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

I found the following algorithm provides a very good statistical distribution. Each input bit affects each output bit with about 50% probability. There are no collisions (each input results in a different output). The algorithm is fast except if the CPU doesn't have a built-in integer multiplication unit. C code (for Java, replace >> with >>> , remove the trailing unsigned u in the constant, and use int instead of uint32_t):

uint32_t hash(uint32_t x) {
    x = ((x >> 16) ^ x) * 0x45d9f3bu;
    x = ((x >> 16) ^ x) * 0x45d9f3bu;
    x = (x >> 16) ^ x;
    return x;
}

The magic number was calculated using a special multi-threaded test program that ran for many hours, which calculates the avalanche effect (the number of output bits that change if a single input bit is changed; should be nearly 16 on average), independence of output bit changes (output bits should not depend on each other), and the probability of a change in each output bit if any input bit is changed. The calculated values are better than the 32-bit finalizer used by MurmurHash, and nearly as good (not quite) as when using AES. A slight advantage is that the same constant is used twice (it did make it slightly faster the last time I tested, not sure if it's still the case).

You can reverse the process (get the input value from the hash) if you replace the 0x45d9f3b with 0x119de1f3 (the multiplicative

There's a nice overview over some hash algorithms at Eternally Confuzzled. I'd recommend Bob Jenkins' one-at-a-time hash which quickly reaches avalanche and therefore can be used for efficient hash table lookup.

The answer depends on a lot of things like:

• Where do you intend to employ it?
• What are you trying to do with the hash?
• Do you need a crytographically secure hash function?

I suggest that you take a look at the Merkle-Damgard family of hash functions like SHA-1 etc