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#### NAME

Bloomfilter - Bloom filters

#### SYNOPSIS

```include "sets.m";
include "bloomfilter.m";

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

#### DESCRIPTION

A Bloom filter is a method of representing a set to support probabilistic membership queries. It uses independent hash functions of members of the set to set elements of a bit-vector. Init should be called first to initialise the module. Filter returns a Set s representing the Bloom filter for the single-member set {d}. K independent hash functions are used, each of range [0, 2^logm), to return a Bloom filter 2^logm bits wide. It is an error if logm is less than 3 or greater than 30.

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)).

#### EXAMPLES

Create a 128 bit-wide bloom filter f representing all the elements 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 12 elements in elems, the probability of a false positive would be 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