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,
11 #include <isl_map_private.h>
12 #include <isl_union_map_private.h>
13 #include <isl_polynomial_private.h>
14 #include <isl_point_private.h>
15 #include <isl_dim_private.h>
18 #include <isl_mat_private.h>
19 #include <isl_config.h>
21 enum isl_fold isl_fold_type_negate(enum isl_fold type)
32 isl_die(NULL, isl_error_internal, "unhandled isl_fold type", abort());
35 static __isl_give isl_qpolynomial_fold *qpolynomial_fold_alloc(
36 enum isl_fold type, __isl_take isl_dim *dim, int n)
38 isl_qpolynomial_fold *fold;
43 isl_assert(dim->ctx, n >= 0, goto error);
44 fold = isl_calloc(dim->ctx, struct isl_qpolynomial_fold,
45 sizeof(struct isl_qpolynomial_fold) +
46 (n - 1) * sizeof(struct isl_qpolynomial *));
62 isl_ctx *isl_qpolynomial_fold_get_ctx(__isl_keep isl_qpolynomial_fold *fold)
64 return fold ? fold->dim->ctx : NULL;
67 __isl_give isl_dim *isl_qpolynomial_fold_get_dim(
68 __isl_keep isl_qpolynomial_fold *fold)
70 return fold ? isl_dim_copy(fold->dim) : NULL;
73 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_reset_dim(
74 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_dim *dim)
78 fold = isl_qpolynomial_fold_cow(fold);
82 for (i = 0; i < fold->n; ++i) {
83 fold->qp[i] = isl_qpolynomial_reset_dim(fold->qp[i],
89 isl_dim_free(fold->dim);
94 isl_qpolynomial_fold_free(fold);
99 int isl_qpolynomial_fold_involves_dims(__isl_keep isl_qpolynomial_fold *fold,
100 enum isl_dim_type type, unsigned first, unsigned n)
106 if (fold->n == 0 || n == 0)
109 for (i = 0; i < fold->n; ++i) {
110 int involves = isl_qpolynomial_involves_dims(fold->qp[i],
112 if (involves < 0 || involves)
118 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_set_dim_name(
119 __isl_take isl_qpolynomial_fold *fold,
120 enum isl_dim_type type, unsigned pos, const char *s)
124 fold = isl_qpolynomial_fold_cow(fold);
127 fold->dim = isl_dim_set_name(fold->dim, type, pos, s);
131 for (i = 0; i < fold->n; ++i) {
132 fold->qp[i] = isl_qpolynomial_set_dim_name(fold->qp[i],
140 isl_qpolynomial_fold_free(fold);
144 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_drop_dims(
145 __isl_take isl_qpolynomial_fold *fold,
146 enum isl_dim_type type, unsigned first, unsigned n)
155 fold = isl_qpolynomial_fold_cow(fold);
158 fold->dim = isl_dim_drop(fold->dim, type, first, n);
162 for (i = 0; i < fold->n; ++i) {
163 fold->qp[i] = isl_qpolynomial_drop_dims(fold->qp[i],
171 isl_qpolynomial_fold_free(fold);
175 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_insert_dims(
176 __isl_take isl_qpolynomial_fold *fold,
177 enum isl_dim_type type, unsigned first, unsigned n)
183 if (n == 0 && !isl_dim_is_named_or_nested(fold->dim, type))
186 fold = isl_qpolynomial_fold_cow(fold);
189 fold->dim = isl_dim_insert(fold->dim, type, first, n);
193 for (i = 0; i < fold->n; ++i) {
194 fold->qp[i] = isl_qpolynomial_insert_dims(fold->qp[i],
202 isl_qpolynomial_fold_free(fold);
206 static int isl_qpolynomial_cst_sign(__isl_keep isl_qpolynomial *qp)
208 struct isl_upoly_cst *cst;
210 cst = isl_upoly_as_cst(qp->upoly);
214 return isl_int_sgn(cst->n) < 0 ? -1 : 1;
217 static int isl_qpolynomial_aff_sign(__isl_keep isl_set *set,
218 __isl_keep isl_qpolynomial *qp)
220 enum isl_lp_result res;
225 aff = isl_qpolynomial_extract_affine(qp);
231 res = isl_set_solve_lp(set, 0, aff->el + 1, aff->el[0],
233 if (res == isl_lp_error)
235 if (res == isl_lp_empty ||
236 (res == isl_lp_ok && !isl_int_is_neg(opt))) {
241 res = isl_set_solve_lp(set, 1, aff->el + 1, aff->el[0],
243 if (res == isl_lp_ok && !isl_int_is_pos(opt))
252 /* Determine, if possible, the sign of the quasipolynomial "qp" on
255 * If qp is a constant, then the problem is trivial.
256 * If qp is linear, then we check if the minimum of the corresponding
257 * affine constraint is non-negative or if the maximum is non-positive.
259 * Otherwise, we check if the outermost variable "v" has a lower bound "l"
260 * in "set". If so, we write qp(v,v') as
262 * q(v,v') * (v - l) + r(v')
264 * if q(v,v') and r(v') have the same known sign, then the original
265 * quasipolynomial has the same sign as well.
272 static int isl_qpolynomial_sign(__isl_keep isl_set *set,
273 __isl_keep isl_qpolynomial *qp)
278 struct isl_upoly_rec *rec;
281 enum isl_lp_result res;
284 is = isl_qpolynomial_is_cst(qp, NULL, NULL);
288 return isl_qpolynomial_cst_sign(qp);
290 is = isl_qpolynomial_is_affine(qp);
294 return isl_qpolynomial_aff_sign(set, qp);
296 if (qp->div->n_row > 0)
299 rec = isl_upoly_as_rec(qp->upoly);
303 d = isl_dim_total(qp->dim);
304 v = isl_vec_alloc(set->ctx, 2 + d);
308 isl_seq_clr(v->el + 1, 1 + d);
309 isl_int_set_si(v->el[0], 1);
310 isl_int_set_si(v->el[2 + qp->upoly->var], 1);
314 res = isl_set_solve_lp(set, 0, v->el + 1, v->el[0], &l, NULL, NULL);
315 if (res == isl_lp_ok) {
316 isl_qpolynomial *min;
317 isl_qpolynomial *base;
318 isl_qpolynomial *r, *q;
321 min = isl_qpolynomial_cst(isl_dim_copy(qp->dim), l);
322 base = isl_qpolynomial_var_pow(isl_dim_copy(qp->dim),
325 r = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), 0,
326 isl_upoly_copy(rec->p[rec->n - 1]));
327 q = isl_qpolynomial_copy(r);
329 for (i = rec->n - 2; i >= 0; --i) {
330 r = isl_qpolynomial_mul(r, isl_qpolynomial_copy(min));
331 t = isl_qpolynomial_alloc(isl_dim_copy(qp->dim), 0,
332 isl_upoly_copy(rec->p[i]));
333 r = isl_qpolynomial_add(r, t);
336 q = isl_qpolynomial_mul(q, isl_qpolynomial_copy(base));
337 q = isl_qpolynomial_add(q, isl_qpolynomial_copy(r));
340 if (isl_qpolynomial_is_zero(q))
341 sgn = isl_qpolynomial_sign(set, r);
342 else if (isl_qpolynomial_is_zero(r))
343 sgn = isl_qpolynomial_sign(set, q);
346 sgn_r = isl_qpolynomial_sign(set, r);
347 sgn_q = isl_qpolynomial_sign(set, q);
352 isl_qpolynomial_free(min);
353 isl_qpolynomial_free(base);
354 isl_qpolynomial_free(q);
355 isl_qpolynomial_free(r);
365 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold_on_domain(
366 __isl_keep isl_set *set,
367 __isl_take isl_qpolynomial_fold *fold1,
368 __isl_take isl_qpolynomial_fold *fold2)
372 struct isl_qpolynomial_fold *res = NULL;
375 if (!fold1 || !fold2)
378 isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
379 isl_assert(fold1->dim->ctx, isl_dim_equal(fold1->dim, fold2->dim),
382 better = fold1->type == isl_fold_max ? -1 : 1;
384 if (isl_qpolynomial_fold_is_empty(fold1)) {
385 isl_qpolynomial_fold_free(fold1);
389 if (isl_qpolynomial_fold_is_empty(fold2)) {
390 isl_qpolynomial_fold_free(fold2);
394 res = qpolynomial_fold_alloc(fold1->type, isl_dim_copy(fold1->dim),
395 fold1->n + fold2->n);
399 for (i = 0; i < fold1->n; ++i) {
400 res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
401 if (!res->qp[res->n])
407 for (i = 0; i < fold2->n; ++i) {
408 for (j = n1 - 1; j >= 0; --j) {
411 d = isl_qpolynomial_sub(
412 isl_qpolynomial_copy(res->qp[j]),
413 isl_qpolynomial_copy(fold2->qp[i]));
414 sgn = isl_qpolynomial_sign(set, d);
415 isl_qpolynomial_free(d);
420 isl_qpolynomial_free(res->qp[j]);
422 res->qp[j] = res->qp[n1 - 1];
424 if (n1 != res->n - 1)
425 res->qp[n1] = res->qp[res->n - 1];
430 res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
431 if (!res->qp[res->n])
436 isl_qpolynomial_fold_free(fold1);
437 isl_qpolynomial_fold_free(fold2);
441 isl_qpolynomial_fold_free(res);
442 isl_qpolynomial_fold_free(fold1);
443 isl_qpolynomial_fold_free(fold2);
447 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_qpolynomial(
448 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_qpolynomial *qp)
455 if (isl_qpolynomial_is_zero(qp)) {
456 isl_qpolynomial_free(qp);
460 fold = isl_qpolynomial_fold_cow(fold);
464 for (i = 0; i < fold->n; ++i) {
465 fold->qp[i] = isl_qpolynomial_add(fold->qp[i],
466 isl_qpolynomial_copy(qp));
471 isl_qpolynomial_free(qp);
474 isl_qpolynomial_fold_free(fold);
475 isl_qpolynomial_free(qp);
479 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_add_on_domain(
480 __isl_keep isl_set *dom,
481 __isl_take isl_qpolynomial_fold *fold1,
482 __isl_take isl_qpolynomial_fold *fold2)
485 isl_qpolynomial_fold *res = NULL;
487 if (!fold1 || !fold2)
490 if (isl_qpolynomial_fold_is_empty(fold1)) {
491 isl_qpolynomial_fold_free(fold1);
495 if (isl_qpolynomial_fold_is_empty(fold2)) {
496 isl_qpolynomial_fold_free(fold2);
500 if (fold1->n == 1 && fold2->n != 1)
501 return isl_qpolynomial_fold_add_on_domain(dom, fold2, fold1);
504 res = isl_qpolynomial_fold_add_qpolynomial(fold1,
505 isl_qpolynomial_copy(fold2->qp[0]));
506 isl_qpolynomial_fold_free(fold2);
510 res = isl_qpolynomial_fold_add_qpolynomial(
511 isl_qpolynomial_fold_copy(fold1),
512 isl_qpolynomial_copy(fold2->qp[0]));
514 for (i = 1; i < fold2->n; ++i) {
515 isl_qpolynomial_fold *res_i;
516 res_i = isl_qpolynomial_fold_add_qpolynomial(
517 isl_qpolynomial_fold_copy(fold1),
518 isl_qpolynomial_copy(fold2->qp[i]));
519 res = isl_qpolynomial_fold_fold_on_domain(dom, res, res_i);
522 isl_qpolynomial_fold_free(fold1);
523 isl_qpolynomial_fold_free(fold2);
526 isl_qpolynomial_fold_free(res);
527 isl_qpolynomial_fold_free(fold1);
528 isl_qpolynomial_fold_free(fold2);
532 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute_equalities(
533 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_basic_set *eq)
540 fold = isl_qpolynomial_fold_cow(fold);
544 for (i = 0; i < fold->n; ++i) {
545 fold->qp[i] = isl_qpolynomial_substitute_equalities(fold->qp[i],
546 isl_basic_set_copy(eq));
551 isl_basic_set_free(eq);
554 isl_basic_set_free(eq);
555 isl_qpolynomial_fold_free(fold);
559 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
560 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *context)
564 if (!fold || !context)
567 fold = isl_qpolynomial_fold_cow(fold);
571 for (i = 0; i < fold->n; ++i) {
572 fold->qp[i] = isl_qpolynomial_gist(fold->qp[i],
573 isl_set_copy(context));
578 isl_set_free(context);
581 isl_set_free(context);
582 isl_qpolynomial_fold_free(fold);
589 #define PW isl_pw_qpolynomial_fold
591 #define EL isl_qpolynomial_fold
593 #define EL_IS_ZERO is_empty
597 #define IS_ZERO is_zero
603 #include <isl_pw_templ.c>
606 #define UNION isl_union_pw_qpolynomial_fold
608 #define PART isl_pw_qpolynomial_fold
610 #define PARTS pw_qpolynomial_fold
612 #include <isl_union_templ.c>
614 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_empty(enum isl_fold type,
615 __isl_take isl_dim *dim)
617 return qpolynomial_fold_alloc(type, dim, 0);
620 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_alloc(
621 enum isl_fold type, __isl_take isl_qpolynomial *qp)
623 isl_qpolynomial_fold *fold;
628 fold = qpolynomial_fold_alloc(type, isl_dim_copy(qp->dim), 1);
637 isl_qpolynomial_fold_free(fold);
638 isl_qpolynomial_free(qp);
642 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
643 __isl_keep isl_qpolynomial_fold *fold)
652 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_dup(
653 __isl_keep isl_qpolynomial_fold *fold)
656 isl_qpolynomial_fold *dup;
660 dup = qpolynomial_fold_alloc(fold->type,
661 isl_dim_copy(fold->dim), fold->n);
666 for (i = 0; i < fold->n; ++i) {
667 dup->qp[i] = isl_qpolynomial_copy(fold->qp[i]);
674 isl_qpolynomial_fold_free(dup);
678 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_cow(
679 __isl_take isl_qpolynomial_fold *fold)
687 return isl_qpolynomial_fold_dup(fold);
690 void isl_qpolynomial_fold_free(__isl_take isl_qpolynomial_fold *fold)
699 for (i = 0; i < fold->n; ++i)
700 isl_qpolynomial_free(fold->qp[i]);
701 isl_dim_free(fold->dim);
705 int isl_qpolynomial_fold_is_empty(__isl_keep isl_qpolynomial_fold *fold)
713 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_fold(
714 __isl_take isl_qpolynomial_fold *fold1,
715 __isl_take isl_qpolynomial_fold *fold2)
718 struct isl_qpolynomial_fold *res = NULL;
720 if (!fold1 || !fold2)
723 isl_assert(fold1->dim->ctx, fold1->type == fold2->type, goto error);
724 isl_assert(fold1->dim->ctx, isl_dim_equal(fold1->dim, fold2->dim),
727 if (isl_qpolynomial_fold_is_empty(fold1)) {
728 isl_qpolynomial_fold_free(fold1);
732 if (isl_qpolynomial_fold_is_empty(fold2)) {
733 isl_qpolynomial_fold_free(fold2);
737 res = qpolynomial_fold_alloc(fold1->type, isl_dim_copy(fold1->dim),
738 fold1->n + fold2->n);
742 for (i = 0; i < fold1->n; ++i) {
743 res->qp[res->n] = isl_qpolynomial_copy(fold1->qp[i]);
744 if (!res->qp[res->n])
749 for (i = 0; i < fold2->n; ++i) {
750 res->qp[res->n] = isl_qpolynomial_copy(fold2->qp[i]);
751 if (!res->qp[res->n])
756 isl_qpolynomial_fold_free(fold1);
757 isl_qpolynomial_fold_free(fold2);
761 isl_qpolynomial_fold_free(res);
762 isl_qpolynomial_fold_free(fold1);
763 isl_qpolynomial_fold_free(fold2);
767 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
768 __isl_take isl_pw_qpolynomial_fold *pw1,
769 __isl_take isl_pw_qpolynomial_fold *pw2)
772 struct isl_pw_qpolynomial_fold *res;
778 isl_assert(pw1->dim->ctx, isl_dim_equal(pw1->dim, pw2->dim), goto error);
780 if (isl_pw_qpolynomial_fold_is_zero(pw1)) {
781 isl_pw_qpolynomial_fold_free(pw1);
785 if (isl_pw_qpolynomial_fold_is_zero(pw2)) {
786 isl_pw_qpolynomial_fold_free(pw2);
790 if (pw1->type != pw2->type)
791 isl_die(pw1->dim->ctx, isl_error_invalid,
792 "fold types don't match", goto error);
794 n = (pw1->n + 1) * (pw2->n + 1);
795 res = isl_pw_qpolynomial_fold_alloc_(isl_dim_copy(pw1->dim),
798 for (i = 0; i < pw1->n; ++i) {
799 set = isl_set_copy(pw1->p[i].set);
800 for (j = 0; j < pw2->n; ++j) {
801 struct isl_set *common;
802 isl_qpolynomial_fold *sum;
803 set = isl_set_subtract(set,
804 isl_set_copy(pw2->p[j].set));
805 common = isl_set_intersect(isl_set_copy(pw1->p[i].set),
806 isl_set_copy(pw2->p[j].set));
807 if (isl_set_plain_is_empty(common)) {
808 isl_set_free(common);
812 sum = isl_qpolynomial_fold_fold_on_domain(common,
813 isl_qpolynomial_fold_copy(pw1->p[i].fold),
814 isl_qpolynomial_fold_copy(pw2->p[j].fold));
816 res = isl_pw_qpolynomial_fold_add_piece(res, common, sum);
818 res = isl_pw_qpolynomial_fold_add_piece(res, set,
819 isl_qpolynomial_fold_copy(pw1->p[i].fold));
822 for (j = 0; j < pw2->n; ++j) {
823 set = isl_set_copy(pw2->p[j].set);
824 for (i = 0; i < pw1->n; ++i)
825 set = isl_set_subtract(set, isl_set_copy(pw1->p[i].set));
826 res = isl_pw_qpolynomial_fold_add_piece(res, set,
827 isl_qpolynomial_fold_copy(pw2->p[j].fold));
830 isl_pw_qpolynomial_fold_free(pw1);
831 isl_pw_qpolynomial_fold_free(pw2);
835 isl_pw_qpolynomial_fold_free(pw1);
836 isl_pw_qpolynomial_fold_free(pw2);
840 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
841 __isl_take isl_union_pw_qpolynomial_fold *u,
842 __isl_take isl_pw_qpolynomial_fold *part)
845 struct isl_hash_table_entry *entry;
847 u = isl_union_pw_qpolynomial_fold_cow(u);
852 isl_assert(u->dim->ctx, isl_dim_match(part->dim, isl_dim_param, u->dim,
853 isl_dim_param), goto error);
855 hash = isl_dim_get_hash(part->dim);
856 entry = isl_hash_table_find(u->dim->ctx, &u->table, hash,
857 &has_dim, part->dim, 1);
864 entry->data = isl_pw_qpolynomial_fold_fold(entry->data,
865 isl_pw_qpolynomial_fold_copy(part));
868 isl_pw_qpolynomial_fold_free(part);
873 isl_pw_qpolynomial_fold_free(part);
874 isl_union_pw_qpolynomial_fold_free(u);
878 static int fold_part(__isl_take isl_pw_qpolynomial_fold *part, void *user)
880 isl_union_pw_qpolynomial_fold **u;
881 u = (isl_union_pw_qpolynomial_fold **)user;
883 *u = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(*u, part);
888 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
889 __isl_take isl_union_pw_qpolynomial_fold *u1,
890 __isl_take isl_union_pw_qpolynomial_fold *u2)
892 u1 = isl_union_pw_qpolynomial_fold_cow(u1);
897 if (isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(u2,
898 &fold_part, &u1) < 0)
901 isl_union_pw_qpolynomial_fold_free(u2);
905 isl_union_pw_qpolynomial_fold_free(u1);
906 isl_union_pw_qpolynomial_fold_free(u2);
910 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_from_pw_qpolynomial(
911 enum isl_fold type, __isl_take isl_pw_qpolynomial *pwqp)
914 isl_pw_qpolynomial_fold *pwf;
919 pwf = isl_pw_qpolynomial_fold_alloc_(isl_dim_copy(pwqp->dim), type,
922 for (i = 0; i < pwqp->n; ++i)
923 pwf = isl_pw_qpolynomial_fold_add_piece(pwf,
924 isl_set_copy(pwqp->p[i].set),
925 isl_qpolynomial_fold_alloc(type,
926 isl_qpolynomial_copy(pwqp->p[i].qp)));
928 isl_pw_qpolynomial_free(pwqp);
933 int isl_qpolynomial_fold_plain_is_equal(__isl_keep isl_qpolynomial_fold *fold1,
934 __isl_keep isl_qpolynomial_fold *fold2)
938 if (!fold1 || !fold2)
941 if (fold1->n != fold2->n)
944 /* We probably want to sort the qps first... */
945 for (i = 0; i < fold1->n; ++i) {
946 int eq = isl_qpolynomial_plain_is_equal(fold1->qp[i], fold2->qp[i]);
954 __isl_give isl_qpolynomial *isl_qpolynomial_fold_eval(
955 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_point *pnt)
961 isl_assert(pnt->dim->ctx, isl_dim_equal(pnt->dim, fold->dim), goto error);
962 isl_assert(pnt->dim->ctx,
963 fold->type == isl_fold_max || fold->type == isl_fold_min,
967 qp = isl_qpolynomial_zero(isl_dim_copy(fold->dim));
970 qp = isl_qpolynomial_eval(isl_qpolynomial_copy(fold->qp[0]),
971 isl_point_copy(pnt));
972 for (i = 1; i < fold->n; ++i) {
973 isl_qpolynomial *qp_i;
974 qp_i = isl_qpolynomial_eval(
975 isl_qpolynomial_copy(fold->qp[i]),
976 isl_point_copy(pnt));
977 if (fold->type == isl_fold_max)
978 qp = isl_qpolynomial_max_cst(qp, qp_i);
980 qp = isl_qpolynomial_min_cst(qp, qp_i);
983 isl_qpolynomial_fold_free(fold);
988 isl_qpolynomial_fold_free(fold);
993 size_t isl_pw_qpolynomial_fold_size(__isl_keep isl_pw_qpolynomial_fold *pwf)
998 for (i = 0; i < pwf->n; ++i)
999 n += pwf->p[i].fold->n;
1004 __isl_give isl_qpolynomial *isl_qpolynomial_fold_opt_on_domain(
1005 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_set *set, int max)
1008 isl_qpolynomial *opt;
1014 isl_dim *dim = isl_dim_copy(fold->dim);
1016 isl_qpolynomial_fold_free(fold);
1017 return isl_qpolynomial_zero(dim);
1020 opt = isl_qpolynomial_opt_on_domain(isl_qpolynomial_copy(fold->qp[0]),
1021 isl_set_copy(set), max);
1022 for (i = 1; i < fold->n; ++i) {
1023 isl_qpolynomial *opt_i;
1024 opt_i = isl_qpolynomial_opt_on_domain(
1025 isl_qpolynomial_copy(fold->qp[i]),
1026 isl_set_copy(set), max);
1028 opt = isl_qpolynomial_max_cst(opt, opt_i);
1030 opt = isl_qpolynomial_min_cst(opt, opt_i);
1034 isl_qpolynomial_fold_free(fold);
1039 isl_qpolynomial_fold_free(fold);
1043 /* Check whether for each quasi-polynomial in "fold2" there is
1044 * a quasi-polynomial in "fold1" that dominates it on "set".
1046 static int qpolynomial_fold_covers_on_domain(__isl_keep isl_set *set,
1047 __isl_keep isl_qpolynomial_fold *fold1,
1048 __isl_keep isl_qpolynomial_fold *fold2)
1053 if (!set || !fold1 || !fold2)
1056 covers = fold1->type == isl_fold_max ? 1 : -1;
1058 for (i = 0; i < fold2->n; ++i) {
1059 for (j = 0; j < fold1->n; ++j) {
1063 d = isl_qpolynomial_sub(
1064 isl_qpolynomial_copy(fold1->qp[j]),
1065 isl_qpolynomial_copy(fold2->qp[i]));
1066 sgn = isl_qpolynomial_sign(set, d);
1067 isl_qpolynomial_free(d);
1078 /* Check whether "pwf1" dominated "pwf2", i.e., the domain of "pwf1" contains
1079 * that of "pwf2" and on each cell, the corresponding fold from pwf1 dominates
1082 int isl_pw_qpolynomial_fold_covers(__isl_keep isl_pw_qpolynomial_fold *pwf1,
1083 __isl_keep isl_pw_qpolynomial_fold *pwf2)
1086 isl_set *dom1, *dom2;
1097 dom1 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf1));
1098 dom2 = isl_pw_qpolynomial_fold_domain(isl_pw_qpolynomial_fold_copy(pwf2));
1099 is_subset = isl_set_is_subset(dom2, dom1);
1103 if (is_subset < 0 || !is_subset)
1106 for (i = 0; i < pwf2->n; ++i) {
1107 for (j = 0; j < pwf1->n; ++j) {
1112 common = isl_set_intersect(isl_set_copy(pwf1->p[j].set),
1113 isl_set_copy(pwf2->p[i].set));
1114 is_empty = isl_set_is_empty(common);
1115 if (is_empty < 0 || is_empty) {
1116 isl_set_free(common);
1121 covers = qpolynomial_fold_covers_on_domain(common,
1122 pwf1->p[j].fold, pwf2->p[i].fold);
1123 isl_set_free(common);
1124 if (covers < 0 || !covers)
1132 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_morph(
1133 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_morph *morph)
1138 if (!fold || !morph)
1141 ctx = fold->dim->ctx;
1142 isl_assert(ctx, isl_dim_equal(fold->dim, morph->dom->dim), goto error);
1144 fold = isl_qpolynomial_fold_cow(fold);
1148 isl_dim_free(fold->dim);
1149 fold->dim = isl_dim_copy(morph->ran->dim);
1153 for (i = 0; i < fold->n; ++i) {
1154 fold->qp[i] = isl_qpolynomial_morph(fold->qp[i],
1155 isl_morph_copy(morph));
1160 isl_morph_free(morph);
1164 isl_qpolynomial_fold_free(fold);
1165 isl_morph_free(morph);
1169 enum isl_fold isl_qpolynomial_fold_get_type(__isl_keep isl_qpolynomial_fold *fold)
1172 return isl_fold_list;
1176 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
1177 __isl_keep isl_union_pw_qpolynomial_fold *upwf)
1180 return isl_fold_list;
1184 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_lift(
1185 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_dim *dim)
1192 if (isl_dim_equal(fold->dim, dim)) {
1197 fold = isl_qpolynomial_fold_cow(fold);
1201 isl_dim_free(fold->dim);
1202 fold->dim = isl_dim_copy(dim);
1206 for (i = 0; i < fold->n; ++i) {
1207 fold->qp[i] = isl_qpolynomial_lift(fold->qp[i],
1217 isl_qpolynomial_fold_free(fold);
1222 int isl_qpolynomial_fold_foreach_qpolynomial(
1223 __isl_keep isl_qpolynomial_fold *fold,
1224 int (*fn)(__isl_take isl_qpolynomial *qp, void *user), void *user)
1231 for (i = 0; i < fold->n; ++i)
1232 if (fn(isl_qpolynomial_copy(fold->qp[i]), user) < 0)
1238 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_move_dims(
1239 __isl_take isl_qpolynomial_fold *fold,
1240 enum isl_dim_type dst_type, unsigned dst_pos,
1241 enum isl_dim_type src_type, unsigned src_pos, unsigned n)
1248 fold = isl_qpolynomial_fold_cow(fold);
1252 fold->dim = isl_dim_move(fold->dim, dst_type, dst_pos,
1253 src_type, src_pos, n);
1257 for (i = 0; i < fold->n; ++i) {
1258 fold->qp[i] = isl_qpolynomial_move_dims(fold->qp[i],
1259 dst_type, dst_pos, src_type, src_pos, n);
1266 isl_qpolynomial_fold_free(fold);
1270 /* For each 0 <= i < "n", replace variable "first" + i of type "type"
1271 * in fold->qp[k] by subs[i].
1273 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_substitute(
1274 __isl_take isl_qpolynomial_fold *fold,
1275 enum isl_dim_type type, unsigned first, unsigned n,
1276 __isl_keep isl_qpolynomial **subs)
1283 fold = isl_qpolynomial_fold_cow(fold);
1287 for (i = 0; i < fold->n; ++i) {
1288 fold->qp[i] = isl_qpolynomial_substitute(fold->qp[i],
1289 type, first, n, subs);
1296 isl_qpolynomial_fold_free(fold);
1300 static int add_pwqp(__isl_take isl_pw_qpolynomial *pwqp, void *user)
1303 isl_pw_qpolynomial_fold *pwf;
1304 isl_union_pw_qpolynomial_fold **upwf;
1306 struct isl_hash_table_entry *entry;
1308 upwf = (isl_union_pw_qpolynomial_fold **)user;
1310 ctx = pwqp->dim->ctx;
1311 hash = isl_dim_get_hash(pwqp->dim);
1312 entry = isl_hash_table_find(ctx, &(*upwf)->table,
1313 hash, &has_dim, pwqp->dim, 1);
1317 pwf = isl_pw_qpolynomial_fold_from_pw_qpolynomial((*upwf)->type, pwqp);
1321 entry->data = isl_pw_qpolynomial_fold_add(entry->data, pwf);
1324 if (isl_pw_qpolynomial_fold_is_zero(entry->data)) {
1325 isl_pw_qpolynomial_fold_free(entry->data);
1326 isl_hash_table_remove(ctx, &(*upwf)->table, entry);
1332 isl_pw_qpolynomial_free(pwqp);
1336 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add_union_pw_qpolynomial(
1337 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1338 __isl_take isl_union_pw_qpolynomial *upwqp)
1340 upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1341 isl_union_pw_qpolynomial_get_dim(upwqp));
1342 upwqp = isl_union_pw_qpolynomial_align_params(upwqp,
1343 isl_union_pw_qpolynomial_fold_get_dim(upwf));
1345 upwf = isl_union_pw_qpolynomial_fold_cow(upwf);
1346 if (!upwf || !upwqp)
1349 if (isl_union_pw_qpolynomial_foreach_pw_qpolynomial(upwqp, &add_pwqp,
1353 isl_union_pw_qpolynomial_free(upwqp);
1357 isl_union_pw_qpolynomial_fold_free(upwf);
1358 isl_union_pw_qpolynomial_free(upwqp);
1362 static int compatible_range(__isl_keep isl_dim *dim1, __isl_keep isl_dim *dim2)
1365 m = isl_dim_match(dim1, isl_dim_param, dim2, isl_dim_param);
1368 return isl_dim_tuple_match(dim1, isl_dim_out, dim2, isl_dim_set);
1371 /* Compute the intersection of the range of the map and the domain
1372 * of the piecewise quasipolynomial reduction and then compute a bound
1373 * on the associated quasipolynomial reduction over all elements
1374 * in this intersection.
1376 * We first introduce some unconstrained dimensions in the
1377 * piecewise quasipolynomial, intersect the resulting domain
1378 * with the wrapped map and the compute the sum.
1380 __isl_give isl_pw_qpolynomial_fold *isl_map_apply_pw_qpolynomial_fold(
1381 __isl_take isl_map *map, __isl_take isl_pw_qpolynomial_fold *pwf,
1391 ctx = isl_map_get_ctx(map);
1395 map_dim = isl_map_get_dim(map);
1396 pwf_dim = isl_pw_qpolynomial_fold_get_dim(pwf);
1397 ok = compatible_range(map_dim, pwf_dim);
1398 isl_dim_free(map_dim);
1399 isl_dim_free(pwf_dim);
1401 isl_die(ctx, isl_error_invalid, "incompatible dimensions",
1404 n_in = isl_map_dim(map, isl_dim_in);
1405 pwf = isl_pw_qpolynomial_fold_insert_dims(pwf, isl_dim_set, 0, n_in);
1407 dom = isl_map_wrap(map);
1408 pwf = isl_pw_qpolynomial_fold_reset_dim(pwf, isl_set_get_dim(dom));
1410 pwf = isl_pw_qpolynomial_fold_intersect_domain(pwf, dom);
1411 pwf = isl_pw_qpolynomial_fold_bound(pwf, tight);
1416 isl_pw_qpolynomial_fold_free(pwf);
1420 __isl_give isl_pw_qpolynomial_fold *isl_set_apply_pw_qpolynomial_fold(
1421 __isl_take isl_set *set, __isl_take isl_pw_qpolynomial_fold *pwf,
1426 map = isl_map_from_range(set);
1427 return isl_map_apply_pw_qpolynomial_fold(map, pwf, tight);
1430 struct isl_apply_fold_data {
1431 isl_union_pw_qpolynomial_fold *upwf;
1432 isl_union_pw_qpolynomial_fold *res;
1437 static int pw_qpolynomial_fold_apply(__isl_take isl_pw_qpolynomial_fold *pwf,
1442 struct isl_apply_fold_data *data = user;
1445 map_dim = isl_map_get_dim(data->map);
1446 pwf_dim = isl_pw_qpolynomial_fold_get_dim(pwf);
1447 ok = compatible_range(map_dim, pwf_dim);
1448 isl_dim_free(map_dim);
1449 isl_dim_free(pwf_dim);
1452 pwf = isl_map_apply_pw_qpolynomial_fold(isl_map_copy(data->map),
1453 pwf, data->tight ? &data->tight : NULL);
1454 data->res = isl_union_pw_qpolynomial_fold_fold_pw_qpolynomial_fold(
1457 isl_pw_qpolynomial_fold_free(pwf);
1462 static int map_apply(__isl_take isl_map *map, void *user)
1464 struct isl_apply_fold_data *data = user;
1468 r = isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1469 data->upwf, &pw_qpolynomial_fold_apply, data);
1475 __isl_give isl_union_pw_qpolynomial_fold *isl_union_map_apply_union_pw_qpolynomial_fold(
1476 __isl_take isl_union_map *umap,
1477 __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1481 struct isl_apply_fold_data data;
1483 upwf = isl_union_pw_qpolynomial_fold_align_params(upwf,
1484 isl_union_map_get_dim(umap));
1485 umap = isl_union_map_align_params(umap,
1486 isl_union_pw_qpolynomial_fold_get_dim(upwf));
1489 data.tight = tight ? 1 : 0;
1490 dim = isl_union_pw_qpolynomial_fold_get_dim(upwf);
1491 type = isl_union_pw_qpolynomial_fold_get_type(upwf);
1492 data.res = isl_union_pw_qpolynomial_fold_zero(dim, type);
1493 if (isl_union_map_foreach_map(umap, &map_apply, &data) < 0)
1496 isl_union_map_free(umap);
1497 isl_union_pw_qpolynomial_fold_free(upwf);
1500 *tight = data.tight;
1504 isl_union_map_free(umap);
1505 isl_union_pw_qpolynomial_fold_free(upwf);
1506 isl_union_pw_qpolynomial_fold_free(data.res);
1510 __isl_give isl_union_pw_qpolynomial_fold *isl_union_set_apply_union_pw_qpolynomial_fold(
1511 __isl_take isl_union_set *uset,
1512 __isl_take isl_union_pw_qpolynomial_fold *upwf, int *tight)
1514 return isl_union_map_apply_union_pw_qpolynomial_fold(uset, upwf, tight);
1517 /* Reorder the dimension of "fold" according to the given reordering.
1519 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_realign(
1520 __isl_take isl_qpolynomial_fold *fold, __isl_take isl_reordering *r)
1524 fold = isl_qpolynomial_fold_cow(fold);
1528 for (i = 0; i < fold->n; ++i) {
1529 fold->qp[i] = isl_qpolynomial_realign(fold->qp[i],
1530 isl_reordering_copy(r));
1535 fold = isl_qpolynomial_fold_reset_dim(fold, isl_dim_copy(r->dim));
1537 isl_reordering_free(r);
1541 isl_qpolynomial_fold_free(fold);
1542 isl_reordering_free(r);
1546 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_mul_isl_int(
1547 __isl_take isl_qpolynomial_fold *fold, isl_int v)
1551 if (isl_int_is_one(v))
1553 if (fold && isl_int_is_zero(v)) {
1554 isl_qpolynomial_fold *zero;
1555 isl_dim *dim = isl_dim_copy(fold->dim);
1556 zero = isl_qpolynomial_fold_empty(fold->type, dim);
1557 isl_qpolynomial_fold_free(fold);
1561 fold = isl_qpolynomial_fold_cow(fold);
1565 if (isl_int_is_neg(v))
1566 fold->type = isl_fold_type_negate(fold->type);
1567 for (i = 0; i < fold->n; ++i) {
1568 fold->qp[i] = isl_qpolynomial_mul_isl_int(fold->qp[i], v);
1575 isl_qpolynomial_fold_free(fold);
1579 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
1580 __isl_take isl_qpolynomial_fold *fold, isl_int v)
1582 return isl_qpolynomial_fold_mul_isl_int(fold, v);