dataflow analysis: don't depend on word size during sorting of sources
[isl.git] / isl_tab_pip.c
blob94b868d29cd103ac6ce1864d6c42eb0dcb1ca1ea
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
5 * Use of this software is governed by the GNU LGPLv2.1 license
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
10 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 #include <isl_ctx_private.h>
14 #include "isl_map_private.h"
15 #include <isl/seq.h>
16 #include "isl_tab.h"
17 #include "isl_sample.h"
18 #include <isl_mat_private.h>
21 * The implementation of parametric integer linear programming in this file
22 * was inspired by the paper "Parametric Integer Programming" and the
23 * report "Solving systems of affine (in)equalities" by Paul Feautrier
24 * (and others).
26 * The strategy used for obtaining a feasible solution is different
27 * from the one used in isl_tab.c. In particular, in isl_tab.c,
28 * upon finding a constraint that is not yet satisfied, we pivot
29 * in a row that increases the constant term of the row holding the
30 * constraint, making sure the sample solution remains feasible
31 * for all the constraints it already satisfied.
32 * Here, we always pivot in the row holding the constraint,
33 * choosing a column that induces the lexicographically smallest
34 * increment to the sample solution.
36 * By starting out from a sample value that is lexicographically
37 * smaller than any integer point in the problem space, the first
38 * feasible integer sample point we find will also be the lexicographically
39 * smallest. If all variables can be assumed to be non-negative,
40 * then the initial sample value may be chosen equal to zero.
41 * However, we will not make this assumption. Instead, we apply
42 * the "big parameter" trick. Any variable x is then not directly
43 * used in the tableau, but instead it is represented by another
44 * variable x' = M + x, where M is an arbitrarily large (positive)
45 * value. x' is therefore always non-negative, whatever the value of x.
46 * Taking as initial sample value x' = 0 corresponds to x = -M,
47 * which is always smaller than any possible value of x.
49 * The big parameter trick is used in the main tableau and
50 * also in the context tableau if isl_context_lex is used.
51 * In this case, each tableaus has its own big parameter.
52 * Before doing any real work, we check if all the parameters
53 * happen to be non-negative. If so, we drop the column corresponding
54 * to M from the initial context tableau.
55 * If isl_context_gbr is used, then the big parameter trick is only
56 * used in the main tableau.
59 struct isl_context;
60 struct isl_context_op {
61 /* detect nonnegative parameters in context and mark them in tab */
62 struct isl_tab *(*detect_nonnegative_parameters)(
63 struct isl_context *context, struct isl_tab *tab);
64 /* return temporary reference to basic set representation of context */
65 struct isl_basic_set *(*peek_basic_set)(struct isl_context *context);
66 /* return temporary reference to tableau representation of context */
67 struct isl_tab *(*peek_tab)(struct isl_context *context);
68 /* add equality; check is 1 if eq may not be valid;
69 * update is 1 if we may want to call ineq_sign on context later.
71 void (*add_eq)(struct isl_context *context, isl_int *eq,
72 int check, int update);
73 /* add inequality; check is 1 if ineq may not be valid;
74 * update is 1 if we may want to call ineq_sign on context later.
76 void (*add_ineq)(struct isl_context *context, isl_int *ineq,
77 int check, int update);
78 /* check sign of ineq based on previous information.
79 * strict is 1 if saturation should be treated as a positive sign.
81 enum isl_tab_row_sign (*ineq_sign)(struct isl_context *context,
82 isl_int *ineq, int strict);
83 /* check if inequality maintains feasibility */
84 int (*test_ineq)(struct isl_context *context, isl_int *ineq);
85 /* return index of a div that corresponds to "div" */
86 int (*get_div)(struct isl_context *context, struct isl_tab *tab,
87 struct isl_vec *div);
88 /* add div "div" to context and return non-negativity */
89 int (*add_div)(struct isl_context *context, struct isl_vec *div);
90 int (*detect_equalities)(struct isl_context *context,
91 struct isl_tab *tab);
92 /* return row index of "best" split */
93 int (*best_split)(struct isl_context *context, struct isl_tab *tab);
94 /* check if context has already been determined to be empty */
95 int (*is_empty)(struct isl_context *context);
96 /* check if context is still usable */
97 int (*is_ok)(struct isl_context *context);
98 /* save a copy/snapshot of context */
99 void *(*save)(struct isl_context *context);
100 /* restore saved context */
101 void (*restore)(struct isl_context *context, void *);
102 /* invalidate context */
103 void (*invalidate)(struct isl_context *context);
104 /* free context */
105 void (*free)(struct isl_context *context);
108 struct isl_context {
109 struct isl_context_op *op;
112 struct isl_context_lex {
113 struct isl_context context;
114 struct isl_tab *tab;
117 struct isl_partial_sol {
118 int level;
119 struct isl_basic_set *dom;
120 struct isl_mat *M;
122 struct isl_partial_sol *next;
125 struct isl_sol;
126 struct isl_sol_callback {
127 struct isl_tab_callback callback;
128 struct isl_sol *sol;
131 /* isl_sol is an interface for constructing a solution to
132 * a parametric integer linear programming problem.
133 * Every time the algorithm reaches a state where a solution
134 * can be read off from the tableau (including cases where the tableau
135 * is empty), the function "add" is called on the isl_sol passed
136 * to find_solutions_main.
138 * The context tableau is owned by isl_sol and is updated incrementally.
140 * There are currently two implementations of this interface,
141 * isl_sol_map, which simply collects the solutions in an isl_map
142 * and (optionally) the parts of the context where there is no solution
143 * in an isl_set, and
144 * isl_sol_for, which calls a user-defined function for each part of
145 * the solution.
147 struct isl_sol {
148 int error;
149 int rational;
150 int level;
151 int max;
152 int n_out;
153 struct isl_context *context;
154 struct isl_partial_sol *partial;
155 void (*add)(struct isl_sol *sol,
156 struct isl_basic_set *dom, struct isl_mat *M);
157 void (*add_empty)(struct isl_sol *sol, struct isl_basic_set *bset);
158 void (*free)(struct isl_sol *sol);
159 struct isl_sol_callback dec_level;
162 static void sol_free(struct isl_sol *sol)
164 struct isl_partial_sol *partial, *next;
165 if (!sol)
166 return;
167 for (partial = sol->partial; partial; partial = next) {
168 next = partial->next;
169 isl_basic_set_free(partial->dom);
170 isl_mat_free(partial->M);
171 free(partial);
173 sol->free(sol);
176 /* Push a partial solution represented by a domain and mapping M
177 * onto the stack of partial solutions.
179 static void sol_push_sol(struct isl_sol *sol,
180 struct isl_basic_set *dom, struct isl_mat *M)
182 struct isl_partial_sol *partial;
184 if (sol->error || !dom)
185 goto error;
187 partial = isl_alloc_type(dom->ctx, struct isl_partial_sol);
188 if (!partial)
189 goto error;
191 partial->level = sol->level;
192 partial->dom = dom;
193 partial->M = M;
194 partial->next = sol->partial;
196 sol->partial = partial;
198 return;
199 error:
200 isl_basic_set_free(dom);
201 sol->error = 1;
204 /* Pop one partial solution from the partial solution stack and
205 * pass it on to sol->add or sol->add_empty.
207 static void sol_pop_one(struct isl_sol *sol)
209 struct isl_partial_sol *partial;
211 partial = sol->partial;
212 sol->partial = partial->next;
214 if (partial->M)
215 sol->add(sol, partial->dom, partial->M);
216 else
217 sol->add_empty(sol, partial->dom);
218 free(partial);
221 /* Return a fresh copy of the domain represented by the context tableau.
223 static struct isl_basic_set *sol_domain(struct isl_sol *sol)
225 struct isl_basic_set *bset;
227 if (sol->error)
228 return NULL;
230 bset = isl_basic_set_dup(sol->context->op->peek_basic_set(sol->context));
231 bset = isl_basic_set_update_from_tab(bset,
232 sol->context->op->peek_tab(sol->context));
234 return bset;
237 /* Check whether two partial solutions have the same mapping, where n_div
238 * is the number of divs that the two partial solutions have in common.
240 static int same_solution(struct isl_partial_sol *s1, struct isl_partial_sol *s2,
241 unsigned n_div)
243 int i;
244 unsigned dim;
246 if (!s1->M != !s2->M)
247 return 0;
248 if (!s1->M)
249 return 1;
251 dim = isl_basic_set_total_dim(s1->dom) - s1->dom->n_div;
253 for (i = 0; i < s1->M->n_row; ++i) {
254 if (isl_seq_first_non_zero(s1->M->row[i]+1+dim+n_div,
255 s1->M->n_col-1-dim-n_div) != -1)
256 return 0;
257 if (isl_seq_first_non_zero(s2->M->row[i]+1+dim+n_div,
258 s2->M->n_col-1-dim-n_div) != -1)
259 return 0;
260 if (!isl_seq_eq(s1->M->row[i], s2->M->row[i], 1+dim+n_div))
261 return 0;
263 return 1;
266 /* Pop all solutions from the partial solution stack that were pushed onto
267 * the stack at levels that are deeper than the current level.
268 * If the two topmost elements on the stack have the same level
269 * and represent the same solution, then their domains are combined.
270 * This combined domain is the same as the current context domain
271 * as sol_pop is called each time we move back to a higher level.
273 static void sol_pop(struct isl_sol *sol)
275 struct isl_partial_sol *partial;
276 unsigned n_div;
278 if (sol->error)
279 return;
281 if (sol->level == 0) {
282 for (partial = sol->partial; partial; partial = sol->partial)
283 sol_pop_one(sol);
284 return;
287 partial = sol->partial;
288 if (!partial)
289 return;
291 if (partial->level <= sol->level)
292 return;
294 if (partial->next && partial->next->level == partial->level) {
295 n_div = isl_basic_set_dim(
296 sol->context->op->peek_basic_set(sol->context),
297 isl_dim_div);
299 if (!same_solution(partial, partial->next, n_div)) {
300 sol_pop_one(sol);
301 sol_pop_one(sol);
302 } else {
303 struct isl_basic_set *bset;
305 bset = sol_domain(sol);
307 isl_basic_set_free(partial->next->dom);
308 partial->next->dom = bset;
309 partial->next->level = sol->level;
311 sol->partial = partial->next;
312 isl_basic_set_free(partial->dom);
313 isl_mat_free(partial->M);
314 free(partial);
316 } else
317 sol_pop_one(sol);
320 static void sol_dec_level(struct isl_sol *sol)
322 if (sol->error)
323 return;
325 sol->level--;
327 sol_pop(sol);
330 static int sol_dec_level_wrap(struct isl_tab_callback *cb)
332 struct isl_sol_callback *callback = (struct isl_sol_callback *)cb;
334 sol_dec_level(callback->sol);
336 return callback->sol->error ? -1 : 0;
339 /* Move down to next level and push callback onto context tableau
340 * to decrease the level again when it gets rolled back across
341 * the current state. That is, dec_level will be called with
342 * the context tableau in the same state as it is when inc_level
343 * is called.
345 static void sol_inc_level(struct isl_sol *sol)
347 struct isl_tab *tab;
349 if (sol->error)
350 return;
352 sol->level++;
353 tab = sol->context->op->peek_tab(sol->context);
354 if (isl_tab_push_callback(tab, &sol->dec_level.callback) < 0)
355 sol->error = 1;
358 static void scale_rows(struct isl_mat *mat, isl_int m, int n_row)
360 int i;
362 if (isl_int_is_one(m))
363 return;
365 for (i = 0; i < n_row; ++i)
366 isl_seq_scale(mat->row[i], mat->row[i], m, mat->n_col);
369 /* Add the solution identified by the tableau and the context tableau.
371 * The layout of the variables is as follows.
372 * tab->n_var is equal to the total number of variables in the input
373 * map (including divs that were copied from the context)
374 * + the number of extra divs constructed
375 * Of these, the first tab->n_param and the last tab->n_div variables
376 * correspond to the variables in the context, i.e.,
377 * tab->n_param + tab->n_div = context_tab->n_var
378 * tab->n_param is equal to the number of parameters and input
379 * dimensions in the input map
380 * tab->n_div is equal to the number of divs in the context
382 * If there is no solution, then call add_empty with a basic set
383 * that corresponds to the context tableau. (If add_empty is NULL,
384 * then do nothing).
386 * If there is a solution, then first construct a matrix that maps
387 * all dimensions of the context to the output variables, i.e.,
388 * the output dimensions in the input map.
389 * The divs in the input map (if any) that do not correspond to any
390 * div in the context do not appear in the solution.
391 * The algorithm will make sure that they have an integer value,
392 * but these values themselves are of no interest.
393 * We have to be careful not to drop or rearrange any divs in the
394 * context because that would change the meaning of the matrix.
396 * To extract the value of the output variables, it should be noted
397 * that we always use a big parameter M in the main tableau and so
398 * the variable stored in this tableau is not an output variable x itself, but
399 * x' = M + x (in case of minimization)
400 * or
401 * x' = M - x (in case of maximization)
402 * If x' appears in a column, then its optimal value is zero,
403 * which means that the optimal value of x is an unbounded number
404 * (-M for minimization and M for maximization).
405 * We currently assume that the output dimensions in the original map
406 * are bounded, so this cannot occur.
407 * Similarly, when x' appears in a row, then the coefficient of M in that
408 * row is necessarily 1.
409 * If the row in the tableau represents
410 * d x' = c + d M + e(y)
411 * then, in case of minimization, the corresponding row in the matrix
412 * will be
413 * a c + a e(y)
414 * with a d = m, the (updated) common denominator of the matrix.
415 * In case of maximization, the row will be
416 * -a c - a e(y)
418 static void sol_add(struct isl_sol *sol, struct isl_tab *tab)
420 struct isl_basic_set *bset = NULL;
421 struct isl_mat *mat = NULL;
422 unsigned off;
423 int row, i;
424 isl_int m;
426 if (sol->error || !tab)
427 goto error;
429 if (tab->empty && !sol->add_empty)
430 return;
432 bset = sol_domain(sol);
434 if (tab->empty) {
435 sol_push_sol(sol, bset, NULL);
436 return;
439 off = 2 + tab->M;
441 mat = isl_mat_alloc(tab->mat->ctx, 1 + sol->n_out,
442 1 + tab->n_param + tab->n_div);
443 if (!mat)
444 goto error;
446 isl_int_init(m);
448 isl_seq_clr(mat->row[0] + 1, mat->n_col - 1);
449 isl_int_set_si(mat->row[0][0], 1);
450 for (row = 0; row < sol->n_out; ++row) {
451 int i = tab->n_param + row;
452 int r, j;
454 isl_seq_clr(mat->row[1 + row], mat->n_col);
455 if (!tab->var[i].is_row) {
456 if (tab->M)
457 isl_die(mat->ctx, isl_error_invalid,
458 "unbounded optimum", goto error2);
459 continue;
462 r = tab->var[i].index;
463 if (tab->M &&
464 isl_int_ne(tab->mat->row[r][2], tab->mat->row[r][0]))
465 isl_die(mat->ctx, isl_error_invalid,
466 "unbounded optimum", goto error2);
467 isl_int_gcd(m, mat->row[0][0], tab->mat->row[r][0]);
468 isl_int_divexact(m, tab->mat->row[r][0], m);
469 scale_rows(mat, m, 1 + row);
470 isl_int_divexact(m, mat->row[0][0], tab->mat->row[r][0]);
471 isl_int_mul(mat->row[1 + row][0], m, tab->mat->row[r][1]);
472 for (j = 0; j < tab->n_param; ++j) {
473 int col;
474 if (tab->var[j].is_row)
475 continue;
476 col = tab->var[j].index;
477 isl_int_mul(mat->row[1 + row][1 + j], m,
478 tab->mat->row[r][off + col]);
480 for (j = 0; j < tab->n_div; ++j) {
481 int col;
482 if (tab->var[tab->n_var - tab->n_div+j].is_row)
483 continue;
484 col = tab->var[tab->n_var - tab->n_div+j].index;
485 isl_int_mul(mat->row[1 + row][1 + tab->n_param + j], m,
486 tab->mat->row[r][off + col]);
488 if (sol->max)
489 isl_seq_neg(mat->row[1 + row], mat->row[1 + row],
490 mat->n_col);
493 isl_int_clear(m);
495 sol_push_sol(sol, bset, mat);
496 return;
497 error2:
498 isl_int_clear(m);
499 error:
500 isl_basic_set_free(bset);
501 isl_mat_free(mat);
502 sol->error = 1;
505 struct isl_sol_map {
506 struct isl_sol sol;
507 struct isl_map *map;
508 struct isl_set *empty;
511 static void sol_map_free(struct isl_sol_map *sol_map)
513 if (!sol_map)
514 return;
515 if (sol_map->sol.context)
516 sol_map->sol.context->op->free(sol_map->sol.context);
517 isl_map_free(sol_map->map);
518 isl_set_free(sol_map->empty);
519 free(sol_map);
522 static void sol_map_free_wrap(struct isl_sol *sol)
524 sol_map_free((struct isl_sol_map *)sol);
527 /* This function is called for parts of the context where there is
528 * no solution, with "bset" corresponding to the context tableau.
529 * Simply add the basic set to the set "empty".
531 static void sol_map_add_empty(struct isl_sol_map *sol,
532 struct isl_basic_set *bset)
534 if (!bset)
535 goto error;
536 isl_assert(bset->ctx, sol->empty, goto error);
538 sol->empty = isl_set_grow(sol->empty, 1);
539 bset = isl_basic_set_simplify(bset);
540 bset = isl_basic_set_finalize(bset);
541 sol->empty = isl_set_add_basic_set(sol->empty, isl_basic_set_copy(bset));
542 if (!sol->empty)
543 goto error;
544 isl_basic_set_free(bset);
545 return;
546 error:
547 isl_basic_set_free(bset);
548 sol->sol.error = 1;
551 static void sol_map_add_empty_wrap(struct isl_sol *sol,
552 struct isl_basic_set *bset)
554 sol_map_add_empty((struct isl_sol_map *)sol, bset);
557 /* Add bset to sol's empty, but only if we are actually collecting
558 * the empty set.
560 static void sol_map_add_empty_if_needed(struct isl_sol_map *sol,
561 struct isl_basic_set *bset)
563 if (sol->empty)
564 sol_map_add_empty(sol, bset);
565 else
566 isl_basic_set_free(bset);
569 /* Given a basic map "dom" that represents the context and an affine
570 * matrix "M" that maps the dimensions of the context to the
571 * output variables, construct a basic map with the same parameters
572 * and divs as the context, the dimensions of the context as input
573 * dimensions and a number of output dimensions that is equal to
574 * the number of output dimensions in the input map.
576 * The constraints and divs of the context are simply copied
577 * from "dom". For each row
578 * x = c + e(y)
579 * an equality
580 * c + e(y) - d x = 0
581 * is added, with d the common denominator of M.
583 static void sol_map_add(struct isl_sol_map *sol,
584 struct isl_basic_set *dom, struct isl_mat *M)
586 int i;
587 struct isl_basic_map *bmap = NULL;
588 isl_basic_set *context_bset;
589 unsigned n_eq;
590 unsigned n_ineq;
591 unsigned nparam;
592 unsigned total;
593 unsigned n_div;
594 unsigned n_out;
596 if (sol->sol.error || !dom || !M)
597 goto error;
599 n_out = sol->sol.n_out;
600 n_eq = dom->n_eq + n_out;
601 n_ineq = dom->n_ineq;
602 n_div = dom->n_div;
603 nparam = isl_basic_set_total_dim(dom) - n_div;
604 total = isl_map_dim(sol->map, isl_dim_all);
605 bmap = isl_basic_map_alloc_dim(isl_map_get_dim(sol->map),
606 n_div, n_eq, 2 * n_div + n_ineq);
607 if (!bmap)
608 goto error;
609 if (sol->sol.rational)
610 ISL_F_SET(bmap, ISL_BASIC_MAP_RATIONAL);
611 for (i = 0; i < dom->n_div; ++i) {
612 int k = isl_basic_map_alloc_div(bmap);
613 if (k < 0)
614 goto error;
615 isl_seq_cpy(bmap->div[k], dom->div[i], 1 + 1 + nparam);
616 isl_seq_clr(bmap->div[k] + 1 + 1 + nparam, total - nparam);
617 isl_seq_cpy(bmap->div[k] + 1 + 1 + total,
618 dom->div[i] + 1 + 1 + nparam, i);
620 for (i = 0; i < dom->n_eq; ++i) {
621 int k = isl_basic_map_alloc_equality(bmap);
622 if (k < 0)
623 goto error;
624 isl_seq_cpy(bmap->eq[k], dom->eq[i], 1 + nparam);
625 isl_seq_clr(bmap->eq[k] + 1 + nparam, total - nparam);
626 isl_seq_cpy(bmap->eq[k] + 1 + total,
627 dom->eq[i] + 1 + nparam, n_div);
629 for (i = 0; i < dom->n_ineq; ++i) {
630 int k = isl_basic_map_alloc_inequality(bmap);
631 if (k < 0)
632 goto error;
633 isl_seq_cpy(bmap->ineq[k], dom->ineq[i], 1 + nparam);
634 isl_seq_clr(bmap->ineq[k] + 1 + nparam, total - nparam);
635 isl_seq_cpy(bmap->ineq[k] + 1 + total,
636 dom->ineq[i] + 1 + nparam, n_div);
638 for (i = 0; i < M->n_row - 1; ++i) {
639 int k = isl_basic_map_alloc_equality(bmap);
640 if (k < 0)
641 goto error;
642 isl_seq_cpy(bmap->eq[k], M->row[1 + i], 1 + nparam);
643 isl_seq_clr(bmap->eq[k] + 1 + nparam, n_out);
644 isl_int_neg(bmap->eq[k][1 + nparam + i], M->row[0][0]);
645 isl_seq_cpy(bmap->eq[k] + 1 + nparam + n_out,
646 M->row[1 + i] + 1 + nparam, n_div);
648 bmap = isl_basic_map_simplify(bmap);
649 bmap = isl_basic_map_finalize(bmap);
650 sol->map = isl_map_grow(sol->map, 1);
651 sol->map = isl_map_add_basic_map(sol->map, bmap);
652 if (!sol->map)
653 goto error;
654 isl_basic_set_free(dom);
655 isl_mat_free(M);
656 return;
657 error:
658 isl_basic_set_free(dom);
659 isl_mat_free(M);
660 isl_basic_map_free(bmap);
661 sol->sol.error = 1;
664 static void sol_map_add_wrap(struct isl_sol *sol,
665 struct isl_basic_set *dom, struct isl_mat *M)
667 sol_map_add((struct isl_sol_map *)sol, dom, M);
671 /* Store the "parametric constant" of row "row" of tableau "tab" in "line",
672 * i.e., the constant term and the coefficients of all variables that
673 * appear in the context tableau.
674 * Note that the coefficient of the big parameter M is NOT copied.
675 * The context tableau may not have a big parameter and even when it
676 * does, it is a different big parameter.
678 static void get_row_parameter_line(struct isl_tab *tab, int row, isl_int *line)
680 int i;
681 unsigned off = 2 + tab->M;
683 isl_int_set(line[0], tab->mat->row[row][1]);
684 for (i = 0; i < tab->n_param; ++i) {
685 if (tab->var[i].is_row)
686 isl_int_set_si(line[1 + i], 0);
687 else {
688 int col = tab->var[i].index;
689 isl_int_set(line[1 + i], tab->mat->row[row][off + col]);
692 for (i = 0; i < tab->n_div; ++i) {
693 if (tab->var[tab->n_var - tab->n_div + i].is_row)
694 isl_int_set_si(line[1 + tab->n_param + i], 0);
695 else {
696 int col = tab->var[tab->n_var - tab->n_div + i].index;
697 isl_int_set(line[1 + tab->n_param + i],
698 tab->mat->row[row][off + col]);
703 /* Check if rows "row1" and "row2" have identical "parametric constants",
704 * as explained above.
705 * In this case, we also insist that the coefficients of the big parameter
706 * be the same as the values of the constants will only be the same
707 * if these coefficients are also the same.
709 static int identical_parameter_line(struct isl_tab *tab, int row1, int row2)
711 int i;
712 unsigned off = 2 + tab->M;
714 if (isl_int_ne(tab->mat->row[row1][1], tab->mat->row[row2][1]))
715 return 0;
717 if (tab->M && isl_int_ne(tab->mat->row[row1][2],
718 tab->mat->row[row2][2]))
719 return 0;
721 for (i = 0; i < tab->n_param + tab->n_div; ++i) {
722 int pos = i < tab->n_param ? i :
723 tab->n_var - tab->n_div + i - tab->n_param;
724 int col;
726 if (tab->var[pos].is_row)
727 continue;
728 col = tab->var[pos].index;
729 if (isl_int_ne(tab->mat->row[row1][off + col],
730 tab->mat->row[row2][off + col]))
731 return 0;
733 return 1;
736 /* Return an inequality that expresses that the "parametric constant"
737 * should be non-negative.
738 * This function is only called when the coefficient of the big parameter
739 * is equal to zero.
741 static struct isl_vec *get_row_parameter_ineq(struct isl_tab *tab, int row)
743 struct isl_vec *ineq;
745 ineq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_param + tab->n_div);
746 if (!ineq)
747 return NULL;
749 get_row_parameter_line(tab, row, ineq->el);
750 if (ineq)
751 ineq = isl_vec_normalize(ineq);
753 return ineq;
756 /* Return a integer division for use in a parametric cut based on the given row.
757 * In particular, let the parametric constant of the row be
759 * \sum_i a_i y_i
761 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
762 * The div returned is equal to
764 * floor(\sum_i {-a_i} y_i) = floor((\sum_i (-a_i mod d) y_i)/d)
766 static struct isl_vec *get_row_parameter_div(struct isl_tab *tab, int row)
768 struct isl_vec *div;
770 div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div);
771 if (!div)
772 return NULL;
774 isl_int_set(div->el[0], tab->mat->row[row][0]);
775 get_row_parameter_line(tab, row, div->el + 1);
776 div = isl_vec_normalize(div);
777 isl_seq_neg(div->el + 1, div->el + 1, div->size - 1);
778 isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1);
780 return div;
783 /* Return a integer division for use in transferring an integrality constraint
784 * to the context.
785 * In particular, let the parametric constant of the row be
787 * \sum_i a_i y_i
789 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
790 * The the returned div is equal to
792 * floor(\sum_i {a_i} y_i) = floor((\sum_i (a_i mod d) y_i)/d)
794 static struct isl_vec *get_row_split_div(struct isl_tab *tab, int row)
796 struct isl_vec *div;
798 div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div);
799 if (!div)
800 return NULL;
802 isl_int_set(div->el[0], tab->mat->row[row][0]);
803 get_row_parameter_line(tab, row, div->el + 1);
804 div = isl_vec_normalize(div);
805 isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1);
807 return div;
810 /* Construct and return an inequality that expresses an upper bound
811 * on the given div.
812 * In particular, if the div is given by
814 * d = floor(e/m)
816 * then the inequality expresses
818 * m d <= e
820 static struct isl_vec *ineq_for_div(struct isl_basic_set *bset, unsigned div)
822 unsigned total;
823 unsigned div_pos;
824 struct isl_vec *ineq;
826 if (!bset)
827 return NULL;
829 total = isl_basic_set_total_dim(bset);
830 div_pos = 1 + total - bset->n_div + div;
832 ineq = isl_vec_alloc(bset->ctx, 1 + total);
833 if (!ineq)
834 return NULL;
836 isl_seq_cpy(ineq->el, bset->div[div] + 1, 1 + total);
837 isl_int_neg(ineq->el[div_pos], bset->div[div][0]);
838 return ineq;
841 /* Given a row in the tableau and a div that was created
842 * using get_row_split_div and that been constrained to equality, i.e.,
844 * d = floor(\sum_i {a_i} y_i) = \sum_i {a_i} y_i
846 * replace the expression "\sum_i {a_i} y_i" in the row by d,
847 * i.e., we subtract "\sum_i {a_i} y_i" and add 1 d.
848 * The coefficients of the non-parameters in the tableau have been
849 * verified to be integral. We can therefore simply replace coefficient b
850 * by floor(b). For the coefficients of the parameters we have
851 * floor(a_i) = a_i - {a_i}, while for the other coefficients, we have
852 * floor(b) = b.
854 static struct isl_tab *set_row_cst_to_div(struct isl_tab *tab, int row, int div)
856 isl_seq_fdiv_q(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
857 tab->mat->row[row][0], 1 + tab->M + tab->n_col);
859 isl_int_set_si(tab->mat->row[row][0], 1);
861 if (tab->var[tab->n_var - tab->n_div + div].is_row) {
862 int drow = tab->var[tab->n_var - tab->n_div + div].index;
864 isl_assert(tab->mat->ctx,
865 isl_int_is_one(tab->mat->row[drow][0]), goto error);
866 isl_seq_combine(tab->mat->row[row] + 1,
867 tab->mat->ctx->one, tab->mat->row[row] + 1,
868 tab->mat->ctx->one, tab->mat->row[drow] + 1,
869 1 + tab->M + tab->n_col);
870 } else {
871 int dcol = tab->var[tab->n_var - tab->n_div + div].index;
873 isl_int_set_si(tab->mat->row[row][2 + tab->M + dcol], 1);
876 return tab;
877 error:
878 isl_tab_free(tab);
879 return NULL;
882 /* Check if the (parametric) constant of the given row is obviously
883 * negative, meaning that we don't need to consult the context tableau.
884 * If there is a big parameter and its coefficient is non-zero,
885 * then this coefficient determines the outcome.
886 * Otherwise, we check whether the constant is negative and
887 * all non-zero coefficients of parameters are negative and
888 * belong to non-negative parameters.
890 static int is_obviously_neg(struct isl_tab *tab, int row)
892 int i;
893 int col;
894 unsigned off = 2 + tab->M;
896 if (tab->M) {
897 if (isl_int_is_pos(tab->mat->row[row][2]))
898 return 0;
899 if (isl_int_is_neg(tab->mat->row[row][2]))
900 return 1;
903 if (isl_int_is_nonneg(tab->mat->row[row][1]))
904 return 0;
905 for (i = 0; i < tab->n_param; ++i) {
906 /* Eliminated parameter */
907 if (tab->var[i].is_row)
908 continue;
909 col = tab->var[i].index;
910 if (isl_int_is_zero(tab->mat->row[row][off + col]))
911 continue;
912 if (!tab->var[i].is_nonneg)
913 return 0;
914 if (isl_int_is_pos(tab->mat->row[row][off + col]))
915 return 0;
917 for (i = 0; i < tab->n_div; ++i) {
918 if (tab->var[tab->n_var - tab->n_div + i].is_row)
919 continue;
920 col = tab->var[tab->n_var - tab->n_div + i].index;
921 if (isl_int_is_zero(tab->mat->row[row][off + col]))
922 continue;
923 if (!tab->var[tab->n_var - tab->n_div + i].is_nonneg)
924 return 0;
925 if (isl_int_is_pos(tab->mat->row[row][off + col]))
926 return 0;
928 return 1;
931 /* Check if the (parametric) constant of the given row is obviously
932 * non-negative, meaning that we don't need to consult the context tableau.
933 * If there is a big parameter and its coefficient is non-zero,
934 * then this coefficient determines the outcome.
935 * Otherwise, we check whether the constant is non-negative and
936 * all non-zero coefficients of parameters are positive and
937 * belong to non-negative parameters.
939 static int is_obviously_nonneg(struct isl_tab *tab, int row)
941 int i;
942 int col;
943 unsigned off = 2 + tab->M;
945 if (tab->M) {
946 if (isl_int_is_pos(tab->mat->row[row][2]))
947 return 1;
948 if (isl_int_is_neg(tab->mat->row[row][2]))
949 return 0;
952 if (isl_int_is_neg(tab->mat->row[row][1]))
953 return 0;
954 for (i = 0; i < tab->n_param; ++i) {
955 /* Eliminated parameter */
956 if (tab->var[i].is_row)
957 continue;
958 col = tab->var[i].index;
959 if (isl_int_is_zero(tab->mat->row[row][off + col]))
960 continue;
961 if (!tab->var[i].is_nonneg)
962 return 0;
963 if (isl_int_is_neg(tab->mat->row[row][off + col]))
964 return 0;
966 for (i = 0; i < tab->n_div; ++i) {
967 if (tab->var[tab->n_var - tab->n_div + i].is_row)
968 continue;
969 col = tab->var[tab->n_var - tab->n_div + i].index;
970 if (isl_int_is_zero(tab->mat->row[row][off + col]))
971 continue;
972 if (!tab->var[tab->n_var - tab->n_div + i].is_nonneg)
973 return 0;
974 if (isl_int_is_neg(tab->mat->row[row][off + col]))
975 return 0;
977 return 1;
980 /* Given a row r and two columns, return the column that would
981 * lead to the lexicographically smallest increment in the sample
982 * solution when leaving the basis in favor of the row.
983 * Pivoting with column c will increment the sample value by a non-negative
984 * constant times a_{V,c}/a_{r,c}, with a_{V,c} the elements of column c
985 * corresponding to the non-parametric variables.
986 * If variable v appears in a column c_v, the a_{v,c} = 1 iff c = c_v,
987 * with all other entries in this virtual row equal to zero.
988 * If variable v appears in a row, then a_{v,c} is the element in column c
989 * of that row.
991 * Let v be the first variable with a_{v,c1}/a_{r,c1} != a_{v,c2}/a_{r,c2}.
992 * Then if a_{v,c1}/a_{r,c1} < a_{v,c2}/a_{r,c2}, i.e.,
993 * a_{v,c2} a_{r,c1} - a_{v,c1} a_{r,c2} > 0, c1 results in the minimal
994 * increment. Otherwise, it's c2.
996 static int lexmin_col_pair(struct isl_tab *tab,
997 int row, int col1, int col2, isl_int tmp)
999 int i;
1000 isl_int *tr;
1002 tr = tab->mat->row[row] + 2 + tab->M;
1004 for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
1005 int s1, s2;
1006 isl_int *r;
1008 if (!tab->var[i].is_row) {
1009 if (tab->var[i].index == col1)
1010 return col2;
1011 if (tab->var[i].index == col2)
1012 return col1;
1013 continue;
1016 if (tab->var[i].index == row)
1017 continue;
1019 r = tab->mat->row[tab->var[i].index] + 2 + tab->M;
1020 s1 = isl_int_sgn(r[col1]);
1021 s2 = isl_int_sgn(r[col2]);
1022 if (s1 == 0 && s2 == 0)
1023 continue;
1024 if (s1 < s2)
1025 return col1;
1026 if (s2 < s1)
1027 return col2;
1029 isl_int_mul(tmp, r[col2], tr[col1]);
1030 isl_int_submul(tmp, r[col1], tr[col2]);
1031 if (isl_int_is_pos(tmp))
1032 return col1;
1033 if (isl_int_is_neg(tmp))
1034 return col2;
1036 return -1;
1039 /* Given a row in the tableau, find and return the column that would
1040 * result in the lexicographically smallest, but positive, increment
1041 * in the sample point.
1042 * If there is no such column, then return tab->n_col.
1043 * If anything goes wrong, return -1.
1045 static int lexmin_pivot_col(struct isl_tab *tab, int row)
1047 int j;
1048 int col = tab->n_col;
1049 isl_int *tr;
1050 isl_int tmp;
1052 tr = tab->mat->row[row] + 2 + tab->M;
1054 isl_int_init(tmp);
1056 for (j = tab->n_dead; j < tab->n_col; ++j) {
1057 if (tab->col_var[j] >= 0 &&
1058 (tab->col_var[j] < tab->n_param ||
1059 tab->col_var[j] >= tab->n_var - tab->n_div))
1060 continue;
1062 if (!isl_int_is_pos(tr[j]))
1063 continue;
1065 if (col == tab->n_col)
1066 col = j;
1067 else
1068 col = lexmin_col_pair(tab, row, col, j, tmp);
1069 isl_assert(tab->mat->ctx, col >= 0, goto error);
1072 isl_int_clear(tmp);
1073 return col;
1074 error:
1075 isl_int_clear(tmp);
1076 return -1;
1079 /* Return the first known violated constraint, i.e., a non-negative
1080 * constraint that currently has an either obviously negative value
1081 * or a previously determined to be negative value.
1083 * If any constraint has a negative coefficient for the big parameter,
1084 * if any, then we return one of these first.
1086 static int first_neg(struct isl_tab *tab)
1088 int row;
1090 if (tab->M)
1091 for (row = tab->n_redundant; row < tab->n_row; ++row) {
1092 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
1093 continue;
1094 if (!isl_int_is_neg(tab->mat->row[row][2]))
1095 continue;
1096 if (tab->row_sign)
1097 tab->row_sign[row] = isl_tab_row_neg;
1098 return row;
1100 for (row = tab->n_redundant; row < tab->n_row; ++row) {
1101 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
1102 continue;
1103 if (tab->row_sign) {
1104 if (tab->row_sign[row] == 0 &&
1105 is_obviously_neg(tab, row))
1106 tab->row_sign[row] = isl_tab_row_neg;
1107 if (tab->row_sign[row] != isl_tab_row_neg)
1108 continue;
1109 } else if (!is_obviously_neg(tab, row))
1110 continue;
1111 return row;
1113 return -1;
1116 /* Check whether the invariant that all columns are lexico-positive
1117 * is satisfied. This function is not called from the current code
1118 * but is useful during debugging.
1120 static void check_lexpos(struct isl_tab *tab)
1122 unsigned off = 2 + tab->M;
1123 int col;
1124 int var;
1125 int row;
1127 for (col = tab->n_dead; col < tab->n_col; ++col) {
1128 if (tab->col_var[col] >= 0 &&
1129 (tab->col_var[col] < tab->n_param ||
1130 tab->col_var[col] >= tab->n_var - tab->n_div))
1131 continue;
1132 for (var = tab->n_param; var < tab->n_var - tab->n_div; ++var) {
1133 if (!tab->var[var].is_row) {
1134 if (tab->var[var].index == col)
1135 break;
1136 else
1137 continue;
1139 row = tab->var[var].index;
1140 if (isl_int_is_zero(tab->mat->row[row][off + col]))
1141 continue;
1142 if (isl_int_is_pos(tab->mat->row[row][off + col]))
1143 break;
1144 fprintf(stderr, "lexneg column %d (row %d)\n",
1145 col, row);
1147 if (var >= tab->n_var - tab->n_div)
1148 fprintf(stderr, "zero column %d\n", col);
1152 /* Report to the caller that the given constraint is part of an encountered
1153 * conflict.
1155 static int report_conflicting_constraint(struct isl_tab *tab, int con)
1157 return tab->conflict(con, tab->conflict_user);
1160 /* Given a conflicting row in the tableau, report all constraints
1161 * involved in the row to the caller. That is, the row itself
1162 * (if represents a constraint) and all constraint columns with
1163 * non-zero (and therefore negative) coefficient.
1165 static int report_conflict(struct isl_tab *tab, int row)
1167 int j;
1168 isl_int *tr;
1170 if (!tab->conflict)
1171 return 0;
1173 if (tab->row_var[row] < 0 &&
1174 report_conflicting_constraint(tab, ~tab->row_var[row]) < 0)
1175 return -1;
1177 tr = tab->mat->row[row] + 2 + tab->M;
1179 for (j = tab->n_dead; j < tab->n_col; ++j) {
1180 if (tab->col_var[j] >= 0 &&
1181 (tab->col_var[j] < tab->n_param ||
1182 tab->col_var[j] >= tab->n_var - tab->n_div))
1183 continue;
1185 if (!isl_int_is_neg(tr[j]))
1186 continue;
1188 if (tab->col_var[j] < 0 &&
1189 report_conflicting_constraint(tab, ~tab->col_var[j]) < 0)
1190 return -1;
1193 return 0;
1196 /* Resolve all known or obviously violated constraints through pivoting.
1197 * In particular, as long as we can find any violated constraint, we
1198 * look for a pivoting column that would result in the lexicographically
1199 * smallest increment in the sample point. If there is no such column
1200 * then the tableau is infeasible.
1202 static int restore_lexmin(struct isl_tab *tab) WARN_UNUSED;
1203 static int restore_lexmin(struct isl_tab *tab)
1205 int row, col;
1207 if (!tab)
1208 return -1;
1209 if (tab->empty)
1210 return 0;
1211 while ((row = first_neg(tab)) != -1) {
1212 col = lexmin_pivot_col(tab, row);
1213 if (col >= tab->n_col) {
1214 if (report_conflict(tab, row) < 0)
1215 return -1;
1216 if (isl_tab_mark_empty(tab) < 0)
1217 return -1;
1218 return 0;
1220 if (col < 0)
1221 return -1;
1222 if (isl_tab_pivot(tab, row, col) < 0)
1223 return -1;
1225 return 0;
1228 /* Given a row that represents an equality, look for an appropriate
1229 * pivoting column.
1230 * In particular, if there are any non-zero coefficients among
1231 * the non-parameter variables, then we take the last of these
1232 * variables. Eliminating this variable in terms of the other
1233 * variables and/or parameters does not influence the property
1234 * that all column in the initial tableau are lexicographically
1235 * positive. The row corresponding to the eliminated variable
1236 * will only have non-zero entries below the diagonal of the
1237 * initial tableau. That is, we transform
1239 * I I
1240 * 1 into a
1241 * I I
1243 * If there is no such non-parameter variable, then we are dealing with
1244 * pure parameter equality and we pick any parameter with coefficient 1 or -1
1245 * for elimination. This will ensure that the eliminated parameter
1246 * always has an integer value whenever all the other parameters are integral.
1247 * If there is no such parameter then we return -1.
1249 static int last_var_col_or_int_par_col(struct isl_tab *tab, int row)
1251 unsigned off = 2 + tab->M;
1252 int i;
1254 for (i = tab->n_var - tab->n_div - 1; i >= 0 && i >= tab->n_param; --i) {
1255 int col;
1256 if (tab->var[i].is_row)
1257 continue;
1258 col = tab->var[i].index;
1259 if (col <= tab->n_dead)
1260 continue;
1261 if (!isl_int_is_zero(tab->mat->row[row][off + col]))
1262 return col;
1264 for (i = tab->n_dead; i < tab->n_col; ++i) {
1265 if (isl_int_is_one(tab->mat->row[row][off + i]))
1266 return i;
1267 if (isl_int_is_negone(tab->mat->row[row][off + i]))
1268 return i;
1270 return -1;
1273 /* Add an equality that is known to be valid to the tableau.
1274 * We first check if we can eliminate a variable or a parameter.
1275 * If not, we add the equality as two inequalities.
1276 * In this case, the equality was a pure parameter equality and there
1277 * is no need to resolve any constraint violations.
1279 static struct isl_tab *add_lexmin_valid_eq(struct isl_tab *tab, isl_int *eq)
1281 int i;
1282 int r;
1284 if (!tab)
1285 return NULL;
1286 r = isl_tab_add_row(tab, eq);
1287 if (r < 0)
1288 goto error;
1290 r = tab->con[r].index;
1291 i = last_var_col_or_int_par_col(tab, r);
1292 if (i < 0) {
1293 tab->con[r].is_nonneg = 1;
1294 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1295 goto error;
1296 isl_seq_neg(eq, eq, 1 + tab->n_var);
1297 r = isl_tab_add_row(tab, eq);
1298 if (r < 0)
1299 goto error;
1300 tab->con[r].is_nonneg = 1;
1301 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1302 goto error;
1303 } else {
1304 if (isl_tab_pivot(tab, r, i) < 0)
1305 goto error;
1306 if (isl_tab_kill_col(tab, i) < 0)
1307 goto error;
1308 tab->n_eq++;
1311 return tab;
1312 error:
1313 isl_tab_free(tab);
1314 return NULL;
1317 /* Check if the given row is a pure constant.
1319 static int is_constant(struct isl_tab *tab, int row)
1321 unsigned off = 2 + tab->M;
1323 return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1324 tab->n_col - tab->n_dead) == -1;
1327 /* Add an equality that may or may not be valid to the tableau.
1328 * If the resulting row is a pure constant, then it must be zero.
1329 * Otherwise, the resulting tableau is empty.
1331 * If the row is not a pure constant, then we add two inequalities,
1332 * each time checking that they can be satisfied.
1333 * In the end we try to use one of the two constraints to eliminate
1334 * a column.
1336 static int add_lexmin_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
1337 static int add_lexmin_eq(struct isl_tab *tab, isl_int *eq)
1339 int r1, r2;
1340 int row;
1341 struct isl_tab_undo *snap;
1343 if (!tab)
1344 return -1;
1345 snap = isl_tab_snap(tab);
1346 r1 = isl_tab_add_row(tab, eq);
1347 if (r1 < 0)
1348 return -1;
1349 tab->con[r1].is_nonneg = 1;
1350 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r1]) < 0)
1351 return -1;
1353 row = tab->con[r1].index;
1354 if (is_constant(tab, row)) {
1355 if (!isl_int_is_zero(tab->mat->row[row][1]) ||
1356 (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))) {
1357 if (isl_tab_mark_empty(tab) < 0)
1358 return -1;
1359 return 0;
1361 if (isl_tab_rollback(tab, snap) < 0)
1362 return -1;
1363 return 0;
1366 if (restore_lexmin(tab) < 0)
1367 return -1;
1368 if (tab->empty)
1369 return 0;
1371 isl_seq_neg(eq, eq, 1 + tab->n_var);
1373 r2 = isl_tab_add_row(tab, eq);
1374 if (r2 < 0)
1375 return -1;
1376 tab->con[r2].is_nonneg = 1;
1377 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r2]) < 0)
1378 return -1;
1380 if (restore_lexmin(tab) < 0)
1381 return -1;
1382 if (tab->empty)
1383 return 0;
1385 if (!tab->con[r1].is_row) {
1386 if (isl_tab_kill_col(tab, tab->con[r1].index) < 0)
1387 return -1;
1388 } else if (!tab->con[r2].is_row) {
1389 if (isl_tab_kill_col(tab, tab->con[r2].index) < 0)
1390 return -1;
1393 if (tab->bmap) {
1394 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
1395 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1396 return -1;
1397 isl_seq_neg(eq, eq, 1 + tab->n_var);
1398 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
1399 isl_seq_neg(eq, eq, 1 + tab->n_var);
1400 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1401 return -1;
1402 if (!tab->bmap)
1403 return -1;
1406 return 0;
1409 /* Add an inequality to the tableau, resolving violations using
1410 * restore_lexmin.
1412 static struct isl_tab *add_lexmin_ineq(struct isl_tab *tab, isl_int *ineq)
1414 int r;
1416 if (!tab)
1417 return NULL;
1418 if (tab->bmap) {
1419 tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
1420 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1421 goto error;
1422 if (!tab->bmap)
1423 goto error;
1425 r = isl_tab_add_row(tab, ineq);
1426 if (r < 0)
1427 goto error;
1428 tab->con[r].is_nonneg = 1;
1429 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1430 goto error;
1431 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1432 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1433 goto error;
1434 return tab;
1437 if (restore_lexmin(tab) < 0)
1438 goto error;
1439 if (!tab->empty && tab->con[r].is_row &&
1440 isl_tab_row_is_redundant(tab, tab->con[r].index))
1441 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1442 goto error;
1443 return tab;
1444 error:
1445 isl_tab_free(tab);
1446 return NULL;
1449 /* Check if the coefficients of the parameters are all integral.
1451 static int integer_parameter(struct isl_tab *tab, int row)
1453 int i;
1454 int col;
1455 unsigned off = 2 + tab->M;
1457 for (i = 0; i < tab->n_param; ++i) {
1458 /* Eliminated parameter */
1459 if (tab->var[i].is_row)
1460 continue;
1461 col = tab->var[i].index;
1462 if (!isl_int_is_divisible_by(tab->mat->row[row][off + col],
1463 tab->mat->row[row][0]))
1464 return 0;
1466 for (i = 0; i < tab->n_div; ++i) {
1467 if (tab->var[tab->n_var - tab->n_div + i].is_row)
1468 continue;
1469 col = tab->var[tab->n_var - tab->n_div + i].index;
1470 if (!isl_int_is_divisible_by(tab->mat->row[row][off + col],
1471 tab->mat->row[row][0]))
1472 return 0;
1474 return 1;
1477 /* Check if the coefficients of the non-parameter variables are all integral.
1479 static int integer_variable(struct isl_tab *tab, int row)
1481 int i;
1482 unsigned off = 2 + tab->M;
1484 for (i = tab->n_dead; i < tab->n_col; ++i) {
1485 if (tab->col_var[i] >= 0 &&
1486 (tab->col_var[i] < tab->n_param ||
1487 tab->col_var[i] >= tab->n_var - tab->n_div))
1488 continue;
1489 if (!isl_int_is_divisible_by(tab->mat->row[row][off + i],
1490 tab->mat->row[row][0]))
1491 return 0;
1493 return 1;
1496 /* Check if the constant term is integral.
1498 static int integer_constant(struct isl_tab *tab, int row)
1500 return isl_int_is_divisible_by(tab->mat->row[row][1],
1501 tab->mat->row[row][0]);
1504 #define I_CST 1 << 0
1505 #define I_PAR 1 << 1
1506 #define I_VAR 1 << 2
1508 /* Check for next (non-parameter) variable after "var" (first if var == -1)
1509 * that is non-integer and therefore requires a cut and return
1510 * the index of the variable.
1511 * For parametric tableaus, there are three parts in a row,
1512 * the constant, the coefficients of the parameters and the rest.
1513 * For each part, we check whether the coefficients in that part
1514 * are all integral and if so, set the corresponding flag in *f.
1515 * If the constant and the parameter part are integral, then the
1516 * current sample value is integral and no cut is required
1517 * (irrespective of whether the variable part is integral).
1519 static int next_non_integer_var(struct isl_tab *tab, int var, int *f)
1521 var = var < 0 ? tab->n_param : var + 1;
1523 for (; var < tab->n_var - tab->n_div; ++var) {
1524 int flags = 0;
1525 int row;
1526 if (!tab->var[var].is_row)
1527 continue;
1528 row = tab->var[var].index;
1529 if (integer_constant(tab, row))
1530 ISL_FL_SET(flags, I_CST);
1531 if (integer_parameter(tab, row))
1532 ISL_FL_SET(flags, I_PAR);
1533 if (ISL_FL_ISSET(flags, I_CST) && ISL_FL_ISSET(flags, I_PAR))
1534 continue;
1535 if (integer_variable(tab, row))
1536 ISL_FL_SET(flags, I_VAR);
1537 *f = flags;
1538 return var;
1540 return -1;
1543 /* Check for first (non-parameter) variable that is non-integer and
1544 * therefore requires a cut and return the corresponding row.
1545 * For parametric tableaus, there are three parts in a row,
1546 * the constant, the coefficients of the parameters and the rest.
1547 * For each part, we check whether the coefficients in that part
1548 * are all integral and if so, set the corresponding flag in *f.
1549 * If the constant and the parameter part are integral, then the
1550 * current sample value is integral and no cut is required
1551 * (irrespective of whether the variable part is integral).
1553 static int first_non_integer_row(struct isl_tab *tab, int *f)
1555 int var = next_non_integer_var(tab, -1, f);
1557 return var < 0 ? -1 : tab->var[var].index;
1560 /* Add a (non-parametric) cut to cut away the non-integral sample
1561 * value of the given row.
1563 * If the row is given by
1565 * m r = f + \sum_i a_i y_i
1567 * then the cut is
1569 * c = - {-f/m} + \sum_i {a_i/m} y_i >= 0
1571 * The big parameter, if any, is ignored, since it is assumed to be big
1572 * enough to be divisible by any integer.
1573 * If the tableau is actually a parametric tableau, then this function
1574 * is only called when all coefficients of the parameters are integral.
1575 * The cut therefore has zero coefficients for the parameters.
1577 * The current value is known to be negative, so row_sign, if it
1578 * exists, is set accordingly.
1580 * Return the row of the cut or -1.
1582 static int add_cut(struct isl_tab *tab, int row)
1584 int i;
1585 int r;
1586 isl_int *r_row;
1587 unsigned off = 2 + tab->M;
1589 if (isl_tab_extend_cons(tab, 1) < 0)
1590 return -1;
1591 r = isl_tab_allocate_con(tab);
1592 if (r < 0)
1593 return -1;
1595 r_row = tab->mat->row[tab->con[r].index];
1596 isl_int_set(r_row[0], tab->mat->row[row][0]);
1597 isl_int_neg(r_row[1], tab->mat->row[row][1]);
1598 isl_int_fdiv_r(r_row[1], r_row[1], tab->mat->row[row][0]);
1599 isl_int_neg(r_row[1], r_row[1]);
1600 if (tab->M)
1601 isl_int_set_si(r_row[2], 0);
1602 for (i = 0; i < tab->n_col; ++i)
1603 isl_int_fdiv_r(r_row[off + i],
1604 tab->mat->row[row][off + i], tab->mat->row[row][0]);
1606 tab->con[r].is_nonneg = 1;
1607 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1608 return -1;
1609 if (tab->row_sign)
1610 tab->row_sign[tab->con[r].index] = isl_tab_row_neg;
1612 return tab->con[r].index;
1615 /* Given a non-parametric tableau, add cuts until an integer
1616 * sample point is obtained or until the tableau is determined
1617 * to be integer infeasible.
1618 * As long as there is any non-integer value in the sample point,
1619 * we add appropriate cuts, if possible, for each of these
1620 * non-integer values and then resolve the violated
1621 * cut constraints using restore_lexmin.
1622 * If one of the corresponding rows is equal to an integral
1623 * combination of variables/constraints plus a non-integral constant,
1624 * then there is no way to obtain an integer point and we return
1625 * a tableau that is marked empty.
1627 static struct isl_tab *cut_to_integer_lexmin(struct isl_tab *tab)
1629 int var;
1630 int row;
1631 int flags;
1633 if (!tab)
1634 return NULL;
1635 if (tab->empty)
1636 return tab;
1638 while ((var = next_non_integer_var(tab, -1, &flags)) != -1) {
1639 do {
1640 if (ISL_FL_ISSET(flags, I_VAR)) {
1641 if (isl_tab_mark_empty(tab) < 0)
1642 goto error;
1643 return tab;
1645 row = tab->var[var].index;
1646 row = add_cut(tab, row);
1647 if (row < 0)
1648 goto error;
1649 } while ((var = next_non_integer_var(tab, var, &flags)) != -1);
1650 if (restore_lexmin(tab) < 0)
1651 goto error;
1652 if (tab->empty)
1653 break;
1655 return tab;
1656 error:
1657 isl_tab_free(tab);
1658 return NULL;
1661 /* Check whether all the currently active samples also satisfy the inequality
1662 * "ineq" (treated as an equality if eq is set).
1663 * Remove those samples that do not.
1665 static struct isl_tab *check_samples(struct isl_tab *tab, isl_int *ineq, int eq)
1667 int i;
1668 isl_int v;
1670 if (!tab)
1671 return NULL;
1673 isl_assert(tab->mat->ctx, tab->bmap, goto error);
1674 isl_assert(tab->mat->ctx, tab->samples, goto error);
1675 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error);
1677 isl_int_init(v);
1678 for (i = tab->n_outside; i < tab->n_sample; ++i) {
1679 int sgn;
1680 isl_seq_inner_product(ineq, tab->samples->row[i],
1681 1 + tab->n_var, &v);
1682 sgn = isl_int_sgn(v);
1683 if (eq ? (sgn == 0) : (sgn >= 0))
1684 continue;
1685 tab = isl_tab_drop_sample(tab, i);
1686 if (!tab)
1687 break;
1689 isl_int_clear(v);
1691 return tab;
1692 error:
1693 isl_tab_free(tab);
1694 return NULL;
1697 /* Check whether the sample value of the tableau is finite,
1698 * i.e., either the tableau does not use a big parameter, or
1699 * all values of the variables are equal to the big parameter plus
1700 * some constant. This constant is the actual sample value.
1702 static int sample_is_finite(struct isl_tab *tab)
1704 int i;
1706 if (!tab->M)
1707 return 1;
1709 for (i = 0; i < tab->n_var; ++i) {
1710 int row;
1711 if (!tab->var[i].is_row)
1712 return 0;
1713 row = tab->var[i].index;
1714 if (isl_int_ne(tab->mat->row[row][0], tab->mat->row[row][2]))
1715 return 0;
1717 return 1;
1720 /* Check if the context tableau of sol has any integer points.
1721 * Leave tab in empty state if no integer point can be found.
1722 * If an integer point can be found and if moreover it is finite,
1723 * then it is added to the list of sample values.
1725 * This function is only called when none of the currently active sample
1726 * values satisfies the most recently added constraint.
1728 static struct isl_tab *check_integer_feasible(struct isl_tab *tab)
1730 struct isl_tab_undo *snap;
1731 int feasible;
1733 if (!tab)
1734 return NULL;
1736 snap = isl_tab_snap(tab);
1737 if (isl_tab_push_basis(tab) < 0)
1738 goto error;
1740 tab = cut_to_integer_lexmin(tab);
1741 if (!tab)
1742 goto error;
1744 if (!tab->empty && sample_is_finite(tab)) {
1745 struct isl_vec *sample;
1747 sample = isl_tab_get_sample_value(tab);
1749 tab = isl_tab_add_sample(tab, sample);
1752 if (!tab->empty && isl_tab_rollback(tab, snap) < 0)
1753 goto error;
1755 return tab;
1756 error:
1757 isl_tab_free(tab);
1758 return NULL;
1761 /* Check if any of the currently active sample values satisfies
1762 * the inequality "ineq" (an equality if eq is set).
1764 static int tab_has_valid_sample(struct isl_tab *tab, isl_int *ineq, int eq)
1766 int i;
1767 isl_int v;
1769 if (!tab)
1770 return -1;
1772 isl_assert(tab->mat->ctx, tab->bmap, return -1);
1773 isl_assert(tab->mat->ctx, tab->samples, return -1);
1774 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, return -1);
1776 isl_int_init(v);
1777 for (i = tab->n_outside; i < tab->n_sample; ++i) {
1778 int sgn;
1779 isl_seq_inner_product(ineq, tab->samples->row[i],
1780 1 + tab->n_var, &v);
1781 sgn = isl_int_sgn(v);
1782 if (eq ? (sgn == 0) : (sgn >= 0))
1783 break;
1785 isl_int_clear(v);
1787 return i < tab->n_sample;
1790 /* Add a div specified by "div" to the tableau "tab" and return
1791 * 1 if the div is obviously non-negative.
1793 static int context_tab_add_div(struct isl_tab *tab, struct isl_vec *div,
1794 int (*add_ineq)(void *user, isl_int *), void *user)
1796 int i;
1797 int r;
1798 struct isl_mat *samples;
1799 int nonneg;
1801 r = isl_tab_add_div(tab, div, add_ineq, user);
1802 if (r < 0)
1803 return -1;
1804 nonneg = tab->var[r].is_nonneg;
1805 tab->var[r].frozen = 1;
1807 samples = isl_mat_extend(tab->samples,
1808 tab->n_sample, 1 + tab->n_var);
1809 tab->samples = samples;
1810 if (!samples)
1811 return -1;
1812 for (i = tab->n_outside; i < samples->n_row; ++i) {
1813 isl_seq_inner_product(div->el + 1, samples->row[i],
1814 div->size - 1, &samples->row[i][samples->n_col - 1]);
1815 isl_int_fdiv_q(samples->row[i][samples->n_col - 1],
1816 samples->row[i][samples->n_col - 1], div->el[0]);
1819 return nonneg;
1822 /* Add a div specified by "div" to both the main tableau and
1823 * the context tableau. In case of the main tableau, we only
1824 * need to add an extra div. In the context tableau, we also
1825 * need to express the meaning of the div.
1826 * Return the index of the div or -1 if anything went wrong.
1828 static int add_div(struct isl_tab *tab, struct isl_context *context,
1829 struct isl_vec *div)
1831 int r;
1832 int nonneg;
1834 if ((nonneg = context->op->add_div(context, div)) < 0)
1835 goto error;
1837 if (!context->op->is_ok(context))
1838 goto error;
1840 if (isl_tab_extend_vars(tab, 1) < 0)
1841 goto error;
1842 r = isl_tab_allocate_var(tab);
1843 if (r < 0)
1844 goto error;
1845 if (nonneg)
1846 tab->var[r].is_nonneg = 1;
1847 tab->var[r].frozen = 1;
1848 tab->n_div++;
1850 return tab->n_div - 1;
1851 error:
1852 context->op->invalidate(context);
1853 return -1;
1856 static int find_div(struct isl_tab *tab, isl_int *div, isl_int denom)
1858 int i;
1859 unsigned total = isl_basic_map_total_dim(tab->bmap);
1861 for (i = 0; i < tab->bmap->n_div; ++i) {
1862 if (isl_int_ne(tab->bmap->div[i][0], denom))
1863 continue;
1864 if (!isl_seq_eq(tab->bmap->div[i] + 1, div, 1 + total))
1865 continue;
1866 return i;
1868 return -1;
1871 /* Return the index of a div that corresponds to "div".
1872 * We first check if we already have such a div and if not, we create one.
1874 static int get_div(struct isl_tab *tab, struct isl_context *context,
1875 struct isl_vec *div)
1877 int d;
1878 struct isl_tab *context_tab = context->op->peek_tab(context);
1880 if (!context_tab)
1881 return -1;
1883 d = find_div(context_tab, div->el + 1, div->el[0]);
1884 if (d != -1)
1885 return d;
1887 return add_div(tab, context, div);
1890 /* Add a parametric cut to cut away the non-integral sample value
1891 * of the give row.
1892 * Let a_i be the coefficients of the constant term and the parameters
1893 * and let b_i be the coefficients of the variables or constraints
1894 * in basis of the tableau.
1895 * Let q be the div q = floor(\sum_i {-a_i} y_i).
1897 * The cut is expressed as
1899 * c = \sum_i -{-a_i} y_i + \sum_i {b_i} x_i + q >= 0
1901 * If q did not already exist in the context tableau, then it is added first.
1902 * If q is in a column of the main tableau then the "+ q" can be accomplished
1903 * by setting the corresponding entry to the denominator of the constraint.
1904 * If q happens to be in a row of the main tableau, then the corresponding
1905 * row needs to be added instead (taking care of the denominators).
1906 * Note that this is very unlikely, but perhaps not entirely impossible.
1908 * The current value of the cut is known to be negative (or at least
1909 * non-positive), so row_sign is set accordingly.
1911 * Return the row of the cut or -1.
1913 static int add_parametric_cut(struct isl_tab *tab, int row,
1914 struct isl_context *context)
1916 struct isl_vec *div;
1917 int d;
1918 int i;
1919 int r;
1920 isl_int *r_row;
1921 int col;
1922 int n;
1923 unsigned off = 2 + tab->M;
1925 if (!context)
1926 return -1;
1928 div = get_row_parameter_div(tab, row);
1929 if (!div)
1930 return -1;
1932 n = tab->n_div;
1933 d = context->op->get_div(context, tab, div);
1934 if (d < 0)
1935 return -1;
1937 if (isl_tab_extend_cons(tab, 1) < 0)
1938 return -1;
1939 r = isl_tab_allocate_con(tab);
1940 if (r < 0)
1941 return -1;
1943 r_row = tab->mat->row[tab->con[r].index];
1944 isl_int_set(r_row[0], tab->mat->row[row][0]);
1945 isl_int_neg(r_row[1], tab->mat->row[row][1]);
1946 isl_int_fdiv_r(r_row[1], r_row[1], tab->mat->row[row][0]);
1947 isl_int_neg(r_row[1], r_row[1]);
1948 if (tab->M)
1949 isl_int_set_si(r_row[2], 0);
1950 for (i = 0; i < tab->n_param; ++i) {
1951 if (tab->var[i].is_row)
1952 continue;
1953 col = tab->var[i].index;
1954 isl_int_neg(r_row[off + col], tab->mat->row[row][off + col]);
1955 isl_int_fdiv_r(r_row[off + col], r_row[off + col],
1956 tab->mat->row[row][0]);
1957 isl_int_neg(r_row[off + col], r_row[off + col]);
1959 for (i = 0; i < tab->n_div; ++i) {
1960 if (tab->var[tab->n_var - tab->n_div + i].is_row)
1961 continue;
1962 col = tab->var[tab->n_var - tab->n_div + i].index;
1963 isl_int_neg(r_row[off + col], tab->mat->row[row][off + col]);
1964 isl_int_fdiv_r(r_row[off + col], r_row[off + col],
1965 tab->mat->row[row][0]);
1966 isl_int_neg(r_row[off + col], r_row[off + col]);
1968 for (i = 0; i < tab->n_col; ++i) {
1969 if (tab->col_var[i] >= 0 &&
1970 (tab->col_var[i] < tab->n_param ||
1971 tab->col_var[i] >= tab->n_var - tab->n_div))
1972 continue;
1973 isl_int_fdiv_r(r_row[off + i],
1974 tab->mat->row[row][off + i], tab->mat->row[row][0]);
1976 if (tab->var[tab->n_var - tab->n_div + d].is_row) {
1977 isl_int gcd;
1978 int d_row = tab->var[tab->n_var - tab->n_div + d].index;
1979 isl_int_init(gcd);
1980 isl_int_gcd(gcd, tab->mat->row[d_row][0], r_row[0]);
1981 isl_int_divexact(r_row[0], r_row[0], gcd);
1982 isl_int_divexact(gcd, tab->mat->row[d_row][0], gcd);
1983 isl_seq_combine(r_row + 1, gcd, r_row + 1,
1984 r_row[0], tab->mat->row[d_row] + 1,
1985 off - 1 + tab->n_col);
1986 isl_int_mul(r_row[0], r_row[0], tab->mat->row[d_row][0]);
1987 isl_int_clear(gcd);
1988 } else {
1989 col = tab->var[tab->n_var - tab->n_div + d].index;
1990 isl_int_set(r_row[off + col], tab->mat->row[row][0]);
1993 tab->con[r].is_nonneg = 1;
1994 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1995 return -1;
1996 if (tab->row_sign)
1997 tab->row_sign[tab->con[r].index] = isl_tab_row_neg;
1999 isl_vec_free(div);
2001 row = tab->con[r].index;
2003 if (d >= n && context->op->detect_equalities(context, tab) < 0)
2004 return -1;
2006 return row;
2009 /* Construct a tableau for bmap that can be used for computing
2010 * the lexicographic minimum (or maximum) of bmap.
2011 * If not NULL, then dom is the domain where the minimum
2012 * should be computed. In this case, we set up a parametric
2013 * tableau with row signs (initialized to "unknown").
2014 * If M is set, then the tableau will use a big parameter.
2015 * If max is set, then a maximum should be computed instead of a minimum.
2016 * This means that for each variable x, the tableau will contain the variable
2017 * x' = M - x, rather than x' = M + x. This in turn means that the coefficient
2018 * of the variables in all constraints are negated prior to adding them
2019 * to the tableau.
2021 static struct isl_tab *tab_for_lexmin(struct isl_basic_map *bmap,
2022 struct isl_basic_set *dom, unsigned M, int max)
2024 int i;
2025 struct isl_tab *tab;
2027 tab = isl_tab_alloc(bmap->ctx, 2 * bmap->n_eq + bmap->n_ineq + 1,
2028 isl_basic_map_total_dim(bmap), M);
2029 if (!tab)
2030 return NULL;
2032 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
2033 if (dom) {
2034 tab->n_param = isl_basic_set_total_dim(dom) - dom->n_div;
2035 tab->n_div = dom->n_div;
2036 tab->row_sign = isl_calloc_array(bmap->ctx,
2037 enum isl_tab_row_sign, tab->mat->n_row);
2038 if (!tab->row_sign)
2039 goto error;
2041 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
2042 if (isl_tab_mark_empty(tab) < 0)
2043 goto error;
2044 return tab;
2047 for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
2048 tab->var[i].is_nonneg = 1;
2049 tab->var[i].frozen = 1;
2051 for (i = 0; i < bmap->n_eq; ++i) {
2052 if (max)
2053 isl_seq_neg(bmap->eq[i] + 1 + tab->n_param,
2054 bmap->eq[i] + 1 + tab->n_param,
2055 tab->n_var - tab->n_param - tab->n_div);
2056 tab = add_lexmin_valid_eq(tab, bmap->eq[i]);
2057 if (max)
2058 isl_seq_neg(bmap->eq[i] + 1 + tab->n_param,
2059 bmap->eq[i] + 1 + tab->n_param,
2060 tab->n_var - tab->n_param - tab->n_div);
2061 if (!tab || tab->empty)
2062 return tab;
2064 if (bmap->n_eq && restore_lexmin(tab) < 0)
2065 goto error;
2066 for (i = 0; i < bmap->n_ineq; ++i) {
2067 if (max)
2068 isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param,
2069 bmap->ineq[i] + 1 + tab->n_param,
2070 tab->n_var - tab->n_param - tab->n_div);
2071 tab = add_lexmin_ineq(tab, bmap->ineq[i]);
2072 if (max)
2073 isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param,
2074 bmap->ineq[i] + 1 + tab->n_param,
2075 tab->n_var - tab->n_param - tab->n_div);
2076 if (!tab || tab->empty)
2077 return tab;
2079 return tab;
2080 error:
2081 isl_tab_free(tab);
2082 return NULL;
2085 /* Given a main tableau where more than one row requires a split,
2086 * determine and return the "best" row to split on.
2088 * Given two rows in the main tableau, if the inequality corresponding
2089 * to the first row is redundant with respect to that of the second row
2090 * in the current tableau, then it is better to split on the second row,
2091 * since in the positive part, both row will be positive.
2092 * (In the negative part a pivot will have to be performed and just about
2093 * anything can happen to the sign of the other row.)
2095 * As a simple heuristic, we therefore select the row that makes the most
2096 * of the other rows redundant.
2098 * Perhaps it would also be useful to look at the number of constraints
2099 * that conflict with any given constraint.
2101 static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
2103 struct isl_tab_undo *snap;
2104 int split;
2105 int row;
2106 int best = -1;
2107 int best_r;
2109 if (isl_tab_extend_cons(context_tab, 2) < 0)
2110 return -1;
2112 snap = isl_tab_snap(context_tab);
2114 for (split = tab->n_redundant; split < tab->n_row; ++split) {
2115 struct isl_tab_undo *snap2;
2116 struct isl_vec *ineq = NULL;
2117 int r = 0;
2118 int ok;
2120 if (!isl_tab_var_from_row(tab, split)->is_nonneg)
2121 continue;
2122 if (tab->row_sign[split] != isl_tab_row_any)
2123 continue;
2125 ineq = get_row_parameter_ineq(tab, split);
2126 if (!ineq)
2127 return -1;
2128 ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
2129 isl_vec_free(ineq);
2130 if (!ok)
2131 return -1;
2133 snap2 = isl_tab_snap(context_tab);
2135 for (row = tab->n_redundant; row < tab->n_row; ++row) {
2136 struct isl_tab_var *var;
2138 if (row == split)
2139 continue;
2140 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
2141 continue;
2142 if (tab->row_sign[row] != isl_tab_row_any)
2143 continue;
2145 ineq = get_row_parameter_ineq(tab, row);
2146 if (!ineq)
2147 return -1;
2148 ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
2149 isl_vec_free(ineq);
2150 if (!ok)
2151 return -1;
2152 var = &context_tab->con[context_tab->n_con - 1];
2153 if (!context_tab->empty &&
2154 !isl_tab_min_at_most_neg_one(context_tab, var))
2155 r++;
2156 if (isl_tab_rollback(context_tab, snap2) < 0)
2157 return -1;
2159 if (best == -1 || r > best_r) {
2160 best = split;
2161 best_r = r;
2163 if (isl_tab_rollback(context_tab, snap) < 0)
2164 return -1;
2167 return best;
2170 static struct isl_basic_set *context_lex_peek_basic_set(
2171 struct isl_context *context)
2173 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2174 if (!clex->tab)
2175 return NULL;
2176 return isl_tab_peek_bset(clex->tab);
2179 static struct isl_tab *context_lex_peek_tab(struct isl_context *context)
2181 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2182 return clex->tab;
2185 static void context_lex_extend(struct isl_context *context, int n)
2187 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2188 if (!clex->tab)
2189 return;
2190 if (isl_tab_extend_cons(clex->tab, n) >= 0)
2191 return;
2192 isl_tab_free(clex->tab);
2193 clex->tab = NULL;
2196 static void context_lex_add_eq(struct isl_context *context, isl_int *eq,
2197 int check, int update)
2199 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2200 if (isl_tab_extend_cons(clex->tab, 2) < 0)
2201 goto error;
2202 if (add_lexmin_eq(clex->tab, eq) < 0)
2203 goto error;
2204 if (check) {
2205 int v = tab_has_valid_sample(clex->tab, eq, 1);
2206 if (v < 0)
2207 goto error;
2208 if (!v)
2209 clex->tab = check_integer_feasible(clex->tab);
2211 if (update)
2212 clex->tab = check_samples(clex->tab, eq, 1);
2213 return;
2214 error:
2215 isl_tab_free(clex->tab);
2216 clex->tab = NULL;
2219 static void context_lex_add_ineq(struct isl_context *context, isl_int *ineq,
2220 int check, int update)
2222 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2223 if (isl_tab_extend_cons(clex->tab, 1) < 0)
2224 goto error;
2225 clex->tab = add_lexmin_ineq(clex->tab, ineq);
2226 if (check) {
2227 int v = tab_has_valid_sample(clex->tab, ineq, 0);
2228 if (v < 0)
2229 goto error;
2230 if (!v)
2231 clex->tab = check_integer_feasible(clex->tab);
2233 if (update)
2234 clex->tab = check_samples(clex->tab, ineq, 0);
2235 return;
2236 error:
2237 isl_tab_free(clex->tab);
2238 clex->tab = NULL;
2241 static int context_lex_add_ineq_wrap(void *user, isl_int *ineq)
2243 struct isl_context *context = (struct isl_context *)user;
2244 context_lex_add_ineq(context, ineq, 0, 0);
2245 return context->op->is_ok(context) ? 0 : -1;
2248 /* Check which signs can be obtained by "ineq" on all the currently
2249 * active sample values. See row_sign for more information.
2251 static enum isl_tab_row_sign tab_ineq_sign(struct isl_tab *tab, isl_int *ineq,
2252 int strict)
2254 int i;
2255 int sgn;
2256 isl_int tmp;
2257 enum isl_tab_row_sign res = isl_tab_row_unknown;
2259 isl_assert(tab->mat->ctx, tab->samples, return isl_tab_row_unknown);
2260 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var,
2261 return isl_tab_row_unknown);
2263 isl_int_init(tmp);
2264 for (i = tab->n_outside; i < tab->n_sample; ++i) {
2265 isl_seq_inner_product(tab->samples->row[i], ineq,
2266 1 + tab->n_var, &tmp);
2267 sgn = isl_int_sgn(tmp);
2268 if (sgn > 0 || (sgn == 0 && strict)) {
2269 if (res == isl_tab_row_unknown)
2270 res = isl_tab_row_pos;
2271 if (res == isl_tab_row_neg)
2272 res = isl_tab_row_any;
2274 if (sgn < 0) {
2275 if (res == isl_tab_row_unknown)
2276 res = isl_tab_row_neg;
2277 if (res == isl_tab_row_pos)
2278 res = isl_tab_row_any;
2280 if (res == isl_tab_row_any)
2281 break;
2283 isl_int_clear(tmp);
2285 return res;
2288 static enum isl_tab_row_sign context_lex_ineq_sign(struct isl_context *context,
2289 isl_int *ineq, int strict)
2291 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2292 return tab_ineq_sign(clex->tab, ineq, strict);
2295 /* Check whether "ineq" can be added to the tableau without rendering
2296 * it infeasible.
2298 static int context_lex_test_ineq(struct isl_context *context, isl_int *ineq)
2300 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2301 struct isl_tab_undo *snap;
2302 int feasible;
2304 if (!clex->tab)
2305 return -1;
2307 if (isl_tab_extend_cons(clex->tab, 1) < 0)
2308 return -1;
2310 snap = isl_tab_snap(clex->tab);
2311 if (isl_tab_push_basis(clex->tab) < 0)
2312 return -1;
2313 clex->tab = add_lexmin_ineq(clex->tab, ineq);
2314 clex->tab = check_integer_feasible(clex->tab);
2315 if (!clex->tab)
2316 return -1;
2317 feasible = !clex->tab->empty;
2318 if (isl_tab_rollback(clex->tab, snap) < 0)
2319 return -1;
2321 return feasible;
2324 static int context_lex_get_div(struct isl_context *context, struct isl_tab *tab,
2325 struct isl_vec *div)
2327 return get_div(tab, context, div);
2330 /* Add a div specified by "div" to the context tableau and return
2331 * 1 if the div is obviously non-negative.
2332 * context_tab_add_div will always return 1, because all variables
2333 * in a isl_context_lex tableau are non-negative.
2334 * However, if we are using a big parameter in the context, then this only
2335 * reflects the non-negativity of the variable used to _encode_ the
2336 * div, i.e., div' = M + div, so we can't draw any conclusions.
2338 static int context_lex_add_div(struct isl_context *context, struct isl_vec *div)
2340 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2341 int nonneg;
2342 nonneg = context_tab_add_div(clex->tab, div,
2343 context_lex_add_ineq_wrap, context);
2344 if (nonneg < 0)
2345 return -1;
2346 if (clex->tab->M)
2347 return 0;
2348 return nonneg;
2351 static int context_lex_detect_equalities(struct isl_context *context,
2352 struct isl_tab *tab)
2354 return 0;
2357 static int context_lex_best_split(struct isl_context *context,
2358 struct isl_tab *tab)
2360 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2361 struct isl_tab_undo *snap;
2362 int r;
2364 snap = isl_tab_snap(clex->tab);
2365 if (isl_tab_push_basis(clex->tab) < 0)
2366 return -1;
2367 r = best_split(tab, clex->tab);
2369 if (r >= 0 && isl_tab_rollback(clex->tab, snap) < 0)
2370 return -1;
2372 return r;
2375 static int context_lex_is_empty(struct isl_context *context)
2377 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2378 if (!clex->tab)
2379 return -1;
2380 return clex->tab->empty;
2383 static void *context_lex_save(struct isl_context *context)
2385 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2386 struct isl_tab_undo *snap;
2388 snap = isl_tab_snap(clex->tab);
2389 if (isl_tab_push_basis(clex->tab) < 0)
2390 return NULL;
2391 if (isl_tab_save_samples(clex->tab) < 0)
2392 return NULL;
2394 return snap;
2397 static void context_lex_restore(struct isl_context *context, void *save)
2399 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2400 if (isl_tab_rollback(clex->tab, (struct isl_tab_undo *)save) < 0) {
2401 isl_tab_free(clex->tab);
2402 clex->tab = NULL;
2406 static int context_lex_is_ok(struct isl_context *context)
2408 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2409 return !!clex->tab;
2412 /* For each variable in the context tableau, check if the variable can
2413 * only attain non-negative values. If so, mark the parameter as non-negative
2414 * in the main tableau. This allows for a more direct identification of some
2415 * cases of violated constraints.
2417 static struct isl_tab *tab_detect_nonnegative_parameters(struct isl_tab *tab,
2418 struct isl_tab *context_tab)
2420 int i;
2421 struct isl_tab_undo *snap;
2422 struct isl_vec *ineq = NULL;
2423 struct isl_tab_var *var;
2424 int n;
2426 if (context_tab->n_var == 0)
2427 return tab;
2429 ineq = isl_vec_alloc(tab->mat->ctx, 1 + context_tab->n_var);
2430 if (!ineq)
2431 goto error;
2433 if (isl_tab_extend_cons(context_tab, 1) < 0)
2434 goto error;
2436 snap = isl_tab_snap(context_tab);
2438 n = 0;
2439 isl_seq_clr(ineq->el, ineq->size);
2440 for (i = 0; i < context_tab->n_var; ++i) {
2441 isl_int_set_si(ineq->el[1 + i], 1);
2442 if (isl_tab_add_ineq(context_tab, ineq->el) < 0)
2443 goto error;
2444 var = &context_tab->con[context_tab->n_con - 1];
2445 if (!context_tab->empty &&
2446 !isl_tab_min_at_most_neg_one(context_tab, var)) {
2447 int j = i;
2448 if (i >= tab->n_param)
2449 j = i - tab->n_param + tab->n_var - tab->n_div;
2450 tab->var[j].is_nonneg = 1;
2451 n++;
2453 isl_int_set_si(ineq->el[1 + i], 0);
2454 if (isl_tab_rollback(context_tab, snap) < 0)
2455 goto error;
2458 if (context_tab->M && n == context_tab->n_var) {
2459 context_tab->mat = isl_mat_drop_cols(context_tab->mat, 2, 1);
2460 context_tab->M = 0;
2463 isl_vec_free(ineq);
2464 return tab;
2465 error:
2466 isl_vec_free(ineq);
2467 isl_tab_free(tab);
2468 return NULL;
2471 static struct isl_tab *context_lex_detect_nonnegative_parameters(
2472 struct isl_context *context, struct isl_tab *tab)
2474 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2475 struct isl_tab_undo *snap;
2477 if (!tab)
2478 return NULL;
2480 snap = isl_tab_snap(clex->tab);
2481 if (isl_tab_push_basis(clex->tab) < 0)
2482 goto error;
2484 tab = tab_detect_nonnegative_parameters(tab, clex->tab);
2486 if (isl_tab_rollback(clex->tab, snap) < 0)
2487 goto error;
2489 return tab;
2490 error:
2491 isl_tab_free(tab);
2492 return NULL;
2495 static void context_lex_invalidate(struct isl_context *context)
2497 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2498 isl_tab_free(clex->tab);
2499 clex->tab = NULL;
2502 static void context_lex_free(struct isl_context *context)
2504 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2505 isl_tab_free(clex->tab);
2506 free(clex);
2509 struct isl_context_op isl_context_lex_op = {
2510 context_lex_detect_nonnegative_parameters,
2511 context_lex_peek_basic_set,
2512 context_lex_peek_tab,
2513 context_lex_add_eq,
2514 context_lex_add_ineq,
2515 context_lex_ineq_sign,
2516 context_lex_test_ineq,
2517 context_lex_get_div,
2518 context_lex_add_div,
2519 context_lex_detect_equalities,
2520 context_lex_best_split,
2521 context_lex_is_empty,
2522 context_lex_is_ok,
2523 context_lex_save,
2524 context_lex_restore,
2525 context_lex_invalidate,
2526 context_lex_free,
2529 static struct isl_tab *context_tab_for_lexmin(struct isl_basic_set *bset)
2531 struct isl_tab *tab;
2533 bset = isl_basic_set_cow(bset);
2534 if (!bset)
2535 return NULL;
2536 tab = tab_for_lexmin((struct isl_basic_map *)bset, NULL, 1, 0);
2537 if (!tab)
2538 goto error;
2539 if (isl_tab_track_bset(tab, bset) < 0)
2540 goto error;
2541 tab = isl_tab_init_samples(tab);
2542 return tab;
2543 error:
2544 isl_basic_set_free(bset);
2545 return NULL;
2548 static struct isl_context *isl_context_lex_alloc(struct isl_basic_set *dom)
2550 struct isl_context_lex *clex;
2552 if (!dom)
2553 return NULL;
2555 clex = isl_alloc_type(dom->ctx, struct isl_context_lex);
2556 if (!clex)
2557 return NULL;
2559 clex->context.op = &isl_context_lex_op;
2561 clex->tab = context_tab_for_lexmin(isl_basic_set_copy(dom));
2562 if (restore_lexmin(clex->tab) < 0)
2563 goto error;
2564 clex->tab = check_integer_feasible(clex->tab);
2565 if (!clex->tab)
2566 goto error;
2568 return &clex->context;
2569 error:
2570 clex->context.op->free(&clex->context);
2571 return NULL;
2574 struct isl_context_gbr {
2575 struct isl_context context;
2576 struct isl_tab *tab;
2577 struct isl_tab *shifted;
2578 struct isl_tab *cone;
2581 static struct isl_tab *context_gbr_detect_nonnegative_parameters(
2582 struct isl_context *context, struct isl_tab *tab)
2584 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2585 if (!tab)
2586 return NULL;
2587 return tab_detect_nonnegative_parameters(tab, cgbr->tab);
2590 static struct isl_basic_set *context_gbr_peek_basic_set(
2591 struct isl_context *context)
2593 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2594 if (!cgbr->tab)
2595 return NULL;
2596 return isl_tab_peek_bset(cgbr->tab);
2599 static struct isl_tab *context_gbr_peek_tab(struct isl_context *context)
2601 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2602 return cgbr->tab;
2605 /* Initialize the "shifted" tableau of the context, which
2606 * contains the constraints of the original tableau shifted
2607 * by the sum of all negative coefficients. This ensures
2608 * that any rational point in the shifted tableau can
2609 * be rounded up to yield an integer point in the original tableau.
2611 static void gbr_init_shifted(struct isl_context_gbr *cgbr)
2613 int i, j;
2614 struct isl_vec *cst;
2615 struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab);
2616 unsigned dim = isl_basic_set_total_dim(bset);
2618 cst = isl_vec_alloc(cgbr->tab->mat->ctx, bset->n_ineq);
2619 if (!cst)
2620 return;
2622 for (i = 0; i < bset->n_ineq; ++i) {
2623 isl_int_set(cst->el[i], bset->ineq[i][0]);
2624 for (j = 0; j < dim; ++j) {
2625 if (!isl_int_is_neg(bset->ineq[i][1 + j]))
2626 continue;
2627 isl_int_add(bset->ineq[i][0], bset->ineq[i][0],
2628 bset->ineq[i][1 + j]);
2632 cgbr->shifted = isl_tab_from_basic_set(bset);
2634 for (i = 0; i < bset->n_ineq; ++i)
2635 isl_int_set(bset->ineq[i][0], cst->el[i]);
2637 isl_vec_free(cst);
2640 /* Check if the shifted tableau is non-empty, and if so
2641 * use the sample point to construct an integer point
2642 * of the context tableau.
2644 static struct isl_vec *gbr_get_shifted_sample(struct isl_context_gbr *cgbr)
2646 struct isl_vec *sample;
2648 if (!cgbr->shifted)
2649 gbr_init_shifted(cgbr);
2650 if (!cgbr->shifted)
2651 return NULL;
2652 if (cgbr->shifted->empty)
2653 return isl_vec_alloc(cgbr->tab->mat->ctx, 0);
2655 sample = isl_tab_get_sample_value(cgbr->shifted);
2656 sample = isl_vec_ceil(sample);
2658 return sample;
2661 static struct isl_basic_set *drop_constant_terms(struct isl_basic_set *bset)
2663 int i;
2665 if (!bset)
2666 return NULL;
2668 for (i = 0; i < bset->n_eq; ++i)
2669 isl_int_set_si(bset->eq[i][0], 0);
2671 for (i = 0; i < bset->n_ineq; ++i)
2672 isl_int_set_si(bset->ineq[i][0], 0);
2674 return bset;
2677 static int use_shifted(struct isl_context_gbr *cgbr)
2679 return cgbr->tab->bmap->n_eq == 0 && cgbr->tab->bmap->n_div == 0;
2682 static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr)
2684 struct isl_basic_set *bset;
2685 struct isl_basic_set *cone;
2687 if (isl_tab_sample_is_integer(cgbr->tab))
2688 return isl_tab_get_sample_value(cgbr->tab);
2690 if (use_shifted(cgbr)) {
2691 struct isl_vec *sample;
2693 sample = gbr_get_shifted_sample(cgbr);
2694 if (!sample || sample->size > 0)
2695 return sample;
2697 isl_vec_free(sample);
2700 if (!cgbr->cone) {
2701 bset = isl_tab_peek_bset(cgbr->tab);
2702 cgbr->cone = isl_tab_from_recession_cone(bset, 0);
2703 if (!cgbr->cone)
2704 return NULL;
2705 if (isl_tab_track_bset(cgbr->cone, isl_basic_set_dup(bset)) < 0)
2706 return NULL;
2708 if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0)
2709 return NULL;
2711 if (cgbr->cone->n_dead == cgbr->cone->n_col) {
2712 struct isl_vec *sample;
2713 struct isl_tab_undo *snap;
2715 if (cgbr->tab->basis) {
2716 if (cgbr->tab->basis->n_col != 1 + cgbr->tab->n_var) {
2717 isl_mat_free(cgbr->tab->basis);
2718 cgbr->tab->basis = NULL;
2720 cgbr->tab->n_zero = 0;
2721 cgbr->tab->n_unbounded = 0;
2724 snap = isl_tab_snap(cgbr->tab);
2726 sample = isl_tab_sample(cgbr->tab);
2728 if (isl_tab_rollback(cgbr->tab, snap) < 0) {
2729 isl_vec_free(sample);
2730 return NULL;
2733 return sample;
2736 cone = isl_basic_set_dup(isl_tab_peek_bset(cgbr->cone));
2737 cone = drop_constant_terms(cone);
2738 cone = isl_basic_set_update_from_tab(cone, cgbr->cone);
2739 cone = isl_basic_set_underlying_set(cone);
2740 cone = isl_basic_set_gauss(cone, NULL);
2742 bset = isl_basic_set_dup(isl_tab_peek_bset(cgbr->tab));
2743 bset = isl_basic_set_update_from_tab(bset, cgbr->tab);
2744 bset = isl_basic_set_underlying_set(bset);
2745 bset = isl_basic_set_gauss(bset, NULL);
2747 return isl_basic_set_sample_with_cone(bset, cone);
2750 static void check_gbr_integer_feasible(struct isl_context_gbr *cgbr)
2752 struct isl_vec *sample;
2754 if (!cgbr->tab)
2755 return;
2757 if (cgbr->tab->empty)
2758 return;
2760 sample = gbr_get_sample(cgbr);
2761 if (!sample)
2762 goto error;
2764 if (sample->size == 0) {
2765 isl_vec_free(sample);
2766 if (isl_tab_mark_empty(cgbr->tab) < 0)
2767 goto error;
2768 return;
2771 cgbr->tab = isl_tab_add_sample(cgbr->tab, sample);
2773 return;
2774 error:
2775 isl_tab_free(cgbr->tab);
2776 cgbr->tab = NULL;
2779 static struct isl_tab *add_gbr_eq(struct isl_tab *tab, isl_int *eq)
2781 int r;
2783 if (!tab)
2784 return NULL;
2786 if (isl_tab_extend_cons(tab, 2) < 0)
2787 goto error;
2789 if (isl_tab_add_eq(tab, eq) < 0)
2790 goto error;
2792 return tab;
2793 error:
2794 isl_tab_free(tab);
2795 return NULL;
2798 static void context_gbr_add_eq(struct isl_context *context, isl_int *eq,
2799 int check, int update)
2801 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2803 cgbr->tab = add_gbr_eq(cgbr->tab, eq);
2805 if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
2806 if (isl_tab_extend_cons(cgbr->cone, 2) < 0)
2807 goto error;
2808 if (isl_tab_add_eq(cgbr->cone, eq) < 0)
2809 goto error;
2812 if (check) {
2813 int v = tab_has_valid_sample(cgbr->tab, eq, 1);
2814 if (v < 0)
2815 goto error;
2816 if (!v)
2817 check_gbr_integer_feasible(cgbr);
2819 if (update)
2820 cgbr->tab = check_samples(cgbr->tab, eq, 1);
2821 return;
2822 error:
2823 isl_tab_free(cgbr->tab);
2824 cgbr->tab = NULL;
2827 static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq)
2829 if (!cgbr->tab)
2830 return;
2832 if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
2833 goto error;
2835 if (isl_tab_add_ineq(cgbr->tab, ineq) < 0)
2836 goto error;
2838 if (cgbr->shifted && !cgbr->shifted->empty && use_shifted(cgbr)) {
2839 int i;
2840 unsigned dim;
2841 dim = isl_basic_map_total_dim(cgbr->tab->bmap);
2843 if (isl_tab_extend_cons(cgbr->shifted, 1) < 0)
2844 goto error;
2846 for (i = 0; i < dim; ++i) {
2847 if (!isl_int_is_neg(ineq[1 + i]))
2848 continue;
2849 isl_int_add(ineq[0], ineq[0], ineq[1 + i]);
2852 if (isl_tab_add_ineq(cgbr->shifted, ineq) < 0)
2853 goto error;
2855 for (i = 0; i < dim; ++i) {
2856 if (!isl_int_is_neg(ineq[1 + i]))
2857 continue;
2858 isl_int_sub(ineq[0], ineq[0], ineq[1 + i]);
2862 if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
2863 if (isl_tab_extend_cons(cgbr->cone, 1) < 0)
2864 goto error;
2865 if (isl_tab_add_ineq(cgbr->cone, ineq) < 0)
2866 goto error;
2869 return;
2870 error:
2871 isl_tab_free(cgbr->tab);
2872 cgbr->tab = NULL;
2875 static void context_gbr_add_ineq(struct isl_context *context, isl_int *ineq,
2876 int check, int update)
2878 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2880 add_gbr_ineq(cgbr, ineq);
2881 if (!cgbr->tab)
2882 return;
2884 if (check) {
2885 int v = tab_has_valid_sample(cgbr->tab, ineq, 0);
2886 if (v < 0)
2887 goto error;
2888 if (!v)
2889 check_gbr_integer_feasible(cgbr);
2891 if (update)
2892 cgbr->tab = check_samples(cgbr->tab, ineq, 0);
2893 return;
2894 error:
2895 isl_tab_free(cgbr->tab);
2896 cgbr->tab = NULL;
2899 static int context_gbr_add_ineq_wrap(void *user, isl_int *ineq)
2901 struct isl_context *context = (struct isl_context *)user;
2902 context_gbr_add_ineq(context, ineq, 0, 0);
2903 return context->op->is_ok(context) ? 0 : -1;
2906 static enum isl_tab_row_sign context_gbr_ineq_sign(struct isl_context *context,
2907 isl_int *ineq, int strict)
2909 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2910 return tab_ineq_sign(cgbr->tab, ineq, strict);
2913 /* Check whether "ineq" can be added to the tableau without rendering
2914 * it infeasible.
2916 static int context_gbr_test_ineq(struct isl_context *context, isl_int *ineq)
2918 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2919 struct isl_tab_undo *snap;
2920 struct isl_tab_undo *shifted_snap = NULL;
2921 struct isl_tab_undo *cone_snap = NULL;
2922 int feasible;
2924 if (!cgbr->tab)
2925 return -1;
2927 if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
2928 return -1;
2930 snap = isl_tab_snap(cgbr->tab);
2931 if (cgbr->shifted)
2932 shifted_snap = isl_tab_snap(cgbr->shifted);
2933 if (cgbr->cone)
2934 cone_snap = isl_tab_snap(cgbr->cone);
2935 add_gbr_ineq(cgbr, ineq);
2936 check_gbr_integer_feasible(cgbr);
2937 if (!cgbr->tab)
2938 return -1;
2939 feasible = !cgbr->tab->empty;
2940 if (isl_tab_rollback(cgbr->tab, snap) < 0)
2941 return -1;
2942 if (shifted_snap) {
2943 if (isl_tab_rollback(cgbr->shifted, shifted_snap))
2944 return -1;
2945 } else if (cgbr->shifted) {
2946 isl_tab_free(cgbr->shifted);
2947 cgbr->shifted = NULL;
2949 if (cone_snap) {
2950 if (isl_tab_rollback(cgbr->cone, cone_snap))
2951 return -1;
2952 } else if (cgbr->cone) {
2953 isl_tab_free(cgbr->cone);
2954 cgbr->cone = NULL;
2957 return feasible;
2960 /* Return the column of the last of the variables associated to
2961 * a column that has a non-zero coefficient.
2962 * This function is called in a context where only coefficients
2963 * of parameters or divs can be non-zero.
2965 static int last_non_zero_var_col(struct isl_tab *tab, isl_int *p)
2967 int i;
2968 int col;
2969 unsigned dim = tab->n_var - tab->n_param - tab->n_div;
2971 if (tab->n_var == 0)
2972 return -1;
2974 for (i = tab->n_var - 1; i >= 0; --i) {
2975 if (i >= tab->n_param && i < tab->n_var - tab->n_div)
2976 continue;
2977 if (tab->var[i].is_row)
2978 continue;
2979 col = tab->var[i].index;
2980 if (!isl_int_is_zero(p[col]))
2981 return col;
2984 return -1;
2987 /* Look through all the recently added equalities in the context
2988 * to see if we can propagate any of them to the main tableau.
2990 * The newly added equalities in the context are encoded as pairs
2991 * of inequalities starting at inequality "first".
2993 * We tentatively add each of these equalities to the main tableau
2994 * and if this happens to result in a row with a final coefficient
2995 * that is one or negative one, we use it to kill a column
2996 * in the main tableau. Otherwise, we discard the tentatively
2997 * added row.
2999 static void propagate_equalities(struct isl_context_gbr *cgbr,
3000 struct isl_tab *tab, unsigned first)
3002 int i;
3003 struct isl_vec *eq = NULL;
3005 eq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
3006 if (!eq)
3007 goto error;
3009 if (isl_tab_extend_cons(tab, (cgbr->tab->bmap->n_ineq - first)/2) < 0)
3010 goto error;
3012 isl_seq_clr(eq->el + 1 + tab->n_param,
3013 tab->n_var - tab->n_param - tab->n_div);
3014 for (i = first; i < cgbr->tab->bmap->n_ineq; i += 2) {
3015 int j;
3016 int r;
3017 struct isl_tab_undo *snap;
3018 snap = isl_tab_snap(tab);
3020 isl_seq_cpy(eq->el, cgbr->tab->bmap->ineq[i], 1 + tab->n_param);
3021 isl_seq_cpy(eq->el + 1 + tab->n_var - tab->n_div,
3022 cgbr->tab->bmap->ineq[i] + 1 + tab->n_param,
3023 tab->n_div);
3025 r = isl_tab_add_row(tab, eq->el);
3026 if (r < 0)
3027 goto error;
3028 r = tab->con[r].index;
3029 j = last_non_zero_var_col(tab, tab->mat->row[r] + 2 + tab->M);
3030 if (j < 0 || j < tab->n_dead ||
3031 !isl_int_is_one(tab->mat->row[r][0]) ||
3032 (!isl_int_is_one(tab->mat->row[r][2 + tab->M + j]) &&
3033 !isl_int_is_negone(tab->mat->row[r][2 + tab->M + j]))) {
3034 if (isl_tab_rollback(tab, snap) < 0)
3035 goto error;
3036 continue;
3038 if (isl_tab_pivot(tab, r, j) < 0)
3039 goto error;
3040 if (isl_tab_kill_col(tab, j) < 0)
3041 goto error;
3043 if (restore_lexmin(tab) < 0)
3044 goto error;
3047 isl_vec_free(eq);
3049 return;
3050 error:
3051 isl_vec_free(eq);
3052 isl_tab_free(cgbr->tab);
3053 cgbr->tab = NULL;
3056 static int context_gbr_detect_equalities(struct isl_context *context,
3057 struct isl_tab *tab)
3059 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3060 struct isl_ctx *ctx;
3061 int i;
3062 enum isl_lp_result res;
3063 unsigned n_ineq;
3065 ctx = cgbr->tab->mat->ctx;
3067 if (!cgbr->cone) {
3068 struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab);
3069 cgbr->cone = isl_tab_from_recession_cone(bset, 0);
3070 if (!cgbr->cone)
3071 goto error;
3072 if (isl_tab_track_bset(cgbr->cone, isl_basic_set_dup(bset)) < 0)
3073 goto error;
3075 if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0)
3076 goto error;
3078 n_ineq = cgbr->tab->bmap->n_ineq;
3079 cgbr->tab = isl_tab_detect_equalities(cgbr->tab, cgbr->cone);
3080 if (cgbr->tab && cgbr->tab->bmap->n_ineq > n_ineq)
3081 propagate_equalities(cgbr, tab, n_ineq);
3083 return 0;
3084 error:
3085 isl_tab_free(cgbr->tab);
3086 cgbr->tab = NULL;
3087 return -1;
3090 static int context_gbr_get_div(struct isl_context *context, struct isl_tab *tab,
3091 struct isl_vec *div)
3093 return get_div(tab, context, div);
3096 static int context_gbr_add_div(struct isl_context *context, struct isl_vec *div)
3098 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3099 if (cgbr->cone) {
3100 int k;
3102 if (isl_tab_extend_cons(cgbr->cone, 3) < 0)
3103 return -1;
3104 if (isl_tab_extend_vars(cgbr->cone, 1) < 0)
3105 return -1;
3106 if (isl_tab_allocate_var(cgbr->cone) <0)
3107 return -1;
3109 cgbr->cone->bmap = isl_basic_map_extend_dim(cgbr->cone->bmap,
3110 isl_basic_map_get_dim(cgbr->cone->bmap), 1, 0, 2);
3111 k = isl_basic_map_alloc_div(cgbr->cone->bmap);
3112 if (k < 0)
3113 return -1;
3114 isl_seq_cpy(cgbr->cone->bmap->div[k], div->el, div->size);
3115 if (isl_tab_push(cgbr->cone, isl_tab_undo_bmap_div) < 0)
3116 return -1;
3118 return context_tab_add_div(cgbr->tab, div,
3119 context_gbr_add_ineq_wrap, context);
3122 static int context_gbr_best_split(struct isl_context *context,
3123 struct isl_tab *tab)
3125 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3126 struct isl_tab_undo *snap;
3127 int r;
3129 snap = isl_tab_snap(cgbr->tab);
3130 r = best_split(tab, cgbr->tab);
3132 if (r >= 0 && isl_tab_rollback(cgbr->tab, snap) < 0)
3133 return -1;
3135 return r;
3138 static int context_gbr_is_empty(struct isl_context *context)
3140 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3141 if (!cgbr->tab)
3142 return -1;
3143 return cgbr->tab->empty;
3146 struct isl_gbr_tab_undo {
3147 struct isl_tab_undo *tab_snap;
3148 struct isl_tab_undo *shifted_snap;
3149 struct isl_tab_undo *cone_snap;
3152 static void *context_gbr_save(struct isl_context *context)
3154 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3155 struct isl_gbr_tab_undo *snap;
3157 snap = isl_alloc_type(cgbr->tab->mat->ctx, struct isl_gbr_tab_undo);
3158 if (!snap)
3159 return NULL;
3161 snap->tab_snap = isl_tab_snap(cgbr->tab);
3162 if (isl_tab_save_samples(cgbr->tab) < 0)
3163 goto error;
3165 if (cgbr->shifted)
3166 snap->shifted_snap = isl_tab_snap(cgbr->shifted);
3167 else
3168 snap->shifted_snap = NULL;
3170 if (cgbr->cone)
3171 snap->cone_snap = isl_tab_snap(cgbr->cone);
3172 else
3173 snap->cone_snap = NULL;
3175 return snap;
3176 error:
3177 free(snap);
3178 return NULL;
3181 static void context_gbr_restore(struct isl_context *context, void *save)
3183 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3184 struct isl_gbr_tab_undo *snap = (struct isl_gbr_tab_undo *)save;
3185 if (!snap)
3186 goto error;
3187 if (isl_tab_rollback(cgbr->tab, snap->tab_snap) < 0) {
3188 isl_tab_free(cgbr->tab);
3189 cgbr->tab = NULL;
3192 if (snap->shifted_snap) {
3193 if (isl_tab_rollback(cgbr->shifted, snap->shifted_snap) < 0)
3194 goto error;
3195 } else if (cgbr->shifted) {
3196 isl_tab_free(cgbr->shifted);
3197 cgbr->shifted = NULL;
3200 if (snap->cone_snap) {
3201 if (isl_tab_rollback(cgbr->cone, snap->cone_snap) < 0)
3202 goto error;
3203 } else if (cgbr->cone) {
3204 isl_tab_free(cgbr->cone);
3205 cgbr->cone = NULL;
3208 free(snap);
3210 return;
3211 error:
3212 free(snap);
3213 isl_tab_free(cgbr->tab);
3214 cgbr->tab = NULL;
3217 static int context_gbr_is_ok(struct isl_context *context)
3219 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3220 return !!cgbr->tab;
3223 static void context_gbr_invalidate(struct isl_context *context)
3225 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3226 isl_tab_free(cgbr->tab);
3227 cgbr->tab = NULL;
3230 static void context_gbr_free(struct isl_context *context)
3232 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3233 isl_tab_free(cgbr->tab);
3234 isl_tab_free(cgbr->shifted);
3235 isl_tab_free(cgbr->cone);
3236 free(cgbr);
3239 struct isl_context_op isl_context_gbr_op = {
3240 context_gbr_detect_nonnegative_parameters,
3241 context_gbr_peek_basic_set,
3242 context_gbr_peek_tab,
3243 context_gbr_add_eq,
3244 context_gbr_add_ineq,
3245 context_gbr_ineq_sign,
3246 context_gbr_test_ineq,
3247 context_gbr_get_div,
3248 context_gbr_add_div,
3249 context_gbr_detect_equalities,
3250 context_gbr_best_split,
3251 context_gbr_is_empty,
3252 context_gbr_is_ok,
3253 context_gbr_save,
3254 context_gbr_restore,
3255 context_gbr_invalidate,
3256 context_gbr_free,
3259 static struct isl_context *isl_context_gbr_alloc(struct isl_basic_set *dom)
3261 struct isl_context_gbr *cgbr;
3263 if (!dom)
3264 return NULL;
3266 cgbr = isl_calloc_type(dom->ctx, struct isl_context_gbr);
3267 if (!cgbr)
3268 return NULL;
3270 cgbr->context.op = &isl_context_gbr_op;
3272 cgbr->shifted = NULL;
3273 cgbr->cone = NULL;
3274 cgbr->tab = isl_tab_from_basic_set(dom);
3275 cgbr->tab = isl_tab_init_samples(cgbr->tab);
3276 if (!cgbr->tab)
3277 goto error;
3278 if (isl_tab_track_bset(cgbr->tab,
3279 isl_basic_set_cow(isl_basic_set_copy(dom))) < 0)
3280 goto error;
3281 check_gbr_integer_feasible(cgbr);
3283 return &cgbr->context;
3284 error:
3285 cgbr->context.op->free(&cgbr->context);
3286 return NULL;
3289 static struct isl_context *isl_context_alloc(struct isl_basic_set *dom)
3291 if (!dom)
3292 return NULL;
3294 if (dom->ctx->opt->context == ISL_CONTEXT_LEXMIN)
3295 return isl_context_lex_alloc(dom);
3296 else
3297 return isl_context_gbr_alloc(dom);
3300 /* Construct an isl_sol_map structure for accumulating the solution.
3301 * If track_empty is set, then we also keep track of the parts
3302 * of the context where there is no solution.
3303 * If max is set, then we are solving a maximization, rather than
3304 * a minimization problem, which means that the variables in the
3305 * tableau have value "M - x" rather than "M + x".
3307 static struct isl_sol_map *sol_map_init(struct isl_basic_map *bmap,
3308 struct isl_basic_set *dom, int track_empty, int max)
3310 struct isl_sol_map *sol_map = NULL;
3312 if (!bmap)
3313 goto error;
3315 sol_map = isl_calloc_type(bmap->ctx, struct isl_sol_map);
3316 if (!sol_map)
3317 goto error;
3319 sol_map->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
3320 sol_map->sol.dec_level.callback.run = &sol_dec_level_wrap;
3321 sol_map->sol.dec_level.sol = &sol_map->sol;
3322 sol_map->sol.max = max;
3323 sol_map->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
3324 sol_map->sol.add = &sol_map_add_wrap;
3325 sol_map->sol.add_empty = track_empty ? &sol_map_add_empty_wrap : NULL;
3326 sol_map->sol.free = &sol_map_free_wrap;
3327 sol_map->map = isl_map_alloc_dim(isl_basic_map_get_dim(bmap), 1,
3328 ISL_MAP_DISJOINT);
3329 if (!sol_map->map)
3330 goto error;
3332 sol_map->sol.context = isl_context_alloc(dom);
3333 if (!sol_map->sol.context)
3334 goto error;
3336 if (track_empty) {
3337 sol_map->empty = isl_set_alloc_dim(isl_basic_set_get_dim(dom),
3338 1, ISL_SET_DISJOINT);
3339 if (!sol_map->empty)
3340 goto error;
3343 isl_basic_set_free(dom);
3344 return sol_map;
3345 error:
3346 isl_basic_set_free(dom);
3347 sol_map_free(sol_map);
3348 return NULL;
3351 /* Check whether all coefficients of (non-parameter) variables
3352 * are non-positive, meaning that no pivots can be performed on the row.
3354 static int is_critical(struct isl_tab *tab, int row)
3356 int j;
3357 unsigned off = 2 + tab->M;
3359 for (j = tab->n_dead; j < tab->n_col; ++j) {
3360 if (tab->col_var[j] >= 0 &&
3361 (tab->col_var[j] < tab->n_param ||
3362 tab->col_var[j] >= tab->n_var - tab->n_div))
3363 continue;
3365 if (isl_int_is_pos(tab->mat->row[row][off + j]))
3366 return 0;
3369 return 1;
3372 /* Check whether the inequality represented by vec is strict over the integers,
3373 * i.e., there are no integer values satisfying the constraint with
3374 * equality. This happens if the gcd of the coefficients is not a divisor
3375 * of the constant term. If so, scale the constraint down by the gcd
3376 * of the coefficients.
3378 static int is_strict(struct isl_vec *vec)
3380 isl_int gcd;
3381 int strict = 0;
3383 isl_int_init(gcd);
3384 isl_seq_gcd(vec->el + 1, vec->size - 1, &gcd);
3385 if (!isl_int_is_one(gcd)) {
3386 strict = !isl_int_is_divisible_by(vec->el[0], gcd);
3387 isl_int_fdiv_q(vec->el[0], vec->el[0], gcd);
3388 isl_seq_scale_down(vec->el + 1, vec->el + 1, gcd, vec->size-1);
3390 isl_int_clear(gcd);
3392 return strict;
3395 /* Determine the sign of the given row of the main tableau.
3396 * The result is one of
3397 * isl_tab_row_pos: always non-negative; no pivot needed
3398 * isl_tab_row_neg: always non-positive; pivot
3399 * isl_tab_row_any: can be both positive and negative; split
3401 * We first handle some simple cases
3402 * - the row sign may be known already
3403 * - the row may be obviously non-negative
3404 * - the parametric constant may be equal to that of another row
3405 * for which we know the sign. This sign will be either "pos" or
3406 * "any". If it had been "neg" then we would have pivoted before.
3408 * If none of these cases hold, we check the value of the row for each
3409 * of the currently active samples. Based on the signs of these values
3410 * we make an initial determination of the sign of the row.
3412 * all zero -> unk(nown)
3413 * all non-negative -> pos
3414 * all non-positive -> neg
3415 * both negative and positive -> all
3417 * If we end up with "all", we are done.
3418 * Otherwise, we perform a check for positive and/or negative
3419 * values as follows.
3421 * samples neg unk pos
3422 * <0 ? Y N Y N
3423 * pos any pos
3424 * >0 ? Y N Y N
3425 * any neg any neg
3427 * There is no special sign for "zero", because we can usually treat zero
3428 * as either non-negative or non-positive, whatever works out best.
3429 * However, if the row is "critical", meaning that pivoting is impossible
3430 * then we don't want to limp zero with the non-positive case, because
3431 * then we we would lose the solution for those values of the parameters
3432 * where the value of the row is zero. Instead, we treat 0 as non-negative
3433 * ensuring a split if the row can attain both zero and negative values.
3434 * The same happens when the original constraint was one that could not
3435 * be satisfied with equality by any integer values of the parameters.
3436 * In this case, we normalize the constraint, but then a value of zero
3437 * for the normalized constraint is actually a positive value for the
3438 * original constraint, so again we need to treat zero as non-negative.
3439 * In both these cases, we have the following decision tree instead:
3441 * all non-negative -> pos
3442 * all negative -> neg
3443 * both negative and non-negative -> all
3445 * samples neg pos
3446 * <0 ? Y N
3447 * any pos
3448 * >=0 ? Y N
3449 * any neg
3451 static enum isl_tab_row_sign row_sign(struct isl_tab *tab,
3452 struct isl_sol *sol, int row)
3454 struct isl_vec *ineq = NULL;
3455 enum isl_tab_row_sign res = isl_tab_row_unknown;
3456 int critical;
3457 int strict;
3458 int row2;
3460 if (tab->row_sign[row] != isl_tab_row_unknown)
3461 return tab->row_sign[row];
3462 if (is_obviously_nonneg(tab, row))
3463 return isl_tab_row_pos;
3464 for (row2 = tab->n_redundant; row2 < tab->n_row; ++row2) {
3465 if (tab->row_sign[row2] == isl_tab_row_unknown)
3466 continue;
3467 if (identical_parameter_line(tab, row, row2))
3468 return tab->row_sign[row2];
3471 critical = is_critical(tab, row);
3473 ineq = get_row_parameter_ineq(tab, row);
3474 if (!ineq)
3475 goto error;
3477 strict = is_strict(ineq);
3479 res = sol->context->op->ineq_sign(sol->context, ineq->el,
3480 critical || strict);
3482 if (res == isl_tab_row_unknown || res == isl_tab_row_pos) {
3483 /* test for negative values */
3484 int feasible;
3485 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3486 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3488 feasible = sol->context->op->test_ineq(sol->context, ineq->el);
3489 if (feasible < 0)
3490 goto error;
3491 if (!feasible)
3492 res = isl_tab_row_pos;
3493 else
3494 res = (res == isl_tab_row_unknown) ? isl_tab_row_neg
3495 : isl_tab_row_any;
3496 if (res == isl_tab_row_neg) {
3497 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3498 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3502 if (res == isl_tab_row_neg) {
3503 /* test for positive values */
3504 int feasible;
3505 if (!critical && !strict)
3506 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3508 feasible = sol->context->op->test_ineq(sol->context, ineq->el);
3509 if (feasible < 0)
3510 goto error;
3511 if (feasible)
3512 res = isl_tab_row_any;
3515 isl_vec_free(ineq);
3516 return res;
3517 error:
3518 isl_vec_free(ineq);
3519 return isl_tab_row_unknown;
3522 static void find_solutions(struct isl_sol *sol, struct isl_tab *tab);
3524 /* Find solutions for values of the parameters that satisfy the given
3525 * inequality.
3527 * We currently take a snapshot of the context tableau that is reset
3528 * when we return from this function, while we make a copy of the main
3529 * tableau, leaving the original main tableau untouched.
3530 * These are fairly arbitrary choices. Making a copy also of the context
3531 * tableau would obviate the need to undo any changes made to it later,
3532 * while taking a snapshot of the main tableau could reduce memory usage.
3533 * If we were to switch to taking a snapshot of the main tableau,
3534 * we would have to keep in mind that we need to save the row signs
3535 * and that we need to do this before saving the current basis
3536 * such that the basis has been restore before we restore the row signs.
3538 static void find_in_pos(struct isl_sol *sol, struct isl_tab *tab, isl_int *ineq)
3540 void *saved;
3542 if (!sol->context)
3543 goto error;
3544 saved = sol->context->op->save(sol->context);
3546 tab = isl_tab_dup(tab);
3547 if (!tab)
3548 goto error;
3550 sol->context->op->add_ineq(sol->context, ineq, 0, 1);
3552 find_solutions(sol, tab);
3554 if (!sol->error)
3555 sol->context->op->restore(sol->context, saved);
3556 return;
3557 error:
3558 sol->error = 1;
3561 /* Record the absence of solutions for those values of the parameters
3562 * that do not satisfy the given inequality with equality.
3564 static void no_sol_in_strict(struct isl_sol *sol,
3565 struct isl_tab *tab, struct isl_vec *ineq)
3567 int empty;
3568 void *saved;
3570 if (!sol->context || sol->error)
3571 goto error;
3572 saved = sol->context->op->save(sol->context);
3574 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3576 sol->context->op->add_ineq(sol->context, ineq->el, 1, 0);
3577 if (!sol->context)
3578 goto error;
3580 empty = tab->empty;
3581 tab->empty = 1;
3582 sol_add(sol, tab);
3583 tab->empty = empty;
3585 isl_int_add_ui(ineq->el[0], ineq->el[0], 1);
3587 sol->context->op->restore(sol->context, saved);
3588 return;
3589 error:
3590 sol->error = 1;
3593 /* Compute the lexicographic minimum of the set represented by the main
3594 * tableau "tab" within the context "sol->context_tab".
3595 * On entry the sample value of the main tableau is lexicographically
3596 * less than or equal to this lexicographic minimum.
3597 * Pivots are performed until a feasible point is found, which is then
3598 * necessarily equal to the minimum, or until the tableau is found to
3599 * be infeasible. Some pivots may need to be performed for only some
3600 * feasible values of the context tableau. If so, the context tableau
3601 * is split into a part where the pivot is needed and a part where it is not.
3603 * Whenever we enter the main loop, the main tableau is such that no
3604 * "obvious" pivots need to be performed on it, where "obvious" means
3605 * that the given row can be seen to be negative without looking at
3606 * the context tableau. In particular, for non-parametric problems,
3607 * no pivots need to be performed on the main tableau.
3608 * The caller of find_solutions is responsible for making this property
3609 * hold prior to the first iteration of the loop, while restore_lexmin
3610 * is called before every other iteration.
3612 * Inside the main loop, we first examine the signs of the rows of
3613 * the main tableau within the context of the context tableau.
3614 * If we find a row that is always non-positive for all values of
3615 * the parameters satisfying the context tableau and negative for at
3616 * least one value of the parameters, we perform the appropriate pivot
3617 * and start over. An exception is the case where no pivot can be
3618 * performed on the row. In this case, we require that the sign of
3619 * the row is negative for all values of the parameters (rather than just
3620 * non-positive). This special case is handled inside row_sign, which
3621 * will say that the row can have any sign if it determines that it can
3622 * attain both negative and zero values.
3624 * If we can't find a row that always requires a pivot, but we can find
3625 * one or more rows that require a pivot for some values of the parameters
3626 * (i.e., the row can attain both positive and negative signs), then we split
3627 * the context tableau into two parts, one where we force the sign to be
3628 * non-negative and one where we force is to be negative.
3629 * The non-negative part is handled by a recursive call (through find_in_pos).
3630 * Upon returning from this call, we continue with the negative part and
3631 * perform the required pivot.
3633 * If no such rows can be found, all rows are non-negative and we have
3634 * found a (rational) feasible point. If we only wanted a rational point
3635 * then we are done.
3636 * Otherwise, we check if all values of the sample point of the tableau
3637 * are integral for the variables. If so, we have found the minimal
3638 * integral point and we are done.
3639 * If the sample point is not integral, then we need to make a distinction
3640 * based on whether the constant term is non-integral or the coefficients
3641 * of the parameters. Furthermore, in order to decide how to handle
3642 * the non-integrality, we also need to know whether the coefficients
3643 * of the other columns in the tableau are integral. This leads
3644 * to the following table. The first two rows do not correspond
3645 * to a non-integral sample point and are only mentioned for completeness.
3647 * constant parameters other
3649 * int int int |
3650 * int int rat | -> no problem
3652 * rat int int -> fail
3654 * rat int rat -> cut
3656 * int rat rat |
3657 * rat rat rat | -> parametric cut
3659 * int rat int |
3660 * rat rat int | -> split context
3662 * If the parametric constant is completely integral, then there is nothing
3663 * to be done. If the constant term is non-integral, but all the other
3664 * coefficient are integral, then there is nothing that can be done
3665 * and the tableau has no integral solution.
3666 * If, on the other hand, one or more of the other columns have rational
3667 * coefficients, but the parameter coefficients are all integral, then
3668 * we can perform a regular (non-parametric) cut.
3669 * Finally, if there is any parameter coefficient that is non-integral,
3670 * then we need to involve the context tableau. There are two cases here.
3671 * If at least one other column has a rational coefficient, then we
3672 * can perform a parametric cut in the main tableau by adding a new
3673 * integer division in the context tableau.
3674 * If all other columns have integral coefficients, then we need to
3675 * enforce that the rational combination of parameters (c + \sum a_i y_i)/m
3676 * is always integral. We do this by introducing an integer division
3677 * q = floor((c + \sum a_i y_i)/m) and stipulating that its argument should
3678 * always be integral in the context tableau, i.e., m q = c + \sum a_i y_i.
3679 * Since q is expressed in the tableau as
3680 * c + \sum a_i y_i - m q >= 0
3681 * -c - \sum a_i y_i + m q + m - 1 >= 0
3682 * it is sufficient to add the inequality
3683 * -c - \sum a_i y_i + m q >= 0
3684 * In the part of the context where this inequality does not hold, the
3685 * main tableau is marked as being empty.
3687 static void find_solutions(struct isl_sol *sol, struct isl_tab *tab)
3689 struct isl_context *context;
3690 int r;
3692 if (!tab || sol->error)
3693 goto error;
3695 context = sol->context;
3697 if (tab->empty)
3698 goto done;
3699 if (context->op->is_empty(context))
3700 goto done;
3702 for (r = 0; r >= 0 && tab && !tab->empty; r = restore_lexmin(tab)) {
3703 int flags;
3704 int row;
3705 enum isl_tab_row_sign sgn;
3706 int split = -1;
3707 int n_split = 0;
3709 for (row = tab->n_redundant; row < tab->n_row; ++row) {
3710 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
3711 continue;
3712 sgn = row_sign(tab, sol, row);
3713 if (!sgn)
3714 goto error;
3715 tab->row_sign[row] = sgn;
3716 if (sgn == isl_tab_row_any)
3717 n_split++;
3718 if (sgn == isl_tab_row_any && split == -1)
3719 split = row;
3720 if (sgn == isl_tab_row_neg)
3721 break;
3723 if (row < tab->n_row)
3724 continue;
3725 if (split != -1) {
3726 struct isl_vec *ineq;
3727 if (n_split != 1)
3728 split = context->op->best_split(context, tab);
3729 if (split < 0)
3730 goto error;
3731 ineq = get_row_parameter_ineq(tab, split);
3732 if (!ineq)
3733 goto error;
3734 is_strict(ineq);
3735 for (row = tab->n_redundant; row < tab->n_row; ++row) {
3736 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
3737 continue;
3738 if (tab->row_sign[row] == isl_tab_row_any)
3739 tab->row_sign[row] = isl_tab_row_unknown;
3741 tab->row_sign[split] = isl_tab_row_pos;
3742 sol_inc_level(sol);
3743 find_in_pos(sol, tab, ineq->el);
3744 tab->row_sign[split] = isl_tab_row_neg;
3745 row = split;
3746 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3747 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3748 if (!sol->error)
3749 context->op->add_ineq(context, ineq->el, 0, 1);
3750 isl_vec_free(ineq);
3751 if (sol->error)
3752 goto error;
3753 continue;
3755 if (tab->rational)
3756 break;
3757 row = first_non_integer_row(tab, &flags);
3758 if (row < 0)
3759 break;
3760 if (ISL_FL_ISSET(flags, I_PAR)) {
3761 if (ISL_FL_ISSET(flags, I_VAR)) {
3762 if (isl_tab_mark_empty(tab) < 0)
3763 goto error;
3764 break;
3766 row = add_cut(tab, row);
3767 } else if (ISL_FL_ISSET(flags, I_VAR)) {
3768 struct isl_vec *div;
3769 struct isl_vec *ineq;
3770 int d;
3771 div = get_row_split_div(tab, row);
3772 if (!div)
3773 goto error;
3774 d = context->op->get_div(context, tab, div);
3775 isl_vec_free(div);
3776 if (d < 0)
3777 goto error;
3778 ineq = ineq_for_div(context->op->peek_basic_set(context), d);
3779 if (!ineq)
3780 goto error;
3781 sol_inc_level(sol);
3782 no_sol_in_strict(sol, tab, ineq);
3783 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3784 context->op->add_ineq(context, ineq->el, 1, 1);
3785 isl_vec_free(ineq);
3786 if (sol->error || !context->op->is_ok(context))
3787 goto error;
3788 tab = set_row_cst_to_div(tab, row, d);
3789 if (context->op->is_empty(context))
3790 break;
3791 } else
3792 row = add_parametric_cut(tab, row, context);
3793 if (row < 0)
3794 goto error;
3796 if (r < 0)
3797 goto error;
3798 done:
3799 sol_add(sol, tab);
3800 isl_tab_free(tab);
3801 return;
3802 error:
3803 isl_tab_free(tab);
3804 sol->error = 1;
3807 /* Compute the lexicographic minimum of the set represented by the main
3808 * tableau "tab" within the context "sol->context_tab".
3810 * As a preprocessing step, we first transfer all the purely parametric
3811 * equalities from the main tableau to the context tableau, i.e.,
3812 * parameters that have been pivoted to a row.
3813 * These equalities are ignored by the main algorithm, because the
3814 * corresponding rows may not be marked as being non-negative.
3815 * In parts of the context where the added equality does not hold,
3816 * the main tableau is marked as being empty.
3818 static void find_solutions_main(struct isl_sol *sol, struct isl_tab *tab)
3820 int row;
3822 if (!tab)
3823 goto error;
3825 sol->level = 0;
3827 for (row = tab->n_redundant; row < tab->n_row; ++row) {
3828 int p;
3829 struct isl_vec *eq;
3831 if (tab->row_var[row] < 0)
3832 continue;
3833 if (tab->row_var[row] >= tab->n_param &&
3834 tab->row_var[row] < tab->n_var - tab->n_div)
3835 continue;
3836 if (tab->row_var[row] < tab->n_param)
3837 p = tab->row_var[row];
3838 else
3839 p = tab->row_var[row]
3840 + tab->n_param - (tab->n_var - tab->n_div);
3842 eq = isl_vec_alloc(tab->mat->ctx, 1+tab->n_param+tab->n_div);
3843 if (!eq)
3844 goto error;
3845 get_row_parameter_line(tab, row, eq->el);
3846 isl_int_neg(eq->el[1 + p], tab->mat->row[row][0]);
3847 eq = isl_vec_normalize(eq);
3849 sol_inc_level(sol);
3850 no_sol_in_strict(sol, tab, eq);
3852 isl_seq_neg(eq->el, eq->el, eq->size);
3853 sol_inc_level(sol);
3854 no_sol_in_strict(sol, tab, eq);
3855 isl_seq_neg(eq->el, eq->el, eq->size);
3857 sol->context->op->add_eq(sol->context, eq->el, 1, 1);
3859 isl_vec_free(eq);
3861 if (isl_tab_mark_redundant(tab, row) < 0)
3862 goto error;
3864 if (sol->context->op->is_empty(sol->context))
3865 break;
3867 row = tab->n_redundant - 1;
3870 find_solutions(sol, tab);
3872 sol->level = 0;
3873 sol_pop(sol);
3875 return;
3876 error:
3877 isl_tab_free(tab);
3878 sol->error = 1;
3881 static void sol_map_find_solutions(struct isl_sol_map *sol_map,
3882 struct isl_tab *tab)
3884 find_solutions_main(&sol_map->sol, tab);
3887 /* Check if integer division "div" of "dom" also occurs in "bmap".
3888 * If so, return its position within the divs.
3889 * If not, return -1.
3891 static int find_context_div(struct isl_basic_map *bmap,
3892 struct isl_basic_set *dom, unsigned div)
3894 int i;
3895 unsigned b_dim = isl_dim_total(bmap->dim);
3896 unsigned d_dim = isl_dim_total(dom->dim);
3898 if (isl_int_is_zero(dom->div[div][0]))
3899 return -1;
3900 if (isl_seq_first_non_zero(dom->div[div] + 2 + d_dim, dom->n_div) != -1)
3901 return -1;
3903 for (i = 0; i < bmap->n_div; ++i) {
3904 if (isl_int_is_zero(bmap->div[i][0]))
3905 continue;
3906 if (isl_seq_first_non_zero(bmap->div[i] + 2 + d_dim,
3907 (b_dim - d_dim) + bmap->n_div) != -1)
3908 continue;
3909 if (isl_seq_eq(bmap->div[i], dom->div[div], 2 + d_dim))
3910 return i;
3912 return -1;
3915 /* The correspondence between the variables in the main tableau,
3916 * the context tableau, and the input map and domain is as follows.
3917 * The first n_param and the last n_div variables of the main tableau
3918 * form the variables of the context tableau.
3919 * In the basic map, these n_param variables correspond to the
3920 * parameters and the input dimensions. In the domain, they correspond
3921 * to the parameters and the set dimensions.
3922 * The n_div variables correspond to the integer divisions in the domain.
3923 * To ensure that everything lines up, we may need to copy some of the
3924 * integer divisions of the domain to the map. These have to be placed
3925 * in the same order as those in the context and they have to be placed
3926 * after any other integer divisions that the map may have.
3927 * This function performs the required reordering.
3929 static struct isl_basic_map *align_context_divs(struct isl_basic_map *bmap,
3930 struct isl_basic_set *dom)
3932 int i;
3933 int common = 0;
3934 int other;
3936 for (i = 0; i < dom->n_div; ++i)
3937 if (find_context_div(bmap, dom, i) != -1)
3938 common++;
3939 other = bmap->n_div - common;
3940 if (dom->n_div - common > 0) {
3941 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
3942 dom->n_div - common, 0, 0);
3943 if (!bmap)
3944 return NULL;
3946 for (i = 0; i < dom->n_div; ++i) {
3947 int pos = find_context_div(bmap, dom, i);
3948 if (pos < 0) {
3949 pos = isl_basic_map_alloc_div(bmap);
3950 if (pos < 0)
3951 goto error;
3952 isl_int_set_si(bmap->div[pos][0], 0);
3954 if (pos != other + i)
3955 isl_basic_map_swap_div(bmap, pos, other + i);
3957 return bmap;
3958 error:
3959 isl_basic_map_free(bmap);
3960 return NULL;
3963 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
3964 * some obvious symmetries.
3966 * We make sure the divs in the domain are properly ordered,
3967 * because they will be added one by one in the given order
3968 * during the construction of the solution map.
3970 static __isl_give isl_map *basic_map_partial_lexopt_base(
3971 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
3972 __isl_give isl_set **empty, int max)
3974 isl_map *result = NULL;
3975 struct isl_tab *tab;
3976 struct isl_sol_map *sol_map = NULL;
3977 struct isl_context *context;
3979 if (dom->n_div) {
3980 dom = isl_basic_set_order_divs(dom);
3981 bmap = align_context_divs(bmap, dom);
3983 sol_map = sol_map_init(bmap, dom, !!empty, max);
3984 if (!sol_map)
3985 goto error;
3987 context = sol_map->sol.context;
3988 if (isl_basic_set_fast_is_empty(context->op->peek_basic_set(context)))
3989 /* nothing */;
3990 else if (isl_basic_map_fast_is_empty(bmap))
3991 sol_map_add_empty_if_needed(sol_map,
3992 isl_basic_set_copy(context->op->peek_basic_set(context)));
3993 else {
3994 tab = tab_for_lexmin(bmap,
3995 context->op->peek_basic_set(context), 1, max);
3996 tab = context->op->detect_nonnegative_parameters(context, tab);
3997 sol_map_find_solutions(sol_map, tab);
3999 if (sol_map->sol.error)
4000 goto error;
4002 result = isl_map_copy(sol_map->map);
4003 if (empty)
4004 *empty = isl_set_copy(sol_map->empty);
4005 sol_free(&sol_map->sol);
4006 isl_basic_map_free(bmap);
4007 return result;
4008 error:
4009 sol_free(&sol_map->sol);
4010 isl_basic_map_free(bmap);
4011 return NULL;
4014 /* Structure used during detection of parallel constraints.
4015 * n_in: number of "input" variables: isl_dim_param + isl_dim_in
4016 * n_out: number of "output" variables: isl_dim_out + isl_dim_div
4017 * val: the coefficients of the output variables
4019 struct isl_constraint_equal_info {
4020 isl_basic_map *bmap;
4021 unsigned n_in;
4022 unsigned n_out;
4023 isl_int *val;
4026 /* Check whether the coefficients of the output variables
4027 * of the constraint in "entry" are equal to info->val.
4029 static int constraint_equal(const void *entry, const void *val)
4031 isl_int **row = (isl_int **)entry;
4032 const struct isl_constraint_equal_info *info = val;
4034 return isl_seq_eq((*row) + 1 + info->n_in, info->val, info->n_out);
4037 /* Check whether "bmap" has a pair of constraints that have
4038 * the same coefficients for the output variables.
4039 * Note that the coefficients of the existentially quantified
4040 * variables need to be zero since the existentially quantified
4041 * of the result are usually not the same as those of the input.
4042 * the isl_dim_out and isl_dim_div dimensions.
4043 * If so, return 1 and return the row indices of the two constraints
4044 * in *first and *second.
4046 static int parallel_constraints(__isl_keep isl_basic_map *bmap,
4047 int *first, int *second)
4049 int i;
4050 isl_ctx *ctx = isl_basic_map_get_ctx(bmap);
4051 struct isl_hash_table *table = NULL;
4052 struct isl_hash_table_entry *entry;
4053 struct isl_constraint_equal_info info;
4054 unsigned n_out;
4055 unsigned n_div;
4057 ctx = isl_basic_map_get_ctx(bmap);
4058 table = isl_hash_table_alloc(ctx, bmap->n_ineq);
4059 if (!table)
4060 goto error;
4062 info.n_in = isl_basic_map_dim(bmap, isl_dim_param) +
4063 isl_basic_map_dim(bmap, isl_dim_in);
4064 info.bmap = bmap;
4065 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4066 n_div = isl_basic_map_dim(bmap, isl_dim_div);
4067 info.n_out = n_out + n_div;
4068 for (i = 0; i < bmap->n_ineq; ++i) {
4069 uint32_t hash;
4071 info.val = bmap->ineq[i] + 1 + info.n_in;
4072 if (isl_seq_first_non_zero(info.val, n_out) < 0)
4073 continue;
4074 if (isl_seq_first_non_zero(info.val + n_out, n_div) >= 0)
4075 continue;
4076 hash = isl_seq_get_hash(info.val, info.n_out);
4077 entry = isl_hash_table_find(ctx, table, hash,
4078 constraint_equal, &info, 1);
4079 if (!entry)
4080 goto error;
4081 if (entry->data)
4082 break;
4083 entry->data = &bmap->ineq[i];
4086 if (i < bmap->n_ineq) {
4087 *first = ((isl_int **)entry->data) - bmap->ineq;
4088 *second = i;
4091 isl_hash_table_free(ctx, table);
4093 return i < bmap->n_ineq;
4094 error:
4095 isl_hash_table_free(ctx, table);
4096 return -1;
4099 /* Given a set of upper bounds on the last "input" variable m,
4100 * construct a set that assigns the minimal upper bound to m, i.e.,
4101 * construct a set that divides the space into cells where one
4102 * of the upper bounds is smaller than all the others and assign
4103 * this upper bound to m.
4105 * In particular, if there are n bounds b_i, then the result
4106 * consists of n basic sets, each one of the form
4108 * m = b_i
4109 * b_i <= b_j for j > i
4110 * b_i < b_j for j < i
4112 static __isl_give isl_set *set_minimum(__isl_take isl_dim *dim,
4113 __isl_take isl_mat *var)
4115 int i, j, k;
4116 isl_basic_set *bset = NULL;
4117 isl_ctx *ctx;
4118 isl_set *set = NULL;
4120 if (!dim || !var)
4121 goto error;
4123 ctx = isl_dim_get_ctx(dim);
4124 set = isl_set_alloc_dim(isl_dim_copy(dim),
4125 var->n_row, ISL_SET_DISJOINT);
4127 for (i = 0; i < var->n_row; ++i) {
4128 bset = isl_basic_set_alloc_dim(isl_dim_copy(dim), 0,
4129 1, var->n_row - 1);
4130 k = isl_basic_set_alloc_equality(bset);
4131 if (k < 0)
4132 goto error;
4133 isl_seq_cpy(bset->eq[k], var->row[i], var->n_col);
4134 isl_int_set_si(bset->eq[k][var->n_col], -1);
4135 for (j = 0; j < var->n_row; ++j) {
4136 if (j == i)
4137 continue;
4138 k = isl_basic_set_alloc_inequality(bset);
4139 if (k < 0)
4140 goto error;
4141 isl_seq_combine(bset->ineq[k], ctx->one, var->row[j],
4142 ctx->negone, var->row[i],
4143 var->n_col);
4144 isl_int_set_si(bset->ineq[k][var->n_col], 0);
4145 if (j < i)
4146 isl_int_sub_ui(bset->ineq[k][0],
4147 bset->ineq[k][0], 1);
4149 bset = isl_basic_set_finalize(bset);
4150 set = isl_set_add_basic_set(set, bset);
4153 isl_dim_free(dim);
4154 isl_mat_free(var);
4155 return set;
4156 error:
4157 isl_basic_set_free(bset);
4158 isl_set_free(set);
4159 isl_dim_free(dim);
4160 isl_mat_free(var);
4161 return NULL;
4164 /* Given that the last input variable of "bmap" represents the minimum
4165 * of the bounds in "cst", check whether we need to split the domain
4166 * based on which bound attains the minimum.
4168 * A split is needed when the minimum appears in an integer division
4169 * or in an equality. Otherwise, it is only needed if it appears in
4170 * an upper bound that is different from the upper bounds on which it
4171 * is defined.
4173 static int need_split_map(__isl_keep isl_basic_map *bmap,
4174 __isl_keep isl_mat *cst)
4176 int i, j;
4177 unsigned total;
4178 unsigned pos;
4180 pos = cst->n_col - 1;
4181 total = isl_basic_map_dim(bmap, isl_dim_all);
4183 for (i = 0; i < bmap->n_div; ++i)
4184 if (!isl_int_is_zero(bmap->div[i][2 + pos]))
4185 return 1;
4187 for (i = 0; i < bmap->n_eq; ++i)
4188 if (!isl_int_is_zero(bmap->eq[i][1 + pos]))
4189 return 1;
4191 for (i = 0; i < bmap->n_ineq; ++i) {
4192 if (isl_int_is_nonneg(bmap->ineq[i][1 + pos]))
4193 continue;
4194 if (!isl_int_is_negone(bmap->ineq[i][1 + pos]))
4195 return 1;
4196 if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + pos + 1,
4197 total - pos - 1) >= 0)
4198 return 1;
4200 for (j = 0; j < cst->n_row; ++j)
4201 if (isl_seq_eq(bmap->ineq[i], cst->row[j], cst->n_col))
4202 break;
4203 if (j >= cst->n_row)
4204 return 1;
4207 return 0;
4210 static int need_split_set(__isl_keep isl_basic_set *bset,
4211 __isl_keep isl_mat *cst)
4213 return need_split_map((isl_basic_map *)bset, cst);
4216 /* Given a set of which the last set variable is the minimum
4217 * of the bounds in "cst", split each basic set in the set
4218 * in pieces where one of the bounds is (strictly) smaller than the others.
4219 * This subdivision is given in "min_expr".
4220 * The variable is subsequently projected out.
4222 * We only do the split when it is needed.
4223 * For example if the last input variable m = min(a,b) and the only
4224 * constraints in the given basic set are lower bounds on m,
4225 * i.e., l <= m = min(a,b), then we can simply project out m
4226 * to obtain l <= a and l <= b, without having to split on whether
4227 * m is equal to a or b.
4229 static __isl_give isl_set *split(__isl_take isl_set *empty,
4230 __isl_take isl_set *min_expr, __isl_take isl_mat *cst)
4232 int n_in;
4233 int i;
4234 isl_dim *dim;
4235 isl_set *res;
4237 if (!empty || !min_expr || !cst)
4238 goto error;
4240 n_in = isl_set_dim(empty, isl_dim_set);
4241 dim = isl_set_get_dim(empty);
4242 dim = isl_dim_drop(dim, isl_dim_set, n_in - 1, 1);
4243 res = isl_set_empty(dim);
4245 for (i = 0; i < empty->n; ++i) {
4246 isl_set *set;
4248 set = isl_set_from_basic_set(isl_basic_set_copy(empty->p[i]));
4249 if (need_split_set(empty->p[i], cst))
4250 set = isl_set_intersect(set, isl_set_copy(min_expr));
4251 set = isl_set_remove_dims(set, isl_dim_set, n_in - 1, 1);
4253 res = isl_set_union_disjoint(res, set);
4256 isl_set_free(empty);
4257 isl_set_free(min_expr);
4258 isl_mat_free(cst);
4259 return res;
4260 error:
4261 isl_set_free(empty);
4262 isl_set_free(min_expr);
4263 isl_mat_free(cst);
4264 return NULL;
4267 /* Given a map of which the last input variable is the minimum
4268 * of the bounds in "cst", split each basic set in the set
4269 * in pieces where one of the bounds is (strictly) smaller than the others.
4270 * This subdivision is given in "min_expr".
4271 * The variable is subsequently projected out.
4273 * The implementation is essentially the same as that of "split".
4275 static __isl_give isl_map *split_domain(__isl_take isl_map *opt,
4276 __isl_take isl_set *min_expr, __isl_take isl_mat *cst)
4278 int n_in;
4279 int i;
4280 isl_dim *dim;
4281 isl_map *res;
4283 if (!opt || !min_expr || !cst)
4284 goto error;
4286 n_in = isl_map_dim(opt, isl_dim_in);
4287 dim = isl_map_get_dim(opt);
4288 dim = isl_dim_drop(dim, isl_dim_in, n_in - 1, 1);
4289 res = isl_map_empty(dim);
4291 for (i = 0; i < opt->n; ++i) {
4292 isl_map *map;
4294 map = isl_map_from_basic_map(isl_basic_map_copy(opt->p[i]));
4295 if (need_split_map(opt->p[i], cst))
4296 map = isl_map_intersect_domain(map,
4297 isl_set_copy(min_expr));
4298 map = isl_map_remove_dims(map, isl_dim_in, n_in - 1, 1);
4300 res = isl_map_union_disjoint(res, map);
4303 isl_map_free(opt);
4304 isl_set_free(min_expr);
4305 isl_mat_free(cst);
4306 return res;
4307 error:
4308 isl_map_free(opt);
4309 isl_set_free(min_expr);
4310 isl_mat_free(cst);
4311 return NULL;
4314 static __isl_give isl_map *basic_map_partial_lexopt(
4315 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
4316 __isl_give isl_set **empty, int max);
4318 /* Given a basic map with at least two parallel constraints (as found
4319 * by the function parallel_constraints), first look for more constraints
4320 * parallel to the two constraint and replace the found list of parallel
4321 * constraints by a single constraint with as "input" part the minimum
4322 * of the input parts of the list of constraints. Then, recursively call
4323 * basic_map_partial_lexopt (possibly finding more parallel constraints)
4324 * and plug in the definition of the minimum in the result.
4326 * More specifically, given a set of constraints
4328 * a x + b_i(p) >= 0
4330 * Replace this set by a single constraint
4332 * a x + u >= 0
4334 * with u a new parameter with constraints
4336 * u <= b_i(p)
4338 * Any solution to the new system is also a solution for the original system
4339 * since
4341 * a x >= -u >= -b_i(p)
4343 * Moreover, m = min_i(b_i(p)) satisfies the constraints on u and can
4344 * therefore be plugged into the solution.
4346 static __isl_give isl_map *basic_map_partial_lexopt_symm(
4347 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
4348 __isl_give isl_set **empty, int max, int first, int second)
4350 int i, n, k;
4351 int *list = NULL;
4352 unsigned n_in, n_out, n_div;
4353 isl_ctx *ctx;
4354 isl_vec *var = NULL;
4355 isl_mat *cst = NULL;
4356 isl_map *opt;
4357 isl_set *min_expr;
4358 isl_dim *map_dim, *set_dim;
4360 map_dim = isl_basic_map_get_dim(bmap);
4361 set_dim = empty ? isl_basic_set_get_dim(dom) : NULL;
4363 n_in = isl_basic_map_dim(bmap, isl_dim_param) +
4364 isl_basic_map_dim(bmap, isl_dim_in);
4365 n_out = isl_basic_map_dim(bmap, isl_dim_all) - n_in;
4367 ctx = isl_basic_map_get_ctx(bmap);
4368 list = isl_alloc_array(ctx, int, bmap->n_ineq);
4369 var = isl_vec_alloc(ctx, n_out);
4370 if (!list || !var)
4371 goto error;
4373 list[0] = first;
4374 list[1] = second;
4375 isl_seq_cpy(var->el, bmap->ineq[first] + 1 + n_in, n_out);
4376 for (i = second + 1, n = 2; i < bmap->n_ineq; ++i) {
4377 if (isl_seq_eq(var->el, bmap->ineq[i] + 1 + n_in, n_out))
4378 list[n++] = i;
4381 cst = isl_mat_alloc(ctx, n, 1 + n_in);
4382 if (!cst)
4383 goto error;
4385 for (i = 0; i < n; ++i)
4386 isl_seq_cpy(cst->row[i], bmap->ineq[list[i]], 1 + n_in);
4388 bmap = isl_basic_map_cow(bmap);
4389 if (!bmap)
4390 goto error;
4391 for (i = n - 1; i >= 0; --i)
4392 if (isl_basic_map_drop_inequality(bmap, list[i]) < 0)
4393 goto error;
4395 bmap = isl_basic_map_add(bmap, isl_dim_in, 1);
4396 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
4397 k = isl_basic_map_alloc_inequality(bmap);
4398 if (k < 0)
4399 goto error;
4400 isl_seq_clr(bmap->ineq[k], 1 + n_in);
4401 isl_int_set_si(bmap->ineq[k][1 + n_in], 1);
4402 isl_seq_cpy(bmap->ineq[k] + 1 + n_in + 1, var->el, n_out);
4403 bmap = isl_basic_map_finalize(bmap);
4405 n_div = isl_basic_set_dim(dom, isl_dim_div);
4406 dom = isl_basic_set_add(dom, isl_dim_set, 1);
4407 dom = isl_basic_set_extend_constraints(dom, 0, n);
4408 for (i = 0; i < n; ++i) {
4409 k = isl_basic_set_alloc_inequality(dom);
4410 if (k < 0)
4411 goto error;
4412 isl_seq_cpy(dom->ineq[k], cst->row[i], 1 + n_in);
4413 isl_int_set_si(dom->ineq[k][1 + n_in], -1);
4414 isl_seq_clr(dom->ineq[k] + 1 + n_in + 1, n_div);
4417 min_expr = set_minimum(isl_basic_set_get_dim(dom), isl_mat_copy(cst));
4419 isl_vec_free(var);
4420 free(list);
4422 opt = basic_map_partial_lexopt(bmap, dom, empty, max);
4424 if (empty) {
4425 *empty = split(*empty,
4426 isl_set_copy(min_expr), isl_mat_copy(cst));
4427 *empty = isl_set_reset_dim(*empty, set_dim);
4430 opt = split_domain(opt, min_expr, cst);
4431 opt = isl_map_reset_dim(opt, map_dim);
4433 return opt;
4434 error:
4435 isl_dim_free(map_dim);
4436 isl_dim_free(set_dim);
4437 isl_mat_free(cst);
4438 isl_vec_free(var);
4439 free(list);
4440 isl_basic_set_free(dom);
4441 isl_basic_map_free(bmap);
4442 return NULL;
4445 /* Recursive part of isl_tab_basic_map_partial_lexopt, after detecting
4446 * equalities and removing redundant constraints.
4448 * We first check if there are any parallel constraints (left).
4449 * If not, we are in the base case.
4450 * If there are parallel constraints, we replace them by a single
4451 * constraint in basic_map_partial_lexopt_symm and then call
4452 * this function recursively to look for more parallel constraints.
4454 static __isl_give isl_map *basic_map_partial_lexopt(
4455 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
4456 __isl_give isl_set **empty, int max)
4458 int par = 0;
4459 int first, second;
4461 if (!bmap)
4462 goto error;
4464 if (bmap->ctx->opt->pip_symmetry)
4465 par = parallel_constraints(bmap, &first, &second);
4466 if (par < 0)
4467 goto error;
4468 if (!par)
4469 return basic_map_partial_lexopt_base(bmap, dom, empty, max);
4471 return basic_map_partial_lexopt_symm(bmap, dom, empty, max,
4472 first, second);
4473 error:
4474 isl_basic_set_free(dom);
4475 isl_basic_map_free(bmap);
4476 return NULL;
4479 /* Compute the lexicographic minimum (or maximum if "max" is set)
4480 * of "bmap" over the domain "dom" and return the result as a map.
4481 * If "empty" is not NULL, then *empty is assigned a set that
4482 * contains those parts of the domain where there is no solution.
4483 * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
4484 * then we compute the rational optimum. Otherwise, we compute
4485 * the integral optimum.
4487 * We perform some preprocessing. As the PILP solver does not
4488 * handle implicit equalities very well, we first make sure all
4489 * the equalities are explicitly available.
4491 * We also add context constraints to the basic map and remove
4492 * redundant constraints. This is only needed because of the
4493 * way we handle simple symmetries. In particular, we currently look
4494 * for symmetries on the constraints, before we set up the main tableau.
4495 * It is then no good to look for symmetries on possibly redundant constraints.
4497 struct isl_map *isl_tab_basic_map_partial_lexopt(
4498 struct isl_basic_map *bmap, struct isl_basic_set *dom,
4499 struct isl_set **empty, int max)
4501 if (empty)
4502 *empty = NULL;
4503 if (!bmap || !dom)
4504 goto error;
4506 isl_assert(bmap->ctx,
4507 isl_basic_map_compatible_domain(bmap, dom), goto error);
4509 if (isl_basic_set_dim(dom, isl_dim_all) == 0)
4510 return basic_map_partial_lexopt(bmap, dom, empty, max);
4512 bmap = isl_basic_map_intersect_domain(bmap, isl_basic_set_copy(dom));
4513 bmap = isl_basic_map_detect_equalities(bmap);
4514 bmap = isl_basic_map_remove_redundancies(bmap);
4516 return basic_map_partial_lexopt(bmap, dom, empty, max);
4517 error:
4518 isl_basic_set_free(dom);
4519 isl_basic_map_free(bmap);
4520 return NULL;
4523 struct isl_sol_for {
4524 struct isl_sol sol;
4525 int (*fn)(__isl_take isl_basic_set *dom,
4526 __isl_take isl_mat *map, void *user);
4527 void *user;
4530 static void sol_for_free(struct isl_sol_for *sol_for)
4532 if (sol_for->sol.context)
4533 sol_for->sol.context->op->free(sol_for->sol.context);
4534 free(sol_for);
4537 static void sol_for_free_wrap(struct isl_sol *sol)
4539 sol_for_free((struct isl_sol_for *)sol);
4542 /* Add the solution identified by the tableau and the context tableau.
4544 * See documentation of sol_add for more details.
4546 * Instead of constructing a basic map, this function calls a user
4547 * defined function with the current context as a basic set and
4548 * an affine matrix representing the relation between the input and output.
4549 * The number of rows in this matrix is equal to one plus the number
4550 * of output variables. The number of columns is equal to one plus
4551 * the total dimension of the context, i.e., the number of parameters,
4552 * input variables and divs. Since some of the columns in the matrix
4553 * may refer to the divs, the basic set is not simplified.
4554 * (Simplification may reorder or remove divs.)
4556 static void sol_for_add(struct isl_sol_for *sol,
4557 struct isl_basic_set *dom, struct isl_mat *M)
4559 if (sol->sol.error || !dom || !M)
4560 goto error;
4562 dom = isl_basic_set_simplify(dom);
4563 dom = isl_basic_set_finalize(dom);
4565 if (sol->fn(isl_basic_set_copy(dom), isl_mat_copy(M), sol->user) < 0)
4566 goto error;
4568 isl_basic_set_free(dom);
4569 isl_mat_free(M);
4570 return;
4571 error:
4572 isl_basic_set_free(dom);
4573 isl_mat_free(M);
4574 sol->sol.error = 1;
4577 static void sol_for_add_wrap(struct isl_sol *sol,
4578 struct isl_basic_set *dom, struct isl_mat *M)
4580 sol_for_add((struct isl_sol_for *)sol, dom, M);
4583 static struct isl_sol_for *sol_for_init(struct isl_basic_map *bmap, int max,
4584 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
4585 void *user),
4586 void *user)
4588 struct isl_sol_for *sol_for = NULL;
4589 struct isl_dim *dom_dim;
4590 struct isl_basic_set *dom = NULL;
4592 sol_for = isl_calloc_type(bmap->ctx, struct isl_sol_for);
4593 if (!sol_for)
4594 goto error;
4596 dom_dim = isl_dim_domain(isl_dim_copy(bmap->dim));
4597 dom = isl_basic_set_universe(dom_dim);
4599 sol_for->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
4600 sol_for->sol.dec_level.callback.run = &sol_dec_level_wrap;
4601 sol_for->sol.dec_level.sol = &sol_for->sol;
4602 sol_for->fn = fn;
4603 sol_for->user = user;
4604 sol_for->sol.max = max;
4605 sol_for->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
4606 sol_for->sol.add = &sol_for_add_wrap;
4607 sol_for->sol.add_empty = NULL;
4608 sol_for->sol.free = &sol_for_free_wrap;
4610 sol_for->sol.context = isl_context_alloc(dom);
4611 if (!sol_for->sol.context)
4612 goto error;
4614 isl_basic_set_free(dom);
4615 return sol_for;
4616 error:
4617 isl_basic_set_free(dom);
4618 sol_for_free(sol_for);
4619 return NULL;
4622 static void sol_for_find_solutions(struct isl_sol_for *sol_for,
4623 struct isl_tab *tab)
4625 find_solutions_main(&sol_for->sol, tab);
4628 int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map *bmap, int max,
4629 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
4630 void *user),
4631 void *user)
4633 struct isl_sol_for *sol_for = NULL;
4635 bmap = isl_basic_map_copy(bmap);
4636 if (!bmap)
4637 return -1;
4639 bmap = isl_basic_map_detect_equalities(bmap);
4640 sol_for = sol_for_init(bmap, max, fn, user);
4642 if (isl_basic_map_fast_is_empty(bmap))
4643 /* nothing */;
4644 else {
4645 struct isl_tab *tab;
4646 struct isl_context *context = sol_for->sol.context;
4647 tab = tab_for_lexmin(bmap,
4648 context->op->peek_basic_set(context), 1, max);
4649 tab = context->op->detect_nonnegative_parameters(context, tab);
4650 sol_for_find_solutions(sol_for, tab);
4651 if (sol_for->sol.error)
4652 goto error;
4655 sol_free(&sol_for->sol);
4656 isl_basic_map_free(bmap);
4657 return 0;
4658 error:
4659 sol_free(&sol_for->sol);
4660 isl_basic_map_free(bmap);
4661 return -1;
4664 int isl_basic_map_foreach_lexmin(__isl_keep isl_basic_map *bmap,
4665 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
4666 void *user),
4667 void *user)
4669 return isl_basic_map_foreach_lexopt(bmap, 0, fn, user);
4672 int isl_basic_map_foreach_lexmax(__isl_keep isl_basic_map *bmap,
4673 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
4674 void *user),
4675 void *user)
4677 return isl_basic_map_foreach_lexopt(bmap, 1, fn, user);
4680 /* Check if the given sequence of len variables starting at pos
4681 * represents a trivial (i.e., zero) solution.
4682 * The variables are assumed to be non-negative and to come in pairs,
4683 * with each pair representing a variable of unrestricted sign.
4684 * The solution is trivial if each such pair in the sequence consists
4685 * of two identical values, meaning that the variable being represented
4686 * has value zero.
4688 static int region_is_trivial(struct isl_tab *tab, int pos, int len)
4690 int i;
4692 if (len == 0)
4693 return 0;
4695 for (i = 0; i < len; i += 2) {
4696 int neg_row;
4697 int pos_row;
4699 neg_row = tab->var[pos + i].is_row ?
4700 tab->var[pos + i].index : -1;
4701 pos_row = tab->var[pos + i + 1].is_row ?
4702 tab->var[pos + i + 1].index : -1;
4704 if ((neg_row < 0 ||
4705 isl_int_is_zero(tab->mat->row[neg_row][1])) &&
4706 (pos_row < 0 ||
4707 isl_int_is_zero(tab->mat->row[pos_row][1])))
4708 continue;
4710 if (neg_row < 0 || pos_row < 0)
4711 return 0;
4712 if (isl_int_ne(tab->mat->row[neg_row][1],
4713 tab->mat->row[pos_row][1]))
4714 return 0;
4717 return 1;
4720 /* Return the index of the first trivial region or -1 if all regions
4721 * are non-trivial.
4723 static int first_trivial_region(struct isl_tab *tab,
4724 int n_region, struct isl_region *region)
4726 int i;
4728 for (i = 0; i < n_region; ++i) {
4729 if (region_is_trivial(tab, region[i].pos, region[i].len))
4730 return i;
4733 return -1;
4736 /* Check if the solution is optimal, i.e., whether the first
4737 * n_op entries are zero.
4739 static int is_optimal(__isl_keep isl_vec *sol, int n_op)
4741 int i;
4743 for (i = 0; i < n_op; ++i)
4744 if (!isl_int_is_zero(sol->el[1 + i]))
4745 return 0;
4746 return 1;
4749 /* Add constraints to "tab" that ensure that any solution is significantly
4750 * better that that represented by "sol". That is, find the first
4751 * relevant (within first n_op) non-zero coefficient and force it (along
4752 * with all previous coefficients) to be zero.
4753 * If the solution is already optimal (all relevant coefficients are zero),
4754 * then just mark the table as empty.
4756 static int force_better_solution(struct isl_tab *tab,
4757 __isl_keep isl_vec *sol, int n_op)
4759 int i;
4760 isl_ctx *ctx;
4761 isl_vec *v = NULL;
4763 if (!sol)
4764 return -1;
4766 for (i = 0; i < n_op; ++i)
4767 if (!isl_int_is_zero(sol->el[1 + i]))
4768 break;
4770 if (i == n_op) {
4771 if (isl_tab_mark_empty(tab) < 0)
4772 return -1;
4773 return 0;
4776 ctx = isl_vec_get_ctx(sol);
4777 v = isl_vec_alloc(ctx, 1 + tab->n_var);
4778 if (!v)
4779 return -1;
4781 for (; i >= 0; --i) {
4782 v = isl_vec_clr(v);
4783 isl_int_set_si(v->el[1 + i], -1);
4784 if (add_lexmin_eq(tab, v->el) < 0)
4785 goto error;
4788 isl_vec_free(v);
4789 return 0;
4790 error:
4791 isl_vec_free(v);
4792 return -1;
4795 struct isl_trivial {
4796 int update;
4797 int region;
4798 int side;
4799 struct isl_tab_undo *snap;
4802 /* Return the lexicographically smallest non-trivial solution of the
4803 * given ILP problem.
4805 * All variables are assumed to be non-negative.
4807 * n_op is the number of initial coordinates to optimize.
4808 * That is, once a solution has been found, we will only continue looking
4809 * for solution that result in significantly better values for those
4810 * initial coordinates. That is, we only continue looking for solutions
4811 * that increase the number of initial zeros in this sequence.
4813 * A solution is non-trivial, if it is non-trivial on each of the
4814 * specified regions. Each region represents a sequence of pairs
4815 * of variables. A solution is non-trivial on such a region if
4816 * at least one of these pairs consists of different values, i.e.,
4817 * such that the non-negative variable represented by the pair is non-zero.
4819 * Whenever a conflict is encountered, all constraints involved are
4820 * reported to the caller through a call to "conflict".
4822 * We perform a simple branch-and-bound backtracking search.
4823 * Each level in the search represents initially trivial region that is forced
4824 * to be non-trivial.
4825 * At each level we consider n cases, where n is the length of the region.
4826 * In terms of the n/2 variables of unrestricted signs being encoded by
4827 * the region, we consider the cases
4828 * x_0 >= 1
4829 * x_0 <= -1
4830 * x_0 = 0 and x_1 >= 1
4831 * x_0 = 0 and x_1 <= -1
4832 * x_0 = 0 and x_1 = 0 and x_2 >= 1
4833 * x_0 = 0 and x_1 = 0 and x_2 <= -1
4834 * ...
4835 * The cases are considered in this order, assuming that each pair
4836 * x_i_a x_i_b represents the value x_i_b - x_i_a.
4837 * That is, x_0 >= 1 is enforced by adding the constraint
4838 * x_0_b - x_0_a >= 1
4840 __isl_give isl_vec *isl_tab_basic_set_non_trivial_lexmin(
4841 __isl_take isl_basic_set *bset, int n_op, int n_region,
4842 struct isl_region *region,
4843 int (*conflict)(int con, void *user), void *user)
4845 int i, j;
4846 int need_update = 0;
4847 int r;
4848 isl_ctx *ctx = isl_basic_set_get_ctx(bset);
4849 isl_vec *v = NULL;
4850 isl_vec *sol = isl_vec_alloc(ctx, 0);
4851 struct isl_tab *tab;
4852 struct isl_trivial *triv = NULL;
4853 int level, init;
4855 tab = tab_for_lexmin(isl_basic_map_from_range(bset), NULL, 0, 0);
4856 if (!tab)
4857 goto error;
4858 tab->conflict = conflict;
4859 tab->conflict_user = user;
4861 v = isl_vec_alloc(ctx, 1 + tab->n_var);
4862 triv = isl_calloc_array(ctx, struct isl_trivial, n_region);
4863 if (!v || !triv)
4864 goto error;
4866 level = 0;
4867 init = 1;
4869 while (level >= 0) {
4870 int side, base;
4872 if (init) {
4873 tab = cut_to_integer_lexmin(tab);
4874 if (!tab)
4875 goto error;
4876 if (tab->empty)
4877 goto backtrack;
4878 r = first_trivial_region(tab, n_region, region);
4879 if (r < 0) {
4880 for (i = 0; i < level; ++i)
4881 triv[i].update = 1;
4882 isl_vec_free(sol);
4883 sol = isl_tab_get_sample_value(tab);
4884 if (!sol)
4885 goto error;
4886 if (is_optimal(sol, n_op))
4887 break;
4888 goto backtrack;
4890 if (level >= n_region)
4891 isl_die(ctx, isl_error_internal,
4892 "nesting level too deep", goto error);
4893 if (isl_tab_extend_cons(tab,
4894 2 * region[r].len + 2 * n_op) < 0)
4895 goto error;
4896 triv[level].region = r;
4897 triv[level].side = 0;
4900 r = triv[level].region;
4901 side = triv[level].side;
4902 base = 2 * (side/2);
4904 if (side >= region[r].len) {
4905 backtrack:
4906 level--;
4907 init = 0;
4908 if (level >= 0)
4909 if (isl_tab_rollback(tab, triv[level].snap) < 0)
4910 goto error;
4911 continue;
4914 if (triv[level].update) {
4915 if (force_better_solution(tab, sol, n_op) < 0)
4916 goto error;
4917 triv[level].update = 0;
4920 if (side == base && base >= 2) {
4921 for (j = base - 2; j < base; ++j) {
4922 v = isl_vec_clr(v);
4923 isl_int_set_si(v->el[1 + region[r].pos + j], 1);
4924 if (add_lexmin_eq(tab, v->el) < 0)
4925 goto error;
4929 triv[level].snap = isl_tab_snap(tab);
4930 if (isl_tab_push_basis(tab) < 0)
4931 goto error;
4933 v = isl_vec_clr(v);
4934 isl_int_set_si(v->el[0], -1);
4935 isl_int_set_si(v->el[1 + region[r].pos + side], -1);
4936 isl_int_set_si(v->el[1 + region[r].pos + (side ^ 1)], 1);
4937 tab = add_lexmin_ineq(tab, v->el);
4939 triv[level].side++;
4940 level++;
4941 init = 1;
4944 free(triv);
4945 isl_vec_free(v);
4946 isl_tab_free(tab);
4947 isl_basic_set_free(bset);
4949 return sol;
4950 error:
4951 free(triv);
4952 isl_vec_free(v);
4953 isl_tab_free(tab);
4954 isl_basic_set_free(bset);
4955 isl_vec_free(sol);
4956 return NULL;
4959 /* Return the lexicographically smallest rational point in "bset",
4960 * assuming that all variables are non-negative.
4961 * If "bset" is empty, then return a zero-length vector.
4963 __isl_give isl_vec *isl_tab_basic_set_non_neg_lexmin(
4964 __isl_take isl_basic_set *bset)
4966 struct isl_tab *tab;
4967 isl_ctx *ctx = isl_basic_set_get_ctx(bset);
4968 isl_vec *sol;
4970 tab = tab_for_lexmin(isl_basic_map_from_range(bset), NULL, 0, 0);
4971 if (!tab)
4972 goto error;
4973 if (tab->empty)
4974 sol = isl_vec_alloc(ctx, 0);
4975 else
4976 sol = isl_tab_get_sample_value(tab);
4977 isl_tab_free(tab);
4978 isl_basic_set_free(bset);
4979 return sol;
4980 error:
4981 isl_tab_free(tab);
4982 isl_basic_set_free(bset);
4983 return NULL;