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% ``The contents of this file are subject to the Erlang Public License,
%% Version 1.1, (the "License"); you may not use this file except in
%% compliance with the License. You should have received a copy of the
%% Erlang Public License along with this software. If not, it can be
%% retrieved via the world wide web at http://www.erlang.org/.
%%
%% Software distributed under the License is distributed on an "AS IS"
%% basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See
%% the License for the specific language governing rights and limitations
%% under the License.
%%
-module(bloom).
-author("Paulo Sergio Almeida <psa@di.uminho.pt>").
-export([sbf/1, sbf/2, sbf/3, sbf/4,
bloom/1, bloom/2,
member/2, add/2,
size/1, capacity/1]).
-export([is_element/2, add_element/2]). % alternative names
-import(math, [log/1, pow/2]).
is_element(E, B) -> member(E, B).
add_element(E, B) -> add(E, B).
%% Based on
%% Scalable Bloom Filters
%% Paulo Sérgio Almeida, Carlos Baquero, Nuno Preguiça, David Hutchison
%% Information Processing Letters
%% Volume 101, Issue 6, 31 March 2007, Pages 255-261
%%
%% Provides scalable bloom filters that can grow indefinitely while
%% ensuring a desired maximum false positive probability. Also provides
%% standard partitioned bloom filters with a maximum capacity. Bit arrays
%% are dimensioned as a power of 2 to enable reusing hash values across
%% filters through bit operations. Double hashing is used (no need for
%% enhanced double hashing for partitioned bloom filters).
%% modified slightly by Justin Sheehy to make it a single file
%% (incorporated the array-based bitarray internally)
-define(W, 27).
-record(bloom, {
e, % error probability
n, % maximum number of elements
mb, % 2^mb = m, the size of each slice (bitvector)
size, % number of elements
a % list of bitvectors
}).
-record(sbf, {
e, % error probability
r, % error probability ratio
s, % log 2 of growth ratio
size, % number of elements
b % list of plain bloom filters
}).
%% Constructors for (fixed capacity) bloom filters
%%
%% N - capacity
%% E - error probability
bloom(N) -> bloom(N, 0.001).
bloom(N, E) when is_number(N), N > 0,
is_float(E), E > 0, E < 1,
N >= 4/E -> % rule of thumb; due to double hashing
bloom(size, N, E).
bloom(Mode, Dim, E) ->
K = 1 + trunc(log2(1/E)),
P = pow(E, 1 / K),
case Mode of
size -> Mb = 1 + trunc(-log2(1 - pow(1 - P, 1 / Dim)));
bits -> Mb = Dim
end,
M = 1 bsl Mb,
N = trunc(log(1-P) / log(1-1/M)),
#bloom{e=E, n=N, mb=Mb, size = 0,
a = [bitarray_new(1 bsl Mb) || _ <- lists:seq(1, K)]}.
log2(X) -> log(X) / log(2).
%% Constructors for scalable bloom filters
%%
%% N - initial capacity before expanding
%% E - error probability
%% S - growth ratio when full (log 2) can be 1, 2 or 3
%% R - tightening ratio of error probability
sbf(N) -> sbf(N, 0.001).
sbf(N, E) -> sbf(N, E, 1).
sbf(N, E, 1) -> sbf(N, E, 1, 0.85);
sbf(N, E, 2) -> sbf(N, E, 2, 0.75);
sbf(N, E, 3) -> sbf(N, E, 3, 0.65).
sbf(N, E, S, R) when is_number(N), N > 0,
is_float(E), E > 0, E < 1,
is_integer(S), S > 0, S < 4,
is_float(R), R > 0, R < 1,
N >= 4/(E*(1-R)) -> % rule of thumb; due to double hashing
#sbf{e=E, s=S, r=R, size=0, b=[bloom(N, E*(1-R))]}.
%% Returns number of elements
%%
size(#bloom{size=Size}) -> Size;
size(#sbf{size=Size}) -> Size.
%% Returns capacity
%%
capacity(#bloom{n=N}) -> N;
capacity(#sbf{}) -> infinity.
%% Test for membership
%%
member(Elem, #bloom{mb=Mb}=B) ->
Hashes = make_hashes(Mb, Elem),
hash_member(Hashes, B);
member(Elem, #sbf{b=[H|_]}=Sbf) ->
Hashes = make_hashes(H#bloom.mb, Elem),
hash_member(Hashes, Sbf).
hash_member(Hashes, #bloom{mb=Mb, a=A}) ->
Mask = 1 bsl Mb -1,
{I1, I0} = make_indexes(Mask, Hashes),
all_set(Mask, I1, I0, A);
hash_member(Hashes, #sbf{b=B}) ->
lists:any(fun(X) -> hash_member(Hashes, X) end, B).
make_hashes(Mb, E) when Mb =< 16 ->
erlang:phash2({E}, 1 bsl 32);
make_hashes(Mb, E) when Mb =< 32 ->
{erlang:phash2({E}, 1 bsl 32), erlang:phash2([E], 1 bsl 32)}.
make_indexes(Mask, {H0, H1}) when Mask > 1 bsl 16 -> masked_pair(Mask, H0, H1);
make_indexes(Mask, {H0, _}) -> make_indexes(Mask, H0);
make_indexes(Mask, H0) -> masked_pair(Mask, H0 bsr 16, H0).
masked_pair(Mask, X, Y) -> {X band Mask, Y band Mask}.
all_set(_Mask, _I1, _I, []) -> true;
all_set(Mask, I1, I, [H|T]) ->
case bitarray_get(I, H) of
true -> all_set(Mask, I1, (I+I1) band Mask, T);
false -> false
end.
%% Adds element to set
%%
add(Elem, #bloom{mb=Mb} = B) ->
Hashes = make_hashes(Mb, Elem),
hash_add(Hashes, B);
add(Elem, #sbf{size=Size, r=R, s=S, b=[H|T]=Bs}=Sbf) ->
#bloom{mb=Mb, e=E, n=N, size=HSize} = H,
Hashes = make_hashes(Mb, Elem),
case hash_member(Hashes, Sbf) of
true -> Sbf;
false ->
case HSize < N of
true -> Sbf#sbf{size=Size+1, b=[hash_add(Hashes, H)|T]};
false ->
B = add(Elem, bloom(bits, Mb + S, E * R)),
Sbf#sbf{size=Size+1, b=[B|Bs]}
end
end.
hash_add(Hashes, #bloom{mb=Mb, a=A, size=Size} = B) ->
Mask = 1 bsl Mb -1,
{I1, I0} = make_indexes(Mask, Hashes),
case all_set(Mask, I1, I0, A) of
true -> B;
false -> B#bloom{size=Size+1, a=set_bits(Mask, I1, I0, A, [])}
end.
set_bits(_Mask, _I1, _I, [], Acc) -> lists:reverse(Acc);
set_bits(Mask, I1, I, [H|T], Acc) ->
set_bits(Mask, I1, (I+I1) band Mask, T, [bitarray_set(I, H) | Acc]).
bitarray_new(N) -> array:new((N-1) div ?W + 1, {default, 0}).
bitarray_set(I, A) ->
AI = I div ?W,
V = array:get(AI, A),
V1 = V bor (1 bsl (I rem ?W)),
array:set(AI, V1, A).
bitarray_get(I, A) ->
AI = I div ?W,
V = array:get(AI, A),
V band (1 bsl (I rem ?W)) =/= 0.
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