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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.�)�ABCMeta�abstractmethod�Number�Complex�Real�Rational�Integralc@seZdZdZdZdZdS)rz�All numbers inherit from this class.
If you just want to check if an argument x is a number, without
caring what kind, use isinstance(x, Number).
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__module__� __qualname__�__doc__� __slots__�__hash__r r r � /usr/lib64/python3.8/numbers.pyr s)� metaclassc@s�eZdZdZdZedd��Zdd�Zeedd���Z eed d
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edd��Zdd�Zdd�Zedd��Zedd��Zedd ��Zed d ��Zed d ��Zed!d"��Zed#d$��Zed%d&��Zed'd(��Zd)S)*rabComplex defines the operations that work on the builtin complex type.
In short, those are: a conversion to complex, .real, .imag, +, -,
*, /, abs(), .conjugate, ==, and !=.
If it is given heterogeneous arguments, and doesn't have special
knowledge about them, it should fall back to the builtin complex
type as described below.
r cCsdS)z<Return a builtin complex instance. Called for complex(self).Nr ��selfr r r� __complex__-szComplex.__complex__cCs|dkS)z)True if self != 0. Called for bool(self).rr rr r r�__bool__1szComplex.__bool__cCst�dS)zXRetrieve the real component of this number.
This should subclass Real.
N��NotImplementedErrorrr r r�real5sz Complex.realcCst�dS)z]Retrieve the imaginary component of this number.
This should subclass Real.
Nrrr r r�imag>sz Complex.imagcCst�dS)z self + otherNr�r�otherr r r�__add__GszComplex.__add__cCst�dS)z other + selfNrrr r r�__radd__LszComplex.__radd__cCst�dS)z-selfNrrr r r�__neg__QszComplex.__neg__cCst�dS)z+selfNrrr r r�__pos__VszComplex.__pos__cCs
|| S)z self - otherr rr r r�__sub__[szComplex.__sub__cCs
| |S)z other - selfr rr r r�__rsub___szComplex.__rsub__cCst�dS)z self * otherNrrr r r�__mul__cszComplex.__mul__cCst�dS)z other * selfNrrr r r�__rmul__hszComplex.__rmul__cCst�dS)z5self / other: Should promote to float when necessary.Nrrr r r� __truediv__mszComplex.__truediv__cCst�dS)z other / selfNrrr r r� __rtruediv__rszComplex.__rtruediv__cCst�dS)zBself**exponent; should promote to float or complex when necessary.Nr)r�exponentr r r�__pow__wszComplex.__pow__cCst�dS)z base ** selfNr)r�baser r r�__rpow__|szComplex.__rpow__cCst�dS)z7Returns the Real distance from 0. Called for abs(self).Nrrr r r�__abs__�szComplex.__abs__cCst�dS)z$(x+y*i).conjugate() returns (x-y*i).Nrrr r r� conjugate�szComplex.conjugatecCst�dS)z
self == otherNrrr r r�__eq__�szComplex.__eq__N)r
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rrrr�propertyrrr r r r r r!r"r#r$r%r'r)r*r+r,r r r rr sN
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edd��Zedd��Zedd��Zedd��Zed d ��Zd d �Zed d!��Zed"d#��Zd$d%�Zd S)'rz�To 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.
r cCst�dS)zTAny Real can be converted to a native float object.
Called for float(self).Nrrr r r� __float__�szReal.__float__cCst�dS)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".
Nrrr r r� __trunc__�s zReal.__trunc__cCst�dS)z$Finds the greatest Integral <= self.Nrrr r r� __floor__�szReal.__floor__cCst�dS)z!Finds the least Integral >= self.Nrrr r r�__ceil__�sz
Real.__ceil__NcCst�dS)z�Rounds 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.
Nr)rZndigitsr r r� __round__�szReal.__round__cCs||||fS)z�divmod(self, other): The pair (self // other, self % other).
Sometimes this can be computed faster than the pair of
operations.
r rr r r�
__divmod__�szReal.__divmod__cCs||||fS)z�divmod(other, self): The pair (self // other, self % other).
Sometimes this can be computed faster than the pair of
operations.
r rr r r� __rdivmod__�szReal.__rdivmod__cCst�dS)z)self // other: The floor() of self/other.Nrrr r r� __floordiv__�szReal.__floordiv__cCst�dS)z)other // self: The floor() of other/self.Nrrr r r�
__rfloordiv__�szReal.__rfloordiv__cCst�dS)z self % otherNrrr r r�__mod__�sz Real.__mod__cCst�dS)z other % selfNrrr r r�__rmod__�sz
Real.__rmod__cCst�dS)zRself < other
< on Reals defines a total ordering, except perhaps for NaN.Nrrr r r�__lt__�sz Real.__lt__cCst�dS)z
self <= otherNrrr r r�__le__�sz Real.__le__cCs tt|��S)z(complex(self) == complex(float(self), 0))�complex�floatrr r rr�szReal.__complex__cCs|
S)z&Real numbers are their real component.r rr r rr�sz Real.realcCsdS)z)Real numbers have no imaginary component.rr rr r rr�sz Real.imagcCs|
S)z Conjugate is a no-op for Reals.r rr r rr+szReal.conjugate)N)r
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c@s<eZdZdZdZeedd���Zeedd���Zdd�Z d S)
rz6.numerator and .denominator should be in lowest terms.r cCst�dS�Nrrr r r� numeratorszRational.numeratorcCst�dSr=rrr r r� denominatorszRational.denominatorcCs |j|jS)a float(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.
)r>r?rr r rr.szRational.__float__N)
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edd��Zedd��Zedd��Zedd��Zed d ��Zed d ��Zd d!�Zed"d#��Zed$d%��ZdS)'rz@Integral adds a conversion to int and the bit-string operations.r cCst�dS)z int(self)Nrrr r r�__int__+szIntegral.__int__cCst|�S)z6Called whenever an index is needed, such as in slicing)�intrr r r� __index__0szIntegral.__index__NcCst�dS)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.
Nr)rr&�modulusr r rr'4s zIntegral.__pow__cCst�dS)z
self << otherNrrr r r�
__lshift__?szIntegral.__lshift__cCst�dS)z
other << selfNrrr r r� __rlshift__DszIntegral.__rlshift__cCst�dS)z
self >> otherNrrr r r�
__rshift__IszIntegral.__rshift__cCst�dS)z
other >> selfNrrr r r� __rrshift__NszIntegral.__rrshift__cCst�dS)z self & otherNrrr r r�__and__SszIntegral.__and__cCst�dS)z other & selfNrrr r r�__rand__XszIntegral.__rand__cCst�dS)z self ^ otherNrrr r r�__xor__]szIntegral.__xor__cCst�dS)z other ^ selfNrrr r r�__rxor__bszIntegral.__rxor__cCst�dS)z self | otherNrrr r r�__or__gszIntegral.__or__cCst�dS)z other | selfNrrr r r�__ror__lszIntegral.__ror__cCst�dS)z~selfNrrr r r�
__invert__qszIntegral.__invert__cCs tt|��S)z float(self) == float(int(self)))r<rArr r rr.wszIntegral.__float__cCs|
S)z"Integers are their own numerators.r rr r rr>{szIntegral.numeratorcCsdS)z!Integers have a denominator of 1.�r rr r rr?�szIntegral.denominator)N)r
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