c_cpp 可逆整数散列函数

Posted 2021-05-14

/*
  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;
}