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lY( @ s d Z d d l m Z m Z d d d d d g Z Gd d d d e Z Gd
d d e Z e j e Gd d d e Z e j e
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d S)z~Abstract Base Classes (ABCs) for numbers, according to PEP 3141.
TODO: Fill out more detailed documentation on the operators. )ABCMetaabstractmethodNumberComplexRealRationalIntegralc @ s" e Z d Z d Z f Z d Z d S)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 &/opt/python35/lib/python3.5/numbers.pyr s metaclassc @ sl e Z d Z d Z f Z e d d Z d d Z e e d d Z e e d d Z
e d
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e d d Z d d Z d d Z e d d Z e d d Z e d d Z e d d Z e d d Z e d d! Z e d" d# Z e d$ d% Z e d& d' Z d( S))r aa 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 heterogenous arguments, and doesn't have special
knowledge about them, it should fall back to the builtin complex
type as described below.
c C s d S)z s z Complex.imagc C s
t d S)z self + otherN)r )r otherr r r __add__G s zComplex.__add__c C s
t d S)z other + selfN)r )r r r r r __radd__L s zComplex.__radd__c C s
t d S)z-selfN)r )r r r r __neg__Q s zComplex.__neg__c C s
t d S)z+selfN)r )r r r r __pos__V s zComplex.__pos__c C s | | S)z self - otherr )r r r r r __sub__[ s zComplex.__sub__c C s | | S)z other - selfr )r r r r r __rsub___ s zComplex.__rsub__c C s
t d S)z self * otherN)r )r r r r r __mul__c s zComplex.__mul__c C s
t d S)z other * selfN)r )r r r r r __rmul__h s zComplex.__rmul__c C s
t d S)z5self / other: Should promote to float when necessary.N)r )r r r r r __truediv__m s zComplex.__truediv__c C s
t d S)z other / selfN)r )r r r r r __rtruediv__r s zComplex.__rtruediv__c C s
t d S)zBself**exponent; should promote to float or complex when necessary.N)r )r exponentr r r __pow__w s zComplex.__pow__c C s
t d S)z base ** selfN)r )r baser r r __rpow__| s zComplex.__rpow__c C s
t d S)z7Returns the Real distance from 0. Called for abs(self).N)r )r r r r __abs__ s zComplex.__abs__c C s
t d S)z$(x+y*i).conjugate() returns (x-y*i).N)r )r r r r conjugate s zComplex.conjugatec C s
t d S)z
self == otherN)r )r r r r r __eq__ s zComplex.__eq__N)r r
r r r
r r r propertyr r r r r r r r r r r! r" r$ r& r' r( r) r r r r r s. c @ s9 e Z d Z d Z f Z e d d Z e d d Z e d d Z e d d Z e d
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e d d Z e d d Z e d d Z e d d Z e d d Z d d Z e d d Z e d! d" Z d# d$ Z d
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.
c C s
t d S)zTAny Real can be converted to a native float object.
Called for float(self).N)r )r r r r __float__ s zReal.__float__c C s
t d S)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".
N)r )r r r r __trunc__ s zReal.__trunc__c C s
t d S)z$Finds the greatest Integral <= self.N)r )r r r r __floor__ s zReal.__floor__c C s
t d S)z!Finds the least Integral >= self.N)r )r r r r __ceil__ s z
Real.__ceil__Nc C s
t d S)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 )r Zndigitsr r r __round__ s zReal.__round__c C s | | | | f S)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 r
__divmod__ s zReal.__divmod__c C s | | | | f S)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 r __rdivmod__ s zReal.__rdivmod__c C s
t d S)z)self // other: The floor() of self/other.N)r )r r r r r __floordiv__ s zReal.__floordiv__c C s
t d S)z)other // self: The floor() of other/self.N)r )r r r r r
__rfloordiv__ s zReal.__rfloordiv__c C s
t d S)z self % otherN)r )r r r r r __mod__ s z Real.__mod__c C s
t d S)z other % selfN)r )r r r r r __rmod__ s z
Real.__rmod__c C s
t d S)zRself < other
< on Reals defines a total ordering, except perhaps for NaN.N)r )r r r r r __lt__ s z Real.__lt__c C s
t d S)z
self <= otherN)r )r r r r r __le__ s z Real.__le__c C s t t | S)z(complex(self) == complex(float(self), 0))complexfloat)r 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 d S)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)r r
r r r
r r+ r, r- r. r/ r0 r1 r2 r3 r4 r5 r6 r7 r r* r r r( r r r r r s(
c @ sX e Z d Z d Z f Z e e d d Z e e d d Z d d Z d S) r z6.numerator and .denominator should be in lowest terms.c C s
t d S)N)r )r r r r numerator s zRational.numeratorc C s
t d S)N)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 c @ sE e Z d Z d Z f Z e d d Z d d Z e d d d Z e d d
Z e d d Z
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e d d Z e d d Z e d d Z e d d Z e d d Z e d d Z d d Z e d! d" Z e d# d$ Z d S)%r z@Integral adds a conversion to int and the bit-string operations.c C s
t d S)z int(self)N)r )r r r r __int__+ s zIntegral.__int__c C s
t | S)z6Called whenever an index is needed, such as in slicing)int)r r r r __index__0 s zIntegral.__index__Nc C s
t d S)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.
N)r )r r# modulusr r r r$ 4 s zIntegral.__pow__c C s
t d S)z
self << otherN)r )r r r r r
__lshift__? s zIntegral.__lshift__c C s
t d S)z
other << selfN)r )r r r r r __rlshift__D s zIntegral.__rlshift__c C s
t d S)z
self >> otherN)r )r r r r r
__rshift__I s zIntegral.__rshift__c C s
t d S)z
other >> selfN)r )r r r r r __rrshift__N s zIntegral.__rrshift__c C s
t d S)z self & otherN)r )r r r r r __and__S s zIntegral.__and__c C s
t d S)z other & selfN)r )r r r r r __rand__X s zIntegral.__rand__c C s
t d S)z self ^ otherN)r )r r r r r __xor__] s zIntegral.__xor__c C s
t d S)z other ^ selfN)r )r r r r r __rxor__b s zIntegral.__rxor__c C s
t d S)z self | otherN)r )r r r r r __or__g s zIntegral.__or__c C s
t d S)z other | selfN)r )r r r r r __ror__l s zIntegral.__ror__c C s
t d S)z~selfN)r )r r r r
__invert__q s zIntegral.__invert__c C s t t | S)z float(self) == float(int(self)))r9 r= )r r r r r+ w s zIntegral.__float__c C s |
S)z"Integers are their own numerators.r )r r r r r: { s zIntegral.numeratorc C s d S)z!Integers have a denominator of 1. r )r r r r r; s zIntegral.denominator)r r
r r r
r r< r> r$ r@ rA rB rC rD rE rF rG rH rI rJ r+ r* r: r; r r r r r & s(
N)r abcr r __all__r r registerr8 r r9 r r r= r r r r s p
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