What integer hash function are good that accepts an integer hash key?

Question

What integer hash function are good that accepts an integer hash key?

Answer 1

I have been using splitmix64 (pointed in Thomas Mueller's answer) ever since I found this thread. However, I recently stumbled upon Pelle Evensen's rrxmrrxmsx_0, which yielded tremendously better statistical distribution than the original MurmurHash3 finalizer and its successors (splitmix64 and other mixes). Here is the code snippet in C:

#include 

static inline uint64_t ror64(uint64_t v, int r) {
    return (v >> r) | (v << (64 - r));
}

uint64_t rrxmrrxmsx_0(uint64_t v) {
    v ^= ror64(v, 25) ^ ror64(v, 50);
    v *= 0xA24BAED4963EE407UL;
    v ^= ror64(v, 24) ^ ror64(v, 49);
    v *= 0x9FB21C651E98DF25UL;
    return v ^ v >> 28;
}

Pelle also provides an in-depth analysis of the 64-bit mixer used in the final step of MurmurHash3 and the more recent variants.