1/*
2 * Copyright 2010      INRIA Saclay
3 *
4 * Use of this software is governed by the MIT license
5 *
6 * Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
7 * Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
8 * 91893 Orsay, France
9 */
10
11#include <isl_map_private.h>
12#include <isl/set.h>
13#include <isl/seq.h>
14#include <isl_tab.h>
15#include <isl_space_private.h>
16#include <isl_morph.h>
17#include <isl_vertices_private.h>
18#include <isl_mat_private.h>
19
20#define SELECTED	1
21#define DESELECTED	-1
22#define UNSELECTED	0
23
24static __isl_give isl_vertices *compute_chambers(__isl_take isl_basic_set *bset,
25	__isl_take isl_vertices *vertices);
26
27__isl_give isl_vertices *isl_vertices_copy(__isl_keep isl_vertices *vertices)
28{
29	if (!vertices)
30		return NULL;
31
32	vertices->ref++;
33	return vertices;
34}
35
36void isl_vertices_free(__isl_take isl_vertices *vertices)
37{
38	int i;
39
40	if (!vertices)
41		return;
42
43	if (--vertices->ref > 0)
44		return;
45
46	for (i = 0; i < vertices->n_vertices; ++i) {
47		isl_basic_set_free(vertices->v[i].vertex);
48		isl_basic_set_free(vertices->v[i].dom);
49	}
50	free(vertices->v);
51
52	for (i = 0; i < vertices->n_chambers; ++i) {
53		free(vertices->c[i].vertices);
54		isl_basic_set_free(vertices->c[i].dom);
55	}
56	free(vertices->c);
57
58	isl_basic_set_free(vertices->bset);
59	free(vertices);
60}
61
62struct isl_vertex_list {
63	struct isl_vertex v;
64	struct isl_vertex_list *next;
65};
66
67static void free_vertex_list(struct isl_vertex_list *list)
68{
69	struct isl_vertex_list *next;
70
71	for (; list; list = next) {
72		next = list->next;
73		isl_basic_set_free(list->v.vertex);
74		isl_basic_set_free(list->v.dom);
75		free(list);
76	}
77}
78
79static __isl_give isl_vertices *vertices_from_list(__isl_keep isl_basic_set *bset,
80	int n_vertices, struct isl_vertex_list *list)
81{
82	int i;
83	struct isl_vertex_list *next;
84	isl_vertices *vertices;
85
86	vertices = isl_calloc_type(bset->ctx, isl_vertices);
87	if (!vertices)
88		goto error;
89	vertices->ref = 1;
90	vertices->bset = isl_basic_set_copy(bset);
91	vertices->v = isl_alloc_array(bset->ctx, struct isl_vertex, n_vertices);
92	if (n_vertices && !vertices->v)
93		goto error;
94	vertices->n_vertices = n_vertices;
95
96	for (i = 0; list; list = next, i++) {
97		next = list->next;
98		vertices->v[i] = list->v;
99		free(list);
100	}
101
102	return vertices;
103error:
104	isl_vertices_free(vertices);
105	free_vertex_list(list);
106	return NULL;
107}
108
109/* Prepend a vertex to the linked list "list" based on the equalities in "tab".
110 */
111static int add_vertex(struct isl_vertex_list **list,
112	__isl_keep isl_basic_set *bset, struct isl_tab *tab)
113{
114	unsigned nvar;
115	unsigned nparam;
116	struct isl_vertex_list *v = NULL;
117
118	if (isl_tab_detect_implicit_equalities(tab) < 0)
119		return -1;
120
121	nvar = isl_basic_set_dim(bset, isl_dim_set);
122	nparam = isl_basic_set_dim(bset, isl_dim_param);
123
124	v = isl_calloc_type(tab->mat->ctx, struct isl_vertex_list);
125	if (!v)
126		goto error;
127
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);
133	if (!v->v.vertex)
134		goto error;
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);
138	if (!v->v.dom)
139		goto error;
140
141	v->next = *list;
142	*list = v;
143
144	return 0;
145error:
146	free_vertex_list(v);
147	return -1;
148}
149
150/* Compute the parametric vertices and the chamber decomposition
151 * of an empty parametric polytope.
152 */
153static __isl_give isl_vertices *vertices_empty(__isl_keep isl_basic_set *bset)
154{
155	isl_vertices *vertices;
156	unsigned nparam;
157
158	if (!bset)
159		return NULL;
160
161	nparam = isl_basic_set_dim(bset, isl_dim_param);
162
163	vertices = isl_calloc_type(bset->ctx, isl_vertices);
164	if (!vertices)
165		return NULL;
166	vertices->bset = isl_basic_set_copy(bset);
167	vertices->ref = 1;
168
169	vertices->n_vertices = 0;
170	vertices->n_chambers = 0;
171
172	return vertices;
173}
174
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
179 * the vertex.
180 */
181static __isl_give isl_vertices *vertices_0D(__isl_keep isl_basic_set *bset)
182{
183	isl_vertices *vertices;
184	unsigned nparam;
185
186	if (!bset)
187		return NULL;
188
189	nparam = isl_basic_set_dim(bset, isl_dim_param);
190
191	vertices = isl_calloc_type(bset->ctx, isl_vertices);
192	if (!vertices)
193		return NULL;
194	vertices->ref = 1;
195	vertices->bset = isl_basic_set_copy(bset);
196
197	vertices->v = isl_calloc_array(bset->ctx, struct isl_vertex, 1);
198	if (!vertices->v)
199		goto error;
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)
204		goto error;
205
206	vertices->c = isl_calloc_array(bset->ctx, struct isl_chamber, 1);
207	if (!vertices->c)
208		goto error;
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)
213		goto error;
214	vertices->c[0].dom = isl_basic_set_copy(vertices->v[0].dom);
215	if (!vertices->c[0].dom)
216		goto error;
217
218	return vertices;
219error:
220	isl_vertices_free(vertices);
221	return NULL;
222}
223
224static int isl_mat_rank(__isl_keep isl_mat *mat)
225{
226	int row, col;
227	isl_mat *H;
228
229	H = isl_mat_left_hermite(isl_mat_copy(mat), 0, NULL, NULL);
230	if (!H)
231		return -1;
232
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]))
236				break;
237		if (row == H->n_row)
238			break;
239	}
240
241	isl_mat_free(H);
242
243	return col;
244}
245
246/* Is the row pointed to by "f" linearly independent of the "n" first
247 * rows in "facets"?
248 */
249static int is_independent(__isl_keep isl_mat *facets, int n, isl_int *f)
250{
251	int rank;
252
253	if (isl_seq_first_non_zero(f, facets->n_col) < 0)
254		return 0;
255
256	isl_seq_cpy(facets->row[n], f, facets->n_col);
257	facets->n_row = n + 1;
258	rank = isl_mat_rank(facets);
259	if (rank < 0)
260		return -1;
261
262	return rank == n + 1;
263}
264
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".
268 *
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.
279 */
280static int can_select(__isl_keep isl_basic_set *bset, int level,
281	struct isl_tab *tab, __isl_keep isl_mat *facets, int selected,
282	int *selection)
283{
284	int i;
285	int indep;
286	unsigned ovar;
287	struct isl_tab_undo *snap;
288
289	if (isl_tab_is_redundant(tab, level))
290		return 0;
291
292	ovar = isl_space_offset(bset->dim, isl_dim_set);
293
294	indep = is_independent(facets, selected, bset->ineq[level] + 1 + ovar);
295	if (indep < 0)
296		return -1;
297	if (!indep)
298		return 0;
299
300	snap = isl_tab_snap(tab);
301	if (isl_tab_select_facet(tab, level) < 0)
302		return -1;
303
304	if (tab->empty) {
305		if (isl_tab_rollback(tab, snap) < 0)
306			return -1;
307		return 0;
308	}
309
310	for (i = 0; i < level; ++i) {
311		int sgn;
312
313		if (selection[i] != DESELECTED)
314			continue;
315
316		if (isl_tab_is_equality(tab, i))
317			sgn = 0;
318		else if (isl_tab_is_redundant(tab, i))
319			sgn = 1;
320		else
321			sgn = isl_tab_sign_of_max(tab, i);
322		if (sgn < -1)
323			return -1;
324		if (sgn <= 0) {
325			if (isl_tab_rollback(tab, snap) < 0)
326				return -1;
327			return 0;
328		}
329	}
330
331	return 1;
332}
333
334/* Compute the parametric vertices and the chamber decomposition
335 * of a parametric polytope that is not full-dimensional.
336 *
337 * Simply map the parametric polytope to a lower dimensional space
338 * and map the resulting vertices back.
339 */
340static __isl_give isl_vertices *lower_dim_vertices(
341	__isl_keep isl_basic_set *bset)
342{
343	isl_morph *morph;
344	isl_vertices *vertices;
345
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);
349
350	vertices = isl_basic_set_compute_vertices(bset);
351	isl_basic_set_free(bset);
352
353	morph = isl_morph_inverse(morph);
354
355	vertices = isl_morph_vertices(morph, vertices);
356
357	return vertices;
358}
359
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
363 * variables.
364 *
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
371 * smallest index.
372 *
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).
385 *
386 * The set variable coefficients of the selected constraints are stored
387 * in the facets matrix.
388 */
389__isl_give isl_vertices *isl_basic_set_compute_vertices(
390	__isl_keep isl_basic_set *bset)
391{
392	struct isl_tab *tab;
393	int level;
394	int init;
395	unsigned nvar;
396	int *selection = NULL;
397	int selected;
398	struct isl_tab_undo **snap = NULL;
399	isl_mat *facets = NULL;
400	struct isl_vertex_list *list = NULL;
401	int n_vertices = 0;
402	isl_vertices *vertices;
403
404	if (!bset)
405		return NULL;
406
407	if (isl_basic_set_plain_is_empty(bset))
408		return vertices_empty(bset);
409
410	if (bset->n_eq != 0)
411		return lower_dim_vertices(bset);
412
413	isl_assert(bset->ctx, isl_basic_set_dim(bset, isl_dim_div) == 0,
414		return NULL);
415
416	if (isl_basic_set_dim(bset, isl_dim_set) == 0)
417		return vertices_0D(bset);
418
419	nvar = isl_basic_set_dim(bset, isl_dim_set);
420
421	bset = isl_basic_set_copy(bset);
422	bset = isl_basic_set_set_rational(bset);
423	if (!bset)
424		return NULL;
425
426	tab = isl_tab_from_basic_set(bset, 0);
427	if (!tab)
428		goto error;
429	tab->strict_redundant = 1;
430
431	if (tab->empty)	{
432		vertices = vertices_empty(bset);
433		isl_basic_set_free(bset);
434		isl_tab_free(tab);
435		return vertices;
436	}
437
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)
442		goto error;
443
444	level = 0;
445	init = 1;
446	selected = 0;
447
448	while (level >= 0) {
449		if (level >= bset->n_ineq ||
450		    (!init && selection[level] != SELECTED)) {
451			--level;
452			init = 0;
453			continue;
454		}
455		if (init) {
456			int ok;
457			snap[level] = isl_tab_snap(tab);
458			ok = can_select(bset, level, tab, facets, selected,
459					selection);
460			if (ok < 0)
461				goto error;
462			if (ok) {
463				selection[level] = SELECTED;
464				selected++;
465			} else
466				selection[level] = UNSELECTED;
467		} else {
468			selection[level] = DESELECTED;
469			selected--;
470			if (isl_tab_rollback(tab, snap[level]) < 0)
471				goto error;
472		}
473		if (selected == nvar) {
474			if (tab->n_dead == nvar) {
475				if (add_vertex(&list, bset, tab) < 0)
476					goto error;
477				n_vertices++;
478			}
479			init = 0;
480			continue;
481		}
482		++level;
483		init = 1;
484	}
485
486	isl_mat_free(facets);
487	free(selection);
488	free(snap);
489
490	isl_tab_free(tab);
491
492	vertices = vertices_from_list(bset, n_vertices, list);
493
494	vertices = compute_chambers(bset, vertices);
495
496	return vertices;
497error:
498	free_vertex_list(list);
499	isl_mat_free(facets);
500	free(selection);
501	free(snap);
502	isl_tab_free(tab);
503	isl_basic_set_free(bset);
504	return NULL;
505}
506
507struct isl_chamber_list {
508	struct isl_chamber c;
509	struct isl_chamber_list *next;
510};
511
512static void free_chamber_list(struct isl_chamber_list *list)
513{
514	struct isl_chamber_list *next;
515
516	for (; list; list = next) {
517		next = list->next;
518		isl_basic_set_free(list->c.dom);
519		free(list->c.vertices);
520		free(list);
521	}
522}
523
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.
526 */
527static int bset_covers_tab(__isl_keep isl_basic_set *bset, struct isl_tab *tab)
528{
529	int i;
530
531	if (!bset || !tab)
532		return -1;
533
534	for (i = 0; i < bset->n_ineq; ++i) {
535		enum isl_ineq_type type = isl_tab_ineq_type(tab, bset->ineq[i]);
536		switch (type) {
537		case isl_ineq_error:		return -1;
538		case isl_ineq_redundant:	continue;
539		default:			return 0;
540		}
541	}
542
543	return 1;
544}
545
546static __isl_give isl_vertices *vertices_add_chambers(
547	__isl_take isl_vertices *vertices, int n_chambers,
548	struct isl_chamber_list *list)
549{
550	int i;
551	isl_ctx *ctx;
552	struct isl_chamber_list *next;
553
554	ctx = isl_vertices_get_ctx(vertices);
555	vertices->c = isl_alloc_array(ctx, struct isl_chamber, n_chambers);
556	if (!vertices->c)
557		goto error;
558	vertices->n_chambers = n_chambers;
559
560	for (i = 0; list; list = next, i++) {
561		next = list->next;
562		vertices->c[i] = list->c;
563		free(list);
564	}
565
566	return vertices;
567error:
568	isl_vertices_free(vertices);
569	free_chamber_list(list);
570	return NULL;
571}
572
573/* Can "tab" be intersected with "bset" without resulting in
574 * a lower-dimensional set.
575 */
576static int can_intersect(struct isl_tab *tab, __isl_keep isl_basic_set *bset)
577{
578	int i;
579	struct isl_tab_undo *snap;
580
581	if (isl_tab_extend_cons(tab, bset->n_ineq) < 0)
582		return -1;
583
584	snap = isl_tab_snap(tab);
585
586	for (i = 0; i < bset->n_ineq; ++i) {
587		if (isl_tab_ineq_type(tab, bset->ineq[i]) == isl_ineq_redundant)
588			continue;
589		if (isl_tab_add_ineq(tab, bset->ineq[i]) < 0)
590			return -1;
591	}
592
593	if (isl_tab_detect_implicit_equalities(tab) < 0)
594		return -1;
595	if (tab->n_dead) {
596		if (isl_tab_rollback(tab, snap) < 0)
597			return -1;
598		return 0;
599	}
600
601	return 1;
602}
603
604static int add_chamber(struct isl_chamber_list **list,
605	__isl_keep isl_vertices *vertices, struct isl_tab *tab, int *selection)
606{
607	int n_frozen;
608	int i, j;
609	int n_vertices = 0;
610	struct isl_tab_undo *snap;
611	struct isl_chamber_list *c = NULL;
612
613	for (i = 0; i < vertices->n_vertices; ++i)
614		if (selection[i])
615			n_vertices++;
616
617	snap = isl_tab_snap(tab);
618
619	for (i = 0; i < tab->n_con && tab->con[i].frozen; ++i)
620		tab->con[i].frozen = 0;
621	n_frozen = i;
622
623	if (isl_tab_detect_redundant(tab) < 0)
624		return -1;
625
626	c = isl_calloc_type(tab->mat->ctx, struct isl_chamber_list);
627	if (!c)
628		goto error;
629	c->c.vertices = isl_alloc_array(tab->mat->ctx, int, n_vertices);
630	if (n_vertices && !c->c.vertices)
631		goto error;
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);
638	if (!c->c.dom)
639		goto error;
640
641	c->c.n_vertices = n_vertices;
642
643	for (i = 0, j = 0; i < vertices->n_vertices; ++i)
644		if (selection[i]) {
645			c->c.vertices[j] = i;
646			j++;
647		}
648
649	c->next = *list;
650	*list = c;
651
652	for (i = 0; i < n_frozen; ++i)
653		tab->con[i].frozen = 1;
654
655	if (isl_tab_rollback(tab, snap) < 0)
656		return -1;
657
658	return 0;
659error:
660	free_chamber_list(c);
661	return -1;
662}
663
664struct 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;
669};
670
671static void free_todo(struct isl_facet_todo *todo)
672{
673	while (todo) {
674		struct isl_facet_todo *next = todo->next;
675
676		isl_tab_free(todo->tab);
677		isl_basic_set_free(todo->bset);
678		isl_vec_free(todo->constraint);
679		free(todo);
680
681		todo = next;
682	}
683}
684
685static struct isl_facet_todo *create_todo(struct isl_tab *tab, int con)
686{
687	int i;
688	int n_frozen;
689	struct isl_tab_undo *snap;
690	struct isl_facet_todo *todo;
691
692	snap = isl_tab_snap(tab);
693
694	for (i = 0; i < tab->n_con && tab->con[i].frozen; ++i)
695		tab->con[i].frozen = 0;
696	n_frozen = i;
697
698	if (isl_tab_detect_redundant(tab) < 0)
699		return NULL;
700
701	todo = isl_calloc_type(tab->mat->ctx, struct isl_facet_todo);
702	if (!todo)
703		return NULL;
704
705	todo->constraint = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
706	if (!todo->constraint)
707		goto error;
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);
715	if (!todo->bset)
716		goto error;
717	ISL_F_SET(todo->bset, ISL_BASIC_SET_NORMALIZED);
718	todo->tab = isl_tab_dup(tab);
719	if (!todo->tab)
720		goto error;
721
722	for (i = 0; i < n_frozen; ++i)
723		tab->con[i].frozen = 1;
724
725	if (isl_tab_rollback(tab, snap) < 0)
726		goto error;
727
728	return todo;
729error:
730	free_todo(todo);
731	return NULL;
732}
733
734/* Create todo items for all interior facets of the chamber represented
735 * by "tab" and collect them in "next".
736 */
737static int init_todo(struct isl_facet_todo **next, struct isl_tab *tab)
738{
739	int i;
740	struct isl_tab_undo *snap;
741	struct isl_facet_todo *todo;
742
743	snap = isl_tab_snap(tab);
744
745	for (i = 0; i < tab->n_con; ++i) {
746		if (tab->con[i].frozen)
747			continue;
748		if (tab->con[i].is_redundant)
749			continue;
750
751		if (isl_tab_select_facet(tab, i) < 0)
752			return -1;
753
754		todo = create_todo(tab, i);
755		if (!todo)
756			return -1;
757
758		todo->next = *next;
759		*next = todo;
760
761		if (isl_tab_rollback(tab, snap) < 0)
762			return -1;
763	}
764
765	return 0;
766}
767
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.
770 */
771static int has_opposite(struct isl_facet_todo *todo,
772	struct isl_facet_todo **list)
773{
774	for (; *list; list = &(*list)->next) {
775		int eq;
776		eq = isl_basic_set_plain_is_equal(todo->bset, (*list)->bset);
777		if (eq < 0)
778			return -1;
779		if (!eq)
780			continue;
781		todo = *list;
782		*list = todo->next;
783		todo->next = NULL;
784		free_todo(todo);
785		return 1;
786	}
787
788	return 0;
789}
790
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.
794 */
795static int update_todo(struct isl_facet_todo *first, struct isl_tab *tab)
796{
797	int i;
798	struct isl_tab_undo *snap;
799	struct isl_facet_todo *todo;
800
801	snap = isl_tab_snap(tab);
802
803	for (i = 0; i < tab->n_con; ++i) {
804		int drop;
805
806		if (tab->con[i].frozen)
807			continue;
808		if (tab->con[i].is_redundant)
809			continue;
810
811		if (isl_tab_select_facet(tab, i) < 0)
812			return -1;
813
814		todo = create_todo(tab, i);
815		if (!todo)
816			return -1;
817
818		drop = has_opposite(todo, &first->next);
819		if (drop < 0)
820			return -1;
821
822		if (drop)
823			free_todo(todo);
824		else {
825			todo->next = first->next;
826			first->next = todo;
827		}
828
829		if (isl_tab_rollback(tab, snap) < 0)
830			return -1;
831	}
832
833	return 0;
834}
835
836/* Compute the chamber decomposition of the parametric polytope respresented
837 * by "bset" given the parametric vertices and their activity domains.
838 *
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.
843 *
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.
848 *
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.
857 */
858static __isl_give isl_vertices *compute_chambers(__isl_take isl_basic_set *bset,
859	__isl_take isl_vertices *vertices)
860{
861	int i;
862	isl_ctx *ctx;
863	isl_vec *sample = NULL;
864	struct isl_tab *tab = NULL;
865	struct isl_tab_undo *snap;
866	int *selection = NULL;
867	int n_chambers = 0;
868	struct isl_chamber_list *list = NULL;
869	struct isl_facet_todo *todo = NULL;
870
871	if (!bset || !vertices)
872		goto error;
873
874	ctx = isl_vertices_get_ctx(vertices);
875	selection = isl_alloc_array(ctx, int, vertices->n_vertices);
876	if (vertices->n_vertices && !selection)
877		goto error;
878
879	bset = isl_basic_set_params(bset);
880
881	tab = isl_tab_from_basic_set(bset, 1);
882	if (!tab)
883		goto error;
884	for (i = 0; i < bset->n_ineq; ++i)
885		if (isl_tab_freeze_constraint(tab, i) < 0)
886			goto error;
887	isl_basic_set_free(bset);
888
889	snap = isl_tab_snap(tab);
890
891	sample = isl_tab_get_sample_value(tab);
892
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)
896			goto error;
897		if (!selection[i])
898			continue;
899		selection[i] = can_intersect(tab, vertices->v[i].dom);
900		if (selection[i] < 0)
901			goto error;
902	}
903
904	if (isl_tab_detect_redundant(tab) < 0)
905		goto error;
906
907	if (add_chamber(&list, vertices, tab, selection) < 0)
908		goto error;
909	n_chambers++;
910
911	if (init_todo(&todo, tab) < 0)
912		goto error;
913
914	while (todo) {
915		struct isl_facet_todo *next;
916
917		if (isl_tab_rollback(tab, snap) < 0)
918			goto error;
919
920		if (isl_tab_add_ineq(tab, todo->constraint->el) < 0)
921			goto error;
922		if (isl_tab_freeze_constraint(tab, tab->n_con - 1) < 0)
923			goto error;
924
925		for (i = 0; i < vertices->n_vertices; ++i) {
926			selection[i] = bset_covers_tab(vertices->v[i].dom,
927							todo->tab);
928			if (selection[i] < 0)
929				goto error;
930			if (!selection[i])
931				continue;
932			selection[i] = can_intersect(tab, vertices->v[i].dom);
933			if (selection[i] < 0)
934				goto error;
935		}
936
937		if (isl_tab_detect_redundant(tab) < 0)
938			goto error;
939
940		if (add_chamber(&list, vertices, tab, selection) < 0)
941			goto error;
942		n_chambers++;
943
944		if (update_todo(todo, tab) < 0)
945			goto error;
946
947		next = todo->next;
948		todo->next = NULL;
949		free_todo(todo);
950		todo = next;
951	}
952
953	isl_vec_free(sample);
954
955	isl_tab_free(tab);
956	free(selection);
957
958	vertices = vertices_add_chambers(vertices, n_chambers, list);
959
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;
963	}
964
965	return vertices;
966error:
967	free_chamber_list(list);
968	free_todo(todo);
969	isl_vec_free(sample);
970	isl_tab_free(tab);
971	free(selection);
972	if (!tab)
973		isl_basic_set_free(bset);
974	isl_vertices_free(vertices);
975	return NULL;
976}
977
978isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex)
979{
980	return vertex ? isl_vertices_get_ctx(vertex->vertices) : NULL;
981}
982
983int isl_vertex_get_id(__isl_keep isl_vertex *vertex)
984{
985	return vertex ? vertex->id : -1;
986}
987
988__isl_give isl_basic_set *isl_vertex_get_domain(__isl_keep isl_vertex *vertex)
989{
990	struct isl_vertex *v;
991
992	if (!vertex)
993		return NULL;
994
995	v = &vertex->vertices->v[vertex->id];
996	if (!v->dom) {
997		v->dom = isl_basic_set_copy(v->vertex);
998		v->dom = isl_basic_set_params(v->dom);
999	}
1000
1001	return isl_basic_set_copy(v->dom);
1002}
1003
1004__isl_give isl_basic_set *isl_vertex_get_expr(__isl_keep isl_vertex *vertex)
1005{
1006	struct isl_vertex *v;
1007
1008	if (!vertex)
1009		return NULL;
1010
1011	v = &vertex->vertices->v[vertex->id];
1012
1013	return isl_basic_set_copy(v->vertex);
1014}
1015
1016static __isl_give isl_vertex *isl_vertex_alloc(__isl_take isl_vertices *vertices,
1017	int id)
1018{
1019	isl_ctx *ctx;
1020	isl_vertex *vertex;
1021
1022	if (!vertices)
1023		return NULL;
1024
1025	ctx = isl_vertices_get_ctx(vertices);
1026	vertex = isl_alloc_type(ctx, isl_vertex);
1027	if (!vertex)
1028		goto error;
1029
1030	vertex->vertices = vertices;
1031	vertex->id = id;
1032
1033	return vertex;
1034error:
1035	isl_vertices_free(vertices);
1036	return NULL;
1037}
1038
1039void isl_vertex_free(__isl_take isl_vertex *vertex)
1040{
1041	if (!vertex)
1042		return;
1043	isl_vertices_free(vertex->vertices);
1044	free(vertex);
1045}
1046
1047__isl_give isl_basic_set *isl_basic_set_set_integral(__isl_take isl_basic_set *bset)
1048{
1049	if (!bset)
1050		return NULL;
1051
1052	if (!ISL_F_ISSET(bset, ISL_BASIC_MAP_RATIONAL))
1053		return bset;
1054
1055	bset = isl_basic_set_cow(bset);
1056	if (!bset)
1057		return NULL;
1058
1059	ISL_F_CLR(bset, ISL_BASIC_MAP_RATIONAL);
1060
1061	return isl_basic_set_finalize(bset);
1062}
1063
1064isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell)
1065{
1066	return cell ? cell->dom->ctx : NULL;
1067}
1068
1069__isl_give isl_basic_set *isl_cell_get_domain(__isl_keep isl_cell *cell)
1070{
1071	return cell ? isl_basic_set_copy(cell->dom) : NULL;
1072}
1073
1074static __isl_give isl_cell *isl_cell_alloc(__isl_take isl_vertices *vertices,
1075	__isl_take isl_basic_set *dom, int id)
1076{
1077	int i;
1078	isl_cell *cell = NULL;
1079
1080	if (!vertices || !dom)
1081		goto error;
1082
1083	cell = isl_calloc_type(dom->ctx, isl_cell);
1084	if (!cell)
1085		goto error;
1086
1087	cell->n_vertices = vertices->c[id].n_vertices;
1088	cell->ids = isl_alloc_array(dom->ctx, int, cell->n_vertices);
1089	if (cell->n_vertices && !cell->ids)
1090		goto error;
1091	for (i = 0; i < cell->n_vertices; ++i)
1092		cell->ids[i] = vertices->c[id].vertices[i];
1093	cell->vertices = vertices;
1094	cell->dom = dom;
1095
1096	return cell;
1097error:
1098	isl_cell_free(cell);
1099	isl_vertices_free(vertices);
1100	isl_basic_set_free(dom);
1101	return NULL;
1102}
1103
1104void isl_cell_free(__isl_take isl_cell *cell)
1105{
1106	if (!cell)
1107		return;
1108
1109	isl_vertices_free(cell->vertices);
1110	free(cell->ids);
1111	isl_basic_set_free(cell->dom);
1112	free(cell);
1113}
1114
1115/* Create a tableau of the cone obtained by first homogenizing the given
1116 * polytope and then making all inequalities strict by setting the
1117 * constant term to -1.
1118 */
1119static struct isl_tab *tab_for_shifted_cone(__isl_keep isl_basic_set *bset)
1120{
1121	int i;
1122	isl_vec *c = NULL;
1123	struct isl_tab *tab;
1124
1125	if (!bset)
1126		return NULL;
1127	tab = isl_tab_alloc(bset->ctx, bset->n_ineq + 1,
1128			    1 + isl_basic_set_total_dim(bset), 0);
1129	if (!tab)
1130		return NULL;
1131	tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
1132	if (ISL_F_ISSET(bset, ISL_BASIC_MAP_EMPTY)) {
1133		if (isl_tab_mark_empty(tab) < 0)
1134			goto error;
1135		return tab;
1136	}
1137
1138	c = isl_vec_alloc(bset->ctx, 1 + 1 + isl_basic_set_total_dim(bset));
1139	if (!c)
1140		goto error;
1141
1142	isl_int_set_si(c->el[0], 0);
1143	for (i = 0; i < bset->n_eq; ++i) {
1144		isl_seq_cpy(c->el + 1, bset->eq[i], c->size - 1);
1145		if (isl_tab_add_eq(tab, c->el) < 0)
1146			goto error;
1147	}
1148
1149	isl_int_set_si(c->el[0], -1);
1150	for (i = 0; i < bset->n_ineq; ++i) {
1151		isl_seq_cpy(c->el + 1, bset->ineq[i], c->size - 1);
1152		if (isl_tab_add_ineq(tab, c->el) < 0)
1153			goto error;
1154		if (tab->empty) {
1155			isl_vec_free(c);
1156			return tab;
1157		}
1158	}
1159
1160	isl_seq_clr(c->el + 1, c->size - 1);
1161	isl_int_set_si(c->el[1], 1);
1162	if (isl_tab_add_ineq(tab, c->el) < 0)
1163		goto error;
1164
1165	isl_vec_free(c);
1166	return tab;
1167error:
1168	isl_vec_free(c);
1169	isl_tab_free(tab);
1170	return NULL;
1171}
1172
1173/* Compute an interior point of "bset" by selecting an interior
1174 * point in homogeneous space and projecting the point back down.
1175 */
1176static __isl_give isl_vec *isl_basic_set_interior_point(
1177	__isl_keep isl_basic_set *bset)
1178{
1179	isl_vec *vec;
1180	struct isl_tab *tab;
1181
1182	tab = tab_for_shifted_cone(bset);
1183	vec = isl_tab_get_sample_value(tab);
1184	isl_tab_free(tab);
1185	if (!vec)
1186		return NULL;
1187
1188	isl_seq_cpy(vec->el, vec->el + 1, vec->size - 1);
1189	vec->size--;
1190
1191	return vec;
1192}
1193
1194/* Call "fn" on all chambers of the parametric polytope with the shared
1195 * facets of neighboring chambers only appearing in one of the chambers.
1196 *
1197 * We pick an interior point from one of the chambers and then make
1198 * all constraints that do not satisfy this point strict.
1199 */
1200int isl_vertices_foreach_disjoint_cell(__isl_keep isl_vertices *vertices,
1201	int (*fn)(__isl_take isl_cell *cell, void *user), void *user)
1202{
1203	int i, j;
1204	isl_vec *vec;
1205	isl_int v;
1206	isl_cell *cell;
1207
1208	if (!vertices)
1209		return -1;
1210
1211	if (vertices->n_chambers == 0)
1212		return 0;
1213
1214	if (vertices->n_chambers == 1) {
1215		isl_basic_set *dom = isl_basic_set_copy(vertices->c[0].dom);
1216		dom = isl_basic_set_set_integral(dom);
1217		cell = isl_cell_alloc(isl_vertices_copy(vertices), dom, 0);
1218		if (!cell)
1219			return -1;
1220		return fn(cell, user);
1221	}
1222
1223	vec = isl_basic_set_interior_point(vertices->c[0].dom);
1224	if (!vec)
1225		return -1;
1226
1227	isl_int_init(v);
1228
1229	for (i = 0; i < vertices->n_chambers; ++i) {
1230		int r;
1231		isl_basic_set *dom = isl_basic_set_copy(vertices->c[i].dom);
1232		dom = isl_basic_set_cow(dom);
1233		if (!dom)
1234			goto error;
1235		for (j = 0; i && j < dom->n_ineq; ++j) {
1236			isl_seq_inner_product(vec->el, dom->ineq[j], vec->size,
1237						&v);
1238			if (!isl_int_is_neg(v))
1239				continue;
1240			isl_int_sub_ui(dom->ineq[j][0], dom->ineq[j][0], 1);
1241		}
1242		dom = isl_basic_set_set_integral(dom);
1243		cell = isl_cell_alloc(isl_vertices_copy(vertices), dom, i);
1244		if (!cell)
1245			goto error;
1246		r = fn(cell, user);
1247		if (r < 0)
1248			goto error;
1249	}
1250
1251	isl_int_clear(v);
1252	isl_vec_free(vec);
1253
1254	return 0;
1255error:
1256	isl_int_clear(v);
1257	isl_vec_free(vec);
1258	return -1;
1259}
1260
1261int isl_vertices_foreach_cell(__isl_keep isl_vertices *vertices,
1262	int (*fn)(__isl_take isl_cell *cell, void *user), void *user)
1263{
1264	int i;
1265	isl_cell *cell;
1266
1267	if (!vertices)
1268		return -1;
1269
1270	if (vertices->n_chambers == 0)
1271		return 0;
1272
1273	for (i = 0; i < vertices->n_chambers; ++i) {
1274		int r;
1275		isl_basic_set *dom = isl_basic_set_copy(vertices->c[i].dom);
1276
1277		cell = isl_cell_alloc(isl_vertices_copy(vertices), dom, i);
1278		if (!cell)
1279			return -1;
1280
1281		r = fn(cell, user);
1282		if (r < 0)
1283			return -1;
1284	}
1285
1286	return 0;
1287}
1288
1289int isl_vertices_foreach_vertex(__isl_keep isl_vertices *vertices,
1290	int (*fn)(__isl_take isl_vertex *vertex, void *user), void *user)
1291{
1292	int i;
1293	isl_vertex *vertex;
1294
1295	if (!vertices)
1296		return -1;
1297
1298	if (vertices->n_vertices == 0)
1299		return 0;
1300
1301	for (i = 0; i < vertices->n_vertices; ++i) {
1302		int r;
1303
1304		vertex = isl_vertex_alloc(isl_vertices_copy(vertices), i);
1305		if (!vertex)
1306			return -1;
1307
1308		r = fn(vertex, user);
1309		if (r < 0)
1310			return -1;
1311	}
1312
1313	return 0;
1314}
1315
1316int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
1317	int (*fn)(__isl_take isl_vertex *vertex, void *user), void *user)
1318{
1319	int i;
1320	isl_vertex *vertex;
1321
1322	if (!cell)
1323		return -1;
1324
1325	if (cell->n_vertices == 0)
1326		return 0;
1327
1328	for (i = 0; i < cell->n_vertices; ++i) {
1329		int r;
1330
1331		vertex = isl_vertex_alloc(isl_vertices_copy(cell->vertices),
1332					  cell->ids[i]);
1333		if (!vertex)
1334			return -1;
1335
1336		r = fn(vertex, user);
1337		if (r < 0)
1338			return -1;
1339	}
1340
1341	return 0;
1342}
1343
1344isl_ctx *isl_vertices_get_ctx(__isl_keep isl_vertices *vertices)
1345{
1346	return vertices ? vertices->bset->ctx : NULL;
1347}
1348
1349int isl_vertices_get_n_vertices(__isl_keep isl_vertices *vertices)
1350{
1351	return vertices ? vertices->n_vertices : -1;
1352}
1353
1354__isl_give isl_vertices *isl_morph_vertices(__isl_take isl_morph *morph,
1355	__isl_take isl_vertices *vertices)
1356{
1357	int i;
1358	isl_morph *param_morph = NULL;
1359
1360	if (!morph || !vertices)
1361		goto error;
1362
1363	isl_assert(vertices->bset->ctx, vertices->ref == 1, goto error);
1364
1365	param_morph = isl_morph_copy(morph);
1366	param_morph = isl_morph_dom_params(param_morph);
1367	param_morph = isl_morph_ran_params(param_morph);
1368
1369	for (i = 0; i < vertices->n_vertices; ++i) {
1370		vertices->v[i].dom = isl_morph_basic_set(
1371			isl_morph_copy(param_morph), vertices->v[i].dom);
1372		vertices->v[i].vertex = isl_morph_basic_set(
1373			isl_morph_copy(morph), vertices->v[i].vertex);
1374		if (!vertices->v[i].vertex)
1375			goto error;
1376	}
1377
1378	for (i = 0; i < vertices->n_chambers; ++i) {
1379		vertices->c[i].dom = isl_morph_basic_set(
1380			isl_morph_copy(param_morph), vertices->c[i].dom);
1381		if (!vertices->c[i].dom)
1382			goto error;
1383	}
1384
1385	isl_morph_free(param_morph);
1386	isl_morph_free(morph);
1387	return vertices;
1388error:
1389	isl_morph_free(param_morph);
1390	isl_morph_free(morph);
1391	isl_vertices_free(vertices);
1392	return NULL;
1393}
1394
1395/* Construct a simplex isl_cell spanned by the vertices with indices in
1396 * "simplex_ids" and "other_ids" and call "fn" on this isl_cell.
1397 */
1398static int call_on_simplex(__isl_keep isl_cell *cell,
1399	int *simplex_ids, int n_simplex, int *other_ids, int n_other,
1400	int (*fn)(__isl_take isl_cell *simplex, void *user), void *user)
1401{
1402	int i;
1403	isl_ctx *ctx;
1404	struct isl_cell *simplex;
1405
1406	ctx = isl_cell_get_ctx(cell);
1407
1408	simplex = isl_calloc_type(ctx, struct isl_cell);
1409	if (!simplex)
1410		return -1;
1411	simplex->vertices = isl_vertices_copy(cell->vertices);
1412	if (!simplex->vertices)
1413		goto error;
1414	simplex->dom = isl_basic_set_copy(cell->dom);
1415	if (!simplex->dom)
1416		goto error;
1417	simplex->n_vertices = n_simplex + n_other;
1418	simplex->ids = isl_alloc_array(ctx, int, simplex->n_vertices);
1419	if (!simplex->ids)
1420		goto error;
1421
1422	for (i = 0; i < n_simplex; ++i)
1423		simplex->ids[i] = simplex_ids[i];
1424	for (i = 0; i < n_other; ++i)
1425		simplex->ids[n_simplex + i] = other_ids[i];
1426
1427	return fn(simplex, user);
1428error:
1429	isl_cell_free(simplex);
1430	return -1;
1431}
1432
1433/* Check whether the parametric vertex described by "vertex"
1434 * lies on the facet corresponding to constraint "facet" of "bset".
1435 * The isl_vec "v" is a temporary vector than can be used by this function.
1436 *
1437 * We eliminate the variables from the facet constraint using the
1438 * equalities defining the vertex and check if the result is identical
1439 * to zero.
1440 *
1441 * It would probably be better to keep track of the constraints defining
1442 * a vertex during the vertex construction so that we could simply look
1443 * it up here.
1444 */
1445static int vertex_on_facet(__isl_keep isl_basic_set *vertex,
1446	__isl_keep isl_basic_set *bset, int facet, __isl_keep isl_vec *v)
1447{
1448	int i;
1449	isl_int m;
1450
1451	isl_seq_cpy(v->el, bset->ineq[facet], v->size);
1452
1453	isl_int_init(m);
1454	for (i = 0; i < vertex->n_eq; ++i) {
1455		int k = isl_seq_last_non_zero(vertex->eq[i], v->size);
1456		isl_seq_elim(v->el, vertex->eq[i], k, v->size, &m);
1457	}
1458	isl_int_clear(m);
1459
1460	return isl_seq_first_non_zero(v->el, v->size) == -1;
1461}
1462
1463/* Triangulate the polytope spanned by the vertices with ids
1464 * in "simplex_ids" and "other_ids" and call "fn" on each of
1465 * the resulting simplices.
1466 * If the input polytope is already a simplex, we simply call "fn".
1467 * Otherwise, we pick a point from "other_ids" and add it to "simplex_ids".
1468 * Then we consider each facet of "bset" that does not contain the point
1469 * we just picked, but does contain some of the other points in "other_ids"
1470 * and call ourselves recursively on the polytope spanned by the new
1471 * "simplex_ids" and those points in "other_ids" that lie on the facet.
1472 */
1473static int triangulate(__isl_keep isl_cell *cell, __isl_keep isl_vec *v,
1474	int *simplex_ids, int n_simplex, int *other_ids, int n_other,
1475	int (*fn)(__isl_take isl_cell *simplex, void *user), void *user)
1476{
1477	int i, j, k;
1478	int d, nparam;
1479	int *ids;
1480	isl_ctx *ctx;
1481	isl_basic_set *vertex;
1482	isl_basic_set *bset;
1483
1484	ctx = isl_cell_get_ctx(cell);
1485	d = isl_basic_set_dim(cell->vertices->bset, isl_dim_set);
1486	nparam = isl_basic_set_dim(cell->vertices->bset, isl_dim_param);
1487
1488	if (n_simplex + n_other == d + 1)
1489		return call_on_simplex(cell, simplex_ids, n_simplex,
1490				       other_ids, n_other, fn, user);
1491
1492	simplex_ids[n_simplex] = other_ids[0];
1493	vertex = cell->vertices->v[other_ids[0]].vertex;
1494	bset = cell->vertices->bset;
1495
1496	ids = isl_alloc_array(ctx, int, n_other - 1);
1497	for (i = 0; i < bset->n_ineq; ++i) {
1498		if (isl_seq_first_non_zero(bset->ineq[i] + 1 + nparam, d) == -1)
1499			continue;
1500		if (vertex_on_facet(vertex, bset, i, v))
1501			continue;
1502
1503		for (j = 1, k = 0; j < n_other; ++j) {
1504			isl_basic_set *ov;
1505			ov = cell->vertices->v[other_ids[j]].vertex;
1506			if (vertex_on_facet(ov, bset, i, v))
1507				ids[k++] = other_ids[j];
1508		}
1509		if (k == 0)
1510			continue;
1511
1512		if (triangulate(cell, v, simplex_ids, n_simplex + 1,
1513				ids, k, fn, user) < 0)
1514			goto error;
1515	}
1516	free(ids);
1517
1518	return 0;
1519error:
1520	free(ids);
1521	return -1;
1522}
1523
1524/* Triangulate the given cell and call "fn" on each of the resulting
1525 * simplices.
1526 */
1527int isl_cell_foreach_simplex(__isl_take isl_cell *cell,
1528	int (*fn)(__isl_take isl_cell *simplex, void *user), void *user)
1529{
1530	int d, total;
1531	int r;
1532	isl_ctx *ctx;
1533	isl_vec *v = NULL;
1534	int *simplex_ids = NULL;
1535
1536	if (!cell)
1537		return -1;
1538
1539	d = isl_basic_set_dim(cell->vertices->bset, isl_dim_set);
1540	total = isl_basic_set_total_dim(cell->vertices->bset);
1541
1542	if (cell->n_vertices == d + 1)
1543		return fn(cell, user);
1544
1545	ctx = isl_cell_get_ctx(cell);
1546	simplex_ids = isl_alloc_array(ctx, int, d + 1);
1547	if (!simplex_ids)
1548		goto error;
1549
1550	v = isl_vec_alloc(ctx, 1 + total);
1551	if (!v)
1552		goto error;
1553
1554	r = triangulate(cell, v, simplex_ids, 0,
1555			cell->ids, cell->n_vertices, fn, user);
1556
1557	isl_vec_free(v);
1558	free(simplex_ids);
1559
1560	isl_cell_free(cell);
1561
1562	return r;
1563error:
1564	free(simplex_ids);
1565	isl_vec_free(v);
1566	isl_cell_free(cell);
1567	return -1;
1568}
1569