add isl_basic_set_get_dim_id
[isl.git] / isl_convex_hull.c
blob2fe4f73962a970877c2bfad3581008e7641c3471
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8 */
10 #include <isl_ctx_private.h>
11 #include <isl_map_private.h>
12 #include <isl/lp.h>
13 #include <isl/map.h>
14 #include <isl_mat_private.h>
15 #include <isl/set.h>
16 #include <isl/seq.h>
17 #include <isl_options_private.h>
18 #include "isl_equalities.h"
19 #include "isl_tab.h"
21 static struct isl_basic_set *uset_convex_hull_wrap_bounded(struct isl_set *set);
23 /* Return 1 if constraint c is redundant with respect to the constraints
24 * in bmap. If c is a lower [upper] bound in some variable and bmap
25 * does not have a lower [upper] bound in that variable, then c cannot
26 * be redundant and we do not need solve any lp.
28 int isl_basic_map_constraint_is_redundant(struct isl_basic_map **bmap,
29 isl_int *c, isl_int *opt_n, isl_int *opt_d)
31 enum isl_lp_result res;
32 unsigned total;
33 int i, j;
35 if (!bmap)
36 return -1;
38 total = isl_basic_map_total_dim(*bmap);
39 for (i = 0; i < total; ++i) {
40 int sign;
41 if (isl_int_is_zero(c[1+i]))
42 continue;
43 sign = isl_int_sgn(c[1+i]);
44 for (j = 0; j < (*bmap)->n_ineq; ++j)
45 if (sign == isl_int_sgn((*bmap)->ineq[j][1+i]))
46 break;
47 if (j == (*bmap)->n_ineq)
48 break;
50 if (i < total)
51 return 0;
53 res = isl_basic_map_solve_lp(*bmap, 0, c, (*bmap)->ctx->one,
54 opt_n, opt_d, NULL);
55 if (res == isl_lp_unbounded)
56 return 0;
57 if (res == isl_lp_error)
58 return -1;
59 if (res == isl_lp_empty) {
60 *bmap = isl_basic_map_set_to_empty(*bmap);
61 return 0;
63 return !isl_int_is_neg(*opt_n);
66 int isl_basic_set_constraint_is_redundant(struct isl_basic_set **bset,
67 isl_int *c, isl_int *opt_n, isl_int *opt_d)
69 return isl_basic_map_constraint_is_redundant(
70 (struct isl_basic_map **)bset, c, opt_n, opt_d);
73 /* Remove redundant
74 * constraints. If the minimal value along the normal of a constraint
75 * is the same if the constraint is removed, then the constraint is redundant.
77 * Alternatively, we could have intersected the basic map with the
78 * corresponding equality and the checked if the dimension was that
79 * of a facet.
81 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
82 __isl_take isl_basic_map *bmap)
84 struct isl_tab *tab;
86 if (!bmap)
87 return NULL;
89 bmap = isl_basic_map_gauss(bmap, NULL);
90 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
91 return bmap;
92 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_NO_REDUNDANT))
93 return bmap;
94 if (bmap->n_ineq <= 1)
95 return bmap;
97 tab = isl_tab_from_basic_map(bmap, 0);
98 if (isl_tab_detect_implicit_equalities(tab) < 0)
99 goto error;
100 if (isl_tab_detect_redundant(tab) < 0)
101 goto error;
102 bmap = isl_basic_map_update_from_tab(bmap, tab);
103 isl_tab_free(tab);
104 ISL_F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
105 ISL_F_SET(bmap, ISL_BASIC_MAP_NO_REDUNDANT);
106 return bmap;
107 error:
108 isl_tab_free(tab);
109 isl_basic_map_free(bmap);
110 return NULL;
113 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
114 __isl_take isl_basic_set *bset)
116 return (struct isl_basic_set *)
117 isl_basic_map_remove_redundancies((struct isl_basic_map *)bset);
120 /* Remove redundant constraints in each of the basic maps.
122 __isl_give isl_map *isl_map_remove_redundancies(__isl_take isl_map *map)
124 return isl_map_inline_foreach_basic_map(map,
125 &isl_basic_map_remove_redundancies);
128 __isl_give isl_set *isl_set_remove_redundancies(__isl_take isl_set *set)
130 return isl_map_remove_redundancies(set);
133 /* Check if the set set is bound in the direction of the affine
134 * constraint c and if so, set the constant term such that the
135 * resulting constraint is a bounding constraint for the set.
137 static int uset_is_bound(struct isl_set *set, isl_int *c, unsigned len)
139 int first;
140 int j;
141 isl_int opt;
142 isl_int opt_denom;
144 isl_int_init(opt);
145 isl_int_init(opt_denom);
146 first = 1;
147 for (j = 0; j < set->n; ++j) {
148 enum isl_lp_result res;
150 if (ISL_F_ISSET(set->p[j], ISL_BASIC_SET_EMPTY))
151 continue;
153 res = isl_basic_set_solve_lp(set->p[j],
154 0, c, set->ctx->one, &opt, &opt_denom, NULL);
155 if (res == isl_lp_unbounded)
156 break;
157 if (res == isl_lp_error)
158 goto error;
159 if (res == isl_lp_empty) {
160 set->p[j] = isl_basic_set_set_to_empty(set->p[j]);
161 if (!set->p[j])
162 goto error;
163 continue;
165 if (first || isl_int_is_neg(opt)) {
166 if (!isl_int_is_one(opt_denom))
167 isl_seq_scale(c, c, opt_denom, len);
168 isl_int_sub(c[0], c[0], opt);
170 first = 0;
172 isl_int_clear(opt);
173 isl_int_clear(opt_denom);
174 return j >= set->n;
175 error:
176 isl_int_clear(opt);
177 isl_int_clear(opt_denom);
178 return -1;
181 __isl_give isl_basic_map *isl_basic_map_set_rational(
182 __isl_take isl_basic_set *bmap)
184 if (!bmap)
185 return NULL;
187 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL))
188 return bmap;
190 bmap = isl_basic_map_cow(bmap);
191 if (!bmap)
192 return NULL;
194 ISL_F_SET(bmap, ISL_BASIC_MAP_RATIONAL);
196 return isl_basic_map_finalize(bmap);
199 __isl_give isl_basic_set *isl_basic_set_set_rational(
200 __isl_take isl_basic_set *bset)
202 return isl_basic_map_set_rational(bset);
205 __isl_give isl_map *isl_map_set_rational(__isl_take isl_map *map)
207 int i;
209 map = isl_map_cow(map);
210 if (!map)
211 return NULL;
212 for (i = 0; i < map->n; ++i) {
213 map->p[i] = isl_basic_map_set_rational(map->p[i]);
214 if (!map->p[i])
215 goto error;
217 return map;
218 error:
219 isl_map_free(map);
220 return NULL;
223 __isl_give isl_set *isl_set_set_rational(__isl_take isl_set *set)
225 return isl_map_set_rational(set);
228 static struct isl_basic_set *isl_basic_set_add_equality(
229 struct isl_basic_set *bset, isl_int *c)
231 int i;
232 unsigned dim;
234 if (!bset)
235 return NULL;
237 if (ISL_F_ISSET(bset, ISL_BASIC_SET_EMPTY))
238 return bset;
240 isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
241 isl_assert(bset->ctx, bset->n_div == 0, goto error);
242 dim = isl_basic_set_n_dim(bset);
243 bset = isl_basic_set_cow(bset);
244 bset = isl_basic_set_extend(bset, 0, dim, 0, 1, 0);
245 i = isl_basic_set_alloc_equality(bset);
246 if (i < 0)
247 goto error;
248 isl_seq_cpy(bset->eq[i], c, 1 + dim);
249 return bset;
250 error:
251 isl_basic_set_free(bset);
252 return NULL;
255 static struct isl_set *isl_set_add_basic_set_equality(struct isl_set *set, isl_int *c)
257 int i;
259 set = isl_set_cow(set);
260 if (!set)
261 return NULL;
262 for (i = 0; i < set->n; ++i) {
263 set->p[i] = isl_basic_set_add_equality(set->p[i], c);
264 if (!set->p[i])
265 goto error;
267 return set;
268 error:
269 isl_set_free(set);
270 return NULL;
273 /* Given a union of basic sets, construct the constraints for wrapping
274 * a facet around one of its ridges.
275 * In particular, if each of n the d-dimensional basic sets i in "set"
276 * contains the origin, satisfies the constraints x_1 >= 0 and x_2 >= 0
277 * and is defined by the constraints
278 * [ 1 ]
279 * A_i [ x ] >= 0
281 * then the resulting set is of dimension n*(1+d) and has as constraints
283 * [ a_i ]
284 * A_i [ x_i ] >= 0
286 * a_i >= 0
288 * \sum_i x_{i,1} = 1
290 static struct isl_basic_set *wrap_constraints(struct isl_set *set)
292 struct isl_basic_set *lp;
293 unsigned n_eq;
294 unsigned n_ineq;
295 int i, j, k;
296 unsigned dim, lp_dim;
298 if (!set)
299 return NULL;
301 dim = 1 + isl_set_n_dim(set);
302 n_eq = 1;
303 n_ineq = set->n;
304 for (i = 0; i < set->n; ++i) {
305 n_eq += set->p[i]->n_eq;
306 n_ineq += set->p[i]->n_ineq;
308 lp = isl_basic_set_alloc(set->ctx, 0, dim * set->n, 0, n_eq, n_ineq);
309 lp = isl_basic_set_set_rational(lp);
310 if (!lp)
311 return NULL;
312 lp_dim = isl_basic_set_n_dim(lp);
313 k = isl_basic_set_alloc_equality(lp);
314 isl_int_set_si(lp->eq[k][0], -1);
315 for (i = 0; i < set->n; ++i) {
316 isl_int_set_si(lp->eq[k][1+dim*i], 0);
317 isl_int_set_si(lp->eq[k][1+dim*i+1], 1);
318 isl_seq_clr(lp->eq[k]+1+dim*i+2, dim-2);
320 for (i = 0; i < set->n; ++i) {
321 k = isl_basic_set_alloc_inequality(lp);
322 isl_seq_clr(lp->ineq[k], 1+lp_dim);
323 isl_int_set_si(lp->ineq[k][1+dim*i], 1);
325 for (j = 0; j < set->p[i]->n_eq; ++j) {
326 k = isl_basic_set_alloc_equality(lp);
327 isl_seq_clr(lp->eq[k], 1+dim*i);
328 isl_seq_cpy(lp->eq[k]+1+dim*i, set->p[i]->eq[j], dim);
329 isl_seq_clr(lp->eq[k]+1+dim*(i+1), dim*(set->n-i-1));
332 for (j = 0; j < set->p[i]->n_ineq; ++j) {
333 k = isl_basic_set_alloc_inequality(lp);
334 isl_seq_clr(lp->ineq[k], 1+dim*i);
335 isl_seq_cpy(lp->ineq[k]+1+dim*i, set->p[i]->ineq[j], dim);
336 isl_seq_clr(lp->ineq[k]+1+dim*(i+1), dim*(set->n-i-1));
339 return lp;
342 /* Given a facet "facet" of the convex hull of "set" and a facet "ridge"
343 * of that facet, compute the other facet of the convex hull that contains
344 * the ridge.
346 * We first transform the set such that the facet constraint becomes
348 * x_1 >= 0
350 * I.e., the facet lies in
352 * x_1 = 0
354 * and on that facet, the constraint that defines the ridge is
356 * x_2 >= 0
358 * (This transformation is not strictly needed, all that is needed is
359 * that the ridge contains the origin.)
361 * Since the ridge contains the origin, the cone of the convex hull
362 * will be of the form
364 * x_1 >= 0
365 * x_2 >= a x_1
367 * with this second constraint defining the new facet.
368 * The constant a is obtained by settting x_1 in the cone of the
369 * convex hull to 1 and minimizing x_2.
370 * Now, each element in the cone of the convex hull is the sum
371 * of elements in the cones of the basic sets.
372 * If a_i is the dilation factor of basic set i, then the problem
373 * we need to solve is
375 * min \sum_i x_{i,2}
376 * st
377 * \sum_i x_{i,1} = 1
378 * a_i >= 0
379 * [ a_i ]
380 * A [ x_i ] >= 0
382 * with
383 * [ 1 ]
384 * A_i [ x_i ] >= 0
386 * the constraints of each (transformed) basic set.
387 * If a = n/d, then the constraint defining the new facet (in the transformed
388 * space) is
390 * -n x_1 + d x_2 >= 0
392 * In the original space, we need to take the same combination of the
393 * corresponding constraints "facet" and "ridge".
395 * If a = -infty = "-1/0", then we just return the original facet constraint.
396 * This means that the facet is unbounded, but has a bounded intersection
397 * with the union of sets.
399 isl_int *isl_set_wrap_facet(__isl_keep isl_set *set,
400 isl_int *facet, isl_int *ridge)
402 int i;
403 isl_ctx *ctx;
404 struct isl_mat *T = NULL;
405 struct isl_basic_set *lp = NULL;
406 struct isl_vec *obj;
407 enum isl_lp_result res;
408 isl_int num, den;
409 unsigned dim;
411 if (!set)
412 return NULL;
413 ctx = set->ctx;
414 set = isl_set_copy(set);
415 set = isl_set_set_rational(set);
417 dim = 1 + isl_set_n_dim(set);
418 T = isl_mat_alloc(ctx, 3, dim);
419 if (!T)
420 goto error;
421 isl_int_set_si(T->row[0][0], 1);
422 isl_seq_clr(T->row[0]+1, dim - 1);
423 isl_seq_cpy(T->row[1], facet, dim);
424 isl_seq_cpy(T->row[2], ridge, dim);
425 T = isl_mat_right_inverse(T);
426 set = isl_set_preimage(set, T);
427 T = NULL;
428 if (!set)
429 goto error;
430 lp = wrap_constraints(set);
431 obj = isl_vec_alloc(ctx, 1 + dim*set->n);
432 if (!obj)
433 goto error;
434 isl_int_set_si(obj->block.data[0], 0);
435 for (i = 0; i < set->n; ++i) {
436 isl_seq_clr(obj->block.data + 1 + dim*i, 2);
437 isl_int_set_si(obj->block.data[1 + dim*i+2], 1);
438 isl_seq_clr(obj->block.data + 1 + dim*i+3, dim-3);
440 isl_int_init(num);
441 isl_int_init(den);
442 res = isl_basic_set_solve_lp(lp, 0,
443 obj->block.data, ctx->one, &num, &den, NULL);
444 if (res == isl_lp_ok) {
445 isl_int_neg(num, num);
446 isl_seq_combine(facet, num, facet, den, ridge, dim);
447 isl_seq_normalize(ctx, facet, dim);
449 isl_int_clear(num);
450 isl_int_clear(den);
451 isl_vec_free(obj);
452 isl_basic_set_free(lp);
453 isl_set_free(set);
454 if (res == isl_lp_error)
455 return NULL;
456 isl_assert(ctx, res == isl_lp_ok || res == isl_lp_unbounded,
457 return NULL);
458 return facet;
459 error:
460 isl_basic_set_free(lp);
461 isl_mat_free(T);
462 isl_set_free(set);
463 return NULL;
466 /* Compute the constraint of a facet of "set".
468 * We first compute the intersection with a bounding constraint
469 * that is orthogonal to one of the coordinate axes.
470 * If the affine hull of this intersection has only one equality,
471 * we have found a facet.
472 * Otherwise, we wrap the current bounding constraint around
473 * one of the equalities of the face (one that is not equal to
474 * the current bounding constraint).
475 * This process continues until we have found a facet.
476 * The dimension of the intersection increases by at least
477 * one on each iteration, so termination is guaranteed.
479 static __isl_give isl_mat *initial_facet_constraint(__isl_keep isl_set *set)
481 struct isl_set *slice = NULL;
482 struct isl_basic_set *face = NULL;
483 int i;
484 unsigned dim = isl_set_n_dim(set);
485 int is_bound;
486 isl_mat *bounds;
488 isl_assert(set->ctx, set->n > 0, goto error);
489 bounds = isl_mat_alloc(set->ctx, 1, 1 + dim);
490 if (!bounds)
491 return NULL;
493 isl_seq_clr(bounds->row[0], dim);
494 isl_int_set_si(bounds->row[0][1 + dim - 1], 1);
495 is_bound = uset_is_bound(set, bounds->row[0], 1 + dim);
496 if (is_bound < 0)
497 goto error;
498 isl_assert(set->ctx, is_bound, goto error);
499 isl_seq_normalize(set->ctx, bounds->row[0], 1 + dim);
500 bounds->n_row = 1;
502 for (;;) {
503 slice = isl_set_copy(set);
504 slice = isl_set_add_basic_set_equality(slice, bounds->row[0]);
505 face = isl_set_affine_hull(slice);
506 if (!face)
507 goto error;
508 if (face->n_eq == 1) {
509 isl_basic_set_free(face);
510 break;
512 for (i = 0; i < face->n_eq; ++i)
513 if (!isl_seq_eq(bounds->row[0], face->eq[i], 1 + dim) &&
514 !isl_seq_is_neg(bounds->row[0],
515 face->eq[i], 1 + dim))
516 break;
517 isl_assert(set->ctx, i < face->n_eq, goto error);
518 if (!isl_set_wrap_facet(set, bounds->row[0], face->eq[i]))
519 goto error;
520 isl_seq_normalize(set->ctx, bounds->row[0], bounds->n_col);
521 isl_basic_set_free(face);
524 return bounds;
525 error:
526 isl_basic_set_free(face);
527 isl_mat_free(bounds);
528 return NULL;
531 /* Given the bounding constraint "c" of a facet of the convex hull of "set",
532 * compute a hyperplane description of the facet, i.e., compute the facets
533 * of the facet.
535 * We compute an affine transformation that transforms the constraint
537 * [ 1 ]
538 * c [ x ] = 0
540 * to the constraint
542 * z_1 = 0
544 * by computing the right inverse U of a matrix that starts with the rows
546 * [ 1 0 ]
547 * [ c ]
549 * Then
550 * [ 1 ] [ 1 ]
551 * [ x ] = U [ z ]
552 * and
553 * [ 1 ] [ 1 ]
554 * [ z ] = Q [ x ]
556 * with Q = U^{-1}
557 * Since z_1 is zero, we can drop this variable as well as the corresponding
558 * column of U to obtain
560 * [ 1 ] [ 1 ]
561 * [ x ] = U' [ z' ]
562 * and
563 * [ 1 ] [ 1 ]
564 * [ z' ] = Q' [ x ]
566 * with Q' equal to Q, but without the corresponding row.
567 * After computing the facets of the facet in the z' space,
568 * we convert them back to the x space through Q.
570 static struct isl_basic_set *compute_facet(struct isl_set *set, isl_int *c)
572 struct isl_mat *m, *U, *Q;
573 struct isl_basic_set *facet = NULL;
574 struct isl_ctx *ctx;
575 unsigned dim;
577 ctx = set->ctx;
578 set = isl_set_copy(set);
579 dim = isl_set_n_dim(set);
580 m = isl_mat_alloc(set->ctx, 2, 1 + dim);
581 if (!m)
582 goto error;
583 isl_int_set_si(m->row[0][0], 1);
584 isl_seq_clr(m->row[0]+1, dim);
585 isl_seq_cpy(m->row[1], c, 1+dim);
586 U = isl_mat_right_inverse(m);
587 Q = isl_mat_right_inverse(isl_mat_copy(U));
588 U = isl_mat_drop_cols(U, 1, 1);
589 Q = isl_mat_drop_rows(Q, 1, 1);
590 set = isl_set_preimage(set, U);
591 facet = uset_convex_hull_wrap_bounded(set);
592 facet = isl_basic_set_preimage(facet, Q);
593 if (facet)
594 isl_assert(ctx, facet->n_eq == 0, goto error);
595 return facet;
596 error:
597 isl_basic_set_free(facet);
598 isl_set_free(set);
599 return NULL;
602 /* Given an initial facet constraint, compute the remaining facets.
603 * We do this by running through all facets found so far and computing
604 * the adjacent facets through wrapping, adding those facets that we
605 * hadn't already found before.
607 * For each facet we have found so far, we first compute its facets
608 * in the resulting convex hull. That is, we compute the ridges
609 * of the resulting convex hull contained in the facet.
610 * We also compute the corresponding facet in the current approximation
611 * of the convex hull. There is no need to wrap around the ridges
612 * in this facet since that would result in a facet that is already
613 * present in the current approximation.
615 * This function can still be significantly optimized by checking which of
616 * the facets of the basic sets are also facets of the convex hull and
617 * using all the facets so far to help in constructing the facets of the
618 * facets
619 * and/or
620 * using the technique in section "3.1 Ridge Generation" of
621 * "Extended Convex Hull" by Fukuda et al.
623 static struct isl_basic_set *extend(struct isl_basic_set *hull,
624 struct isl_set *set)
626 int i, j, f;
627 int k;
628 struct isl_basic_set *facet = NULL;
629 struct isl_basic_set *hull_facet = NULL;
630 unsigned dim;
632 if (!hull)
633 return NULL;
635 isl_assert(set->ctx, set->n > 0, goto error);
637 dim = isl_set_n_dim(set);
639 for (i = 0; i < hull->n_ineq; ++i) {
640 facet = compute_facet(set, hull->ineq[i]);
641 facet = isl_basic_set_add_equality(facet, hull->ineq[i]);
642 facet = isl_basic_set_gauss(facet, NULL);
643 facet = isl_basic_set_normalize_constraints(facet);
644 hull_facet = isl_basic_set_copy(hull);
645 hull_facet = isl_basic_set_add_equality(hull_facet, hull->ineq[i]);
646 hull_facet = isl_basic_set_gauss(hull_facet, NULL);
647 hull_facet = isl_basic_set_normalize_constraints(hull_facet);
648 if (!facet || !hull_facet)
649 goto error;
650 hull = isl_basic_set_cow(hull);
651 hull = isl_basic_set_extend_space(hull,
652 isl_space_copy(hull->dim), 0, 0, facet->n_ineq);
653 if (!hull)
654 goto error;
655 for (j = 0; j < facet->n_ineq; ++j) {
656 for (f = 0; f < hull_facet->n_ineq; ++f)
657 if (isl_seq_eq(facet->ineq[j],
658 hull_facet->ineq[f], 1 + dim))
659 break;
660 if (f < hull_facet->n_ineq)
661 continue;
662 k = isl_basic_set_alloc_inequality(hull);
663 if (k < 0)
664 goto error;
665 isl_seq_cpy(hull->ineq[k], hull->ineq[i], 1+dim);
666 if (!isl_set_wrap_facet(set, hull->ineq[k], facet->ineq[j]))
667 goto error;
669 isl_basic_set_free(hull_facet);
670 isl_basic_set_free(facet);
672 hull = isl_basic_set_simplify(hull);
673 hull = isl_basic_set_finalize(hull);
674 return hull;
675 error:
676 isl_basic_set_free(hull_facet);
677 isl_basic_set_free(facet);
678 isl_basic_set_free(hull);
679 return NULL;
682 /* Special case for computing the convex hull of a one dimensional set.
683 * We simply collect the lower and upper bounds of each basic set
684 * and the biggest of those.
686 static struct isl_basic_set *convex_hull_1d(struct isl_set *set)
688 struct isl_mat *c = NULL;
689 isl_int *lower = NULL;
690 isl_int *upper = NULL;
691 int i, j, k;
692 isl_int a, b;
693 struct isl_basic_set *hull;
695 for (i = 0; i < set->n; ++i) {
696 set->p[i] = isl_basic_set_simplify(set->p[i]);
697 if (!set->p[i])
698 goto error;
700 set = isl_set_remove_empty_parts(set);
701 if (!set)
702 goto error;
703 isl_assert(set->ctx, set->n > 0, goto error);
704 c = isl_mat_alloc(set->ctx, 2, 2);
705 if (!c)
706 goto error;
708 if (set->p[0]->n_eq > 0) {
709 isl_assert(set->ctx, set->p[0]->n_eq == 1, goto error);
710 lower = c->row[0];
711 upper = c->row[1];
712 if (isl_int_is_pos(set->p[0]->eq[0][1])) {
713 isl_seq_cpy(lower, set->p[0]->eq[0], 2);
714 isl_seq_neg(upper, set->p[0]->eq[0], 2);
715 } else {
716 isl_seq_neg(lower, set->p[0]->eq[0], 2);
717 isl_seq_cpy(upper, set->p[0]->eq[0], 2);
719 } else {
720 for (j = 0; j < set->p[0]->n_ineq; ++j) {
721 if (isl_int_is_pos(set->p[0]->ineq[j][1])) {
722 lower = c->row[0];
723 isl_seq_cpy(lower, set->p[0]->ineq[j], 2);
724 } else {
725 upper = c->row[1];
726 isl_seq_cpy(upper, set->p[0]->ineq[j], 2);
731 isl_int_init(a);
732 isl_int_init(b);
733 for (i = 0; i < set->n; ++i) {
734 struct isl_basic_set *bset = set->p[i];
735 int has_lower = 0;
736 int has_upper = 0;
738 for (j = 0; j < bset->n_eq; ++j) {
739 has_lower = 1;
740 has_upper = 1;
741 if (lower) {
742 isl_int_mul(a, lower[0], bset->eq[j][1]);
743 isl_int_mul(b, lower[1], bset->eq[j][0]);
744 if (isl_int_lt(a, b) && isl_int_is_pos(bset->eq[j][1]))
745 isl_seq_cpy(lower, bset->eq[j], 2);
746 if (isl_int_gt(a, b) && isl_int_is_neg(bset->eq[j][1]))
747 isl_seq_neg(lower, bset->eq[j], 2);
749 if (upper) {
750 isl_int_mul(a, upper[0], bset->eq[j][1]);
751 isl_int_mul(b, upper[1], bset->eq[j][0]);
752 if (isl_int_lt(a, b) && isl_int_is_pos(bset->eq[j][1]))
753 isl_seq_neg(upper, bset->eq[j], 2);
754 if (isl_int_gt(a, b) && isl_int_is_neg(bset->eq[j][1]))
755 isl_seq_cpy(upper, bset->eq[j], 2);
758 for (j = 0; j < bset->n_ineq; ++j) {
759 if (isl_int_is_pos(bset->ineq[j][1]))
760 has_lower = 1;
761 if (isl_int_is_neg(bset->ineq[j][1]))
762 has_upper = 1;
763 if (lower && isl_int_is_pos(bset->ineq[j][1])) {
764 isl_int_mul(a, lower[0], bset->ineq[j][1]);
765 isl_int_mul(b, lower[1], bset->ineq[j][0]);
766 if (isl_int_lt(a, b))
767 isl_seq_cpy(lower, bset->ineq[j], 2);
769 if (upper && isl_int_is_neg(bset->ineq[j][1])) {
770 isl_int_mul(a, upper[0], bset->ineq[j][1]);
771 isl_int_mul(b, upper[1], bset->ineq[j][0]);
772 if (isl_int_gt(a, b))
773 isl_seq_cpy(upper, bset->ineq[j], 2);
776 if (!has_lower)
777 lower = NULL;
778 if (!has_upper)
779 upper = NULL;
781 isl_int_clear(a);
782 isl_int_clear(b);
784 hull = isl_basic_set_alloc(set->ctx, 0, 1, 0, 0, 2);
785 hull = isl_basic_set_set_rational(hull);
786 if (!hull)
787 goto error;
788 if (lower) {
789 k = isl_basic_set_alloc_inequality(hull);
790 isl_seq_cpy(hull->ineq[k], lower, 2);
792 if (upper) {
793 k = isl_basic_set_alloc_inequality(hull);
794 isl_seq_cpy(hull->ineq[k], upper, 2);
796 hull = isl_basic_set_finalize(hull);
797 isl_set_free(set);
798 isl_mat_free(c);
799 return hull;
800 error:
801 isl_set_free(set);
802 isl_mat_free(c);
803 return NULL;
806 static struct isl_basic_set *convex_hull_0d(struct isl_set *set)
808 struct isl_basic_set *convex_hull;
810 if (!set)
811 return NULL;
813 if (isl_set_is_empty(set))
814 convex_hull = isl_basic_set_empty(isl_space_copy(set->dim));
815 else
816 convex_hull = isl_basic_set_universe(isl_space_copy(set->dim));
817 isl_set_free(set);
818 return convex_hull;
821 /* Compute the convex hull of a pair of basic sets without any parameters or
822 * integer divisions using Fourier-Motzkin elimination.
823 * The convex hull is the set of all points that can be written as
824 * the sum of points from both basic sets (in homogeneous coordinates).
825 * We set up the constraints in a space with dimensions for each of
826 * the three sets and then project out the dimensions corresponding
827 * to the two original basic sets, retaining only those corresponding
828 * to the convex hull.
830 static struct isl_basic_set *convex_hull_pair_elim(struct isl_basic_set *bset1,
831 struct isl_basic_set *bset2)
833 int i, j, k;
834 struct isl_basic_set *bset[2];
835 struct isl_basic_set *hull = NULL;
836 unsigned dim;
838 if (!bset1 || !bset2)
839 goto error;
841 dim = isl_basic_set_n_dim(bset1);
842 hull = isl_basic_set_alloc(bset1->ctx, 0, 2 + 3 * dim, 0,
843 1 + dim + bset1->n_eq + bset2->n_eq,
844 2 + bset1->n_ineq + bset2->n_ineq);
845 bset[0] = bset1;
846 bset[1] = bset2;
847 for (i = 0; i < 2; ++i) {
848 for (j = 0; j < bset[i]->n_eq; ++j) {
849 k = isl_basic_set_alloc_equality(hull);
850 if (k < 0)
851 goto error;
852 isl_seq_clr(hull->eq[k], (i+1) * (1+dim));
853 isl_seq_clr(hull->eq[k]+(i+2)*(1+dim), (1-i)*(1+dim));
854 isl_seq_cpy(hull->eq[k]+(i+1)*(1+dim), bset[i]->eq[j],
855 1+dim);
857 for (j = 0; j < bset[i]->n_ineq; ++j) {
858 k = isl_basic_set_alloc_inequality(hull);
859 if (k < 0)
860 goto error;
861 isl_seq_clr(hull->ineq[k], (i+1) * (1+dim));
862 isl_seq_clr(hull->ineq[k]+(i+2)*(1+dim), (1-i)*(1+dim));
863 isl_seq_cpy(hull->ineq[k]+(i+1)*(1+dim),
864 bset[i]->ineq[j], 1+dim);
866 k = isl_basic_set_alloc_inequality(hull);
867 if (k < 0)
868 goto error;
869 isl_seq_clr(hull->ineq[k], 1+2+3*dim);
870 isl_int_set_si(hull->ineq[k][(i+1)*(1+dim)], 1);
872 for (j = 0; j < 1+dim; ++j) {
873 k = isl_basic_set_alloc_equality(hull);
874 if (k < 0)
875 goto error;
876 isl_seq_clr(hull->eq[k], 1+2+3*dim);
877 isl_int_set_si(hull->eq[k][j], -1);
878 isl_int_set_si(hull->eq[k][1+dim+j], 1);
879 isl_int_set_si(hull->eq[k][2*(1+dim)+j], 1);
881 hull = isl_basic_set_set_rational(hull);
882 hull = isl_basic_set_remove_dims(hull, isl_dim_set, dim, 2*(1+dim));
883 hull = isl_basic_set_remove_redundancies(hull);
884 isl_basic_set_free(bset1);
885 isl_basic_set_free(bset2);
886 return hull;
887 error:
888 isl_basic_set_free(bset1);
889 isl_basic_set_free(bset2);
890 isl_basic_set_free(hull);
891 return NULL;
894 /* Is the set bounded for each value of the parameters?
896 int isl_basic_set_is_bounded(__isl_keep isl_basic_set *bset)
898 struct isl_tab *tab;
899 int bounded;
901 if (!bset)
902 return -1;
903 if (isl_basic_set_plain_is_empty(bset))
904 return 1;
906 tab = isl_tab_from_recession_cone(bset, 1);
907 bounded = isl_tab_cone_is_bounded(tab);
908 isl_tab_free(tab);
909 return bounded;
912 /* Is the image bounded for each value of the parameters and
913 * the domain variables?
915 int isl_basic_map_image_is_bounded(__isl_keep isl_basic_map *bmap)
917 unsigned nparam = isl_basic_map_dim(bmap, isl_dim_param);
918 unsigned n_in = isl_basic_map_dim(bmap, isl_dim_in);
919 int bounded;
921 bmap = isl_basic_map_copy(bmap);
922 bmap = isl_basic_map_cow(bmap);
923 bmap = isl_basic_map_move_dims(bmap, isl_dim_param, nparam,
924 isl_dim_in, 0, n_in);
925 bounded = isl_basic_set_is_bounded((isl_basic_set *)bmap);
926 isl_basic_map_free(bmap);
928 return bounded;
931 /* Is the set bounded for each value of the parameters?
933 int isl_set_is_bounded(__isl_keep isl_set *set)
935 int i;
937 if (!set)
938 return -1;
940 for (i = 0; i < set->n; ++i) {
941 int bounded = isl_basic_set_is_bounded(set->p[i]);
942 if (!bounded || bounded < 0)
943 return bounded;
945 return 1;
948 /* Compute the lineality space of the convex hull of bset1 and bset2.
950 * We first compute the intersection of the recession cone of bset1
951 * with the negative of the recession cone of bset2 and then compute
952 * the linear hull of the resulting cone.
954 static struct isl_basic_set *induced_lineality_space(
955 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
957 int i, k;
958 struct isl_basic_set *lin = NULL;
959 unsigned dim;
961 if (!bset1 || !bset2)
962 goto error;
964 dim = isl_basic_set_total_dim(bset1);
965 lin = isl_basic_set_alloc_space(isl_basic_set_get_space(bset1), 0,
966 bset1->n_eq + bset2->n_eq,
967 bset1->n_ineq + bset2->n_ineq);
968 lin = isl_basic_set_set_rational(lin);
969 if (!lin)
970 goto error;
971 for (i = 0; i < bset1->n_eq; ++i) {
972 k = isl_basic_set_alloc_equality(lin);
973 if (k < 0)
974 goto error;
975 isl_int_set_si(lin->eq[k][0], 0);
976 isl_seq_cpy(lin->eq[k] + 1, bset1->eq[i] + 1, dim);
978 for (i = 0; i < bset1->n_ineq; ++i) {
979 k = isl_basic_set_alloc_inequality(lin);
980 if (k < 0)
981 goto error;
982 isl_int_set_si(lin->ineq[k][0], 0);
983 isl_seq_cpy(lin->ineq[k] + 1, bset1->ineq[i] + 1, dim);
985 for (i = 0; i < bset2->n_eq; ++i) {
986 k = isl_basic_set_alloc_equality(lin);
987 if (k < 0)
988 goto error;
989 isl_int_set_si(lin->eq[k][0], 0);
990 isl_seq_neg(lin->eq[k] + 1, bset2->eq[i] + 1, dim);
992 for (i = 0; i < bset2->n_ineq; ++i) {
993 k = isl_basic_set_alloc_inequality(lin);
994 if (k < 0)
995 goto error;
996 isl_int_set_si(lin->ineq[k][0], 0);
997 isl_seq_neg(lin->ineq[k] + 1, bset2->ineq[i] + 1, dim);
1000 isl_basic_set_free(bset1);
1001 isl_basic_set_free(bset2);
1002 return isl_basic_set_affine_hull(lin);
1003 error:
1004 isl_basic_set_free(lin);
1005 isl_basic_set_free(bset1);
1006 isl_basic_set_free(bset2);
1007 return NULL;
1010 static struct isl_basic_set *uset_convex_hull(struct isl_set *set);
1012 /* Given a set and a linear space "lin" of dimension n > 0,
1013 * project the linear space from the set, compute the convex hull
1014 * and then map the set back to the original space.
1016 * Let
1018 * M x = 0
1020 * describe the linear space. We first compute the Hermite normal
1021 * form H = M U of M = H Q, to obtain
1023 * H Q x = 0
1025 * The last n rows of H will be zero, so the last n variables of x' = Q x
1026 * are the one we want to project out. We do this by transforming each
1027 * basic set A x >= b to A U x' >= b and then removing the last n dimensions.
1028 * After computing the convex hull in x'_1, i.e., A' x'_1 >= b',
1029 * we transform the hull back to the original space as A' Q_1 x >= b',
1030 * with Q_1 all but the last n rows of Q.
1032 static struct isl_basic_set *modulo_lineality(struct isl_set *set,
1033 struct isl_basic_set *lin)
1035 unsigned total = isl_basic_set_total_dim(lin);
1036 unsigned lin_dim;
1037 struct isl_basic_set *hull;
1038 struct isl_mat *M, *U, *Q;
1040 if (!set || !lin)
1041 goto error;
1042 lin_dim = total - lin->n_eq;
1043 M = isl_mat_sub_alloc6(set->ctx, lin->eq, 0, lin->n_eq, 1, total);
1044 M = isl_mat_left_hermite(M, 0, &U, &Q);
1045 if (!M)
1046 goto error;
1047 isl_mat_free(M);
1048 isl_basic_set_free(lin);
1050 Q = isl_mat_drop_rows(Q, Q->n_row - lin_dim, lin_dim);
1052 U = isl_mat_lin_to_aff(U);
1053 Q = isl_mat_lin_to_aff(Q);
1055 set = isl_set_preimage(set, U);
1056 set = isl_set_remove_dims(set, isl_dim_set, total - lin_dim, lin_dim);
1057 hull = uset_convex_hull(set);
1058 hull = isl_basic_set_preimage(hull, Q);
1060 return hull;
1061 error:
1062 isl_basic_set_free(lin);
1063 isl_set_free(set);
1064 return NULL;
1067 /* Given two polyhedra with as constraints h_{ij} x >= 0 in homegeneous space,
1068 * set up an LP for solving
1070 * \sum_j \alpha_{1j} h_{1j} = \sum_j \alpha_{2j} h_{2j}
1072 * \alpha{i0} corresponds to the (implicit) positivity constraint 1 >= 0
1073 * The next \alpha{ij} correspond to the equalities and come in pairs.
1074 * The final \alpha{ij} correspond to the inequalities.
1076 static struct isl_basic_set *valid_direction_lp(
1077 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
1079 isl_space *dim;
1080 struct isl_basic_set *lp;
1081 unsigned d;
1082 int n;
1083 int i, j, k;
1085 if (!bset1 || !bset2)
1086 goto error;
1087 d = 1 + isl_basic_set_total_dim(bset1);
1088 n = 2 +
1089 2 * bset1->n_eq + bset1->n_ineq + 2 * bset2->n_eq + bset2->n_ineq;
1090 dim = isl_space_set_alloc(bset1->ctx, 0, n);
1091 lp = isl_basic_set_alloc_space(dim, 0, d, n);
1092 if (!lp)
1093 goto error;
1094 for (i = 0; i < n; ++i) {
1095 k = isl_basic_set_alloc_inequality(lp);
1096 if (k < 0)
1097 goto error;
1098 isl_seq_clr(lp->ineq[k] + 1, n);
1099 isl_int_set_si(lp->ineq[k][0], -1);
1100 isl_int_set_si(lp->ineq[k][1 + i], 1);
1102 for (i = 0; i < d; ++i) {
1103 k = isl_basic_set_alloc_equality(lp);
1104 if (k < 0)
1105 goto error;
1106 n = 0;
1107 isl_int_set_si(lp->eq[k][n], 0); n++;
1108 /* positivity constraint 1 >= 0 */
1109 isl_int_set_si(lp->eq[k][n], i == 0); n++;
1110 for (j = 0; j < bset1->n_eq; ++j) {
1111 isl_int_set(lp->eq[k][n], bset1->eq[j][i]); n++;
1112 isl_int_neg(lp->eq[k][n], bset1->eq[j][i]); n++;
1114 for (j = 0; j < bset1->n_ineq; ++j) {
1115 isl_int_set(lp->eq[k][n], bset1->ineq[j][i]); n++;
1117 /* positivity constraint 1 >= 0 */
1118 isl_int_set_si(lp->eq[k][n], -(i == 0)); n++;
1119 for (j = 0; j < bset2->n_eq; ++j) {
1120 isl_int_neg(lp->eq[k][n], bset2->eq[j][i]); n++;
1121 isl_int_set(lp->eq[k][n], bset2->eq[j][i]); n++;
1123 for (j = 0; j < bset2->n_ineq; ++j) {
1124 isl_int_neg(lp->eq[k][n], bset2->ineq[j][i]); n++;
1127 lp = isl_basic_set_gauss(lp, NULL);
1128 isl_basic_set_free(bset1);
1129 isl_basic_set_free(bset2);
1130 return lp;
1131 error:
1132 isl_basic_set_free(bset1);
1133 isl_basic_set_free(bset2);
1134 return NULL;
1137 /* Compute a vector s in the homogeneous space such that <s, r> > 0
1138 * for all rays in the homogeneous space of the two cones that correspond
1139 * to the input polyhedra bset1 and bset2.
1141 * We compute s as a vector that satisfies
1143 * s = \sum_j \alpha_{ij} h_{ij} for i = 1,2 (*)
1145 * with h_{ij} the normals of the facets of polyhedron i
1146 * (including the "positivity constraint" 1 >= 0) and \alpha_{ij}
1147 * strictly positive numbers. For simplicity we impose \alpha_{ij} >= 1.
1148 * We first set up an LP with as variables the \alpha{ij}.
1149 * In this formulation, for each polyhedron i,
1150 * the first constraint is the positivity constraint, followed by pairs
1151 * of variables for the equalities, followed by variables for the inequalities.
1152 * We then simply pick a feasible solution and compute s using (*).
1154 * Note that we simply pick any valid direction and make no attempt
1155 * to pick a "good" or even the "best" valid direction.
1157 static struct isl_vec *valid_direction(
1158 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
1160 struct isl_basic_set *lp;
1161 struct isl_tab *tab;
1162 struct isl_vec *sample = NULL;
1163 struct isl_vec *dir;
1164 unsigned d;
1165 int i;
1166 int n;
1168 if (!bset1 || !bset2)
1169 goto error;
1170 lp = valid_direction_lp(isl_basic_set_copy(bset1),
1171 isl_basic_set_copy(bset2));
1172 tab = isl_tab_from_basic_set(lp, 0);
1173 sample = isl_tab_get_sample_value(tab);
1174 isl_tab_free(tab);
1175 isl_basic_set_free(lp);
1176 if (!sample)
1177 goto error;
1178 d = isl_basic_set_total_dim(bset1);
1179 dir = isl_vec_alloc(bset1->ctx, 1 + d);
1180 if (!dir)
1181 goto error;
1182 isl_seq_clr(dir->block.data + 1, dir->size - 1);
1183 n = 1;
1184 /* positivity constraint 1 >= 0 */
1185 isl_int_set(dir->block.data[0], sample->block.data[n]); n++;
1186 for (i = 0; i < bset1->n_eq; ++i) {
1187 isl_int_sub(sample->block.data[n],
1188 sample->block.data[n], sample->block.data[n+1]);
1189 isl_seq_combine(dir->block.data,
1190 bset1->ctx->one, dir->block.data,
1191 sample->block.data[n], bset1->eq[i], 1 + d);
1193 n += 2;
1195 for (i = 0; i < bset1->n_ineq; ++i)
1196 isl_seq_combine(dir->block.data,
1197 bset1->ctx->one, dir->block.data,
1198 sample->block.data[n++], bset1->ineq[i], 1 + d);
1199 isl_vec_free(sample);
1200 isl_seq_normalize(bset1->ctx, dir->el, dir->size);
1201 isl_basic_set_free(bset1);
1202 isl_basic_set_free(bset2);
1203 return dir;
1204 error:
1205 isl_vec_free(sample);
1206 isl_basic_set_free(bset1);
1207 isl_basic_set_free(bset2);
1208 return NULL;
1211 /* Given a polyhedron b_i + A_i x >= 0 and a map T = S^{-1},
1212 * compute b_i' + A_i' x' >= 0, with
1214 * [ b_i A_i ] [ y' ] [ y' ]
1215 * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
1217 * In particular, add the "positivity constraint" and then perform
1218 * the mapping.
1220 static struct isl_basic_set *homogeneous_map(struct isl_basic_set *bset,
1221 struct isl_mat *T)
1223 int k;
1225 if (!bset)
1226 goto error;
1227 bset = isl_basic_set_extend_constraints(bset, 0, 1);
1228 k = isl_basic_set_alloc_inequality(bset);
1229 if (k < 0)
1230 goto error;
1231 isl_seq_clr(bset->ineq[k] + 1, isl_basic_set_total_dim(bset));
1232 isl_int_set_si(bset->ineq[k][0], 1);
1233 bset = isl_basic_set_preimage(bset, T);
1234 return bset;
1235 error:
1236 isl_mat_free(T);
1237 isl_basic_set_free(bset);
1238 return NULL;
1241 /* Compute the convex hull of a pair of basic sets without any parameters or
1242 * integer divisions, where the convex hull is known to be pointed,
1243 * but the basic sets may be unbounded.
1245 * We turn this problem into the computation of a convex hull of a pair
1246 * _bounded_ polyhedra by "changing the direction of the homogeneous
1247 * dimension". This idea is due to Matthias Koeppe.
1249 * Consider the cones in homogeneous space that correspond to the
1250 * input polyhedra. The rays of these cones are also rays of the
1251 * polyhedra if the coordinate that corresponds to the homogeneous
1252 * dimension is zero. That is, if the inner product of the rays
1253 * with the homogeneous direction is zero.
1254 * The cones in the homogeneous space can also be considered to
1255 * correspond to other pairs of polyhedra by chosing a different
1256 * homogeneous direction. To ensure that both of these polyhedra
1257 * are bounded, we need to make sure that all rays of the cones
1258 * correspond to vertices and not to rays.
1259 * Let s be a direction such that <s, r> > 0 for all rays r of both cones.
1260 * Then using s as a homogeneous direction, we obtain a pair of polytopes.
1261 * The vector s is computed in valid_direction.
1263 * Note that we need to consider _all_ rays of the cones and not just
1264 * the rays that correspond to rays in the polyhedra. If we were to
1265 * only consider those rays and turn them into vertices, then we
1266 * may inadvertently turn some vertices into rays.
1268 * The standard homogeneous direction is the unit vector in the 0th coordinate.
1269 * We therefore transform the two polyhedra such that the selected
1270 * direction is mapped onto this standard direction and then proceed
1271 * with the normal computation.
1272 * Let S be a non-singular square matrix with s as its first row,
1273 * then we want to map the polyhedra to the space
1275 * [ y' ] [ y ] [ y ] [ y' ]
1276 * [ x' ] = S [ x ] i.e., [ x ] = S^{-1} [ x' ]
1278 * We take S to be the unimodular completion of s to limit the growth
1279 * of the coefficients in the following computations.
1281 * Let b_i + A_i x >= 0 be the constraints of polyhedron i.
1282 * We first move to the homogeneous dimension
1284 * b_i y + A_i x >= 0 [ b_i A_i ] [ y ] [ 0 ]
1285 * y >= 0 or [ 1 0 ] [ x ] >= [ 0 ]
1287 * Then we change directoin
1289 * [ b_i A_i ] [ y' ] [ y' ]
1290 * [ 1 0 ] S^{-1} [ x' ] >= 0 or [ b_i' A_i' ] [ x' ] >= 0
1292 * Then we compute the convex hull of the polytopes b_i' + A_i' x' >= 0
1293 * resulting in b' + A' x' >= 0, which we then convert back
1295 * [ y ] [ y ]
1296 * [ b' A' ] S [ x ] >= 0 or [ b A ] [ x ] >= 0
1298 * The polyhedron b + A x >= 0 is then the convex hull of the input polyhedra.
1300 static struct isl_basic_set *convex_hull_pair_pointed(
1301 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
1303 struct isl_ctx *ctx = NULL;
1304 struct isl_vec *dir = NULL;
1305 struct isl_mat *T = NULL;
1306 struct isl_mat *T2 = NULL;
1307 struct isl_basic_set *hull;
1308 struct isl_set *set;
1310 if (!bset1 || !bset2)
1311 goto error;
1312 ctx = bset1->ctx;
1313 dir = valid_direction(isl_basic_set_copy(bset1),
1314 isl_basic_set_copy(bset2));
1315 if (!dir)
1316 goto error;
1317 T = isl_mat_alloc(bset1->ctx, dir->size, dir->size);
1318 if (!T)
1319 goto error;
1320 isl_seq_cpy(T->row[0], dir->block.data, dir->size);
1321 T = isl_mat_unimodular_complete(T, 1);
1322 T2 = isl_mat_right_inverse(isl_mat_copy(T));
1324 bset1 = homogeneous_map(bset1, isl_mat_copy(T2));
1325 bset2 = homogeneous_map(bset2, T2);
1326 set = isl_set_alloc_space(isl_basic_set_get_space(bset1), 2, 0);
1327 set = isl_set_add_basic_set(set, bset1);
1328 set = isl_set_add_basic_set(set, bset2);
1329 hull = uset_convex_hull(set);
1330 hull = isl_basic_set_preimage(hull, T);
1332 isl_vec_free(dir);
1334 return hull;
1335 error:
1336 isl_vec_free(dir);
1337 isl_basic_set_free(bset1);
1338 isl_basic_set_free(bset2);
1339 return NULL;
1342 static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set);
1343 static struct isl_basic_set *modulo_affine_hull(
1344 struct isl_set *set, struct isl_basic_set *affine_hull);
1346 /* Compute the convex hull of a pair of basic sets without any parameters or
1347 * integer divisions.
1349 * This function is called from uset_convex_hull_unbounded, which
1350 * means that the complete convex hull is unbounded. Some pairs
1351 * of basic sets may still be bounded, though.
1352 * They may even lie inside a lower dimensional space, in which
1353 * case they need to be handled inside their affine hull since
1354 * the main algorithm assumes that the result is full-dimensional.
1356 * If the convex hull of the two basic sets would have a non-trivial
1357 * lineality space, we first project out this lineality space.
1359 static struct isl_basic_set *convex_hull_pair(struct isl_basic_set *bset1,
1360 struct isl_basic_set *bset2)
1362 isl_basic_set *lin, *aff;
1363 int bounded1, bounded2;
1365 if (bset1->ctx->opt->convex == ISL_CONVEX_HULL_FM)
1366 return convex_hull_pair_elim(bset1, bset2);
1368 aff = isl_set_affine_hull(isl_basic_set_union(isl_basic_set_copy(bset1),
1369 isl_basic_set_copy(bset2)));
1370 if (!aff)
1371 goto error;
1372 if (aff->n_eq != 0)
1373 return modulo_affine_hull(isl_basic_set_union(bset1, bset2), aff);
1374 isl_basic_set_free(aff);
1376 bounded1 = isl_basic_set_is_bounded(bset1);
1377 bounded2 = isl_basic_set_is_bounded(bset2);
1379 if (bounded1 < 0 || bounded2 < 0)
1380 goto error;
1382 if (bounded1 && bounded2)
1383 uset_convex_hull_wrap(isl_basic_set_union(bset1, bset2));
1385 if (bounded1 || bounded2)
1386 return convex_hull_pair_pointed(bset1, bset2);
1388 lin = induced_lineality_space(isl_basic_set_copy(bset1),
1389 isl_basic_set_copy(bset2));
1390 if (!lin)
1391 goto error;
1392 if (isl_basic_set_is_universe(lin)) {
1393 isl_basic_set_free(bset1);
1394 isl_basic_set_free(bset2);
1395 return lin;
1397 if (lin->n_eq < isl_basic_set_total_dim(lin)) {
1398 struct isl_set *set;
1399 set = isl_set_alloc_space(isl_basic_set_get_space(bset1), 2, 0);
1400 set = isl_set_add_basic_set(set, bset1);
1401 set = isl_set_add_basic_set(set, bset2);
1402 return modulo_lineality(set, lin);
1404 isl_basic_set_free(lin);
1406 return convex_hull_pair_pointed(bset1, bset2);
1407 error:
1408 isl_basic_set_free(bset1);
1409 isl_basic_set_free(bset2);
1410 return NULL;
1413 /* Compute the lineality space of a basic set.
1414 * We currently do not allow the basic set to have any divs.
1415 * We basically just drop the constants and turn every inequality
1416 * into an equality.
1418 struct isl_basic_set *isl_basic_set_lineality_space(struct isl_basic_set *bset)
1420 int i, k;
1421 struct isl_basic_set *lin = NULL;
1422 unsigned dim;
1424 if (!bset)
1425 goto error;
1426 isl_assert(bset->ctx, bset->n_div == 0, goto error);
1427 dim = isl_basic_set_total_dim(bset);
1429 lin = isl_basic_set_alloc_space(isl_basic_set_get_space(bset), 0, dim, 0);
1430 if (!lin)
1431 goto error;
1432 for (i = 0; i < bset->n_eq; ++i) {
1433 k = isl_basic_set_alloc_equality(lin);
1434 if (k < 0)
1435 goto error;
1436 isl_int_set_si(lin->eq[k][0], 0);
1437 isl_seq_cpy(lin->eq[k] + 1, bset->eq[i] + 1, dim);
1439 lin = isl_basic_set_gauss(lin, NULL);
1440 if (!lin)
1441 goto error;
1442 for (i = 0; i < bset->n_ineq && lin->n_eq < dim; ++i) {
1443 k = isl_basic_set_alloc_equality(lin);
1444 if (k < 0)
1445 goto error;
1446 isl_int_set_si(lin->eq[k][0], 0);
1447 isl_seq_cpy(lin->eq[k] + 1, bset->ineq[i] + 1, dim);
1448 lin = isl_basic_set_gauss(lin, NULL);
1449 if (!lin)
1450 goto error;
1452 isl_basic_set_free(bset);
1453 return lin;
1454 error:
1455 isl_basic_set_free(lin);
1456 isl_basic_set_free(bset);
1457 return NULL;
1460 /* Compute the (linear) hull of the lineality spaces of the basic sets in the
1461 * "underlying" set "set".
1463 static struct isl_basic_set *uset_combined_lineality_space(struct isl_set *set)
1465 int i;
1466 struct isl_set *lin = NULL;
1468 if (!set)
1469 return NULL;
1470 if (set->n == 0) {
1471 isl_space *dim = isl_set_get_space(set);
1472 isl_set_free(set);
1473 return isl_basic_set_empty(dim);
1476 lin = isl_set_alloc_space(isl_set_get_space(set), set->n, 0);
1477 for (i = 0; i < set->n; ++i)
1478 lin = isl_set_add_basic_set(lin,
1479 isl_basic_set_lineality_space(isl_basic_set_copy(set->p[i])));
1480 isl_set_free(set);
1481 return isl_set_affine_hull(lin);
1484 /* Compute the convex hull of a set without any parameters or
1485 * integer divisions.
1486 * In each step, we combined two basic sets until only one
1487 * basic set is left.
1488 * The input basic sets are assumed not to have a non-trivial
1489 * lineality space. If any of the intermediate results has
1490 * a non-trivial lineality space, it is projected out.
1492 static struct isl_basic_set *uset_convex_hull_unbounded(struct isl_set *set)
1494 struct isl_basic_set *convex_hull = NULL;
1496 convex_hull = isl_set_copy_basic_set(set);
1497 set = isl_set_drop_basic_set(set, convex_hull);
1498 if (!set)
1499 goto error;
1500 while (set->n > 0) {
1501 struct isl_basic_set *t;
1502 t = isl_set_copy_basic_set(set);
1503 if (!t)
1504 goto error;
1505 set = isl_set_drop_basic_set(set, t);
1506 if (!set)
1507 goto error;
1508 convex_hull = convex_hull_pair(convex_hull, t);
1509 if (set->n == 0)
1510 break;
1511 t = isl_basic_set_lineality_space(isl_basic_set_copy(convex_hull));
1512 if (!t)
1513 goto error;
1514 if (isl_basic_set_is_universe(t)) {
1515 isl_basic_set_free(convex_hull);
1516 convex_hull = t;
1517 break;
1519 if (t->n_eq < isl_basic_set_total_dim(t)) {
1520 set = isl_set_add_basic_set(set, convex_hull);
1521 return modulo_lineality(set, t);
1523 isl_basic_set_free(t);
1525 isl_set_free(set);
1526 return convex_hull;
1527 error:
1528 isl_set_free(set);
1529 isl_basic_set_free(convex_hull);
1530 return NULL;
1533 /* Compute an initial hull for wrapping containing a single initial
1534 * facet.
1535 * This function assumes that the given set is bounded.
1537 static struct isl_basic_set *initial_hull(struct isl_basic_set *hull,
1538 struct isl_set *set)
1540 struct isl_mat *bounds = NULL;
1541 unsigned dim;
1542 int k;
1544 if (!hull)
1545 goto error;
1546 bounds = initial_facet_constraint(set);
1547 if (!bounds)
1548 goto error;
1549 k = isl_basic_set_alloc_inequality(hull);
1550 if (k < 0)
1551 goto error;
1552 dim = isl_set_n_dim(set);
1553 isl_assert(set->ctx, 1 + dim == bounds->n_col, goto error);
1554 isl_seq_cpy(hull->ineq[k], bounds->row[0], bounds->n_col);
1555 isl_mat_free(bounds);
1557 return hull;
1558 error:
1559 isl_basic_set_free(hull);
1560 isl_mat_free(bounds);
1561 return NULL;
1564 struct max_constraint {
1565 struct isl_mat *c;
1566 int count;
1567 int ineq;
1570 static int max_constraint_equal(const void *entry, const void *val)
1572 struct max_constraint *a = (struct max_constraint *)entry;
1573 isl_int *b = (isl_int *)val;
1575 return isl_seq_eq(a->c->row[0] + 1, b, a->c->n_col - 1);
1578 static void update_constraint(struct isl_ctx *ctx, struct isl_hash_table *table,
1579 isl_int *con, unsigned len, int n, int ineq)
1581 struct isl_hash_table_entry *entry;
1582 struct max_constraint *c;
1583 uint32_t c_hash;
1585 c_hash = isl_seq_get_hash(con + 1, len);
1586 entry = isl_hash_table_find(ctx, table, c_hash, max_constraint_equal,
1587 con + 1, 0);
1588 if (!entry)
1589 return;
1590 c = entry->data;
1591 if (c->count < n) {
1592 isl_hash_table_remove(ctx, table, entry);
1593 return;
1595 c->count++;
1596 if (isl_int_gt(c->c->row[0][0], con[0]))
1597 return;
1598 if (isl_int_eq(c->c->row[0][0], con[0])) {
1599 if (ineq)
1600 c->ineq = ineq;
1601 return;
1603 c->c = isl_mat_cow(c->c);
1604 isl_int_set(c->c->row[0][0], con[0]);
1605 c->ineq = ineq;
1608 /* Check whether the constraint hash table "table" constains the constraint
1609 * "con".
1611 static int has_constraint(struct isl_ctx *ctx, struct isl_hash_table *table,
1612 isl_int *con, unsigned len, int n)
1614 struct isl_hash_table_entry *entry;
1615 struct max_constraint *c;
1616 uint32_t c_hash;
1618 c_hash = isl_seq_get_hash(con + 1, len);
1619 entry = isl_hash_table_find(ctx, table, c_hash, max_constraint_equal,
1620 con + 1, 0);
1621 if (!entry)
1622 return 0;
1623 c = entry->data;
1624 if (c->count < n)
1625 return 0;
1626 return isl_int_eq(c->c->row[0][0], con[0]);
1629 /* Check for inequality constraints of a basic set without equalities
1630 * such that the same or more stringent copies of the constraint appear
1631 * in all of the basic sets. Such constraints are necessarily facet
1632 * constraints of the convex hull.
1634 * If the resulting basic set is by chance identical to one of
1635 * the basic sets in "set", then we know that this basic set contains
1636 * all other basic sets and is therefore the convex hull of set.
1637 * In this case we set *is_hull to 1.
1639 static struct isl_basic_set *common_constraints(struct isl_basic_set *hull,
1640 struct isl_set *set, int *is_hull)
1642 int i, j, s, n;
1643 int min_constraints;
1644 int best;
1645 struct max_constraint *constraints = NULL;
1646 struct isl_hash_table *table = NULL;
1647 unsigned total;
1649 *is_hull = 0;
1651 for (i = 0; i < set->n; ++i)
1652 if (set->p[i]->n_eq == 0)
1653 break;
1654 if (i >= set->n)
1655 return hull;
1656 min_constraints = set->p[i]->n_ineq;
1657 best = i;
1658 for (i = best + 1; i < set->n; ++i) {
1659 if (set->p[i]->n_eq != 0)
1660 continue;
1661 if (set->p[i]->n_ineq >= min_constraints)
1662 continue;
1663 min_constraints = set->p[i]->n_ineq;
1664 best = i;
1666 constraints = isl_calloc_array(hull->ctx, struct max_constraint,
1667 min_constraints);
1668 if (!constraints)
1669 return hull;
1670 table = isl_alloc_type(hull->ctx, struct isl_hash_table);
1671 if (isl_hash_table_init(hull->ctx, table, min_constraints))
1672 goto error;
1674 total = isl_space_dim(set->dim, isl_dim_all);
1675 for (i = 0; i < set->p[best]->n_ineq; ++i) {
1676 constraints[i].c = isl_mat_sub_alloc6(hull->ctx,
1677 set->p[best]->ineq + i, 0, 1, 0, 1 + total);
1678 if (!constraints[i].c)
1679 goto error;
1680 constraints[i].ineq = 1;
1682 for (i = 0; i < min_constraints; ++i) {
1683 struct isl_hash_table_entry *entry;
1684 uint32_t c_hash;
1685 c_hash = isl_seq_get_hash(constraints[i].c->row[0] + 1, total);
1686 entry = isl_hash_table_find(hull->ctx, table, c_hash,
1687 max_constraint_equal, constraints[i].c->row[0] + 1, 1);
1688 if (!entry)
1689 goto error;
1690 isl_assert(hull->ctx, !entry->data, goto error);
1691 entry->data = &constraints[i];
1694 n = 0;
1695 for (s = 0; s < set->n; ++s) {
1696 if (s == best)
1697 continue;
1699 for (i = 0; i < set->p[s]->n_eq; ++i) {
1700 isl_int *eq = set->p[s]->eq[i];
1701 for (j = 0; j < 2; ++j) {
1702 isl_seq_neg(eq, eq, 1 + total);
1703 update_constraint(hull->ctx, table,
1704 eq, total, n, 0);
1707 for (i = 0; i < set->p[s]->n_ineq; ++i) {
1708 isl_int *ineq = set->p[s]->ineq[i];
1709 update_constraint(hull->ctx, table, ineq, total, n,
1710 set->p[s]->n_eq == 0);
1712 ++n;
1715 for (i = 0; i < min_constraints; ++i) {
1716 if (constraints[i].count < n)
1717 continue;
1718 if (!constraints[i].ineq)
1719 continue;
1720 j = isl_basic_set_alloc_inequality(hull);
1721 if (j < 0)
1722 goto error;
1723 isl_seq_cpy(hull->ineq[j], constraints[i].c->row[0], 1 + total);
1726 for (s = 0; s < set->n; ++s) {
1727 if (set->p[s]->n_eq)
1728 continue;
1729 if (set->p[s]->n_ineq != hull->n_ineq)
1730 continue;
1731 for (i = 0; i < set->p[s]->n_ineq; ++i) {
1732 isl_int *ineq = set->p[s]->ineq[i];
1733 if (!has_constraint(hull->ctx, table, ineq, total, n))
1734 break;
1736 if (i == set->p[s]->n_ineq)
1737 *is_hull = 1;
1740 isl_hash_table_clear(table);
1741 for (i = 0; i < min_constraints; ++i)
1742 isl_mat_free(constraints[i].c);
1743 free(constraints);
1744 free(table);
1745 return hull;
1746 error:
1747 isl_hash_table_clear(table);
1748 free(table);
1749 if (constraints)
1750 for (i = 0; i < min_constraints; ++i)
1751 isl_mat_free(constraints[i].c);
1752 free(constraints);
1753 return hull;
1756 /* Create a template for the convex hull of "set" and fill it up
1757 * obvious facet constraints, if any. If the result happens to
1758 * be the convex hull of "set" then *is_hull is set to 1.
1760 static struct isl_basic_set *proto_hull(struct isl_set *set, int *is_hull)
1762 struct isl_basic_set *hull;
1763 unsigned n_ineq;
1764 int i;
1766 n_ineq = 1;
1767 for (i = 0; i < set->n; ++i) {
1768 n_ineq += set->p[i]->n_eq;
1769 n_ineq += set->p[i]->n_ineq;
1771 hull = isl_basic_set_alloc_space(isl_space_copy(set->dim), 0, 0, n_ineq);
1772 hull = isl_basic_set_set_rational(hull);
1773 if (!hull)
1774 return NULL;
1775 return common_constraints(hull, set, is_hull);
1778 static struct isl_basic_set *uset_convex_hull_wrap(struct isl_set *set)
1780 struct isl_basic_set *hull;
1781 int is_hull;
1783 hull = proto_hull(set, &is_hull);
1784 if (hull && !is_hull) {
1785 if (hull->n_ineq == 0)
1786 hull = initial_hull(hull, set);
1787 hull = extend(hull, set);
1789 isl_set_free(set);
1791 return hull;
1794 /* Compute the convex hull of a set without any parameters or
1795 * integer divisions. Depending on whether the set is bounded,
1796 * we pass control to the wrapping based convex hull or
1797 * the Fourier-Motzkin elimination based convex hull.
1798 * We also handle a few special cases before checking the boundedness.
1800 static struct isl_basic_set *uset_convex_hull(struct isl_set *set)
1802 struct isl_basic_set *convex_hull = NULL;
1803 struct isl_basic_set *lin;
1805 if (isl_set_n_dim(set) == 0)
1806 return convex_hull_0d(set);
1808 set = isl_set_coalesce(set);
1809 set = isl_set_set_rational(set);
1811 if (!set)
1812 goto error;
1813 if (!set)
1814 return NULL;
1815 if (set->n == 1) {
1816 convex_hull = isl_basic_set_copy(set->p[0]);
1817 isl_set_free(set);
1818 return convex_hull;
1820 if (isl_set_n_dim(set) == 1)
1821 return convex_hull_1d(set);
1823 if (isl_set_is_bounded(set) &&
1824 set->ctx->opt->convex == ISL_CONVEX_HULL_WRAP)
1825 return uset_convex_hull_wrap(set);
1827 lin = uset_combined_lineality_space(isl_set_copy(set));
1828 if (!lin)
1829 goto error;
1830 if (isl_basic_set_is_universe(lin)) {
1831 isl_set_free(set);
1832 return lin;
1834 if (lin->n_eq < isl_basic_set_total_dim(lin))
1835 return modulo_lineality(set, lin);
1836 isl_basic_set_free(lin);
1838 return uset_convex_hull_unbounded(set);
1839 error:
1840 isl_set_free(set);
1841 isl_basic_set_free(convex_hull);
1842 return NULL;
1845 /* This is the core procedure, where "set" is a "pure" set, i.e.,
1846 * without parameters or divs and where the convex hull of set is
1847 * known to be full-dimensional.
1849 static struct isl_basic_set *uset_convex_hull_wrap_bounded(struct isl_set *set)
1851 struct isl_basic_set *convex_hull = NULL;
1853 if (!set)
1854 goto error;
1856 if (isl_set_n_dim(set) == 0) {
1857 convex_hull = isl_basic_set_universe(isl_space_copy(set->dim));
1858 isl_set_free(set);
1859 convex_hull = isl_basic_set_set_rational(convex_hull);
1860 return convex_hull;
1863 set = isl_set_set_rational(set);
1864 set = isl_set_coalesce(set);
1865 if (!set)
1866 goto error;
1867 if (set->n == 1) {
1868 convex_hull = isl_basic_set_copy(set->p[0]);
1869 isl_set_free(set);
1870 convex_hull = isl_basic_map_remove_redundancies(convex_hull);
1871 return convex_hull;
1873 if (isl_set_n_dim(set) == 1)
1874 return convex_hull_1d(set);
1876 return uset_convex_hull_wrap(set);
1877 error:
1878 isl_set_free(set);
1879 return NULL;
1882 /* Compute the convex hull of set "set" with affine hull "affine_hull",
1883 * We first remove the equalities (transforming the set), compute the
1884 * convex hull of the transformed set and then add the equalities back
1885 * (after performing the inverse transformation.
1887 static struct isl_basic_set *modulo_affine_hull(
1888 struct isl_set *set, struct isl_basic_set *affine_hull)
1890 struct isl_mat *T;
1891 struct isl_mat *T2;
1892 struct isl_basic_set *dummy;
1893 struct isl_basic_set *convex_hull;
1895 dummy = isl_basic_set_remove_equalities(
1896 isl_basic_set_copy(affine_hull), &T, &T2);
1897 if (!dummy)
1898 goto error;
1899 isl_basic_set_free(dummy);
1900 set = isl_set_preimage(set, T);
1901 convex_hull = uset_convex_hull(set);
1902 convex_hull = isl_basic_set_preimage(convex_hull, T2);
1903 convex_hull = isl_basic_set_intersect(convex_hull, affine_hull);
1904 return convex_hull;
1905 error:
1906 isl_basic_set_free(affine_hull);
1907 isl_set_free(set);
1908 return NULL;
1911 /* Compute the convex hull of a map.
1913 * The implementation was inspired by "Extended Convex Hull" by Fukuda et al.,
1914 * specifically, the wrapping of facets to obtain new facets.
1916 struct isl_basic_map *isl_map_convex_hull(struct isl_map *map)
1918 struct isl_basic_set *bset;
1919 struct isl_basic_map *model = NULL;
1920 struct isl_basic_set *affine_hull = NULL;
1921 struct isl_basic_map *convex_hull = NULL;
1922 struct isl_set *set = NULL;
1923 struct isl_ctx *ctx;
1925 if (!map)
1926 goto error;
1928 ctx = map->ctx;
1929 if (map->n == 0) {
1930 convex_hull = isl_basic_map_empty_like_map(map);
1931 isl_map_free(map);
1932 return convex_hull;
1935 map = isl_map_detect_equalities(map);
1936 map = isl_map_align_divs(map);
1937 if (!map)
1938 goto error;
1939 model = isl_basic_map_copy(map->p[0]);
1940 set = isl_map_underlying_set(map);
1941 if (!set)
1942 goto error;
1944 affine_hull = isl_set_affine_hull(isl_set_copy(set));
1945 if (!affine_hull)
1946 goto error;
1947 if (affine_hull->n_eq != 0)
1948 bset = modulo_affine_hull(set, affine_hull);
1949 else {
1950 isl_basic_set_free(affine_hull);
1951 bset = uset_convex_hull(set);
1954 convex_hull = isl_basic_map_overlying_set(bset, model);
1955 if (!convex_hull)
1956 return NULL;
1958 ISL_F_SET(convex_hull, ISL_BASIC_MAP_NO_IMPLICIT);
1959 ISL_F_SET(convex_hull, ISL_BASIC_MAP_ALL_EQUALITIES);
1960 ISL_F_CLR(convex_hull, ISL_BASIC_MAP_RATIONAL);
1961 return convex_hull;
1962 error:
1963 isl_set_free(set);
1964 isl_basic_map_free(model);
1965 return NULL;
1968 struct isl_basic_set *isl_set_convex_hull(struct isl_set *set)
1970 return (struct isl_basic_set *)
1971 isl_map_convex_hull((struct isl_map *)set);
1974 __isl_give isl_basic_map *isl_map_polyhedral_hull(__isl_take isl_map *map)
1976 isl_basic_map *hull;
1978 hull = isl_map_convex_hull(map);
1979 return isl_basic_map_remove_divs(hull);
1982 __isl_give isl_basic_set *isl_set_polyhedral_hull(__isl_take isl_set *set)
1984 return (isl_basic_set *)isl_map_polyhedral_hull((isl_map *)set);
1987 struct sh_data_entry {
1988 struct isl_hash_table *table;
1989 struct isl_tab *tab;
1992 /* Holds the data needed during the simple hull computation.
1993 * In particular,
1994 * n the number of basic sets in the original set
1995 * hull_table a hash table of already computed constraints
1996 * in the simple hull
1997 * p for each basic set,
1998 * table a hash table of the constraints
1999 * tab the tableau corresponding to the basic set
2001 struct sh_data {
2002 struct isl_ctx *ctx;
2003 unsigned n;
2004 struct isl_hash_table *hull_table;
2005 struct sh_data_entry p[1];
2008 static void sh_data_free(struct sh_data *data)
2010 int i;
2012 if (!data)
2013 return;
2014 isl_hash_table_free(data->ctx, data->hull_table);
2015 for (i = 0; i < data->n; ++i) {
2016 isl_hash_table_free(data->ctx, data->p[i].table);
2017 isl_tab_free(data->p[i].tab);
2019 free(data);
2022 struct ineq_cmp_data {
2023 unsigned len;
2024 isl_int *p;
2027 static int has_ineq(const void *entry, const void *val)
2029 isl_int *row = (isl_int *)entry;
2030 struct ineq_cmp_data *v = (struct ineq_cmp_data *)val;
2032 return isl_seq_eq(row + 1, v->p + 1, v->len) ||
2033 isl_seq_is_neg(row + 1, v->p + 1, v->len);
2036 static int hash_ineq(struct isl_ctx *ctx, struct isl_hash_table *table,
2037 isl_int *ineq, unsigned len)
2039 uint32_t c_hash;
2040 struct ineq_cmp_data v;
2041 struct isl_hash_table_entry *entry;
2043 v.len = len;
2044 v.p = ineq;
2045 c_hash = isl_seq_get_hash(ineq + 1, len);
2046 entry = isl_hash_table_find(ctx, table, c_hash, has_ineq, &v, 1);
2047 if (!entry)
2048 return - 1;
2049 entry->data = ineq;
2050 return 0;
2053 /* Fill hash table "table" with the constraints of "bset".
2054 * Equalities are added as two inequalities.
2055 * The value in the hash table is a pointer to the (in)equality of "bset".
2057 static int hash_basic_set(struct isl_hash_table *table,
2058 struct isl_basic_set *bset)
2060 int i, j;
2061 unsigned dim = isl_basic_set_total_dim(bset);
2063 for (i = 0; i < bset->n_eq; ++i) {
2064 for (j = 0; j < 2; ++j) {
2065 isl_seq_neg(bset->eq[i], bset->eq[i], 1 + dim);
2066 if (hash_ineq(bset->ctx, table, bset->eq[i], dim) < 0)
2067 return -1;
2070 for (i = 0; i < bset->n_ineq; ++i) {
2071 if (hash_ineq(bset->ctx, table, bset->ineq[i], dim) < 0)
2072 return -1;
2074 return 0;
2077 static struct sh_data *sh_data_alloc(struct isl_set *set, unsigned n_ineq)
2079 struct sh_data *data;
2080 int i;
2082 data = isl_calloc(set->ctx, struct sh_data,
2083 sizeof(struct sh_data) +
2084 (set->n - 1) * sizeof(struct sh_data_entry));
2085 if (!data)
2086 return NULL;
2087 data->ctx = set->ctx;
2088 data->n = set->n;
2089 data->hull_table = isl_hash_table_alloc(set->ctx, n_ineq);
2090 if (!data->hull_table)
2091 goto error;
2092 for (i = 0; i < set->n; ++i) {
2093 data->p[i].table = isl_hash_table_alloc(set->ctx,
2094 2 * set->p[i]->n_eq + set->p[i]->n_ineq);
2095 if (!data->p[i].table)
2096 goto error;
2097 if (hash_basic_set(data->p[i].table, set->p[i]) < 0)
2098 goto error;
2100 return data;
2101 error:
2102 sh_data_free(data);
2103 return NULL;
2106 /* Check if inequality "ineq" is a bound for basic set "j" or if
2107 * it can be relaxed (by increasing the constant term) to become
2108 * a bound for that basic set. In the latter case, the constant
2109 * term is updated.
2110 * Return 1 if "ineq" is a bound
2111 * 0 if "ineq" may attain arbitrarily small values on basic set "j"
2112 * -1 if some error occurred
2114 static int is_bound(struct sh_data *data, struct isl_set *set, int j,
2115 isl_int *ineq)
2117 enum isl_lp_result res;
2118 isl_int opt;
2120 if (!data->p[j].tab) {
2121 data->p[j].tab = isl_tab_from_basic_set(set->p[j], 0);
2122 if (!data->p[j].tab)
2123 return -1;
2126 isl_int_init(opt);
2128 res = isl_tab_min(data->p[j].tab, ineq, data->ctx->one,
2129 &opt, NULL, 0);
2130 if (res == isl_lp_ok && isl_int_is_neg(opt))
2131 isl_int_sub(ineq[0], ineq[0], opt);
2133 isl_int_clear(opt);
2135 return (res == isl_lp_ok || res == isl_lp_empty) ? 1 :
2136 res == isl_lp_unbounded ? 0 : -1;
2139 /* Check if inequality "ineq" from basic set "i" can be relaxed to
2140 * become a bound on the whole set. If so, add the (relaxed) inequality
2141 * to "hull".
2143 * We first check if "hull" already contains a translate of the inequality.
2144 * If so, we are done.
2145 * Then, we check if any of the previous basic sets contains a translate
2146 * of the inequality. If so, then we have already considered this
2147 * inequality and we are done.
2148 * Otherwise, for each basic set other than "i", we check if the inequality
2149 * is a bound on the basic set.
2150 * For previous basic sets, we know that they do not contain a translate
2151 * of the inequality, so we directly call is_bound.
2152 * For following basic sets, we first check if a translate of the
2153 * inequality appears in its description and if so directly update
2154 * the inequality accordingly.
2156 static struct isl_basic_set *add_bound(struct isl_basic_set *hull,
2157 struct sh_data *data, struct isl_set *set, int i, isl_int *ineq)
2159 uint32_t c_hash;
2160 struct ineq_cmp_data v;
2161 struct isl_hash_table_entry *entry;
2162 int j, k;
2164 if (!hull)
2165 return NULL;
2167 v.len = isl_basic_set_total_dim(hull);
2168 v.p = ineq;
2169 c_hash = isl_seq_get_hash(ineq + 1, v.len);
2171 entry = isl_hash_table_find(hull->ctx, data->hull_table, c_hash,
2172 has_ineq, &v, 0);
2173 if (entry)
2174 return hull;
2176 for (j = 0; j < i; ++j) {
2177 entry = isl_hash_table_find(hull->ctx, data->p[j].table,
2178 c_hash, has_ineq, &v, 0);
2179 if (entry)
2180 break;
2182 if (j < i)
2183 return hull;
2185 k = isl_basic_set_alloc_inequality(hull);
2186 isl_seq_cpy(hull->ineq[k], ineq, 1 + v.len);
2187 if (k < 0)
2188 goto error;
2190 for (j = 0; j < i; ++j) {
2191 int bound;
2192 bound = is_bound(data, set, j, hull->ineq[k]);
2193 if (bound < 0)
2194 goto error;
2195 if (!bound)
2196 break;
2198 if (j < i) {
2199 isl_basic_set_free_inequality(hull, 1);
2200 return hull;
2203 for (j = i + 1; j < set->n; ++j) {
2204 int bound, neg;
2205 isl_int *ineq_j;
2206 entry = isl_hash_table_find(hull->ctx, data->p[j].table,
2207 c_hash, has_ineq, &v, 0);
2208 if (entry) {
2209 ineq_j = entry->data;
2210 neg = isl_seq_is_neg(ineq_j + 1,
2211 hull->ineq[k] + 1, v.len);
2212 if (neg)
2213 isl_int_neg(ineq_j[0], ineq_j[0]);
2214 if (isl_int_gt(ineq_j[0], hull->ineq[k][0]))
2215 isl_int_set(hull->ineq[k][0], ineq_j[0]);
2216 if (neg)
2217 isl_int_neg(ineq_j[0], ineq_j[0]);
2218 continue;
2220 bound = is_bound(data, set, j, hull->ineq[k]);
2221 if (bound < 0)
2222 goto error;
2223 if (!bound)
2224 break;
2226 if (j < set->n) {
2227 isl_basic_set_free_inequality(hull, 1);
2228 return hull;
2231 entry = isl_hash_table_find(hull->ctx, data->hull_table, c_hash,
2232 has_ineq, &v, 1);
2233 if (!entry)
2234 goto error;
2235 entry->data = hull->ineq[k];
2237 return hull;
2238 error:
2239 isl_basic_set_free(hull);
2240 return NULL;
2243 /* Check if any inequality from basic set "i" can be relaxed to
2244 * become a bound on the whole set. If so, add the (relaxed) inequality
2245 * to "hull".
2247 static struct isl_basic_set *add_bounds(struct isl_basic_set *bset,
2248 struct sh_data *data, struct isl_set *set, int i)
2250 int j, k;
2251 unsigned dim = isl_basic_set_total_dim(bset);
2253 for (j = 0; j < set->p[i]->n_eq; ++j) {
2254 for (k = 0; k < 2; ++k) {
2255 isl_seq_neg(set->p[i]->eq[j], set->p[i]->eq[j], 1+dim);
2256 bset = add_bound(bset, data, set, i, set->p[i]->eq[j]);
2259 for (j = 0; j < set->p[i]->n_ineq; ++j)
2260 bset = add_bound(bset, data, set, i, set->p[i]->ineq[j]);
2261 return bset;
2264 /* Compute a superset of the convex hull of set that is described
2265 * by only translates of the constraints in the constituents of set.
2267 static struct isl_basic_set *uset_simple_hull(struct isl_set *set)
2269 struct sh_data *data = NULL;
2270 struct isl_basic_set *hull = NULL;
2271 unsigned n_ineq;
2272 int i;
2274 if (!set)
2275 return NULL;
2277 n_ineq = 0;
2278 for (i = 0; i < set->n; ++i) {
2279 if (!set->p[i])
2280 goto error;
2281 n_ineq += 2 * set->p[i]->n_eq + set->p[i]->n_ineq;
2284 hull = isl_basic_set_alloc_space(isl_space_copy(set->dim), 0, 0, n_ineq);
2285 if (!hull)
2286 goto error;
2288 data = sh_data_alloc(set, n_ineq);
2289 if (!data)
2290 goto error;
2292 for (i = 0; i < set->n; ++i)
2293 hull = add_bounds(hull, data, set, i);
2295 sh_data_free(data);
2296 isl_set_free(set);
2298 return hull;
2299 error:
2300 sh_data_free(data);
2301 isl_basic_set_free(hull);
2302 isl_set_free(set);
2303 return NULL;
2306 /* Compute a superset of the convex hull of map that is described
2307 * by only translates of the constraints in the constituents of map.
2309 struct isl_basic_map *isl_map_simple_hull(struct isl_map *map)
2311 struct isl_set *set = NULL;
2312 struct isl_basic_map *model = NULL;
2313 struct isl_basic_map *hull;
2314 struct isl_basic_map *affine_hull;
2315 struct isl_basic_set *bset = NULL;
2317 if (!map)
2318 return NULL;
2319 if (map->n == 0) {
2320 hull = isl_basic_map_empty_like_map(map);
2321 isl_map_free(map);
2322 return hull;
2324 if (map->n == 1) {
2325 hull = isl_basic_map_copy(map->p[0]);
2326 isl_map_free(map);
2327 return hull;
2330 map = isl_map_detect_equalities(map);
2331 affine_hull = isl_map_affine_hull(isl_map_copy(map));
2332 map = isl_map_align_divs(map);
2333 model = isl_basic_map_copy(map->p[0]);
2335 set = isl_map_underlying_set(map);
2337 bset = uset_simple_hull(set);
2339 hull = isl_basic_map_overlying_set(bset, model);
2341 hull = isl_basic_map_intersect(hull, affine_hull);
2342 hull = isl_basic_map_remove_redundancies(hull);
2344 if (!hull)
2345 return NULL;
2346 ISL_F_SET(hull, ISL_BASIC_MAP_NO_IMPLICIT);
2347 ISL_F_SET(hull, ISL_BASIC_MAP_ALL_EQUALITIES);
2349 return hull;
2352 struct isl_basic_set *isl_set_simple_hull(struct isl_set *set)
2354 return (struct isl_basic_set *)
2355 isl_map_simple_hull((struct isl_map *)set);
2358 /* Given a set "set", return parametric bounds on the dimension "dim".
2360 static struct isl_basic_set *set_bounds(struct isl_set *set, int dim)
2362 unsigned set_dim = isl_set_dim(set, isl_dim_set);
2363 set = isl_set_copy(set);
2364 set = isl_set_eliminate_dims(set, dim + 1, set_dim - (dim + 1));
2365 set = isl_set_eliminate_dims(set, 0, dim);
2366 return isl_set_convex_hull(set);
2369 /* Computes a "simple hull" and then check if each dimension in the
2370 * resulting hull is bounded by a symbolic constant. If not, the
2371 * hull is intersected with the corresponding bounds on the whole set.
2373 struct isl_basic_set *isl_set_bounded_simple_hull(struct isl_set *set)
2375 int i, j;
2376 struct isl_basic_set *hull;
2377 unsigned nparam, left;
2378 int removed_divs = 0;
2380 hull = isl_set_simple_hull(isl_set_copy(set));
2381 if (!hull)
2382 goto error;
2384 nparam = isl_basic_set_dim(hull, isl_dim_param);
2385 for (i = 0; i < isl_basic_set_dim(hull, isl_dim_set); ++i) {
2386 int lower = 0, upper = 0;
2387 struct isl_basic_set *bounds;
2389 left = isl_basic_set_total_dim(hull) - nparam - i - 1;
2390 for (j = 0; j < hull->n_eq; ++j) {
2391 if (isl_int_is_zero(hull->eq[j][1 + nparam + i]))
2392 continue;
2393 if (isl_seq_first_non_zero(hull->eq[j]+1+nparam+i+1,
2394 left) == -1)
2395 break;
2397 if (j < hull->n_eq)
2398 continue;
2400 for (j = 0; j < hull->n_ineq; ++j) {
2401 if (isl_int_is_zero(hull->ineq[j][1 + nparam + i]))
2402 continue;
2403 if (isl_seq_first_non_zero(hull->ineq[j]+1+nparam+i+1,
2404 left) != -1 ||
2405 isl_seq_first_non_zero(hull->ineq[j]+1+nparam,
2406 i) != -1)
2407 continue;
2408 if (isl_int_is_pos(hull->ineq[j][1 + nparam + i]))
2409 lower = 1;
2410 else
2411 upper = 1;
2412 if (lower && upper)
2413 break;
2416 if (lower && upper)
2417 continue;
2419 if (!removed_divs) {
2420 set = isl_set_remove_divs(set);
2421 if (!set)
2422 goto error;
2423 removed_divs = 1;
2425 bounds = set_bounds(set, i);
2426 hull = isl_basic_set_intersect(hull, bounds);
2427 if (!hull)
2428 goto error;
2431 isl_set_free(set);
2432 return hull;
2433 error:
2434 isl_set_free(set);
2435 return NULL;