add isl_aff_scale_down_ui
[isl.git] / isl_sample.c
blob9c9fb6d6971de53ec2c7fb377f1960dbf78e98be
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8 */
10 #include <isl_ctx_private.h>
11 #include <isl_map_private.h>
12 #include "isl_sample.h"
13 #include "isl_sample_piplib.h"
14 #include <isl/vec.h>
15 #include <isl/mat.h>
16 #include <isl/seq.h>
17 #include "isl_equalities.h"
18 #include "isl_tab.h"
19 #include "isl_basis_reduction.h"
20 #include <isl_factorization.h>
21 #include <isl_point_private.h>
23 static struct isl_vec *empty_sample(struct isl_basic_set *bset)
25 struct isl_vec *vec;
27 vec = isl_vec_alloc(bset->ctx, 0);
28 isl_basic_set_free(bset);
29 return vec;
32 /* Construct a zero sample of the same dimension as bset.
33 * As a special case, if bset is zero-dimensional, this
34 * function creates a zero-dimensional sample point.
36 static struct isl_vec *zero_sample(struct isl_basic_set *bset)
38 unsigned dim;
39 struct isl_vec *sample;
41 dim = isl_basic_set_total_dim(bset);
42 sample = isl_vec_alloc(bset->ctx, 1 + dim);
43 if (sample) {
44 isl_int_set_si(sample->el[0], 1);
45 isl_seq_clr(sample->el + 1, dim);
47 isl_basic_set_free(bset);
48 return sample;
51 static struct isl_vec *interval_sample(struct isl_basic_set *bset)
53 int i;
54 isl_int t;
55 struct isl_vec *sample;
57 bset = isl_basic_set_simplify(bset);
58 if (!bset)
59 return NULL;
60 if (isl_basic_set_plain_is_empty(bset))
61 return empty_sample(bset);
62 if (bset->n_eq == 0 && bset->n_ineq == 0)
63 return zero_sample(bset);
65 sample = isl_vec_alloc(bset->ctx, 2);
66 if (!sample)
67 goto error;
68 if (!bset)
69 return NULL;
70 isl_int_set_si(sample->block.data[0], 1);
72 if (bset->n_eq > 0) {
73 isl_assert(bset->ctx, bset->n_eq == 1, goto error);
74 isl_assert(bset->ctx, bset->n_ineq == 0, goto error);
75 if (isl_int_is_one(bset->eq[0][1]))
76 isl_int_neg(sample->el[1], bset->eq[0][0]);
77 else {
78 isl_assert(bset->ctx, isl_int_is_negone(bset->eq[0][1]),
79 goto error);
80 isl_int_set(sample->el[1], bset->eq[0][0]);
82 isl_basic_set_free(bset);
83 return sample;
86 isl_int_init(t);
87 if (isl_int_is_one(bset->ineq[0][1]))
88 isl_int_neg(sample->block.data[1], bset->ineq[0][0]);
89 else
90 isl_int_set(sample->block.data[1], bset->ineq[0][0]);
91 for (i = 1; i < bset->n_ineq; ++i) {
92 isl_seq_inner_product(sample->block.data,
93 bset->ineq[i], 2, &t);
94 if (isl_int_is_neg(t))
95 break;
97 isl_int_clear(t);
98 if (i < bset->n_ineq) {
99 isl_vec_free(sample);
100 return empty_sample(bset);
103 isl_basic_set_free(bset);
104 return sample;
105 error:
106 isl_basic_set_free(bset);
107 isl_vec_free(sample);
108 return NULL;
111 static struct isl_mat *independent_bounds(struct isl_basic_set *bset)
113 int i, j, n;
114 struct isl_mat *dirs = NULL;
115 struct isl_mat *bounds = NULL;
116 unsigned dim;
118 if (!bset)
119 return NULL;
121 dim = isl_basic_set_n_dim(bset);
122 bounds = isl_mat_alloc(bset->ctx, 1+dim, 1+dim);
123 if (!bounds)
124 return NULL;
126 isl_int_set_si(bounds->row[0][0], 1);
127 isl_seq_clr(bounds->row[0]+1, dim);
128 bounds->n_row = 1;
130 if (bset->n_ineq == 0)
131 return bounds;
133 dirs = isl_mat_alloc(bset->ctx, dim, dim);
134 if (!dirs) {
135 isl_mat_free(bounds);
136 return NULL;
138 isl_seq_cpy(dirs->row[0], bset->ineq[0]+1, dirs->n_col);
139 isl_seq_cpy(bounds->row[1], bset->ineq[0], bounds->n_col);
140 for (j = 1, n = 1; n < dim && j < bset->n_ineq; ++j) {
141 int pos;
143 isl_seq_cpy(dirs->row[n], bset->ineq[j]+1, dirs->n_col);
145 pos = isl_seq_first_non_zero(dirs->row[n], dirs->n_col);
146 if (pos < 0)
147 continue;
148 for (i = 0; i < n; ++i) {
149 int pos_i;
150 pos_i = isl_seq_first_non_zero(dirs->row[i], dirs->n_col);
151 if (pos_i < pos)
152 continue;
153 if (pos_i > pos)
154 break;
155 isl_seq_elim(dirs->row[n], dirs->row[i], pos,
156 dirs->n_col, NULL);
157 pos = isl_seq_first_non_zero(dirs->row[n], dirs->n_col);
158 if (pos < 0)
159 break;
161 if (pos < 0)
162 continue;
163 if (i < n) {
164 int k;
165 isl_int *t = dirs->row[n];
166 for (k = n; k > i; --k)
167 dirs->row[k] = dirs->row[k-1];
168 dirs->row[i] = t;
170 ++n;
171 isl_seq_cpy(bounds->row[n], bset->ineq[j], bounds->n_col);
173 isl_mat_free(dirs);
174 bounds->n_row = 1+n;
175 return bounds;
178 static void swap_inequality(struct isl_basic_set *bset, int a, int b)
180 isl_int *t = bset->ineq[a];
181 bset->ineq[a] = bset->ineq[b];
182 bset->ineq[b] = t;
185 /* Skew into positive orthant and project out lineality space.
187 * We perform a unimodular transformation that turns a selected
188 * maximal set of linearly independent bounds into constraints
189 * on the first dimensions that impose that these first dimensions
190 * are non-negative. In particular, the constraint matrix is lower
191 * triangular with positive entries on the diagonal and negative
192 * entries below.
193 * If "bset" has a lineality space then these constraints (and therefore
194 * all constraints in bset) only involve the first dimensions.
195 * The remaining dimensions then do not appear in any constraints and
196 * we can select any value for them, say zero. We therefore project
197 * out this final dimensions and plug in the value zero later. This
198 * is accomplished by simply dropping the final columns of
199 * the unimodular transformation.
201 static struct isl_basic_set *isl_basic_set_skew_to_positive_orthant(
202 struct isl_basic_set *bset, struct isl_mat **T)
204 struct isl_mat *U = NULL;
205 struct isl_mat *bounds = NULL;
206 int i, j;
207 unsigned old_dim, new_dim;
209 *T = NULL;
210 if (!bset)
211 return NULL;
213 isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0, goto error);
214 isl_assert(bset->ctx, bset->n_div == 0, goto error);
215 isl_assert(bset->ctx, bset->n_eq == 0, goto error);
217 old_dim = isl_basic_set_n_dim(bset);
218 /* Try to move (multiples of) unit rows up. */
219 for (i = 0, j = 0; i < bset->n_ineq; ++i) {
220 int pos = isl_seq_first_non_zero(bset->ineq[i]+1, old_dim);
221 if (pos < 0)
222 continue;
223 if (isl_seq_first_non_zero(bset->ineq[i]+1+pos+1,
224 old_dim-pos-1) >= 0)
225 continue;
226 if (i != j)
227 swap_inequality(bset, i, j);
228 ++j;
230 bounds = independent_bounds(bset);
231 if (!bounds)
232 goto error;
233 new_dim = bounds->n_row - 1;
234 bounds = isl_mat_left_hermite(bounds, 1, &U, NULL);
235 if (!bounds)
236 goto error;
237 U = isl_mat_drop_cols(U, 1 + new_dim, old_dim - new_dim);
238 bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
239 if (!bset)
240 goto error;
241 *T = U;
242 isl_mat_free(bounds);
243 return bset;
244 error:
245 isl_mat_free(bounds);
246 isl_mat_free(U);
247 isl_basic_set_free(bset);
248 return NULL;
251 /* Find a sample integer point, if any, in bset, which is known
252 * to have equalities. If bset contains no integer points, then
253 * return a zero-length vector.
254 * We simply remove the known equalities, compute a sample
255 * in the resulting bset, using the specified recurse function,
256 * and then transform the sample back to the original space.
258 static struct isl_vec *sample_eq(struct isl_basic_set *bset,
259 struct isl_vec *(*recurse)(struct isl_basic_set *))
261 struct isl_mat *T;
262 struct isl_vec *sample;
264 if (!bset)
265 return NULL;
267 bset = isl_basic_set_remove_equalities(bset, &T, NULL);
268 sample = recurse(bset);
269 if (!sample || sample->size == 0)
270 isl_mat_free(T);
271 else
272 sample = isl_mat_vec_product(T, sample);
273 return sample;
276 /* Return a matrix containing the equalities of the tableau
277 * in constraint form. The tableau is assumed to have
278 * an associated bset that has been kept up-to-date.
280 static struct isl_mat *tab_equalities(struct isl_tab *tab)
282 int i, j;
283 int n_eq;
284 struct isl_mat *eq;
285 struct isl_basic_set *bset;
287 if (!tab)
288 return NULL;
290 bset = isl_tab_peek_bset(tab);
291 isl_assert(tab->mat->ctx, bset, return NULL);
293 n_eq = tab->n_var - tab->n_col + tab->n_dead;
294 if (tab->empty || n_eq == 0)
295 return isl_mat_alloc(tab->mat->ctx, 0, tab->n_var);
296 if (n_eq == tab->n_var)
297 return isl_mat_identity(tab->mat->ctx, tab->n_var);
299 eq = isl_mat_alloc(tab->mat->ctx, n_eq, tab->n_var);
300 if (!eq)
301 return NULL;
302 for (i = 0, j = 0; i < tab->n_con; ++i) {
303 if (tab->con[i].is_row)
304 continue;
305 if (tab->con[i].index >= 0 && tab->con[i].index >= tab->n_dead)
306 continue;
307 if (i < bset->n_eq)
308 isl_seq_cpy(eq->row[j], bset->eq[i] + 1, tab->n_var);
309 else
310 isl_seq_cpy(eq->row[j],
311 bset->ineq[i - bset->n_eq] + 1, tab->n_var);
312 ++j;
314 isl_assert(bset->ctx, j == n_eq, goto error);
315 return eq;
316 error:
317 isl_mat_free(eq);
318 return NULL;
321 /* Compute and return an initial basis for the bounded tableau "tab".
323 * If the tableau is either full-dimensional or zero-dimensional,
324 * the we simply return an identity matrix.
325 * Otherwise, we construct a basis whose first directions correspond
326 * to equalities.
328 static struct isl_mat *initial_basis(struct isl_tab *tab)
330 int n_eq;
331 struct isl_mat *eq;
332 struct isl_mat *Q;
334 tab->n_unbounded = 0;
335 tab->n_zero = n_eq = tab->n_var - tab->n_col + tab->n_dead;
336 if (tab->empty || n_eq == 0 || n_eq == tab->n_var)
337 return isl_mat_identity(tab->mat->ctx, 1 + tab->n_var);
339 eq = tab_equalities(tab);
340 eq = isl_mat_left_hermite(eq, 0, NULL, &Q);
341 if (!eq)
342 return NULL;
343 isl_mat_free(eq);
345 Q = isl_mat_lin_to_aff(Q);
346 return Q;
349 /* Given a tableau representing a set, find and return
350 * an integer point in the set, if there is any.
352 * We perform a depth first search
353 * for an integer point, by scanning all possible values in the range
354 * attained by a basis vector, where an initial basis may have been set
355 * by the calling function. Otherwise an initial basis that exploits
356 * the equalities in the tableau is created.
357 * tab->n_zero is currently ignored and is clobbered by this function.
359 * The tableau is allowed to have unbounded direction, but then
360 * the calling function needs to set an initial basis, with the
361 * unbounded directions last and with tab->n_unbounded set
362 * to the number of unbounded directions.
363 * Furthermore, the calling functions needs to add shifted copies
364 * of all constraints involving unbounded directions to ensure
365 * that any feasible rational value in these directions can be rounded
366 * up to yield a feasible integer value.
367 * In particular, let B define the given basis x' = B x
368 * and let T be the inverse of B, i.e., X = T x'.
369 * Let a x + c >= 0 be a constraint of the set represented by the tableau,
370 * or a T x' + c >= 0 in terms of the given basis. Assume that
371 * the bounded directions have an integer value, then we can safely
372 * round up the values for the unbounded directions if we make sure
373 * that x' not only satisfies the original constraint, but also
374 * the constraint "a T x' + c + s >= 0" with s the sum of all
375 * negative values in the last n_unbounded entries of "a T".
376 * The calling function therefore needs to add the constraint
377 * a x + c + s >= 0. The current function then scans the first
378 * directions for an integer value and once those have been found,
379 * it can compute "T ceil(B x)" to yield an integer point in the set.
380 * Note that during the search, the first rows of B may be changed
381 * by a basis reduction, but the last n_unbounded rows of B remain
382 * unaltered and are also not mixed into the first rows.
384 * The search is implemented iteratively. "level" identifies the current
385 * basis vector. "init" is true if we want the first value at the current
386 * level and false if we want the next value.
388 * The initial basis is the identity matrix. If the range in some direction
389 * contains more than one integer value, we perform basis reduction based
390 * on the value of ctx->opt->gbr
391 * - ISL_GBR_NEVER: never perform basis reduction
392 * - ISL_GBR_ONCE: only perform basis reduction the first
393 * time such a range is encountered
394 * - ISL_GBR_ALWAYS: always perform basis reduction when
395 * such a range is encountered
397 * When ctx->opt->gbr is set to ISL_GBR_ALWAYS, then we allow the basis
398 * reduction computation to return early. That is, as soon as it
399 * finds a reasonable first direction.
401 struct isl_vec *isl_tab_sample(struct isl_tab *tab)
403 unsigned dim;
404 unsigned gbr;
405 struct isl_ctx *ctx;
406 struct isl_vec *sample;
407 struct isl_vec *min;
408 struct isl_vec *max;
409 enum isl_lp_result res;
410 int level;
411 int init;
412 int reduced;
413 struct isl_tab_undo **snap;
415 if (!tab)
416 return NULL;
417 if (tab->empty)
418 return isl_vec_alloc(tab->mat->ctx, 0);
420 if (!tab->basis)
421 tab->basis = initial_basis(tab);
422 if (!tab->basis)
423 return NULL;
424 isl_assert(tab->mat->ctx, tab->basis->n_row == tab->n_var + 1,
425 return NULL);
426 isl_assert(tab->mat->ctx, tab->basis->n_col == tab->n_var + 1,
427 return NULL);
429 ctx = tab->mat->ctx;
430 dim = tab->n_var;
431 gbr = ctx->opt->gbr;
433 if (tab->n_unbounded == tab->n_var) {
434 sample = isl_tab_get_sample_value(tab);
435 sample = isl_mat_vec_product(isl_mat_copy(tab->basis), sample);
436 sample = isl_vec_ceil(sample);
437 sample = isl_mat_vec_inverse_product(isl_mat_copy(tab->basis),
438 sample);
439 return sample;
442 if (isl_tab_extend_cons(tab, dim + 1) < 0)
443 return NULL;
445 min = isl_vec_alloc(ctx, dim);
446 max = isl_vec_alloc(ctx, dim);
447 snap = isl_alloc_array(ctx, struct isl_tab_undo *, dim);
449 if (!min || !max || !snap)
450 goto error;
452 level = 0;
453 init = 1;
454 reduced = 0;
456 while (level >= 0) {
457 int empty = 0;
458 if (init) {
459 res = isl_tab_min(tab, tab->basis->row[1 + level],
460 ctx->one, &min->el[level], NULL, 0);
461 if (res == isl_lp_empty)
462 empty = 1;
463 isl_assert(ctx, res != isl_lp_unbounded, goto error);
464 if (res == isl_lp_error)
465 goto error;
466 if (!empty && isl_tab_sample_is_integer(tab))
467 break;
468 isl_seq_neg(tab->basis->row[1 + level] + 1,
469 tab->basis->row[1 + level] + 1, dim);
470 res = isl_tab_min(tab, tab->basis->row[1 + level],
471 ctx->one, &max->el[level], NULL, 0);
472 isl_seq_neg(tab->basis->row[1 + level] + 1,
473 tab->basis->row[1 + level] + 1, dim);
474 isl_int_neg(max->el[level], max->el[level]);
475 if (res == isl_lp_empty)
476 empty = 1;
477 isl_assert(ctx, res != isl_lp_unbounded, goto error);
478 if (res == isl_lp_error)
479 goto error;
480 if (!empty && isl_tab_sample_is_integer(tab))
481 break;
482 if (!empty && !reduced &&
483 ctx->opt->gbr != ISL_GBR_NEVER &&
484 isl_int_lt(min->el[level], max->el[level])) {
485 unsigned gbr_only_first;
486 if (ctx->opt->gbr == ISL_GBR_ONCE)
487 ctx->opt->gbr = ISL_GBR_NEVER;
488 tab->n_zero = level;
489 gbr_only_first = ctx->opt->gbr_only_first;
490 ctx->opt->gbr_only_first =
491 ctx->opt->gbr == ISL_GBR_ALWAYS;
492 tab = isl_tab_compute_reduced_basis(tab);
493 ctx->opt->gbr_only_first = gbr_only_first;
494 if (!tab || !tab->basis)
495 goto error;
496 reduced = 1;
497 continue;
499 reduced = 0;
500 snap[level] = isl_tab_snap(tab);
501 } else
502 isl_int_add_ui(min->el[level], min->el[level], 1);
504 if (empty || isl_int_gt(min->el[level], max->el[level])) {
505 level--;
506 init = 0;
507 if (level >= 0)
508 if (isl_tab_rollback(tab, snap[level]) < 0)
509 goto error;
510 continue;
512 isl_int_neg(tab->basis->row[1 + level][0], min->el[level]);
513 if (isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]) < 0)
514 goto error;
515 isl_int_set_si(tab->basis->row[1 + level][0], 0);
516 if (level + tab->n_unbounded < dim - 1) {
517 ++level;
518 init = 1;
519 continue;
521 break;
524 if (level >= 0) {
525 sample = isl_tab_get_sample_value(tab);
526 if (!sample)
527 goto error;
528 if (tab->n_unbounded && !isl_int_is_one(sample->el[0])) {
529 sample = isl_mat_vec_product(isl_mat_copy(tab->basis),
530 sample);
531 sample = isl_vec_ceil(sample);
532 sample = isl_mat_vec_inverse_product(
533 isl_mat_copy(tab->basis), sample);
535 } else
536 sample = isl_vec_alloc(ctx, 0);
538 ctx->opt->gbr = gbr;
539 isl_vec_free(min);
540 isl_vec_free(max);
541 free(snap);
542 return sample;
543 error:
544 ctx->opt->gbr = gbr;
545 isl_vec_free(min);
546 isl_vec_free(max);
547 free(snap);
548 return NULL;
551 static struct isl_vec *sample_bounded(struct isl_basic_set *bset);
553 /* Compute a sample point of the given basic set, based on the given,
554 * non-trivial factorization.
556 static __isl_give isl_vec *factored_sample(__isl_take isl_basic_set *bset,
557 __isl_take isl_factorizer *f)
559 int i, n;
560 isl_vec *sample = NULL;
561 isl_ctx *ctx;
562 unsigned nparam;
563 unsigned nvar;
565 ctx = isl_basic_set_get_ctx(bset);
566 if (!ctx)
567 goto error;
569 nparam = isl_basic_set_dim(bset, isl_dim_param);
570 nvar = isl_basic_set_dim(bset, isl_dim_set);
572 sample = isl_vec_alloc(ctx, 1 + isl_basic_set_total_dim(bset));
573 if (!sample)
574 goto error;
575 isl_int_set_si(sample->el[0], 1);
577 bset = isl_morph_basic_set(isl_morph_copy(f->morph), bset);
579 for (i = 0, n = 0; i < f->n_group; ++i) {
580 isl_basic_set *bset_i;
581 isl_vec *sample_i;
583 bset_i = isl_basic_set_copy(bset);
584 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
585 nparam + n + f->len[i], nvar - n - f->len[i]);
586 bset_i = isl_basic_set_drop_constraints_involving(bset_i,
587 nparam, n);
588 bset_i = isl_basic_set_drop(bset_i, isl_dim_set,
589 n + f->len[i], nvar - n - f->len[i]);
590 bset_i = isl_basic_set_drop(bset_i, isl_dim_set, 0, n);
592 sample_i = sample_bounded(bset_i);
593 if (!sample_i)
594 goto error;
595 if (sample_i->size == 0) {
596 isl_basic_set_free(bset);
597 isl_factorizer_free(f);
598 isl_vec_free(sample);
599 return sample_i;
601 isl_seq_cpy(sample->el + 1 + nparam + n,
602 sample_i->el + 1, f->len[i]);
603 isl_vec_free(sample_i);
605 n += f->len[i];
608 f->morph = isl_morph_inverse(f->morph);
609 sample = isl_morph_vec(isl_morph_copy(f->morph), sample);
611 isl_basic_set_free(bset);
612 isl_factorizer_free(f);
613 return sample;
614 error:
615 isl_basic_set_free(bset);
616 isl_factorizer_free(f);
617 isl_vec_free(sample);
618 return NULL;
621 /* Given a basic set that is known to be bounded, find and return
622 * an integer point in the basic set, if there is any.
624 * After handling some trivial cases, we construct a tableau
625 * and then use isl_tab_sample to find a sample, passing it
626 * the identity matrix as initial basis.
628 static struct isl_vec *sample_bounded(struct isl_basic_set *bset)
630 unsigned dim;
631 struct isl_ctx *ctx;
632 struct isl_vec *sample;
633 struct isl_tab *tab = NULL;
634 isl_factorizer *f;
636 if (!bset)
637 return NULL;
639 if (isl_basic_set_plain_is_empty(bset))
640 return empty_sample(bset);
642 dim = isl_basic_set_total_dim(bset);
643 if (dim == 0)
644 return zero_sample(bset);
645 if (dim == 1)
646 return interval_sample(bset);
647 if (bset->n_eq > 0)
648 return sample_eq(bset, sample_bounded);
650 f = isl_basic_set_factorizer(bset);
651 if (!f)
652 goto error;
653 if (f->n_group != 0)
654 return factored_sample(bset, f);
655 isl_factorizer_free(f);
657 ctx = bset->ctx;
659 tab = isl_tab_from_basic_set(bset);
660 if (tab && tab->empty) {
661 isl_tab_free(tab);
662 ISL_F_SET(bset, ISL_BASIC_SET_EMPTY);
663 sample = isl_vec_alloc(bset->ctx, 0);
664 isl_basic_set_free(bset);
665 return sample;
668 if (isl_tab_track_bset(tab, isl_basic_set_copy(bset)) < 0)
669 goto error;
670 if (!ISL_F_ISSET(bset, ISL_BASIC_SET_NO_IMPLICIT))
671 if (isl_tab_detect_implicit_equalities(tab) < 0)
672 goto error;
674 sample = isl_tab_sample(tab);
675 if (!sample)
676 goto error;
678 if (sample->size > 0) {
679 isl_vec_free(bset->sample);
680 bset->sample = isl_vec_copy(sample);
683 isl_basic_set_free(bset);
684 isl_tab_free(tab);
685 return sample;
686 error:
687 isl_basic_set_free(bset);
688 isl_tab_free(tab);
689 return NULL;
692 /* Given a basic set "bset" and a value "sample" for the first coordinates
693 * of bset, plug in these values and drop the corresponding coordinates.
695 * We do this by computing the preimage of the transformation
697 * [ 1 0 ]
698 * x = [ s 0 ] x'
699 * [ 0 I ]
701 * where [1 s] is the sample value and I is the identity matrix of the
702 * appropriate dimension.
704 static struct isl_basic_set *plug_in(struct isl_basic_set *bset,
705 struct isl_vec *sample)
707 int i;
708 unsigned total;
709 struct isl_mat *T;
711 if (!bset || !sample)
712 goto error;
714 total = isl_basic_set_total_dim(bset);
715 T = isl_mat_alloc(bset->ctx, 1 + total, 1 + total - (sample->size - 1));
716 if (!T)
717 goto error;
719 for (i = 0; i < sample->size; ++i) {
720 isl_int_set(T->row[i][0], sample->el[i]);
721 isl_seq_clr(T->row[i] + 1, T->n_col - 1);
723 for (i = 0; i < T->n_col - 1; ++i) {
724 isl_seq_clr(T->row[sample->size + i], T->n_col);
725 isl_int_set_si(T->row[sample->size + i][1 + i], 1);
727 isl_vec_free(sample);
729 bset = isl_basic_set_preimage(bset, T);
730 return bset;
731 error:
732 isl_basic_set_free(bset);
733 isl_vec_free(sample);
734 return NULL;
737 /* Given a basic set "bset", return any (possibly non-integer) point
738 * in the basic set.
740 static struct isl_vec *rational_sample(struct isl_basic_set *bset)
742 struct isl_tab *tab;
743 struct isl_vec *sample;
745 if (!bset)
746 return NULL;
748 tab = isl_tab_from_basic_set(bset);
749 sample = isl_tab_get_sample_value(tab);
750 isl_tab_free(tab);
752 isl_basic_set_free(bset);
754 return sample;
757 /* Given a linear cone "cone" and a rational point "vec",
758 * construct a polyhedron with shifted copies of the constraints in "cone",
759 * i.e., a polyhedron with "cone" as its recession cone, such that each
760 * point x in this polyhedron is such that the unit box positioned at x
761 * lies entirely inside the affine cone 'vec + cone'.
762 * Any rational point in this polyhedron may therefore be rounded up
763 * to yield an integer point that lies inside said affine cone.
765 * Denote the constraints of cone by "<a_i, x> >= 0" and the rational
766 * point "vec" by v/d.
767 * Let b_i = <a_i, v>. Then the affine cone 'vec + cone' is given
768 * by <a_i, x> - b/d >= 0.
769 * The polyhedron <a_i, x> - ceil{b/d} >= 0 is a subset of this affine cone.
770 * We prefer this polyhedron over the actual affine cone because it doesn't
771 * require a scaling of the constraints.
772 * If each of the vertices of the unit cube positioned at x lies inside
773 * this polyhedron, then the whole unit cube at x lies inside the affine cone.
774 * We therefore impose that x' = x + \sum e_i, for any selection of unit
775 * vectors lies inside the polyhedron, i.e.,
777 * <a_i, x'> - ceil{b/d} = <a_i, x> + sum a_i - ceil{b/d} >= 0
779 * The most stringent of these constraints is the one that selects
780 * all negative a_i, so the polyhedron we are looking for has constraints
782 * <a_i, x> + sum_{a_i < 0} a_i - ceil{b/d} >= 0
784 * Note that if cone were known to have only non-negative rays
785 * (which can be accomplished by a unimodular transformation),
786 * then we would only have to check the points x' = x + e_i
787 * and we only have to add the smallest negative a_i (if any)
788 * instead of the sum of all negative a_i.
790 static struct isl_basic_set *shift_cone(struct isl_basic_set *cone,
791 struct isl_vec *vec)
793 int i, j, k;
794 unsigned total;
796 struct isl_basic_set *shift = NULL;
798 if (!cone || !vec)
799 goto error;
801 isl_assert(cone->ctx, cone->n_eq == 0, goto error);
803 total = isl_basic_set_total_dim(cone);
805 shift = isl_basic_set_alloc_dim(isl_basic_set_get_dim(cone),
806 0, 0, cone->n_ineq);
808 for (i = 0; i < cone->n_ineq; ++i) {
809 k = isl_basic_set_alloc_inequality(shift);
810 if (k < 0)
811 goto error;
812 isl_seq_cpy(shift->ineq[k] + 1, cone->ineq[i] + 1, total);
813 isl_seq_inner_product(shift->ineq[k] + 1, vec->el + 1, total,
814 &shift->ineq[k][0]);
815 isl_int_cdiv_q(shift->ineq[k][0],
816 shift->ineq[k][0], vec->el[0]);
817 isl_int_neg(shift->ineq[k][0], shift->ineq[k][0]);
818 for (j = 0; j < total; ++j) {
819 if (isl_int_is_nonneg(shift->ineq[k][1 + j]))
820 continue;
821 isl_int_add(shift->ineq[k][0],
822 shift->ineq[k][0], shift->ineq[k][1 + j]);
826 isl_basic_set_free(cone);
827 isl_vec_free(vec);
829 return isl_basic_set_finalize(shift);
830 error:
831 isl_basic_set_free(shift);
832 isl_basic_set_free(cone);
833 isl_vec_free(vec);
834 return NULL;
837 /* Given a rational point vec in a (transformed) basic set,
838 * such that cone is the recession cone of the original basic set,
839 * "round up" the rational point to an integer point.
841 * We first check if the rational point just happens to be integer.
842 * If not, we transform the cone in the same way as the basic set,
843 * pick a point x in this cone shifted to the rational point such that
844 * the whole unit cube at x is also inside this affine cone.
845 * Then we simply round up the coordinates of x and return the
846 * resulting integer point.
848 static struct isl_vec *round_up_in_cone(struct isl_vec *vec,
849 struct isl_basic_set *cone, struct isl_mat *U)
851 unsigned total;
853 if (!vec || !cone || !U)
854 goto error;
856 isl_assert(vec->ctx, vec->size != 0, goto error);
857 if (isl_int_is_one(vec->el[0])) {
858 isl_mat_free(U);
859 isl_basic_set_free(cone);
860 return vec;
863 total = isl_basic_set_total_dim(cone);
864 cone = isl_basic_set_preimage(cone, U);
865 cone = isl_basic_set_remove_dims(cone, isl_dim_set,
866 0, total - (vec->size - 1));
868 cone = shift_cone(cone, vec);
870 vec = rational_sample(cone);
871 vec = isl_vec_ceil(vec);
872 return vec;
873 error:
874 isl_mat_free(U);
875 isl_vec_free(vec);
876 isl_basic_set_free(cone);
877 return NULL;
880 /* Concatenate two integer vectors, i.e., two vectors with denominator
881 * (stored in element 0) equal to 1.
883 static struct isl_vec *vec_concat(struct isl_vec *vec1, struct isl_vec *vec2)
885 struct isl_vec *vec;
887 if (!vec1 || !vec2)
888 goto error;
889 isl_assert(vec1->ctx, vec1->size > 0, goto error);
890 isl_assert(vec2->ctx, vec2->size > 0, goto error);
891 isl_assert(vec1->ctx, isl_int_is_one(vec1->el[0]), goto error);
892 isl_assert(vec2->ctx, isl_int_is_one(vec2->el[0]), goto error);
894 vec = isl_vec_alloc(vec1->ctx, vec1->size + vec2->size - 1);
895 if (!vec)
896 goto error;
898 isl_seq_cpy(vec->el, vec1->el, vec1->size);
899 isl_seq_cpy(vec->el + vec1->size, vec2->el + 1, vec2->size - 1);
901 isl_vec_free(vec1);
902 isl_vec_free(vec2);
904 return vec;
905 error:
906 isl_vec_free(vec1);
907 isl_vec_free(vec2);
908 return NULL;
911 /* Give a basic set "bset" with recession cone "cone", compute and
912 * return an integer point in bset, if any.
914 * If the recession cone is full-dimensional, then we know that
915 * bset contains an infinite number of integer points and it is
916 * fairly easy to pick one of them.
917 * If the recession cone is not full-dimensional, then we first
918 * transform bset such that the bounded directions appear as
919 * the first dimensions of the transformed basic set.
920 * We do this by using a unimodular transformation that transforms
921 * the equalities in the recession cone to equalities on the first
922 * dimensions.
924 * The transformed set is then projected onto its bounded dimensions.
925 * Note that to compute this projection, we can simply drop all constraints
926 * involving any of the unbounded dimensions since these constraints
927 * cannot be combined to produce a constraint on the bounded dimensions.
928 * To see this, assume that there is such a combination of constraints
929 * that produces a constraint on the bounded dimensions. This means
930 * that some combination of the unbounded dimensions has both an upper
931 * bound and a lower bound in terms of the bounded dimensions, but then
932 * this combination would be a bounded direction too and would have been
933 * transformed into a bounded dimensions.
935 * We then compute a sample value in the bounded dimensions.
936 * If no such value can be found, then the original set did not contain
937 * any integer points and we are done.
938 * Otherwise, we plug in the value we found in the bounded dimensions,
939 * project out these bounded dimensions and end up with a set with
940 * a full-dimensional recession cone.
941 * A sample point in this set is computed by "rounding up" any
942 * rational point in the set.
944 * The sample points in the bounded and unbounded dimensions are
945 * then combined into a single sample point and transformed back
946 * to the original space.
948 __isl_give isl_vec *isl_basic_set_sample_with_cone(
949 __isl_take isl_basic_set *bset, __isl_take isl_basic_set *cone)
951 unsigned total;
952 unsigned cone_dim;
953 struct isl_mat *M, *U;
954 struct isl_vec *sample;
955 struct isl_vec *cone_sample;
956 struct isl_ctx *ctx;
957 struct isl_basic_set *bounded;
959 if (!bset || !cone)
960 goto error;
962 ctx = bset->ctx;
963 total = isl_basic_set_total_dim(cone);
964 cone_dim = total - cone->n_eq;
966 M = isl_mat_sub_alloc6(bset->ctx, cone->eq, 0, cone->n_eq, 1, total);
967 M = isl_mat_left_hermite(M, 0, &U, NULL);
968 if (!M)
969 goto error;
970 isl_mat_free(M);
972 U = isl_mat_lin_to_aff(U);
973 bset = isl_basic_set_preimage(bset, isl_mat_copy(U));
975 bounded = isl_basic_set_copy(bset);
976 bounded = isl_basic_set_drop_constraints_involving(bounded,
977 total - cone_dim, cone_dim);
978 bounded = isl_basic_set_drop_dims(bounded, total - cone_dim, cone_dim);
979 sample = sample_bounded(bounded);
980 if (!sample || sample->size == 0) {
981 isl_basic_set_free(bset);
982 isl_basic_set_free(cone);
983 isl_mat_free(U);
984 return sample;
986 bset = plug_in(bset, isl_vec_copy(sample));
987 cone_sample = rational_sample(bset);
988 cone_sample = round_up_in_cone(cone_sample, cone, isl_mat_copy(U));
989 sample = vec_concat(sample, cone_sample);
990 sample = isl_mat_vec_product(U, sample);
991 return sample;
992 error:
993 isl_basic_set_free(cone);
994 isl_basic_set_free(bset);
995 return NULL;
998 static void vec_sum_of_neg(struct isl_vec *v, isl_int *s)
1000 int i;
1002 isl_int_set_si(*s, 0);
1004 for (i = 0; i < v->size; ++i)
1005 if (isl_int_is_neg(v->el[i]))
1006 isl_int_add(*s, *s, v->el[i]);
1009 /* Given a tableau "tab", a tableau "tab_cone" that corresponds
1010 * to the recession cone and the inverse of a new basis U = inv(B),
1011 * with the unbounded directions in B last,
1012 * add constraints to "tab" that ensure any rational value
1013 * in the unbounded directions can be rounded up to an integer value.
1015 * The new basis is given by x' = B x, i.e., x = U x'.
1016 * For any rational value of the last tab->n_unbounded coordinates
1017 * in the update tableau, the value that is obtained by rounding
1018 * up this value should be contained in the original tableau.
1019 * For any constraint "a x + c >= 0", we therefore need to add
1020 * a constraint "a x + c + s >= 0", with s the sum of all negative
1021 * entries in the last elements of "a U".
1023 * Since we are not interested in the first entries of any of the "a U",
1024 * we first drop the columns of U that correpond to bounded directions.
1026 static int tab_shift_cone(struct isl_tab *tab,
1027 struct isl_tab *tab_cone, struct isl_mat *U)
1029 int i;
1030 isl_int v;
1031 struct isl_basic_set *bset = NULL;
1033 if (tab && tab->n_unbounded == 0) {
1034 isl_mat_free(U);
1035 return 0;
1037 isl_int_init(v);
1038 if (!tab || !tab_cone || !U)
1039 goto error;
1040 bset = isl_tab_peek_bset(tab_cone);
1041 U = isl_mat_drop_cols(U, 0, tab->n_var - tab->n_unbounded);
1042 for (i = 0; i < bset->n_ineq; ++i) {
1043 int ok;
1044 struct isl_vec *row = NULL;
1045 if (isl_tab_is_equality(tab_cone, tab_cone->n_eq + i))
1046 continue;
1047 row = isl_vec_alloc(bset->ctx, tab_cone->n_var);
1048 if (!row)
1049 goto error;
1050 isl_seq_cpy(row->el, bset->ineq[i] + 1, tab_cone->n_var);
1051 row = isl_vec_mat_product(row, isl_mat_copy(U));
1052 if (!row)
1053 goto error;
1054 vec_sum_of_neg(row, &v);
1055 isl_vec_free(row);
1056 if (isl_int_is_zero(v))
1057 continue;
1058 tab = isl_tab_extend(tab, 1);
1059 isl_int_add(bset->ineq[i][0], bset->ineq[i][0], v);
1060 ok = isl_tab_add_ineq(tab, bset->ineq[i]) >= 0;
1061 isl_int_sub(bset->ineq[i][0], bset->ineq[i][0], v);
1062 if (!ok)
1063 goto error;
1066 isl_mat_free(U);
1067 isl_int_clear(v);
1068 return 0;
1069 error:
1070 isl_mat_free(U);
1071 isl_int_clear(v);
1072 return -1;
1075 /* Compute and return an initial basis for the possibly
1076 * unbounded tableau "tab". "tab_cone" is a tableau
1077 * for the corresponding recession cone.
1078 * Additionally, add constraints to "tab" that ensure
1079 * that any rational value for the unbounded directions
1080 * can be rounded up to an integer value.
1082 * If the tableau is bounded, i.e., if the recession cone
1083 * is zero-dimensional, then we just use inital_basis.
1084 * Otherwise, we construct a basis whose first directions
1085 * correspond to equalities, followed by bounded directions,
1086 * i.e., equalities in the recession cone.
1087 * The remaining directions are then unbounded.
1089 int isl_tab_set_initial_basis_with_cone(struct isl_tab *tab,
1090 struct isl_tab *tab_cone)
1092 struct isl_mat *eq;
1093 struct isl_mat *cone_eq;
1094 struct isl_mat *U, *Q;
1096 if (!tab || !tab_cone)
1097 return -1;
1099 if (tab_cone->n_col == tab_cone->n_dead) {
1100 tab->basis = initial_basis(tab);
1101 return tab->basis ? 0 : -1;
1104 eq = tab_equalities(tab);
1105 if (!eq)
1106 return -1;
1107 tab->n_zero = eq->n_row;
1108 cone_eq = tab_equalities(tab_cone);
1109 eq = isl_mat_concat(eq, cone_eq);
1110 if (!eq)
1111 return -1;
1112 tab->n_unbounded = tab->n_var - (eq->n_row - tab->n_zero);
1113 eq = isl_mat_left_hermite(eq, 0, &U, &Q);
1114 if (!eq)
1115 return -1;
1116 isl_mat_free(eq);
1117 tab->basis = isl_mat_lin_to_aff(Q);
1118 if (tab_shift_cone(tab, tab_cone, U) < 0)
1119 return -1;
1120 if (!tab->basis)
1121 return -1;
1122 return 0;
1125 /* Compute and return a sample point in bset using generalized basis
1126 * reduction. We first check if the input set has a non-trivial
1127 * recession cone. If so, we perform some extra preprocessing in
1128 * sample_with_cone. Otherwise, we directly perform generalized basis
1129 * reduction.
1131 static struct isl_vec *gbr_sample(struct isl_basic_set *bset)
1133 unsigned dim;
1134 struct isl_basic_set *cone;
1136 dim = isl_basic_set_total_dim(bset);
1138 cone = isl_basic_set_recession_cone(isl_basic_set_copy(bset));
1139 if (!cone)
1140 goto error;
1142 if (cone->n_eq < dim)
1143 return isl_basic_set_sample_with_cone(bset, cone);
1145 isl_basic_set_free(cone);
1146 return sample_bounded(bset);
1147 error:
1148 isl_basic_set_free(bset);
1149 return NULL;
1152 static struct isl_vec *pip_sample(struct isl_basic_set *bset)
1154 struct isl_mat *T;
1155 struct isl_ctx *ctx;
1156 struct isl_vec *sample;
1158 bset = isl_basic_set_skew_to_positive_orthant(bset, &T);
1159 if (!bset)
1160 return NULL;
1162 ctx = bset->ctx;
1163 sample = isl_pip_basic_set_sample(bset);
1165 if (sample && sample->size != 0)
1166 sample = isl_mat_vec_product(T, sample);
1167 else
1168 isl_mat_free(T);
1170 return sample;
1173 static struct isl_vec *basic_set_sample(struct isl_basic_set *bset, int bounded)
1175 struct isl_ctx *ctx;
1176 unsigned dim;
1177 if (!bset)
1178 return NULL;
1180 ctx = bset->ctx;
1181 if (isl_basic_set_plain_is_empty(bset))
1182 return empty_sample(bset);
1184 dim = isl_basic_set_n_dim(bset);
1185 isl_assert(ctx, isl_basic_set_n_param(bset) == 0, goto error);
1186 isl_assert(ctx, bset->n_div == 0, goto error);
1188 if (bset->sample && bset->sample->size == 1 + dim) {
1189 int contains = isl_basic_set_contains(bset, bset->sample);
1190 if (contains < 0)
1191 goto error;
1192 if (contains) {
1193 struct isl_vec *sample = isl_vec_copy(bset->sample);
1194 isl_basic_set_free(bset);
1195 return sample;
1198 isl_vec_free(bset->sample);
1199 bset->sample = NULL;
1201 if (bset->n_eq > 0)
1202 return sample_eq(bset, bounded ? isl_basic_set_sample_bounded
1203 : isl_basic_set_sample_vec);
1204 if (dim == 0)
1205 return zero_sample(bset);
1206 if (dim == 1)
1207 return interval_sample(bset);
1209 switch (bset->ctx->opt->ilp_solver) {
1210 case ISL_ILP_PIP:
1211 return pip_sample(bset);
1212 case ISL_ILP_GBR:
1213 return bounded ? sample_bounded(bset) : gbr_sample(bset);
1215 isl_assert(bset->ctx, 0, );
1216 error:
1217 isl_basic_set_free(bset);
1218 return NULL;
1221 __isl_give isl_vec *isl_basic_set_sample_vec(__isl_take isl_basic_set *bset)
1223 return basic_set_sample(bset, 0);
1226 /* Compute an integer sample in "bset", where the caller guarantees
1227 * that "bset" is bounded.
1229 struct isl_vec *isl_basic_set_sample_bounded(struct isl_basic_set *bset)
1231 return basic_set_sample(bset, 1);
1234 __isl_give isl_basic_set *isl_basic_set_from_vec(__isl_take isl_vec *vec)
1236 int i;
1237 int k;
1238 struct isl_basic_set *bset = NULL;
1239 struct isl_ctx *ctx;
1240 unsigned dim;
1242 if (!vec)
1243 return NULL;
1244 ctx = vec->ctx;
1245 isl_assert(ctx, vec->size != 0, goto error);
1247 bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
1248 if (!bset)
1249 goto error;
1250 dim = isl_basic_set_n_dim(bset);
1251 for (i = dim - 1; i >= 0; --i) {
1252 k = isl_basic_set_alloc_equality(bset);
1253 if (k < 0)
1254 goto error;
1255 isl_seq_clr(bset->eq[k], 1 + dim);
1256 isl_int_neg(bset->eq[k][0], vec->el[1 + i]);
1257 isl_int_set(bset->eq[k][1 + i], vec->el[0]);
1259 bset->sample = vec;
1261 return bset;
1262 error:
1263 isl_basic_set_free(bset);
1264 isl_vec_free(vec);
1265 return NULL;
1268 __isl_give isl_basic_map *isl_basic_map_sample(__isl_take isl_basic_map *bmap)
1270 struct isl_basic_set *bset;
1271 struct isl_vec *sample_vec;
1273 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
1274 sample_vec = isl_basic_set_sample_vec(bset);
1275 if (!sample_vec)
1276 goto error;
1277 if (sample_vec->size == 0) {
1278 struct isl_basic_map *sample;
1279 sample = isl_basic_map_empty_like(bmap);
1280 isl_vec_free(sample_vec);
1281 isl_basic_map_free(bmap);
1282 return sample;
1284 bset = isl_basic_set_from_vec(sample_vec);
1285 return isl_basic_map_overlying_set(bset, bmap);
1286 error:
1287 isl_basic_map_free(bmap);
1288 return NULL;
1291 __isl_give isl_basic_map *isl_map_sample(__isl_take isl_map *map)
1293 int i;
1294 isl_basic_map *sample = NULL;
1296 if (!map)
1297 goto error;
1299 for (i = 0; i < map->n; ++i) {
1300 sample = isl_basic_map_sample(isl_basic_map_copy(map->p[i]));
1301 if (!sample)
1302 goto error;
1303 if (!ISL_F_ISSET(sample, ISL_BASIC_MAP_EMPTY))
1304 break;
1305 isl_basic_map_free(sample);
1307 if (i == map->n)
1308 sample = isl_basic_map_empty_like_map(map);
1309 isl_map_free(map);
1310 return sample;
1311 error:
1312 isl_map_free(map);
1313 return NULL;
1316 __isl_give isl_basic_set *isl_set_sample(__isl_take isl_set *set)
1318 return (isl_basic_set *) isl_map_sample((isl_map *)set);
1321 __isl_give isl_point *isl_basic_set_sample_point(__isl_take isl_basic_set *bset)
1323 isl_vec *vec;
1324 isl_dim *dim;
1326 dim = isl_basic_set_get_dim(bset);
1327 bset = isl_basic_set_underlying_set(bset);
1328 vec = isl_basic_set_sample_vec(bset);
1330 return isl_point_alloc(dim, vec);
1333 __isl_give isl_point *isl_set_sample_point(__isl_take isl_set *set)
1335 int i;
1336 isl_point *pnt;
1338 if (!set)
1339 return NULL;
1341 for (i = 0; i < set->n; ++i) {
1342 pnt = isl_basic_set_sample_point(isl_basic_set_copy(set->p[i]));
1343 if (!pnt)
1344 goto error;
1345 if (!isl_point_is_void(pnt))
1346 break;
1347 isl_point_free(pnt);
1349 if (i == set->n)
1350 pnt = isl_point_void(isl_set_get_dim(set));
1352 isl_set_free(set);
1353 return pnt;
1354 error:
1355 isl_set_free(set);
1356 return NULL;