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 int isl_mat_rank(__isl_keep isl_mat
*mat
)
237 H
= isl_mat_left_hermite(isl_mat_copy(mat
), 0, NULL
, NULL
);
241 for (col
= 0; col
< H
->n_col
; ++col
) {
242 for (row
= 0; row
< H
->n_row
; ++row
)
243 if (!isl_int_is_zero(H
->row
[row
][col
]))
254 /* Is the row pointed to by "f" linearly independent of the "n" first
257 static int is_independent(__isl_keep isl_mat
*facets
, int n
, isl_int
*f
)
261 if (isl_seq_first_non_zero(f
, facets
->n_col
) < 0)
264 isl_seq_cpy(facets
->row
[n
], f
, facets
->n_col
);
265 facets
->n_row
= n
+ 1;
266 rank
= isl_mat_rank(facets
);
270 return rank
== n
+ 1;
273 /* Check whether we can select constraint "level", given the current selection
274 * reflected by facets in "tab", the rows of "facets" and the earlier
275 * "selected" elements of "selection".
277 * If the constraint is (strictly) redundant in the tableau, selecting it would
278 * result in an empty tableau, so it can't be selected.
279 * If the set variable part of the constraint is not linearly independent
280 * of the set variable parts of the already selected constraints,
281 * the constraint cannot be selected.
282 * If selecting the constraint results in an empty tableau, the constraint
283 * cannot be selected.
284 * Finally, if selecting the constraint results in some explicitly
285 * deselected constraints turning into equalities, then the corresponding
286 * vertices have already been generated, so the constraint cannot be selected.
288 static int can_select(__isl_keep isl_basic_set
*bset
, int level
,
289 struct isl_tab
*tab
, __isl_keep isl_mat
*facets
, int selected
,
295 struct isl_tab_undo
*snap
;
297 if (isl_tab_is_redundant(tab
, level
))
300 ovar
= isl_space_offset(bset
->dim
, isl_dim_set
);
302 indep
= is_independent(facets
, selected
, bset
->ineq
[level
] + 1 + ovar
);
308 snap
= isl_tab_snap(tab
);
309 if (isl_tab_select_facet(tab
, level
) < 0)
313 if (isl_tab_rollback(tab
, snap
) < 0)
318 for (i
= 0; i
< level
; ++i
) {
321 if (selection
[i
] != DESELECTED
)
324 if (isl_tab_is_equality(tab
, i
))
326 else if (isl_tab_is_redundant(tab
, i
))
329 sgn
= isl_tab_sign_of_max(tab
, i
);
333 if (isl_tab_rollback(tab
, snap
) < 0)
342 /* Compute the parametric vertices and the chamber decomposition
343 * of a parametric polytope that is not full-dimensional.
345 * Simply map the parametric polytope to a lower dimensional space
346 * and map the resulting vertices back.
348 static __isl_give isl_vertices
*lower_dim_vertices(
349 __isl_keep isl_basic_set
*bset
)
352 isl_vertices
*vertices
;
354 bset
= isl_basic_set_copy(bset
);
355 morph
= isl_basic_set_full_compression(bset
);
356 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
358 vertices
= isl_basic_set_compute_vertices(bset
);
359 isl_basic_set_free(bset
);
361 morph
= isl_morph_inverse(morph
);
363 vertices
= isl_morph_vertices(morph
, vertices
);
368 /* Compute the parametric vertices and the chamber decomposition
369 * of the parametric polytope defined using the same constraints
370 * as "bset". "bset" is assumed to have no existentially quantified
373 * The vertices themselves are computed in a fairly simplistic way.
374 * We simply run through all combinations of d constraints,
375 * with d the number of set variables, and check if those d constraints
376 * define a vertex. To avoid the generation of duplicate vertices,
377 * which we may happen if a vertex is defined by more that d constraints,
378 * we make sure we only generate the vertex for the d constraints with
381 * We set up a tableau and keep track of which facets have been
382 * selected. The tableau is marked strict_redundant so that we can be
383 * sure that any constraint that is marked redundant (and that is not
384 * also marked zero) is not an equality.
385 * If a constraint is marked DESELECTED, it means the constraint was
386 * SELECTED before (in combination with the same selection of earlier
387 * constraints). If such a deselected constraint turns out to be an
388 * equality, then any vertex that may still be found with the current
389 * selection has already been generated when the constraint was selected.
390 * A constraint is marked UNSELECTED when there is no way selecting
391 * the constraint could lead to a vertex (in combination with the current
392 * selection of earlier constraints).
394 * The set variable coefficients of the selected constraints are stored
395 * in the facets matrix.
397 __isl_give isl_vertices
*isl_basic_set_compute_vertices(
398 __isl_keep isl_basic_set
*bset
)
404 int *selection
= NULL
;
406 struct isl_tab_undo
**snap
= NULL
;
407 isl_mat
*facets
= NULL
;
408 struct isl_vertex_list
*list
= NULL
;
410 isl_vertices
*vertices
;
415 if (isl_basic_set_plain_is_empty(bset
))
416 return vertices_empty(bset
);
419 return lower_dim_vertices(bset
);
421 isl_assert(bset
->ctx
, isl_basic_set_dim(bset
, isl_dim_div
) == 0,
424 if (isl_basic_set_dim(bset
, isl_dim_set
) == 0)
425 return vertices_0D(bset
);
427 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
429 bset
= isl_basic_set_copy(bset
);
430 bset
= isl_basic_set_set_rational(bset
);
434 tab
= isl_tab_from_basic_set(bset
, 0);
437 tab
->strict_redundant
= 1;
440 vertices
= vertices_empty(bset
);
441 isl_basic_set_free(bset
);
446 selection
= isl_alloc_array(bset
->ctx
, int, bset
->n_ineq
);
447 snap
= isl_alloc_array(bset
->ctx
, struct isl_tab_undo
*, bset
->n_ineq
);
448 facets
= isl_mat_alloc(bset
->ctx
, nvar
, nvar
);
449 if ((bset
->n_ineq
&& (!selection
|| !snap
)) || !facets
)
457 if (level
>= bset
->n_ineq
||
458 (!init
&& selection
[level
] != SELECTED
)) {
465 snap
[level
] = isl_tab_snap(tab
);
466 ok
= can_select(bset
, level
, tab
, facets
, selected
,
471 selection
[level
] = SELECTED
;
474 selection
[level
] = UNSELECTED
;
476 selection
[level
] = DESELECTED
;
478 if (isl_tab_rollback(tab
, snap
[level
]) < 0)
481 if (selected
== nvar
) {
482 if (tab
->n_dead
== nvar
) {
483 isl_bool added
= add_vertex(&list
, bset
, tab
);
496 isl_mat_free(facets
);
502 vertices
= vertices_from_list(bset
, n_vertices
, list
);
504 vertices
= compute_chambers(bset
, vertices
);
508 free_vertex_list(list
);
509 isl_mat_free(facets
);
513 isl_basic_set_free(bset
);
517 struct isl_chamber_list
{
518 struct isl_chamber c
;
519 struct isl_chamber_list
*next
;
522 static void free_chamber_list(struct isl_chamber_list
*list
)
524 struct isl_chamber_list
*next
;
526 for (; list
; list
= next
) {
528 isl_basic_set_free(list
->c
.dom
);
529 free(list
->c
.vertices
);
534 /* Check whether the basic set "bset" is a superset of the basic set described
535 * by "tab", i.e., check whether all constraints of "bset" are redundant.
537 static isl_bool
bset_covers_tab(__isl_keep isl_basic_set
*bset
,
543 return isl_bool_error
;
545 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
546 enum isl_ineq_type type
= isl_tab_ineq_type(tab
, bset
->ineq
[i
]);
548 case isl_ineq_error
: return isl_bool_error
;
549 case isl_ineq_redundant
: continue;
550 default: return isl_bool_false
;
554 return isl_bool_true
;
557 static __isl_give isl_vertices
*vertices_add_chambers(
558 __isl_take isl_vertices
*vertices
, int n_chambers
,
559 struct isl_chamber_list
*list
)
563 struct isl_chamber_list
*next
;
565 ctx
= isl_vertices_get_ctx(vertices
);
566 vertices
->c
= isl_alloc_array(ctx
, struct isl_chamber
, n_chambers
);
569 vertices
->n_chambers
= n_chambers
;
571 for (i
= 0; list
; list
= next
, i
++) {
573 vertices
->c
[i
] = list
->c
;
579 isl_vertices_free(vertices
);
580 free_chamber_list(list
);
584 /* Can "tab" be intersected with "bset" without resulting in
585 * a lower-dimensional set.
586 * "bset" itself is assumed to be full-dimensional.
588 static isl_bool
can_intersect(struct isl_tab
*tab
,
589 __isl_keep isl_basic_set
*bset
)
592 struct isl_tab_undo
*snap
;
595 isl_die(isl_basic_set_get_ctx(bset
), isl_error_internal
,
596 "expecting full-dimensional input",
597 return isl_bool_error
);
599 if (isl_tab_extend_cons(tab
, bset
->n_ineq
) < 0)
600 return isl_bool_error
;
602 snap
= isl_tab_snap(tab
);
604 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
605 if (isl_tab_ineq_type(tab
, bset
->ineq
[i
]) == isl_ineq_redundant
)
607 if (isl_tab_add_ineq(tab
, bset
->ineq
[i
]) < 0)
608 return isl_bool_error
;
611 if (isl_tab_detect_implicit_equalities(tab
) < 0)
612 return isl_bool_error
;
614 if (isl_tab_rollback(tab
, snap
) < 0)
615 return isl_bool_error
;
616 return isl_bool_false
;
619 return isl_bool_true
;
622 static int add_chamber(struct isl_chamber_list
**list
,
623 __isl_keep isl_vertices
*vertices
, struct isl_tab
*tab
, int *selection
)
628 struct isl_tab_undo
*snap
;
629 struct isl_chamber_list
*c
= NULL
;
631 for (i
= 0; i
< vertices
->n_vertices
; ++i
)
635 snap
= isl_tab_snap(tab
);
637 for (i
= 0; i
< tab
->n_con
&& tab
->con
[i
].frozen
; ++i
)
638 tab
->con
[i
].frozen
= 0;
641 if (isl_tab_detect_redundant(tab
) < 0)
644 c
= isl_calloc_type(tab
->mat
->ctx
, struct isl_chamber_list
);
647 c
->c
.vertices
= isl_alloc_array(tab
->mat
->ctx
, int, n_vertices
);
648 if (n_vertices
&& !c
->c
.vertices
)
650 c
->c
.dom
= isl_basic_set_copy(isl_tab_peek_bset(tab
));
651 c
->c
.dom
= isl_basic_set_set_rational(c
->c
.dom
);
652 c
->c
.dom
= isl_basic_set_cow(c
->c
.dom
);
653 c
->c
.dom
= isl_basic_set_update_from_tab(c
->c
.dom
, tab
);
654 c
->c
.dom
= isl_basic_set_simplify(c
->c
.dom
);
655 c
->c
.dom
= isl_basic_set_finalize(c
->c
.dom
);
659 c
->c
.n_vertices
= n_vertices
;
661 for (i
= 0, j
= 0; i
< vertices
->n_vertices
; ++i
)
663 c
->c
.vertices
[j
] = i
;
670 for (i
= 0; i
< n_frozen
; ++i
)
671 tab
->con
[i
].frozen
= 1;
673 if (isl_tab_rollback(tab
, snap
) < 0)
678 free_chamber_list(c
);
682 struct isl_facet_todo
{
683 struct isl_tab
*tab
; /* A tableau representation of the facet */
684 isl_basic_set
*bset
; /* A normalized basic set representation */
685 isl_vec
*constraint
; /* Constraint pointing to the other side */
686 struct isl_facet_todo
*next
;
689 static void free_todo(struct isl_facet_todo
*todo
)
692 struct isl_facet_todo
*next
= todo
->next
;
694 isl_tab_free(todo
->tab
);
695 isl_basic_set_free(todo
->bset
);
696 isl_vec_free(todo
->constraint
);
703 static struct isl_facet_todo
*create_todo(struct isl_tab
*tab
, int con
)
707 struct isl_tab_undo
*snap
;
708 struct isl_facet_todo
*todo
;
710 snap
= isl_tab_snap(tab
);
712 for (i
= 0; i
< tab
->n_con
&& tab
->con
[i
].frozen
; ++i
)
713 tab
->con
[i
].frozen
= 0;
716 if (isl_tab_detect_redundant(tab
) < 0)
719 todo
= isl_calloc_type(tab
->mat
->ctx
, struct isl_facet_todo
);
723 todo
->constraint
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
724 if (!todo
->constraint
)
726 isl_seq_neg(todo
->constraint
->el
, tab
->bmap
->ineq
[con
], 1 + tab
->n_var
);
727 todo
->bset
= isl_basic_set_copy(isl_tab_peek_bset(tab
));
728 todo
->bset
= isl_basic_set_set_rational(todo
->bset
);
729 todo
->bset
= isl_basic_set_cow(todo
->bset
);
730 todo
->bset
= isl_basic_set_update_from_tab(todo
->bset
, tab
);
731 todo
->bset
= isl_basic_set_simplify(todo
->bset
);
732 todo
->bset
= isl_basic_set_sort_constraints(todo
->bset
);
735 ISL_F_SET(todo
->bset
, ISL_BASIC_SET_NORMALIZED
);
736 todo
->tab
= isl_tab_dup(tab
);
740 for (i
= 0; i
< n_frozen
; ++i
)
741 tab
->con
[i
].frozen
= 1;
743 if (isl_tab_rollback(tab
, snap
) < 0)
752 /* Create todo items for all interior facets of the chamber represented
753 * by "tab" and collect them in "next".
755 static int init_todo(struct isl_facet_todo
**next
, struct isl_tab
*tab
)
758 struct isl_tab_undo
*snap
;
759 struct isl_facet_todo
*todo
;
761 snap
= isl_tab_snap(tab
);
763 for (i
= 0; i
< tab
->n_con
; ++i
) {
764 if (tab
->con
[i
].frozen
)
766 if (tab
->con
[i
].is_redundant
)
769 if (isl_tab_select_facet(tab
, i
) < 0)
772 todo
= create_todo(tab
, i
);
779 if (isl_tab_rollback(tab
, snap
) < 0)
786 /* Does the linked list contain a todo item that is the opposite of "todo".
787 * If so, return 1 and remove the opposite todo item.
789 static int has_opposite(struct isl_facet_todo
*todo
,
790 struct isl_facet_todo
**list
)
792 for (; *list
; list
= &(*list
)->next
) {
794 eq
= isl_basic_set_plain_is_equal(todo
->bset
, (*list
)->bset
);
809 /* Create todo items for all interior facets of the chamber represented
810 * by "tab" and collect them in first->next, taking care to cancel
811 * opposite todo items.
813 static int update_todo(struct isl_facet_todo
*first
, struct isl_tab
*tab
)
816 struct isl_tab_undo
*snap
;
817 struct isl_facet_todo
*todo
;
819 snap
= isl_tab_snap(tab
);
821 for (i
= 0; i
< tab
->n_con
; ++i
) {
824 if (tab
->con
[i
].frozen
)
826 if (tab
->con
[i
].is_redundant
)
829 if (isl_tab_select_facet(tab
, i
) < 0)
832 todo
= create_todo(tab
, i
);
836 drop
= has_opposite(todo
, &first
->next
);
843 todo
->next
= first
->next
;
847 if (isl_tab_rollback(tab
, snap
) < 0)
854 /* Compute the chamber decomposition of the parametric polytope respresented
855 * by "bset" given the parametric vertices and their activity domains.
857 * We are only interested in full-dimensional chambers.
858 * Each of these chambers is the intersection of the activity domains of
859 * one or more vertices and the union of all chambers is equal to the
860 * projection of the entire parametric polytope onto the parameter space.
862 * We first create an initial chamber by intersecting as many activity
863 * domains as possible without ending up with an empty or lower-dimensional
864 * set. As a minor optimization, we only consider those activity domains
865 * that contain some arbitrary point.
867 * For each of the interior facets of the chamber, we construct a todo item,
868 * containing the facet and a constraint containing the other side of the facet,
869 * for constructing the chamber on the other side.
870 * While their are any todo items left, we pick a todo item and
871 * create the required chamber by intersecting all activity domains
872 * that contain the facet and have a full-dimensional intersection with
873 * the other side of the facet. For each of the interior facets, we
874 * again create todo items, taking care to cancel opposite todo items.
876 static __isl_give isl_vertices
*compute_chambers(__isl_take isl_basic_set
*bset
,
877 __isl_take isl_vertices
*vertices
)
881 isl_vec
*sample
= NULL
;
882 struct isl_tab
*tab
= NULL
;
883 struct isl_tab_undo
*snap
;
884 int *selection
= NULL
;
886 struct isl_chamber_list
*list
= NULL
;
887 struct isl_facet_todo
*todo
= NULL
;
889 if (!bset
|| !vertices
)
892 ctx
= isl_vertices_get_ctx(vertices
);
893 selection
= isl_alloc_array(ctx
, int, vertices
->n_vertices
);
894 if (vertices
->n_vertices
&& !selection
)
897 bset
= isl_basic_set_params(bset
);
899 tab
= isl_tab_from_basic_set(bset
, 1);
902 for (i
= 0; i
< bset
->n_ineq
; ++i
)
903 if (isl_tab_freeze_constraint(tab
, i
) < 0)
905 isl_basic_set_free(bset
);
907 snap
= isl_tab_snap(tab
);
909 sample
= isl_tab_get_sample_value(tab
);
911 for (i
= 0; i
< vertices
->n_vertices
; ++i
) {
912 selection
[i
] = isl_basic_set_contains(vertices
->v
[i
].dom
, sample
);
913 if (selection
[i
] < 0)
917 selection
[i
] = can_intersect(tab
, vertices
->v
[i
].dom
);
918 if (selection
[i
] < 0)
922 if (isl_tab_detect_redundant(tab
) < 0)
925 if (add_chamber(&list
, vertices
, tab
, selection
) < 0)
929 if (init_todo(&todo
, tab
) < 0)
933 struct isl_facet_todo
*next
;
935 if (isl_tab_rollback(tab
, snap
) < 0)
938 if (isl_tab_add_ineq(tab
, todo
->constraint
->el
) < 0)
940 if (isl_tab_freeze_constraint(tab
, tab
->n_con
- 1) < 0)
943 for (i
= 0; i
< vertices
->n_vertices
; ++i
) {
944 selection
[i
] = bset_covers_tab(vertices
->v
[i
].dom
,
946 if (selection
[i
] < 0)
950 selection
[i
] = can_intersect(tab
, vertices
->v
[i
].dom
);
951 if (selection
[i
] < 0)
955 if (isl_tab_detect_redundant(tab
) < 0)
958 if (add_chamber(&list
, vertices
, tab
, selection
) < 0)
962 if (update_todo(todo
, tab
) < 0)
971 isl_vec_free(sample
);
976 vertices
= vertices_add_chambers(vertices
, n_chambers
, list
);
978 for (i
= 0; vertices
&& i
< vertices
->n_vertices
; ++i
) {
979 isl_basic_set_free(vertices
->v
[i
].dom
);
980 vertices
->v
[i
].dom
= NULL
;
985 free_chamber_list(list
);
987 isl_vec_free(sample
);
991 isl_basic_set_free(bset
);
992 isl_vertices_free(vertices
);
996 isl_ctx
*isl_vertex_get_ctx(__isl_keep isl_vertex
*vertex
)
998 return vertex
? isl_vertices_get_ctx(vertex
->vertices
) : NULL
;
1001 int isl_vertex_get_id(__isl_keep isl_vertex
*vertex
)
1003 return vertex
? vertex
->id
: -1;
1006 /* Return the activity domain of the vertex "vertex".
1008 __isl_give isl_basic_set
*isl_vertex_get_domain(__isl_keep isl_vertex
*vertex
)
1010 struct isl_vertex
*v
;
1015 v
= &vertex
->vertices
->v
[vertex
->id
];
1017 v
->dom
= isl_basic_set_copy(v
->vertex
);
1018 v
->dom
= isl_basic_set_params(v
->dom
);
1019 v
->dom
= isl_basic_set_set_integral(v
->dom
);
1022 return isl_basic_set_copy(v
->dom
);
1025 /* Return a multiple quasi-affine expression describing the vertex "vertex"
1026 * in terms of the parameters,
1028 __isl_give isl_multi_aff
*isl_vertex_get_expr(__isl_keep isl_vertex
*vertex
)
1030 struct isl_vertex
*v
;
1031 isl_basic_set
*bset
;
1036 v
= &vertex
->vertices
->v
[vertex
->id
];
1038 bset
= isl_basic_set_copy(v
->vertex
);
1039 return isl_multi_aff_from_basic_set_equalities(bset
);
1042 static __isl_give isl_vertex
*isl_vertex_alloc(__isl_take isl_vertices
*vertices
,
1051 ctx
= isl_vertices_get_ctx(vertices
);
1052 vertex
= isl_alloc_type(ctx
, isl_vertex
);
1056 vertex
->vertices
= vertices
;
1061 isl_vertices_free(vertices
);
1065 void isl_vertex_free(__isl_take isl_vertex
*vertex
)
1069 isl_vertices_free(vertex
->vertices
);
1073 isl_ctx
*isl_cell_get_ctx(__isl_keep isl_cell
*cell
)
1075 return cell
? cell
->dom
->ctx
: NULL
;
1078 __isl_give isl_basic_set
*isl_cell_get_domain(__isl_keep isl_cell
*cell
)
1080 return cell
? isl_basic_set_copy(cell
->dom
) : NULL
;
1083 static __isl_give isl_cell
*isl_cell_alloc(__isl_take isl_vertices
*vertices
,
1084 __isl_take isl_basic_set
*dom
, int id
)
1087 isl_cell
*cell
= NULL
;
1089 if (!vertices
|| !dom
)
1092 cell
= isl_calloc_type(dom
->ctx
, isl_cell
);
1096 cell
->n_vertices
= vertices
->c
[id
].n_vertices
;
1097 cell
->ids
= isl_alloc_array(dom
->ctx
, int, cell
->n_vertices
);
1098 if (cell
->n_vertices
&& !cell
->ids
)
1100 for (i
= 0; i
< cell
->n_vertices
; ++i
)
1101 cell
->ids
[i
] = vertices
->c
[id
].vertices
[i
];
1102 cell
->vertices
= vertices
;
1107 isl_cell_free(cell
);
1108 isl_vertices_free(vertices
);
1109 isl_basic_set_free(dom
);
1113 void isl_cell_free(__isl_take isl_cell
*cell
)
1118 isl_vertices_free(cell
->vertices
);
1120 isl_basic_set_free(cell
->dom
);
1124 /* Create a tableau of the cone obtained by first homogenizing the given
1125 * polytope and then making all inequalities strict by setting the
1126 * constant term to -1.
1128 static struct isl_tab
*tab_for_shifted_cone(__isl_keep isl_basic_set
*bset
)
1132 struct isl_tab
*tab
;
1136 tab
= isl_tab_alloc(bset
->ctx
, bset
->n_eq
+ bset
->n_ineq
+ 1,
1137 1 + isl_basic_set_total_dim(bset
), 0);
1140 tab
->rational
= ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
);
1141 if (ISL_F_ISSET(bset
, ISL_BASIC_MAP_EMPTY
)) {
1142 if (isl_tab_mark_empty(tab
) < 0)
1147 c
= isl_vec_alloc(bset
->ctx
, 1 + 1 + isl_basic_set_total_dim(bset
));
1151 isl_int_set_si(c
->el
[0], 0);
1152 for (i
= 0; i
< bset
->n_eq
; ++i
) {
1153 isl_seq_cpy(c
->el
+ 1, bset
->eq
[i
], c
->size
- 1);
1154 if (isl_tab_add_eq(tab
, c
->el
) < 0)
1158 isl_int_set_si(c
->el
[0], -1);
1159 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
1160 isl_seq_cpy(c
->el
+ 1, bset
->ineq
[i
], c
->size
- 1);
1161 if (isl_tab_add_ineq(tab
, c
->el
) < 0)
1169 isl_seq_clr(c
->el
+ 1, c
->size
- 1);
1170 isl_int_set_si(c
->el
[1], 1);
1171 if (isl_tab_add_ineq(tab
, c
->el
) < 0)
1182 /* Compute an interior point of "bset" by selecting an interior
1183 * point in homogeneous space and projecting the point back down.
1185 static __isl_give isl_vec
*isl_basic_set_interior_point(
1186 __isl_keep isl_basic_set
*bset
)
1189 struct isl_tab
*tab
;
1191 tab
= tab_for_shifted_cone(bset
);
1192 vec
= isl_tab_get_sample_value(tab
);
1197 isl_seq_cpy(vec
->el
, vec
->el
+ 1, vec
->size
- 1);
1203 /* Call "fn" on all chambers of the parametric polytope with the shared
1204 * facets of neighboring chambers only appearing in one of the chambers.
1206 * We pick an interior point from one of the chambers and then make
1207 * all constraints that do not satisfy this point strict.
1208 * For constraints that saturate the interior point, the sign
1209 * of the first non-zero coefficient is used to determine which
1210 * of the two (internal) constraints should be tightened.
1212 isl_stat
isl_vertices_foreach_disjoint_cell(__isl_keep isl_vertices
*vertices
,
1213 isl_stat (*fn
)(__isl_take isl_cell
*cell
, void *user
), void *user
)
1220 return isl_stat_error
;
1222 if (vertices
->n_chambers
== 0)
1225 if (vertices
->n_chambers
== 1) {
1226 isl_basic_set
*dom
= isl_basic_set_copy(vertices
->c
[0].dom
);
1227 dom
= isl_basic_set_set_integral(dom
);
1228 cell
= isl_cell_alloc(isl_vertices_copy(vertices
), dom
, 0);
1230 return isl_stat_error
;
1231 return fn(cell
, user
);
1234 vec
= isl_basic_set_interior_point(vertices
->c
[0].dom
);
1236 return isl_stat_error
;
1238 for (i
= 0; i
< vertices
->n_chambers
; ++i
) {
1240 isl_basic_set
*dom
= isl_basic_set_copy(vertices
->c
[i
].dom
);
1242 dom
= isl_basic_set_tighten_outward(dom
, vec
);
1243 dom
= isl_basic_set_set_integral(dom
);
1244 cell
= isl_cell_alloc(isl_vertices_copy(vertices
), dom
, i
);
1257 return isl_stat_error
;
1260 isl_stat
isl_vertices_foreach_cell(__isl_keep isl_vertices
*vertices
,
1261 isl_stat (*fn
)(__isl_take isl_cell
*cell
, void *user
), void *user
)
1267 return isl_stat_error
;
1269 if (vertices
->n_chambers
== 0)
1272 for (i
= 0; i
< vertices
->n_chambers
; ++i
) {
1274 isl_basic_set
*dom
= isl_basic_set_copy(vertices
->c
[i
].dom
);
1276 cell
= isl_cell_alloc(isl_vertices_copy(vertices
), dom
, i
);
1278 return isl_stat_error
;
1282 return isl_stat_error
;
1288 isl_stat
isl_vertices_foreach_vertex(__isl_keep isl_vertices
*vertices
,
1289 isl_stat (*fn
)(__isl_take isl_vertex
*vertex
, void *user
), void *user
)
1295 return isl_stat_error
;
1297 if (vertices
->n_vertices
== 0)
1300 for (i
= 0; i
< vertices
->n_vertices
; ++i
) {
1303 vertex
= isl_vertex_alloc(isl_vertices_copy(vertices
), i
);
1305 return isl_stat_error
;
1307 r
= fn(vertex
, user
);
1309 return isl_stat_error
;
1315 isl_stat
isl_cell_foreach_vertex(__isl_keep isl_cell
*cell
,
1316 isl_stat (*fn
)(__isl_take isl_vertex
*vertex
, void *user
), void *user
)
1322 return isl_stat_error
;
1324 if (cell
->n_vertices
== 0)
1327 for (i
= 0; i
< cell
->n_vertices
; ++i
) {
1330 vertex
= isl_vertex_alloc(isl_vertices_copy(cell
->vertices
),
1333 return isl_stat_error
;
1335 r
= fn(vertex
, user
);
1337 return isl_stat_error
;
1343 isl_ctx
*isl_vertices_get_ctx(__isl_keep isl_vertices
*vertices
)
1345 return vertices
? vertices
->bset
->ctx
: NULL
;
1348 int isl_vertices_get_n_vertices(__isl_keep isl_vertices
*vertices
)
1350 return vertices
? vertices
->n_vertices
: -1;
1353 __isl_give isl_vertices
*isl_morph_vertices(__isl_take isl_morph
*morph
,
1354 __isl_take isl_vertices
*vertices
)
1357 isl_morph
*param_morph
= NULL
;
1359 if (!morph
|| !vertices
)
1362 isl_assert(vertices
->bset
->ctx
, vertices
->ref
== 1, goto error
);
1364 param_morph
= isl_morph_copy(morph
);
1365 param_morph
= isl_morph_dom_params(param_morph
);
1366 param_morph
= isl_morph_ran_params(param_morph
);
1368 for (i
= 0; i
< vertices
->n_vertices
; ++i
) {
1369 vertices
->v
[i
].dom
= isl_morph_basic_set(
1370 isl_morph_copy(param_morph
), vertices
->v
[i
].dom
);
1371 vertices
->v
[i
].vertex
= isl_morph_basic_set(
1372 isl_morph_copy(morph
), vertices
->v
[i
].vertex
);
1373 if (!vertices
->v
[i
].vertex
)
1377 for (i
= 0; i
< vertices
->n_chambers
; ++i
) {
1378 vertices
->c
[i
].dom
= isl_morph_basic_set(
1379 isl_morph_copy(param_morph
), vertices
->c
[i
].dom
);
1380 if (!vertices
->c
[i
].dom
)
1384 isl_morph_free(param_morph
);
1385 isl_morph_free(morph
);
1388 isl_morph_free(param_morph
);
1389 isl_morph_free(morph
);
1390 isl_vertices_free(vertices
);
1394 /* Construct a simplex isl_cell spanned by the vertices with indices in
1395 * "simplex_ids" and "other_ids" and call "fn" on this isl_cell.
1397 static isl_stat
call_on_simplex(__isl_keep isl_cell
*cell
,
1398 int *simplex_ids
, int n_simplex
, int *other_ids
, int n_other
,
1399 isl_stat (*fn
)(__isl_take isl_cell
*simplex
, void *user
), void *user
)
1403 struct isl_cell
*simplex
;
1405 ctx
= isl_cell_get_ctx(cell
);
1407 simplex
= isl_calloc_type(ctx
, struct isl_cell
);
1409 return isl_stat_error
;
1410 simplex
->vertices
= isl_vertices_copy(cell
->vertices
);
1411 if (!simplex
->vertices
)
1413 simplex
->dom
= isl_basic_set_copy(cell
->dom
);
1416 simplex
->n_vertices
= n_simplex
+ n_other
;
1417 simplex
->ids
= isl_alloc_array(ctx
, int, simplex
->n_vertices
);
1421 for (i
= 0; i
< n_simplex
; ++i
)
1422 simplex
->ids
[i
] = simplex_ids
[i
];
1423 for (i
= 0; i
< n_other
; ++i
)
1424 simplex
->ids
[n_simplex
+ i
] = other_ids
[i
];
1426 return fn(simplex
, user
);
1428 isl_cell_free(simplex
);
1429 return isl_stat_error
;
1432 /* Check whether the parametric vertex described by "vertex"
1433 * lies on the facet corresponding to constraint "facet" of "bset".
1434 * The isl_vec "v" is a temporary vector than can be used by this function.
1436 * We eliminate the variables from the facet constraint using the
1437 * equalities defining the vertex and check if the result is identical
1440 * It would probably be better to keep track of the constraints defining
1441 * a vertex during the vertex construction so that we could simply look
1444 static int vertex_on_facet(__isl_keep isl_basic_set
*vertex
,
1445 __isl_keep isl_basic_set
*bset
, int facet
, __isl_keep isl_vec
*v
)
1450 isl_seq_cpy(v
->el
, bset
->ineq
[facet
], v
->size
);
1453 for (i
= 0; i
< vertex
->n_eq
; ++i
) {
1454 int k
= isl_seq_last_non_zero(vertex
->eq
[i
], v
->size
);
1455 isl_seq_elim(v
->el
, vertex
->eq
[i
], k
, v
->size
, &m
);
1459 return isl_seq_first_non_zero(v
->el
, v
->size
) == -1;
1462 /* Triangulate the polytope spanned by the vertices with ids
1463 * in "simplex_ids" and "other_ids" and call "fn" on each of
1464 * the resulting simplices.
1465 * If the input polytope is already a simplex, we simply call "fn".
1466 * Otherwise, we pick a point from "other_ids" and add it to "simplex_ids".
1467 * Then we consider each facet of "bset" that does not contain the point
1468 * we just picked, but does contain some of the other points in "other_ids"
1469 * and call ourselves recursively on the polytope spanned by the new
1470 * "simplex_ids" and those points in "other_ids" that lie on the facet.
1472 static isl_stat
triangulate(__isl_keep isl_cell
*cell
, __isl_keep isl_vec
*v
,
1473 int *simplex_ids
, int n_simplex
, int *other_ids
, int n_other
,
1474 isl_stat (*fn
)(__isl_take isl_cell
*simplex
, void *user
), void *user
)
1480 isl_basic_set
*vertex
;
1481 isl_basic_set
*bset
;
1483 ctx
= isl_cell_get_ctx(cell
);
1484 d
= isl_basic_set_dim(cell
->vertices
->bset
, isl_dim_set
);
1485 nparam
= isl_basic_set_dim(cell
->vertices
->bset
, isl_dim_param
);
1487 if (n_simplex
+ n_other
== d
+ 1)
1488 return call_on_simplex(cell
, simplex_ids
, n_simplex
,
1489 other_ids
, n_other
, fn
, user
);
1491 simplex_ids
[n_simplex
] = other_ids
[0];
1492 vertex
= cell
->vertices
->v
[other_ids
[0]].vertex
;
1493 bset
= cell
->vertices
->bset
;
1495 ids
= isl_alloc_array(ctx
, int, n_other
- 1);
1498 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
1499 if (isl_seq_first_non_zero(bset
->ineq
[i
] + 1 + nparam
, d
) == -1)
1501 if (vertex_on_facet(vertex
, bset
, i
, v
))
1504 for (j
= 1, k
= 0; j
< n_other
; ++j
) {
1506 ov
= cell
->vertices
->v
[other_ids
[j
]].vertex
;
1507 if (vertex_on_facet(ov
, bset
, i
, v
))
1508 ids
[k
++] = other_ids
[j
];
1513 if (triangulate(cell
, v
, simplex_ids
, n_simplex
+ 1,
1514 ids
, k
, fn
, user
) < 0)
1522 return isl_stat_error
;
1525 /* Triangulate the given cell and call "fn" on each of the resulting
1528 isl_stat
isl_cell_foreach_simplex(__isl_take isl_cell
*cell
,
1529 isl_stat (*fn
)(__isl_take isl_cell
*simplex
, void *user
), void *user
)
1535 int *simplex_ids
= NULL
;
1538 return isl_stat_error
;
1540 d
= isl_basic_set_dim(cell
->vertices
->bset
, isl_dim_set
);
1541 total
= isl_basic_set_total_dim(cell
->vertices
->bset
);
1543 if (cell
->n_vertices
== d
+ 1)
1544 return fn(cell
, user
);
1546 ctx
= isl_cell_get_ctx(cell
);
1547 simplex_ids
= isl_alloc_array(ctx
, int, d
+ 1);
1551 v
= isl_vec_alloc(ctx
, 1 + total
);
1555 r
= triangulate(cell
, v
, simplex_ids
, 0,
1556 cell
->ids
, cell
->n_vertices
, fn
, user
);
1561 isl_cell_free(cell
);
1567 isl_cell_free(cell
);
1568 return isl_stat_error
;