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o il( @ s d Z ddlmZmZ g dZG dd dedZG dd deZee G d d d eZ e e G d d d e Z G d d de 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 @ s e Zd ZdZdZdZdS )r zAll 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 s r ) metaclassc @ s e Zd ZdZdZedd Zdd Zeedd Z eed d Z ed d Z ed d Z edd Z edd Zdd Zdd Zedd Zedd Zedd Zed d Zed d Zed!d" Zed#d$ Zed%d& Zed'd( Zd)S )*r af 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 heterogeneous arguments, and doesn't have special knowledge about them, it should fall back to the builtin complex type as described below. r c C dS )z<Return a builtin complex instance. Called for complex(self).Nr selfr r r __complex__- s zComplex.__complex__c C s | dkS )z)True if self != 0. Called for bool(self).r r r r r r __bool__1 zComplex.__bool__c C t )zXRetrieve the real component of this number. This should subclass Real. NotImplementedErrorr r r r real5 z Complex.realc C r )z]Retrieve the imaginary component of this number. This should subclass Real. r r r r r imag> r z Complex.imagc C r )z self + otherr r otherr r r __add__G zComplex.__add__c C r )z other + selfr r r r r __radd__L r! zComplex.__radd__c C r )z-selfr r r r r __neg__Q r! zComplex.__neg__c C r )z+selfr r r r r __pos__V r! zComplex.__pos__c C s | | S )z self - otherr r r r r __sub__[ zComplex.__sub__c C s | | S )z other - selfr r r r r __rsub___ r& zComplex.__rsub__c C r )z self * otherr r r r r __mul__c r! zComplex.__mul__c C r )z other * selfr r r r r __rmul__h r! zComplex.__rmul__c C r )z5self / other: Should promote to float when necessary.r r r r r __truediv__m r! zComplex.__truediv__c C r )z other / selfr r r r r __rtruediv__r r! zComplex.__rtruediv__c C r )zBself**exponent; should promote to float or complex when necessary.r )r exponentr r r __pow__w r! zComplex.__pow__c C r )z base ** selfr )r baser r r __rpow__| r! zComplex.__rpow__c C r )z7Returns the Real distance from 0. Called for abs(self).r r r r r __abs__ r! zComplex.__abs__c C r )z$(x+y*i).conjugate() returns (x-y*i).r r r r r conjugate r! zComplex.conjugatec C r )z self == otherr r r r r __eq__ r! zComplex.__eq__N)r r r r r r r r propertyr r r r" r# r$ r% r' r( r) r* r+ r- r/ r0 r1 r2 r r r r r sP r c @ s e Zd ZdZdZedd Zedd Zedd Zed d Z ed&d d Z dd Z dd Z edd Z edd Zedd Zedd Zedd Zed d Zd d Zed d! Zed"d# Zd$d% Zd S )'r zTo Complex, Real adds the operations that work on real numbers. In short, those are: a conversion to float, trunc(), divmod, %, <, <=, >, and >=. Real also provides defaults for the derived operations. r c C r )zTAny Real can be converted to a native float object. Called for float(self).r r r r r __float__ zReal.__float__c C r )aG trunc(self): Truncates self to an Integral. Returns an Integral i such that: * i>0 iff self>0; * abs(i) <= abs(self); * for any Integral j satisfying the first two conditions, abs(i) >= abs(j) [i.e. i has "maximal" abs among those]. i.e. "truncate towards 0". r r r r r __trunc__ s zReal.__trunc__c C r )z$Finds the greatest Integral <= self.r r r r r __floor__ r! zReal.__floor__c C r )z!Finds the least Integral >= self.r r r r r __ceil__ r! z Real.__ceil__Nc C r )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 )r ndigitsr r r __round__ r zReal.__round__c C s | | | | fS )zdivmod(self, other): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. r r r r r __divmod__ zReal.__divmod__c C s || || fS )zdivmod(other, self): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. r r r r r __rdivmod__ r< zReal.__rdivmod__c C r )z)self // other: The floor() of self/other.r r r r r __floordiv__ r! zReal.__floordiv__c C r )z)other // self: The floor() of other/self.r r r r r __rfloordiv__ r! zReal.__rfloordiv__c C r )z self % otherr r r r r __mod__ r! z Real.__mod__c C r )z other % selfr r r r r __rmod__ r! z Real.__rmod__c C r )zRself < other < on Reals defines a total ordering, except perhaps for NaN.r r r r r __lt__ r5 z Real.__lt__c C r )z self <= otherr r r r r __le__ r! z Real.__le__c C t t| S )z(complex(self) == complex(float(self), 0))complexfloatr r r r r zReal.__complex__c C | S )z&Real numbers are their real component.r r r r r r z Real.realc C r )z)Real numbers have no imaginary component.r r r r r r r r! z Real.imagc C rH )z Conjugate is a no-op for Reals.r r r r r r1 s zReal.conjugateN)r r r r r r r4 r6 r7 r8 r: r; r= r> r? r@ rA rB rC r r3 r r r1 r r r r r sB r c @ s< e Zd ZdZdZeedd Zeedd Zdd Z d S ) r z6.numerator and .denominator should be in lowest terms.r c C r rJ r r r r r numerator r! zRational.numeratorc C r rJ r r r r r denominator r! zRational.denominatorc C s t | jt | j S )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. )intrK rL r r r r r4 s zRational.__float__N) r r r r r r3 r rK rL r4 r r r r r s r c @ s e Zd ZdZdZedd Zdd Zed&dd Zed d Z ed d Z edd Z edd Z edd Z edd Zedd Zedd Zedd Zed d Zed d Zd d! Zed"d# Zed$d% ZdS )'r zIntegral adds methods that work on integral numbers. In short, these are conversion to int, pow with modulus, and the bit-string operations. r c C r )z int(self)r r r r r __int__/ r! zIntegral.__int__c C s t | S )z6Called whenever an index is needed, such as in slicing)rM r r r r __index__4 r zIntegral.__index__Nc C r )a4 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. r )r r, modulusr r r r- 8 s zIntegral.__pow__c C r )z self << otherr r r r r __lshift__C r! zIntegral.__lshift__c C r )z other << selfr r r r r __rlshift__H r! zIntegral.__rlshift__c C r )z self >> otherr r r r r __rshift__M r! zIntegral.__rshift__c C r )z other >> selfr r r r r __rrshift__R r! zIntegral.__rrshift__c C r )z self & otherr r r r r __and__W r! zIntegral.__and__c C r )z other & selfr r r r r __rand__\ r! zIntegral.__rand__c C r )z self ^ otherr r r r r __xor__a r! zIntegral.__xor__c C r )z other ^ selfr r r r r __rxor__f r! zIntegral.__rxor__c C r )z self | otherr r r r r __or__k r! zIntegral.__or__c C r )z other | selfr r r r r __ror__p r! zIntegral.__ror__c C r )z~selfr r r r r __invert__u r! zIntegral.__invert__c C rD )z float(self) == float(int(self)))rF rM r r r r r4 { rG zIntegral.__float__c C rH )z"Integers are their own numerators.r r r r r rK rI zIntegral.numeratorc C r )z!Integers have a denominator of 1. r r r r r rL r! zIntegral.denominatorrJ )r r r r r r rN rO r- rQ rR rS rT rU rV rW rX rY rZ r[ r4 r3 rK rL r r r r r & sF r N)r abcr r __all__r r registerrE r rF r r rM r r r r <module> s p uc