> 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?

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

If mask = 0xfff...fff then a/b will be swapped, otherwise if mask = 0 then they'll remain the same.

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.

[0] https://en.wikipedia.org/wiki/Nim