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;
33 static unsigned basic_set_offset(struct isl_basic_set *bset,
34 enum isl_dim_type type)
36 struct isl_dim *dim = bset->dim;
38 case isl_dim_param: return 1;
39 case isl_dim_in: return 1 + dim->nparam;
40 case isl_dim_out: return 1 + dim->nparam + dim->n_in;
41 case isl_dim_div: return 1 + dim->nparam + dim->n_in + dim->n_out;
45 struct isl_constraint *isl_basic_map_constraint(struct isl_basic_map *bmap,
48 struct isl_constraint *constraint;
53 constraint = isl_alloc_type(bmap->ctx, struct isl_constraint);
57 constraint->ctx = bmap->ctx;
58 isl_ctx_ref(constraint->ctx);
60 constraint->bmap = bmap;
61 constraint->line = line;
65 isl_basic_map_free(bmap);
69 struct isl_constraint *isl_basic_set_constraint(struct isl_basic_set *bset,
72 return isl_basic_map_constraint((struct isl_basic_map *)bset, line);
75 struct isl_constraint *isl_equality_alloc(struct isl_dim *dim)
77 struct isl_basic_map *bmap;
82 bmap = isl_basic_map_alloc_dim(dim, 0, 1, 0);
86 isl_basic_map_alloc_equality(bmap);
87 isl_seq_clr(bmap->eq[0], 1 + isl_basic_map_total_dim(bmap));
88 return isl_basic_map_constraint(bmap, &bmap->eq[0]);
91 struct isl_constraint *isl_inequality_alloc(struct isl_dim *dim)
93 struct isl_basic_map *bmap;
98 bmap = isl_basic_map_alloc_dim(dim, 0, 0, 1);
102 isl_basic_map_alloc_inequality(bmap);
103 isl_seq_clr(bmap->ineq[0], 1 + isl_basic_map_total_dim(bmap));
104 return isl_basic_map_constraint(bmap, &bmap->ineq[0]);
107 struct isl_constraint *isl_constraint_dup(struct isl_constraint *c)
109 struct isl_basic_map *bmap;
116 eq = c->line < c->bmap->eq + c->bmap->n_eq;
117 i = eq ? c->line - c->bmap->eq : c->line - c->bmap->ineq;
118 bmap = isl_basic_map_copy(c->bmap);
121 return isl_basic_map_constraint(bmap, eq ? bmap->eq + i : bmap->ineq + i);
124 struct isl_constraint *isl_constraint_cow(struct isl_constraint *c)
132 return isl_constraint_dup(c);
135 struct isl_constraint *isl_constraint_copy(struct isl_constraint *constraint)
144 void isl_constraint_free(struct isl_constraint *c)
152 isl_basic_map_free(c->bmap);
153 isl_ctx_deref(c->ctx);
157 __isl_give isl_constraint *isl_basic_map_first_constraint(
158 __isl_take isl_basic_map *bmap)
164 return isl_basic_map_constraint(bmap, &bmap->eq[0]);
166 if (bmap->n_ineq > 0)
167 return isl_basic_map_constraint(bmap, &bmap->ineq[0]);
169 isl_basic_map_free(bmap);
173 __isl_give isl_constraint *isl_basic_set_first_constraint(
174 __isl_take isl_basic_set *bset)
176 return isl_basic_map_first_constraint((struct isl_basic_map *)bset);
179 struct isl_constraint *isl_constraint_next(struct isl_constraint *c)
181 c = isl_constraint_cow(c);
182 if (c->line >= c->bmap->eq) {
184 if (c->line < c->bmap->eq + c->bmap->n_eq)
186 c->line = c->bmap->ineq;
189 if (c->line < c->bmap->ineq + c->bmap->n_ineq)
191 isl_constraint_free(c);
195 int isl_basic_map_foreach_constraint(__isl_keep isl_basic_map *bmap,
196 int (*fn)(__isl_take isl_constraint *c, void *user), void *user)
199 struct isl_constraint *c;
204 for (i = 0; i < bmap->n_eq; ++i) {
205 c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
213 for (i = 0; i < bmap->n_ineq; ++i) {
214 c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
225 int isl_basic_set_foreach_constraint(__isl_keep isl_basic_set *bset,
226 int (*fn)(__isl_take isl_constraint *c, void *user), void *user)
228 return isl_basic_map_foreach_constraint((isl_basic_map *)bset, fn, user);
231 int isl_constraint_is_equal(struct isl_constraint *constraint1,
232 struct isl_constraint *constraint2)
234 if (!constraint1 || !constraint2)
236 return constraint1->bmap == constraint2->bmap &&
237 constraint1->line == constraint2->line;
240 struct isl_basic_map *isl_basic_map_add_constraint(
241 struct isl_basic_map *bmap, struct isl_constraint *constraint)
243 if (!bmap || !constraint)
246 isl_assert(constraint->ctx,
247 isl_dim_equal(bmap->dim, constraint->bmap->dim), goto error);
249 bmap = isl_basic_map_intersect(bmap,
250 isl_basic_map_from_constraint(constraint));
253 isl_basic_map_free(bmap);
254 isl_constraint_free(constraint);
258 struct isl_basic_set *isl_basic_set_add_constraint(
259 struct isl_basic_set *bset, struct isl_constraint *constraint)
261 return (struct isl_basic_set *)
262 isl_basic_map_add_constraint((struct isl_basic_map *)bset,
266 struct isl_constraint *isl_constraint_add_div(struct isl_constraint *constraint,
267 struct isl_div *div, int *pos)
269 if (!constraint || !div)
272 isl_assert(constraint->ctx,
273 isl_dim_equal(div->bmap->dim, constraint->bmap->dim), goto error);
274 isl_assert(constraint->ctx,
275 constraint->bmap->n_eq + constraint->bmap->n_ineq == 1, goto error);
277 constraint->bmap = isl_basic_map_cow(constraint->bmap);
278 constraint->bmap = isl_basic_map_extend_dim(constraint->bmap,
279 isl_dim_copy(constraint->bmap->dim), 1, 0, 0);
280 if (!constraint->bmap)
282 constraint->line = &constraint->bmap->eq[0];
283 *pos = isl_basic_map_alloc_div(constraint->bmap);
286 isl_seq_cpy(constraint->bmap->div[*pos], div->line[0],
287 1 + 1 + isl_basic_map_total_dim(constraint->bmap));
291 isl_constraint_free(constraint);
296 int isl_constraint_dim(struct isl_constraint *constraint,
297 enum isl_dim_type type)
301 return n(constraint, type);
304 void isl_constraint_get_constant(struct isl_constraint *constraint, isl_int *v)
308 isl_int_set(*v, constraint->line[0][0]);
311 void isl_constraint_get_coefficient(struct isl_constraint *constraint,
312 enum isl_dim_type type, int pos, isl_int *v)
317 isl_assert(constraint->ctx, pos < n(constraint, type), return);
318 isl_int_set(*v, constraint->line[0][offset(constraint, type) + pos]);
321 struct isl_div *isl_constraint_div(struct isl_constraint *constraint, int pos)
326 isl_assert(constraint->ctx, pos < n(constraint, isl_dim_div),
328 isl_assert(constraint->ctx,
329 !isl_int_is_zero(constraint->bmap->div[pos][0]), return NULL);
330 return isl_basic_map_div(isl_basic_map_copy(constraint->bmap), pos);
333 void isl_constraint_set_constant(struct isl_constraint *constraint, isl_int v)
337 isl_int_set(constraint->line[0][0], v);
340 void isl_constraint_set_coefficient(struct isl_constraint *constraint,
341 enum isl_dim_type type, int pos, isl_int v)
346 isl_assert(constraint->ctx, pos < n(constraint, type), return);
347 isl_int_set(constraint->line[0][offset(constraint, type) + pos], v);
350 void isl_constraint_clear(struct isl_constraint *constraint)
356 total = isl_basic_map_total_dim(constraint->bmap);
357 isl_seq_clr(constraint->line[0], 1 + total);
360 struct isl_constraint *isl_constraint_negate(struct isl_constraint *constraint)
367 isl_assert(constraint->ctx, !isl_constraint_is_equality(constraint),
369 isl_assert(constraint->ctx, constraint->bmap->ref == 1, goto error);
370 total = isl_basic_map_total_dim(constraint->bmap);
371 isl_seq_neg(constraint->line[0], constraint->line[0], 1 + total);
372 isl_int_sub_ui(constraint->line[0][0], constraint->line[0][0], 1);
373 ISL_F_CLR(constraint->bmap, ISL_BASIC_MAP_NORMALIZED);
376 isl_constraint_free(constraint);
380 int isl_constraint_is_equality(struct isl_constraint *constraint)
384 return constraint->line >= constraint->bmap->eq;
387 __isl_give isl_basic_map *isl_basic_map_from_constraint(
388 __isl_take isl_constraint *constraint)
391 struct isl_basic_map *bmap;
398 if (constraint->bmap->n_eq + constraint->bmap->n_ineq == 1) {
399 bmap = isl_basic_map_copy(constraint->bmap);
400 isl_constraint_free(constraint);
404 bmap = isl_basic_map_universe_like(constraint->bmap);
405 bmap = isl_basic_map_align_divs(bmap, constraint->bmap);
406 bmap = isl_basic_map_cow(bmap);
407 bmap = isl_basic_map_extend_constraints(bmap, 1, 1);
408 if (isl_constraint_is_equality(constraint)) {
409 k = isl_basic_map_alloc_equality(bmap);
415 k = isl_basic_map_alloc_inequality(bmap);
420 total = isl_basic_map_total_dim(bmap);
421 isl_seq_cpy(c, constraint->line[0], 1 + total);
422 isl_constraint_free(constraint);
425 isl_constraint_free(constraint);
426 isl_basic_map_free(bmap);
430 struct isl_basic_set *isl_basic_set_from_constraint(
431 struct isl_constraint *constraint)
436 isl_assert(constraint->ctx,n(constraint, isl_dim_in) == 0, goto error);
437 return (isl_basic_set *)isl_basic_map_from_constraint(constraint);
439 isl_constraint_free(constraint);
443 int isl_basic_set_has_defining_equality(
444 struct isl_basic_set *bset, enum isl_dim_type type, int pos,
445 struct isl_constraint **c)
453 offset = basic_set_offset(bset, type);
454 total = isl_basic_set_total_dim(bset);
455 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
456 for (i = 0; i < bset->n_eq; ++i)
457 if (!isl_int_is_zero(bset->eq[i][offset + pos]) &&
458 isl_seq_first_non_zero(bset->eq[i]+offset+pos+1,
459 1+total-offset-pos-1) == -1) {
460 *c= isl_basic_set_constraint(isl_basic_set_copy(bset),
467 int isl_basic_set_has_defining_inequalities(
468 struct isl_basic_set *bset, enum isl_dim_type type, int pos,
469 struct isl_constraint **lower,
470 struct isl_constraint **upper)
476 isl_int **lower_line, **upper_line;
480 offset = basic_set_offset(bset, type);
481 total = isl_basic_set_total_dim(bset);
482 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
484 for (i = 0; i < bset->n_ineq; ++i) {
485 if (isl_int_is_zero(bset->ineq[i][offset + pos]))
487 if (isl_int_is_one(bset->ineq[i][offset + pos]))
489 if (isl_int_is_negone(bset->ineq[i][offset + pos]))
491 if (isl_seq_first_non_zero(bset->ineq[i]+offset+pos+1,
492 1+total-offset-pos-1) != -1)
494 for (j = i + 1; j < bset->n_ineq; ++j) {
495 if (!isl_seq_is_neg(bset->ineq[i]+1, bset->ineq[j]+1,
498 isl_int_add(m, bset->ineq[i][0], bset->ineq[j][0]);
499 if (isl_int_abs_ge(m, bset->ineq[i][offset+pos]))
502 if (isl_int_is_pos(bset->ineq[i][offset+pos])) {
503 lower_line = &bset->ineq[i];
504 upper_line = &bset->ineq[j];
506 lower_line = &bset->ineq[j];
507 upper_line = &bset->ineq[i];
509 *lower = isl_basic_set_constraint(
510 isl_basic_set_copy(bset), lower_line);
511 *upper = isl_basic_set_constraint(
512 isl_basic_set_copy(bset), upper_line);
523 /* Given two constraints "a" and "b" on the variable at position "abs_pos"
524 * (in "a" and "b"), add a constraint to "bset" that ensures that the
525 * bound implied by "a" is (strictly) larger than the bound implied by "b".
527 * If both constraints imply lower bounds, then this means that "a" is
528 * active in the result.
529 * If both constraints imply upper bounds, then this means that "b" is
530 * active in the result.
532 static __isl_give isl_basic_set *add_larger_bound_constraint(
533 __isl_take isl_basic_set *bset, isl_int *a, isl_int *b,
534 unsigned abs_pos, int strict)
540 k = isl_basic_set_alloc_inequality(bset);
544 total = isl_basic_set_dim(bset, isl_dim_all);
547 isl_int_neg(t, b[1 + abs_pos]);
549 isl_seq_combine(bset->ineq[k], t, a, a[1 + abs_pos], b, 1 + abs_pos);
550 isl_seq_combine(bset->ineq[k] + 1 + abs_pos,
551 t, a + 1 + abs_pos + 1, a[1 + abs_pos], b + 1 + abs_pos + 1,
555 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
561 isl_basic_set_free(bset);
565 /* Add constraints to "context" that ensure that "u" is the smallest
566 * (and therefore active) upper bound on "abs_pos" in "bset" and return
567 * the resulting basic set.
569 static __isl_give isl_basic_set *set_smallest_upper_bound(
570 __isl_keep isl_basic_set *context,
571 __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_upper, int u)
575 context = isl_basic_set_copy(context);
576 context = isl_basic_set_cow(context);
578 context = isl_basic_set_extend_constraints(context, 0, n_upper - 1);
580 for (j = 0; j < bset->n_ineq; ++j) {
583 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
585 context = add_larger_bound_constraint(context,
586 bset->ineq[j], bset->ineq[u], abs_pos, j > u);
589 context = isl_basic_set_simplify(context);
590 context = isl_basic_set_finalize(context);
595 /* Add constraints to "context" that ensure that "u" is the largest
596 * (and therefore active) upper bound on "abs_pos" in "bset" and return
597 * the resulting basic set.
599 static __isl_give isl_basic_set *set_largest_lower_bound(
600 __isl_keep isl_basic_set *context,
601 __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_lower, int l)
605 context = isl_basic_set_copy(context);
606 context = isl_basic_set_cow(context);
608 context = isl_basic_set_extend_constraints(context, 0, n_lower - 1);
610 for (j = 0; j < bset->n_ineq; ++j) {
613 if (!isl_int_is_pos(bset->ineq[j][1 + abs_pos]))
615 context = add_larger_bound_constraint(context,
616 bset->ineq[l], bset->ineq[j], abs_pos, j > l);
619 context = isl_basic_set_simplify(context);
620 context = isl_basic_set_finalize(context);
625 static int foreach_upper_bound(__isl_keep isl_basic_set *bset,
626 enum isl_dim_type type, unsigned abs_pos,
627 __isl_take isl_basic_set *context, int n_upper,
628 int (*fn)(__isl_take isl_constraint *lower,
629 __isl_take isl_constraint *upper,
630 __isl_take isl_basic_set *bset, void *user), void *user)
632 isl_basic_set *context_i;
633 isl_constraint *upper = NULL;
636 for (i = 0; i < bset->n_ineq; ++i) {
637 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
640 context_i = set_smallest_upper_bound(context, bset,
641 abs_pos, n_upper, i);
642 if (isl_basic_set_is_empty(context_i)) {
643 isl_basic_set_free(context_i);
646 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
648 if (!upper || !context_i)
650 if (fn(NULL, upper, context_i, user) < 0)
654 isl_basic_set_free(context);
656 if (i < bset->n_ineq)
661 isl_constraint_free(upper);
662 isl_basic_set_free(context_i);
663 isl_basic_set_free(context);
667 static int foreach_lower_bound(__isl_keep isl_basic_set *bset,
668 enum isl_dim_type type, unsigned abs_pos,
669 __isl_take isl_basic_set *context, int n_lower,
670 int (*fn)(__isl_take isl_constraint *lower,
671 __isl_take isl_constraint *upper,
672 __isl_take isl_basic_set *bset, void *user), void *user)
674 isl_basic_set *context_i;
675 isl_constraint *lower = NULL;
678 for (i = 0; i < bset->n_ineq; ++i) {
679 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
682 context_i = set_largest_lower_bound(context, bset,
683 abs_pos, n_lower, i);
684 if (isl_basic_set_is_empty(context_i)) {
685 isl_basic_set_free(context_i);
688 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
690 if (!lower || !context_i)
692 if (fn(lower, NULL, context_i, user) < 0)
696 isl_basic_set_free(context);
698 if (i < bset->n_ineq)
703 isl_constraint_free(lower);
704 isl_basic_set_free(context_i);
705 isl_basic_set_free(context);
709 static int foreach_bound_pair(__isl_keep isl_basic_set *bset,
710 enum isl_dim_type type, unsigned abs_pos,
711 __isl_take isl_basic_set *context, int n_lower, int n_upper,
712 int (*fn)(__isl_take isl_constraint *lower,
713 __isl_take isl_constraint *upper,
714 __isl_take isl_basic_set *bset, void *user), void *user)
716 isl_basic_set *context_i, *context_j;
717 isl_constraint *lower = NULL;
718 isl_constraint *upper = NULL;
721 for (i = 0; i < bset->n_ineq; ++i) {
722 if (!isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
725 context_i = set_largest_lower_bound(context, bset,
726 abs_pos, n_lower, i);
727 if (isl_basic_set_is_empty(context_i)) {
728 isl_basic_set_free(context_i);
732 for (j = 0; j < bset->n_ineq; ++j) {
733 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
736 context_j = set_smallest_upper_bound(context_i, bset,
737 abs_pos, n_upper, j);
738 context_j = isl_basic_set_extend_constraints(context_j,
740 context_j = add_larger_bound_constraint(context_j,
741 bset->ineq[i], bset->ineq[j], abs_pos, 0);
742 context_j = isl_basic_set_simplify(context_j);
743 context_j = isl_basic_set_finalize(context_j);
744 if (isl_basic_set_is_empty(context_j)) {
745 isl_basic_set_free(context_j);
748 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
750 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
752 if (!lower || !upper || !context_j)
754 if (fn(lower, upper, context_j, user) < 0)
758 isl_basic_set_free(context_i);
760 if (j < bset->n_ineq)
764 isl_basic_set_free(context);
766 if (i < bset->n_ineq)
771 isl_constraint_free(lower);
772 isl_constraint_free(upper);
773 isl_basic_set_free(context_i);
774 isl_basic_set_free(context_j);
775 isl_basic_set_free(context);
779 /* For each pair of lower and upper bounds on the variable "pos"
780 * of type "type", call "fn" with these lower and upper bounds and the
781 * set of constraints on the remaining variables where these bounds
782 * are active, i.e., (stricly) larger/smaller than the other lower/upper bounds.
784 * If the designated variable is equal to an affine combination of the
785 * other variables then fn is called with both lower and upper
786 * set to the corresponding equality.
788 * If there is no lower (or upper) bound, then NULL is passed
789 * as the corresponding bound.
791 * We first check if the variable is involved in any equality.
792 * If not, we count the number of lower and upper bounds and
795 int isl_basic_set_foreach_bound_pair(__isl_keep isl_basic_set *bset,
796 enum isl_dim_type type, unsigned pos,
797 int (*fn)(__isl_take isl_constraint *lower,
798 __isl_take isl_constraint *upper,
799 __isl_take isl_basic_set *bset, void *user), void *user)
802 isl_constraint *lower = NULL;
803 isl_constraint *upper = NULL;
804 isl_basic_set *context = NULL;
806 int n_lower, n_upper;
810 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
811 isl_assert(bset->ctx, type == isl_dim_param || type == isl_dim_set,
815 if (type == isl_dim_set)
816 abs_pos += isl_basic_set_dim(bset, isl_dim_param);
818 for (i = 0; i < bset->n_eq; ++i) {
819 if (isl_int_is_zero(bset->eq[i][1 + abs_pos]))
822 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
824 upper = isl_constraint_copy(lower);
825 context = isl_basic_set_remove(isl_basic_set_copy(bset),
827 if (!lower || !upper || !context)
829 return fn(lower, upper, context, user);
834 for (i = 0; i < bset->n_ineq; ++i) {
835 if (isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
837 else if (isl_int_is_neg(bset->ineq[i][1 + abs_pos]))
841 context = isl_basic_set_copy(bset);
842 context = isl_basic_set_cow(context);
845 for (i = context->n_ineq - 1; i >= 0; --i)
846 if (!isl_int_is_zero(context->ineq[i][1 + abs_pos]))
847 isl_basic_set_drop_inequality(context, i);
849 context = isl_basic_set_drop(context, type, pos, 1);
850 if (!n_lower && !n_upper)
851 return fn(NULL, NULL, context, user);
853 return foreach_upper_bound(bset, type, abs_pos, context, n_upper,
856 return foreach_lower_bound(bset, type, abs_pos, context, n_lower,
858 return foreach_bound_pair(bset, type, abs_pos, context, n_lower, n_upper,
861 isl_constraint_free(lower);
862 isl_constraint_free(upper);
863 isl_basic_set_free(context);