o fl(@sdZddlmZmZgdZGdddedZGdddeZeeGd d d eZ e e Gd d d e Z Gd dde Z e e dS)z~Abstract Base Classes (ABCs) for numbers, according to PEP 3141. TODO: Fill out more detailed documentation on the operators.)ABCMetaabstractmethod)NumberComplexRealRationalIntegralc@seZdZdZdZdZdS)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__r r r /usr/lib/python3.10/numbers.pyr sr) metaclassc@seZdZdZdZeddZddZeeddZ eed d Z ed d Z ed dZ eddZ eddZddZddZeddZeddZeddZeddZedd Zed!d"Zed#d$Zed%d&Zed'd(Zd)S)*rafComplex defines the operations that work on the builtin complex type. In short, those are: a conversion to complex, .real, .imag, +, -, *, /, **, abs(), .conjugate, ==, and !=. If it is given heterogeneous arguments, and doesn't have special knowledge about them, it should fall back to the builtin complex type as described below. r cCdS)zrz Complex.imagcCr)z self + otherrrotherr r r__add__GzComplex.__add__cCr)z other + selfrrr r r__radd__Lr!zComplex.__radd__cCr)z-selfrrr r r__neg__Qr!zComplex.__neg__cCr)z+selfrrr r r__pos__Vr!zComplex.__pos__cCs || S)z self - otherr rr r r__sub__[ zComplex.__sub__cCs | |S)z other - selfr rr r r__rsub___r&zComplex.__rsub__cCr)z self * otherrrr r r__mul__cr!zComplex.__mul__cCr)z other * selfrrr r r__rmul__hr!zComplex.__rmul__cCr)z5self / other: Should promote to float when necessary.rrr r r __truediv__mr!zComplex.__truediv__cCr)z other / selfrrr r r __rtruediv__rr!zComplex.__rtruediv__cCr)zBself**exponent; should promote to float or complex when necessary.r)rexponentr r r__pow__wr!zComplex.__pow__cCr)z base ** selfr)rbaser r r__rpow__|r!zComplex.__rpow__cCr)z7Returns the Real distance from 0. Called for abs(self).rrr r r__abs__r!zComplex.__abs__cCr)z$(x+y*i).conjugate() returns (x-y*i).rrr r r conjugater!zComplex.conjugatecCr)z self == otherrrr r r__eq__r!zComplex.__eq__N)r r r r rrrrpropertyrrr r"r#r$r%r'r(r)r*r+r-r/r0r1r2r r r rr sP                rc@seZdZdZdZeddZeddZeddZed d Z ed&d d Z ddZ ddZ eddZ eddZeddZeddZeddZeddZddZed d!Zed"d#Zd$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. r cCr)zTAny Real can be converted to a native float object. Called for float(self).rrr r r __float__zReal.__float__cCr)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". rrr r r __trunc__s zReal.__trunc__cCr)z$Finds the greatest Integral <= self.rrr r r __floor__r!zReal.__floor__cCr)z!Finds the least Integral >= self.rrr r r__ceil__r!z Real.__ceil__NcCr)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. r)rndigitsr r r __round__rzReal.__round__cCs||||fS)zdivmod(self, other): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. r rr r r __divmod__zReal.__divmod__cCs||||fS)zdivmod(other, self): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. r rr r r __rdivmod__r<zReal.__rdivmod__cCr)z)self // other: The floor() of self/other.rrr r r __floordiv__r!zReal.__floordiv__cCr)z)other // self: The floor() of other/self.rrr r r __rfloordiv__r!zReal.__rfloordiv__cCr)z self % otherrrr r r__mod__r!z Real.__mod__cCr)z other % selfrrr r r__rmod__r!z Real.__rmod__cCr)zRself < other < on Reals defines a total ordering, except perhaps for NaN.rrr r r__lt__r5z Real.__lt__cCr)z self <= otherrrr r r__le__r!z Real.__le__cC tt|S)z(complex(self) == complex(float(self), 0))complexfloatrr r rr zReal.__complex__cC| S)z&Real numbers are their real component.r rr r rrz Real.realcCr)z)Real numbers have no imaginary component.rr rr r rrr!z Real.imagcCrH)zConjugate is a no-op for Reals.r rr r rr1szReal.conjugateN)r r r r rrr4r6r7r8r:r;r=r>r?r@rArBrCrr3rrr1r r r rrsB              rc@s<eZdZdZdZeeddZeeddZddZ d S) rz6.numerator and .denominator should be in lowest terms.r cCrrJrrr r r numeratorr!zRational.numeratorcCrrJrrr r r denominatorr!zRational.denominatorcCst|jt|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. )intrKrLrr r rr4szRational.__float__N) r r r r rr3rrKrLr4r r r rr s   rc@seZdZdZdZeddZddZed&dd Zed d Z ed d Z eddZ eddZ eddZ eddZeddZeddZeddZeddZeddZd d!Zed"d#Zed$d%ZdS)'rzIntegral adds methods that work on integral numbers. In short, these are conversion to int, pow with modulus, and the bit-string operations. r cCr)z int(self)rrr r r__int__/r!zIntegral.__int__cCst|S)z6Called whenever an index is needed, such as in slicing)rMrr r r __index__4rzIntegral.__index__NcCr)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. r)rr,modulusr r rr-8s zIntegral.__pow__cCr)z self << otherrrr r r __lshift__Cr!zIntegral.__lshift__cCr)z other << selfrrr r r __rlshift__Hr!zIntegral.__rlshift__cCr)z self >> otherrrr r r __rshift__Mr!zIntegral.__rshift__cCr)z other >> selfrrr r r __rrshift__Rr!zIntegral.__rrshift__cCr)z self & otherrrr r r__and__Wr!zIntegral.__and__cCr)z other & selfrrr r r__rand__\r!zIntegral.__rand__cCr)z self ^ otherrrr r r__xor__ar!zIntegral.__xor__cCr)z other ^ selfrrr r r__rxor__fr!zIntegral.__rxor__cCr)z self | otherrrr r r__or__kr!zIntegral.__or__cCr)z other | selfrrr r r__ror__pr!zIntegral.__ror__cCr)z~selfrrr r r __invert__ur!zIntegral.__invert__cCrD)zfloat(self) == float(int(self)))rFrMrr r rr4{rGzIntegral.__float__cCrH)z"Integers are their own numerators.r rr r rrKrIzIntegral.numeratorcCr)z!Integers have a denominator of 1.r rr r rrLr!zIntegral.denominatorrJ)r r r r rrrNrOr-rQrRrSrTrUrVrWrXrYrZr[r4r3rKrLr r r rr&sF              rN)r abcrr__all__rrregisterrErrFrrrMr r r rs p uc