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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
>>>
)%�Decimal�Context�DecimalTuple�DefaultContext�BasicContext�ExtendedContext�DecimalException�Clamped�InvalidOperation�DivisionByZero�Inexact�Rounded�	Subnormal�Overflow�	Underflow�FloatOperation�DivisionImpossible�InvalidContext�ConversionSyntax�DivisionUndefined�
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    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).)

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    from DecimalException.
    cGsdSr)r*��self�contextr+r*r*r,�handle�szDecimalException.handleN��__name__�
__module__�__qualname__�__doc__r3r*r*r*r,r�src@seZdZdZdS)ra)Exponent of a 0 changed to fit bounds.

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    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�r5r6r7r8r*r*r*r,r�src@seZdZdZdd�ZdS)r	a0An invalid operation was performed.

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    -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
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    cGs,|r(t|dj|djdd�}|�|�StS)Nr'�nT)�_dec_from_triple�_sign�_int�_fix_nan�_NaN)r1r2r+�ansr*r*r,r3�s
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    cGstSr)�r?r0r*r*r,r3szConversionSyntax.handleNr4r*r*r*r,rsrc@seZdZdZdd�ZdS)r
a�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.

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    cGst|Sr))�_SignedInfinity�r1r2�signr+r*r*r,r3szDivisionByZero.handleNr4r*r*r*r,r

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c@seZdZdZdd�ZdS)rz�Cannot perform the division adequately.

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    cGstSr)rAr0r*r*r,r3"szDivisionImpossible.handleNr4r*r*r*r,rsrc@seZdZdZdd�ZdS)rz�Undefined result of division.

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    cGstSr)rAr0r*r*r,r3-szDivisionUndefined.handleNr4r*r*r*r,r%src@seZdZdZdS)ra�Had to round, losing information.

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    Nr9r*r*r*r,r0src@seZdZdZdd�ZdS)ra�Invalid context.  Unknown rounding, for example.

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    cGstSr)rAr0r*r*r,r3GszInvalidContext.handleNr4r*r*r*r,r<s
rc@seZdZdZdS)ra�Number got rounded (not  necessarily changed during rounding).

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    result in all cases is unchanged.

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    Nr9r*r*r*r,rJsrc@seZdZdZdS)r
a�Exponent < Emin before rounding.

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    Nr9r*r*r*r,r
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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
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    cGs�|jttttfvrt|S|dkrR|jtkr4t|St|d|j|j	|jd�S|dkr�|jt
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�zOverflow.handleNr4r*r*r*r,rasrc@seZdZdZdS)raxNumerical underflow with result rounded to 0.

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    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
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    Nr9r*r*r*r,r�src@seZdZdZdS)ra�Enable stricter semantics for mixing floats and Decimals.

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    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
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    Nr9r*r*r*r,r�srZdecimal_contextcCs6z
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rcCs,|tttfvr|��}|��t�|�dS)z%Set this thread's context to context.N)rrr�copy�clear_flagsrIrLrMr*r*r,r�srcCs|durt�}t|�S)abReturn a context manager for a copy of the supplied context

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             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)r�_ContextManager)�ctxr*r*r,r�s$rc
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        >>> Decimal('3.14')              # string input
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        >>> 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
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        >>> Decimal('  3.14  \n')        # leading and trailing whitespace okay
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        �_�NzInvalid literal for Decimal: %rrD�-r/r'�intZfrac�exprTF�diag�signal�Nr:�FT�ztInvalid tuple size in creation of Decimal from list or tuple.  The list or tuple should have exactly three elements.�r'r/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.��	zTThe second value in the tuple must be composed of integers in the range 0 through 9.�r:r\zUThe third value in the tuple must be an integer, or one of the strings 'F', 'n', 'N'.�;strict semantics for mixing floats and Decimals are enabledzCannot convert %r to Decimal)!�object�__new__�
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(


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zDecimal.__new__cCs�t|t�r,|dkrdnd}d}tt|��}nzt|t�r�t�|�sJt�|�rV|t|��St�	d|�dkrld}nd}t|��
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|||�}|tur�|S||�SdS)a.Converts a float to a decimal number, exactly.

        Note that Decimal.from_float(0.1) is not the same as Decimal('0.1').
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        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'))
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        >>> Decimal.from_float(-0.0)
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zDecimal.from_floatcCs(|jr$|j}|dkrdS|dkr$dSdS)zrReturns whether the number is not actually one.

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        compare_signal, __le__, __lt__, __ge__, __gt__.

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        >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3'))
        Decimal('-1')
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        Decimal('0')
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        Decimal('1')
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        Decimal('-1')
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        Decimal('1.50')
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        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')
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        >>> 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'))
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        >>> ExtendedContext.divide(5, 5)
        Decimal('1')
        >>> ExtendedContext.divide(Decimal(5), 5)
        Decimal('1')
        >>> ExtendedContext.divide(5, Decimal(5))
        Decimal('1')
        Tr�rMr�N)r�r�r�ryr�r*r*r,�divides
zContext.dividecCs8t|dd�}|j||d�}|tur0td|��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')
        Tr�rMr�N)r�r�r�ryr�r*r*r,�
divide_int+s
zContext.divide_intcCs8t|dd�}|j||d�}|tur0td|��n|SdS)a�Return (a // b, a % b).

        >>> ExtendedContext.divmod(Decimal(8), Decimal(3))
        (Decimal('2'), Decimal('2'))
        >>> ExtendedContext.divmod(Decimal(8), Decimal(4))
        (Decimal('2'), Decimal('0'))
        >>> ExtendedContext.divmod(8, 4)
        (Decimal('2'), Decimal('0'))
        >>> ExtendedContext.divmod(Decimal(8), 4)
        (Decimal('2'), Decimal('0'))
        >>> ExtendedContext.divmod(8, Decimal(4))
        (Decimal('2'), Decimal('0'))
        Tr�rMr�N)r�r�r�ryr�r*r*r,r�Bs
zContext.divmodcCst|dd�}|j|d�S)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')
        Tr�rM)r�rYr�r*r*r,rYWszContext.expcCst|dd�}|j|||d�S)aReturns a multiplied by b, plus c.

        The first two operands are multiplied together, using multiply,
        the third operand is then added to the result of that
        multiplication, using add, all with only one final rounding.

        >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7'))
        Decimal('22')
        >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7'))
        Decimal('-8')
        >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578'))
        Decimal('1.38435736E+12')
        >>> ExtendedContext.fma(1, 3, 4)
        Decimal('7')
        >>> ExtendedContext.fma(1, Decimal(3), 4)
        Decimal('7')
        >>> ExtendedContext.fma(1, 3, Decimal(4))
        Decimal('7')
        Tr�rM)r�r)r1r0rwrJr*r*r,roszContext.fmacCst|t�std��|��S)aReturn True if the operand is canonical; otherwise return False.

        Currently, the encoding of a Decimal instance is always
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        True
        z/is_canonical requires a Decimal as an argument.)rfrryrZr�r*r*r,rZ�s	
zContext.is_canonicalcCst|dd�}|��S)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
        Tr�)r�r[r�r*r*r,r[�szContext.is_finitecCst|dd�}|��S)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
        Tr�)r�rAr�r*r*r,rA�szContext.is_infinitecCst|dd�}|��S)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
        Tr�)r�r�r�r*r*r,r��s
zContext.is_nancCst|dd�}|j|d�S)a�Return True if the operand is a normal number;
        otherwise return False.

        >>> c = ExtendedContext.copy()
        >>> c.Emin = -999
        >>> c.Emax = 999
        >>> c.is_normal(Decimal('2.50'))
        True
        >>> c.is_normal(Decimal('0.1E-999'))
        False
        >>> c.is_normal(Decimal('0.00'))
        False
        >>> c.is_normal(Decimal('-Inf'))
        False
        >>> c.is_normal(Decimal('NaN'))
        False
        >>> c.is_normal(1)
        True
        Tr�rM)r�r]r�r*r*r,r]�szContext.is_normalcCst|dd�}|��S)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
        Tr�)r�r�r�r*r*r,r��szContext.is_qnancCst|dd�}|��S)a�Return True if the operand is negative; otherwise return False.

        >>> ExtendedContext.is_signed(Decimal('2.50'))
        False
        >>> ExtendedContext.is_signed(Decimal('-12'))
        True
        >>> ExtendedContext.is_signed(Decimal('-0'))
        True
        >>> ExtendedContext.is_signed(8)
        False
        >>> ExtendedContext.is_signed(-8)
        True
        Tr�)r�r^r�r*r*r,r^�szContext.is_signedcCst|dd�}|��S)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
        Tr�)r�r�r�r*r*r,r��s
zContext.is_snancCst|dd�}|j|d�S)a�Return True if the operand is subnormal; otherwise return False.

        >>> c = ExtendedContext.copy()
        >>> c.Emin = -999
        >>> c.Emax = 999
        >>> c.is_subnormal(Decimal('2.50'))
        False
        >>> c.is_subnormal(Decimal('0.1E-999'))
        True
        >>> c.is_subnormal(Decimal('0.00'))
        False
        >>> c.is_subnormal(Decimal('-Inf'))
        False
        >>> c.is_subnormal(Decimal('NaN'))
        False
        >>> c.is_subnormal(1)
        False
        Tr�rM)r�r_r�r*r*r,r_szContext.is_subnormalcCst|dd�}|��S)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
        Tr�)r�r`r�r*r*r,r`%szContext.is_zerocCst|dd�}|j|d�S)a�Returns the natural (base e) logarithm of the operand.

        >>> c = ExtendedContext.copy()
        >>> c.Emin = -999
        >>> c.Emax = 999
        >>> c.ln(Decimal('0'))
        Decimal('-Infinity')
        >>> c.ln(Decimal('1.000'))
        Decimal('0')
        >>> c.ln(Decimal('2.71828183'))
        Decimal('1.00000000')
        >>> c.ln(Decimal('10'))
        Decimal('2.30258509')
        >>> c.ln(Decimal('+Infinity'))
        Decimal('Infinity')
        >>> c.ln(1)
        Decimal('0')
        Tr�rM)r�rjr�r*r*r,rj6sz
Context.lncCst|dd�}|j|d�S)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')
        Tr�rM)r�rmr�r*r*r,rmLsz
Context.log10cCst|dd�}|j|d�S)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')
        Tr�rM)r�rnr�r*r*r,rnhszContext.logbcCst|dd�}|j||d�S)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')
        Tr�rM)r�r|r�r*r*r,r|�szContext.logical_andcCst|dd�}|j|d�S)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')
        Tr�rM)r�r~r�r*r*r,r~�szContext.logical_invertcCst|dd�}|j||d�S)a�Applies the logical operation 'or' between each operand's digits.

        The operands must be both logical numbers.

        >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0'))
        Decimal('0')
        >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1'))
        Decimal('1')
        >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0'))
        Decimal('1')
        >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1'))
        Decimal('1')
        >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010'))
        Decimal('1110')
        >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10'))
        Decimal('1110')
        >>> ExtendedContext.logical_or(110, 1101)
        Decimal('1111')
        >>> ExtendedContext.logical_or(Decimal(110), 1101)
        Decimal('1111')
        >>> ExtendedContext.logical_or(110, Decimal(1101))
        Decimal('1111')
        Tr�rM)r�rr�r*r*r,r�szContext.logical_orcCst|dd�}|j||d�S)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')
        Tr�rM)r�r}r�r*r*r,r}�szContext.logical_xorcCst|dd�}|j||d�S)a�max compares two values numerically and returns the maximum.

        If either operand is a NaN then the general rules apply.
        Otherwise, the operands are compared as though by the compare
        operation.  If they are numerically equal then the left-hand operand
        is chosen as the result.  Otherwise the maximum (closer to positive
        infinity) of the two operands is chosen as the result.

        >>> ExtendedContext.max(Decimal('3'), Decimal('2'))
        Decimal('3')
        >>> ExtendedContext.max(Decimal('-10'), Decimal('3'))
        Decimal('3')
        >>> ExtendedContext.max(Decimal('1.0'), Decimal('1'))
        Decimal('1')
        >>> ExtendedContext.max(Decimal('7'), Decimal('NaN'))
        Decimal('7')
        >>> ExtendedContext.max(1, 2)
        Decimal('2')
        >>> ExtendedContext.max(Decimal(1), 2)
        Decimal('2')
        >>> ExtendedContext.max(1, Decimal(2))
        Decimal('2')
        Tr�rM)r�r�r�r*r*r,r��szContext.maxcCst|dd�}|j||d�S)a�Compares the values numerically with their sign ignored.

        >>> ExtendedContext.max_mag(Decimal('7'), Decimal('NaN'))
        Decimal('7')
        >>> ExtendedContext.max_mag(Decimal('7'), Decimal('-10'))
        Decimal('-10')
        >>> ExtendedContext.max_mag(1, -2)
        Decimal('-2')
        >>> ExtendedContext.max_mag(Decimal(1), -2)
        Decimal('-2')
        >>> ExtendedContext.max_mag(1, Decimal(-2))
        Decimal('-2')
        Tr�rM)r�r�r�r*r*r,r�szContext.max_magcCst|dd�}|j||d�S)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')
        Tr�rM)r�r�r�r*r*r,r�szContext.mincCst|dd�}|j||d�S)a�Compares the values numerically with their sign ignored.

        >>> ExtendedContext.min_mag(Decimal('3'), Decimal('-2'))
        Decimal('-2')
        >>> ExtendedContext.min_mag(Decimal('-3'), Decimal('NaN'))
        Decimal('-3')
        >>> ExtendedContext.min_mag(1, -2)
        Decimal('1')
        >>> ExtendedContext.min_mag(Decimal(1), -2)
        Decimal('1')
        >>> ExtendedContext.min_mag(1, Decimal(-2))
        Decimal('1')
        Tr�rM)r�r�r�r*r*r,r�-szContext.min_magcCst|dd�}|j|d�S)a�Minus corresponds to unary prefix minus in Python.

        The operation is evaluated using the same rules as subtract; the
        operation minus(a) is calculated as subtract('0', a) where the '0'
        has the same exponent as the operand.

        >>> ExtendedContext.minus(Decimal('1.3'))
        Decimal('-1.3')
        >>> ExtendedContext.minus(Decimal('-1.3'))
        Decimal('1.3')
        >>> ExtendedContext.minus(1)
        Decimal('-1')
        Tr�rM)r�r�r�r*r*r,�minus>sz
Context.minuscCs8t|dd�}|j||d�}|tur0td|��n|SdS)a�multiply multiplies two operands.

        If either operand is a special value then the general rules apply.
        Otherwise, the operands are multiplied together
        ('long multiplication'), resulting in a number which may be as long as
        the sum of the lengths of the two operands.

        >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3'))
        Decimal('3.60')
        >>> ExtendedContext.multiply(Decimal('7'), Decimal('3'))
        Decimal('21')
        >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8'))
        Decimal('0.72')
        >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0'))
        Decimal('-0.0')
        >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321'))
        Decimal('4.28135971E+11')
        >>> ExtendedContext.multiply(7, 7)
        Decimal('49')
        >>> ExtendedContext.multiply(Decimal(7), 7)
        Decimal('49')
        >>> ExtendedContext.multiply(7, Decimal(7))
        Decimal('49')
        Tr�rMr�N)r�r�r�ryr�r*r*r,�multiplyOs
zContext.multiplycCst|dd�}|j|d�S)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')
        Tr�rM)r�r�r�r*r*r,r�oszContext.next_minuscCst|dd�}|j|d�S)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')
        Tr�rM)r�r�r�r*r*r,r��szContext.next_pluscCst|dd�}|j||d�S)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')
        Tr�rM)r�r�r�r*r*r,r��s zContext.next_towardcCst|dd�}|j|d�S)a�normalize reduces an operand to its simplest form.

        Essentially a plus operation with all trailing zeros removed from the
        result.

        >>> ExtendedContext.normalize(Decimal('2.1'))
        Decimal('2.1')
        >>> ExtendedContext.normalize(Decimal('-2.0'))
        Decimal('-2')
        >>> ExtendedContext.normalize(Decimal('1.200'))
        Decimal('1.2')
        >>> ExtendedContext.normalize(Decimal('-120'))
        Decimal('-1.2E+2')
        >>> ExtendedContext.normalize(Decimal('120.00'))
        Decimal('1.2E+2')
        >>> ExtendedContext.normalize(Decimal('0.00'))
        Decimal('0')
        >>> ExtendedContext.normalize(6)
        Decimal('6')
        Tr�rM)r�r?r�r*r*r,r?�szContext.normalizecCst|dd�}|j|d�S)a�Returns an indication of the class of the operand.

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

        >>> c = ExtendedContext.copy()
        >>> c.Emin = -999
        >>> c.Emax = 999
        >>> c.number_class(Decimal('Infinity'))
        '+Infinity'
        >>> c.number_class(Decimal('1E-10'))
        '+Normal'
        >>> c.number_class(Decimal('2.50'))
        '+Normal'
        >>> c.number_class(Decimal('0.1E-999'))
        '+Subnormal'
        >>> c.number_class(Decimal('0'))
        '+Zero'
        >>> c.number_class(Decimal('-0'))
        '-Zero'
        >>> c.number_class(Decimal('-0.1E-999'))
        '-Subnormal'
        >>> c.number_class(Decimal('-1E-10'))
        '-Normal'
        >>> c.number_class(Decimal('-2.50'))
        '-Normal'
        >>> c.number_class(Decimal('-Infinity'))
        '-Infinity'
        >>> c.number_class(Decimal('NaN'))
        'NaN'
        >>> c.number_class(Decimal('-NaN'))
        'NaN'
        >>> c.number_class(Decimal('sNaN'))
        'sNaN'
        >>> c.number_class(123)
        '+Normal'
        Tr�rM)r�r�r�r*r*r,r��s/zContext.number_classcCst|dd�}|j|d�S)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')
        Tr�rM)r�r�r�r*r*r,�plusszContext.pluscCs:t|dd�}|j|||d�}|tur2td|��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')
        Tr�rMr�N)r�r;r�ry)r1r0rwrr�r*r*r,�powers
Iz
Context.powercCst|dd�}|j||d�S)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')
        Tr�rM)r�rr�r*r*r,res7zContext.quantizecCstd�S)zkJust returns 10, as this is Decimal, :)

        >>> ExtendedContext.radix()
        Decimal('10')
        r�r�r�r*r*r,r��sz
Context.radixcCs8t|dd�}|j||d�}|tur0td|��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')
        Tr�rMr�N)r�r�r�ryr�r*r*r,r��s
zContext.remaindercCst|dd�}|j||d�S)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')
        Tr�rM)r�r�r�r*r*r,r��szContext.remainder_nearcCst|dd�}|j||d�S)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')
        Tr�rM)r�r�r�r*r*r,r��szContext.rotatecCst|dd�}|�|�S)a�Returns True if the two operands have the same exponent.

        The result is never affected by either the sign or the coefficient of
        either operand.

        >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001'))
        False
        >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01'))
        True
        >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1'))
        False
        >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf'))
        True
        >>> ExtendedContext.same_quantum(10000, -1)
        True
        >>> ExtendedContext.same_quantum(Decimal(10000), -1)
        True
        >>> ExtendedContext.same_quantum(10000, Decimal(-1))
        True
        Tr�)r�rBr�r*r*r,rBszContext.same_quantumcCst|dd�}|j||d�S)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')
        Tr�rM)r�r�r�r*r*r,r�$szContext.scalebcCst|dd�}|j||d�S)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')
        Tr�rM)r�r�r�r*r*r,r�7sz
Context.shiftcCst|dd�}|j|d�S)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
        Tr�rM)r�rLr�r*r*r,rLUszContext.sqrtcCs8t|dd�}|j||d�}|tur0td|��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')
        Tr�rMr�N)r�r�r�ryr�r*r*r,�subtractus
zContext.subtractcCst|dd�}|j|d�S)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'

        Tr�rM)r�r�r�r*r*r,r��szContext.to_eng_stringcCst|dd�}|j|d�S)zyConverts a number to a string, using scientific notation.

        The operation is not affected by the context.
        Tr�rM)r�r�r�r*r*r,�
to_sci_string�szContext.to_sci_stringcCst|dd�}|j|d�S)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')
        Tr�rM)r�rFr�r*r*r,rF�szContext.to_integral_exactcCst|dd�}|j|d�S)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')
        Tr�rM)r�rr�r*r*r,r�szContext.to_integral_value)	NNNNNNNNN)N)rT)N)Xr5r6r7r8r�r�r�r�r�r�r�rOr�rGrNr�rkr�r�r�r�r�r�rHr�r�ror�r�rQr�rRrNrVr�r�r�rWr�r�r�rYrrZr[rAr�r]r�r^r�r_r`rjrmrnr|r~rr}r�r�r�r�r�r�r�r�r�r?r�r�r�rr�r�r�r�rBr�r�rLr�r�r�rFrr�r*r*r*r,rs��
$



$#


%
 #2
P:&" rc@s"eZdZdZddd�Zdd�ZdS)rp�rDrXrYNcCsf|durd|_d|_d|_nFt|t�rD|j|_t|j�|_|j|_n|d|_|d|_|d|_dS)Nr'r/r`)rDrXrYrfrr<r=rR)r1r{r*r*r,r��s



z_WorkRep.__init__cCsd|j|j|jfS)Nz(%r, %r, %r)r�r�r*r*r,r�sz_WorkRep.__repr__)N)r5r6r7r�r�r�r*r*r*r,rp�s
rpcCs�|j|jkr|}|}n|}|}tt|j��}tt|j��}|jtd||d�}||jd|krpd|_||_|jd|j|j9_|j|_||fS)zcNormalizes op1, op2 to have the same exp and length of coefficient.

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    r�r`r/r�)rYrmrgrXr�)r�r�rG�tmpr�Ztmp_lenZ	other_lenrYr*r*r,r�sr�cCsb|dkrdS|dkr |d|Stt|��}t|�t|�d��}||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
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    30000
    >>> _decimal_lshift_exact(300, -999999999)  # returns None

    r'r�rTN)rgrorm�rstrip)r:r�Zstr_nZval_nr*r*r,r&(sr&cCsB|dks|dkrtd��d}||kr>||||d?}}q|S)z�Closest integer to the square root of the positive integer n.  a is
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    r'z3Both arguments to _sqrt_nearest should be positive.r/)rs)r:r0rwr*r*r,�
_sqrt_nearest=sr�cCs2d|>||?}}|d||d@|d@|kS)z�Given an integer x and a nonnegative integer shift, return closest
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    r`r/)r�)r0rwr�r�r*r*r,�_div_nearestTsr�r c		Cs�||}d}||kr(t|�||>|ksD||krxt|�||?|krxt||d>|t||t||�|��}|d7}qtdtt|��d|�}t||�}t||�}t|ddd�D]}t||�t|||�}q�t|||�S)a�Integer approximation to M*log(x/M), with absolute error boundable
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    between the approximation and the exact result is at most 22.  For
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Cs�|d7}tt|��}||||dk}|dkr�d|}|||}|dkrZ|d|9}nt|d|�}t||�}t|�}t|||�}||}	nd}t|d|�}	t|	|d�S)z�Given integers c, e and p with c > 0, p >= 0, compute an integer
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rlc	Cs�|d7}tt|��}||||dk}|dkrr|||}|dkrR|d|9}nt|d|�}t|d|�}nd}|r�ttt|���d}||dkr�t|t||�d|�}q�d}nd}t||d�S)z�Given integers c, e and p with c > 0, compute an integer
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    Returns integers d, f such that:

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      (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
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fS)a5Given 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.)

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22 Jul 2025 8.33 AM
root / linksafe
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__future__.cpython-39.opt-1.pyc
4.042 KB
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__future__.cpython-39.opt-2.pyc
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__future__.cpython-39.pyc
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__phello__.foo.cpython-39.opt-1.pyc
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_aix_support.cpython-39.opt-1.pyc
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_aix_support.cpython-39.opt-2.pyc
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_aix_support.cpython-39.pyc
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_bootlocale.cpython-39.opt-1.pyc
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_bootlocale.cpython-39.opt-2.pyc
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_bootsubprocess.cpython-39.pyc
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_collections_abc.cpython-39.opt-1.pyc
31 KB
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_collections_abc.cpython-39.opt-2.pyc
25.639 KB
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_collections_abc.cpython-39.pyc
31 KB
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_compat_pickle.cpython-39.opt-1.pyc
5.32 KB
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_compat_pickle.cpython-39.opt-2.pyc
5.32 KB
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_compat_pickle.cpython-39.pyc
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_compression.cpython-39.opt-1.pyc
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_compression.cpython-39.opt-2.pyc
3.903 KB
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_compression.cpython-39.pyc
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7.46 KB
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_markupbase.cpython-39.opt-2.pyc
7.091 KB
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_markupbase.cpython-39.pyc
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_osx_support.cpython-39.opt-1.pyc
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_osx_support.cpython-39.opt-2.pyc
8.696 KB
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4.538 KB
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3.354 KB
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4.56 KB
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_pydecimal.cpython-39.opt-1.pyc
156.861 KB
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_pydecimal.cpython-39.pyc
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_pyio.cpython-39.opt-2.pyc
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_strptime.cpython-39.pyc
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_sysconfigdata__linux_x86_64-linux-gnu.cpython-39.opt-1.pyc
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_sysconfigdata__linux_x86_64-linux-gnu.cpython-39.opt-2.pyc
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_sysconfigdata__linux_x86_64-linux-gnu.cpython-39.pyc
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_sysconfigdata_d_linux_x86_64-linux-gnu.cpython-39.opt-1.pyc
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_sysconfigdata_d_linux_x86_64-linux-gnu.cpython-39.opt-2.pyc
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_sysconfigdata_d_linux_x86_64-linux-gnu.cpython-39.pyc
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_threading_local.cpython-39.opt-1.pyc
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_threading_local.cpython-39.opt-2.pyc
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_threading_local.cpython-39.pyc
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_weakrefset.cpython-39.opt-1.pyc
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_weakrefset.cpython-39.opt-2.pyc
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_weakrefset.cpython-39.pyc
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abc.cpython-39.opt-1.pyc
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abc.cpython-39.opt-2.pyc
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abc.cpython-39.pyc
5.652 KB
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aifc.cpython-39.opt-1.pyc
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aifc.cpython-39.opt-2.pyc
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aifc.cpython-39.pyc
24.687 KB
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antigravity.cpython-39.opt-1.pyc
0.813 KB
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antigravity.cpython-39.opt-2.pyc
0.672 KB
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antigravity.cpython-39.pyc
0.813 KB
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argparse.cpython-39.opt-1.pyc
62.066 KB
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argparse.cpython-39.opt-2.pyc
52.922 KB
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argparse.cpython-39.pyc
62.175 KB
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ast.cpython-39.opt-1.pyc
51.118 KB
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ast.cpython-39.opt-2.pyc
42.773 KB
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ast.cpython-39.pyc
51.168 KB
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asynchat.cpython-39.opt-1.pyc
6.675 KB
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asynchat.cpython-39.opt-2.pyc
5.332 KB
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asynchat.cpython-39.pyc
6.675 KB
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asyncore.cpython-39.opt-1.pyc
15.673 KB
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asyncore.cpython-39.opt-2.pyc
14.497 KB
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asyncore.cpython-39.pyc
15.673 KB
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base64.cpython-39.opt-1.pyc
15.953 KB
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base64.cpython-39.opt-2.pyc
10.563 KB
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base64.cpython-39.pyc
16.082 KB
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bdb.cpython-39.opt-1.pyc
23.978 KB
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bdb.cpython-39.opt-2.pyc
15.152 KB
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bdb.cpython-39.pyc
23.978 KB
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binhex.cpython-39.opt-1.pyc
12.674 KB
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binhex.cpython-39.opt-2.pyc
12.152 KB
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binhex.cpython-39.pyc
12.674 KB
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bisect.cpython-39.opt-1.pyc
2.308 KB
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bisect.cpython-39.opt-2.pyc
1.026 KB
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bisect.cpython-39.pyc
2.308 KB
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bz2.cpython-39.opt-1.pyc
11.287 KB
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bz2.cpython-39.opt-2.pyc
6.389 KB
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bz2.cpython-39.pyc
11.287 KB
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cProfile.cpython-39.opt-1.pyc
5.009 KB
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cProfile.cpython-39.opt-2.pyc
4.559 KB
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cProfile.cpython-39.pyc
5.009 KB
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calendar.cpython-39.opt-1.pyc
26.41 KB
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calendar.cpython-39.opt-2.pyc
21.926 KB
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calendar.cpython-39.pyc
26.41 KB
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cgi.cpython-39.opt-1.pyc
25.874 KB
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cgi.cpython-39.opt-2.pyc
17.646 KB
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cgi.cpython-39.pyc
25.874 KB
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cgitb.cpython-39.opt-1.pyc
9.96 KB
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cgitb.cpython-39.opt-2.pyc
8.398 KB
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cgitb.cpython-39.pyc
9.96 KB
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chunk.cpython-39.opt-1.pyc
4.74 KB
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chunk.cpython-39.opt-2.pyc
2.646 KB
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chunk.cpython-39.pyc
4.74 KB
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cmd.cpython-39.opt-1.pyc
12.392 KB
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cmd.cpython-39.opt-2.pyc
7.094 KB
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cmd.cpython-39.pyc
12.392 KB
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code.cpython-39.opt-1.pyc
9.696 KB
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code.cpython-39.opt-2.pyc
4.549 KB
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code.cpython-39.pyc
9.696 KB
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codecs.cpython-39.opt-1.pyc
33.106 KB
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codecs.cpython-39.opt-2.pyc
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codecs.cpython-39.pyc
33.106 KB
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codeop.cpython-39.opt-1.pyc
6.319 KB
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codeop.cpython-39.opt-2.pyc
2.354 KB
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codeop.cpython-39.pyc
6.319 KB
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colorsys.cpython-39.opt-1.pyc
3.196 KB
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colorsys.cpython-39.opt-2.pyc
2.604 KB
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colorsys.cpython-39.pyc
3.196 KB
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compileall.cpython-39.opt-1.pyc
12.307 KB
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compileall.cpython-39.opt-2.pyc
9.124 KB
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compileall.cpython-39.pyc
12.307 KB
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