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 for (i = 0; i < bmap->n_eq; ++i) {
207 c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
215 for (i = 0; i < bmap->n_ineq; ++i) {
216 c = isl_basic_map_constraint(isl_basic_map_copy(bmap),
227 int isl_basic_set_foreach_constraint(__isl_keep isl_basic_set *bset,
228 int (*fn)(__isl_take isl_constraint *c, void *user), void *user)
230 return isl_basic_map_foreach_constraint((isl_basic_map *)bset, fn, user);
233 int isl_constraint_is_equal(struct isl_constraint *constraint1,
234 struct isl_constraint *constraint2)
236 if (!constraint1 || !constraint2)
238 return constraint1->bmap == constraint2->bmap &&
239 constraint1->line == constraint2->line;
242 struct isl_basic_map *isl_basic_map_add_constraint(
243 struct isl_basic_map *bmap, struct isl_constraint *constraint)
245 if (!bmap || !constraint)
248 isl_assert(constraint->ctx,
249 isl_dim_equal(bmap->dim, constraint->bmap->dim), goto error);
251 bmap = isl_basic_map_intersect(bmap,
252 isl_basic_map_from_constraint(constraint));
255 isl_basic_map_free(bmap);
256 isl_constraint_free(constraint);
260 struct isl_basic_set *isl_basic_set_add_constraint(
261 struct isl_basic_set *bset, struct isl_constraint *constraint)
263 return (struct isl_basic_set *)
264 isl_basic_map_add_constraint((struct isl_basic_map *)bset,
268 struct isl_constraint *isl_constraint_add_div(struct isl_constraint *constraint,
269 struct isl_div *div, int *pos)
271 if (!constraint || !div)
274 isl_assert(constraint->ctx,
275 isl_dim_equal(div->bmap->dim, constraint->bmap->dim), goto error);
276 isl_assert(constraint->ctx,
277 constraint->bmap->n_eq + constraint->bmap->n_ineq == 1, goto error);
279 constraint->bmap = isl_basic_map_cow(constraint->bmap);
280 constraint->bmap = isl_basic_map_extend_dim(constraint->bmap,
281 isl_dim_copy(constraint->bmap->dim), 1, 0, 0);
282 if (!constraint->bmap)
284 constraint->line = &constraint->bmap->eq[0];
285 *pos = isl_basic_map_alloc_div(constraint->bmap);
288 isl_seq_cpy(constraint->bmap->div[*pos], div->line[0],
289 1 + 1 + isl_basic_map_total_dim(constraint->bmap));
293 isl_constraint_free(constraint);
298 int isl_constraint_dim(struct isl_constraint *constraint,
299 enum isl_dim_type type)
303 return n(constraint, type);
306 void isl_constraint_get_constant(struct isl_constraint *constraint, isl_int *v)
310 isl_int_set(*v, constraint->line[0][0]);
313 void isl_constraint_get_coefficient(struct isl_constraint *constraint,
314 enum isl_dim_type type, int pos, isl_int *v)
319 isl_assert(constraint->ctx, pos < n(constraint, type), return);
320 isl_int_set(*v, constraint->line[0][offset(constraint, type) + pos]);
323 struct isl_div *isl_constraint_div(struct isl_constraint *constraint, int pos)
328 isl_assert(constraint->ctx, pos < n(constraint, isl_dim_div),
330 isl_assert(constraint->ctx,
331 !isl_int_is_zero(constraint->bmap->div[pos][0]), return NULL);
332 return isl_basic_map_div(isl_basic_map_copy(constraint->bmap), pos);
335 void isl_constraint_set_constant(struct isl_constraint *constraint, isl_int v)
339 isl_int_set(constraint->line[0][0], v);
342 void isl_constraint_set_coefficient(struct isl_constraint *constraint,
343 enum isl_dim_type type, int pos, isl_int v)
348 isl_assert(constraint->ctx, pos < n(constraint, type), return);
349 isl_int_set(constraint->line[0][offset(constraint, type) + pos], v);
352 void isl_constraint_clear(struct isl_constraint *constraint)
358 total = isl_basic_map_total_dim(constraint->bmap);
359 isl_seq_clr(constraint->line[0], 1 + total);
362 struct isl_constraint *isl_constraint_negate(struct isl_constraint *constraint)
369 isl_assert(constraint->ctx, !isl_constraint_is_equality(constraint),
371 isl_assert(constraint->ctx, constraint->bmap->ref == 1, goto error);
372 total = isl_basic_map_total_dim(constraint->bmap);
373 isl_seq_neg(constraint->line[0], constraint->line[0], 1 + total);
374 isl_int_sub_ui(constraint->line[0][0], constraint->line[0][0], 1);
375 ISL_F_CLR(constraint->bmap, ISL_BASIC_MAP_NORMALIZED);
378 isl_constraint_free(constraint);
382 int isl_constraint_is_equality(struct isl_constraint *constraint)
386 return constraint->line >= constraint->bmap->eq;
389 __isl_give isl_basic_map *isl_basic_map_from_constraint(
390 __isl_take isl_constraint *constraint)
393 struct isl_basic_map *bmap;
400 if (constraint->bmap->n_eq + constraint->bmap->n_ineq == 1) {
401 bmap = isl_basic_map_copy(constraint->bmap);
402 isl_constraint_free(constraint);
406 bmap = isl_basic_map_universe_like(constraint->bmap);
407 bmap = isl_basic_map_align_divs(bmap, constraint->bmap);
408 bmap = isl_basic_map_cow(bmap);
409 bmap = isl_basic_map_extend_constraints(bmap, 1, 1);
410 if (isl_constraint_is_equality(constraint)) {
411 k = isl_basic_map_alloc_equality(bmap);
417 k = isl_basic_map_alloc_inequality(bmap);
422 total = isl_basic_map_total_dim(bmap);
423 isl_seq_cpy(c, constraint->line[0], 1 + total);
424 isl_constraint_free(constraint);
425 bmap = isl_basic_map_finalize(bmap);
428 isl_constraint_free(constraint);
429 isl_basic_map_free(bmap);
433 struct isl_basic_set *isl_basic_set_from_constraint(
434 struct isl_constraint *constraint)
439 isl_assert(constraint->ctx,n(constraint, isl_dim_in) == 0, goto error);
440 return (isl_basic_set *)isl_basic_map_from_constraint(constraint);
442 isl_constraint_free(constraint);
446 int isl_basic_set_has_defining_equality(
447 struct isl_basic_set *bset, enum isl_dim_type type, int pos,
448 struct isl_constraint **c)
456 offset = basic_set_offset(bset, type);
457 total = isl_basic_set_total_dim(bset);
458 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
459 for (i = 0; i < bset->n_eq; ++i)
460 if (!isl_int_is_zero(bset->eq[i][offset + pos]) &&
461 isl_seq_first_non_zero(bset->eq[i]+offset+pos+1,
462 1+total-offset-pos-1) == -1) {
463 *c= isl_basic_set_constraint(isl_basic_set_copy(bset),
470 int isl_basic_set_has_defining_inequalities(
471 struct isl_basic_set *bset, enum isl_dim_type type, int pos,
472 struct isl_constraint **lower,
473 struct isl_constraint **upper)
479 isl_int **lower_line, **upper_line;
483 offset = basic_set_offset(bset, type);
484 total = isl_basic_set_total_dim(bset);
485 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
487 for (i = 0; i < bset->n_ineq; ++i) {
488 if (isl_int_is_zero(bset->ineq[i][offset + pos]))
490 if (isl_int_is_one(bset->ineq[i][offset + pos]))
492 if (isl_int_is_negone(bset->ineq[i][offset + pos]))
494 if (isl_seq_first_non_zero(bset->ineq[i]+offset+pos+1,
495 1+total-offset-pos-1) != -1)
497 for (j = i + 1; j < bset->n_ineq; ++j) {
498 if (!isl_seq_is_neg(bset->ineq[i]+1, bset->ineq[j]+1,
501 isl_int_add(m, bset->ineq[i][0], bset->ineq[j][0]);
502 if (isl_int_abs_ge(m, bset->ineq[i][offset+pos]))
505 if (isl_int_is_pos(bset->ineq[i][offset+pos])) {
506 lower_line = &bset->ineq[i];
507 upper_line = &bset->ineq[j];
509 lower_line = &bset->ineq[j];
510 upper_line = &bset->ineq[i];
512 *lower = isl_basic_set_constraint(
513 isl_basic_set_copy(bset), lower_line);
514 *upper = isl_basic_set_constraint(
515 isl_basic_set_copy(bset), upper_line);
526 /* Given two constraints "a" and "b" on the variable at position "abs_pos"
527 * (in "a" and "b"), add a constraint to "bset" that ensures that the
528 * bound implied by "a" is (strictly) larger than the bound implied by "b".
530 * If both constraints imply lower bounds, then this means that "a" is
531 * active in the result.
532 * If both constraints imply upper bounds, then this means that "b" is
533 * active in the result.
535 static __isl_give isl_basic_set *add_larger_bound_constraint(
536 __isl_take isl_basic_set *bset, isl_int *a, isl_int *b,
537 unsigned abs_pos, int strict)
543 k = isl_basic_set_alloc_inequality(bset);
547 total = isl_basic_set_dim(bset, isl_dim_all);
550 isl_int_neg(t, b[1 + abs_pos]);
552 isl_seq_combine(bset->ineq[k], t, a, a[1 + abs_pos], b, 1 + abs_pos);
553 isl_seq_combine(bset->ineq[k] + 1 + abs_pos,
554 t, a + 1 + abs_pos + 1, a[1 + abs_pos], b + 1 + abs_pos + 1,
558 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
564 isl_basic_set_free(bset);
568 /* Add constraints to "context" that ensure that "u" is the smallest
569 * (and therefore active) upper bound on "abs_pos" in "bset" and return
570 * the resulting basic set.
572 static __isl_give isl_basic_set *set_smallest_upper_bound(
573 __isl_keep isl_basic_set *context,
574 __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_upper, int u)
578 context = isl_basic_set_copy(context);
579 context = isl_basic_set_cow(context);
581 context = isl_basic_set_extend_constraints(context, 0, n_upper - 1);
583 for (j = 0; j < bset->n_ineq; ++j) {
586 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
588 context = add_larger_bound_constraint(context,
589 bset->ineq[j], bset->ineq[u], abs_pos, j > u);
592 context = isl_basic_set_simplify(context);
593 context = isl_basic_set_finalize(context);
598 /* Add constraints to "context" that ensure that "u" is the largest
599 * (and therefore active) upper bound on "abs_pos" in "bset" and return
600 * the resulting basic set.
602 static __isl_give isl_basic_set *set_largest_lower_bound(
603 __isl_keep isl_basic_set *context,
604 __isl_keep isl_basic_set *bset, unsigned abs_pos, int n_lower, int l)
608 context = isl_basic_set_copy(context);
609 context = isl_basic_set_cow(context);
611 context = isl_basic_set_extend_constraints(context, 0, n_lower - 1);
613 for (j = 0; j < bset->n_ineq; ++j) {
616 if (!isl_int_is_pos(bset->ineq[j][1 + abs_pos]))
618 context = add_larger_bound_constraint(context,
619 bset->ineq[l], bset->ineq[j], abs_pos, j > l);
622 context = isl_basic_set_simplify(context);
623 context = isl_basic_set_finalize(context);
628 static int foreach_upper_bound(__isl_keep isl_basic_set *bset,
629 enum isl_dim_type type, unsigned abs_pos,
630 __isl_take isl_basic_set *context, int n_upper,
631 int (*fn)(__isl_take isl_constraint *lower,
632 __isl_take isl_constraint *upper,
633 __isl_take isl_basic_set *bset, void *user), void *user)
635 isl_basic_set *context_i;
636 isl_constraint *upper = NULL;
639 for (i = 0; i < bset->n_ineq; ++i) {
640 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
643 context_i = set_smallest_upper_bound(context, bset,
644 abs_pos, n_upper, i);
645 if (isl_basic_set_is_empty(context_i)) {
646 isl_basic_set_free(context_i);
649 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
651 if (!upper || !context_i)
653 if (fn(NULL, upper, context_i, user) < 0)
657 isl_basic_set_free(context);
659 if (i < bset->n_ineq)
664 isl_constraint_free(upper);
665 isl_basic_set_free(context_i);
666 isl_basic_set_free(context);
670 static int foreach_lower_bound(__isl_keep isl_basic_set *bset,
671 enum isl_dim_type type, unsigned abs_pos,
672 __isl_take isl_basic_set *context, int n_lower,
673 int (*fn)(__isl_take isl_constraint *lower,
674 __isl_take isl_constraint *upper,
675 __isl_take isl_basic_set *bset, void *user), void *user)
677 isl_basic_set *context_i;
678 isl_constraint *lower = NULL;
681 for (i = 0; i < bset->n_ineq; ++i) {
682 if (isl_int_is_zero(bset->ineq[i][1 + abs_pos]))
685 context_i = set_largest_lower_bound(context, bset,
686 abs_pos, n_lower, i);
687 if (isl_basic_set_is_empty(context_i)) {
688 isl_basic_set_free(context_i);
691 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
693 if (!lower || !context_i)
695 if (fn(lower, NULL, context_i, user) < 0)
699 isl_basic_set_free(context);
701 if (i < bset->n_ineq)
706 isl_constraint_free(lower);
707 isl_basic_set_free(context_i);
708 isl_basic_set_free(context);
712 static int foreach_bound_pair(__isl_keep isl_basic_set *bset,
713 enum isl_dim_type type, unsigned abs_pos,
714 __isl_take isl_basic_set *context, int n_lower, int n_upper,
715 int (*fn)(__isl_take isl_constraint *lower,
716 __isl_take isl_constraint *upper,
717 __isl_take isl_basic_set *bset, void *user), void *user)
719 isl_basic_set *context_i, *context_j;
720 isl_constraint *lower = NULL;
721 isl_constraint *upper = NULL;
724 for (i = 0; i < bset->n_ineq; ++i) {
725 if (!isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
728 context_i = set_largest_lower_bound(context, bset,
729 abs_pos, n_lower, i);
730 if (isl_basic_set_is_empty(context_i)) {
731 isl_basic_set_free(context_i);
735 for (j = 0; j < bset->n_ineq; ++j) {
736 if (!isl_int_is_neg(bset->ineq[j][1 + abs_pos]))
739 context_j = set_smallest_upper_bound(context_i, bset,
740 abs_pos, n_upper, j);
741 context_j = isl_basic_set_extend_constraints(context_j,
743 context_j = add_larger_bound_constraint(context_j,
744 bset->ineq[i], bset->ineq[j], abs_pos, 0);
745 context_j = isl_basic_set_simplify(context_j);
746 context_j = isl_basic_set_finalize(context_j);
747 if (isl_basic_set_is_empty(context_j)) {
748 isl_basic_set_free(context_j);
751 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
753 upper = isl_basic_set_constraint(isl_basic_set_copy(bset),
755 if (!lower || !upper || !context_j)
757 if (fn(lower, upper, context_j, user) < 0)
761 isl_basic_set_free(context_i);
763 if (j < bset->n_ineq)
767 isl_basic_set_free(context);
769 if (i < bset->n_ineq)
774 isl_constraint_free(lower);
775 isl_constraint_free(upper);
776 isl_basic_set_free(context_i);
777 isl_basic_set_free(context_j);
778 isl_basic_set_free(context);
782 /* For each pair of lower and upper bounds on the variable "pos"
783 * of type "type", call "fn" with these lower and upper bounds and the
784 * set of constraints on the remaining variables where these bounds
785 * are active, i.e., (stricly) larger/smaller than the other lower/upper bounds.
787 * If the designated variable is equal to an affine combination of the
788 * other variables then fn is called with both lower and upper
789 * set to the corresponding equality.
791 * If there is no lower (or upper) bound, then NULL is passed
792 * as the corresponding bound.
794 * We first check if the variable is involved in any equality.
795 * If not, we count the number of lower and upper bounds and
798 int isl_basic_set_foreach_bound_pair(__isl_keep isl_basic_set *bset,
799 enum isl_dim_type type, unsigned pos,
800 int (*fn)(__isl_take isl_constraint *lower,
801 __isl_take isl_constraint *upper,
802 __isl_take isl_basic_set *bset, void *user), void *user)
805 isl_constraint *lower = NULL;
806 isl_constraint *upper = NULL;
807 isl_basic_set *context = NULL;
809 int n_lower, n_upper;
813 isl_assert(bset->ctx, pos < isl_basic_set_dim(bset, type), return -1);
814 isl_assert(bset->ctx, type == isl_dim_param || type == isl_dim_set,
818 if (type == isl_dim_set)
819 abs_pos += isl_basic_set_dim(bset, isl_dim_param);
821 for (i = 0; i < bset->n_eq; ++i) {
822 if (isl_int_is_zero(bset->eq[i][1 + abs_pos]))
825 lower = isl_basic_set_constraint(isl_basic_set_copy(bset),
827 upper = isl_constraint_copy(lower);
828 context = isl_basic_set_remove(isl_basic_set_copy(bset),
830 if (!lower || !upper || !context)
832 return fn(lower, upper, context, user);
837 for (i = 0; i < bset->n_ineq; ++i) {
838 if (isl_int_is_pos(bset->ineq[i][1 + abs_pos]))
840 else if (isl_int_is_neg(bset->ineq[i][1 + abs_pos]))
844 context = isl_basic_set_copy(bset);
845 context = isl_basic_set_cow(context);
848 for (i = context->n_ineq - 1; i >= 0; --i)
849 if (!isl_int_is_zero(context->ineq[i][1 + abs_pos]))
850 isl_basic_set_drop_inequality(context, i);
852 context = isl_basic_set_drop(context, type, pos, 1);
853 if (!n_lower && !n_upper)
854 return fn(NULL, NULL, context, user);
856 return foreach_upper_bound(bset, type, abs_pos, context, n_upper,
859 return foreach_lower_bound(bset, type, abs_pos, context, n_lower,
861 return foreach_bound_pair(bset, type, abs_pos, context, n_lower, n_upper,
864 isl_constraint_free(lower);
865 isl_constraint_free(upper);
866 isl_basic_set_free(context);