­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ 3 \(@sdZddlmZmZdddddgZGddded ZGd ddeZejeGd ddeZ e je Gd dde Z Gd dde Z e je dS)z~Abstract Base Classes (ABCs) for numbers, according to PEP 3141. TODO: Fill out more detailed documentation on the operators.)ABCMetaabstractmethodNumberComplexRealRationalIntegralc@seZdZdZfZdZdS)rzAll 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__rr/usr/lib64/python3.6/numbers.pyr s) metaclassc@seZdZdZfZeddZddZeeddZ eedd Z ed d Z ed d Z eddZ eddZddZddZeddZeddZeddZeddZeddZed d!Zed"d#Zed$d%Zed&d'Zd(S))raaComplex defines the operations that work on the builtin complex type. In short, those are: a conversion to complex, .real, .imag, +, -, *, /, abs(), .conjugate, ==, and !=. If it is given heterogenous arguments, and doesn't have special knowledge about them, it should fall back to the builtin complex type as described below. cCsdS)zsz Complex.imagcCstdS)z self + otherN)r)rotherrrr__add__GszComplex.__add__cCstdS)z other + selfN)r)rrrrr__radd__LszComplex.__radd__cCstdS)z-selfN)r)rrrr__neg__QszComplex.__neg__cCstdS)z+selfN)r)rrrr__pos__VszComplex.__pos__cCs || S)z self - otherr)rrrrr__sub__[szComplex.__sub__cCs | |S)z other - selfr)rrrrr__rsub___szComplex.__rsub__cCstdS)z self * otherN)r)rrrrr__mul__cszComplex.__mul__cCstdS)z other * selfN)r)rrrrr__rmul__hszComplex.__rmul__cCstdS)z5self / other: Should promote to float when necessary.N)r)rrrrr __truediv__mszComplex.__truediv__cCstdS)z other / selfN)r)rrrrr __rtruediv__rszComplex.__rtruediv__cCstdS)zBself**exponent; should promote to float or complex when necessary.N)r)rexponentrrr__pow__wszComplex.__pow__cCstdS)z base ** selfN)r)rbaserrr__rpow__|szComplex.__rpow__cCstdS)z7Returns the Real distance from 0. Called for abs(self).N)r)rrrr__abs__szComplex.__abs__cCstdS)z$(x+y*i).conjugate() returns (x-y*i).N)r)rrrr conjugateszComplex.conjugatecCstdS)z self == otherN)r)rrrrr__eq__szComplex.__eq__N)r r r r r rrrpropertyrrrrrrrrrr r!r"r$r&r'r(r)rrrrr s.              c@seZdZdZfZeddZeddZeddZedd Z ed%d d Z d dZ ddZ eddZ eddZeddZeddZeddZeddZddZedd Zed!d"Zd#d$Zd S)&rzTo 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. cCstdS)zTAny Real can be converted to a native float object. Called for float(self).N)r)rrrr __float__szReal.__float__cCstdS)aGtrunc(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)rrrr __trunc__s zReal.__trunc__cCstdS)z$Finds the greatest Integral <= self.N)r)rrrr __floor__szReal.__floor__cCstdS)z!Finds the least Integral >= self.N)r)rrrr__ceil__sz Real.__ceil__NcCstdS)zRounds 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)rZndigitsrrr __round__szReal.__round__cCs||||fS)zdivmod(self, other): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. r)rrrrr __divmod__szReal.__divmod__cCs||||fS)zdivmod(other, self): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. r)rrrrr __rdivmod__szReal.__rdivmod__cCstdS)z)self // other: The floor() of self/other.N)r)rrrrr __floordiv__szReal.__floordiv__cCstdS)z)other // self: The floor() of other/self.N)r)rrrrr __rfloordiv__szReal.__rfloordiv__cCstdS)z self % otherN)r)rrrrr__mod__sz Real.__mod__cCstdS)z other % selfN)r)rrrrr__rmod__sz Real.__rmod__cCstdS)zRself < other < on Reals defines a total ordering, except perhaps for NaN.N)r)rrrrr__lt__sz Real.__lt__cCstdS)z self <= otherN)r)rrrrr__le__sz Real.__le__cCs tt|S)z(complex(self) == complex(float(self), 0))complexfloat)rrrrrszReal.__complex__cCs| S)z&Real numbers are their real component.r)rrrrrsz Real.realcCsdS)z)Real numbers have no imaginary component.rr)rrrrrsz Real.imagcCs| S)zConjugate is a no-op for Reals.r)rrrrr(szReal.conjugate)N)r r r r r rr+r,r-r.r/r0r1r2r3r4r5r6r7rr*rrr(rrrrrs(            c@s<eZdZdZfZeeddZeeddZddZ dS) rz6.numerator and .denominator should be in lowest terms.cCstdS)N)r)rrrr numeratorszRational.numeratorcCstdS)N)r)rrrr denominatorszRational.denominatorcCs |j|jS)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;)rrrrr+szRational.__float__N) r r r r r r*rr:r;r+rrrrr sc@seZdZdZfZeddZddZed%ddZed d Z ed d Z ed dZ eddZ eddZ eddZeddZeddZeddZeddZeddZdd Zed!d"Zed#d$ZdS)&rz@Integral adds a conversion to int and the bit-string operations.cCstdS)z int(self)N)r)rrrr__int__+szIntegral.__int__cCst|S)z6Called whenever an index is needed, such as in slicing)int)rrrr __index__0szIntegral.__index__NcCstdS)a4self ** 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)rr#modulusrrrr$4s zIntegral.__pow__cCstdS)z self << otherN)r)rrrrr __lshift__?szIntegral.__lshift__cCstdS)z other << selfN)r)rrrrr __rlshift__DszIntegral.__rlshift__cCstdS)z self >> otherN)r)rrrrr __rshift__IszIntegral.__rshift__cCstdS)z other >> selfN)r)rrrrr __rrshift__NszIntegral.__rrshift__cCstdS)z self & otherN)r)rrrrr__and__SszIntegral.__and__cCstdS)z other & selfN)r)rrrrr__rand__XszIntegral.__rand__cCstdS)z self ^ otherN)r)rrrrr__xor__]szIntegral.__xor__cCstdS)z other ^ selfN)r)rrrrr__rxor__bszIntegral.__rxor__cCstdS)z self | otherN)r)rrrrr__or__gszIntegral.__or__cCstdS)z other | selfN)r)rrrrr__ror__lszIntegral.__ror__cCstdS)z~selfN)r)rrrr __invert__qszIntegral.__invert__cCs tt|S)zfloat(self) == float(int(self)))r9r=)rrrrr+wszIntegral.__float__cCs| S)z"Integers are their own numerators.r)rrrrr:{szIntegral.numeratorcCsdS)z!Integers have a denominator of 1.r)rrrrr;szIntegral.denominator)N)r r r r r rr<r>r$r@rArBrCrDrErFrGrHrIrJr+r*r:r;rrrrr&s(             N)r abcrr__all__rrregisterr8rr9rrr=rrrrsp u _