I converted all parameter integers to 64 bit values to allow for larger filters. This is a change that breaks backwards-compatibility with older filters. I added a 64-bit value at the beginning of the filter to store the file version (currently 1) and additional flags, which we can use in the future to ensure backwards-compatibility.

I also noticed that the false positive probability was higher than anticipated for large filter values, which I found to be related to the hash generation. Before, the hashes were generated following the method outlined in Adam Kirsch et. al. (https://www.eecs.harvard.edu/~michaelm/postscripts/tr-02-05.pdf), however their method of generating k hash values from two initial ones seems to be suboptimal and does not produce a fully uniform distribution. I replaced it with a scheme that borrows from PRNG schemes by generating an initial value hn using a FNV hash and then in each round sets hn = hn*g % m, where m is a large prime number and g is a primitive root of m. As long as the number of bits in the filter is smaller than m (which for all practical purposes it is) we can use this method to generate k hash values using an initial seed value generated via FNV.

I did this when noticing problems while converting the Have I Been Pwned database into a Bloom filter.