Invertible integer hash functions

/* For any 1<k<=64, let mask=(1<<k)-1. hash_64() is a bijection on [0,1<<k), which means hash_64(x, mask)==hash_64(y, mask) if and only if x==y. hash_64i() is the inversion of hash_64(): hash_64i(hash_64(x, mask), mask) == hash_64(hash_64i(x, mask), mask) == x. */

// Thomas Wang's integer hash functions. See https://gist.github.com/lh3/59882d6b96166dfc3d8d for a snapshot. uint64_t hash_64(uint64_t key, uint64_t mask) { key = (~key + (key << 21)) & mask; // key = (key << 21) - key - 1; key = key ^ key >> 24; key = ((key + (key << 3)) + (key << 8)) & mask; // key * 265 key = key ^ key >> 14; key = ((key + (key << 2)) + (key << 4)) & mask; // key * 21 key = key ^ key >> 28; key = (key + (key << 31)) & mask; return key; }

// The inversion of hash_64(). Modified from https://naml.us/blog/tag/invertible uint64_t hash_64i(uint64_t key, uint64_t mask) { uint64_t tmp;

// Invert key = key + (key << 31)
tmp = (key - (key << 31));
key = (key - (tmp << 31)) & mask;

// Invert key = key ^ (key >> 28)
tmp = key ^ key >> 28;
key = key ^ tmp >> 28;

// Invert key *= 21
key = (key * 14933078535860113213ull) & mask;

// Invert key = key ^ (key >> 14)
tmp = key ^ key >> 14;
tmp = key ^ tmp >> 14;
tmp = key ^ tmp >> 14;
key = key ^ tmp >> 14;

// Invert key *= 265
key = (key * 15244667743933553977ull) & mask;

// Invert key = key ^ (key >> 24)
tmp = key ^ key >> 24;
key = key ^ tmp >> 24;

// Invert key = (~key) + (key << 21)
tmp = ~key;
tmp = ~(key - (tmp << 21));
tmp = ~(key - (tmp << 21));
key = ~(key - (tmp << 21)) & mask;

return key;

}