I’ve used Thomas Wang’s integer hash functions for years for various purposes. Using techniques invented by Bob Jenkins for general hashing (e.g., hashes of strings), Wang derived several hash specialized for fixed size integer input. His 64-bit version is

uint64_t hash(uint64_t key) {
  key = (~key) + (key << 21); // key = (key << 21) - key - 1;
  key = key ^ (key >> 24);
  key = (key + (key << 3)) + (key << 8); // key * 265
  key = key ^ (key >> 14);
  key = (key + (key << 2)) + (key << 4); // key * 21
  key = key ^ (key >> 28);
  key = key + (key << 31);
  return key;
}

Key properties include avalanche (changing any input bit changes about half of the output bits) and invertibility. Recently I wanted to make explicit use of the inverse, in order to verify that zero would never arise as the hash of a given set of inputs. This property would allow me to initialize the hash table in question (which takes up several gigabytes) with zeros and avoid an explicit occupied bit on each entry. Thus, I needed inverse_hash(0).