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� y)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 � � e Zd ZdZdZdZy)r z�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).
� N)�__name__�
__module__� __qualname__�__doc__� __slots__�__hash__r � �m/build/snapcraft-certbot-817459ae66b3942307a8b35b87e7f45e/parts/certbot/install/usr/lib/python3.12/numbers.pyr r % s � ��
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� � Zed� � Zed� � Zed� � Zed� � Zed� � Zed� � Zed� � Zed� � Zy)r af Complex 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 c � � y)z<Return a builtin complex instance. Called for complex(self).Nr ��selfs r � __complex__zComplex.__complex__F s � r c � � | dk7 S )z)True if self != 0. Called for bool(self).r r r s r �__bool__zComplex.__bool__J s � ��q�y�r c � � t �)zXRetrieve the real component of this number.
This should subclass Real.
��NotImplementedErrorr s r �realz Complex.realN �
� � "�!r c � � t �)z]Retrieve the imaginary component of this number.
This should subclass Real.
r r s r �imagz Complex.imagW r r c � � t �)z self + otherr �r �others r �__add__zComplex.__add__` �
� � "�!r c � � t �)z other + selfr r$ s r �__radd__zComplex.__radd__e r' r c � � t �)z-selfr r s r �__neg__zComplex.__neg__j r' r c � � t �)z+selfr r s r �__pos__zComplex.__pos__o r' r c � � | | z S )z self - otherr r$ s r �__sub__zComplex.__sub__t s � ��u�f�}� r c � � | |z S )z other - selfr r$ s r �__rsub__zComplex.__rsub__x s � ��u�u�}� r c � � t �)z self * otherr r$ s r �__mul__zComplex.__mul__| r' r c � � t �)z other * selfr r$ s r �__rmul__zComplex.__rmul__� r' r c � � t �)z5self / other: Should promote to float when necessary.r r$ s r � __truediv__zComplex.__truediv__� r' r c � � t �)z other / selfr r$ s r � __rtruediv__zComplex.__rtruediv__� r' r c � � t �)zDself ** exponent; should promote to float or complex when necessary.r )r �exponents r �__pow__zComplex.__pow__� r' r c � � t �)z base ** selfr )r �bases r �__rpow__zComplex.__rpow__� r' r c � � t �)z7Returns the Real distance from 0. Called for abs(self).r r s r �__abs__zComplex.__abs__� r' r c � � t �)z$(x+y*i).conjugate() returns (x-y*i).r r s r � conjugatezComplex.conjugate� r' r c � � t �)z
self == otherr r$ s r �__eq__zComplex.__eq__� r' r N)r r
r r r r r r �propertyr r" r& r) r+ r- r/ r1 r3 r5 r7 r9 r< r? rA rC rE r r r r r 9 sm � �� �I��K� �K�� ��"� � �"� ��"� � �"� �"� �"� �"� �"� �"� �"� �"� �"� � � �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"r r c � � e Zd ZdZdZed� � Zed� � Zed� � Zed� � Z edd�� Z
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� � Zed� � Zed� � Zed� � Zd� Zed� � Zed� � Zd� Zy)r z�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 c � � t �)zTAny Real can be converted to a native float object.
Called for float(self).r r s r � __float__zReal.__float__� �
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"�!r c � � t �)aK trunc(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".
r r s r � __trunc__zReal.__trunc__� s
� � "�!r c � � t �)z$Finds the greatest Integral <= self.r r s r � __floor__zReal.__floor__� r' r c � � t �)z!Finds the least Integral >= self.r r s r �__ceil__z
Real.__ceil__� r' r Nc � � t �)z�Rounds self to ndigits decimal places, defaulting to 0.
If ndigits is omitted or None, returns an Integral, otherwise
returns a Real. Rounds half toward even.
r )r �ndigitss r � __round__zReal.__round__� r r c � � | |z | |z fS )z�divmod(self, other): The pair (self // other, self % other).
Sometimes this can be computed faster than the pair of
operations.
r r$ s r �
__divmod__zReal.__divmod__� s � � ��
�t�e�|�,�,r c � � || z || z fS )z�divmod(other, self): The pair (other // self, other % self).
Sometimes this can be computed faster than the pair of
operations.
r r$ s r � __rdivmod__zReal.__rdivmod__� s � � ��
�u�t�|�,�,r c � � t �)z)self // other: The floor() of self/other.r r$ s r � __floordiv__zReal.__floordiv__� r' r c � � t �)z)other // self: The floor() of other/self.r r$ s r �
__rfloordiv__zReal.__rfloordiv__� r' r c � � t �)z self % otherr r$ s r �__mod__z Real.__mod__� r' r c � � t �)z other % selfr r$ s r �__rmod__z
Real.__rmod__� r' r c � � t �)zRself < other
< on Reals defines a total ordering, except perhaps for NaN.r r$ s r �__lt__z Real.__lt__ rJ r c � � t �)z
self <= otherr r$ s r �__le__z Real.__le__ r' r c �* � t t | � � S )z(complex(self) == complex(float(self), 0))�complex�floatr s r r zReal.__complex__ s � ��u�T�{�#�#r c � � | �S )z&Real numbers are their real component.r r s r r z Real.real � � � �u� r c � � y)z)Real numbers have no imaginary component.r r r s r r" z Real.imag � � � r c � � | �S )z Conjugate is a no-op for Reals.r r s r rC zReal.conjugate s � ��u� r �N)r r
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$� �� �� �� ��r r c �N � e Zd ZdZdZeed� � � Zeed� � � Zd� Z y)r z6.numerator and .denominator should be in lowest terms.r c � � t �rl r r s r � numeratorzRational.numerator) r' r c � � t �rl r r s r � denominatorzRational.denominator. r' r c �X � t | j � t | j � z S )a float(self) = self.numerator / self.denominator
It's important that this conversion use the integer's "true"
division rather than casting one side to float before dividing
so that ratios of huge integers convert without overflowing.
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� � Zed� � Zed� � Zed� � Zed� � Zd� Zed� � Zed� � Zy)r z�Integral adds methods that work on integral numbers.
In short, these are conversion to int, pow with modulus, and the
bit-string operations.
r c � � t �)z int(self)r r s r �__int__zIntegral.__int__H r' r c � � t | � S )z6Called whenever an index is needed, such as in slicing)rs r s r � __index__zIntegral.__index__M s � ��4�y�r Nc � � t �)a4 self ** exponent % modulus, but maybe faster.
Accept the modulus argument if you want to support the
3-argument version of pow(). Raise a TypeError if exponent < 0
or any argument isn't Integral. Otherwise, just implement the
2-argument version described in Complex.
r )r r; �moduluss r r< zIntegral.__pow__Q s
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self << otherr r$ s r �
__lshift__zIntegral.__lshift__\ r' r c � � t �)z
other << selfr r$ s r � __rlshift__zIntegral.__rlshift__a r' r c � � t �)z
self >> otherr r$ s r �
__rshift__zIntegral.__rshift__f r' r c � � t �)z
other >> selfr r$ s r � __rrshift__zIntegral.__rrshift__k r' r c � � t �)z self & otherr r$ s r �__and__zIntegral.__and__p r' r c � � t �)z other & selfr r$ s r �__rand__zIntegral.__rand__u r' r c � � t �)z self ^ otherr r$ s r �__xor__zIntegral.__xor__z r' r c � � t �)z other ^ selfr r$ s r �__rxor__zIntegral.__rxor__ r' r c � � t �)z self | otherr r$ s r �__or__zIntegral.__or__� r' r c � � t �)z other | selfr r$ s r �__ror__zIntegral.__ror__� r' r c � � t �)z~selfr r s r �
__invert__zIntegral.__invert__� r' r c �* � t t | � � S )z float(self) == float(int(self)))rf rs r s r rI zIntegral.__float__� s � ��S��Y� � r c � � | �S )z"Integers are their own numerators.r r s r ro zIntegral.numerator� rh r c � � y)z!Integers have a denominator of 1.� r r s r rq zIntegral.denominator� rj r rl )r r
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