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/* SparseSet implementation.
Copyright (C) 2007-2018 Free Software Foundation, Inc.
Contributed by Peter Bergner <>
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
for more details.
You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING3. If not see
<>. */
/* 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:
* 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. */
typedef struct sparseset_def
SPARSESET_ELT_TYPE *dense; /* Dense array. */
SPARSESET_ELT_TYPE *sparse; /* Sparse array. */
SPARSESET_ELT_TYPE members; /* Number of elements. */
SPARSESET_ELT_TYPE size; /* Maximum number of elements. */
SPARSESET_ELT_TYPE iter; /* Iterator index. */
unsigned char iter_inc; /* Iteration increment amount. */
bool iterating;
SPARSESET_ELT_TYPE elms[2]; /* Combined dense and sparse arrays. */
} *sparseset;
#define sparseset_free(MAP) free(MAP)
extern sparseset sparseset_alloc (SPARSESET_ELT_TYPE n_elms);
extern void sparseset_clear_bit (sparseset, SPARSESET_ELT_TYPE);
extern void sparseset_copy (sparseset, sparseset);
extern void sparseset_and (sparseset, sparseset, sparseset);
extern void sparseset_and_compl (sparseset, sparseset, sparseset);
extern void sparseset_ior (sparseset, sparseset, sparseset);
extern bool sparseset_equal_p (sparseset, sparseset);
/* Operation: S = {}
Clear the set of all elements. */
static inline void
sparseset_clear (sparseset s)
s->members = 0;
s->iterating = false;
/* Return the number of elements currently in the set. */
static inline SPARSESET_ELT_TYPE
sparseset_cardinality (sparseset s)
return s->members;
/* Return the maximum number of elements this set can hold. */
static inline SPARSESET_ELT_TYPE
sparseset_size (sparseset s)
return s->size;
/* Return true if e is a member of the set S, otherwise return false. */
static inline bool
sparseset_bit_p (sparseset s, SPARSESET_ELT_TYPE e)
gcc_checking_assert (e < s->size);
idx = s->sparse[e];
return idx < s->members && s->dense[idx] == e;
/* Low level insertion routine not meant for use outside of sparseset.[ch].
Assumes E is valid and not already a member of the set S. */
static inline void
sparseset_insert_bit (sparseset s, SPARSESET_ELT_TYPE e, SPARSESET_ELT_TYPE idx)
s->sparse[e] = idx;
s->dense[idx] = e;
/* Operation: S = S + {e}
Insert E into the set S, if it isn't already a member. */
static inline void
sparseset_set_bit (sparseset s, SPARSESET_ELT_TYPE e)
if (!sparseset_bit_p (s, e))
sparseset_insert_bit (s, e, s->members++);
/* Return and remove the last member added to the set S. */
static inline SPARSESET_ELT_TYPE
sparseset_pop (sparseset s)
SPARSESET_ELT_TYPE mem = s->members;
gcc_checking_assert (mem != 0);
s->members = mem - 1;
return s->dense[s->members];
static inline void
sparseset_iter_init (sparseset s)
s->iter = 0;
s->iter_inc = 1;
s->iterating = true;
static inline bool
sparseset_iter_p (sparseset s)
if (s->iterating && s->iter < s->members)
return true;
return s->iterating = false;
static inline SPARSESET_ELT_TYPE
sparseset_iter_elm (sparseset s)
return s->dense[s->iter];
static inline void
sparseset_iter_next (sparseset s)
s->iter += s->iter_inc;
s->iter_inc = 1;
for (sparseset_iter_init (SPARSESET); \
sparseset_iter_p (SPARSESET) \
&& (((ITER) = sparseset_iter_elm (SPARSESET)) || 1); \
sparseset_iter_next (SPARSESET))
#endif /* GCC_SPARSESET_H */