isl_handle_error: fix type of error argument
[isl.git] / isl_tab_pip.c
blob74564db37279e6ec98c08ba2dc00dc8c528eb70a
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>
19 #include <isl_aff_private.h>
20 #include <isl_options_private.h>
21 #include <isl_config.h>
24 * The implementation of parametric integer linear programming in this file
25 * was inspired by the paper "Parametric Integer Programming" and the
26 * report "Solving systems of affine (in)equalities" by Paul Feautrier
27 * (and others).
29 * The strategy used for obtaining a feasible solution is different
30 * from the one used in isl_tab.c. In particular, in isl_tab.c,
31 * upon finding a constraint that is not yet satisfied, we pivot
32 * in a row that increases the constant term of the row holding the
33 * constraint, making sure the sample solution remains feasible
34 * for all the constraints it already satisfied.
35 * Here, we always pivot in the row holding the constraint,
36 * choosing a column that induces the lexicographically smallest
37 * increment to the sample solution.
39 * By starting out from a sample value that is lexicographically
40 * smaller than any integer point in the problem space, the first
41 * feasible integer sample point we find will also be the lexicographically
42 * smallest. If all variables can be assumed to be non-negative,
43 * then the initial sample value may be chosen equal to zero.
44 * However, we will not make this assumption. Instead, we apply
45 * the "big parameter" trick. Any variable x is then not directly
46 * used in the tableau, but instead it is represented by another
47 * variable x' = M + x, where M is an arbitrarily large (positive)
48 * value. x' is therefore always non-negative, whatever the value of x.
49 * Taking as initial sample value x' = 0 corresponds to x = -M,
50 * which is always smaller than any possible value of x.
52 * The big parameter trick is used in the main tableau and
53 * also in the context tableau if isl_context_lex is used.
54 * In this case, each tableaus has its own big parameter.
55 * Before doing any real work, we check if all the parameters
56 * happen to be non-negative. If so, we drop the column corresponding
57 * to M from the initial context tableau.
58 * If isl_context_gbr is used, then the big parameter trick is only
59 * used in the main tableau.
62 struct isl_context;
63 struct isl_context_op {
64 /* detect nonnegative parameters in context and mark them in tab */
65 struct isl_tab *(*detect_nonnegative_parameters)(
66 struct isl_context *context, struct isl_tab *tab);
67 /* return temporary reference to basic set representation of context */
68 struct isl_basic_set *(*peek_basic_set)(struct isl_context *context);
69 /* return temporary reference to tableau representation of context */
70 struct isl_tab *(*peek_tab)(struct isl_context *context);
71 /* add equality; check is 1 if eq may not be valid;
72 * update is 1 if we may want to call ineq_sign on context later.
74 void (*add_eq)(struct isl_context *context, isl_int *eq,
75 int check, int update);
76 /* add inequality; check is 1 if ineq may not be valid;
77 * update is 1 if we may want to call ineq_sign on context later.
79 void (*add_ineq)(struct isl_context *context, isl_int *ineq,
80 int check, int update);
81 /* check sign of ineq based on previous information.
82 * strict is 1 if saturation should be treated as a positive sign.
84 enum isl_tab_row_sign (*ineq_sign)(struct isl_context *context,
85 isl_int *ineq, int strict);
86 /* check if inequality maintains feasibility */
87 int (*test_ineq)(struct isl_context *context, isl_int *ineq);
88 /* return index of a div that corresponds to "div" */
89 int (*get_div)(struct isl_context *context, struct isl_tab *tab,
90 struct isl_vec *div);
91 /* add div "div" to context and return non-negativity */
92 int (*add_div)(struct isl_context *context, struct isl_vec *div);
93 int (*detect_equalities)(struct isl_context *context,
94 struct isl_tab *tab);
95 /* return row index of "best" split */
96 int (*best_split)(struct isl_context *context, struct isl_tab *tab);
97 /* check if context has already been determined to be empty */
98 int (*is_empty)(struct isl_context *context);
99 /* check if context is still usable */
100 int (*is_ok)(struct isl_context *context);
101 /* save a copy/snapshot of context */
102 void *(*save)(struct isl_context *context);
103 /* restore saved context */
104 void (*restore)(struct isl_context *context, void *);
105 /* invalidate context */
106 void (*invalidate)(struct isl_context *context);
107 /* free context */
108 void (*free)(struct isl_context *context);
111 struct isl_context {
112 struct isl_context_op *op;
115 struct isl_context_lex {
116 struct isl_context context;
117 struct isl_tab *tab;
120 struct isl_partial_sol {
121 int level;
122 struct isl_basic_set *dom;
123 struct isl_mat *M;
125 struct isl_partial_sol *next;
128 struct isl_sol;
129 struct isl_sol_callback {
130 struct isl_tab_callback callback;
131 struct isl_sol *sol;
134 /* isl_sol is an interface for constructing a solution to
135 * a parametric integer linear programming problem.
136 * Every time the algorithm reaches a state where a solution
137 * can be read off from the tableau (including cases where the tableau
138 * is empty), the function "add" is called on the isl_sol passed
139 * to find_solutions_main.
141 * The context tableau is owned by isl_sol and is updated incrementally.
143 * There are currently two implementations of this interface,
144 * isl_sol_map, which simply collects the solutions in an isl_map
145 * and (optionally) the parts of the context where there is no solution
146 * in an isl_set, and
147 * isl_sol_for, which calls a user-defined function for each part of
148 * the solution.
150 struct isl_sol {
151 int error;
152 int rational;
153 int level;
154 int max;
155 int n_out;
156 struct isl_context *context;
157 struct isl_partial_sol *partial;
158 void (*add)(struct isl_sol *sol,
159 struct isl_basic_set *dom, struct isl_mat *M);
160 void (*add_empty)(struct isl_sol *sol, struct isl_basic_set *bset);
161 void (*free)(struct isl_sol *sol);
162 struct isl_sol_callback dec_level;
165 static void sol_free(struct isl_sol *sol)
167 struct isl_partial_sol *partial, *next;
168 if (!sol)
169 return;
170 for (partial = sol->partial; partial; partial = next) {
171 next = partial->next;
172 isl_basic_set_free(partial->dom);
173 isl_mat_free(partial->M);
174 free(partial);
176 sol->free(sol);
179 /* Push a partial solution represented by a domain and mapping M
180 * onto the stack of partial solutions.
182 static void sol_push_sol(struct isl_sol *sol,
183 struct isl_basic_set *dom, struct isl_mat *M)
185 struct isl_partial_sol *partial;
187 if (sol->error || !dom)
188 goto error;
190 partial = isl_alloc_type(dom->ctx, struct isl_partial_sol);
191 if (!partial)
192 goto error;
194 partial->level = sol->level;
195 partial->dom = dom;
196 partial->M = M;
197 partial->next = sol->partial;
199 sol->partial = partial;
201 return;
202 error:
203 isl_basic_set_free(dom);
204 sol->error = 1;
207 /* Pop one partial solution from the partial solution stack and
208 * pass it on to sol->add or sol->add_empty.
210 static void sol_pop_one(struct isl_sol *sol)
212 struct isl_partial_sol *partial;
214 partial = sol->partial;
215 sol->partial = partial->next;
217 if (partial->M)
218 sol->add(sol, partial->dom, partial->M);
219 else
220 sol->add_empty(sol, partial->dom);
221 free(partial);
224 /* Return a fresh copy of the domain represented by the context tableau.
226 static struct isl_basic_set *sol_domain(struct isl_sol *sol)
228 struct isl_basic_set *bset;
230 if (sol->error)
231 return NULL;
233 bset = isl_basic_set_dup(sol->context->op->peek_basic_set(sol->context));
234 bset = isl_basic_set_update_from_tab(bset,
235 sol->context->op->peek_tab(sol->context));
237 return bset;
240 /* Check whether two partial solutions have the same mapping, where n_div
241 * is the number of divs that the two partial solutions have in common.
243 static int same_solution(struct isl_partial_sol *s1, struct isl_partial_sol *s2,
244 unsigned n_div)
246 int i;
247 unsigned dim;
249 if (!s1->M != !s2->M)
250 return 0;
251 if (!s1->M)
252 return 1;
254 dim = isl_basic_set_total_dim(s1->dom) - s1->dom->n_div;
256 for (i = 0; i < s1->M->n_row; ++i) {
257 if (isl_seq_first_non_zero(s1->M->row[i]+1+dim+n_div,
258 s1->M->n_col-1-dim-n_div) != -1)
259 return 0;
260 if (isl_seq_first_non_zero(s2->M->row[i]+1+dim+n_div,
261 s2->M->n_col-1-dim-n_div) != -1)
262 return 0;
263 if (!isl_seq_eq(s1->M->row[i], s2->M->row[i], 1+dim+n_div))
264 return 0;
266 return 1;
269 /* Pop all solutions from the partial solution stack that were pushed onto
270 * the stack at levels that are deeper than the current level.
271 * If the two topmost elements on the stack have the same level
272 * and represent the same solution, then their domains are combined.
273 * This combined domain is the same as the current context domain
274 * as sol_pop is called each time we move back to a higher level.
276 static void sol_pop(struct isl_sol *sol)
278 struct isl_partial_sol *partial;
279 unsigned n_div;
281 if (sol->error)
282 return;
284 if (sol->level == 0) {
285 for (partial = sol->partial; partial; partial = sol->partial)
286 sol_pop_one(sol);
287 return;
290 partial = sol->partial;
291 if (!partial)
292 return;
294 if (partial->level <= sol->level)
295 return;
297 if (partial->next && partial->next->level == partial->level) {
298 n_div = isl_basic_set_dim(
299 sol->context->op->peek_basic_set(sol->context),
300 isl_dim_div);
302 if (!same_solution(partial, partial->next, n_div)) {
303 sol_pop_one(sol);
304 sol_pop_one(sol);
305 } else {
306 struct isl_basic_set *bset;
308 bset = sol_domain(sol);
310 isl_basic_set_free(partial->next->dom);
311 partial->next->dom = bset;
312 partial->next->level = sol->level;
314 sol->partial = partial->next;
315 isl_basic_set_free(partial->dom);
316 isl_mat_free(partial->M);
317 free(partial);
319 } else
320 sol_pop_one(sol);
323 static void sol_dec_level(struct isl_sol *sol)
325 if (sol->error)
326 return;
328 sol->level--;
330 sol_pop(sol);
333 static int sol_dec_level_wrap(struct isl_tab_callback *cb)
335 struct isl_sol_callback *callback = (struct isl_sol_callback *)cb;
337 sol_dec_level(callback->sol);
339 return callback->sol->error ? -1 : 0;
342 /* Move down to next level and push callback onto context tableau
343 * to decrease the level again when it gets rolled back across
344 * the current state. That is, dec_level will be called with
345 * the context tableau in the same state as it is when inc_level
346 * is called.
348 static void sol_inc_level(struct isl_sol *sol)
350 struct isl_tab *tab;
352 if (sol->error)
353 return;
355 sol->level++;
356 tab = sol->context->op->peek_tab(sol->context);
357 if (isl_tab_push_callback(tab, &sol->dec_level.callback) < 0)
358 sol->error = 1;
361 static void scale_rows(struct isl_mat *mat, isl_int m, int n_row)
363 int i;
365 if (isl_int_is_one(m))
366 return;
368 for (i = 0; i < n_row; ++i)
369 isl_seq_scale(mat->row[i], mat->row[i], m, mat->n_col);
372 /* Add the solution identified by the tableau and the context tableau.
374 * The layout of the variables is as follows.
375 * tab->n_var is equal to the total number of variables in the input
376 * map (including divs that were copied from the context)
377 * + the number of extra divs constructed
378 * Of these, the first tab->n_param and the last tab->n_div variables
379 * correspond to the variables in the context, i.e.,
380 * tab->n_param + tab->n_div = context_tab->n_var
381 * tab->n_param is equal to the number of parameters and input
382 * dimensions in the input map
383 * tab->n_div is equal to the number of divs in the context
385 * If there is no solution, then call add_empty with a basic set
386 * that corresponds to the context tableau. (If add_empty is NULL,
387 * then do nothing).
389 * If there is a solution, then first construct a matrix that maps
390 * all dimensions of the context to the output variables, i.e.,
391 * the output dimensions in the input map.
392 * The divs in the input map (if any) that do not correspond to any
393 * div in the context do not appear in the solution.
394 * The algorithm will make sure that they have an integer value,
395 * but these values themselves are of no interest.
396 * We have to be careful not to drop or rearrange any divs in the
397 * context because that would change the meaning of the matrix.
399 * To extract the value of the output variables, it should be noted
400 * that we always use a big parameter M in the main tableau and so
401 * the variable stored in this tableau is not an output variable x itself, but
402 * x' = M + x (in case of minimization)
403 * or
404 * x' = M - x (in case of maximization)
405 * If x' appears in a column, then its optimal value is zero,
406 * which means that the optimal value of x is an unbounded number
407 * (-M for minimization and M for maximization).
408 * We currently assume that the output dimensions in the original map
409 * are bounded, so this cannot occur.
410 * Similarly, when x' appears in a row, then the coefficient of M in that
411 * row is necessarily 1.
412 * If the row in the tableau represents
413 * d x' = c + d M + e(y)
414 * then, in case of minimization, the corresponding row in the matrix
415 * will be
416 * a c + a e(y)
417 * with a d = m, the (updated) common denominator of the matrix.
418 * In case of maximization, the row will be
419 * -a c - a e(y)
421 static void sol_add(struct isl_sol *sol, struct isl_tab *tab)
423 struct isl_basic_set *bset = NULL;
424 struct isl_mat *mat = NULL;
425 unsigned off;
426 int row;
427 isl_int m;
429 if (sol->error || !tab)
430 goto error;
432 if (tab->empty && !sol->add_empty)
433 return;
434 if (sol->context->op->is_empty(sol->context))
435 return;
437 bset = sol_domain(sol);
439 if (tab->empty) {
440 sol_push_sol(sol, bset, NULL);
441 return;
444 off = 2 + tab->M;
446 mat = isl_mat_alloc(tab->mat->ctx, 1 + sol->n_out,
447 1 + tab->n_param + tab->n_div);
448 if (!mat)
449 goto error;
451 isl_int_init(m);
453 isl_seq_clr(mat->row[0] + 1, mat->n_col - 1);
454 isl_int_set_si(mat->row[0][0], 1);
455 for (row = 0; row < sol->n_out; ++row) {
456 int i = tab->n_param + row;
457 int r, j;
459 isl_seq_clr(mat->row[1 + row], mat->n_col);
460 if (!tab->var[i].is_row) {
461 if (tab->M)
462 isl_die(mat->ctx, isl_error_invalid,
463 "unbounded optimum", goto error2);
464 continue;
467 r = tab->var[i].index;
468 if (tab->M &&
469 isl_int_ne(tab->mat->row[r][2], tab->mat->row[r][0]))
470 isl_die(mat->ctx, isl_error_invalid,
471 "unbounded optimum", goto error2);
472 isl_int_gcd(m, mat->row[0][0], tab->mat->row[r][0]);
473 isl_int_divexact(m, tab->mat->row[r][0], m);
474 scale_rows(mat, m, 1 + row);
475 isl_int_divexact(m, mat->row[0][0], tab->mat->row[r][0]);
476 isl_int_mul(mat->row[1 + row][0], m, tab->mat->row[r][1]);
477 for (j = 0; j < tab->n_param; ++j) {
478 int col;
479 if (tab->var[j].is_row)
480 continue;
481 col = tab->var[j].index;
482 isl_int_mul(mat->row[1 + row][1 + j], m,
483 tab->mat->row[r][off + col]);
485 for (j = 0; j < tab->n_div; ++j) {
486 int col;
487 if (tab->var[tab->n_var - tab->n_div+j].is_row)
488 continue;
489 col = tab->var[tab->n_var - tab->n_div+j].index;
490 isl_int_mul(mat->row[1 + row][1 + tab->n_param + j], m,
491 tab->mat->row[r][off + col]);
493 if (sol->max)
494 isl_seq_neg(mat->row[1 + row], mat->row[1 + row],
495 mat->n_col);
498 isl_int_clear(m);
500 sol_push_sol(sol, bset, mat);
501 return;
502 error2:
503 isl_int_clear(m);
504 error:
505 isl_basic_set_free(bset);
506 isl_mat_free(mat);
507 sol->error = 1;
510 struct isl_sol_map {
511 struct isl_sol sol;
512 struct isl_map *map;
513 struct isl_set *empty;
516 static void sol_map_free(struct isl_sol_map *sol_map)
518 if (!sol_map)
519 return;
520 if (sol_map->sol.context)
521 sol_map->sol.context->op->free(sol_map->sol.context);
522 isl_map_free(sol_map->map);
523 isl_set_free(sol_map->empty);
524 free(sol_map);
527 static void sol_map_free_wrap(struct isl_sol *sol)
529 sol_map_free((struct isl_sol_map *)sol);
532 /* This function is called for parts of the context where there is
533 * no solution, with "bset" corresponding to the context tableau.
534 * Simply add the basic set to the set "empty".
536 static void sol_map_add_empty(struct isl_sol_map *sol,
537 struct isl_basic_set *bset)
539 if (!bset)
540 goto error;
541 isl_assert(bset->ctx, sol->empty, goto error);
543 sol->empty = isl_set_grow(sol->empty, 1);
544 bset = isl_basic_set_simplify(bset);
545 bset = isl_basic_set_finalize(bset);
546 sol->empty = isl_set_add_basic_set(sol->empty, isl_basic_set_copy(bset));
547 if (!sol->empty)
548 goto error;
549 isl_basic_set_free(bset);
550 return;
551 error:
552 isl_basic_set_free(bset);
553 sol->sol.error = 1;
556 static void sol_map_add_empty_wrap(struct isl_sol *sol,
557 struct isl_basic_set *bset)
559 sol_map_add_empty((struct isl_sol_map *)sol, bset);
562 /* Given a basic map "dom" that represents the context and an affine
563 * matrix "M" that maps the dimensions of the context to the
564 * output variables, construct a basic map with the same parameters
565 * and divs as the context, the dimensions of the context as input
566 * dimensions and a number of output dimensions that is equal to
567 * the number of output dimensions in the input map.
569 * The constraints and divs of the context are simply copied
570 * from "dom". For each row
571 * x = c + e(y)
572 * an equality
573 * c + e(y) - d x = 0
574 * is added, with d the common denominator of M.
576 static void sol_map_add(struct isl_sol_map *sol,
577 struct isl_basic_set *dom, struct isl_mat *M)
579 int i;
580 struct isl_basic_map *bmap = NULL;
581 unsigned n_eq;
582 unsigned n_ineq;
583 unsigned nparam;
584 unsigned total;
585 unsigned n_div;
586 unsigned n_out;
588 if (sol->sol.error || !dom || !M)
589 goto error;
591 n_out = sol->sol.n_out;
592 n_eq = dom->n_eq + n_out;
593 n_ineq = dom->n_ineq;
594 n_div = dom->n_div;
595 nparam = isl_basic_set_total_dim(dom) - n_div;
596 total = isl_map_dim(sol->map, isl_dim_all);
597 bmap = isl_basic_map_alloc_space(isl_map_get_space(sol->map),
598 n_div, n_eq, 2 * n_div + n_ineq);
599 if (!bmap)
600 goto error;
601 if (sol->sol.rational)
602 ISL_F_SET(bmap, ISL_BASIC_MAP_RATIONAL);
603 for (i = 0; i < dom->n_div; ++i) {
604 int k = isl_basic_map_alloc_div(bmap);
605 if (k < 0)
606 goto error;
607 isl_seq_cpy(bmap->div[k], dom->div[i], 1 + 1 + nparam);
608 isl_seq_clr(bmap->div[k] + 1 + 1 + nparam, total - nparam);
609 isl_seq_cpy(bmap->div[k] + 1 + 1 + total,
610 dom->div[i] + 1 + 1 + nparam, i);
612 for (i = 0; i < dom->n_eq; ++i) {
613 int k = isl_basic_map_alloc_equality(bmap);
614 if (k < 0)
615 goto error;
616 isl_seq_cpy(bmap->eq[k], dom->eq[i], 1 + nparam);
617 isl_seq_clr(bmap->eq[k] + 1 + nparam, total - nparam);
618 isl_seq_cpy(bmap->eq[k] + 1 + total,
619 dom->eq[i] + 1 + nparam, n_div);
621 for (i = 0; i < dom->n_ineq; ++i) {
622 int k = isl_basic_map_alloc_inequality(bmap);
623 if (k < 0)
624 goto error;
625 isl_seq_cpy(bmap->ineq[k], dom->ineq[i], 1 + nparam);
626 isl_seq_clr(bmap->ineq[k] + 1 + nparam, total - nparam);
627 isl_seq_cpy(bmap->ineq[k] + 1 + total,
628 dom->ineq[i] + 1 + nparam, n_div);
630 for (i = 0; i < M->n_row - 1; ++i) {
631 int k = isl_basic_map_alloc_equality(bmap);
632 if (k < 0)
633 goto error;
634 isl_seq_cpy(bmap->eq[k], M->row[1 + i], 1 + nparam);
635 isl_seq_clr(bmap->eq[k] + 1 + nparam, n_out);
636 isl_int_neg(bmap->eq[k][1 + nparam + i], M->row[0][0]);
637 isl_seq_cpy(bmap->eq[k] + 1 + nparam + n_out,
638 M->row[1 + i] + 1 + nparam, n_div);
640 bmap = isl_basic_map_simplify(bmap);
641 bmap = isl_basic_map_finalize(bmap);
642 sol->map = isl_map_grow(sol->map, 1);
643 sol->map = isl_map_add_basic_map(sol->map, bmap);
644 isl_basic_set_free(dom);
645 isl_mat_free(M);
646 if (!sol->map)
647 sol->sol.error = 1;
648 return;
649 error:
650 isl_basic_set_free(dom);
651 isl_mat_free(M);
652 isl_basic_map_free(bmap);
653 sol->sol.error = 1;
656 static void sol_map_add_wrap(struct isl_sol *sol,
657 struct isl_basic_set *dom, struct isl_mat *M)
659 sol_map_add((struct isl_sol_map *)sol, dom, M);
663 /* Store the "parametric constant" of row "row" of tableau "tab" in "line",
664 * i.e., the constant term and the coefficients of all variables that
665 * appear in the context tableau.
666 * Note that the coefficient of the big parameter M is NOT copied.
667 * The context tableau may not have a big parameter and even when it
668 * does, it is a different big parameter.
670 static void get_row_parameter_line(struct isl_tab *tab, int row, isl_int *line)
672 int i;
673 unsigned off = 2 + tab->M;
675 isl_int_set(line[0], tab->mat->row[row][1]);
676 for (i = 0; i < tab->n_param; ++i) {
677 if (tab->var[i].is_row)
678 isl_int_set_si(line[1 + i], 0);
679 else {
680 int col = tab->var[i].index;
681 isl_int_set(line[1 + i], tab->mat->row[row][off + col]);
684 for (i = 0; i < tab->n_div; ++i) {
685 if (tab->var[tab->n_var - tab->n_div + i].is_row)
686 isl_int_set_si(line[1 + tab->n_param + i], 0);
687 else {
688 int col = tab->var[tab->n_var - tab->n_div + i].index;
689 isl_int_set(line[1 + tab->n_param + i],
690 tab->mat->row[row][off + col]);
695 /* Check if rows "row1" and "row2" have identical "parametric constants",
696 * as explained above.
697 * In this case, we also insist that the coefficients of the big parameter
698 * be the same as the values of the constants will only be the same
699 * if these coefficients are also the same.
701 static int identical_parameter_line(struct isl_tab *tab, int row1, int row2)
703 int i;
704 unsigned off = 2 + tab->M;
706 if (isl_int_ne(tab->mat->row[row1][1], tab->mat->row[row2][1]))
707 return 0;
709 if (tab->M && isl_int_ne(tab->mat->row[row1][2],
710 tab->mat->row[row2][2]))
711 return 0;
713 for (i = 0; i < tab->n_param + tab->n_div; ++i) {
714 int pos = i < tab->n_param ? i :
715 tab->n_var - tab->n_div + i - tab->n_param;
716 int col;
718 if (tab->var[pos].is_row)
719 continue;
720 col = tab->var[pos].index;
721 if (isl_int_ne(tab->mat->row[row1][off + col],
722 tab->mat->row[row2][off + col]))
723 return 0;
725 return 1;
728 /* Return an inequality that expresses that the "parametric constant"
729 * should be non-negative.
730 * This function is only called when the coefficient of the big parameter
731 * is equal to zero.
733 static struct isl_vec *get_row_parameter_ineq(struct isl_tab *tab, int row)
735 struct isl_vec *ineq;
737 ineq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_param + tab->n_div);
738 if (!ineq)
739 return NULL;
741 get_row_parameter_line(tab, row, ineq->el);
742 if (ineq)
743 ineq = isl_vec_normalize(ineq);
745 return ineq;
748 /* Normalize a div expression of the form
750 * [(g*f(x) + c)/(g * m)]
752 * with c the constant term and f(x) the remaining coefficients, to
754 * [(f(x) + [c/g])/m]
756 static void normalize_div(__isl_keep isl_vec *div)
758 isl_ctx *ctx = isl_vec_get_ctx(div);
759 int len = div->size - 2;
761 isl_seq_gcd(div->el + 2, len, &ctx->normalize_gcd);
762 isl_int_gcd(ctx->normalize_gcd, ctx->normalize_gcd, div->el[0]);
764 if (isl_int_is_one(ctx->normalize_gcd))
765 return;
767 isl_int_divexact(div->el[0], div->el[0], ctx->normalize_gcd);
768 isl_int_fdiv_q(div->el[1], div->el[1], ctx->normalize_gcd);
769 isl_seq_scale_down(div->el + 2, div->el + 2, ctx->normalize_gcd, len);
772 /* Return a integer division for use in a parametric cut based on the given row.
773 * In particular, let the parametric constant of the row be
775 * \sum_i a_i y_i
777 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
778 * The div returned is equal to
780 * floor(\sum_i {-a_i} y_i) = floor((\sum_i (-a_i mod d) y_i)/d)
782 static struct isl_vec *get_row_parameter_div(struct isl_tab *tab, int row)
784 struct isl_vec *div;
786 div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div);
787 if (!div)
788 return NULL;
790 isl_int_set(div->el[0], tab->mat->row[row][0]);
791 get_row_parameter_line(tab, row, div->el + 1);
792 normalize_div(div);
793 isl_seq_neg(div->el + 1, div->el + 1, div->size - 1);
794 isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1);
796 return div;
799 /* Return a integer division for use in transferring an integrality constraint
800 * to the context.
801 * In particular, let the parametric constant of the row be
803 * \sum_i a_i y_i
805 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
806 * The the returned div is equal to
808 * floor(\sum_i {a_i} y_i) = floor((\sum_i (a_i mod d) y_i)/d)
810 static struct isl_vec *get_row_split_div(struct isl_tab *tab, int row)
812 struct isl_vec *div;
814 div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div);
815 if (!div)
816 return NULL;
818 isl_int_set(div->el[0], tab->mat->row[row][0]);
819 get_row_parameter_line(tab, row, div->el + 1);
820 normalize_div(div);
821 isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1);
823 return div;
826 /* Construct and return an inequality that expresses an upper bound
827 * on the given div.
828 * In particular, if the div is given by
830 * d = floor(e/m)
832 * then the inequality expresses
834 * m d <= e
836 static struct isl_vec *ineq_for_div(struct isl_basic_set *bset, unsigned div)
838 unsigned total;
839 unsigned div_pos;
840 struct isl_vec *ineq;
842 if (!bset)
843 return NULL;
845 total = isl_basic_set_total_dim(bset);
846 div_pos = 1 + total - bset->n_div + div;
848 ineq = isl_vec_alloc(bset->ctx, 1 + total);
849 if (!ineq)
850 return NULL;
852 isl_seq_cpy(ineq->el, bset->div[div] + 1, 1 + total);
853 isl_int_neg(ineq->el[div_pos], bset->div[div][0]);
854 return ineq;
857 /* Given a row in the tableau and a div that was created
858 * using get_row_split_div and that has been constrained to equality, i.e.,
860 * d = floor(\sum_i {a_i} y_i) = \sum_i {a_i} y_i
862 * replace the expression "\sum_i {a_i} y_i" in the row by d,
863 * i.e., we subtract "\sum_i {a_i} y_i" and add 1 d.
864 * The coefficients of the non-parameters in the tableau have been
865 * verified to be integral. We can therefore simply replace coefficient b
866 * by floor(b). For the coefficients of the parameters we have
867 * floor(a_i) = a_i - {a_i}, while for the other coefficients, we have
868 * floor(b) = b.
870 static struct isl_tab *set_row_cst_to_div(struct isl_tab *tab, int row, int div)
872 isl_seq_fdiv_q(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
873 tab->mat->row[row][0], 1 + tab->M + tab->n_col);
875 isl_int_set_si(tab->mat->row[row][0], 1);
877 if (tab->var[tab->n_var - tab->n_div + div].is_row) {
878 int drow = tab->var[tab->n_var - tab->n_div + div].index;
880 isl_assert(tab->mat->ctx,
881 isl_int_is_one(tab->mat->row[drow][0]), goto error);
882 isl_seq_combine(tab->mat->row[row] + 1,
883 tab->mat->ctx->one, tab->mat->row[row] + 1,
884 tab->mat->ctx->one, tab->mat->row[drow] + 1,
885 1 + tab->M + tab->n_col);
886 } else {
887 int dcol = tab->var[tab->n_var - tab->n_div + div].index;
889 isl_int_add_ui(tab->mat->row[row][2 + tab->M + dcol],
890 tab->mat->row[row][2 + tab->M + dcol], 1);
893 return tab;
894 error:
895 isl_tab_free(tab);
896 return NULL;
899 /* Check if the (parametric) constant of the given row is obviously
900 * negative, meaning that we don't need to consult the context tableau.
901 * If there is a big parameter and its coefficient is non-zero,
902 * then this coefficient determines the outcome.
903 * Otherwise, we check whether the constant is negative and
904 * all non-zero coefficients of parameters are negative and
905 * belong to non-negative parameters.
907 static int is_obviously_neg(struct isl_tab *tab, int row)
909 int i;
910 int col;
911 unsigned off = 2 + tab->M;
913 if (tab->M) {
914 if (isl_int_is_pos(tab->mat->row[row][2]))
915 return 0;
916 if (isl_int_is_neg(tab->mat->row[row][2]))
917 return 1;
920 if (isl_int_is_nonneg(tab->mat->row[row][1]))
921 return 0;
922 for (i = 0; i < tab->n_param; ++i) {
923 /* Eliminated parameter */
924 if (tab->var[i].is_row)
925 continue;
926 col = tab->var[i].index;
927 if (isl_int_is_zero(tab->mat->row[row][off + col]))
928 continue;
929 if (!tab->var[i].is_nonneg)
930 return 0;
931 if (isl_int_is_pos(tab->mat->row[row][off + col]))
932 return 0;
934 for (i = 0; i < tab->n_div; ++i) {
935 if (tab->var[tab->n_var - tab->n_div + i].is_row)
936 continue;
937 col = tab->var[tab->n_var - tab->n_div + i].index;
938 if (isl_int_is_zero(tab->mat->row[row][off + col]))
939 continue;
940 if (!tab->var[tab->n_var - tab->n_div + i].is_nonneg)
941 return 0;
942 if (isl_int_is_pos(tab->mat->row[row][off + col]))
943 return 0;
945 return 1;
948 /* Check if the (parametric) constant of the given row is obviously
949 * non-negative, meaning that we don't need to consult the context tableau.
950 * If there is a big parameter and its coefficient is non-zero,
951 * then this coefficient determines the outcome.
952 * Otherwise, we check whether the constant is non-negative and
953 * all non-zero coefficients of parameters are positive and
954 * belong to non-negative parameters.
956 static int is_obviously_nonneg(struct isl_tab *tab, int row)
958 int i;
959 int col;
960 unsigned off = 2 + tab->M;
962 if (tab->M) {
963 if (isl_int_is_pos(tab->mat->row[row][2]))
964 return 1;
965 if (isl_int_is_neg(tab->mat->row[row][2]))
966 return 0;
969 if (isl_int_is_neg(tab->mat->row[row][1]))
970 return 0;
971 for (i = 0; i < tab->n_param; ++i) {
972 /* Eliminated parameter */
973 if (tab->var[i].is_row)
974 continue;
975 col = tab->var[i].index;
976 if (isl_int_is_zero(tab->mat->row[row][off + col]))
977 continue;
978 if (!tab->var[i].is_nonneg)
979 return 0;
980 if (isl_int_is_neg(tab->mat->row[row][off + col]))
981 return 0;
983 for (i = 0; i < tab->n_div; ++i) {
984 if (tab->var[tab->n_var - tab->n_div + i].is_row)
985 continue;
986 col = tab->var[tab->n_var - tab->n_div + i].index;
987 if (isl_int_is_zero(tab->mat->row[row][off + col]))
988 continue;
989 if (!tab->var[tab->n_var - tab->n_div + i].is_nonneg)
990 return 0;
991 if (isl_int_is_neg(tab->mat->row[row][off + col]))
992 return 0;
994 return 1;
997 /* Given a row r and two columns, return the column that would
998 * lead to the lexicographically smallest increment in the sample
999 * solution when leaving the basis in favor of the row.
1000 * Pivoting with column c will increment the sample value by a non-negative
1001 * constant times a_{V,c}/a_{r,c}, with a_{V,c} the elements of column c
1002 * corresponding to the non-parametric variables.
1003 * If variable v appears in a column c_v, the a_{v,c} = 1 iff c = c_v,
1004 * with all other entries in this virtual row equal to zero.
1005 * If variable v appears in a row, then a_{v,c} is the element in column c
1006 * of that row.
1008 * Let v be the first variable with a_{v,c1}/a_{r,c1} != a_{v,c2}/a_{r,c2}.
1009 * Then if a_{v,c1}/a_{r,c1} < a_{v,c2}/a_{r,c2}, i.e.,
1010 * a_{v,c2} a_{r,c1} - a_{v,c1} a_{r,c2} > 0, c1 results in the minimal
1011 * increment. Otherwise, it's c2.
1013 static int lexmin_col_pair(struct isl_tab *tab,
1014 int row, int col1, int col2, isl_int tmp)
1016 int i;
1017 isl_int *tr;
1019 tr = tab->mat->row[row] + 2 + tab->M;
1021 for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
1022 int s1, s2;
1023 isl_int *r;
1025 if (!tab->var[i].is_row) {
1026 if (tab->var[i].index == col1)
1027 return col2;
1028 if (tab->var[i].index == col2)
1029 return col1;
1030 continue;
1033 if (tab->var[i].index == row)
1034 continue;
1036 r = tab->mat->row[tab->var[i].index] + 2 + tab->M;
1037 s1 = isl_int_sgn(r[col1]);
1038 s2 = isl_int_sgn(r[col2]);
1039 if (s1 == 0 && s2 == 0)
1040 continue;
1041 if (s1 < s2)
1042 return col1;
1043 if (s2 < s1)
1044 return col2;
1046 isl_int_mul(tmp, r[col2], tr[col1]);
1047 isl_int_submul(tmp, r[col1], tr[col2]);
1048 if (isl_int_is_pos(tmp))
1049 return col1;
1050 if (isl_int_is_neg(tmp))
1051 return col2;
1053 return -1;
1056 /* Given a row in the tableau, find and return the column that would
1057 * result in the lexicographically smallest, but positive, increment
1058 * in the sample point.
1059 * If there is no such column, then return tab->n_col.
1060 * If anything goes wrong, return -1.
1062 static int lexmin_pivot_col(struct isl_tab *tab, int row)
1064 int j;
1065 int col = tab->n_col;
1066 isl_int *tr;
1067 isl_int tmp;
1069 tr = tab->mat->row[row] + 2 + tab->M;
1071 isl_int_init(tmp);
1073 for (j = tab->n_dead; j < tab->n_col; ++j) {
1074 if (tab->col_var[j] >= 0 &&
1075 (tab->col_var[j] < tab->n_param ||
1076 tab->col_var[j] >= tab->n_var - tab->n_div))
1077 continue;
1079 if (!isl_int_is_pos(tr[j]))
1080 continue;
1082 if (col == tab->n_col)
1083 col = j;
1084 else
1085 col = lexmin_col_pair(tab, row, col, j, tmp);
1086 isl_assert(tab->mat->ctx, col >= 0, goto error);
1089 isl_int_clear(tmp);
1090 return col;
1091 error:
1092 isl_int_clear(tmp);
1093 return -1;
1096 /* Return the first known violated constraint, i.e., a non-negative
1097 * constraint that currently has an either obviously negative value
1098 * or a previously determined to be negative value.
1100 * If any constraint has a negative coefficient for the big parameter,
1101 * if any, then we return one of these first.
1103 static int first_neg(struct isl_tab *tab)
1105 int row;
1107 if (tab->M)
1108 for (row = tab->n_redundant; row < tab->n_row; ++row) {
1109 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
1110 continue;
1111 if (!isl_int_is_neg(tab->mat->row[row][2]))
1112 continue;
1113 if (tab->row_sign)
1114 tab->row_sign[row] = isl_tab_row_neg;
1115 return row;
1117 for (row = tab->n_redundant; row < tab->n_row; ++row) {
1118 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
1119 continue;
1120 if (tab->row_sign) {
1121 if (tab->row_sign[row] == 0 &&
1122 is_obviously_neg(tab, row))
1123 tab->row_sign[row] = isl_tab_row_neg;
1124 if (tab->row_sign[row] != isl_tab_row_neg)
1125 continue;
1126 } else if (!is_obviously_neg(tab, row))
1127 continue;
1128 return row;
1130 return -1;
1133 /* Check whether the invariant that all columns are lexico-positive
1134 * is satisfied. This function is not called from the current code
1135 * but is useful during debugging.
1137 static void check_lexpos(struct isl_tab *tab) __attribute__ ((unused));
1138 static void check_lexpos(struct isl_tab *tab)
1140 unsigned off = 2 + tab->M;
1141 int col;
1142 int var;
1143 int row;
1145 for (col = tab->n_dead; col < tab->n_col; ++col) {
1146 if (tab->col_var[col] >= 0 &&
1147 (tab->col_var[col] < tab->n_param ||
1148 tab->col_var[col] >= tab->n_var - tab->n_div))
1149 continue;
1150 for (var = tab->n_param; var < tab->n_var - tab->n_div; ++var) {
1151 if (!tab->var[var].is_row) {
1152 if (tab->var[var].index == col)
1153 break;
1154 else
1155 continue;
1157 row = tab->var[var].index;
1158 if (isl_int_is_zero(tab->mat->row[row][off + col]))
1159 continue;
1160 if (isl_int_is_pos(tab->mat->row[row][off + col]))
1161 break;
1162 fprintf(stderr, "lexneg column %d (row %d)\n",
1163 col, row);
1165 if (var >= tab->n_var - tab->n_div)
1166 fprintf(stderr, "zero column %d\n", col);
1170 /* Report to the caller that the given constraint is part of an encountered
1171 * conflict.
1173 static int report_conflicting_constraint(struct isl_tab *tab, int con)
1175 return tab->conflict(con, tab->conflict_user);
1178 /* Given a conflicting row in the tableau, report all constraints
1179 * involved in the row to the caller. That is, the row itself
1180 * (if it represents a constraint) and all constraint columns with
1181 * non-zero (and therefore negative) coefficients.
1183 static int report_conflict(struct isl_tab *tab, int row)
1185 int j;
1186 isl_int *tr;
1188 if (!tab->conflict)
1189 return 0;
1191 if (tab->row_var[row] < 0 &&
1192 report_conflicting_constraint(tab, ~tab->row_var[row]) < 0)
1193 return -1;
1195 tr = tab->mat->row[row] + 2 + tab->M;
1197 for (j = tab->n_dead; j < tab->n_col; ++j) {
1198 if (tab->col_var[j] >= 0 &&
1199 (tab->col_var[j] < tab->n_param ||
1200 tab->col_var[j] >= tab->n_var - tab->n_div))
1201 continue;
1203 if (!isl_int_is_neg(tr[j]))
1204 continue;
1206 if (tab->col_var[j] < 0 &&
1207 report_conflicting_constraint(tab, ~tab->col_var[j]) < 0)
1208 return -1;
1211 return 0;
1214 /* Resolve all known or obviously violated constraints through pivoting.
1215 * In particular, as long as we can find any violated constraint, we
1216 * look for a pivoting column that would result in the lexicographically
1217 * smallest increment in the sample point. If there is no such column
1218 * then the tableau is infeasible.
1220 static int restore_lexmin(struct isl_tab *tab) WARN_UNUSED;
1221 static int restore_lexmin(struct isl_tab *tab)
1223 int row, col;
1225 if (!tab)
1226 return -1;
1227 if (tab->empty)
1228 return 0;
1229 while ((row = first_neg(tab)) != -1) {
1230 col = lexmin_pivot_col(tab, row);
1231 if (col >= tab->n_col) {
1232 if (report_conflict(tab, row) < 0)
1233 return -1;
1234 if (isl_tab_mark_empty(tab) < 0)
1235 return -1;
1236 return 0;
1238 if (col < 0)
1239 return -1;
1240 if (isl_tab_pivot(tab, row, col) < 0)
1241 return -1;
1243 return 0;
1246 /* Given a row that represents an equality, look for an appropriate
1247 * pivoting column.
1248 * In particular, if there are any non-zero coefficients among
1249 * the non-parameter variables, then we take the last of these
1250 * variables. Eliminating this variable in terms of the other
1251 * variables and/or parameters does not influence the property
1252 * that all column in the initial tableau are lexicographically
1253 * positive. The row corresponding to the eliminated variable
1254 * will only have non-zero entries below the diagonal of the
1255 * initial tableau. That is, we transform
1257 * I I
1258 * 1 into a
1259 * I I
1261 * If there is no such non-parameter variable, then we are dealing with
1262 * pure parameter equality and we pick any parameter with coefficient 1 or -1
1263 * for elimination. This will ensure that the eliminated parameter
1264 * always has an integer value whenever all the other parameters are integral.
1265 * If there is no such parameter then we return -1.
1267 static int last_var_col_or_int_par_col(struct isl_tab *tab, int row)
1269 unsigned off = 2 + tab->M;
1270 int i;
1272 for (i = tab->n_var - tab->n_div - 1; i >= 0 && i >= tab->n_param; --i) {
1273 int col;
1274 if (tab->var[i].is_row)
1275 continue;
1276 col = tab->var[i].index;
1277 if (col <= tab->n_dead)
1278 continue;
1279 if (!isl_int_is_zero(tab->mat->row[row][off + col]))
1280 return col;
1282 for (i = tab->n_dead; i < tab->n_col; ++i) {
1283 if (isl_int_is_one(tab->mat->row[row][off + i]))
1284 return i;
1285 if (isl_int_is_negone(tab->mat->row[row][off + i]))
1286 return i;
1288 return -1;
1291 /* Add an equality that is known to be valid to the tableau.
1292 * We first check if we can eliminate a variable or a parameter.
1293 * If not, we add the equality as two inequalities.
1294 * In this case, the equality was a pure parameter equality and there
1295 * is no need to resolve any constraint violations.
1297 static struct isl_tab *add_lexmin_valid_eq(struct isl_tab *tab, isl_int *eq)
1299 int i;
1300 int r;
1302 if (!tab)
1303 return NULL;
1304 r = isl_tab_add_row(tab, eq);
1305 if (r < 0)
1306 goto error;
1308 r = tab->con[r].index;
1309 i = last_var_col_or_int_par_col(tab, r);
1310 if (i < 0) {
1311 tab->con[r].is_nonneg = 1;
1312 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1313 goto error;
1314 isl_seq_neg(eq, eq, 1 + tab->n_var);
1315 r = isl_tab_add_row(tab, eq);
1316 if (r < 0)
1317 goto error;
1318 tab->con[r].is_nonneg = 1;
1319 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1320 goto error;
1321 } else {
1322 if (isl_tab_pivot(tab, r, i) < 0)
1323 goto error;
1324 if (isl_tab_kill_col(tab, i) < 0)
1325 goto error;
1326 tab->n_eq++;
1329 return tab;
1330 error:
1331 isl_tab_free(tab);
1332 return NULL;
1335 /* Check if the given row is a pure constant.
1337 static int is_constant(struct isl_tab *tab, int row)
1339 unsigned off = 2 + tab->M;
1341 return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1342 tab->n_col - tab->n_dead) == -1;
1345 /* Add an equality that may or may not be valid to the tableau.
1346 * If the resulting row is a pure constant, then it must be zero.
1347 * Otherwise, the resulting tableau is empty.
1349 * If the row is not a pure constant, then we add two inequalities,
1350 * each time checking that they can be satisfied.
1351 * In the end we try to use one of the two constraints to eliminate
1352 * a column.
1354 static int add_lexmin_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
1355 static int add_lexmin_eq(struct isl_tab *tab, isl_int *eq)
1357 int r1, r2;
1358 int row;
1359 struct isl_tab_undo *snap;
1361 if (!tab)
1362 return -1;
1363 snap = isl_tab_snap(tab);
1364 r1 = isl_tab_add_row(tab, eq);
1365 if (r1 < 0)
1366 return -1;
1367 tab->con[r1].is_nonneg = 1;
1368 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r1]) < 0)
1369 return -1;
1371 row = tab->con[r1].index;
1372 if (is_constant(tab, row)) {
1373 if (!isl_int_is_zero(tab->mat->row[row][1]) ||
1374 (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))) {
1375 if (isl_tab_mark_empty(tab) < 0)
1376 return -1;
1377 return 0;
1379 if (isl_tab_rollback(tab, snap) < 0)
1380 return -1;
1381 return 0;
1384 if (restore_lexmin(tab) < 0)
1385 return -1;
1386 if (tab->empty)
1387 return 0;
1389 isl_seq_neg(eq, eq, 1 + tab->n_var);
1391 r2 = isl_tab_add_row(tab, eq);
1392 if (r2 < 0)
1393 return -1;
1394 tab->con[r2].is_nonneg = 1;
1395 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r2]) < 0)
1396 return -1;
1398 if (restore_lexmin(tab) < 0)
1399 return -1;
1400 if (tab->empty)
1401 return 0;
1403 if (!tab->con[r1].is_row) {
1404 if (isl_tab_kill_col(tab, tab->con[r1].index) < 0)
1405 return -1;
1406 } else if (!tab->con[r2].is_row) {
1407 if (isl_tab_kill_col(tab, tab->con[r2].index) < 0)
1408 return -1;
1411 if (tab->bmap) {
1412 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
1413 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1414 return -1;
1415 isl_seq_neg(eq, eq, 1 + tab->n_var);
1416 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
1417 isl_seq_neg(eq, eq, 1 + tab->n_var);
1418 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1419 return -1;
1420 if (!tab->bmap)
1421 return -1;
1424 return 0;
1427 /* Add an inequality to the tableau, resolving violations using
1428 * restore_lexmin.
1430 static struct isl_tab *add_lexmin_ineq(struct isl_tab *tab, isl_int *ineq)
1432 int r;
1434 if (!tab)
1435 return NULL;
1436 if (tab->bmap) {
1437 tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
1438 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1439 goto error;
1440 if (!tab->bmap)
1441 goto error;
1443 r = isl_tab_add_row(tab, ineq);
1444 if (r < 0)
1445 goto error;
1446 tab->con[r].is_nonneg = 1;
1447 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1448 goto error;
1449 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1450 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1451 goto error;
1452 return tab;
1455 if (restore_lexmin(tab) < 0)
1456 goto error;
1457 if (!tab->empty && tab->con[r].is_row &&
1458 isl_tab_row_is_redundant(tab, tab->con[r].index))
1459 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1460 goto error;
1461 return tab;
1462 error:
1463 isl_tab_free(tab);
1464 return NULL;
1467 /* Check if the coefficients of the parameters are all integral.
1469 static int integer_parameter(struct isl_tab *tab, int row)
1471 int i;
1472 int col;
1473 unsigned off = 2 + tab->M;
1475 for (i = 0; i < tab->n_param; ++i) {
1476 /* Eliminated parameter */
1477 if (tab->var[i].is_row)
1478 continue;
1479 col = tab->var[i].index;
1480 if (!isl_int_is_divisible_by(tab->mat->row[row][off + col],
1481 tab->mat->row[row][0]))
1482 return 0;
1484 for (i = 0; i < tab->n_div; ++i) {
1485 if (tab->var[tab->n_var - tab->n_div + i].is_row)
1486 continue;
1487 col = tab->var[tab->n_var - tab->n_div + i].index;
1488 if (!isl_int_is_divisible_by(tab->mat->row[row][off + col],
1489 tab->mat->row[row][0]))
1490 return 0;
1492 return 1;
1495 /* Check if the coefficients of the non-parameter variables are all integral.
1497 static int integer_variable(struct isl_tab *tab, int row)
1499 int i;
1500 unsigned off = 2 + tab->M;
1502 for (i = tab->n_dead; i < tab->n_col; ++i) {
1503 if (tab->col_var[i] >= 0 &&
1504 (tab->col_var[i] < tab->n_param ||
1505 tab->col_var[i] >= tab->n_var - tab->n_div))
1506 continue;
1507 if (!isl_int_is_divisible_by(tab->mat->row[row][off + i],
1508 tab->mat->row[row][0]))
1509 return 0;
1511 return 1;
1514 /* Check if the constant term is integral.
1516 static int integer_constant(struct isl_tab *tab, int row)
1518 return isl_int_is_divisible_by(tab->mat->row[row][1],
1519 tab->mat->row[row][0]);
1522 #define I_CST 1 << 0
1523 #define I_PAR 1 << 1
1524 #define I_VAR 1 << 2
1526 /* Check for next (non-parameter) variable after "var" (first if var == -1)
1527 * that is non-integer and therefore requires a cut and return
1528 * the index of the variable.
1529 * For parametric tableaus, there are three parts in a row,
1530 * the constant, the coefficients of the parameters and the rest.
1531 * For each part, we check whether the coefficients in that part
1532 * are all integral and if so, set the corresponding flag in *f.
1533 * If the constant and the parameter part are integral, then the
1534 * current sample value is integral and no cut is required
1535 * (irrespective of whether the variable part is integral).
1537 static int next_non_integer_var(struct isl_tab *tab, int var, int *f)
1539 var = var < 0 ? tab->n_param : var + 1;
1541 for (; var < tab->n_var - tab->n_div; ++var) {
1542 int flags = 0;
1543 int row;
1544 if (!tab->var[var].is_row)
1545 continue;
1546 row = tab->var[var].index;
1547 if (integer_constant(tab, row))
1548 ISL_FL_SET(flags, I_CST);
1549 if (integer_parameter(tab, row))
1550 ISL_FL_SET(flags, I_PAR);
1551 if (ISL_FL_ISSET(flags, I_CST) && ISL_FL_ISSET(flags, I_PAR))
1552 continue;
1553 if (integer_variable(tab, row))
1554 ISL_FL_SET(flags, I_VAR);
1555 *f = flags;
1556 return var;
1558 return -1;
1561 /* Check for first (non-parameter) variable that is non-integer and
1562 * therefore requires a cut and return the corresponding row.
1563 * For parametric tableaus, there are three parts in a row,
1564 * the constant, the coefficients of the parameters and the rest.
1565 * For each part, we check whether the coefficients in that part
1566 * are all integral and if so, set the corresponding flag in *f.
1567 * If the constant and the parameter part are integral, then the
1568 * current sample value is integral and no cut is required
1569 * (irrespective of whether the variable part is integral).
1571 static int first_non_integer_row(struct isl_tab *tab, int *f)
1573 int var = next_non_integer_var(tab, -1, f);
1575 return var < 0 ? -1 : tab->var[var].index;
1578 /* Add a (non-parametric) cut to cut away the non-integral sample
1579 * value of the given row.
1581 * If the row is given by
1583 * m r = f + \sum_i a_i y_i
1585 * then the cut is
1587 * c = - {-f/m} + \sum_i {a_i/m} y_i >= 0
1589 * The big parameter, if any, is ignored, since it is assumed to be big
1590 * enough to be divisible by any integer.
1591 * If the tableau is actually a parametric tableau, then this function
1592 * is only called when all coefficients of the parameters are integral.
1593 * The cut therefore has zero coefficients for the parameters.
1595 * The current value is known to be negative, so row_sign, if it
1596 * exists, is set accordingly.
1598 * Return the row of the cut or -1.
1600 static int add_cut(struct isl_tab *tab, int row)
1602 int i;
1603 int r;
1604 isl_int *r_row;
1605 unsigned off = 2 + tab->M;
1607 if (isl_tab_extend_cons(tab, 1) < 0)
1608 return -1;
1609 r = isl_tab_allocate_con(tab);
1610 if (r < 0)
1611 return -1;
1613 r_row = tab->mat->row[tab->con[r].index];
1614 isl_int_set(r_row[0], tab->mat->row[row][0]);
1615 isl_int_neg(r_row[1], tab->mat->row[row][1]);
1616 isl_int_fdiv_r(r_row[1], r_row[1], tab->mat->row[row][0]);
1617 isl_int_neg(r_row[1], r_row[1]);
1618 if (tab->M)
1619 isl_int_set_si(r_row[2], 0);
1620 for (i = 0; i < tab->n_col; ++i)
1621 isl_int_fdiv_r(r_row[off + i],
1622 tab->mat->row[row][off + i], tab->mat->row[row][0]);
1624 tab->con[r].is_nonneg = 1;
1625 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1626 return -1;
1627 if (tab->row_sign)
1628 tab->row_sign[tab->con[r].index] = isl_tab_row_neg;
1630 return tab->con[r].index;
1633 #define CUT_ALL 1
1634 #define CUT_ONE 0
1636 /* Given a non-parametric tableau, add cuts until an integer
1637 * sample point is obtained or until the tableau is determined
1638 * to be integer infeasible.
1639 * As long as there is any non-integer value in the sample point,
1640 * we add appropriate cuts, if possible, for each of these
1641 * non-integer values and then resolve the violated
1642 * cut constraints using restore_lexmin.
1643 * If one of the corresponding rows is equal to an integral
1644 * combination of variables/constraints plus a non-integral constant,
1645 * then there is no way to obtain an integer point and we return
1646 * a tableau that is marked empty.
1647 * The parameter cutting_strategy controls the strategy used when adding cuts
1648 * to remove non-integer points. CUT_ALL adds all possible cuts
1649 * before continuing the search. CUT_ONE adds only one cut at a time.
1651 static struct isl_tab *cut_to_integer_lexmin(struct isl_tab *tab,
1652 int cutting_strategy)
1654 int var;
1655 int row;
1656 int flags;
1658 if (!tab)
1659 return NULL;
1660 if (tab->empty)
1661 return tab;
1663 while ((var = next_non_integer_var(tab, -1, &flags)) != -1) {
1664 do {
1665 if (ISL_FL_ISSET(flags, I_VAR)) {
1666 if (isl_tab_mark_empty(tab) < 0)
1667 goto error;
1668 return tab;
1670 row = tab->var[var].index;
1671 row = add_cut(tab, row);
1672 if (row < 0)
1673 goto error;
1674 if (cutting_strategy == CUT_ONE)
1675 break;
1676 } while ((var = next_non_integer_var(tab, var, &flags)) != -1);
1677 if (restore_lexmin(tab) < 0)
1678 goto error;
1679 if (tab->empty)
1680 break;
1682 return tab;
1683 error:
1684 isl_tab_free(tab);
1685 return NULL;
1688 /* Check whether all the currently active samples also satisfy the inequality
1689 * "ineq" (treated as an equality if eq is set).
1690 * Remove those samples that do not.
1692 static struct isl_tab *check_samples(struct isl_tab *tab, isl_int *ineq, int eq)
1694 int i;
1695 isl_int v;
1697 if (!tab)
1698 return NULL;
1700 isl_assert(tab->mat->ctx, tab->bmap, goto error);
1701 isl_assert(tab->mat->ctx, tab->samples, goto error);
1702 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error);
1704 isl_int_init(v);
1705 for (i = tab->n_outside; i < tab->n_sample; ++i) {
1706 int sgn;
1707 isl_seq_inner_product(ineq, tab->samples->row[i],
1708 1 + tab->n_var, &v);
1709 sgn = isl_int_sgn(v);
1710 if (eq ? (sgn == 0) : (sgn >= 0))
1711 continue;
1712 tab = isl_tab_drop_sample(tab, i);
1713 if (!tab)
1714 break;
1716 isl_int_clear(v);
1718 return tab;
1719 error:
1720 isl_tab_free(tab);
1721 return NULL;
1724 /* Check whether the sample value of the tableau is finite,
1725 * i.e., either the tableau does not use a big parameter, or
1726 * all values of the variables are equal to the big parameter plus
1727 * some constant. This constant is the actual sample value.
1729 static int sample_is_finite(struct isl_tab *tab)
1731 int i;
1733 if (!tab->M)
1734 return 1;
1736 for (i = 0; i < tab->n_var; ++i) {
1737 int row;
1738 if (!tab->var[i].is_row)
1739 return 0;
1740 row = tab->var[i].index;
1741 if (isl_int_ne(tab->mat->row[row][0], tab->mat->row[row][2]))
1742 return 0;
1744 return 1;
1747 /* Check if the context tableau of sol has any integer points.
1748 * Leave tab in empty state if no integer point can be found.
1749 * If an integer point can be found and if moreover it is finite,
1750 * then it is added to the list of sample values.
1752 * This function is only called when none of the currently active sample
1753 * values satisfies the most recently added constraint.
1755 static struct isl_tab *check_integer_feasible(struct isl_tab *tab)
1757 struct isl_tab_undo *snap;
1759 if (!tab)
1760 return NULL;
1762 snap = isl_tab_snap(tab);
1763 if (isl_tab_push_basis(tab) < 0)
1764 goto error;
1766 tab = cut_to_integer_lexmin(tab, CUT_ALL);
1767 if (!tab)
1768 goto error;
1770 if (!tab->empty && sample_is_finite(tab)) {
1771 struct isl_vec *sample;
1773 sample = isl_tab_get_sample_value(tab);
1775 tab = isl_tab_add_sample(tab, sample);
1778 if (!tab->empty && isl_tab_rollback(tab, snap) < 0)
1779 goto error;
1781 return tab;
1782 error:
1783 isl_tab_free(tab);
1784 return NULL;
1787 /* Check if any of the currently active sample values satisfies
1788 * the inequality "ineq" (an equality if eq is set).
1790 static int tab_has_valid_sample(struct isl_tab *tab, isl_int *ineq, int eq)
1792 int i;
1793 isl_int v;
1795 if (!tab)
1796 return -1;
1798 isl_assert(tab->mat->ctx, tab->bmap, return -1);
1799 isl_assert(tab->mat->ctx, tab->samples, return -1);
1800 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, return -1);
1802 isl_int_init(v);
1803 for (i = tab->n_outside; i < tab->n_sample; ++i) {
1804 int sgn;
1805 isl_seq_inner_product(ineq, tab->samples->row[i],
1806 1 + tab->n_var, &v);
1807 sgn = isl_int_sgn(v);
1808 if (eq ? (sgn == 0) : (sgn >= 0))
1809 break;
1811 isl_int_clear(v);
1813 return i < tab->n_sample;
1816 /* Add a div specified by "div" to the tableau "tab" and return
1817 * 1 if the div is obviously non-negative.
1819 static int context_tab_add_div(struct isl_tab *tab, struct isl_vec *div,
1820 int (*add_ineq)(void *user, isl_int *), void *user)
1822 int i;
1823 int r;
1824 struct isl_mat *samples;
1825 int nonneg;
1827 r = isl_tab_add_div(tab, div, add_ineq, user);
1828 if (r < 0)
1829 return -1;
1830 nonneg = tab->var[r].is_nonneg;
1831 tab->var[r].frozen = 1;
1833 samples = isl_mat_extend(tab->samples,
1834 tab->n_sample, 1 + tab->n_var);
1835 tab->samples = samples;
1836 if (!samples)
1837 return -1;
1838 for (i = tab->n_outside; i < samples->n_row; ++i) {
1839 isl_seq_inner_product(div->el + 1, samples->row[i],
1840 div->size - 1, &samples->row[i][samples->n_col - 1]);
1841 isl_int_fdiv_q(samples->row[i][samples->n_col - 1],
1842 samples->row[i][samples->n_col - 1], div->el[0]);
1845 return nonneg;
1848 /* Add a div specified by "div" to both the main tableau and
1849 * the context tableau. In case of the main tableau, we only
1850 * need to add an extra div. In the context tableau, we also
1851 * need to express the meaning of the div.
1852 * Return the index of the div or -1 if anything went wrong.
1854 static int add_div(struct isl_tab *tab, struct isl_context *context,
1855 struct isl_vec *div)
1857 int r;
1858 int nonneg;
1860 if ((nonneg = context->op->add_div(context, div)) < 0)
1861 goto error;
1863 if (!context->op->is_ok(context))
1864 goto error;
1866 if (isl_tab_extend_vars(tab, 1) < 0)
1867 goto error;
1868 r = isl_tab_allocate_var(tab);
1869 if (r < 0)
1870 goto error;
1871 if (nonneg)
1872 tab->var[r].is_nonneg = 1;
1873 tab->var[r].frozen = 1;
1874 tab->n_div++;
1876 return tab->n_div - 1;
1877 error:
1878 context->op->invalidate(context);
1879 return -1;
1882 static int find_div(struct isl_tab *tab, isl_int *div, isl_int denom)
1884 int i;
1885 unsigned total = isl_basic_map_total_dim(tab->bmap);
1887 for (i = 0; i < tab->bmap->n_div; ++i) {
1888 if (isl_int_ne(tab->bmap->div[i][0], denom))
1889 continue;
1890 if (!isl_seq_eq(tab->bmap->div[i] + 1, div, 1 + total))
1891 continue;
1892 return i;
1894 return -1;
1897 /* Return the index of a div that corresponds to "div".
1898 * We first check if we already have such a div and if not, we create one.
1900 static int get_div(struct isl_tab *tab, struct isl_context *context,
1901 struct isl_vec *div)
1903 int d;
1904 struct isl_tab *context_tab = context->op->peek_tab(context);
1906 if (!context_tab)
1907 return -1;
1909 d = find_div(context_tab, div->el + 1, div->el[0]);
1910 if (d != -1)
1911 return d;
1913 return add_div(tab, context, div);
1916 /* Add a parametric cut to cut away the non-integral sample value
1917 * of the give row.
1918 * Let a_i be the coefficients of the constant term and the parameters
1919 * and let b_i be the coefficients of the variables or constraints
1920 * in basis of the tableau.
1921 * Let q be the div q = floor(\sum_i {-a_i} y_i).
1923 * The cut is expressed as
1925 * c = \sum_i -{-a_i} y_i + \sum_i {b_i} x_i + q >= 0
1927 * If q did not already exist in the context tableau, then it is added first.
1928 * If q is in a column of the main tableau then the "+ q" can be accomplished
1929 * by setting the corresponding entry to the denominator of the constraint.
1930 * If q happens to be in a row of the main tableau, then the corresponding
1931 * row needs to be added instead (taking care of the denominators).
1932 * Note that this is very unlikely, but perhaps not entirely impossible.
1934 * The current value of the cut is known to be negative (or at least
1935 * non-positive), so row_sign is set accordingly.
1937 * Return the row of the cut or -1.
1939 static int add_parametric_cut(struct isl_tab *tab, int row,
1940 struct isl_context *context)
1942 struct isl_vec *div;
1943 int d;
1944 int i;
1945 int r;
1946 isl_int *r_row;
1947 int col;
1948 int n;
1949 unsigned off = 2 + tab->M;
1951 if (!context)
1952 return -1;
1954 div = get_row_parameter_div(tab, row);
1955 if (!div)
1956 return -1;
1958 n = tab->n_div;
1959 d = context->op->get_div(context, tab, div);
1960 if (d < 0)
1961 return -1;
1963 if (isl_tab_extend_cons(tab, 1) < 0)
1964 return -1;
1965 r = isl_tab_allocate_con(tab);
1966 if (r < 0)
1967 return -1;
1969 r_row = tab->mat->row[tab->con[r].index];
1970 isl_int_set(r_row[0], tab->mat->row[row][0]);
1971 isl_int_neg(r_row[1], tab->mat->row[row][1]);
1972 isl_int_fdiv_r(r_row[1], r_row[1], tab->mat->row[row][0]);
1973 isl_int_neg(r_row[1], r_row[1]);
1974 if (tab->M)
1975 isl_int_set_si(r_row[2], 0);
1976 for (i = 0; i < tab->n_param; ++i) {
1977 if (tab->var[i].is_row)
1978 continue;
1979 col = tab->var[i].index;
1980 isl_int_neg(r_row[off + col], tab->mat->row[row][off + col]);
1981 isl_int_fdiv_r(r_row[off + col], r_row[off + col],
1982 tab->mat->row[row][0]);
1983 isl_int_neg(r_row[off + col], r_row[off + col]);
1985 for (i = 0; i < tab->n_div; ++i) {
1986 if (tab->var[tab->n_var - tab->n_div + i].is_row)
1987 continue;
1988 col = tab->var[tab->n_var - tab->n_div + i].index;
1989 isl_int_neg(r_row[off + col], tab->mat->row[row][off + col]);
1990 isl_int_fdiv_r(r_row[off + col], r_row[off + col],
1991 tab->mat->row[row][0]);
1992 isl_int_neg(r_row[off + col], r_row[off + col]);
1994 for (i = 0; i < tab->n_col; ++i) {
1995 if (tab->col_var[i] >= 0 &&
1996 (tab->col_var[i] < tab->n_param ||
1997 tab->col_var[i] >= tab->n_var - tab->n_div))
1998 continue;
1999 isl_int_fdiv_r(r_row[off + i],
2000 tab->mat->row[row][off + i], tab->mat->row[row][0]);
2002 if (tab->var[tab->n_var - tab->n_div + d].is_row) {
2003 isl_int gcd;
2004 int d_row = tab->var[tab->n_var - tab->n_div + d].index;
2005 isl_int_init(gcd);
2006 isl_int_gcd(gcd, tab->mat->row[d_row][0], r_row[0]);
2007 isl_int_divexact(r_row[0], r_row[0], gcd);
2008 isl_int_divexact(gcd, tab->mat->row[d_row][0], gcd);
2009 isl_seq_combine(r_row + 1, gcd, r_row + 1,
2010 r_row[0], tab->mat->row[d_row] + 1,
2011 off - 1 + tab->n_col);
2012 isl_int_mul(r_row[0], r_row[0], tab->mat->row[d_row][0]);
2013 isl_int_clear(gcd);
2014 } else {
2015 col = tab->var[tab->n_var - tab->n_div + d].index;
2016 isl_int_set(r_row[off + col], tab->mat->row[row][0]);
2019 tab->con[r].is_nonneg = 1;
2020 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
2021 return -1;
2022 if (tab->row_sign)
2023 tab->row_sign[tab->con[r].index] = isl_tab_row_neg;
2025 isl_vec_free(div);
2027 row = tab->con[r].index;
2029 if (d >= n && context->op->detect_equalities(context, tab) < 0)
2030 return -1;
2032 return row;
2035 /* Construct a tableau for bmap that can be used for computing
2036 * the lexicographic minimum (or maximum) of bmap.
2037 * If not NULL, then dom is the domain where the minimum
2038 * should be computed. In this case, we set up a parametric
2039 * tableau with row signs (initialized to "unknown").
2040 * If M is set, then the tableau will use a big parameter.
2041 * If max is set, then a maximum should be computed instead of a minimum.
2042 * This means that for each variable x, the tableau will contain the variable
2043 * x' = M - x, rather than x' = M + x. This in turn means that the coefficient
2044 * of the variables in all constraints are negated prior to adding them
2045 * to the tableau.
2047 static struct isl_tab *tab_for_lexmin(struct isl_basic_map *bmap,
2048 struct isl_basic_set *dom, unsigned M, int max)
2050 int i;
2051 struct isl_tab *tab;
2053 tab = isl_tab_alloc(bmap->ctx, 2 * bmap->n_eq + bmap->n_ineq + 1,
2054 isl_basic_map_total_dim(bmap), M);
2055 if (!tab)
2056 return NULL;
2058 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
2059 if (dom) {
2060 tab->n_param = isl_basic_set_total_dim(dom) - dom->n_div;
2061 tab->n_div = dom->n_div;
2062 tab->row_sign = isl_calloc_array(bmap->ctx,
2063 enum isl_tab_row_sign, tab->mat->n_row);
2064 if (!tab->row_sign)
2065 goto error;
2067 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
2068 if (isl_tab_mark_empty(tab) < 0)
2069 goto error;
2070 return tab;
2073 for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
2074 tab->var[i].is_nonneg = 1;
2075 tab->var[i].frozen = 1;
2077 for (i = 0; i < bmap->n_eq; ++i) {
2078 if (max)
2079 isl_seq_neg(bmap->eq[i] + 1 + tab->n_param,
2080 bmap->eq[i] + 1 + tab->n_param,
2081 tab->n_var - tab->n_param - tab->n_div);
2082 tab = add_lexmin_valid_eq(tab, bmap->eq[i]);
2083 if (max)
2084 isl_seq_neg(bmap->eq[i] + 1 + tab->n_param,
2085 bmap->eq[i] + 1 + tab->n_param,
2086 tab->n_var - tab->n_param - tab->n_div);
2087 if (!tab || tab->empty)
2088 return tab;
2090 if (bmap->n_eq && restore_lexmin(tab) < 0)
2091 goto error;
2092 for (i = 0; i < bmap->n_ineq; ++i) {
2093 if (max)
2094 isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param,
2095 bmap->ineq[i] + 1 + tab->n_param,
2096 tab->n_var - tab->n_param - tab->n_div);
2097 tab = add_lexmin_ineq(tab, bmap->ineq[i]);
2098 if (max)
2099 isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param,
2100 bmap->ineq[i] + 1 + tab->n_param,
2101 tab->n_var - tab->n_param - tab->n_div);
2102 if (!tab || tab->empty)
2103 return tab;
2105 return tab;
2106 error:
2107 isl_tab_free(tab);
2108 return NULL;
2111 /* Given a main tableau where more than one row requires a split,
2112 * determine and return the "best" row to split on.
2114 * Given two rows in the main tableau, if the inequality corresponding
2115 * to the first row is redundant with respect to that of the second row
2116 * in the current tableau, then it is better to split on the second row,
2117 * since in the positive part, both row will be positive.
2118 * (In the negative part a pivot will have to be performed and just about
2119 * anything can happen to the sign of the other row.)
2121 * As a simple heuristic, we therefore select the row that makes the most
2122 * of the other rows redundant.
2124 * Perhaps it would also be useful to look at the number of constraints
2125 * that conflict with any given constraint.
2127 static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
2129 struct isl_tab_undo *snap;
2130 int split;
2131 int row;
2132 int best = -1;
2133 int best_r;
2135 if (isl_tab_extend_cons(context_tab, 2) < 0)
2136 return -1;
2138 snap = isl_tab_snap(context_tab);
2140 for (split = tab->n_redundant; split < tab->n_row; ++split) {
2141 struct isl_tab_undo *snap2;
2142 struct isl_vec *ineq = NULL;
2143 int r = 0;
2144 int ok;
2146 if (!isl_tab_var_from_row(tab, split)->is_nonneg)
2147 continue;
2148 if (tab->row_sign[split] != isl_tab_row_any)
2149 continue;
2151 ineq = get_row_parameter_ineq(tab, split);
2152 if (!ineq)
2153 return -1;
2154 ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
2155 isl_vec_free(ineq);
2156 if (!ok)
2157 return -1;
2159 snap2 = isl_tab_snap(context_tab);
2161 for (row = tab->n_redundant; row < tab->n_row; ++row) {
2162 struct isl_tab_var *var;
2164 if (row == split)
2165 continue;
2166 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
2167 continue;
2168 if (tab->row_sign[row] != isl_tab_row_any)
2169 continue;
2171 ineq = get_row_parameter_ineq(tab, row);
2172 if (!ineq)
2173 return -1;
2174 ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
2175 isl_vec_free(ineq);
2176 if (!ok)
2177 return -1;
2178 var = &context_tab->con[context_tab->n_con - 1];
2179 if (!context_tab->empty &&
2180 !isl_tab_min_at_most_neg_one(context_tab, var))
2181 r++;
2182 if (isl_tab_rollback(context_tab, snap2) < 0)
2183 return -1;
2185 if (best == -1 || r > best_r) {
2186 best = split;
2187 best_r = r;
2189 if (isl_tab_rollback(context_tab, snap) < 0)
2190 return -1;
2193 return best;
2196 static struct isl_basic_set *context_lex_peek_basic_set(
2197 struct isl_context *context)
2199 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2200 if (!clex->tab)
2201 return NULL;
2202 return isl_tab_peek_bset(clex->tab);
2205 static struct isl_tab *context_lex_peek_tab(struct isl_context *context)
2207 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2208 return clex->tab;
2211 static void context_lex_add_eq(struct isl_context *context, isl_int *eq,
2212 int check, int update)
2214 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2215 if (isl_tab_extend_cons(clex->tab, 2) < 0)
2216 goto error;
2217 if (add_lexmin_eq(clex->tab, eq) < 0)
2218 goto error;
2219 if (check) {
2220 int v = tab_has_valid_sample(clex->tab, eq, 1);
2221 if (v < 0)
2222 goto error;
2223 if (!v)
2224 clex->tab = check_integer_feasible(clex->tab);
2226 if (update)
2227 clex->tab = check_samples(clex->tab, eq, 1);
2228 return;
2229 error:
2230 isl_tab_free(clex->tab);
2231 clex->tab = NULL;
2234 static void context_lex_add_ineq(struct isl_context *context, isl_int *ineq,
2235 int check, int update)
2237 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2238 if (isl_tab_extend_cons(clex->tab, 1) < 0)
2239 goto error;
2240 clex->tab = add_lexmin_ineq(clex->tab, ineq);
2241 if (check) {
2242 int v = tab_has_valid_sample(clex->tab, ineq, 0);
2243 if (v < 0)
2244 goto error;
2245 if (!v)
2246 clex->tab = check_integer_feasible(clex->tab);
2248 if (update)
2249 clex->tab = check_samples(clex->tab, ineq, 0);
2250 return;
2251 error:
2252 isl_tab_free(clex->tab);
2253 clex->tab = NULL;
2256 static int context_lex_add_ineq_wrap(void *user, isl_int *ineq)
2258 struct isl_context *context = (struct isl_context *)user;
2259 context_lex_add_ineq(context, ineq, 0, 0);
2260 return context->op->is_ok(context) ? 0 : -1;
2263 /* Check which signs can be obtained by "ineq" on all the currently
2264 * active sample values. See row_sign for more information.
2266 static enum isl_tab_row_sign tab_ineq_sign(struct isl_tab *tab, isl_int *ineq,
2267 int strict)
2269 int i;
2270 int sgn;
2271 isl_int tmp;
2272 enum isl_tab_row_sign res = isl_tab_row_unknown;
2274 isl_assert(tab->mat->ctx, tab->samples, return isl_tab_row_unknown);
2275 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var,
2276 return isl_tab_row_unknown);
2278 isl_int_init(tmp);
2279 for (i = tab->n_outside; i < tab->n_sample; ++i) {
2280 isl_seq_inner_product(tab->samples->row[i], ineq,
2281 1 + tab->n_var, &tmp);
2282 sgn = isl_int_sgn(tmp);
2283 if (sgn > 0 || (sgn == 0 && strict)) {
2284 if (res == isl_tab_row_unknown)
2285 res = isl_tab_row_pos;
2286 if (res == isl_tab_row_neg)
2287 res = isl_tab_row_any;
2289 if (sgn < 0) {
2290 if (res == isl_tab_row_unknown)
2291 res = isl_tab_row_neg;
2292 if (res == isl_tab_row_pos)
2293 res = isl_tab_row_any;
2295 if (res == isl_tab_row_any)
2296 break;
2298 isl_int_clear(tmp);
2300 return res;
2303 static enum isl_tab_row_sign context_lex_ineq_sign(struct isl_context *context,
2304 isl_int *ineq, int strict)
2306 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2307 return tab_ineq_sign(clex->tab, ineq, strict);
2310 /* Check whether "ineq" can be added to the tableau without rendering
2311 * it infeasible.
2313 static int context_lex_test_ineq(struct isl_context *context, isl_int *ineq)
2315 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2316 struct isl_tab_undo *snap;
2317 int feasible;
2319 if (!clex->tab)
2320 return -1;
2322 if (isl_tab_extend_cons(clex->tab, 1) < 0)
2323 return -1;
2325 snap = isl_tab_snap(clex->tab);
2326 if (isl_tab_push_basis(clex->tab) < 0)
2327 return -1;
2328 clex->tab = add_lexmin_ineq(clex->tab, ineq);
2329 clex->tab = check_integer_feasible(clex->tab);
2330 if (!clex->tab)
2331 return -1;
2332 feasible = !clex->tab->empty;
2333 if (isl_tab_rollback(clex->tab, snap) < 0)
2334 return -1;
2336 return feasible;
2339 static int context_lex_get_div(struct isl_context *context, struct isl_tab *tab,
2340 struct isl_vec *div)
2342 return get_div(tab, context, div);
2345 /* Add a div specified by "div" to the context tableau and return
2346 * 1 if the div is obviously non-negative.
2347 * context_tab_add_div will always return 1, because all variables
2348 * in a isl_context_lex tableau are non-negative.
2349 * However, if we are using a big parameter in the context, then this only
2350 * reflects the non-negativity of the variable used to _encode_ the
2351 * div, i.e., div' = M + div, so we can't draw any conclusions.
2353 static int context_lex_add_div(struct isl_context *context, struct isl_vec *div)
2355 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2356 int nonneg;
2357 nonneg = context_tab_add_div(clex->tab, div,
2358 context_lex_add_ineq_wrap, context);
2359 if (nonneg < 0)
2360 return -1;
2361 if (clex->tab->M)
2362 return 0;
2363 return nonneg;
2366 static int context_lex_detect_equalities(struct isl_context *context,
2367 struct isl_tab *tab)
2369 return 0;
2372 static int context_lex_best_split(struct isl_context *context,
2373 struct isl_tab *tab)
2375 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2376 struct isl_tab_undo *snap;
2377 int r;
2379 snap = isl_tab_snap(clex->tab);
2380 if (isl_tab_push_basis(clex->tab) < 0)
2381 return -1;
2382 r = best_split(tab, clex->tab);
2384 if (r >= 0 && isl_tab_rollback(clex->tab, snap) < 0)
2385 return -1;
2387 return r;
2390 static int context_lex_is_empty(struct isl_context *context)
2392 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2393 if (!clex->tab)
2394 return -1;
2395 return clex->tab->empty;
2398 static void *context_lex_save(struct isl_context *context)
2400 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2401 struct isl_tab_undo *snap;
2403 snap = isl_tab_snap(clex->tab);
2404 if (isl_tab_push_basis(clex->tab) < 0)
2405 return NULL;
2406 if (isl_tab_save_samples(clex->tab) < 0)
2407 return NULL;
2409 return snap;
2412 static void context_lex_restore(struct isl_context *context, void *save)
2414 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2415 if (isl_tab_rollback(clex->tab, (struct isl_tab_undo *)save) < 0) {
2416 isl_tab_free(clex->tab);
2417 clex->tab = NULL;
2421 static int context_lex_is_ok(struct isl_context *context)
2423 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2424 return !!clex->tab;
2427 /* For each variable in the context tableau, check if the variable can
2428 * only attain non-negative values. If so, mark the parameter as non-negative
2429 * in the main tableau. This allows for a more direct identification of some
2430 * cases of violated constraints.
2432 static struct isl_tab *tab_detect_nonnegative_parameters(struct isl_tab *tab,
2433 struct isl_tab *context_tab)
2435 int i;
2436 struct isl_tab_undo *snap;
2437 struct isl_vec *ineq = NULL;
2438 struct isl_tab_var *var;
2439 int n;
2441 if (context_tab->n_var == 0)
2442 return tab;
2444 ineq = isl_vec_alloc(tab->mat->ctx, 1 + context_tab->n_var);
2445 if (!ineq)
2446 goto error;
2448 if (isl_tab_extend_cons(context_tab, 1) < 0)
2449 goto error;
2451 snap = isl_tab_snap(context_tab);
2453 n = 0;
2454 isl_seq_clr(ineq->el, ineq->size);
2455 for (i = 0; i < context_tab->n_var; ++i) {
2456 isl_int_set_si(ineq->el[1 + i], 1);
2457 if (isl_tab_add_ineq(context_tab, ineq->el) < 0)
2458 goto error;
2459 var = &context_tab->con[context_tab->n_con - 1];
2460 if (!context_tab->empty &&
2461 !isl_tab_min_at_most_neg_one(context_tab, var)) {
2462 int j = i;
2463 if (i >= tab->n_param)
2464 j = i - tab->n_param + tab->n_var - tab->n_div;
2465 tab->var[j].is_nonneg = 1;
2466 n++;
2468 isl_int_set_si(ineq->el[1 + i], 0);
2469 if (isl_tab_rollback(context_tab, snap) < 0)
2470 goto error;
2473 if (context_tab->M && n == context_tab->n_var) {
2474 context_tab->mat = isl_mat_drop_cols(context_tab->mat, 2, 1);
2475 context_tab->M = 0;
2478 isl_vec_free(ineq);
2479 return tab;
2480 error:
2481 isl_vec_free(ineq);
2482 isl_tab_free(tab);
2483 return NULL;
2486 static struct isl_tab *context_lex_detect_nonnegative_parameters(
2487 struct isl_context *context, struct isl_tab *tab)
2489 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2490 struct isl_tab_undo *snap;
2492 if (!tab)
2493 return NULL;
2495 snap = isl_tab_snap(clex->tab);
2496 if (isl_tab_push_basis(clex->tab) < 0)
2497 goto error;
2499 tab = tab_detect_nonnegative_parameters(tab, clex->tab);
2501 if (isl_tab_rollback(clex->tab, snap) < 0)
2502 goto error;
2504 return tab;
2505 error:
2506 isl_tab_free(tab);
2507 return NULL;
2510 static void context_lex_invalidate(struct isl_context *context)
2512 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2513 isl_tab_free(clex->tab);
2514 clex->tab = NULL;
2517 static void context_lex_free(struct isl_context *context)
2519 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2520 isl_tab_free(clex->tab);
2521 free(clex);
2524 struct isl_context_op isl_context_lex_op = {
2525 context_lex_detect_nonnegative_parameters,
2526 context_lex_peek_basic_set,
2527 context_lex_peek_tab,
2528 context_lex_add_eq,
2529 context_lex_add_ineq,
2530 context_lex_ineq_sign,
2531 context_lex_test_ineq,
2532 context_lex_get_div,
2533 context_lex_add_div,
2534 context_lex_detect_equalities,
2535 context_lex_best_split,
2536 context_lex_is_empty,
2537 context_lex_is_ok,
2538 context_lex_save,
2539 context_lex_restore,
2540 context_lex_invalidate,
2541 context_lex_free,
2544 static struct isl_tab *context_tab_for_lexmin(struct isl_basic_set *bset)
2546 struct isl_tab *tab;
2548 if (!bset)
2549 return NULL;
2550 tab = tab_for_lexmin((struct isl_basic_map *)bset, NULL, 1, 0);
2551 if (!tab)
2552 goto error;
2553 if (isl_tab_track_bset(tab, bset) < 0)
2554 goto error;
2555 tab = isl_tab_init_samples(tab);
2556 return tab;
2557 error:
2558 isl_basic_set_free(bset);
2559 return NULL;
2562 static struct isl_context *isl_context_lex_alloc(struct isl_basic_set *dom)
2564 struct isl_context_lex *clex;
2566 if (!dom)
2567 return NULL;
2569 clex = isl_alloc_type(dom->ctx, struct isl_context_lex);
2570 if (!clex)
2571 return NULL;
2573 clex->context.op = &isl_context_lex_op;
2575 clex->tab = context_tab_for_lexmin(isl_basic_set_copy(dom));
2576 if (restore_lexmin(clex->tab) < 0)
2577 goto error;
2578 clex->tab = check_integer_feasible(clex->tab);
2579 if (!clex->tab)
2580 goto error;
2582 return &clex->context;
2583 error:
2584 clex->context.op->free(&clex->context);
2585 return NULL;
2588 struct isl_context_gbr {
2589 struct isl_context context;
2590 struct isl_tab *tab;
2591 struct isl_tab *shifted;
2592 struct isl_tab *cone;
2595 static struct isl_tab *context_gbr_detect_nonnegative_parameters(
2596 struct isl_context *context, struct isl_tab *tab)
2598 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2599 if (!tab)
2600 return NULL;
2601 return tab_detect_nonnegative_parameters(tab, cgbr->tab);
2604 static struct isl_basic_set *context_gbr_peek_basic_set(
2605 struct isl_context *context)
2607 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2608 if (!cgbr->tab)
2609 return NULL;
2610 return isl_tab_peek_bset(cgbr->tab);
2613 static struct isl_tab *context_gbr_peek_tab(struct isl_context *context)
2615 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2616 return cgbr->tab;
2619 /* Initialize the "shifted" tableau of the context, which
2620 * contains the constraints of the original tableau shifted
2621 * by the sum of all negative coefficients. This ensures
2622 * that any rational point in the shifted tableau can
2623 * be rounded up to yield an integer point in the original tableau.
2625 static void gbr_init_shifted(struct isl_context_gbr *cgbr)
2627 int i, j;
2628 struct isl_vec *cst;
2629 struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab);
2630 unsigned dim = isl_basic_set_total_dim(bset);
2632 cst = isl_vec_alloc(cgbr->tab->mat->ctx, bset->n_ineq);
2633 if (!cst)
2634 return;
2636 for (i = 0; i < bset->n_ineq; ++i) {
2637 isl_int_set(cst->el[i], bset->ineq[i][0]);
2638 for (j = 0; j < dim; ++j) {
2639 if (!isl_int_is_neg(bset->ineq[i][1 + j]))
2640 continue;
2641 isl_int_add(bset->ineq[i][0], bset->ineq[i][0],
2642 bset->ineq[i][1 + j]);
2646 cgbr->shifted = isl_tab_from_basic_set(bset, 0);
2648 for (i = 0; i < bset->n_ineq; ++i)
2649 isl_int_set(bset->ineq[i][0], cst->el[i]);
2651 isl_vec_free(cst);
2654 /* Check if the shifted tableau is non-empty, and if so
2655 * use the sample point to construct an integer point
2656 * of the context tableau.
2658 static struct isl_vec *gbr_get_shifted_sample(struct isl_context_gbr *cgbr)
2660 struct isl_vec *sample;
2662 if (!cgbr->shifted)
2663 gbr_init_shifted(cgbr);
2664 if (!cgbr->shifted)
2665 return NULL;
2666 if (cgbr->shifted->empty)
2667 return isl_vec_alloc(cgbr->tab->mat->ctx, 0);
2669 sample = isl_tab_get_sample_value(cgbr->shifted);
2670 sample = isl_vec_ceil(sample);
2672 return sample;
2675 static struct isl_basic_set *drop_constant_terms(struct isl_basic_set *bset)
2677 int i;
2679 if (!bset)
2680 return NULL;
2682 for (i = 0; i < bset->n_eq; ++i)
2683 isl_int_set_si(bset->eq[i][0], 0);
2685 for (i = 0; i < bset->n_ineq; ++i)
2686 isl_int_set_si(bset->ineq[i][0], 0);
2688 return bset;
2691 static int use_shifted(struct isl_context_gbr *cgbr)
2693 return cgbr->tab->bmap->n_eq == 0 && cgbr->tab->bmap->n_div == 0;
2696 static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr)
2698 struct isl_basic_set *bset;
2699 struct isl_basic_set *cone;
2701 if (isl_tab_sample_is_integer(cgbr->tab))
2702 return isl_tab_get_sample_value(cgbr->tab);
2704 if (use_shifted(cgbr)) {
2705 struct isl_vec *sample;
2707 sample = gbr_get_shifted_sample(cgbr);
2708 if (!sample || sample->size > 0)
2709 return sample;
2711 isl_vec_free(sample);
2714 if (!cgbr->cone) {
2715 bset = isl_tab_peek_bset(cgbr->tab);
2716 cgbr->cone = isl_tab_from_recession_cone(bset, 0);
2717 if (!cgbr->cone)
2718 return NULL;
2719 if (isl_tab_track_bset(cgbr->cone,
2720 isl_basic_set_copy(bset)) < 0)
2721 return NULL;
2723 if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0)
2724 return NULL;
2726 if (cgbr->cone->n_dead == cgbr->cone->n_col) {
2727 struct isl_vec *sample;
2728 struct isl_tab_undo *snap;
2730 if (cgbr->tab->basis) {
2731 if (cgbr->tab->basis->n_col != 1 + cgbr->tab->n_var) {
2732 isl_mat_free(cgbr->tab->basis);
2733 cgbr->tab->basis = NULL;
2735 cgbr->tab->n_zero = 0;
2736 cgbr->tab->n_unbounded = 0;
2739 snap = isl_tab_snap(cgbr->tab);
2741 sample = isl_tab_sample(cgbr->tab);
2743 if (isl_tab_rollback(cgbr->tab, snap) < 0) {
2744 isl_vec_free(sample);
2745 return NULL;
2748 return sample;
2751 cone = isl_basic_set_dup(isl_tab_peek_bset(cgbr->cone));
2752 cone = drop_constant_terms(cone);
2753 cone = isl_basic_set_update_from_tab(cone, cgbr->cone);
2754 cone = isl_basic_set_underlying_set(cone);
2755 cone = isl_basic_set_gauss(cone, NULL);
2757 bset = isl_basic_set_dup(isl_tab_peek_bset(cgbr->tab));
2758 bset = isl_basic_set_update_from_tab(bset, cgbr->tab);
2759 bset = isl_basic_set_underlying_set(bset);
2760 bset = isl_basic_set_gauss(bset, NULL);
2762 return isl_basic_set_sample_with_cone(bset, cone);
2765 static void check_gbr_integer_feasible(struct isl_context_gbr *cgbr)
2767 struct isl_vec *sample;
2769 if (!cgbr->tab)
2770 return;
2772 if (cgbr->tab->empty)
2773 return;
2775 sample = gbr_get_sample(cgbr);
2776 if (!sample)
2777 goto error;
2779 if (sample->size == 0) {
2780 isl_vec_free(sample);
2781 if (isl_tab_mark_empty(cgbr->tab) < 0)
2782 goto error;
2783 return;
2786 cgbr->tab = isl_tab_add_sample(cgbr->tab, sample);
2788 return;
2789 error:
2790 isl_tab_free(cgbr->tab);
2791 cgbr->tab = NULL;
2794 static struct isl_tab *add_gbr_eq(struct isl_tab *tab, isl_int *eq)
2796 if (!tab)
2797 return NULL;
2799 if (isl_tab_extend_cons(tab, 2) < 0)
2800 goto error;
2802 if (isl_tab_add_eq(tab, eq) < 0)
2803 goto error;
2805 return tab;
2806 error:
2807 isl_tab_free(tab);
2808 return NULL;
2811 static void context_gbr_add_eq(struct isl_context *context, isl_int *eq,
2812 int check, int update)
2814 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2816 cgbr->tab = add_gbr_eq(cgbr->tab, eq);
2818 if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
2819 if (isl_tab_extend_cons(cgbr->cone, 2) < 0)
2820 goto error;
2821 if (isl_tab_add_eq(cgbr->cone, eq) < 0)
2822 goto error;
2825 if (check) {
2826 int v = tab_has_valid_sample(cgbr->tab, eq, 1);
2827 if (v < 0)
2828 goto error;
2829 if (!v)
2830 check_gbr_integer_feasible(cgbr);
2832 if (update)
2833 cgbr->tab = check_samples(cgbr->tab, eq, 1);
2834 return;
2835 error:
2836 isl_tab_free(cgbr->tab);
2837 cgbr->tab = NULL;
2840 static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq)
2842 if (!cgbr->tab)
2843 return;
2845 if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
2846 goto error;
2848 if (isl_tab_add_ineq(cgbr->tab, ineq) < 0)
2849 goto error;
2851 if (cgbr->shifted && !cgbr->shifted->empty && use_shifted(cgbr)) {
2852 int i;
2853 unsigned dim;
2854 dim = isl_basic_map_total_dim(cgbr->tab->bmap);
2856 if (isl_tab_extend_cons(cgbr->shifted, 1) < 0)
2857 goto error;
2859 for (i = 0; i < dim; ++i) {
2860 if (!isl_int_is_neg(ineq[1 + i]))
2861 continue;
2862 isl_int_add(ineq[0], ineq[0], ineq[1 + i]);
2865 if (isl_tab_add_ineq(cgbr->shifted, ineq) < 0)
2866 goto error;
2868 for (i = 0; i < dim; ++i) {
2869 if (!isl_int_is_neg(ineq[1 + i]))
2870 continue;
2871 isl_int_sub(ineq[0], ineq[0], ineq[1 + i]);
2875 if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
2876 if (isl_tab_extend_cons(cgbr->cone, 1) < 0)
2877 goto error;
2878 if (isl_tab_add_ineq(cgbr->cone, ineq) < 0)
2879 goto error;
2882 return;
2883 error:
2884 isl_tab_free(cgbr->tab);
2885 cgbr->tab = NULL;
2888 static void context_gbr_add_ineq(struct isl_context *context, isl_int *ineq,
2889 int check, int update)
2891 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2893 add_gbr_ineq(cgbr, ineq);
2894 if (!cgbr->tab)
2895 return;
2897 if (check) {
2898 int v = tab_has_valid_sample(cgbr->tab, ineq, 0);
2899 if (v < 0)
2900 goto error;
2901 if (!v)
2902 check_gbr_integer_feasible(cgbr);
2904 if (update)
2905 cgbr->tab = check_samples(cgbr->tab, ineq, 0);
2906 return;
2907 error:
2908 isl_tab_free(cgbr->tab);
2909 cgbr->tab = NULL;
2912 static int context_gbr_add_ineq_wrap(void *user, isl_int *ineq)
2914 struct isl_context *context = (struct isl_context *)user;
2915 context_gbr_add_ineq(context, ineq, 0, 0);
2916 return context->op->is_ok(context) ? 0 : -1;
2919 static enum isl_tab_row_sign context_gbr_ineq_sign(struct isl_context *context,
2920 isl_int *ineq, int strict)
2922 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2923 return tab_ineq_sign(cgbr->tab, ineq, strict);
2926 /* Check whether "ineq" can be added to the tableau without rendering
2927 * it infeasible.
2929 static int context_gbr_test_ineq(struct isl_context *context, isl_int *ineq)
2931 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2932 struct isl_tab_undo *snap;
2933 struct isl_tab_undo *shifted_snap = NULL;
2934 struct isl_tab_undo *cone_snap = NULL;
2935 int feasible;
2937 if (!cgbr->tab)
2938 return -1;
2940 if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
2941 return -1;
2943 snap = isl_tab_snap(cgbr->tab);
2944 if (cgbr->shifted)
2945 shifted_snap = isl_tab_snap(cgbr->shifted);
2946 if (cgbr->cone)
2947 cone_snap = isl_tab_snap(cgbr->cone);
2948 add_gbr_ineq(cgbr, ineq);
2949 check_gbr_integer_feasible(cgbr);
2950 if (!cgbr->tab)
2951 return -1;
2952 feasible = !cgbr->tab->empty;
2953 if (isl_tab_rollback(cgbr->tab, snap) < 0)
2954 return -1;
2955 if (shifted_snap) {
2956 if (isl_tab_rollback(cgbr->shifted, shifted_snap))
2957 return -1;
2958 } else if (cgbr->shifted) {
2959 isl_tab_free(cgbr->shifted);
2960 cgbr->shifted = NULL;
2962 if (cone_snap) {
2963 if (isl_tab_rollback(cgbr->cone, cone_snap))
2964 return -1;
2965 } else if (cgbr->cone) {
2966 isl_tab_free(cgbr->cone);
2967 cgbr->cone = NULL;
2970 return feasible;
2973 /* Return the column of the last of the variables associated to
2974 * a column that has a non-zero coefficient.
2975 * This function is called in a context where only coefficients
2976 * of parameters or divs can be non-zero.
2978 static int last_non_zero_var_col(struct isl_tab *tab, isl_int *p)
2980 int i;
2981 int col;
2983 if (tab->n_var == 0)
2984 return -1;
2986 for (i = tab->n_var - 1; i >= 0; --i) {
2987 if (i >= tab->n_param && i < tab->n_var - tab->n_div)
2988 continue;
2989 if (tab->var[i].is_row)
2990 continue;
2991 col = tab->var[i].index;
2992 if (!isl_int_is_zero(p[col]))
2993 return col;
2996 return -1;
2999 /* Look through all the recently added equalities in the context
3000 * to see if we can propagate any of them to the main tableau.
3002 * The newly added equalities in the context are encoded as pairs
3003 * of inequalities starting at inequality "first".
3005 * We tentatively add each of these equalities to the main tableau
3006 * and if this happens to result in a row with a final coefficient
3007 * that is one or negative one, we use it to kill a column
3008 * in the main tableau. Otherwise, we discard the tentatively
3009 * added row.
3011 static void propagate_equalities(struct isl_context_gbr *cgbr,
3012 struct isl_tab *tab, unsigned first)
3014 int i;
3015 struct isl_vec *eq = NULL;
3017 eq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
3018 if (!eq)
3019 goto error;
3021 if (isl_tab_extend_cons(tab, (cgbr->tab->bmap->n_ineq - first)/2) < 0)
3022 goto error;
3024 isl_seq_clr(eq->el + 1 + tab->n_param,
3025 tab->n_var - tab->n_param - tab->n_div);
3026 for (i = first; i < cgbr->tab->bmap->n_ineq; i += 2) {
3027 int j;
3028 int r;
3029 struct isl_tab_undo *snap;
3030 snap = isl_tab_snap(tab);
3032 isl_seq_cpy(eq->el, cgbr->tab->bmap->ineq[i], 1 + tab->n_param);
3033 isl_seq_cpy(eq->el + 1 + tab->n_var - tab->n_div,
3034 cgbr->tab->bmap->ineq[i] + 1 + tab->n_param,
3035 tab->n_div);
3037 r = isl_tab_add_row(tab, eq->el);
3038 if (r < 0)
3039 goto error;
3040 r = tab->con[r].index;
3041 j = last_non_zero_var_col(tab, tab->mat->row[r] + 2 + tab->M);
3042 if (j < 0 || j < tab->n_dead ||
3043 !isl_int_is_one(tab->mat->row[r][0]) ||
3044 (!isl_int_is_one(tab->mat->row[r][2 + tab->M + j]) &&
3045 !isl_int_is_negone(tab->mat->row[r][2 + tab->M + j]))) {
3046 if (isl_tab_rollback(tab, snap) < 0)
3047 goto error;
3048 continue;
3050 if (isl_tab_pivot(tab, r, j) < 0)
3051 goto error;
3052 if (isl_tab_kill_col(tab, j) < 0)
3053 goto error;
3055 if (restore_lexmin(tab) < 0)
3056 goto error;
3059 isl_vec_free(eq);
3061 return;
3062 error:
3063 isl_vec_free(eq);
3064 isl_tab_free(cgbr->tab);
3065 cgbr->tab = NULL;
3068 static int context_gbr_detect_equalities(struct isl_context *context,
3069 struct isl_tab *tab)
3071 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3072 struct isl_ctx *ctx;
3073 unsigned n_ineq;
3075 ctx = cgbr->tab->mat->ctx;
3077 if (!cgbr->cone) {
3078 struct isl_basic_set *bset = isl_tab_peek_bset(cgbr->tab);
3079 cgbr->cone = isl_tab_from_recession_cone(bset, 0);
3080 if (!cgbr->cone)
3081 goto error;
3082 if (isl_tab_track_bset(cgbr->cone,
3083 isl_basic_set_copy(bset)) < 0)
3084 goto error;
3086 if (isl_tab_detect_implicit_equalities(cgbr->cone) < 0)
3087 goto error;
3089 n_ineq = cgbr->tab->bmap->n_ineq;
3090 cgbr->tab = isl_tab_detect_equalities(cgbr->tab, cgbr->cone);
3091 if (cgbr->tab && cgbr->tab->bmap->n_ineq > n_ineq)
3092 propagate_equalities(cgbr, tab, n_ineq);
3094 return 0;
3095 error:
3096 isl_tab_free(cgbr->tab);
3097 cgbr->tab = NULL;
3098 return -1;
3101 static int context_gbr_get_div(struct isl_context *context, struct isl_tab *tab,
3102 struct isl_vec *div)
3104 return get_div(tab, context, div);
3107 static int context_gbr_add_div(struct isl_context *context, struct isl_vec *div)
3109 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3110 if (cgbr->cone) {
3111 int k;
3113 if (isl_tab_extend_cons(cgbr->cone, 3) < 0)
3114 return -1;
3115 if (isl_tab_extend_vars(cgbr->cone, 1) < 0)
3116 return -1;
3117 if (isl_tab_allocate_var(cgbr->cone) <0)
3118 return -1;
3120 cgbr->cone->bmap = isl_basic_map_extend_space(cgbr->cone->bmap,
3121 isl_basic_map_get_space(cgbr->cone->bmap), 1, 0, 2);
3122 k = isl_basic_map_alloc_div(cgbr->cone->bmap);
3123 if (k < 0)
3124 return -1;
3125 isl_seq_cpy(cgbr->cone->bmap->div[k], div->el, div->size);
3126 if (isl_tab_push(cgbr->cone, isl_tab_undo_bmap_div) < 0)
3127 return -1;
3129 return context_tab_add_div(cgbr->tab, div,
3130 context_gbr_add_ineq_wrap, context);
3133 static int context_gbr_best_split(struct isl_context *context,
3134 struct isl_tab *tab)
3136 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3137 struct isl_tab_undo *snap;
3138 int r;
3140 snap = isl_tab_snap(cgbr->tab);
3141 r = best_split(tab, cgbr->tab);
3143 if (r >= 0 && isl_tab_rollback(cgbr->tab, snap) < 0)
3144 return -1;
3146 return r;
3149 static int context_gbr_is_empty(struct isl_context *context)
3151 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3152 if (!cgbr->tab)
3153 return -1;
3154 return cgbr->tab->empty;
3157 struct isl_gbr_tab_undo {
3158 struct isl_tab_undo *tab_snap;
3159 struct isl_tab_undo *shifted_snap;
3160 struct isl_tab_undo *cone_snap;
3163 static void *context_gbr_save(struct isl_context *context)
3165 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3166 struct isl_gbr_tab_undo *snap;
3168 snap = isl_alloc_type(cgbr->tab->mat->ctx, struct isl_gbr_tab_undo);
3169 if (!snap)
3170 return NULL;
3172 snap->tab_snap = isl_tab_snap(cgbr->tab);
3173 if (isl_tab_save_samples(cgbr->tab) < 0)
3174 goto error;
3176 if (cgbr->shifted)
3177 snap->shifted_snap = isl_tab_snap(cgbr->shifted);
3178 else
3179 snap->shifted_snap = NULL;
3181 if (cgbr->cone)
3182 snap->cone_snap = isl_tab_snap(cgbr->cone);
3183 else
3184 snap->cone_snap = NULL;
3186 return snap;
3187 error:
3188 free(snap);
3189 return NULL;
3192 static void context_gbr_restore(struct isl_context *context, void *save)
3194 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3195 struct isl_gbr_tab_undo *snap = (struct isl_gbr_tab_undo *)save;
3196 if (!snap)
3197 goto error;
3198 if (isl_tab_rollback(cgbr->tab, snap->tab_snap) < 0) {
3199 isl_tab_free(cgbr->tab);
3200 cgbr->tab = NULL;
3203 if (snap->shifted_snap) {
3204 if (isl_tab_rollback(cgbr->shifted, snap->shifted_snap) < 0)
3205 goto error;
3206 } else if (cgbr->shifted) {
3207 isl_tab_free(cgbr->shifted);
3208 cgbr->shifted = NULL;
3211 if (snap->cone_snap) {
3212 if (isl_tab_rollback(cgbr->cone, snap->cone_snap) < 0)
3213 goto error;
3214 } else if (cgbr->cone) {
3215 isl_tab_free(cgbr->cone);
3216 cgbr->cone = NULL;
3219 free(snap);
3221 return;
3222 error:
3223 free(snap);
3224 isl_tab_free(cgbr->tab);
3225 cgbr->tab = NULL;
3228 static int context_gbr_is_ok(struct isl_context *context)
3230 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3231 return !!cgbr->tab;
3234 static void context_gbr_invalidate(struct isl_context *context)
3236 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3237 isl_tab_free(cgbr->tab);
3238 cgbr->tab = NULL;
3241 static void context_gbr_free(struct isl_context *context)
3243 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3244 isl_tab_free(cgbr->tab);
3245 isl_tab_free(cgbr->shifted);
3246 isl_tab_free(cgbr->cone);
3247 free(cgbr);
3250 struct isl_context_op isl_context_gbr_op = {
3251 context_gbr_detect_nonnegative_parameters,
3252 context_gbr_peek_basic_set,
3253 context_gbr_peek_tab,
3254 context_gbr_add_eq,
3255 context_gbr_add_ineq,
3256 context_gbr_ineq_sign,
3257 context_gbr_test_ineq,
3258 context_gbr_get_div,
3259 context_gbr_add_div,
3260 context_gbr_detect_equalities,
3261 context_gbr_best_split,
3262 context_gbr_is_empty,
3263 context_gbr_is_ok,
3264 context_gbr_save,
3265 context_gbr_restore,
3266 context_gbr_invalidate,
3267 context_gbr_free,
3270 static struct isl_context *isl_context_gbr_alloc(struct isl_basic_set *dom)
3272 struct isl_context_gbr *cgbr;
3274 if (!dom)
3275 return NULL;
3277 cgbr = isl_calloc_type(dom->ctx, struct isl_context_gbr);
3278 if (!cgbr)
3279 return NULL;
3281 cgbr->context.op = &isl_context_gbr_op;
3283 cgbr->shifted = NULL;
3284 cgbr->cone = NULL;
3285 cgbr->tab = isl_tab_from_basic_set(dom, 1);
3286 cgbr->tab = isl_tab_init_samples(cgbr->tab);
3287 if (!cgbr->tab)
3288 goto error;
3289 check_gbr_integer_feasible(cgbr);
3291 return &cgbr->context;
3292 error:
3293 cgbr->context.op->free(&cgbr->context);
3294 return NULL;
3297 static struct isl_context *isl_context_alloc(struct isl_basic_set *dom)
3299 if (!dom)
3300 return NULL;
3302 if (dom->ctx->opt->context == ISL_CONTEXT_LEXMIN)
3303 return isl_context_lex_alloc(dom);
3304 else
3305 return isl_context_gbr_alloc(dom);
3308 /* Construct an isl_sol_map structure for accumulating the solution.
3309 * If track_empty is set, then we also keep track of the parts
3310 * of the context where there is no solution.
3311 * If max is set, then we are solving a maximization, rather than
3312 * a minimization problem, which means that the variables in the
3313 * tableau have value "M - x" rather than "M + x".
3315 static struct isl_sol *sol_map_init(struct isl_basic_map *bmap,
3316 struct isl_basic_set *dom, int track_empty, int max)
3318 struct isl_sol_map *sol_map = NULL;
3320 if (!bmap)
3321 goto error;
3323 sol_map = isl_calloc_type(bmap->ctx, struct isl_sol_map);
3324 if (!sol_map)
3325 goto error;
3327 sol_map->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
3328 sol_map->sol.dec_level.callback.run = &sol_dec_level_wrap;
3329 sol_map->sol.dec_level.sol = &sol_map->sol;
3330 sol_map->sol.max = max;
3331 sol_map->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
3332 sol_map->sol.add = &sol_map_add_wrap;
3333 sol_map->sol.add_empty = track_empty ? &sol_map_add_empty_wrap : NULL;
3334 sol_map->sol.free = &sol_map_free_wrap;
3335 sol_map->map = isl_map_alloc_space(isl_basic_map_get_space(bmap), 1,
3336 ISL_MAP_DISJOINT);
3337 if (!sol_map->map)
3338 goto error;
3340 sol_map->sol.context = isl_context_alloc(dom);
3341 if (!sol_map->sol.context)
3342 goto error;
3344 if (track_empty) {
3345 sol_map->empty = isl_set_alloc_space(isl_basic_set_get_space(dom),
3346 1, ISL_SET_DISJOINT);
3347 if (!sol_map->empty)
3348 goto error;
3351 isl_basic_set_free(dom);
3352 return &sol_map->sol;
3353 error:
3354 isl_basic_set_free(dom);
3355 sol_map_free(sol_map);
3356 return NULL;
3359 /* Check whether all coefficients of (non-parameter) variables
3360 * are non-positive, meaning that no pivots can be performed on the row.
3362 static int is_critical(struct isl_tab *tab, int row)
3364 int j;
3365 unsigned off = 2 + tab->M;
3367 for (j = tab->n_dead; j < tab->n_col; ++j) {
3368 if (tab->col_var[j] >= 0 &&
3369 (tab->col_var[j] < tab->n_param ||
3370 tab->col_var[j] >= tab->n_var - tab->n_div))
3371 continue;
3373 if (isl_int_is_pos(tab->mat->row[row][off + j]))
3374 return 0;
3377 return 1;
3380 /* Check whether the inequality represented by vec is strict over the integers,
3381 * i.e., there are no integer values satisfying the constraint with
3382 * equality. This happens if the gcd of the coefficients is not a divisor
3383 * of the constant term. If so, scale the constraint down by the gcd
3384 * of the coefficients.
3386 static int is_strict(struct isl_vec *vec)
3388 isl_int gcd;
3389 int strict = 0;
3391 isl_int_init(gcd);
3392 isl_seq_gcd(vec->el + 1, vec->size - 1, &gcd);
3393 if (!isl_int_is_one(gcd)) {
3394 strict = !isl_int_is_divisible_by(vec->el[0], gcd);
3395 isl_int_fdiv_q(vec->el[0], vec->el[0], gcd);
3396 isl_seq_scale_down(vec->el + 1, vec->el + 1, gcd, vec->size-1);
3398 isl_int_clear(gcd);
3400 return strict;
3403 /* Determine the sign of the given row of the main tableau.
3404 * The result is one of
3405 * isl_tab_row_pos: always non-negative; no pivot needed
3406 * isl_tab_row_neg: always non-positive; pivot
3407 * isl_tab_row_any: can be both positive and negative; split
3409 * We first handle some simple cases
3410 * - the row sign may be known already
3411 * - the row may be obviously non-negative
3412 * - the parametric constant may be equal to that of another row
3413 * for which we know the sign. This sign will be either "pos" or
3414 * "any". If it had been "neg" then we would have pivoted before.
3416 * If none of these cases hold, we check the value of the row for each
3417 * of the currently active samples. Based on the signs of these values
3418 * we make an initial determination of the sign of the row.
3420 * all zero -> unk(nown)
3421 * all non-negative -> pos
3422 * all non-positive -> neg
3423 * both negative and positive -> all
3425 * If we end up with "all", we are done.
3426 * Otherwise, we perform a check for positive and/or negative
3427 * values as follows.
3429 * samples neg unk pos
3430 * <0 ? Y N Y N
3431 * pos any pos
3432 * >0 ? Y N Y N
3433 * any neg any neg
3435 * There is no special sign for "zero", because we can usually treat zero
3436 * as either non-negative or non-positive, whatever works out best.
3437 * However, if the row is "critical", meaning that pivoting is impossible
3438 * then we don't want to limp zero with the non-positive case, because
3439 * then we we would lose the solution for those values of the parameters
3440 * where the value of the row is zero. Instead, we treat 0 as non-negative
3441 * ensuring a split if the row can attain both zero and negative values.
3442 * The same happens when the original constraint was one that could not
3443 * be satisfied with equality by any integer values of the parameters.
3444 * In this case, we normalize the constraint, but then a value of zero
3445 * for the normalized constraint is actually a positive value for the
3446 * original constraint, so again we need to treat zero as non-negative.
3447 * In both these cases, we have the following decision tree instead:
3449 * all non-negative -> pos
3450 * all negative -> neg
3451 * both negative and non-negative -> all
3453 * samples neg pos
3454 * <0 ? Y N
3455 * any pos
3456 * >=0 ? Y N
3457 * any neg
3459 static enum isl_tab_row_sign row_sign(struct isl_tab *tab,
3460 struct isl_sol *sol, int row)
3462 struct isl_vec *ineq = NULL;
3463 enum isl_tab_row_sign res = isl_tab_row_unknown;
3464 int critical;
3465 int strict;
3466 int row2;
3468 if (tab->row_sign[row] != isl_tab_row_unknown)
3469 return tab->row_sign[row];
3470 if (is_obviously_nonneg(tab, row))
3471 return isl_tab_row_pos;
3472 for (row2 = tab->n_redundant; row2 < tab->n_row; ++row2) {
3473 if (tab->row_sign[row2] == isl_tab_row_unknown)
3474 continue;
3475 if (identical_parameter_line(tab, row, row2))
3476 return tab->row_sign[row2];
3479 critical = is_critical(tab, row);
3481 ineq = get_row_parameter_ineq(tab, row);
3482 if (!ineq)
3483 goto error;
3485 strict = is_strict(ineq);
3487 res = sol->context->op->ineq_sign(sol->context, ineq->el,
3488 critical || strict);
3490 if (res == isl_tab_row_unknown || res == isl_tab_row_pos) {
3491 /* test for negative values */
3492 int feasible;
3493 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3494 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3496 feasible = sol->context->op->test_ineq(sol->context, ineq->el);
3497 if (feasible < 0)
3498 goto error;
3499 if (!feasible)
3500 res = isl_tab_row_pos;
3501 else
3502 res = (res == isl_tab_row_unknown) ? isl_tab_row_neg
3503 : isl_tab_row_any;
3504 if (res == isl_tab_row_neg) {
3505 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3506 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3510 if (res == isl_tab_row_neg) {
3511 /* test for positive values */
3512 int feasible;
3513 if (!critical && !strict)
3514 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3516 feasible = sol->context->op->test_ineq(sol->context, ineq->el);
3517 if (feasible < 0)
3518 goto error;
3519 if (feasible)
3520 res = isl_tab_row_any;
3523 isl_vec_free(ineq);
3524 return res;
3525 error:
3526 isl_vec_free(ineq);
3527 return isl_tab_row_unknown;
3530 static void find_solutions(struct isl_sol *sol, struct isl_tab *tab);
3532 /* Find solutions for values of the parameters that satisfy the given
3533 * inequality.
3535 * We currently take a snapshot of the context tableau that is reset
3536 * when we return from this function, while we make a copy of the main
3537 * tableau, leaving the original main tableau untouched.
3538 * These are fairly arbitrary choices. Making a copy also of the context
3539 * tableau would obviate the need to undo any changes made to it later,
3540 * while taking a snapshot of the main tableau could reduce memory usage.
3541 * If we were to switch to taking a snapshot of the main tableau,
3542 * we would have to keep in mind that we need to save the row signs
3543 * and that we need to do this before saving the current basis
3544 * such that the basis has been restore before we restore the row signs.
3546 static void find_in_pos(struct isl_sol *sol, struct isl_tab *tab, isl_int *ineq)
3548 void *saved;
3550 if (!sol->context)
3551 goto error;
3552 saved = sol->context->op->save(sol->context);
3554 tab = isl_tab_dup(tab);
3555 if (!tab)
3556 goto error;
3558 sol->context->op->add_ineq(sol->context, ineq, 0, 1);
3560 find_solutions(sol, tab);
3562 if (!sol->error)
3563 sol->context->op->restore(sol->context, saved);
3564 return;
3565 error:
3566 sol->error = 1;
3569 /* Record the absence of solutions for those values of the parameters
3570 * that do not satisfy the given inequality with equality.
3572 static void no_sol_in_strict(struct isl_sol *sol,
3573 struct isl_tab *tab, struct isl_vec *ineq)
3575 int empty;
3576 void *saved;
3578 if (!sol->context || sol->error)
3579 goto error;
3580 saved = sol->context->op->save(sol->context);
3582 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3584 sol->context->op->add_ineq(sol->context, ineq->el, 1, 0);
3585 if (!sol->context)
3586 goto error;
3588 empty = tab->empty;
3589 tab->empty = 1;
3590 sol_add(sol, tab);
3591 tab->empty = empty;
3593 isl_int_add_ui(ineq->el[0], ineq->el[0], 1);
3595 sol->context->op->restore(sol->context, saved);
3596 return;
3597 error:
3598 sol->error = 1;
3601 /* Compute the lexicographic minimum of the set represented by the main
3602 * tableau "tab" within the context "sol->context_tab".
3603 * On entry the sample value of the main tableau is lexicographically
3604 * less than or equal to this lexicographic minimum.
3605 * Pivots are performed until a feasible point is found, which is then
3606 * necessarily equal to the minimum, or until the tableau is found to
3607 * be infeasible. Some pivots may need to be performed for only some
3608 * feasible values of the context tableau. If so, the context tableau
3609 * is split into a part where the pivot is needed and a part where it is not.
3611 * Whenever we enter the main loop, the main tableau is such that no
3612 * "obvious" pivots need to be performed on it, where "obvious" means
3613 * that the given row can be seen to be negative without looking at
3614 * the context tableau. In particular, for non-parametric problems,
3615 * no pivots need to be performed on the main tableau.
3616 * The caller of find_solutions is responsible for making this property
3617 * hold prior to the first iteration of the loop, while restore_lexmin
3618 * is called before every other iteration.
3620 * Inside the main loop, we first examine the signs of the rows of
3621 * the main tableau within the context of the context tableau.
3622 * If we find a row that is always non-positive for all values of
3623 * the parameters satisfying the context tableau and negative for at
3624 * least one value of the parameters, we perform the appropriate pivot
3625 * and start over. An exception is the case where no pivot can be
3626 * performed on the row. In this case, we require that the sign of
3627 * the row is negative for all values of the parameters (rather than just
3628 * non-positive). This special case is handled inside row_sign, which
3629 * will say that the row can have any sign if it determines that it can
3630 * attain both negative and zero values.
3632 * If we can't find a row that always requires a pivot, but we can find
3633 * one or more rows that require a pivot for some values of the parameters
3634 * (i.e., the row can attain both positive and negative signs), then we split
3635 * the context tableau into two parts, one where we force the sign to be
3636 * non-negative and one where we force is to be negative.
3637 * The non-negative part is handled by a recursive call (through find_in_pos).
3638 * Upon returning from this call, we continue with the negative part and
3639 * perform the required pivot.
3641 * If no such rows can be found, all rows are non-negative and we have
3642 * found a (rational) feasible point. If we only wanted a rational point
3643 * then we are done.
3644 * Otherwise, we check if all values of the sample point of the tableau
3645 * are integral for the variables. If so, we have found the minimal
3646 * integral point and we are done.
3647 * If the sample point is not integral, then we need to make a distinction
3648 * based on whether the constant term is non-integral or the coefficients
3649 * of the parameters. Furthermore, in order to decide how to handle
3650 * the non-integrality, we also need to know whether the coefficients
3651 * of the other columns in the tableau are integral. This leads
3652 * to the following table. The first two rows do not correspond
3653 * to a non-integral sample point and are only mentioned for completeness.
3655 * constant parameters other
3657 * int int int |
3658 * int int rat | -> no problem
3660 * rat int int -> fail
3662 * rat int rat -> cut
3664 * int rat rat |
3665 * rat rat rat | -> parametric cut
3667 * int rat int |
3668 * rat rat int | -> split context
3670 * If the parametric constant is completely integral, then there is nothing
3671 * to be done. If the constant term is non-integral, but all the other
3672 * coefficient are integral, then there is nothing that can be done
3673 * and the tableau has no integral solution.
3674 * If, on the other hand, one or more of the other columns have rational
3675 * coefficients, but the parameter coefficients are all integral, then
3676 * we can perform a regular (non-parametric) cut.
3677 * Finally, if there is any parameter coefficient that is non-integral,
3678 * then we need to involve the context tableau. There are two cases here.
3679 * If at least one other column has a rational coefficient, then we
3680 * can perform a parametric cut in the main tableau by adding a new
3681 * integer division in the context tableau.
3682 * If all other columns have integral coefficients, then we need to
3683 * enforce that the rational combination of parameters (c + \sum a_i y_i)/m
3684 * is always integral. We do this by introducing an integer division
3685 * q = floor((c + \sum a_i y_i)/m) and stipulating that its argument should
3686 * always be integral in the context tableau, i.e., m q = c + \sum a_i y_i.
3687 * Since q is expressed in the tableau as
3688 * c + \sum a_i y_i - m q >= 0
3689 * -c - \sum a_i y_i + m q + m - 1 >= 0
3690 * it is sufficient to add the inequality
3691 * -c - \sum a_i y_i + m q >= 0
3692 * In the part of the context where this inequality does not hold, the
3693 * main tableau is marked as being empty.
3695 static void find_solutions(struct isl_sol *sol, struct isl_tab *tab)
3697 struct isl_context *context;
3698 int r;
3700 if (!tab || sol->error)
3701 goto error;
3703 context = sol->context;
3705 if (tab->empty)
3706 goto done;
3707 if (context->op->is_empty(context))
3708 goto done;
3710 for (r = 0; r >= 0 && tab && !tab->empty; r = restore_lexmin(tab)) {
3711 int flags;
3712 int row;
3713 enum isl_tab_row_sign sgn;
3714 int split = -1;
3715 int n_split = 0;
3717 for (row = tab->n_redundant; row < tab->n_row; ++row) {
3718 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
3719 continue;
3720 sgn = row_sign(tab, sol, row);
3721 if (!sgn)
3722 goto error;
3723 tab->row_sign[row] = sgn;
3724 if (sgn == isl_tab_row_any)
3725 n_split++;
3726 if (sgn == isl_tab_row_any && split == -1)
3727 split = row;
3728 if (sgn == isl_tab_row_neg)
3729 break;
3731 if (row < tab->n_row)
3732 continue;
3733 if (split != -1) {
3734 struct isl_vec *ineq;
3735 if (n_split != 1)
3736 split = context->op->best_split(context, tab);
3737 if (split < 0)
3738 goto error;
3739 ineq = get_row_parameter_ineq(tab, split);
3740 if (!ineq)
3741 goto error;
3742 is_strict(ineq);
3743 for (row = tab->n_redundant; row < tab->n_row; ++row) {
3744 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
3745 continue;
3746 if (tab->row_sign[row] == isl_tab_row_any)
3747 tab->row_sign[row] = isl_tab_row_unknown;
3749 tab->row_sign[split] = isl_tab_row_pos;
3750 sol_inc_level(sol);
3751 find_in_pos(sol, tab, ineq->el);
3752 tab->row_sign[split] = isl_tab_row_neg;
3753 row = split;
3754 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3755 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3756 if (!sol->error)
3757 context->op->add_ineq(context, ineq->el, 0, 1);
3758 isl_vec_free(ineq);
3759 if (sol->error)
3760 goto error;
3761 continue;
3763 if (tab->rational)
3764 break;
3765 row = first_non_integer_row(tab, &flags);
3766 if (row < 0)
3767 break;
3768 if (ISL_FL_ISSET(flags, I_PAR)) {
3769 if (ISL_FL_ISSET(flags, I_VAR)) {
3770 if (isl_tab_mark_empty(tab) < 0)
3771 goto error;
3772 break;
3774 row = add_cut(tab, row);
3775 } else if (ISL_FL_ISSET(flags, I_VAR)) {
3776 struct isl_vec *div;
3777 struct isl_vec *ineq;
3778 int d;
3779 div = get_row_split_div(tab, row);
3780 if (!div)
3781 goto error;
3782 d = context->op->get_div(context, tab, div);
3783 isl_vec_free(div);
3784 if (d < 0)
3785 goto error;
3786 ineq = ineq_for_div(context->op->peek_basic_set(context), d);
3787 if (!ineq)
3788 goto error;
3789 sol_inc_level(sol);
3790 no_sol_in_strict(sol, tab, ineq);
3791 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3792 context->op->add_ineq(context, ineq->el, 1, 1);
3793 isl_vec_free(ineq);
3794 if (sol->error || !context->op->is_ok(context))
3795 goto error;
3796 tab = set_row_cst_to_div(tab, row, d);
3797 if (context->op->is_empty(context))
3798 break;
3799 } else
3800 row = add_parametric_cut(tab, row, context);
3801 if (row < 0)
3802 goto error;
3804 if (r < 0)
3805 goto error;
3806 done:
3807 sol_add(sol, tab);
3808 isl_tab_free(tab);
3809 return;
3810 error:
3811 isl_tab_free(tab);
3812 sol->error = 1;
3815 /* Compute the lexicographic minimum of the set represented by the main
3816 * tableau "tab" within the context "sol->context_tab".
3818 * As a preprocessing step, we first transfer all the purely parametric
3819 * equalities from the main tableau to the context tableau, i.e.,
3820 * parameters that have been pivoted to a row.
3821 * These equalities are ignored by the main algorithm, because the
3822 * corresponding rows may not be marked as being non-negative.
3823 * In parts of the context where the added equality does not hold,
3824 * the main tableau is marked as being empty.
3826 static void find_solutions_main(struct isl_sol *sol, struct isl_tab *tab)
3828 int row;
3830 if (!tab)
3831 goto error;
3833 sol->level = 0;
3835 for (row = tab->n_redundant; row < tab->n_row; ++row) {
3836 int p;
3837 struct isl_vec *eq;
3839 if (tab->row_var[row] < 0)
3840 continue;
3841 if (tab->row_var[row] >= tab->n_param &&
3842 tab->row_var[row] < tab->n_var - tab->n_div)
3843 continue;
3844 if (tab->row_var[row] < tab->n_param)
3845 p = tab->row_var[row];
3846 else
3847 p = tab->row_var[row]
3848 + tab->n_param - (tab->n_var - tab->n_div);
3850 eq = isl_vec_alloc(tab->mat->ctx, 1+tab->n_param+tab->n_div);
3851 if (!eq)
3852 goto error;
3853 get_row_parameter_line(tab, row, eq->el);
3854 isl_int_neg(eq->el[1 + p], tab->mat->row[row][0]);
3855 eq = isl_vec_normalize(eq);
3857 sol_inc_level(sol);
3858 no_sol_in_strict(sol, tab, eq);
3860 isl_seq_neg(eq->el, eq->el, eq->size);
3861 sol_inc_level(sol);
3862 no_sol_in_strict(sol, tab, eq);
3863 isl_seq_neg(eq->el, eq->el, eq->size);
3865 sol->context->op->add_eq(sol->context, eq->el, 1, 1);
3867 isl_vec_free(eq);
3869 if (isl_tab_mark_redundant(tab, row) < 0)
3870 goto error;
3872 if (sol->context->op->is_empty(sol->context))
3873 break;
3875 row = tab->n_redundant - 1;
3878 find_solutions(sol, tab);
3880 sol->level = 0;
3881 sol_pop(sol);
3883 return;
3884 error:
3885 isl_tab_free(tab);
3886 sol->error = 1;
3889 /* Check if integer division "div" of "dom" also occurs in "bmap".
3890 * If so, return its position within the divs.
3891 * If not, return -1.
3893 static int find_context_div(struct isl_basic_map *bmap,
3894 struct isl_basic_set *dom, unsigned div)
3896 int i;
3897 unsigned b_dim = isl_space_dim(bmap->dim, isl_dim_all);
3898 unsigned d_dim = isl_space_dim(dom->dim, isl_dim_all);
3900 if (isl_int_is_zero(dom->div[div][0]))
3901 return -1;
3902 if (isl_seq_first_non_zero(dom->div[div] + 2 + d_dim, dom->n_div) != -1)
3903 return -1;
3905 for (i = 0; i < bmap->n_div; ++i) {
3906 if (isl_int_is_zero(bmap->div[i][0]))
3907 continue;
3908 if (isl_seq_first_non_zero(bmap->div[i] + 2 + d_dim,
3909 (b_dim - d_dim) + bmap->n_div) != -1)
3910 continue;
3911 if (isl_seq_eq(bmap->div[i], dom->div[div], 2 + d_dim))
3912 return i;
3914 return -1;
3917 /* The correspondence between the variables in the main tableau,
3918 * the context tableau, and the input map and domain is as follows.
3919 * The first n_param and the last n_div variables of the main tableau
3920 * form the variables of the context tableau.
3921 * In the basic map, these n_param variables correspond to the
3922 * parameters and the input dimensions. In the domain, they correspond
3923 * to the parameters and the set dimensions.
3924 * The n_div variables correspond to the integer divisions in the domain.
3925 * To ensure that everything lines up, we may need to copy some of the
3926 * integer divisions of the domain to the map. These have to be placed
3927 * in the same order as those in the context and they have to be placed
3928 * after any other integer divisions that the map may have.
3929 * This function performs the required reordering.
3931 static struct isl_basic_map *align_context_divs(struct isl_basic_map *bmap,
3932 struct isl_basic_set *dom)
3934 int i;
3935 int common = 0;
3936 int other;
3938 for (i = 0; i < dom->n_div; ++i)
3939 if (find_context_div(bmap, dom, i) != -1)
3940 common++;
3941 other = bmap->n_div - common;
3942 if (dom->n_div - common > 0) {
3943 bmap = isl_basic_map_extend_space(bmap, isl_space_copy(bmap->dim),
3944 dom->n_div - common, 0, 0);
3945 if (!bmap)
3946 return NULL;
3948 for (i = 0; i < dom->n_div; ++i) {
3949 int pos = find_context_div(bmap, dom, i);
3950 if (pos < 0) {
3951 pos = isl_basic_map_alloc_div(bmap);
3952 if (pos < 0)
3953 goto error;
3954 isl_int_set_si(bmap->div[pos][0], 0);
3956 if (pos != other + i)
3957 isl_basic_map_swap_div(bmap, pos, other + i);
3959 return bmap;
3960 error:
3961 isl_basic_map_free(bmap);
3962 return NULL;
3965 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
3966 * some obvious symmetries.
3968 * We make sure the divs in the domain are properly ordered,
3969 * because they will be added one by one in the given order
3970 * during the construction of the solution map.
3972 static struct isl_sol *basic_map_partial_lexopt_base(
3973 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
3974 __isl_give isl_set **empty, int max,
3975 struct isl_sol *(*init)(__isl_keep isl_basic_map *bmap,
3976 __isl_take isl_basic_set *dom, int track_empty, int max))
3978 struct isl_tab *tab;
3979 struct isl_sol *sol = NULL;
3980 struct isl_context *context;
3982 if (dom->n_div) {
3983 dom = isl_basic_set_order_divs(dom);
3984 bmap = align_context_divs(bmap, dom);
3986 sol = init(bmap, dom, !!empty, max);
3987 if (!sol)
3988 goto error;
3990 context = sol->context;
3991 if (isl_basic_set_plain_is_empty(context->op->peek_basic_set(context)))
3992 /* nothing */;
3993 else if (isl_basic_map_plain_is_empty(bmap)) {
3994 if (sol->add_empty)
3995 sol->add_empty(sol,
3996 isl_basic_set_copy(context->op->peek_basic_set(context)));
3997 } else {
3998 tab = tab_for_lexmin(bmap,
3999 context->op->peek_basic_set(context), 1, max);
4000 tab = context->op->detect_nonnegative_parameters(context, tab);
4001 find_solutions_main(sol, tab);
4003 if (sol->error)
4004 goto error;
4006 isl_basic_map_free(bmap);
4007 return sol;
4008 error:
4009 sol_free(sol);
4010 isl_basic_map_free(bmap);
4011 return NULL;
4014 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
4015 * some obvious symmetries.
4017 * We call basic_map_partial_lexopt_base and extract the results.
4019 static __isl_give isl_map *basic_map_partial_lexopt_base_map(
4020 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
4021 __isl_give isl_set **empty, int max)
4023 isl_map *result = NULL;
4024 struct isl_sol *sol;
4025 struct isl_sol_map *sol_map;
4027 sol = basic_map_partial_lexopt_base(bmap, dom, empty, max,
4028 &sol_map_init);
4029 if (!sol)
4030 return NULL;
4031 sol_map = (struct isl_sol_map *) sol;
4033 result = isl_map_copy(sol_map->map);
4034 if (empty)
4035 *empty = isl_set_copy(sol_map->empty);
4036 sol_free(&sol_map->sol);
4037 return result;
4040 /* Structure used during detection of parallel constraints.
4041 * n_in: number of "input" variables: isl_dim_param + isl_dim_in
4042 * n_out: number of "output" variables: isl_dim_out + isl_dim_div
4043 * val: the coefficients of the output variables
4045 struct isl_constraint_equal_info {
4046 isl_basic_map *bmap;
4047 unsigned n_in;
4048 unsigned n_out;
4049 isl_int *val;
4052 /* Check whether the coefficients of the output variables
4053 * of the constraint in "entry" are equal to info->val.
4055 static int constraint_equal(const void *entry, const void *val)
4057 isl_int **row = (isl_int **)entry;
4058 const struct isl_constraint_equal_info *info = val;
4060 return isl_seq_eq((*row) + 1 + info->n_in, info->val, info->n_out);
4063 /* Check whether "bmap" has a pair of constraints that have
4064 * the same coefficients for the output variables.
4065 * Note that the coefficients of the existentially quantified
4066 * variables need to be zero since the existentially quantified
4067 * of the result are usually not the same as those of the input.
4068 * the isl_dim_out and isl_dim_div dimensions.
4069 * If so, return 1 and return the row indices of the two constraints
4070 * in *first and *second.
4072 static int parallel_constraints(__isl_keep isl_basic_map *bmap,
4073 int *first, int *second)
4075 int i;
4076 isl_ctx *ctx = isl_basic_map_get_ctx(bmap);
4077 struct isl_hash_table *table = NULL;
4078 struct isl_hash_table_entry *entry;
4079 struct isl_constraint_equal_info info;
4080 unsigned n_out;
4081 unsigned n_div;
4083 ctx = isl_basic_map_get_ctx(bmap);
4084 table = isl_hash_table_alloc(ctx, bmap->n_ineq);
4085 if (!table)
4086 goto error;
4088 info.n_in = isl_basic_map_dim(bmap, isl_dim_param) +
4089 isl_basic_map_dim(bmap, isl_dim_in);
4090 info.bmap = bmap;
4091 n_out = isl_basic_map_dim(bmap, isl_dim_out);
4092 n_div = isl_basic_map_dim(bmap, isl_dim_div);
4093 info.n_out = n_out + n_div;
4094 for (i = 0; i < bmap->n_ineq; ++i) {
4095 uint32_t hash;
4097 info.val = bmap->ineq[i] + 1 + info.n_in;
4098 if (isl_seq_first_non_zero(info.val, n_out) < 0)
4099 continue;
4100 if (isl_seq_first_non_zero(info.val + n_out, n_div) >= 0)
4101 continue;
4102 hash = isl_seq_get_hash(info.val, info.n_out);
4103 entry = isl_hash_table_find(ctx, table, hash,
4104 constraint_equal, &info, 1);
4105 if (!entry)
4106 goto error;
4107 if (entry->data)
4108 break;
4109 entry->data = &bmap->ineq[i];
4112 if (i < bmap->n_ineq) {
4113 *first = ((isl_int **)entry->data) - bmap->ineq;
4114 *second = i;
4117 isl_hash_table_free(ctx, table);
4119 return i < bmap->n_ineq;
4120 error:
4121 isl_hash_table_free(ctx, table);
4122 return -1;
4125 /* Given a set of upper bounds in "var", add constraints to "bset"
4126 * that make the i-th bound smallest.
4128 * In particular, if there are n bounds b_i, then add the constraints
4130 * b_i <= b_j for j > i
4131 * b_i < b_j for j < i
4133 static __isl_give isl_basic_set *select_minimum(__isl_take isl_basic_set *bset,
4134 __isl_keep isl_mat *var, int i)
4136 isl_ctx *ctx;
4137 int j, k;
4139 ctx = isl_mat_get_ctx(var);
4141 for (j = 0; j < var->n_row; ++j) {
4142 if (j == i)
4143 continue;
4144 k = isl_basic_set_alloc_inequality(bset);
4145 if (k < 0)
4146 goto error;
4147 isl_seq_combine(bset->ineq[k], ctx->one, var->row[j],
4148 ctx->negone, var->row[i], var->n_col);
4149 isl_int_set_si(bset->ineq[k][var->n_col], 0);
4150 if (j < i)
4151 isl_int_sub_ui(bset->ineq[k][0], bset->ineq[k][0], 1);
4154 bset = isl_basic_set_finalize(bset);
4156 return bset;
4157 error:
4158 isl_basic_set_free(bset);
4159 return NULL;
4162 /* Given a set of upper bounds on the last "input" variable m,
4163 * construct a set that assigns the minimal upper bound to m, i.e.,
4164 * construct a set that divides the space into cells where one
4165 * of the upper bounds is smaller than all the others and assign
4166 * this upper bound to m.
4168 * In particular, if there are n bounds b_i, then the result
4169 * consists of n basic sets, each one of the form
4171 * m = b_i
4172 * b_i <= b_j for j > i
4173 * b_i < b_j for j < i
4175 static __isl_give isl_set *set_minimum(__isl_take isl_space *dim,
4176 __isl_take isl_mat *var)
4178 int i, k;
4179 isl_basic_set *bset = NULL;
4180 isl_ctx *ctx;
4181 isl_set *set = NULL;
4183 if (!dim || !var)
4184 goto error;
4186 ctx = isl_space_get_ctx(dim);
4187 set = isl_set_alloc_space(isl_space_copy(dim),
4188 var->n_row, ISL_SET_DISJOINT);
4190 for (i = 0; i < var->n_row; ++i) {
4191 bset = isl_basic_set_alloc_space(isl_space_copy(dim), 0,
4192 1, var->n_row - 1);
4193 k = isl_basic_set_alloc_equality(bset);
4194 if (k < 0)
4195 goto error;
4196 isl_seq_cpy(bset->eq[k], var->row[i], var->n_col);
4197 isl_int_set_si(bset->eq[k][var->n_col], -1);
4198 bset = select_minimum(bset, var, i);
4199 set = isl_set_add_basic_set(set, bset);
4202 isl_space_free(dim);
4203 isl_mat_free(var);
4204 return set;
4205 error:
4206 isl_basic_set_free(bset);
4207 isl_set_free(set);
4208 isl_space_free(dim);
4209 isl_mat_free(var);
4210 return NULL;
4213 /* Given that the last input variable of "bmap" represents the minimum
4214 * of the bounds in "cst", check whether we need to split the domain
4215 * based on which bound attains the minimum.
4217 * A split is needed when the minimum appears in an integer division
4218 * or in an equality. Otherwise, it is only needed if it appears in
4219 * an upper bound that is different from the upper bounds on which it
4220 * is defined.
4222 static int need_split_basic_map(__isl_keep isl_basic_map *bmap,
4223 __isl_keep isl_mat *cst)
4225 int i, j;
4226 unsigned total;
4227 unsigned pos;
4229 pos = cst->n_col - 1;
4230 total = isl_basic_map_dim(bmap, isl_dim_all);
4232 for (i = 0; i < bmap->n_div; ++i)
4233 if (!isl_int_is_zero(bmap->div[i][2 + pos]))
4234 return 1;
4236 for (i = 0; i < bmap->n_eq; ++i)
4237 if (!isl_int_is_zero(bmap->eq[i][1 + pos]))
4238 return 1;
4240 for (i = 0; i < bmap->n_ineq; ++i) {
4241 if (isl_int_is_nonneg(bmap->ineq[i][1 + pos]))
4242 continue;
4243 if (!isl_int_is_negone(bmap->ineq[i][1 + pos]))
4244 return 1;
4245 if (isl_seq_first_non_zero(bmap->ineq[i] + 1 + pos + 1,
4246 total - pos - 1) >= 0)
4247 return 1;
4249 for (j = 0; j < cst->n_row; ++j)
4250 if (isl_seq_eq(bmap->ineq[i], cst->row[j], cst->n_col))
4251 break;
4252 if (j >= cst->n_row)
4253 return 1;
4256 return 0;
4259 /* Given that the last set variable of "bset" represents the minimum
4260 * of the bounds in "cst", check whether we need to split the domain
4261 * based on which bound attains the minimum.
4263 * We simply call need_split_basic_map here. This is safe because
4264 * the position of the minimum is computed from "cst" and not
4265 * from "bmap".
4267 static int need_split_basic_set(__isl_keep isl_basic_set *bset,
4268 __isl_keep isl_mat *cst)
4270 return need_split_basic_map((isl_basic_map *)bset, cst);
4273 /* Given that the last set variable of "set" represents the minimum
4274 * of the bounds in "cst", check whether we need to split the domain
4275 * based on which bound attains the minimum.
4277 static int need_split_set(__isl_keep isl_set *set, __isl_keep isl_mat *cst)
4279 int i;
4281 for (i = 0; i < set->n; ++i)
4282 if (need_split_basic_set(set->p[i], cst))
4283 return 1;
4285 return 0;
4288 /* Given a set of which the last set variable is the minimum
4289 * of the bounds in "cst", split each basic set in the set
4290 * in pieces where one of the bounds is (strictly) smaller than the others.
4291 * This subdivision is given in "min_expr".
4292 * The variable is subsequently projected out.
4294 * We only do the split when it is needed.
4295 * For example if the last input variable m = min(a,b) and the only
4296 * constraints in the given basic set are lower bounds on m,
4297 * i.e., l <= m = min(a,b), then we can simply project out m
4298 * to obtain l <= a and l <= b, without having to split on whether
4299 * m is equal to a or b.
4301 static __isl_give isl_set *split(__isl_take isl_set *empty,
4302 __isl_take isl_set *min_expr, __isl_take isl_mat *cst)
4304 int n_in;
4305 int i;
4306 isl_space *dim;
4307 isl_set *res;
4309 if (!empty || !min_expr || !cst)
4310 goto error;
4312 n_in = isl_set_dim(empty, isl_dim_set);
4313 dim = isl_set_get_space(empty);
4314 dim = isl_space_drop_dims(dim, isl_dim_set, n_in - 1, 1);
4315 res = isl_set_empty(dim);
4317 for (i = 0; i < empty->n; ++i) {
4318 isl_set *set;
4320 set = isl_set_from_basic_set(isl_basic_set_copy(empty->p[i]));
4321 if (need_split_basic_set(empty->p[i], cst))
4322 set = isl_set_intersect(set, isl_set_copy(min_expr));
4323 set = isl_set_remove_dims(set, isl_dim_set, n_in - 1, 1);
4325 res = isl_set_union_disjoint(res, set);
4328 isl_set_free(empty);
4329 isl_set_free(min_expr);
4330 isl_mat_free(cst);
4331 return res;
4332 error:
4333 isl_set_free(empty);
4334 isl_set_free(min_expr);
4335 isl_mat_free(cst);
4336 return NULL;
4339 /* Given a map of which the last input variable is the minimum
4340 * of the bounds in "cst", split each basic set in the set
4341 * in pieces where one of the bounds is (strictly) smaller than the others.
4342 * This subdivision is given in "min_expr".
4343 * The variable is subsequently projected out.
4345 * The implementation is essentially the same as that of "split".
4347 static __isl_give isl_map *split_domain(__isl_take isl_map *opt,
4348 __isl_take isl_set *min_expr, __isl_take isl_mat *cst)
4350 int n_in;
4351 int i;
4352 isl_space *dim;
4353 isl_map *res;
4355 if (!opt || !min_expr || !cst)
4356 goto error;
4358 n_in = isl_map_dim(opt, isl_dim_in);
4359 dim = isl_map_get_space(opt);
4360 dim = isl_space_drop_dims(dim, isl_dim_in, n_in - 1, 1);
4361 res = isl_map_empty(dim);
4363 for (i = 0; i < opt->n; ++i) {
4364 isl_map *map;
4366 map = isl_map_from_basic_map(isl_basic_map_copy(opt->p[i]));
4367 if (need_split_basic_map(opt->p[i], cst))
4368 map = isl_map_intersect_domain(map,
4369 isl_set_copy(min_expr));
4370 map = isl_map_remove_dims(map, isl_dim_in, n_in - 1, 1);
4372 res = isl_map_union_disjoint(res, map);
4375 isl_map_free(opt);
4376 isl_set_free(min_expr);
4377 isl_mat_free(cst);
4378 return res;
4379 error:
4380 isl_map_free(opt);
4381 isl_set_free(min_expr);
4382 isl_mat_free(cst);
4383 return NULL;
4386 static __isl_give isl_map *basic_map_partial_lexopt(
4387 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
4388 __isl_give isl_set **empty, int max);
4390 union isl_lex_res {
4391 void *p;
4392 isl_map *map;
4393 isl_pw_multi_aff *pma;
4396 /* This function is called from basic_map_partial_lexopt_symm.
4397 * The last variable of "bmap" and "dom" corresponds to the minimum
4398 * of the bounds in "cst". "map_space" is the space of the original
4399 * input relation (of basic_map_partial_lexopt_symm) and "set_space"
4400 * is the space of the original domain.
4402 * We recursively call basic_map_partial_lexopt and then plug in
4403 * the definition of the minimum in the result.
4405 static __isl_give union isl_lex_res basic_map_partial_lexopt_symm_map_core(
4406 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
4407 __isl_give isl_set **empty, int max, __isl_take isl_mat *cst,
4408 __isl_take isl_space *map_space, __isl_take isl_space *set_space)
4410 isl_map *opt;
4411 isl_set *min_expr;
4412 union isl_lex_res res;
4414 min_expr = set_minimum(isl_basic_set_get_space(dom), isl_mat_copy(cst));
4416 opt = basic_map_partial_lexopt(bmap, dom, empty, max);
4418 if (empty) {
4419 *empty = split(*empty,
4420 isl_set_copy(min_expr), isl_mat_copy(cst));
4421 *empty = isl_set_reset_space(*empty, set_space);
4424 opt = split_domain(opt, min_expr, cst);
4425 opt = isl_map_reset_space(opt, map_space);
4427 res.map = opt;
4428 return res;
4431 /* Given a basic map with at least two parallel constraints (as found
4432 * by the function parallel_constraints), first look for more constraints
4433 * parallel to the two constraint and replace the found list of parallel
4434 * constraints by a single constraint with as "input" part the minimum
4435 * of the input parts of the list of constraints. Then, recursively call
4436 * basic_map_partial_lexopt (possibly finding more parallel constraints)
4437 * and plug in the definition of the minimum in the result.
4439 * More specifically, given a set of constraints
4441 * a x + b_i(p) >= 0
4443 * Replace this set by a single constraint
4445 * a x + u >= 0
4447 * with u a new parameter with constraints
4449 * u <= b_i(p)
4451 * Any solution to the new system is also a solution for the original system
4452 * since
4454 * a x >= -u >= -b_i(p)
4456 * Moreover, m = min_i(b_i(p)) satisfies the constraints on u and can
4457 * therefore be plugged into the solution.
4459 static union isl_lex_res basic_map_partial_lexopt_symm(
4460 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
4461 __isl_give isl_set **empty, int max, int first, int second,
4462 __isl_give union isl_lex_res (*core)(__isl_take isl_basic_map *bmap,
4463 __isl_take isl_basic_set *dom,
4464 __isl_give isl_set **empty,
4465 int max, __isl_take isl_mat *cst,
4466 __isl_take isl_space *map_space,
4467 __isl_take isl_space *set_space))
4469 int i, n, k;
4470 int *list = NULL;
4471 unsigned n_in, n_out, n_div;
4472 isl_ctx *ctx;
4473 isl_vec *var = NULL;
4474 isl_mat *cst = NULL;
4475 isl_space *map_space, *set_space;
4476 union isl_lex_res res;
4478 map_space = isl_basic_map_get_space(bmap);
4479 set_space = empty ? isl_basic_set_get_space(dom) : NULL;
4481 n_in = isl_basic_map_dim(bmap, isl_dim_param) +
4482 isl_basic_map_dim(bmap, isl_dim_in);
4483 n_out = isl_basic_map_dim(bmap, isl_dim_all) - n_in;
4485 ctx = isl_basic_map_get_ctx(bmap);
4486 list = isl_alloc_array(ctx, int, bmap->n_ineq);
4487 var = isl_vec_alloc(ctx, n_out);
4488 if (!list || !var)
4489 goto error;
4491 list[0] = first;
4492 list[1] = second;
4493 isl_seq_cpy(var->el, bmap->ineq[first] + 1 + n_in, n_out);
4494 for (i = second + 1, n = 2; i < bmap->n_ineq; ++i) {
4495 if (isl_seq_eq(var->el, bmap->ineq[i] + 1 + n_in, n_out))
4496 list[n++] = i;
4499 cst = isl_mat_alloc(ctx, n, 1 + n_in);
4500 if (!cst)
4501 goto error;
4503 for (i = 0; i < n; ++i)
4504 isl_seq_cpy(cst->row[i], bmap->ineq[list[i]], 1 + n_in);
4506 bmap = isl_basic_map_cow(bmap);
4507 if (!bmap)
4508 goto error;
4509 for (i = n - 1; i >= 0; --i)
4510 if (isl_basic_map_drop_inequality(bmap, list[i]) < 0)
4511 goto error;
4513 bmap = isl_basic_map_add(bmap, isl_dim_in, 1);
4514 bmap = isl_basic_map_extend_constraints(bmap, 0, 1);
4515 k = isl_basic_map_alloc_inequality(bmap);
4516 if (k < 0)
4517 goto error;
4518 isl_seq_clr(bmap->ineq[k], 1 + n_in);
4519 isl_int_set_si(bmap->ineq[k][1 + n_in], 1);
4520 isl_seq_cpy(bmap->ineq[k] + 1 + n_in + 1, var->el, n_out);
4521 bmap = isl_basic_map_finalize(bmap);
4523 n_div = isl_basic_set_dim(dom, isl_dim_div);
4524 dom = isl_basic_set_add(dom, isl_dim_set, 1);
4525 dom = isl_basic_set_extend_constraints(dom, 0, n);
4526 for (i = 0; i < n; ++i) {
4527 k = isl_basic_set_alloc_inequality(dom);
4528 if (k < 0)
4529 goto error;
4530 isl_seq_cpy(dom->ineq[k], cst->row[i], 1 + n_in);
4531 isl_int_set_si(dom->ineq[k][1 + n_in], -1);
4532 isl_seq_clr(dom->ineq[k] + 1 + n_in + 1, n_div);
4535 isl_vec_free(var);
4536 free(list);
4538 return core(bmap, dom, empty, max, cst, map_space, set_space);
4539 error:
4540 isl_space_free(map_space);
4541 isl_space_free(set_space);
4542 isl_mat_free(cst);
4543 isl_vec_free(var);
4544 free(list);
4545 isl_basic_set_free(dom);
4546 isl_basic_map_free(bmap);
4547 res.p = NULL;
4548 return res;
4551 static __isl_give isl_map *basic_map_partial_lexopt_symm_map(
4552 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
4553 __isl_give isl_set **empty, int max, int first, int second)
4555 return basic_map_partial_lexopt_symm(bmap, dom, empty, max,
4556 first, second, &basic_map_partial_lexopt_symm_map_core).map;
4559 /* Recursive part of isl_tab_basic_map_partial_lexopt, after detecting
4560 * equalities and removing redundant constraints.
4562 * We first check if there are any parallel constraints (left).
4563 * If not, we are in the base case.
4564 * If there are parallel constraints, we replace them by a single
4565 * constraint in basic_map_partial_lexopt_symm and then call
4566 * this function recursively to look for more parallel constraints.
4568 static __isl_give isl_map *basic_map_partial_lexopt(
4569 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
4570 __isl_give isl_set **empty, int max)
4572 int par = 0;
4573 int first, second;
4575 if (!bmap)
4576 goto error;
4578 if (bmap->ctx->opt->pip_symmetry)
4579 par = parallel_constraints(bmap, &first, &second);
4580 if (par < 0)
4581 goto error;
4582 if (!par)
4583 return basic_map_partial_lexopt_base_map(bmap, dom, empty, max);
4585 return basic_map_partial_lexopt_symm_map(bmap, dom, empty, max,
4586 first, second);
4587 error:
4588 isl_basic_set_free(dom);
4589 isl_basic_map_free(bmap);
4590 return NULL;
4593 /* Compute the lexicographic minimum (or maximum if "max" is set)
4594 * of "bmap" over the domain "dom" and return the result as a map.
4595 * If "empty" is not NULL, then *empty is assigned a set that
4596 * contains those parts of the domain where there is no solution.
4597 * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
4598 * then we compute the rational optimum. Otherwise, we compute
4599 * the integral optimum.
4601 * We perform some preprocessing. As the PILP solver does not
4602 * handle implicit equalities very well, we first make sure all
4603 * the equalities are explicitly available.
4605 * We also add context constraints to the basic map and remove
4606 * redundant constraints. This is only needed because of the
4607 * way we handle simple symmetries. In particular, we currently look
4608 * for symmetries on the constraints, before we set up the main tableau.
4609 * It is then no good to look for symmetries on possibly redundant constraints.
4611 struct isl_map *isl_tab_basic_map_partial_lexopt(
4612 struct isl_basic_map *bmap, struct isl_basic_set *dom,
4613 struct isl_set **empty, int max)
4615 if (empty)
4616 *empty = NULL;
4617 if (!bmap || !dom)
4618 goto error;
4620 isl_assert(bmap->ctx,
4621 isl_basic_map_compatible_domain(bmap, dom), goto error);
4623 if (isl_basic_set_dim(dom, isl_dim_all) == 0)
4624 return basic_map_partial_lexopt(bmap, dom, empty, max);
4626 bmap = isl_basic_map_intersect_domain(bmap, isl_basic_set_copy(dom));
4627 bmap = isl_basic_map_detect_equalities(bmap);
4628 bmap = isl_basic_map_remove_redundancies(bmap);
4630 return basic_map_partial_lexopt(bmap, dom, empty, max);
4631 error:
4632 isl_basic_set_free(dom);
4633 isl_basic_map_free(bmap);
4634 return NULL;
4637 struct isl_sol_for {
4638 struct isl_sol sol;
4639 int (*fn)(__isl_take isl_basic_set *dom,
4640 __isl_take isl_aff_list *list, void *user);
4641 void *user;
4644 static void sol_for_free(struct isl_sol_for *sol_for)
4646 if (sol_for->sol.context)
4647 sol_for->sol.context->op->free(sol_for->sol.context);
4648 free(sol_for);
4651 static void sol_for_free_wrap(struct isl_sol *sol)
4653 sol_for_free((struct isl_sol_for *)sol);
4656 /* Add the solution identified by the tableau and the context tableau.
4658 * See documentation of sol_add for more details.
4660 * Instead of constructing a basic map, this function calls a user
4661 * defined function with the current context as a basic set and
4662 * a list of affine expressions representing the relation between
4663 * the input and output. The space over which the affine expressions
4664 * are defined is the same as that of the domain. The number of
4665 * affine expressions in the list is equal to the number of output variables.
4667 static void sol_for_add(struct isl_sol_for *sol,
4668 struct isl_basic_set *dom, struct isl_mat *M)
4670 int i;
4671 isl_ctx *ctx;
4672 isl_local_space *ls;
4673 isl_aff *aff;
4674 isl_aff_list *list;
4676 if (sol->sol.error || !dom || !M)
4677 goto error;
4679 ctx = isl_basic_set_get_ctx(dom);
4680 ls = isl_basic_set_get_local_space(dom);
4681 list = isl_aff_list_alloc(ctx, M->n_row - 1);
4682 for (i = 1; i < M->n_row; ++i) {
4683 aff = isl_aff_alloc(isl_local_space_copy(ls));
4684 if (aff) {
4685 isl_int_set(aff->v->el[0], M->row[0][0]);
4686 isl_seq_cpy(aff->v->el + 1, M->row[i], M->n_col);
4688 aff = isl_aff_normalize(aff);
4689 list = isl_aff_list_add(list, aff);
4691 isl_local_space_free(ls);
4693 dom = isl_basic_set_finalize(dom);
4695 if (sol->fn(isl_basic_set_copy(dom), list, sol->user) < 0)
4696 goto error;
4698 isl_basic_set_free(dom);
4699 isl_mat_free(M);
4700 return;
4701 error:
4702 isl_basic_set_free(dom);
4703 isl_mat_free(M);
4704 sol->sol.error = 1;
4707 static void sol_for_add_wrap(struct isl_sol *sol,
4708 struct isl_basic_set *dom, struct isl_mat *M)
4710 sol_for_add((struct isl_sol_for *)sol, dom, M);
4713 static struct isl_sol_for *sol_for_init(struct isl_basic_map *bmap, int max,
4714 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
4715 void *user),
4716 void *user)
4718 struct isl_sol_for *sol_for = NULL;
4719 isl_space *dom_dim;
4720 struct isl_basic_set *dom = NULL;
4722 sol_for = isl_calloc_type(bmap->ctx, struct isl_sol_for);
4723 if (!sol_for)
4724 goto error;
4726 dom_dim = isl_space_domain(isl_space_copy(bmap->dim));
4727 dom = isl_basic_set_universe(dom_dim);
4729 sol_for->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
4730 sol_for->sol.dec_level.callback.run = &sol_dec_level_wrap;
4731 sol_for->sol.dec_level.sol = &sol_for->sol;
4732 sol_for->fn = fn;
4733 sol_for->user = user;
4734 sol_for->sol.max = max;
4735 sol_for->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
4736 sol_for->sol.add = &sol_for_add_wrap;
4737 sol_for->sol.add_empty = NULL;
4738 sol_for->sol.free = &sol_for_free_wrap;
4740 sol_for->sol.context = isl_context_alloc(dom);
4741 if (!sol_for->sol.context)
4742 goto error;
4744 isl_basic_set_free(dom);
4745 return sol_for;
4746 error:
4747 isl_basic_set_free(dom);
4748 sol_for_free(sol_for);
4749 return NULL;
4752 static void sol_for_find_solutions(struct isl_sol_for *sol_for,
4753 struct isl_tab *tab)
4755 find_solutions_main(&sol_for->sol, tab);
4758 int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map *bmap, int max,
4759 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
4760 void *user),
4761 void *user)
4763 struct isl_sol_for *sol_for = NULL;
4765 bmap = isl_basic_map_copy(bmap);
4766 if (!bmap)
4767 return -1;
4769 bmap = isl_basic_map_detect_equalities(bmap);
4770 sol_for = sol_for_init(bmap, max, fn, user);
4772 if (isl_basic_map_plain_is_empty(bmap))
4773 /* nothing */;
4774 else {
4775 struct isl_tab *tab;
4776 struct isl_context *context = sol_for->sol.context;
4777 tab = tab_for_lexmin(bmap,
4778 context->op->peek_basic_set(context), 1, max);
4779 tab = context->op->detect_nonnegative_parameters(context, tab);
4780 sol_for_find_solutions(sol_for, tab);
4781 if (sol_for->sol.error)
4782 goto error;
4785 sol_free(&sol_for->sol);
4786 isl_basic_map_free(bmap);
4787 return 0;
4788 error:
4789 sol_free(&sol_for->sol);
4790 isl_basic_map_free(bmap);
4791 return -1;
4794 int isl_basic_set_foreach_lexopt(__isl_keep isl_basic_set *bset, int max,
4795 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_aff_list *list,
4796 void *user),
4797 void *user)
4799 return isl_basic_map_foreach_lexopt(bset, max, fn, user);
4802 /* Check if the given sequence of len variables starting at pos
4803 * represents a trivial (i.e., zero) solution.
4804 * The variables are assumed to be non-negative and to come in pairs,
4805 * with each pair representing a variable of unrestricted sign.
4806 * The solution is trivial if each such pair in the sequence consists
4807 * of two identical values, meaning that the variable being represented
4808 * has value zero.
4810 static int region_is_trivial(struct isl_tab *tab, int pos, int len)
4812 int i;
4814 if (len == 0)
4815 return 0;
4817 for (i = 0; i < len; i += 2) {
4818 int neg_row;
4819 int pos_row;
4821 neg_row = tab->var[pos + i].is_row ?
4822 tab->var[pos + i].index : -1;
4823 pos_row = tab->var[pos + i + 1].is_row ?
4824 tab->var[pos + i + 1].index : -1;
4826 if ((neg_row < 0 ||
4827 isl_int_is_zero(tab->mat->row[neg_row][1])) &&
4828 (pos_row < 0 ||
4829 isl_int_is_zero(tab->mat->row[pos_row][1])))
4830 continue;
4832 if (neg_row < 0 || pos_row < 0)
4833 return 0;
4834 if (isl_int_ne(tab->mat->row[neg_row][1],
4835 tab->mat->row[pos_row][1]))
4836 return 0;
4839 return 1;
4842 /* Return the index of the first trivial region or -1 if all regions
4843 * are non-trivial.
4845 static int first_trivial_region(struct isl_tab *tab,
4846 int n_region, struct isl_region *region)
4848 int i;
4850 for (i = 0; i < n_region; ++i) {
4851 if (region_is_trivial(tab, region[i].pos, region[i].len))
4852 return i;
4855 return -1;
4858 /* Check if the solution is optimal, i.e., whether the first
4859 * n_op entries are zero.
4861 static int is_optimal(__isl_keep isl_vec *sol, int n_op)
4863 int i;
4865 for (i = 0; i < n_op; ++i)
4866 if (!isl_int_is_zero(sol->el[1 + i]))
4867 return 0;
4868 return 1;
4871 /* Add constraints to "tab" that ensure that any solution is significantly
4872 * better that that represented by "sol". That is, find the first
4873 * relevant (within first n_op) non-zero coefficient and force it (along
4874 * with all previous coefficients) to be zero.
4875 * If the solution is already optimal (all relevant coefficients are zero),
4876 * then just mark the table as empty.
4878 static int force_better_solution(struct isl_tab *tab,
4879 __isl_keep isl_vec *sol, int n_op)
4881 int i;
4882 isl_ctx *ctx;
4883 isl_vec *v = NULL;
4885 if (!sol)
4886 return -1;
4888 for (i = 0; i < n_op; ++i)
4889 if (!isl_int_is_zero(sol->el[1 + i]))
4890 break;
4892 if (i == n_op) {
4893 if (isl_tab_mark_empty(tab) < 0)
4894 return -1;
4895 return 0;
4898 ctx = isl_vec_get_ctx(sol);
4899 v = isl_vec_alloc(ctx, 1 + tab->n_var);
4900 if (!v)
4901 return -1;
4903 for (; i >= 0; --i) {
4904 v = isl_vec_clr(v);
4905 isl_int_set_si(v->el[1 + i], -1);
4906 if (add_lexmin_eq(tab, v->el) < 0)
4907 goto error;
4910 isl_vec_free(v);
4911 return 0;
4912 error:
4913 isl_vec_free(v);
4914 return -1;
4917 struct isl_trivial {
4918 int update;
4919 int region;
4920 int side;
4921 struct isl_tab_undo *snap;
4924 /* Return the lexicographically smallest non-trivial solution of the
4925 * given ILP problem.
4927 * All variables are assumed to be non-negative.
4929 * n_op is the number of initial coordinates to optimize.
4930 * That is, once a solution has been found, we will only continue looking
4931 * for solution that result in significantly better values for those
4932 * initial coordinates. That is, we only continue looking for solutions
4933 * that increase the number of initial zeros in this sequence.
4935 * A solution is non-trivial, if it is non-trivial on each of the
4936 * specified regions. Each region represents a sequence of pairs
4937 * of variables. A solution is non-trivial on such a region if
4938 * at least one of these pairs consists of different values, i.e.,
4939 * such that the non-negative variable represented by the pair is non-zero.
4941 * Whenever a conflict is encountered, all constraints involved are
4942 * reported to the caller through a call to "conflict".
4944 * We perform a simple branch-and-bound backtracking search.
4945 * Each level in the search represents initially trivial region that is forced
4946 * to be non-trivial.
4947 * At each level we consider n cases, where n is the length of the region.
4948 * In terms of the n/2 variables of unrestricted signs being encoded by
4949 * the region, we consider the cases
4950 * x_0 >= 1
4951 * x_0 <= -1
4952 * x_0 = 0 and x_1 >= 1
4953 * x_0 = 0 and x_1 <= -1
4954 * x_0 = 0 and x_1 = 0 and x_2 >= 1
4955 * x_0 = 0 and x_1 = 0 and x_2 <= -1
4956 * ...
4957 * The cases are considered in this order, assuming that each pair
4958 * x_i_a x_i_b represents the value x_i_b - x_i_a.
4959 * That is, x_0 >= 1 is enforced by adding the constraint
4960 * x_0_b - x_0_a >= 1
4962 __isl_give isl_vec *isl_tab_basic_set_non_trivial_lexmin(
4963 __isl_take isl_basic_set *bset, int n_op, int n_region,
4964 struct isl_region *region,
4965 int (*conflict)(int con, void *user), void *user)
4967 int i, j;
4968 int r;
4969 isl_ctx *ctx = isl_basic_set_get_ctx(bset);
4970 isl_vec *v = NULL;
4971 isl_vec *sol = isl_vec_alloc(ctx, 0);
4972 struct isl_tab *tab;
4973 struct isl_trivial *triv = NULL;
4974 int level, init;
4976 tab = tab_for_lexmin(bset, NULL, 0, 0);
4977 if (!tab)
4978 goto error;
4979 tab->conflict = conflict;
4980 tab->conflict_user = user;
4982 v = isl_vec_alloc(ctx, 1 + tab->n_var);
4983 triv = isl_calloc_array(ctx, struct isl_trivial, n_region);
4984 if (!v || !triv)
4985 goto error;
4987 level = 0;
4988 init = 1;
4990 while (level >= 0) {
4991 int side, base;
4993 if (init) {
4994 tab = cut_to_integer_lexmin(tab, CUT_ONE);
4995 if (!tab)
4996 goto error;
4997 if (tab->empty)
4998 goto backtrack;
4999 r = first_trivial_region(tab, n_region, region);
5000 if (r < 0) {
5001 for (i = 0; i < level; ++i)
5002 triv[i].update = 1;
5003 isl_vec_free(sol);
5004 sol = isl_tab_get_sample_value(tab);
5005 if (!sol)
5006 goto error;
5007 if (is_optimal(sol, n_op))
5008 break;
5009 goto backtrack;
5011 if (level >= n_region)
5012 isl_die(ctx, isl_error_internal,
5013 "nesting level too deep", goto error);
5014 if (isl_tab_extend_cons(tab,
5015 2 * region[r].len + 2 * n_op) < 0)
5016 goto error;
5017 triv[level].region = r;
5018 triv[level].side = 0;
5021 r = triv[level].region;
5022 side = triv[level].side;
5023 base = 2 * (side/2);
5025 if (side >= region[r].len) {
5026 backtrack:
5027 level--;
5028 init = 0;
5029 if (level >= 0)
5030 if (isl_tab_rollback(tab, triv[level].snap) < 0)
5031 goto error;
5032 continue;
5035 if (triv[level].update) {
5036 if (force_better_solution(tab, sol, n_op) < 0)
5037 goto error;
5038 triv[level].update = 0;
5041 if (side == base && base >= 2) {
5042 for (j = base - 2; j < base; ++j) {
5043 v = isl_vec_clr(v);
5044 isl_int_set_si(v->el[1 + region[r].pos + j], 1);
5045 if (add_lexmin_eq(tab, v->el) < 0)
5046 goto error;
5050 triv[level].snap = isl_tab_snap(tab);
5051 if (isl_tab_push_basis(tab) < 0)
5052 goto error;
5054 v = isl_vec_clr(v);
5055 isl_int_set_si(v->el[0], -1);
5056 isl_int_set_si(v->el[1 + region[r].pos + side], -1);
5057 isl_int_set_si(v->el[1 + region[r].pos + (side ^ 1)], 1);
5058 tab = add_lexmin_ineq(tab, v->el);
5060 triv[level].side++;
5061 level++;
5062 init = 1;
5065 free(triv);
5066 isl_vec_free(v);
5067 isl_tab_free(tab);
5068 isl_basic_set_free(bset);
5070 return sol;
5071 error:
5072 free(triv);
5073 isl_vec_free(v);
5074 isl_tab_free(tab);
5075 isl_basic_set_free(bset);
5076 isl_vec_free(sol);
5077 return NULL;
5080 /* Return the lexicographically smallest rational point in "bset",
5081 * assuming that all variables are non-negative.
5082 * If "bset" is empty, then return a zero-length vector.
5084 __isl_give isl_vec *isl_tab_basic_set_non_neg_lexmin(
5085 __isl_take isl_basic_set *bset)
5087 struct isl_tab *tab;
5088 isl_ctx *ctx = isl_basic_set_get_ctx(bset);
5089 isl_vec *sol;
5091 tab = tab_for_lexmin(bset, NULL, 0, 0);
5092 if (!tab)
5093 goto error;
5094 if (tab->empty)
5095 sol = isl_vec_alloc(ctx, 0);
5096 else
5097 sol = isl_tab_get_sample_value(tab);
5098 isl_tab_free(tab);
5099 isl_basic_set_free(bset);
5100 return sol;
5101 error:
5102 isl_tab_free(tab);
5103 isl_basic_set_free(bset);
5104 return NULL;
5107 struct isl_sol_pma {
5108 struct isl_sol sol;
5109 isl_pw_multi_aff *pma;
5110 isl_set *empty;
5113 static void sol_pma_free(struct isl_sol_pma *sol_pma)
5115 if (!sol_pma)
5116 return;
5117 if (sol_pma->sol.context)
5118 sol_pma->sol.context->op->free(sol_pma->sol.context);
5119 isl_pw_multi_aff_free(sol_pma->pma);
5120 isl_set_free(sol_pma->empty);
5121 free(sol_pma);
5124 /* This function is called for parts of the context where there is
5125 * no solution, with "bset" corresponding to the context tableau.
5126 * Simply add the basic set to the set "empty".
5128 static void sol_pma_add_empty(struct isl_sol_pma *sol,
5129 __isl_take isl_basic_set *bset)
5131 if (!bset)
5132 goto error;
5133 isl_assert(bset->ctx, sol->empty, goto error);
5135 sol->empty = isl_set_grow(sol->empty, 1);
5136 bset = isl_basic_set_simplify(bset);
5137 bset = isl_basic_set_finalize(bset);
5138 sol->empty = isl_set_add_basic_set(sol->empty, bset);
5139 if (!sol->empty)
5140 sol->sol.error = 1;
5141 return;
5142 error:
5143 isl_basic_set_free(bset);
5144 sol->sol.error = 1;
5147 /* Given a basic map "dom" that represents the context and an affine
5148 * matrix "M" that maps the dimensions of the context to the
5149 * output variables, construct an isl_pw_multi_aff with a single
5150 * cell corresponding to "dom" and affine expressions copied from "M".
5152 static void sol_pma_add(struct isl_sol_pma *sol,
5153 __isl_take isl_basic_set *dom, __isl_take isl_mat *M)
5155 int i;
5156 isl_local_space *ls;
5157 isl_aff *aff;
5158 isl_multi_aff *maff;
5159 isl_pw_multi_aff *pma;
5161 maff = isl_multi_aff_alloc(isl_pw_multi_aff_get_space(sol->pma));
5162 ls = isl_basic_set_get_local_space(dom);
5163 for (i = 1; i < M->n_row; ++i) {
5164 aff = isl_aff_alloc(isl_local_space_copy(ls));
5165 if (aff) {
5166 isl_int_set(aff->v->el[0], M->row[0][0]);
5167 isl_seq_cpy(aff->v->el + 1, M->row[i], M->n_col);
5169 aff = isl_aff_normalize(aff);
5170 maff = isl_multi_aff_set_aff(maff, i - 1, aff);
5172 isl_local_space_free(ls);
5173 isl_mat_free(M);
5174 dom = isl_basic_set_simplify(dom);
5175 dom = isl_basic_set_finalize(dom);
5176 pma = isl_pw_multi_aff_alloc(isl_set_from_basic_set(dom), maff);
5177 sol->pma = isl_pw_multi_aff_add_disjoint(sol->pma, pma);
5178 if (!sol->pma)
5179 sol->sol.error = 1;
5182 static void sol_pma_free_wrap(struct isl_sol *sol)
5184 sol_pma_free((struct isl_sol_pma *)sol);
5187 static void sol_pma_add_empty_wrap(struct isl_sol *sol,
5188 __isl_take isl_basic_set *bset)
5190 sol_pma_add_empty((struct isl_sol_pma *)sol, bset);
5193 static void sol_pma_add_wrap(struct isl_sol *sol,
5194 __isl_take isl_basic_set *dom, __isl_take isl_mat *M)
5196 sol_pma_add((struct isl_sol_pma *)sol, dom, M);
5199 /* Construct an isl_sol_pma structure for accumulating the solution.
5200 * If track_empty is set, then we also keep track of the parts
5201 * of the context where there is no solution.
5202 * If max is set, then we are solving a maximization, rather than
5203 * a minimization problem, which means that the variables in the
5204 * tableau have value "M - x" rather than "M + x".
5206 static struct isl_sol *sol_pma_init(__isl_keep isl_basic_map *bmap,
5207 __isl_take isl_basic_set *dom, int track_empty, int max)
5209 struct isl_sol_pma *sol_pma = NULL;
5211 if (!bmap)
5212 goto error;
5214 sol_pma = isl_calloc_type(bmap->ctx, struct isl_sol_pma);
5215 if (!sol_pma)
5216 goto error;
5218 sol_pma->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
5219 sol_pma->sol.dec_level.callback.run = &sol_dec_level_wrap;
5220 sol_pma->sol.dec_level.sol = &sol_pma->sol;
5221 sol_pma->sol.max = max;
5222 sol_pma->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
5223 sol_pma->sol.add = &sol_pma_add_wrap;
5224 sol_pma->sol.add_empty = track_empty ? &sol_pma_add_empty_wrap : NULL;
5225 sol_pma->sol.free = &sol_pma_free_wrap;
5226 sol_pma->pma = isl_pw_multi_aff_empty(isl_basic_map_get_space(bmap));
5227 if (!sol_pma->pma)
5228 goto error;
5230 sol_pma->sol.context = isl_context_alloc(dom);
5231 if (!sol_pma->sol.context)
5232 goto error;
5234 if (track_empty) {
5235 sol_pma->empty = isl_set_alloc_space(isl_basic_set_get_space(dom),
5236 1, ISL_SET_DISJOINT);
5237 if (!sol_pma->empty)
5238 goto error;
5241 isl_basic_set_free(dom);
5242 return &sol_pma->sol;
5243 error:
5244 isl_basic_set_free(dom);
5245 sol_pma_free(sol_pma);
5246 return NULL;
5249 /* Base case of isl_tab_basic_map_partial_lexopt, after removing
5250 * some obvious symmetries.
5252 * We call basic_map_partial_lexopt_base and extract the results.
5254 static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_base_pma(
5255 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5256 __isl_give isl_set **empty, int max)
5258 isl_pw_multi_aff *result = NULL;
5259 struct isl_sol *sol;
5260 struct isl_sol_pma *sol_pma;
5262 sol = basic_map_partial_lexopt_base(bmap, dom, empty, max,
5263 &sol_pma_init);
5264 if (!sol)
5265 return NULL;
5266 sol_pma = (struct isl_sol_pma *) sol;
5268 result = isl_pw_multi_aff_copy(sol_pma->pma);
5269 if (empty)
5270 *empty = isl_set_copy(sol_pma->empty);
5271 sol_free(&sol_pma->sol);
5272 return result;
5275 /* Given that the last input variable of "maff" represents the minimum
5276 * of some bounds, check whether we need to plug in the expression
5277 * of the minimum.
5279 * In particular, check if the last input variable appears in any
5280 * of the expressions in "maff".
5282 static int need_substitution(__isl_keep isl_multi_aff *maff)
5284 int i;
5285 unsigned pos;
5287 pos = isl_multi_aff_dim(maff, isl_dim_in) - 1;
5289 for (i = 0; i < maff->n; ++i)
5290 if (isl_aff_involves_dims(maff->p[i], isl_dim_in, pos, 1))
5291 return 1;
5293 return 0;
5296 /* Given a set of upper bounds on the last "input" variable m,
5297 * construct a piecewise affine expression that selects
5298 * the minimal upper bound to m, i.e.,
5299 * divide the space into cells where one
5300 * of the upper bounds is smaller than all the others and select
5301 * this upper bound on that cell.
5303 * In particular, if there are n bounds b_i, then the result
5304 * consists of n cell, each one of the form
5306 * b_i <= b_j for j > i
5307 * b_i < b_j for j < i
5309 * The affine expression on this cell is
5311 * b_i
5313 static __isl_give isl_pw_aff *set_minimum_pa(__isl_take isl_space *space,
5314 __isl_take isl_mat *var)
5316 int i;
5317 isl_aff *aff = NULL;
5318 isl_basic_set *bset = NULL;
5319 isl_ctx *ctx;
5320 isl_pw_aff *paff = NULL;
5321 isl_space *pw_space;
5322 isl_local_space *ls = NULL;
5324 if (!space || !var)
5325 goto error;
5327 ctx = isl_space_get_ctx(space);
5328 ls = isl_local_space_from_space(isl_space_copy(space));
5329 pw_space = isl_space_copy(space);
5330 pw_space = isl_space_from_domain(pw_space);
5331 pw_space = isl_space_add_dims(pw_space, isl_dim_out, 1);
5332 paff = isl_pw_aff_alloc_size(pw_space, var->n_row);
5334 for (i = 0; i < var->n_row; ++i) {
5335 isl_pw_aff *paff_i;
5337 aff = isl_aff_alloc(isl_local_space_copy(ls));
5338 bset = isl_basic_set_alloc_space(isl_space_copy(space), 0,
5339 0, var->n_row - 1);
5340 if (!aff || !bset)
5341 goto error;
5342 isl_int_set_si(aff->v->el[0], 1);
5343 isl_seq_cpy(aff->v->el + 1, var->row[i], var->n_col);
5344 isl_int_set_si(aff->v->el[1 + var->n_col], 0);
5345 bset = select_minimum(bset, var, i);
5346 paff_i = isl_pw_aff_alloc(isl_set_from_basic_set(bset), aff);
5347 paff = isl_pw_aff_add_disjoint(paff, paff_i);
5350 isl_local_space_free(ls);
5351 isl_space_free(space);
5352 isl_mat_free(var);
5353 return paff;
5354 error:
5355 isl_aff_free(aff);
5356 isl_basic_set_free(bset);
5357 isl_pw_aff_free(paff);
5358 isl_local_space_free(ls);
5359 isl_space_free(space);
5360 isl_mat_free(var);
5361 return NULL;
5364 /* Given a piecewise multi-affine expression of which the last input variable
5365 * is the minimum of the bounds in "cst", plug in the value of the minimum.
5366 * This minimum expression is given in "min_expr_pa".
5367 * The set "min_expr" contains the same information, but in the form of a set.
5368 * The variable is subsequently projected out.
5370 * The implementation is similar to those of "split" and "split_domain".
5371 * If the variable appears in a given expression, then minimum expression
5372 * is plugged in. Otherwise, if the variable appears in the constraints
5373 * and a split is required, then the domain is split. Otherwise, no split
5374 * is performed.
5376 static __isl_give isl_pw_multi_aff *split_domain_pma(
5377 __isl_take isl_pw_multi_aff *opt, __isl_take isl_pw_aff *min_expr_pa,
5378 __isl_take isl_set *min_expr, __isl_take isl_mat *cst)
5380 int n_in;
5381 int i;
5382 isl_space *space;
5383 isl_pw_multi_aff *res;
5385 if (!opt || !min_expr || !cst)
5386 goto error;
5388 n_in = isl_pw_multi_aff_dim(opt, isl_dim_in);
5389 space = isl_pw_multi_aff_get_space(opt);
5390 space = isl_space_drop_dims(space, isl_dim_in, n_in - 1, 1);
5391 res = isl_pw_multi_aff_empty(space);
5393 for (i = 0; i < opt->n; ++i) {
5394 isl_pw_multi_aff *pma;
5396 pma = isl_pw_multi_aff_alloc(isl_set_copy(opt->p[i].set),
5397 isl_multi_aff_copy(opt->p[i].maff));
5398 if (need_substitution(opt->p[i].maff))
5399 pma = isl_pw_multi_aff_substitute(pma,
5400 isl_dim_in, n_in - 1, min_expr_pa);
5401 else if (need_split_set(opt->p[i].set, cst))
5402 pma = isl_pw_multi_aff_intersect_domain(pma,
5403 isl_set_copy(min_expr));
5404 pma = isl_pw_multi_aff_project_out(pma,
5405 isl_dim_in, n_in - 1, 1);
5407 res = isl_pw_multi_aff_add_disjoint(res, pma);
5410 isl_pw_multi_aff_free(opt);
5411 isl_pw_aff_free(min_expr_pa);
5412 isl_set_free(min_expr);
5413 isl_mat_free(cst);
5414 return res;
5415 error:
5416 isl_pw_multi_aff_free(opt);
5417 isl_pw_aff_free(min_expr_pa);
5418 isl_set_free(min_expr);
5419 isl_mat_free(cst);
5420 return NULL;
5423 static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_pma(
5424 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5425 __isl_give isl_set **empty, int max);
5427 /* This function is called from basic_map_partial_lexopt_symm.
5428 * The last variable of "bmap" and "dom" corresponds to the minimum
5429 * of the bounds in "cst". "map_space" is the space of the original
5430 * input relation (of basic_map_partial_lexopt_symm) and "set_space"
5431 * is the space of the original domain.
5433 * We recursively call basic_map_partial_lexopt and then plug in
5434 * the definition of the minimum in the result.
5436 static __isl_give union isl_lex_res basic_map_partial_lexopt_symm_pma_core(
5437 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5438 __isl_give isl_set **empty, int max, __isl_take isl_mat *cst,
5439 __isl_take isl_space *map_space, __isl_take isl_space *set_space)
5441 isl_pw_multi_aff *opt;
5442 isl_pw_aff *min_expr_pa;
5443 isl_set *min_expr;
5444 union isl_lex_res res;
5446 min_expr = set_minimum(isl_basic_set_get_space(dom), isl_mat_copy(cst));
5447 min_expr_pa = set_minimum_pa(isl_basic_set_get_space(dom),
5448 isl_mat_copy(cst));
5450 opt = basic_map_partial_lexopt_pma(bmap, dom, empty, max);
5452 if (empty) {
5453 *empty = split(*empty,
5454 isl_set_copy(min_expr), isl_mat_copy(cst));
5455 *empty = isl_set_reset_space(*empty, set_space);
5458 opt = split_domain_pma(opt, min_expr_pa, min_expr, cst);
5459 opt = isl_pw_multi_aff_reset_space(opt, map_space);
5461 res.pma = opt;
5462 return res;
5465 static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_symm_pma(
5466 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5467 __isl_give isl_set **empty, int max, int first, int second)
5469 return basic_map_partial_lexopt_symm(bmap, dom, empty, max,
5470 first, second, &basic_map_partial_lexopt_symm_pma_core).pma;
5473 /* Recursive part of isl_basic_map_partial_lexopt_pw_multi_aff, after detecting
5474 * equalities and removing redundant constraints.
5476 * We first check if there are any parallel constraints (left).
5477 * If not, we are in the base case.
5478 * If there are parallel constraints, we replace them by a single
5479 * constraint in basic_map_partial_lexopt_symm_pma and then call
5480 * this function recursively to look for more parallel constraints.
5482 static __isl_give isl_pw_multi_aff *basic_map_partial_lexopt_pma(
5483 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5484 __isl_give isl_set **empty, int max)
5486 int par = 0;
5487 int first, second;
5489 if (!bmap)
5490 goto error;
5492 if (bmap->ctx->opt->pip_symmetry)
5493 par = parallel_constraints(bmap, &first, &second);
5494 if (par < 0)
5495 goto error;
5496 if (!par)
5497 return basic_map_partial_lexopt_base_pma(bmap, dom, empty, max);
5499 return basic_map_partial_lexopt_symm_pma(bmap, dom, empty, max,
5500 first, second);
5501 error:
5502 isl_basic_set_free(dom);
5503 isl_basic_map_free(bmap);
5504 return NULL;
5507 /* Compute the lexicographic minimum (or maximum if "max" is set)
5508 * of "bmap" over the domain "dom" and return the result as a piecewise
5509 * multi-affine expression.
5510 * If "empty" is not NULL, then *empty is assigned a set that
5511 * contains those parts of the domain where there is no solution.
5512 * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
5513 * then we compute the rational optimum. Otherwise, we compute
5514 * the integral optimum.
5516 * We perform some preprocessing. As the PILP solver does not
5517 * handle implicit equalities very well, we first make sure all
5518 * the equalities are explicitly available.
5520 * We also add context constraints to the basic map and remove
5521 * redundant constraints. This is only needed because of the
5522 * way we handle simple symmetries. In particular, we currently look
5523 * for symmetries on the constraints, before we set up the main tableau.
5524 * It is then no good to look for symmetries on possibly redundant constraints.
5526 __isl_give isl_pw_multi_aff *isl_basic_map_partial_lexopt_pw_multi_aff(
5527 __isl_take isl_basic_map *bmap, __isl_take isl_basic_set *dom,
5528 __isl_give isl_set **empty, int max)
5530 if (empty)
5531 *empty = NULL;
5532 if (!bmap || !dom)
5533 goto error;
5535 isl_assert(bmap->ctx,
5536 isl_basic_map_compatible_domain(bmap, dom), goto error);
5538 if (isl_basic_set_dim(dom, isl_dim_all) == 0)
5539 return basic_map_partial_lexopt_pma(bmap, dom, empty, max);
5541 bmap = isl_basic_map_intersect_domain(bmap, isl_basic_set_copy(dom));
5542 bmap = isl_basic_map_detect_equalities(bmap);
5543 bmap = isl_basic_map_remove_redundancies(bmap);
5545 return basic_map_partial_lexopt_pma(bmap, dom, empty, max);
5546 error:
5547 isl_basic_set_free(dom);
5548 isl_basic_map_free(bmap);
5549 return NULL;