Python __xor__() Magic Method

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object.__xor__(self, other)

The Python __xor__() method implements the built-in Bitwise XOR ^ operation. So, when you cal x ^ y, Python attempts to call x.__xor__(y). If the method is not implemented, Python first attempts to call __rxor__ on the right operand and if this isn’t implemented either, it raises a TypeError.

We call this a “Dunder Method” for Double Underscore Method” (also called “magic method”). To get a list of all dunder methods with explanation, check out our dunder cheat sheet article on this blog.

Background Bitwise XOR ^

Python’s bitwise XOR operator performs logical XOR on each bit position on the binary representations of integers x and y.

Each output bit evaluates to 1 if and only if exactly one of the two input bits at the same position are 1.

For example, the integer expression 4 ^ 3 is translated to the binary operation 0100 ^ 0011 which results in 0111 because for the last three positions exactly one bit is 1.

In this example, you apply the bitwise XOR operator to two integers 32 and 16:

>>> 32 ^ 16

The expression 32 ^ 16 operates on the bit representations "0100000" (decimal 32) and "0010000" (decimal 16) and performs bitwise XOR resulting in binary "0110000" (decimal 48):

First Operand x100000
Second Operand y010000
x ^ y110000

To understand this operation in detail, feel free to read over our tutorial or watch the following video:

Python Bitwise XOR ^ Operator

Example Custom __xor__()

In the following example, you create a custom class Data and overwrite the __xor__() magic method so that it returns a dummy string when trying to calculate the bitwise XOR operation.

class Data:
    def __xor__(self, other):
        return '... my result of XOR ...'

a = Data()
b = Data()

print(a ^ b)
# ... my result of XOR ...

If you hadn’t defined the __xor__() method, Python would’ve raised a TypeError.

TypeError: unsupported operand type(s) for ^

Consider the following code snippet where you try to calculate the bitwise XOR operation on custom objects without defining the dunder method __xor__():

class Data:

a = Data()
b = Data()

print(a ^ b)

Running this leads to the following error message on my computer:

Traceback (most recent call last):
  File "C:\Users\xcent\Desktop\", line 8, in <module>
    print(a ^ b)
TypeError: unsupported operand type(s) for ^: 'Data' and 'Data'

The reason for this error is that the __xor__() method has never been defined—and it is not defined for a custom object by default. So, to resolve the TypeError: unsupported operand type(s) for ^, you need to provide the __xor__(self, other) method in your class definition as shown previously:

class Data:
    def __xor__(self, other):
        return '... my result of XOR ...'

Of course, you’d use another return value in practice as explained in the “Background” section.

Python __xor__ vs __rxor__

Say, you want to calculate the ^ operation on two custom objects x and y:

print(x ^ y)

Python first tries to call the left object’s __xor__() method x.__xor__(y). But this may fail for two reasons:

  1. The method x.__xor__() is not implemented in the first place, or
  2. The method x.__xor__() is implemented but returns a NotImplemented value indicating that the data types are incompatible.

If this fails, Python tries to fix it by calling the y.__rxor__() for reverse bitwise XOR on the right operand y.

If the reverse bitwise XOR method is implemented, Python knows that it doesn’t run into a potential problem of a non-commutative operation. If it would just execute y.__xor__(x) instead of x.__xor__(y), the result would be wrong because the operation may be non-commutative when defined as a custom operation. That’s why y.__rxor__(x) is needed.

So, the difference between x.__xor__(y) and x.__rxor__(y) is that the former calculates x ^ y whereas the latter calculates y ^ x — both calling the respective method defined on the object x.

You can see this in effect here where we attempt to call the operation on the left operand x—but as it’s not implemented, Python simply calls the reverse operation on the right operand y.

class Data_1:

class Data_2:
    def __rxor__(self, other):
        return 'called reverse bitwise XOR'

x = Data_1()
y = Data_2()

print(x ^ y)
# called reverse bitwise XOR


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