numbers — Numeric abstract base classes¶New in version 2.6. The numbers module (PEP 3141) defines a hierarchy of numeric abstract base classes which progressively define more operations. None of the types defined in this module can be instantiated.
The numeric tower¶
Notes for type implementors¶Implementors 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. For example, fractions.Fraction implements hash() as follows: def __hash__(self):
if self.denominator == 1:
# Get integers right.
return hash(self.numerator)
# Expensive check, but definitely correct.
if self == float(self):
return hash(float(self))
else:
# Use tuple's hash to avoid a high collision rate on
# simple fractions.
return hash((self.numerator, self.denominator))
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 Complex and Real with: class MyFoo(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 Integral, this means that __add__() and __radd__() should be defined as: class MyIntegral(Integral):
def __add__(self, other):
if isinstance(other, MyIntegral):
return do_my_adding_stuff(self, other)
elif isinstance(other, OtherTypeIKnowAbout):
return do_my_other_adding_stuff(self, other)
else:
return NotImplemented
def __radd__(self, other):
if isinstance(other, MyIntegral):
return do_my_adding_stuff(other, self)
elif isinstance(other, OtherTypeIKnowAbout):
return do_my_other_adding_stuff(other, self)
elif isinstance(other, Integral):
return int(other) + int(self)
elif isinstance(other, Real):
return float(other) + float(self)
elif isinstance(other, Complex):
return complex(other) + complex(self)
else:
return NotImplemented
There are 5 different cases for a mixed-type operation on subclasses of Complex. 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<:Complex and B<:Real without sharing any other knowledge, then the appropriate shared operation is the one involving the built in complex, and both __radd__() 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, fractions.Fraction uses: def _operator_fallbacks(monomorphic_operator, fallback_operator):
def forward(a, b):
if isinstance(b, (int, long, Fraction)):
return monomorphic_operator(a, b)
elif isinstance(b, float):
return fallback_operator(float(a), b)
elif isinstance(b, complex):
return fallback_operator(complex(a), b)
else:
return NotImplemented
forward.__name__ = '__' + fallback_operator.__name__ + '__'
forward.__doc__ = monomorphic_operator.__doc__
def reverse(b, a):
if isinstance(a, Rational):
# Includes ints.
return monomorphic_operator(a, b)
elif isinstance(a, numbers.Real):
return fallback_operator(float(a), float(b))
elif isinstance(a, numbers.Complex):
return fallback_operator(complex(a), complex(b))
else:
return NotImplemented
reverse.__name__ = '__r' + fallback_operator.__name__ + '__'
reverse.__doc__ = monomorphic_operator.__doc__
return forward, reverse
def _add(a, b):
"""a + b"""
return Fraction(a.numerator * b.denominator +
b.numerator * a.denominator,
a.denominator * b.denominator)
__add__, __radd__ = _operator_fallbacks(_add, operator.add)
# ...
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