2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
5 * Use of this software is governed by the GNU LGPLv2.1 license
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
10 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 #include "isl_map_private.h"
17 #define STATUS_ERROR -1
18 #define STATUS_REDUNDANT 1
19 #define STATUS_VALID 2
20 #define STATUS_SEPARATE 3
22 #define STATUS_ADJ_EQ 5
23 #define STATUS_ADJ_INEQ 6
25 static int status_in(isl_int *ineq, struct isl_tab *tab)
27 enum isl_ineq_type type = isl_tab_ineq_type(tab, ineq);
29 case isl_ineq_error: return STATUS_ERROR;
30 case isl_ineq_redundant: return STATUS_VALID;
31 case isl_ineq_separate: return STATUS_SEPARATE;
32 case isl_ineq_cut: return STATUS_CUT;
33 case isl_ineq_adj_eq: return STATUS_ADJ_EQ;
34 case isl_ineq_adj_ineq: return STATUS_ADJ_INEQ;
38 /* Compute the position of the equalities of basic map "i"
39 * with respect to basic map "j".
40 * The resulting array has twice as many entries as the number
41 * of equalities corresponding to the two inequalties to which
42 * each equality corresponds.
44 static int *eq_status_in(struct isl_map *map, int i, int j,
45 struct isl_tab **tabs)
48 int *eq = isl_calloc_array(map->ctx, int, 2 * map->p[i]->n_eq);
51 dim = isl_basic_map_total_dim(map->p[i]);
52 for (k = 0; k < map->p[i]->n_eq; ++k) {
53 for (l = 0; l < 2; ++l) {
54 isl_seq_neg(map->p[i]->eq[k], map->p[i]->eq[k], 1+dim);
55 eq[2 * k + l] = status_in(map->p[i]->eq[k], tabs[j]);
56 if (eq[2 * k + l] == STATUS_ERROR)
59 if (eq[2 * k] == STATUS_SEPARATE ||
60 eq[2 * k + 1] == STATUS_SEPARATE)
70 /* Compute the position of the inequalities of basic map "i"
71 * with respect to basic map "j".
73 static int *ineq_status_in(struct isl_map *map, int i, int j,
74 struct isl_tab **tabs)
77 unsigned n_eq = map->p[i]->n_eq;
78 int *ineq = isl_calloc_array(map->ctx, int, map->p[i]->n_ineq);
80 for (k = 0; k < map->p[i]->n_ineq; ++k) {
81 if (isl_tab_is_redundant(tabs[i], n_eq + k)) {
82 ineq[k] = STATUS_REDUNDANT;
85 ineq[k] = status_in(map->p[i]->ineq[k], tabs[j]);
86 if (ineq[k] == STATUS_ERROR)
88 if (ineq[k] == STATUS_SEPARATE)
98 static int any(int *con, unsigned len, int status)
102 for (i = 0; i < len ; ++i)
103 if (con[i] == status)
108 static int count(int *con, unsigned len, int status)
113 for (i = 0; i < len ; ++i)
114 if (con[i] == status)
119 static int all(int *con, unsigned len, int status)
123 for (i = 0; i < len ; ++i) {
124 if (con[i] == STATUS_REDUNDANT)
126 if (con[i] != status)
132 static void drop(struct isl_map *map, int i, struct isl_tab **tabs)
134 isl_basic_map_free(map->p[i]);
135 isl_tab_free(tabs[i]);
137 if (i != map->n - 1) {
138 map->p[i] = map->p[map->n - 1];
139 tabs[i] = tabs[map->n - 1];
141 tabs[map->n - 1] = NULL;
145 /* Replace the pair of basic maps i and j by the basic map bounded
146 * by the valid constraints in both basic maps and the constraint
147 * in extra (if not NULL).
149 static int fuse(struct isl_map *map, int i, int j,
150 struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j,
151 __isl_keep isl_mat *extra)
154 struct isl_basic_map *fused = NULL;
155 struct isl_tab *fused_tab = NULL;
156 unsigned total = isl_basic_map_total_dim(map->p[i]);
157 unsigned extra_rows = extra ? extra->n_row : 0;
159 fused = isl_basic_map_alloc_dim(isl_dim_copy(map->p[i]->dim),
161 map->p[i]->n_eq + map->p[j]->n_eq,
162 map->p[i]->n_ineq + map->p[j]->n_ineq + extra_rows);
166 for (k = 0; k < map->p[i]->n_eq; ++k) {
167 if (eq_i && (eq_i[2 * k] != STATUS_VALID ||
168 eq_i[2 * k + 1] != STATUS_VALID))
170 l = isl_basic_map_alloc_equality(fused);
173 isl_seq_cpy(fused->eq[l], map->p[i]->eq[k], 1 + total);
176 for (k = 0; k < map->p[j]->n_eq; ++k) {
177 if (eq_j && (eq_j[2 * k] != STATUS_VALID ||
178 eq_j[2 * k + 1] != STATUS_VALID))
180 l = isl_basic_map_alloc_equality(fused);
183 isl_seq_cpy(fused->eq[l], map->p[j]->eq[k], 1 + total);
186 for (k = 0; k < map->p[i]->n_ineq; ++k) {
187 if (ineq_i[k] != STATUS_VALID)
189 l = isl_basic_map_alloc_inequality(fused);
192 isl_seq_cpy(fused->ineq[l], map->p[i]->ineq[k], 1 + total);
195 for (k = 0; k < map->p[j]->n_ineq; ++k) {
196 if (ineq_j[k] != STATUS_VALID)
198 l = isl_basic_map_alloc_inequality(fused);
201 isl_seq_cpy(fused->ineq[l], map->p[j]->ineq[k], 1 + total);
204 for (k = 0; k < map->p[i]->n_div; ++k) {
205 int l = isl_basic_map_alloc_div(fused);
208 isl_seq_cpy(fused->div[l], map->p[i]->div[k], 1 + 1 + total);
211 for (k = 0; k < extra_rows; ++k) {
212 l = isl_basic_map_alloc_inequality(fused);
215 isl_seq_cpy(fused->ineq[l], extra->row[k], 1 + total);
218 fused = isl_basic_map_gauss(fused, NULL);
219 ISL_F_SET(fused, ISL_BASIC_MAP_FINAL);
220 if (ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_RATIONAL) &&
221 ISL_F_ISSET(map->p[j], ISL_BASIC_MAP_RATIONAL))
222 ISL_F_SET(fused, ISL_BASIC_MAP_RATIONAL);
224 fused_tab = isl_tab_from_basic_map(fused);
225 if (isl_tab_detect_redundant(fused_tab) < 0)
228 isl_basic_map_free(map->p[i]);
230 isl_tab_free(tabs[i]);
236 isl_tab_free(fused_tab);
237 isl_basic_map_free(fused);
241 /* Given a pair of basic maps i and j such that all constraints are either
242 * "valid" or "cut", check if the facets corresponding to the "cut"
243 * constraints of i lie entirely within basic map j.
244 * If so, replace the pair by the basic map consisting of the valid
245 * constraints in both basic maps.
247 * To see that we are not introducing any extra points, call the
248 * two basic maps A and B and the resulting map U and let x
249 * be an element of U \setminus ( A \cup B ).
250 * Then there is a pair of cut constraints c_1 and c_2 in A and B such that x
251 * violates them. Let X be the intersection of U with the opposites
252 * of these constraints. Then x \in X.
253 * The facet corresponding to c_1 contains the corresponding facet of A.
254 * This facet is entirely contained in B, so c_2 is valid on the facet.
255 * However, since it is also (part of) a facet of X, -c_2 is also valid
256 * on the facet. This means c_2 is saturated on the facet, so c_1 and
257 * c_2 must be opposites of each other, but then x could not violate
260 static int check_facets(struct isl_map *map, int i, int j,
261 struct isl_tab **tabs, int *ineq_i, int *ineq_j)
264 struct isl_tab_undo *snap;
265 unsigned n_eq = map->p[i]->n_eq;
267 snap = isl_tab_snap(tabs[i]);
269 for (k = 0; k < map->p[i]->n_ineq; ++k) {
270 if (ineq_i[k] != STATUS_CUT)
272 tabs[i] = isl_tab_select_facet(tabs[i], n_eq + k);
273 for (l = 0; l < map->p[j]->n_ineq; ++l) {
275 if (ineq_j[l] != STATUS_CUT)
277 stat = status_in(map->p[j]->ineq[l], tabs[i]);
278 if (stat != STATUS_VALID)
281 if (isl_tab_rollback(tabs[i], snap) < 0)
283 if (l < map->p[j]->n_ineq)
287 if (k < map->p[i]->n_ineq)
290 return fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
293 /* Both basic maps have at least one inequality with and adjacent
294 * (but opposite) inequality in the other basic map.
295 * Check that there are no cut constraints and that there is only
296 * a single pair of adjacent inequalities.
297 * If so, we can replace the pair by a single basic map described
298 * by all but the pair of adjacent inequalities.
299 * Any additional points introduced lie strictly between the two
300 * adjacent hyperplanes and can therefore be integral.
309 * The test for a single pair of adjancent inequalities is important
310 * for avoiding the combination of two basic maps like the following
320 static int check_adj_ineq(struct isl_map *map, int i, int j,
321 struct isl_tab **tabs, int *ineq_i, int *ineq_j)
325 if (any(ineq_i, map->p[i]->n_ineq, STATUS_CUT) ||
326 any(ineq_j, map->p[j]->n_ineq, STATUS_CUT))
329 else if (count(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) == 1 &&
330 count(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ) == 1)
331 changed = fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
332 /* else ADJ INEQ TOO MANY */
337 /* Check if basic map "i" contains the basic map represented
338 * by the tableau "tab".
340 static int contains(struct isl_map *map, int i, int *ineq_i,
346 dim = isl_basic_map_total_dim(map->p[i]);
347 for (k = 0; k < map->p[i]->n_eq; ++k) {
348 for (l = 0; l < 2; ++l) {
350 isl_seq_neg(map->p[i]->eq[k], map->p[i]->eq[k], 1+dim);
351 stat = status_in(map->p[i]->eq[k], tab);
352 if (stat != STATUS_VALID)
357 for (k = 0; k < map->p[i]->n_ineq; ++k) {
359 if (ineq_i[k] == STATUS_REDUNDANT)
361 stat = status_in(map->p[i]->ineq[k], tab);
362 if (stat != STATUS_VALID)
368 /* Basic map "i" has an inequality "k" that is adjacent to some equality
369 * of basic map "j". All the other inequalities are valid for "j".
370 * Check if basic map "j" forms an extension of basic map "i".
372 * In particular, we relax constraint "k", compute the corresponding
373 * facet and check whether it is included in the other basic map.
374 * If so, we know that relaxing the constraint extends the basic
375 * map with exactly the other basic map (we already know that this
376 * other basic map is included in the extension, because there
377 * were no "cut" inequalities in "i") and we can replace the
378 * two basic maps by thie extension.
386 static int is_extension(struct isl_map *map, int i, int j, int k,
387 struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
391 struct isl_tab_undo *snap, *snap2;
392 unsigned n_eq = map->p[i]->n_eq;
394 snap = isl_tab_snap(tabs[i]);
395 tabs[i] = isl_tab_relax(tabs[i], n_eq + k);
396 snap2 = isl_tab_snap(tabs[i]);
397 tabs[i] = isl_tab_select_facet(tabs[i], n_eq + k);
398 super = contains(map, j, ineq_j, tabs[i]);
400 if (isl_tab_rollback(tabs[i], snap2) < 0)
402 map->p[i] = isl_basic_map_cow(map->p[i]);
405 isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
406 ISL_F_SET(map->p[i], ISL_BASIC_MAP_FINAL);
410 if (isl_tab_rollback(tabs[i], snap) < 0)
416 /* For each non-redundant constraint in "bmap" (as determined by "tab"),
417 * wrap the constraint around "bound" such that it includes the whole
418 * set "set" and append the resulting constraint to "wraps".
419 * "wraps" is assumed to have been pre-allocated to the appropriate size.
420 * wraps->n_row is the number of actual wrapped constraints that have
422 * If any of the wrapping problems results in a constraint that is
423 * identical to "bound", then this means that "set" is unbounded in such
424 * way that no wrapping is possible. If this happens then wraps->n_row
427 static int add_wraps(__isl_keep isl_mat *wraps, __isl_keep isl_basic_map *bmap,
428 struct isl_tab *tab, isl_int *bound, __isl_keep isl_set *set)
432 unsigned total = isl_basic_map_total_dim(bmap);
436 for (l = 0; l < bmap->n_ineq; ++l) {
437 if (isl_seq_is_neg(bound, bmap->ineq[l], 1 + total))
439 if (isl_seq_eq(bound, bmap->ineq[l], 1 + total))
441 if (isl_tab_is_redundant(tab, bmap->n_eq + l))
444 isl_seq_cpy(wraps->row[w], bound, 1 + total);
445 if (!isl_set_wrap_facet(set, wraps->row[w], bmap->ineq[l]))
447 if (isl_seq_eq(wraps->row[w], bound, 1 + total))
451 for (l = 0; l < bmap->n_eq; ++l) {
452 if (isl_seq_is_neg(bound, bmap->eq[l], 1 + total))
454 if (isl_seq_eq(bound, bmap->eq[l], 1 + total))
457 isl_seq_cpy(wraps->row[w], bound, 1 + total);
458 isl_seq_neg(wraps->row[w + 1], bmap->eq[l], 1 + total);
459 if (!isl_set_wrap_facet(set, wraps->row[w], wraps->row[w + 1]))
461 if (isl_seq_eq(wraps->row[w], bound, 1 + total))
465 isl_seq_cpy(wraps->row[w], bound, 1 + total);
466 if (!isl_set_wrap_facet(set, wraps->row[w], bmap->eq[l]))
468 if (isl_seq_eq(wraps->row[w], bound, 1 + total))
480 /* Check if the constraints in "wraps" from "first" until the last
481 * are all valid for the basic set represented by "tab".
482 * If not, wraps->n_row is set to zero.
484 static int check_wraps(__isl_keep isl_mat *wraps, int first,
489 for (i = first; i < wraps->n_row; ++i) {
490 enum isl_ineq_type type;
491 type = isl_tab_ineq_type(tab, wraps->row[i]);
492 if (type == isl_ineq_error)
494 if (type == isl_ineq_redundant)
503 /* Return a set that corresponds to the non-redudant constraints
504 * (as recorded in tab) of bmap.
506 * It's important to remove the redundant constraints as some
507 * of the other constraints may have been modified after the
508 * constraints were marked redundant.
509 * In particular, a constraint may have been relaxed.
510 * Redundant constraints are ignored when a constraint is relaxed
511 * and should therefore continue to be ignored ever after.
512 * Otherwise, the relaxation might be thwarted by some of
515 static __isl_give isl_set *set_from_updated_bmap(__isl_keep isl_basic_map *bmap,
518 bmap = isl_basic_map_copy(bmap);
519 bmap = isl_basic_map_cow(bmap);
520 bmap = isl_basic_map_update_from_tab(bmap, tab);
521 return isl_set_from_basic_set(isl_basic_map_underlying_set(bmap));
524 /* Given a basic set i with a constraint k that is adjacent to either the
525 * whole of basic set j or a facet of basic set j, check if we can wrap
526 * both the facet corresponding to k and the facet of j (or the whole of j)
527 * around their ridges to include the other set.
528 * If so, replace the pair of basic sets by their union.
530 * All constraints of i (except k) are assumed to be valid for j.
532 * However, the constraints of j may not be valid for i and so
533 * we have to check that the wrapping constraints for j are valid for i.
535 * In the case where j has a facet adjacent to i, tab[j] is assumed
536 * to have been restricted to this facet, so that the non-redundant
537 * constraints in tab[j] are the ridges of the facet.
538 * Note that for the purpose of wrapping, it does not matter whether
539 * we wrap the ridges of i around the whole of j or just around
540 * the facet since all the other constraints are assumed to be valid for j.
541 * In practice, we wrap to include the whole of j.
550 static int can_wrap_in_facet(struct isl_map *map, int i, int j, int k,
551 struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
554 struct isl_mat *wraps = NULL;
555 struct isl_set *set_i = NULL;
556 struct isl_set *set_j = NULL;
557 struct isl_vec *bound = NULL;
558 unsigned total = isl_basic_map_total_dim(map->p[i]);
559 struct isl_tab_undo *snap;
562 set_i = set_from_updated_bmap(map->p[i], tabs[i]);
563 set_j = set_from_updated_bmap(map->p[j], tabs[j]);
564 wraps = isl_mat_alloc(map->ctx, 2 * (map->p[i]->n_eq + map->p[j]->n_eq) +
565 map->p[i]->n_ineq + map->p[j]->n_ineq,
567 bound = isl_vec_alloc(map->ctx, 1 + total);
568 if (!set_i || !set_j || !wraps || !bound)
571 isl_seq_cpy(bound->el, map->p[i]->ineq[k], 1 + total);
572 isl_int_add_ui(bound->el[0], bound->el[0], 1);
574 isl_seq_cpy(wraps->row[0], bound->el, 1 + total);
577 if (add_wraps(wraps, map->p[j], tabs[j], bound->el, set_i) < 0)
582 snap = isl_tab_snap(tabs[i]);
584 tabs[i] = isl_tab_select_facet(tabs[i], map->p[i]->n_eq + k);
585 if (isl_tab_detect_redundant(tabs[i]) < 0)
588 isl_seq_neg(bound->el, map->p[i]->ineq[k], 1 + total);
591 if (add_wraps(wraps, map->p[i], tabs[i], bound->el, set_j) < 0)
594 if (isl_tab_rollback(tabs[i], snap) < 0)
596 if (check_wraps(wraps, n, tabs[i]) < 0)
601 changed = fuse(map, i, j, tabs, eq_i, ineq_i, eq_j, ineq_j, wraps);
620 /* Given two basic sets i and j such that i has exactly one cut constraint,
621 * check if we can wrap the corresponding facet around its ridges to include
622 * the other basic set (and nothing else).
623 * If so, replace the pair by their union.
625 * We first check if j has a facet adjacent to the cut constraint of i.
626 * If so, we try to wrap in the facet.
634 static int can_wrap_in_set(struct isl_map *map, int i, int j,
635 struct isl_tab **tabs, int *ineq_i, int *ineq_j)
639 unsigned total = isl_basic_map_total_dim(map->p[i]);
640 struct isl_tab_undo *snap;
642 for (k = 0; k < map->p[i]->n_ineq; ++k)
643 if (ineq_i[k] == STATUS_CUT)
646 isl_assert(map->ctx, k < map->p[i]->n_ineq, return -1);
648 isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
649 for (l = 0; l < map->p[j]->n_ineq; ++l) {
650 if (isl_tab_is_redundant(tabs[j], map->p[j]->n_eq + l))
652 if (isl_seq_eq(map->p[i]->ineq[k],
653 map->p[j]->ineq[l], 1 + total))
656 isl_int_sub_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
658 if (l >= map->p[j]->n_ineq)
661 snap = isl_tab_snap(tabs[j]);
662 tabs[j] = isl_tab_select_facet(tabs[j], map->p[j]->n_eq + l);
663 if (isl_tab_detect_redundant(tabs[j]) < 0)
666 changed = can_wrap_in_facet(map, i, j, k, tabs, NULL, ineq_i, NULL, ineq_j);
668 if (!changed && isl_tab_rollback(tabs[j], snap) < 0)
674 /* Check if either i or j has a single cut constraint that can
675 * be used to wrap in (a facet of) the other basic set.
676 * if so, replace the pair by their union.
678 static int check_wrap(struct isl_map *map, int i, int j,
679 struct isl_tab **tabs, int *ineq_i, int *ineq_j)
683 if (count(ineq_i, map->p[i]->n_ineq, STATUS_CUT) == 1)
684 changed = can_wrap_in_set(map, i, j, tabs, ineq_i, ineq_j);
688 if (count(ineq_j, map->p[j]->n_ineq, STATUS_CUT) == 1)
689 changed = can_wrap_in_set(map, j, i, tabs, ineq_j, ineq_i);
693 /* At least one of the basic maps has an equality that is adjacent
694 * to inequality. Make sure that only one of the basic maps has
695 * such an equality and that the other basic map has exactly one
696 * inequality adjacent to an equality.
697 * We call the basic map that has the inequality "i" and the basic
698 * map that has the equality "j".
699 * If "i" has any "cut" (in)equality, then relaxing the inequality
700 * by one would not result in a basic map that contains the other
703 static int check_adj_eq(struct isl_map *map, int i, int j,
704 struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
709 if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ) &&
710 any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ))
711 /* ADJ EQ TOO MANY */
714 if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ))
715 return check_adj_eq(map, j, i, tabs,
716 eq_j, ineq_j, eq_i, ineq_i);
718 /* j has an equality adjacent to an inequality in i */
720 if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT))
722 if (any(ineq_i, map->p[i]->n_ineq, STATUS_CUT))
725 if (count(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ) != 1 ||
726 count(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_EQ) != 1 ||
727 any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_EQ) ||
728 any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
729 any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ))
730 /* ADJ EQ TOO MANY */
733 for (k = 0; k < map->p[i]->n_ineq ; ++k)
734 if (ineq_i[k] == STATUS_ADJ_EQ)
737 changed = is_extension(map, i, j, k, tabs, eq_i, ineq_i, eq_j, ineq_j);
741 changed = can_wrap_in_facet(map, i, j, k, tabs, eq_i, ineq_i, eq_j, ineq_j);
746 /* Check if the union of the given pair of basic maps
747 * can be represented by a single basic map.
748 * If so, replace the pair by the single basic map and return 1.
749 * Otherwise, return 0;
751 * We first check the effect of each constraint of one basic map
752 * on the other basic map.
753 * The constraint may be
754 * redundant the constraint is redundant in its own
755 * basic map and should be ignore and removed
757 * valid all (integer) points of the other basic map
758 * satisfy the constraint
759 * separate no (integer) point of the other basic map
760 * satisfies the constraint
761 * cut some but not all points of the other basic map
762 * satisfy the constraint
763 * adj_eq the given constraint is adjacent (on the outside)
764 * to an equality of the other basic map
765 * adj_ineq the given constraint is adjacent (on the outside)
766 * to an inequality of the other basic map
768 * We consider six cases in which we can replace the pair by a single
769 * basic map. We ignore all "redundant" constraints.
771 * 1. all constraints of one basic map are valid
772 * => the other basic map is a subset and can be removed
774 * 2. all constraints of both basic maps are either "valid" or "cut"
775 * and the facets corresponding to the "cut" constraints
776 * of one of the basic maps lies entirely inside the other basic map
777 * => the pair can be replaced by a basic map consisting
778 * of the valid constraints in both basic maps
780 * 3. there is a single pair of adjacent inequalities
781 * (all other constraints are "valid")
782 * => the pair can be replaced by a basic map consisting
783 * of the valid constraints in both basic maps
785 * 4. there is a single adjacent pair of an inequality and an equality,
786 * the other constraints of the basic map containing the inequality are
787 * "valid". Moreover, if the inequality the basic map is relaxed
788 * and then turned into an equality, then resulting facet lies
789 * entirely inside the other basic map
790 * => the pair can be replaced by the basic map containing
791 * the inequality, with the inequality relaxed.
793 * 5. there is a single adjacent pair of an inequality and an equality,
794 * the other constraints of the basic map containing the inequality are
795 * "valid". Moreover, the facets corresponding to both
796 * the inequality and the equality can be wrapped around their
797 * ridges to include the other basic map
798 * => the pair can be replaced by a basic map consisting
799 * of the valid constraints in both basic maps together
800 * with all wrapping constraints
802 * 6. one of the basic maps has a single cut constraint and
803 * the other basic map has a constraint adjacent to this constraint.
804 * Moreover, the facets corresponding to both constraints
805 * can be wrapped around their ridges to include the other basic map
806 * => the pair can be replaced by a basic map consisting
807 * of the valid constraints in both basic maps together
808 * with all wrapping constraints
810 * Throughout the computation, we maintain a collection of tableaus
811 * corresponding to the basic maps. When the basic maps are dropped
812 * or combined, the tableaus are modified accordingly.
814 static int coalesce_pair(struct isl_map *map, int i, int j,
815 struct isl_tab **tabs)
823 eq_i = eq_status_in(map, i, j, tabs);
824 if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ERROR))
826 if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_SEPARATE))
829 eq_j = eq_status_in(map, j, i, tabs);
830 if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_ERROR))
832 if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_SEPARATE))
835 ineq_i = ineq_status_in(map, i, j, tabs);
836 if (any(ineq_i, map->p[i]->n_ineq, STATUS_ERROR))
838 if (any(ineq_i, map->p[i]->n_ineq, STATUS_SEPARATE))
841 ineq_j = ineq_status_in(map, j, i, tabs);
842 if (any(ineq_j, map->p[j]->n_ineq, STATUS_ERROR))
844 if (any(ineq_j, map->p[j]->n_ineq, STATUS_SEPARATE))
847 if (all(eq_i, 2 * map->p[i]->n_eq, STATUS_VALID) &&
848 all(ineq_i, map->p[i]->n_ineq, STATUS_VALID)) {
851 } else if (all(eq_j, 2 * map->p[j]->n_eq, STATUS_VALID) &&
852 all(ineq_j, map->p[j]->n_ineq, STATUS_VALID)) {
855 } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_EQ) ||
856 any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_EQ)) {
858 } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ) ||
859 any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ)) {
860 changed = check_adj_eq(map, i, j, tabs,
861 eq_i, ineq_i, eq_j, ineq_j);
862 } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) ||
863 any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT)) {
865 } else if (any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_EQ) ||
866 any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_EQ)) {
869 } else if (any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
870 any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ)) {
871 changed = check_adj_ineq(map, i, j, tabs, ineq_i, ineq_j);
873 changed = check_facets(map, i, j, tabs, ineq_i, ineq_j);
875 changed = check_wrap(map, i, j, tabs, ineq_i, ineq_j);
892 static struct isl_map *coalesce(struct isl_map *map, struct isl_tab **tabs)
896 for (i = map->n - 2; i >= 0; --i)
898 for (j = i + 1; j < map->n; ++j) {
900 changed = coalesce_pair(map, i, j, tabs);
912 /* For each pair of basic maps in the map, check if the union of the two
913 * can be represented by a single basic map.
914 * If so, replace the pair by the single basic map and start over.
916 struct isl_map *isl_map_coalesce(struct isl_map *map)
920 struct isl_tab **tabs = NULL;
928 map = isl_map_align_divs(map);
930 tabs = isl_calloc_array(map->ctx, struct isl_tab *, map->n);
935 for (i = 0; i < map->n; ++i) {
936 tabs[i] = isl_tab_from_basic_map(map->p[i]);
939 if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_IMPLICIT))
940 tabs[i] = isl_tab_detect_implicit_equalities(tabs[i]);
941 if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_REDUNDANT))
942 if (isl_tab_detect_redundant(tabs[i]) < 0)
945 for (i = map->n - 1; i >= 0; --i)
949 map = coalesce(map, tabs);
952 for (i = 0; i < map->n; ++i) {
953 map->p[i] = isl_basic_map_update_from_tab(map->p[i],
955 map->p[i] = isl_basic_map_finalize(map->p[i]);
958 ISL_F_SET(map->p[i], ISL_BASIC_MAP_NO_IMPLICIT);
959 ISL_F_SET(map->p[i], ISL_BASIC_MAP_NO_REDUNDANT);
962 for (i = 0; i < n; ++i)
963 isl_tab_free(tabs[i]);
970 for (i = 0; i < n; ++i)
971 isl_tab_free(tabs[i]);
976 /* For each pair of basic sets in the set, check if the union of the two
977 * can be represented by a single basic set.
978 * If so, replace the pair by the single basic set and start over.
980 struct isl_set *isl_set_coalesce(struct isl_set *set)
982 return (struct isl_set *)isl_map_coalesce((struct isl_map *)set);