What is the purpose of the Parity Flag on a CPU?

Question

Some CPUs (notably x86 CPUs) feature a parity flag on their status register. This flag indicates whether the number of bits of the result of an operation is odd or even.

Answer 1

There's one practical micro-optimization achievable with parity -- that's bit swapping as used eg in fourier transform address generation using the butterfly kernel.

To swap bits 7 and 0, one can exploit parity of (a&0x81) followed by conditional (a^=0x81). Repeat for bits 6/1, 5/2 and 4/3.