2 * Copyright 2010 INRIA Saclay
4 * Use of this software is governed by the MIT 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_aff_private.h>
16 #include <isl_space_private.h>
17 #include <isl_morph.h>
18 #include <isl_vertices_private.h>
19 #include <isl_mat_private.h>
20 #include <isl_vec_private.h>
26 static __isl_give isl_vertices
*compute_chambers(__isl_take isl_basic_set
*bset
,
27 __isl_take isl_vertices
*vertices
);
29 __isl_give isl_vertices
*isl_vertices_copy(__isl_keep isl_vertices
*vertices
)
38 __isl_null isl_vertices
*isl_vertices_free(__isl_take isl_vertices
*vertices
)
45 if (--vertices
->ref
> 0)
48 for (i
= 0; i
< vertices
->n_vertices
; ++i
) {
49 isl_basic_set_free(vertices
->v
[i
].vertex
);
50 isl_basic_set_free(vertices
->v
[i
].dom
);
54 for (i
= 0; i
< vertices
->n_chambers
; ++i
) {
55 free(vertices
->c
[i
].vertices
);
56 isl_basic_set_free(vertices
->c
[i
].dom
);
60 isl_basic_set_free(vertices
->bset
);
66 struct isl_vertex_list
{
68 struct isl_vertex_list
*next
;
71 static struct isl_vertex_list
*free_vertex_list(struct isl_vertex_list
*list
)
73 struct isl_vertex_list
*next
;
75 for (; list
; list
= next
) {
77 isl_basic_set_free(list
->v
.vertex
);
78 isl_basic_set_free(list
->v
.dom
);
85 static __isl_give isl_vertices
*vertices_from_list(__isl_keep isl_basic_set
*bset
,
86 int n_vertices
, struct isl_vertex_list
*list
)
89 struct isl_vertex_list
*next
;
90 isl_vertices
*vertices
;
92 vertices
= isl_calloc_type(bset
->ctx
, isl_vertices
);
96 vertices
->bset
= isl_basic_set_copy(bset
);
97 vertices
->v
= isl_alloc_array(bset
->ctx
, struct isl_vertex
, n_vertices
);
98 if (n_vertices
&& !vertices
->v
)
100 vertices
->n_vertices
= n_vertices
;
102 for (i
= 0; list
; list
= next
, i
++) {
104 vertices
->v
[i
] = list
->v
;
110 isl_vertices_free(vertices
);
111 free_vertex_list(list
);
115 /* Prepend a vertex to the linked list "list" based on the equalities in "tab".
116 * Return isl_bool_true if the vertex was actually added and
117 * isl_bool_false otherwise.
118 * In particular, vertices with a lower-dimensional activity domain are
119 * not added to the list because they would not be included in any chamber.
120 * Return isl_bool_error on error.
122 static isl_bool
add_vertex(struct isl_vertex_list
**list
,
123 __isl_keep isl_basic_set
*bset
, struct isl_tab
*tab
)
126 struct isl_vertex_list
*v
= NULL
;
128 if (isl_tab_detect_implicit_equalities(tab
) < 0)
129 return isl_bool_error
;
131 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
133 v
= isl_calloc_type(tab
->mat
->ctx
, struct isl_vertex_list
);
137 v
->v
.vertex
= isl_basic_set_copy(bset
);
138 v
->v
.vertex
= isl_basic_set_cow(v
->v
.vertex
);
139 v
->v
.vertex
= isl_basic_set_update_from_tab(v
->v
.vertex
, tab
);
140 v
->v
.vertex
= isl_basic_set_simplify(v
->v
.vertex
);
141 v
->v
.vertex
= isl_basic_set_finalize(v
->v
.vertex
);
144 isl_assert(bset
->ctx
, v
->v
.vertex
->n_eq
>= nvar
, goto error
);
145 v
->v
.dom
= isl_basic_set_copy(v
->v
.vertex
);
146 v
->v
.dom
= isl_basic_set_params(v
->v
.dom
);
150 if (v
->v
.dom
->n_eq
> 0) {
152 return isl_bool_false
;
158 return isl_bool_true
;
161 return isl_bool_error
;
164 /* Compute the parametric vertices and the chamber decomposition
165 * of an empty parametric polytope.
167 static __isl_give isl_vertices
*vertices_empty(__isl_keep isl_basic_set
*bset
)
169 isl_vertices
*vertices
;
174 vertices
= isl_calloc_type(bset
->ctx
, isl_vertices
);
177 vertices
->bset
= isl_basic_set_copy(bset
);
180 vertices
->n_vertices
= 0;
181 vertices
->n_chambers
= 0;
186 /* Compute the parametric vertices and the chamber decomposition
187 * of the parametric polytope defined using the same constraints
188 * as "bset" in the 0D case.
189 * There is exactly one 0D vertex and a single chamber containing
192 static __isl_give isl_vertices
*vertices_0D(__isl_keep isl_basic_set
*bset
)
194 isl_vertices
*vertices
;
199 vertices
= isl_calloc_type(bset
->ctx
, isl_vertices
);
203 vertices
->bset
= isl_basic_set_copy(bset
);
205 vertices
->v
= isl_calloc_array(bset
->ctx
, struct isl_vertex
, 1);
208 vertices
->n_vertices
= 1;
209 vertices
->v
[0].vertex
= isl_basic_set_copy(bset
);
210 vertices
->v
[0].dom
= isl_basic_set_params(isl_basic_set_copy(bset
));
211 if (!vertices
->v
[0].vertex
|| !vertices
->v
[0].dom
)
214 vertices
->c
= isl_calloc_array(bset
->ctx
, struct isl_chamber
, 1);
217 vertices
->n_chambers
= 1;
218 vertices
->c
[0].n_vertices
= 1;
219 vertices
->c
[0].vertices
= isl_calloc_array(bset
->ctx
, int, 1);
220 if (!vertices
->c
[0].vertices
)
222 vertices
->c
[0].dom
= isl_basic_set_copy(vertices
->v
[0].dom
);
223 if (!vertices
->c
[0].dom
)
228 isl_vertices_free(vertices
);
232 /* Is the row pointed to by "f" linearly independent of the "n" first
235 static isl_bool
is_independent(__isl_keep isl_mat
*facets
, int n
, isl_int
*f
)
239 if (isl_seq_first_non_zero(f
, facets
->n_col
) < 0)
240 return isl_bool_false
;
242 isl_seq_cpy(facets
->row
[n
], f
, facets
->n_col
);
243 facets
->n_row
= n
+ 1;
244 rank
= isl_mat_rank(facets
);
246 return isl_bool_error
;
248 return rank
== n
+ 1;
251 /* Check whether we can select constraint "level", given the current selection
252 * reflected by facets in "tab", the rows of "facets" and the earlier
253 * "selected" elements of "selection".
255 * If the constraint is (strictly) redundant in the tableau, selecting it would
256 * result in an empty tableau, so it can't be selected.
257 * If the set variable part of the constraint is not linearly independent
258 * of the set variable parts of the already selected constraints,
259 * the constraint cannot be selected.
260 * If selecting the constraint results in an empty tableau, the constraint
261 * cannot be selected.
262 * Finally, if selecting the constraint results in some explicitly
263 * deselected constraints turning into equalities, then the corresponding
264 * vertices have already been generated, so the constraint cannot be selected.
266 static isl_bool
can_select(__isl_keep isl_basic_set
*bset
, int level
,
267 struct isl_tab
*tab
, __isl_keep isl_mat
*facets
, int selected
,
273 struct isl_tab_undo
*snap
;
275 if (isl_tab_is_redundant(tab
, level
))
276 return isl_bool_false
;
278 ovar
= isl_space_offset(bset
->dim
, isl_dim_set
);
280 indep
= is_independent(facets
, selected
, bset
->ineq
[level
] + 1 + ovar
);
281 if (indep
< 0 || !indep
)
284 snap
= isl_tab_snap(tab
);
285 if (isl_tab_select_facet(tab
, level
) < 0)
286 return isl_bool_error
;
289 if (isl_tab_rollback(tab
, snap
) < 0)
290 return isl_bool_error
;
291 return isl_bool_false
;
294 for (i
= 0; i
< level
; ++i
) {
297 if (selection
[i
] != DESELECTED
)
300 if (isl_tab_is_equality(tab
, i
))
302 else if (isl_tab_is_redundant(tab
, i
))
305 sgn
= isl_tab_sign_of_max(tab
, i
);
307 return isl_bool_error
;
309 if (isl_tab_rollback(tab
, snap
) < 0)
310 return isl_bool_error
;
311 return isl_bool_false
;
315 return isl_bool_true
;
318 /* Compute the parametric vertices and the chamber decomposition
319 * of a parametric polytope that is not full-dimensional.
321 * Simply map the parametric polytope to a lower dimensional space
322 * and map the resulting vertices back.
324 static __isl_give isl_vertices
*lower_dim_vertices(
325 __isl_keep isl_basic_set
*bset
)
328 isl_vertices
*vertices
;
330 bset
= isl_basic_set_copy(bset
);
331 morph
= isl_basic_set_full_compression(bset
);
332 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
334 vertices
= isl_basic_set_compute_vertices(bset
);
335 isl_basic_set_free(bset
);
337 morph
= isl_morph_inverse(morph
);
339 vertices
= isl_morph_vertices(morph
, vertices
);
344 /* Compute the parametric vertices and the chamber decomposition
345 * of the parametric polytope defined using the same constraints
346 * as "bset". "bset" is assumed to have no existentially quantified
349 * The vertices themselves are computed in a fairly simplistic way.
350 * We simply run through all combinations of d constraints,
351 * with d the number of set variables, and check if those d constraints
352 * define a vertex. To avoid the generation of duplicate vertices,
353 * which we may happen if a vertex is defined by more that d constraints,
354 * we make sure we only generate the vertex for the d constraints with
357 * We set up a tableau and keep track of which facets have been
358 * selected. The tableau is marked strict_redundant so that we can be
359 * sure that any constraint that is marked redundant (and that is not
360 * also marked zero) is not an equality.
361 * If a constraint is marked DESELECTED, it means the constraint was
362 * SELECTED before (in combination with the same selection of earlier
363 * constraints). If such a deselected constraint turns out to be an
364 * equality, then any vertex that may still be found with the current
365 * selection has already been generated when the constraint was selected.
366 * A constraint is marked UNSELECTED when there is no way selecting
367 * the constraint could lead to a vertex (in combination with the current
368 * selection of earlier constraints).
370 * The set variable coefficients of the selected constraints are stored
371 * in the facets matrix.
373 __isl_give isl_vertices
*isl_basic_set_compute_vertices(
374 __isl_keep isl_basic_set
*bset
)
380 int *selection
= NULL
;
382 struct isl_tab_undo
**snap
= NULL
;
383 isl_mat
*facets
= NULL
;
384 struct isl_vertex_list
*list
= NULL
;
386 isl_vertices
*vertices
;
391 if (isl_basic_set_plain_is_empty(bset
))
392 return vertices_empty(bset
);
395 return lower_dim_vertices(bset
);
397 if (isl_basic_set_check_no_locals(bset
) < 0)
400 if (isl_basic_set_dim(bset
, isl_dim_set
) == 0)
401 return vertices_0D(bset
);
403 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
405 bset
= isl_basic_set_copy(bset
);
406 bset
= isl_basic_set_set_rational(bset
);
410 tab
= isl_tab_from_basic_set(bset
, 0);
413 tab
->strict_redundant
= 1;
416 vertices
= vertices_empty(bset
);
417 isl_basic_set_free(bset
);
422 selection
= isl_alloc_array(bset
->ctx
, int, bset
->n_ineq
);
423 snap
= isl_alloc_array(bset
->ctx
, struct isl_tab_undo
*, bset
->n_ineq
);
424 facets
= isl_mat_alloc(bset
->ctx
, nvar
, nvar
);
425 if ((bset
->n_ineq
&& (!selection
|| !snap
)) || !facets
)
433 if (level
>= bset
->n_ineq
||
434 (!init
&& selection
[level
] != SELECTED
)) {
441 snap
[level
] = isl_tab_snap(tab
);
442 ok
= can_select(bset
, level
, tab
, facets
, selected
,
447 selection
[level
] = SELECTED
;
450 selection
[level
] = UNSELECTED
;
452 selection
[level
] = DESELECTED
;
454 if (isl_tab_rollback(tab
, snap
[level
]) < 0)
457 if (selected
== nvar
) {
458 if (tab
->n_dead
== nvar
) {
459 isl_bool added
= add_vertex(&list
, bset
, tab
);
472 isl_mat_free(facets
);
478 vertices
= vertices_from_list(bset
, n_vertices
, list
);
480 vertices
= compute_chambers(bset
, vertices
);
484 free_vertex_list(list
);
485 isl_mat_free(facets
);
489 isl_basic_set_free(bset
);
493 struct isl_chamber_list
{
494 struct isl_chamber c
;
495 struct isl_chamber_list
*next
;
498 static void free_chamber_list(struct isl_chamber_list
*list
)
500 struct isl_chamber_list
*next
;
502 for (; list
; list
= next
) {
504 isl_basic_set_free(list
->c
.dom
);
505 free(list
->c
.vertices
);
510 /* Check whether the basic set "bset" is a superset of the basic set described
511 * by "tab", i.e., check whether all constraints of "bset" are redundant.
513 static isl_bool
bset_covers_tab(__isl_keep isl_basic_set
*bset
,
519 return isl_bool_error
;
521 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
522 enum isl_ineq_type type
= isl_tab_ineq_type(tab
, bset
->ineq
[i
]);
524 case isl_ineq_error
: return isl_bool_error
;
525 case isl_ineq_redundant
: continue;
526 default: return isl_bool_false
;
530 return isl_bool_true
;
533 static __isl_give isl_vertices
*vertices_add_chambers(
534 __isl_take isl_vertices
*vertices
, int n_chambers
,
535 struct isl_chamber_list
*list
)
539 struct isl_chamber_list
*next
;
541 ctx
= isl_vertices_get_ctx(vertices
);
542 vertices
->c
= isl_alloc_array(ctx
, struct isl_chamber
, n_chambers
);
545 vertices
->n_chambers
= n_chambers
;
547 for (i
= 0; list
; list
= next
, i
++) {
549 vertices
->c
[i
] = list
->c
;
555 isl_vertices_free(vertices
);
556 free_chamber_list(list
);
560 /* Can "tab" be intersected with "bset" without resulting in
561 * a lower-dimensional set.
562 * "bset" itself is assumed to be full-dimensional.
564 static isl_bool
can_intersect(struct isl_tab
*tab
,
565 __isl_keep isl_basic_set
*bset
)
568 struct isl_tab_undo
*snap
;
571 isl_die(isl_basic_set_get_ctx(bset
), isl_error_internal
,
572 "expecting full-dimensional input",
573 return isl_bool_error
);
575 if (isl_tab_extend_cons(tab
, bset
->n_ineq
) < 0)
576 return isl_bool_error
;
578 snap
= isl_tab_snap(tab
);
580 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
581 if (isl_tab_ineq_type(tab
, bset
->ineq
[i
]) == isl_ineq_redundant
)
583 if (isl_tab_add_ineq(tab
, bset
->ineq
[i
]) < 0)
584 return isl_bool_error
;
587 if (isl_tab_detect_implicit_equalities(tab
) < 0)
588 return isl_bool_error
;
590 if (isl_tab_rollback(tab
, snap
) < 0)
591 return isl_bool_error
;
592 return isl_bool_false
;
595 return isl_bool_true
;
598 static int add_chamber(struct isl_chamber_list
**list
,
599 __isl_keep isl_vertices
*vertices
, struct isl_tab
*tab
, int *selection
)
604 struct isl_tab_undo
*snap
;
605 struct isl_chamber_list
*c
= NULL
;
607 for (i
= 0; i
< vertices
->n_vertices
; ++i
)
611 snap
= isl_tab_snap(tab
);
613 for (i
= 0; i
< tab
->n_con
&& tab
->con
[i
].frozen
; ++i
)
614 tab
->con
[i
].frozen
= 0;
617 if (isl_tab_detect_redundant(tab
) < 0)
620 c
= isl_calloc_type(tab
->mat
->ctx
, struct isl_chamber_list
);
623 c
->c
.vertices
= isl_alloc_array(tab
->mat
->ctx
, int, n_vertices
);
624 if (n_vertices
&& !c
->c
.vertices
)
626 c
->c
.dom
= isl_basic_set_copy(isl_tab_peek_bset(tab
));
627 c
->c
.dom
= isl_basic_set_set_rational(c
->c
.dom
);
628 c
->c
.dom
= isl_basic_set_cow(c
->c
.dom
);
629 c
->c
.dom
= isl_basic_set_update_from_tab(c
->c
.dom
, tab
);
630 c
->c
.dom
= isl_basic_set_simplify(c
->c
.dom
);
631 c
->c
.dom
= isl_basic_set_finalize(c
->c
.dom
);
635 c
->c
.n_vertices
= n_vertices
;
637 for (i
= 0, j
= 0; i
< vertices
->n_vertices
; ++i
)
639 c
->c
.vertices
[j
] = i
;
646 for (i
= 0; i
< n_frozen
; ++i
)
647 tab
->con
[i
].frozen
= 1;
649 if (isl_tab_rollback(tab
, snap
) < 0)
654 free_chamber_list(c
);
658 struct isl_facet_todo
{
659 struct isl_tab
*tab
; /* A tableau representation of the facet */
660 isl_basic_set
*bset
; /* A normalized basic set representation */
661 isl_vec
*constraint
; /* Constraint pointing to the other side */
662 struct isl_facet_todo
*next
;
665 static void free_todo(struct isl_facet_todo
*todo
)
668 struct isl_facet_todo
*next
= todo
->next
;
670 isl_tab_free(todo
->tab
);
671 isl_basic_set_free(todo
->bset
);
672 isl_vec_free(todo
->constraint
);
679 static struct isl_facet_todo
*create_todo(struct isl_tab
*tab
, int con
)
683 struct isl_tab_undo
*snap
;
684 struct isl_facet_todo
*todo
;
686 snap
= isl_tab_snap(tab
);
688 for (i
= 0; i
< tab
->n_con
&& tab
->con
[i
].frozen
; ++i
)
689 tab
->con
[i
].frozen
= 0;
692 if (isl_tab_detect_redundant(tab
) < 0)
695 todo
= isl_calloc_type(tab
->mat
->ctx
, struct isl_facet_todo
);
699 todo
->constraint
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
700 if (!todo
->constraint
)
702 isl_seq_neg(todo
->constraint
->el
, tab
->bmap
->ineq
[con
], 1 + tab
->n_var
);
703 todo
->bset
= isl_basic_set_copy(isl_tab_peek_bset(tab
));
704 todo
->bset
= isl_basic_set_set_rational(todo
->bset
);
705 todo
->bset
= isl_basic_set_cow(todo
->bset
);
706 todo
->bset
= isl_basic_set_update_from_tab(todo
->bset
, tab
);
707 todo
->bset
= isl_basic_set_simplify(todo
->bset
);
708 todo
->bset
= isl_basic_set_sort_constraints(todo
->bset
);
711 ISL_F_SET(todo
->bset
, ISL_BASIC_SET_NO_REDUNDANT
);
712 todo
->tab
= isl_tab_dup(tab
);
716 for (i
= 0; i
< n_frozen
; ++i
)
717 tab
->con
[i
].frozen
= 1;
719 if (isl_tab_rollback(tab
, snap
) < 0)
728 /* Create todo items for all interior facets of the chamber represented
729 * by "tab" and collect them in "next".
731 static int init_todo(struct isl_facet_todo
**next
, struct isl_tab
*tab
)
734 struct isl_tab_undo
*snap
;
735 struct isl_facet_todo
*todo
;
737 snap
= isl_tab_snap(tab
);
739 for (i
= 0; i
< tab
->n_con
; ++i
) {
740 if (tab
->con
[i
].frozen
)
742 if (tab
->con
[i
].is_redundant
)
745 if (isl_tab_select_facet(tab
, i
) < 0)
748 todo
= create_todo(tab
, i
);
755 if (isl_tab_rollback(tab
, snap
) < 0)
762 /* Does the linked list contain a todo item that is the opposite of "todo".
763 * If so, return 1 and remove the opposite todo item.
765 static int has_opposite(struct isl_facet_todo
*todo
,
766 struct isl_facet_todo
**list
)
768 for (; *list
; list
= &(*list
)->next
) {
770 eq
= isl_basic_set_plain_is_equal(todo
->bset
, (*list
)->bset
);
785 /* Create todo items for all interior facets of the chamber represented
786 * by "tab" and collect them in first->next, taking care to cancel
787 * opposite todo items.
789 static int update_todo(struct isl_facet_todo
*first
, struct isl_tab
*tab
)
792 struct isl_tab_undo
*snap
;
793 struct isl_facet_todo
*todo
;
795 snap
= isl_tab_snap(tab
);
797 for (i
= 0; i
< tab
->n_con
; ++i
) {
800 if (tab
->con
[i
].frozen
)
802 if (tab
->con
[i
].is_redundant
)
805 if (isl_tab_select_facet(tab
, i
) < 0)
808 todo
= create_todo(tab
, i
);
812 drop
= has_opposite(todo
, &first
->next
);
819 todo
->next
= first
->next
;
823 if (isl_tab_rollback(tab
, snap
) < 0)
830 /* Compute the chamber decomposition of the parametric polytope respresented
831 * by "bset" given the parametric vertices and their activity domains.
833 * We are only interested in full-dimensional chambers.
834 * Each of these chambers is the intersection of the activity domains of
835 * one or more vertices and the union of all chambers is equal to the
836 * projection of the entire parametric polytope onto the parameter space.
838 * We first create an initial chamber by intersecting as many activity
839 * domains as possible without ending up with an empty or lower-dimensional
840 * set. As a minor optimization, we only consider those activity domains
841 * that contain some arbitrary point.
843 * For each of the interior facets of the chamber, we construct a todo item,
844 * containing the facet and a constraint containing the other side of the facet,
845 * for constructing the chamber on the other side.
846 * While their are any todo items left, we pick a todo item and
847 * create the required chamber by intersecting all activity domains
848 * that contain the facet and have a full-dimensional intersection with
849 * the other side of the facet. For each of the interior facets, we
850 * again create todo items, taking care to cancel opposite todo items.
852 static __isl_give isl_vertices
*compute_chambers(__isl_take isl_basic_set
*bset
,
853 __isl_take isl_vertices
*vertices
)
857 isl_vec
*sample
= NULL
;
858 struct isl_tab
*tab
= NULL
;
859 struct isl_tab_undo
*snap
;
860 int *selection
= NULL
;
862 struct isl_chamber_list
*list
= NULL
;
863 struct isl_facet_todo
*todo
= NULL
;
865 if (!bset
|| !vertices
)
868 ctx
= isl_vertices_get_ctx(vertices
);
869 selection
= isl_alloc_array(ctx
, int, vertices
->n_vertices
);
870 if (vertices
->n_vertices
&& !selection
)
873 bset
= isl_basic_set_params(bset
);
875 tab
= isl_tab_from_basic_set(bset
, 1);
878 for (i
= 0; i
< bset
->n_ineq
; ++i
)
879 if (isl_tab_freeze_constraint(tab
, i
) < 0)
881 isl_basic_set_free(bset
);
883 snap
= isl_tab_snap(tab
);
885 sample
= isl_tab_get_sample_value(tab
);
887 for (i
= 0; i
< vertices
->n_vertices
; ++i
) {
888 selection
[i
] = isl_basic_set_contains(vertices
->v
[i
].dom
, sample
);
889 if (selection
[i
] < 0)
893 selection
[i
] = can_intersect(tab
, vertices
->v
[i
].dom
);
894 if (selection
[i
] < 0)
898 if (isl_tab_detect_redundant(tab
) < 0)
901 if (add_chamber(&list
, vertices
, tab
, selection
) < 0)
905 if (init_todo(&todo
, tab
) < 0)
909 struct isl_facet_todo
*next
;
911 if (isl_tab_rollback(tab
, snap
) < 0)
914 if (isl_tab_add_ineq(tab
, todo
->constraint
->el
) < 0)
916 if (isl_tab_freeze_constraint(tab
, tab
->n_con
- 1) < 0)
919 for (i
= 0; i
< vertices
->n_vertices
; ++i
) {
920 selection
[i
] = bset_covers_tab(vertices
->v
[i
].dom
,
922 if (selection
[i
] < 0)
926 selection
[i
] = can_intersect(tab
, vertices
->v
[i
].dom
);
927 if (selection
[i
] < 0)
931 if (isl_tab_detect_redundant(tab
) < 0)
934 if (add_chamber(&list
, vertices
, tab
, selection
) < 0)
938 if (update_todo(todo
, tab
) < 0)
947 isl_vec_free(sample
);
952 vertices
= vertices_add_chambers(vertices
, n_chambers
, list
);
954 for (i
= 0; vertices
&& i
< vertices
->n_vertices
; ++i
) {
955 isl_basic_set_free(vertices
->v
[i
].dom
);
956 vertices
->v
[i
].dom
= NULL
;
961 free_chamber_list(list
);
963 isl_vec_free(sample
);
967 isl_basic_set_free(bset
);
968 isl_vertices_free(vertices
);
972 isl_ctx
*isl_vertex_get_ctx(__isl_keep isl_vertex
*vertex
)
974 return vertex
? isl_vertices_get_ctx(vertex
->vertices
) : NULL
;
977 int isl_vertex_get_id(__isl_keep isl_vertex
*vertex
)
979 return vertex
? vertex
->id
: -1;
982 /* Return the activity domain of the vertex "vertex".
984 __isl_give isl_basic_set
*isl_vertex_get_domain(__isl_keep isl_vertex
*vertex
)
986 struct isl_vertex
*v
;
991 v
= &vertex
->vertices
->v
[vertex
->id
];
993 v
->dom
= isl_basic_set_copy(v
->vertex
);
994 v
->dom
= isl_basic_set_params(v
->dom
);
995 v
->dom
= isl_basic_set_set_integral(v
->dom
);
998 return isl_basic_set_copy(v
->dom
);
1001 /* Return a multiple quasi-affine expression describing the vertex "vertex"
1002 * in terms of the parameters,
1004 __isl_give isl_multi_aff
*isl_vertex_get_expr(__isl_keep isl_vertex
*vertex
)
1006 struct isl_vertex
*v
;
1007 isl_basic_set
*bset
;
1012 v
= &vertex
->vertices
->v
[vertex
->id
];
1014 bset
= isl_basic_set_copy(v
->vertex
);
1015 return isl_multi_aff_from_basic_set_equalities(bset
);
1018 static __isl_give isl_vertex
*isl_vertex_alloc(__isl_take isl_vertices
*vertices
,
1027 ctx
= isl_vertices_get_ctx(vertices
);
1028 vertex
= isl_alloc_type(ctx
, isl_vertex
);
1032 vertex
->vertices
= vertices
;
1037 isl_vertices_free(vertices
);
1041 __isl_null isl_vertex
*isl_vertex_free(__isl_take isl_vertex
*vertex
)
1045 isl_vertices_free(vertex
->vertices
);
1051 isl_ctx
*isl_cell_get_ctx(__isl_keep isl_cell
*cell
)
1053 return cell
? cell
->dom
->ctx
: NULL
;
1056 __isl_give isl_basic_set
*isl_cell_get_domain(__isl_keep isl_cell
*cell
)
1058 return cell
? isl_basic_set_copy(cell
->dom
) : NULL
;
1061 static __isl_give isl_cell
*isl_cell_alloc(__isl_take isl_vertices
*vertices
,
1062 __isl_take isl_basic_set
*dom
, int id
)
1065 isl_cell
*cell
= NULL
;
1067 if (!vertices
|| !dom
)
1070 cell
= isl_calloc_type(dom
->ctx
, isl_cell
);
1074 cell
->n_vertices
= vertices
->c
[id
].n_vertices
;
1075 cell
->ids
= isl_alloc_array(dom
->ctx
, int, cell
->n_vertices
);
1076 if (cell
->n_vertices
&& !cell
->ids
)
1078 for (i
= 0; i
< cell
->n_vertices
; ++i
)
1079 cell
->ids
[i
] = vertices
->c
[id
].vertices
[i
];
1080 cell
->vertices
= vertices
;
1085 isl_cell_free(cell
);
1086 isl_vertices_free(vertices
);
1087 isl_basic_set_free(dom
);
1091 __isl_null isl_cell
*isl_cell_free(__isl_take isl_cell
*cell
)
1096 isl_vertices_free(cell
->vertices
);
1098 isl_basic_set_free(cell
->dom
);
1104 /* Create a tableau of the cone obtained by first homogenizing the given
1105 * polytope and then making all inequalities strict by setting the
1106 * constant term to -1.
1108 static struct isl_tab
*tab_for_shifted_cone(__isl_keep isl_basic_set
*bset
)
1112 struct isl_tab
*tab
;
1116 tab
= isl_tab_alloc(bset
->ctx
, bset
->n_eq
+ bset
->n_ineq
+ 1,
1117 1 + isl_basic_set_total_dim(bset
), 0);
1120 tab
->rational
= ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
);
1121 if (ISL_F_ISSET(bset
, ISL_BASIC_MAP_EMPTY
)) {
1122 if (isl_tab_mark_empty(tab
) < 0)
1127 c
= isl_vec_alloc(bset
->ctx
, 1 + 1 + isl_basic_set_total_dim(bset
));
1131 isl_int_set_si(c
->el
[0], 0);
1132 for (i
= 0; i
< bset
->n_eq
; ++i
) {
1133 isl_seq_cpy(c
->el
+ 1, bset
->eq
[i
], c
->size
- 1);
1134 if (isl_tab_add_eq(tab
, c
->el
) < 0)
1138 isl_int_set_si(c
->el
[0], -1);
1139 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
1140 isl_seq_cpy(c
->el
+ 1, bset
->ineq
[i
], c
->size
- 1);
1141 if (isl_tab_add_ineq(tab
, c
->el
) < 0)
1149 isl_seq_clr(c
->el
+ 1, c
->size
- 1);
1150 isl_int_set_si(c
->el
[1], 1);
1151 if (isl_tab_add_ineq(tab
, c
->el
) < 0)
1162 /* Compute an interior point of "bset" by selecting an interior
1163 * point in homogeneous space and projecting the point back down.
1165 static __isl_give isl_vec
*isl_basic_set_interior_point(
1166 __isl_keep isl_basic_set
*bset
)
1169 struct isl_tab
*tab
;
1171 tab
= tab_for_shifted_cone(bset
);
1172 vec
= isl_tab_get_sample_value(tab
);
1177 isl_seq_cpy(vec
->el
, vec
->el
+ 1, vec
->size
- 1);
1183 /* Call "fn" on all chambers of the parametric polytope with the shared
1184 * facets of neighboring chambers only appearing in one of the chambers.
1186 * We pick an interior point from one of the chambers and then make
1187 * all constraints that do not satisfy this point strict.
1188 * For constraints that saturate the interior point, the sign
1189 * of the first non-zero coefficient is used to determine which
1190 * of the two (internal) constraints should be tightened.
1192 isl_stat
isl_vertices_foreach_disjoint_cell(__isl_keep isl_vertices
*vertices
,
1193 isl_stat (*fn
)(__isl_take isl_cell
*cell
, void *user
), void *user
)
1200 return isl_stat_error
;
1202 if (vertices
->n_chambers
== 0)
1205 if (vertices
->n_chambers
== 1) {
1206 isl_basic_set
*dom
= isl_basic_set_copy(vertices
->c
[0].dom
);
1207 dom
= isl_basic_set_set_integral(dom
);
1208 cell
= isl_cell_alloc(isl_vertices_copy(vertices
), dom
, 0);
1210 return isl_stat_error
;
1211 return fn(cell
, user
);
1214 vec
= isl_basic_set_interior_point(vertices
->c
[0].dom
);
1216 return isl_stat_error
;
1218 for (i
= 0; i
< vertices
->n_chambers
; ++i
) {
1220 isl_basic_set
*dom
= isl_basic_set_copy(vertices
->c
[i
].dom
);
1222 dom
= isl_basic_set_tighten_outward(dom
, vec
);
1223 dom
= isl_basic_set_set_integral(dom
);
1224 cell
= isl_cell_alloc(isl_vertices_copy(vertices
), dom
, i
);
1237 return isl_stat_error
;
1240 isl_stat
isl_vertices_foreach_cell(__isl_keep isl_vertices
*vertices
,
1241 isl_stat (*fn
)(__isl_take isl_cell
*cell
, void *user
), void *user
)
1247 return isl_stat_error
;
1249 if (vertices
->n_chambers
== 0)
1252 for (i
= 0; i
< vertices
->n_chambers
; ++i
) {
1254 isl_basic_set
*dom
= isl_basic_set_copy(vertices
->c
[i
].dom
);
1256 cell
= isl_cell_alloc(isl_vertices_copy(vertices
), dom
, i
);
1258 return isl_stat_error
;
1262 return isl_stat_error
;
1268 isl_stat
isl_vertices_foreach_vertex(__isl_keep isl_vertices
*vertices
,
1269 isl_stat (*fn
)(__isl_take isl_vertex
*vertex
, void *user
), void *user
)
1275 return isl_stat_error
;
1277 if (vertices
->n_vertices
== 0)
1280 for (i
= 0; i
< vertices
->n_vertices
; ++i
) {
1283 vertex
= isl_vertex_alloc(isl_vertices_copy(vertices
), i
);
1285 return isl_stat_error
;
1287 r
= fn(vertex
, user
);
1289 return isl_stat_error
;
1295 isl_stat
isl_cell_foreach_vertex(__isl_keep isl_cell
*cell
,
1296 isl_stat (*fn
)(__isl_take isl_vertex
*vertex
, void *user
), void *user
)
1302 return isl_stat_error
;
1304 if (cell
->n_vertices
== 0)
1307 for (i
= 0; i
< cell
->n_vertices
; ++i
) {
1310 vertex
= isl_vertex_alloc(isl_vertices_copy(cell
->vertices
),
1313 return isl_stat_error
;
1315 r
= fn(vertex
, user
);
1317 return isl_stat_error
;
1323 isl_ctx
*isl_vertices_get_ctx(__isl_keep isl_vertices
*vertices
)
1325 return vertices
? vertices
->bset
->ctx
: NULL
;
1328 int isl_vertices_get_n_vertices(__isl_keep isl_vertices
*vertices
)
1330 return vertices
? vertices
->n_vertices
: -1;
1333 __isl_give isl_vertices
*isl_morph_vertices(__isl_take isl_morph
*morph
,
1334 __isl_take isl_vertices
*vertices
)
1337 isl_morph
*param_morph
= NULL
;
1339 if (!morph
|| !vertices
)
1342 isl_assert(vertices
->bset
->ctx
, vertices
->ref
== 1, goto error
);
1344 param_morph
= isl_morph_copy(morph
);
1345 param_morph
= isl_morph_dom_params(param_morph
);
1346 param_morph
= isl_morph_ran_params(param_morph
);
1348 for (i
= 0; i
< vertices
->n_vertices
; ++i
) {
1349 vertices
->v
[i
].dom
= isl_morph_basic_set(
1350 isl_morph_copy(param_morph
), vertices
->v
[i
].dom
);
1351 vertices
->v
[i
].vertex
= isl_morph_basic_set(
1352 isl_morph_copy(morph
), vertices
->v
[i
].vertex
);
1353 if (!vertices
->v
[i
].vertex
)
1357 for (i
= 0; i
< vertices
->n_chambers
; ++i
) {
1358 vertices
->c
[i
].dom
= isl_morph_basic_set(
1359 isl_morph_copy(param_morph
), vertices
->c
[i
].dom
);
1360 if (!vertices
->c
[i
].dom
)
1364 isl_morph_free(param_morph
);
1365 isl_morph_free(morph
);
1368 isl_morph_free(param_morph
);
1369 isl_morph_free(morph
);
1370 isl_vertices_free(vertices
);
1374 /* Construct a simplex isl_cell spanned by the vertices with indices in
1375 * "simplex_ids" and "other_ids" and call "fn" on this isl_cell.
1377 static isl_stat
call_on_simplex(__isl_keep isl_cell
*cell
,
1378 int *simplex_ids
, int n_simplex
, int *other_ids
, int n_other
,
1379 isl_stat (*fn
)(__isl_take isl_cell
*simplex
, void *user
), void *user
)
1383 struct isl_cell
*simplex
;
1385 ctx
= isl_cell_get_ctx(cell
);
1387 simplex
= isl_calloc_type(ctx
, struct isl_cell
);
1389 return isl_stat_error
;
1390 simplex
->vertices
= isl_vertices_copy(cell
->vertices
);
1391 if (!simplex
->vertices
)
1393 simplex
->dom
= isl_basic_set_copy(cell
->dom
);
1396 simplex
->n_vertices
= n_simplex
+ n_other
;
1397 simplex
->ids
= isl_alloc_array(ctx
, int, simplex
->n_vertices
);
1401 for (i
= 0; i
< n_simplex
; ++i
)
1402 simplex
->ids
[i
] = simplex_ids
[i
];
1403 for (i
= 0; i
< n_other
; ++i
)
1404 simplex
->ids
[n_simplex
+ i
] = other_ids
[i
];
1406 return fn(simplex
, user
);
1408 isl_cell_free(simplex
);
1409 return isl_stat_error
;
1412 /* Check whether the parametric vertex described by "vertex"
1413 * lies on the facet corresponding to constraint "facet" of "bset".
1414 * The isl_vec "v" is a temporary vector than can be used by this function.
1416 * We eliminate the variables from the facet constraint using the
1417 * equalities defining the vertex and check if the result is identical
1420 * It would probably be better to keep track of the constraints defining
1421 * a vertex during the vertex construction so that we could simply look
1424 static int vertex_on_facet(__isl_keep isl_basic_set
*vertex
,
1425 __isl_keep isl_basic_set
*bset
, int facet
, __isl_keep isl_vec
*v
)
1430 isl_seq_cpy(v
->el
, bset
->ineq
[facet
], v
->size
);
1433 for (i
= 0; i
< vertex
->n_eq
; ++i
) {
1434 int k
= isl_seq_last_non_zero(vertex
->eq
[i
], v
->size
);
1435 isl_seq_elim(v
->el
, vertex
->eq
[i
], k
, v
->size
, &m
);
1439 return isl_seq_first_non_zero(v
->el
, v
->size
) == -1;
1442 /* Triangulate the polytope spanned by the vertices with ids
1443 * in "simplex_ids" and "other_ids" and call "fn" on each of
1444 * the resulting simplices.
1445 * If the input polytope is already a simplex, we simply call "fn".
1446 * Otherwise, we pick a point from "other_ids" and add it to "simplex_ids".
1447 * Then we consider each facet of "bset" that does not contain the point
1448 * we just picked, but does contain some of the other points in "other_ids"
1449 * and call ourselves recursively on the polytope spanned by the new
1450 * "simplex_ids" and those points in "other_ids" that lie on the facet.
1452 static isl_stat
triangulate(__isl_keep isl_cell
*cell
, __isl_keep isl_vec
*v
,
1453 int *simplex_ids
, int n_simplex
, int *other_ids
, int n_other
,
1454 isl_stat (*fn
)(__isl_take isl_cell
*simplex
, void *user
), void *user
)
1460 isl_basic_set
*vertex
;
1461 isl_basic_set
*bset
;
1463 ctx
= isl_cell_get_ctx(cell
);
1464 d
= isl_basic_set_dim(cell
->vertices
->bset
, isl_dim_set
);
1465 nparam
= isl_basic_set_dim(cell
->vertices
->bset
, isl_dim_param
);
1467 if (n_simplex
+ n_other
== d
+ 1)
1468 return call_on_simplex(cell
, simplex_ids
, n_simplex
,
1469 other_ids
, n_other
, fn
, user
);
1471 simplex_ids
[n_simplex
] = other_ids
[0];
1472 vertex
= cell
->vertices
->v
[other_ids
[0]].vertex
;
1473 bset
= cell
->vertices
->bset
;
1475 ids
= isl_alloc_array(ctx
, int, n_other
- 1);
1478 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
1479 if (isl_seq_first_non_zero(bset
->ineq
[i
] + 1 + nparam
, d
) == -1)
1481 if (vertex_on_facet(vertex
, bset
, i
, v
))
1484 for (j
= 1, k
= 0; j
< n_other
; ++j
) {
1486 ov
= cell
->vertices
->v
[other_ids
[j
]].vertex
;
1487 if (vertex_on_facet(ov
, bset
, i
, v
))
1488 ids
[k
++] = other_ids
[j
];
1493 if (triangulate(cell
, v
, simplex_ids
, n_simplex
+ 1,
1494 ids
, k
, fn
, user
) < 0)
1502 return isl_stat_error
;
1505 /* Triangulate the given cell and call "fn" on each of the resulting
1508 isl_stat
isl_cell_foreach_simplex(__isl_take isl_cell
*cell
,
1509 isl_stat (*fn
)(__isl_take isl_cell
*simplex
, void *user
), void *user
)
1515 int *simplex_ids
= NULL
;
1518 return isl_stat_error
;
1520 d
= isl_basic_set_dim(cell
->vertices
->bset
, isl_dim_set
);
1521 total
= isl_basic_set_total_dim(cell
->vertices
->bset
);
1523 if (cell
->n_vertices
== d
+ 1)
1524 return fn(cell
, user
);
1526 ctx
= isl_cell_get_ctx(cell
);
1527 simplex_ids
= isl_alloc_array(ctx
, int, d
+ 1);
1531 v
= isl_vec_alloc(ctx
, 1 + total
);
1535 r
= triangulate(cell
, v
, simplex_ids
, 0,
1536 cell
->ids
, cell
->n_vertices
, fn
, user
);
1541 isl_cell_free(cell
);
1547 isl_cell_free(cell
);
1548 return isl_stat_error
;