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 int isl_constraint_is_div_constraint(__isl_keep isl_constraint *constraint)
398 if (isl_constraint_is_equality(constraint))
400 for (i = 0; i < constraint->bmap->n_div; ++i) {
401 if (isl_int_is_zero(constraint->bmap->div[i][0]))
403 if (isl_basic_map_is_div_constraint(constraint->bmap,
404 constraint->line[0], i))
411 /* We manually set ISL_BASIC_SET_FINAL instead of calling
412 * isl_basic_map_finalize because we want to keep the position
413 * of the divs and we therefore do not want to throw away redundant divs.
414 * This is arguably a bit fragile.
416 __isl_give isl_basic_map *isl_basic_map_from_constraint(
417 __isl_take isl_constraint *constraint)
420 struct isl_basic_map *bmap;
427 if (constraint->bmap->n_eq == 1 && constraint->bmap->n_ineq == 0) {
428 bmap = isl_basic_map_copy(constraint->bmap);
429 isl_constraint_free(constraint);
433 bmap = isl_basic_map_universe_like(constraint->bmap);
434 bmap = isl_basic_map_align_divs(bmap, constraint->bmap);
435 bmap = isl_basic_map_cow(bmap);
436 bmap = isl_basic_map_extend_constraints(bmap, 1, 1);
437 if (isl_constraint_is_equality(constraint)) {
438 k = isl_basic_map_alloc_equality(bmap);
444 k = isl_basic_map_alloc_inequality(bmap);
449 total = isl_basic_map_total_dim(bmap);
450 isl_seq_cpy(c, constraint->line[0], 1 + total);
451 isl_constraint_free(constraint);
453 ISL_F_SET(bmap, ISL_BASIC_SET_FINAL);
456 isl_constraint_free(constraint);
457 isl_basic_map_free(bmap);
461 struct isl_basic_set *isl_basic_set_from_constraint(
462 struct isl_constraint *constraint)
467 isl_assert(constraint->ctx,n(constraint, isl_dim_in) == 0, goto error);
468 return (isl_basic_set *)isl_basic_map_from_constraint(constraint);
470 isl_constraint_free(constraint);
474 int isl_basic_set_has_defining_equality(
475 struct isl_basic_set *bset, enum isl_dim_type type, int pos,
476 struct isl_constraint **c)
484 offset = basic_set_offset(bset, type);
485 total = isl_basic_set_total_dim(bset);
486 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
487 for (i = 0; i < bset->n_eq; ++i)
488 if (!isl_int_is_zero(bset->eq[i][offset + pos]) &&
489 isl_seq_first_non_zero(bset->eq[i]+offset+pos+1,
490 1+total-offset-pos-1) == -1) {
491 *c= isl_basic_set_constraint(isl_basic_set_copy(bset),
498 int isl_basic_set_has_defining_inequalities(
499 struct isl_basic_set *bset, enum isl_dim_type type, int pos,
500 struct isl_constraint **lower,
501 struct isl_constraint **upper)
507 isl_int **lower_line, **upper_line;
511 offset = basic_set_offset(bset, type);
512 total = isl_basic_set_total_dim(bset);
513 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
515 for (i = 0; i < bset->n_ineq; ++i) {
516 if (isl_int_is_zero(bset->ineq[i][offset + pos]))
518 if (isl_int_is_one(bset->ineq[i][offset + pos]))
520 if (isl_int_is_negone(bset->ineq[i][offset + pos]))
522 if (isl_seq_first_non_zero(bset->ineq[i]+offset+pos+1,
523 1+total-offset-pos-1) != -1)
525 for (j = i + 1; j < bset->n_ineq; ++j) {
526 if (!isl_seq_is_neg(bset->ineq[i]+1, bset->ineq[j]+1,
529 isl_int_add(m, bset->ineq[i][0], bset->ineq[j][0]);
530 if (isl_int_abs_ge(m, bset->ineq[i][offset+pos]))
533 if (isl_int_is_pos(bset->ineq[i][offset+pos])) {
534 lower_line = &bset->ineq[i];
535 upper_line = &bset->ineq[j];
537 lower_line = &bset->ineq[j];
538 upper_line = &bset->ineq[i];
540 *lower = isl_basic_set_constraint(
541 isl_basic_set_copy(bset), lower_line);
542 *upper = isl_basic_set_constraint(
543 isl_basic_set_copy(bset), upper_line);
554 /* Given two constraints "a" and "b" on the variable at position "abs_pos"
555 * (in "a" and "b"), add a constraint to "bset" that ensures that the
556 * bound implied by "a" is (strictly) larger than the bound implied by "b".
558 * If both constraints imply lower bounds, then this means that "a" is
559 * active in the result.
560 * If both constraints imply upper bounds, then this means that "b" is
561 * active in the result.
563 static __isl_give isl_basic_set *add_larger_bound_constraint(
564 __isl_take isl_basic_set *bset, isl_int *a, isl_int *b,
565 unsigned abs_pos, int strict)
571 k = isl_basic_set_alloc_inequality(bset);
575 total = isl_basic_set_dim(bset, isl_dim_all);
578 isl_int_neg(t, b[1 + abs_pos]);
580 isl_seq_combine(bset->ineq[k], t, a, a[1 + abs_pos], b, 1 + abs_pos);
581 isl_seq_combine(bset->ineq[k] + 1 + abs_pos,
582 t, a + 1 + abs_pos + 1, a[1 + abs_pos], b + 1 + abs_pos + 1,
586 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
592 isl_basic_set_free(bset);
596 /* Add constraints to "context" that ensure that "u" is the smallest
597 * (and therefore active) upper bound on "abs_pos" in "bset" and return
598 * the resulting basic set.
600 static __isl_give isl_basic_set *set_smallest_upper_bound(
601 __isl_keep isl_basic_set *context,
602 __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_upper, int u)
606 context = isl_basic_set_copy(context);
607 context = isl_basic_set_cow(context);
609 context = isl_basic_set_extend_constraints(context, 0, n_upper - 1);
611 for (j = 0; j < bset->n_ineq; ++j) {
614 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
616 context = add_larger_bound_constraint(context,
617 bset->ineq[j], bset->ineq[u], abs_pos, j > u);
620 context = isl_basic_set_simplify(context);
621 context = isl_basic_set_finalize(context);
626 /* Add constraints to "context" that ensure that "u" is the largest
627 * (and therefore active) upper bound on "abs_pos" in "bset" and return
628 * the resulting basic set.
630 static __isl_give isl_basic_set *set_largest_lower_bound(
631 __isl_keep isl_basic_set *context,
632 __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_lower, int l)
636 context = isl_basic_set_copy(context);
637 context = isl_basic_set_cow(context);
639 context = isl_basic_set_extend_constraints(context, 0, n_lower - 1);
641 for (j = 0; j < bset->n_ineq; ++j) {
644 if (!isl_int_is_pos(bset->ineq[j][1 + abs_pos]))
646 context = add_larger_bound_constraint(context,
647 bset->ineq[l], bset->ineq[j], abs_pos, j > l);
650 context = isl_basic_set_simplify(context);
651 context = isl_basic_set_finalize(context);
656 static int foreach_upper_bound(__isl_keep isl_basic_set *bset,
657 enum isl_dim_type type, unsigned abs_pos,
658 __isl_take isl_basic_set *context, int n_upper,
659 int (*fn)(__isl_take isl_constraint *lower,
660 __isl_take isl_constraint *upper,
661 __isl_take isl_basic_set *bset, void *user), void *user)
663 isl_basic_set *context_i;
664 isl_constraint *upper = NULL;
667 for (i = 0; i < bset->n_ineq; ++i) {
668 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
671 context_i = set_smallest_upper_bound(context, bset,
672 abs_pos, n_upper, i);
673 if (isl_basic_set_is_empty(context_i)) {
674 isl_basic_set_free(context_i);
677 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
679 if (!upper || !context_i)
681 if (fn(NULL, upper, context_i, user) < 0)
685 isl_basic_set_free(context);
687 if (i < bset->n_ineq)
692 isl_constraint_free(upper);
693 isl_basic_set_free(context_i);
694 isl_basic_set_free(context);
698 static int foreach_lower_bound(__isl_keep isl_basic_set *bset,
699 enum isl_dim_type type, unsigned abs_pos,
700 __isl_take isl_basic_set *context, int n_lower,
701 int (*fn)(__isl_take isl_constraint *lower,
702 __isl_take isl_constraint *upper,
703 __isl_take isl_basic_set *bset, void *user), void *user)
705 isl_basic_set *context_i;
706 isl_constraint *lower = NULL;
709 for (i = 0; i < bset->n_ineq; ++i) {
710 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
713 context_i = set_largest_lower_bound(context, bset,
714 abs_pos, n_lower, i);
715 if (isl_basic_set_is_empty(context_i)) {
716 isl_basic_set_free(context_i);
719 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
721 if (!lower || !context_i)
723 if (fn(lower, NULL, context_i, user) < 0)
727 isl_basic_set_free(context);
729 if (i < bset->n_ineq)
734 isl_constraint_free(lower);
735 isl_basic_set_free(context_i);
736 isl_basic_set_free(context);
740 static int foreach_bound_pair(__isl_keep isl_basic_set *bset,
741 enum isl_dim_type type, unsigned abs_pos,
742 __isl_take isl_basic_set *context, int n_lower, int n_upper,
743 int (*fn)(__isl_take isl_constraint *lower,
744 __isl_take isl_constraint *upper,
745 __isl_take isl_basic_set *bset, void *user), void *user)
747 isl_basic_set *context_i, *context_j;
748 isl_constraint *lower = NULL;
749 isl_constraint *upper = NULL;
752 for (i = 0; i < bset->n_ineq; ++i) {
753 if (!isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
756 context_i = set_largest_lower_bound(context, bset,
757 abs_pos, n_lower, i);
758 if (isl_basic_set_is_empty(context_i)) {
759 isl_basic_set_free(context_i);
763 for (j = 0; j < bset->n_ineq; ++j) {
764 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
767 context_j = set_smallest_upper_bound(context_i, bset,
768 abs_pos, n_upper, j);
769 context_j = isl_basic_set_extend_constraints(context_j,
771 context_j = add_larger_bound_constraint(context_j,
772 bset->ineq[i], bset->ineq[j], abs_pos, 0);
773 context_j = isl_basic_set_simplify(context_j);
774 context_j = isl_basic_set_finalize(context_j);
775 if (isl_basic_set_is_empty(context_j)) {
776 isl_basic_set_free(context_j);
779 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
781 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
783 if (!lower || !upper || !context_j)
785 if (fn(lower, upper, context_j, user) < 0)
789 isl_basic_set_free(context_i);
791 if (j < bset->n_ineq)
795 isl_basic_set_free(context);
797 if (i < bset->n_ineq)
802 isl_constraint_free(lower);
803 isl_constraint_free(upper);
804 isl_basic_set_free(context_i);
805 isl_basic_set_free(context_j);
806 isl_basic_set_free(context);
810 /* For each pair of lower and upper bounds on the variable "pos"
811 * of type "type", call "fn" with these lower and upper bounds and the
812 * set of constraints on the remaining variables where these bounds
813 * are active, i.e., (stricly) larger/smaller than the other lower/upper bounds.
815 * If the designated variable is equal to an affine combination of the
816 * other variables then fn is called with both lower and upper
817 * set to the corresponding equality.
819 * If there is no lower (or upper) bound, then NULL is passed
820 * as the corresponding bound.
822 * We first check if the variable is involved in any equality.
823 * If not, we count the number of lower and upper bounds and
826 int isl_basic_set_foreach_bound_pair(__isl_keep isl_basic_set *bset,
827 enum isl_dim_type type, unsigned pos,
828 int (*fn)(__isl_take isl_constraint *lower,
829 __isl_take isl_constraint *upper,
830 __isl_take isl_basic_set *bset, void *user), void *user)
833 isl_constraint *lower = NULL;
834 isl_constraint *upper = NULL;
835 isl_basic_set *context = NULL;
837 int n_lower, n_upper;
841 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
842 isl_assert(bset->ctx, type == isl_dim_param || type == isl_dim_set,
846 if (type == isl_dim_set)
847 abs_pos += isl_basic_set_dim(bset, isl_dim_param);
849 for (i = 0; i < bset->n_eq; ++i) {
850 if (isl_int_is_zero(bset->eq[i][1 + abs_pos]))
853 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
855 upper = isl_constraint_copy(lower);
856 context = isl_basic_set_remove(isl_basic_set_copy(bset),
858 if (!lower || !upper || !context)
860 return fn(lower, upper, context, user);
865 for (i = 0; i < bset->n_ineq; ++i) {
866 if (isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
868 else if (isl_int_is_neg(bset->ineq[i][1 + abs_pos]))
872 context = isl_basic_set_copy(bset);
873 context = isl_basic_set_cow(context);
876 for (i = context->n_ineq - 1; i >= 0; --i)
877 if (!isl_int_is_zero(context->ineq[i][1 + abs_pos]))
878 isl_basic_set_drop_inequality(context, i);
880 context = isl_basic_set_drop(context, type, pos, 1);
881 if (!n_lower && !n_upper)
882 return fn(NULL, NULL, context, user);
884 return foreach_upper_bound(bset, type, abs_pos, context, n_upper,
887 return foreach_lower_bound(bset, type, abs_pos, context, n_lower,
889 return foreach_bound_pair(bset, type, abs_pos, context, n_lower, n_upper,
892 isl_constraint_free(lower);
893 isl_constraint_free(upper);
894 isl_basic_set_free(context);