Emulating Numeric types in Python
Last Updated :
15 Jul, 2025
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. |
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