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(root)/
lib/
python3.11/
__pycache__/
numbers.cpython-311.opt-1.pyc

el(.dZddlmZmZgdZGddeZGddeZeeGd	d
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dS)z~Abstract Base Classes (ABCs) for numbers, according to PEP 3141.

TODO: Fill out more detailed documentation on the operators.)ABCMetaabstractmethod)NumberComplexRealRationalIntegralceZdZdZdZdZdS)rzAll numbers inherit from this class.

    If you just want to check if an argument x is a number, without
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__module____qualname____doc__	__slots____hash__r;/BuggyBox/python/3.11.7/bootstrap/lib/python3.11/numbers.pyrrs&
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ZedZedZedZedZedZedZedZedZdS)rafComplex defines the operations that work on the builtin complex type.

    In short, those are: a conversion to complex, .real, .imag, +, -,
    *, /, **, abs(), .conjugate, ==, and !=.

    If it is given heterogeneous arguments, and doesn't have special
    knowledge about them, it should fall back to the builtin complex
    type as described below.
    rcdS)z<Return a builtin complex instance. Called for complex(self).Nrselfs r__complex__zComplex.__complex__-src|dkS)z)True if self != 0. Called for bool(self).rrrs r__bool__zComplex.__bool__1sqyrct)zXRetrieve the real component of this number.

        This should subclass Real.
        NotImplementedErrorrs rrealzComplex.real5
"!rct)z]Retrieve the imaginary component of this number.

        This should subclass Real.
        rrs rimagzComplex.imag>r rct)zself + otherrrothers  r__add__zComplex.__add__G
"!rct)zother + selfrr$s  r__radd__zComplex.__radd__Lr'rct)z-selfrrs r__neg__zComplex.__neg__Qr'rct)z+selfrrs r__pos__zComplex.__pos__Vr'rc||zS)zself - otherrr$s  r__sub__zComplex.__sub__[suf}rc||zS)zother - selfrr$s  r__rsub__zComplex.__rsub___suu}rct)zself * otherrr$s  r__mul__zComplex.__mul__cr'rct)zother * selfrr$s  r__rmul__zComplex.__rmul__hr'rct)z5self / other: Should promote to float when necessary.rr$s  r__truediv__zComplex.__truediv__mr'rct)zother / selfrr$s  r__rtruediv__zComplex.__rtruediv__rr'rct)zBself**exponent; should promote to float or complex when necessary.r)rexponents  r__pow__zComplex.__pow__wr'rct)zbase ** selfr)rbases  r__rpow__zComplex.__rpow__|r'rct)z7Returns the Real distance from 0. Called for abs(self).rrs r__abs__zComplex.__abs__r'rct)z$(x+y*i).conjugate() returns (x-y*i).rrs r	conjugatezComplex.conjugater'rct)z
self == otherrr$s  r__eq__zComplex.__eq__r'rN)rr
rrrrrrpropertyrr"r&r)r+r-r/r1r3r5r7r9r<r?rArCrErrrrr sIKK^K""^X"""^X"""^"""^"""^"""^"""^"""^"""^"""^"""^"""^"""^"""^"""^"""rrcNeZdZdZdZedZedZedZedZ	eddZ
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ZedZedZedZdZedZedZdZdS)rzTo Complex, Real adds the operations that work on real numbers.

    In short, those are: a conversion to float, trunc(), divmod,
    %, <, <=, >, and >=.

    Real also provides defaults for the derived operations.
    rct)zTAny Real can be converted to a native float object.

        Called for float(self).rrs r	__float__zReal.__float__

"!rct)aGtrunc(self): Truncates self to an Integral.

        Returns an Integral i such that:
          * i>0 iff self>0;
          * abs(i) <= abs(self);
          * for any Integral j satisfying the first two conditions,
            abs(i) >= abs(j) [i.e. i has "maximal" abs among those].
        i.e. "truncate towards 0".
        rrs r	__trunc__zReal.__trunc__s
"!rct)z$Finds the greatest Integral <= self.rrs r	__floor__zReal.__floor__r'rct)z!Finds the least Integral >= self.rrs r__ceil__z
Real.__ceil__r'rNct)zRounds self to ndigits decimal places, defaulting to 0.

        If ndigits is omitted or None, returns an Integral, otherwise
        returns a Real. Rounds half toward even.
        r)rndigitss  r	__round__zReal.__round__r rc||z||zfS)zdivmod(self, other): The pair (self // other, self % other).

        Sometimes this can be computed faster than the pair of
        operations.
        rr$s  r
__divmod__zReal.__divmod__s
te|,,rc||z||zfS)zdivmod(other, self): The pair (self // other, self % other).

        Sometimes this can be computed faster than the pair of
        operations.
        rr$s  r__rdivmod__zReal.__rdivmod__s
ut|,,rct)z)self // other: The floor() of self/other.rr$s  r__floordiv__zReal.__floordiv__r'rct)z)other // self: The floor() of other/self.rr$s  r
__rfloordiv__zReal.__rfloordiv__r'rct)zself % otherrr$s  r__mod__zReal.__mod__r'rct)zother % selfrr$s  r__rmod__z
Real.__rmod__r'rct)zRself < other

        < on Reals defines a total ordering, except perhaps for NaN.rr$s  r__lt__zReal.__lt__rJrct)z
self <= otherrr$s  r__le__zReal.__le__r'rc:tt|S)z(complex(self) == complex(float(self), 0))complexfloatrs rrzReal.__complex__suT{{###rc|
S)z&Real numbers are their real component.rrs rrz	Real.realurcdS)z)Real numbers have no imaginary component.rrrs rr"z	Real.imag	qrc|
S)zConjugate is a no-op for Reals.rrs rrCzReal.conjugates	urN)rr
rrrrrIrLrNrPrSrUrWrYr[r]r_rarcrrFrr"rCrrrrrsI""^"
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"^
"""^"""^""""^"------""^"""^"""^"""^"""^"""^"
$$$XXrrcheZdZdZdZeedZeedZdZ	dS)rz6.numerator and .denominator should be in lowest terms.rctrlrrs r	numeratorzRational.numeratorr'rctrlrrs rdenominatorzRational.denominatorr'rcTt|jt|jzS)afloat(self) = self.numerator / self.denominator

        It's important that this conversion use the integer's "true"
        division rather than casting one side to float before dividing
        so that ratios of huge integers convert without overflowing.

        )introrqrs rrIzRational.__float__s$4>""S)9%:%:::rN)
rr
rrrrFrrorqrIrrrrrsv@@I
""^X"""^X";;;;;rrcneZdZdZdZedZdZeddZedZ	edZ
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ZedZedZedZedZdZedZedZdS)r	zIntegral adds methods that work on integral numbers.

    In short, these are conversion to int, pow with modulus, and the
    bit-string operations.
    rct)z	int(self)rrs r__int__zIntegral.__int__/r'rc t|S)z6Called whenever an index is needed, such as in slicing)rsrs r	__index__zIntegral.__index__4s4yyrNct)a4self ** exponent % modulus, but maybe faster.

        Accept the modulus argument if you want to support the
        3-argument version of pow(). Raise a TypeError if exponent < 0
        or any argument isn't Integral. Otherwise, just implement the
        2-argument version described in Complex.
        r)rr;moduluss   rr<zIntegral.__pow__8s
"!rct)z
self << otherrr$s  r
__lshift__zIntegral.__lshift__Cr'rct)z
other << selfrr$s  r__rlshift__zIntegral.__rlshift__Hr'rct)z
self >> otherrr$s  r
__rshift__zIntegral.__rshift__Mr'rct)z
other >> selfrr$s  r__rrshift__zIntegral.__rrshift__Rr'rct)zself & otherrr$s  r__and__zIntegral.__and__Wr'rct)zother & selfrr$s  r__rand__zIntegral.__rand__\r'rct)zself ^ otherrr$s  r__xor__zIntegral.__xor__ar'rct)zother ^ selfrr$s  r__rxor__zIntegral.__rxor__fr'rct)zself | otherrr$s  r__or__zIntegral.__or__kr'rct)zother | selfrr$s  r__ror__zIntegral.__ror__pr'rct)z~selfrrs r
__invert__zIntegral.__invert__ur'rc:tt|S)zfloat(self) == float(int(self)))rfrsrs rrIzIntegral.__float__{sSYYrc|
S)z"Integers are their own numerators.rrs rrozIntegral.numeratorrhrcdS)z!Integers have a denominator of 1.rrs rrqzIntegral.denominatorrjrrl)rr
rrrrrvrxr<r|r~rrrrrrrrrrIrFrorqrrrr	r	&sI""^""""^"""^"""^"""^"""^"""^"""^"""^"""^"""^"""^"""^"
   XXrr	N)rabcrr__all__rrregisterrerrfrr	rsrrr<module>rsn@@('''''''
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