Source code:
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The numbers module (
) defines a hierarchy of numeric
which progressively define more operations. None of the types defined in this module are intended to be instantiated.
classnumbers.Number
The root of the numeric hierarchy. If you just want to check if an argument x is a number, without caring what kind, use isinstance(x,Number).
The numeric tower
classnumbers.Complex
Subclasses of this type describe complex numbers and include the operations that work on the built-in
type. These are: conversions to complex and
,
,
, +, -, *, /, **,
,
, ==, and !=. All except - and != are abstract.
real
Abstract. Retrieves the real component of this number.
imag
Abstract. Retrieves the imaginary component of this number.
abstractmethodconjugate()
Abstract. Returns the complex conjugate. For example, (1+3j).conjugate()==(1-3j).
classnumbers.Real
To
, Real adds the operations that work on real numbers.
In short, those are: a conversion to
,
,
,
,
,
, //, %, <, <=, >, and >=.
Real also provides defaults for
,
,
, and
.
classnumbers.Rational
Subtypes
and adds
and
properties. It also provides a default for
.
The
and
values should be instances of
and should be in lowest terms with denominator positive.
numerator
Abstract. The numerator of this rational number.
denominator
Abstract. The denominator of this rational number.
classnumbers.Integral
Subtypes
and adds a conversion to
. Provides defaults for
,
, and
. Adds abstract methods for
with modulus and bit-string operations: <<, >>, &, ^, |, ~.
Notes for type implementers
Implementers should be careful to make equal numbers equal and hash them to the same values. This may be subtle if there are two different extensions of the real numbers. See also
.
Adding More Numeric ABCs
There are, of course, more possible ABCs for numbers, and this would be a poor hierarchy if it precluded the possibility of adding those. You can add MyFoo between
and
with:
classMyFoo(Complex):...MyFoo.register(Real)Implementing the arithmetic operations
We want to implement the arithmetic operations so that mixed-mode operations either call an implementation whose author knew about the types of both arguments, or convert both to the nearest built in type and do the operation there. For subtypes of
, this means that
and
should be defined as:
classMyIntegral(Integral):def__add__(self,other):ifisinstance(other,MyIntegral):returndo_my_adding_stuff(self,other)elifisinstance(other,OtherTypeIKnowAbout):returndo_my_other_adding_stuff(self,other)else:returnNotImplementeddef__radd__(self,other):ifisinstance(other,MyIntegral):returndo_my_adding_stuff(other,self)elifisinstance(other,OtherTypeIKnowAbout):returndo_my_other_adding_stuff(other,self)elifisinstance(other,Integral):returnint(other)+int(self)elifisinstance(other,Real):returnfloat(other)+float(self)elifisinstance(other,Complex):returncomplex(other)+complex(self)else:returnNotImplementedThere are 5 different cases for a mixed-type operation on subclasses of
. I’ll refer to all of the above code that doesn’t refer to MyIntegral and OtherTypeIKnowAbout as “boilerplate”. a will be an instance of A, which is a subtype of Complex (a:A<:Complex), and b:B<:Complex. I’ll consider a+b:
If A defines an
which accepts b, all is well.
If A falls back to the boilerplate code, and it were to return a value from
, we’d miss the possibility that B defines a more intelligent
, so the boilerplate should return
from __add__(). (Or A may not implement __add__() at all.)
Then B’s
gets a chance. If it accepts a, all is well.
If it falls back to the boilerplate, there are no more possible methods to try, so this is where the default implementation should live.
If B<:A, Python tries B.__radd__ before A.__add__. This is ok, because it was implemented with knowledge of A, so it can handle those instances before delegating to
.
If A<:Complex and B<:Real without sharing any other knowledge, then the appropriate shared operation is the one involving the built in
, and both
s land there, so a+b==b+a.
Because most of the operations on any given type will be very similar, it can be useful to define a helper function which generates the forward and reverse instances of any given operator. For example,
uses:
def_operator_fallbacks(monomorphic_operator,fallback_operator):defforward(a,b):ifisinstance(b,(int,Fraction)):returnmonomorphic_operator(a,b)elifisinstance(b,float):returnfallback_operator(float(a),b)elifisinstance(b,complex):returnfallback_operator(complex(a),b)else:returnNotImplementedforward.__name__='__'+fallback_operator.__name__+'__'forward.__doc__=monomorphic_operator.__doc__defreverse(b,a):ifisinstance(a,Rational):# Includes ints.returnmonomorphic_operator(a,b)elifisinstance(a,Real):returnfallback_operator(float(a),float(b))elifisinstance(a,Complex):returnfallback_operator(complex(a),complex(b))else:returnNotImplementedreverse.__name__='__r'+fallback_operator.__name__+'__'reverse.__doc__=monomorphic_operator.__doc__returnforward,reversedef_add(a,b):"""a + b"""returnFraction(a.numerator*b.denominator+b.numerator*a.denominator,a.denominator*b.denominator)__add__,__radd__=_operator_fallbacks(_add,operator.add)# ...