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� � YZ e j e � e j e � d S( s~ Abstract Base Classes (ABCs) for numbers, according to PEP 3141.
TODO: Fill out more detailed documentation on the operators.i����( t division( t ABCMetat abstractmethodt abstractpropertyt Numbert Complext Realt Rationalt Integralc B s e Z d Z e Z d Z d Z RS( s� 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( t __name__t
__module__t __doc__R t
__metaclass__t __slots__t Nonet __hash__( ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyR
s c B sF e Z d Z d Z e d � � Z d � Z e d � � Z e d � � Z e d � � Z
e d � � Z e d � � Z e d � � Z
d � Z d
� Z e d � � Z e d � � Z e d
� � Z e d � � Z e d � � Z e d � � Z e d � � Z e d � � Z e d � � Z e d � � Z e d � � Z d � Z RS( sa 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( s< Return a builtin complex instance. Called for complex(self).N( ( t self( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __complex__/ t c C s
| d k S( s) True if self != 0. Called for bool(self).i ( ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __nonzero__4 s c C s
t � d S( sX Retrieve the real component of this number.
This should subclass Real.
N( t NotImplementedError( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt real8 s c C s
t � d S( s] Retrieve the imaginary component of this number.
This should subclass Real.
N( R ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt imag@ s c C s
t � d S( s self + otherN( R ( R t other( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __add__H s c C s
t � d S( s other + selfN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __radd__M s c C s
t � d S( s -selfN( R ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __neg__R s c C s
t � d S( s +selfN( R ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __pos__W s c C s | | S( s self - other( ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __sub__\ s c C s | | S( s other - self( ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __rsub__` s c C s
t � d S( s self * otherN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __mul__d s c C s
t � d S( s other * selfN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __rmul__i s c C s
t � d S( sP self / other without __future__ division
May promote to float.
N( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __div__n s c C s
t � d S( s( other / self without __future__ divisionN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __rdiv__v s c C s
t � d S( s` self / other with __future__ division.
Should promote to float when necessary.
N( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __truediv__{ s c C s
t � d S( s% other / self with __future__ divisionN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __rtruediv__� s c C s
t � d S( sB self**exponent; should promote to float or complex when necessary.N( R ( R t exponent( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __pow__� s c C s
t � d S( s base ** selfN( R ( R t base( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __rpow__� s c C s
t � d S( s7 Returns the Real distance from 0. Called for abs(self).N( R ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __abs__� s c C s
t � d S( s$ (x+y*i).conjugate() returns (x-y*i).N( R ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt conjugate� s c C s
t � d S( s
self == otherN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __eq__� s c C s | | k S( s
self != other( ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __ne__� s ( ( R R
R R
R R R R R R R R R R R R R R R R! R" R# R% R' R( R) R* R+ ( ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyR " s0 c B s� e Z d Z d Z e d � � Z e d � � Z d � Z d � Z e d � � Z e d � � Z
e d � � Z e d � � Z e d � � Z
e d
� � Z d � Z e d � � Z e d
� � Z d � Z RS( s� 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( sT Any Real can be converted to a native float object.
Called for float(self).N( R ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __float__� s c C s
t � d S( sG 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 ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __trunc__� s c C s | | | | f S( s� divmod(self, other): The pair (self // other, self % other).
Sometimes this can be computed faster than the pair of
operations.
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__divmod__� s c C s | | | | f S( s� divmod(other, self): The pair (self // other, self % other).
Sometimes this can be computed faster than the pair of
operations.
( ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __rdivmod__� s c C s
t � d S( s) self // other: The floor() of self/other.N( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __floordiv__� s c C s
t � d S( s) other // self: The floor() of other/self.N( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt
__rfloordiv__� s c C s
t � d S( s self % otherN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __mod__� s c C s
t � d S( s other % selfN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __rmod__� s c C s
t � d S( sR self < other
< on Reals defines a total ordering, except perhaps for NaN.N( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __lt__� s c C s
t � d S( s
self <= otherN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __le__� s c C s t t | � � S( s( complex(self) == complex(float(self), 0)( t complext float( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyR � s c C s |
S( s& Real numbers are their real component.( ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyR � s c C s d S( s) Real numbers have no imaginary component.i ( ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyR s c C s |
S( s Conjugate is a no-op for Reals.( ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyR) s ( ( R R
R R
R R, R- R. R/ R0 R1 R2 R3 R4 R5 R t propertyR R R) ( ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyR � s
c B s; e Z d Z d Z e d � � Z e d � � Z d � Z RS( s6 .numerator and .denominator should be in lowest terms.c C s
t � d S( N( R ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt numerator s c C s
t � d S( N( R ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt denominator s c C s | j | j S( s 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.
( R9 R: ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyR, s ( ( R R
R R
R R9 R: R, ( ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyR s
c B s
e Z d Z d Z e d � � Z d � Z e d d � � Z e d � � Z e d � � Z
e d � � Z e d � � Z e d � � Z
e d � � Z e d
� � Z e d � � Z e d � � Z e d
� � Z e d � � Z d � Z e d � � Z e d � � Z RS( sA Integral adds a conversion to long and the bit-string operations.c C s
t � d S( s
long(self)N( R ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __long__, s c C s
t | � S( s6 Called whenever an index is needed, such as in slicing( t long( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __index__1 s c C s
t � d S( s4 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$ t modulus( ( s' /opt/RZpython2/lib/python2.7/numbers.pyR% 5 s c C s
t � d S( s
self << otherN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt
__lshift__@ s c C s
t � d S( s
other << selfN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __rlshift__E s c C s
t � d S( s
self >> otherN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt
__rshift__J s c C s
t � d S( s
other >> selfN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __rrshift__O s c C s
t � d S( s self & otherN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __and__T s c C s
t � d S( s other & selfN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __rand__Y s c C s
t � d S( s self ^ otherN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __xor__^ s c C s
t � d S( s other ^ selfN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __rxor__c s c C s
t � d S( s self | otherN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __or__h s c C s
t � d S( s other | selfN( R ( R R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt __ror__m s c C s
t � d S( s ~selfN( R ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt
__invert__r s c C s t t | � � S( s float(self) == float(long(self))( R7 R< ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyR, x s c C s |
S( s" Integers are their own numerators.( ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyR9 | s c C s d S( s! Integers have a denominator of 1.i ( ( R ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyR: � s ( N( R R
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R R; R= R R% R? R@ RA RB RC RD RE RF RG RH RI R, R8 R9 R: ( ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyR ' s(
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__future__R t abcR R R t __all__t objectR R t registerR6 R R7 R R t intR< ( ( ( s' /opt/RZpython2/lib/python2.7/numbers.pyt <module> s �
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