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

For random hash values, some engineers said golden ratio prime number(2654435761) is a bad choice, with my testing results, I found that it's not true; instead, 2654435761 distributes the hash values pretty good.

#define MCR_HashTableSize 2^10

unsigned int
Hash_UInt_GRPrimeNumber(unsigned int key)
{
  key = key*2654435761 & (MCR_HashTableSize - 1)
  return key;
}

The hash table size must be a power of two.

I have written a test program to evaluate many hash functions for integers, the results show that GRPrimeNumber is a pretty good choice.

I have tried:

1. total_data_entry_number / total_bucket_number = 2, 3, 4; where total_bucket_number = hash table size;
2. map hash value domain into bucket index domain; that is, convert hash value into bucket index by Logical And Operation with (hash_table_size - 1), as shown in Hash_UInt_GRPrimeNumber();
3. calculate the collision number of each bucket;
4. record the bucket that has not been mapped, that is, an empty bucket;
5. find out the max collision number of all buckets; that is, the longest chain length;

With my testing results, I found that Golden Ratio Prime Number always has the fewer empty buckets or zero empty bucket and the shortest collision chain length.

Some hash functions for integers are claimed to be good, but the testing results show that when the total_data_entry / total_bucket_number = 3, the longest chain length is bigger than 10(max collision number > 10), and many buckets are not mapped(empty buckets), which is very bad, compared with the result of zero empty bucket and longest chain length 3 by Golden Ratio Prime Number Hashing.

BTW, with my testing results, I found one version of shifting-xor hash functions is pretty good(It's shared by mikera).

unsigned int Hash_UInt_M3(unsigned int key)
{
  key ^= (key << 13);
  key ^= (key >> 17);    
  key ^= (key << 5); 
  return key;
}