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.
172 * We perform a unimodular transformation that turns a selected
173 * maximal set of linearly independent bounds into constraints
174 * on the first dimensions that impose that these first dimensions
175 * are non-negative. In particular, the constraint matrix is lower
176 * triangular with positive entries on the diagonal and negative
178 * If "bset" has a lineality space then these constraints (and therefore
179 * all constraints in bset) only involve the first dimensions.
180 * The remaining dimensions then do not appear in any constraints and
181 * we can select any value for them, say zero. We therefore project
182 * out this final dimensions and plug in the value zero later. This
183 * is accomplished by simply dropping the final columns of
184 * the unimodular transformation.
186 static struct isl_basic_set
*isl_basic_set_skew_to_positive_orthant(
187 struct isl_basic_set
*bset
, struct isl_mat
**T
)
189 struct isl_mat
*U
= NULL
;
190 struct isl_mat
*bounds
= NULL
;
192 unsigned old_dim
, new_dim
;
200 isl_assert(ctx
, isl_basic_set_n_param(bset
) == 0, goto error
);
201 isl_assert(ctx
, bset
->n_div
== 0, goto error
);
202 isl_assert(ctx
, bset
->n_eq
== 0, goto error
);
204 old_dim
= isl_basic_set_n_dim(bset
);
205 /* Try to move (multiples of) unit rows up. */
206 for (i
= 0, j
= 0; i
< bset
->n_ineq
; ++i
) {
207 int pos
= isl_seq_first_non_zero(bset
->ineq
[i
]+1, old_dim
);
210 if (isl_seq_first_non_zero(bset
->ineq
[i
]+1+pos
+1,
214 swap_inequality(bset
, i
, j
);
217 bounds
= independent_bounds(ctx
, bset
);
220 new_dim
= bounds
->n_row
- 1;
221 bounds
= isl_mat_left_hermite(ctx
, bounds
, 1, &U
, NULL
);
224 U
= isl_mat_drop_cols(ctx
, U
, 1 + new_dim
, old_dim
- new_dim
);
225 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(ctx
, U
));
229 isl_mat_free(ctx
, bounds
);
232 isl_mat_free(ctx
, bounds
);
233 isl_mat_free(ctx
, U
);
234 isl_basic_set_free(bset
);
238 /* Find a sample integer point, if any, in bset, which is known
239 * to have equalities. If bset contains no integer points, then
240 * return a zero-length vector.
241 * We simply remove the known equalities, compute a sample
242 * in the resulting bset, using the specified recurse function,
243 * and then transform the sample back to the original space.
245 static struct isl_vec
*sample_eq(struct isl_basic_set
*bset
,
246 struct isl_vec
*(*recurse
)(struct isl_basic_set
*))
249 struct isl_vec
*sample
;
256 bset
= isl_basic_set_remove_equalities(bset
, &T
, NULL
);
257 sample
= recurse(bset
);
258 if (!sample
|| sample
->size
== 0)
259 isl_mat_free(ctx
, T
);
261 sample
= isl_mat_vec_product(ctx
, T
, sample
);
265 /* Given a basic set "bset" and an affine function "f"/"denom",
266 * check if bset is bounded and non-empty and if so, return the minimal
267 * and maximal value attained by the affine function in "min" and "max".
268 * The minimal value is rounded up to the nearest integer, while the
269 * maximal value is rounded down.
270 * The return value indicates whether the set was empty or unbounded.
272 * If we happen to find an integer point while looking for the minimal
273 * or maximal value, then we record that value in "bset" and return early.
275 static enum isl_lp_result
basic_set_range(struct isl_basic_set
*bset
,
276 isl_int
*f
, isl_int denom
, isl_int
*min
, isl_int
*max
)
280 enum isl_lp_result res
;
284 if (isl_basic_set_fast_is_empty(bset
))
287 tab
= isl_tab_from_basic_set(bset
);
288 res
= isl_tab_min(bset
->ctx
, tab
, f
, denom
, min
, NULL
, 0);
289 if (res
!= isl_lp_ok
)
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
);
297 isl_int_set(*max
, *min
);
301 dim
= isl_basic_set_total_dim(bset
);
302 isl_seq_neg(f
, f
, 1 + dim
);
303 res
= isl_tab_min(bset
->ctx
, tab
, f
, denom
, max
, NULL
, 0);
304 isl_seq_neg(f
, f
, 1 + dim
);
305 isl_int_neg(*max
, *max
);
307 if (isl_tab_sample_is_integer(bset
->ctx
, tab
)) {
308 isl_vec_free(bset
->sample
);
309 bset
->sample
= isl_tab_get_sample_value(bset
->ctx
, tab
);
315 isl_tab_free(bset
->ctx
, tab
);
318 isl_tab_free(bset
->ctx
, tab
);
322 /* Perform a basis reduction on "bset" and return the inverse of
323 * the new basis, i.e., an affine mapping from the new coordinates to the old,
326 static struct isl_basic_set
*basic_set_reduced(struct isl_basic_set
*bset
,
330 unsigned gbr_only_first
;
338 gbr_only_first
= ctx
->gbr_only_first
;
339 ctx
->gbr_only_first
= 1;
340 *T
= isl_basic_set_reduced_basis(bset
);
341 ctx
->gbr_only_first
= gbr_only_first
;
343 *T
= isl_mat_lin_to_aff(bset
->ctx
, *T
);
344 *T
= isl_mat_right_inverse(bset
->ctx
, *T
);
346 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(bset
->ctx
, *T
));
352 isl_mat_free(ctx
, *T
);
357 static struct isl_vec
*sample_bounded(struct isl_basic_set
*bset
);
359 /* Given a basic set "bset" whose first coordinate ranges between
360 * "min" and "max", step through all values from min to max, until
361 * the slice of bset with the first coordinate fixed to one of these
362 * values contains an integer point. If such a point is found, return it.
363 * If none of the slices contains any integer point, then bset itself
364 * doesn't contain any integer point and an empty sample is returned.
366 static struct isl_vec
*sample_scan(struct isl_basic_set
*bset
,
367 isl_int min
, isl_int max
)
370 struct isl_basic_set
*slice
= NULL
;
371 struct isl_vec
*sample
= NULL
;
374 total
= isl_basic_set_total_dim(bset
);
377 for (isl_int_set(tmp
, min
); isl_int_le(tmp
, max
);
378 isl_int_add_ui(tmp
, tmp
, 1)) {
381 slice
= isl_basic_set_copy(bset
);
382 slice
= isl_basic_set_cow(slice
);
383 slice
= isl_basic_set_extend_constraints(slice
, 1, 0);
384 k
= isl_basic_set_alloc_equality(slice
);
387 isl_int_set(slice
->eq
[k
][0], tmp
);
388 isl_int_set_si(slice
->eq
[k
][1], -1);
389 isl_seq_clr(slice
->eq
[k
] + 2, total
- 1);
390 slice
= isl_basic_set_simplify(slice
);
391 sample
= sample_bounded(slice
);
395 if (sample
->size
> 0)
397 isl_vec_free(sample
);
401 sample
= empty_sample(bset
);
403 isl_basic_set_free(bset
);
407 isl_basic_set_free(bset
);
408 isl_basic_set_free(slice
);
413 /* Given a basic set that is known to be bounded, find and return
414 * an integer point in the basic set, if there is any.
416 * After handling some trivial cases, we check the range of the
417 * first coordinate. If this coordinate can only attain one integer
418 * value, we are happy. Otherwise, we perform basis reduction and
419 * determine the new range.
421 * Then we step through all possible values in the range in sample_scan.
423 * If any basis reduction was performed, the sample value found, if any,
424 * is transformed back to the original space.
426 static struct isl_vec
*sample_bounded(struct isl_basic_set
*bset
)
430 struct isl_vec
*sample
;
431 struct isl_vec
*obj
= NULL
;
432 struct isl_mat
*T
= NULL
;
434 enum isl_lp_result res
;
439 if (isl_basic_set_fast_is_empty(bset
))
440 return empty_sample(bset
);
443 dim
= isl_basic_set_total_dim(bset
);
445 return zero_sample(bset
);
447 return interval_sample(bset
);
449 return sample_eq(bset
, sample_bounded
);
453 obj
= isl_vec_alloc(bset
->ctx
, 1 + dim
);
456 isl_seq_clr(obj
->el
, 1+ dim
);
457 isl_int_set_si(obj
->el
[1], 1);
459 res
= basic_set_range(bset
, obj
->el
, bset
->ctx
->one
, &min
, &max
);
460 if (res
== isl_lp_error
)
462 isl_assert(bset
->ctx
, res
!= isl_lp_unbounded
, goto error
);
464 sample
= isl_vec_copy(bset
->sample
);
465 isl_basic_set_free(bset
);
468 if (res
== isl_lp_empty
|| isl_int_lt(max
, min
)) {
469 sample
= empty_sample(bset
);
473 if (isl_int_ne(min
, max
)) {
474 bset
= basic_set_reduced(bset
, &T
);
478 res
= basic_set_range(bset
, obj
->el
, bset
->ctx
->one
, &min
, &max
);
479 if (res
== isl_lp_error
)
481 isl_assert(bset
->ctx
, res
!= isl_lp_unbounded
, goto error
);
483 sample
= isl_vec_copy(bset
->sample
);
484 isl_basic_set_free(bset
);
487 if (res
== isl_lp_empty
|| isl_int_lt(max
, min
)) {
488 sample
= empty_sample(bset
);
493 sample
= sample_scan(bset
, min
, max
);
496 if (!sample
|| sample
->size
== 0)
497 isl_mat_free(ctx
, T
);
499 sample
= isl_mat_vec_product(ctx
, T
, sample
);
506 isl_mat_free(ctx
, T
);
507 isl_basic_set_free(bset
);
514 /* Given a basic set "bset" and a value "sample" for the first coordinates
515 * of bset, plug in these values and drop the corresponding coordinates.
517 * We do this by computing the preimage of the transformation
523 * where [1 s] is the sample value and I is the identity matrix of the
524 * appropriate dimension.
526 static struct isl_basic_set
*plug_in(struct isl_basic_set
*bset
,
527 struct isl_vec
*sample
)
533 if (!bset
|| !sample
)
536 total
= isl_basic_set_total_dim(bset
);
537 T
= isl_mat_alloc(bset
->ctx
, 1 + total
, 1 + total
- (sample
->size
- 1));
541 for (i
= 0; i
< sample
->size
; ++i
) {
542 isl_int_set(T
->row
[i
][0], sample
->el
[i
]);
543 isl_seq_clr(T
->row
[i
] + 1, T
->n_col
- 1);
545 for (i
= 0; i
< T
->n_col
- 1; ++i
) {
546 isl_seq_clr(T
->row
[sample
->size
+ i
], T
->n_col
);
547 isl_int_set_si(T
->row
[sample
->size
+ i
][1 + i
], 1);
549 isl_vec_free(sample
);
551 bset
= isl_basic_set_preimage(bset
, T
);
554 isl_basic_set_free(bset
);
555 isl_vec_free(sample
);
559 /* Given a basic set "bset", return any (possibly non-integer) point
562 static struct isl_vec
*rational_sample(struct isl_basic_set
*bset
)
565 struct isl_vec
*sample
;
570 tab
= isl_tab_from_basic_set(bset
);
571 sample
= isl_tab_get_sample_value(bset
->ctx
, tab
);
572 isl_tab_free(bset
->ctx
, tab
);
574 isl_basic_set_free(bset
);
579 /* Given a rational vector, with the denominator in the first element
580 * of the vector, round up all coordinates.
582 struct isl_vec
*isl_vec_ceil(struct isl_vec
*vec
)
586 vec
= isl_vec_cow(vec
);
590 isl_seq_cdiv_q(vec
->el
+ 1, vec
->el
+ 1, vec
->el
[0], vec
->size
- 1);
592 isl_int_set_si(vec
->el
[0], 1);
597 /* Given a linear cone "cone" and a rational point "vec",
598 * construct a polyhedron with shifted copies of the constraints in "cone",
599 * i.e., a polyhedron with "cone" as its recession cone, such that each
600 * point x in this polyhedron is such that the unit box positioned at x
601 * lies entirely inside the affine cone 'vec + cone'.
602 * Any rational point in this polyhedron may therefore be rounded up
603 * to yield an integer point that lies inside said affine cone.
605 * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
606 * point "vec" by v/d.
607 * Let b_i = <a_i, v>. Then the affine cone 'vec + cone' is given
608 * by <a_i, x> - b/d >= 0.
609 * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
610 * We prefer this polyhedron over the actual affine cone because it doesn't
611 * require a scaling of the constraints.
612 * If each of the vertices of the unit cube positioned at x lies inside
613 * this polyhedron, then the whole unit cube at x lies inside the affine cone.
614 * We therefore impose that x' = x + \sum e_i, for any selection of unit
615 * vectors lies inside the polyhedron, i.e.,
617 * <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
619 * The most stringent of these constraints is the one that selects
620 * all negative a_i, so the polyhedron we are looking for has constraints
622 * <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
624 * Note that if cone were known to have only non-negative rays
625 * (which can be accomplished by a unimodular transformation),
626 * then we would only have to check the points x' = x + e_i
627 * and we only have to add the smallest negative a_i (if any)
628 * instead of the sum of all negative a_i.
630 static struct isl_basic_set
*shift_cone(struct isl_basic_set
*cone
,
636 struct isl_basic_set
*shift
= NULL
;
641 isl_assert(cone
->ctx
, cone
->n_eq
== 0, goto error
);
643 total
= isl_basic_set_total_dim(cone
);
645 shift
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(cone
),
648 for (i
= 0; i
< cone
->n_ineq
; ++i
) {
649 k
= isl_basic_set_alloc_inequality(shift
);
652 isl_seq_cpy(shift
->ineq
[k
] + 1, cone
->ineq
[i
] + 1, total
);
653 isl_seq_inner_product(shift
->ineq
[k
] + 1, vec
->el
+ 1, total
,
655 isl_int_cdiv_q(shift
->ineq
[k
][0],
656 shift
->ineq
[k
][0], vec
->el
[0]);
657 isl_int_neg(shift
->ineq
[k
][0], shift
->ineq
[k
][0]);
658 for (j
= 0; j
< total
; ++j
) {
659 if (isl_int_is_nonneg(shift
->ineq
[k
][1 + j
]))
661 isl_int_add(shift
->ineq
[k
][0],
662 shift
->ineq
[k
][0], shift
->ineq
[k
][1 + j
]);
666 isl_basic_set_free(cone
);
669 return isl_basic_set_finalize(shift
);
671 isl_basic_set_free(shift
);
672 isl_basic_set_free(cone
);
677 /* Given a rational point vec in a (transformed) basic set,
678 * such that cone is the recession cone of the original basic set,
679 * "round up" the rational point to an integer point.
681 * We first check if the rational point just happens to be integer.
682 * If not, we transform the cone in the same way as the basic set,
683 * pick a point x in this cone shifted to the rational point such that
684 * the whole unit cube at x is also inside this affine cone.
685 * Then we simply round up the coordinates of x and return the
686 * resulting integer point.
688 static struct isl_vec
*round_up_in_cone(struct isl_vec
*vec
,
689 struct isl_basic_set
*cone
, struct isl_mat
*U
)
693 if (!vec
|| !cone
|| !U
)
696 isl_assert(vec
->ctx
, vec
->size
!= 0, goto error
);
697 if (isl_int_is_one(vec
->el
[0])) {
698 isl_mat_free(vec
->ctx
, U
);
699 isl_basic_set_free(cone
);
703 total
= isl_basic_set_total_dim(cone
);
704 cone
= isl_basic_set_preimage(cone
, U
);
705 cone
= isl_basic_set_remove_dims(cone
, 0, total
- (vec
->size
- 1));
707 cone
= shift_cone(cone
, vec
);
709 vec
= rational_sample(cone
);
710 vec
= isl_vec_ceil(vec
);
713 isl_mat_free(vec
? vec
->ctx
: cone
? cone
->ctx
: NULL
, U
);
715 isl_basic_set_free(cone
);
719 /* Concatenate two integer vectors, i.e., two vectors with denominator
720 * (stored in element 0) equal to 1.
722 static struct isl_vec
*vec_concat(struct isl_vec
*vec1
, struct isl_vec
*vec2
)
728 isl_assert(vec1
->ctx
, vec1
->size
> 0, goto error
);
729 isl_assert(vec2
->ctx
, vec2
->size
> 0, goto error
);
730 isl_assert(vec1
->ctx
, isl_int_is_one(vec1
->el
[0]), goto error
);
731 isl_assert(vec2
->ctx
, isl_int_is_one(vec2
->el
[0]), goto error
);
733 vec
= isl_vec_alloc(vec1
->ctx
, vec1
->size
+ vec2
->size
- 1);
737 isl_seq_cpy(vec
->el
, vec1
->el
, vec1
->size
);
738 isl_seq_cpy(vec
->el
+ vec1
->size
, vec2
->el
+ 1, vec2
->size
- 1);
750 /* Drop all constraints in bset that involve any of the dimensions
751 * first to first+n-1.
753 static struct isl_basic_set
*drop_constraints_involving
754 (struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
761 bset
= isl_basic_set_cow(bset
);
763 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
) {
764 if (isl_seq_first_non_zero(bset
->ineq
[i
] + 1 + first
, n
) == -1)
766 isl_basic_set_drop_inequality(bset
, i
);
772 /* Give a basic set "bset" with recession cone "cone", compute and
773 * return an integer point in bset, if any.
775 * If the recession cone is full-dimensional, then we know that
776 * bset contains an infinite number of integer points and it is
777 * fairly easy to pick one of them.
778 * If the recession cone is not full-dimensional, then we first
779 * transform bset such that the bounded directions appear as
780 * the first dimensions of the transformed basic set.
781 * We do this by using a unimodular transformation that transforms
782 * the equalities in the recession cone to equalities on the first
785 * The transformed set is then projected onto its bounded dimensions.
786 * Note that to compute this projection, we can simply drop all constraints
787 * involving any of the unbounded dimensions since these constraints
788 * cannot be combined to produce a constraint on the bounded dimensions.
789 * To see this, assume that there is such a combination of constraints
790 * that produces a constraint on the bounded dimensions. This means
791 * that some combination of the unbounded dimensions has both an upper
792 * bound and a lower bound in terms of the bounded dimensions, but then
793 * this combination would be a bounded direction too and would have been
794 * transformed into a bounded dimensions.
796 * We then compute a sample value in the bounded dimensions.
797 * If no such value can be found, then the original set did not contain
798 * any integer points and we are done.
799 * Otherwise, we plug in the value we found in the bounded dimensions,
800 * project out these bounded dimensions and end up with a set with
801 * a full-dimensional recession cone.
802 * A sample point in this set is computed by "rounding up" any
803 * rational point in the set.
805 * The sample points in the bounded and unbounded dimensions are
806 * then combined into a single sample point and transformed back
807 * to the original space.
809 static struct isl_vec
*sample_with_cone(struct isl_basic_set
*bset
,
810 struct isl_basic_set
*cone
)
814 struct isl_mat
*M
, *U
;
815 struct isl_vec
*sample
;
816 struct isl_vec
*cone_sample
;
818 struct isl_basic_set
*bounded
;
824 total
= isl_basic_set_total_dim(cone
);
825 cone_dim
= total
- cone
->n_eq
;
827 M
= isl_mat_sub_alloc(bset
->ctx
, cone
->eq
, 0, cone
->n_eq
, 1, total
);
828 M
= isl_mat_left_hermite(bset
->ctx
, M
, 0, &U
, NULL
);
831 isl_mat_free(bset
->ctx
, M
);
833 U
= isl_mat_lin_to_aff(bset
->ctx
, U
);
834 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(bset
->ctx
, U
));
836 bounded
= isl_basic_set_copy(bset
);
837 bounded
= drop_constraints_involving(bounded
, total
- cone_dim
, cone_dim
);
838 bounded
= isl_basic_set_drop_dims(bounded
, total
- cone_dim
, cone_dim
);
839 sample
= sample_bounded(bounded
);
840 if (!sample
|| sample
->size
== 0) {
841 isl_basic_set_free(bset
);
842 isl_basic_set_free(cone
);
843 isl_mat_free(ctx
, U
);
846 bset
= plug_in(bset
, isl_vec_copy(sample
));
847 cone_sample
= rational_sample(bset
);
848 cone_sample
= round_up_in_cone(cone_sample
, cone
, isl_mat_copy(ctx
, U
));
849 sample
= vec_concat(sample
, cone_sample
);
850 sample
= isl_mat_vec_product(ctx
, U
, sample
);
853 isl_basic_set_free(cone
);
854 isl_basic_set_free(bset
);
858 /* Compute and return a sample point in bset using generalized basis
859 * reduction. We first check if the input set has a non-trivial
860 * recession cone. If so, we perform some extra preprocessing in
861 * sample_with_cone. Otherwise, we directly perform generalized basis
864 static struct isl_vec
*gbr_sample(struct isl_basic_set
*bset
)
867 struct isl_basic_set
*cone
;
869 dim
= isl_basic_set_total_dim(bset
);
871 cone
= isl_basic_set_recession_cone(isl_basic_set_copy(bset
));
873 if (cone
->n_eq
< dim
)
874 return sample_with_cone(bset
, cone
);
876 isl_basic_set_free(cone
);
877 return sample_bounded(bset
);
880 static struct isl_vec
*pip_sample(struct isl_basic_set
*bset
)
884 struct isl_vec
*sample
;
886 bset
= isl_basic_set_skew_to_positive_orthant(bset
, &T
);
891 sample
= isl_pip_basic_set_sample(bset
);
893 if (sample
&& sample
->size
!= 0)
894 sample
= isl_mat_vec_product(ctx
, T
, sample
);
896 isl_mat_free(ctx
, T
);
901 struct isl_vec
*isl_basic_set_sample(struct isl_basic_set
*bset
)
909 if (isl_basic_set_fast_is_empty(bset
))
910 return empty_sample(bset
);
912 dim
= isl_basic_set_n_dim(bset
);
913 isl_assert(ctx
, isl_basic_set_n_param(bset
) == 0, goto error
);
914 isl_assert(ctx
, bset
->n_div
== 0, goto error
);
916 if (bset
->sample
&& bset
->sample
->size
== 1 + dim
) {
917 int contains
= isl_basic_set_contains(bset
, bset
->sample
);
921 struct isl_vec
*sample
= isl_vec_copy(bset
->sample
);
922 isl_basic_set_free(bset
);
926 isl_vec_free(bset
->sample
);
930 return sample_eq(bset
, isl_basic_set_sample
);
932 return zero_sample(bset
);
934 return interval_sample(bset
);
936 switch (bset
->ctx
->ilp_solver
) {
938 return pip_sample(bset
);
940 return gbr_sample(bset
);
942 isl_assert(bset
->ctx
, 0, );
944 isl_basic_set_free(bset
);