XOR Swap Algorithm - Proof of Correctness

Proof of Correctness

The binary operation XOR over bit strings of length exhibits the following properties (where denotes XOR):

  • L1. Commutativity:
  • L2. Associativity:
  • L3. Identity exists: there is a bit string, 0, (of length N) such that for any
  • L4. Each element is its own inverse: for each, .

Suppose that we have two distinct registers R1 and R2 as in the table below, with initial values A and B respectively. We perform the operations below in sequence, and reduce our results using the properties listed above.

Step Operation Register 1 Register 2 Reduction
0 Initial value
1 R1 := R1 XOR R2
2 R2 := R1 XOR R2 L2
L4
L3
3 R1 := R1 XOR R2 L1
L2
L4
L3

Read more about this topic:  XOR Swap Algorithm

Famous quotes containing the words proof of, proof and/or correctness:

    Ah! I have penetrated to those meadows on the morning of many a first spring day, jumping from hummock to hummock, from willow root to willow root, when the wild river valley and the woods were bathed in so pure and bright a light as would have waked the dead, if they had been slumbering in their graves, as some suppose. There needs no stronger proof of immortality. All things must live in such a light. O Death, where was thy sting? O Grave, where was thy victory, then?
    Henry David Thoreau (1817–1862)

    Talk shows are proof that conversation is dead.
    Mason Cooley (b. 1927)

    Rather would I have the love songs of romantic ages, rather Don Juan and Madame Venus, rather an elopement by ladder and rope on a moonlight night, followed by the father’s curse, mother’s moans, and the moral comments of neighbors, than correctness and propriety measured by yardsticks.
    Emma Goldman (1869–1940)