numbers — Numeric abstract base classes

Código fuente: Lib/numbers.py

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 are intended to be instantiated.

class numbers.Number

La raíz de la jerarquía numérica. Si desea validar si un argumento x es un número, sin importar su tipo, use isinstance(x, Number).

La torre numérica

class numbers.Complex

Las subclases de este tipo describen números complejos e incluyen las operaciones que funcionan en el tipo complex integrado. Estos son: conversiones a complex y bool, real, imag, +, -, *, /, **, abs(), conjugate(), == y !=. Todos excepto - y != son abstractos.

real

Abstracto. Recupera el componente real de este número.

imag

Abstracto. Recupera el componente imaginario de este número.

abstractmethod conjugate()

Abstracto. Retorna el complejo conjugado. Por ejemplo, (1+3j).conjugate() == (1-3j).

class numbers.Real

To Complex, Real adds the operations that work on real numbers.

En resumen, estos son: conversiones a float, math.trunc(), round(), math.floor(), math.ceil(), divmod(), //, %, <, <=, >, y >=.

Real también proporciona valores predeterminados para complex(), real, imag, y conjugate().

class numbers.Rational

Subtipos Real y agrega propiedades de numerator y denominator. También proporciona un valor predeterminado para float().

Los valores del numerator y del denominator deben ser instancias de Integral y deben estar en términos mínimos con denominator positivo.

numerator

Abstract. The numerator of this rational number.

denominator

Abstract. The denominator of this rational number.

class numbers.Integral

Subtipos Rational y agrega una conversión a int. Proporciona valores predeterminados para float(), numerator y denominator. Agrega métodos abstractos para pow() con operaciones de módulo y cadena de bits: <<, >>, &, ^, |, ~.

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 Hashing of numeric types.

Adding more numeric ABCs

Por supuesto, hay más ABCs posibles para los números, y esto sería una jerarquía deficiente si se excluye la posibilidad de añadirlos. Puede usar MyFoo entre Complex y Real así:

class MyFoo(Complex): ...
MyFoo.register(Real)

Implementar operaciones aritméticas

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. All of the above code that doesn’t refer to MyIntegral and OtherTypeIKnowAbout is referred to as «boilerplate».

In this description, a is an instance of A and b is an instance of B, where A and B are both subtypes of Complex. Consider a + b:

  1. If A defines an __add__() which accepts b, all is well.

  2. If A falls back to the boilerplate code, and it were to return a value from __add__(), we’d miss the possibility that B defines a more intelligent __radd__(), so the boilerplate should return NotImplemented from __add__(). (Or A may not implement __add__() at all.)

  3. Then B’s __radd__() gets a chance. If it accepts a, all is well.

  4. Si se vuelve a caer en el código repetitivo, no hay más posibles métodos para probar, por lo que acá debería vivir la implementación predeterminada.

  5. If B is a subtype of 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 Complex.

If A is a subtype of Complex and B is a subtype of 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.

Dado que la mayoría de las operaciones en un tipo determinado serán muy similares, puede ser útil definir una función auxiliar que genere las instancias forward y reverse de cualquier operador dado. Por ejemplo, fractions.Fraction así:

def _operator_fallbacks(monomorphic_operator, fallback_operator):
    def forward(a, b):
        if isinstance(b, (int, 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, Real):
            return fallback_operator(float(a), float(b))
        elif isinstance(a, 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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