# Python __rxor__() Magic Method

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## Syntax

`object.__rxor__(self, other)`

The Python `__rxor__()` method implements the reverse Bitwise XOR ^ operation with reflected, swapped operands. So, when you call `x ^ y`, Python attempts to call `x.__xor__(y)`. If the method is not implemented, Python 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
48```

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):

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

## 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:
pass

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
```

References:

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