= Bloomfilter: Bloom filters     include "sets.m";    include "bloomfilter.m";    bloomfilter := load Bloomfilter Bloomfilter->PATH;     init:   fn();    filter: fn(d: array of byte, logm, k: int): Sets->Set; A  Bloom  filter is a method of representing a set to supportprobabilistic membership queries. It  uses  independent  hashfunctions of members of the set to set elements of a bit-vec‐tor.  Init should be called first to initialise  the  module.Filter  returns a Set s representing the Bloom filter for thesingle-member set {d}.   K  independent  hash  functions  areused,  each  of  range  [0, 2^logm), to return a Bloom filter2^logm bits wide. It is an error if logm is less  than  3  orgreater than 30. Bloom  filters  can be combined by set union.  The set repre‐sented by Bloom filter a is not a  subset  of  another  b  ifthere  are  any  members  in  a that are not in b.  Together,logm, k, and n (the number of members in the  set)  determinethe  false  positve  rate  (the probability that a membershiptest will not eliminate a member that is not in fact  in  theset).   The  probability of a false positive is approximately(1-e^(-kn/(2^logm))^k.  For a given false positive rate, f, auseful   formula  to  determine  appropriate  parameters  is:k=ceil(-log₂(f)), and logm=ceil(log₂(nk)). == examplesCreate a 128 bit-wide bloom filter  f  representing  all  theelements in the string array elems, with k=6.    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));Test whether the string s is a member of f.  If there were 12elements in elems, the probability of a false positive  wouldbe approximately 0.0063.    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); == source/appl/lib/bloomfilter.b == see ALSOsets(2)