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� � �e�- � �� � S r SSKJrJr / SQr " S S\S9r " S S\5 r\R \5 " S S \5 r \ R \ 5 " S S \ 5 r " S S\ 5 r \ R \ 5 g)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 � � \ rS rSrSrSrSrSrg)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__�__firstlineno__�__doc__� __slots__�__hash__�__static_attributes__r � �-/opt/imh/python3.13/lib/python3.13/numbers.pyr r % s � �� �I� �Hr r )� metaclassc �B � \ rS rSrSrSr\S 5 rS r\ \S 5 5 r \ \S 5 5 r \S 5 r \S 5 r \S 5 r\S 5 rS rS r\S 5 r\S 5 r\S 5 r\S 5 r\S 5 r\S 5 r\S 5 r\S 5 r\S 5 rSrg)r �9 aN 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 � � g)z<Return a builtin complex instance. Called for complex(self).Nr ��selfs r � __complex__�Complex.__complex__F s � r c � � U S:g $ )z)True if self != 0. Called for bool(self).r r r s r �__bool__�Complex.__bool__J s � ��q�y�r c � � [ e)zHRetrieve the real component of this number. This should subclass Real. ��NotImplementedErrorr s r �real� Complex.realN � � � "�!r c � � [ e)zMRetrieve the imaginary component of this number. This should subclass Real. r# r s r �imag� Complex.imagW r' r c � � [ e)z self + otherr# �r �others r �__add__�Complex.__add__` � � � "�!r c � � [ e)z other + selfr# r, s r �__radd__�Complex.__radd__e r0 r c � � [ e)z-selfr# r s r �__neg__�Complex.__neg__j r0 r c � � [ e)z+selfr# r s r �__pos__�Complex.__pos__o r0 r c � � X* - $ )z self - otherr r, s r �__sub__�Complex.__sub__t s � ��f�}� r c � � U * U- $ )z other - selfr r, s r �__rsub__�Complex.__rsub__x s � ��u�u�}� r c � � [ e)z self * otherr# r, s r �__mul__�Complex.__mul__| r0 r c � � [ e)z other * selfr# r, s r �__rmul__�Complex.__rmul__� r0 r c � � [ e)z5self / other: Should promote to float when necessary.r# r, s r � __truediv__�Complex.__truediv__� r0 r c � � [ e)z other / selfr# r, s r � __rtruediv__�Complex.__rtruediv__� r0 r c � � [ e)zDself ** exponent; should promote to float or complex when necessary.r# )r �exponents r �__pow__�Complex.__pow__� r0 r c � � [ e)z base ** selfr# )r �bases r �__rpow__�Complex.__rpow__� r0 r c � � [ e)z7Returns the Real distance from 0. Called for abs(self).r# r s r �__abs__�Complex.__abs__� r0 r c � � [ e)z$(x+y*i).conjugate() returns (x-y*i).r# r s r � conjugate�Complex.conjugate� r0 r c � � [ e)z self == otherr# r, s r �__eq__�Complex.__eq__� r0 r N) r r r r r r r r r �propertyr% r) r. r2 r5 r8 r; r> rA rD rG rJ rN rR rU rX r[ r r r r r r 9 sm � �� �I��K� �K�� ��"� � �"� ��"� � �"� �"� �"� �"� �"� �"� �"� �"� �"� � � �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"r r c � � \ rS rSrSrSr\S 5 r\S 5 r\S 5 r \S 5 r \SS j5 r S r S r \S 5 r\S 5 r\S 5 r\S 5 r\S 5 r\S 5 rS r\S 5 r\S 5 rS rSrg)r � z�To Complex, Real adds the operations that work on real numbers. In short, those are: a conversion to float, trunc(), divmod, %, <, <=, >, and >=. Real also provides defaults for the derived operations. r c � � [ e)zLAny Real can be converted to a native float object. Called for float(self).r# r s r � __float__�Real.__float__� � � � "�!r c � � [ e)a trunc(self): Truncates self to an Integral. Returns an Integral i such that: * i > 0 iff self > 0; * abs(i) <= abs(self); * for any Integral j satisfying the first two conditions, abs(i) >= abs(j) [i.e. i has "maximal" abs among those]. i.e. "truncate towards 0". r# r s r � __trunc__�Real.__trunc__� s � � "�!r c � � [ e)z$Finds the greatest Integral <= self.r# r s r � __floor__�Real.__floor__� r0 r c � � [ e)z!Finds the least Integral >= self.r# r s r �__ceil__� Real.__ceil__� r0 r Nc � � [ e)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__�Real.__round__� r' r c � � X- X- 4$ )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__�Real.__divmod__� s � � � �t�|�,�,r c � � X- X- 4$ )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__�Real.__rdivmod__� s � � � �u�|�,�,r c � � [ e)z)self // other: The floor() of self/other.r# r, s r � __floordiv__�Real.__floordiv__� r0 r c � � [ e)z)other // self: The floor() of other/self.r# r, s r � __rfloordiv__�Real.__rfloordiv__� r0 r c � � [ e)z self % otherr# r, s r �__mod__� Real.__mod__� r0 r c � � [ e)z other % selfr# r, s r �__rmod__� Real.__rmod__� r0 r c � � [ e)zJself < other < on Reals defines a total ordering, except perhaps for NaN.r# r, s r �__lt__� Real.__lt__ rc r c � � [ e)z self <= otherr# r, s r �__le__� Real.__le__ r0 r c �* � [ [ U 5 5 $ )z(complex(self) == complex(float(self), 0))�complex�floatr s r r �Real.__complex__ s � ��u�T�{�#�#r c � � U 7$ )z&Real numbers are their real component.r r s r r% � Real.real � � � �u� r c � � g)z)Real numbers have no imaginary component.r r r s r r) � Real.imag � � � r c � � U 7$ )z Conjugate is a no-op for Reals.r r s r rX �Real.conjugate s � ��u� r �N)r r r r r r r ra re rh rk ro rr ru rx r{ r~ r� r� r� r r] r% r) rX r r r r r r � s$ � �� �I��"� �"� � "� � "� �"� �"� �"� �"� �"� �"�-�-� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� $� �� �� �� ��r r c �V � \ rS rSrSrSr\\S 5 5 r\\S 5 5 r S r Sr g)r i$ z�To Real, Rational adds numerator and denominator properties. The numerator and denominator values should be in lowest terms, with a positive denominator. r c � � [ e)z3The numerator of a rational number in lowest terms.r# r s r � numerator�Rational.numerator- s � � "�!r c � � [ e)z\The denominator of a rational number in lowest terms. This denominator should be positive. r# r s r � denominator�Rational.denominator3 r' r c �X � [ U R 5 [ U R 5 - $ )z�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. )�intr� r� r s r ra �Rational.__float__= s# � � �4�>�>�"�S��)9�)9�%:�:�:r N) r r r r r r r] r r� r� ra r r r r r r $ sI � �� �I� ��"� � �"� ��"� � �"�;r r c � � \ rS rSrSrSr\S 5 rS r\SS j5 r \S 5 r \S 5 r \S 5 r \S 5 r \S 5 r\S 5 r\S 5 r\S 5 r\S 5 r\S 5 r\S 5 rS r\S 5 r\S 5 rSrg)r iH 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 � � [ e)z int(self)r# r s r �__int__�Integral.__int__Q r0 r c � � [ U 5 $ )z6Called whenever an index is needed, such as in slicing)r� r s r � __index__�Integral.__index__V s � ��4�y�r Nc � � [ e)a 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 rM �moduluss r rN �Integral.__pow__Z s � � "�!r c � � [ e)z self << otherr# r, s r � __lshift__�Integral.__lshift__e r0 r c � � [ e)z other << selfr# r, s r � __rlshift__�Integral.__rlshift__j r0 r c � � [ e)z self >> otherr# r, s r � __rshift__�Integral.__rshift__o r0 r c � � [ e)z other >> selfr# r, s r � __rrshift__�Integral.__rrshift__t r0 r c � � [ e)z self & otherr# r, s r �__and__�Integral.__and__y r0 r c � � [ e)z other & selfr# r, s r �__rand__�Integral.__rand__~ r0 r c � � [ e)z self ^ otherr# r, s r �__xor__�Integral.__xor__� r0 r c � � [ e)z other ^ selfr# r, s r �__rxor__�Integral.__rxor__� r0 r c � � [ e)z self | otherr# r, s r �__or__�Integral.__or__� r0 r c � � [ e)z other | selfr# r, s r �__ror__�Integral.__ror__� r0 r c � � [ e)z~selfr# r s r � __invert__�Integral.__invert__� r0 r c �* � [ [ U 5 5 $ )z float(self) == float(int(self)))r� r� r s r ra �Integral.__float__� s � ��S��Y� � r c � � U 7$ )z"Integers are their own numerators.r r s r r� �Integral.numerator� r� r c � � g)z!Integers have a denominator of 1.� r r s r r� �Integral.denominator� r� r r� )r r r r r r r r� r� rN r� r� r� r� r� r� r� r� r� r� r� ra r] r� r� r r r r r r H sB � �� �I��"� �"�� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� � �� �� �� �r r N)r �abcr r �__all__r r �registerr� r r� r r r� r r r �<module>r� s� ��@�: (� ?�� �w� �(n"�f� n"�` � � �� �s�7� s�j � � �e� �!;�t� !;�Ha�x� a�F � � �#� r
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