3).sqrt()
1.73205080756887729
>>> print Decimal(3) ** 123
4.85192780976896427E+58
>>> inf = Decimal(1) / Decimal(0)
>>> print inf
Infinity
>>> neginf = Decimal(-1) / Decimal(0)
>>> print neginf
-Infinity
>>> print neginf + inf
NaN
>>> print neginf * inf
-Infinity
>>> print dig / 0
Infinity
>>> getcontext().traps[DivisionByZero] = 1
>>> print dig / 0
Traceback (most recent call last):
  ...
  ...
  ...
DivisionByZero: x / 0
>>> c = Context()
>>> c.traps[InvalidOperation] = 0
>>> print c.flags[InvalidOperation]
0
>>> c.divide(Decimal(0), Decimal(0))
Decimal("NaN")
>>> c.traps[InvalidOperation] = 1
>>> print c.flags[InvalidOperation]
1
>>> c.flags[InvalidOperation] = 0
>>> print c.flags[InvalidOperation]
0
>>> print c.divide(Decimal(0), Decimal(0))
Traceback (most recent call last):
  ...
  ...
  ...
InvalidOperation: 0 / 0
>>> print c.flags[InvalidOperation]
1
>>> c.flags[InvalidOperation] = 0
>>> c.traps[InvalidOperation] = 0
>>> print c.divide(Decimal(0), Decimal(0))
NaN
>>> print c.flags[InvalidOperation]
1
>>>
tDecimaltContexttDefaultContexttBasicContexttExtendedContexttDecimalExceptiontClampedtInvalidOperationtDivisionByZerotInexacttRoundedt	SubnormaltOverflowt	Underflowt
ROUND_DOWNt
ROUND_HALF_UPtROUND_HALF_EVENt
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ROUND_05UPt
setcontextt
getcontexttlocalcontexti    NcBseZdZdДZRS(s-Base exception class.

    Used exceptions derive from this.
    If an exception derives from another exception besides this (such as
    Underflow (Inexact, Rounded, Subnormal) that indicates that it is only
    called if the others are present.  This isn't actually used for
    anything, though.

    handle  -- Called when context._raise_error is called and the
               trap_enabler is set.  First argument is self, second is the
               context.  More arguments can be given, those being after
               the explanation in _raise_error (For example,
               context._raise_error(NewError, '(-x)!', self._sign) would
               call NewError().handle(context, self._sign).)

    To define a new exception, it should be sufficient to have it derive
    from DecimalException.
    cGsdS(N((tselftcontexttargs((s#/usr/local/lib/python2.5/decimal.pythandleкs(t__name__t
__module__t__doc__R(((s#/usr/local/lib/python2.5/decimal.pyRЧscBseZdZRS(s)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").
    (RRR(((s#/usr/local/lib/python2.5/decimal.pyRоs
cBseZdZdДZRS(s0An 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?|o4t|di|didtГ}|i|ГSntS(Nitn(t_dec_from_triplet_signt_inttTruet_fix_nantNaN(RRRtans((s#/usr/local/lib/python2.5/decimal.pyR╤s#(RRRR(((s#/usr/local/lib/python2.5/decimal.pyR║stConversionSyntaxcBseZdZdДZRS(s▌Trying to convert badly formed string.

    This occurs and signals invalid-operation if an string is being
    converted to a number and it does not conform to the numeric string
    syntax.  The result is [0,qNaN].
    cGstS(N(R&(RRR((s#/usr/local/lib/python2.5/decimal.pyR▐s(RRRR(((s#/usr/local/lib/python2.5/decimal.pyR(╫scBseZdZdДZRS(s▓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.
    cGst|S(N(tInfsign(RRtsignR((s#/usr/local/lib/python2.5/decimal.pyRюs(RRRR(((s#/usr/local/lib/python2.5/decimal.pyRсstDivisionImpossiblecBseZdZdДZRS(sєCannot 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&(RRR((s#/usr/local/lib/python2.5/decimal.pyR∙s(RRRR(((s#/usr/local/lib/python2.5/decimal.pyR+ёstDivisionUndefinedcBseZdZdДZRS(sюUndefined 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&(RRR((s#/usr/local/lib/python2.5/decimal.pyRs(RRRR(((s#/usr/local/lib/python2.5/decimal.pyR,№scBseZdZRS(sнHad 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.
    (RRR(((s#/usr/local/lib/python2.5/decimal.pyR	s
tInvalidContextcBseZdZdДZRS(sьInvalid 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&(RRR((s#/usr/local/lib/python2.5/decimal.pyRs(RRRR(((s#/usr/local/lib/python2.5/decimal.pyR-s	cBseZdZRS(s┘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.
    (RRR(((s#/usr/local/lib/python2.5/decimal.pyR
!s
cBseZdZRS(sШExponent < 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.
    (RRR(((s#/usr/local/lib/python2.5/decimal.pyR-s	cBseZdZdДZRS(sNumerical 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.
    cGs╨|ittttfjot|Sn|djoE|itjot|Snt|d|i|i	|idГSn|djoE|it
jot|Snt|d|i|i	|idГSndS(Nit9i(troundingRRRRR)RR!tprectEmaxR(RRR*R((s#/usr/local/lib/python2.5/decimal.pyRNs

(RRRR(((s#/usr/local/lib/python2.5/decimal.pyR8scBseZdZRS(sxNumerical 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.
    (RRR(((s#/usr/local/lib/python2.5/decimal.pyR
^s
t
MockThreadingcBseZedДZRS(cCs|itS(N(tmodulesR(Rtsys((s#/usr/local/lib/python2.5/decimal.pytlocalЕs(RRR4R5(((s#/usr/local/lib/python2.5/decimal.pyR2Дst__decimal_context__cCsC|tttfjo|iГ}|iГn|tiГ_dS(s%Set this thread's context to context.N(RRRtcopytclear_flagst	threadingt
currentThreadR6(R((s#/usr/local/lib/python2.5/decimal.pyRФscCsGytiГiSWn/tj
o#tГ}|tiГ_|SnXdS(s═Returns this thread's context.

        If this thread does not yet have a context, returns
        a new context and sets this thread's context.
        New contexts are copies of DefaultContext.
        N(R9R:R6tAttributeErrorR(R((s#/usr/local/lib/python2.5/decimal.pyRЫs	cCs;y|iSWn)tj
otГ}||_|SnXdS(s═Returns this thread's context.

        If this thread does not yet have a context, returns
        a new context and sets this thread's context.
        New contexts are copies of DefaultContext.
        N(R6R;R(t_localR((s#/usr/local/lib/python2.5/decimal.pyRпs		cCs=|tttfjo|iГ}|iГn||_dS(s%Set this thread's context to context.N(RRRR7R8R6(RR<((s#/usr/local/lib/python2.5/decimal.pyR╜scCs$|djo
tГ}nt|ГS(sReturn 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

    N(tNoneRt_ContextManager(tctx((s#/usr/local/lib/python2.5/decimal.pyR╞s(

cBsСeZdZdmZddndДZdДZdДZdndnd	ДZd
ДZ	dДZ
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dДZdДZdДZedndДZdndДZdndДZdndДZedndДZdndДZeZdndДZdndДZdndДZeZdndДZeZdДZ dndДZ!e!Z"dndДZ#dndДZ$dnd ДZ%dnd!ДZ&dnd"ДZ'dnd#ДZ(dnd$ДZ)d%ДZ*d&ДZ+d'ДZ,d(ДZ-d)ДZ.hZ/d*ДZ0d+ДZ1d,ДZ2d-ДZ3d.ДZ4d/ДZ5d0ДZ6d1ДZ7dnd2ДZ8dnd3ДZ9d4ДZ:dndnd5ДZ;dnd6ДZ<dnd7ДZ=dndned8ДZ>d9ДZ?d:ДZ@dndnd;ДZAdndnd<ДZBeBZCdnd=ДZDdnd>ДZEdnd?ДZFd@ДZGdAДZHdBДZIdndCДZJdndDДZKdEДZLdFДZMdGДZNdHДZOdIДZPdndJДZQdKДZRdLДZSdMДZTdNДZUdndOДZVdPДZWdQДZXdRДZYdndSДZZdTДZ[dUДZ\dndVДZ]dWДZ^dndXДZ_dndYДZ`dZДZad[ДZbdnd\ДZcdnd]ДZddnd^ДZednd_ДZfdnd`ДZgdndaДZhdndbДZidndcДZjdnddДZkdndeДZldfДZmdndgДZndndhДZodndiДZpdjДZqdkДZrdlДZsRS(os,Floating point class for decimal arithmetic.t_expR#R"t_is_specialt0cCs ti|Г}t|tГo╗t|Г}|djo2|djo
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ГqqбtdГВqбW|ddjo5ditt|	ГГ|_|d|_t|_nft|dttfГo?ditt|	pdgГГ|_|d|_t|_n
tdГВ|Snt|t Гot!ddГВnt!d|ГВdS(sКCreate a decimal point instance.

        >>> Decimal('3.14')              # string input
        Decimal("3.14")
        >>> Decimal((0, (3, 1, 4), -2))  # tuple (sign, digit_tuple, exponent)
        Decimal("3.14")
        >>> Decimal(314)                 # int or long
        Decimal("314")
        >>> Decimal(Decimal(314))        # another decimal instance
        Decimal("314")
        sInvalid literal for Decimal: %rR*t-iitinttfractexpRBtdiagtsignaltNR tFistInvalid tuple size in creation of Decimal from list or tuple.  The list or tuple should have exactly three elements.s|Invalid sign.  The first value in the tuple should be an integer; either 0 for a positive number or 1 for a negative number.ii	sTThe second value in the tuple must be composed of integers in the range 0 through 9.tsUThe third value in the tuple must be an integer, or one of the strings 'F', 'n', 'N'.s"Cannot convert float to Decimal.  s#First convert the float to a stringsCannot convert %r to DecimalN(ii(R RI("tobjectt__new__t
isinstancet
basestringt_parserR=Rt_raise_errorR(tgroupR"RDtstrtlstripR#tlenR@tFalseRAR$tlongtabsRt_WorkRepR*RFtlistttuplet
ValueErrortappendtjointmaptfloatt	TypeError(tclstvalueRRtmtintparttfracpartRFRGtdigitstdigit((s#/usr/local/lib/python2.5/decimal.pyRM¤sд


	
	

#	



			

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%

cCsE|io7|i}|djodSqA|djodSqAndS(srReturns whether the number is not actually one.

        0 if a number
        1 if NaN
        2 if sNaN
        R iRIii(RAR@(RRF((s#/usr/local/lib/python2.5/decimal.pyt_isnanМs
	

cCs.|idjo|iodSndSndS(syReturns whether the number is infinite

        0 if finite or not a number
        1 if +INF
        -1 if -INF
        RJi    ii(R@R"(R((s#/usr/local/lib/python2.5/decimal.pyt_isinfinityЫs

cCs╠|iГ}|djo
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|iГ}|p|oЛ|djo
tГ}n|djo|itd|ГSn|djo|itd|ГSn|o|i|ГSn|i|ГSndS(s╜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.
        itsNaNiN(RiR=RVRRQRR%(RtotherRtself_is_nantother_is_nan((s#/usr/local/lib/python2.5/decimal.pyt_check_nansиs"





cCs|ip
|idjS(suReturn True if self is nonzero; otherwise return False.

        NaNs and infinities are considered nonzero.
        RB(RAR#(R((s#/usr/local/lib/python2.5/decimal.pyt__nonzero__╚scCsЙt|Г}|tjodSn|ip
|io?|iГp
|iГodSnt|iГ|iГГSn|p|pdSqЪd|iSn|pd|iSn|i|ijodSn|i|ijodSn|iГ}|iГ}||joR|id|i	|i	}|id|i	|i	}t||Гd|iSn)||jod|iSn
d|iSdS(Niii    RB(
t_convert_othertNotImplementedRARitcmpRjR"tadjustedR#R@(RRlt
self_adjustedtother_adjustedtself_paddedtother_padded((s#/usr/local/lib/python2.5/decimal.pyt__cmp__╧s4


cCs4t|tttfГptSn|i|ГdjS(Ni(RNRRDRWRrRy(RRl((s#/usr/local/lib/python2.5/decimal.pyt__eq__ўscCs4t|tttfГptSn|i|ГdjS(Ni(RNRRDRWRrRy(RRl((s#/usr/local/lib/python2.5/decimal.pyt__ne__№scCset|dtГ}|ip|o/|io%|i||Г}|o|SqRnt|i|ГГS(sнCompares one to another.

        -1 => a < b
        0  => a = b
        1  => a > b
        NaN => one is NaN
        Like __cmp__, but returns Decimal instances.
        traiseit(RqR$RARoRRy(RRlRR'((s#/usr/local/lib/python2.5/decimal.pytcompares	cCs┬|io1|iГotdГВntt|ГГSn|pdSn|iГo9t|iГГ}td|i|i	d|i
ГSnt|i|it
|iГ|iidГfГS(sx.__hash__() <==> hash(x)sCannot hash a NaN value.ii    i
RB(RARiRathashRSt
_isintegerRYtto_integral_valueR*RDRFR"R@RUR#trstrip(Rtop((s#/usr/local/lib/python2.5/decimal.pyt__hash__s


'	cCs%|ittt|iГГ|ifS(seRepresents the number as a triple tuple.

        To show the internals exactly as they are.
        (R"R[R_RDR#R@(R((s#/usr/local/lib/python2.5/decimal.pytas_tuple,scCsdt|ГS(s0Represents the number as an instance of Decimal.s
Decimal("%s")(RS(R((s#/usr/local/lib/python2.5/decimal.pyt__repr__3sc	Cs▐ddg|i}|ioR|idjo|dSqo|idjo|d|iSqo|d|iSn|it|iГ}|idjo|d	jo
|}nJ|p
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}n9|idjo|d
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|i|}||jo
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tГ}nddg|id||}||||S(sЦReturn string representation of the number in scientific notation.

        Captures all of the information in the underlying representation.
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    cCs|iГ|_dS(N(R7tnew_context(RRg((s#/usr/local/lib/python2.5/decimal.pyt__init__)
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cCst|iГdS(N(RRi(Rtttvttb((s#/usr/local/lib/python2.5/decimal.pyt__exit__/
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s		c
BsсeZdZdNdNdNdNdNdNdNddNdД	ZdДZdДZdДZdДZeZ	dNdДZ
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ДZdДZddДZdДZdДZdДZdДZdДZdДZdДZdДZdДZdДZdДZdДZdДZdДZ dДZ!d ДZ"d!ДZ#d"ДZ$d#ДZ%d$ДZ&d%ДZ'd&ДZ(d'ДZ)d(ДZ*d)ДZ+d*ДZ,d+ДZ-d,ДZ.d-ДZ/d.ДZ0d/ДZ1d0ДZ2d1ДZ3d2ДZ4d3ДZ5d4ДZ6d5ДZ7d6ДZ8d7ДZ9d8ДZ:d9ДZ;d:ДZ<d;ДZ=d<ДZ>d=ДZ?d>ДZ@dNd?ДZAd@ДZBdAДZCdBДZDdCДZEdDДZFdEДZGdFДZHdGДZIdHДZJdIДZKdJДZLdKДZMdLДZNdMДZOeOZPRS(OsчContains 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 incremented.
             (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)
    ic
Cs=|djo
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tit	t
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ГГГqрt||
|ГqрW|`dS(N(R=RNtdictt_signalstlocalstitemstsetattrt_copyR7R─RR(RR0R/ttrapstflagsR√R1RКR└t_ignored_flagsR=R╜t_[2]tnametval((s#/usr/local/lib/python2.5/decimal.pyRhE
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&cCsцg}|idt|ГГg}|iiГD]!\}}|o||iq1q1~}|iddi|ГdГg}|iiГD]!\}}|o||iqНqН~}|iddi|ГdГdi|ГdS(sShow the current context.saContext(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)dsflags=[s, t]straps=[t)(R]tvarsRvRrRR^Ru(RR╜R=tfRltnamesRxRk((s#/usr/local/lib/python2.5/decimal.pyRЕ[
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c
CsCt|i|i|i|i|i|i|i|i|i	Г	}|S(s!Returns a shallow copy from self.(
RR0R/RuRvR√R1RКR└Rw(Rtnc((s#/usr/local/lib/python2.5/decimal.pyRl
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CsOt|i|i|iiГ|iiГ|i|i|i|i	|i
Г	}|S(sReturns a deep copy from self.(RR0R/RuR7RvR√R1RКR└Rw(RRБ((s#/usr/local/lib/python2.5/decimal.pyR7s
scGs~ti||Г}||ijo|Гi||МSn|i|cd7<|i|p|Гi||МSn||ВdS(s-Handles an error

        If the flag is in _ignored_flags, returns the default response.
        Otherwise, it increments the flag, then, if the corresponding
        trap_enabler is set, it reaises the exception.  Otherwise, it returns
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        iN(t_condition_maptgetRwRRvRu(Rt	conditiontexplanationRterror((s#/usr/local/lib/python2.5/decimal.pyRQ{
scCs
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scGs |it|Г|_t|ГS(s$Ignore the flags, if they are raised(RwRZ(RRv((s#/usr/local/lib/python2.5/decimal.pyRЗХ
scGsT|o(t|dttfГo|d}nx|D]}|ii|Гq6WdS(s+Stop ignoring the flags, if they are raisediN(RNR[RZRwtremove(RRvRА((s#/usr/local/lib/python2.5/decimal.pyt
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!cCstdГВdS(sA Context cannot be hashed.sCannot hash a Context.N(Ra(R((s#/usr/local/lib/python2.5/decimal.pyRГг
scCst|i|idГS(s!Returns Etiny (= Emin - prec + 1)i(RDR√R0(R((s#/usr/local/lib/python2.5/decimal.pyRжи
scCst|i|idГS(s,Returns maximum exponent (= Emax - prec + 1)i(RDR1R0(R((s#/usr/local/lib/python2.5/decimal.pyR├м
scCs|i}||_|S(s╙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.
        (R/(RRZR/((s#/usr/local/lib/python2.5/decimal.pyR
░
s		RBcCs`t|d|Г}|iГo4t|iГ|i|ijo|itdГSn|i|ГS(s9Creates a new Decimal instance but using self as context.Rsdiagnostic info too long in NaN(	RRiRUR#R0R└RQR(RТ(RR)RV((s#/usr/local/lib/python2.5/decimal.pytcreate_decimal├
s
-	cCs|id|ГS(s"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")
        R(RЦ(RRї((s#/usr/local/lib/python2.5/decimal.pyRX╠
scCs|i|d|ГS(sцReturn 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")
        R(RЯ(RRїR>((s#/usr/local/lib/python2.5/decimal.pytadd▐
scCst|i|ГГS(N(RSRТ(RRї((s#/usr/local/lib/python2.5/decimal.pyt_applyш
scCs|id|ГS(s√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")
        R(R(RRї((s#/usr/local/lib/python2.5/decimal.pyRы
s	cCs|i|d|ГS(s│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")
        R(R}(RRїR>((s#/usr/local/lib/python2.5/decimal.pyR}Ў
scCs|i|d|ГS(sTCompares 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
        R(R(RRїR>((s#/usr/local/lib/python2.5/decimal.pyRscCs
|i|ГS(sGCompares 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")
        (R(RRїR>((s#/usr/local/lib/python2.5/decimal.pyR/scCs
|i|ГS(sгCompares two operands using their abstract representation ignoring sign.

        Like compare_total, but with operand's sign ignored and assumed to be 0.
        (R(RRїR>((s#/usr/local/lib/python2.5/decimal.pyREscCs
|iГS(s╪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")
        (RР(RRї((s#/usr/local/lib/python2.5/decimal.pyRРLscCs
t|ГS(s╥Returns a copy of the decimal objet.

        >>> ExtendedContext.copy_decimal(Decimal('2.1'))
        Decimal("2.1")
        >>> ExtendedContext.copy_decimal(Decimal('-1.00'))
        Decimal("-1.00")
        (R(RRї((s#/usr/local/lib/python2.5/decimal.pytcopy_decimalVscCs
|iГS(sчReturns 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")
        (RС(RRї((s#/usr/local/lib/python2.5/decimal.pyRС`scCs
|i|ГS(s>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")
        (R(RRїR>((s#/usr/local/lib/python2.5/decimal.pyRjscCs|i|d|ГS(s╝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")
        R(Rм(RRїR>((s#/usr/local/lib/python2.5/decimal.pytdivide{scCs|i|d|ГS(sTDivides 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")
        R(R╣(RRїR>((s#/usr/local/lib/python2.5/decimal.pyt
divide_intХs
cCs|i|d|ГS(NR(R│(RRїR>((s#/usr/local/lib/python2.5/decimal.pyRзбscCs|id|ГS(sяReturns 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")
        R(RF(RRї((s#/usr/local/lib/python2.5/decimal.pyRFдscCs|i||d|ГS(s@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")
        R(R█(RRїR>R((s#/usr/local/lib/python2.5/decimal.pyR█╣scCs
|iГS(sReturn 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
        (R!(RRї((s#/usr/local/lib/python2.5/decimal.pyR!╔s	cCs
|iГS(sЎReturn 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
        (R"(RRї((s#/usr/local/lib/python2.5/decimal.pyR"╘scCs
|iГS(sReturn 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
        (R	(RRї((s#/usr/local/lib/python2.5/decimal.pyR	чs
cCs
|iГS(sReturn 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
        (R(RRї((s#/usr/local/lib/python2.5/decimal.pyRєscCs|id|ГS(s╟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
        R(R#(RRї((s#/usr/local/lib/python2.5/decimal.pyR#scCs
|iГS(sReturn 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
        (R$(RRї((s#/usr/local/lib/python2.5/decimal.pyR$s
cCs
|iГS(sReturn 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
        (R%(RRї((s#/usr/local/lib/python2.5/decimal.pyR% s
cCs
|iГS(sReturn 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
        (R&(RRї((s#/usr/local/lib/python2.5/decimal.pyR&,scCs|id|ГS(s╚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
        R(R'(RRї((s#/usr/local/lib/python2.5/decimal.pyR'9scCs
|iГS(sReturn 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
        (R((RRї((s#/usr/local/lib/python2.5/decimal.pyR(Ls
cCs|id|ГS(s╒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")
        R(R0(RRї((s#/usr/local/lib/python2.5/decimal.pyR0XscCs|id|ГS(sGReturns 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")
        R(R3(RRї((s#/usr/local/lib/python2.5/decimal.pyR3kscCs|id|ГS(sЖ 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")
        R(R4(RRї((s#/usr/local/lib/python2.5/decimal.pyR4ВscCs|i|d|ГS(sдApplies 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")
        R(R?(RRїR>((s#/usr/local/lib/python2.5/decimal.pyR?ХscCs|id|ГS(s╜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")
        R(RA(RRї((s#/usr/local/lib/python2.5/decimal.pyRAйscCs|i|d|ГS(sЯApplies 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")
        R(RC(RRїR>((s#/usr/local/lib/python2.5/decimal.pyRC╣scCs|i|d|ГS(sеApplies 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")
        R(R@(RRїR>((s#/usr/local/lib/python2.5/decimal.pyR@═scCs|i|d|ГS(sєmax compares two values numerically and returns the maximum.

        If either operand is a NaN then the general rules apply.
        Otherwise, the operands are compared as as though by the compare
        operation.  If they are numerically equal then the left-hand operand
        is chosen as the result.  Otherwise the maximum (closer to positive
        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")
        R(RШ(RRїR>((s#/usr/local/lib/python2.5/decimal.pyRШсscCs|i|d|ГS(s8Compares the values numerically with their sign ignored.R(RD(RRїR>((s#/usr/local/lib/python2.5/decimal.pyRDїscCs|i|d|ГS(sўmin compares two values numerically and returns the minimum.

        If either operand is a NaN then the general rules apply.
        Otherwise, the operands are compared as as though by the compare
        operation.  If they are numerically equal then the left-hand operand
        is chosen as the result.  Otherwise the minimum (closer to negative
        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")
        R(RЧ(RRїR>((s#/usr/local/lib/python2.5/decimal.pyRЧ∙scCs|i|d|ГS(s8Compares the values numerically with their sign ignored.R(RE(RRїR>((s#/usr/local/lib/python2.5/decimal.pyRE
scCs|id|ГS(sУMinus 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")
        R(RУ(RRї((s#/usr/local/lib/python2.5/decimal.pytminusscCs|i|d|ГS(smultiply 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")
        R(Rе(RRїR>((s#/usr/local/lib/python2.5/decimal.pytmultiplyscCs|id|ГS(sчReturns 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")
        R(RH(RRї((s#/usr/local/lib/python2.5/decimal.pyRH4scCs|id|ГS(sцReturns 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")
        R(RI(RRї((s#/usr/local/lib/python2.5/decimal.pyRIEscCs|i|d|ГS(sёReturns 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")
        R(RK(RRїR>((s#/usr/local/lib/python2.5/decimal.pyRKVscCs|id|ГS(sunormalize 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")
        R(R(RRї((s#/usr/local/lib/python2.5/decimal.pyRrscCs|id|ГS(s▓Returns an indication of the class of the operand.

        The class is one of the following strings:
          -sNaN
          -NaN
          -Infinity
          -Normal
          -Subnormal
          -Zero
          +Zero
          +Subnormal
          +Normal
          +Infinity

        >>> c = Context(ExtendedContext)
        >>> c.Emin = -999
        >>> c.Emax = 999
        >>> c.number_class(Decimal('Infinity'))
        '+Infinity'
        >>> c.number_class(Decimal('1E-10'))
        '+Normal'
        >>> c.number_class(Decimal('2.50'))
        '+Normal'
        >>> c.number_class(Decimal('0.1E-999'))
        '+Subnormal'
        >>> c.number_class(Decimal('0'))
        '+Zero'
        >>> c.number_class(Decimal('-0'))
        '-Zero'
        >>> c.number_class(Decimal('-0.1E-999'))
        '-Subnormal'
        >>> c.number_class(Decimal('-1E-10'))
        '-Normal'
        >>> c.number_class(Decimal('-2.50'))
        '-Normal'
        >>> c.number_class(Decimal('-Infinity'))
        '-Infinity'
        >>> c.number_class(Decimal('NaN'))
        'NaN'
        >>> c.number_class(Decimal('-NaN'))
        'NaN'
        >>> c.number_class(Decimal('sNaN'))
        'sNaN'
        R(RM(RRї((s#/usr/local/lib/python2.5/decimal.pyRMЗs-cCs|id|ГS(sДPlus 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")
        R(RФ(RRї((s#/usr/local/lib/python2.5/decimal.pytplus╢scCs|i||d|ГS(s1
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")
        R(R(RRїR>R▀((s#/usr/local/lib/python2.5/decimal.pytpower─sCcCs|i|d|ГS(sC	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")
        R(R(RRїR>((s#/usr/local/lib/python2.5/decimal.pyR	s1cCs
tdГS(skJust returns 10, as this is Decimal, :)

        >>> ExtendedContext.radix()
        Decimal("10")
        i
(R(R((s#/usr/local/lib/python2.5/decimal.pyRN<scCs|i|d|ГS(s>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")
        R(R╡(RRїR>((s#/usr/local/lib/python2.5/decimal.pyRкDscCs|i|d|ГS(s`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")
        R(R╕(RRїR>((s#/usr/local/lib/python2.5/decimal.pyR╕_scCs|i|d|ГS(s[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")
        R(RS(RRїR>((s#/usr/local/lib/python2.5/decimal.pyRSzscCs
|i|ГS(sReturns 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
        (R
(RRїR>((s#/usr/local/lib/python2.5/decimal.pyR
РscCs|i|d|ГS(s^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")
        R(RW(RRїR>((s#/usr/local/lib/python2.5/decimal.pyRWбs
cCs|i|d|ГS(sЕReturns 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")
        R(Rй(RRїR>((s#/usr/local/lib/python2.5/decimal.pyRйнscCs|id|ГS(sdSquare root of a non-negative number to context precision.

        If the result must be inexact, it is rounded using the round-half-even
        algorithm.

        >>> ExtendedContext.sqrt(Decimal('0'))
        Decimal("0")
        >>> ExtendedContext.sqrt(Decimal('-0'))
        Decimal("-0")
        >>> ExtendedContext.sqrt(Decimal('0.39'))
        Decimal("0.624499800")
        >>> ExtendedContext.sqrt(Decimal('100'))
        Decimal("10")
        >>> ExtendedContext.sqrt(Decimal('1'))
        Decimal("1")
        >>> ExtendedContext.sqrt(Decimal('1.0'))
        Decimal("1.0")
        >>> ExtendedContext.sqrt(Decimal('1.00'))
        Decimal("1.0")
        >>> ExtendedContext.sqrt(Decimal('7'))
        Decimal("2.64575131")
        >>> ExtendedContext.sqrt(Decimal('10'))
        Decimal("3.16227766")
        >>> ExtendedContext.prec
        9
        R(R(RRї((s#/usr/local/lib/python2.5/decimal.pyR─scCs|i|d|ГS(sTReturn 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")
        R(Rа(RRїR>((s#/usr/local/lib/python2.5/decimal.pytsubtractсs
cCs|id|ГS(syConverts a number to a string, using scientific notation.

        The operation is not affected by the context.
        R(RП(RRї((s#/usr/local/lib/python2.5/decimal.pyRПэscCs|id|ГS(syConverts a number to a string, using scientific notation.

        The operation is not affected by the context.
        R(RО(RRї((s#/usr/local/lib/python2.5/decimal.pyt
to_sci_stringЇscCs|id|ГS(skRounds 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")
        R(R(RRї((s#/usr/local/lib/python2.5/decimal.pyR√scCs|id|ГS(sLRounds 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")
        R(RА(RRї((s#/usr/local/lib/python2.5/decimal.pyRАsN(QRRRR=RhRЕR8RR7R[RQRFRЗRЙRГRжR├R
RКRXRЛRМRR}RRRRРRНRСRRОRПRзRFR█R!R"R	RR#R$R%R&R'R(R0R3R4R?RARCR@RШRDRЧRERРRСRHRIRKRRMRТRУRRNRкR╕RSR
RWRйRRФRПRХRRАRc(((s#/usr/local/lib/python2.5/decimal.pyR2
sд														
							
	
	
										
				
																				/	E	3													RYcBs)eZdZddДZdДZeZRS(R*RDRFcCsХ|djod|_d|_d|_nft|tГo.|i|_t|iГ|_|i|_n(|d|_|d|_|d|_dS(Niii(	R=R*RDRFRNRR"R#R@(RRc((s#/usr/local/lib/python2.5/decimal.pyRh=s
		


cCsd|i|i|ifS(Ns(%r, %r, %r)(R*RDRF(R((s#/usr/local/lib/python2.5/decimal.pyRЕLs(ssignsintsexpN(RRR^R=RhRЕRО(((s#/usr/local/lib/python2.5/decimal.pyRY7s	icCs╪|i|ijo|}|}n
|}|}tt|iГГ}tt|iГГ}|itd||dГ}||id|jod|_||_n|id|i|i9_|i|_||fS(scNormalizes op1, op2 to have the same exp and length of coefficient.

    Done during addition.
    i    iii
(RFRURSRDRЧ(RЬRЭR0ttmpRlttmp_lent	other_lenRF((s#/usr/local/lib/python2.5/decimal.pyRЪSs
	
iRBiRвit2t3t4t5t6t7t8R.RїR>RRVRИR~cCsA|djotdГВnd|}dt|Г||dS(s[Number of bits in binary representation of the positive integer n,
    or 0 if n == 0.
    is-The argument to _nbits should be nonnegative.s%xi(R\RU(R t
correctionthex_n((s#/usr/local/lib/python2.5/decimal.pyRхvs

cCsc|djp
|djotdГВnd}x,||jo||||d?}}q3W|S(sєClosest 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.

    is3Both arguments to _sqrt_nearest should be positive.i(R\(R RїR>((s#/usr/local/lib/python2.5/decimal.pyt
_sqrt_nearestГs
cCs7d|>||?}}|d||d@|d@|jS(sЙGiven an integer x and a nonnegative integer shift, return closest
    integer to x / 2**shift; use round-to-even in case of a tie.

    lii((RшRйR>Rо((s#/usr/local/lib/python2.5/decimal.pyt_rshift_nearestТscCs/t||Г\}}|d||d@|jS(saClosest integer to a/b, a and b positive integers; rounds to even
    in the case of a tie.

    ii(Rз(RїR>RоRп((s#/usr/local/lib/python2.5/decimal.pyt_div_nearestЪsic		CsH||}d}xа||jo!tt|ГГ||>|jp(||jodt|Г||?|joItt||Гd>|t||t||Г|ГГ}|d7}qWtdtt|ГГd|Г}t||Г}t||Г}x>t|dddГD]&}t||Гt|||Г}q
Wt|||ГS(s╔Integer approximation to M*log(x/M), with absolute error boundable
    in terms only of x/M.

    Given positive integers x and M, return an integer approximation to
    M * log(x/M).  For L = 8 and 0.1 <= x/M <= 10 the difference
    between the approximation and the exact result is at most 22.  For
    L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15.  In
    both cases these are upper bounds on the error; it will usually be
    much smaller.iiiЎ   ii    (	RWRXRдRвRгRDRURSR▐(	RшtMtLRыtRtTtyshifttwtk((s#/usr/local/lib/python2.5/decimal.pyt_ilogвs
.('%$c
Csє|d7}tt|ГГ}||||dj}|djoЗd|}|||}|djo|d|9}nt|d|Г}t||Г}t|Г}t|||Г}||}	nd}t|d|Г}	t|	|dГS(s╛Given integers c, e and p with c > 0, p >= 0, compute an integer
    approximation to 10**p * log10(c*10**e), with an absolute error of
    at most 1.  Assumes that c*10**e is not exactly 1.iiii
id(RURSRдRмt
_log10_digitstdiv_nearest(
RRИRчRR~RеRлtlog_dtlog_10tlog_tenpower((s#/usr/local/lib/python2.5/decimal.pyR2╥s 


c	Cs|d7}tt|ГГ}||||dj}|djoX|||}|djo|d|9}nt|d|Г}t|d|Г}nd}|o\ttt|ГГГd}||djo%t|t||Гd|Г}qd}nd}t||dГS(s┤Given integers c, e and p with c > 0, compute an integer
    approximation to 10**p * log(c*10**e), with an absolute error of
    at most 1.  Assumes that c*10**e is not exactly 1.iiii
id(RURSRдRмRXRн(	RRИRчRR~RлRпRt	f_log_ten((s#/usr/local/lib/python2.5/decimal.pyR.Їs"


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t
_Log10MemoizecBs eZdZdДZdДZRS(s╛Class to compute, store, and allow retrieval of, digits of the
    constant log(10) = 2.302585....  This constant is needed by
    Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.cCs
d|_dS(Nt/23025850929940456840179914546843642076011014886(Rg(R((s#/usr/local/lib/python2.5/decimal.pyRh$scCs╨|djotdГВn|t|iГjoИd}xeto]d||d}tttd||ГdГГ}||d|joPn|d7}q<W|idГd |_nt|i|d	 ГS(
stGiven an integer p >= 0, return floor(10**p)*log(10).

        For example, self.getdigits(3) returns 2302.
        isp should be nonnegativeii
iidRBi    i(	R\RURgR$RSRдRмRБRD(RRчRRеRg((s#/usr/local/lib/python2.5/decimal.pyt	getdigits's	
"(RRRRhR╡(((s#/usr/local/lib/python2.5/decimal.pyR│ s	c	Csюtt|Г|>|Г}tdtt|ГГd|Г}t||Г}t|Г|>}x9t|dddГD]!}t|||||Г}quWxIt|dddГD]1}t|Г|d>}t||||Г}q▒W||S(sыGiven integers x and M, M > 0, such that x/M is small in absolute
    value, compute an integer approximation to M*exp(x/M).  For 0 <=
    x/M <= 2.4, the absolute error in the result is bounded by 60 (and
    is usually much smaller).iЎ   iiii    i(RхRWRDRURSRдR▐(	RшRеRжRзRиRыtMshiftRуRл((s#/usr/local/lib/python2.5/decimal.pyt_iexpEs%c	Cs┼|d7}td|tt|ГГdГ}||}||}|djo|d|}n|d|}t|t|ГГ\}}t|d|Г}tt|d|ГdГ||dfS(s╨Compute an approximation to exp(c*10**e), with p decimal places of
    precision.

    Returns integers d, f such that:

      10**(p-1) <= d <= 10**p, and
      (d-1)*10**f < exp(c*10**e) < (d+1)*10**f

    In other words, d*10**f is an approximation to exp(c*10**e) with p
    digits of precision, and with an error in d of at most 1.  This is
    almost, but not quite, the same as the error being < 1ulp: when d
    = 10**(p-1) the error could be up to 10 ulp.iiii
iшi(RШRURSRзRнRдR╖(	RRИRчRRоRйtcshifttquotRЇ((s#/usr/local/lib/python2.5/decimal.pyRjs
#


cCs0ttt|ГГГ|}t||||dГ}||}|djo||d|}nt||d|Г}|djodtt|ГГ|dj|djjo!d|ddd|}	}
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|	|
fS(s5Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and
    y = yc*10**ye, compute x**y.  Returns a pair of integers (c, e) such that:

      10**(p-1) <= c <= 10**p, and
      (c-1)*10**e < x**y < (c+1)*10**e

    in other words, c*10**e is an approximation to x**y with p digits
    of precision, and with an error in c of at most 1.  (This is
    almost, but not quite, the same as the error being < 1ulp: when c
    == 10**(p-1) we can only guarantee error < 10ulp.)

    We assume that: x is positive and not equal to 1, and y is nonzero.
    iii
(RURSRXR.RдR(RщRъRьRэRчR>tlxcRйtpcRиRF((s#/usr/local/lib/python2.5/decimal.pyR·Оs


)!!
idiFi5i(iiii
icCsC|djotdГВnt|Г}dt|Г||dS(s@Compute a lower bound for 100*log10(c) for a positive integer c.is0The argument to _log10_lb should be nonnegative.id(R\RSRU(RRаtstr_c((s#/usr/local/lib/python2.5/decimal.pyRц╕s
cCs[t|tГo|Snt|ttfГot|ГSn|otd|ГВntS(s]Convert other to Decimal.

    Verifies that it's ok to use in an implicit construction.
    sUnable to convert %s to Decimal(RNRRDRWRaRr(RlR|((s#/usr/local/lib/python2.5/decimal.pyRq├sR0iR/RuRvR1i ╔Ъ;R√i6e─RКi	sж     # A numeric string consists of:
#    \s*
    (?P<sign>[-+])?           # an optional sign, followed by either...
    (
        (?=\d|\.\d)           # ...a number (with at least one digit)
        (?P<int>\d*)          # consisting of a (possibly empty) integer part
        (\.(?P<frac>\d*))?    # followed by an optional fractional part
        (E(?P<exp>[-+]?\d+))? # followed by an optional exponent, or...
    |
        Inf(inity)?           # ...an infinity, or...
    |
        (?P<signal>s)?        # ...an (optionally signaling)
        NaN                   # NaN
        (?P<diag>\d*)         # with (possibly empty) diagnostic information.
    )
#    \s*
    $
s0*$s50*$R-s-InfR&t__main__(bRt__all__R7RtRRRRRRRRtArithmeticErrorRRRR(tZeroDivisionErrorRR+R,R	R-R
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