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� �� f�( c @ s� d Z d d l m Z m Z d d d d d g Z Gd d � d d e �Z Gd d � d e � Z e j e � Gd d � d e � Z e j e � Gd d � d e � Z Gd d � d e � Z e j e � d S( u~ Abstract Base Classes (ABCs) for numbers, according to PEP 3141. TODO: Fill out more detailed documentation on the operators.i ( u ABCMetau abstractmethodu Numberu Complexu Realu Rationalu Integralc B s& | Ee Z d Z d Z f Z d Z d S( u Numberu� 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( u __name__u __module__u __qualname__u __doc__u __slots__u Noneu __hash__( u __locals__( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu Number s u metaclassc B s| | Ee Z d Z d Z f Z e d d � � Z d d � Z e e d d � � � Z e e d d � � � Z e d 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( d) � Z d* S(+ u Complexua 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( u< Return a builtin complex instance. Called for complex(self).N( ( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __complex__- s u Complex.__complex__c C s | d k S( u) True if self != 0. Called for bool(self).i ( ( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __bool__1 s u Complex.__bool__c C s t � d S( uX Retrieve the real component of this number. This should subclass Real. N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu real5 s u Complex.realc C s t � d S( u] Retrieve the imaginary component of this number. This should subclass Real. N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu imag> s u Complex.imagc C s t � d S( u self + otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __add__G s u Complex.__add__c C s t � d S( u other + selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __radd__L s u Complex.__radd__c C s t � d S( u -selfN( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __neg__Q s u Complex.__neg__c C s t � d S( u +selfN( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __pos__V s u Complex.__pos__c C s | | S( u self - other( ( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __sub__[ s u Complex.__sub__c C s | | S( u other - self( ( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rsub___ s u Complex.__rsub__c C s t � d S( u self * otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __mul__c s u Complex.__mul__c C s t � d S( u other * selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rmul__h s u Complex.__rmul__c C s t � d S( u5 self / other: Should promote to float when necessary.N( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __truediv__m s u Complex.__truediv__c C s t � d S( u other / selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rtruediv__r s u Complex.__rtruediv__c C s t � d S( uB self**exponent; should promote to float or complex when necessary.N( u NotImplementedError( u selfu exponent( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __pow__w s u Complex.__pow__c C s t � d S( u base ** selfN( u NotImplementedError( u selfu base( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rpow__| s u Complex.__rpow__c C s t � d S( u7 Returns the Real distance from 0. Called for abs(self).N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __abs__� s u Complex.__abs__c C s t � d S( u$ (x+y*i).conjugate() returns (x-y*i).N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu conjugate� s u Complex.conjugatec C s t � d S( u self == otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __eq__� s u Complex.__eq__c C s | | k S( u self != other( ( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __ne__� s u Complex.__ne__N( u __name__u __module__u __qualname__u __doc__u __slots__u abstractmethodu __complex__u __bool__u propertyu realu imagu __add__u __radd__u __neg__u __pos__u __sub__u __rsub__u __mul__u __rmul__u __truediv__u __rtruediv__u __pow__u __rpow__u __abs__u conjugateu __eq__u __ne__( u __locals__( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu Complex s0 c B s= | Ee 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(% u Realu� 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( uT Any Real can be converted to a native float object. Called for float(self).N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __float__� s u Real.__float__c C s t � d S( uG 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( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __trunc__� s u Real.__trunc__c C s t � d S( u$ Finds the greatest Integral <= self.N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __floor__� s u Real.__floor__c C s t � d S( u! Finds the least Integral >= self.N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __ceil__� s u Real.__ceil__c C s t � d S( u� 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( u NotImplementedError( u selfu ndigits( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __round__� s u Real.__round__c C s | | | | f S( u� divmod(self, other): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. ( ( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __divmod__� s u Real.__divmod__c C s | | | | f S( u� divmod(other, self): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. ( ( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rdivmod__� s u Real.__rdivmod__c C s t � d S( u) self // other: The floor() of self/other.N( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __floordiv__� s u Real.__floordiv__c C s t � d S( u) other // self: The floor() of other/self.N( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rfloordiv__� s u Real.__rfloordiv__c C s t � d S( u self % otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __mod__� s u Real.__mod__c C s t � d S( u other % selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rmod__� s u Real.__rmod__c C s t � d S( uR self < other < on Reals defines a total ordering, except perhaps for NaN.N( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __lt__� s u Real.__lt__c C s t � d S( u self <= otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __le__� s u Real.__le__c C s t t | � � S( u( complex(self) == complex(float(self), 0)( u complexu float( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __complex__� s u Real.__complex__c C s | S( u& Real numbers are their real component.( ( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu real� s u Real.realc C s d S( u) Real numbers have no imaginary component.i ( ( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu imag s u Real.imagc C s | S( u Conjugate is a no-op for Reals.( ( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu conjugate s u Real.conjugateN( u __name__u __module__u __qualname__u __doc__u __slots__u abstractmethodu __float__u __trunc__u __floor__u __ceil__u Noneu __round__u __divmod__u __rdivmod__u __floordiv__u __rfloordiv__u __mod__u __rmod__u __lt__u __le__u __complex__u propertyu realu imagu conjugate( u __locals__( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu Real� s( c B s\ | Ee Z d Z d Z f Z e e d d � � � Z e e d d � � � Z d d � Z d S( u Rationalu6 .numerator and .denominator should be in lowest terms.c C s t � d S( N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu numerator s u Rational.numeratorc C s t � d S( N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu denominator s u Rational.denominatorc C s | j | j S( u 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. ( u numeratoru denominator( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __float__ s u Rational.__float__N( u __name__u __module__u __qualname__u __doc__u __slots__u propertyu abstractmethodu numeratoru denominatoru __float__( u __locals__( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu Rational s c B sI | Ee 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(% u Integralu@ Integral adds a conversion to int and the bit-string operations.c C s t � d S( u int(self)N( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __int__0 s u Integral.__int__c C s t | � S( u6 Called whenever an index is needed, such as in slicing( u int( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __index__5 s u Integral.__index__c C s t � d S( u4 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( u NotImplementedError( u selfu exponentu modulus( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __pow__9 s u Integral.__pow__c C s t � d S( u self << otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __lshift__D s u Integral.__lshift__c C s t � d S( u other << selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rlshift__I s u Integral.__rlshift__c C s t � d S( u self >> otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rshift__N s u Integral.__rshift__c C s t � d S( u other >> selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rrshift__S s u Integral.__rrshift__c C s t � d S( u self & otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __and__X s u Integral.__and__c C s t � d S( u other & selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rand__] s u Integral.__rand__c C s t � d S( u self ^ otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __xor__b s u Integral.__xor__c C s t � d S( u other ^ selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __rxor__g s u Integral.__rxor__c C s t � d S( u self | otherN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __or__l s u Integral.__or__c C s t � d S( u other | selfN( u NotImplementedError( u selfu other( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __ror__q s u Integral.__ror__c C s t � d S( u ~selfN( u NotImplementedError( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __invert__v s u Integral.__invert__c C s t t | � � S( u float(self) == float(int(self))( u floatu int( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu __float__| s u Integral.__float__c C s | S( u" Integers are their own numerators.( ( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu numerator� s u Integral.numeratorc C s d S( u! Integers have a denominator of 1.i ( ( u self( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu denominator� s u Integral.denominatorN( u __name__u __module__u __qualname__u __doc__u __slots__u abstractmethodu __int__u __index__u Noneu __pow__u __lshift__u __rlshift__u __rshift__u __rrshift__u __and__u __rand__u __xor__u __rxor__u __or__u __ror__u __invert__u __float__u propertyu numeratoru denominator( u __locals__( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu Integral+ s( N( u __doc__u abcu ABCMetau abstractmethodu __all__u Numberu Complexu registeru complexu Realu floatu Rationalu Integralu int( ( ( u, /opt/alt/python33/lib64/python3.3/numbers.pyu <module> s u u _
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