you will need to use a hashing algorithm that can handle a sufficiently large number of items
I didn't expect SHA256 to be so slow. I just tested a simple bash loop, and get less than 1000 hashes per second. That won't scale well to 40 billion inputs.
Is it absolutely necessary to hash the inputs with SHA256, or can a different algorithm be used for the bloom filter, such that we can create a different hash type Z(inputs) = Y(SHA256(inputs)) and thus save computational time?
Of course, Z() and Y() do not need to be cryptographic, and it would be better if they weren't.
I'll need to check the academic archives if such transfusion of a hashed output has ever been explored (let alone discovered).