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_ctx
*ctx
,
96 struct isl_basic_set
*bset
)
99 struct isl_mat
*dirs
= NULL
;
105 dim
= isl_basic_set_n_dim(bset
);
106 if (bset
->n_ineq
== 0)
107 return isl_mat_alloc(ctx
, 0, dim
);
109 dirs
= isl_mat_alloc(ctx
, dim
, dim
);
112 isl_seq_cpy(dirs
->row
[0], bset
->ineq
[0]+1, dirs
->n_col
);
113 for (j
= 1, n
= 1; n
< dim
&& j
< bset
->n_ineq
; ++j
) {
116 isl_seq_cpy(dirs
->row
[n
], bset
->ineq
[j
]+1, dirs
->n_col
);
118 pos
= isl_seq_first_non_zero(dirs
->row
[n
], dirs
->n_col
);
121 for (i
= 0; i
< n
; ++i
) {
123 pos_i
= isl_seq_first_non_zero(dirs
->row
[i
], dirs
->n_col
);
128 isl_seq_elim(dirs
->row
[n
], dirs
->row
[i
], pos
,
130 pos
= isl_seq_first_non_zero(dirs
->row
[n
], dirs
->n_col
);
138 isl_int
*t
= dirs
->row
[n
];
139 for (k
= n
; k
> i
; --k
)
140 dirs
->row
[k
] = dirs
->row
[k
-1];
149 /* Find a sample integer point, if any, in bset, which is known
150 * to have equalities. If bset contains no integer points, then
151 * return a zero-length vector.
152 * We simply remove the known equalities, compute a sample
153 * in the resulting bset, using the specified recurse function,
154 * and then transform the sample back to the original space.
156 static struct isl_vec
*sample_eq(struct isl_basic_set
*bset
,
157 struct isl_vec
*(*recurse
)(struct isl_basic_set
*))
160 struct isl_vec
*sample
;
167 bset
= isl_basic_set_remove_equalities(bset
, &T
, NULL
);
168 sample
= recurse(bset
);
169 if (!sample
|| sample
->size
== 0)
170 isl_mat_free(ctx
, T
);
172 sample
= isl_mat_vec_product(ctx
, T
, sample
);
176 /* Given a basic set "bset" and an affine function "f"/"denom",
177 * check if bset is bounded and non-empty and if so, return the minimal
178 * and maximal value attained by the affine function in "min" and "max".
179 * The minimal value is rounded up to the nearest integer, while the
180 * maximal value is rounded down.
181 * The return value indicates whether the set was empty or unbounded.
183 static enum isl_lp_result
basic_set_range(struct isl_basic_set
*bset
,
184 isl_int
*f
, isl_int denom
, isl_int
*min
, isl_int
*max
)
188 enum isl_lp_result res
;
192 if (isl_basic_set_fast_is_empty(bset
))
195 tab
= isl_tab_from_basic_set(bset
);
196 res
= isl_tab_min(bset
->ctx
, tab
, f
, denom
, min
, NULL
, 0);
197 if (res
!= isl_lp_ok
) {
198 isl_tab_free(bset
->ctx
, tab
);
201 dim
= isl_basic_set_total_dim(bset
);
202 isl_seq_neg(f
, f
, 1 + dim
);
203 res
= isl_tab_min(bset
->ctx
, tab
, f
, denom
, max
, NULL
, 0);
204 isl_seq_neg(f
, f
, 1 + dim
);
205 isl_int_neg(*max
, *max
);
207 isl_tab_free(bset
->ctx
, tab
);
211 /* Perform a basis reduction on "bset" and return the inverse of
212 * the new basis, i.e., an affine mapping from the new coordinates to the old,
215 static struct isl_basic_set
*basic_set_reduced(struct isl_basic_set
*bset
,
219 unsigned gbr_only_first
;
227 gbr_only_first
= ctx
->gbr_only_first
;
228 ctx
->gbr_only_first
= 1;
229 *T
= isl_basic_set_reduced_basis(bset
);
230 ctx
->gbr_only_first
= gbr_only_first
;
232 *T
= isl_mat_lin_to_aff(bset
->ctx
, *T
);
233 *T
= isl_mat_right_inverse(bset
->ctx
, *T
);
235 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(bset
->ctx
, *T
));
241 isl_mat_free(ctx
, *T
);
246 static struct isl_vec
*sample_bounded(struct isl_basic_set
*bset
);
248 /* Given a basic set "bset" whose first coordinate ranges between
249 * "min" and "max", step through all values from min to max, until
250 * the slice of bset with the first coordinate fixed to one of these
251 * values contains an integer point. If such a point is found, return it.
252 * If none of the slices contains any integer point, then bset itself
253 * doesn't contain any integer point and an empty sample is returned.
255 static struct isl_vec
*sample_scan(struct isl_basic_set
*bset
,
256 isl_int min
, isl_int max
)
259 struct isl_basic_set
*slice
= NULL
;
260 struct isl_vec
*sample
= NULL
;
263 total
= isl_basic_set_total_dim(bset
);
266 for (isl_int_set(tmp
, min
); isl_int_le(tmp
, max
);
267 isl_int_add_ui(tmp
, tmp
, 1)) {
270 slice
= isl_basic_set_copy(bset
);
271 slice
= isl_basic_set_cow(slice
);
272 slice
= isl_basic_set_extend_constraints(slice
, 1, 0);
273 k
= isl_basic_set_alloc_equality(slice
);
276 isl_int_set(slice
->eq
[k
][0], tmp
);
277 isl_int_set_si(slice
->eq
[k
][1], -1);
278 isl_seq_clr(slice
->eq
[k
] + 2, total
- 1);
279 slice
= isl_basic_set_simplify(slice
);
280 sample
= sample_bounded(slice
);
284 if (sample
->size
> 0)
286 isl_vec_free(sample
);
290 sample
= empty_sample(bset
);
292 isl_basic_set_free(bset
);
296 isl_basic_set_free(bset
);
297 isl_basic_set_free(slice
);
302 /* Given a basic set that is known to be bounded, find and return
303 * an integer point in the basic set, if there is any.
305 * After handling some trivial cases, we check the range of the
306 * first coordinate. If this coordinate can only attain one integer
307 * value, we are happy. Otherwise, we perform basis reduction and
308 * determine the new range.
310 * Then we step through all possible values in the range in sample_scan.
312 * If any basis reduction was performed, the sample value found, if any,
313 * is transformed back to the original space.
315 static struct isl_vec
*sample_bounded(struct isl_basic_set
*bset
)
319 struct isl_vec
*sample
;
320 struct isl_vec
*obj
= NULL
;
321 struct isl_mat
*T
= NULL
;
323 enum isl_lp_result res
;
328 if (isl_basic_set_fast_is_empty(bset
))
329 return empty_sample(bset
);
332 dim
= isl_basic_set_total_dim(bset
);
334 return zero_sample(bset
);
336 return interval_sample(bset
);
338 return sample_eq(bset
, sample_bounded
);
342 obj
= isl_vec_alloc(bset
->ctx
, 1 + dim
);
345 isl_seq_clr(obj
->el
, 1+ dim
);
346 isl_int_set_si(obj
->el
[1], 1);
348 res
= basic_set_range(bset
, obj
->el
, bset
->ctx
->one
, &min
, &max
);
349 if (res
== isl_lp_error
)
351 isl_assert(bset
->ctx
, res
!= isl_lp_unbounded
, goto error
);
352 if (res
== isl_lp_empty
|| isl_int_lt(max
, min
)) {
353 sample
= empty_sample(bset
);
357 if (isl_int_ne(min
, max
)) {
358 bset
= basic_set_reduced(bset
, &T
);
362 res
= basic_set_range(bset
, obj
->el
, bset
->ctx
->one
, &min
, &max
);
363 if (res
== isl_lp_error
)
365 isl_assert(bset
->ctx
, res
!= isl_lp_unbounded
, goto error
);
366 if (res
== isl_lp_empty
|| isl_int_lt(max
, min
)) {
367 sample
= empty_sample(bset
);
372 sample
= sample_scan(bset
, min
, max
);
375 if (!sample
|| sample
->size
== 0)
376 isl_mat_free(ctx
, T
);
378 sample
= isl_mat_vec_product(ctx
, T
, sample
);
385 isl_mat_free(ctx
, T
);
386 isl_basic_set_free(bset
);
393 /* Given a basic set "bset" and a value "sample" for the first coordinates
394 * of bset, plug in these values and drop the corresponding coordinates.
396 * We do this by computing the preimage of the transformation
402 * where [1 s] is the sample value and I is the identity matrix of the
403 * appropriate dimension.
405 static struct isl_basic_set
*plug_in(struct isl_basic_set
*bset
,
406 struct isl_vec
*sample
)
412 if (!bset
|| !sample
)
415 total
= isl_basic_set_total_dim(bset
);
416 T
= isl_mat_alloc(bset
->ctx
, 1 + total
, 1 + total
- (sample
->size
- 1));
420 for (i
= 0; i
< sample
->size
; ++i
) {
421 isl_int_set(T
->row
[i
][0], sample
->el
[i
]);
422 isl_seq_clr(T
->row
[i
] + 1, T
->n_col
- 1);
424 for (i
= 0; i
< T
->n_col
- 1; ++i
) {
425 isl_seq_clr(T
->row
[sample
->size
+ i
], T
->n_col
);
426 isl_int_set_si(T
->row
[sample
->size
+ i
][1 + i
], 1);
428 isl_vec_free(sample
);
430 bset
= isl_basic_set_preimage(bset
, T
);
433 isl_basic_set_free(bset
);
434 isl_vec_free(sample
);
438 /* Given a basic set "bset", return any (possibly non-integer) point
441 static struct isl_vec
*rational_sample(struct isl_basic_set
*bset
)
444 struct isl_vec
*sample
;
449 tab
= isl_tab_from_basic_set(bset
);
450 sample
= isl_tab_get_sample_value(bset
->ctx
, tab
);
451 isl_tab_free(bset
->ctx
, tab
);
453 isl_basic_set_free(bset
);
458 /* Given a rational vector, with the denominator in the first element
459 * of the vector, round up all coordinates.
461 struct isl_vec
*isl_vec_ceil(struct isl_vec
*vec
)
465 vec
= isl_vec_cow(vec
);
469 isl_seq_cdiv_q(vec
->el
+ 1, vec
->el
+ 1, vec
->el
[0], vec
->size
- 1);
471 isl_int_set_si(vec
->el
[0], 1);
476 /* Given a linear cone "cone" and a rational point "vec",
477 * construct a polyhedron with shifted copies of the constraints in "cone",
478 * i.e., a polyhedron with "cone" as its recession cone, such that each
479 * point x in this polyhedron is such that the unit box positioned at x
480 * lies entirely inside the affine cone 'vec + cone'.
481 * Any rational point in this polyhedron may therefore be rounded up
482 * to yield an integer point that lies inside said affine cone.
484 * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
485 * point "vec" by v/d.
486 * Let b_i = <a_i, v>. Then the affine cone 'vec + cone' is given
487 * by <a_i, x> - b/d >= 0.
488 * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
489 * We prefer this polyhedron over the actual affine cone because it doesn't
490 * require a scaling of the constraints.
491 * If each of the vertices of the unit cube positioned at x lies inside
492 * this polyhedron, then the whole unit cube at x lies inside the affine cone.
493 * We therefore impose that x' = x + \sum e_i, for any selection of unit
494 * vectors lies inside the polyhedron, i.e.,
496 * <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
498 * The most stringent of these constraints is the one that selects
499 * all negative a_i, so the polyhedron we are looking for has constraints
501 * <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
503 * Note that if cone were known to have only non-negative rays
504 * (which can be accomplished by a unimodular transformation),
505 * then we would only have to check the points x' = x + e_i
506 * and we only have to add the smallest negative a_i (if any)
507 * instead of the sum of all negative a_i.
509 static struct isl_basic_set
*shift_cone(struct isl_basic_set
*cone
,
515 struct isl_basic_set
*shift
= NULL
;
520 isl_assert(cone
->ctx
, cone
->n_eq
== 0, goto error
);
522 total
= isl_basic_set_total_dim(cone
);
524 shift
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(cone
),
527 for (i
= 0; i
< cone
->n_ineq
; ++i
) {
528 k
= isl_basic_set_alloc_inequality(shift
);
531 isl_seq_cpy(shift
->ineq
[k
] + 1, cone
->ineq
[i
] + 1, total
);
532 isl_seq_inner_product(shift
->ineq
[k
] + 1, vec
->el
+ 1, total
,
534 isl_int_cdiv_q(shift
->ineq
[k
][0],
535 shift
->ineq
[k
][0], vec
->el
[0]);
536 isl_int_neg(shift
->ineq
[k
][0], shift
->ineq
[k
][0]);
537 for (j
= 0; j
< total
; ++j
) {
538 if (isl_int_is_nonneg(shift
->ineq
[k
][1 + j
]))
540 isl_int_add(shift
->ineq
[k
][0],
541 shift
->ineq
[k
][0], shift
->ineq
[k
][1 + j
]);
545 isl_basic_set_free(cone
);
548 return isl_basic_set_finalize(shift
);
550 isl_basic_set_free(shift
);
551 isl_basic_set_free(cone
);
556 /* Given a rational point vec in a (transformed) basic set,
557 * such that cone is the recession cone of the original basic set,
558 * "round up" the rational point to an integer point.
560 * We first check if the rational point just happens to be integer.
561 * If not, we transform the cone in the same way as the basic set,
562 * pick a point x in this cone shifted to the rational point such that
563 * the whole unit cube at x is also inside this affine cone.
564 * Then we simply round up the coordinates of x and return the
565 * resulting integer point.
567 static struct isl_vec
*round_up_in_cone(struct isl_vec
*vec
,
568 struct isl_basic_set
*cone
, struct isl_mat
*U
)
572 if (!vec
|| !cone
|| !U
)
575 isl_assert(vec
->ctx
, vec
->size
!= 0, goto error
);
576 if (isl_int_is_one(vec
->el
[0])) {
577 isl_mat_free(vec
->ctx
, U
);
578 isl_basic_set_free(cone
);
582 total
= isl_basic_set_total_dim(cone
);
583 cone
= isl_basic_set_preimage(cone
, U
);
584 cone
= isl_basic_set_remove_dims(cone
, 0, total
- (vec
->size
- 1));
586 cone
= shift_cone(cone
, vec
);
588 vec
= rational_sample(cone
);
589 vec
= isl_vec_ceil(vec
);
592 isl_mat_free(vec
? vec
->ctx
: cone
? cone
->ctx
: NULL
, U
);
594 isl_basic_set_free(cone
);
598 /* Concatenate two integer vectors, i.e., two vectors with denominator
599 * (stored in element 0) equal to 1.
601 static struct isl_vec
*vec_concat(struct isl_vec
*vec1
, struct isl_vec
*vec2
)
607 isl_assert(vec1
->ctx
, vec1
->size
> 0, goto error
);
608 isl_assert(vec2
->ctx
, vec2
->size
> 0, goto error
);
609 isl_assert(vec1
->ctx
, isl_int_is_one(vec1
->el
[0]), goto error
);
610 isl_assert(vec2
->ctx
, isl_int_is_one(vec2
->el
[0]), goto error
);
612 vec
= isl_vec_alloc(vec1
->ctx
, vec1
->size
+ vec2
->size
- 1);
616 isl_seq_cpy(vec
->el
, vec1
->el
, vec1
->size
);
617 isl_seq_cpy(vec
->el
+ vec1
->size
, vec2
->el
+ 1, vec2
->size
- 1);
629 /* Drop all constraints in bset that involve any of the dimensions
630 * first to first+n-1.
632 static struct isl_basic_set
*drop_constraints_involving
633 (struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
640 bset
= isl_basic_set_cow(bset
);
642 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
) {
643 if (isl_seq_first_non_zero(bset
->ineq
[i
] + 1 + first
, n
) == -1)
645 isl_basic_set_drop_inequality(bset
, i
);
651 /* Give a basic set "bset" with recession cone "cone", compute and
652 * return an integer point in bset, if any.
654 * If the recession cone is full-dimensional, then we know that
655 * bset contains an infinite number of integer points and it is
656 * fairly easy to pick one of them.
657 * If the recession cone is not full-dimensional, then we first
658 * transform bset such that the bounded directions appear as
659 * the first dimensions of the transformed basic set.
660 * We do this by using a unimodular transformation that transforms
661 * the equalities in the recession cone to equalities on the first
664 * The transformed set is then projected onto its bounded dimensions.
665 * Note that to compute this projection, we can simply drop all constraints
666 * involving any of the unbounded dimensions since these constraints
667 * cannot be combined to produce a constraint on the bounded dimensions.
668 * To see this, assume that there is such a combination of constraints
669 * that produces a constraint on the bounded dimensions. This means
670 * that some combination of the unbounded dimensions has both an upper
671 * bound and a lower bound in terms of the bounded dimensions, but then
672 * this combination would be a bounded direction too and would have been
673 * transformed into a bounded dimensions.
675 * We then compute a sample value in the bounded dimensions.
676 * If no such value can be found, then the original set did not contain
677 * any integer points and we are done.
678 * Otherwise, we plug in the value we found in the bounded dimensions,
679 * project out these bounded dimensions and end up with a set with
680 * a full-dimensional recession cone.
681 * A sample point in this set is computed by "rounding up" any
682 * rational point in the set.
684 * The sample points in the bounded and unbounded dimensions are
685 * then combined into a single sample point and transformed back
686 * to the original space.
688 static struct isl_vec
*sample_with_cone(struct isl_basic_set
*bset
,
689 struct isl_basic_set
*cone
)
693 struct isl_mat
*M
, *U
;
694 struct isl_vec
*sample
;
695 struct isl_vec
*cone_sample
;
697 struct isl_basic_set
*bounded
;
703 total
= isl_basic_set_total_dim(cone
);
704 cone_dim
= total
- cone
->n_eq
;
706 M
= isl_mat_sub_alloc(bset
->ctx
, cone
->eq
, 0, cone
->n_eq
, 1, total
);
707 M
= isl_mat_left_hermite(bset
->ctx
, M
, 0, &U
, NULL
);
710 isl_mat_free(bset
->ctx
, M
);
712 U
= isl_mat_lin_to_aff(bset
->ctx
, U
);
713 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(bset
->ctx
, U
));
715 bounded
= isl_basic_set_copy(bset
);
716 bounded
= drop_constraints_involving(bounded
, total
- cone_dim
, cone_dim
);
717 bounded
= isl_basic_set_drop_dims(bounded
, total
- cone_dim
, cone_dim
);
718 sample
= sample_bounded(bounded
);
719 if (!sample
|| sample
->size
== 0) {
720 isl_basic_set_free(bset
);
721 isl_basic_set_free(cone
);
722 isl_mat_free(ctx
, U
);
725 bset
= plug_in(bset
, isl_vec_copy(sample
));
726 cone_sample
= rational_sample(bset
);
727 cone_sample
= round_up_in_cone(cone_sample
, cone
, isl_mat_copy(ctx
, U
));
728 sample
= vec_concat(sample
, cone_sample
);
729 sample
= isl_mat_vec_product(ctx
, U
, sample
);
732 isl_basic_set_free(cone
);
733 isl_basic_set_free(bset
);
737 /* Compute and return a sample point in bset using generalized basis
738 * reduction. We first check if the input set has a non-trivial
739 * recession cone. If so, we perform some extra preprocessing in
740 * sample_with_cone. Otherwise, we directly perform generalized basis
743 static struct isl_vec
*gbr_sample_no_lineality(struct isl_basic_set
*bset
)
746 struct isl_basic_set
*cone
;
748 dim
= isl_basic_set_total_dim(bset
);
750 cone
= isl_basic_set_recession_cone(isl_basic_set_copy(bset
));
752 if (cone
->n_eq
< dim
)
753 return sample_with_cone(bset
, cone
);
755 isl_basic_set_free(cone
);
756 return sample_bounded(bset
);
759 static struct isl_vec
*sample_no_lineality(struct isl_basic_set
*bset
)
763 if (isl_basic_set_fast_is_empty(bset
))
764 return empty_sample(bset
);
766 return sample_eq(bset
, sample_no_lineality
);
767 dim
= isl_basic_set_total_dim(bset
);
769 return zero_sample(bset
);
771 return interval_sample(bset
);
773 switch (bset
->ctx
->ilp_solver
) {
775 return isl_pip_basic_set_sample(bset
);
777 return gbr_sample_no_lineality(bset
);
779 isl_assert(bset
->ctx
, 0, );
780 isl_basic_set_free(bset
);
784 /* Compute an integer point in "bset" with a lineality space that
785 * is orthogonal to the constraints in "bounds".
787 * We first perform a unimodular transformation on bset that
788 * make the constraints in bounds (and therefore all constraints in bset)
789 * only involve the first dimensions. The remaining dimensions
790 * then do not appear in any constraints and we can select any value
791 * for them, say zero. We therefore project out this final dimensions
792 * and plug in the value zero later. This is accomplished by simply
793 * dropping the final columns of the unimodular transformation.
795 static struct isl_vec
*sample_lineality(struct isl_basic_set
*bset
,
796 struct isl_mat
*bounds
)
798 struct isl_mat
*U
= NULL
;
799 unsigned old_dim
, new_dim
;
800 struct isl_vec
*sample
;
803 if (!bset
|| !bounds
)
807 old_dim
= isl_basic_set_n_dim(bset
);
808 new_dim
= bounds
->n_row
;
809 bounds
= isl_mat_left_hermite(ctx
, bounds
, 0, &U
, NULL
);
812 U
= isl_mat_lin_to_aff(ctx
, U
);
813 U
= isl_mat_drop_cols(ctx
, U
, 1 + new_dim
, old_dim
- new_dim
);
814 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(ctx
, U
));
817 isl_mat_free(ctx
, bounds
);
819 sample
= sample_no_lineality(bset
);
820 if (sample
&& sample
->size
!= 0)
821 sample
= isl_mat_vec_product(ctx
, U
, sample
);
823 isl_mat_free(ctx
, U
);
826 isl_mat_free(ctx
, bounds
);
827 isl_mat_free(ctx
, U
);
828 isl_basic_set_free(bset
);
832 struct isl_vec
*isl_basic_set_sample(struct isl_basic_set
*bset
)
835 struct isl_mat
*bounds
;
841 if (isl_basic_set_fast_is_empty(bset
))
842 return empty_sample(bset
);
844 dim
= isl_basic_set_n_dim(bset
);
845 isl_assert(ctx
, isl_basic_set_n_param(bset
) == 0, goto error
);
846 isl_assert(ctx
, bset
->n_div
== 0, goto error
);
848 if (bset
->sample
&& bset
->sample
->size
== 1 + dim
) {
849 int contains
= isl_basic_set_contains(bset
, bset
->sample
);
853 struct isl_vec
*sample
= isl_vec_copy(bset
->sample
);
854 isl_basic_set_free(bset
);
858 isl_vec_free(bset
->sample
);
862 return sample_eq(bset
, isl_basic_set_sample
);
864 return zero_sample(bset
);
866 return interval_sample(bset
);
867 bounds
= independent_bounds(ctx
, bset
);
871 if (bounds
->n_row
== 0) {
872 isl_mat_free(ctx
, bounds
);
873 return zero_sample(bset
);
875 if (bounds
->n_row
< dim
)
876 return sample_lineality(bset
, bounds
);
878 isl_mat_free(ctx
, bounds
);
879 return sample_no_lineality(bset
);
881 isl_basic_set_free(bset
);