2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
13 #include "isl_map_private.h"
15 #include <isl_point_private.h>
17 static void expand_constraint(isl_vec *v, unsigned dim,
18 isl_int *c, int *div_map, unsigned n_div)
22 isl_seq_cpy(v->el, c, 1 + dim);
23 isl_seq_clr(v->el + 1 + dim, v->size - (1 + dim));
25 for (i = 0; i < n_div; ++i)
26 isl_int_set(v->el[1 + dim + div_map[i]], c[1 + dim + i]);
29 /* Add all constraints of bmap to tab. The equalities of bmap
30 * are added as a pair of inequalities.
32 static int tab_add_constraints(struct isl_tab *tab,
33 __isl_keep isl_basic_map *bmap, int *div_map)
44 tab_total = isl_basic_map_total_dim(tab->bmap);
45 bmap_total = isl_basic_map_total_dim(bmap);
46 dim = isl_dim_total(tab->bmap->dim);
48 if (isl_tab_extend_cons(tab, 2 * bmap->n_eq + bmap->n_ineq) < 0)
51 v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
53 for (i = 0; i < bmap->n_eq; ++i) {
54 expand_constraint(v, dim, bmap->eq[i], div_map, bmap->n_div);
55 if (isl_tab_add_ineq(tab, v->el) < 0)
57 isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
58 expand_constraint(v, dim, bmap->eq[i], div_map, bmap->n_div);
59 if (isl_tab_add_ineq(tab, v->el) < 0)
61 isl_seq_neg(bmap->eq[i], bmap->eq[i], 1 + bmap_total);
66 for (i = 0; i < bmap->n_ineq; ++i) {
67 expand_constraint(v, dim, bmap->ineq[i], div_map, bmap->n_div);
68 if (isl_tab_add_ineq(tab, v->el) < 0)
81 /* Add a specific constraint of bmap (or its opposite) to tab.
82 * The position of the constraint is specified by "c", where
83 * the equalities of bmap are counted twice, once for the inequality
84 * that is equal to the equality, and once for its negation.
86 static int tab_add_constraint(struct isl_tab *tab,
87 __isl_keep isl_basic_map *bmap, int *div_map, int c, int oppose)
98 tab_total = isl_basic_map_total_dim(tab->bmap);
99 bmap_total = isl_basic_map_total_dim(bmap);
100 dim = isl_dim_total(tab->bmap->dim);
102 v = isl_vec_alloc(bmap->ctx, 1 + tab_total);
106 if (c < 2 * bmap->n_eq) {
107 if ((c % 2) != oppose)
108 isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
111 isl_int_sub_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
112 expand_constraint(v, dim, bmap->eq[c/2], div_map, bmap->n_div);
113 r = isl_tab_add_ineq(tab, v->el);
115 isl_int_add_ui(bmap->eq[c/2][0], bmap->eq[c/2][0], 1);
116 if ((c % 2) != oppose)
117 isl_seq_neg(bmap->eq[c/2], bmap->eq[c/2],
122 isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
124 isl_int_sub_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
126 expand_constraint(v, dim, bmap->ineq[c], div_map, bmap->n_div);
127 r = isl_tab_add_ineq(tab, v->el);
129 isl_int_add_ui(bmap->ineq[c][0], bmap->ineq[c][0], 1);
130 isl_seq_neg(bmap->ineq[c], bmap->ineq[c],
139 static int tab_add_divs(struct isl_tab *tab, __isl_keep isl_basic_map *bmap,
153 *div_map = isl_alloc_array(bmap->ctx, int, bmap->n_div);
157 total = isl_basic_map_total_dim(tab->bmap);
158 dim = total - tab->bmap->n_div;
159 vec = isl_vec_alloc(bmap->ctx, 2 + total + bmap->n_div);
163 for (i = 0; i < bmap->n_div; ++i) {
164 isl_seq_cpy(vec->el, bmap->div[i], 2 + dim);
165 isl_seq_clr(vec->el + 2 + dim, tab->bmap->n_div);
166 for (j = 0; j < i; ++j)
167 isl_int_set(vec->el[2 + dim + (*div_map)[j]],
168 bmap->div[i][2 + dim + j]);
169 for (j = 0; j < tab->bmap->n_div; ++j)
170 if (isl_seq_eq(tab->bmap->div[j],
171 vec->el, 2 + dim + tab->bmap->n_div))
174 if (j == tab->bmap->n_div) {
175 vec->size = 2 + dim + tab->bmap->n_div;
176 if (isl_tab_add_div(tab, vec, NULL, NULL) < 0)
190 /* Freeze all constraints of tableau tab.
192 static int tab_freeze_constraints(struct isl_tab *tab)
196 for (i = 0; i < tab->n_con; ++i)
197 if (isl_tab_freeze_constraint(tab, i) < 0)
203 /* Check for redundant constraints starting at offset.
204 * Put the indices of the redundant constraints in index
205 * and return the number of redundant constraints.
207 static int n_non_redundant(struct isl_tab *tab, int offset, int **index)
210 int n_test = tab->n_con - offset;
212 if (isl_tab_detect_redundant(tab) < 0)
216 *index = isl_alloc_array(tab->mat->ctx, int, n_test);
220 for (n = 0, i = 0; i < n_test; ++i) {
222 r = isl_tab_is_redundant(tab, offset + i);
233 /* basic_map_collect_diff calls add on each of the pieces of
234 * the set difference between bmap and map until the add method
235 * return a negative value.
237 struct isl_diff_collector {
238 int (*add)(struct isl_diff_collector *dc,
239 __isl_take isl_basic_map *bmap);
242 /* Compute the set difference between bmap and map and call
243 * dc->add on each of the piece until this function returns
245 * Return 0 on success and -1 on error. dc->add returning
246 * a negative value is treated as an error, but the calling
247 * function can interpret the results based on the state of dc.
249 * Assumes that both bmap and map have known divs.
251 * The difference is computed by a backtracking algorithm.
252 * Each level corresponds to a basic map in "map".
253 * When a node in entered for the first time, we check
254 * if the corresonding basic map intersects the current piece
255 * of "bmap". If not, we move to the next level.
256 * Otherwise, we split the current piece into as many
257 * pieces as there are non-redundant constraints of the current
258 * basic map in the intersection. Each of these pieces is
259 * handled by a child of the current node.
260 * In particular, if there are n non-redundant constraints,
261 * then for each 0 <= i < n, a piece is cut off by adding
262 * constraints 0 <= j < i and adding the opposite of constraint i.
263 * If there are no non-redundant constraints, meaning that the current
264 * piece is a subset of the current basic map, then we simply backtrack.
266 * In the leaves, we check if the remaining piece has any integer points
267 * and if so, pass it along to dc->add. As a special case, if nothing
268 * has been removed when we end up in a leaf, we simply pass along
269 * the original basic map.
271 static int basic_map_collect_diff(__isl_take isl_basic_map *bmap,
272 __isl_take isl_map *map, struct isl_diff_collector *dc)
279 struct isl_tab *tab = NULL;
280 struct isl_tab_undo **snap = NULL;
284 int **div_map = NULL;
286 empty = isl_basic_map_is_empty(bmap);
288 isl_basic_map_free(bmap);
290 return empty < 0 ? -1 : 0;
293 bmap = isl_basic_map_cow(bmap);
294 map = isl_map_cow(map);
299 snap = isl_alloc_array(map->ctx, struct isl_tab_undo *, map->n);
300 k = isl_alloc_array(map->ctx, int, map->n);
301 n = isl_alloc_array(map->ctx, int, map->n);
302 index = isl_calloc_array(map->ctx, int *, map->n);
303 div_map = isl_calloc_array(map->ctx, int *, map->n);
304 if (!snap || !k || !n || !index || !div_map)
307 bmap = isl_basic_map_order_divs(bmap);
308 map = isl_map_order_divs(map);
310 tab = isl_tab_from_basic_map(bmap);
311 if (isl_tab_track_bmap(tab, isl_basic_map_copy(bmap)) < 0)
319 if (level >= map->n) {
321 struct isl_basic_map *bm;
323 if (dc->add(dc, isl_basic_map_copy(bmap)) < 0)
327 bm = isl_basic_map_copy(tab->bmap);
328 bm = isl_basic_map_cow(bm);
329 bm = isl_basic_map_update_from_tab(bm, tab);
330 bm = isl_basic_map_simplify(bm);
331 bm = isl_basic_map_finalize(bm);
332 empty = isl_basic_map_is_empty(bm);
334 isl_basic_map_free(bm);
335 else if (dc->add(dc, bm) < 0)
345 struct isl_tab_undo *snap2;
346 snap2 = isl_tab_snap(tab);
347 if (tab_add_divs(tab, map->p[level],
348 &div_map[level]) < 0)
351 snap[level] = isl_tab_snap(tab);
352 if (tab_freeze_constraints(tab) < 0)
354 if (tab_add_constraints(tab, map->p[level],
360 if (isl_tab_rollback(tab, snap2) < 0)
366 n[level] = n_non_redundant(tab, offset, &index[level]);
374 if (isl_tab_rollback(tab, snap[level]) < 0)
376 if (tab_add_constraint(tab, map->p[level],
377 div_map[level], index[level][0], 1) < 0)
382 if (k[level] + 1 >= n[level]) {
386 if (isl_tab_rollback(tab, snap[level]) < 0)
388 if (tab_add_constraint(tab, map->p[level],
390 index[level][k[level]], 0) < 0)
392 snap[level] = isl_tab_snap(tab);
394 if (tab_add_constraint(tab, map->p[level],
396 index[level][k[level]], 1) < 0)
408 for (i = 0; index && i < map->n; ++i)
411 for (i = 0; div_map && i < map->n; ++i)
415 isl_basic_map_free(bmap);
424 for (i = 0; index && i < map->n; ++i)
427 for (i = 0; div_map && i < map->n; ++i)
430 isl_basic_map_free(bmap);
435 /* A diff collector that actually collects all parts of the
436 * set difference in the field diff.
438 struct isl_subtract_diff_collector {
439 struct isl_diff_collector dc;
440 struct isl_map *diff;
443 /* isl_subtract_diff_collector callback.
445 static int basic_map_subtract_add(struct isl_diff_collector *dc,
446 __isl_take isl_basic_map *bmap)
448 struct isl_subtract_diff_collector *sdc;
449 sdc = (struct isl_subtract_diff_collector *)dc;
451 sdc->diff = isl_map_union_disjoint(sdc->diff,
452 isl_map_from_basic_map(bmap));
454 return sdc->diff ? 0 : -1;
457 /* Return the set difference between bmap and map.
459 static __isl_give isl_map *basic_map_subtract(__isl_take isl_basic_map *bmap,
460 __isl_take isl_map *map)
462 struct isl_subtract_diff_collector sdc;
463 sdc.dc.add = &basic_map_subtract_add;
464 sdc.diff = isl_map_empty_like_basic_map(bmap);
465 if (basic_map_collect_diff(bmap, map, &sdc.dc) < 0) {
466 isl_map_free(sdc.diff);
472 /* Return the set difference between map1 and map2.
473 * (U_i A_i) \ (U_j B_j) is computed as U_i (A_i \ (U_j B_j))
475 struct isl_map *isl_map_subtract(struct isl_map *map1, struct isl_map *map2)
478 struct isl_map *diff;
483 isl_assert(map1->ctx, isl_dim_equal(map1->dim, map2->dim), goto error);
485 if (isl_map_is_empty(map2)) {
490 map1 = isl_map_compute_divs(map1);
491 map2 = isl_map_compute_divs(map2);
495 map1 = isl_map_remove_empty_parts(map1);
496 map2 = isl_map_remove_empty_parts(map2);
498 diff = isl_map_empty_like(map1);
499 for (i = 0; i < map1->n; ++i) {
501 d = basic_map_subtract(isl_basic_map_copy(map1->p[i]),
503 if (ISL_F_ISSET(map1, ISL_MAP_DISJOINT))
504 diff = isl_map_union_disjoint(diff, d);
506 diff = isl_map_union(diff, d);
519 struct isl_set *isl_set_subtract(struct isl_set *set1, struct isl_set *set2)
521 return (struct isl_set *)
523 (struct isl_map *)set1, (struct isl_map *)set2);
526 /* A diff collector that aborts as soon as its add function is called,
527 * setting empty to 0.
529 struct isl_is_empty_diff_collector {
530 struct isl_diff_collector dc;
534 /* isl_is_empty_diff_collector callback.
536 static int basic_map_is_empty_add(struct isl_diff_collector *dc,
537 __isl_take isl_basic_map *bmap)
539 struct isl_is_empty_diff_collector *edc;
540 edc = (struct isl_is_empty_diff_collector *)dc;
544 isl_basic_map_free(bmap);
548 /* Check if bmap \ map is empty by computing this set difference
549 * and breaking off as soon as the difference is known to be non-empty.
551 static int basic_map_diff_is_empty(__isl_keep isl_basic_map *bmap,
552 __isl_keep isl_map *map)
555 struct isl_is_empty_diff_collector edc;
557 r = isl_basic_map_fast_is_empty(bmap);
561 edc.dc.add = &basic_map_is_empty_add;
563 r = basic_map_collect_diff(isl_basic_map_copy(bmap),
564 isl_map_copy(map), &edc.dc);
568 return r < 0 ? -1 : 1;
571 /* Check if map1 \ map2 is empty by checking if the set difference is empty
572 * for each of the basic maps in map1.
574 static int map_diff_is_empty(__isl_keep isl_map *map1, __isl_keep isl_map *map2)
582 for (i = 0; i < map1->n; ++i) {
583 is_empty = basic_map_diff_is_empty(map1->p[i], map2);
584 if (is_empty < 0 || !is_empty)
591 /* Return 1 if "bmap" contains a single element.
593 int isl_basic_map_is_singleton(__isl_keep isl_basic_map *bmap)
601 return bmap->n_eq == isl_basic_map_total_dim(bmap);
604 /* Return 1 if "map" contains a single element.
606 int isl_map_is_singleton(__isl_keep isl_map *map)
613 return isl_basic_map_is_singleton(map->p[0]);
616 /* Given a singleton basic map, extract the single element
619 static __isl_give isl_point *singleton_extract_point(
620 __isl_keep isl_basic_map *bmap)
624 struct isl_vec *point;
630 dim = isl_basic_map_total_dim(bmap);
631 isl_assert(bmap->ctx, bmap->n_eq == dim, return NULL);
632 point = isl_vec_alloc(bmap->ctx, 1 + dim);
638 isl_int_set_si(point->el[0], 1);
639 for (j = 0; j < bmap->n_eq; ++j) {
642 isl_assert(bmap->ctx,
643 isl_seq_first_non_zero(bmap->eq[j] + 1, i) == -1,
645 isl_assert(bmap->ctx,
646 isl_int_is_one(bmap->eq[j][1 + i]) ||
647 isl_int_is_negone(bmap->eq[j][1 + i]),
649 isl_assert(bmap->ctx,
650 isl_seq_first_non_zero(bmap->eq[j]+1+i+1, dim-i-1) == -1,
653 isl_int_gcd(m, point->el[0], bmap->eq[j][1 + i]);
654 isl_int_divexact(m, bmap->eq[j][1 + i], m);
656 isl_seq_scale(point->el, point->el, m, 1 + i);
657 isl_int_divexact(m, point->el[0], bmap->eq[j][1 + i]);
659 isl_int_mul(point->el[1 + i], m, bmap->eq[j][0]);
663 return isl_point_alloc(isl_basic_map_get_dim(bmap), point);
670 /* Return 1 is the singleton map "map1" is a subset of "map2",
671 * i.e., if the single element of "map1" is also an element of "map2".
673 static int map_is_singleton_subset(__isl_keep isl_map *map1,
674 __isl_keep isl_map *map2)
678 struct isl_point *point;
685 point = singleton_extract_point(map1->p[0]);
689 for (i = 0; i < map2->n; ++i) {
690 is_subset = isl_basic_map_contains_point(map2->p[i], point);
695 isl_point_free(point);
699 int isl_map_is_subset(struct isl_map *map1, struct isl_map *map2)
702 struct isl_map *diff;
707 if (isl_map_is_empty(map1))
710 if (isl_map_is_empty(map2))
713 if (isl_map_fast_is_universe(map2))
716 map1 = isl_map_compute_divs(isl_map_copy(map1));
717 map2 = isl_map_compute_divs(isl_map_copy(map2));
718 if (isl_map_is_singleton(map1)) {
719 is_subset = map_is_singleton_subset(map1, map2);
724 is_subset = map_diff_is_empty(map1, map2);
731 int isl_set_is_subset(struct isl_set *set1, struct isl_set *set2)
733 return isl_map_is_subset(
734 (struct isl_map *)set1, (struct isl_map *)set2);
737 __isl_give isl_map *isl_map_make_disjoint(__isl_take isl_map *map)
740 struct isl_subtract_diff_collector sdc;
741 sdc.dc.add = &basic_map_subtract_add;
745 if (ISL_F_ISSET(map, ISL_MAP_DISJOINT))
750 map = isl_map_compute_divs(map);
751 map = isl_map_remove_empty_parts(map);
753 if (!map || map->n <= 1)
756 sdc.diff = isl_map_from_basic_map(isl_basic_map_copy(map->p[0]));
758 for (i = 1; i < map->n; ++i) {
759 struct isl_basic_map *bmap = isl_basic_map_copy(map->p[i]);
760 struct isl_map *copy = isl_map_copy(sdc.diff);
761 if (basic_map_collect_diff(bmap, copy, &sdc.dc) < 0) {
762 isl_map_free(sdc.diff);
773 __isl_give isl_set *isl_set_make_disjoint(__isl_take isl_set *set)
775 return (struct isl_set *)isl_map_make_disjoint((struct isl_map *)set);
778 __isl_give isl_set *isl_set_complement(__isl_take isl_set *set)
785 universe = isl_set_universe(isl_set_get_dim(set));
787 return isl_set_subtract(universe, set);