Is there a category of hash functions that hash a 64/32 bit input to exactly 64/32 bits output, such that all inputs are uniquely preserved? This could be an interesting property for a hash table of integers, because a hash match implies a key match.
Even if you used such a bijective hash, your hash table would have to have 2^32 available buckets in order for the hash match to be all you need for lookup. Or 2^64 for 64-bit… which is why nobody really does this. (And if you did this, why even hash the input? The input integer could just be the key, and you’re basically using a really big sparse array.)
I agree that for standard hash tables this won’t work. However, I recently read about “Ideal Hash Trees” [0], that preserves the entire hash. That design also requires all bits to be “random” because it lacks the usual prime division.
> However, if you can use a permutation as a hash function, you might be fine with just using the identity function.
This certainly isn't true for 8-bit characters using ASCII.
The top-bit of all ASCII strings is always zero, its effectively a wasted bit. Permuting all ASCII characters to randomly use all 8-bits means a better distribution in virtually any hash-based data-structure. (ex: 64 slot hashtable will have fewer collisions after you permute the 7-bit ASCII into an 8-bit random permutation)
Linear congruential generators in some cases can do that, though more often they are used to convert n bits of input data into a uniform distribution over a range from 0-m. For instance simulating chance in a game (dice rolls, or % probability).
Excellent tutorial for bitwise arithmetic this is. The key is the motivation you receive from the prospect of being able to do something that seems "l33t".
But only 3 so far.