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"
15 #include <isl/options.h>
17 #include <isl_mat_private.h>
19 #define STATUS_ERROR -1
20 #define STATUS_REDUNDANT 1
21 #define STATUS_VALID 2
22 #define STATUS_SEPARATE 3
24 #define STATUS_ADJ_EQ 5
25 #define STATUS_ADJ_INEQ 6
27 static int status_in(isl_int *ineq, struct isl_tab *tab)
29 enum isl_ineq_type type = isl_tab_ineq_type(tab, ineq);
32 case isl_ineq_error: return STATUS_ERROR;
33 case isl_ineq_redundant: return STATUS_VALID;
34 case isl_ineq_separate: return STATUS_SEPARATE;
35 case isl_ineq_cut: return STATUS_CUT;
36 case isl_ineq_adj_eq: return STATUS_ADJ_EQ;
37 case isl_ineq_adj_ineq: return STATUS_ADJ_INEQ;
41 /* Compute the position of the equalities of basic map "bmap_i"
42 * with respect to the basic map represented by "tab_j".
43 * The resulting array has twice as many entries as the number
44 * of equalities corresponding to the two inequalties to which
45 * each equality corresponds.
47 static int *eq_status_in(__isl_keep isl_basic_map *bmap_i,
48 struct isl_tab *tab_j)
51 int *eq = isl_calloc_array(bmap_i->ctx, int, 2 * bmap_i->n_eq);
54 dim = isl_basic_map_total_dim(bmap_i);
55 for (k = 0; k < bmap_i->n_eq; ++k) {
56 for (l = 0; l < 2; ++l) {
57 isl_seq_neg(bmap_i->eq[k], bmap_i->eq[k], 1+dim);
58 eq[2 * k + l] = status_in(bmap_i->eq[k], tab_j);
59 if (eq[2 * k + l] == STATUS_ERROR)
62 if (eq[2 * k] == STATUS_SEPARATE ||
63 eq[2 * k + 1] == STATUS_SEPARATE)
73 /* Compute the position of the inequalities of basic map "bmap_i"
74 * (also represented by "tab_i") with respect to the basic map
75 * represented by "tab_j".
77 static int *ineq_status_in(__isl_keep isl_basic_map *bmap_i,
78 struct isl_tab *tab_i, struct isl_tab *tab_j)
81 unsigned n_eq = bmap_i->n_eq;
82 int *ineq = isl_calloc_array(bmap_i->ctx, int, bmap_i->n_ineq);
84 for (k = 0; k < bmap_i->n_ineq; ++k) {
85 if (isl_tab_is_redundant(tab_i, n_eq + k)) {
86 ineq[k] = STATUS_REDUNDANT;
89 ineq[k] = status_in(bmap_i->ineq[k], tab_j);
90 if (ineq[k] == STATUS_ERROR)
92 if (ineq[k] == STATUS_SEPARATE)
102 static int any(int *con, unsigned len, int status)
106 for (i = 0; i < len ; ++i)
107 if (con[i] == status)
112 static int count(int *con, unsigned len, int status)
117 for (i = 0; i < len ; ++i)
118 if (con[i] == status)
123 static int all(int *con, unsigned len, int status)
127 for (i = 0; i < len ; ++i) {
128 if (con[i] == STATUS_REDUNDANT)
130 if (con[i] != status)
136 static void drop(struct isl_map *map, int i, struct isl_tab **tabs)
138 isl_basic_map_free(map->p[i]);
139 isl_tab_free(tabs[i]);
141 if (i != map->n - 1) {
142 map->p[i] = map->p[map->n - 1];
143 tabs[i] = tabs[map->n - 1];
145 tabs[map->n - 1] = NULL;
149 /* Replace the pair of basic maps i and j by the basic map bounded
150 * by the valid constraints in both basic maps and the constraint
151 * in extra (if not NULL).
153 static int fuse(struct isl_map *map, int i, int j,
154 struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j,
155 __isl_keep isl_mat *extra)
158 struct isl_basic_map *fused = NULL;
159 struct isl_tab *fused_tab = NULL;
160 unsigned total = isl_basic_map_total_dim(map->p[i]);
161 unsigned extra_rows = extra ? extra->n_row : 0;
163 fused = isl_basic_map_alloc_space(isl_space_copy(map->p[i]->dim),
165 map->p[i]->n_eq + map->p[j]->n_eq,
166 map->p[i]->n_ineq + map->p[j]->n_ineq + extra_rows);
170 for (k = 0; k < map->p[i]->n_eq; ++k) {
171 if (eq_i && (eq_i[2 * k] != STATUS_VALID ||
172 eq_i[2 * k + 1] != STATUS_VALID))
174 l = isl_basic_map_alloc_equality(fused);
177 isl_seq_cpy(fused->eq[l], map->p[i]->eq[k], 1 + total);
180 for (k = 0; k < map->p[j]->n_eq; ++k) {
181 if (eq_j && (eq_j[2 * k] != STATUS_VALID ||
182 eq_j[2 * k + 1] != STATUS_VALID))
184 l = isl_basic_map_alloc_equality(fused);
187 isl_seq_cpy(fused->eq[l], map->p[j]->eq[k], 1 + total);
190 for (k = 0; k < map->p[i]->n_ineq; ++k) {
191 if (ineq_i[k] != STATUS_VALID)
193 l = isl_basic_map_alloc_inequality(fused);
196 isl_seq_cpy(fused->ineq[l], map->p[i]->ineq[k], 1 + total);
199 for (k = 0; k < map->p[j]->n_ineq; ++k) {
200 if (ineq_j[k] != STATUS_VALID)
202 l = isl_basic_map_alloc_inequality(fused);
205 isl_seq_cpy(fused->ineq[l], map->p[j]->ineq[k], 1 + total);
208 for (k = 0; k < map->p[i]->n_div; ++k) {
209 int l = isl_basic_map_alloc_div(fused);
212 isl_seq_cpy(fused->div[l], map->p[i]->div[k], 1 + 1 + total);
215 for (k = 0; k < extra_rows; ++k) {
216 l = isl_basic_map_alloc_inequality(fused);
219 isl_seq_cpy(fused->ineq[l], extra->row[k], 1 + total);
222 fused = isl_basic_map_gauss(fused, NULL);
223 ISL_F_SET(fused, ISL_BASIC_MAP_FINAL);
224 if (ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_RATIONAL) &&
225 ISL_F_ISSET(map->p[j], ISL_BASIC_MAP_RATIONAL))
226 ISL_F_SET(fused, ISL_BASIC_MAP_RATIONAL);
228 fused_tab = isl_tab_from_basic_map(fused, 0);
229 if (isl_tab_detect_redundant(fused_tab) < 0)
232 isl_basic_map_free(map->p[i]);
234 isl_tab_free(tabs[i]);
240 isl_tab_free(fused_tab);
241 isl_basic_map_free(fused);
245 /* Given a pair of basic maps i and j such that all constraints are either
246 * "valid" or "cut", check if the facets corresponding to the "cut"
247 * constraints of i lie entirely within basic map j.
248 * If so, replace the pair by the basic map consisting of the valid
249 * constraints in both basic maps.
251 * To see that we are not introducing any extra points, call the
252 * two basic maps A and B and the resulting map U and let x
253 * be an element of U \setminus ( A \cup B ).
254 * Then there is a pair of cut constraints c_1 and c_2 in A and B such that x
255 * violates them. Let X be the intersection of U with the opposites
256 * of these constraints. Then x \in X.
257 * The facet corresponding to c_1 contains the corresponding facet of A.
258 * This facet is entirely contained in B, so c_2 is valid on the facet.
259 * However, since it is also (part of) a facet of X, -c_2 is also valid
260 * on the facet. This means c_2 is saturated on the facet, so c_1 and
261 * c_2 must be opposites of each other, but then x could not violate
264 static int check_facets(struct isl_map *map, int i, int j,
265 struct isl_tab **tabs, int *ineq_i, int *ineq_j)
268 struct isl_tab_undo *snap;
269 unsigned n_eq = map->p[i]->n_eq;
271 snap = isl_tab_snap(tabs[i]);
273 for (k = 0; k < map->p[i]->n_ineq; ++k) {
274 if (ineq_i[k] != STATUS_CUT)
276 if (isl_tab_select_facet(tabs[i], n_eq + k) < 0)
278 for (l = 0; l < map->p[j]->n_ineq; ++l) {
280 if (ineq_j[l] != STATUS_CUT)
282 stat = status_in(map->p[j]->ineq[l], tabs[i]);
283 if (stat != STATUS_VALID)
286 if (isl_tab_rollback(tabs[i], snap) < 0)
288 if (l < map->p[j]->n_ineq)
292 if (k < map->p[i]->n_ineq)
295 return fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
298 /* Both basic maps have at least one inequality with and adjacent
299 * (but opposite) inequality in the other basic map.
300 * Check that there are no cut constraints and that there is only
301 * a single pair of adjacent inequalities.
302 * If so, we can replace the pair by a single basic map described
303 * by all but the pair of adjacent inequalities.
304 * Any additional points introduced lie strictly between the two
305 * adjacent hyperplanes and can therefore be integral.
314 * The test for a single pair of adjancent inequalities is important
315 * for avoiding the combination of two basic maps like the following
325 static int check_adj_ineq(struct isl_map *map, int i, int j,
326 struct isl_tab **tabs, int *ineq_i, int *ineq_j)
330 if (any(ineq_i, map->p[i]->n_ineq, STATUS_CUT) ||
331 any(ineq_j, map->p[j]->n_ineq, STATUS_CUT))
334 else if (count(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) == 1 &&
335 count(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ) == 1)
336 changed = fuse(map, i, j, tabs, NULL, ineq_i, NULL, ineq_j, NULL);
337 /* else ADJ INEQ TOO MANY */
342 /* Check if basic map "i" contains the basic map represented
343 * by the tableau "tab".
345 static int contains(struct isl_map *map, int i, int *ineq_i,
351 dim = isl_basic_map_total_dim(map->p[i]);
352 for (k = 0; k < map->p[i]->n_eq; ++k) {
353 for (l = 0; l < 2; ++l) {
355 isl_seq_neg(map->p[i]->eq[k], map->p[i]->eq[k], 1+dim);
356 stat = status_in(map->p[i]->eq[k], tab);
357 if (stat != STATUS_VALID)
362 for (k = 0; k < map->p[i]->n_ineq; ++k) {
364 if (ineq_i[k] == STATUS_REDUNDANT)
366 stat = status_in(map->p[i]->ineq[k], tab);
367 if (stat != STATUS_VALID)
373 /* Basic map "i" has an inequality "k" that is adjacent to some equality
374 * of basic map "j". All the other inequalities are valid for "j".
375 * Check if basic map "j" forms an extension of basic map "i".
377 * In particular, we relax constraint "k", compute the corresponding
378 * facet and check whether it is included in the other basic map.
379 * If so, we know that relaxing the constraint extends the basic
380 * map with exactly the other basic map (we already know that this
381 * other basic map is included in the extension, because there
382 * were no "cut" inequalities in "i") and we can replace the
383 * two basic maps by thie extension.
391 static int is_extension(struct isl_map *map, int i, int j, int k,
392 struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
396 struct isl_tab_undo *snap, *snap2;
397 unsigned n_eq = map->p[i]->n_eq;
399 if (isl_tab_is_equality(tabs[i], n_eq + k))
402 snap = isl_tab_snap(tabs[i]);
403 tabs[i] = isl_tab_relax(tabs[i], n_eq + k);
404 snap2 = isl_tab_snap(tabs[i]);
405 if (isl_tab_select_facet(tabs[i], n_eq + k) < 0)
407 super = contains(map, j, ineq_j, tabs[i]);
409 if (isl_tab_rollback(tabs[i], snap2) < 0)
411 map->p[i] = isl_basic_map_cow(map->p[i]);
414 isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
415 ISL_F_SET(map->p[i], ISL_BASIC_MAP_FINAL);
419 if (isl_tab_rollback(tabs[i], snap) < 0)
425 /* Data structure that keeps track of the wrapping constraints
426 * and of information to bound the coefficients of those constraints.
428 * bound is set if we want to apply a bound on the coefficients
429 * mat contains the wrapping constraints
430 * max is the bound on the coefficients (if bound is set)
438 /* Update wraps->max to be greater than or equal to the coefficients
439 * in the equalities and inequalities of bmap that can be removed if we end up
442 static void wraps_update_max(struct isl_wraps *wraps,
443 __isl_keep isl_basic_map *bmap, int *eq, int *ineq)
447 unsigned total = isl_basic_map_total_dim(bmap);
451 for (k = 0; k < bmap->n_eq; ++k) {
452 if (eq[2 * k] == STATUS_VALID &&
453 eq[2 * k + 1] == STATUS_VALID)
455 isl_seq_abs_max(bmap->eq[k] + 1, total, &max_k);
456 if (isl_int_abs_gt(max_k, wraps->max))
457 isl_int_set(wraps->max, max_k);
460 for (k = 0; k < bmap->n_ineq; ++k) {
461 if (ineq[k] == STATUS_VALID || ineq[k] == STATUS_REDUNDANT)
463 isl_seq_abs_max(bmap->ineq[k] + 1, total, &max_k);
464 if (isl_int_abs_gt(max_k, wraps->max))
465 isl_int_set(wraps->max, max_k);
468 isl_int_clear(max_k);
471 /* Initialize the isl_wraps data structure.
472 * If we want to bound the coefficients of the wrapping constraints,
473 * we set wraps->max to the largest coefficient
474 * in the equalities and inequalities that can be removed if we end up
477 static void wraps_init(struct isl_wraps *wraps, __isl_take isl_mat *mat,
478 __isl_keep isl_map *map, int i, int j,
479 int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
487 ctx = isl_mat_get_ctx(mat);
488 wraps->bound = isl_options_get_coalesce_bounded_wrapping(ctx);
491 isl_int_init(wraps->max);
492 isl_int_set_si(wraps->max, 0);
493 wraps_update_max(wraps, map->p[i], eq_i, ineq_i);
494 wraps_update_max(wraps, map->p[j], eq_j, ineq_j);
497 /* Free the contents of the isl_wraps data structure.
499 static void wraps_free(struct isl_wraps *wraps)
501 isl_mat_free(wraps->mat);
503 isl_int_clear(wraps->max);
506 /* Is the wrapping constraint in row "row" allowed?
508 * If wraps->bound is set, we check that none of the coefficients
509 * is greater than wraps->max.
511 static int allow_wrap(struct isl_wraps *wraps, int row)
518 for (i = 1; i < wraps->mat->n_col; ++i)
519 if (isl_int_abs_gt(wraps->mat->row[row][i], wraps->max))
525 /* For each non-redundant constraint in "bmap" (as determined by "tab"),
526 * wrap the constraint around "bound" such that it includes the whole
527 * set "set" and append the resulting constraint to "wraps".
528 * "wraps" is assumed to have been pre-allocated to the appropriate size.
529 * wraps->n_row is the number of actual wrapped constraints that have
531 * If any of the wrapping problems results in a constraint that is
532 * identical to "bound", then this means that "set" is unbounded in such
533 * way that no wrapping is possible. If this happens then wraps->n_row
535 * Similarly, if we want to bound the coefficients of the wrapping
536 * constraints and a newly added wrapping constraint does not
537 * satisfy the bound, then wraps->n_row is also reset to zero.
539 static int add_wraps(struct isl_wraps *wraps, __isl_keep isl_basic_map *bmap,
540 struct isl_tab *tab, isl_int *bound, __isl_keep isl_set *set)
544 unsigned total = isl_basic_map_total_dim(bmap);
546 w = wraps->mat->n_row;
548 for (l = 0; l < bmap->n_ineq; ++l) {
549 if (isl_seq_is_neg(bound, bmap->ineq[l], 1 + total))
551 if (isl_seq_eq(bound, bmap->ineq[l], 1 + total))
553 if (isl_tab_is_redundant(tab, bmap->n_eq + l))
556 isl_seq_cpy(wraps->mat->row[w], bound, 1 + total);
557 if (!isl_set_wrap_facet(set, wraps->mat->row[w], bmap->ineq[l]))
559 if (isl_seq_eq(wraps->mat->row[w], bound, 1 + total))
561 if (!allow_wrap(wraps, w))
565 for (l = 0; l < bmap->n_eq; ++l) {
566 if (isl_seq_is_neg(bound, bmap->eq[l], 1 + total))
568 if (isl_seq_eq(bound, bmap->eq[l], 1 + total))
571 isl_seq_cpy(wraps->mat->row[w], bound, 1 + total);
572 isl_seq_neg(wraps->mat->row[w + 1], bmap->eq[l], 1 + total);
573 if (!isl_set_wrap_facet(set, wraps->mat->row[w],
574 wraps->mat->row[w + 1]))
576 if (isl_seq_eq(wraps->mat->row[w], bound, 1 + total))
578 if (!allow_wrap(wraps, w))
582 isl_seq_cpy(wraps->mat->row[w], bound, 1 + total);
583 if (!isl_set_wrap_facet(set, wraps->mat->row[w], bmap->eq[l]))
585 if (isl_seq_eq(wraps->mat->row[w], bound, 1 + total))
587 if (!allow_wrap(wraps, w))
592 wraps->mat->n_row = w;
595 wraps->mat->n_row = 0;
599 /* Check if the constraints in "wraps" from "first" until the last
600 * are all valid for the basic set represented by "tab".
601 * If not, wraps->n_row is set to zero.
603 static int check_wraps(__isl_keep isl_mat *wraps, int first,
608 for (i = first; i < wraps->n_row; ++i) {
609 enum isl_ineq_type type;
610 type = isl_tab_ineq_type(tab, wraps->row[i]);
611 if (type == isl_ineq_error)
613 if (type == isl_ineq_redundant)
622 /* Return a set that corresponds to the non-redudant constraints
623 * (as recorded in tab) of bmap.
625 * It's important to remove the redundant constraints as some
626 * of the other constraints may have been modified after the
627 * constraints were marked redundant.
628 * In particular, a constraint may have been relaxed.
629 * Redundant constraints are ignored when a constraint is relaxed
630 * and should therefore continue to be ignored ever after.
631 * Otherwise, the relaxation might be thwarted by some of
634 static __isl_give isl_set *set_from_updated_bmap(__isl_keep isl_basic_map *bmap,
637 bmap = isl_basic_map_copy(bmap);
638 bmap = isl_basic_map_cow(bmap);
639 bmap = isl_basic_map_update_from_tab(bmap, tab);
640 return isl_set_from_basic_set(isl_basic_map_underlying_set(bmap));
643 /* Given a basic set i with a constraint k that is adjacent to either the
644 * whole of basic set j or a facet of basic set j, check if we can wrap
645 * both the facet corresponding to k and the facet of j (or the whole of j)
646 * around their ridges to include the other set.
647 * If so, replace the pair of basic sets by their union.
649 * All constraints of i (except k) are assumed to be valid for j.
651 * However, the constraints of j may not be valid for i and so
652 * we have to check that the wrapping constraints for j are valid for i.
654 * In the case where j has a facet adjacent to i, tab[j] is assumed
655 * to have been restricted to this facet, so that the non-redundant
656 * constraints in tab[j] are the ridges of the facet.
657 * Note that for the purpose of wrapping, it does not matter whether
658 * we wrap the ridges of i around the whole of j or just around
659 * the facet since all the other constraints are assumed to be valid for j.
660 * In practice, we wrap to include the whole of j.
669 static int can_wrap_in_facet(struct isl_map *map, int i, int j, int k,
670 struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
673 struct isl_wraps wraps;
675 struct isl_set *set_i = NULL;
676 struct isl_set *set_j = NULL;
677 struct isl_vec *bound = NULL;
678 unsigned total = isl_basic_map_total_dim(map->p[i]);
679 struct isl_tab_undo *snap;
682 set_i = set_from_updated_bmap(map->p[i], tabs[i]);
683 set_j = set_from_updated_bmap(map->p[j], tabs[j]);
684 mat = isl_mat_alloc(map->ctx, 2 * (map->p[i]->n_eq + map->p[j]->n_eq) +
685 map->p[i]->n_ineq + map->p[j]->n_ineq,
687 wraps_init(&wraps, mat, map, i, j, eq_i, ineq_i, eq_j, ineq_j);
688 bound = isl_vec_alloc(map->ctx, 1 + total);
689 if (!set_i || !set_j || !wraps.mat || !bound)
692 isl_seq_cpy(bound->el, map->p[i]->ineq[k], 1 + total);
693 isl_int_add_ui(bound->el[0], bound->el[0], 1);
695 isl_seq_cpy(wraps.mat->row[0], bound->el, 1 + total);
696 wraps.mat->n_row = 1;
698 if (add_wraps(&wraps, map->p[j], tabs[j], bound->el, set_i) < 0)
700 if (!wraps.mat->n_row)
703 snap = isl_tab_snap(tabs[i]);
705 if (isl_tab_select_facet(tabs[i], map->p[i]->n_eq + k) < 0)
707 if (isl_tab_detect_redundant(tabs[i]) < 0)
710 isl_seq_neg(bound->el, map->p[i]->ineq[k], 1 + total);
712 n = wraps.mat->n_row;
713 if (add_wraps(&wraps, map->p[i], tabs[i], bound->el, set_j) < 0)
716 if (isl_tab_rollback(tabs[i], snap) < 0)
718 if (check_wraps(wraps.mat, n, tabs[i]) < 0)
720 if (!wraps.mat->n_row)
723 changed = fuse(map, i, j, tabs, eq_i, ineq_i, eq_j, ineq_j, wraps.mat);
742 /* Set the is_redundant property of the "n" constraints in "cuts",
744 * This is a fairly tricky operation as it bypasses isl_tab.c.
745 * The reason we want to temporarily mark some constraints redundant
746 * is that we want to ignore them in add_wraps.
748 * Initially all cut constraints are non-redundant, but the
749 * selection of a facet right before the call to this function
750 * may have made some of them redundant.
751 * Likewise, the same constraints are marked non-redundant
752 * in the second call to this function, before they are officially
753 * made non-redundant again in the subsequent rollback.
755 static void set_is_redundant(struct isl_tab *tab, unsigned n_eq,
756 int *cuts, int n, int k, int v)
760 for (l = 0; l < n; ++l) {
763 tab->con[n_eq + cuts[l]].is_redundant = v;
767 /* Given a pair of basic maps i and j such that j sticks out
768 * of i at n cut constraints, each time by at most one,
769 * try to compute wrapping constraints and replace the two
770 * basic maps by a single basic map.
771 * The other constraints of i are assumed to be valid for j.
773 * The facets of i corresponding to the cut constraints are
774 * wrapped around their ridges, except those ridges determined
775 * by any of the other cut constraints.
776 * The intersections of cut constraints need to be ignored
777 * as the result of wrapping one cut constraint around another
778 * would result in a constraint cutting the union.
779 * In each case, the facets are wrapped to include the union
780 * of the two basic maps.
782 * The pieces of j that lie at an offset of exactly one from
783 * one of the cut constraints of i are wrapped around their edges.
784 * Here, there is no need to ignore intersections because we
785 * are wrapping around the union of the two basic maps.
787 * If any wrapping fails, i.e., if we cannot wrap to touch
788 * the union, then we give up.
789 * Otherwise, the pair of basic maps is replaced by their union.
791 static int wrap_in_facets(struct isl_map *map, int i, int j,
792 int *cuts, int n, struct isl_tab **tabs,
793 int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
796 struct isl_wraps wraps;
799 isl_vec *bound = NULL;
800 unsigned total = isl_basic_map_total_dim(map->p[i]);
803 struct isl_tab_undo *snap_i, *snap_j;
805 if (isl_tab_extend_cons(tabs[j], 1) < 0)
808 max_wrap = 2 * (map->p[i]->n_eq + map->p[j]->n_eq) +
809 map->p[i]->n_ineq + map->p[j]->n_ineq;
812 set = isl_set_union(set_from_updated_bmap(map->p[i], tabs[i]),
813 set_from_updated_bmap(map->p[j], tabs[j]));
814 mat = isl_mat_alloc(map->ctx, max_wrap, 1 + total);
815 wraps_init(&wraps, mat, map, i, j, eq_i, ineq_i, eq_j, ineq_j);
816 bound = isl_vec_alloc(map->ctx, 1 + total);
817 if (!set || !wraps.mat || !bound)
820 snap_i = isl_tab_snap(tabs[i]);
821 snap_j = isl_tab_snap(tabs[j]);
823 wraps.mat->n_row = 0;
825 for (k = 0; k < n; ++k) {
826 if (isl_tab_select_facet(tabs[i], map->p[i]->n_eq + cuts[k]) < 0)
828 if (isl_tab_detect_redundant(tabs[i]) < 0)
830 set_is_redundant(tabs[i], map->p[i]->n_eq, cuts, n, k, 1);
832 isl_seq_neg(bound->el, map->p[i]->ineq[cuts[k]], 1 + total);
833 if (!tabs[i]->empty &&
834 add_wraps(&wraps, map->p[i], tabs[i], bound->el, set) < 0)
837 set_is_redundant(tabs[i], map->p[i]->n_eq, cuts, n, k, 0);
838 if (isl_tab_rollback(tabs[i], snap_i) < 0)
843 if (!wraps.mat->n_row)
846 isl_seq_cpy(bound->el, map->p[i]->ineq[cuts[k]], 1 + total);
847 isl_int_add_ui(bound->el[0], bound->el[0], 1);
848 if (isl_tab_add_eq(tabs[j], bound->el) < 0)
850 if (isl_tab_detect_redundant(tabs[j]) < 0)
853 if (!tabs[j]->empty &&
854 add_wraps(&wraps, map->p[j], tabs[j], bound->el, set) < 0)
857 if (isl_tab_rollback(tabs[j], snap_j) < 0)
860 if (!wraps.mat->n_row)
865 changed = fuse(map, i, j, tabs,
866 eq_i, ineq_i, eq_j, ineq_j, wraps.mat);
880 /* Given two basic sets i and j such that i has no cut equalities,
881 * check if relaxing all the cut inequalities of i by one turns
882 * them into valid constraint for j and check if we can wrap in
883 * the bits that are sticking out.
884 * If so, replace the pair by their union.
886 * We first check if all relaxed cut inequalities of i are valid for j
887 * and then try to wrap in the intersections of the relaxed cut inequalities
890 * During this wrapping, we consider the points of j that lie at a distance
891 * of exactly 1 from i. In particular, we ignore the points that lie in
892 * between this lower-dimensional space and the basic map i.
893 * We can therefore only apply this to integer maps.
919 * Wrapping can fail if the result of wrapping one of the facets
920 * around its edges does not produce any new facet constraint.
921 * In particular, this happens when we try to wrap in unbounded sets.
923 * _______________________________________________________________________
927 * |_| |_________________________________________________________________
930 * The following is not an acceptable result of coalescing the above two
931 * sets as it includes extra integer points.
932 * _______________________________________________________________________
937 * \______________________________________________________________________
939 static int can_wrap_in_set(struct isl_map *map, int i, int j,
940 struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
947 if (ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_RATIONAL) ||
948 ISL_F_ISSET(map->p[j], ISL_BASIC_MAP_RATIONAL))
951 n = count(ineq_i, map->p[i]->n_ineq, STATUS_CUT);
955 cuts = isl_alloc_array(map->ctx, int, n);
959 for (k = 0, m = 0; m < n; ++k) {
960 enum isl_ineq_type type;
962 if (ineq_i[k] != STATUS_CUT)
965 isl_int_add_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
966 type = isl_tab_ineq_type(tabs[j], map->p[i]->ineq[k]);
967 isl_int_sub_ui(map->p[i]->ineq[k][0], map->p[i]->ineq[k][0], 1);
968 if (type == isl_ineq_error)
970 if (type != isl_ineq_redundant)
977 changed = wrap_in_facets(map, i, j, cuts, n, tabs,
978 eq_i, ineq_i, eq_j, ineq_j);
988 /* Check if either i or j has a single cut constraint that can
989 * be used to wrap in (a facet of) the other basic set.
990 * if so, replace the pair by their union.
992 static int check_wrap(struct isl_map *map, int i, int j,
993 struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
997 if (!any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT))
998 changed = can_wrap_in_set(map, i, j, tabs,
999 eq_i, ineq_i, eq_j, ineq_j);
1003 if (!any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT))
1004 changed = can_wrap_in_set(map, j, i, tabs,
1005 eq_j, ineq_j, eq_i, ineq_i);
1009 /* At least one of the basic maps has an equality that is adjacent
1010 * to inequality. Make sure that only one of the basic maps has
1011 * such an equality and that the other basic map has exactly one
1012 * inequality adjacent to an equality.
1013 * We call the basic map that has the inequality "i" and the basic
1014 * map that has the equality "j".
1015 * If "i" has any "cut" (in)equality, then relaxing the inequality
1016 * by one would not result in a basic map that contains the other
1019 static int check_adj_eq(struct isl_map *map, int i, int j,
1020 struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
1025 if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ) &&
1026 any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ))
1027 /* ADJ EQ TOO MANY */
1030 if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ))
1031 return check_adj_eq(map, j, i, tabs,
1032 eq_j, ineq_j, eq_i, ineq_i);
1034 /* j has an equality adjacent to an inequality in i */
1036 if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT))
1038 if (any(ineq_i, map->p[i]->n_ineq, STATUS_CUT))
1041 if (count(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_EQ) != 1 ||
1042 any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_EQ) ||
1043 any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
1044 any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ))
1045 /* ADJ EQ TOO MANY */
1048 for (k = 0; k < map->p[i]->n_ineq ; ++k)
1049 if (ineq_i[k] == STATUS_ADJ_EQ)
1052 changed = is_extension(map, i, j, k, tabs, eq_i, ineq_i, eq_j, ineq_j);
1056 if (count(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ) != 1)
1059 changed = can_wrap_in_facet(map, i, j, k, tabs, eq_i, ineq_i, eq_j, ineq_j);
1064 /* The two basic maps lie on adjacent hyperplanes. In particular,
1065 * basic map "i" has an equality that lies parallel to basic map "j".
1066 * Check if we can wrap the facets around the parallel hyperplanes
1067 * to include the other set.
1069 * We perform basically the same operations as can_wrap_in_facet,
1070 * except that we don't need to select a facet of one of the sets.
1076 * We only allow one equality of "i" to be adjacent to an equality of "j"
1077 * to avoid coalescing
1079 * [m, n] -> { [x, y] -> [x, 1 + y] : x >= 1 and y >= 1 and
1080 * x <= 10 and y <= 10;
1081 * [x, y] -> [1 + x, y] : x >= 1 and x <= 20 and
1082 * y >= 5 and y <= 15 }
1086 * [m, n] -> { [x, y] -> [x2, y2] : x >= 1 and 10y2 <= 20 - x + 10y and
1087 * 4y2 >= 5 + 3y and 5y2 <= 15 + 4y and
1088 * y2 <= 1 + x + y - x2 and y2 >= y and
1089 * y2 >= 1 + x + y - x2 }
1091 static int check_eq_adj_eq(struct isl_map *map, int i, int j,
1092 struct isl_tab **tabs, int *eq_i, int *ineq_i, int *eq_j, int *ineq_j)
1096 struct isl_wraps wraps;
1098 struct isl_set *set_i = NULL;
1099 struct isl_set *set_j = NULL;
1100 struct isl_vec *bound = NULL;
1101 unsigned total = isl_basic_map_total_dim(map->p[i]);
1103 if (count(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_EQ) != 1)
1106 for (k = 0; k < 2 * map->p[i]->n_eq ; ++k)
1107 if (eq_i[k] == STATUS_ADJ_EQ)
1110 set_i = set_from_updated_bmap(map->p[i], tabs[i]);
1111 set_j = set_from_updated_bmap(map->p[j], tabs[j]);
1112 mat = isl_mat_alloc(map->ctx, 2 * (map->p[i]->n_eq + map->p[j]->n_eq) +
1113 map->p[i]->n_ineq + map->p[j]->n_ineq,
1115 wraps_init(&wraps, mat, map, i, j, eq_i, ineq_i, eq_j, ineq_j);
1116 bound = isl_vec_alloc(map->ctx, 1 + total);
1117 if (!set_i || !set_j || !wraps.mat || !bound)
1121 isl_seq_neg(bound->el, map->p[i]->eq[k / 2], 1 + total);
1123 isl_seq_cpy(bound->el, map->p[i]->eq[k / 2], 1 + total);
1124 isl_int_add_ui(bound->el[0], bound->el[0], 1);
1126 isl_seq_cpy(wraps.mat->row[0], bound->el, 1 + total);
1127 wraps.mat->n_row = 1;
1129 if (add_wraps(&wraps, map->p[j], tabs[j], bound->el, set_i) < 0)
1131 if (!wraps.mat->n_row)
1134 isl_int_sub_ui(bound->el[0], bound->el[0], 1);
1135 isl_seq_neg(bound->el, bound->el, 1 + total);
1137 isl_seq_cpy(wraps.mat->row[wraps.mat->n_row], bound->el, 1 + total);
1140 if (add_wraps(&wraps, map->p[i], tabs[i], bound->el, set_j) < 0)
1142 if (!wraps.mat->n_row)
1145 changed = fuse(map, i, j, tabs, eq_i, ineq_i, eq_j, ineq_j, wraps.mat);
1148 error: changed = -1;
1153 isl_set_free(set_i);
1154 isl_set_free(set_j);
1155 isl_vec_free(bound);
1160 /* Check if the union of the given pair of basic maps
1161 * can be represented by a single basic map.
1162 * If so, replace the pair by the single basic map and return 1.
1163 * Otherwise, return 0;
1165 * We first check the effect of each constraint of one basic map
1166 * on the other basic map.
1167 * The constraint may be
1168 * redundant the constraint is redundant in its own
1169 * basic map and should be ignore and removed
1171 * valid all (integer) points of the other basic map
1172 * satisfy the constraint
1173 * separate no (integer) point of the other basic map
1174 * satisfies the constraint
1175 * cut some but not all points of the other basic map
1176 * satisfy the constraint
1177 * adj_eq the given constraint is adjacent (on the outside)
1178 * to an equality of the other basic map
1179 * adj_ineq the given constraint is adjacent (on the outside)
1180 * to an inequality of the other basic map
1182 * We consider seven cases in which we can replace the pair by a single
1183 * basic map. We ignore all "redundant" constraints.
1185 * 1. all constraints of one basic map are valid
1186 * => the other basic map is a subset and can be removed
1188 * 2. all constraints of both basic maps are either "valid" or "cut"
1189 * and the facets corresponding to the "cut" constraints
1190 * of one of the basic maps lies entirely inside the other basic map
1191 * => the pair can be replaced by a basic map consisting
1192 * of the valid constraints in both basic maps
1194 * 3. there is a single pair of adjacent inequalities
1195 * (all other constraints are "valid")
1196 * => the pair can be replaced by a basic map consisting
1197 * of the valid constraints in both basic maps
1199 * 4. there is a single adjacent pair of an inequality and an equality,
1200 * the other constraints of the basic map containing the inequality are
1201 * "valid". Moreover, if the inequality the basic map is relaxed
1202 * and then turned into an equality, then resulting facet lies
1203 * entirely inside the other basic map
1204 * => the pair can be replaced by the basic map containing
1205 * the inequality, with the inequality relaxed.
1207 * 5. there is a single adjacent pair of an inequality and an equality,
1208 * the other constraints of the basic map containing the inequality are
1209 * "valid". Moreover, the facets corresponding to both
1210 * the inequality and the equality can be wrapped around their
1211 * ridges to include the other basic map
1212 * => the pair can be replaced by a basic map consisting
1213 * of the valid constraints in both basic maps together
1214 * with all wrapping constraints
1216 * 6. one of the basic maps extends beyond the other by at most one.
1217 * Moreover, the facets corresponding to the cut constraints and
1218 * the pieces of the other basic map at offset one from these cut
1219 * constraints can be wrapped around their ridges to include
1220 * the union of the two basic maps
1221 * => the pair can be replaced by a basic map consisting
1222 * of the valid constraints in both basic maps together
1223 * with all wrapping constraints
1225 * 7. the two basic maps live in adjacent hyperplanes. In principle
1226 * such sets can always be combined through wrapping, but we impose
1227 * that there is only one such pair, to avoid overeager coalescing.
1229 * Throughout the computation, we maintain a collection of tableaus
1230 * corresponding to the basic maps. When the basic maps are dropped
1231 * or combined, the tableaus are modified accordingly.
1233 static int coalesce_pair(struct isl_map *map, int i, int j,
1234 struct isl_tab **tabs)
1242 eq_i = eq_status_in(map->p[i], tabs[j]);
1245 if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ERROR))
1247 if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_SEPARATE))
1250 eq_j = eq_status_in(map->p[j], tabs[i]);
1253 if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_ERROR))
1255 if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_SEPARATE))
1258 ineq_i = ineq_status_in(map->p[i], tabs[i], tabs[j]);
1261 if (any(ineq_i, map->p[i]->n_ineq, STATUS_ERROR))
1263 if (any(ineq_i, map->p[i]->n_ineq, STATUS_SEPARATE))
1266 ineq_j = ineq_status_in(map->p[j], tabs[j], tabs[i]);
1269 if (any(ineq_j, map->p[j]->n_ineq, STATUS_ERROR))
1271 if (any(ineq_j, map->p[j]->n_ineq, STATUS_SEPARATE))
1274 if (all(eq_i, 2 * map->p[i]->n_eq, STATUS_VALID) &&
1275 all(ineq_i, map->p[i]->n_ineq, STATUS_VALID)) {
1278 } else if (all(eq_j, 2 * map->p[j]->n_eq, STATUS_VALID) &&
1279 all(ineq_j, map->p[j]->n_ineq, STATUS_VALID)) {
1282 } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_EQ)) {
1283 changed = check_eq_adj_eq(map, i, j, tabs,
1284 eq_i, ineq_i, eq_j, ineq_j);
1285 } else if (any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_EQ)) {
1286 changed = check_eq_adj_eq(map, j, i, tabs,
1287 eq_j, ineq_j, eq_i, ineq_i);
1288 } else if (any(eq_i, 2 * map->p[i]->n_eq, STATUS_ADJ_INEQ) ||
1289 any(eq_j, 2 * map->p[j]->n_eq, STATUS_ADJ_INEQ)) {
1290 changed = check_adj_eq(map, i, j, tabs,
1291 eq_i, ineq_i, eq_j, ineq_j);
1292 } else if (any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_EQ) ||
1293 any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_EQ)) {
1296 } else if (any(ineq_i, map->p[i]->n_ineq, STATUS_ADJ_INEQ) ||
1297 any(ineq_j, map->p[j]->n_ineq, STATUS_ADJ_INEQ)) {
1298 if (!any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) &&
1299 !any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT))
1300 changed = check_adj_ineq(map, i, j, tabs,
1303 if (!any(eq_i, 2 * map->p[i]->n_eq, STATUS_CUT) &&
1304 !any(eq_j, 2 * map->p[j]->n_eq, STATUS_CUT))
1305 changed = check_facets(map, i, j, tabs, ineq_i, ineq_j);
1307 changed = check_wrap(map, i, j, tabs,
1308 eq_i, ineq_i, eq_j, ineq_j);
1325 static struct isl_map *coalesce(struct isl_map *map, struct isl_tab **tabs)
1329 for (i = map->n - 2; i >= 0; --i)
1331 for (j = i + 1; j < map->n; ++j) {
1333 changed = coalesce_pair(map, i, j, tabs);
1345 /* For each pair of basic maps in the map, check if the union of the two
1346 * can be represented by a single basic map.
1347 * If so, replace the pair by the single basic map and start over.
1349 struct isl_map *isl_map_coalesce(struct isl_map *map)
1353 struct isl_tab **tabs = NULL;
1355 map = isl_map_remove_empty_parts(map);
1362 map = isl_map_align_divs(map);
1364 tabs = isl_calloc_array(map->ctx, struct isl_tab *, map->n);
1369 for (i = 0; i < map->n; ++i) {
1370 tabs[i] = isl_tab_from_basic_map(map->p[i], 0);
1373 if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_IMPLICIT))
1374 if (isl_tab_detect_implicit_equalities(tabs[i]) < 0)
1376 if (!ISL_F_ISSET(map->p[i], ISL_BASIC_MAP_NO_REDUNDANT))
1377 if (isl_tab_detect_redundant(tabs[i]) < 0)
1380 for (i = map->n - 1; i >= 0; --i)
1384 map = coalesce(map, tabs);
1387 for (i = 0; i < map->n; ++i) {
1388 map->p[i] = isl_basic_map_update_from_tab(map->p[i],
1390 map->p[i] = isl_basic_map_finalize(map->p[i]);
1393 ISL_F_SET(map->p[i], ISL_BASIC_MAP_NO_IMPLICIT);
1394 ISL_F_SET(map->p[i], ISL_BASIC_MAP_NO_REDUNDANT);
1397 for (i = 0; i < n; ++i)
1398 isl_tab_free(tabs[i]);
1405 for (i = 0; i < n; ++i)
1406 isl_tab_free(tabs[i]);
1412 /* For each pair of basic sets in the set, check if the union of the two
1413 * can be represented by a single basic set.
1414 * If so, replace the pair by the single basic set and start over.
1416 struct isl_set *isl_set_coalesce(struct isl_set *set)
1418 return (struct isl_set *)isl_map_coalesce((struct isl_map *)set);