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->eq[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 __isl_give isl_basic_map *isl_basic_map_from_constraint(
393 __isl_take isl_constraint *constraint)
396 struct isl_basic_map *bmap;
403 if (constraint->bmap->n_eq + constraint->bmap->n_ineq == 1) {
404 bmap = isl_basic_map_copy(constraint->bmap);
405 isl_constraint_free(constraint);
409 bmap = isl_basic_map_universe_like(constraint->bmap);
410 bmap = isl_basic_map_align_divs(bmap, constraint->bmap);
411 bmap = isl_basic_map_cow(bmap);
412 bmap = isl_basic_map_extend_constraints(bmap, 1, 1);
413 if (isl_constraint_is_equality(constraint)) {
414 k = isl_basic_map_alloc_equality(bmap);
420 k = isl_basic_map_alloc_inequality(bmap);
425 total = isl_basic_map_total_dim(bmap);
426 isl_seq_cpy(c, constraint->line[0], 1 + total);
427 isl_constraint_free(constraint);
428 bmap = isl_basic_map_finalize(bmap);
431 isl_constraint_free(constraint);
432 isl_basic_map_free(bmap);
436 struct isl_basic_set *isl_basic_set_from_constraint(
437 struct isl_constraint *constraint)
442 isl_assert(constraint->ctx,n(constraint, isl_dim_in) == 0, goto error);
443 return (isl_basic_set *)isl_basic_map_from_constraint(constraint);
445 isl_constraint_free(constraint);
449 int isl_basic_set_has_defining_equality(
450 struct isl_basic_set *bset, enum isl_dim_type type, int pos,
451 struct isl_constraint **c)
459 offset = basic_set_offset(bset, type);
460 total = isl_basic_set_total_dim(bset);
461 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
462 for (i = 0; i < bset->n_eq; ++i)
463 if (!isl_int_is_zero(bset->eq[i][offset + pos]) &&
464 isl_seq_first_non_zero(bset->eq[i]+offset+pos+1,
465 1+total-offset-pos-1) == -1) {
466 *c= isl_basic_set_constraint(isl_basic_set_copy(bset),
473 int isl_basic_set_has_defining_inequalities(
474 struct isl_basic_set *bset, enum isl_dim_type type, int pos,
475 struct isl_constraint **lower,
476 struct isl_constraint **upper)
482 isl_int **lower_line, **upper_line;
486 offset = basic_set_offset(bset, type);
487 total = isl_basic_set_total_dim(bset);
488 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
490 for (i = 0; i < bset->n_ineq; ++i) {
491 if (isl_int_is_zero(bset->ineq[i][offset + pos]))
493 if (isl_int_is_one(bset->ineq[i][offset + pos]))
495 if (isl_int_is_negone(bset->ineq[i][offset + pos]))
497 if (isl_seq_first_non_zero(bset->ineq[i]+offset+pos+1,
498 1+total-offset-pos-1) != -1)
500 for (j = i + 1; j < bset->n_ineq; ++j) {
501 if (!isl_seq_is_neg(bset->ineq[i]+1, bset->ineq[j]+1,
504 isl_int_add(m, bset->ineq[i][0], bset->ineq[j][0]);
505 if (isl_int_abs_ge(m, bset->ineq[i][offset+pos]))
508 if (isl_int_is_pos(bset->ineq[i][offset+pos])) {
509 lower_line = &bset->ineq[i];
510 upper_line = &bset->ineq[j];
512 lower_line = &bset->ineq[j];
513 upper_line = &bset->ineq[i];
515 *lower = isl_basic_set_constraint(
516 isl_basic_set_copy(bset), lower_line);
517 *upper = isl_basic_set_constraint(
518 isl_basic_set_copy(bset), upper_line);
529 /* Given two constraints "a" and "b" on the variable at position "abs_pos"
530 * (in "a" and "b"), add a constraint to "bset" that ensures that the
531 * bound implied by "a" is (strictly) larger than the bound implied by "b".
533 * If both constraints imply lower bounds, then this means that "a" is
534 * active in the result.
535 * If both constraints imply upper bounds, then this means that "b" is
536 * active in the result.
538 static __isl_give isl_basic_set *add_larger_bound_constraint(
539 __isl_take isl_basic_set *bset, isl_int *a, isl_int *b,
540 unsigned abs_pos, int strict)
546 k = isl_basic_set_alloc_inequality(bset);
550 total = isl_basic_set_dim(bset, isl_dim_all);
553 isl_int_neg(t, b[1 + abs_pos]);
555 isl_seq_combine(bset->ineq[k], t, a, a[1 + abs_pos], b, 1 + abs_pos);
556 isl_seq_combine(bset->ineq[k] + 1 + abs_pos,
557 t, a + 1 + abs_pos + 1, a[1 + abs_pos], b + 1 + abs_pos + 1,
561 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
567 isl_basic_set_free(bset);
571 /* Add constraints to "context" that ensure that "u" is the smallest
572 * (and therefore active) upper bound on "abs_pos" in "bset" and return
573 * the resulting basic set.
575 static __isl_give isl_basic_set *set_smallest_upper_bound(
576 __isl_keep isl_basic_set *context,
577 __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_upper, int u)
581 context = isl_basic_set_copy(context);
582 context = isl_basic_set_cow(context);
584 context = isl_basic_set_extend_constraints(context, 0, n_upper - 1);
586 for (j = 0; j < bset->n_ineq; ++j) {
589 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
591 context = add_larger_bound_constraint(context,
592 bset->ineq[j], bset->ineq[u], abs_pos, j > u);
595 context = isl_basic_set_simplify(context);
596 context = isl_basic_set_finalize(context);
601 /* Add constraints to "context" that ensure that "u" is the largest
602 * (and therefore active) upper bound on "abs_pos" in "bset" and return
603 * the resulting basic set.
605 static __isl_give isl_basic_set *set_largest_lower_bound(
606 __isl_keep isl_basic_set *context,
607 __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_lower, int l)
611 context = isl_basic_set_copy(context);
612 context = isl_basic_set_cow(context);
614 context = isl_basic_set_extend_constraints(context, 0, n_lower - 1);
616 for (j = 0; j < bset->n_ineq; ++j) {
619 if (!isl_int_is_pos(bset->ineq[j][1 + abs_pos]))
621 context = add_larger_bound_constraint(context,
622 bset->ineq[l], bset->ineq[j], abs_pos, j > l);
625 context = isl_basic_set_simplify(context);
626 context = isl_basic_set_finalize(context);
631 static int foreach_upper_bound(__isl_keep isl_basic_set *bset,
632 enum isl_dim_type type, unsigned abs_pos,
633 __isl_take isl_basic_set *context, int n_upper,
634 int (*fn)(__isl_take isl_constraint *lower,
635 __isl_take isl_constraint *upper,
636 __isl_take isl_basic_set *bset, void *user), void *user)
638 isl_basic_set *context_i;
639 isl_constraint *upper = NULL;
642 for (i = 0; i < bset->n_ineq; ++i) {
643 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
646 context_i = set_smallest_upper_bound(context, bset,
647 abs_pos, n_upper, i);
648 if (isl_basic_set_is_empty(context_i)) {
649 isl_basic_set_free(context_i);
652 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
654 if (!upper || !context_i)
656 if (fn(NULL, upper, context_i, user) < 0)
660 isl_basic_set_free(context);
662 if (i < bset->n_ineq)
667 isl_constraint_free(upper);
668 isl_basic_set_free(context_i);
669 isl_basic_set_free(context);
673 static int foreach_lower_bound(__isl_keep isl_basic_set *bset,
674 enum isl_dim_type type, unsigned abs_pos,
675 __isl_take isl_basic_set *context, int n_lower,
676 int (*fn)(__isl_take isl_constraint *lower,
677 __isl_take isl_constraint *upper,
678 __isl_take isl_basic_set *bset, void *user), void *user)
680 isl_basic_set *context_i;
681 isl_constraint *lower = NULL;
684 for (i = 0; i < bset->n_ineq; ++i) {
685 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
688 context_i = set_largest_lower_bound(context, bset,
689 abs_pos, n_lower, i);
690 if (isl_basic_set_is_empty(context_i)) {
691 isl_basic_set_free(context_i);
694 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
696 if (!lower || !context_i)
698 if (fn(lower, NULL, context_i, user) < 0)
702 isl_basic_set_free(context);
704 if (i < bset->n_ineq)
709 isl_constraint_free(lower);
710 isl_basic_set_free(context_i);
711 isl_basic_set_free(context);
715 static int foreach_bound_pair(__isl_keep isl_basic_set *bset,
716 enum isl_dim_type type, unsigned abs_pos,
717 __isl_take isl_basic_set *context, int n_lower, int n_upper,
718 int (*fn)(__isl_take isl_constraint *lower,
719 __isl_take isl_constraint *upper,
720 __isl_take isl_basic_set *bset, void *user), void *user)
722 isl_basic_set *context_i, *context_j;
723 isl_constraint *lower = NULL;
724 isl_constraint *upper = NULL;
727 for (i = 0; i < bset->n_ineq; ++i) {
728 if (!isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
731 context_i = set_largest_lower_bound(context, bset,
732 abs_pos, n_lower, i);
733 if (isl_basic_set_is_empty(context_i)) {
734 isl_basic_set_free(context_i);
738 for (j = 0; j < bset->n_ineq; ++j) {
739 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
742 context_j = set_smallest_upper_bound(context_i, bset,
743 abs_pos, n_upper, j);
744 context_j = isl_basic_set_extend_constraints(context_j,
746 context_j = add_larger_bound_constraint(context_j,
747 bset->ineq[i], bset->ineq[j], abs_pos, 0);
748 context_j = isl_basic_set_simplify(context_j);
749 context_j = isl_basic_set_finalize(context_j);
750 if (isl_basic_set_is_empty(context_j)) {
751 isl_basic_set_free(context_j);
754 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
756 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
758 if (!lower || !upper || !context_j)
760 if (fn(lower, upper, context_j, user) < 0)
764 isl_basic_set_free(context_i);
766 if (j < bset->n_ineq)
770 isl_basic_set_free(context);
772 if (i < bset->n_ineq)
777 isl_constraint_free(lower);
778 isl_constraint_free(upper);
779 isl_basic_set_free(context_i);
780 isl_basic_set_free(context_j);
781 isl_basic_set_free(context);
785 /* For each pair of lower and upper bounds on the variable "pos"
786 * of type "type", call "fn" with these lower and upper bounds and the
787 * set of constraints on the remaining variables where these bounds
788 * are active, i.e., (stricly) larger/smaller than the other lower/upper bounds.
790 * If the designated variable is equal to an affine combination of the
791 * other variables then fn is called with both lower and upper
792 * set to the corresponding equality.
794 * If there is no lower (or upper) bound, then NULL is passed
795 * as the corresponding bound.
797 * We first check if the variable is involved in any equality.
798 * If not, we count the number of lower and upper bounds and
801 int isl_basic_set_foreach_bound_pair(__isl_keep isl_basic_set *bset,
802 enum isl_dim_type type, unsigned pos,
803 int (*fn)(__isl_take isl_constraint *lower,
804 __isl_take isl_constraint *upper,
805 __isl_take isl_basic_set *bset, void *user), void *user)
808 isl_constraint *lower = NULL;
809 isl_constraint *upper = NULL;
810 isl_basic_set *context = NULL;
812 int n_lower, n_upper;
816 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
817 isl_assert(bset->ctx, type == isl_dim_param || type == isl_dim_set,
821 if (type == isl_dim_set)
822 abs_pos += isl_basic_set_dim(bset, isl_dim_param);
824 for (i = 0; i < bset->n_eq; ++i) {
825 if (isl_int_is_zero(bset->eq[i][1 + abs_pos]))
828 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
830 upper = isl_constraint_copy(lower);
831 context = isl_basic_set_remove(isl_basic_set_copy(bset),
833 if (!lower || !upper || !context)
835 return fn(lower, upper, context, user);
840 for (i = 0; i < bset->n_ineq; ++i) {
841 if (isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
843 else if (isl_int_is_neg(bset->ineq[i][1 + abs_pos]))
847 context = isl_basic_set_copy(bset);
848 context = isl_basic_set_cow(context);
851 for (i = context->n_ineq - 1; i >= 0; --i)
852 if (!isl_int_is_zero(context->ineq[i][1 + abs_pos]))
853 isl_basic_set_drop_inequality(context, i);
855 context = isl_basic_set_drop(context, type, pos, 1);
856 if (!n_lower && !n_upper)
857 return fn(NULL, NULL, context, user);
859 return foreach_upper_bound(bset, type, abs_pos, context, n_upper,
862 return foreach_lower_bound(bset, type, abs_pos, context, n_lower,
864 return foreach_bound_pair(bset, type, abs_pos, context, n_lower, n_upper,
867 isl_constraint_free(lower);
868 isl_constraint_free(upper);
869 isl_basic_set_free(context);