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a DOgb( @ 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/lib64/python3.9/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 s 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 s zComplex.__bool__c C s t dS )zXRetrieve the real component of this number. This should subclass Real. NNotImplementedErrorr r r r real5 s z Complex.realc C s t dS )z]Retrieve the imaginary component of this number. This should subclass Real. Nr r r r r imag> s z Complex.imagc C s t dS )z self + otherNr r otherr r r __add__G s zComplex.__add__c C s t dS )z other + selfNr r r r r __radd__L s zComplex.__radd__c C s t dS )z-selfNr r r r r __neg__Q s zComplex.__neg__c C s t dS )z+selfNr r r r r __pos__V s zComplex.__pos__c C s | | S )z self - otherr r r r r __sub__[ s zComplex.__sub__c C s | | S )z other - selfr r r r r __rsub___ s zComplex.__rsub__c C s t dS )z self * otherNr r r r r __mul__c s zComplex.__mul__c C s t dS )z other * selfNr r r r r __rmul__h s zComplex.__rmul__c C s t dS )z5self / other: Should promote to float when necessary.Nr r r r r __truediv__m s zComplex.__truediv__c C s t dS )z other / selfNr r r r r __rtruediv__r s zComplex.__rtruediv__c C s t dS )zBself**exponent; should promote to float or complex when necessary.Nr )r exponentr r r __pow__w s zComplex.__pow__c C s t dS )z base ** selfNr )r baser r r __rpow__| s zComplex.__rpow__c C s t dS )z7Returns the Real distance from 0. Called for abs(self).Nr r r r r __abs__ s zComplex.__abs__c C s t dS )z$(x+y*i).conjugate() returns (x-y*i).Nr r r r r conjugate s zComplex.conjugatec C s t dS )z self == otherNr r r r r __eq__ s zComplex.__eq__N)r r r r r r r r propertyr r r r r r r r! r" r# r$ r% r' r) r* r+ r, r r r r r sN 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$d% Zd S )'r zTo Complex, Real adds the operations that work on real numbers. In short, those are: a conversion to float, trunc(), divmod, %, <, <=, >, and >=. Real also provides defaults for the derived operations. r c C s t dS )zTAny Real can be converted to a native float object. Called for float(self).Nr r r r r __float__ s zReal.__float__c C s t dS )aG trunc(self): Truncates self to an Integral. Returns an Integral i such that: * i>0 iff self>0; * abs(i) <= abs(self); * for any Integral j satisfying the first two conditions, abs(i) >= abs(j) [i.e. i has "maximal" abs among those]. i.e. "truncate towards 0". Nr r r r r __trunc__ s zReal.__trunc__c C s t dS )z$Finds the greatest Integral <= self.Nr r r r r __floor__ s zReal.__floor__c C s t dS )z!Finds the least Integral >= self.Nr r r r r __ceil__ s z Real.__ceil__Nc C s t dS )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. Nr )r ndigitsr r r __round__ s 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__ s 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__ s zReal.__rdivmod__c C s t dS )z)self // other: The floor() of self/other.Nr r r r r __floordiv__ s zReal.__floordiv__c C s t dS )z)other // self: The floor() of other/self.Nr r r r r __rfloordiv__ s zReal.__rfloordiv__c C s t dS )z self % otherNr r r r r __mod__ s z Real.__mod__c C s t dS )z other % selfNr r r r r __rmod__ s z Real.__rmod__c C s t dS )zRself < other < on Reals defines a total ordering, except perhaps for NaN.Nr r r r r __lt__ s z Real.__lt__c C s t dS )z self <= otherNr r r r r __le__ s z Real.__le__c C s t t| S )z(complex(self) == complex(float(self), 0))complexfloatr r r r r s zReal.__complex__c C s | S )z&Real numbers are their real component.r r r r r r s z Real.realc C s dS )z)Real numbers have no imaginary component.r r r r r r r s z Real.imagc C s | S )z Conjugate is a no-op for Reals.r r r r r r+ s zReal.conjugate)N)r r r r r r r. r/ r0 r1 r3 r4 r5 r6 r7 r8 r9 r: r; r r- r r r+ r r r r r s@ r c @ s< e Zd ZdZdZeedd Zeedd Zdd Z d S ) r z6.numerator and .denominator should be in lowest terms.r c C s t d S Nr r r r r numerator s zRational.numeratorc C s t d S r> r r r r r denominator s zRational.denominatorc C s | j | 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. )r? r@ r r r r r. s zRational.__float__N) r r r r r r- r r? r@ r. 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 s t dS )z int(self)Nr r r r r __int__/ s zIntegral.__int__c C s t | S )z6Called whenever an index is needed, such as in slicing)intr r r r __index__4 s zIntegral.__index__Nc C s t dS )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. Nr )r r& modulusr r r r' 8 s zIntegral.__pow__c C s t dS )z self << otherNr r r r r __lshift__C s zIntegral.__lshift__c C s t dS )z other << selfNr r r r r __rlshift__H s zIntegral.__rlshift__c C s t dS )z self >> otherNr r r r r __rshift__M s zIntegral.__rshift__c C s t dS )z other >> selfNr r r r r __rrshift__R s zIntegral.__rrshift__c C s t dS )z self & otherNr r r r r __and__W s zIntegral.__and__c C s t dS )z other & selfNr r r r r __rand__\ s zIntegral.__rand__c C s t dS )z self ^ otherNr r r r r __xor__a s zIntegral.__xor__c C s t dS )z other ^ selfNr r r r r __rxor__f s zIntegral.__rxor__c C s t dS )z self | otherNr r r r r __or__k s zIntegral.__or__c C s t dS )z other | selfNr r r r r __ror__p s zIntegral.__ror__c C s t dS )z~selfNr r r r r __invert__u s zIntegral.__invert__c C s t t| S )z float(self) == float(int(self)))r= rB r r r r r. { s zIntegral.__float__c C s | S )z"Integers are their own numerators.r r r r r r? s zIntegral.numeratorc C s dS )z!Integers have a denominator of 1. r r r r r r@ s zIntegral.denominator)N)r r r r r r rA rC r' rE rF rG rH rI rJ rK rL rM rN rO r. r- r? r@ r r r r r & sD r N)r abcr r __all__r r registerr< r r= r r rB r r r r <module> s p u c