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1 office 1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8 */
9  
10 #include <isl_ctx_private.h>
11 #include <isl_map_private.h>
12 #include "isl_sample.h"
13 #include "isl_sample_piplib.h"
14 #include <isl/vec.h>
15 #include <isl/mat.h>
16 #include <isl/seq.h>
17 #include "isl_equalities.h"
18 #include "isl_tab.h"
19 #include "isl_basis_reduction.h"
20 #include <isl_factorization.h>
21 #include <isl_point_private.h>
22 #include <isl_options_private.h>
23  
24 static struct isl_vec *empty_sample(struct isl_basic_set *bset)
25 {
26 struct isl_vec *vec;
27  
28 vec = isl_vec_alloc(bset->ctx, 0);
29 isl_basic_set_free(bset);
30 return vec;
31 }
32  
33 /* Construct a zero sample of the same dimension as bset.
34 * As a special case, if bset is zero-dimensional, this
35 * function creates a zero-dimensional sample point.
36 */
37 static struct isl_vec *zero_sample(struct isl_basic_set *bset)
38 {
39 unsigned dim;
40 struct isl_vec *sample;
41  
42 dim = isl_basic_set_total_dim(bset);
43 sample = isl_vec_alloc(bset->ctx, 1 + dim);
44 if (sample) {
45 isl_int_set_si(sample->el[0], 1);
46 isl_seq_clr(sample->el + 1, dim);
47 }
48 isl_basic_set_free(bset);
49 return sample;
50 }
51  
52 static struct isl_vec *interval_sample(struct isl_basic_set *bset)
53 {
54 int i;
55 isl_int t;
56 struct isl_vec *sample;
57  
58 bset = isl_basic_set_simplify(bset);
59 if (!bset)
60 return NULL;
61 if (isl_basic_set_plain_is_empty(bset))
62 return empty_sample(bset);
63 if (bset->n_eq == 0 && bset->n_ineq == 0)
64 return zero_sample(bset);
65  
66 sample = isl_vec_alloc(bset->ctx, 2);
67 if (!sample)
68 goto error;
69 if (!bset)
70 return NULL;
71 isl_int_set_si(sample->block.data[0], 1);
72  
73 if (bset->n_eq > 0) {
74 isl_assert(bset->ctx, bset->n_eq == 1, goto error);
75 isl_assert(bset->ctx, bset->n_ineq == 0, goto error);
76 if (isl_int_is_one(bset->eq[0][1]))
77 isl_int_neg(sample->el[1], bset->eq[0][0]);
78 else {
79 isl_assert(bset->ctx, isl_int_is_negone(bset->eq[0][1]),
80 goto error);
81 isl_int_set(sample->el[1], bset->eq[0][0]);
82 }
83 isl_basic_set_free(bset);
84 return sample;
85 }
86  
87 isl_int_init(t);
88 if (isl_int_is_one(bset->ineq[0][1]))
89 isl_int_neg(sample->block.data[1], bset->ineq[0][0]);
90 else
91 isl_int_set(sample->block.data[1], bset->ineq[0][0]);
92 for (i = 1; i < bset->n_ineq; ++i) {
93 isl_seq_inner_product(sample->block.data,
94 bset->ineq[i], 2, &t);
95 if (isl_int_is_neg(t))
96 break;
97 }
98 isl_int_clear(t);
99 if (i < bset->n_ineq) {
100 isl_vec_free(sample);
101 return empty_sample(bset);
102 }
103  
104 isl_basic_set_free(bset);
105 return sample;
106 error:
107 isl_basic_set_free(bset);
108 isl_vec_free(sample);
109 return NULL;
110 }
111  
112 static struct isl_mat *independent_bounds(struct isl_basic_set *bset)
113 {
114 int i, j, n;
115 struct isl_mat *dirs = NULL;
116 struct isl_mat *bounds = NULL;
117 unsigned dim;
118  
119 if (!bset)
120 return NULL;
121  
122 dim = isl_basic_set_n_dim(bset);
123 bounds = isl_mat_alloc(bset->ctx, 1+dim, 1+dim);
124 if (!bounds)
125 return NULL;
126  
127 isl_int_set_si(bounds->row[0][0], 1);
128 isl_seq_clr(bounds->row[0]+1, dim);
129 bounds->n_row = 1;
130  
131 if (bset->n_ineq == 0)
132 return bounds;
133  
134 dirs = isl_mat_alloc(bset->ctx, dim, dim);
135 if (!dirs) {
136 isl_mat_free(bounds);
137 return NULL;
138 }
139 isl_seq_cpy(dirs->row[0], bset->ineq[0]+1, dirs->n_col);
140 isl_seq_cpy(bounds->row[1], bset->ineq[0], bounds->n_col);
141 for (j = 1, n = 1; n < dim && j < bset->n_ineq; ++j) {
142 int pos;
143  
144 isl_seq_cpy(dirs->row[n], bset->ineq[j]+1, dirs->n_col);
145  
146 pos = isl_seq_first_non_zero(dirs->row[n], dirs->n_col);
147 if (pos < 0)
148 continue;
149 for (i = 0; i < n; ++i) {
150 int pos_i;
151 pos_i = isl_seq_first_non_zero(dirs->row[i], dirs->n_col);
152 if (pos_i < pos)
153 continue;
154 if (pos_i > pos)
155 break;
156 isl_seq_elim(dirs->row[n], dirs->row[i], pos,
157 dirs->n_col, NULL);
158 pos = isl_seq_first_non_zero(dirs->row[n], dirs->n_col);
159 if (pos < 0)
160 break;
161 }
162 if (pos < 0)
163 continue;
164 if (i < n) {
165 int k;
166 isl_int *t = dirs->row[n];
167 for (k = n; k > i; --k)
168 dirs->row[k] = dirs->row[k-1];
169 dirs->row[i] = t;
170 }
171 ++n;
172 isl_seq_cpy(bounds->row[n], bset->ineq[j], bounds->n_col);
173 }
174 isl_mat_free(dirs);
175 bounds->n_row = 1+n;
176 return bounds;
177 }
178  
179 static void swap_inequality(struct isl_basic_set *bset, int a, int b)
180 {
181 isl_int *t = bset->ineq[a];
182 bset->ineq[a] = bset->ineq[b];
183 bset->ineq[b] = t;
184 }
185  
186 /* Skew into positive orthant and project out lineality space.
187 *
188 * We perform a unimodular transformation that turns a selected
189 * maximal set of linearly independent bounds into constraints
190 * on the first dimensions that impose that these first dimensions
191 * are non-negative. In particular, the constraint matrix is lower
192 * triangular with positive entries on the diagonal and negative
193 * entries below.
194 * If "bset" has a lineality space then these constraints (and therefore
195 * all constraints in bset) only involve the first dimensions.
196 * The remaining dimensions then do not appear in any constraints and
197 * we can select any value for them, say zero. We therefore project
198 * out this final dimensions and plug in the value zero later. This
199 * is accomplished by simply dropping the final columns of
200 * the unimodular transformation.
201 */
202 static struct isl_basic_set *isl_basic_set_skew_to_positive_orthant(
203 struct isl_basic_set *bset, struct isl_mat **T)
204 {
205 struct isl_mat *U = NULL;
206 struct isl_mat *bounds = NULL;
207 int i, j;
208 unsigned old_dim, new_dim;
209  
210 *T = NULL;
211 if (!bset)
212 return NULL;
213  
214 isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
215 isl_assert(bset->ctx, bset->n_div == 0, goto error);
216 isl_assert(bset->ctx, bset->n_eq == 0, goto error);
217  
218 old_dim = isl_basic_set_n_dim(bset);
219 /* Try to move (multiples of) unit rows up. */
220 for (i = 0, j = 0; i < bset->n_ineq; ++i) {
221 int pos = isl_seq_first_non_zero(bset->ineq[i]+1, old_dim);
222 if (pos < 0)
223 continue;
224 if (isl_seq_first_non_zero(bset->ineq[i]+1+pos+1,
225 old_dim-pos-1) >= 0)
226 continue;
227 if (i != j)
228 swap_inequality(bset, i, j);
229 ++j;
230 }
231 bounds = independent_bounds(bset);
232 if (!bounds)
233 goto error;
234 new_dim = bounds->n_row - 1;
235 bounds = isl_mat_left_hermite(bounds, 1, &U, NULL);
236 if (!bounds)
237 goto error;
238 U = isl_mat_drop_cols(U, 1 + new_dim, old_dim - new_dim);
239 bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
240 if (!bset)
241 goto error;
242 *T = U;
243 isl_mat_free(bounds);
244 return bset;
245 error:
246 isl_mat_free(bounds);
247 isl_mat_free(U);
248 isl_basic_set_free(bset);
249 return NULL;
250 }
251  
252 /* Find a sample integer point, if any, in bset, which is known
253 * to have equalities. If bset contains no integer points, then
254 * return a zero-length vector.
255 * We simply remove the known equalities, compute a sample
256 * in the resulting bset, using the specified recurse function,
257 * and then transform the sample back to the original space.
258 */
259 static struct isl_vec *sample_eq(struct isl_basic_set *bset,
260 struct isl_vec *(*recurse)(struct isl_basic_set *))
261 {
262 struct isl_mat *T;
263 struct isl_vec *sample;
264  
265 if (!bset)
266 return NULL;
267  
268 bset = isl_basic_set_remove_equalities(bset, &T, NULL);
269 sample = recurse(bset);
270 if (!sample || sample->size == 0)
271 isl_mat_free(T);
272 else
273 sample = isl_mat_vec_product(T, sample);
274 return sample;
275 }
276  
277 /* Return a matrix containing the equalities of the tableau
278 * in constraint form. The tableau is assumed to have
279 * an associated bset that has been kept up-to-date.
280 */
281 static struct isl_mat *tab_equalities(struct isl_tab *tab)
282 {
283 int i, j;
284 int n_eq;
285 struct isl_mat *eq;
286 struct isl_basic_set *bset;
287  
288 if (!tab)
289 return NULL;
290  
291 bset = isl_tab_peek_bset(tab);
292 isl_assert(tab->mat->ctx, bset, return NULL);
293  
294 n_eq = tab->n_var - tab->n_col + tab->n_dead;
295 if (tab->empty || n_eq == 0)
296 return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var);
297 if (n_eq == tab->n_var)
298 return isl_mat_identity(tab->mat->ctx, tab->n_var);
299  
300 eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var);
301 if (!eq)
302 return NULL;
303 for (i = 0, j = 0; i < tab->n_con; ++i) {
304 if (tab->con[i].is_row)
305 continue;
306 if (tab->con[i].index >= 0 && tab->con[i].index >= tab->n_dead)
307 continue;
308 if (i < bset->n_eq)
309 isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var);
310 else
311 isl_seq_cpy(eq->row[j],
312 bset->ineq[i - bset->n_eq] + 1, tab->n_var);
313 ++j;
314 }
315 isl_assert(bset->ctx, j == n_eq, goto error);
316 return eq;
317 error:
318 isl_mat_free(eq);
319 return NULL;
320 }
321  
322 /* Compute and return an initial basis for the bounded tableau "tab".
323 *
324 * If the tableau is either full-dimensional or zero-dimensional,
325 * the we simply return an identity matrix.
326 * Otherwise, we construct a basis whose first directions correspond
327 * to equalities.
328 */
329 static struct isl_mat *initial_basis(struct isl_tab *tab)
330 {
331 int n_eq;
332 struct isl_mat *eq;
333 struct isl_mat *Q;
334  
335 tab->n_unbounded = 0;
336 tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
337 if (tab->empty || n_eq == 0 || n_eq == tab->n_var)
338 return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
339  
340 eq = tab_equalities(tab);
341 eq = isl_mat_left_hermite(eq, 0, NULL, &Q);
342 if (!eq)
343 return NULL;
344 isl_mat_free(eq);
345  
346 Q = isl_mat_lin_to_aff(Q);
347 return Q;
348 }
349  
350 /* Given a tableau representing a set, find and return
351 * an integer point in the set, if there is any.
352 *
353 * We perform a depth first search
354 * for an integer point, by scanning all possible values in the range
355 * attained by a basis vector, where an initial basis may have been set
356 * by the calling function. Otherwise an initial basis that exploits
357 * the equalities in the tableau is created.
358 * tab->n_zero is currently ignored and is clobbered by this function.
359 *
360 * The tableau is allowed to have unbounded direction, but then
361 * the calling function needs to set an initial basis, with the
362 * unbounded directions last and with tab->n_unbounded set
363 * to the number of unbounded directions.
364 * Furthermore, the calling functions needs to add shifted copies
365 * of all constraints involving unbounded directions to ensure
366 * that any feasible rational value in these directions can be rounded
367 * up to yield a feasible integer value.
368 * In particular, let B define the given basis x' = B x
369 * and let T be the inverse of B, i.e., X = T x'.
370 * Let a x + c >= 0 be a constraint of the set represented by the tableau,
371 * or a T x' + c >= 0 in terms of the given basis. Assume that
372 * the bounded directions have an integer value, then we can safely
373 * round up the values for the unbounded directions if we make sure
374 * that x' not only satisfies the original constraint, but also
375 * the constraint "a T x' + c + s >= 0" with s the sum of all
376 * negative values in the last n_unbounded entries of "a T".
377 * The calling function therefore needs to add the constraint
378 * a x + c + s >= 0. The current function then scans the first
379 * directions for an integer value and once those have been found,
380 * it can compute "T ceil(B x)" to yield an integer point in the set.
381 * Note that during the search, the first rows of B may be changed
382 * by a basis reduction, but the last n_unbounded rows of B remain
383 * unaltered and are also not mixed into the first rows.
384 *
385 * The search is implemented iteratively. "level" identifies the current
386 * basis vector. "init" is true if we want the first value at the current
387 * level and false if we want the next value.
388 *
389 * The initial basis is the identity matrix. If the range in some direction
390 * contains more than one integer value, we perform basis reduction based
391 * on the value of ctx->opt->gbr
392 * - ISL_GBR_NEVER: never perform basis reduction
393 * - ISL_GBR_ONCE: only perform basis reduction the first
394 * time such a range is encountered
395 * - ISL_GBR_ALWAYS: always perform basis reduction when
396 * such a range is encountered
397 *
398 * When ctx->opt->gbr is set to ISL_GBR_ALWAYS, then we allow the basis
399 * reduction computation to return early. That is, as soon as it
400 * finds a reasonable first direction.
401 */
402 struct isl_vec *isl_tab_sample(struct isl_tab *tab)
403 {
404 unsigned dim;
405 unsigned gbr;
406 struct isl_ctx *ctx;
407 struct isl_vec *sample;
408 struct isl_vec *min;
409 struct isl_vec *max;
410 enum isl_lp_result res;
411 int level;
412 int init;
413 int reduced;
414 struct isl_tab_undo **snap;
415  
416 if (!tab)
417 return NULL;
418 if (tab->empty)
419 return isl_vec_alloc(tab->mat->ctx, 0);
420  
421 if (!tab->basis)
422 tab->basis = initial_basis(tab);
423 if (!tab->basis)
424 return NULL;
425 isl_assert(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1,
426 return NULL);
427 isl_assert(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1,
428 return NULL);
429  
430 ctx = tab->mat->ctx;
431 dim = tab->n_var;
432 gbr = ctx->opt->gbr;
433  
434 if (tab->n_unbounded == tab->n_var) {
435 sample = isl_tab_get_sample_value(tab);
436 sample = isl_mat_vec_product(isl_mat_copy(tab->basis), sample);
437 sample = isl_vec_ceil(sample);
438 sample = isl_mat_vec_inverse_product(isl_mat_copy(tab->basis),
439 sample);
440 return sample;
441 }
442  
443 if (isl_tab_extend_cons(tab, dim + 1) < 0)
444 return NULL;
445  
446 min = isl_vec_alloc(ctx, dim);
447 max = isl_vec_alloc(ctx, dim);
448 snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim);
449  
450 if (!min || !max || !snap)
451 goto error;
452  
453 level = 0;
454 init = 1;
455 reduced = 0;
456  
457 while (level >= 0) {
458 int empty = 0;
459 if (init) {
460 res = isl_tab_min(tab, tab->basis->row[1 + level],
461 ctx->one, &min->el[level], NULL, 0);
462 if (res == isl_lp_empty)
463 empty = 1;
464 isl_assert(ctx, res != isl_lp_unbounded, goto error);
465 if (res == isl_lp_error)
466 goto error;
467 if (!empty && isl_tab_sample_is_integer(tab))
468 break;
469 isl_seq_neg(tab->basis->row[1 + level] + 1,
470 tab->basis->row[1 + level] + 1, dim);
471 res = isl_tab_min(tab, tab->basis->row[1 + level],
472 ctx->one, &max->el[level], NULL, 0);
473 isl_seq_neg(tab->basis->row[1 + level] + 1,
474 tab->basis->row[1 + level] + 1, dim);
475 isl_int_neg(max->el[level], max->el[level]);
476 if (res == isl_lp_empty)
477 empty = 1;
478 isl_assert(ctx, res != isl_lp_unbounded, goto error);
479 if (res == isl_lp_error)
480 goto error;
481 if (!empty && isl_tab_sample_is_integer(tab))
482 break;
483 if (!empty && !reduced &&
484 ctx->opt->gbr != ISL_GBR_NEVER &&
485 isl_int_lt(min->el[level], max->el[level])) {
486 unsigned gbr_only_first;
487 if (ctx->opt->gbr == ISL_GBR_ONCE)
488 ctx->opt->gbr = ISL_GBR_NEVER;
489 tab->n_zero = level;
490 gbr_only_first = ctx->opt->gbr_only_first;
491 ctx->opt->gbr_only_first =
492 ctx->opt->gbr == ISL_GBR_ALWAYS;
493 tab = isl_tab_compute_reduced_basis(tab);
494 ctx->opt->gbr_only_first = gbr_only_first;
495 if (!tab || !tab->basis)
496 goto error;
497 reduced = 1;
498 continue;
499 }
500 reduced = 0;
501 snap[level] = isl_tab_snap(tab);
502 } else
503 isl_int_add_ui(min->el[level], min->el[level], 1);
504  
505 if (empty || isl_int_gt(min->el[level], max->el[level])) {
506 level--;
507 init = 0;
508 if (level >= 0)
509 if (isl_tab_rollback(tab, snap[level]) < 0)
510 goto error;
511 continue;
512 }
513 isl_int_neg(tab->basis->row[1 + level][0], min->el[level]);
514 if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
515 goto error;
516 isl_int_set_si(tab->basis->row[1 + level][0], 0);
517 if (level + tab->n_unbounded < dim - 1) {
518 ++level;
519 init = 1;
520 continue;
521 }
522 break;
523 }
524  
525 if (level >= 0) {
526 sample = isl_tab_get_sample_value(tab);
527 if (!sample)
528 goto error;
529 if (tab->n_unbounded && !isl_int_is_one(sample->el[0])) {
530 sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
531 sample);
532 sample = isl_vec_ceil(sample);
533 sample = isl_mat_vec_inverse_product(
534 isl_mat_copy(tab->basis), sample);
535 }
536 } else
537 sample = isl_vec_alloc(ctx, 0);
538  
539 ctx->opt->gbr = gbr;
540 isl_vec_free(min);
541 isl_vec_free(max);
542 free(snap);
543 return sample;
544 error:
545 ctx->opt->gbr = gbr;
546 isl_vec_free(min);
547 isl_vec_free(max);
548 free(snap);
549 return NULL;
550 }
551  
552 static struct isl_vec *sample_bounded(struct isl_basic_set *bset);
553  
554 /* Compute a sample point of the given basic set, based on the given,
555 * non-trivial factorization.
556 */
557 static __isl_give isl_vec *factored_sample(__isl_take isl_basic_set *bset,
558 __isl_take isl_factorizer *f)
559 {
560 int i, n;
561 isl_vec *sample = NULL;
562 isl_ctx *ctx;
563 unsigned nparam;
564 unsigned nvar;
565  
566 ctx = isl_basic_set_get_ctx(bset);
567 if (!ctx)
568 goto error;
569  
570 nparam = isl_basic_set_dim(bset, isl_dim_param);
571 nvar = isl_basic_set_dim(bset, isl_dim_set);
572  
573 sample = isl_vec_alloc(ctx, 1 + isl_basic_set_total_dim(bset));
574 if (!sample)
575 goto error;
576 isl_int_set_si(sample->el[0], 1);
577  
578 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
579  
580 for (i = 0, n = 0; i < f->n_group; ++i) {
581 isl_basic_set *bset_i;
582 isl_vec *sample_i;
583  
584 bset_i = isl_basic_set_copy(bset);
585 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
586 nparam + n + f->len[i], nvar - n - f->len[i]);
587 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
588 nparam, n);
589 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
590 n + f->len[i], nvar - n - f->len[i]);
591 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
592  
593 sample_i = sample_bounded(bset_i);
594 if (!sample_i)
595 goto error;
596 if (sample_i->size == 0) {
597 isl_basic_set_free(bset);
598 isl_factorizer_free(f);
599 isl_vec_free(sample);
600 return sample_i;
601 }
602 isl_seq_cpy(sample->el + 1 + nparam + n,
603 sample_i->el + 1, f->len[i]);
604 isl_vec_free(sample_i);
605  
606 n += f->len[i];
607 }
608  
609 f->morph = isl_morph_inverse(f->morph);
610 sample = isl_morph_vec(isl_morph_copy(f->morph), sample);
611  
612 isl_basic_set_free(bset);
613 isl_factorizer_free(f);
614 return sample;
615 error:
616 isl_basic_set_free(bset);
617 isl_factorizer_free(f);
618 isl_vec_free(sample);
619 return NULL;
620 }
621  
622 /* Given a basic set that is known to be bounded, find and return
623 * an integer point in the basic set, if there is any.
624 *
625 * After handling some trivial cases, we construct a tableau
626 * and then use isl_tab_sample to find a sample, passing it
627 * the identity matrix as initial basis.
628 */
629 static struct isl_vec *sample_bounded(struct isl_basic_set *bset)
630 {
631 unsigned dim;
632 struct isl_ctx *ctx;
633 struct isl_vec *sample;
634 struct isl_tab *tab = NULL;
635 isl_factorizer *f;
636  
637 if (!bset)
638 return NULL;
639  
640 if (isl_basic_set_plain_is_empty(bset))
641 return empty_sample(bset);
642  
643 dim = isl_basic_set_total_dim(bset);
644 if (dim == 0)
645 return zero_sample(bset);
646 if (dim == 1)
647 return interval_sample(bset);
648 if (bset->n_eq > 0)
649 return sample_eq(bset, sample_bounded);
650  
651 f = isl_basic_set_factorizer(bset);
652 if (!f)
653 goto error;
654 if (f->n_group != 0)
655 return factored_sample(bset, f);
656 isl_factorizer_free(f);
657  
658 ctx = bset->ctx;
659  
660 tab = isl_tab_from_basic_set(bset, 1);
661 if (tab && tab->empty) {
662 isl_tab_free(tab);
663 ISL_F_SET(bset, ISL_BASIC_SET_EMPTY);
664 sample = isl_vec_alloc(bset->ctx, 0);
665 isl_basic_set_free(bset);
666 return sample;
667 }
668  
669 if (!ISL_F_ISSET(bset, ISL_BASIC_SET_NO_IMPLICIT))
670 if (isl_tab_detect_implicit_equalities(tab) < 0)
671 goto error;
672  
673 sample = isl_tab_sample(tab);
674 if (!sample)
675 goto error;
676  
677 if (sample->size > 0) {
678 isl_vec_free(bset->sample);
679 bset->sample = isl_vec_copy(sample);
680 }
681  
682 isl_basic_set_free(bset);
683 isl_tab_free(tab);
684 return sample;
685 error:
686 isl_basic_set_free(bset);
687 isl_tab_free(tab);
688 return NULL;
689 }
690  
691 /* Given a basic set "bset" and a value "sample" for the first coordinates
692 * of bset, plug in these values and drop the corresponding coordinates.
693 *
694 * We do this by computing the preimage of the transformation
695 *
696 * [ 1 0 ]
697 * x = [ s 0 ] x'
698 * [ 0 I ]
699 *
700 * where [1 s] is the sample value and I is the identity matrix of the
701 * appropriate dimension.
702 */
703 static struct isl_basic_set *plug_in(struct isl_basic_set *bset,
704 struct isl_vec *sample)
705 {
706 int i;
707 unsigned total;
708 struct isl_mat *T;
709  
710 if (!bset || !sample)
711 goto error;
712  
713 total = isl_basic_set_total_dim(bset);
714 T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
715 if (!T)
716 goto error;
717  
718 for (i = 0; i < sample->size; ++i) {
719 isl_int_set(T->row[i][0], sample->el[i]);
720 isl_seq_clr(T->row[i] + 1, T->n_col - 1);
721 }
722 for (i = 0; i < T->n_col - 1; ++i) {
723 isl_seq_clr(T->row[sample->size + i], T->n_col);
724 isl_int_set_si(T->row[sample->size + i][1 + i], 1);
725 }
726 isl_vec_free(sample);
727  
728 bset = isl_basic_set_preimage(bset, T);
729 return bset;
730 error:
731 isl_basic_set_free(bset);
732 isl_vec_free(sample);
733 return NULL;
734 }
735  
736 /* Given a basic set "bset", return any (possibly non-integer) point
737 * in the basic set.
738 */
739 static struct isl_vec *rational_sample(struct isl_basic_set *bset)
740 {
741 struct isl_tab *tab;
742 struct isl_vec *sample;
743  
744 if (!bset)
745 return NULL;
746  
747 tab = isl_tab_from_basic_set(bset, 0);
748 sample = isl_tab_get_sample_value(tab);
749 isl_tab_free(tab);
750  
751 isl_basic_set_free(bset);
752  
753 return sample;
754 }
755  
756 /* Given a linear cone "cone" and a rational point "vec",
757 * construct a polyhedron with shifted copies of the constraints in "cone",
758 * i.e., a polyhedron with "cone" as its recession cone, such that each
759 * point x in this polyhedron is such that the unit box positioned at x
760 * lies entirely inside the affine cone 'vec + cone'.
761 * Any rational point in this polyhedron may therefore be rounded up
762 * to yield an integer point that lies inside said affine cone.
763 *
764 * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
765 * point "vec" by v/d.
766 * Let b_i = <a_i, v>. Then the affine cone 'vec + cone' is given
767 * by <a_i, x> - b/d >= 0.
768 * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
769 * We prefer this polyhedron over the actual affine cone because it doesn't
770 * require a scaling of the constraints.
771 * If each of the vertices of the unit cube positioned at x lies inside
772 * this polyhedron, then the whole unit cube at x lies inside the affine cone.
773 * We therefore impose that x' = x + \sum e_i, for any selection of unit
774 * vectors lies inside the polyhedron, i.e.,
775 *
776 * <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
777 *
778 * The most stringent of these constraints is the one that selects
779 * all negative a_i, so the polyhedron we are looking for has constraints
780 *
781 * <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
782 *
783 * Note that if cone were known to have only non-negative rays
784 * (which can be accomplished by a unimodular transformation),
785 * then we would only have to check the points x' = x + e_i
786 * and we only have to add the smallest negative a_i (if any)
787 * instead of the sum of all negative a_i.
788 */
789 static struct isl_basic_set *shift_cone(struct isl_basic_set *cone,
790 struct isl_vec *vec)
791 {
792 int i, j, k;
793 unsigned total;
794  
795 struct isl_basic_set *shift = NULL;
796  
797 if (!cone || !vec)
798 goto error;
799  
800 isl_assert(cone->ctx, cone->n_eq == 0, goto error);
801  
802 total = isl_basic_set_total_dim(cone);
803  
804 shift = isl_basic_set_alloc_space(isl_basic_set_get_space(cone),
805 0, 0, cone->n_ineq);
806  
807 for (i = 0; i < cone->n_ineq; ++i) {
808 k = isl_basic_set_alloc_inequality(shift);
809 if (k < 0)
810 goto error;
811 isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
812 isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
813 &shift->ineq[k][0]);
814 isl_int_cdiv_q(shift->ineq[k][0],
815 shift->ineq[k][0], vec->el[0]);
816 isl_int_neg(shift->ineq[k][0], shift->ineq[k][0]);
817 for (j = 0; j < total; ++j) {
818 if (isl_int_is_nonneg(shift->ineq[k][1 + j]))
819 continue;
820 isl_int_add(shift->ineq[k][0],
821 shift->ineq[k][0], shift->ineq[k][1 + j]);
822 }
823 }
824  
825 isl_basic_set_free(cone);
826 isl_vec_free(vec);
827  
828 return isl_basic_set_finalize(shift);
829 error:
830 isl_basic_set_free(shift);
831 isl_basic_set_free(cone);
832 isl_vec_free(vec);
833 return NULL;
834 }
835  
836 /* Given a rational point vec in a (transformed) basic set,
837 * such that cone is the recession cone of the original basic set,
838 * "round up" the rational point to an integer point.
839 *
840 * We first check if the rational point just happens to be integer.
841 * If not, we transform the cone in the same way as the basic set,
842 * pick a point x in this cone shifted to the rational point such that
843 * the whole unit cube at x is also inside this affine cone.
844 * Then we simply round up the coordinates of x and return the
845 * resulting integer point.
846 */
847 static struct isl_vec *round_up_in_cone(struct isl_vec *vec,
848 struct isl_basic_set *cone, struct isl_mat *U)
849 {
850 unsigned total;
851  
852 if (!vec || !cone || !U)
853 goto error;
854  
855 isl_assert(vec->ctx, vec->size != 0, goto error);
856 if (isl_int_is_one(vec->el[0])) {
857 isl_mat_free(U);
858 isl_basic_set_free(cone);
859 return vec;
860 }
861  
862 total = isl_basic_set_total_dim(cone);
863 cone = isl_basic_set_preimage(cone, U);
864 cone = isl_basic_set_remove_dims(cone, isl_dim_set,
865 0, total - (vec->size - 1));
866  
867 cone = shift_cone(cone, vec);
868  
869 vec = rational_sample(cone);
870 vec = isl_vec_ceil(vec);
871 return vec;
872 error:
873 isl_mat_free(U);
874 isl_vec_free(vec);
875 isl_basic_set_free(cone);
876 return NULL;
877 }
878  
879 /* Concatenate two integer vectors, i.e., two vectors with denominator
880 * (stored in element 0) equal to 1.
881 */
882 static struct isl_vec *vec_concat(struct isl_vec *vec1, struct isl_vec *vec2)
883 {
884 struct isl_vec *vec;
885  
886 if (!vec1 || !vec2)
887 goto error;
888 isl_assert(vec1->ctx, vec1->size > 0, goto error);
889 isl_assert(vec2->ctx, vec2->size > 0, goto error);
890 isl_assert(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error);
891 isl_assert(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error);
892  
893 vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
894 if (!vec)
895 goto error;
896  
897 isl_seq_cpy(vec->el, vec1->el, vec1->size);
898 isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
899  
900 isl_vec_free(vec1);
901 isl_vec_free(vec2);
902  
903 return vec;
904 error:
905 isl_vec_free(vec1);
906 isl_vec_free(vec2);
907 return NULL;
908 }
909  
910 /* Give a basic set "bset" with recession cone "cone", compute and
911 * return an integer point in bset, if any.
912 *
913 * If the recession cone is full-dimensional, then we know that
914 * bset contains an infinite number of integer points and it is
915 * fairly easy to pick one of them.
916 * If the recession cone is not full-dimensional, then we first
917 * transform bset such that the bounded directions appear as
918 * the first dimensions of the transformed basic set.
919 * We do this by using a unimodular transformation that transforms
920 * the equalities in the recession cone to equalities on the first
921 * dimensions.
922 *
923 * The transformed set is then projected onto its bounded dimensions.
924 * Note that to compute this projection, we can simply drop all constraints
925 * involving any of the unbounded dimensions since these constraints
926 * cannot be combined to produce a constraint on the bounded dimensions.
927 * To see this, assume that there is such a combination of constraints
928 * that produces a constraint on the bounded dimensions. This means
929 * that some combination of the unbounded dimensions has both an upper
930 * bound and a lower bound in terms of the bounded dimensions, but then
931 * this combination would be a bounded direction too and would have been
932 * transformed into a bounded dimensions.
933 *
934 * We then compute a sample value in the bounded dimensions.
935 * If no such value can be found, then the original set did not contain
936 * any integer points and we are done.
937 * Otherwise, we plug in the value we found in the bounded dimensions,
938 * project out these bounded dimensions and end up with a set with
939 * a full-dimensional recession cone.
940 * A sample point in this set is computed by "rounding up" any
941 * rational point in the set.
942 *
943 * The sample points in the bounded and unbounded dimensions are
944 * then combined into a single sample point and transformed back
945 * to the original space.
946 */
947 __isl_give isl_vec *isl_basic_set_sample_with_cone(
948 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *cone)
949 {
950 unsigned total;
951 unsigned cone_dim;
952 struct isl_mat *M, *U;
953 struct isl_vec *sample;
954 struct isl_vec *cone_sample;
955 struct isl_ctx *ctx;
956 struct isl_basic_set *bounded;
957  
958 if (!bset || !cone)
959 goto error;
960  
961 ctx = bset->ctx;
962 total = isl_basic_set_total_dim(cone);
963 cone_dim = total - cone->n_eq;
964  
965 M = isl_mat_sub_alloc6(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
966 M = isl_mat_left_hermite(M, 0, &U, NULL);
967 if (!M)
968 goto error;
969 isl_mat_free(M);
970  
971 U = isl_mat_lin_to_aff(U);
972 bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
973  
974 bounded = isl_basic_set_copy(bset);
975 bounded = isl_basic_set_drop_constraints_involving(bounded,
976 total - cone_dim, cone_dim);
977 bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
978 sample = sample_bounded(bounded);
979 if (!sample || sample->size == 0) {
980 isl_basic_set_free(bset);
981 isl_basic_set_free(cone);
982 isl_mat_free(U);
983 return sample;
984 }
985 bset = plug_in(bset, isl_vec_copy(sample));
986 cone_sample = rational_sample(bset);
987 cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
988 sample = vec_concat(sample, cone_sample);
989 sample = isl_mat_vec_product(U, sample);
990 return sample;
991 error:
992 isl_basic_set_free(cone);
993 isl_basic_set_free(bset);
994 return NULL;
995 }
996  
997 static void vec_sum_of_neg(struct isl_vec *v, isl_int *s)
998 {
999 int i;
1000  
1001 isl_int_set_si(*s, 0);
1002  
1003 for (i = 0; i < v->size; ++i)
1004 if (isl_int_is_neg(v->el[i]))
1005 isl_int_add(*s, *s, v->el[i]);
1006 }
1007  
1008 /* Given a tableau "tab", a tableau "tab_cone" that corresponds
1009 * to the recession cone and the inverse of a new basis U = inv(B),
1010 * with the unbounded directions in B last,
1011 * add constraints to "tab" that ensure any rational value
1012 * in the unbounded directions can be rounded up to an integer value.
1013 *
1014 * The new basis is given by x' = B x, i.e., x = U x'.
1015 * For any rational value of the last tab->n_unbounded coordinates
1016 * in the update tableau, the value that is obtained by rounding
1017 * up this value should be contained in the original tableau.
1018 * For any constraint "a x + c >= 0", we therefore need to add
1019 * a constraint "a x + c + s >= 0", with s the sum of all negative
1020 * entries in the last elements of "a U".
1021 *
1022 * Since we are not interested in the first entries of any of the "a U",
1023 * we first drop the columns of U that correpond to bounded directions.
1024 */
1025 static int tab_shift_cone(struct isl_tab *tab,
1026 struct isl_tab *tab_cone, struct isl_mat *U)
1027 {
1028 int i;
1029 isl_int v;
1030 struct isl_basic_set *bset = NULL;
1031  
1032 if (tab && tab->n_unbounded == 0) {
1033 isl_mat_free(U);
1034 return 0;
1035 }
1036 isl_int_init(v);
1037 if (!tab || !tab_cone || !U)
1038 goto error;
1039 bset = isl_tab_peek_bset(tab_cone);
1040 U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded);
1041 for (i = 0; i < bset->n_ineq; ++i) {
1042 int ok;
1043 struct isl_vec *row = NULL;
1044 if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i))
1045 continue;
1046 row = isl_vec_alloc(bset->ctx, tab_cone->n_var);
1047 if (!row)
1048 goto error;
1049 isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var);
1050 row = isl_vec_mat_product(row, isl_mat_copy(U));
1051 if (!row)
1052 goto error;
1053 vec_sum_of_neg(row, &v);
1054 isl_vec_free(row);
1055 if (isl_int_is_zero(v))
1056 continue;
1057 tab = isl_tab_extend(tab, 1);
1058 isl_int_add(bset->ineq[i][0], bset->ineq[i][0], v);
1059 ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0;
1060 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v);
1061 if (!ok)
1062 goto error;
1063 }
1064  
1065 isl_mat_free(U);
1066 isl_int_clear(v);
1067 return 0;
1068 error:
1069 isl_mat_free(U);
1070 isl_int_clear(v);
1071 return -1;
1072 }
1073  
1074 /* Compute and return an initial basis for the possibly
1075 * unbounded tableau "tab". "tab_cone" is a tableau
1076 * for the corresponding recession cone.
1077 * Additionally, add constraints to "tab" that ensure
1078 * that any rational value for the unbounded directions
1079 * can be rounded up to an integer value.
1080 *
1081 * If the tableau is bounded, i.e., if the recession cone
1082 * is zero-dimensional, then we just use inital_basis.
1083 * Otherwise, we construct a basis whose first directions
1084 * correspond to equalities, followed by bounded directions,
1085 * i.e., equalities in the recession cone.
1086 * The remaining directions are then unbounded.
1087 */
1088 int isl_tab_set_initial_basis_with_cone(struct isl_tab *tab,
1089 struct isl_tab *tab_cone)
1090 {
1091 struct isl_mat *eq;
1092 struct isl_mat *cone_eq;
1093 struct isl_mat *U, *Q;
1094  
1095 if (!tab || !tab_cone)
1096 return -1;
1097  
1098 if (tab_cone->n_col == tab_cone->n_dead) {
1099 tab->basis = initial_basis(tab);
1100 return tab->basis ? 0 : -1;
1101 }
1102  
1103 eq = tab_equalities(tab);
1104 if (!eq)
1105 return -1;
1106 tab->n_zero = eq->n_row;
1107 cone_eq = tab_equalities(tab_cone);
1108 eq = isl_mat_concat(eq, cone_eq);
1109 if (!eq)
1110 return -1;
1111 tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero);
1112 eq = isl_mat_left_hermite(eq, 0, &U, &Q);
1113 if (!eq)
1114 return -1;
1115 isl_mat_free(eq);
1116 tab->basis = isl_mat_lin_to_aff(Q);
1117 if (tab_shift_cone(tab, tab_cone, U) < 0)
1118 return -1;
1119 if (!tab->basis)
1120 return -1;
1121 return 0;
1122 }
1123  
1124 /* Compute and return a sample point in bset using generalized basis
1125 * reduction. We first check if the input set has a non-trivial
1126 * recession cone. If so, we perform some extra preprocessing in
1127 * sample_with_cone. Otherwise, we directly perform generalized basis
1128 * reduction.
1129 */
1130 static struct isl_vec *gbr_sample(struct isl_basic_set *bset)
1131 {
1132 unsigned dim;
1133 struct isl_basic_set *cone;
1134  
1135 dim = isl_basic_set_total_dim(bset);
1136  
1137 cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
1138 if (!cone)
1139 goto error;
1140  
1141 if (cone->n_eq < dim)
1142 return isl_basic_set_sample_with_cone(bset, cone);
1143  
1144 isl_basic_set_free(cone);
1145 return sample_bounded(bset);
1146 error:
1147 isl_basic_set_free(bset);
1148 return NULL;
1149 }
1150  
1151 static struct isl_vec *pip_sample(struct isl_basic_set *bset)
1152 {
1153 struct isl_mat *T;
1154 struct isl_ctx *ctx;
1155 struct isl_vec *sample;
1156  
1157 bset = isl_basic_set_skew_to_positive_orthant(bset, &T);
1158 if (!bset)
1159 return NULL;
1160  
1161 ctx = bset->ctx;
1162 sample = isl_pip_basic_set_sample(bset);
1163  
1164 if (sample && sample->size != 0)
1165 sample = isl_mat_vec_product(T, sample);
1166 else
1167 isl_mat_free(T);
1168  
1169 return sample;
1170 }
1171  
1172 static struct isl_vec *basic_set_sample(struct isl_basic_set *bset, int bounded)
1173 {
1174 struct isl_ctx *ctx;
1175 unsigned dim;
1176 if (!bset)
1177 return NULL;
1178  
1179 ctx = bset->ctx;
1180 if (isl_basic_set_plain_is_empty(bset))
1181 return empty_sample(bset);
1182  
1183 dim = isl_basic_set_n_dim(bset);
1184 isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
1185 isl_assert(ctx, bset->n_div == 0, goto error);
1186  
1187 if (bset->sample && bset->sample->size == 1 + dim) {
1188 int contains = isl_basic_set_contains(bset, bset->sample);
1189 if (contains < 0)
1190 goto error;
1191 if (contains) {
1192 struct isl_vec *sample = isl_vec_copy(bset->sample);
1193 isl_basic_set_free(bset);
1194 return sample;
1195 }
1196 }
1197 isl_vec_free(bset->sample);
1198 bset->sample = NULL;
1199  
1200 if (bset->n_eq > 0)
1201 return sample_eq(bset, bounded ? isl_basic_set_sample_bounded
1202 : isl_basic_set_sample_vec);
1203 if (dim == 0)
1204 return zero_sample(bset);
1205 if (dim == 1)
1206 return interval_sample(bset);
1207  
1208 switch (bset->ctx->opt->ilp_solver) {
1209 case ISL_ILP_PIP:
1210 return pip_sample(bset);
1211 case ISL_ILP_GBR:
1212 return bounded ? sample_bounded(bset) : gbr_sample(bset);
1213 }
1214 isl_assert(bset->ctx, 0, );
1215 error:
1216 isl_basic_set_free(bset);
1217 return NULL;
1218 }
1219  
1220 __isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_set *bset)
1221 {
1222 return basic_set_sample(bset, 0);
1223 }
1224  
1225 /* Compute an integer sample in "bset", where the caller guarantees
1226 * that "bset" is bounded.
1227 */
1228 struct isl_vec *isl_basic_set_sample_bounded(struct isl_basic_set *bset)
1229 {
1230 return basic_set_sample(bset, 1);
1231 }
1232  
1233 __isl_give isl_basic_set *isl_basic_set_from_vec(__isl_take isl_vec *vec)
1234 {
1235 int i;
1236 int k;
1237 struct isl_basic_set *bset = NULL;
1238 struct isl_ctx *ctx;
1239 unsigned dim;
1240  
1241 if (!vec)
1242 return NULL;
1243 ctx = vec->ctx;
1244 isl_assert(ctx, vec->size != 0, goto error);
1245  
1246 bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
1247 if (!bset)
1248 goto error;
1249 dim = isl_basic_set_n_dim(bset);
1250 for (i = dim - 1; i >= 0; --i) {
1251 k = isl_basic_set_alloc_equality(bset);
1252 if (k < 0)
1253 goto error;
1254 isl_seq_clr(bset->eq[k], 1 + dim);
1255 isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
1256 isl_int_set(bset->eq[k][1 + i], vec->el[0]);
1257 }
1258 bset->sample = vec;
1259  
1260 return bset;
1261 error:
1262 isl_basic_set_free(bset);
1263 isl_vec_free(vec);
1264 return NULL;
1265 }
1266  
1267 __isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap)
1268 {
1269 struct isl_basic_set *bset;
1270 struct isl_vec *sample_vec;
1271  
1272 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1273 sample_vec = isl_basic_set_sample_vec(bset);
1274 if (!sample_vec)
1275 goto error;
1276 if (sample_vec->size == 0) {
1277 struct isl_basic_map *sample;
1278 sample = isl_basic_map_empty_like(bmap);
1279 isl_vec_free(sample_vec);
1280 isl_basic_map_free(bmap);
1281 return sample;
1282 }
1283 bset = isl_basic_set_from_vec(sample_vec);
1284 return isl_basic_map_overlying_set(bset, bmap);
1285 error:
1286 isl_basic_map_free(bmap);
1287 return NULL;
1288 }
1289  
1290 __isl_give isl_basic_set *isl_basic_set_sample(__isl_take isl_basic_set *bset)
1291 {
1292 return isl_basic_map_sample(bset);
1293 }
1294  
1295 __isl_give isl_basic_map *isl_map_sample(__isl_take isl_map *map)
1296 {
1297 int i;
1298 isl_basic_map *sample = NULL;
1299  
1300 if (!map)
1301 goto error;
1302  
1303 for (i = 0; i < map->n; ++i) {
1304 sample = isl_basic_map_sample(isl_basic_map_copy(map->p[i]));
1305 if (!sample)
1306 goto error;
1307 if (!ISL_F_ISSET(sample, ISL_BASIC_MAP_EMPTY))
1308 break;
1309 isl_basic_map_free(sample);
1310 }
1311 if (i == map->n)
1312 sample = isl_basic_map_empty_like_map(map);
1313 isl_map_free(map);
1314 return sample;
1315 error:
1316 isl_map_free(map);
1317 return NULL;
1318 }
1319  
1320 __isl_give isl_basic_set *isl_set_sample(__isl_take isl_set *set)
1321 {
1322 return (isl_basic_set *) isl_map_sample((isl_map *)set);
1323 }
1324  
1325 __isl_give isl_point *isl_basic_set_sample_point(__isl_take isl_basic_set *bset)
1326 {
1327 isl_vec *vec;
1328 isl_space *dim;
1329  
1330 dim = isl_basic_set_get_space(bset);
1331 bset = isl_basic_set_underlying_set(bset);
1332 vec = isl_basic_set_sample_vec(bset);
1333  
1334 return isl_point_alloc(dim, vec);
1335 }
1336  
1337 __isl_give isl_point *isl_set_sample_point(__isl_take isl_set *set)
1338 {
1339 int i;
1340 isl_point *pnt;
1341  
1342 if (!set)
1343 return NULL;
1344  
1345 for (i = 0; i < set->n; ++i) {
1346 pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i]));
1347 if (!pnt)
1348 goto error;
1349 if (!isl_point_is_void(pnt))
1350 break;
1351 isl_point_free(pnt);
1352 }
1353 if (i == set->n)
1354 pnt = isl_point_void(isl_set_get_space(set));
1355  
1356 isl_set_free(set);
1357 return pnt;
1358 error:
1359 isl_set_free(set);
1360 return NULL;
1361 }