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
;
100 struct isl_mat
*bounds
= NULL
;
106 dim
= isl_basic_set_n_dim(bset
);
107 bounds
= isl_mat_alloc(ctx
, 1+dim
, 1+dim
);
111 isl_int_set_si(bounds
->row
[0][0], 1);
112 isl_seq_clr(bounds
->row
[0]+1, dim
);
115 if (bset
->n_ineq
== 0)
118 dirs
= isl_mat_alloc(ctx
, dim
, dim
);
120 isl_mat_free(ctx
, bounds
);
123 isl_seq_cpy(dirs
->row
[0], bset
->ineq
[0]+1, dirs
->n_col
);
124 isl_seq_cpy(bounds
->row
[1], bset
->ineq
[0], bounds
->n_col
);
125 for (j
= 1, n
= 1; n
< dim
&& j
< bset
->n_ineq
; ++j
) {
128 isl_seq_cpy(dirs
->row
[n
], bset
->ineq
[j
]+1, dirs
->n_col
);
130 pos
= isl_seq_first_non_zero(dirs
->row
[n
], dirs
->n_col
);
133 for (i
= 0; i
< n
; ++i
) {
135 pos_i
= isl_seq_first_non_zero(dirs
->row
[i
], dirs
->n_col
);
140 isl_seq_elim(dirs
->row
[n
], dirs
->row
[i
], pos
,
142 pos
= isl_seq_first_non_zero(dirs
->row
[n
], dirs
->n_col
);
150 isl_int
*t
= dirs
->row
[n
];
151 for (k
= n
; k
> i
; --k
)
152 dirs
->row
[k
] = dirs
->row
[k
-1];
156 isl_seq_cpy(bounds
->row
[n
], bset
->ineq
[j
], bounds
->n_col
);
158 isl_mat_free(ctx
, dirs
);
163 static void swap_inequality(struct isl_basic_set
*bset
, int a
, int b
)
165 isl_int
*t
= bset
->ineq
[a
];
166 bset
->ineq
[a
] = bset
->ineq
[b
];
170 /* Skew into positive orthant and project out lineality space */
171 static struct isl_basic_set
*isl_basic_set_skew_to_positive_orthant(
172 struct isl_basic_set
*bset
, struct isl_mat
**T
)
174 struct isl_mat
*U
= NULL
;
175 struct isl_mat
*bounds
= NULL
;
177 unsigned old_dim
, new_dim
;
185 isl_assert(ctx
, isl_basic_set_n_param(bset
) == 0, goto error
);
186 isl_assert(ctx
, bset
->n_div
== 0, goto error
);
187 isl_assert(ctx
, bset
->n_eq
== 0, goto error
);
189 old_dim
= isl_basic_set_n_dim(bset
);
190 /* Try to move (multiples of) unit rows up. */
191 for (i
= 0, j
= 0; i
< bset
->n_ineq
; ++i
) {
192 int pos
= isl_seq_first_non_zero(bset
->ineq
[i
]+1, old_dim
);
195 if (isl_seq_first_non_zero(bset
->ineq
[i
]+1+pos
+1,
199 swap_inequality(bset
, i
, j
);
202 bounds
= independent_bounds(ctx
, bset
);
205 new_dim
= bounds
->n_row
- 1;
206 bounds
= isl_mat_left_hermite(ctx
, bounds
, 1, &U
, NULL
);
209 U
= isl_mat_drop_cols(ctx
, U
, 1 + new_dim
, old_dim
- new_dim
);
210 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(ctx
, U
));
214 isl_mat_free(ctx
, bounds
);
217 isl_mat_free(ctx
, bounds
);
218 isl_mat_free(ctx
, U
);
219 isl_basic_set_free(bset
);
223 /* Find a sample integer point, if any, in bset, which is known
224 * to have equalities. If bset contains no integer points, then
225 * return a zero-length vector.
226 * We simply remove the known equalities, compute a sample
227 * in the resulting bset, using the specified recurse function,
228 * and then transform the sample back to the original space.
230 static struct isl_vec
*sample_eq(struct isl_basic_set
*bset
,
231 struct isl_vec
*(*recurse
)(struct isl_basic_set
*))
234 struct isl_vec
*sample
;
241 bset
= isl_basic_set_remove_equalities(bset
, &T
, NULL
);
242 sample
= recurse(bset
);
243 if (!sample
|| sample
->size
== 0)
244 isl_mat_free(ctx
, T
);
246 sample
= isl_mat_vec_product(ctx
, T
, sample
);
250 /* Given a basic set "bset" and an affine function "f"/"denom",
251 * check if bset is bounded and non-empty and if so, return the minimal
252 * and maximal value attained by the affine function in "min" and "max".
253 * The minimal value is rounded up to the nearest integer, while the
254 * maximal value is rounded down.
255 * The return value indicates whether the set was empty or unbounded.
257 * If we happen to find an integer point while looking for the minimal
258 * or maximal value, then we record that value in "bset" and return early.
260 static enum isl_lp_result
basic_set_range(struct isl_basic_set
*bset
,
261 isl_int
*f
, isl_int denom
, isl_int
*min
, isl_int
*max
)
265 enum isl_lp_result res
;
269 if (isl_basic_set_fast_is_empty(bset
))
272 tab
= isl_tab_from_basic_set(bset
);
273 res
= isl_tab_min(bset
->ctx
, tab
, f
, denom
, min
, NULL
, 0);
274 if (res
!= isl_lp_ok
)
277 if (isl_tab_sample_is_integer(bset
->ctx
, tab
)) {
278 isl_vec_free(bset
->sample
);
279 bset
->sample
= isl_tab_get_sample_value(bset
->ctx
, tab
);
282 isl_int_set(*max
, *min
);
286 dim
= isl_basic_set_total_dim(bset
);
287 isl_seq_neg(f
, f
, 1 + dim
);
288 res
= isl_tab_min(bset
->ctx
, tab
, f
, denom
, max
, NULL
, 0);
289 isl_seq_neg(f
, f
, 1 + dim
);
290 isl_int_neg(*max
, *max
);
292 if (isl_tab_sample_is_integer(bset
->ctx
, tab
)) {
293 isl_vec_free(bset
->sample
);
294 bset
->sample
= isl_tab_get_sample_value(bset
->ctx
, tab
);
300 isl_tab_free(bset
->ctx
, tab
);
303 isl_tab_free(bset
->ctx
, tab
);
307 /* Perform a basis reduction on "bset" and return the inverse of
308 * the new basis, i.e., an affine mapping from the new coordinates to the old,
311 static struct isl_basic_set
*basic_set_reduced(struct isl_basic_set
*bset
,
315 unsigned gbr_only_first
;
323 gbr_only_first
= ctx
->gbr_only_first
;
324 ctx
->gbr_only_first
= 1;
325 *T
= isl_basic_set_reduced_basis(bset
);
326 ctx
->gbr_only_first
= gbr_only_first
;
328 *T
= isl_mat_lin_to_aff(bset
->ctx
, *T
);
329 *T
= isl_mat_right_inverse(bset
->ctx
, *T
);
331 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(bset
->ctx
, *T
));
337 isl_mat_free(ctx
, *T
);
342 static struct isl_vec
*sample_bounded(struct isl_basic_set
*bset
);
344 /* Given a basic set "bset" whose first coordinate ranges between
345 * "min" and "max", step through all values from min to max, until
346 * the slice of bset with the first coordinate fixed to one of these
347 * values contains an integer point. If such a point is found, return it.
348 * If none of the slices contains any integer point, then bset itself
349 * doesn't contain any integer point and an empty sample is returned.
351 static struct isl_vec
*sample_scan(struct isl_basic_set
*bset
,
352 isl_int min
, isl_int max
)
355 struct isl_basic_set
*slice
= NULL
;
356 struct isl_vec
*sample
= NULL
;
359 total
= isl_basic_set_total_dim(bset
);
362 for (isl_int_set(tmp
, min
); isl_int_le(tmp
, max
);
363 isl_int_add_ui(tmp
, tmp
, 1)) {
366 slice
= isl_basic_set_copy(bset
);
367 slice
= isl_basic_set_cow(slice
);
368 slice
= isl_basic_set_extend_constraints(slice
, 1, 0);
369 k
= isl_basic_set_alloc_equality(slice
);
372 isl_int_set(slice
->eq
[k
][0], tmp
);
373 isl_int_set_si(slice
->eq
[k
][1], -1);
374 isl_seq_clr(slice
->eq
[k
] + 2, total
- 1);
375 slice
= isl_basic_set_simplify(slice
);
376 sample
= sample_bounded(slice
);
380 if (sample
->size
> 0)
382 isl_vec_free(sample
);
386 sample
= empty_sample(bset
);
388 isl_basic_set_free(bset
);
392 isl_basic_set_free(bset
);
393 isl_basic_set_free(slice
);
398 /* Given a basic set that is known to be bounded, find and return
399 * an integer point in the basic set, if there is any.
401 * After handling some trivial cases, we check the range of the
402 * first coordinate. If this coordinate can only attain one integer
403 * value, we are happy. Otherwise, we perform basis reduction and
404 * determine the new range.
406 * Then we step through all possible values in the range in sample_scan.
408 * If any basis reduction was performed, the sample value found, if any,
409 * is transformed back to the original space.
411 static struct isl_vec
*sample_bounded(struct isl_basic_set
*bset
)
415 struct isl_vec
*sample
;
416 struct isl_vec
*obj
= NULL
;
417 struct isl_mat
*T
= NULL
;
419 enum isl_lp_result res
;
424 if (isl_basic_set_fast_is_empty(bset
))
425 return empty_sample(bset
);
428 dim
= isl_basic_set_total_dim(bset
);
430 return zero_sample(bset
);
432 return interval_sample(bset
);
434 return sample_eq(bset
, sample_bounded
);
438 obj
= isl_vec_alloc(bset
->ctx
, 1 + dim
);
441 isl_seq_clr(obj
->el
, 1+ dim
);
442 isl_int_set_si(obj
->el
[1], 1);
444 res
= basic_set_range(bset
, obj
->el
, bset
->ctx
->one
, &min
, &max
);
445 if (res
== isl_lp_error
)
447 isl_assert(bset
->ctx
, res
!= isl_lp_unbounded
, goto error
);
449 sample
= isl_vec_copy(bset
->sample
);
450 isl_basic_set_free(bset
);
453 if (res
== isl_lp_empty
|| isl_int_lt(max
, min
)) {
454 sample
= empty_sample(bset
);
458 if (isl_int_ne(min
, max
)) {
459 bset
= basic_set_reduced(bset
, &T
);
463 res
= basic_set_range(bset
, obj
->el
, bset
->ctx
->one
, &min
, &max
);
464 if (res
== isl_lp_error
)
466 isl_assert(bset
->ctx
, res
!= isl_lp_unbounded
, goto error
);
468 sample
= isl_vec_copy(bset
->sample
);
469 isl_basic_set_free(bset
);
472 if (res
== isl_lp_empty
|| isl_int_lt(max
, min
)) {
473 sample
= empty_sample(bset
);
478 sample
= sample_scan(bset
, min
, max
);
481 if (!sample
|| sample
->size
== 0)
482 isl_mat_free(ctx
, T
);
484 sample
= isl_mat_vec_product(ctx
, T
, sample
);
491 isl_mat_free(ctx
, T
);
492 isl_basic_set_free(bset
);
499 /* Given a basic set "bset" and a value "sample" for the first coordinates
500 * of bset, plug in these values and drop the corresponding coordinates.
502 * We do this by computing the preimage of the transformation
508 * where [1 s] is the sample value and I is the identity matrix of the
509 * appropriate dimension.
511 static struct isl_basic_set
*plug_in(struct isl_basic_set
*bset
,
512 struct isl_vec
*sample
)
518 if (!bset
|| !sample
)
521 total
= isl_basic_set_total_dim(bset
);
522 T
= isl_mat_alloc(bset
->ctx
, 1 + total
, 1 + total
- (sample
->size
- 1));
526 for (i
= 0; i
< sample
->size
; ++i
) {
527 isl_int_set(T
->row
[i
][0], sample
->el
[i
]);
528 isl_seq_clr(T
->row
[i
] + 1, T
->n_col
- 1);
530 for (i
= 0; i
< T
->n_col
- 1; ++i
) {
531 isl_seq_clr(T
->row
[sample
->size
+ i
], T
->n_col
);
532 isl_int_set_si(T
->row
[sample
->size
+ i
][1 + i
], 1);
534 isl_vec_free(sample
);
536 bset
= isl_basic_set_preimage(bset
, T
);
539 isl_basic_set_free(bset
);
540 isl_vec_free(sample
);
544 /* Given a basic set "bset", return any (possibly non-integer) point
547 static struct isl_vec
*rational_sample(struct isl_basic_set
*bset
)
550 struct isl_vec
*sample
;
555 tab
= isl_tab_from_basic_set(bset
);
556 sample
= isl_tab_get_sample_value(bset
->ctx
, tab
);
557 isl_tab_free(bset
->ctx
, tab
);
559 isl_basic_set_free(bset
);
564 /* Given a rational vector, with the denominator in the first element
565 * of the vector, round up all coordinates.
567 struct isl_vec
*isl_vec_ceil(struct isl_vec
*vec
)
571 vec
= isl_vec_cow(vec
);
575 isl_seq_cdiv_q(vec
->el
+ 1, vec
->el
+ 1, vec
->el
[0], vec
->size
- 1);
577 isl_int_set_si(vec
->el
[0], 1);
582 /* Given a linear cone "cone" and a rational point "vec",
583 * construct a polyhedron with shifted copies of the constraints in "cone",
584 * i.e., a polyhedron with "cone" as its recession cone, such that each
585 * point x in this polyhedron is such that the unit box positioned at x
586 * lies entirely inside the affine cone 'vec + cone'.
587 * Any rational point in this polyhedron may therefore be rounded up
588 * to yield an integer point that lies inside said affine cone.
590 * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
591 * point "vec" by v/d.
592 * Let b_i = <a_i, v>. Then the affine cone 'vec + cone' is given
593 * by <a_i, x> - b/d >= 0.
594 * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
595 * We prefer this polyhedron over the actual affine cone because it doesn't
596 * require a scaling of the constraints.
597 * If each of the vertices of the unit cube positioned at x lies inside
598 * this polyhedron, then the whole unit cube at x lies inside the affine cone.
599 * We therefore impose that x' = x + \sum e_i, for any selection of unit
600 * vectors lies inside the polyhedron, i.e.,
602 * <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
604 * The most stringent of these constraints is the one that selects
605 * all negative a_i, so the polyhedron we are looking for has constraints
607 * <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
609 * Note that if cone were known to have only non-negative rays
610 * (which can be accomplished by a unimodular transformation),
611 * then we would only have to check the points x' = x + e_i
612 * and we only have to add the smallest negative a_i (if any)
613 * instead of the sum of all negative a_i.
615 static struct isl_basic_set
*shift_cone(struct isl_basic_set
*cone
,
621 struct isl_basic_set
*shift
= NULL
;
626 isl_assert(cone
->ctx
, cone
->n_eq
== 0, goto error
);
628 total
= isl_basic_set_total_dim(cone
);
630 shift
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(cone
),
633 for (i
= 0; i
< cone
->n_ineq
; ++i
) {
634 k
= isl_basic_set_alloc_inequality(shift
);
637 isl_seq_cpy(shift
->ineq
[k
] + 1, cone
->ineq
[i
] + 1, total
);
638 isl_seq_inner_product(shift
->ineq
[k
] + 1, vec
->el
+ 1, total
,
640 isl_int_cdiv_q(shift
->ineq
[k
][0],
641 shift
->ineq
[k
][0], vec
->el
[0]);
642 isl_int_neg(shift
->ineq
[k
][0], shift
->ineq
[k
][0]);
643 for (j
= 0; j
< total
; ++j
) {
644 if (isl_int_is_nonneg(shift
->ineq
[k
][1 + j
]))
646 isl_int_add(shift
->ineq
[k
][0],
647 shift
->ineq
[k
][0], shift
->ineq
[k
][1 + j
]);
651 isl_basic_set_free(cone
);
654 return isl_basic_set_finalize(shift
);
656 isl_basic_set_free(shift
);
657 isl_basic_set_free(cone
);
662 /* Given a rational point vec in a (transformed) basic set,
663 * such that cone is the recession cone of the original basic set,
664 * "round up" the rational point to an integer point.
666 * We first check if the rational point just happens to be integer.
667 * If not, we transform the cone in the same way as the basic set,
668 * pick a point x in this cone shifted to the rational point such that
669 * the whole unit cube at x is also inside this affine cone.
670 * Then we simply round up the coordinates of x and return the
671 * resulting integer point.
673 static struct isl_vec
*round_up_in_cone(struct isl_vec
*vec
,
674 struct isl_basic_set
*cone
, struct isl_mat
*U
)
678 if (!vec
|| !cone
|| !U
)
681 isl_assert(vec
->ctx
, vec
->size
!= 0, goto error
);
682 if (isl_int_is_one(vec
->el
[0])) {
683 isl_mat_free(vec
->ctx
, U
);
684 isl_basic_set_free(cone
);
688 total
= isl_basic_set_total_dim(cone
);
689 cone
= isl_basic_set_preimage(cone
, U
);
690 cone
= isl_basic_set_remove_dims(cone
, 0, total
- (vec
->size
- 1));
692 cone
= shift_cone(cone
, vec
);
694 vec
= rational_sample(cone
);
695 vec
= isl_vec_ceil(vec
);
698 isl_mat_free(vec
? vec
->ctx
: cone
? cone
->ctx
: NULL
, U
);
700 isl_basic_set_free(cone
);
704 /* Concatenate two integer vectors, i.e., two vectors with denominator
705 * (stored in element 0) equal to 1.
707 static struct isl_vec
*vec_concat(struct isl_vec
*vec1
, struct isl_vec
*vec2
)
713 isl_assert(vec1
->ctx
, vec1
->size
> 0, goto error
);
714 isl_assert(vec2
->ctx
, vec2
->size
> 0, goto error
);
715 isl_assert(vec1
->ctx
, isl_int_is_one(vec1
->el
[0]), goto error
);
716 isl_assert(vec2
->ctx
, isl_int_is_one(vec2
->el
[0]), goto error
);
718 vec
= isl_vec_alloc(vec1
->ctx
, vec1
->size
+ vec2
->size
- 1);
722 isl_seq_cpy(vec
->el
, vec1
->el
, vec1
->size
);
723 isl_seq_cpy(vec
->el
+ vec1
->size
, vec2
->el
+ 1, vec2
->size
- 1);
735 /* Drop all constraints in bset that involve any of the dimensions
736 * first to first+n-1.
738 static struct isl_basic_set
*drop_constraints_involving
739 (struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
746 bset
= isl_basic_set_cow(bset
);
748 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
) {
749 if (isl_seq_first_non_zero(bset
->ineq
[i
] + 1 + first
, n
) == -1)
751 isl_basic_set_drop_inequality(bset
, i
);
757 /* Give a basic set "bset" with recession cone "cone", compute and
758 * return an integer point in bset, if any.
760 * If the recession cone is full-dimensional, then we know that
761 * bset contains an infinite number of integer points and it is
762 * fairly easy to pick one of them.
763 * If the recession cone is not full-dimensional, then we first
764 * transform bset such that the bounded directions appear as
765 * the first dimensions of the transformed basic set.
766 * We do this by using a unimodular transformation that transforms
767 * the equalities in the recession cone to equalities on the first
770 * The transformed set is then projected onto its bounded dimensions.
771 * Note that to compute this projection, we can simply drop all constraints
772 * involving any of the unbounded dimensions since these constraints
773 * cannot be combined to produce a constraint on the bounded dimensions.
774 * To see this, assume that there is such a combination of constraints
775 * that produces a constraint on the bounded dimensions. This means
776 * that some combination of the unbounded dimensions has both an upper
777 * bound and a lower bound in terms of the bounded dimensions, but then
778 * this combination would be a bounded direction too and would have been
779 * transformed into a bounded dimensions.
781 * We then compute a sample value in the bounded dimensions.
782 * If no such value can be found, then the original set did not contain
783 * any integer points and we are done.
784 * Otherwise, we plug in the value we found in the bounded dimensions,
785 * project out these bounded dimensions and end up with a set with
786 * a full-dimensional recession cone.
787 * A sample point in this set is computed by "rounding up" any
788 * rational point in the set.
790 * The sample points in the bounded and unbounded dimensions are
791 * then combined into a single sample point and transformed back
792 * to the original space.
794 static struct isl_vec
*sample_with_cone(struct isl_basic_set
*bset
,
795 struct isl_basic_set
*cone
)
799 struct isl_mat
*M
, *U
;
800 struct isl_vec
*sample
;
801 struct isl_vec
*cone_sample
;
803 struct isl_basic_set
*bounded
;
809 total
= isl_basic_set_total_dim(cone
);
810 cone_dim
= total
- cone
->n_eq
;
812 M
= isl_mat_sub_alloc(bset
->ctx
, cone
->eq
, 0, cone
->n_eq
, 1, total
);
813 M
= isl_mat_left_hermite(bset
->ctx
, M
, 0, &U
, NULL
);
816 isl_mat_free(bset
->ctx
, M
);
818 U
= isl_mat_lin_to_aff(bset
->ctx
, U
);
819 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(bset
->ctx
, U
));
821 bounded
= isl_basic_set_copy(bset
);
822 bounded
= drop_constraints_involving(bounded
, total
- cone_dim
, cone_dim
);
823 bounded
= isl_basic_set_drop_dims(bounded
, total
- cone_dim
, cone_dim
);
824 sample
= sample_bounded(bounded
);
825 if (!sample
|| sample
->size
== 0) {
826 isl_basic_set_free(bset
);
827 isl_basic_set_free(cone
);
828 isl_mat_free(ctx
, U
);
831 bset
= plug_in(bset
, isl_vec_copy(sample
));
832 cone_sample
= rational_sample(bset
);
833 cone_sample
= round_up_in_cone(cone_sample
, cone
, isl_mat_copy(ctx
, U
));
834 sample
= vec_concat(sample
, cone_sample
);
835 sample
= isl_mat_vec_product(ctx
, U
, sample
);
838 isl_basic_set_free(cone
);
839 isl_basic_set_free(bset
);
843 /* Compute and return a sample point in bset using generalized basis
844 * reduction. We first check if the input set has a non-trivial
845 * recession cone. If so, we perform some extra preprocessing in
846 * sample_with_cone. Otherwise, we directly perform generalized basis
849 static struct isl_vec
*gbr_sample_no_lineality(struct isl_basic_set
*bset
)
852 struct isl_basic_set
*cone
;
854 dim
= isl_basic_set_total_dim(bset
);
856 cone
= isl_basic_set_recession_cone(isl_basic_set_copy(bset
));
858 if (cone
->n_eq
< dim
)
859 return sample_with_cone(bset
, cone
);
861 isl_basic_set_free(cone
);
862 return sample_bounded(bset
);
865 static struct isl_vec
*pip_sample_no_lineality(struct isl_basic_set
*bset
)
869 struct isl_vec
*sample
;
871 bset
= isl_basic_set_skew_to_positive_orthant(bset
, &T
);
876 sample
= isl_pip_basic_set_sample(bset
);
878 if (sample
&& sample
->size
!= 0)
879 sample
= isl_mat_vec_product(ctx
, T
, sample
);
881 isl_mat_free(ctx
, T
);
886 static struct isl_vec
*sample_no_lineality(struct isl_basic_set
*bset
)
890 if (isl_basic_set_fast_is_empty(bset
))
891 return empty_sample(bset
);
893 return sample_eq(bset
, sample_no_lineality
);
894 dim
= isl_basic_set_total_dim(bset
);
896 return zero_sample(bset
);
898 return interval_sample(bset
);
900 switch (bset
->ctx
->ilp_solver
) {
902 return pip_sample_no_lineality(bset
);
904 return gbr_sample_no_lineality(bset
);
906 isl_assert(bset
->ctx
, 0, );
907 isl_basic_set_free(bset
);
911 /* Compute an integer point in "bset" with a lineality space that
912 * is orthogonal to the constraints in "bounds".
914 * We first perform a unimodular transformation on bset that
915 * make the constraints in bounds (and therefore all constraints in bset)
916 * only involve the first dimensions. The remaining dimensions
917 * then do not appear in any constraints and we can select any value
918 * for them, say zero. We therefore project out this final dimensions
919 * and plug in the value zero later. This is accomplished by simply
920 * dropping the final columns of the unimodular transformation.
922 static struct isl_vec
*sample_lineality(struct isl_basic_set
*bset
,
923 struct isl_mat
*bounds
)
925 struct isl_mat
*U
= NULL
;
926 unsigned old_dim
, new_dim
;
927 struct isl_vec
*sample
;
930 if (!bset
|| !bounds
)
934 old_dim
= isl_basic_set_n_dim(bset
);
935 new_dim
= bounds
->n_row
- 1;
936 bounds
= isl_mat_left_hermite(ctx
, bounds
, 0, &U
, NULL
);
939 U
= isl_mat_drop_cols(ctx
, U
, 1 + new_dim
, old_dim
- new_dim
);
940 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(ctx
, U
));
943 isl_mat_free(ctx
, bounds
);
945 sample
= sample_no_lineality(bset
);
946 if (sample
&& sample
->size
!= 0)
947 sample
= isl_mat_vec_product(ctx
, U
, sample
);
949 isl_mat_free(ctx
, U
);
952 isl_mat_free(ctx
, bounds
);
953 isl_mat_free(ctx
, U
);
954 isl_basic_set_free(bset
);
958 struct isl_vec
*isl_basic_set_sample(struct isl_basic_set
*bset
)
961 struct isl_mat
*bounds
;
967 if (isl_basic_set_fast_is_empty(bset
))
968 return empty_sample(bset
);
970 dim
= isl_basic_set_n_dim(bset
);
971 isl_assert(ctx
, isl_basic_set_n_param(bset
) == 0, goto error
);
972 isl_assert(ctx
, bset
->n_div
== 0, goto error
);
974 if (bset
->sample
&& bset
->sample
->size
== 1 + dim
) {
975 int contains
= isl_basic_set_contains(bset
, bset
->sample
);
979 struct isl_vec
*sample
= isl_vec_copy(bset
->sample
);
980 isl_basic_set_free(bset
);
984 isl_vec_free(bset
->sample
);
988 return sample_eq(bset
, isl_basic_set_sample
);
990 return zero_sample(bset
);
992 return interval_sample(bset
);
993 bounds
= independent_bounds(ctx
, bset
);
997 if (bounds
->n_row
== 1) {
998 isl_mat_free(ctx
, bounds
);
999 return zero_sample(bset
);
1001 if (bounds
->n_row
< 1 + dim
)
1002 return sample_lineality(bset
, bounds
);
1004 isl_mat_free(ctx
, bounds
);
1005 return sample_no_lineality(bset
);
1007 isl_basic_set_free(bset
);