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 void 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
);
64 struct isl_vertex_list
{
66 struct isl_vertex_list
*next
;
69 static void free_vertex_list(struct isl_vertex_list
*list
)
71 struct isl_vertex_list
*next
;
73 for (; list
; list
= next
) {
75 isl_basic_set_free(list
->v
.vertex
);
76 isl_basic_set_free(list
->v
.dom
);
81 static __isl_give isl_vertices
*vertices_from_list(__isl_keep isl_basic_set
*bset
,
82 int n_vertices
, struct isl_vertex_list
*list
)
85 struct isl_vertex_list
*next
;
86 isl_vertices
*vertices
;
88 vertices
= isl_calloc_type(bset
->ctx
, isl_vertices
);
92 vertices
->bset
= isl_basic_set_copy(bset
);
93 vertices
->v
= isl_alloc_array(bset
->ctx
, struct isl_vertex
, n_vertices
);
94 if (n_vertices
&& !vertices
->v
)
96 vertices
->n_vertices
= n_vertices
;
98 for (i
= 0; list
; list
= next
, i
++) {
100 vertices
->v
[i
] = list
->v
;
106 isl_vertices_free(vertices
);
107 free_vertex_list(list
);
111 /* Prepend a vertex to the linked list "list" based on the equalities in "tab".
113 static int add_vertex(struct isl_vertex_list
**list
,
114 __isl_keep isl_basic_set
*bset
, struct isl_tab
*tab
)
117 struct isl_vertex_list
*v
= NULL
;
119 if (isl_tab_detect_implicit_equalities(tab
) < 0)
122 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
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_params(v
->v
.dom
);
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 vertices
->v
[0].dom
= isl_basic_set_params(isl_basic_set_copy(bset
));
203 if (!vertices
->v
[0].vertex
|| !vertices
->v
[0].dom
)
206 vertices
->c
= isl_calloc_array(bset
->ctx
, struct isl_chamber
, 1);
209 vertices
->n_chambers
= 1;
210 vertices
->c
[0].n_vertices
= 1;
211 vertices
->c
[0].vertices
= isl_calloc_array(bset
->ctx
, int, 1);
212 if (!vertices
->c
[0].vertices
)
214 vertices
->c
[0].dom
= isl_basic_set_copy(vertices
->v
[0].dom
);
215 if (!vertices
->c
[0].dom
)
220 isl_vertices_free(vertices
);
224 static int isl_mat_rank(__isl_keep isl_mat
*mat
)
229 H
= isl_mat_left_hermite(isl_mat_copy(mat
), 0, NULL
, NULL
);
233 for (col
= 0; col
< H
->n_col
; ++col
) {
234 for (row
= 0; row
< H
->n_row
; ++row
)
235 if (!isl_int_is_zero(H
->row
[row
][col
]))
246 /* Is the row pointed to by "f" linearly independent of the "n" first
249 static int is_independent(__isl_keep isl_mat
*facets
, int n
, isl_int
*f
)
253 if (isl_seq_first_non_zero(f
, facets
->n_col
) < 0)
256 isl_seq_cpy(facets
->row
[n
], f
, facets
->n_col
);
257 facets
->n_row
= n
+ 1;
258 rank
= isl_mat_rank(facets
);
262 return rank
== n
+ 1;
265 /* Check whether we can select constraint "level", given the current selection
266 * reflected by facets in "tab", the rows of "facets" and the earlier
267 * "selected" elements of "selection".
269 * If the constraint is (strictly) redundant in the tableau, selecting it would
270 * result in an empty tableau, so it can't be selected.
271 * If the set variable part of the constraint is not linearly indepedent
272 * of the set variable parts of the already selected constraints,
273 * the constraint cannot be selected.
274 * If selecting the constraint results in an empty tableau, the constraint
275 * cannot be selected.
276 * Finally, if selecting the constraint results in some explicitly
277 * deselected constraints turning into equalities, then the corresponding
278 * vertices have already been generated, so the constraint cannot be selected.
280 static int can_select(__isl_keep isl_basic_set
*bset
, int level
,
281 struct isl_tab
*tab
, __isl_keep isl_mat
*facets
, int selected
,
287 struct isl_tab_undo
*snap
;
289 if (isl_tab_is_redundant(tab
, level
))
292 ovar
= isl_space_offset(bset
->dim
, isl_dim_set
);
294 indep
= is_independent(facets
, selected
, bset
->ineq
[level
] + 1 + ovar
);
300 snap
= isl_tab_snap(tab
);
301 if (isl_tab_select_facet(tab
, level
) < 0)
305 if (isl_tab_rollback(tab
, snap
) < 0)
310 for (i
= 0; i
< level
; ++i
) {
313 if (selection
[i
] != DESELECTED
)
316 if (isl_tab_is_equality(tab
, i
))
318 else if (isl_tab_is_redundant(tab
, i
))
321 sgn
= isl_tab_sign_of_max(tab
, i
);
325 if (isl_tab_rollback(tab
, snap
) < 0)
334 /* Compute the parametric vertices and the chamber decomposition
335 * of a parametric polytope that is not full-dimensional.
337 * Simply map the parametric polytope to a lower dimensional space
338 * and map the resulting vertices back.
340 static __isl_give isl_vertices
*lower_dim_vertices(
341 __isl_keep isl_basic_set
*bset
)
344 isl_vertices
*vertices
;
346 bset
= isl_basic_set_copy(bset
);
347 morph
= isl_basic_set_full_compression(bset
);
348 bset
= isl_morph_basic_set(isl_morph_copy(morph
), bset
);
350 vertices
= isl_basic_set_compute_vertices(bset
);
351 isl_basic_set_free(bset
);
353 morph
= isl_morph_inverse(morph
);
355 vertices
= isl_morph_vertices(morph
, vertices
);
360 /* Compute the parametric vertices and the chamber decomposition
361 * of the parametric polytope defined using the same constraints
362 * as "bset". "bset" is assumed to have no existentially quantified
365 * The vertices themselves are computed in a fairly simplistic way.
366 * We simply run through all combinations of d constraints,
367 * with d the number of set variables, and check if those d constraints
368 * define a vertex. To avoid the generation of duplicate vertices,
369 * which we may happen if a vertex is defined by more that d constraints,
370 * we make sure we only generate the vertex for the d constraints with
373 * We set up a tableau and keep track of which facets have been
374 * selected. The tableau is marked strict_redundant so that we can be
375 * sure that any constraint that is marked redundant (and that is not
376 * also marked zero) is not an equality.
377 * If a constraint is marked DESELECTED, it means the constraint was
378 * SELECTED before (in combination with the same selection of earlier
379 * constraints). If such a deselected constraint turns out to be an
380 * equality, then any vertex that may still be found with the current
381 * selection has already been generated when the constraint was selected.
382 * A constraint is marked UNSELECTED when there is no way selecting
383 * the constraint could lead to a vertex (in combination with the current
384 * selection of earlier constraints).
386 * The set variable coefficients of the selected constraints are stored
387 * in the facets matrix.
389 __isl_give isl_vertices
*isl_basic_set_compute_vertices(
390 __isl_keep isl_basic_set
*bset
)
396 int *selection
= NULL
;
398 struct isl_tab_undo
**snap
= NULL
;
399 isl_mat
*facets
= NULL
;
400 struct isl_vertex_list
*list
= NULL
;
402 isl_vertices
*vertices
;
407 if (isl_basic_set_plain_is_empty(bset
))
408 return vertices_empty(bset
);
411 return lower_dim_vertices(bset
);
413 isl_assert(bset
->ctx
, isl_basic_set_dim(bset
, isl_dim_div
) == 0,
416 if (isl_basic_set_dim(bset
, isl_dim_set
) == 0)
417 return vertices_0D(bset
);
419 nvar
= isl_basic_set_dim(bset
, isl_dim_set
);
421 bset
= isl_basic_set_copy(bset
);
422 bset
= isl_basic_set_set_rational(bset
);
426 tab
= isl_tab_from_basic_set(bset
, 0);
429 tab
->strict_redundant
= 1;
432 vertices
= vertices_empty(bset
);
433 isl_basic_set_free(bset
);
438 selection
= isl_alloc_array(bset
->ctx
, int, bset
->n_ineq
);
439 snap
= isl_alloc_array(bset
->ctx
, struct isl_tab_undo
*, bset
->n_ineq
);
440 facets
= isl_mat_alloc(bset
->ctx
, nvar
, nvar
);
441 if ((bset
->n_ineq
&& (!selection
|| !snap
)) || !facets
)
449 if (level
>= bset
->n_ineq
||
450 (!init
&& selection
[level
] != SELECTED
)) {
457 snap
[level
] = isl_tab_snap(tab
);
458 ok
= can_select(bset
, level
, tab
, facets
, selected
,
463 selection
[level
] = SELECTED
;
466 selection
[level
] = UNSELECTED
;
468 selection
[level
] = DESELECTED
;
470 if (isl_tab_rollback(tab
, snap
[level
]) < 0)
473 if (selected
== nvar
) {
474 if (tab
->n_dead
== nvar
) {
475 if (add_vertex(&list
, bset
, tab
) < 0)
486 isl_mat_free(facets
);
492 vertices
= vertices_from_list(bset
, n_vertices
, list
);
494 vertices
= compute_chambers(bset
, vertices
);
498 free_vertex_list(list
);
499 isl_mat_free(facets
);
503 isl_basic_set_free(bset
);
507 struct isl_chamber_list
{
508 struct isl_chamber c
;
509 struct isl_chamber_list
*next
;
512 static void free_chamber_list(struct isl_chamber_list
*list
)
514 struct isl_chamber_list
*next
;
516 for (; list
; list
= next
) {
518 isl_basic_set_free(list
->c
.dom
);
519 free(list
->c
.vertices
);
524 /* Check whether the basic set "bset" is a superset of the basic set described
525 * by "tab", i.e., check whether all constraints of "bset" are redundant.
527 static int bset_covers_tab(__isl_keep isl_basic_set
*bset
, struct isl_tab
*tab
)
534 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
535 enum isl_ineq_type type
= isl_tab_ineq_type(tab
, bset
->ineq
[i
]);
537 case isl_ineq_error
: return -1;
538 case isl_ineq_redundant
: continue;
546 static __isl_give isl_vertices
*vertices_add_chambers(
547 __isl_take isl_vertices
*vertices
, int n_chambers
,
548 struct isl_chamber_list
*list
)
552 struct isl_chamber_list
*next
;
554 ctx
= isl_vertices_get_ctx(vertices
);
555 vertices
->c
= isl_alloc_array(ctx
, struct isl_chamber
, n_chambers
);
558 vertices
->n_chambers
= n_chambers
;
560 for (i
= 0; list
; list
= next
, i
++) {
562 vertices
->c
[i
] = list
->c
;
568 isl_vertices_free(vertices
);
569 free_chamber_list(list
);
573 /* Can "tab" be intersected with "bset" without resulting in
574 * a lower-dimensional set.
576 static int can_intersect(struct isl_tab
*tab
, __isl_keep isl_basic_set
*bset
)
579 struct isl_tab_undo
*snap
;
581 if (isl_tab_extend_cons(tab
, bset
->n_ineq
) < 0)
584 snap
= isl_tab_snap(tab
);
586 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
587 if (isl_tab_ineq_type(tab
, bset
->ineq
[i
]) == isl_ineq_redundant
)
589 if (isl_tab_add_ineq(tab
, bset
->ineq
[i
]) < 0)
593 if (isl_tab_detect_implicit_equalities(tab
) < 0)
596 if (isl_tab_rollback(tab
, snap
) < 0)
604 static int add_chamber(struct isl_chamber_list
**list
,
605 __isl_keep isl_vertices
*vertices
, struct isl_tab
*tab
, int *selection
)
610 struct isl_tab_undo
*snap
;
611 struct isl_chamber_list
*c
= NULL
;
613 for (i
= 0; i
< vertices
->n_vertices
; ++i
)
617 snap
= isl_tab_snap(tab
);
619 for (i
= 0; i
< tab
->n_con
&& tab
->con
[i
].frozen
; ++i
)
620 tab
->con
[i
].frozen
= 0;
623 if (isl_tab_detect_redundant(tab
) < 0)
626 c
= isl_calloc_type(tab
->mat
->ctx
, struct isl_chamber_list
);
629 c
->c
.vertices
= isl_alloc_array(tab
->mat
->ctx
, int, n_vertices
);
630 if (n_vertices
&& !c
->c
.vertices
)
632 c
->c
.dom
= isl_basic_set_from_basic_map(isl_basic_map_copy(tab
->bmap
));
633 c
->c
.dom
= isl_basic_set_set_rational(c
->c
.dom
);
634 c
->c
.dom
= isl_basic_set_cow(c
->c
.dom
);
635 c
->c
.dom
= isl_basic_set_update_from_tab(c
->c
.dom
, tab
);
636 c
->c
.dom
= isl_basic_set_simplify(c
->c
.dom
);
637 c
->c
.dom
= isl_basic_set_finalize(c
->c
.dom
);
641 c
->c
.n_vertices
= n_vertices
;
643 for (i
= 0, j
= 0; i
< vertices
->n_vertices
; ++i
)
645 c
->c
.vertices
[j
] = i
;
652 for (i
= 0; i
< n_frozen
; ++i
)
653 tab
->con
[i
].frozen
= 1;
655 if (isl_tab_rollback(tab
, snap
) < 0)
660 free_chamber_list(c
);
664 struct isl_facet_todo
{
665 struct isl_tab
*tab
; /* A tableau representation of the facet */
666 isl_basic_set
*bset
; /* A normalized basic set representation */
667 isl_vec
*constraint
; /* Constraint pointing to the other side */
668 struct isl_facet_todo
*next
;
671 static void free_todo(struct isl_facet_todo
*todo
)
674 struct isl_facet_todo
*next
= todo
->next
;
676 isl_tab_free(todo
->tab
);
677 isl_basic_set_free(todo
->bset
);
678 isl_vec_free(todo
->constraint
);
685 static struct isl_facet_todo
*create_todo(struct isl_tab
*tab
, int con
)
689 struct isl_tab_undo
*snap
;
690 struct isl_facet_todo
*todo
;
692 snap
= isl_tab_snap(tab
);
694 for (i
= 0; i
< tab
->n_con
&& tab
->con
[i
].frozen
; ++i
)
695 tab
->con
[i
].frozen
= 0;
698 if (isl_tab_detect_redundant(tab
) < 0)
701 todo
= isl_calloc_type(tab
->mat
->ctx
, struct isl_facet_todo
);
705 todo
->constraint
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
706 if (!todo
->constraint
)
708 isl_seq_neg(todo
->constraint
->el
, tab
->bmap
->ineq
[con
], 1 + tab
->n_var
);
709 todo
->bset
= isl_basic_set_from_basic_map(isl_basic_map_copy(tab
->bmap
));
710 todo
->bset
= isl_basic_set_set_rational(todo
->bset
);
711 todo
->bset
= isl_basic_set_cow(todo
->bset
);
712 todo
->bset
= isl_basic_set_update_from_tab(todo
->bset
, tab
);
713 todo
->bset
= isl_basic_set_simplify(todo
->bset
);
714 todo
->bset
= isl_basic_set_sort_constraints(todo
->bset
);
717 ISL_F_SET(todo
->bset
, ISL_BASIC_SET_NORMALIZED
);
718 todo
->tab
= isl_tab_dup(tab
);
722 for (i
= 0; i
< n_frozen
; ++i
)
723 tab
->con
[i
].frozen
= 1;
725 if (isl_tab_rollback(tab
, snap
) < 0)
734 /* Create todo items for all interior facets of the chamber represented
735 * by "tab" and collect them in "next".
737 static int init_todo(struct isl_facet_todo
**next
, struct isl_tab
*tab
)
740 struct isl_tab_undo
*snap
;
741 struct isl_facet_todo
*todo
;
743 snap
= isl_tab_snap(tab
);
745 for (i
= 0; i
< tab
->n_con
; ++i
) {
746 if (tab
->con
[i
].frozen
)
748 if (tab
->con
[i
].is_redundant
)
751 if (isl_tab_select_facet(tab
, i
) < 0)
754 todo
= create_todo(tab
, i
);
761 if (isl_tab_rollback(tab
, snap
) < 0)
768 /* Does the linked list contain a todo item that is the opposite of "todo".
769 * If so, return 1 and remove the opposite todo item.
771 static int has_opposite(struct isl_facet_todo
*todo
,
772 struct isl_facet_todo
**list
)
774 for (; *list
; list
= &(*list
)->next
) {
776 eq
= isl_basic_set_plain_is_equal(todo
->bset
, (*list
)->bset
);
791 /* Create todo items for all interior facets of the chamber represented
792 * by "tab" and collect them in first->next, taking care to cancel
793 * opposite todo items.
795 static int update_todo(struct isl_facet_todo
*first
, struct isl_tab
*tab
)
798 struct isl_tab_undo
*snap
;
799 struct isl_facet_todo
*todo
;
801 snap
= isl_tab_snap(tab
);
803 for (i
= 0; i
< tab
->n_con
; ++i
) {
806 if (tab
->con
[i
].frozen
)
808 if (tab
->con
[i
].is_redundant
)
811 if (isl_tab_select_facet(tab
, i
) < 0)
814 todo
= create_todo(tab
, i
);
818 drop
= has_opposite(todo
, &first
->next
);
825 todo
->next
= first
->next
;
829 if (isl_tab_rollback(tab
, snap
) < 0)
836 /* Compute the chamber decomposition of the parametric polytope respresented
837 * by "bset" given the parametric vertices and their activity domains.
839 * We are only interested in full-dimensional chambers.
840 * Each of these chambers is the intersection of the activity domains of
841 * one or more vertices and the union of all chambers is equal to the
842 * projection of the entire parametric polytope onto the parameter space.
844 * We first create an initial chamber by intersecting as many activity
845 * domains as possible without ending up with an empty or lower-dimensional
846 * set. As a minor optimization, we only consider those activity domains
847 * that contain some arbitrary point.
849 * For each of interior facets of the chamber, we construct a todo item,
850 * containing the facet and a constraint containing the other side of the facet,
851 * for constructing the chamber on the other side.
852 * While their are any todo items left, we pick a todo item and
853 * create the required chamber by intersecting all activity domains
854 * that contain the facet and have a full-dimensional intersection with
855 * the other side of the facet. For each of the interior facets, we
856 * again create todo items, taking care to cancel opposite todo items.
858 static __isl_give isl_vertices
*compute_chambers(__isl_take isl_basic_set
*bset
,
859 __isl_take isl_vertices
*vertices
)
863 isl_vec
*sample
= NULL
;
864 struct isl_tab
*tab
= NULL
;
865 struct isl_tab_undo
*snap
;
866 int *selection
= NULL
;
868 struct isl_chamber_list
*list
= NULL
;
869 struct isl_facet_todo
*todo
= NULL
;
871 if (!bset
|| !vertices
)
874 ctx
= isl_vertices_get_ctx(vertices
);
875 selection
= isl_alloc_array(ctx
, int, vertices
->n_vertices
);
876 if (vertices
->n_vertices
&& !selection
)
879 bset
= isl_basic_set_params(bset
);
881 tab
= isl_tab_from_basic_set(bset
, 1);
884 for (i
= 0; i
< bset
->n_ineq
; ++i
)
885 if (isl_tab_freeze_constraint(tab
, i
) < 0)
887 isl_basic_set_free(bset
);
889 snap
= isl_tab_snap(tab
);
891 sample
= isl_tab_get_sample_value(tab
);
893 for (i
= 0; i
< vertices
->n_vertices
; ++i
) {
894 selection
[i
] = isl_basic_set_contains(vertices
->v
[i
].dom
, sample
);
895 if (selection
[i
] < 0)
899 selection
[i
] = can_intersect(tab
, vertices
->v
[i
].dom
);
900 if (selection
[i
] < 0)
904 if (isl_tab_detect_redundant(tab
) < 0)
907 if (add_chamber(&list
, vertices
, tab
, selection
) < 0)
911 if (init_todo(&todo
, tab
) < 0)
915 struct isl_facet_todo
*next
;
917 if (isl_tab_rollback(tab
, snap
) < 0)
920 if (isl_tab_add_ineq(tab
, todo
->constraint
->el
) < 0)
922 if (isl_tab_freeze_constraint(tab
, tab
->n_con
- 1) < 0)
925 for (i
= 0; i
< vertices
->n_vertices
; ++i
) {
926 selection
[i
] = bset_covers_tab(vertices
->v
[i
].dom
,
928 if (selection
[i
] < 0)
932 selection
[i
] = can_intersect(tab
, vertices
->v
[i
].dom
);
933 if (selection
[i
] < 0)
937 if (isl_tab_detect_redundant(tab
) < 0)
940 if (add_chamber(&list
, vertices
, tab
, selection
) < 0)
944 if (update_todo(todo
, tab
) < 0)
953 isl_vec_free(sample
);
958 vertices
= vertices_add_chambers(vertices
, n_chambers
, list
);
960 for (i
= 0; vertices
&& i
< vertices
->n_vertices
; ++i
) {
961 isl_basic_set_free(vertices
->v
[i
].dom
);
962 vertices
->v
[i
].dom
= NULL
;
967 free_chamber_list(list
);
969 isl_vec_free(sample
);
973 isl_basic_set_free(bset
);
974 isl_vertices_free(vertices
);
978 isl_ctx
*isl_vertex_get_ctx(__isl_keep isl_vertex
*vertex
)
980 return vertex
? isl_vertices_get_ctx(vertex
->vertices
) : NULL
;
983 int isl_vertex_get_id(__isl_keep isl_vertex
*vertex
)
985 return vertex
? vertex
->id
: -1;
988 __isl_give isl_basic_set
*isl_basic_set_set_integral(__isl_take isl_basic_set
*bset
)
993 if (!ISL_F_ISSET(bset
, ISL_BASIC_MAP_RATIONAL
))
996 bset
= isl_basic_set_cow(bset
);
1000 ISL_F_CLR(bset
, ISL_BASIC_MAP_RATIONAL
);
1002 return isl_basic_set_finalize(bset
);
1005 /* Return the activity domain of the vertex "vertex".
1007 __isl_give isl_basic_set
*isl_vertex_get_domain(__isl_keep isl_vertex
*vertex
)
1009 struct isl_vertex
*v
;
1014 v
= &vertex
->vertices
->v
[vertex
->id
];
1016 v
->dom
= isl_basic_set_copy(v
->vertex
);
1017 v
->dom
= isl_basic_set_params(v
->dom
);
1018 v
->dom
= isl_basic_set_set_integral(v
->dom
);
1021 return isl_basic_set_copy(v
->dom
);
1024 /* Return a multiple quasi-affine expression describing the vertex "vertex"
1025 * in terms of the parameters,
1027 __isl_give isl_multi_aff
*isl_vertex_get_expr(__isl_keep isl_vertex
*vertex
)
1029 struct isl_vertex
*v
;
1030 isl_basic_set
*bset
;
1035 v
= &vertex
->vertices
->v
[vertex
->id
];
1037 bset
= isl_basic_set_copy(v
->vertex
);
1038 return isl_multi_aff_from_basic_set_equalities(bset
);
1041 static __isl_give isl_vertex
*isl_vertex_alloc(__isl_take isl_vertices
*vertices
,
1050 ctx
= isl_vertices_get_ctx(vertices
);
1051 vertex
= isl_alloc_type(ctx
, isl_vertex
);
1055 vertex
->vertices
= vertices
;
1060 isl_vertices_free(vertices
);
1064 void isl_vertex_free(__isl_take isl_vertex
*vertex
)
1068 isl_vertices_free(vertex
->vertices
);
1072 isl_ctx
*isl_cell_get_ctx(__isl_keep isl_cell
*cell
)
1074 return cell
? cell
->dom
->ctx
: NULL
;
1077 __isl_give isl_basic_set
*isl_cell_get_domain(__isl_keep isl_cell
*cell
)
1079 return cell
? isl_basic_set_copy(cell
->dom
) : NULL
;
1082 static __isl_give isl_cell
*isl_cell_alloc(__isl_take isl_vertices
*vertices
,
1083 __isl_take isl_basic_set
*dom
, int id
)
1086 isl_cell
*cell
= NULL
;
1088 if (!vertices
|| !dom
)
1091 cell
= isl_calloc_type(dom
->ctx
, isl_cell
);
1095 cell
->n_vertices
= vertices
->c
[id
].n_vertices
;
1096 cell
->ids
= isl_alloc_array(dom
->ctx
, int, cell
->n_vertices
);
1097 if (cell
->n_vertices
&& !cell
->ids
)
1099 for (i
= 0; i
< cell
->n_vertices
; ++i
)
1100 cell
->ids
[i
] = vertices
->c
[id
].vertices
[i
];
1101 cell
->vertices
= vertices
;
1106 isl_cell_free(cell
);
1107 isl_vertices_free(vertices
);
1108 isl_basic_set_free(dom
);
1112 void isl_cell_free(__isl_take isl_cell
*cell
)
1117 isl_vertices_free(cell
->vertices
);
1119 isl_basic_set_free(cell
->dom
);
1123 /* Create a tableau of the cone obtained by first homogenizing the given
1124 * polytope and then making all inequalities strict by setting the
1125 * constant term to -1.
1127 static struct isl_tab
*tab_for_shifted_cone(__isl_keep isl_basic_set
*bset
)
1131 struct isl_tab
*tab
;
1135 tab
= isl_tab_alloc(bset
->ctx
, bset
->n_ineq
+ 1,
1136 1 + isl_basic_set_total_dim(bset
), 0);
1139 tab
->rational
= ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
);
1140 if (ISL_F_ISSET(bset
, ISL_BASIC_MAP_EMPTY
)) {
1141 if (isl_tab_mark_empty(tab
) < 0)
1146 c
= isl_vec_alloc(bset
->ctx
, 1 + 1 + isl_basic_set_total_dim(bset
));
1150 isl_int_set_si(c
->el
[0], 0);
1151 for (i
= 0; i
< bset
->n_eq
; ++i
) {
1152 isl_seq_cpy(c
->el
+ 1, bset
->eq
[i
], c
->size
- 1);
1153 if (isl_tab_add_eq(tab
, c
->el
) < 0)
1157 isl_int_set_si(c
->el
[0], -1);
1158 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
1159 isl_seq_cpy(c
->el
+ 1, bset
->ineq
[i
], c
->size
- 1);
1160 if (isl_tab_add_ineq(tab
, c
->el
) < 0)
1168 isl_seq_clr(c
->el
+ 1, c
->size
- 1);
1169 isl_int_set_si(c
->el
[1], 1);
1170 if (isl_tab_add_ineq(tab
, c
->el
) < 0)
1181 /* Compute an interior point of "bset" by selecting an interior
1182 * point in homogeneous space and projecting the point back down.
1184 static __isl_give isl_vec
*isl_basic_set_interior_point(
1185 __isl_keep isl_basic_set
*bset
)
1188 struct isl_tab
*tab
;
1190 tab
= tab_for_shifted_cone(bset
);
1191 vec
= isl_tab_get_sample_value(tab
);
1196 isl_seq_cpy(vec
->el
, vec
->el
+ 1, vec
->size
- 1);
1202 /* Call "fn" on all chambers of the parametric polytope with the shared
1203 * facets of neighboring chambers only appearing in one of the chambers.
1205 * We pick an interior point from one of the chambers and then make
1206 * all constraints that do not satisfy this point strict.
1208 int isl_vertices_foreach_disjoint_cell(__isl_keep isl_vertices
*vertices
,
1209 int (*fn
)(__isl_take isl_cell
*cell
, void *user
), void *user
)
1219 if (vertices
->n_chambers
== 0)
1222 if (vertices
->n_chambers
== 1) {
1223 isl_basic_set
*dom
= isl_basic_set_copy(vertices
->c
[0].dom
);
1224 dom
= isl_basic_set_set_integral(dom
);
1225 cell
= isl_cell_alloc(isl_vertices_copy(vertices
), dom
, 0);
1228 return fn(cell
, user
);
1231 vec
= isl_basic_set_interior_point(vertices
->c
[0].dom
);
1237 for (i
= 0; i
< vertices
->n_chambers
; ++i
) {
1239 isl_basic_set
*dom
= isl_basic_set_copy(vertices
->c
[i
].dom
);
1240 dom
= isl_basic_set_cow(dom
);
1243 for (j
= 0; i
&& j
< dom
->n_ineq
; ++j
) {
1244 isl_seq_inner_product(vec
->el
, dom
->ineq
[j
], vec
->size
,
1246 if (!isl_int_is_neg(v
))
1248 isl_int_sub_ui(dom
->ineq
[j
][0], dom
->ineq
[j
][0], 1);
1250 dom
= isl_basic_set_set_integral(dom
);
1251 cell
= isl_cell_alloc(isl_vertices_copy(vertices
), dom
, i
);
1269 int isl_vertices_foreach_cell(__isl_keep isl_vertices
*vertices
,
1270 int (*fn
)(__isl_take isl_cell
*cell
, void *user
), void *user
)
1278 if (vertices
->n_chambers
== 0)
1281 for (i
= 0; i
< vertices
->n_chambers
; ++i
) {
1283 isl_basic_set
*dom
= isl_basic_set_copy(vertices
->c
[i
].dom
);
1285 cell
= isl_cell_alloc(isl_vertices_copy(vertices
), dom
, i
);
1297 int isl_vertices_foreach_vertex(__isl_keep isl_vertices
*vertices
,
1298 int (*fn
)(__isl_take isl_vertex
*vertex
, void *user
), void *user
)
1306 if (vertices
->n_vertices
== 0)
1309 for (i
= 0; i
< vertices
->n_vertices
; ++i
) {
1312 vertex
= isl_vertex_alloc(isl_vertices_copy(vertices
), i
);
1316 r
= fn(vertex
, user
);
1324 int isl_cell_foreach_vertex(__isl_keep isl_cell
*cell
,
1325 int (*fn
)(__isl_take isl_vertex
*vertex
, void *user
), void *user
)
1333 if (cell
->n_vertices
== 0)
1336 for (i
= 0; i
< cell
->n_vertices
; ++i
) {
1339 vertex
= isl_vertex_alloc(isl_vertices_copy(cell
->vertices
),
1344 r
= fn(vertex
, user
);
1352 isl_ctx
*isl_vertices_get_ctx(__isl_keep isl_vertices
*vertices
)
1354 return vertices
? vertices
->bset
->ctx
: NULL
;
1357 int isl_vertices_get_n_vertices(__isl_keep isl_vertices
*vertices
)
1359 return vertices
? vertices
->n_vertices
: -1;
1362 __isl_give isl_vertices
*isl_morph_vertices(__isl_take isl_morph
*morph
,
1363 __isl_take isl_vertices
*vertices
)
1366 isl_morph
*param_morph
= NULL
;
1368 if (!morph
|| !vertices
)
1371 isl_assert(vertices
->bset
->ctx
, vertices
->ref
== 1, goto error
);
1373 param_morph
= isl_morph_copy(morph
);
1374 param_morph
= isl_morph_dom_params(param_morph
);
1375 param_morph
= isl_morph_ran_params(param_morph
);
1377 for (i
= 0; i
< vertices
->n_vertices
; ++i
) {
1378 vertices
->v
[i
].dom
= isl_morph_basic_set(
1379 isl_morph_copy(param_morph
), vertices
->v
[i
].dom
);
1380 vertices
->v
[i
].vertex
= isl_morph_basic_set(
1381 isl_morph_copy(morph
), vertices
->v
[i
].vertex
);
1382 if (!vertices
->v
[i
].vertex
)
1386 for (i
= 0; i
< vertices
->n_chambers
; ++i
) {
1387 vertices
->c
[i
].dom
= isl_morph_basic_set(
1388 isl_morph_copy(param_morph
), vertices
->c
[i
].dom
);
1389 if (!vertices
->c
[i
].dom
)
1393 isl_morph_free(param_morph
);
1394 isl_morph_free(morph
);
1397 isl_morph_free(param_morph
);
1398 isl_morph_free(morph
);
1399 isl_vertices_free(vertices
);
1403 /* Construct a simplex isl_cell spanned by the vertices with indices in
1404 * "simplex_ids" and "other_ids" and call "fn" on this isl_cell.
1406 static int call_on_simplex(__isl_keep isl_cell
*cell
,
1407 int *simplex_ids
, int n_simplex
, int *other_ids
, int n_other
,
1408 int (*fn
)(__isl_take isl_cell
*simplex
, void *user
), void *user
)
1412 struct isl_cell
*simplex
;
1414 ctx
= isl_cell_get_ctx(cell
);
1416 simplex
= isl_calloc_type(ctx
, struct isl_cell
);
1419 simplex
->vertices
= isl_vertices_copy(cell
->vertices
);
1420 if (!simplex
->vertices
)
1422 simplex
->dom
= isl_basic_set_copy(cell
->dom
);
1425 simplex
->n_vertices
= n_simplex
+ n_other
;
1426 simplex
->ids
= isl_alloc_array(ctx
, int, simplex
->n_vertices
);
1430 for (i
= 0; i
< n_simplex
; ++i
)
1431 simplex
->ids
[i
] = simplex_ids
[i
];
1432 for (i
= 0; i
< n_other
; ++i
)
1433 simplex
->ids
[n_simplex
+ i
] = other_ids
[i
];
1435 return fn(simplex
, user
);
1437 isl_cell_free(simplex
);
1441 /* Check whether the parametric vertex described by "vertex"
1442 * lies on the facet corresponding to constraint "facet" of "bset".
1443 * The isl_vec "v" is a temporary vector than can be used by this function.
1445 * We eliminate the variables from the facet constraint using the
1446 * equalities defining the vertex and check if the result is identical
1449 * It would probably be better to keep track of the constraints defining
1450 * a vertex during the vertex construction so that we could simply look
1453 static int vertex_on_facet(__isl_keep isl_basic_set
*vertex
,
1454 __isl_keep isl_basic_set
*bset
, int facet
, __isl_keep isl_vec
*v
)
1459 isl_seq_cpy(v
->el
, bset
->ineq
[facet
], v
->size
);
1462 for (i
= 0; i
< vertex
->n_eq
; ++i
) {
1463 int k
= isl_seq_last_non_zero(vertex
->eq
[i
], v
->size
);
1464 isl_seq_elim(v
->el
, vertex
->eq
[i
], k
, v
->size
, &m
);
1468 return isl_seq_first_non_zero(v
->el
, v
->size
) == -1;
1471 /* Triangulate the polytope spanned by the vertices with ids
1472 * in "simplex_ids" and "other_ids" and call "fn" on each of
1473 * the resulting simplices.
1474 * If the input polytope is already a simplex, we simply call "fn".
1475 * Otherwise, we pick a point from "other_ids" and add it to "simplex_ids".
1476 * Then we consider each facet of "bset" that does not contain the point
1477 * we just picked, but does contain some of the other points in "other_ids"
1478 * and call ourselves recursively on the polytope spanned by the new
1479 * "simplex_ids" and those points in "other_ids" that lie on the facet.
1481 static int triangulate(__isl_keep isl_cell
*cell
, __isl_keep isl_vec
*v
,
1482 int *simplex_ids
, int n_simplex
, int *other_ids
, int n_other
,
1483 int (*fn
)(__isl_take isl_cell
*simplex
, void *user
), void *user
)
1489 isl_basic_set
*vertex
;
1490 isl_basic_set
*bset
;
1492 ctx
= isl_cell_get_ctx(cell
);
1493 d
= isl_basic_set_dim(cell
->vertices
->bset
, isl_dim_set
);
1494 nparam
= isl_basic_set_dim(cell
->vertices
->bset
, isl_dim_param
);
1496 if (n_simplex
+ n_other
== d
+ 1)
1497 return call_on_simplex(cell
, simplex_ids
, n_simplex
,
1498 other_ids
, n_other
, fn
, user
);
1500 simplex_ids
[n_simplex
] = other_ids
[0];
1501 vertex
= cell
->vertices
->v
[other_ids
[0]].vertex
;
1502 bset
= cell
->vertices
->bset
;
1504 ids
= isl_alloc_array(ctx
, int, n_other
- 1);
1505 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
1506 if (isl_seq_first_non_zero(bset
->ineq
[i
] + 1 + nparam
, d
) == -1)
1508 if (vertex_on_facet(vertex
, bset
, i
, v
))
1511 for (j
= 1, k
= 0; j
< n_other
; ++j
) {
1513 ov
= cell
->vertices
->v
[other_ids
[j
]].vertex
;
1514 if (vertex_on_facet(ov
, bset
, i
, v
))
1515 ids
[k
++] = other_ids
[j
];
1520 if (triangulate(cell
, v
, simplex_ids
, n_simplex
+ 1,
1521 ids
, k
, fn
, user
) < 0)
1532 /* Triangulate the given cell and call "fn" on each of the resulting
1535 int isl_cell_foreach_simplex(__isl_take isl_cell
*cell
,
1536 int (*fn
)(__isl_take isl_cell
*simplex
, void *user
), void *user
)
1542 int *simplex_ids
= NULL
;
1547 d
= isl_basic_set_dim(cell
->vertices
->bset
, isl_dim_set
);
1548 total
= isl_basic_set_total_dim(cell
->vertices
->bset
);
1550 if (cell
->n_vertices
== d
+ 1)
1551 return fn(cell
, user
);
1553 ctx
= isl_cell_get_ctx(cell
);
1554 simplex_ids
= isl_alloc_array(ctx
, int, d
+ 1);
1558 v
= isl_vec_alloc(ctx
, 1 + total
);
1562 r
= triangulate(cell
, v
, simplex_ids
, 0,
1563 cell
->ids
, cell
->n_vertices
, fn
, user
);
1568 isl_cell_free(cell
);
1574 isl_cell_free(cell
);