File: //lib/python3.10/__pycache__/numbers.cpython-310.pyc
o
E�hl( � @ s� d Z ddlmZmZ g d�ZG dd� ded�ZG dd� de�Ze�e� G d d
� d
e�Z e �e
� G d d � d e �Z G d
d� de �Z e �e
� 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 @ s e Zd ZdZdZdZdS )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 r r � /usr/lib/python3.10/numbers.pyr s r )� metaclassc @ s� e Zd ZdZdZedd� �Zdd� Zeedd� ��Z eed d
� ��Z
ed d � �Z ed
d� �Z edd� �Z
edd� �Zdd� Zdd� Zedd� �Zedd� �Zedd � �Zed d � �Zed d � �Zed!d"� �Zed#d$� �Zed%d&� �Zed'd(� �Zd)S )*r af Complex defines the operations that work on the builtin complex type.
In short, those are: a conversion to complex, .real, .imag, +, -,
*, /, **, abs(), .conjugate, ==, and !=.
If it is given heterogeneous arguments, and doesn't have special
knowledge about them, it should fall back to the builtin complex
type as described below.
r c C � dS )z<Return a builtin complex instance. Called for complex(self).Nr ��selfr r r � __complex__- s zComplex.__complex__c C s | dkS )z)True if self != 0. Called for bool(self).r r r r r r �__bool__1 � zComplex.__bool__c C � t �)zXRetrieve the real component of this number.
This should subclass Real.
��NotImplementedErrorr r r r �real5 � z Complex.realc C r )z]Retrieve the imaginary component of this number.
This should subclass Real.
r r r r r �imag> r z Complex.imagc C r )z self + otherr �r �otherr r r �__add__G � zComplex.__add__c C r )z other + selfr r r r r �__radd__L r! zComplex.__radd__c C r )z-selfr r r r r �__neg__Q r! zComplex.__neg__c C r )z+selfr r r r r �__pos__V r! zComplex.__pos__c C s
| | S )z self - otherr r r r r �__sub__[ �
zComplex.__sub__c C s
| | S )z other - selfr r r r r �__rsub___ r& zComplex.__rsub__c C r )z self * otherr r r r r �__mul__c r! zComplex.__mul__c C r )z other * selfr r r r r �__rmul__h r! zComplex.__rmul__c C r )z5self / other: Should promote to float when necessary.r r r r r � __truediv__m r! zComplex.__truediv__c C r )z other / selfr r r r r � __rtruediv__r r! zComplex.__rtruediv__c C r )zBself**exponent; should promote to float or complex when necessary.r )r �exponentr r r �__pow__w r! zComplex.__pow__c C r )z base ** selfr )r �baser r r �__rpow__| r! zComplex.__rpow__c C r )z7Returns the Real distance from 0. Called for abs(self).r r r r r �__abs__� r! zComplex.__abs__c C r )z$(x+y*i).conjugate() returns (x-y*i).r r r r r � conjugate� r! zComplex.conjugatec C r )z
self == otherr r r r r �__eq__� r! zComplex.__eq__N)r
r r r
r r r r �propertyr r r r" r# r$ r% r' r( r) r* r+ r- r/ r0 r1 r2 r r r r r sP
r c @ s� e Zd ZdZdZedd� �Zedd� �Zedd� �Zed d
� �Z ed&d d
��Z
dd� Z dd� Z edd� �Z
edd� �Zedd� �Zedd� �Zedd� �Zed d � �Zd d � Zed d!� �Zed"d#� �Zd$d%� Zd S )'r z�To Complex, Real adds the operations that work on real numbers.
In short, those are: a conversion to float, trunc(), divmod,
%, <, <=, >, and >=.
Real also provides defaults for the derived operations.
r c C r )zTAny Real can be converted to a native float object.
Called for float(self).r r r r r � __float__� � zReal.__float__c C r )aG trunc(self): Truncates self to an Integral.
Returns an Integral i such that:
* i>0 iff self>0;
* abs(i) <= abs(self);
* for any Integral j satisfying the first two conditions,
abs(i) >= abs(j) [i.e. i has "maximal" abs among those].
i.e. "truncate towards 0".
r r r r r � __trunc__� s zReal.__trunc__c C r )z$Finds the greatest Integral <= self.r r r r r � __floor__� r! zReal.__floor__c C r )z!Finds the least Integral >= self.r r r r r �__ceil__� r! z
Real.__ceil__Nc C r )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 �ndigitsr r r � __round__� r zReal.__round__c C s | | | | fS )z�divmod(self, other): The pair (self // other, self % other).
Sometimes this can be computed faster than the pair of
operations.
r r r r r �
__divmod__� � zReal.__divmod__c C s || || fS )z�divmod(other, self): The pair (self // other, self % other).
Sometimes this can be computed faster than the pair of
operations.
r r r r r � __rdivmod__� r< zReal.__rdivmod__c C r )z)self // other: The floor() of self/other.r r r r r � __floordiv__� r! zReal.__floordiv__c C r )z)other // self: The floor() of other/self.r r r r r �
__rfloordiv__� r! zReal.__rfloordiv__c C r )z self % otherr r r r r �__mod__� r! z Real.__mod__c C r )z other % selfr r r r r �__rmod__� r! z
Real.__rmod__c C r )zRself < other
< on Reals defines a total ordering, except perhaps for NaN.r r r r r �__lt__� r5 z Real.__lt__c C r )z
self <= otherr r r r r �__le__� r! z Real.__le__c C � t t| ��S )z(complex(self) == complex(float(self), 0))�complex�floatr r r r r � � zReal.__complex__c C � |
S )z&Real numbers are their real component.r r r r r r � � z Real.realc C r )z)Real numbers have no imaginary component.r r r r r r r � r! z Real.imagc C rH )z Conjugate is a no-op for Reals.r r r r r r1 s zReal.conjugate�N)r
r r r
r r r4 r6 r7 r8 r: r; r= r> r? r@ rA rB rC r r3 r r r1 r r r r r � sB
r c @ s< e Zd ZdZdZeedd� ��Zeedd� ��Zdd� Z d S )
r z6.numerator and .denominator should be in lowest terms.r c C r rJ r r r r r � numerator r! zRational.numeratorc C r rJ r r r r r � denominator r! zRational.denominatorc C s t | j�t | j� 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.
)�intrK rL r r r r r4 s zRational.__float__N)
r
r r r
r r3 r rK rL r4 r r r r r s r c @ s� e Zd ZdZdZedd� �Zdd� Zed&dd ��Zed
d � �Z ed d
� �Z
edd� �Z edd� �Z edd� �Z
edd� �Zedd� �Zedd� �Zedd� �Zed d � �Zed d � �Zd d!� Zed"d#� �Zed$d%� �ZdS )'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 C r )z int(self)r r r r r �__int__/ r! zIntegral.__int__c C s t | �S )z6Called whenever an index is needed, such as in slicing)rM r r r r � __index__4 r zIntegral.__index__Nc C r )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, �modulusr r r r- 8 s zIntegral.__pow__c C r )z
self << otherr r r r r �
__lshift__C r! zIntegral.__lshift__c C r )z
other << selfr r r r r � __rlshift__H r! zIntegral.__rlshift__c C r )z
self >> otherr r r r r �
__rshift__M r! zIntegral.__rshift__c C r )z
other >> selfr r r r r � __rrshift__R r! zIntegral.__rrshift__c C r )z self & otherr r r r r �__and__W r! zIntegral.__and__c C r )z other & selfr r r r r �__rand__\ r! zIntegral.__rand__c C r )z self ^ otherr r r r r �__xor__a r! zIntegral.__xor__c C r )z other ^ selfr r r r r �__rxor__f r! zIntegral.__rxor__c C r )z self | otherr r r r r �__or__k r! zIntegral.__or__c C r )z other | selfr r r r r �__ror__p r! zIntegral.__ror__c C r )z~selfr r r r r �
__invert__u r! zIntegral.__invert__c C rD )z float(self) == float(int(self)))rF rM r r r r r4 { rG zIntegral.__float__c C rH )z"Integers are their own numerators.r r r r r rK rI zIntegral.numeratorc C r )z!Integers have a denominator of 1.� r r r r r rL � r! zIntegral.denominatorrJ )r
r r r
r r rN rO r- rQ rR rS rT rU rV rW rX rY rZ r[ r4 r3 rK rL r r r r r & sF
r N)r
�abcr r �__all__r r �registerrE r rF r r rM r r r r �<module> s
p
uc