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,
14 #include <isl_map_private.h>
15 #include <isl_dim_private.h>
16 #include <isl_morph.h>
17 #include <isl_vertices_private.h>
18 #include <isl_mat_private.h>
24 static __isl_give isl_vertices *compute_chambers(__isl_take isl_basic_set *bset,
25 __isl_take isl_vertices *vertices);
27 __isl_give isl_vertices *isl_vertices_copy(__isl_keep isl_vertices *vertices)
36 void isl_vertices_free(__isl_take isl_vertices *vertices)
43 if (--vertices->ref > 0)
46 for (i = 0; i < vertices->n_vertices; ++i) {
47 isl_basic_set_free(vertices->v[i].vertex);
48 isl_basic_set_free(vertices->v[i].dom);
52 for (i = 0; i < vertices->n_chambers; ++i) {
53 free(vertices->c[i].vertices);
54 isl_basic_set_free(vertices->c[i].dom);
58 isl_basic_set_free(vertices->bset);
62 struct isl_vertex_list {
64 struct isl_vertex_list *next;
67 static void free_vertex_list(struct isl_vertex_list *list)
69 struct isl_vertex_list *next;
71 for (; list; list = next) {
73 isl_basic_set_free(list->v.vertex);
74 isl_basic_set_free(list->v.dom);
79 static __isl_give isl_vertices *vertices_from_list(__isl_keep isl_basic_set *bset,
80 int n_vertices, struct isl_vertex_list *list)
83 struct isl_vertex_list *next;
84 isl_vertices *vertices;
86 vertices = isl_calloc_type(bset->ctx, isl_vertices);
90 vertices->bset = isl_basic_set_copy(bset);
91 vertices->v = isl_alloc_array(bset->ctx, struct isl_vertex, n_vertices);
94 vertices->n_vertices = n_vertices;
96 for (i = 0; list; list = next, i++) {
98 vertices->v[i] = list->v;
105 free_vertex_list(list);
109 /* Prepend a vertex to the linked list "list" based on the equalities in "tab".
111 static int add_vertex(struct isl_vertex_list **list,
112 __isl_keep isl_basic_set *bset, struct isl_tab *tab)
116 struct isl_vertex_list *v = NULL;
118 if (isl_tab_detect_implicit_equalities(tab) < 0)
121 nvar = isl_basic_set_dim(bset, isl_dim_set);
122 nparam = isl_basic_set_dim(bset, isl_dim_param);
124 v = isl_calloc_type(tab->mat->ctx, struct isl_vertex_list);
128 v->v.vertex = isl_basic_set_copy(bset);
129 v->v.vertex = isl_basic_set_cow(v->v.vertex);
130 v->v.vertex = isl_basic_set_update_from_tab(v->v.vertex, tab);
131 v->v.vertex = isl_basic_set_simplify(v->v.vertex);
132 v->v.vertex = isl_basic_set_finalize(v->v.vertex);
135 isl_assert(bset->ctx, v->v.vertex->n_eq >= nvar, goto error);
136 v->v.dom = isl_basic_set_copy(v->v.vertex);
137 v->v.dom = isl_basic_set_project_out(v->v.dom, isl_dim_set, 0, nvar);
150 /* Compute the parametric vertices and the chamber decomposition
151 * of an empty parametric polytope.
153 static __isl_give isl_vertices *vertices_empty(__isl_keep isl_basic_set *bset)
155 isl_vertices *vertices;
161 nparam = isl_basic_set_dim(bset, isl_dim_param);
163 vertices = isl_calloc_type(bset->ctx, isl_vertices);
166 vertices->bset = isl_basic_set_copy(bset);
169 vertices->n_vertices = 0;
170 vertices->n_chambers = 0;
175 /* Compute the parametric vertices and the chamber decomposition
176 * of the parametric polytope defined using the same constraints
177 * as "bset" in the 0D case.
178 * There is exactly one 0D vertex and a single chamber containing
181 static __isl_give isl_vertices *vertices_0D(__isl_keep isl_basic_set *bset)
183 isl_vertices *vertices;
189 nparam = isl_basic_set_dim(bset, isl_dim_param);
191 vertices = isl_calloc_type(bset->ctx, isl_vertices);
195 vertices->bset = isl_basic_set_copy(bset);
197 vertices->v = isl_calloc_array(bset->ctx, struct isl_vertex, 1);
200 vertices->n_vertices = 1;
201 vertices->v[0].vertex = isl_basic_set_copy(bset);
202 if (!vertices->v[0].vertex)
205 vertices->c = isl_calloc_array(bset->ctx, struct isl_chamber, 1);
208 vertices->n_chambers = 1;
209 vertices->c[0].n_vertices = 1;
210 vertices->c[0].vertices = isl_calloc_array(bset->ctx, int, 1);
211 if (!vertices->c[0].vertices)
213 vertices->c[0].dom = isl_basic_set_copy(bset);
214 if (!vertices->c[0].dom)
219 isl_vertices_free(vertices);
223 static int isl_mat_rank(__isl_keep isl_mat *mat)
228 H = isl_mat_left_hermite(isl_mat_copy(mat), 0, NULL, NULL);
232 for (col = 0; col < H->n_col; ++col) {
233 for (row = 0; row < H->n_row; ++row)
234 if (!isl_int_is_zero(H->row[row][col]))
245 /* Is the row pointed to by "f" linearly independent of the "n" first
248 static int is_independent(__isl_keep isl_mat *facets, int n, isl_int *f)
252 if (isl_seq_first_non_zero(f, facets->n_col) < 0)
255 isl_seq_cpy(facets->row[n], f, facets->n_col);
256 facets->n_row = n + 1;
257 rank = isl_mat_rank(facets);
261 return rank == n + 1;
264 /* Check whether we can select constraint "level", given the current selection
265 * reflected by facets in "tab", the rows of "facets" and the earlier
266 * "selected" elements of "selection".
268 * If the constraint is (strictly) redundant in the tableau, selecting it would
269 * result in an empty tableau, so it can't be selected.
270 * If the set variable part of the constraint is not linearly indepedent
271 * of the set variable parts of the already selected constraints,
272 * the constraint cannot be selected.
273 * If selecting the constraint results in an empty tableau, the constraint
274 * cannot be selected.
275 * Finally, if selecting the constraint results in some explicitly
276 * deselected constraints turning into equalities, then the corresponding
277 * vertices have already been generated, so the constraint cannot be selected.
279 static int can_select(__isl_keep isl_basic_set *bset, int level,
280 struct isl_tab *tab, __isl_keep isl_mat *facets, int selected,
286 struct isl_tab_undo *snap;
288 if (isl_tab_is_redundant(tab, level))
291 ovar = isl_dim_offset(bset->dim, isl_dim_set);
293 indep = is_independent(facets, selected, bset->ineq[level] + 1 + ovar);
299 snap = isl_tab_snap(tab);
300 if (isl_tab_select_facet(tab, level) < 0)
304 if (isl_tab_rollback(tab, snap) < 0)
309 for (i = 0; i < level; ++i) {
312 if (selection[i] != DESELECTED)
315 if (isl_tab_is_equality(tab, i))
317 else if (isl_tab_is_redundant(tab, i))
320 sgn = isl_tab_sign_of_max(tab, i);
324 if (isl_tab_rollback(tab, snap) < 0)
333 /* Compute the parametric vertices and the chamber decomposition
334 * of a parametric polytope that is not full-dimensional.
336 * Simply map the parametric polytope to a lower dimensional space
337 * and map the resulting vertices back.
339 static __isl_give isl_vertices *lower_dim_vertices(
340 __isl_keep isl_basic_set *bset)
343 isl_vertices *vertices;
345 bset = isl_basic_set_copy(bset);
346 morph = isl_basic_set_full_compression(bset);
347 bset = isl_morph_basic_set(isl_morph_copy(morph), bset);
349 vertices = isl_basic_set_compute_vertices(bset);
350 isl_basic_set_free(bset);
352 morph = isl_morph_inverse(morph);
354 vertices = isl_morph_vertices(morph, vertices);
359 /* Compute the parametric vertices and the chamber decomposition
360 * of the parametric polytope defined using the same constraints
361 * as "bset". "bset" is assumed to have no existentially quantified
364 * The vertices themselves are computed in a fairly simplistic way.
365 * We simply run through all combinations of d constraints,
366 * with d the number of set variables, and check if those d constraints
367 * define a vertex. To avoid the generation of duplicate vertices,
368 * which we may happen if a vertex is defined by more that d constraints,
369 * we make sure we only generate the vertex for the d constraints with
372 * We set up a tableau and keep track of which facets have been
373 * selected. The tableau is marked strict_redundant so that we can be
374 * sure that any constraint that is marked redundant (and that is not
375 * also marked zero) is not an equality.
376 * If a constraint is marked DESELECTED, it means the constraint was
377 * SELECTED before (in combination with the same selection of earlier
378 * constraints). If such a deselected constraint turns out to be an
379 * equality, then any vertex that may still be found with the current
380 * selection has already been generated when the constraint was selected.
381 * A constraint is marked UNSELECTED when there is no way selecting
382 * the constraint could lead to a vertex (in combination with the current
383 * selection of earlier constraints).
385 * The set variable coefficients of the selected constraints are stored
386 * in the facets matrix.
388 __isl_give isl_vertices *isl_basic_set_compute_vertices(
389 __isl_keep isl_basic_set *bset)
397 struct isl_tab_undo **snap;
399 struct isl_vertex_list *list = NULL;
401 isl_vertices *vertices;
406 if (isl_basic_set_fast_is_empty(bset))
407 return vertices_empty(bset);
410 return lower_dim_vertices(bset);
412 isl_assert(bset->ctx, isl_basic_set_dim(bset, isl_dim_div) == 0,
415 if (isl_basic_set_dim(bset, isl_dim_set) == 0)
416 return vertices_0D(bset);
418 nvar = isl_basic_set_dim(bset, isl_dim_set);
420 bset = isl_basic_set_copy(bset);
421 bset = isl_basic_set_set_rational(bset);
425 tab = isl_tab_from_basic_set(bset);
428 tab->strict_redundant = 1;
431 vertices = vertices_empty(bset);
432 isl_basic_set_free(bset);
437 selection = isl_alloc_array(bset->ctx, int, bset->n_ineq);
438 snap = isl_alloc_array(bset->ctx, struct isl_tab_undo *, bset->n_ineq);
439 facets = isl_mat_alloc(bset->ctx, nvar, nvar);
440 if (!selection || !snap || !facets)
448 if (level >= bset->n_ineq ||
449 (!init && selection[level] != SELECTED)) {
456 snap[level] = isl_tab_snap(tab);
457 ok = can_select(bset, level, tab, facets, selected,
462 selection[level] = SELECTED;
465 selection[level] = UNSELECTED;
467 selection[level] = DESELECTED;
469 if (isl_tab_rollback(tab, snap[level]) < 0)
472 if (selected == nvar) {
473 if (tab->n_dead == nvar) {
474 if (add_vertex(&list, bset, tab) < 0)
485 isl_mat_free(facets);
491 vertices = vertices_from_list(bset, n_vertices, list);
493 vertices = compute_chambers(bset, vertices);
497 isl_mat_free(facets);
501 isl_basic_set_free(bset);
505 struct isl_chamber_list {
506 struct isl_chamber c;
507 struct isl_chamber_list *next;
510 static void free_chamber_list(struct isl_chamber_list *list)
512 struct isl_chamber_list *next;
514 for (; list; list = next) {
516 isl_basic_set_free(list->c.dom);
517 free(list->c.vertices);
522 /* Check whether the basic set "bset" is a superset of the basic set described
523 * by "tab", i.e., check whether all constraints of "bset" are redundant.
525 static int bset_covers_tab(__isl_keep isl_basic_set *bset, struct isl_tab *tab)
532 for (i = 0; i < bset->n_ineq; ++i) {
533 enum isl_ineq_type type = isl_tab_ineq_type(tab, bset->ineq[i]);
535 case isl_ineq_error: return -1;
536 case isl_ineq_redundant: continue;
544 static __isl_give isl_vertices *vertices_add_chambers(
545 __isl_take isl_vertices *vertices, int n_chambers,
546 struct isl_chamber_list *list)
549 struct isl_chamber_list *next;
551 vertices->c = isl_alloc_array(vertices->ctx, struct isl_chamber, n_chambers);
554 vertices->n_chambers = n_chambers;
556 for (i = 0; list; list = next, i++) {
558 vertices->c[i] = list->c;
564 isl_vertices_free(vertices);
565 free_chamber_list(list);
569 /* Can "tab" be intersected with "bset" without resulting in
570 * a lower-dimensional set.
572 static int can_intersect(struct isl_tab *tab, __isl_keep isl_basic_set *bset)
575 struct isl_tab_undo *snap;
577 if (isl_tab_extend_cons(tab, bset->n_ineq) < 0)
580 snap = isl_tab_snap(tab);
582 for (i = 0; i < bset->n_ineq; ++i) {
583 if (isl_tab_ineq_type(tab, bset->ineq[i]) == isl_ineq_redundant)
585 if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
589 if (isl_tab_detect_implicit_equalities(tab) < 0)
592 if (isl_tab_rollback(tab, snap) < 0)
600 static int add_chamber(struct isl_chamber_list **list,
601 __isl_keep isl_vertices *vertices, struct isl_tab *tab, int *selection)
606 struct isl_tab_undo *snap;
607 struct isl_chamber_list *c = NULL;
609 for (i = 0; i < vertices->n_vertices; ++i)
613 snap = isl_tab_snap(tab);
615 for (i = 0; i < tab->n_con && tab->con[i].frozen; ++i)
616 tab->con[i].frozen = 0;
619 if (isl_tab_detect_redundant(tab) < 0)
622 c = isl_calloc_type(tab->mat->ctx, struct isl_chamber_list);
625 c->c.vertices = isl_alloc_array(tab->mat->ctx, int, n_vertices);
628 c->c.dom = isl_basic_set_from_basic_map(isl_basic_map_copy(tab->bmap));
629 c->c.dom = isl_basic_set_set_rational(c->c.dom);
630 c->c.dom = isl_basic_set_cow(c->c.dom);
631 c->c.dom = isl_basic_set_update_from_tab(c->c.dom, tab);
632 c->c.dom = isl_basic_set_simplify(c->c.dom);
633 c->c.dom = isl_basic_set_finalize(c->c.dom);
637 c->c.n_vertices = n_vertices;
639 for (i = 0, j = 0; i < vertices->n_vertices; ++i)
641 c->c.vertices[j] = i;
648 for (i = 0; i < n_frozen; ++i)
649 tab->con[i].frozen = 1;
651 if (isl_tab_rollback(tab, snap) < 0)
656 free_chamber_list(c);
660 struct isl_facet_todo {
661 struct isl_tab *tab; /* A tableau representation of the facet */
662 isl_basic_set *bset; /* A normalized basic set representation */
663 isl_vec *constraint; /* Constraint pointing to the other side */
664 struct isl_facet_todo *next;
667 static void free_todo(struct isl_facet_todo *todo)
670 struct isl_facet_todo *next = todo->next;
672 isl_tab_free(todo->tab);
673 isl_basic_set_free(todo->bset);
674 isl_vec_free(todo->constraint);
681 static struct isl_facet_todo *create_todo(struct isl_tab *tab, int con)
685 struct isl_tab_undo *snap;
686 struct isl_facet_todo *todo;
688 snap = isl_tab_snap(tab);
690 for (i = 0; i < tab->n_con && tab->con[i].frozen; ++i)
691 tab->con[i].frozen = 0;
694 if (isl_tab_detect_redundant(tab) < 0)
697 todo = isl_calloc_type(tab->mat->ctx, struct isl_facet_todo);
701 todo->constraint = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
702 if (!todo->constraint)
704 isl_seq_neg(todo->constraint->el, tab->bmap->ineq[con], 1 + tab->n_var);
705 todo->bset = isl_basic_set_from_basic_map(isl_basic_map_copy(tab->bmap));
706 todo->bset = isl_basic_set_set_rational(todo->bset);
707 todo->bset = isl_basic_set_cow(todo->bset);
708 todo->bset = isl_basic_set_update_from_tab(todo->bset, tab);
709 todo->bset = isl_basic_set_simplify(todo->bset);
710 todo->bset = isl_basic_set_sort_constraints(todo->bset);
713 ISL_F_SET(todo->bset, ISL_BASIC_SET_NORMALIZED);
714 todo->tab = isl_tab_dup(tab);
718 for (i = 0; i < n_frozen; ++i)
719 tab->con[i].frozen = 1;
721 if (isl_tab_rollback(tab, snap) < 0)
730 /* Create todo items for all interior facets of the chamber represented
731 * by "tab" and collect them in "next".
733 static int init_todo(struct isl_facet_todo **next, struct isl_tab *tab)
736 struct isl_tab_undo *snap;
737 struct isl_facet_todo *todo;
739 snap = isl_tab_snap(tab);
741 for (i = 0; i < tab->n_con; ++i) {
742 if (tab->con[i].frozen)
744 if (tab->con[i].is_redundant)
747 if (isl_tab_select_facet(tab, i) < 0)
750 todo = create_todo(tab, i);
757 if (isl_tab_rollback(tab, snap) < 0)
764 /* Does the linked list contain a todo item that is the opposite of "todo".
765 * If so, return 1 and remove the opposite todo item.
767 static int has_opposite(struct isl_facet_todo *todo,
768 struct isl_facet_todo **list)
770 for (; *list; list = &(*list)->next) {
772 eq = isl_basic_set_fast_is_equal(todo->bset, (*list)->bset);
787 /* Create todo items for all interior facets of the chamber represented
788 * by "tab" and collect them in first->next, taking care to cancel
789 * opposite todo items.
791 static int update_todo(struct isl_facet_todo *first, struct isl_tab *tab)
794 struct isl_tab_undo *snap;
795 struct isl_facet_todo *todo;
797 snap = isl_tab_snap(tab);
799 for (i = 0; i < tab->n_con; ++i) {
802 if (tab->con[i].frozen)
804 if (tab->con[i].is_redundant)
807 if (isl_tab_select_facet(tab, i) < 0)
810 todo = create_todo(tab, i);
814 drop = has_opposite(todo, &first->next);
821 todo->next = first->next;
825 if (isl_tab_rollback(tab, snap) < 0)
832 /* Compute the chamber decomposition of the parametric polytope respresented
833 * by "bset" given the parametric vertices and their activity domains.
835 * We are only interested in full-dimensional chambers.
836 * Each of these chambers is the intersection of the activity domains of
837 * one or more vertices and the union of all chambers is equal to the
838 * projection of the entire parametric polytope onto the parameter space.
840 * We first create an initial chamber by intersecting as many activity
841 * domains as possible without ending up with an empty or lower-dimensional
842 * set. As a minor optimization, we only consider those activity domains
843 * that contain some arbitrary point.
845 * For each of interior facets of the chamber, we construct a todo item,
846 * containing the facet and a constraint containing the other side of the facet,
847 * for constructing the chamber on the other side.
848 * While their are any todo items left, we pick a todo item and
849 * create the required chamber by intersecting all activity domains
850 * that contain the facet and have a full-dimensional intersection with
851 * the other side of the facet. For each of the interior facets, we
852 * again create todo items, taking care to cancel opposite todo items.
854 static __isl_give isl_vertices *compute_chambers(__isl_take isl_basic_set *bset,
855 __isl_take isl_vertices *vertices)
858 isl_vec *sample = NULL;
859 struct isl_tab *tab = NULL;
860 struct isl_tab_undo *snap;
862 int *selection = NULL;
864 struct isl_chamber_list *list = NULL;
865 struct isl_facet_todo *todo = NULL;
867 if (!bset || !vertices)
870 selection = isl_alloc_array(vertices->ctx, int, vertices->n_vertices);
874 nvar = isl_basic_set_dim(bset, isl_dim_set);
875 bset = isl_basic_set_project_out(bset, isl_dim_set, 0, nvar);
877 tab = isl_tab_from_basic_set(bset);
878 for (i = 0; i < bset->n_ineq; ++i)
879 if (isl_tab_freeze_constraint(tab, i) < 0)
881 if (isl_tab_track_bset(tab, bset) < 0)
884 snap = isl_tab_snap(tab);
886 sample = isl_tab_get_sample_value(tab);
888 for (i = 0; i < vertices->n_vertices; ++i) {
889 selection[i] = isl_basic_set_contains(vertices->v[i].dom, sample);
890 if (selection[i] < 0)
894 selection[i] = can_intersect(tab, vertices->v[i].dom);
895 if (selection[i] < 0)
899 if (isl_tab_detect_redundant(tab) < 0)
902 if (add_chamber(&list, vertices, tab, selection) < 0)
906 if (init_todo(&todo, tab) < 0)
910 struct isl_facet_todo *next;
912 if (isl_tab_rollback(tab, snap) < 0)
915 if (isl_tab_add_ineq(tab, todo->constraint->el) < 0)
917 if (isl_tab_freeze_constraint(tab, tab->n_con - 1) < 0)
920 for (i = 0; i < vertices->n_vertices; ++i) {
921 selection[i] = bset_covers_tab(vertices->v[i].dom,
923 if (selection[i] < 0)
927 selection[i] = can_intersect(tab, vertices->v[i].dom);
928 if (selection[i] < 0)
932 if (isl_tab_detect_redundant(tab) < 0)
935 if (add_chamber(&list, vertices, tab, selection) < 0)
939 if (update_todo(todo, tab) < 0)
948 isl_vec_free(sample);
953 vertices = vertices_add_chambers(vertices, n_chambers, list);
955 for (i = 0; vertices && i < vertices->n_vertices; ++i) {
956 isl_basic_set_free(vertices->v[i].dom);
957 vertices->v[i].dom = NULL;
962 free_chamber_list(list);
964 isl_vec_free(sample);
968 isl_basic_set_free(bset);
969 isl_vertices_free(vertices);
973 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex)
975 return vertex ? isl_vertices_get_ctx(vertex->vertices) : NULL;
978 int isl_vertex_get_id(__isl_keep isl_vertex *vertex)
980 return vertex ? vertex->id : -1;
983 __isl_give isl_basic_set *isl_vertex_get_domain(__isl_keep isl_vertex *vertex)
985 struct isl_vertex *v;
990 v = &vertex->vertices->v[vertex->id];
993 nvar = isl_basic_set_dim(v->vertex, isl_dim_set);
994 v->dom = isl_basic_set_copy(v->vertex);
995 v->dom = isl_basic_set_project_out(v->dom, isl_dim_set, 0, nvar);
998 return isl_basic_set_copy(v->dom);
1001 __isl_give isl_basic_set *isl_vertex_get_expr(__isl_keep isl_vertex *vertex)
1003 struct isl_vertex *v;
1008 v = &vertex->vertices->v[vertex->id];
1010 return isl_basic_set_copy(v->vertex);
1013 static __isl_give isl_vertex *isl_vertex_alloc(__isl_take isl_vertices *vertices,
1021 vertex = isl_alloc_type(vertices->ctx, isl_vertex);
1025 vertex->vertices = vertices;
1030 isl_vertices_free(vertices);
1034 void isl_vertex_free(__isl_take isl_vertex *vertex)
1038 isl_vertices_free(vertex->vertices);
1042 __isl_give isl_basic_set *isl_basic_set_set_integral(__isl_take isl_basic_set *bset)
1047 if (!ISL_F_ISSET(bset, ISL_BASIC_MAP_RATIONAL))
1050 bset = isl_basic_set_cow(bset);
1054 ISL_F_CLR(bset, ISL_BASIC_MAP_RATIONAL);
1056 return isl_basic_set_finalize(bset);
1059 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell)
1061 return cell ? cell->dom->ctx : NULL;
1064 __isl_give isl_basic_set *isl_cell_get_domain(__isl_keep isl_cell *cell)
1066 return cell ? isl_basic_set_copy(cell->dom) : NULL;
1069 static __isl_give isl_cell *isl_cell_alloc(__isl_take isl_vertices *vertices,
1070 __isl_take isl_basic_set *dom, int id)
1073 isl_cell *cell = NULL;
1075 if (!vertices || !dom)
1078 cell = isl_calloc_type(dom->ctx, isl_cell);
1082 cell->n_vertices = vertices->c[id].n_vertices;
1083 cell->ids = isl_alloc_array(dom->ctx, int, cell->n_vertices);
1086 for (i = 0; i < cell->n_vertices; ++i)
1087 cell->ids[i] = vertices->c[id].vertices[i];
1088 cell->vertices = vertices;
1093 isl_cell_free(cell);
1094 isl_vertices_free(vertices);
1095 isl_basic_set_free(dom);
1099 void isl_cell_free(__isl_take isl_cell *cell)
1104 isl_vertices_free(cell->vertices);
1106 isl_basic_set_free(cell->dom);
1110 /* Create a tableau of the cone obtained by first homogenizing the given
1111 * polytope and then making all inequalities strict by setting the
1112 * constant term to -1.
1114 static struct isl_tab *tab_for_shifted_cone(__isl_keep isl_basic_set *bset)
1118 struct isl_tab *tab;
1122 tab = isl_tab_alloc(bset->ctx, bset->n_ineq + 1,
1123 1 + isl_basic_set_total_dim(bset), 0);
1126 tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
1127 if (ISL_F_ISSET(bset, ISL_BASIC_MAP_EMPTY)) {
1128 if (isl_tab_mark_empty(tab) < 0)
1133 c = isl_vec_alloc(bset->ctx, 1 + 1 + isl_basic_set_total_dim(bset));
1137 isl_int_set_si(c->el[0], 0);
1138 for (i = 0; i < bset->n_eq; ++i) {
1139 isl_seq_cpy(c->el + 1, bset->eq[i], c->size - 1);
1140 if (isl_tab_add_eq(tab, c->el) < 0)
1144 isl_int_set_si(c->el[0], -1);
1145 for (i = 0; i < bset->n_ineq; ++i) {
1146 isl_seq_cpy(c->el + 1, bset->ineq[i], c->size - 1);
1147 if (isl_tab_add_ineq(tab, c->el) < 0)
1155 isl_seq_clr(c->el + 1, c->size - 1);
1156 isl_int_set_si(c->el[1], 1);
1157 if (isl_tab_add_ineq(tab, c->el) < 0)
1168 /* Compute an interior point of "bset" by selecting an interior
1169 * point in homogeneous space and projecting the point back down.
1171 static __isl_give isl_vec *isl_basic_set_interior_point(
1172 __isl_keep isl_basic_set *bset)
1175 struct isl_tab *tab;
1177 tab = tab_for_shifted_cone(bset);
1178 vec = isl_tab_get_sample_value(tab);
1183 isl_seq_cpy(vec->el, vec->el + 1, vec->size - 1);
1189 /* Call "fn" on all chambers of the parametric polytope with the shared
1190 * facets of neighboring chambers only appearing in one of the chambers.
1192 * We pick an interior point from one of the chambers and then make
1193 * all constraints that do not satisfy this point strict.
1195 int isl_vertices_foreach_disjoint_cell(__isl_keep isl_vertices *vertices,
1196 int (*fn)(__isl_take isl_cell *cell, void *user), void *user)
1206 if (vertices->n_chambers == 0)
1209 if (vertices->n_chambers == 1) {
1210 isl_basic_set *dom = isl_basic_set_copy(vertices->c[0].dom);
1211 dom = isl_basic_set_set_integral(dom);
1212 cell = isl_cell_alloc(isl_vertices_copy(vertices), dom, 0);
1215 return fn(cell, user);
1218 vec = isl_basic_set_interior_point(vertices->c[0].dom);
1224 for (i = 0; i < vertices->n_chambers; ++i) {
1226 isl_basic_set *dom = isl_basic_set_copy(vertices->c[i].dom);
1227 dom = isl_basic_set_cow(dom);
1230 for (j = 0; i && j < dom->n_ineq; ++j) {
1231 isl_seq_inner_product(vec->el, dom->ineq[j], vec->size,
1233 if (!isl_int_is_neg(v))
1235 isl_int_sub_ui(dom->ineq[j][0], dom->ineq[j][0], 1);
1237 dom = isl_basic_set_set_integral(dom);
1238 cell = isl_cell_alloc(isl_vertices_copy(vertices), dom, i);
1256 int isl_vertices_foreach_cell(__isl_keep isl_vertices *vertices,
1257 int (*fn)(__isl_take isl_cell *cell, void *user), void *user)
1265 if (vertices->n_chambers == 0)
1268 for (i = 0; i < vertices->n_chambers; ++i) {
1270 isl_basic_set *dom = isl_basic_set_copy(vertices->c[i].dom);
1272 cell = isl_cell_alloc(isl_vertices_copy(vertices), dom, i);
1284 int isl_vertices_foreach_vertex(__isl_keep isl_vertices *vertices,
1285 int (*fn)(__isl_take isl_vertex *vertex, void *user), void *user)
1293 if (vertices->n_vertices == 0)
1296 for (i = 0; i < vertices->n_vertices; ++i) {
1299 vertex = isl_vertex_alloc(isl_vertices_copy(vertices), i);
1303 r = fn(vertex, user);
1311 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
1312 int (*fn)(__isl_take isl_vertex *vertex, void *user), void *user)
1320 if (cell->n_vertices == 0)
1323 for (i = 0; i < cell->n_vertices; ++i) {
1326 vertex = isl_vertex_alloc(isl_vertices_copy(cell->vertices),
1331 r = fn(vertex, user);
1339 isl_ctx *isl_vertices_get_ctx(__isl_keep isl_vertices *vertices)
1341 return vertices ? vertices->bset->ctx : NULL;
1344 int isl_vertices_get_n_vertices(__isl_keep isl_vertices *vertices)
1346 return vertices ? vertices->n_vertices : -1;
1349 __isl_give isl_vertices *isl_morph_vertices(__isl_take isl_morph *morph,
1350 __isl_take isl_vertices *vertices)
1353 isl_morph *param_morph = NULL;
1355 if (!morph || !vertices)
1358 isl_assert(vertices->bset->ctx, vertices->ref == 1, goto error);
1360 param_morph = isl_morph_copy(morph);
1361 param_morph = isl_morph_remove_dom_dims(param_morph, isl_dim_set,
1362 0, isl_morph_dom_dim(morph, isl_dim_set));
1363 param_morph = isl_morph_remove_ran_dims(param_morph, isl_dim_set,
1364 0, isl_morph_ran_dim(morph, isl_dim_set));
1366 for (i = 0; i < vertices->n_vertices; ++i) {
1367 vertices->v[i].dom = isl_morph_basic_set(
1368 isl_morph_copy(param_morph), vertices->v[i].dom);
1369 vertices->v[i].vertex = isl_morph_basic_set(
1370 isl_morph_copy(morph), vertices->v[i].vertex);
1371 if (!vertices->v[i].vertex)
1375 for (i = 0; i < vertices->n_chambers; ++i) {
1376 vertices->c[i].dom = isl_morph_basic_set(
1377 isl_morph_copy(param_morph), vertices->c[i].dom);
1378 if (!vertices->c[i].dom)
1382 isl_morph_free(param_morph);
1383 isl_morph_free(morph);
1386 isl_morph_free(param_morph);
1387 isl_morph_free(morph);
1388 isl_vertices_free(vertices);
1392 /* Construct a simplex isl_cell spanned by the vertices with indices in
1393 * "simplex_ids" and "other_ids" and call "fn" on this isl_cell.
1395 static int call_on_simplex(__isl_keep isl_cell *cell,
1396 int *simplex_ids, int n_simplex, int *other_ids, int n_other,
1397 int (*fn)(__isl_take isl_cell *simplex, void *user), void *user)
1401 struct isl_cell *simplex;
1403 ctx = isl_cell_get_ctx(cell);
1405 simplex = isl_calloc_type(ctx, struct isl_cell);
1408 simplex->vertices = isl_vertices_copy(cell->vertices);
1409 if (!simplex->vertices)
1411 simplex->dom = isl_basic_set_copy(cell->dom);
1414 simplex->n_vertices = n_simplex + n_other;
1415 simplex->ids = isl_alloc_array(ctx, int, simplex->n_vertices);
1419 for (i = 0; i < n_simplex; ++i)
1420 simplex->ids[i] = simplex_ids[i];
1421 for (i = 0; i < n_other; ++i)
1422 simplex->ids[n_simplex + i] = other_ids[i];
1424 return fn(simplex, user);
1426 isl_cell_free(simplex);
1430 /* Check whether the parametric vertex described by "vertex"
1431 * lies on the facet corresponding to constraint "facet" of "bset".
1432 * The isl_vec "v" is a temporary vector than can be used by this function.
1434 * We eliminate the variables from the facet constraint using the
1435 * equalities defining the vertex and check if the result is identical
1438 * It would probably be better to keep track of the constraints defining
1439 * a vertex during the vertex construction so that we could simply look
1442 static int vertex_on_facet(__isl_keep isl_basic_set *vertex,
1443 __isl_keep isl_basic_set *bset, int facet, __isl_keep isl_vec *v)
1448 isl_seq_cpy(v->el, bset->ineq[facet], v->size);
1451 for (i = 0; i < vertex->n_eq; ++i) {
1452 int k = isl_seq_last_non_zero(vertex->eq[i], v->size);
1453 isl_seq_elim(v->el, vertex->eq[i], k, v->size, &m);
1457 return isl_seq_first_non_zero(v->el, v->size) == -1;
1460 /* Triangulate the polytope spanned by the vertices with ids
1461 * in "simplex_ids" and "other_ids" and call "fn" on each of
1462 * the resulting simplices.
1463 * If the input polytope is already a simplex, we simply call "fn".
1464 * Otherwise, we pick a point from "other_ids" and add it to "simplex_ids".
1465 * Then we consider each facet of "bset" that does not contain the point
1466 * we just picked, but does contain some of the other points in "other_ids"
1467 * and call ourselves recursively on the polytope spanned by the new
1468 * "simplex_ids" and those points in "other_ids" that lie on the facet.
1470 static int triangulate(__isl_keep isl_cell *cell, __isl_keep isl_vec *v,
1471 int *simplex_ids, int n_simplex, int *other_ids, int n_other,
1472 int (*fn)(__isl_take isl_cell *simplex, void *user), void *user)
1477 isl_basic_set *vertex;
1478 isl_basic_set *bset;
1480 d = isl_basic_set_dim(cell->vertices->bset, isl_dim_set);
1481 nparam = isl_basic_set_dim(cell->vertices->bset, isl_dim_param);
1483 if (n_simplex + n_other == d + 1)
1484 return call_on_simplex(cell, simplex_ids, n_simplex,
1485 other_ids, n_other, fn, user);
1487 simplex_ids[n_simplex] = other_ids[0];
1488 vertex = cell->vertices->v[other_ids[0]].vertex;
1489 bset = cell->vertices->bset;
1491 ids = isl_alloc_array(ctx, int, n_other - 1);
1492 for (i = 0; i < bset->n_ineq; ++i) {
1493 if (isl_seq_first_non_zero(bset->ineq[i] + 1 + nparam, d) == -1)
1495 if (vertex_on_facet(vertex, bset, i, v))
1498 for (j = 1, k = 0; j < n_other; ++j) {
1500 ov = cell->vertices->v[other_ids[j]].vertex;
1501 if (vertex_on_facet(ov, bset, i, v))
1502 ids[k++] = other_ids[j];
1507 if (triangulate(cell, v, simplex_ids, n_simplex + 1,
1508 ids, k, fn, user) < 0)
1519 /* Triangulate the given cell and call "fn" on each of the resulting
1522 int isl_cell_foreach_simplex(__isl_take isl_cell *cell,
1523 int (*fn)(__isl_take isl_cell *simplex, void *user), void *user)
1529 int *simplex_ids = NULL;
1534 d = isl_basic_set_dim(cell->vertices->bset, isl_dim_set);
1535 total = isl_basic_set_total_dim(cell->vertices->bset);
1537 if (cell->n_vertices == d + 1)
1538 return fn(cell, user);
1540 ctx = isl_cell_get_ctx(cell);
1541 simplex_ids = isl_alloc_array(ctx, int, d + 1);
1545 v = isl_vec_alloc(ctx, 1 + total);
1549 r = triangulate(cell, v, simplex_ids, 0,
1550 cell->ids, cell->n_vertices, fn, user);
1555 isl_cell_free(cell);
1561 isl_cell_free(cell);