2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
12 #include <isl_map_private.h>
13 #include <isl_union_map_private.h>
14 #include <isl_polynomial_private.h>
15 #include <isl_point_private.h>
16 #include <isl_space_private.h>
19 #include <isl_mat_private.h>
20 #include <isl_config.h>
22 enum isl_fold isl_fold_type_negate(enum isl_fold type)
33 isl_die(NULL, isl_error_internal, "unhandled isl_fold type", abort());
36 static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
37 enum isl_fold type, __isl_take isl_space *dim, int n)
39 isl_qpolynomial_fold *fold;
44 isl_assert(dim->ctx, n >= 0, goto error);
45 fold = isl_calloc(dim->ctx, struct isl_qpolynomial_fold,
46 sizeof(struct isl_qpolynomial_fold) +
47 (n - 1) * sizeof(struct isl_qpolynomial *));
63 isl_ctx *isl_qpolynomial_fold_get_ctx(__isl_keep isl_qpolynomial_fold *fold)
65 return fold ? fold->dim->ctx : NULL;
68 __isl_give isl_space *isl_qpolynomial_fold_get_domain_space(
69 __isl_keep isl_qpolynomial_fold *fold)
71 return fold ? isl_space_copy(fold->dim) : NULL;
74 __isl_give isl_space *isl_qpolynomial_fold_get_space(
75 __isl_keep isl_qpolynomial_fold *fold)
80 space = isl_space_copy(fold->dim);
81 space = isl_space_from_domain(space);
82 space = isl_space_add_dims(space, isl_dim_out, 1);
86 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_domain_space(
87 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
91 fold = isl_qpolynomial_fold_cow(fold);
95 for (i = 0; i < fold->n; ++i) {
96 fold->qp[i] = isl_qpolynomial_reset_domain_space(fold->qp[i],
102 isl_space_free(fold->dim);
107 isl_qpolynomial_fold_free(fold);
112 /* Reset the space of "fold". This function is called from isl_pw_templ.c
113 * and doesn't know if the space of an element object is represented
114 * directly or through its domain. It therefore passes along both.
116 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_space_and_domain(
117 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *space,
118 __isl_take isl_space *domain)
120 isl_space_free(space);
121 return isl_qpolynomial_fold_reset_domain_space(fold, domain);
124 int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold *fold,
125 enum isl_dim_type type, unsigned first, unsigned n)
131 if (fold->n == 0 || n == 0)
134 for (i = 0; i < fold->n; ++i) {
135 int involves = isl_qpolynomial_involves_dims(fold->qp[i],
137 if (involves < 0 || involves)
143 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_set_dim_name(
144 __isl_take isl_qpolynomial_fold *fold,
145 enum isl_dim_type type, unsigned pos, const char *s)
149 fold = isl_qpolynomial_fold_cow(fold);
152 fold->dim = isl_space_set_dim_name(fold->dim, type, pos, s);
156 for (i = 0; i < fold->n; ++i) {
157 fold->qp[i] = isl_qpolynomial_set_dim_name(fold->qp[i],
165 isl_qpolynomial_fold_free(fold);
169 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_drop_dims(
170 __isl_take isl_qpolynomial_fold *fold,
171 enum isl_dim_type type, unsigned first, unsigned n)
174 enum isl_dim_type set_type;
181 set_type = type == isl_dim_in ? isl_dim_set : type;
183 fold = isl_qpolynomial_fold_cow(fold);
186 fold->dim = isl_space_drop_dims(fold->dim, set_type, first, n);
190 for (i = 0; i < fold->n; ++i) {
191 fold->qp[i] = isl_qpolynomial_drop_dims(fold->qp[i],
199 isl_qpolynomial_fold_free(fold);
203 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_insert_dims(
204 __isl_take isl_qpolynomial_fold *fold,
205 enum isl_dim_type type, unsigned first, unsigned n)
211 if (n == 0 && !isl_space_is_named_or_nested(fold->dim, type))
214 fold = isl_qpolynomial_fold_cow(fold);
217 fold->dim = isl_space_insert_dims(fold->dim, type, first, n);
221 for (i = 0; i < fold->n; ++i) {
222 fold->qp[i] = isl_qpolynomial_insert_dims(fold->qp[i],
230 isl_qpolynomial_fold_free(fold);
234 static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial *qp)
236 struct isl_upoly_cst *cst;
238 cst = isl_upoly_as_cst(qp->upoly);
242 return isl_int_sgn(cst->n) < 0 ? -1 : 1;
245 static int isl_qpolynomial_aff_sign(__isl_keep isl_set *set,
246 __isl_keep isl_qpolynomial *qp)
248 enum isl_lp_result res;
253 aff = isl_qpolynomial_extract_affine(qp);
259 res = isl_set_solve_lp(set, 0, aff->el + 1, aff->el[0],
261 if (res == isl_lp_error)
263 if (res == isl_lp_empty ||
264 (res == isl_lp_ok && !isl_int_is_neg(opt))) {
269 res = isl_set_solve_lp(set, 1, aff->el + 1, aff->el[0],
271 if (res == isl_lp_ok && !isl_int_is_pos(opt))
280 /* Determine, if possible, the sign of the quasipolynomial "qp" on
283 * If qp is a constant, then the problem is trivial.
284 * If qp is linear, then we check if the minimum of the corresponding
285 * affine constraint is non-negative or if the maximum is non-positive.
287 * Otherwise, we check if the outermost variable "v" has a lower bound "l"
288 * in "set". If so, we write qp(v,v') as
290 * q(v,v') * (v - l) + r(v')
292 * if q(v,v') and r(v') have the same known sign, then the original
293 * quasipolynomial has the same sign as well.
300 static int isl_qpolynomial_sign(__isl_keep isl_set *set,
301 __isl_keep isl_qpolynomial *qp)
306 struct isl_upoly_rec *rec;
309 enum isl_lp_result res;
312 is = isl_qpolynomial_is_cst(qp, NULL, NULL);
316 return isl_qpolynomial_cst_sign(qp);
318 is = isl_qpolynomial_is_affine(qp);
322 return isl_qpolynomial_aff_sign(set, qp);
324 if (qp->div->n_row > 0)
327 rec = isl_upoly_as_rec(qp->upoly);
331 d = isl_space_dim(qp->dim, isl_dim_all);
332 v = isl_vec_alloc(set->ctx, 2 + d);
336 isl_seq_clr(v->el + 1, 1 + d);
337 isl_int_set_si(v->el[0], 1);
338 isl_int_set_si(v->el[2 + qp->upoly->var], 1);
342 res = isl_set_solve_lp(set, 0, v->el + 1, v->el[0], &l, NULL, NULL);
343 if (res == isl_lp_ok) {
344 isl_qpolynomial *min;
345 isl_qpolynomial *base;
346 isl_qpolynomial *r, *q;
349 min = isl_qpolynomial_cst_on_domain(isl_space_copy(qp->dim), l);
350 base = isl_qpolynomial_var_pow_on_domain(isl_space_copy(qp->dim),
353 r = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
354 isl_upoly_copy(rec->p[rec->n - 1]));
355 q = isl_qpolynomial_copy(r);
357 for (i = rec->n - 2; i >= 0; --i) {
358 r = isl_qpolynomial_mul(r, isl_qpolynomial_copy(min));
359 t = isl_qpolynomial_alloc(isl_space_copy(qp->dim), 0,
360 isl_upoly_copy(rec->p[i]));
361 r = isl_qpolynomial_add(r, t);
364 q = isl_qpolynomial_mul(q, isl_qpolynomial_copy(base));
365 q = isl_qpolynomial_add(q, isl_qpolynomial_copy(r));
368 if (isl_qpolynomial_is_zero(q))
369 sgn = isl_qpolynomial_sign(set, r);
370 else if (isl_qpolynomial_is_zero(r))
371 sgn = isl_qpolynomial_sign(set, q);
374 sgn_r = isl_qpolynomial_sign(set, r);
375 sgn_q = isl_qpolynomial_sign(set, q);
380 isl_qpolynomial_free(min);
381 isl_qpolynomial_free(base);
382 isl_qpolynomial_free(q);
383 isl_qpolynomial_free(r);
393 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold_on_domain(
394 __isl_keep isl_set *set,
395 __isl_take isl_qpolynomial_fold *fold1,
396 __isl_take isl_qpolynomial_fold *fold2)
400 struct isl_qpolynomial_fold *res = NULL;
403 if (!fold1 || !fold2)
406 isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
407 isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
410 better = fold1->type == isl_fold_max ? -1 : 1;
412 if (isl_qpolynomial_fold_is_empty(fold1)) {
413 isl_qpolynomial_fold_free(fold1);
417 if (isl_qpolynomial_fold_is_empty(fold2)) {
418 isl_qpolynomial_fold_free(fold2);
422 res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
423 fold1->n + fold2->n);
427 for (i = 0; i < fold1->n; ++i) {
428 res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
429 if (!res->qp[res->n])
435 for (i = 0; i < fold2->n; ++i) {
436 for (j = n1 - 1; j >= 0; --j) {
439 d = isl_qpolynomial_sub(
440 isl_qpolynomial_copy(res->qp[j]),
441 isl_qpolynomial_copy(fold2->qp[i]));
442 sgn = isl_qpolynomial_sign(set, d);
443 isl_qpolynomial_free(d);
448 isl_qpolynomial_free(res->qp[j]);
450 res->qp[j] = res->qp[n1 - 1];
452 if (n1 != res->n - 1)
453 res->qp[n1] = res->qp[res->n - 1];
458 res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
459 if (!res->qp[res->n])
464 isl_qpolynomial_fold_free(fold1);
465 isl_qpolynomial_fold_free(fold2);
469 isl_qpolynomial_fold_free(res);
470 isl_qpolynomial_fold_free(fold1);
471 isl_qpolynomial_fold_free(fold2);
475 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_qpolynomial(
476 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_qpolynomial *qp)
483 if (isl_qpolynomial_is_zero(qp)) {
484 isl_qpolynomial_free(qp);
488 fold = isl_qpolynomial_fold_cow(fold);
492 for (i = 0; i < fold->n; ++i) {
493 fold->qp[i] = isl_qpolynomial_add(fold->qp[i],
494 isl_qpolynomial_copy(qp));
499 isl_qpolynomial_free(qp);
502 isl_qpolynomial_fold_free(fold);
503 isl_qpolynomial_free(qp);
507 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_on_domain(
508 __isl_keep isl_set *dom,
509 __isl_take isl_qpolynomial_fold *fold1,
510 __isl_take isl_qpolynomial_fold *fold2)
513 isl_qpolynomial_fold *res = NULL;
515 if (!fold1 || !fold2)
518 if (isl_qpolynomial_fold_is_empty(fold1)) {
519 isl_qpolynomial_fold_free(fold1);
523 if (isl_qpolynomial_fold_is_empty(fold2)) {
524 isl_qpolynomial_fold_free(fold2);
528 if (fold1->n == 1 && fold2->n != 1)
529 return isl_qpolynomial_fold_add_on_domain(dom, fold2, fold1);
532 res = isl_qpolynomial_fold_add_qpolynomial(fold1,
533 isl_qpolynomial_copy(fold2->qp[0]));
534 isl_qpolynomial_fold_free(fold2);
538 res = isl_qpolynomial_fold_add_qpolynomial(
539 isl_qpolynomial_fold_copy(fold1),
540 isl_qpolynomial_copy(fold2->qp[0]));
542 for (i = 1; i < fold2->n; ++i) {
543 isl_qpolynomial_fold *res_i;
544 res_i = isl_qpolynomial_fold_add_qpolynomial(
545 isl_qpolynomial_fold_copy(fold1),
546 isl_qpolynomial_copy(fold2->qp[i]));
547 res = isl_qpolynomial_fold_fold_on_domain(dom, res, res_i);
550 isl_qpolynomial_fold_free(fold1);
551 isl_qpolynomial_fold_free(fold2);
554 isl_qpolynomial_fold_free(res);
555 isl_qpolynomial_fold_free(fold1);
556 isl_qpolynomial_fold_free(fold2);
560 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute_equalities(
561 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_basic_set *eq)
568 fold = isl_qpolynomial_fold_cow(fold);
572 for (i = 0; i < fold->n; ++i) {
573 fold->qp[i] = isl_qpolynomial_substitute_equalities(fold->qp[i],
574 isl_basic_set_copy(eq));
579 isl_basic_set_free(eq);
582 isl_basic_set_free(eq);
583 isl_qpolynomial_fold_free(fold);
587 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
588 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
592 if (!fold || !context)
595 fold = isl_qpolynomial_fold_cow(fold);
599 for (i = 0; i < fold->n; ++i) {
600 fold->qp[i] = isl_qpolynomial_gist(fold->qp[i],
601 isl_set_copy(context));
606 isl_set_free(context);
609 isl_set_free(context);
610 isl_qpolynomial_fold_free(fold);
614 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
615 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
617 isl_space *space = isl_qpolynomial_fold_get_domain_space(fold);
618 isl_set *dom_context = isl_set_universe(space);
619 dom_context = isl_set_intersect_params(dom_context, context);
620 return isl_qpolynomial_fold_gist(fold, dom_context);
626 #define PW isl_pw_qpolynomial_fold
628 #define EL isl_qpolynomial_fold
630 #define EL_IS_ZERO is_empty
634 #define IS_ZERO is_zero
640 #include <isl_pw_templ.c>
643 #define UNION isl_union_pw_qpolynomial_fold
645 #define PART isl_pw_qpolynomial_fold
647 #define PARTS pw_qpolynomial_fold
650 #include <isl_union_templ.c>
652 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
653 __isl_take isl_space *dim)
655 return qpolynomial_fold_alloc(type, dim, 0);
658 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_alloc(
659 enum isl_fold type, __isl_take isl_qpolynomial *qp)
661 isl_qpolynomial_fold *fold;
666 fold = qpolynomial_fold_alloc(type, isl_space_copy(qp->dim), 1);
675 isl_qpolynomial_fold_free(fold);
676 isl_qpolynomial_free(qp);
680 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
681 __isl_keep isl_qpolynomial_fold *fold)
690 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_dup(
691 __isl_keep isl_qpolynomial_fold *fold)
694 isl_qpolynomial_fold *dup;
698 dup = qpolynomial_fold_alloc(fold->type,
699 isl_space_copy(fold->dim), fold->n);
704 for (i = 0; i < fold->n; ++i) {
705 dup->qp[i] = isl_qpolynomial_copy(fold->qp[i]);
712 isl_qpolynomial_fold_free(dup);
716 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_cow(
717 __isl_take isl_qpolynomial_fold *fold)
725 return isl_qpolynomial_fold_dup(fold);
728 void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold *fold)
737 for (i = 0; i < fold->n; ++i)
738 isl_qpolynomial_free(fold->qp[i]);
739 isl_space_free(fold->dim);
743 int isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold *fold)
751 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
752 __isl_take isl_qpolynomial_fold *fold1,
753 __isl_take isl_qpolynomial_fold *fold2)
756 struct isl_qpolynomial_fold *res = NULL;
758 if (!fold1 || !fold2)
761 isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
762 isl_assert(fold1->dim->ctx, isl_space_is_equal(fold1->dim, fold2->dim),
765 if (isl_qpolynomial_fold_is_empty(fold1)) {
766 isl_qpolynomial_fold_free(fold1);
770 if (isl_qpolynomial_fold_is_empty(fold2)) {
771 isl_qpolynomial_fold_free(fold2);
775 res = qpolynomial_fold_alloc(fold1->type, isl_space_copy(fold1->dim),
776 fold1->n + fold2->n);
780 for (i = 0; i < fold1->n; ++i) {
781 res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
782 if (!res->qp[res->n])
787 for (i = 0; i < fold2->n; ++i) {
788 res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
789 if (!res->qp[res->n])
794 isl_qpolynomial_fold_free(fold1);
795 isl_qpolynomial_fold_free(fold2);
799 isl_qpolynomial_fold_free(res);
800 isl_qpolynomial_fold_free(fold1);
801 isl_qpolynomial_fold_free(fold2);
805 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
806 __isl_take isl_pw_qpolynomial_fold *pw1,
807 __isl_take isl_pw_qpolynomial_fold *pw2)
810 struct isl_pw_qpolynomial_fold *res;
816 isl_assert(pw1->dim->ctx, isl_space_is_equal(pw1->dim, pw2->dim), goto error);
818 if (isl_pw_qpolynomial_fold_is_zero(pw1)) {
819 isl_pw_qpolynomial_fold_free(pw1);
823 if (isl_pw_qpolynomial_fold_is_zero(pw2)) {
824 isl_pw_qpolynomial_fold_free(pw2);
828 if (pw1->type != pw2->type)
829 isl_die(pw1->dim->ctx, isl_error_invalid,
830 "fold types don't match", goto error);
832 n = (pw1->n + 1) * (pw2->n + 1);
833 res = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pw1->dim),
836 for (i = 0; i < pw1->n; ++i) {
837 set = isl_set_copy(pw1->p[i].set);
838 for (j = 0; j < pw2->n; ++j) {
839 struct isl_set *common;
840 isl_qpolynomial_fold *sum;
841 set = isl_set_subtract(set,
842 isl_set_copy(pw2->p[j].set));
843 common = isl_set_intersect(isl_set_copy(pw1->p[i].set),
844 isl_set_copy(pw2->p[j].set));
845 if (isl_set_plain_is_empty(common)) {
846 isl_set_free(common);
850 sum = isl_qpolynomial_fold_fold_on_domain(common,
851 isl_qpolynomial_fold_copy(pw1->p[i].fold),
852 isl_qpolynomial_fold_copy(pw2->p[j].fold));
854 res = isl_pw_qpolynomial_fold_add_piece(res, common, sum);
856 res = isl_pw_qpolynomial_fold_add_piece(res, set,
857 isl_qpolynomial_fold_copy(pw1->p[i].fold));
860 for (j = 0; j < pw2->n; ++j) {
861 set = isl_set_copy(pw2->p[j].set);
862 for (i = 0; i < pw1->n; ++i)
863 set = isl_set_subtract(set, isl_set_copy(pw1->p[i].set));
864 res = isl_pw_qpolynomial_fold_add_piece(res, set,
865 isl_qpolynomial_fold_copy(pw2->p[j].fold));
868 isl_pw_qpolynomial_fold_free(pw1);
869 isl_pw_qpolynomial_fold_free(pw2);
873 isl_pw_qpolynomial_fold_free(pw1);
874 isl_pw_qpolynomial_fold_free(pw2);
878 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
879 __isl_take isl_union_pw_qpolynomial_fold *u,
880 __isl_take isl_pw_qpolynomial_fold *part)
883 struct isl_hash_table_entry *entry;
885 u = isl_union_pw_qpolynomial_fold_cow(u);
890 isl_assert(u->dim->ctx, isl_space_match(part->dim, isl_dim_param, u->dim,
891 isl_dim_param), goto error);
893 hash = isl_space_get_hash(part->dim);
894 entry = isl_hash_table_find(u->dim->ctx, &u->table, hash,
895 &has_dim, part->dim, 1);
902 entry->data = isl_pw_qpolynomial_fold_fold(entry->data,
903 isl_pw_qpolynomial_fold_copy(part));
906 isl_pw_qpolynomial_fold_free(part);
911 isl_pw_qpolynomial_fold_free(part);
912 isl_union_pw_qpolynomial_fold_free(u);
916 static int fold_part(__isl_take isl_pw_qpolynomial_fold *part, void *user)
918 isl_union_pw_qpolynomial_fold **u;
919 u = (isl_union_pw_qpolynomial_fold **)user;
921 *u = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u, part);
926 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
927 __isl_take isl_union_pw_qpolynomial_fold *u1,
928 __isl_take isl_union_pw_qpolynomial_fold *u2)
930 u1 = isl_union_pw_qpolynomial_fold_cow(u1);
935 if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2,
936 &fold_part, &u1) < 0)
939 isl_union_pw_qpolynomial_fold_free(u2);
943 isl_union_pw_qpolynomial_fold_free(u1);
944 isl_union_pw_qpolynomial_fold_free(u2);
948 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
949 enum isl_fold type, __isl_take isl_pw_qpolynomial *pwqp)
952 isl_pw_qpolynomial_fold *pwf;
957 pwf = isl_pw_qpolynomial_fold_alloc_size(isl_space_copy(pwqp->dim),
960 for (i = 0; i < pwqp->n; ++i)
961 pwf = isl_pw_qpolynomial_fold_add_piece(pwf,
962 isl_set_copy(pwqp->p[i].set),
963 isl_qpolynomial_fold_alloc(type,
964 isl_qpolynomial_copy(pwqp->p[i].qp)));
966 isl_pw_qpolynomial_free(pwqp);
971 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
972 __isl_take isl_pw_qpolynomial_fold *pwf1,
973 __isl_take isl_pw_qpolynomial_fold *pwf2)
975 return isl_pw_qpolynomial_fold_union_add_(pwf1, pwf2);
978 int isl_qpolynomial_fold_plain_is_equal(__isl_keep isl_qpolynomial_fold *fold1,
979 __isl_keep isl_qpolynomial_fold *fold2)
983 if (!fold1 || !fold2)
986 if (fold1->n != fold2->n)
989 /* We probably want to sort the qps first... */
990 for (i = 0; i < fold1->n; ++i) {
991 int eq = isl_qpolynomial_plain_is_equal(fold1->qp[i], fold2->qp[i]);
999 __isl_give isl_qpolynomial *isl_qpolynomial_fold_eval(
1000 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_point *pnt)
1002 isl_qpolynomial *qp;
1006 isl_assert(pnt->dim->ctx, isl_space_is_equal(pnt->dim, fold->dim), goto error);
1007 isl_assert(pnt->dim->ctx,
1008 fold->type == isl_fold_max || fold->type == isl_fold_min,
1012 qp = isl_qpolynomial_zero_on_domain(isl_space_copy(fold->dim));
1015 qp = isl_qpolynomial_eval(isl_qpolynomial_copy(fold->qp[0]),
1016 isl_point_copy(pnt));
1017 for (i = 1; i < fold->n; ++i) {
1018 isl_qpolynomial *qp_i;
1019 qp_i = isl_qpolynomial_eval(
1020 isl_qpolynomial_copy(fold->qp[i]),
1021 isl_point_copy(pnt));
1022 if (fold->type == isl_fold_max)
1023 qp = isl_qpolynomial_max_cst(qp, qp_i);
1025 qp = isl_qpolynomial_min_cst(qp, qp_i);
1028 isl_qpolynomial_fold_free(fold);
1029 isl_point_free(pnt);
1033 isl_qpolynomial_fold_free(fold);
1034 isl_point_free(pnt);
1038 size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold *pwf)
1043 for (i = 0; i < pwf->n; ++i)
1044 n += pwf->p[i].fold->n;
1049 __isl_give isl_qpolynomial *isl_qpolynomial_fold_opt_on_domain(
1050 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *set, int max)
1053 isl_qpolynomial *opt;
1059 isl_space *dim = isl_space_copy(fold->dim);
1061 isl_qpolynomial_fold_free(fold);
1062 return isl_qpolynomial_zero_on_domain(dim);
1065 opt = isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold->qp[0]),
1066 isl_set_copy(set), max);
1067 for (i = 1; i < fold->n; ++i) {
1068 isl_qpolynomial *opt_i;
1069 opt_i = isl_qpolynomial_opt_on_domain(
1070 isl_qpolynomial_copy(fold->qp[i]),
1071 isl_set_copy(set), max);
1073 opt = isl_qpolynomial_max_cst(opt, opt_i);
1075 opt = isl_qpolynomial_min_cst(opt, opt_i);
1079 isl_qpolynomial_fold_free(fold);
1084 isl_qpolynomial_fold_free(fold);
1088 /* Check whether for each quasi-polynomial in "fold2" there is
1089 * a quasi-polynomial in "fold1" that dominates it on "set".
1091 static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set *set,
1092 __isl_keep isl_qpolynomial_fold *fold1,
1093 __isl_keep isl_qpolynomial_fold *fold2)
1098 if (!set || !fold1 || !fold2)
1101 covers = fold1->type == isl_fold_max ? 1 : -1;
1103 for (i = 0; i < fold2->n; ++i) {
1104 for (j = 0; j < fold1->n; ++j) {
1108 d = isl_qpolynomial_sub(
1109 isl_qpolynomial_copy(fold1->qp[j]),
1110 isl_qpolynomial_copy(fold2->qp[i]));
1111 sgn = isl_qpolynomial_sign(set, d);
1112 isl_qpolynomial_free(d);
1123 /* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
1124 * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
1127 int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold *pwf1,
1128 __isl_keep isl_pw_qpolynomial_fold *pwf2)
1131 isl_set *dom1, *dom2;
1142 dom1 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1));
1143 dom2 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2));
1144 is_subset = isl_set_is_subset(dom2, dom1);
1148 if (is_subset < 0 || !is_subset)
1151 for (i = 0; i < pwf2->n; ++i) {
1152 for (j = 0; j < pwf1->n; ++j) {
1157 common = isl_set_intersect(isl_set_copy(pwf1->p[j].set),
1158 isl_set_copy(pwf2->p[i].set));
1159 is_empty = isl_set_is_empty(common);
1160 if (is_empty < 0 || is_empty) {
1161 isl_set_free(common);
1166 covers = qpolynomial_fold_covers_on_domain(common,
1167 pwf1->p[j].fold, pwf2->p[i].fold);
1168 isl_set_free(common);
1169 if (covers < 0 || !covers)
1177 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_morph_domain(
1178 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_morph *morph)
1183 if (!fold || !morph)
1186 ctx = fold->dim->ctx;
1187 isl_assert(ctx, isl_space_is_equal(fold->dim, morph->dom->dim), goto error);
1189 fold = isl_qpolynomial_fold_cow(fold);
1193 isl_space_free(fold->dim);
1194 fold->dim = isl_space_copy(morph->ran->dim);
1198 for (i = 0; i < fold->n; ++i) {
1199 fold->qp[i] = isl_qpolynomial_morph_domain(fold->qp[i],
1200 isl_morph_copy(morph));
1205 isl_morph_free(morph);
1209 isl_qpolynomial_fold_free(fold);
1210 isl_morph_free(morph);
1214 enum isl_fold isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold *fold)
1217 return isl_fold_list;
1221 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
1222 __isl_keep isl_union_pw_qpolynomial_fold *upwf)
1225 return isl_fold_list;
1229 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_lift(
1230 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_space *dim)
1237 if (isl_space_is_equal(fold->dim, dim)) {
1238 isl_space_free(dim);
1242 fold = isl_qpolynomial_fold_cow(fold);
1246 isl_space_free(fold->dim);
1247 fold->dim = isl_space_copy(dim);
1251 for (i = 0; i < fold->n; ++i) {
1252 fold->qp[i] = isl_qpolynomial_lift(fold->qp[i],
1253 isl_space_copy(dim));
1258 isl_space_free(dim);
1262 isl_qpolynomial_fold_free(fold);
1263 isl_space_free(dim);
1267 int isl_qpolynomial_fold_foreach_qpolynomial(
1268 __isl_keep isl_qpolynomial_fold *fold,
1269 int (*fn)(__isl_take isl_qpolynomial *qp, void *user), void *user)
1276 for (i = 0; i < fold->n; ++i)
1277 if (fn(isl_qpolynomial_copy(fold->qp[i]), user) < 0)
1283 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_move_dims(
1284 __isl_take isl_qpolynomial_fold *fold,
1285 enum isl_dim_type dst_type, unsigned dst_pos,
1286 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
1293 fold = isl_qpolynomial_fold_cow(fold);
1297 fold->dim = isl_space_move_dims(fold->dim, dst_type, dst_pos,
1298 src_type, src_pos, n);
1302 for (i = 0; i < fold->n; ++i) {
1303 fold->qp[i] = isl_qpolynomial_move_dims(fold->qp[i],
1304 dst_type, dst_pos, src_type, src_pos, n);
1311 isl_qpolynomial_fold_free(fold);
1315 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
1316 * in fold->qp[k] by subs[i].
1318 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute(
1319 __isl_take isl_qpolynomial_fold *fold,
1320 enum isl_dim_type type, unsigned first, unsigned n,
1321 __isl_keep isl_qpolynomial **subs)
1328 fold = isl_qpolynomial_fold_cow(fold);
1332 for (i = 0; i < fold->n; ++i) {
1333 fold->qp[i] = isl_qpolynomial_substitute(fold->qp[i],
1334 type, first, n, subs);
1341 isl_qpolynomial_fold_free(fold);
1345 static int add_pwqp(__isl_take isl_pw_qpolynomial *pwqp, void *user)
1348 isl_pw_qpolynomial_fold *pwf;
1349 isl_union_pw_qpolynomial_fold **upwf;
1351 struct isl_hash_table_entry *entry;
1353 upwf = (isl_union_pw_qpolynomial_fold **)user;
1355 ctx = pwqp->dim->ctx;
1356 hash = isl_space_get_hash(pwqp->dim);
1357 entry = isl_hash_table_find(ctx, &(*upwf)->table,
1358 hash, &has_dim, pwqp->dim, 1);
1362 pwf = isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf)->type, pwqp);
1366 entry->data = isl_pw_qpolynomial_fold_add(entry->data, pwf);
1369 if (isl_pw_qpolynomial_fold_is_zero(entry->data)) {
1370 isl_pw_qpolynomial_fold_free(entry->data);
1371 isl_hash_table_remove(ctx, &(*upwf)->table, entry);
1377 isl_pw_qpolynomial_free(pwqp);
1381 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
1382 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1383 __isl_take isl_union_pw_qpolynomial *upwqp)
1385 upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1386 isl_union_pw_qpolynomial_get_space(upwqp));
1387 upwqp = isl_union_pw_qpolynomial_align_params(upwqp,
1388 isl_union_pw_qpolynomial_fold_get_space(upwf));
1390 upwf = isl_union_pw_qpolynomial_fold_cow(upwf);
1391 if (!upwf || !upwqp)
1394 if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp, &add_pwqp,
1398 isl_union_pw_qpolynomial_free(upwqp);
1402 isl_union_pw_qpolynomial_fold_free(upwf);
1403 isl_union_pw_qpolynomial_free(upwqp);
1407 static int join_compatible(__isl_keep isl_space *dim1, __isl_keep isl_space *dim2)
1410 m = isl_space_match(dim1, isl_dim_param, dim2, isl_dim_param);
1413 return isl_space_tuple_match(dim1, isl_dim_out, dim2, isl_dim_in);
1416 /* Compute the intersection of the range of the map and the domain
1417 * of the piecewise quasipolynomial reduction and then compute a bound
1418 * on the associated quasipolynomial reduction over all elements
1419 * in this intersection.
1421 * We first introduce some unconstrained dimensions in the
1422 * piecewise quasipolynomial, intersect the resulting domain
1423 * with the wrapped map and the compute the sum.
1425 __isl_give isl_pw_qpolynomial_fold *isl_map_apply_pw_qpolynomial_fold(
1426 __isl_take isl_map *map, __isl_take isl_pw_qpolynomial_fold *pwf,
1436 ctx = isl_map_get_ctx(map);
1440 map_dim = isl_map_get_space(map);
1441 pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
1442 ok = join_compatible(map_dim, pwf_dim);
1443 isl_space_free(map_dim);
1444 isl_space_free(pwf_dim);
1446 isl_die(ctx, isl_error_invalid, "incompatible dimensions",
1449 n_in = isl_map_dim(map, isl_dim_in);
1450 pwf = isl_pw_qpolynomial_fold_insert_dims(pwf, isl_dim_in, 0, n_in);
1452 dom = isl_map_wrap(map);
1453 pwf = isl_pw_qpolynomial_fold_reset_domain_space(pwf,
1454 isl_set_get_space(dom));
1456 pwf = isl_pw_qpolynomial_fold_intersect_domain(pwf, dom);
1457 pwf = isl_pw_qpolynomial_fold_bound(pwf, tight);
1462 isl_pw_qpolynomial_fold_free(pwf);
1466 __isl_give isl_pw_qpolynomial_fold *isl_set_apply_pw_qpolynomial_fold(
1467 __isl_take isl_set *set, __isl_take isl_pw_qpolynomial_fold *pwf,
1470 return isl_map_apply_pw_qpolynomial_fold(set, pwf, tight);
1473 struct isl_apply_fold_data {
1474 isl_union_pw_qpolynomial_fold *upwf;
1475 isl_union_pw_qpolynomial_fold *res;
1480 static int pw_qpolynomial_fold_apply(__isl_take isl_pw_qpolynomial_fold *pwf,
1485 struct isl_apply_fold_data *data = user;
1488 map_dim = isl_map_get_space(data->map);
1489 pwf_dim = isl_pw_qpolynomial_fold_get_space(pwf);
1490 ok = join_compatible(map_dim, pwf_dim);
1491 isl_space_free(map_dim);
1492 isl_space_free(pwf_dim);
1495 pwf = isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data->map),
1496 pwf, data->tight ? &data->tight : NULL);
1497 data->res = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
1500 isl_pw_qpolynomial_fold_free(pwf);
1505 static int map_apply(__isl_take isl_map *map, void *user)
1507 struct isl_apply_fold_data *data = user;
1511 r = isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1512 data->upwf, &pw_qpolynomial_fold_apply, data);
1518 __isl_give isl_union_pw_qpolynomial_fold *isl_union_map_apply_union_pw_qpolynomial_fold(
1519 __isl_take isl_union_map *umap,
1520 __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1524 struct isl_apply_fold_data data;
1526 upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1527 isl_union_map_get_space(umap));
1528 umap = isl_union_map_align_params(umap,
1529 isl_union_pw_qpolynomial_fold_get_space(upwf));
1532 data.tight = tight ? 1 : 0;
1533 dim = isl_union_pw_qpolynomial_fold_get_space(upwf);
1534 type = isl_union_pw_qpolynomial_fold_get_type(upwf);
1535 data.res = isl_union_pw_qpolynomial_fold_zero(dim, type);
1536 if (isl_union_map_foreach_map(umap, &map_apply, &data) < 0)
1539 isl_union_map_free(umap);
1540 isl_union_pw_qpolynomial_fold_free(upwf);
1543 *tight = data.tight;
1547 isl_union_map_free(umap);
1548 isl_union_pw_qpolynomial_fold_free(upwf);
1549 isl_union_pw_qpolynomial_fold_free(data.res);
1553 __isl_give isl_union_pw_qpolynomial_fold *isl_union_set_apply_union_pw_qpolynomial_fold(
1554 __isl_take isl_union_set *uset,
1555 __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1557 return isl_union_map_apply_union_pw_qpolynomial_fold(uset, upwf, tight);
1560 /* Reorder the dimension of "fold" according to the given reordering.
1562 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_realign_domain(
1563 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_reordering *r)
1567 fold = isl_qpolynomial_fold_cow(fold);
1571 for (i = 0; i < fold->n; ++i) {
1572 fold->qp[i] = isl_qpolynomial_realign_domain(fold->qp[i],
1573 isl_reordering_copy(r));
1578 fold = isl_qpolynomial_fold_reset_domain_space(fold,
1579 isl_space_copy(r->dim));
1581 isl_reordering_free(r);
1585 isl_qpolynomial_fold_free(fold);
1586 isl_reordering_free(r);
1590 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_mul_isl_int(
1591 __isl_take isl_qpolynomial_fold *fold, isl_int v)
1595 if (isl_int_is_one(v))
1597 if (fold && isl_int_is_zero(v)) {
1598 isl_qpolynomial_fold *zero;
1599 isl_space *dim = isl_space_copy(fold->dim);
1600 zero = isl_qpolynomial_fold_empty(fold->type, dim);
1601 isl_qpolynomial_fold_free(fold);
1605 fold = isl_qpolynomial_fold_cow(fold);
1609 if (isl_int_is_neg(v))
1610 fold->type = isl_fold_type_negate(fold->type);
1611 for (i = 0; i < fold->n; ++i) {
1612 fold->qp[i] = isl_qpolynomial_mul_isl_int(fold->qp[i], v);
1619 isl_qpolynomial_fold_free(fold);
1623 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
1624 __isl_take isl_qpolynomial_fold *fold, isl_int v)
1626 return isl_qpolynomial_fold_mul_isl_int(fold, v);