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 tableau that is known to represent a bounded set, find and return
261 * an integer point in the set, if there is any.
263 * We perform a depth first search
264 * for an integer point, by scanning all possible values in the range
265 * attained by a basis vector, where the initial basis is assumed
266 * to have been set by the calling function.
267 * tab->n_zero is currently ignored and is clobbered by this function.
269 * The search is implemented iteratively. "level" identifies the current
270 * basis vector. "init" is true if we want the first value at the current
271 * level and false if we want the next value.
273 * The initial basis is the identity matrix. If the range in some direction
274 * contains more than one integer value, we perform basis reduction based
275 * on the value of ctx->gbr
276 * - ISL_GBR_NEVER: never perform basis reduction
277 * - ISL_GBR_ONCE: only perform basis reduction the first
278 * time such a range is encountered
279 * - ISL_GBR_ALWAYS: always perform basis reduction when
280 * such a range is encountered
282 * When ctx->gbr is set to ISL_GBR_ALWAYS, then we allow the basis
283 * reduction computation to return early. That is, as soon as it
284 * finds a reasonable first direction.
286 struct isl_vec
*isl_tab_sample(struct isl_tab
*tab
)
291 struct isl_vec
*sample
;
294 enum isl_lp_result res
;
298 struct isl_tab_undo
**snap
;
303 return isl_vec_alloc(tab
->mat
->ctx
, 0);
309 isl_assert(ctx
, tab
->basis
, return NULL
);
311 if (isl_tab_extend_cons(tab
, dim
+ 1) < 0)
314 min
= isl_vec_alloc(ctx
, dim
);
315 max
= isl_vec_alloc(ctx
, dim
);
316 snap
= isl_alloc_array(ctx
, struct isl_tab_undo
*, dim
);
318 if (!min
|| !max
|| !snap
)
328 res
= isl_tab_min(tab
, tab
->basis
->row
[1 + level
],
329 ctx
->one
, &min
->el
[level
], NULL
, 0);
330 if (res
== isl_lp_empty
)
332 isl_assert(ctx
, res
!= isl_lp_unbounded
, goto error
);
333 if (res
== isl_lp_error
)
335 if (!empty
&& isl_tab_sample_is_integer(tab
))
337 isl_seq_neg(tab
->basis
->row
[1 + level
] + 1,
338 tab
->basis
->row
[1 + level
] + 1, dim
);
339 res
= isl_tab_min(tab
, tab
->basis
->row
[1 + level
],
340 ctx
->one
, &max
->el
[level
], NULL
, 0);
341 isl_seq_neg(tab
->basis
->row
[1 + level
] + 1,
342 tab
->basis
->row
[1 + level
] + 1, dim
);
343 isl_int_neg(max
->el
[level
], max
->el
[level
]);
344 if (res
== isl_lp_empty
)
346 isl_assert(ctx
, res
!= isl_lp_unbounded
, goto error
);
347 if (res
== isl_lp_error
)
349 if (!empty
&& isl_tab_sample_is_integer(tab
))
351 if (!empty
&& !reduced
&& ctx
->gbr
!= ISL_GBR_NEVER
&&
352 isl_int_lt(min
->el
[level
], max
->el
[level
])) {
353 unsigned gbr_only_first
;
354 if (ctx
->gbr
== ISL_GBR_ONCE
)
355 ctx
->gbr
= ISL_GBR_NEVER
;
357 gbr_only_first
= ctx
->gbr_only_first
;
358 ctx
->gbr_only_first
=
359 ctx
->gbr
== ISL_GBR_ALWAYS
;
360 tab
= isl_tab_compute_reduced_basis(tab
);
361 ctx
->gbr_only_first
= gbr_only_first
;
362 if (!tab
|| !tab
->basis
)
368 snap
[level
] = isl_tab_snap(tab
);
370 isl_int_add_ui(min
->el
[level
], min
->el
[level
], 1);
372 if (empty
|| isl_int_gt(min
->el
[level
], max
->el
[level
])) {
376 isl_tab_rollback(tab
, snap
[level
]);
379 isl_int_neg(tab
->basis
->row
[1 + level
][0], min
->el
[level
]);
380 tab
= isl_tab_add_valid_eq(tab
, tab
->basis
->row
[1 + level
]);
381 isl_int_set_si(tab
->basis
->row
[1 + level
][0], 0);
382 if (level
< dim
- 1) {
391 sample
= isl_tab_get_sample_value(tab
);
393 sample
= isl_vec_alloc(ctx
, 0);
408 /* Given a basic set that is known to be bounded, find and return
409 * an integer point in the basic set, if there is any.
411 * After handling some trivial cases, we construct a tableau
412 * and then use isl_tab_sample to find a sample, passing it
413 * the identity matrix as initial basis.
415 static struct isl_vec
*sample_bounded(struct isl_basic_set
*bset
)
419 struct isl_vec
*sample
;
420 struct isl_tab
*tab
= NULL
;
425 if (isl_basic_set_fast_is_empty(bset
))
426 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 tab
= isl_tab_from_basic_set(bset
);
442 tab
->basis
= isl_mat_identity(bset
->ctx
, 1 + dim
);
446 sample
= isl_tab_sample(tab
);
450 if (sample
->size
> 0) {
451 isl_vec_free(bset
->sample
);
452 bset
->sample
= isl_vec_copy(sample
);
455 isl_basic_set_free(bset
);
459 isl_basic_set_free(bset
);
464 /* Given a basic set "bset" and a value "sample" for the first coordinates
465 * of bset, plug in these values and drop the corresponding coordinates.
467 * We do this by computing the preimage of the transformation
473 * where [1 s] is the sample value and I is the identity matrix of the
474 * appropriate dimension.
476 static struct isl_basic_set
*plug_in(struct isl_basic_set
*bset
,
477 struct isl_vec
*sample
)
483 if (!bset
|| !sample
)
486 total
= isl_basic_set_total_dim(bset
);
487 T
= isl_mat_alloc(bset
->ctx
, 1 + total
, 1 + total
- (sample
->size
- 1));
491 for (i
= 0; i
< sample
->size
; ++i
) {
492 isl_int_set(T
->row
[i
][0], sample
->el
[i
]);
493 isl_seq_clr(T
->row
[i
] + 1, T
->n_col
- 1);
495 for (i
= 0; i
< T
->n_col
- 1; ++i
) {
496 isl_seq_clr(T
->row
[sample
->size
+ i
], T
->n_col
);
497 isl_int_set_si(T
->row
[sample
->size
+ i
][1 + i
], 1);
499 isl_vec_free(sample
);
501 bset
= isl_basic_set_preimage(bset
, T
);
504 isl_basic_set_free(bset
);
505 isl_vec_free(sample
);
509 /* Given a basic set "bset", return any (possibly non-integer) point
512 static struct isl_vec
*rational_sample(struct isl_basic_set
*bset
)
515 struct isl_vec
*sample
;
520 tab
= isl_tab_from_basic_set(bset
);
521 sample
= isl_tab_get_sample_value(tab
);
524 isl_basic_set_free(bset
);
529 /* Given a linear cone "cone" and a rational point "vec",
530 * construct a polyhedron with shifted copies of the constraints in "cone",
531 * i.e., a polyhedron with "cone" as its recession cone, such that each
532 * point x in this polyhedron is such that the unit box positioned at x
533 * lies entirely inside the affine cone 'vec + cone'.
534 * Any rational point in this polyhedron may therefore be rounded up
535 * to yield an integer point that lies inside said affine cone.
537 * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
538 * point "vec" by v/d.
539 * Let b_i = <a_i, v>. Then the affine cone 'vec + cone' is given
540 * by <a_i, x> - b/d >= 0.
541 * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
542 * We prefer this polyhedron over the actual affine cone because it doesn't
543 * require a scaling of the constraints.
544 * If each of the vertices of the unit cube positioned at x lies inside
545 * this polyhedron, then the whole unit cube at x lies inside the affine cone.
546 * We therefore impose that x' = x + \sum e_i, for any selection of unit
547 * vectors lies inside the polyhedron, i.e.,
549 * <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
551 * The most stringent of these constraints is the one that selects
552 * all negative a_i, so the polyhedron we are looking for has constraints
554 * <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
556 * Note that if cone were known to have only non-negative rays
557 * (which can be accomplished by a unimodular transformation),
558 * then we would only have to check the points x' = x + e_i
559 * and we only have to add the smallest negative a_i (if any)
560 * instead of the sum of all negative a_i.
562 static struct isl_basic_set
*shift_cone(struct isl_basic_set
*cone
,
568 struct isl_basic_set
*shift
= NULL
;
573 isl_assert(cone
->ctx
, cone
->n_eq
== 0, goto error
);
575 total
= isl_basic_set_total_dim(cone
);
577 shift
= isl_basic_set_alloc_dim(isl_basic_set_get_dim(cone
),
580 for (i
= 0; i
< cone
->n_ineq
; ++i
) {
581 k
= isl_basic_set_alloc_inequality(shift
);
584 isl_seq_cpy(shift
->ineq
[k
] + 1, cone
->ineq
[i
] + 1, total
);
585 isl_seq_inner_product(shift
->ineq
[k
] + 1, vec
->el
+ 1, total
,
587 isl_int_cdiv_q(shift
->ineq
[k
][0],
588 shift
->ineq
[k
][0], vec
->el
[0]);
589 isl_int_neg(shift
->ineq
[k
][0], shift
->ineq
[k
][0]);
590 for (j
= 0; j
< total
; ++j
) {
591 if (isl_int_is_nonneg(shift
->ineq
[k
][1 + j
]))
593 isl_int_add(shift
->ineq
[k
][0],
594 shift
->ineq
[k
][0], shift
->ineq
[k
][1 + j
]);
598 isl_basic_set_free(cone
);
601 return isl_basic_set_finalize(shift
);
603 isl_basic_set_free(shift
);
604 isl_basic_set_free(cone
);
609 /* Given a rational point vec in a (transformed) basic set,
610 * such that cone is the recession cone of the original basic set,
611 * "round up" the rational point to an integer point.
613 * We first check if the rational point just happens to be integer.
614 * If not, we transform the cone in the same way as the basic set,
615 * pick a point x in this cone shifted to the rational point such that
616 * the whole unit cube at x is also inside this affine cone.
617 * Then we simply round up the coordinates of x and return the
618 * resulting integer point.
620 static struct isl_vec
*round_up_in_cone(struct isl_vec
*vec
,
621 struct isl_basic_set
*cone
, struct isl_mat
*U
)
625 if (!vec
|| !cone
|| !U
)
628 isl_assert(vec
->ctx
, vec
->size
!= 0, goto error
);
629 if (isl_int_is_one(vec
->el
[0])) {
631 isl_basic_set_free(cone
);
635 total
= isl_basic_set_total_dim(cone
);
636 cone
= isl_basic_set_preimage(cone
, U
);
637 cone
= isl_basic_set_remove_dims(cone
, 0, total
- (vec
->size
- 1));
639 cone
= shift_cone(cone
, vec
);
641 vec
= rational_sample(cone
);
642 vec
= isl_vec_ceil(vec
);
647 isl_basic_set_free(cone
);
651 /* Concatenate two integer vectors, i.e., two vectors with denominator
652 * (stored in element 0) equal to 1.
654 static struct isl_vec
*vec_concat(struct isl_vec
*vec1
, struct isl_vec
*vec2
)
660 isl_assert(vec1
->ctx
, vec1
->size
> 0, goto error
);
661 isl_assert(vec2
->ctx
, vec2
->size
> 0, goto error
);
662 isl_assert(vec1
->ctx
, isl_int_is_one(vec1
->el
[0]), goto error
);
663 isl_assert(vec2
->ctx
, isl_int_is_one(vec2
->el
[0]), goto error
);
665 vec
= isl_vec_alloc(vec1
->ctx
, vec1
->size
+ vec2
->size
- 1);
669 isl_seq_cpy(vec
->el
, vec1
->el
, vec1
->size
);
670 isl_seq_cpy(vec
->el
+ vec1
->size
, vec2
->el
+ 1, vec2
->size
- 1);
682 /* Drop all constraints in bset that involve any of the dimensions
683 * first to first+n-1.
685 static struct isl_basic_set
*drop_constraints_involving
686 (struct isl_basic_set
*bset
, unsigned first
, unsigned n
)
693 bset
= isl_basic_set_cow(bset
);
695 for (i
= bset
->n_ineq
- 1; i
>= 0; --i
) {
696 if (isl_seq_first_non_zero(bset
->ineq
[i
] + 1 + first
, n
) == -1)
698 isl_basic_set_drop_inequality(bset
, i
);
704 /* Give a basic set "bset" with recession cone "cone", compute and
705 * return an integer point in bset, if any.
707 * If the recession cone is full-dimensional, then we know that
708 * bset contains an infinite number of integer points and it is
709 * fairly easy to pick one of them.
710 * If the recession cone is not full-dimensional, then we first
711 * transform bset such that the bounded directions appear as
712 * the first dimensions of the transformed basic set.
713 * We do this by using a unimodular transformation that transforms
714 * the equalities in the recession cone to equalities on the first
717 * The transformed set is then projected onto its bounded dimensions.
718 * Note that to compute this projection, we can simply drop all constraints
719 * involving any of the unbounded dimensions since these constraints
720 * cannot be combined to produce a constraint on the bounded dimensions.
721 * To see this, assume that there is such a combination of constraints
722 * that produces a constraint on the bounded dimensions. This means
723 * that some combination of the unbounded dimensions has both an upper
724 * bound and a lower bound in terms of the bounded dimensions, but then
725 * this combination would be a bounded direction too and would have been
726 * transformed into a bounded dimensions.
728 * We then compute a sample value in the bounded dimensions.
729 * If no such value can be found, then the original set did not contain
730 * any integer points and we are done.
731 * Otherwise, we plug in the value we found in the bounded dimensions,
732 * project out these bounded dimensions and end up with a set with
733 * a full-dimensional recession cone.
734 * A sample point in this set is computed by "rounding up" any
735 * rational point in the set.
737 * The sample points in the bounded and unbounded dimensions are
738 * then combined into a single sample point and transformed back
739 * to the original space.
741 __isl_give isl_vec
*isl_basic_set_sample_with_cone(
742 __isl_take isl_basic_set
*bset
, __isl_take isl_basic_set
*cone
)
746 struct isl_mat
*M
, *U
;
747 struct isl_vec
*sample
;
748 struct isl_vec
*cone_sample
;
750 struct isl_basic_set
*bounded
;
756 total
= isl_basic_set_total_dim(cone
);
757 cone_dim
= total
- cone
->n_eq
;
759 M
= isl_mat_sub_alloc(bset
->ctx
, cone
->eq
, 0, cone
->n_eq
, 1, total
);
760 M
= isl_mat_left_hermite(M
, 0, &U
, NULL
);
765 U
= isl_mat_lin_to_aff(U
);
766 bset
= isl_basic_set_preimage(bset
, isl_mat_copy(U
));
768 bounded
= isl_basic_set_copy(bset
);
769 bounded
= drop_constraints_involving(bounded
, total
- cone_dim
, cone_dim
);
770 bounded
= isl_basic_set_drop_dims(bounded
, total
- cone_dim
, cone_dim
);
771 sample
= sample_bounded(bounded
);
772 if (!sample
|| sample
->size
== 0) {
773 isl_basic_set_free(bset
);
774 isl_basic_set_free(cone
);
778 bset
= plug_in(bset
, isl_vec_copy(sample
));
779 cone_sample
= rational_sample(bset
);
780 cone_sample
= round_up_in_cone(cone_sample
, cone
, isl_mat_copy(U
));
781 sample
= vec_concat(sample
, cone_sample
);
782 sample
= isl_mat_vec_product(U
, sample
);
785 isl_basic_set_free(cone
);
786 isl_basic_set_free(bset
);
790 /* Compute and return a sample point in bset using generalized basis
791 * reduction. We first check if the input set has a non-trivial
792 * recession cone. If so, we perform some extra preprocessing in
793 * sample_with_cone. Otherwise, we directly perform generalized basis
796 static struct isl_vec
*gbr_sample(struct isl_basic_set
*bset
)
799 struct isl_basic_set
*cone
;
801 dim
= isl_basic_set_total_dim(bset
);
803 cone
= isl_basic_set_recession_cone(isl_basic_set_copy(bset
));
805 if (cone
->n_eq
< dim
)
806 return isl_basic_set_sample_with_cone(bset
, cone
);
808 isl_basic_set_free(cone
);
809 return sample_bounded(bset
);
812 static struct isl_vec
*pip_sample(struct isl_basic_set
*bset
)
816 struct isl_vec
*sample
;
818 bset
= isl_basic_set_skew_to_positive_orthant(bset
, &T
);
823 sample
= isl_pip_basic_set_sample(bset
);
825 if (sample
&& sample
->size
!= 0)
826 sample
= isl_mat_vec_product(T
, sample
);
833 static struct isl_vec
*basic_set_sample(struct isl_basic_set
*bset
, int bounded
)
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
, bounded
? isl_basic_set_sample_bounded
863 : isl_basic_set_sample_vec
);
865 return zero_sample(bset
);
867 return interval_sample(bset
);
869 switch (bset
->ctx
->ilp_solver
) {
871 return pip_sample(bset
);
873 return bounded
? sample_bounded(bset
) : gbr_sample(bset
);
875 isl_assert(bset
->ctx
, 0, );
877 isl_basic_set_free(bset
);
881 __isl_give isl_vec
*isl_basic_set_sample_vec(__isl_take isl_basic_set
*bset
)
883 return basic_set_sample(bset
, 0);
886 /* Compute an integer sample in "bset", where the caller guarantees
887 * that "bset" is bounded.
889 struct isl_vec
*isl_basic_set_sample_bounded(struct isl_basic_set
*bset
)
891 return basic_set_sample(bset
, 1);
894 __isl_give isl_basic_set
*isl_basic_set_from_vec(__isl_take isl_vec
*vec
)
898 struct isl_basic_set
*bset
= NULL
;
905 isl_assert(ctx
, vec
->size
!= 0, goto error
);
907 bset
= isl_basic_set_alloc(ctx
, 0, vec
->size
- 1, 0, vec
->size
- 1, 0);
910 dim
= isl_basic_set_n_dim(bset
);
911 for (i
= dim
- 1; i
>= 0; --i
) {
912 k
= isl_basic_set_alloc_equality(bset
);
915 isl_seq_clr(bset
->eq
[k
], 1 + dim
);
916 isl_int_neg(bset
->eq
[k
][0], vec
->el
[1 + i
]);
917 isl_int_set(bset
->eq
[k
][1 + i
], vec
->el
[0]);
923 isl_basic_set_free(bset
);
928 __isl_give isl_basic_map
*isl_basic_map_sample(__isl_take isl_basic_map
*bmap
)
930 struct isl_basic_set
*bset
;
931 struct isl_vec
*sample_vec
;
933 bset
= isl_basic_map_underlying_set(isl_basic_map_copy(bmap
));
934 sample_vec
= isl_basic_set_sample_vec(bset
);
937 if (sample_vec
->size
== 0) {
938 struct isl_basic_map
*sample
;
939 sample
= isl_basic_map_empty_like(bmap
);
940 isl_vec_free(sample_vec
);
941 isl_basic_map_free(bmap
);
944 bset
= isl_basic_set_from_vec(sample_vec
);
945 return isl_basic_map_overlying_set(bset
, bmap
);
947 isl_basic_map_free(bmap
);
951 __isl_give isl_basic_map
*isl_map_sample(__isl_take isl_map
*map
)
954 isl_basic_map
*sample
= NULL
;
959 for (i
= 0; i
< map
->n
; ++i
) {
960 sample
= isl_basic_map_sample(isl_basic_map_copy(map
->p
[i
]));
963 if (!ISL_F_ISSET(sample
, ISL_BASIC_MAP_EMPTY
))
965 isl_basic_map_free(sample
);
968 sample
= isl_basic_map_empty_like_map(map
);
976 __isl_give isl_basic_set
*isl_set_sample(__isl_take isl_set
*set
)
978 return (isl_basic_set
*) isl_map_sample((isl_map
*)set
);