privately export isl_set_combined_lineality_space
[isl.git] / isl_ilp.c
blobeee294ea07fb187a919f7e706b459510112d68ce
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the MIT 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/ilp.h>
13 #include <isl/union_set.h>
14 #include "isl_sample.h"
15 #include <isl_seq.h>
16 #include "isl_equalities.h"
17 #include <isl_aff_private.h>
18 #include <isl_local_space_private.h>
19 #include <isl_mat_private.h>
20 #include <isl_val_private.h>
21 #include <isl_vec_private.h>
22 #include <isl_lp_private.h>
23 #include <isl_ilp_private.h>
24 #include <isl/deprecated/ilp_int.h>
26 /* Given a basic set "bset", construct a basic set U such that for
27 * each element x in U, the whole unit box positioned at x is inside
28 * the given basic set.
29 * Note that U may not contain all points that satisfy this property.
31 * We simply add the sum of all negative coefficients to the constant
32 * term. This ensures that if x satisfies the resulting constraints,
33 * then x plus any sum of unit vectors satisfies the original constraints.
35 static __isl_give isl_basic_set *unit_box_base_points(
36 __isl_take isl_basic_set *bset)
38 int i, j, k;
39 struct isl_basic_set *unit_box = NULL;
40 unsigned total;
42 if (!bset)
43 goto error;
45 if (bset->n_eq != 0) {
46 isl_space *space = isl_basic_set_get_space(bset);
47 isl_basic_set_free(bset);
48 return isl_basic_set_empty(space);
51 total = isl_basic_set_total_dim(bset);
52 unit_box = isl_basic_set_alloc_space(isl_basic_set_get_space(bset),
53 0, 0, bset->n_ineq);
55 for (i = 0; i < bset->n_ineq; ++i) {
56 k = isl_basic_set_alloc_inequality(unit_box);
57 if (k < 0)
58 goto error;
59 isl_seq_cpy(unit_box->ineq[k], bset->ineq[i], 1 + total);
60 for (j = 0; j < total; ++j) {
61 if (isl_int_is_nonneg(unit_box->ineq[k][1 + j]))
62 continue;
63 isl_int_add(unit_box->ineq[k][0],
64 unit_box->ineq[k][0], unit_box->ineq[k][1 + j]);
68 isl_basic_set_free(bset);
69 return unit_box;
70 error:
71 isl_basic_set_free(bset);
72 isl_basic_set_free(unit_box);
73 return NULL;
76 /* Find an integer point in "bset", preferably one that is
77 * close to minimizing "f".
79 * We first check if we can easily put unit boxes inside bset.
80 * If so, we take the best base point of any of the unit boxes we can find
81 * and round it up to the nearest integer.
82 * If not, we simply pick any integer point in "bset".
84 static __isl_give isl_vec *initial_solution(__isl_keep isl_basic_set *bset,
85 isl_int *f)
87 enum isl_lp_result res;
88 struct isl_basic_set *unit_box;
89 struct isl_vec *sol;
91 unit_box = unit_box_base_points(isl_basic_set_copy(bset));
93 res = isl_basic_set_solve_lp(unit_box, 0, f, bset->ctx->one,
94 NULL, NULL, &sol);
95 if (res == isl_lp_ok) {
96 isl_basic_set_free(unit_box);
97 return isl_vec_ceil(sol);
100 isl_basic_set_free(unit_box);
102 return isl_basic_set_sample_vec(isl_basic_set_copy(bset));
105 /* Restrict "bset" to those points with values for f in the interval [l, u].
107 static __isl_give isl_basic_set *add_bounds(__isl_take isl_basic_set *bset,
108 isl_int *f, isl_int l, isl_int u)
110 int k;
111 unsigned total;
113 total = isl_basic_set_total_dim(bset);
114 bset = isl_basic_set_extend_constraints(bset, 0, 2);
116 k = isl_basic_set_alloc_inequality(bset);
117 if (k < 0)
118 goto error;
119 isl_seq_cpy(bset->ineq[k], f, 1 + total);
120 isl_int_sub(bset->ineq[k][0], bset->ineq[k][0], l);
122 k = isl_basic_set_alloc_inequality(bset);
123 if (k < 0)
124 goto error;
125 isl_seq_neg(bset->ineq[k], f, 1 + total);
126 isl_int_add(bset->ineq[k][0], bset->ineq[k][0], u);
128 return bset;
129 error:
130 isl_basic_set_free(bset);
131 return NULL;
134 /* Find an integer point in "bset" that minimizes f (in any) such that
135 * the value of f lies inside the interval [l, u].
136 * Return this integer point if it can be found.
137 * Otherwise, return sol.
139 * We perform a number of steps until l > u.
140 * In each step, we look for an integer point with value in either
141 * the whole interval [l, u] or half of the interval [l, l+floor(u-l-1/2)].
142 * The choice depends on whether we have found an integer point in the
143 * previous step. If so, we look for the next point in half of the remaining
144 * interval.
145 * If we find a point, the current solution is updated and u is set
146 * to its value minus 1.
147 * If no point can be found, we update l to the upper bound of the interval
148 * we checked (u or l+floor(u-l-1/2)) plus 1.
150 static __isl_give isl_vec *solve_ilp_search(__isl_keep isl_basic_set *bset,
151 isl_int *f, isl_int *opt, __isl_take isl_vec *sol, isl_int l, isl_int u)
153 isl_int tmp;
154 int divide = 1;
156 isl_int_init(tmp);
158 while (isl_int_le(l, u)) {
159 struct isl_basic_set *slice;
160 struct isl_vec *sample;
162 if (!divide)
163 isl_int_set(tmp, u);
164 else {
165 isl_int_sub(tmp, u, l);
166 isl_int_fdiv_q_ui(tmp, tmp, 2);
167 isl_int_add(tmp, tmp, l);
169 slice = add_bounds(isl_basic_set_copy(bset), f, l, tmp);
170 sample = isl_basic_set_sample_vec(slice);
171 if (!sample) {
172 isl_vec_free(sol);
173 sol = NULL;
174 break;
176 if (sample->size > 0) {
177 isl_vec_free(sol);
178 sol = sample;
179 isl_seq_inner_product(f, sol->el, sol->size, opt);
180 isl_int_sub_ui(u, *opt, 1);
181 divide = 1;
182 } else {
183 isl_vec_free(sample);
184 if (!divide)
185 break;
186 isl_int_add_ui(l, tmp, 1);
187 divide = 0;
191 isl_int_clear(tmp);
193 return sol;
196 /* Find an integer point in "bset" that minimizes f (if any).
197 * If sol_p is not NULL then the integer point is returned in *sol_p.
198 * The optimal value of f is returned in *opt.
200 * The algorithm maintains a currently best solution and an interval [l, u]
201 * of values of f for which integer solutions could potentially still be found.
202 * The initial value of the best solution so far is any solution.
203 * The initial value of l is minimal value of f over the rationals
204 * (rounded up to the nearest integer).
205 * The initial value of u is the value of f at the initial solution minus 1.
207 * We then call solve_ilp_search to perform a binary search on the interval.
209 static enum isl_lp_result solve_ilp(__isl_keep isl_basic_set *bset,
210 isl_int *f, isl_int *opt, __isl_give isl_vec **sol_p)
212 enum isl_lp_result res;
213 isl_int l, u;
214 struct isl_vec *sol;
216 res = isl_basic_set_solve_lp(bset, 0, f, bset->ctx->one,
217 opt, NULL, &sol);
218 if (res == isl_lp_ok && isl_int_is_one(sol->el[0])) {
219 if (sol_p)
220 *sol_p = sol;
221 else
222 isl_vec_free(sol);
223 return isl_lp_ok;
225 isl_vec_free(sol);
226 if (res == isl_lp_error || res == isl_lp_empty)
227 return res;
229 sol = initial_solution(bset, f);
230 if (!sol)
231 return isl_lp_error;
232 if (sol->size == 0) {
233 isl_vec_free(sol);
234 return isl_lp_empty;
236 if (res == isl_lp_unbounded) {
237 isl_vec_free(sol);
238 return isl_lp_unbounded;
241 isl_int_init(l);
242 isl_int_init(u);
244 isl_int_set(l, *opt);
246 isl_seq_inner_product(f, sol->el, sol->size, opt);
247 isl_int_sub_ui(u, *opt, 1);
249 sol = solve_ilp_search(bset, f, opt, sol, l, u);
250 if (!sol)
251 res = isl_lp_error;
253 isl_int_clear(l);
254 isl_int_clear(u);
256 if (sol_p)
257 *sol_p = sol;
258 else
259 isl_vec_free(sol);
261 return res;
264 static enum isl_lp_result solve_ilp_with_eq(__isl_keep isl_basic_set *bset,
265 int max, isl_int *f, isl_int *opt, __isl_give isl_vec **sol_p)
267 unsigned dim;
268 enum isl_lp_result res;
269 struct isl_mat *T = NULL;
270 struct isl_vec *v;
272 bset = isl_basic_set_copy(bset);
273 dim = isl_basic_set_total_dim(bset);
274 v = isl_vec_alloc(bset->ctx, 1 + dim);
275 if (!v)
276 goto error;
277 isl_seq_cpy(v->el, f, 1 + dim);
278 bset = isl_basic_set_remove_equalities(bset, &T, NULL);
279 v = isl_vec_mat_product(v, isl_mat_copy(T));
280 if (!v)
281 goto error;
282 res = isl_basic_set_solve_ilp(bset, max, v->el, opt, sol_p);
283 isl_vec_free(v);
284 if (res == isl_lp_ok && sol_p) {
285 *sol_p = isl_mat_vec_product(T, *sol_p);
286 if (!*sol_p)
287 res = isl_lp_error;
288 } else
289 isl_mat_free(T);
290 isl_basic_set_free(bset);
291 return res;
292 error:
293 isl_mat_free(T);
294 isl_basic_set_free(bset);
295 return isl_lp_error;
298 /* Find an integer point in "bset" that minimizes (or maximizes if max is set)
299 * f (if any).
300 * If sol_p is not NULL then the integer point is returned in *sol_p.
301 * The optimal value of f is returned in *opt.
303 * If there is any equality among the points in "bset", then we first
304 * project it out. Otherwise, we continue with solve_ilp above.
306 enum isl_lp_result isl_basic_set_solve_ilp(__isl_keep isl_basic_set *bset,
307 int max, isl_int *f, isl_int *opt, __isl_give isl_vec **sol_p)
309 unsigned dim;
310 enum isl_lp_result res;
312 if (!bset)
313 return isl_lp_error;
314 if (sol_p)
315 *sol_p = NULL;
317 isl_assert(bset->ctx, isl_basic_set_n_param(bset) == 0,
318 return isl_lp_error);
320 if (isl_basic_set_plain_is_empty(bset))
321 return isl_lp_empty;
323 if (bset->n_eq)
324 return solve_ilp_with_eq(bset, max, f, opt, sol_p);
326 dim = isl_basic_set_total_dim(bset);
328 if (max)
329 isl_seq_neg(f, f, 1 + dim);
331 res = solve_ilp(bset, f, opt, sol_p);
333 if (max) {
334 isl_seq_neg(f, f, 1 + dim);
335 isl_int_neg(*opt, *opt);
338 return res;
341 static enum isl_lp_result basic_set_opt(__isl_keep isl_basic_set *bset, int max,
342 __isl_keep isl_aff *obj, isl_int *opt)
344 enum isl_lp_result res;
346 if (!obj)
347 return isl_lp_error;
348 bset = isl_basic_set_copy(bset);
349 bset = isl_basic_set_underlying_set(bset);
350 res = isl_basic_set_solve_ilp(bset, max, obj->v->el + 1, opt, NULL);
351 isl_basic_set_free(bset);
352 return res;
355 static __isl_give isl_mat *extract_divs(__isl_keep isl_basic_set *bset)
357 int i;
358 isl_ctx *ctx = isl_basic_set_get_ctx(bset);
359 isl_mat *div;
361 div = isl_mat_alloc(ctx, bset->n_div,
362 1 + 1 + isl_basic_set_total_dim(bset));
363 if (!div)
364 return NULL;
366 for (i = 0; i < bset->n_div; ++i)
367 isl_seq_cpy(div->row[i], bset->div[i], div->n_col);
369 return div;
372 enum isl_lp_result isl_basic_set_opt(__isl_keep isl_basic_set *bset, int max,
373 __isl_keep isl_aff *obj, isl_int *opt)
375 int *exp1 = NULL;
376 int *exp2 = NULL;
377 isl_ctx *ctx;
378 isl_mat *bset_div = NULL;
379 isl_mat *div = NULL;
380 enum isl_lp_result res;
381 int bset_n_div, obj_n_div;
383 if (!bset || !obj)
384 return isl_lp_error;
386 ctx = isl_aff_get_ctx(obj);
387 if (!isl_space_is_equal(bset->dim, obj->ls->dim))
388 isl_die(ctx, isl_error_invalid,
389 "spaces don't match", return isl_lp_error);
390 if (!isl_int_is_one(obj->v->el[0]))
391 isl_die(ctx, isl_error_unsupported,
392 "expecting integer affine expression",
393 return isl_lp_error);
395 bset_n_div = isl_basic_set_dim(bset, isl_dim_div);
396 obj_n_div = isl_aff_dim(obj, isl_dim_div);
397 if (bset_n_div == 0 && obj_n_div == 0)
398 return basic_set_opt(bset, max, obj, opt);
400 bset = isl_basic_set_copy(bset);
401 obj = isl_aff_copy(obj);
403 bset_div = extract_divs(bset);
404 exp1 = isl_alloc_array(ctx, int, bset_n_div);
405 exp2 = isl_alloc_array(ctx, int, obj_n_div);
406 if (!bset_div || (bset_n_div && !exp1) || (obj_n_div && !exp2))
407 goto error;
409 div = isl_merge_divs(bset_div, obj->ls->div, exp1, exp2);
411 bset = isl_basic_set_expand_divs(bset, isl_mat_copy(div), exp1);
412 obj = isl_aff_expand_divs(obj, isl_mat_copy(div), exp2);
414 res = basic_set_opt(bset, max, obj, opt);
416 isl_mat_free(bset_div);
417 isl_mat_free(div);
418 free(exp1);
419 free(exp2);
420 isl_basic_set_free(bset);
421 isl_aff_free(obj);
423 return res;
424 error:
425 isl_mat_free(div);
426 isl_mat_free(bset_div);
427 free(exp1);
428 free(exp2);
429 isl_basic_set_free(bset);
430 isl_aff_free(obj);
431 return isl_lp_error;
434 /* Compute the minimum (maximum if max is set) of the integer affine
435 * expression obj over the points in set and put the result in *opt.
437 * The parameters are assumed to have been aligned.
439 static enum isl_lp_result isl_set_opt_aligned(__isl_keep isl_set *set, int max,
440 __isl_keep isl_aff *obj, isl_int *opt)
442 int i;
443 enum isl_lp_result res;
444 int empty = 1;
445 isl_int opt_i;
447 if (!set || !obj)
448 return isl_lp_error;
449 if (set->n == 0)
450 return isl_lp_empty;
452 res = isl_basic_set_opt(set->p[0], max, obj, opt);
453 if (res == isl_lp_error || res == isl_lp_unbounded)
454 return res;
455 if (set->n == 1)
456 return res;
457 if (res == isl_lp_ok)
458 empty = 0;
460 isl_int_init(opt_i);
461 for (i = 1; i < set->n; ++i) {
462 res = isl_basic_set_opt(set->p[i], max, obj, &opt_i);
463 if (res == isl_lp_error || res == isl_lp_unbounded) {
464 isl_int_clear(opt_i);
465 return res;
467 if (res == isl_lp_empty)
468 continue;
469 empty = 0;
470 if (max ? isl_int_gt(opt_i, *opt) : isl_int_lt(opt_i, *opt))
471 isl_int_set(*opt, opt_i);
473 isl_int_clear(opt_i);
475 return empty ? isl_lp_empty : isl_lp_ok;
478 /* Compute the minimum (maximum if max is set) of the integer affine
479 * expression obj over the points in set and put the result in *opt.
481 enum isl_lp_result isl_set_opt(__isl_keep isl_set *set, int max,
482 __isl_keep isl_aff *obj, isl_int *opt)
484 enum isl_lp_result res;
485 isl_bool aligned;
487 if (!set || !obj)
488 return isl_lp_error;
490 aligned = isl_set_space_has_equal_params(set, obj->ls->dim);
491 if (aligned < 0)
492 return isl_lp_error;
493 if (aligned)
494 return isl_set_opt_aligned(set, max, obj, opt);
496 set = isl_set_copy(set);
497 obj = isl_aff_copy(obj);
498 set = isl_set_align_params(set, isl_aff_get_domain_space(obj));
499 obj = isl_aff_align_params(obj, isl_set_get_space(set));
501 res = isl_set_opt_aligned(set, max, obj, opt);
503 isl_set_free(set);
504 isl_aff_free(obj);
506 return res;
509 enum isl_lp_result isl_basic_set_max(__isl_keep isl_basic_set *bset,
510 __isl_keep isl_aff *obj, isl_int *opt)
512 return isl_basic_set_opt(bset, 1, obj, opt);
515 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
516 __isl_keep isl_aff *obj, isl_int *opt)
518 return isl_set_opt(set, 1, obj, opt);
521 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
522 __isl_keep isl_aff *obj, isl_int *opt)
524 return isl_set_opt(set, 0, obj, opt);
527 /* Convert the result of a function that returns an isl_lp_result
528 * to an isl_val. The numerator of "v" is set to the optimal value
529 * if lp_res is isl_lp_ok. "max" is set if a maximum was computed.
531 * Return "v" with denominator set to 1 if lp_res is isl_lp_ok.
532 * Return NULL on error.
533 * Return a NaN if lp_res is isl_lp_empty.
534 * Return infinity or negative infinity if lp_res is isl_lp_unbounded,
535 * depending on "max".
537 static __isl_give isl_val *convert_lp_result(enum isl_lp_result lp_res,
538 __isl_take isl_val *v, int max)
540 isl_ctx *ctx;
542 if (lp_res == isl_lp_ok) {
543 isl_int_set_si(v->d, 1);
544 return isl_val_normalize(v);
546 ctx = isl_val_get_ctx(v);
547 isl_val_free(v);
548 if (lp_res == isl_lp_error)
549 return NULL;
550 if (lp_res == isl_lp_empty)
551 return isl_val_nan(ctx);
552 if (max)
553 return isl_val_infty(ctx);
554 else
555 return isl_val_neginfty(ctx);
558 /* Return the minimum (maximum if max is set) of the integer affine
559 * expression "obj" over the points in "bset".
561 * Return infinity or negative infinity if the optimal value is unbounded and
562 * NaN if "bset" is empty.
564 * Call isl_basic_set_opt and translate the results.
566 __isl_give isl_val *isl_basic_set_opt_val(__isl_keep isl_basic_set *bset,
567 int max, __isl_keep isl_aff *obj)
569 isl_ctx *ctx;
570 isl_val *res;
571 enum isl_lp_result lp_res;
573 if (!bset || !obj)
574 return NULL;
576 ctx = isl_aff_get_ctx(obj);
577 res = isl_val_alloc(ctx);
578 if (!res)
579 return NULL;
580 lp_res = isl_basic_set_opt(bset, max, obj, &res->n);
581 return convert_lp_result(lp_res, res, max);
584 /* Return the maximum of the integer affine
585 * expression "obj" over the points in "bset".
587 * Return infinity or negative infinity if the optimal value is unbounded and
588 * NaN if "bset" is empty.
590 __isl_give isl_val *isl_basic_set_max_val(__isl_keep isl_basic_set *bset,
591 __isl_keep isl_aff *obj)
593 return isl_basic_set_opt_val(bset, 1, obj);
596 /* Return the minimum (maximum if max is set) of the integer affine
597 * expression "obj" over the points in "set".
599 * Return infinity or negative infinity if the optimal value is unbounded and
600 * NaN if "set" is empty.
602 * Call isl_set_opt and translate the results.
604 __isl_give isl_val *isl_set_opt_val(__isl_keep isl_set *set, int max,
605 __isl_keep isl_aff *obj)
607 isl_ctx *ctx;
608 isl_val *res;
609 enum isl_lp_result lp_res;
611 if (!set || !obj)
612 return NULL;
614 ctx = isl_aff_get_ctx(obj);
615 res = isl_val_alloc(ctx);
616 if (!res)
617 return NULL;
618 lp_res = isl_set_opt(set, max, obj, &res->n);
619 return convert_lp_result(lp_res, res, max);
622 /* Return the minimum of the integer affine
623 * expression "obj" over the points in "set".
625 * Return infinity or negative infinity if the optimal value is unbounded and
626 * NaN if "set" is empty.
628 __isl_give isl_val *isl_set_min_val(__isl_keep isl_set *set,
629 __isl_keep isl_aff *obj)
631 return isl_set_opt_val(set, 0, obj);
634 /* Return the maximum of the integer affine
635 * expression "obj" over the points in "set".
637 * Return infinity or negative infinity if the optimal value is unbounded and
638 * NaN if "set" is empty.
640 __isl_give isl_val *isl_set_max_val(__isl_keep isl_set *set,
641 __isl_keep isl_aff *obj)
643 return isl_set_opt_val(set, 1, obj);
646 /* Return the optimum (min or max depending on "max") of "v1" and "v2",
647 * where either may be NaN, signifying an uninitialized value.
648 * That is, if either is NaN, then return the other one.
650 static __isl_give isl_val *val_opt(__isl_take isl_val *v1,
651 __isl_take isl_val *v2, int max)
653 if (!v1 || !v2)
654 goto error;
655 if (isl_val_is_nan(v1)) {
656 isl_val_free(v1);
657 return v2;
659 if (isl_val_is_nan(v2)) {
660 isl_val_free(v2);
661 return v1;
663 if (max)
664 return isl_val_max(v1, v2);
665 else
666 return isl_val_min(v1, v2);
667 error:
668 isl_val_free(v1);
669 isl_val_free(v2);
670 return NULL;
673 /* Internal data structure for isl_set_opt_pw_aff.
675 * "max" is set if the maximum should be computed.
676 * "set" is the set over which the optimum should be computed.
677 * "res" contains the current optimum and is initialized to NaN.
679 struct isl_set_opt_data {
680 int max;
681 isl_set *set;
683 isl_val *res;
686 /* Update the optimum in data->res with respect to the affine function
687 * "aff" defined over "set".
689 static isl_stat piece_opt(__isl_take isl_set *set, __isl_take isl_aff *aff,
690 void *user)
692 struct isl_set_opt_data *data = user;
693 isl_val *opt;
695 set = isl_set_intersect(set, isl_set_copy(data->set));
696 opt = isl_set_opt_val(set, data->max, aff);
697 isl_set_free(set);
698 isl_aff_free(aff);
700 data->res = val_opt(data->res, opt, data->max);
701 if (!data->res)
702 return isl_stat_error;
704 return isl_stat_ok;
707 /* Return the minimum (maximum if "max" is set) of the integer piecewise affine
708 * expression "obj" over the points in "set".
710 * Return infinity or negative infinity if the optimal value is unbounded and
711 * NaN if the intersection of "set" with the domain of "obj" is empty.
713 * Initialize the result to NaN and then update it for each of the pieces
714 * in "obj".
716 static __isl_give isl_val *isl_set_opt_pw_aff(__isl_keep isl_set *set, int max,
717 __isl_keep isl_pw_aff *obj)
719 struct isl_set_opt_data data = { max, set };
721 data.res = isl_val_nan(isl_set_get_ctx(set));
722 if (isl_pw_aff_foreach_piece(obj, &piece_opt, &data) < 0)
723 return isl_val_free(data.res);
725 return data.res;
728 /* Internal data structure for isl_union_set_opt_union_pw_aff.
730 * "max" is set if the maximum should be computed.
731 * "obj" is the objective function that needs to be optimized.
732 * "res" contains the current optimum and is initialized to NaN.
734 struct isl_union_set_opt_data {
735 int max;
736 isl_union_pw_aff *obj;
738 isl_val *res;
741 /* Update the optimum in data->res with the optimum over "set".
742 * Do so by first extracting the matching objective function
743 * from data->obj.
745 static isl_stat set_opt(__isl_take isl_set *set, void *user)
747 struct isl_union_set_opt_data *data = user;
748 isl_space *space;
749 isl_pw_aff *pa;
750 isl_val *opt;
752 space = isl_set_get_space(set);
753 space = isl_space_from_domain(space);
754 space = isl_space_add_dims(space, isl_dim_out, 1);
755 pa = isl_union_pw_aff_extract_pw_aff(data->obj, space);
756 opt = isl_set_opt_pw_aff(set, data->max, pa);
757 isl_pw_aff_free(pa);
758 isl_set_free(set);
760 data->res = val_opt(data->res, opt, data->max);
761 if (!data->res)
762 return isl_stat_error;
764 return isl_stat_ok;
767 /* Return the minimum (maximum if "max" is set) of the integer piecewise affine
768 * expression "obj" over the points in "uset".
770 * Return infinity or negative infinity if the optimal value is unbounded and
771 * NaN if the intersection of "uset" with the domain of "obj" is empty.
773 * Initialize the result to NaN and then update it for each of the sets
774 * in "uset".
776 static __isl_give isl_val *isl_union_set_opt_union_pw_aff(
777 __isl_keep isl_union_set *uset, int max,
778 __isl_keep isl_union_pw_aff *obj)
780 struct isl_union_set_opt_data data = { max, obj };
782 data.res = isl_val_nan(isl_union_set_get_ctx(uset));
783 if (isl_union_set_foreach_set(uset, &set_opt, &data) < 0)
784 return isl_val_free(data.res);
786 return data.res;
789 /* Return a list of minima (maxima if "max" is set) over the points in "uset"
790 * for each of the expressions in "obj".
792 * An element in the list is infinity or negative infinity if the optimal
793 * value of the corresponding expression is unbounded and
794 * NaN if the intersection of "uset" with the domain of the expression
795 * is empty.
797 * Iterate over all the expressions in "obj" and collect the results.
799 static __isl_give isl_multi_val *isl_union_set_opt_multi_union_pw_aff(
800 __isl_keep isl_union_set *uset, int max,
801 __isl_keep isl_multi_union_pw_aff *obj)
803 int i, n;
804 isl_multi_val *mv;
806 if (!uset || !obj)
807 return NULL;
809 n = isl_multi_union_pw_aff_dim(obj, isl_dim_set);
810 mv = isl_multi_val_zero(isl_multi_union_pw_aff_get_space(obj));
812 for (i = 0; i < n; ++i) {
813 isl_val *v;
814 isl_union_pw_aff *upa;
816 upa = isl_multi_union_pw_aff_get_union_pw_aff(obj, i);
817 v = isl_union_set_opt_union_pw_aff(uset, max, upa);
818 isl_union_pw_aff_free(upa);
819 mv = isl_multi_val_set_val(mv, i, v);
822 return mv;
825 /* Return a list of minima over the points in "uset"
826 * for each of the expressions in "obj".
828 * An element in the list is infinity or negative infinity if the optimal
829 * value of the corresponding expression is unbounded and
830 * NaN if the intersection of "uset" with the domain of the expression
831 * is empty.
833 __isl_give isl_multi_val *isl_union_set_min_multi_union_pw_aff(
834 __isl_keep isl_union_set *uset, __isl_keep isl_multi_union_pw_aff *obj)
836 return isl_union_set_opt_multi_union_pw_aff(uset, 0, obj);