Emulating Numeric types in Python

Last Updated : 27 Feb, 2023

The following are the functions which can be defined to emulate numeric type objects.

Methods to implement Binary operations on same type of objects :

These functions will make no change in the calling object rather they will return a new numeric object of same type after performing certain operation on the calling object. Following are the methods to implement arithmetic binary operations.

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)

The __pow__() is defined to accept a third optional argument so as to support the ternary version of pow() function. Also if any of above method does not support the operation it should return NotImplemented .

Methods to implement Binary operations on different type of objects :

If type of object at left (callable object) is different than following methods can be used to perform arithmetic binary operations :

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)

For example, if in a.__sub__(b), a is not of numeric type as of b then this method will return NotImplemented, then to perform a – b we will call a.__rsub__(b).

Methods to implement arithmetic assignment operations :

These methods are used to implement the arithmetic assignment operations. They will not return a new object rather they will assign the new value in calling object itself. Like x.__imul__(y) will be performed as x = x * y. Following are the corresponding operations to each method.

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)

Methods to implement unary arithmetic operations :

Following are the methods to implement unary arithmetic operations like, negative of a number, inverse of a number etc.

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)

Some other important methods :

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.