It seems like the authors wanted to use a single hash for performance (?). Maybe they correctly determined that naive Bloom filters have poor cache locality and reinvented block bloom filters from there.

Overall, I think block bloom filters should be the default most people reach for. They completely solve the cache locality issues (single cache miss per element lookup), and they sacrifice only like 10–15% space increase to do it. I had a simple implementation running at something like 20ns per query with maybe k=9. It would be about 9x that for native Bloom filters.

There’s some discussion in the article about using a single hash to come up with various indexing locations, but it’s simpler to just think of block bloom filters as:

1. Hash-0 gets you the block index

2. Hash-1 through hash-k get you the bits inside the block

If your implementation slices up a single hash to divide it into multiple smaller hashes, that’s fine.