ï¿½ !A?hl(ï¿½ï¿½.ï¿½dZddlmZmZgdï¿½ZGdï¿½deï¿½ï¿½ï¿½ZGdï¿½deï¿½ï¿½Zeï¿½eï¿½ï¿½Gd ï¿½d eï¿½ï¿½Z e ï¿½e ï¿½ï¿½Gdï¿½de ï¿½ï¿½ZGd ï¿½deï¿½ï¿½Zeï¿½e ï¿½ï¿½dS)z~Abstract Base Classes (ABCs) for numbers, according to PEP 3141. TODO: Fill out more detailed documentation on the operators.ï¿½)ï¿½ABCMetaï¿½abstractmethod)ï¿½Numberï¿½Complexï¿½Realï¿½Rationalï¿½Integralcï¿½ï¿½eZdZdZdZdZdS)rzï¿½All 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). ï¿½N)ï¿½__name__ï¿½ __module__ï¿½__qualname__ï¿½__doc__ï¿½ __slots__ï¿½__hash__rï¿½ï¿½4/opt/alt/python-internal/lib64/python3.11/numbers.pyrrs&ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ ï¿½Iï¿½ï¿½Hï¿½Hï¿½Hrr)ï¿½ metaclasscï¿½ï¿½eZdZdZdZedï¿½ï¿½ï¿½Zdï¿½Zeedï¿½ï¿½ï¿½ï¿½ï¿½Z eedï¿½ï¿½ï¿½ï¿½ï¿½Z edï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zed ï¿½ï¿½ï¿½Z ed ï¿½ï¿½ï¿½Zdï¿½Zdï¿½Zed ï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½ZdS)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. rcï¿½ï¿½dS)zr rcï¿½ï¿½tï¿½)zself + otherrï¿½rï¿½others rï¿½__add__zComplex.__add__Gï¿½ ï¿½ï¿½"ï¿½!rcï¿½ï¿½tï¿½)zother + selfrr$s rï¿½__radd__zComplex.__radd__Lr'rcï¿½ï¿½tï¿½)z-selfrrs rï¿½__neg__zComplex.__neg__Qr'rcï¿½ï¿½tï¿½)z+selfrrs rï¿½__pos__zComplex.__pos__Vr'rcï¿½ï¿½||zS)zself - otherrr$s rï¿½__sub__zComplex.__sub__[sï¿½ï¿½ï¿½uï¿½fï¿½}ï¿½rcï¿½ï¿½||zS)zother - selfrr$s rï¿½__rsub__zComplex.__rsub___sï¿½ï¿½ï¿½uï¿½uï¿½}ï¿½rcï¿½ï¿½tï¿½)zself * otherrr$s rï¿½__mul__zComplex.__mul__cr'rcï¿½ï¿½tï¿½)zother * selfrr$s rï¿½__rmul__zComplex.__rmul__hr'rcï¿½ï¿½tï¿½)z5self / other: Should promote to float when necessary.rr$s rï¿½__truediv__zComplex.__truediv__mr'rcï¿½ï¿½tï¿½)zother / selfrr$s rï¿½__rtruediv__zComplex.__rtruediv__rr'rcï¿½ï¿½tï¿½)zBself**exponent; should promote to float or complex when necessary.r)rï¿½exponents rï¿½__pow__zComplex.__pow__wr'rcï¿½ï¿½tï¿½)zbase ** selfr)rï¿½bases rï¿½__rpow__zComplex.__rpow__|r'rcï¿½ï¿½tï¿½)z7Returns the Real distance from 0. Called for abs(self).rrs rï¿½__abs__zComplex.__abs__ï¿½r'rcï¿½ï¿½tï¿½)z$(x+y*i).conjugate() returns (x-y*i).rrs rï¿½ conjugatezComplex.conjugateï¿½r'rcï¿½ï¿½tï¿½)z self == otherrr$s rï¿½__eq__zComplex.__eq__ï¿½r'rN)rr rrrrrrï¿½propertyrr"r&r)r+r-r/r1r3r5r7r9r<r?rArCrErrrrr sï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½Iï¿½ï¿½Kï¿½Kï¿½ï¿½^ï¿½Kï¿½ï¿½ï¿½ï¿½ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½ï¿½Xï¿½"ï¿½ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½ï¿½Xï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½"ï¿½"rrcï¿½Nï¿½eZdZdZdZedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Z eddï¿½ï¿½ï¿½Z d ï¿½Zd ï¿½Zedï¿½ï¿½ï¿½Z edï¿½ï¿½ï¿½Zed ï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zdï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zdï¿½ZdS)rzï¿½To Complex, Real adds the operations that work on real numbers. In short, those are: a conversion to float, trunc(), divmod, %, <, <=, >, and >=. Real also provides defaults for the derived operations. rcï¿½ï¿½tï¿½)zTAny Real can be converted to a native float object. Called for float(self).rrs rï¿½ __float__zReal.__float__ï¿½ï¿½ ï¿½ï¿½ "ï¿½!rcï¿½ï¿½tï¿½)aGtrunc(self): Truncates self to an Integral. Returns an Integral i such that: * i>0 iff self>0; * abs(i) <= abs(self); * for any Integral j satisfying the first two conditions, abs(i) >= abs(j) [i.e. i has "maximal" abs among those]. i.e. "truncate towards 0". rrs rï¿½ __trunc__zReal.__trunc__ï¿½s ï¿½ï¿½"ï¿½!rcï¿½ï¿½tï¿½)z$Finds the greatest Integral <= self.rrs rï¿½ __floor__zReal.__floor__ï¿½r'rcï¿½ï¿½tï¿½)z!Finds the least Integral >= self.rrs rï¿½__ceil__z Real.__ceil__ï¿½r'rNcï¿½ï¿½tï¿½)zï¿½Rounds 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)rï¿½ndigitss rï¿½ __round__zReal.__round__ï¿½r rcï¿½ï¿½||z||zfS)zï¿½divmod(self, other): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. rr$s rï¿½ __divmod__zReal.__divmod__ï¿½sï¿½ï¿½ï¿½ï¿½ ï¿½tï¿½eï¿½|ï¿½,ï¿½,rcï¿½ï¿½||z||zfS)zï¿½divmod(other, self): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. rr$s rï¿½__rdivmod__zReal.__rdivmod__ï¿½sï¿½ï¿½ï¿½ï¿½ ï¿½uï¿½tï¿½|ï¿½,ï¿½,rcï¿½ï¿½tï¿½)z)self // other: The floor() of self/other.rr$s rï¿½__floordiv__zReal.__floordiv__ï¿½r'rcï¿½ï¿½tï¿½)z)other // self: The floor() of other/self.rr$s rï¿½ __rfloordiv__zReal.__rfloordiv__ï¿½r'rcï¿½ï¿½tï¿½)zself % otherrr$s rï¿½__mod__zReal.__mod__ï¿½r'rcï¿½ï¿½tï¿½)zother % selfrr$s rï¿½__rmod__z Real.__rmod__ï¿½r'rcï¿½ï¿½tï¿½)zRself < other < on Reals defines a total ordering, except perhaps for NaN.rr$s rï¿½__lt__zReal.__lt__ï¿½rJrcï¿½ï¿½tï¿½)z self <= otherrr$s rï¿½__le__zReal.__le__ï¿½r'rcï¿½:ï¿½tt|ï¿½ï¿½ï¿½ï¿½S)z(complex(self) == complex(float(self), 0))ï¿½complexï¿½floatrs rrzReal.__complex__ï¿½sï¿½ï¿½ï¿½uï¿½Tï¿½{ï¿½{ï¿½#ï¿½#ï¿½#rcï¿½ï¿½| S)z&Real numbers are their real component.rrs rrz Real.realï¿½ï¿½ï¿½ï¿½ï¿½uï¿½rcï¿½ï¿½dS)z)Real numbers have no imaginary component.rrrs rr"z Real.imagï¿½ï¿½ ï¿½ï¿½ï¿½qrcï¿½ï¿½| S)zConjugate is a no-op for Reals.rrs rrCzReal.conjugates ï¿½ï¿½ï¿½uï¿½rï¿½N)rr rrrrrIrLrNrPrSrUrWrYr[r]r_rarcrrFrr"rCrrrrrï¿½sï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½Iï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½ "ï¿½ "ï¿½ï¿½^ï¿½ "ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½-ï¿½-ï¿½-ï¿½-ï¿½-ï¿½-ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ $ï¿½$ï¿½$ï¿½ï¿½ï¿½ï¿½ï¿½Xï¿½ï¿½ï¿½ï¿½ï¿½ï¿½Xï¿½ï¿½ï¿½ï¿½ï¿½ï¿½rrcï¿½hï¿½eZdZdZdZeedï¿½ï¿½ï¿½ï¿½ï¿½Zeedï¿½ï¿½ï¿½ï¿½ï¿½Zdï¿½Z dS)rz6.numerator and .denominator should be in lowest terms.rcï¿½ï¿½tï¿½rlrrs rï¿½ numeratorzRational.numeratorr'rcï¿½ï¿½tï¿½rlrrs rï¿½denominatorzRational.denominatorr'rcï¿½Tï¿½t|jï¿½ï¿½t|jï¿½ï¿½zS)afloat(self) = self.numerator / self.denominator It's important that this conversion use the integer's "true" division rather than casting one side to float before dividing so that ratios of huge integers convert without overflowing. )ï¿½introrqrs rrIzRational.__float__s$ï¿½ï¿½ï¿½4ï¿½>ï¿½"ï¿½"ï¿½Sï¿½ï¿½)9ï¿½%:ï¿½%:ï¿½:ï¿½:rN) rr rrrrFrrorqrIrrrrrsvï¿½ï¿½ï¿½ï¿½ï¿½ï¿½@ï¿½@ï¿½ï¿½Iï¿½ ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½ï¿½Xï¿½"ï¿½ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½ï¿½Xï¿½"ï¿½;ï¿½;ï¿½;ï¿½;ï¿½;rrcï¿½nï¿½eZdZdZdZedï¿½ï¿½ï¿½Zdï¿½Zeddï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Z edï¿½ï¿½ï¿½Z ed ï¿½ï¿½ï¿½Zed ï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Z edï¿½ï¿½ï¿½Zed ï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½Zdï¿½Zedï¿½ï¿½ï¿½Zedï¿½ï¿½ï¿½ZdS)r zï¿½Integral adds methods that work on integral numbers. In short, these are conversion to int, pow with modulus, and the bit-string operations. rcï¿½ï¿½tï¿½)z int(self)rrs rï¿½__int__zIntegral.__int__/r'rcï¿½ ï¿½t|ï¿½ï¿½S)z6Called whenever an index is needed, such as in slicing)rsrs rï¿½ __index__zIntegral.__index__4sï¿½ï¿½ï¿½4ï¿½yï¿½yï¿½rNcï¿½ï¿½tï¿½)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;ï¿½moduluss rr<zIntegral.__pow__8s ï¿½ï¿½"ï¿½!rcï¿½ï¿½tï¿½)z self << otherrr$s rï¿½ __lshift__zIntegral.__lshift__Cr'rcï¿½ï¿½tï¿½)z other << selfrr$s rï¿½__rlshift__zIntegral.__rlshift__Hr'rcï¿½ï¿½tï¿½)z self >> otherrr$s rï¿½ __rshift__zIntegral.__rshift__Mr'rcï¿½ï¿½tï¿½)z other >> selfrr$s rï¿½__rrshift__zIntegral.__rrshift__Rr'rcï¿½ï¿½tï¿½)zself & otherrr$s rï¿½__and__zIntegral.__and__Wr'rcï¿½ï¿½tï¿½)zother & selfrr$s rï¿½__rand__zIntegral.__rand__\r'rcï¿½ï¿½tï¿½)zself ^ otherrr$s rï¿½__xor__zIntegral.__xor__ar'rcï¿½ï¿½tï¿½)zother ^ selfrr$s rï¿½__rxor__zIntegral.__rxor__fr'rcï¿½ï¿½tï¿½)zself | otherrr$s rï¿½__or__zIntegral.__or__kr'rcï¿½ï¿½tï¿½)zother | selfrr$s rï¿½__ror__zIntegral.__ror__pr'rcï¿½ï¿½tï¿½)z~selfrrs rï¿½ __invert__zIntegral.__invert__ur'rcï¿½:ï¿½tt|ï¿½ï¿½ï¿½ï¿½S)zfloat(self) == float(int(self)))rfrsrs rrIzIntegral.__float__{sï¿½ï¿½ï¿½Sï¿½ï¿½Yï¿½Yï¿½ï¿½ï¿½rcï¿½ï¿½| S)z"Integers are their own numerators.rrs rrozIntegral.numeratorrhrcï¿½ï¿½dS)z!Integers have a denominator of 1.ï¿½rrs rrqzIntegral.denominatorï¿½rjrrl)rr rrrrrvrxr<r|r~rï¿½rï¿½rï¿½rï¿½rï¿½rï¿½rï¿½rï¿½rï¿½rIrFrorqrrrr r &sï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½Iï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½ï¿½ï¿½ï¿½"ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ï¿½"ï¿½"ï¿½ï¿½^ï¿½"ï¿½ ï¿½ ï¿½ ï¿½ï¿½ï¿½ï¿½ï¿½Xï¿½ï¿½ï¿½ï¿½ï¿½ï¿½Xï¿½ï¿½ï¿½rr N)rï¿½abcrrï¿½__all__rrï¿½registerrerrfrr rsrrrï¿½rï¿½snï¿½ï¿½@ï¿½@ï¿½(ï¿½'ï¿½'ï¿½'ï¿½'ï¿½'ï¿½'ï¿½'ï¿½ ?ï¿½ ?ï¿½ ?ï¿½ï¿½ ï¿½ ï¿½ ï¿½ ï¿½ ï¿½wï¿½ ï¿½ ï¿½ ï¿½ ï¿½(n"ï¿½n"ï¿½n"ï¿½n"ï¿½n"ï¿½fï¿½n"ï¿½n"ï¿½n"ï¿½`ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½sï¿½sï¿½sï¿½sï¿½sï¿½7ï¿½sï¿½sï¿½sï¿½jï¿½ ï¿½ ï¿½eï¿½ï¿½ï¿½ï¿½;ï¿½;ï¿½;ï¿½;ï¿½;ï¿½tï¿½;ï¿½;ï¿½;ï¿½6aï¿½aï¿½aï¿½aï¿½aï¿½xï¿½aï¿½aï¿½aï¿½F ï¿½ï¿½ï¿½#ï¿½ï¿½ï¿½ï¿½ï¿½r