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Edit File: numbers.pyc
� NY~gc @ s� d Z d d l m Z d d l m Z m Z m Z d d d d d g Z d e f d � � YZ d e f d � � YZ e j e � d e f d � � YZ e j e � d e f d � � YZ d e f d � � 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/alt/python27/lib64/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/alt/python27/lib64/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/alt/python27/lib64/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/alt/python27/lib64/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/alt/python27/lib64/python2.7/numbers.pyt imag@ s c C s t � d S( s self + otherN( R ( R t other( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __add__H s c C s t � d S( s other + selfN( R ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __radd__M s c C s t � d S( s -selfN( R ( R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __neg__R s c C s t � d S( s +selfN( R ( R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __pos__W s c C s | | S( s self - other( ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __sub__\ s c C s | | S( s other - self( ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __rsub__` s c C s t � d S( s self * otherN( R ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __mul__d s c C s t � d S( s other * selfN( R ( R R ( ( s, /opt/alt/python27/lib64/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/alt/python27/lib64/python2.7/numbers.pyt __div__n s c C s t � d S( s( other / self without __future__ divisionN( R ( R R ( ( s, /opt/alt/python27/lib64/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/alt/python27/lib64/python2.7/numbers.pyt __truediv__{ s c C s t � d S( s% other / self with __future__ divisionN( R ( R R ( ( s, /opt/alt/python27/lib64/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/alt/python27/lib64/python2.7/numbers.pyt __pow__� s c C s t � d S( s base ** selfN( R ( R t base( ( s, /opt/alt/python27/lib64/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/alt/python27/lib64/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/alt/python27/lib64/python2.7/numbers.pyt conjugate� s c C s t � d S( s self == otherN( R ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __eq__� s c C s | | k S( s self != other( ( R R ( ( s, /opt/alt/python27/lib64/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/alt/python27/lib64/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/alt/python27/lib64/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/alt/python27/lib64/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. ( ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __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/alt/python27/lib64/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/alt/python27/lib64/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/alt/python27/lib64/python2.7/numbers.pyt __rfloordiv__� s c C s t � d S( s self % otherN( R ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __mod__� s c C s t � d S( s other % selfN( R ( R R ( ( s, /opt/alt/python27/lib64/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/alt/python27/lib64/python2.7/numbers.pyt __lt__� s c C s t � d S( s self <= otherN( R ( R R ( ( s, /opt/alt/python27/lib64/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/alt/python27/lib64/python2.7/numbers.pyR � s c C s | S( s& Real numbers are their real component.( ( R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyR � s c C s d S( s) Real numbers have no imaginary component.i ( ( R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyR s c C s | S( s Conjugate is a no-op for Reals.( ( R ( ( s, /opt/alt/python27/lib64/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/alt/python27/lib64/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/alt/python27/lib64/python2.7/numbers.pyt numerator s c C s t � d S( N( R ( R ( ( s, /opt/alt/python27/lib64/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/alt/python27/lib64/python2.7/numbers.pyR, s ( ( R R R R R R9 R: R, ( ( ( s, /opt/alt/python27/lib64/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/alt/python27/lib64/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/alt/python27/lib64/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/alt/python27/lib64/python2.7/numbers.pyR% 5 s c C s t � d S( s self << otherN( R ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __lshift__@ s c C s t � d S( s other << selfN( R ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __rlshift__E s c C s t � d S( s self >> otherN( R ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __rshift__J s c C s t � d S( s other >> selfN( R ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __rrshift__O s c C s t � d S( s self & otherN( R ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __and__T s c C s t � d S( s other & selfN( R ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __rand__Y s c C s t � d S( s self ^ otherN( R ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __xor__^ s c C s t � d S( s other ^ selfN( R ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __rxor__c s c C s t � d S( s self | otherN( R ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __or__h s c C s t � d S( s other | selfN( R ( R R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __ror__m s c C s t � d S( s ~selfN( R ( R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt __invert__r s c C s t t | � � S( s float(self) == float(long(self))( R7 R< ( R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyR, x s c C s | S( s" Integers are their own numerators.( ( R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyR9 | s c C s d S( s! Integers have a denominator of 1.i ( ( R ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyR: � s ( N( R R R R R R; R= R R% R? R@ RA RB RC RD RE RF RG RH RI R, R8 R9 R: ( ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyR ' s( N( R t __future__R t abcR R R t __all__t objectR R t registerR6 R R7 R R t intR< ( ( ( s, /opt/alt/python27/lib64/python2.7/numbers.pyt <module> s � b _