For me it falls in the obfuscated-C quadrant for code. Performance implications aside, it's just not the kind of "self-documenting" code I like lying around in my sources. (And I'll take clarity of purpose over performance every day.)
We didn't get into the deeper question of benchmarking it vs. a three-register swap, because I suspect the latter would be handled entirely by register renaming and end up being faster due to not requiring allocation of an ALU unit. Difficult to benchmark that because in order for it to make a difference, you'd need to surround it with other arithmetic instructions.
A meta question is why this persists. It has the right qualities for a "party trick": slightly esoteric piece of knowledge, not actually that hard to understand when you do know about it, but unintuitive enough that most people don't spontaneously reinvent it.
See also: https://en.wikipedia.org/wiki/Fast_inverse_square_root , which requires a bit more maths.
The other classic use of XOR - cursor overdrawing - has also long since gone away. It used to be possible to easily draw a cursor on a monochrome display by XORing it in, then to move it you simply XOR it again, restoring the original image.
void swap(unsigned* a, unsigned* b)
{
*a = *a + *b;
*b = *a - *b;
*a = *a - *b;
}
Yes, error correction.
You have some packets of data a, b, c. Add one additional packet z that is computed as z = a ^ b ^ c. Now whenever one of a, b or c gets corrupted or lost, it can be reconstructed by computing the XOR of all the others.
So if b is lost: b = a ^ c ^ z. This works for any packet, but only one. If multiple are lost, this will fail.
There are way better error correction algorithms, but I like the simplicity of this one.
a = the bits of some song or movie
b = pure noise
Store c = a^b.
Give b to a friend. Throw away a.
Now both you and your friend have a bit vector of pure noise. Together you can produce the copyrighted work. But nobody is liable.
> https://ansuz.sooke.bc.ca/entry/23
> https://ansuz.sooke.bc.ca/entry/24
As these article outline, the legal situation is much more complicated (and unintuitive to people who are used to "computer science thinking").
There is no trace back from pure noise to the original work.
Colour of bits is just magical thinking.
No law exists "physically".
Otherwise: Even in Computer Science the situation is more complicated, as is explained in the linked articles). Relevant excerpt from the first linked article:
"Child pornography is an interesting case because I find myself, and I think many people in the computing community will find themselves, on the opposite side of the Colourful/Colour-blind gap from where I would normally be. In copyright I spend a lot of time explaining why Colour doesn't exist and it doesn't matter where the bits came from. But when it comes to child pornography, I think maybe Colour should make a difference - if we're going to ban it at all, it should matter where it came from. Whether any children were actually involved, who did or didn't give consent, in short: what Colour the bits are. The other side takes the opposite tack: child pornography is dangerous by its very existence, and it doesn't matter where it came from. They're claiming that whether some bits are child pornography or not, and if so, whether they're illegal or not, should be entirely determined by (strictly a function of) the bits themselves. Legality, at least under the obscenity law, should not involve Colour distinctions.
[...]
The computer science applications of Colour seem to be mostly specific to security. Suppose your computer is infected with a worm or virus. You want to disinfect it. What do you do? You boot it up from original write-protected install media. Sure, you have a copy of the operating system on the drive already, but you can't use that copy - it's the wrong Colour. Then you go through a process of replacing files, maybe examining files, swapping disks around and carefully write-protecting them; throughout, you're maintaining information on the Colour of each part of the system and each disk until you've isolated the questionable files and everything else is known to be the "not infected with virus" Colour. Note that developers of Web applications in Perl use a similar scorekeeping system to keep track of which bits are "tainted" by influence from user input.
When we use Colour like that to protect ourselves against viruses or malicious input, we're using the Colour to conservatively approximate a difficult or impossible to compute function of the bits. Either our operating system is infected, or it is not. A given sequence of bits either is an infected file or isn't, and the same sequence of bits will always be either infected or not. Disinfecting a file changes the bits. Infected or not is a function, not a Colour. The trouble is that because any of our files might be infected including the tools we would use to test for infection, we can't reliably compute the "is infected" function, so we use Colour to approximate "is infected" with something that we can compute and manage - namely "might be infected". Note that "might be infected" is not a function; the same file can be "might be infected" or "not (might be infected)" depending on where it came from. That is a Colour.
[...]
Random numbers have a Colour different from that of non-random numbers. [...]
Note my terminology - I spoke of "randomly generated" numbers. Conscientious cryptographers refuse to use the term "random numbers". They'll persistently and annoyingly correct you to say "randomly generated numbers" instead, because it's not the numbers that are or are not random, it's the source of the numbers that is or is not random. If you have numbers that are supposed to come from a random source and you start testing them to make sure they're really "random", and you throw out the ones that seem not to be, then you end up reducing the Shannon entropy of the source, violating the constraints of the one-time pad if that's relevant to your application, and generally harming security. I just threw a bunch of math terms at you in that sentence and I don't plan to explain them here, but all cryptographers understand that it's not the numbers that matter when you're talking about randomness. What matters is where the numbers came from - that is, exactly, their Colour.
So if we think we understand cryptography, we ought to be able to understand that Colour is something real even though it is also true that bits by themselves do not have Colour. I think it's time for computer people to take Colour more seriously - if only so that we can better explain to the lawyers why they must give up their dream of enforcing Colour inside Friend Computer, where Colour does not and cannot exist."
That's the whole point of encryption.
(unless you're an AI company, in which case you can copy the whole internet just fine)
How many ways could they do this? Could they note in court that they found you getting your copy from a "super secure no liability legal loophole" piracy service? Could they just get B's side, whether through subpoena or whatever mechanism you have to communicate with B? (You must, since your file is "just noise" and useless to you as it is)
[1] Achieving Multi-Port Memory Performance on Single-Port Memory with Coding Techniques - https://arxiv.org/abs/2001.09599
[2] https://people.csail.mit.edu/ml/pubs/fpga12_xor.pdfA few months ago, I had a rare occasion of trying to explain them to a relative who had just bought a fancy NAS and wanted help setting it up.
a^=b^=a^=b;
Which allegedly saves you 0.5 seconds of typing in competitive programming competitions from 20 years ago and is known to work reliably (on MinGW under Windows XP).
Bonus authenticity: use `a^=a` to zero a register in a single x86 instruction (and makes a real difference for compiler toolchains 30+ years old).
For real now, a very useful application of XOR is its relation to the Nim game [0], which comes in very handy if you need to save your village from an ancient disgruntled Chinese emperor.
> a^=b^=a^=b;
I believe this is defined in C++ since C++17, but still undefined in C.
Modern compilers will still use xor for zeroing registers on their own.
For instance: https://godbolt.org/z/n5n35xjqx
Variable a(register esi) is first initialized to 42 with mov and then cleared to zero using xor.
tmp = (a ^ b) & mask
a ^= tmp
b ^= tmp
One extension that I ran into, and which I think forms a nice problem is the following:
Just like the XOR swap trick can be used to swap to variables (and let's just say that they're bools), it can be extended to implement any permutation of the variables: suppose that the permutation is written as a composition of n transpositions (i.e., swaps of pairs), and that is the minimal number of transpositions that let's you do that. Each transposition can be implemented by 3 XORs, by the XOR swap trick for pairs, and so the full permutation can be implemented by 3n XORs. Now here's the question: Is it possible to come up with a way of doing it with less than 3n, or can we find a permutation that has a shortcut through XOR-land (not allowing any other kinds of instructions)? In other words, is XOR-swapping XOR-optimal?
I'm not going to spoil it, but only last year a paper was published in the quantum information literature that contains an answer [0]. I ended up making a little game where you get to play around with XOR-optimizing not only permutations, but general linear reversible circuits. [1]
[0] https://link.springer.com/article/10.1007/s11128-025-04831-5
Yes there are false positives, and the false negative of all-zero/all-equal, but the test can be useful in a "bloom filter" type case.
Have used it in dynamic firewalling rules ... one can do something pretty close to a JA3/JA4 TLS fingerprint in eBPF with that (to match the cipher lists).
Things like "add with saturation" and the special AES instructions.
It'll break eventually. If it matters, write the simd yourself. It'll probably be 2-50x better than the compiler anyways.
The article makes the same point as well at the end:
It is the kind of technique which might have been occasionally useful in the 1980s, but now is only useful for cute interview questions and as a curiosity.
https://lemire.me/blog/2022/01/21/swar-explained-parsing-eig...
(See also the wacky way in which ARM "load immediate" works)
For some reason this reminds me of the Fourier transform. I wonder if it can be performed with XOR tricks and no complicated arithmetic?
Solution: xor is just addition mod 2. Write the numbers in base n and do digit-wise addition mod n (ie without carry). Very intuitive way to see the xor trick.