1 #include "isl_sample.h"
2 #include "isl_sample_piplib.h"
6 #include "isl_map_private.h"
7 #include "isl_equalities.h"
9 #include "isl_basis_reduction.h"
11 static struct isl_vec *empty_sample(struct isl_basic_set *bset)
15 vec = isl_vec_alloc(bset->ctx, 0);
16 isl_basic_set_free(bset);
20 /* Construct a zero sample of the same dimension as bset.
21 * As a special case, if bset is zero-dimensional, this
22 * function creates a zero-dimensional sample point.
24 static struct isl_vec *zero_sample(struct isl_basic_set *bset)
27 struct isl_vec *sample;
29 dim = isl_basic_set_total_dim(bset);
30 sample = isl_vec_alloc(bset->ctx, 1 + dim);
32 isl_int_set_si(sample->el[0], 1);
33 isl_seq_clr(sample->el + 1, dim);
35 isl_basic_set_free(bset);
39 static struct isl_vec *interval_sample(struct isl_basic_set *bset)
43 struct isl_vec *sample;
45 bset = isl_basic_set_simplify(bset);
48 if (isl_basic_set_fast_is_empty(bset))
49 return empty_sample(bset);
50 if (bset->n_eq == 0 && bset->n_ineq == 0)
51 return zero_sample(bset);
53 sample = isl_vec_alloc(bset->ctx, 2);
54 isl_int_set_si(sample->block.data[0], 1);
57 isl_assert(bset->ctx, bset->n_eq == 1, goto error);
58 isl_assert(bset->ctx, bset->n_ineq == 0, goto error);
59 if (isl_int_is_one(bset->eq[0][1]))
60 isl_int_neg(sample->el[1], bset->eq[0][0]);
62 isl_assert(bset->ctx, isl_int_is_negone(bset->eq[0][1]),
64 isl_int_set(sample->el[1], bset->eq[0][0]);
66 isl_basic_set_free(bset);
71 if (isl_int_is_one(bset->ineq[0][1]))
72 isl_int_neg(sample->block.data[1], bset->ineq[0][0]);
74 isl_int_set(sample->block.data[1], bset->ineq[0][0]);
75 for (i = 1; i < bset->n_ineq; ++i) {
76 isl_seq_inner_product(sample->block.data,
77 bset->ineq[i], 2, &t);
78 if (isl_int_is_neg(t))
82 if (i < bset->n_ineq) {
84 return empty_sample(bset);
87 isl_basic_set_free(bset);
90 isl_basic_set_free(bset);
95 static struct isl_mat *independent_bounds(struct isl_basic_set *bset)
98 struct isl_mat *dirs = NULL;
99 struct isl_mat *bounds = NULL;
105 dim = isl_basic_set_n_dim(bset);
106 bounds = isl_mat_alloc(bset->ctx, 1+dim, 1+dim);
110 isl_int_set_si(bounds->row[0][0], 1);
111 isl_seq_clr(bounds->row[0]+1, dim);
114 if (bset->n_ineq == 0)
117 dirs = isl_mat_alloc(bset->ctx, dim, dim);
119 isl_mat_free(bounds);
122 isl_seq_cpy(dirs->row[0], bset->ineq[0]+1, dirs->n_col);
123 isl_seq_cpy(bounds->row[1], bset->ineq[0], bounds->n_col);
124 for (j = 1, n = 1; n < dim && j < bset->n_ineq; ++j) {
127 isl_seq_cpy(dirs->row[n], bset->ineq[j]+1, dirs->n_col);
129 pos = isl_seq_first_non_zero(dirs->row[n], dirs->n_col);
132 for (i = 0; i < n; ++i) {
134 pos_i = isl_seq_first_non_zero(dirs->row[i], dirs->n_col);
139 isl_seq_elim(dirs->row[n], dirs->row[i], pos,
141 pos = isl_seq_first_non_zero(dirs->row[n], dirs->n_col);
149 isl_int *t = dirs->row[n];
150 for (k = n; k > i; --k)
151 dirs->row[k] = dirs->row[k-1];
155 isl_seq_cpy(bounds->row[n], bset->ineq[j], bounds->n_col);
162 static void swap_inequality(struct isl_basic_set *bset, int a, int b)
164 isl_int *t = bset->ineq[a];
165 bset->ineq[a] = bset->ineq[b];
169 /* Skew into positive orthant and project out lineality space.
171 * We perform a unimodular transformation that turns a selected
172 * maximal set of linearly independent bounds into constraints
173 * on the first dimensions that impose that these first dimensions
174 * are non-negative. In particular, the constraint matrix is lower
175 * triangular with positive entries on the diagonal and negative
177 * If "bset" has a lineality space then these constraints (and therefore
178 * all constraints in bset) only involve the first dimensions.
179 * The remaining dimensions then do not appear in any constraints and
180 * we can select any value for them, say zero. We therefore project
181 * out this final dimensions and plug in the value zero later. This
182 * is accomplished by simply dropping the final columns of
183 * the unimodular transformation.
185 static struct isl_basic_set *isl_basic_set_skew_to_positive_orthant(
186 struct isl_basic_set *bset, struct isl_mat **T)
188 struct isl_mat *U = NULL;
189 struct isl_mat *bounds = NULL;
191 unsigned old_dim, new_dim;
197 isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
198 isl_assert(bset->ctx, bset->n_div == 0, goto error);
199 isl_assert(bset->ctx, bset->n_eq == 0, goto error);
201 old_dim = isl_basic_set_n_dim(bset);
202 /* Try to move (multiples of) unit rows up. */
203 for (i = 0, j = 0; i < bset->n_ineq; ++i) {
204 int pos = isl_seq_first_non_zero(bset->ineq[i]+1, old_dim);
207 if (isl_seq_first_non_zero(bset->ineq[i]+1+pos+1,
211 swap_inequality(bset, i, j);
214 bounds = independent_bounds(bset);
217 new_dim = bounds->n_row - 1;
218 bounds = isl_mat_left_hermite(bounds, 1, &U, NULL);
221 U = isl_mat_drop_cols(U, 1 + new_dim, old_dim - new_dim);
222 bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
226 isl_mat_free(bounds);
229 isl_mat_free(bounds);
231 isl_basic_set_free(bset);
235 /* Find a sample integer point, if any, in bset, which is known
236 * to have equalities. If bset contains no integer points, then
237 * return a zero-length vector.
238 * We simply remove the known equalities, compute a sample
239 * in the resulting bset, using the specified recurse function,
240 * and then transform the sample back to the original space.
242 static struct isl_vec *sample_eq(struct isl_basic_set *bset,
243 struct isl_vec *(*recurse)(struct isl_basic_set *))
246 struct isl_vec *sample;
251 bset = isl_basic_set_remove_equalities(bset, &T, NULL);
252 sample = recurse(bset);
253 if (!sample || sample->size == 0)
256 sample = isl_mat_vec_product(T, sample);
260 /* Given a basic set "bset" and an affine function "f"/"denom",
261 * check if bset is bounded and non-empty and if so, return the minimal
262 * and maximal value attained by the affine function in "min" and "max".
263 * The minimal value is rounded up to the nearest integer, while the
264 * maximal value is rounded down.
265 * The return value indicates whether the set was empty or unbounded.
267 * If we happen to find an integer point while looking for the minimal
268 * or maximal value, then we record that value in "bset" and return early.
270 static enum isl_lp_result basic_set_range(struct isl_basic_set *bset,
271 isl_int *f, isl_int denom, isl_int *min, isl_int *max)
275 enum isl_lp_result res;
279 if (isl_basic_set_fast_is_empty(bset))
282 tab = isl_tab_from_basic_set(bset);
283 res = isl_tab_min(tab, f, denom, min, NULL, 0);
284 if (res != isl_lp_ok)
287 if (isl_tab_sample_is_integer(tab)) {
288 isl_vec_free(bset->sample);
289 bset->sample = isl_tab_get_sample_value(tab);
292 isl_int_set(*max, *min);
296 dim = isl_basic_set_total_dim(bset);
297 isl_seq_neg(f, f, 1 + dim);
298 res = isl_tab_min(tab, f, denom, max, NULL, 0);
299 isl_seq_neg(f, f, 1 + dim);
300 isl_int_neg(*max, *max);
302 if (isl_tab_sample_is_integer(tab)) {
303 isl_vec_free(bset->sample);
304 bset->sample = isl_tab_get_sample_value(tab);
317 /* Perform a basis reduction on "bset" and return the inverse of
318 * the new basis, i.e., an affine mapping from the new coordinates to the old,
321 static struct isl_basic_set *basic_set_reduced(struct isl_basic_set *bset,
324 unsigned gbr_only_first;
330 gbr_only_first = bset->ctx->gbr_only_first;
331 bset->ctx->gbr_only_first = 1;
332 *T = isl_basic_set_reduced_basis(bset);
333 bset->ctx->gbr_only_first = gbr_only_first;
335 *T = isl_mat_lin_to_aff(*T);
336 *T = isl_mat_right_inverse(*T);
338 bset = isl_basic_set_preimage(bset, isl_mat_copy(*T));
349 static struct isl_vec *sample_bounded(struct isl_basic_set *bset);
351 /* Given a basic set "bset" whose first coordinate ranges between
352 * "min" and "max", step through all values from min to max, until
353 * the slice of bset with the first coordinate fixed to one of these
354 * values contains an integer point. If such a point is found, return it.
355 * If none of the slices contains any integer point, then bset itself
356 * doesn't contain any integer point and an empty sample is returned.
358 static struct isl_vec *sample_scan(struct isl_basic_set *bset,
359 isl_int min, isl_int max)
362 struct isl_basic_set *slice = NULL;
363 struct isl_vec *sample = NULL;
366 total = isl_basic_set_total_dim(bset);
369 for (isl_int_set(tmp, min); isl_int_le(tmp, max);
370 isl_int_add_ui(tmp, tmp, 1)) {
373 slice = isl_basic_set_copy(bset);
374 slice = isl_basic_set_cow(slice);
375 slice = isl_basic_set_extend_constraints(slice, 1, 0);
376 k = isl_basic_set_alloc_equality(slice);
379 isl_int_set(slice->eq[k][0], tmp);
380 isl_int_set_si(slice->eq[k][1], -1);
381 isl_seq_clr(slice->eq[k] + 2, total - 1);
382 slice = isl_basic_set_simplify(slice);
383 sample = sample_bounded(slice);
387 if (sample->size > 0)
389 isl_vec_free(sample);
393 sample = empty_sample(bset);
395 isl_basic_set_free(bset);
399 isl_basic_set_free(bset);
400 isl_basic_set_free(slice);
405 /* Given a basic set that is known to be bounded, find and return
406 * an integer point in the basic set, if there is any.
408 * After handling some trivial cases, we check the range of the
409 * first coordinate. If this coordinate can only attain one integer
410 * value, we are happy. Otherwise, we perform basis reduction and
411 * determine the new range.
413 * Then we step through all possible values in the range in sample_scan.
415 * If any basis reduction was performed, the sample value found, if any,
416 * is transformed back to the original space.
418 static struct isl_vec *sample_bounded(struct isl_basic_set *bset)
421 struct isl_vec *sample;
422 struct isl_vec *obj = NULL;
423 struct isl_mat *T = NULL;
425 enum isl_lp_result res;
430 if (isl_basic_set_fast_is_empty(bset))
431 return empty_sample(bset);
433 dim = isl_basic_set_total_dim(bset);
435 return zero_sample(bset);
437 return interval_sample(bset);
439 return sample_eq(bset, sample_bounded);
443 obj = isl_vec_alloc(bset->ctx, 1 + dim);
446 isl_seq_clr(obj->el, 1+ dim);
447 isl_int_set_si(obj->el[1], 1);
449 res = basic_set_range(bset, obj->el, bset->ctx->one, &min, &max);
450 if (res == isl_lp_error)
452 isl_assert(bset->ctx, res != isl_lp_unbounded, goto error);
454 sample = isl_vec_copy(bset->sample);
455 isl_basic_set_free(bset);
458 if (res == isl_lp_empty || isl_int_lt(max, min)) {
459 sample = empty_sample(bset);
463 if (isl_int_ne(min, max)) {
464 bset = basic_set_reduced(bset, &T);
468 res = basic_set_range(bset, obj->el, bset->ctx->one, &min, &max);
469 if (res == isl_lp_error)
471 isl_assert(bset->ctx, res != isl_lp_unbounded, goto error);
473 sample = isl_vec_copy(bset->sample);
474 isl_basic_set_free(bset);
477 if (res == isl_lp_empty || isl_int_lt(max, min)) {
478 sample = empty_sample(bset);
483 sample = sample_scan(bset, min, max);
486 if (!sample || sample->size == 0)
489 sample = isl_mat_vec_product(T, sample);
497 isl_basic_set_free(bset);
504 /* Given a basic set "bset" and a value "sample" for the first coordinates
505 * of bset, plug in these values and drop the corresponding coordinates.
507 * We do this by computing the preimage of the transformation
513 * where [1 s] is the sample value and I is the identity matrix of the
514 * appropriate dimension.
516 static struct isl_basic_set *plug_in(struct isl_basic_set *bset,
517 struct isl_vec *sample)
523 if (!bset || !sample)
526 total = isl_basic_set_total_dim(bset);
527 T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
531 for (i = 0; i < sample->size; ++i) {
532 isl_int_set(T->row[i][0], sample->el[i]);
533 isl_seq_clr(T->row[i] + 1, T->n_col - 1);
535 for (i = 0; i < T->n_col - 1; ++i) {
536 isl_seq_clr(T->row[sample->size + i], T->n_col);
537 isl_int_set_si(T->row[sample->size + i][1 + i], 1);
539 isl_vec_free(sample);
541 bset = isl_basic_set_preimage(bset, T);
544 isl_basic_set_free(bset);
545 isl_vec_free(sample);
549 /* Given a basic set "bset", return any (possibly non-integer) point
552 static struct isl_vec *rational_sample(struct isl_basic_set *bset)
555 struct isl_vec *sample;
560 tab = isl_tab_from_basic_set(bset);
561 sample = isl_tab_get_sample_value(tab);
564 isl_basic_set_free(bset);
569 /* Given a rational vector, with the denominator in the first element
570 * of the vector, round up all coordinates.
572 struct isl_vec *isl_vec_ceil(struct isl_vec *vec)
576 vec = isl_vec_cow(vec);
580 isl_seq_cdiv_q(vec->el + 1, vec->el + 1, vec->el[0], vec->size - 1);
582 isl_int_set_si(vec->el[0], 1);
587 /* Given a linear cone "cone" and a rational point "vec",
588 * construct a polyhedron with shifted copies of the constraints in "cone",
589 * i.e., a polyhedron with "cone" as its recession cone, such that each
590 * point x in this polyhedron is such that the unit box positioned at x
591 * lies entirely inside the affine cone 'vec + cone'.
592 * Any rational point in this polyhedron may therefore be rounded up
593 * to yield an integer point that lies inside said affine cone.
595 * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
596 * point "vec" by v/d.
597 * Let b_i = <a_i, v>. Then the affine cone 'vec + cone' is given
598 * by <a_i, x> - b/d >= 0.
599 * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
600 * We prefer this polyhedron over the actual affine cone because it doesn't
601 * require a scaling of the constraints.
602 * If each of the vertices of the unit cube positioned at x lies inside
603 * this polyhedron, then the whole unit cube at x lies inside the affine cone.
604 * We therefore impose that x' = x + \sum e_i, for any selection of unit
605 * vectors lies inside the polyhedron, i.e.,
607 * <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
609 * The most stringent of these constraints is the one that selects
610 * all negative a_i, so the polyhedron we are looking for has constraints
612 * <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
614 * Note that if cone were known to have only non-negative rays
615 * (which can be accomplished by a unimodular transformation),
616 * then we would only have to check the points x' = x + e_i
617 * and we only have to add the smallest negative a_i (if any)
618 * instead of the sum of all negative a_i.
620 static struct isl_basic_set *shift_cone(struct isl_basic_set *cone,
626 struct isl_basic_set *shift = NULL;
631 isl_assert(cone->ctx, cone->n_eq == 0, goto error);
633 total = isl_basic_set_total_dim(cone);
635 shift = isl_basic_set_alloc_dim(isl_basic_set_get_dim(cone),
638 for (i = 0; i < cone->n_ineq; ++i) {
639 k = isl_basic_set_alloc_inequality(shift);
642 isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
643 isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
645 isl_int_cdiv_q(shift->ineq[k][0],
646 shift->ineq[k][0], vec->el[0]);
647 isl_int_neg(shift->ineq[k][0], shift->ineq[k][0]);
648 for (j = 0; j < total; ++j) {
649 if (isl_int_is_nonneg(shift->ineq[k][1 + j]))
651 isl_int_add(shift->ineq[k][0],
652 shift->ineq[k][0], shift->ineq[k][1 + j]);
656 isl_basic_set_free(cone);
659 return isl_basic_set_finalize(shift);
661 isl_basic_set_free(shift);
662 isl_basic_set_free(cone);
667 /* Given a rational point vec in a (transformed) basic set,
668 * such that cone is the recession cone of the original basic set,
669 * "round up" the rational point to an integer point.
671 * We first check if the rational point just happens to be integer.
672 * If not, we transform the cone in the same way as the basic set,
673 * pick a point x in this cone shifted to the rational point such that
674 * the whole unit cube at x is also inside this affine cone.
675 * Then we simply round up the coordinates of x and return the
676 * resulting integer point.
678 static struct isl_vec *round_up_in_cone(struct isl_vec *vec,
679 struct isl_basic_set *cone, struct isl_mat *U)
683 if (!vec || !cone || !U)
686 isl_assert(vec->ctx, vec->size != 0, goto error);
687 if (isl_int_is_one(vec->el[0])) {
689 isl_basic_set_free(cone);
693 total = isl_basic_set_total_dim(cone);
694 cone = isl_basic_set_preimage(cone, U);
695 cone = isl_basic_set_remove_dims(cone, 0, total - (vec->size - 1));
697 cone = shift_cone(cone, vec);
699 vec = rational_sample(cone);
700 vec = isl_vec_ceil(vec);
705 isl_basic_set_free(cone);
709 /* Concatenate two integer vectors, i.e., two vectors with denominator
710 * (stored in element 0) equal to 1.
712 static struct isl_vec *vec_concat(struct isl_vec *vec1, struct isl_vec *vec2)
718 isl_assert(vec1->ctx, vec1->size > 0, goto error);
719 isl_assert(vec2->ctx, vec2->size > 0, goto error);
720 isl_assert(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error);
721 isl_assert(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error);
723 vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
727 isl_seq_cpy(vec->el, vec1->el, vec1->size);
728 isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
740 /* Drop all constraints in bset that involve any of the dimensions
741 * first to first+n-1.
743 static struct isl_basic_set *drop_constraints_involving
744 (struct isl_basic_set *bset, unsigned first, unsigned n)
751 bset = isl_basic_set_cow(bset);
753 for (i = bset->n_ineq - 1; i >= 0; --i) {
754 if (isl_seq_first_non_zero(bset->ineq[i] + 1 + first, n) == -1)
756 isl_basic_set_drop_inequality(bset, i);
762 /* Give a basic set "bset" with recession cone "cone", compute and
763 * return an integer point in bset, if any.
765 * If the recession cone is full-dimensional, then we know that
766 * bset contains an infinite number of integer points and it is
767 * fairly easy to pick one of them.
768 * If the recession cone is not full-dimensional, then we first
769 * transform bset such that the bounded directions appear as
770 * the first dimensions of the transformed basic set.
771 * We do this by using a unimodular transformation that transforms
772 * the equalities in the recession cone to equalities on the first
775 * The transformed set is then projected onto its bounded dimensions.
776 * Note that to compute this projection, we can simply drop all constraints
777 * involving any of the unbounded dimensions since these constraints
778 * cannot be combined to produce a constraint on the bounded dimensions.
779 * To see this, assume that there is such a combination of constraints
780 * that produces a constraint on the bounded dimensions. This means
781 * that some combination of the unbounded dimensions has both an upper
782 * bound and a lower bound in terms of the bounded dimensions, but then
783 * this combination would be a bounded direction too and would have been
784 * transformed into a bounded dimensions.
786 * We then compute a sample value in the bounded dimensions.
787 * If no such value can be found, then the original set did not contain
788 * any integer points and we are done.
789 * Otherwise, we plug in the value we found in the bounded dimensions,
790 * project out these bounded dimensions and end up with a set with
791 * a full-dimensional recession cone.
792 * A sample point in this set is computed by "rounding up" any
793 * rational point in the set.
795 * The sample points in the bounded and unbounded dimensions are
796 * then combined into a single sample point and transformed back
797 * to the original space.
799 static struct isl_vec *sample_with_cone(struct isl_basic_set *bset,
800 struct isl_basic_set *cone)
804 struct isl_mat *M, *U;
805 struct isl_vec *sample;
806 struct isl_vec *cone_sample;
808 struct isl_basic_set *bounded;
814 total = isl_basic_set_total_dim(cone);
815 cone_dim = total - cone->n_eq;
817 M = isl_mat_sub_alloc(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
818 M = isl_mat_left_hermite(M, 0, &U, NULL);
823 U = isl_mat_lin_to_aff(U);
824 bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
826 bounded = isl_basic_set_copy(bset);
827 bounded = drop_constraints_involving(bounded, total - cone_dim, cone_dim);
828 bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
829 sample = sample_bounded(bounded);
830 if (!sample || sample->size == 0) {
831 isl_basic_set_free(bset);
832 isl_basic_set_free(cone);
836 bset = plug_in(bset, isl_vec_copy(sample));
837 cone_sample = rational_sample(bset);
838 cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
839 sample = vec_concat(sample, cone_sample);
840 sample = isl_mat_vec_product(U, sample);
843 isl_basic_set_free(cone);
844 isl_basic_set_free(bset);
848 /* Compute and return a sample point in bset using generalized basis
849 * reduction. We first check if the input set has a non-trivial
850 * recession cone. If so, we perform some extra preprocessing in
851 * sample_with_cone. Otherwise, we directly perform generalized basis
854 static struct isl_vec *gbr_sample(struct isl_basic_set *bset)
857 struct isl_basic_set *cone;
859 dim = isl_basic_set_total_dim(bset);
861 cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
863 if (cone->n_eq < dim)
864 return sample_with_cone(bset, cone);
866 isl_basic_set_free(cone);
867 return sample_bounded(bset);
870 static struct isl_vec *pip_sample(struct isl_basic_set *bset)
874 struct isl_vec *sample;
876 bset = isl_basic_set_skew_to_positive_orthant(bset, &T);
881 sample = isl_pip_basic_set_sample(bset);
883 if (sample && sample->size != 0)
884 sample = isl_mat_vec_product(T, sample);
891 struct isl_vec *isl_basic_set_sample(struct isl_basic_set *bset)
899 if (isl_basic_set_fast_is_empty(bset))
900 return empty_sample(bset);
902 dim = isl_basic_set_n_dim(bset);
903 isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
904 isl_assert(ctx, bset->n_div == 0, goto error);
906 if (bset->sample && bset->sample->size == 1 + dim) {
907 int contains = isl_basic_set_contains(bset, bset->sample);
911 struct isl_vec *sample = isl_vec_copy(bset->sample);
912 isl_basic_set_free(bset);
916 isl_vec_free(bset->sample);
920 return sample_eq(bset, isl_basic_set_sample);
922 return zero_sample(bset);
924 return interval_sample(bset);
926 switch (bset->ctx->ilp_solver) {
928 return pip_sample(bset);
930 return gbr_sample(bset);
932 isl_assert(bset->ctx, 0, );
934 isl_basic_set_free(bset);