Ю м fЮ(c@s═dZddlmZmZdddddgZGddДdd eГZGd dДdeГZejeГGddДdeГZ e je ГGddДde ГZGd dДdeГZeje ГdS(u~Abstract Base Classes (ABCs) for numbers, according to PEP 3141. TODO: Fill out more detailed documentation on the operators.i(uABCMetauabstractmethoduNumberuComplexuRealuRationaluIntegralcBs&|EeZdZdZfZdZdS(uNumberuЯAll 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__uNoneu__hash__(u __locals__((u,/opt/alt/python33/lib64/python3.3/numbers.pyuNumbersu metaclasscBs||EeZdZdZfZeddДГZddДZeeddДГГZ eedd ДГГZ ed dДГZedd ДГZeddДГZ eddДГZddДZddДZeddДГZeddДГZeddДГZeddДГZeddДГZed d!ДГZed"d#ДГZed$d%ДГZed&d'ДГZd(d)ДZd*S(+uComplexuaComplex 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. cCsdS(u<Return a builtin complex instance. Called for complex(self).N((uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__complex__-suComplex.__complex__cCs |dkS(u)True if self != 0. Called for bool(self).i((uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__bool__1suComplex.__bool__cCs tВdS(uXRetrieve the real component of this number. This should subclass Real. N(uNotImplementedError(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyureal5suComplex.realcCs tВdS(u]Retrieve the imaginary component of this number. This should subclass Real. N(uNotImplementedError(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyuimag>suComplex.imagcCs tВdS(uself + otherN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__add__GsuComplex.__add__cCs tВdS(uother + selfN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__radd__LsuComplex.__radd__cCs tВdS(u-selfN(uNotImplementedError(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__neg__QsuComplex.__neg__cCs tВdS(u+selfN(uNotImplementedError(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__pos__VsuComplex.__pos__cCs ||S(uself - other((uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__sub__[suComplex.__sub__cCs ||S(uother - self((uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__rsub___suComplex.__rsub__cCs tВdS(uself * otherN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__mul__csuComplex.__mul__cCs tВdS(uother * selfN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__rmul__hsuComplex.__rmul__cCs tВdS(u5self / other: Should promote to float when necessary.N(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__truediv__msuComplex.__truediv__cCs tВdS(uother / selfN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__rtruediv__rsuComplex.__rtruediv__cCs tВdS(uBself**exponent; should promote to float or complex when necessary.N(uNotImplementedError(uselfuexponent((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__pow__wsuComplex.__pow__cCs tВdS(ubase ** selfN(uNotImplementedError(uselfubase((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__rpow__|suComplex.__rpow__cCs tВdS(u7Returns the Real distance from 0. Called for abs(self).N(uNotImplementedError(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__abs__БsuComplex.__abs__cCs tВdS(u$(x+y*i).conjugate() returns (x-y*i).N(uNotImplementedError(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu conjugateЖsuComplex.conjugatecCs tВdS(u self == otherN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__eq__ЛsuComplex.__eq__cCs||kS(u self != other((uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__ne__РsuComplex.__ne__N(u__name__u __module__u__qualname__u__doc__u __slots__uabstractmethodu__complex__u__bool__upropertyurealuimagu__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.pyuComplex s0 cBs=|EeZdZdZfZeddДГZeddДГZeddДГZedd ДГZ ed$d dДГZdd ДZddДZ eddДГZeddДГZeddДГZeddДГZeddДГZeddДГZddДZeddДГZed d!ДГZd"d#ДZd$S(%uRealu▄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. cCs tВdS(uTAny Real can be converted to a native float object. Called for float(self).N(uNotImplementedError(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu __float__гsuReal.__float__cCs tВdS(uGtrunc(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(uNotImplementedError(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu __trunc__кsuReal.__trunc__cCs tВdS(u$Finds the greatest Integral <= self.N(uNotImplementedError(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu __floor__╖suReal.__floor__cCs tВdS(u!Finds the least Integral >= self.N(uNotImplementedError(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__ceil__╝su Real.__ceil__cCs tВdS(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(uNotImplementedError(uselfundigits((u,/opt/alt/python33/lib64/python3.3/numbers.pyu __round__┴suReal.__round__cCs||||fS(uЩdivmod(self, other): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. ((uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu __divmod__╩suReal.__divmod__cCs||||fS(uЩdivmod(other, self): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. ((uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__rdivmod__╥suReal.__rdivmod__cCs tВdS(u)self // other: The floor() of self/other.N(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__floordiv__┌suReal.__floordiv__cCs tВdS(u)other // self: The floor() of other/self.N(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu __rfloordiv__▀suReal.__rfloordiv__cCs tВdS(uself % otherN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__mod__фsuReal.__mod__cCs tВdS(uother % selfN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__rmod__щsu Real.__rmod__cCs tВdS(uRself < other < on Reals defines a total ordering, except perhaps for NaN.N(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__lt__юsuReal.__lt__cCs tВdS(u self <= otherN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__le__їsuReal.__le__cCstt|ГГS(u(complex(self) == complex(float(self), 0)(ucomplexufloat(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__complex__√suReal.__complex__cCs| S(u&Real numbers are their real component.((uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyureal su Real.realcCsdS(u)Real numbers have no imaginary component.i((uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyuimagsu Real.imagcCs| S(uConjugate is a no-op for Reals.((uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu conjugate suReal.conjugateN(u__name__u __module__u__qualname__u__doc__u __slots__uabstractmethodu __float__u __trunc__u __floor__u__ceil__uNoneu __round__u __divmod__u__rdivmod__u__floordiv__u __rfloordiv__u__mod__u__rmod__u__lt__u__le__u__complex__upropertyurealuimagu conjugate(u __locals__((u,/opt/alt/python33/lib64/python3.3/numbers.pyuRealШs( cBs\|EeZdZdZfZeeddДГГZeeddДГГZddДZ dS( uRationalu6.numerator and .denominator should be in lowest terms.cCs tВdS(N(uNotImplementedError(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu numeratorsuRational.numeratorcCs tВdS(N(uNotImplementedError(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyudenominatorsuRational.denominatorcCs|j|jS(ufloat(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 numeratorudenominator(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu __float__ suRational.__float__N( u__name__u __module__u__qualname__u__doc__u __slots__upropertyuabstractmethodu numeratorudenominatoru __float__(u __locals__((u,/opt/alt/python33/lib64/python3.3/numbers.pyuRationalscBsI|EeZdZdZfZeddДГZddДZed$ddДГZ edd ДГZ ed dДГZedd ДГZeddДГZ eddДГZeddДГZeddДГZeddДГZeddДГZeddДГZeddДГZddДZed d!ДГZed"d#ДГZd$S(%uIntegralu@Integral adds a conversion to int and the bit-string operations.cCs tВdS(u int(self)N(uNotImplementedError(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__int__0suIntegral.__int__cCs t|ГS(u6Called whenever an index is needed, such as in slicing(uint(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu __index__5suIntegral.__index__cCs tВdS(u4self ** 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(uNotImplementedError(uselfuexponentumodulus((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__pow__9s uIntegral.__pow__cCs tВdS(u self << otherN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu __lshift__DsuIntegral.__lshift__cCs tВdS(u other << selfN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__rlshift__IsuIntegral.__rlshift__cCs tВdS(u self >> otherN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu __rshift__NsuIntegral.__rshift__cCs tВdS(u other >> selfN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__rrshift__SsuIntegral.__rrshift__cCs tВdS(uself & otherN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__and__XsuIntegral.__and__cCs tВdS(uother & selfN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__rand__]suIntegral.__rand__cCs tВdS(uself ^ otherN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__xor__bsuIntegral.__xor__cCs tВdS(uother ^ selfN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__rxor__gsuIntegral.__rxor__cCs tВdS(uself | otherN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__or__lsuIntegral.__or__cCs tВdS(uother | selfN(uNotImplementedError(uselfuother((u,/opt/alt/python33/lib64/python3.3/numbers.pyu__ror__qsuIntegral.__ror__cCs tВdS(u~selfN(uNotImplementedError(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu __invert__vsuIntegral.__invert__cCstt|ГГS(ufloat(self) == float(int(self))(ufloatuint(uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu __float__|suIntegral.__float__cCs| S(u"Integers are their own numerators.((uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyu numeratorАsuIntegral.numeratorcCsdS(u!Integers have a denominator of 1.i((uself((u,/opt/alt/python33/lib64/python3.3/numbers.pyudenominatorЕsuIntegral.denominatorN(u__name__u __module__u__qualname__u__doc__u __slots__uabstractmethodu__int__u __index__uNoneu__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__upropertyu numeratorudenominator(u __locals__((u,/opt/alt/python33/lib64/python3.3/numbers.pyuIntegral+s( N(u__doc__uabcuABCMetauabstractmethodu__all__uNumberuComplexuregisterucomplexuRealufloatuRationaluIntegraluint(((u,/opt/alt/python33/lib64/python3.3/numbers.pyusu u _