alt Hacker NewsToo much discussion of the XOR swap trick
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> Are there other XOR tricks?
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.
The XOR trick is only cool in its undefined-behavior form:
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.
xor swap trick was useful in older simd (sse1/sse2) when based on some condition you want to swap values or not:
tmp = (a ^ b) & mask
a ^= tmp
b ^= tmp
The XOR swap trick also features in the compilation/synthesis of quantum algorithms, where the XOR instruction (in the form of a CNOT gate) is fundamental in many architectures, and where native swapping need not be available.
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
Used to do this in assembly back when registers actually mattered. Today it mostly hurts readability more than anything.
Xor swap trick has perfect profile for underhanded C contests. It generally works until a specific condition triggers its failure. The condition is "the arguments are aliases", so for example XOR_SWAP(a[i], a[j]) when i=j.
I would remark that modern CPUs don't use physical registers, so swapping should be just a register rename op, and this kind of bithacking only applies to old machines.
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.
Such tricks were maybe useful 40 years ago while writing assembly code manually or while using a dumb compiler with no optimizations. But nowadays such tricks are near to useless. All useful ones (like optimizing division by 2 via bitshift ) are already implemented as compiler optimizations. Others shouldn't be used in order to avoid making optimizer's job harder.
30 years ago, when I wanted to 0 a register in assembly I used something like xor ah, ah because it was a bit more performant.
You can use this same property of xor to make a double-linked list using just one pointer per item, which is xor of the previous and next item addresses!
> given a list where every value appears exactly twice except one, XOR all the values together and the duplicates cancel out, leaving the unique element
For some reason this reminds me of the Fourier transform. I wonder if it can be performed with XOR tricks and no complicated arithmetic?
The fun bit is right at the start when the author notices that the compiler spots this and optimizes it away.
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.