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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).
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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$(x+y*i).conjugate() returns (x-y*i).r# r s r � conjugate�Complex.conjugate� r0 r c � � [ e)z
self == otherr# r, s r �__eq__�Complex.__eq__� r0 r N) r
r r r r r r r r �propertyr% r) r. r2 r5 r8 r; r> rA rD rG rJ rN rR rU rX r[ r r r r r r 9 sm � �� �I��K� �K�� ��"� � �"� ��"� � �"� �"� �"� �"� �"� �"� �"� �"� �"� � � �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"� �"r r c � � \ rS rSrSrSr\S 5 r\S 5 r\S 5 r \S 5 r
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5 r\S 5 r\S 5 r\S 5 r\S 5 rS r\S 5 r\S 5 rS rSrg)r � z�To Complex, Real adds the operations that work on real numbers.
In short, those are: a conversion to float, trunc(), divmod,
%, <, <=, >, and >=.
Real also provides defaults for the derived operations.
r c � � [ e)zLAny Real can be converted to a native float object.
Called for float(self).r# r s r � __float__�Real.__float__� �
� �
"�!r c � � [ e)a trunc(self): Truncates self to an Integral.
Returns an Integral i such that:
* i > 0 iff self > 0;
* abs(i) <= abs(self);
* for any Integral j satisfying the first two conditions,
abs(i) >= abs(j) [i.e. i has "maximal" abs among those].
i.e. "truncate towards 0".
r# r s r � __trunc__�Real.__trunc__� s
� � "�!r c � � [ e)z$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��"� �"� �
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$� �� �� �� ��r r c �V � \ rS rSrSrSr\\S 5 5 r\\S 5 5 r S r
Sr g)r i$ z6.numerator and .denominator should be in lowest terms.r c � � [ er� r# r s r � numerator�Rational.numerator) r0 r c � � [ er� r# r s r � denominator�Rational.denominator. r0 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__4 s# � � �4�>�>�"�S��)9�)9�%:�:�:r N) r
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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 i? 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__H r0 r c � � [ U 5 $ )z6Called whenever an index is needed, such as in slicing)r� r s r � __index__�Integral.__index__M 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__Q s
� � "�!r c � � [ e)z
self << otherr# r, s r �
__lshift__�Integral.__lshift__\ r0 r c � � [ e)z
other << selfr# r, s r � __rlshift__�Integral.__rlshift__a r0 r c � � [ e)z
self >> otherr# r, s r �
__rshift__�Integral.__rshift__f r0 r c � � [ e)z
other >> selfr# r, s r � __rrshift__�Integral.__rrshift__k r0 r c � � [ e)z self & otherr# r, s r �__and__�Integral.__and__p r0 r c � � [ e)z other & selfr# r, s r �__rand__�Integral.__rand__u r0 r c � � [ e)z self ^ otherr# r, s r �__xor__�Integral.__xor__z 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
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