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� d S)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 Z d Z d Z f Z d Z d S)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 � /usr/lib/python3.5/numbers.pyr s � metaclassc @ sl e Z d Z d Z f Z e d d � � Z d d � Z e e d d � � � Z e e d d � � � Z
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d � � Z e d d
� � Z e d d � � Z
e d d � � Z d d � Z d d � Z e d d � � Z e d d � � Z e d d � � Z e d d � � Z e d d � � Z e d d! � � Z e d" d# � � Z e d$ d% � � Z e d& d' � � Z d( S))r aa 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 heterogenous arguments, and doesn't have special
knowledge about them, it should fall back to the builtin complex
type as described below.
c C s d S)z<Return a builtin complex instance. Called for complex(self).Nr )�selfr r r � __complex__- s zComplex.__complex__c C s
| d k S)z)True if self != 0. Called for bool(self).r r )r r r r �__bool__1 s zComplex.__bool__c C s
t � d S)zXRetrieve the real component of this number.
This should subclass Real.
N)�NotImplementedError)r r r r �real5 s z Complex.realc C s
t � d S)z]Retrieve the imaginary component of this number.
This should subclass Real.
N)r )r r r r �imag> s z Complex.imagc C s
t � d S)z self + otherN)r )r �otherr r r �__add__G s zComplex.__add__c C s
t � d S)z other + selfN)r )r r r r r �__radd__L s zComplex.__radd__c C s
t � d S)z-selfN)r )r r r r �__neg__Q s zComplex.__neg__c C s
t � d S)z+selfN)r )r r r r �__pos__V s zComplex.__pos__c C s | | S)z self - otherr )r r r r r �__sub__[ s zComplex.__sub__c C s | | S)z other - selfr )r r r r r �__rsub___ s zComplex.__rsub__c C s
t � d S)z self * otherN)r )r r r r r �__mul__c s zComplex.__mul__c C s
t � d S)z other * selfN)r )r r r r r �__rmul__h s zComplex.__rmul__c C s
t � d S)z5self / other: Should promote to float when necessary.N)r )r r r r r � __truediv__m s zComplex.__truediv__c C s
t � d S)z other / selfN)r )r r r r r � __rtruediv__r s zComplex.__rtruediv__c C s
t � d S)zBself**exponent; should promote to float or complex when necessary.N)r )r �exponentr r r �__pow__w s zComplex.__pow__c C s
t � d S)z base ** selfN)r )r �baser r r �__rpow__| s zComplex.__rpow__c C s
t � d S)z7Returns the Real distance from 0. Called for abs(self).N)r )r r r r �__abs__� s zComplex.__abs__c C s
t � d S)z$(x+y*i).conjugate() returns (x-y*i).N)r )r r r r � conjugate� s zComplex.conjugatec C s
t � d S)z
self == otherN)r )r r r r r �__eq__� s zComplex.__eq__N)r r
r r r
r r r �propertyr r r r r r r r r r r! r" r$ r& r' r( r) r r r r r s. c @ s9 e Z d Z d Z f Z e d d � � Z e d d � � Z e d d � � Z e d d � � Z e d
d d � � Z
d
d � Z d d � Z e d d � � Z
e d d � � Z e d d � � Z e d d � � Z e d d � � Z e d d � � Z d d � Z e d d � � Z e d! d" � � Z d# d$ � Z d
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.
c C s
t � d S)zTAny Real can be converted to a native float object.
Called for float(self).N)r )r r r r � __float__� s zReal.__float__c C s
t � d S)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".
N)r )r r r r � __trunc__� s zReal.__trunc__c C s
t � d S)z$Finds the greatest Integral <= self.N)r )r r r r � __floor__� s zReal.__floor__c C s
t � d S)z!Finds the least Integral >= self.N)r )r r r r �__ceil__� s z
Real.__ceil__Nc C s
t � d S)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.
N)r )r Zndigitsr r r � __round__� s zReal.__round__c C s | | | | f S)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 r �
__divmod__� s zReal.__divmod__c C s | | | | f S)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 r � __rdivmod__� s zReal.__rdivmod__c C s
t � d S)z)self // other: The floor() of self/other.N)r )r r r r r � __floordiv__� s zReal.__floordiv__c C s
t � d S)z)other // self: The floor() of other/self.N)r )r r r r r �
__rfloordiv__� s zReal.__rfloordiv__c C s
t � d S)z self % otherN)r )r r r r r �__mod__� s z Real.__mod__c C s
t � d S)z other % selfN)r )r r r r r �__rmod__� s z
Real.__rmod__c C s
t � d S)zRself < other
< on Reals defines a total ordering, except perhaps for NaN.N)r )r r r r r �__lt__� s z Real.__lt__c C s
t � d S)z
self <= otherN)r )r r r r r �__le__� s z Real.__le__c C s t t | � � S)z(complex(self) == complex(float(self), 0))�complex�float)r r r r r � s zReal.__complex__c C s |
S)z&Real numbers are their real component.r )r r r r r � s z Real.realc C s d S)z)Real numbers have no imaginary component.r r )r r r r r � s z Real.imagc C s |
S)z Conjugate is a no-op for Reals.r )r r r r r( s zReal.conjugate)r r
r r r
r r+ r, r- r. r/ r0 r1 r2 r3 r4 r5 r6 r7 r r* r r r( r r r r r � s(
c @ sX e Z d Z d Z f Z e e d d � � � Z e e d d � � � Z d d � Z d S) r z6.numerator and .denominator should be in lowest terms.c C s
t � d S)N)r )r r r r � numerator s zRational.numeratorc C s
t � d S)N)r )r r r r � denominator s zRational.denominatorc C s | j | 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.
)r: r; )r r r r r+ s zRational.__float__N)
r r
r r r
r* r r: r; r+ r r r r r s c @ sE e Z d Z d Z f Z e d d � � Z d d � Z e d d d � � Z e d d
� � Z e d d � � Z
e d
d � � Z e d d � � Z e d d � � Z
e d d � � Z e d d � � Z e d d � � Z e d d � � Z e d d � � Z e d d � � Z d d � Z e d! d" � � Z e d# d$ � � Z d S)%r z@Integral adds a conversion to int and the bit-string operations.c C s
t � d S)z int(self)N)r )r r r r �__int__+ s zIntegral.__int__c C s
t | � S)z6Called whenever an index is needed, such as in slicing)�int)r r r r � __index__0 s zIntegral.__index__Nc C s
t � d S)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.
N)r )r r# �modulusr r r r$ 4 s zIntegral.__pow__c C s
t � d S)z
self << otherN)r )r r r r r �
__lshift__? s zIntegral.__lshift__c C s
t � d S)z
other << selfN)r )r r r r r � __rlshift__D s zIntegral.__rlshift__c C s
t � d S)z
self >> otherN)r )r r r r r �
__rshift__I s zIntegral.__rshift__c C s
t � d S)z
other >> selfN)r )r r r r r � __rrshift__N s zIntegral.__rrshift__c C s
t � d S)z self & otherN)r )r r r r r �__and__S s zIntegral.__and__c C s
t � d S)z other & selfN)r )r r r r r �__rand__X s zIntegral.__rand__c C s
t � d S)z self ^ otherN)r )r r r r r �__xor__] s zIntegral.__xor__c C s
t � d S)z other ^ selfN)r )r r r r r �__rxor__b s zIntegral.__rxor__c C s
t � d S)z self | otherN)r )r r r r r �__or__g s zIntegral.__or__c C s
t � d S)z other | selfN)r )r r r r r �__ror__l s zIntegral.__ror__c C s
t � d S)z~selfN)r )r r r r �
__invert__q s zIntegral.__invert__c C s t t | � � S)z float(self) == float(int(self)))r9 r= )r r r r r+ w s zIntegral.__float__c C s |
S)z"Integers are their own numerators.r )r r r r r: { s zIntegral.numeratorc C s d S)z!Integers have a denominator of 1.� r )r r r r r; � s zIntegral.denominator)r r
r r r
r r< r> r$ r@ rA rB rC rD rE rF rG rH rI rJ r+ r* r: r; r r r r r & s(
N)r �abcr r �__all__r r �registerr8 r r9 r r r= r r r r �<module> s p
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