在Python中模拟数字类型

以下是可以定义为模拟数字类型对象的函数。

在相同类型的对象上实现二进制操作的方法：

这些函数不会对调用对象进行任何更改，而是在对调用对象执行某些操作后返回一个相同类型的新数字对象。以下是实现算术二进制运算的方法。

Method	Operation
object.__add__(self, other)	+ (Addition)
object.__sub__(self, other)	– (Subtraction)
object.__mul__(self, other)	* (Multiplication)
object.__matmul__(self, other)	@ (Matrix multiplication)
object.__truediv__(self, other)	/ (True division)
object.__floordiv__(self, other)	// (Floor division)
object.__mod__(self, other)	% (Modulus or remainder)
object.__divmod__(self, other)	divmod()
object.__pow__(self, other[, modulo])	** (power)
object.__lshift__(self, other)	<< (Bit wise left shift)
object.__rshift__(self, other)	>> (Bit wise right shift)
object.__and__(self, other)	& (Bit wise AND operation)
object.__xor__(self, other)	^ (Exclusive OR operation)
object.__or__(self, other)	| (Bit wise OR operation)

__pow__() 被定义为接受第三个可选参数，以支持 pow()函数的三元版本。此外，如果上述任何方法不支持该操作，它应该返回NotImplemented 。

在不同类型的对象上实现二进制操作的方法：

如果左侧的对象类型（可收集对象）不同，则可以使用以下方法执行算术二进制运算：

Method	Operation
object.__radd__(self, other)	+ (Addition)
object.__rsub__(self, other)	– (Subtraction)
object.__rmul__(self, other)	* (Multiplication)
object.__rmatmul__(self, other)	@ (Matrix multiplication)
object.__rtruediv__(self, other)	/ (True division)
object.__rfloordiv__(self, other)	// (Floor division)
object.__rmod__(self, other)	% (Modulus or remainder)
object.__rdivmod__(self, other)	divmod()
object.__rpow__(self, other[, modulo])	** (pow() or power of number)
object.__rlshift__(self, other)	<< (Bit wise left shift)
object.__rrshift__(self, other)	>> (Bit wise right shift)
object.__rand__(self, other)	& (Bit wise AND operation)
object.__rxor__(self, other)	^ (Exclusive OR operation)
object.__ror__(self, other)	| (Bit wise OR operation)

例如，如果在 a.__sub__(b) 中，a 与 b 一样不是数字类型，那么此方法将返回NotImplemented，然后要执行 a – b，我们将调用 a.__rsub__(b)。

实现算术赋值操作的方法：

这些方法用于实现算术赋值操作。它们不会返回新对象，而是会在调用对象本身时分配新值。就像x.__imul__(y)将被执行为x = x * y 。以下是每种方法的对应操作。

Method	Operation
object.__iadd__(self, other)	+= (Addition assignment)
object.__isub__(self, other)	-= (Subtraction assignment)
object.__imul__(self, other)	*= (Multiplication assignment)
object.__imatmul__(self, other)	@= (Matrix multiplication assignment)
object.__itruediv__(self, other)	/= (True division assignment)
object.__ifloordiv__(self, other)	//= (Floor division assignment)
object.__imod__(self, other)	%= (Modulus or remainder assignment)
object.__ipow__(self, other[, modulo])	**= (power of number assignment)
object.__ilshift__(self, other)	<<= (Bit wise left shift assignment)
object.__irshift__(self, other)	>>= (Bit wise right shift assignment)
object.__iand__(self, other)	&= (Bit wise AND operation assignment)
object.__ixor__(self, other)	^= (Exclusive OR operation assignment)
object.__ior__(self, other)	|= (Bit wise OR operation assignment)

实现一元算术运算的方法：

以下是实现一元算术运算的方法，例如数字的负数、数字的倒数等。

Method	Operation
object.__neg__(self)	– (unary minus)
object.__pos__(self)	+ (unary plus)
object.__abs__(self)	abs() in-built function
object.__invert__(self)	~ (complement of a number)

其他一些重要的方法：

Method	Description
object.__index__(self)	Called to implement operator.index() function, also used to convert a numeric type object to integer type,   or we can say if __int__(), __float__() or __complex__() is not defined then int(), float() and complex() falls  under __index__().
object.__round__(self, ndigits)	To implement the round() function, the second optional argument tells up to how many decimal places  we want to round the numeric value.
object.__trunc__(self)	To implement trunc() function.
object.__floor__(self)	To implement floor() function.
object.__ceil__(self)	To implement ceil() function.