The core of the function is as follows:
static U64 XXH64_round(U64 acc, U64 input)
{
acc += input * PRIME64_2;
acc = XXH_rotl64(acc, 31);
acc *= PRIME64_1;
return acc;
}
My own experiments show that multiplication is a great function for hashing. Multiplication however only spreads the bits in "one direction" (towards the most-significant bit), and very poorly spreads bits towards the LSB.
Rotations, as well as a 2nd multiplication, are helpful at spreading the bits around better.
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The 64-bit version is somewhat interesting to me, but the 32-bit version probably has more potential for optimization. 32-bit vectorized multiplication exists in AVX2, so the 32-bit version probably can be vectorized. I'd expect the 32-bit version (if vectorized) would be faster, but the 64-bit version probably mixes the bits around better.
Overall looks like a decent design. Uses ILP with 4x state variables (state->v1, state->v2, etc. etc. to allow CPUs to process these multiplications in parallel). Multiply + rotation + multiplication is good from my personal experiments, but the numbers chosen need to be carefully chosen.
Prime numbers are probably not necessary: they just need to be odd numbers to ensure invertibility (Ex: I've achieved decent mixing by multiplying with 0xAAAAAAAA5, which probably isn't a prime number). I'm curious how the prime-constants were selected. There could be some potential for "better numbers" for mixing, depending on how PRIME64_1 and PRIME64_2 were chosen.
Overall checks all of my boxes with regards to good design. Nice! I'm just curious about some details.
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I'll note that in my experiments, multiplication seems to "mix" better with XOR, rather than with ADD. I haven't done any tests with this hash yet, but I'm curious how changing the "+=" into "^=" would have on the statistical strength of the hash function.