SparseSet implementation. Copyright (C) 2007-2013 Free Software Foundation, Inc. Contributed by Peter Bergner bergn.nosp@m.er@v.nosp@m.net.i.nosp@m.bm.c.nosp@m.om
This file is part of GCC.
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You should have received a copy of the GNU General Public License along with GCC; see the file COPYING3. If not see http://www.gnu.org/licenses/. Implementation of the Briggs and Torczon sparse set representation. The sparse set representation was first published in:
"An Efficient Representation for Sparse Sets", ACM LOPLAS, Vol. 2, Nos. 1-4, March-December 1993, Pages 59-69.
The sparse set representation is suitable for integer sets with a fixed-size universe. Two vectors are used to store the members of the set. If an element I is in the set, then sparse[I] is the index of I in the dense vector, and dense[sparse[I]] == I. The dense vector works like a stack. The size of the stack is the cardinality of the set.
The following operations can be performed in O(1) time:
clear : sparseset_clear
cardinality : sparseset_cardinality
set_size : sparseset_size
member_p : sparseset_bit_p
add_member : sparseset_set_bit
remove_member : sparseset_clear_bit
choose_one : sparseset_pop
Additionally, the sparse set representation supports enumeration of the members in O(N) time, where n is the number of members in the set. The members of the set are stored cache-friendly in the dense vector. This makes it a competitive choice for iterating over relatively sparse sets requiring operations:
forall : EXECUTE_IF_SET_IN_SPARSESET
set_copy : sparseset_copy
set_intersection : sparseset_and
set_union : sparseset_ior
set_difference : sparseset_and_compl
set_disjuction : (not implemented)
set_compare : sparseset_equal_p
NB: It is OK to use remove_member during EXECUTE_IF_SET_IN_SPARSESET. The iterator is updated for it.
Based on the efficiency of these operations, this representation of sparse sets will often be superior to alternatives such as simple bitmaps, linked-list bitmaps, array bitmaps, balanced binary trees, hash tables, linked lists, etc., if the set is sufficiently sparse. In the LOPLAS paper the cut-off point where sparse sets became faster than simple bitmaps (see sbitmap.h) when N / U < 64 (where U is the size of the universe of the set).
Because the set universe is fixed, the set cannot be resized. For sparse sets with initially unknown size, linked-list bitmaps are a better choice, see bitmap.h.
Sparse sets storage requirements are relatively large: O(U) with a larger constant than sbitmaps (if the storage requirement for an sbitmap with universe U is S, then the storage required for a sparse set for the same universe are 2*HOST_BITS_PER_WIDEST_FAST_INT * S). Accessing the sparse vector is not very cache-friendly, but iterating over the members in the set is cache-friendly because only the dense vector is used. Data Structure used for the SparseSet representation.