9.1. numbers — 数值抽象基类 ¶

9.1.1. The numeric tower ¶

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 ¶

To 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, which should be in lowest terms. With these, it provides a default for float() .

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 ** and bit-string operations: << , >> , & , ^ , | , ~ .

9.1.2. 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))
								

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

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
									

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)
# ...