`numbers` — 数值抽象基类 ¶

源代码： Lib/numbers.py

The numbers 模块 ( PEP 3141 ) 定义层次结构为数值抽象基类 which progressively define more operations. None of the types defined in this module are intended to be instantiated.

class numbers. 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) .

数值塔 ¶

class numbers. Complex ¶

Subclasses of this type describe complex numbers and include the operations that work on the built-in complex type. These are: conversions to complex and bool , real , imag , + , - , * , / , ** , abs() , conjugate() , == ，和 != . All except - and != are abstract.

real ¶: Abstract. Retrieves the real component of this number.

imag ¶: Abstract. Retrieves the imaginary component of this number.

abstractmethod conjugate ( ) ¶: Abstract. Returns the complex conjugate. For example, (1+3j).conjugate() == (1-3j) .

class numbers. Real ¶

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

In short, those are: a conversion to float , math.trunc() , round() , math.floor() , math.ceil() , divmod() , // , % , < , <= , > ，和 >= .

Real also provides defaults for complex() , real , imag ，和 conjugate() .

class numbers. Rational ¶

子类型 Real and adds numerator and denominator properties. It also provides a default for float() .

The numerator and denominator values should be instances of Integral and should be in lowest terms with denominator positive.

numerator ¶: 抽象。

denominator ¶: 抽象。

class numbers. Integral ¶: 子类型 Rational and adds a conversion to int . Provides defaults for float() , numerator ，和 denominator . Adds abstract methods for pow() 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. For example, fractions.Fraction 实现 hash() 如下：

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))

添加更多数值 ABC ¶

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 采用：

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

实现算术运算 ¶

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 )，和 b : B <: Complex . I’ll consider a + b :

若 A defines an __add__() which accepts b , all is well.
若 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.)
Then B ’s __radd__() 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.
若 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 .

若 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 使用：

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)
# ...

内容表

numbers — 数值抽象基类
- 数值塔
- Notes for type implementers
  - 添加更多数值 ABC
  - 实现算术运算

上一话题

数值和数学模块

下一话题

math — 数学函数

本页

报告 Bug
展示源

快速搜索

键入搜索术语或模块、类、函数名称。

首页
Python 3.12.4
索引
模块
下一
上一
Python 标准库
数值和数学模块
numbers — 数值抽象基类