/* Part of SWI-Prolog Author: Jan Wielemaker E-mail: J.Wielemaker@vu.nl WWW: http://www.swi-prolog.org Copyright (c) 2005-2024, VU University Amsterdam CWI, Amsterdam SWI-Prolog Solutions b.v. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ :- module(nb_set, [ empty_nb_set/1, % -EmptySet add_nb_set/2, % +Key, !Set add_nb_set/3, % +Key, !Set, ?New size_nb_set/2, % +Set, -Size nb_set_to_list/2, % +Set, -List gen_nb_set/2 % +Set, -Key ]). :- autoload(library(terms), [term_factorized/3]). :- use_module(library(debug), [assertion/1]). /** Non-backtrackable sets This library provides a non-backtrackabe _set_ of terms that are variants of each other. It is primarily intended to implement distinct/1 from library(solution_sequences). The set is implemented as a hash table that is built using non-backtrackable primitives, notably nb_setarg/3. The original version of this library used binary trees which provides immediate ordering. As the trees were not balanced, performance could get really poor. The complexity of balancing trees using non-backtrackable primitives is too high. The next iteration used _open hash tables_, while the current incarnation uses _closed hash tables_, providing better perfomance and less space usage. @author Jan Wielemaker */ initial_capacity(4). % initial hash-table size %! empty_nb_set(-Set) % % Create an empty non-backtrackable set. empty_nb_set(NbSet) :- initial_capacity(Capacity), Empty = empty(1), '$filled_array'(Buckets, buckets, Capacity, Empty), NbSet = nb_set(Empty, Capacity, 0, Buckets). %! add_nb_set(+Key, !Set) is det. %! add_nb_set(+Key, !Set, ?New) is semidet. % % Insert Key into the set. If a variant (see =@=/2) of Key is % already in the set, the set is unchanged and New is unified with % `false`. Otherwise, New is unified with `true` and a _copy of_ % Key is added to the set. % % @tbd Computing the hash for cyclic terms is performed with % the help of term_factorized/3, which performs rather % poorly. add_nb_set(Key, Set) :- add_nb_set(Key, Set, _). add_nb_set(Key, Set, New) :- Set = nb_set(Empty, Capacity, Size, Buckets), key_hash(Key, Hash), index(Hash, Capacity, KIndex), arg(KIndex, Buckets, StoredKey), ( same_term(StoredKey, Empty) -> !, New = true, nb_setarg(KIndex, Buckets, Key), NSize is Size+1, nb_setarg(3, Set, NSize), ( NSize > Capacity//2 -> rehash(Set) ; true ) ; Key =@= StoredKey -> !, New = false ). %! index(+Hash, +Capacity, -Index) is nondet. % % Generate candidate values for Index, starting from `Hash mod % Capacity`, round tripping to 1 when Capacity is reached. index(Hash, Capacity, KIndex) :- KIndex0 is (Hash mod Capacity) + 1, next(KIndex0, Capacity, KIndex). next(KIndex, _, KIndex). next(KIndex0, Capacity, KIndex) :- KIndex1 is 1+(KIndex0 mod Capacity), next(KIndex1, Capacity, KIndex). rehash(Set) :- Set = nb_set(Empty, Capacity, Size, Buckets), NCapacity is Capacity*2, '$filled_array'(NBuckets, buckets, NCapacity, Empty), nb_setarg(2, Set, NCapacity), nb_setarg(3, Set, 0), nb_linkarg(4, Set, NBuckets), forall(between(1, Capacity, I), reinsert(I, Empty, Buckets, Set)), arg(3, Set, NewSize), assertion(NewSize == Size). :- det(reinsert/4). reinsert(KIndex, Empty, Buckets, Set) :- arg(KIndex, Buckets, Key), ( same_term(Key, Empty) -> true ; add_nb_set(Key, Set, true) ). %! hash_key(+Key, -Hash:integer) is det. % % Compute a hash for Term. Note that variant_hash/2 currently does % not handle cyclic terms, so use term_factorized/3 to get rid of % the cycles. This means that this library is rather slow when % cyclic terms are involved. :- if(catch((A = f(A), variant_hash(A,_)), _, fail)). key_hash(Key, Hash) :- variant_hash(Key, Hash). :- else. key_hash(Key, Hash) :- acyclic_term(Key), !, variant_hash(Key, Hash). key_hash(Key, Hash) :- term_factorized(Key, Skeleton, Substiution), variant_hash(Skeleton+Substiution, Hash). :- endif. %! nb_set_to_list(+NBSet, -OrdSet) is det. %! nb_set_to_list(-NBSet, +List) is det. % % Get the elements of a an nb_set. OrdSet is sorted to the standard % order of terms, providing a set representation that is compatible to % library(ordsets). nb_set_to_list(NBSet, Set), NBSet = nb_set(Empty, Capacity, _Size, Buckets) => buckets_to_list(1, Empty, Capacity, Buckets, List0), sort(List0, Set). buckets_to_list(KIndex, Empty, Capacity, Buckets, List) :- ( arg(KIndex, Buckets, Key) -> ( same_term(Empty, Key) -> KIndex1 is KIndex+1, buckets_to_list(KIndex1, Empty, Capacity, Buckets, List) ; List = [Key|List1], KIndex1 is KIndex+2, buckets_to_list(KIndex1, Empty, Capacity, Buckets, List1) ) ; List = [] ). %! gen_nb_set(+Set, -Key) is nondet. % % Enumerate the members of a set in the standard order of terms. gen_nb_set(nb_set(Empty, Capacity, _Size, Buckets), Key) => between(1, Capacity, KIndex), arg(KIndex, Buckets, Key), \+ same_term(Empty, Key). %! size_nb_set(+Set, -Size) is det. % % Unify Size with the number of elements in the set size_nb_set(nb_set(_Empty, _Capacity, Sz, _Buckets), Size) => Size = Sz.