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_constraint.h>
15 #include "isl_map_private.h"
17 static unsigned n(struct isl_constraint *c, enum isl_dim_type type)
19 return isl_basic_map_dim(c->bmap, type);
22 static unsigned offset(struct isl_constraint *c, enum isl_dim_type type)
24 struct isl_dim *dim = c->bmap->dim;
26 case isl_dim_param: return 1;
27 case isl_dim_in: return 1 + dim->nparam;
28 case isl_dim_out: return 1 + dim->nparam + dim->n_in;
29 case isl_dim_div: return 1 + dim->nparam + dim->n_in + dim->n_out;
34 static unsigned basic_set_offset(struct isl_basic_set *bset,
35 enum isl_dim_type type)
37 struct isl_dim *dim = bset->dim;
39 case isl_dim_param: return 1;
40 case isl_dim_in: return 1 + dim->nparam;
41 case isl_dim_out: return 1 + dim->nparam + dim->n_in;
42 case isl_dim_div: return 1 + dim->nparam + dim->n_in + dim->n_out;
47 struct isl_constraint *isl_basic_map_constraint(struct isl_basic_map *bmap,
50 struct isl_constraint *constraint;
55 constraint = isl_alloc_type(bmap->ctx, struct isl_constraint);
59 constraint->ctx = bmap->ctx;
60 isl_ctx_ref(constraint->ctx);
62 constraint->bmap = bmap;
63 constraint->line = line;
67 isl_basic_map_free(bmap);
71 struct isl_constraint *isl_basic_set_constraint(struct isl_basic_set *bset,
74 return isl_basic_map_constraint((struct isl_basic_map *)bset, line);
77 struct isl_constraint *isl_equality_alloc(struct isl_dim *dim)
79 struct isl_basic_map *bmap;
84 bmap = isl_basic_map_alloc_dim(dim, 0, 1, 0);
88 isl_basic_map_alloc_equality(bmap);
89 isl_seq_clr(bmap->eq[0], 1 + isl_basic_map_total_dim(bmap));
90 return isl_basic_map_constraint(bmap, &bmap->eq[0]);
93 struct isl_constraint *isl_inequality_alloc(struct isl_dim *dim)
95 struct isl_basic_map *bmap;
100 bmap = isl_basic_map_alloc_dim(dim, 0, 0, 1);
104 isl_basic_map_alloc_inequality(bmap);
105 isl_seq_clr(bmap->ineq[0], 1 + isl_basic_map_total_dim(bmap));
106 return isl_basic_map_constraint(bmap, &bmap->ineq[0]);
109 struct isl_constraint *isl_constraint_dup(struct isl_constraint *c)
111 struct isl_basic_map *bmap;
118 eq = c->line < c->bmap->eq + c->bmap->n_eq;
119 i = eq ? c->line - c->bmap->eq : c->line - c->bmap->ineq;
120 bmap = isl_basic_map_copy(c->bmap);
123 return isl_basic_map_constraint(bmap, eq ? bmap->eq + i : bmap->ineq + i);
126 struct isl_constraint *isl_constraint_cow(struct isl_constraint *c)
134 return isl_constraint_dup(c);
137 struct isl_constraint *isl_constraint_copy(struct isl_constraint *constraint)
146 void isl_constraint_free(struct isl_constraint *c)
154 isl_basic_map_free(c->bmap);
155 isl_ctx_deref(c->ctx);
159 __isl_give isl_constraint *isl_basic_map_first_constraint(
160 __isl_take isl_basic_map *bmap)
166 return isl_basic_map_constraint(bmap, &bmap->eq[0]);
168 if (bmap->n_ineq > 0)
169 return isl_basic_map_constraint(bmap, &bmap->ineq[0]);
171 isl_basic_map_free(bmap);
175 __isl_give isl_constraint *isl_basic_set_first_constraint(
176 __isl_take isl_basic_set *bset)
178 return isl_basic_map_first_constraint((struct isl_basic_map *)bset);
181 struct isl_constraint *isl_constraint_next(struct isl_constraint *c)
183 c = isl_constraint_cow(c);
184 if (c->line >= c->bmap->eq) {
186 if (c->line < c->bmap->eq + c->bmap->n_eq)
188 c->line = c->bmap->ineq;
191 if (c->line < c->bmap->ineq + c->bmap->n_ineq)
193 isl_constraint_free(c);
197 int isl_basic_map_foreach_constraint(__isl_keep isl_basic_map *bmap,
198 int (*fn)(__isl_take isl_constraint *c, void *user), void *user)
201 struct isl_constraint *c;
206 isl_assert(bmap->ctx, ISL_F_ISSET(bmap, ISL_BASIC_MAP_FINAL),
209 for (i = 0; i < bmap->n_eq; ++i) {
210 c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
218 for (i = 0; i < bmap->n_ineq; ++i) {
219 c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
230 int isl_basic_set_foreach_constraint(__isl_keep isl_basic_set *bset,
231 int (*fn)(__isl_take isl_constraint *c, void *user), void *user)
233 return isl_basic_map_foreach_constraint((isl_basic_map *)bset, fn, user);
236 int isl_constraint_is_equal(struct isl_constraint *constraint1,
237 struct isl_constraint *constraint2)
239 if (!constraint1 || !constraint2)
241 return constraint1->bmap == constraint2->bmap &&
242 constraint1->line == constraint2->line;
245 struct isl_basic_map *isl_basic_map_add_constraint(
246 struct isl_basic_map *bmap, struct isl_constraint *constraint)
248 if (!bmap || !constraint)
251 isl_assert(constraint->ctx,
252 isl_dim_equal(bmap->dim, constraint->bmap->dim), goto error);
254 bmap = isl_basic_map_intersect(bmap,
255 isl_basic_map_from_constraint(constraint));
258 isl_basic_map_free(bmap);
259 isl_constraint_free(constraint);
263 struct isl_basic_set *isl_basic_set_add_constraint(
264 struct isl_basic_set *bset, struct isl_constraint *constraint)
266 return (struct isl_basic_set *)
267 isl_basic_map_add_constraint((struct isl_basic_map *)bset,
271 struct isl_constraint *isl_constraint_add_div(struct isl_constraint *constraint,
272 struct isl_div *div, int *pos)
274 if (!constraint || !div)
277 isl_assert(constraint->ctx,
278 isl_dim_equal(div->bmap->dim, constraint->bmap->dim), goto error);
279 isl_assert(constraint->ctx,
280 constraint->bmap->n_eq + constraint->bmap->n_ineq == 1, goto error);
282 constraint->bmap = isl_basic_map_cow(constraint->bmap);
283 constraint->bmap = isl_basic_map_extend_dim(constraint->bmap,
284 isl_dim_copy(constraint->bmap->dim), 1, 0, 0);
285 if (!constraint->bmap)
287 constraint->line = &constraint->bmap->ineq[0];
288 *pos = isl_basic_map_alloc_div(constraint->bmap);
291 isl_seq_cpy(constraint->bmap->div[*pos], div->line[0],
292 1 + 1 + isl_basic_map_total_dim(constraint->bmap));
296 isl_constraint_free(constraint);
301 int isl_constraint_dim(struct isl_constraint *constraint,
302 enum isl_dim_type type)
306 return n(constraint, type);
309 void isl_constraint_get_constant(struct isl_constraint *constraint, isl_int *v)
313 isl_int_set(*v, constraint->line[0][0]);
316 void isl_constraint_get_coefficient(struct isl_constraint *constraint,
317 enum isl_dim_type type, int pos, isl_int *v)
322 isl_assert(constraint->ctx, pos < n(constraint, type), return);
323 isl_int_set(*v, constraint->line[0][offset(constraint, type) + pos]);
326 struct isl_div *isl_constraint_div(struct isl_constraint *constraint, int pos)
331 isl_assert(constraint->ctx, pos < n(constraint, isl_dim_div),
333 isl_assert(constraint->ctx,
334 !isl_int_is_zero(constraint->bmap->div[pos][0]), return NULL);
335 return isl_basic_map_div(isl_basic_map_copy(constraint->bmap), pos);
338 void isl_constraint_set_constant(struct isl_constraint *constraint, isl_int v)
342 isl_int_set(constraint->line[0][0], v);
345 void isl_constraint_set_coefficient(struct isl_constraint *constraint,
346 enum isl_dim_type type, int pos, isl_int v)
351 isl_assert(constraint->ctx, pos < n(constraint, type), return);
352 isl_int_set(constraint->line[0][offset(constraint, type) + pos], v);
355 void isl_constraint_clear(struct isl_constraint *constraint)
361 total = isl_basic_map_total_dim(constraint->bmap);
362 isl_seq_clr(constraint->line[0], 1 + total);
365 struct isl_constraint *isl_constraint_negate(struct isl_constraint *constraint)
372 isl_assert(constraint->ctx, !isl_constraint_is_equality(constraint),
374 isl_assert(constraint->ctx, constraint->bmap->ref == 1, goto error);
375 total = isl_basic_map_total_dim(constraint->bmap);
376 isl_seq_neg(constraint->line[0], constraint->line[0], 1 + total);
377 isl_int_sub_ui(constraint->line[0][0], constraint->line[0][0], 1);
378 ISL_F_CLR(constraint->bmap, ISL_BASIC_MAP_NORMALIZED);
381 isl_constraint_free(constraint);
385 int isl_constraint_is_equality(struct isl_constraint *constraint)
389 return constraint->line >= constraint->bmap->eq;
392 /* We manually set ISL_BASIC_SET_FINAL instead of calling
393 * isl_basic_map_finalize because we want to keep the position
394 * of the divs and we therefore do not want to throw away redundant divs.
395 * This is arguably a bit fragile.
397 __isl_give isl_basic_map *isl_basic_map_from_constraint(
398 __isl_take isl_constraint *constraint)
401 struct isl_basic_map *bmap;
408 if (constraint->bmap->n_eq == 1 && constraint->bmap->n_ineq == 0) {
409 bmap = isl_basic_map_copy(constraint->bmap);
410 isl_constraint_free(constraint);
414 bmap = isl_basic_map_universe_like(constraint->bmap);
415 bmap = isl_basic_map_align_divs(bmap, constraint->bmap);
416 bmap = isl_basic_map_cow(bmap);
417 bmap = isl_basic_map_extend_constraints(bmap, 1, 1);
418 if (isl_constraint_is_equality(constraint)) {
419 k = isl_basic_map_alloc_equality(bmap);
425 k = isl_basic_map_alloc_inequality(bmap);
430 total = isl_basic_map_total_dim(bmap);
431 isl_seq_cpy(c, constraint->line[0], 1 + total);
432 isl_constraint_free(constraint);
434 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
437 isl_constraint_free(constraint);
438 isl_basic_map_free(bmap);
442 struct isl_basic_set *isl_basic_set_from_constraint(
443 struct isl_constraint *constraint)
448 isl_assert(constraint->ctx,n(constraint, isl_dim_in) == 0, goto error);
449 return (isl_basic_set *)isl_basic_map_from_constraint(constraint);
451 isl_constraint_free(constraint);
455 int isl_basic_set_has_defining_equality(
456 struct isl_basic_set *bset, enum isl_dim_type type, int pos,
457 struct isl_constraint **c)
465 offset = basic_set_offset(bset, type);
466 total = isl_basic_set_total_dim(bset);
467 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
468 for (i = 0; i < bset->n_eq; ++i)
469 if (!isl_int_is_zero(bset->eq[i][offset + pos]) &&
470 isl_seq_first_non_zero(bset->eq[i]+offset+pos+1,
471 1+total-offset-pos-1) == -1) {
472 *c= isl_basic_set_constraint(isl_basic_set_copy(bset),
479 int isl_basic_set_has_defining_inequalities(
480 struct isl_basic_set *bset, enum isl_dim_type type, int pos,
481 struct isl_constraint **lower,
482 struct isl_constraint **upper)
488 isl_int **lower_line, **upper_line;
492 offset = basic_set_offset(bset, type);
493 total = isl_basic_set_total_dim(bset);
494 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
496 for (i = 0; i < bset->n_ineq; ++i) {
497 if (isl_int_is_zero(bset->ineq[i][offset + pos]))
499 if (isl_int_is_one(bset->ineq[i][offset + pos]))
501 if (isl_int_is_negone(bset->ineq[i][offset + pos]))
503 if (isl_seq_first_non_zero(bset->ineq[i]+offset+pos+1,
504 1+total-offset-pos-1) != -1)
506 for (j = i + 1; j < bset->n_ineq; ++j) {
507 if (!isl_seq_is_neg(bset->ineq[i]+1, bset->ineq[j]+1,
510 isl_int_add(m, bset->ineq[i][0], bset->ineq[j][0]);
511 if (isl_int_abs_ge(m, bset->ineq[i][offset+pos]))
514 if (isl_int_is_pos(bset->ineq[i][offset+pos])) {
515 lower_line = &bset->ineq[i];
516 upper_line = &bset->ineq[j];
518 lower_line = &bset->ineq[j];
519 upper_line = &bset->ineq[i];
521 *lower = isl_basic_set_constraint(
522 isl_basic_set_copy(bset), lower_line);
523 *upper = isl_basic_set_constraint(
524 isl_basic_set_copy(bset), upper_line);
535 /* Given two constraints "a" and "b" on the variable at position "abs_pos"
536 * (in "a" and "b"), add a constraint to "bset" that ensures that the
537 * bound implied by "a" is (strictly) larger than the bound implied by "b".
539 * If both constraints imply lower bounds, then this means that "a" is
540 * active in the result.
541 * If both constraints imply upper bounds, then this means that "b" is
542 * active in the result.
544 static __isl_give isl_basic_set *add_larger_bound_constraint(
545 __isl_take isl_basic_set *bset, isl_int *a, isl_int *b,
546 unsigned abs_pos, int strict)
552 k = isl_basic_set_alloc_inequality(bset);
556 total = isl_basic_set_dim(bset, isl_dim_all);
559 isl_int_neg(t, b[1 + abs_pos]);
561 isl_seq_combine(bset->ineq[k], t, a, a[1 + abs_pos], b, 1 + abs_pos);
562 isl_seq_combine(bset->ineq[k] + 1 + abs_pos,
563 t, a + 1 + abs_pos + 1, a[1 + abs_pos], b + 1 + abs_pos + 1,
567 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
573 isl_basic_set_free(bset);
577 /* Add constraints to "context" that ensure that "u" is the smallest
578 * (and therefore active) upper bound on "abs_pos" in "bset" and return
579 * the resulting basic set.
581 static __isl_give isl_basic_set *set_smallest_upper_bound(
582 __isl_keep isl_basic_set *context,
583 __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_upper, int u)
587 context = isl_basic_set_copy(context);
588 context = isl_basic_set_cow(context);
590 context = isl_basic_set_extend_constraints(context, 0, n_upper - 1);
592 for (j = 0; j < bset->n_ineq; ++j) {
595 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
597 context = add_larger_bound_constraint(context,
598 bset->ineq[j], bset->ineq[u], abs_pos, j > u);
601 context = isl_basic_set_simplify(context);
602 context = isl_basic_set_finalize(context);
607 /* Add constraints to "context" that ensure that "u" is the largest
608 * (and therefore active) upper bound on "abs_pos" in "bset" and return
609 * the resulting basic set.
611 static __isl_give isl_basic_set *set_largest_lower_bound(
612 __isl_keep isl_basic_set *context,
613 __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_lower, int l)
617 context = isl_basic_set_copy(context);
618 context = isl_basic_set_cow(context);
620 context = isl_basic_set_extend_constraints(context, 0, n_lower - 1);
622 for (j = 0; j < bset->n_ineq; ++j) {
625 if (!isl_int_is_pos(bset->ineq[j][1 + abs_pos]))
627 context = add_larger_bound_constraint(context,
628 bset->ineq[l], bset->ineq[j], abs_pos, j > l);
631 context = isl_basic_set_simplify(context);
632 context = isl_basic_set_finalize(context);
637 static int foreach_upper_bound(__isl_keep isl_basic_set *bset,
638 enum isl_dim_type type, unsigned abs_pos,
639 __isl_take isl_basic_set *context, int n_upper,
640 int (*fn)(__isl_take isl_constraint *lower,
641 __isl_take isl_constraint *upper,
642 __isl_take isl_basic_set *bset, void *user), void *user)
644 isl_basic_set *context_i;
645 isl_constraint *upper = NULL;
648 for (i = 0; i < bset->n_ineq; ++i) {
649 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
652 context_i = set_smallest_upper_bound(context, bset,
653 abs_pos, n_upper, i);
654 if (isl_basic_set_is_empty(context_i)) {
655 isl_basic_set_free(context_i);
658 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
660 if (!upper || !context_i)
662 if (fn(NULL, upper, context_i, user) < 0)
666 isl_basic_set_free(context);
668 if (i < bset->n_ineq)
673 isl_constraint_free(upper);
674 isl_basic_set_free(context_i);
675 isl_basic_set_free(context);
679 static int foreach_lower_bound(__isl_keep isl_basic_set *bset,
680 enum isl_dim_type type, unsigned abs_pos,
681 __isl_take isl_basic_set *context, int n_lower,
682 int (*fn)(__isl_take isl_constraint *lower,
683 __isl_take isl_constraint *upper,
684 __isl_take isl_basic_set *bset, void *user), void *user)
686 isl_basic_set *context_i;
687 isl_constraint *lower = NULL;
690 for (i = 0; i < bset->n_ineq; ++i) {
691 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
694 context_i = set_largest_lower_bound(context, bset,
695 abs_pos, n_lower, i);
696 if (isl_basic_set_is_empty(context_i)) {
697 isl_basic_set_free(context_i);
700 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
702 if (!lower || !context_i)
704 if (fn(lower, NULL, context_i, user) < 0)
708 isl_basic_set_free(context);
710 if (i < bset->n_ineq)
715 isl_constraint_free(lower);
716 isl_basic_set_free(context_i);
717 isl_basic_set_free(context);
721 static int foreach_bound_pair(__isl_keep isl_basic_set *bset,
722 enum isl_dim_type type, unsigned abs_pos,
723 __isl_take isl_basic_set *context, int n_lower, int n_upper,
724 int (*fn)(__isl_take isl_constraint *lower,
725 __isl_take isl_constraint *upper,
726 __isl_take isl_basic_set *bset, void *user), void *user)
728 isl_basic_set *context_i, *context_j;
729 isl_constraint *lower = NULL;
730 isl_constraint *upper = NULL;
733 for (i = 0; i < bset->n_ineq; ++i) {
734 if (!isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
737 context_i = set_largest_lower_bound(context, bset,
738 abs_pos, n_lower, i);
739 if (isl_basic_set_is_empty(context_i)) {
740 isl_basic_set_free(context_i);
744 for (j = 0; j < bset->n_ineq; ++j) {
745 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
748 context_j = set_smallest_upper_bound(context_i, bset,
749 abs_pos, n_upper, j);
750 context_j = isl_basic_set_extend_constraints(context_j,
752 context_j = add_larger_bound_constraint(context_j,
753 bset->ineq[i], bset->ineq[j], abs_pos, 0);
754 context_j = isl_basic_set_simplify(context_j);
755 context_j = isl_basic_set_finalize(context_j);
756 if (isl_basic_set_is_empty(context_j)) {
757 isl_basic_set_free(context_j);
760 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
762 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
764 if (!lower || !upper || !context_j)
766 if (fn(lower, upper, context_j, user) < 0)
770 isl_basic_set_free(context_i);
772 if (j < bset->n_ineq)
776 isl_basic_set_free(context);
778 if (i < bset->n_ineq)
783 isl_constraint_free(lower);
784 isl_constraint_free(upper);
785 isl_basic_set_free(context_i);
786 isl_basic_set_free(context_j);
787 isl_basic_set_free(context);
791 /* For each pair of lower and upper bounds on the variable "pos"
792 * of type "type", call "fn" with these lower and upper bounds and the
793 * set of constraints on the remaining variables where these bounds
794 * are active, i.e., (stricly) larger/smaller than the other lower/upper bounds.
796 * If the designated variable is equal to an affine combination of the
797 * other variables then fn is called with both lower and upper
798 * set to the corresponding equality.
800 * If there is no lower (or upper) bound, then NULL is passed
801 * as the corresponding bound.
803 * We first check if the variable is involved in any equality.
804 * If not, we count the number of lower and upper bounds and
807 int isl_basic_set_foreach_bound_pair(__isl_keep isl_basic_set *bset,
808 enum isl_dim_type type, unsigned pos,
809 int (*fn)(__isl_take isl_constraint *lower,
810 __isl_take isl_constraint *upper,
811 __isl_take isl_basic_set *bset, void *user), void *user)
814 isl_constraint *lower = NULL;
815 isl_constraint *upper = NULL;
816 isl_basic_set *context = NULL;
818 int n_lower, n_upper;
822 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
823 isl_assert(bset->ctx, type == isl_dim_param || type == isl_dim_set,
827 if (type == isl_dim_set)
828 abs_pos += isl_basic_set_dim(bset, isl_dim_param);
830 for (i = 0; i < bset->n_eq; ++i) {
831 if (isl_int_is_zero(bset->eq[i][1 + abs_pos]))
834 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
836 upper = isl_constraint_copy(lower);
837 context = isl_basic_set_remove(isl_basic_set_copy(bset),
839 if (!lower || !upper || !context)
841 return fn(lower, upper, context, user);
846 for (i = 0; i < bset->n_ineq; ++i) {
847 if (isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
849 else if (isl_int_is_neg(bset->ineq[i][1 + abs_pos]))
853 context = isl_basic_set_copy(bset);
854 context = isl_basic_set_cow(context);
857 for (i = context->n_ineq - 1; i >= 0; --i)
858 if (!isl_int_is_zero(context->ineq[i][1 + abs_pos]))
859 isl_basic_set_drop_inequality(context, i);
861 context = isl_basic_set_drop(context, type, pos, 1);
862 if (!n_lower && !n_upper)
863 return fn(NULL, NULL, context, user);
865 return foreach_upper_bound(bset, type, abs_pos, context, n_upper,
868 return foreach_lower_bound(bset, type, abs_pos, context, n_lower,
870 return foreach_bound_pair(bset, type, abs_pos, context, n_lower, n_upper,
873 isl_constraint_free(lower);
874 isl_constraint_free(upper);
875 isl_basic_set_free(context);