numbers --- 数字的抽象基类

源代码： Lib/numbers.py

---

numbers 模块 (PEP 3141) 定义了数字 抽象基类 的层次结构，其中逐级定义了更多操作。 此模块中所定义的类型都不可被实例化。

class numbers.Number

数字的层次结构的基础。如果你只想确认参数 x 是不是数字而不关心其类型，则使用``isinstance(x, Number)``。

数字的层次

class numbers.Complex

内置在类型 complex 里的子类描述了复数和它的运算操作。这些操作有：转化至 complex 和 bool， real、 imag、+、-、*、/、 abs()、 conjugate()、 == 和 !=。 所有的异常，- 和 != ，都是抽象的。

real

抽象的。得到该数字的实数部分。

imag

抽象的。得到该数字的虚数部分。

abstractmethod conjugate()

抽象的。返回共轭复数。例如 (1+3j).conjugate() == (1-3j)。

class numbers.Real

相对于 Complex，Real 加入了只有实数才能进行的操作。

简单的说，它们是：转化至 float，math.trunc()、 round()、 math.floor()、 math.ceil()、 divmod()、 //、 %、 <、 <=、 >、 和 >=。

实数同样默认支持 complex()、 real、 imag 和 conjugate()。

class numbers.Rational

子类型 Real 并加入 numerator 和 denominator 两种属性，这两种属性应该属于最低的级别。加入后，这默认支持 float()。

numerator

摘要。

denominator

摘要。

class numbers.Integral

子类型 Rational 加上转化至 int。 默认支持 float()、 numerator 和 denominator。 在 ** 中加入抽象方法和比特字符串的操作： <<、 >>、 &、 ^、 |、 ~。

类型接口注释。

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:

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. If it falls back to the boilerplate, there are no more possible methods to try, so this is where the default implementation should live.

5. 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 Complex.

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, 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)

# ...