include "sets.m";
include "bloomfilter.m";
bloomfilter := load Bloomfilter Bloomfilter->PATH;

init:   fn();
filter: fn(d: array of byte, logm, k: int): Sets->Set;

Bloom filters can be combined by set union. The set represented by Bloom filter a is not a subset of another b if there are any members in a that are not in b. Together, logm, k, and n (the number of members in the set) determine the false positve rate (the probability that a membership test will not eliminate a member that is not in fact in the set). The probability of a false positive is approximately (1-e^(-kn/(2^logm))^k. For a given false positive rate, f, a useful formula to determine appropriate parameters is: k=ceil(-log₂(f)), and logm=ceil(log₂(nk)).

    A, B, None: import Sets;
    for(i:=0; i<len elems; i++)
        f = f.X(A|B, filter(array of byte elems[i], 7, 6));

    if(filter(array of byte s, 7, 6).X(A&~B, f).eq(None))
        sys->print("'%s' might be a member of f\n", s);