isl_tab_detect_redundant: return status instead of isl_tab *
[isl.git] / isl_tab_pip.c
blob8f3311cf6a365784302918af9d7a4c153c3594e7
1 #include "isl_map_private.h"
2 #include "isl_seq.h"
3 #include "isl_tab.h"
4 #include "isl_sample.h"
6 /*
7 * The implementation of parametric integer linear programming in this file
8 * was inspired by the paper "Parametric Integer Programming" and the
9 * report "Solving systems of affine (in)equalities" by Paul Feautrier
10 * (and others).
12 * The strategy used for obtaining a feasible solution is different
13 * from the one used in isl_tab.c. In particular, in isl_tab.c,
14 * upon finding a constraint that is not yet satisfied, we pivot
15 * in a row that increases the constant term of row holding the
16 * constraint, making sure the sample solution remains feasible
17 * for all the constraints it already satisfied.
18 * Here, we always pivot in the row holding the constraint,
19 * choosing a column that induces the lexicographically smallest
20 * increment to the sample solution.
22 * By starting out from a sample value that is lexicographically
23 * smaller than any integer point in the problem space, the first
24 * feasible integer sample point we find will also be the lexicographically
25 * smallest. If all variables can be assumed to be non-negative,
26 * then the initial sample value may be chosen equal to zero.
27 * However, we will not make this assumption. Instead, we apply
28 * the "big parameter" trick. Any variable x is then not directly
29 * used in the tableau, but instead it its represented by another
30 * variable x' = M + x, where M is an arbitrarily large (positive)
31 * value. x' is therefore always non-negative, whatever the value of x.
32 * Taking as initial smaple value x' = 0 corresponds to x = -M,
33 * which is always smaller than any possible value of x.
35 * The big parameter trick is used in the main tableau and
36 * also in the context tableau if isl_context_lex is used.
37 * In this case, each tableaus has its own big parameter.
38 * Before doing any real work, we check if all the parameters
39 * happen to be non-negative. If so, we drop the column corresponding
40 * to M from the initial context tableau.
41 * If isl_context_gbr is used, then the big parameter trick is only
42 * used in the main tableau.
45 struct isl_context;
46 struct isl_context_op {
47 /* detect nonnegative parameters in context and mark them in tab */
48 struct isl_tab *(*detect_nonnegative_parameters)(
49 struct isl_context *context, struct isl_tab *tab);
50 /* return temporary reference to basic set representation of context */
51 struct isl_basic_set *(*peek_basic_set)(struct isl_context *context);
52 /* return temporary reference to tableau representation of context */
53 struct isl_tab *(*peek_tab)(struct isl_context *context);
54 /* add equality; check is 1 if eq may not be valid;
55 * update is 1 if we may want to call ineq_sign on context later.
57 void (*add_eq)(struct isl_context *context, isl_int *eq,
58 int check, int update);
59 /* add inequality; check is 1 if ineq may not be valid;
60 * update is 1 if we may want to call ineq_sign on context later.
62 void (*add_ineq)(struct isl_context *context, isl_int *ineq,
63 int check, int update);
64 /* check sign of ineq based on previous information.
65 * strict is 1 if saturation should be treated as a positive sign.
67 enum isl_tab_row_sign (*ineq_sign)(struct isl_context *context,
68 isl_int *ineq, int strict);
69 /* check if inequality maintains feasibility */
70 int (*test_ineq)(struct isl_context *context, isl_int *ineq);
71 /* return index of a div that corresponds to "div" */
72 int (*get_div)(struct isl_context *context, struct isl_tab *tab,
73 struct isl_vec *div);
74 /* add div "div" to context and return index and non-negativity */
75 int (*add_div)(struct isl_context *context, struct isl_vec *div,
76 int *nonneg);
77 int (*detect_equalities)(struct isl_context *context,
78 struct isl_tab *tab);
79 /* return row index of "best" split */
80 int (*best_split)(struct isl_context *context, struct isl_tab *tab);
81 /* check if context has already been determined to be empty */
82 int (*is_empty)(struct isl_context *context);
83 /* check if context is still usable */
84 int (*is_ok)(struct isl_context *context);
85 /* save a copy/snapshot of context */
86 void *(*save)(struct isl_context *context);
87 /* restore saved context */
88 void (*restore)(struct isl_context *context, void *);
89 /* invalidate context */
90 void (*invalidate)(struct isl_context *context);
91 /* free context */
92 void (*free)(struct isl_context *context);
95 struct isl_context {
96 struct isl_context_op *op;
99 struct isl_context_lex {
100 struct isl_context context;
101 struct isl_tab *tab;
104 struct isl_partial_sol {
105 int level;
106 struct isl_basic_set *dom;
107 struct isl_mat *M;
109 struct isl_partial_sol *next;
112 struct isl_sol;
113 struct isl_sol_callback {
114 struct isl_tab_callback callback;
115 struct isl_sol *sol;
118 /* isl_sol is an interface for constructing a solution to
119 * a parametric integer linear programming problem.
120 * Every time the algorithm reaches a state where a solution
121 * can be read off from the tableau (including cases where the tableau
122 * is empty), the function "add" is called on the isl_sol passed
123 * to find_solutions_main.
125 * The context tableau is owned by isl_sol and is updated incrementally.
127 * There are currently two implementations of this interface,
128 * isl_sol_map, which simply collects the solutions in an isl_map
129 * and (optionally) the parts of the context where there is no solution
130 * in an isl_set, and
131 * isl_sol_for, which calls a user-defined function for each part of
132 * the solution.
134 struct isl_sol {
135 int error;
136 int rational;
137 int level;
138 int max;
139 int n_out;
140 struct isl_context *context;
141 struct isl_partial_sol *partial;
142 void (*add)(struct isl_sol *sol,
143 struct isl_basic_set *dom, struct isl_mat *M);
144 void (*add_empty)(struct isl_sol *sol, struct isl_basic_set *bset);
145 void (*free)(struct isl_sol *sol);
146 struct isl_sol_callback dec_level;
149 static void sol_free(struct isl_sol *sol)
151 struct isl_partial_sol *partial, *next;
152 if (!sol)
153 return;
154 for (partial = sol->partial; partial; partial = next) {
155 next = partial->next;
156 isl_basic_set_free(partial->dom);
157 isl_mat_free(partial->M);
158 free(partial);
160 sol->free(sol);
163 /* Push a partial solution represented by a domain and mapping M
164 * onto the stack of partial solutions.
166 static void sol_push_sol(struct isl_sol *sol,
167 struct isl_basic_set *dom, struct isl_mat *M)
169 struct isl_partial_sol *partial;
171 if (sol->error || !dom)
172 goto error;
174 partial = isl_alloc_type(dom->ctx, struct isl_partial_sol);
175 if (!partial)
176 goto error;
178 partial->level = sol->level;
179 partial->dom = dom;
180 partial->M = M;
181 partial->next = sol->partial;
183 sol->partial = partial;
185 return;
186 error:
187 isl_basic_set_free(dom);
188 sol->error = 1;
191 /* Pop one partial solution from the partial solution stack and
192 * pass it on to sol->add or sol->add_empty.
194 static void sol_pop_one(struct isl_sol *sol)
196 struct isl_partial_sol *partial;
198 partial = sol->partial;
199 sol->partial = partial->next;
201 if (partial->M)
202 sol->add(sol, partial->dom, partial->M);
203 else
204 sol->add_empty(sol, partial->dom);
205 free(partial);
208 /* Return a fresh copy of the domain represented by the context tableau.
210 static struct isl_basic_set *sol_domain(struct isl_sol *sol)
212 struct isl_basic_set *bset;
214 if (sol->error)
215 return NULL;
217 bset = isl_basic_set_dup(sol->context->op->peek_basic_set(sol->context));
218 bset = isl_basic_set_update_from_tab(bset,
219 sol->context->op->peek_tab(sol->context));
221 return bset;
224 /* Check whether two partial solutions have the same mapping, where n_div
225 * is the number of divs that the two partial solutions have in common.
227 static int same_solution(struct isl_partial_sol *s1, struct isl_partial_sol *s2,
228 unsigned n_div)
230 int i;
231 unsigned dim;
233 if (!s1->M != !s2->M)
234 return 0;
235 if (!s1->M)
236 return 1;
238 dim = isl_basic_set_total_dim(s1->dom) - s1->dom->n_div;
240 for (i = 0; i < s1->M->n_row; ++i) {
241 if (isl_seq_first_non_zero(s1->M->row[i]+1+dim+n_div,
242 s1->M->n_col-1-dim-n_div) != -1)
243 return 0;
244 if (isl_seq_first_non_zero(s2->M->row[i]+1+dim+n_div,
245 s2->M->n_col-1-dim-n_div) != -1)
246 return 0;
247 if (!isl_seq_eq(s1->M->row[i], s2->M->row[i], 1+dim+n_div))
248 return 0;
250 return 1;
253 /* Pop all solutions from the partial solution stack that were pushed onto
254 * the stack at levels that are deeper than the current level.
255 * If the two topmost elements on the stack have the same level
256 * and represent the same solution, then their domains are combined.
257 * This combined domain is the same as the current context domain
258 * as sol_pop is called each time we move back to a higher level.
260 static void sol_pop(struct isl_sol *sol)
262 struct isl_partial_sol *partial;
263 unsigned n_div;
265 if (sol->error)
266 return;
268 if (sol->level == 0) {
269 for (partial = sol->partial; partial; partial = sol->partial)
270 sol_pop_one(sol);
271 return;
274 partial = sol->partial;
275 if (!partial)
276 return;
278 if (partial->level <= sol->level)
279 return;
281 if (partial->next && partial->next->level == partial->level) {
282 n_div = isl_basic_set_dim(
283 sol->context->op->peek_basic_set(sol->context),
284 isl_dim_div);
286 if (!same_solution(partial, partial->next, n_div)) {
287 sol_pop_one(sol);
288 sol_pop_one(sol);
289 } else {
290 struct isl_basic_set *bset;
292 bset = sol_domain(sol);
294 isl_basic_set_free(partial->next->dom);
295 partial->next->dom = bset;
296 partial->next->level = sol->level;
298 sol->partial = partial->next;
299 isl_basic_set_free(partial->dom);
300 isl_mat_free(partial->M);
301 free(partial);
303 } else
304 sol_pop_one(sol);
307 static void sol_dec_level(struct isl_sol *sol)
309 if (sol->error)
310 return;
312 sol->level--;
314 sol_pop(sol);
317 static int sol_dec_level_wrap(struct isl_tab_callback *cb)
319 struct isl_sol_callback *callback = (struct isl_sol_callback *)cb;
321 sol_dec_level(callback->sol);
323 return callback->sol->error ? -1 : 0;
326 /* Move down to next level and push callback onto context tableau
327 * to decrease the level again when it gets rolled back across
328 * the current state. That is, dec_level will be called with
329 * the context tableau in the same state as it is when inc_level
330 * is called.
332 static void sol_inc_level(struct isl_sol *sol)
334 struct isl_tab *tab;
336 if (sol->error)
337 return;
339 sol->level++;
340 tab = sol->context->op->peek_tab(sol->context);
341 if (isl_tab_push_callback(tab, &sol->dec_level.callback) < 0)
342 sol->error = 1;
345 static void scale_rows(struct isl_mat *mat, isl_int m, int n_row)
347 int i;
349 if (isl_int_is_one(m))
350 return;
352 for (i = 0; i < n_row; ++i)
353 isl_seq_scale(mat->row[i], mat->row[i], m, mat->n_col);
356 /* Add the solution identified by the tableau and the context tableau.
358 * The layout of the variables is as follows.
359 * tab->n_var is equal to the total number of variables in the input
360 * map (including divs that were copied from the context)
361 * + the number of extra divs constructed
362 * Of these, the first tab->n_param and the last tab->n_div variables
363 * correspond to the variables in the context, i.e.,
364 * tab->n_param + tab->n_div = context_tab->n_var
365 * tab->n_param is equal to the number of parameters and input
366 * dimensions in the input map
367 * tab->n_div is equal to the number of divs in the context
369 * If there is no solution, then call add_empty with a basic set
370 * that corresponds to the context tableau. (If add_empty is NULL,
371 * then do nothing).
373 * If there is a solution, then first construct a matrix that maps
374 * all dimensions of the context to the output variables, i.e.,
375 * the output dimensions in the input map.
376 * The divs in the input map (if any) that do not correspond to any
377 * div in the context do not appear in the solution.
378 * The algorithm will make sure that they have an integer value,
379 * but these values themselves are of no interest.
380 * We have to be careful not to drop or rearrange any divs in the
381 * context because that would change the meaning of the matrix.
383 * To extract the value of the output variables, it should be noted
384 * that we always use a big parameter M in the main tableau and so
385 * the variable stored in this tableau is not an output variable x itself, but
386 * x' = M + x (in case of minimization)
387 * or
388 * x' = M - x (in case of maximization)
389 * If x' appears in a column, then its optimal value is zero,
390 * which means that the optimal value of x is an unbounded number
391 * (-M for minimization and M for maximization).
392 * We currently assume that the output dimensions in the original map
393 * are bounded, so this cannot occur.
394 * Similarly, when x' appears in a row, then the coefficient of M in that
395 * row is necessarily 1.
396 * If the row in the tableau represents
397 * d x' = c + d M + e(y)
398 * then, in case of minimization, the corresponding row in the matrix
399 * will be
400 * a c + a e(y)
401 * with a d = m, the (updated) common denominator of the matrix.
402 * In case of maximization, the row will be
403 * -a c - a e(y)
405 static void sol_add(struct isl_sol *sol, struct isl_tab *tab)
407 struct isl_basic_set *bset = NULL;
408 struct isl_mat *mat = NULL;
409 unsigned off;
410 int row, i;
411 isl_int m;
413 if (sol->error || !tab)
414 goto error;
416 if (tab->empty && !sol->add_empty)
417 return;
419 bset = sol_domain(sol);
421 if (tab->empty) {
422 sol_push_sol(sol, bset, NULL);
423 return;
426 off = 2 + tab->M;
428 mat = isl_mat_alloc(tab->mat->ctx, 1 + sol->n_out,
429 1 + tab->n_param + tab->n_div);
430 if (!mat)
431 goto error;
433 isl_int_init(m);
435 isl_seq_clr(mat->row[0] + 1, mat->n_col - 1);
436 isl_int_set_si(mat->row[0][0], 1);
437 for (row = 0; row < sol->n_out; ++row) {
438 int i = tab->n_param + row;
439 int r, j;
441 isl_seq_clr(mat->row[1 + row], mat->n_col);
442 if (!tab->var[i].is_row) {
443 /* no unbounded */
444 isl_assert(mat->ctx, !tab->M, goto error2);
445 continue;
448 r = tab->var[i].index;
449 /* no unbounded */
450 if (tab->M)
451 isl_assert(mat->ctx, isl_int_eq(tab->mat->row[r][2],
452 tab->mat->row[r][0]),
453 goto error2);
454 isl_int_gcd(m, mat->row[0][0], tab->mat->row[r][0]);
455 isl_int_divexact(m, tab->mat->row[r][0], m);
456 scale_rows(mat, m, 1 + row);
457 isl_int_divexact(m, mat->row[0][0], tab->mat->row[r][0]);
458 isl_int_mul(mat->row[1 + row][0], m, tab->mat->row[r][1]);
459 for (j = 0; j < tab->n_param; ++j) {
460 int col;
461 if (tab->var[j].is_row)
462 continue;
463 col = tab->var[j].index;
464 isl_int_mul(mat->row[1 + row][1 + j], m,
465 tab->mat->row[r][off + col]);
467 for (j = 0; j < tab->n_div; ++j) {
468 int col;
469 if (tab->var[tab->n_var - tab->n_div+j].is_row)
470 continue;
471 col = tab->var[tab->n_var - tab->n_div+j].index;
472 isl_int_mul(mat->row[1 + row][1 + tab->n_param + j], m,
473 tab->mat->row[r][off + col]);
475 if (sol->max)
476 isl_seq_neg(mat->row[1 + row], mat->row[1 + row],
477 mat->n_col);
480 isl_int_clear(m);
482 sol_push_sol(sol, bset, mat);
483 return;
484 error2:
485 isl_int_clear(m);
486 error:
487 isl_basic_set_free(bset);
488 isl_mat_free(mat);
489 sol_free(sol);
492 struct isl_sol_map {
493 struct isl_sol sol;
494 struct isl_map *map;
495 struct isl_set *empty;
498 static void sol_map_free(struct isl_sol_map *sol_map)
500 if (sol_map->sol.context)
501 sol_map->sol.context->op->free(sol_map->sol.context);
502 isl_map_free(sol_map->map);
503 isl_set_free(sol_map->empty);
504 free(sol_map);
507 static void sol_map_free_wrap(struct isl_sol *sol)
509 sol_map_free((struct isl_sol_map *)sol);
512 /* This function is called for parts of the context where there is
513 * no solution, with "bset" corresponding to the context tableau.
514 * Simply add the basic set to the set "empty".
516 static void sol_map_add_empty(struct isl_sol_map *sol,
517 struct isl_basic_set *bset)
519 if (!bset)
520 goto error;
521 isl_assert(bset->ctx, sol->empty, goto error);
523 sol->empty = isl_set_grow(sol->empty, 1);
524 bset = isl_basic_set_simplify(bset);
525 bset = isl_basic_set_finalize(bset);
526 sol->empty = isl_set_add(sol->empty, isl_basic_set_copy(bset));
527 if (!sol->empty)
528 goto error;
529 isl_basic_set_free(bset);
530 return;
531 error:
532 isl_basic_set_free(bset);
533 sol->sol.error = 1;
536 static void sol_map_add_empty_wrap(struct isl_sol *sol,
537 struct isl_basic_set *bset)
539 sol_map_add_empty((struct isl_sol_map *)sol, bset);
542 /* Given a basic map "dom" that represents the context and an affine
543 * matrix "M" that maps the dimensions of the context to the
544 * output variables, construct a basic map with the same parameters
545 * and divs as the context, the dimensions of the context as input
546 * dimensions and a number of output dimensions that is equal to
547 * the number of output dimensions in the input map.
549 * The constraints and divs of the context are simply copied
550 * from "dom". For each row
551 * x = c + e(y)
552 * an equality
553 * c + e(y) - d x = 0
554 * is added, with d the common denominator of M.
556 static void sol_map_add(struct isl_sol_map *sol,
557 struct isl_basic_set *dom, struct isl_mat *M)
559 int i;
560 struct isl_basic_map *bmap = NULL;
561 isl_basic_set *context_bset;
562 unsigned n_eq;
563 unsigned n_ineq;
564 unsigned nparam;
565 unsigned total;
566 unsigned n_div;
567 unsigned n_out;
569 if (sol->sol.error || !dom || !M)
570 goto error;
572 n_out = sol->sol.n_out;
573 n_eq = dom->n_eq + n_out;
574 n_ineq = dom->n_ineq;
575 n_div = dom->n_div;
576 nparam = isl_basic_set_total_dim(dom) - n_div;
577 total = isl_map_dim(sol->map, isl_dim_all);
578 bmap = isl_basic_map_alloc_dim(isl_map_get_dim(sol->map),
579 n_div, n_eq, 2 * n_div + n_ineq);
580 if (!bmap)
581 goto error;
582 if (sol->sol.rational)
583 ISL_F_SET(bmap, ISL_BASIC_MAP_RATIONAL);
584 for (i = 0; i < dom->n_div; ++i) {
585 int k = isl_basic_map_alloc_div(bmap);
586 if (k < 0)
587 goto error;
588 isl_seq_cpy(bmap->div[k], dom->div[i], 1 + 1 + nparam);
589 isl_seq_clr(bmap->div[k] + 1 + 1 + nparam, total - nparam);
590 isl_seq_cpy(bmap->div[k] + 1 + 1 + total,
591 dom->div[i] + 1 + 1 + nparam, i);
593 for (i = 0; i < dom->n_eq; ++i) {
594 int k = isl_basic_map_alloc_equality(bmap);
595 if (k < 0)
596 goto error;
597 isl_seq_cpy(bmap->eq[k], dom->eq[i], 1 + nparam);
598 isl_seq_clr(bmap->eq[k] + 1 + nparam, total - nparam);
599 isl_seq_cpy(bmap->eq[k] + 1 + total,
600 dom->eq[i] + 1 + nparam, n_div);
602 for (i = 0; i < dom->n_ineq; ++i) {
603 int k = isl_basic_map_alloc_inequality(bmap);
604 if (k < 0)
605 goto error;
606 isl_seq_cpy(bmap->ineq[k], dom->ineq[i], 1 + nparam);
607 isl_seq_clr(bmap->ineq[k] + 1 + nparam, total - nparam);
608 isl_seq_cpy(bmap->ineq[k] + 1 + total,
609 dom->ineq[i] + 1 + nparam, n_div);
611 for (i = 0; i < M->n_row - 1; ++i) {
612 int k = isl_basic_map_alloc_equality(bmap);
613 if (k < 0)
614 goto error;
615 isl_seq_cpy(bmap->eq[k], M->row[1 + i], 1 + nparam);
616 isl_seq_clr(bmap->eq[k] + 1 + nparam, n_out);
617 isl_int_neg(bmap->eq[k][1 + nparam + i], M->row[0][0]);
618 isl_seq_cpy(bmap->eq[k] + 1 + nparam + n_out,
619 M->row[1 + i] + 1 + nparam, n_div);
621 bmap = isl_basic_map_simplify(bmap);
622 bmap = isl_basic_map_finalize(bmap);
623 sol->map = isl_map_grow(sol->map, 1);
624 sol->map = isl_map_add(sol->map, bmap);
625 if (!sol->map)
626 goto error;
627 isl_basic_set_free(dom);
628 isl_mat_free(M);
629 return;
630 error:
631 isl_basic_set_free(dom);
632 isl_mat_free(M);
633 isl_basic_map_free(bmap);
634 sol->sol.error = 1;
637 static void sol_map_add_wrap(struct isl_sol *sol,
638 struct isl_basic_set *dom, struct isl_mat *M)
640 sol_map_add((struct isl_sol_map *)sol, dom, M);
644 /* Store the "parametric constant" of row "row" of tableau "tab" in "line",
645 * i.e., the constant term and the coefficients of all variables that
646 * appear in the context tableau.
647 * Note that the coefficient of the big parameter M is NOT copied.
648 * The context tableau may not have a big parameter and even when it
649 * does, it is a different big parameter.
651 static void get_row_parameter_line(struct isl_tab *tab, int row, isl_int *line)
653 int i;
654 unsigned off = 2 + tab->M;
656 isl_int_set(line[0], tab->mat->row[row][1]);
657 for (i = 0; i < tab->n_param; ++i) {
658 if (tab->var[i].is_row)
659 isl_int_set_si(line[1 + i], 0);
660 else {
661 int col = tab->var[i].index;
662 isl_int_set(line[1 + i], tab->mat->row[row][off + col]);
665 for (i = 0; i < tab->n_div; ++i) {
666 if (tab->var[tab->n_var - tab->n_div + i].is_row)
667 isl_int_set_si(line[1 + tab->n_param + i], 0);
668 else {
669 int col = tab->var[tab->n_var - tab->n_div + i].index;
670 isl_int_set(line[1 + tab->n_param + i],
671 tab->mat->row[row][off + col]);
676 /* Check if rows "row1" and "row2" have identical "parametric constants",
677 * as explained above.
678 * In this case, we also insist that the coefficients of the big parameter
679 * be the same as the values of the constants will only be the same
680 * if these coefficients are also the same.
682 static int identical_parameter_line(struct isl_tab *tab, int row1, int row2)
684 int i;
685 unsigned off = 2 + tab->M;
687 if (isl_int_ne(tab->mat->row[row1][1], tab->mat->row[row2][1]))
688 return 0;
690 if (tab->M && isl_int_ne(tab->mat->row[row1][2],
691 tab->mat->row[row2][2]))
692 return 0;
694 for (i = 0; i < tab->n_param + tab->n_div; ++i) {
695 int pos = i < tab->n_param ? i :
696 tab->n_var - tab->n_div + i - tab->n_param;
697 int col;
699 if (tab->var[pos].is_row)
700 continue;
701 col = tab->var[pos].index;
702 if (isl_int_ne(tab->mat->row[row1][off + col],
703 tab->mat->row[row2][off + col]))
704 return 0;
706 return 1;
709 /* Return an inequality that expresses that the "parametric constant"
710 * should be non-negative.
711 * This function is only called when the coefficient of the big parameter
712 * is equal to zero.
714 static struct isl_vec *get_row_parameter_ineq(struct isl_tab *tab, int row)
716 struct isl_vec *ineq;
718 ineq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_param + tab->n_div);
719 if (!ineq)
720 return NULL;
722 get_row_parameter_line(tab, row, ineq->el);
723 if (ineq)
724 ineq = isl_vec_normalize(ineq);
726 return ineq;
729 /* Return a integer division for use in a parametric cut based on the given row.
730 * In particular, let the parametric constant of the row be
732 * \sum_i a_i y_i
734 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
735 * The div returned is equal to
737 * floor(\sum_i {-a_i} y_i) = floor((\sum_i (-a_i mod d) y_i)/d)
739 static struct isl_vec *get_row_parameter_div(struct isl_tab *tab, int row)
741 struct isl_vec *div;
743 div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div);
744 if (!div)
745 return NULL;
747 isl_int_set(div->el[0], tab->mat->row[row][0]);
748 get_row_parameter_line(tab, row, div->el + 1);
749 div = isl_vec_normalize(div);
750 isl_seq_neg(div->el + 1, div->el + 1, div->size - 1);
751 isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1);
753 return div;
756 /* Return a integer division for use in transferring an integrality constraint
757 * to the context.
758 * In particular, let the parametric constant of the row be
760 * \sum_i a_i y_i
762 * where y_0 = 1, but none of the y_i corresponds to the big parameter M.
763 * The the returned div is equal to
765 * floor(\sum_i {a_i} y_i) = floor((\sum_i (a_i mod d) y_i)/d)
767 static struct isl_vec *get_row_split_div(struct isl_tab *tab, int row)
769 struct isl_vec *div;
771 div = isl_vec_alloc(tab->mat->ctx, 1 + 1 + tab->n_param + tab->n_div);
772 if (!div)
773 return NULL;
775 isl_int_set(div->el[0], tab->mat->row[row][0]);
776 get_row_parameter_line(tab, row, div->el + 1);
777 div = isl_vec_normalize(div);
778 isl_seq_fdiv_r(div->el + 1, div->el + 1, div->el[0], div->size - 1);
780 return div;
783 /* Construct and return an inequality that expresses an upper bound
784 * on the given div.
785 * In particular, if the div is given by
787 * d = floor(e/m)
789 * then the inequality expresses
791 * m d <= e
793 static struct isl_vec *ineq_for_div(struct isl_basic_set *bset, unsigned div)
795 unsigned total;
796 unsigned div_pos;
797 struct isl_vec *ineq;
799 if (!bset)
800 return NULL;
802 total = isl_basic_set_total_dim(bset);
803 div_pos = 1 + total - bset->n_div + div;
805 ineq = isl_vec_alloc(bset->ctx, 1 + total);
806 if (!ineq)
807 return NULL;
809 isl_seq_cpy(ineq->el, bset->div[div] + 1, 1 + total);
810 isl_int_neg(ineq->el[div_pos], bset->div[div][0]);
811 return ineq;
814 /* Given a row in the tableau and a div that was created
815 * using get_row_split_div and that been constrained to equality, i.e.,
817 * d = floor(\sum_i {a_i} y_i) = \sum_i {a_i} y_i
819 * replace the expression "\sum_i {a_i} y_i" in the row by d,
820 * i.e., we subtract "\sum_i {a_i} y_i" and add 1 d.
821 * The coefficients of the non-parameters in the tableau have been
822 * verified to be integral. We can therefore simply replace coefficient b
823 * by floor(b). For the coefficients of the parameters we have
824 * floor(a_i) = a_i - {a_i}, while for the other coefficients, we have
825 * floor(b) = b.
827 static struct isl_tab *set_row_cst_to_div(struct isl_tab *tab, int row, int div)
829 isl_seq_fdiv_q(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
830 tab->mat->row[row][0], 1 + tab->M + tab->n_col);
832 isl_int_set_si(tab->mat->row[row][0], 1);
834 if (tab->var[tab->n_var - tab->n_div + div].is_row) {
835 int drow = tab->var[tab->n_var - tab->n_div + div].index;
837 isl_assert(tab->mat->ctx,
838 isl_int_is_one(tab->mat->row[drow][0]), goto error);
839 isl_seq_combine(tab->mat->row[row] + 1,
840 tab->mat->ctx->one, tab->mat->row[row] + 1,
841 tab->mat->ctx->one, tab->mat->row[drow] + 1,
842 1 + tab->M + tab->n_col);
843 } else {
844 int dcol = tab->var[tab->n_var - tab->n_div + div].index;
846 isl_int_set_si(tab->mat->row[row][2 + tab->M + dcol], 1);
849 return tab;
850 error:
851 isl_tab_free(tab);
852 return NULL;
855 /* Check if the (parametric) constant of the given row is obviously
856 * negative, meaning that we don't need to consult the context tableau.
857 * If there is a big parameter and its coefficient is non-zero,
858 * then this coefficient determines the outcome.
859 * Otherwise, we check whether the constant is negative and
860 * all non-zero coefficients of parameters are negative and
861 * belong to non-negative parameters.
863 static int is_obviously_neg(struct isl_tab *tab, int row)
865 int i;
866 int col;
867 unsigned off = 2 + tab->M;
869 if (tab->M) {
870 if (isl_int_is_pos(tab->mat->row[row][2]))
871 return 0;
872 if (isl_int_is_neg(tab->mat->row[row][2]))
873 return 1;
876 if (isl_int_is_nonneg(tab->mat->row[row][1]))
877 return 0;
878 for (i = 0; i < tab->n_param; ++i) {
879 /* Eliminated parameter */
880 if (tab->var[i].is_row)
881 continue;
882 col = tab->var[i].index;
883 if (isl_int_is_zero(tab->mat->row[row][off + col]))
884 continue;
885 if (!tab->var[i].is_nonneg)
886 return 0;
887 if (isl_int_is_pos(tab->mat->row[row][off + col]))
888 return 0;
890 for (i = 0; i < tab->n_div; ++i) {
891 if (tab->var[tab->n_var - tab->n_div + i].is_row)
892 continue;
893 col = tab->var[tab->n_var - tab->n_div + i].index;
894 if (isl_int_is_zero(tab->mat->row[row][off + col]))
895 continue;
896 if (!tab->var[tab->n_var - tab->n_div + i].is_nonneg)
897 return 0;
898 if (isl_int_is_pos(tab->mat->row[row][off + col]))
899 return 0;
901 return 1;
904 /* Check if the (parametric) constant of the given row is obviously
905 * non-negative, meaning that we don't need to consult the context tableau.
906 * If there is a big parameter and its coefficient is non-zero,
907 * then this coefficient determines the outcome.
908 * Otherwise, we check whether the constant is non-negative and
909 * all non-zero coefficients of parameters are positive and
910 * belong to non-negative parameters.
912 static int is_obviously_nonneg(struct isl_tab *tab, int row)
914 int i;
915 int col;
916 unsigned off = 2 + tab->M;
918 if (tab->M) {
919 if (isl_int_is_pos(tab->mat->row[row][2]))
920 return 1;
921 if (isl_int_is_neg(tab->mat->row[row][2]))
922 return 0;
925 if (isl_int_is_neg(tab->mat->row[row][1]))
926 return 0;
927 for (i = 0; i < tab->n_param; ++i) {
928 /* Eliminated parameter */
929 if (tab->var[i].is_row)
930 continue;
931 col = tab->var[i].index;
932 if (isl_int_is_zero(tab->mat->row[row][off + col]))
933 continue;
934 if (!tab->var[i].is_nonneg)
935 return 0;
936 if (isl_int_is_neg(tab->mat->row[row][off + col]))
937 return 0;
939 for (i = 0; i < tab->n_div; ++i) {
940 if (tab->var[tab->n_var - tab->n_div + i].is_row)
941 continue;
942 col = tab->var[tab->n_var - tab->n_div + i].index;
943 if (isl_int_is_zero(tab->mat->row[row][off + col]))
944 continue;
945 if (!tab->var[tab->n_var - tab->n_div + i].is_nonneg)
946 return 0;
947 if (isl_int_is_neg(tab->mat->row[row][off + col]))
948 return 0;
950 return 1;
953 /* Given a row r and two columns, return the column that would
954 * lead to the lexicographically smallest increment in the sample
955 * solution when leaving the basis in favor of the row.
956 * Pivoting with column c will increment the sample value by a non-negative
957 * constant times a_{V,c}/a_{r,c}, with a_{V,c} the elements of column c
958 * corresponding to the non-parametric variables.
959 * If variable v appears in a column c_v, the a_{v,c} = 1 iff c = c_v,
960 * with all other entries in this virtual row equal to zero.
961 * If variable v appears in a row, then a_{v,c} is the element in column c
962 * of that row.
964 * Let v be the first variable with a_{v,c1}/a_{r,c1} != a_{v,c2}/a_{r,c2}.
965 * Then if a_{v,c1}/a_{r,c1} < a_{v,c2}/a_{r,c2}, i.e.,
966 * a_{v,c2} a_{r,c1} - a_{v,c1} a_{r,c2} > 0, c1 results in the minimal
967 * increment. Otherwise, it's c2.
969 static int lexmin_col_pair(struct isl_tab *tab,
970 int row, int col1, int col2, isl_int tmp)
972 int i;
973 isl_int *tr;
975 tr = tab->mat->row[row] + 2 + tab->M;
977 for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
978 int s1, s2;
979 isl_int *r;
981 if (!tab->var[i].is_row) {
982 if (tab->var[i].index == col1)
983 return col2;
984 if (tab->var[i].index == col2)
985 return col1;
986 continue;
989 if (tab->var[i].index == row)
990 continue;
992 r = tab->mat->row[tab->var[i].index] + 2 + tab->M;
993 s1 = isl_int_sgn(r[col1]);
994 s2 = isl_int_sgn(r[col2]);
995 if (s1 == 0 && s2 == 0)
996 continue;
997 if (s1 < s2)
998 return col1;
999 if (s2 < s1)
1000 return col2;
1002 isl_int_mul(tmp, r[col2], tr[col1]);
1003 isl_int_submul(tmp, r[col1], tr[col2]);
1004 if (isl_int_is_pos(tmp))
1005 return col1;
1006 if (isl_int_is_neg(tmp))
1007 return col2;
1009 return -1;
1012 /* Given a row in the tableau, find and return the column that would
1013 * result in the lexicographically smallest, but positive, increment
1014 * in the sample point.
1015 * If there is no such column, then return tab->n_col.
1016 * If anything goes wrong, return -1.
1018 static int lexmin_pivot_col(struct isl_tab *tab, int row)
1020 int j;
1021 int col = tab->n_col;
1022 isl_int *tr;
1023 isl_int tmp;
1025 tr = tab->mat->row[row] + 2 + tab->M;
1027 isl_int_init(tmp);
1029 for (j = tab->n_dead; j < tab->n_col; ++j) {
1030 if (tab->col_var[j] >= 0 &&
1031 (tab->col_var[j] < tab->n_param ||
1032 tab->col_var[j] >= tab->n_var - tab->n_div))
1033 continue;
1035 if (!isl_int_is_pos(tr[j]))
1036 continue;
1038 if (col == tab->n_col)
1039 col = j;
1040 else
1041 col = lexmin_col_pair(tab, row, col, j, tmp);
1042 isl_assert(tab->mat->ctx, col >= 0, goto error);
1045 isl_int_clear(tmp);
1046 return col;
1047 error:
1048 isl_int_clear(tmp);
1049 return -1;
1052 /* Return the first known violated constraint, i.e., a non-negative
1053 * contraint that currently has an either obviously negative value
1054 * or a previously determined to be negative value.
1056 * If any constraint has a negative coefficient for the big parameter,
1057 * if any, then we return one of these first.
1059 static int first_neg(struct isl_tab *tab)
1061 int row;
1063 if (tab->M)
1064 for (row = tab->n_redundant; row < tab->n_row; ++row) {
1065 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
1066 continue;
1067 if (isl_int_is_neg(tab->mat->row[row][2]))
1068 return row;
1070 for (row = tab->n_redundant; row < tab->n_row; ++row) {
1071 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
1072 continue;
1073 if (tab->row_sign) {
1074 if (tab->row_sign[row] == 0 &&
1075 is_obviously_neg(tab, row))
1076 tab->row_sign[row] = isl_tab_row_neg;
1077 if (tab->row_sign[row] != isl_tab_row_neg)
1078 continue;
1079 } else if (!is_obviously_neg(tab, row))
1080 continue;
1081 return row;
1083 return -1;
1086 /* Resolve all known or obviously violated constraints through pivoting.
1087 * In particular, as long as we can find any violated constraint, we
1088 * look for a pivoting column that would result in the lexicographicallly
1089 * smallest increment in the sample point. If there is no such column
1090 * then the tableau is infeasible.
1092 static struct isl_tab *restore_lexmin(struct isl_tab *tab) WARN_UNUSED;
1093 static struct isl_tab *restore_lexmin(struct isl_tab *tab)
1095 int row, col;
1097 if (!tab)
1098 return NULL;
1099 if (tab->empty)
1100 return tab;
1101 while ((row = first_neg(tab)) != -1) {
1102 col = lexmin_pivot_col(tab, row);
1103 if (col >= tab->n_col) {
1104 if (isl_tab_mark_empty(tab) < 0)
1105 goto error;
1106 return tab;
1108 if (col < 0)
1109 goto error;
1110 if (isl_tab_pivot(tab, row, col) < 0)
1111 goto error;
1113 return tab;
1114 error:
1115 isl_tab_free(tab);
1116 return NULL;
1119 /* Given a row that represents an equality, look for an appropriate
1120 * pivoting column.
1121 * In particular, if there are any non-zero coefficients among
1122 * the non-parameter variables, then we take the last of these
1123 * variables. Eliminating this variable in terms of the other
1124 * variables and/or parameters does not influence the property
1125 * that all column in the initial tableau are lexicographically
1126 * positive. The row corresponding to the eliminated variable
1127 * will only have non-zero entries below the diagonal of the
1128 * initial tableau. That is, we transform
1130 * I I
1131 * 1 into a
1132 * I I
1134 * If there is no such non-parameter variable, then we are dealing with
1135 * pure parameter equality and we pick any parameter with coefficient 1 or -1
1136 * for elimination. This will ensure that the eliminated parameter
1137 * always has an integer value whenever all the other parameters are integral.
1138 * If there is no such parameter then we return -1.
1140 static int last_var_col_or_int_par_col(struct isl_tab *tab, int row)
1142 unsigned off = 2 + tab->M;
1143 int i;
1145 for (i = tab->n_var - tab->n_div - 1; i >= 0 && i >= tab->n_param; --i) {
1146 int col;
1147 if (tab->var[i].is_row)
1148 continue;
1149 col = tab->var[i].index;
1150 if (col <= tab->n_dead)
1151 continue;
1152 if (!isl_int_is_zero(tab->mat->row[row][off + col]))
1153 return col;
1155 for (i = tab->n_dead; i < tab->n_col; ++i) {
1156 if (isl_int_is_one(tab->mat->row[row][off + i]))
1157 return i;
1158 if (isl_int_is_negone(tab->mat->row[row][off + i]))
1159 return i;
1161 return -1;
1164 /* Add an equality that is known to be valid to the tableau.
1165 * We first check if we can eliminate a variable or a parameter.
1166 * If not, we add the equality as two inequalities.
1167 * In this case, the equality was a pure parameter equality and there
1168 * is no need to resolve any constraint violations.
1170 static struct isl_tab *add_lexmin_valid_eq(struct isl_tab *tab, isl_int *eq)
1172 int i;
1173 int r;
1175 if (!tab)
1176 return NULL;
1177 r = isl_tab_add_row(tab, eq);
1178 if (r < 0)
1179 goto error;
1181 r = tab->con[r].index;
1182 i = last_var_col_or_int_par_col(tab, r);
1183 if (i < 0) {
1184 tab->con[r].is_nonneg = 1;
1185 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1186 goto error;
1187 isl_seq_neg(eq, eq, 1 + tab->n_var);
1188 r = isl_tab_add_row(tab, eq);
1189 if (r < 0)
1190 goto error;
1191 tab->con[r].is_nonneg = 1;
1192 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1193 goto error;
1194 } else {
1195 if (isl_tab_pivot(tab, r, i) < 0)
1196 goto error;
1197 if (isl_tab_kill_col(tab, i) < 0)
1198 goto error;
1199 tab->n_eq++;
1201 tab = restore_lexmin(tab);
1204 return tab;
1205 error:
1206 isl_tab_free(tab);
1207 return NULL;
1210 /* Check if the given row is a pure constant.
1212 static int is_constant(struct isl_tab *tab, int row)
1214 unsigned off = 2 + tab->M;
1216 return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1217 tab->n_col - tab->n_dead) == -1;
1220 /* Add an equality that may or may not be valid to the tableau.
1221 * If the resulting row is a pure constant, then it must be zero.
1222 * Otherwise, the resulting tableau is empty.
1224 * If the row is not a pure constant, then we add two inequalities,
1225 * each time checking that they can be satisfied.
1226 * In the end we try to use one of the two constraints to eliminate
1227 * a column.
1229 static struct isl_tab *add_lexmin_eq(struct isl_tab *tab, isl_int *eq) WARN_UNUSED;
1230 static struct isl_tab *add_lexmin_eq(struct isl_tab *tab, isl_int *eq)
1232 int r1, r2;
1233 int row;
1234 struct isl_tab_undo *snap;
1236 if (!tab)
1237 return NULL;
1238 snap = isl_tab_snap(tab);
1239 r1 = isl_tab_add_row(tab, eq);
1240 if (r1 < 0)
1241 goto error;
1242 tab->con[r1].is_nonneg = 1;
1243 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r1]) < 0)
1244 goto error;
1246 row = tab->con[r1].index;
1247 if (is_constant(tab, row)) {
1248 if (!isl_int_is_zero(tab->mat->row[row][1]) ||
1249 (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))) {
1250 if (isl_tab_mark_empty(tab) < 0)
1251 goto error;
1252 return tab;
1254 if (isl_tab_rollback(tab, snap) < 0)
1255 goto error;
1256 return tab;
1259 tab = restore_lexmin(tab);
1260 if (!tab || tab->empty)
1261 return tab;
1263 isl_seq_neg(eq, eq, 1 + tab->n_var);
1265 r2 = isl_tab_add_row(tab, eq);
1266 if (r2 < 0)
1267 goto error;
1268 tab->con[r2].is_nonneg = 1;
1269 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r2]) < 0)
1270 goto error;
1272 tab = restore_lexmin(tab);
1273 if (!tab || tab->empty)
1274 return tab;
1276 if (!tab->con[r1].is_row) {
1277 if (isl_tab_kill_col(tab, tab->con[r1].index) < 0)
1278 goto error;
1279 } else if (!tab->con[r2].is_row) {
1280 if (isl_tab_kill_col(tab, tab->con[r2].index) < 0)
1281 goto error;
1282 } else if (isl_int_is_zero(tab->mat->row[tab->con[r1].index][1])) {
1283 unsigned off = 2 + tab->M;
1284 int i;
1285 int row = tab->con[r1].index;
1286 i = isl_seq_first_non_zero(tab->mat->row[row]+off+tab->n_dead,
1287 tab->n_col - tab->n_dead);
1288 if (i != -1) {
1289 if (isl_tab_pivot(tab, row, tab->n_dead + i) < 0)
1290 goto error;
1291 if (isl_tab_kill_col(tab, tab->n_dead + i) < 0)
1292 goto error;
1296 if (tab->bset) {
1297 tab->bset = isl_basic_set_add_ineq(tab->bset, eq);
1298 if (isl_tab_push(tab, isl_tab_undo_bset_ineq) < 0)
1299 goto error;
1300 isl_seq_neg(eq, eq, 1 + tab->n_var);
1301 tab->bset = isl_basic_set_add_ineq(tab->bset, eq);
1302 isl_seq_neg(eq, eq, 1 + tab->n_var);
1303 if (isl_tab_push(tab, isl_tab_undo_bset_ineq) < 0)
1304 goto error;
1305 if (!tab->bset)
1306 goto error;
1309 return tab;
1310 error:
1311 isl_tab_free(tab);
1312 return NULL;
1315 /* Add an inequality to the tableau, resolving violations using
1316 * restore_lexmin.
1318 static struct isl_tab *add_lexmin_ineq(struct isl_tab *tab, isl_int *ineq)
1320 int r;
1322 if (!tab)
1323 return NULL;
1324 if (tab->bset) {
1325 tab->bset = isl_basic_set_add_ineq(tab->bset, ineq);
1326 if (isl_tab_push(tab, isl_tab_undo_bset_ineq) < 0)
1327 goto error;
1328 if (!tab->bset)
1329 goto error;
1331 r = isl_tab_add_row(tab, ineq);
1332 if (r < 0)
1333 goto error;
1334 tab->con[r].is_nonneg = 1;
1335 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1336 goto error;
1337 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1338 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1339 goto error;
1340 return tab;
1343 tab = restore_lexmin(tab);
1344 if (tab && !tab->empty && tab->con[r].is_row &&
1345 isl_tab_row_is_redundant(tab, tab->con[r].index))
1346 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1347 goto error;
1348 return tab;
1349 error:
1350 isl_tab_free(tab);
1351 return NULL;
1354 /* Check if the coefficients of the parameters are all integral.
1356 static int integer_parameter(struct isl_tab *tab, int row)
1358 int i;
1359 int col;
1360 unsigned off = 2 + tab->M;
1362 for (i = 0; i < tab->n_param; ++i) {
1363 /* Eliminated parameter */
1364 if (tab->var[i].is_row)
1365 continue;
1366 col = tab->var[i].index;
1367 if (!isl_int_is_divisible_by(tab->mat->row[row][off + col],
1368 tab->mat->row[row][0]))
1369 return 0;
1371 for (i = 0; i < tab->n_div; ++i) {
1372 if (tab->var[tab->n_var - tab->n_div + i].is_row)
1373 continue;
1374 col = tab->var[tab->n_var - tab->n_div + i].index;
1375 if (!isl_int_is_divisible_by(tab->mat->row[row][off + col],
1376 tab->mat->row[row][0]))
1377 return 0;
1379 return 1;
1382 /* Check if the coefficients of the non-parameter variables are all integral.
1384 static int integer_variable(struct isl_tab *tab, int row)
1386 int i;
1387 unsigned off = 2 + tab->M;
1389 for (i = tab->n_dead; i < tab->n_col; ++i) {
1390 if (tab->col_var[i] >= 0 &&
1391 (tab->col_var[i] < tab->n_param ||
1392 tab->col_var[i] >= tab->n_var - tab->n_div))
1393 continue;
1394 if (!isl_int_is_divisible_by(tab->mat->row[row][off + i],
1395 tab->mat->row[row][0]))
1396 return 0;
1398 return 1;
1401 /* Check if the constant term is integral.
1403 static int integer_constant(struct isl_tab *tab, int row)
1405 return isl_int_is_divisible_by(tab->mat->row[row][1],
1406 tab->mat->row[row][0]);
1409 #define I_CST 1 << 0
1410 #define I_PAR 1 << 1
1411 #define I_VAR 1 << 2
1413 /* Check for first (non-parameter) variable that is non-integer and
1414 * therefore requires a cut.
1415 * For parametric tableaus, there are three parts in a row,
1416 * the constant, the coefficients of the parameters and the rest.
1417 * For each part, we check whether the coefficients in that part
1418 * are all integral and if so, set the corresponding flag in *f.
1419 * If the constant and the parameter part are integral, then the
1420 * current sample value is integral and no cut is required
1421 * (irrespective of whether the variable part is integral).
1423 static int first_non_integer(struct isl_tab *tab, int *f)
1425 int i;
1427 for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
1428 int flags = 0;
1429 int row;
1430 if (!tab->var[i].is_row)
1431 continue;
1432 row = tab->var[i].index;
1433 if (integer_constant(tab, row))
1434 ISL_FL_SET(flags, I_CST);
1435 if (integer_parameter(tab, row))
1436 ISL_FL_SET(flags, I_PAR);
1437 if (ISL_FL_ISSET(flags, I_CST) && ISL_FL_ISSET(flags, I_PAR))
1438 continue;
1439 if (integer_variable(tab, row))
1440 ISL_FL_SET(flags, I_VAR);
1441 *f = flags;
1442 return row;
1444 return -1;
1447 /* Add a (non-parametric) cut to cut away the non-integral sample
1448 * value of the given row.
1450 * If the row is given by
1452 * m r = f + \sum_i a_i y_i
1454 * then the cut is
1456 * c = - {-f/m} + \sum_i {a_i/m} y_i >= 0
1458 * The big parameter, if any, is ignored, since it is assumed to be big
1459 * enough to be divisible by any integer.
1460 * If the tableau is actually a parametric tableau, then this function
1461 * is only called when all coefficients of the parameters are integral.
1462 * The cut therefore has zero coefficients for the parameters.
1464 * The current value is known to be negative, so row_sign, if it
1465 * exists, is set accordingly.
1467 * Return the row of the cut or -1.
1469 static int add_cut(struct isl_tab *tab, int row)
1471 int i;
1472 int r;
1473 isl_int *r_row;
1474 unsigned off = 2 + tab->M;
1476 if (isl_tab_extend_cons(tab, 1) < 0)
1477 return -1;
1478 r = isl_tab_allocate_con(tab);
1479 if (r < 0)
1480 return -1;
1482 r_row = tab->mat->row[tab->con[r].index];
1483 isl_int_set(r_row[0], tab->mat->row[row][0]);
1484 isl_int_neg(r_row[1], tab->mat->row[row][1]);
1485 isl_int_fdiv_r(r_row[1], r_row[1], tab->mat->row[row][0]);
1486 isl_int_neg(r_row[1], r_row[1]);
1487 if (tab->M)
1488 isl_int_set_si(r_row[2], 0);
1489 for (i = 0; i < tab->n_col; ++i)
1490 isl_int_fdiv_r(r_row[off + i],
1491 tab->mat->row[row][off + i], tab->mat->row[row][0]);
1493 tab->con[r].is_nonneg = 1;
1494 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1495 return -1;
1496 if (tab->row_sign)
1497 tab->row_sign[tab->con[r].index] = isl_tab_row_neg;
1499 return tab->con[r].index;
1502 /* Given a non-parametric tableau, add cuts until an integer
1503 * sample point is obtained or until the tableau is determined
1504 * to be integer infeasible.
1505 * As long as there is any non-integer value in the sample point,
1506 * we add an appropriate cut, if possible and resolve the violated
1507 * cut constraint using restore_lexmin.
1508 * If one of the corresponding rows is equal to an integral
1509 * combination of variables/constraints plus a non-integral constant,
1510 * then there is no way to obtain an integer point an we return
1511 * a tableau that is marked empty.
1513 static struct isl_tab *cut_to_integer_lexmin(struct isl_tab *tab)
1515 int row;
1516 int flags;
1518 if (!tab)
1519 return NULL;
1520 if (tab->empty)
1521 return tab;
1523 while ((row = first_non_integer(tab, &flags)) != -1) {
1524 if (ISL_FL_ISSET(flags, I_VAR)) {
1525 if (isl_tab_mark_empty(tab) < 0)
1526 goto error;
1527 return tab;
1529 row = add_cut(tab, row);
1530 if (row < 0)
1531 goto error;
1532 tab = restore_lexmin(tab);
1533 if (!tab || tab->empty)
1534 break;
1536 return tab;
1537 error:
1538 isl_tab_free(tab);
1539 return NULL;
1542 /* Check whether all the currently active samples also satisfy the inequality
1543 * "ineq" (treated as an equality if eq is set).
1544 * Remove those samples that do not.
1546 static struct isl_tab *check_samples(struct isl_tab *tab, isl_int *ineq, int eq)
1548 int i;
1549 isl_int v;
1551 if (!tab)
1552 return NULL;
1554 isl_assert(tab->mat->ctx, tab->bset, goto error);
1555 isl_assert(tab->mat->ctx, tab->samples, goto error);
1556 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, goto error);
1558 isl_int_init(v);
1559 for (i = tab->n_outside; i < tab->n_sample; ++i) {
1560 int sgn;
1561 isl_seq_inner_product(ineq, tab->samples->row[i],
1562 1 + tab->n_var, &v);
1563 sgn = isl_int_sgn(v);
1564 if (eq ? (sgn == 0) : (sgn >= 0))
1565 continue;
1566 tab = isl_tab_drop_sample(tab, i);
1567 if (!tab)
1568 break;
1570 isl_int_clear(v);
1572 return tab;
1573 error:
1574 isl_tab_free(tab);
1575 return NULL;
1578 /* Check whether the sample value of the tableau is finite,
1579 * i.e., either the tableau does not use a big parameter, or
1580 * all values of the variables are equal to the big parameter plus
1581 * some constant. This constant is the actual sample value.
1583 static int sample_is_finite(struct isl_tab *tab)
1585 int i;
1587 if (!tab->M)
1588 return 1;
1590 for (i = 0; i < tab->n_var; ++i) {
1591 int row;
1592 if (!tab->var[i].is_row)
1593 return 0;
1594 row = tab->var[i].index;
1595 if (isl_int_ne(tab->mat->row[row][0], tab->mat->row[row][2]))
1596 return 0;
1598 return 1;
1601 /* Check if the context tableau of sol has any integer points.
1602 * Leave tab in empty state if no integer point can be found.
1603 * If an integer point can be found and if moreover it is finite,
1604 * then it is added to the list of sample values.
1606 * This function is only called when none of the currently active sample
1607 * values satisfies the most recently added constraint.
1609 static struct isl_tab *check_integer_feasible(struct isl_tab *tab)
1611 struct isl_tab_undo *snap;
1612 int feasible;
1614 if (!tab)
1615 return NULL;
1617 snap = isl_tab_snap(tab);
1618 if (isl_tab_push_basis(tab) < 0)
1619 goto error;
1621 tab = cut_to_integer_lexmin(tab);
1622 if (!tab)
1623 goto error;
1625 if (!tab->empty && sample_is_finite(tab)) {
1626 struct isl_vec *sample;
1628 sample = isl_tab_get_sample_value(tab);
1630 tab = isl_tab_add_sample(tab, sample);
1633 if (!tab->empty && isl_tab_rollback(tab, snap) < 0)
1634 goto error;
1636 return tab;
1637 error:
1638 isl_tab_free(tab);
1639 return NULL;
1642 /* Check if any of the currently active sample values satisfies
1643 * the inequality "ineq" (an equality if eq is set).
1645 static int tab_has_valid_sample(struct isl_tab *tab, isl_int *ineq, int eq)
1647 int i;
1648 isl_int v;
1650 if (!tab)
1651 return -1;
1653 isl_assert(tab->mat->ctx, tab->bset, return -1);
1654 isl_assert(tab->mat->ctx, tab->samples, return -1);
1655 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, return -1);
1657 isl_int_init(v);
1658 for (i = tab->n_outside; i < tab->n_sample; ++i) {
1659 int sgn;
1660 isl_seq_inner_product(ineq, tab->samples->row[i],
1661 1 + tab->n_var, &v);
1662 sgn = isl_int_sgn(v);
1663 if (eq ? (sgn == 0) : (sgn >= 0))
1664 break;
1666 isl_int_clear(v);
1668 return i < tab->n_sample;
1671 /* For a div d = floor(f/m), add the constraints
1673 * f - m d >= 0
1674 * -(f-(m-1)) + m d >= 0
1676 * Note that the second constraint is the negation of
1678 * f - m d >= m
1680 static void add_div_constraints(struct isl_context *context, unsigned div)
1682 unsigned total;
1683 unsigned div_pos;
1684 struct isl_vec *ineq;
1685 struct isl_basic_set *bset;
1687 bset = context->op->peek_basic_set(context);
1688 if (!bset)
1689 goto error;
1691 total = isl_basic_set_total_dim(bset);
1692 div_pos = 1 + total - bset->n_div + div;
1694 ineq = ineq_for_div(bset, div);
1695 if (!ineq)
1696 goto error;
1698 context->op->add_ineq(context, ineq->el, 0, 0);
1700 isl_seq_neg(ineq->el, bset->div[div] + 1, 1 + total);
1701 isl_int_set(ineq->el[div_pos], bset->div[div][0]);
1702 isl_int_add(ineq->el[0], ineq->el[0], ineq->el[div_pos]);
1703 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
1705 context->op->add_ineq(context, ineq->el, 0, 0);
1707 isl_vec_free(ineq);
1709 return;
1710 error:
1711 context->op->invalidate(context);
1714 /* Add a div specifed by "div" to the tableau "tab" and return
1715 * the index of the new div. *nonneg is set to 1 if the div
1716 * is obviously non-negative.
1718 static int context_tab_add_div(struct isl_tab *tab, struct isl_vec *div,
1719 int *nonneg)
1721 int i;
1722 int r;
1723 int k;
1724 struct isl_mat *samples;
1726 for (i = 0; i < tab->n_var; ++i) {
1727 if (isl_int_is_zero(div->el[2 + i]))
1728 continue;
1729 if (!tab->var[i].is_nonneg)
1730 break;
1732 *nonneg = i == tab->n_var;
1734 if (isl_tab_extend_cons(tab, 3) < 0)
1735 return -1;
1736 if (isl_tab_extend_vars(tab, 1) < 0)
1737 return -1;
1738 r = isl_tab_allocate_var(tab);
1739 if (r < 0)
1740 return -1;
1741 if (*nonneg)
1742 tab->var[r].is_nonneg = 1;
1743 tab->var[r].frozen = 1;
1745 samples = isl_mat_extend(tab->samples,
1746 tab->n_sample, 1 + tab->n_var);
1747 tab->samples = samples;
1748 if (!samples)
1749 return -1;
1750 for (i = tab->n_outside; i < samples->n_row; ++i) {
1751 isl_seq_inner_product(div->el + 1, samples->row[i],
1752 div->size - 1, &samples->row[i][samples->n_col - 1]);
1753 isl_int_fdiv_q(samples->row[i][samples->n_col - 1],
1754 samples->row[i][samples->n_col - 1], div->el[0]);
1757 tab->bset = isl_basic_set_extend_dim(tab->bset,
1758 isl_basic_set_get_dim(tab->bset), 1, 0, 2);
1759 k = isl_basic_set_alloc_div(tab->bset);
1760 if (k < 0)
1761 return -1;
1762 isl_seq_cpy(tab->bset->div[k], div->el, div->size);
1763 if (isl_tab_push(tab, isl_tab_undo_bset_div) < 0)
1764 return -1;
1766 return k;
1769 /* Add a div specified by "div" to both the main tableau and
1770 * the context tableau. In case of the main tableau, we only
1771 * need to add an extra div. In the context tableau, we also
1772 * need to express the meaning of the div.
1773 * Return the index of the div or -1 if anything went wrong.
1775 static int add_div(struct isl_tab *tab, struct isl_context *context,
1776 struct isl_vec *div)
1778 int r;
1779 int k;
1780 int nonneg;
1782 k = context->op->add_div(context, div, &nonneg);
1783 if (k < 0)
1784 goto error;
1786 add_div_constraints(context, k);
1787 if (!context->op->is_ok(context))
1788 goto error;
1790 if (isl_tab_extend_vars(tab, 1) < 0)
1791 goto error;
1792 r = isl_tab_allocate_var(tab);
1793 if (r < 0)
1794 goto error;
1795 if (nonneg)
1796 tab->var[r].is_nonneg = 1;
1797 tab->var[r].frozen = 1;
1798 tab->n_div++;
1800 return tab->n_div - 1;
1801 error:
1802 context->op->invalidate(context);
1803 return -1;
1806 static int find_div(struct isl_tab *tab, isl_int *div, isl_int denom)
1808 int i;
1809 unsigned total = isl_basic_set_total_dim(tab->bset);
1811 for (i = 0; i < tab->bset->n_div; ++i) {
1812 if (isl_int_ne(tab->bset->div[i][0], denom))
1813 continue;
1814 if (!isl_seq_eq(tab->bset->div[i] + 1, div, total))
1815 continue;
1816 return i;
1818 return -1;
1821 /* Return the index of a div that corresponds to "div".
1822 * We first check if we already have such a div and if not, we create one.
1824 static int get_div(struct isl_tab *tab, struct isl_context *context,
1825 struct isl_vec *div)
1827 int d;
1828 struct isl_tab *context_tab = context->op->peek_tab(context);
1830 if (!context_tab)
1831 return -1;
1833 d = find_div(context_tab, div->el + 1, div->el[0]);
1834 if (d != -1)
1835 return d;
1837 return add_div(tab, context, div);
1840 /* Add a parametric cut to cut away the non-integral sample value
1841 * of the give row.
1842 * Let a_i be the coefficients of the constant term and the parameters
1843 * and let b_i be the coefficients of the variables or constraints
1844 * in basis of the tableau.
1845 * Let q be the div q = floor(\sum_i {-a_i} y_i).
1847 * The cut is expressed as
1849 * c = \sum_i -{-a_i} y_i + \sum_i {b_i} x_i + q >= 0
1851 * If q did not already exist in the context tableau, then it is added first.
1852 * If q is in a column of the main tableau then the "+ q" can be accomplished
1853 * by setting the corresponding entry to the denominator of the constraint.
1854 * If q happens to be in a row of the main tableau, then the corresponding
1855 * row needs to be added instead (taking care of the denominators).
1856 * Note that this is very unlikely, but perhaps not entirely impossible.
1858 * The current value of the cut is known to be negative (or at least
1859 * non-positive), so row_sign is set accordingly.
1861 * Return the row of the cut or -1.
1863 static int add_parametric_cut(struct isl_tab *tab, int row,
1864 struct isl_context *context)
1866 struct isl_vec *div;
1867 int d;
1868 int i;
1869 int r;
1870 isl_int *r_row;
1871 int col;
1872 int n;
1873 unsigned off = 2 + tab->M;
1875 if (!context)
1876 return -1;
1878 div = get_row_parameter_div(tab, row);
1879 if (!div)
1880 return -1;
1882 n = tab->n_div;
1883 d = context->op->get_div(context, tab, div);
1884 if (d < 0)
1885 return -1;
1887 if (isl_tab_extend_cons(tab, 1) < 0)
1888 return -1;
1889 r = isl_tab_allocate_con(tab);
1890 if (r < 0)
1891 return -1;
1893 r_row = tab->mat->row[tab->con[r].index];
1894 isl_int_set(r_row[0], tab->mat->row[row][0]);
1895 isl_int_neg(r_row[1], tab->mat->row[row][1]);
1896 isl_int_fdiv_r(r_row[1], r_row[1], tab->mat->row[row][0]);
1897 isl_int_neg(r_row[1], r_row[1]);
1898 if (tab->M)
1899 isl_int_set_si(r_row[2], 0);
1900 for (i = 0; i < tab->n_param; ++i) {
1901 if (tab->var[i].is_row)
1902 continue;
1903 col = tab->var[i].index;
1904 isl_int_neg(r_row[off + col], tab->mat->row[row][off + col]);
1905 isl_int_fdiv_r(r_row[off + col], r_row[off + col],
1906 tab->mat->row[row][0]);
1907 isl_int_neg(r_row[off + col], r_row[off + col]);
1909 for (i = 0; i < tab->n_div; ++i) {
1910 if (tab->var[tab->n_var - tab->n_div + i].is_row)
1911 continue;
1912 col = tab->var[tab->n_var - tab->n_div + i].index;
1913 isl_int_neg(r_row[off + col], tab->mat->row[row][off + col]);
1914 isl_int_fdiv_r(r_row[off + col], r_row[off + col],
1915 tab->mat->row[row][0]);
1916 isl_int_neg(r_row[off + col], r_row[off + col]);
1918 for (i = 0; i < tab->n_col; ++i) {
1919 if (tab->col_var[i] >= 0 &&
1920 (tab->col_var[i] < tab->n_param ||
1921 tab->col_var[i] >= tab->n_var - tab->n_div))
1922 continue;
1923 isl_int_fdiv_r(r_row[off + i],
1924 tab->mat->row[row][off + i], tab->mat->row[row][0]);
1926 if (tab->var[tab->n_var - tab->n_div + d].is_row) {
1927 isl_int gcd;
1928 int d_row = tab->var[tab->n_var - tab->n_div + d].index;
1929 isl_int_init(gcd);
1930 isl_int_gcd(gcd, tab->mat->row[d_row][0], r_row[0]);
1931 isl_int_divexact(r_row[0], r_row[0], gcd);
1932 isl_int_divexact(gcd, tab->mat->row[d_row][0], gcd);
1933 isl_seq_combine(r_row + 1, gcd, r_row + 1,
1934 r_row[0], tab->mat->row[d_row] + 1,
1935 off - 1 + tab->n_col);
1936 isl_int_mul(r_row[0], r_row[0], tab->mat->row[d_row][0]);
1937 isl_int_clear(gcd);
1938 } else {
1939 col = tab->var[tab->n_var - tab->n_div + d].index;
1940 isl_int_set(r_row[off + col], tab->mat->row[row][0]);
1943 tab->con[r].is_nonneg = 1;
1944 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1945 return -1;
1946 if (tab->row_sign)
1947 tab->row_sign[tab->con[r].index] = isl_tab_row_neg;
1949 isl_vec_free(div);
1951 row = tab->con[r].index;
1953 if (d >= n && context->op->detect_equalities(context, tab) < 0)
1954 return -1;
1956 return row;
1959 /* Construct a tableau for bmap that can be used for computing
1960 * the lexicographic minimum (or maximum) of bmap.
1961 * If not NULL, then dom is the domain where the minimum
1962 * should be computed. In this case, we set up a parametric
1963 * tableau with row signs (initialized to "unknown").
1964 * If M is set, then the tableau will use a big parameter.
1965 * If max is set, then a maximum should be computed instead of a minimum.
1966 * This means that for each variable x, the tableau will contain the variable
1967 * x' = M - x, rather than x' = M + x. This in turn means that the coefficient
1968 * of the variables in all constraints are negated prior to adding them
1969 * to the tableau.
1971 static struct isl_tab *tab_for_lexmin(struct isl_basic_map *bmap,
1972 struct isl_basic_set *dom, unsigned M, int max)
1974 int i;
1975 struct isl_tab *tab;
1977 tab = isl_tab_alloc(bmap->ctx, 2 * bmap->n_eq + bmap->n_ineq + 1,
1978 isl_basic_map_total_dim(bmap), M);
1979 if (!tab)
1980 return NULL;
1982 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
1983 if (dom) {
1984 tab->n_param = isl_basic_set_total_dim(dom) - dom->n_div;
1985 tab->n_div = dom->n_div;
1986 tab->row_sign = isl_calloc_array(bmap->ctx,
1987 enum isl_tab_row_sign, tab->mat->n_row);
1988 if (!tab->row_sign)
1989 goto error;
1991 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
1992 if (isl_tab_mark_empty(tab) < 0)
1993 goto error;
1994 return tab;
1997 for (i = tab->n_param; i < tab->n_var - tab->n_div; ++i) {
1998 tab->var[i].is_nonneg = 1;
1999 tab->var[i].frozen = 1;
2001 for (i = 0; i < bmap->n_eq; ++i) {
2002 if (max)
2003 isl_seq_neg(bmap->eq[i] + 1 + tab->n_param,
2004 bmap->eq[i] + 1 + tab->n_param,
2005 tab->n_var - tab->n_param - tab->n_div);
2006 tab = add_lexmin_valid_eq(tab, bmap->eq[i]);
2007 if (max)
2008 isl_seq_neg(bmap->eq[i] + 1 + tab->n_param,
2009 bmap->eq[i] + 1 + tab->n_param,
2010 tab->n_var - tab->n_param - tab->n_div);
2011 if (!tab || tab->empty)
2012 return tab;
2014 for (i = 0; i < bmap->n_ineq; ++i) {
2015 if (max)
2016 isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param,
2017 bmap->ineq[i] + 1 + tab->n_param,
2018 tab->n_var - tab->n_param - tab->n_div);
2019 tab = add_lexmin_ineq(tab, bmap->ineq[i]);
2020 if (max)
2021 isl_seq_neg(bmap->ineq[i] + 1 + tab->n_param,
2022 bmap->ineq[i] + 1 + tab->n_param,
2023 tab->n_var - tab->n_param - tab->n_div);
2024 if (!tab || tab->empty)
2025 return tab;
2027 return tab;
2028 error:
2029 isl_tab_free(tab);
2030 return NULL;
2033 /* Given a main tableau where more than one row requires a split,
2034 * determine and return the "best" row to split on.
2036 * Given two rows in the main tableau, if the inequality corresponding
2037 * to the first row is redundant with respect to that of the second row
2038 * in the current tableau, then it is better to split on the second row,
2039 * since in the positive part, both row will be positive.
2040 * (In the negative part a pivot will have to be performed and just about
2041 * anything can happen to the sign of the other row.)
2043 * As a simple heuristic, we therefore select the row that makes the most
2044 * of the other rows redundant.
2046 * Perhaps it would also be useful to look at the number of constraints
2047 * that conflict with any given constraint.
2049 static int best_split(struct isl_tab *tab, struct isl_tab *context_tab)
2051 struct isl_tab_undo *snap;
2052 int split;
2053 int row;
2054 int best = -1;
2055 int best_r;
2057 if (isl_tab_extend_cons(context_tab, 2) < 0)
2058 return -1;
2060 snap = isl_tab_snap(context_tab);
2062 for (split = tab->n_redundant; split < tab->n_row; ++split) {
2063 struct isl_tab_undo *snap2;
2064 struct isl_vec *ineq = NULL;
2065 int r = 0;
2066 int ok;
2068 if (!isl_tab_var_from_row(tab, split)->is_nonneg)
2069 continue;
2070 if (tab->row_sign[split] != isl_tab_row_any)
2071 continue;
2073 ineq = get_row_parameter_ineq(tab, split);
2074 if (!ineq)
2075 return -1;
2076 ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
2077 isl_vec_free(ineq);
2078 if (!ok)
2079 return -1;
2081 snap2 = isl_tab_snap(context_tab);
2083 for (row = tab->n_redundant; row < tab->n_row; ++row) {
2084 struct isl_tab_var *var;
2086 if (row == split)
2087 continue;
2088 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
2089 continue;
2090 if (tab->row_sign[row] != isl_tab_row_any)
2091 continue;
2093 ineq = get_row_parameter_ineq(tab, row);
2094 if (!ineq)
2095 return -1;
2096 ok = isl_tab_add_ineq(context_tab, ineq->el) >= 0;
2097 isl_vec_free(ineq);
2098 if (!ok)
2099 return -1;
2100 var = &context_tab->con[context_tab->n_con - 1];
2101 if (!context_tab->empty &&
2102 !isl_tab_min_at_most_neg_one(context_tab, var))
2103 r++;
2104 if (isl_tab_rollback(context_tab, snap2) < 0)
2105 return -1;
2107 if (best == -1 || r > best_r) {
2108 best = split;
2109 best_r = r;
2111 if (isl_tab_rollback(context_tab, snap) < 0)
2112 return -1;
2115 return best;
2118 static struct isl_basic_set *context_lex_peek_basic_set(
2119 struct isl_context *context)
2121 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2122 if (!clex->tab)
2123 return NULL;
2124 return clex->tab->bset;
2127 static struct isl_tab *context_lex_peek_tab(struct isl_context *context)
2129 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2130 return clex->tab;
2133 static void context_lex_extend(struct isl_context *context, int n)
2135 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2136 if (!clex->tab)
2137 return;
2138 if (isl_tab_extend_cons(clex->tab, n) >= 0)
2139 return;
2140 isl_tab_free(clex->tab);
2141 clex->tab = NULL;
2144 static void context_lex_add_eq(struct isl_context *context, isl_int *eq,
2145 int check, int update)
2147 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2148 if (isl_tab_extend_cons(clex->tab, 2) < 0)
2149 goto error;
2150 clex->tab = add_lexmin_eq(clex->tab, eq);
2151 if (check) {
2152 int v = tab_has_valid_sample(clex->tab, eq, 1);
2153 if (v < 0)
2154 goto error;
2155 if (!v)
2156 clex->tab = check_integer_feasible(clex->tab);
2158 if (update)
2159 clex->tab = check_samples(clex->tab, eq, 1);
2160 return;
2161 error:
2162 isl_tab_free(clex->tab);
2163 clex->tab = NULL;
2166 static void context_lex_add_ineq(struct isl_context *context, isl_int *ineq,
2167 int check, int update)
2169 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2170 if (isl_tab_extend_cons(clex->tab, 1) < 0)
2171 goto error;
2172 clex->tab = add_lexmin_ineq(clex->tab, ineq);
2173 if (check) {
2174 int v = tab_has_valid_sample(clex->tab, ineq, 0);
2175 if (v < 0)
2176 goto error;
2177 if (!v)
2178 clex->tab = check_integer_feasible(clex->tab);
2180 if (update)
2181 clex->tab = check_samples(clex->tab, ineq, 0);
2182 return;
2183 error:
2184 isl_tab_free(clex->tab);
2185 clex->tab = NULL;
2188 /* Check which signs can be obtained by "ineq" on all the currently
2189 * active sample values. See row_sign for more information.
2191 static enum isl_tab_row_sign tab_ineq_sign(struct isl_tab *tab, isl_int *ineq,
2192 int strict)
2194 int i;
2195 int sgn;
2196 isl_int tmp;
2197 int res = isl_tab_row_unknown;
2199 isl_assert(tab->mat->ctx, tab->samples, return 0);
2200 isl_assert(tab->mat->ctx, tab->samples->n_col == 1 + tab->n_var, return 0);
2202 isl_int_init(tmp);
2203 for (i = tab->n_outside; i < tab->n_sample; ++i) {
2204 isl_seq_inner_product(tab->samples->row[i], ineq,
2205 1 + tab->n_var, &tmp);
2206 sgn = isl_int_sgn(tmp);
2207 if (sgn > 0 || (sgn == 0 && strict)) {
2208 if (res == isl_tab_row_unknown)
2209 res = isl_tab_row_pos;
2210 if (res == isl_tab_row_neg)
2211 res = isl_tab_row_any;
2213 if (sgn < 0) {
2214 if (res == isl_tab_row_unknown)
2215 res = isl_tab_row_neg;
2216 if (res == isl_tab_row_pos)
2217 res = isl_tab_row_any;
2219 if (res == isl_tab_row_any)
2220 break;
2222 isl_int_clear(tmp);
2224 return res;
2227 static enum isl_tab_row_sign context_lex_ineq_sign(struct isl_context *context,
2228 isl_int *ineq, int strict)
2230 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2231 return tab_ineq_sign(clex->tab, ineq, strict);
2234 /* Check whether "ineq" can be added to the tableau without rendering
2235 * it infeasible.
2237 static int context_lex_test_ineq(struct isl_context *context, isl_int *ineq)
2239 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2240 struct isl_tab_undo *snap;
2241 int feasible;
2243 if (!clex->tab)
2244 return -1;
2246 if (isl_tab_extend_cons(clex->tab, 1) < 0)
2247 return -1;
2249 snap = isl_tab_snap(clex->tab);
2250 if (isl_tab_push_basis(clex->tab) < 0)
2251 return -1;
2252 clex->tab = add_lexmin_ineq(clex->tab, ineq);
2253 clex->tab = check_integer_feasible(clex->tab);
2254 if (!clex->tab)
2255 return -1;
2256 feasible = !clex->tab->empty;
2257 if (isl_tab_rollback(clex->tab, snap) < 0)
2258 return -1;
2260 return feasible;
2263 static int context_lex_get_div(struct isl_context *context, struct isl_tab *tab,
2264 struct isl_vec *div)
2266 return get_div(tab, context, div);
2269 static int context_lex_add_div(struct isl_context *context, struct isl_vec *div,
2270 int *nonneg)
2272 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2273 return context_tab_add_div(clex->tab, div, nonneg);
2276 static int context_lex_detect_equalities(struct isl_context *context,
2277 struct isl_tab *tab)
2279 return 0;
2282 static int context_lex_best_split(struct isl_context *context,
2283 struct isl_tab *tab)
2285 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2286 struct isl_tab_undo *snap;
2287 int r;
2289 snap = isl_tab_snap(clex->tab);
2290 if (isl_tab_push_basis(clex->tab) < 0)
2291 return -1;
2292 r = best_split(tab, clex->tab);
2294 if (isl_tab_rollback(clex->tab, snap) < 0)
2295 return -1;
2297 return r;
2300 static int context_lex_is_empty(struct isl_context *context)
2302 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2303 if (!clex->tab)
2304 return -1;
2305 return clex->tab->empty;
2308 static void *context_lex_save(struct isl_context *context)
2310 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2311 struct isl_tab_undo *snap;
2313 snap = isl_tab_snap(clex->tab);
2314 if (isl_tab_push_basis(clex->tab) < 0)
2315 return NULL;
2316 if (isl_tab_save_samples(clex->tab) < 0)
2317 return NULL;
2319 return snap;
2322 static void context_lex_restore(struct isl_context *context, void *save)
2324 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2325 if (isl_tab_rollback(clex->tab, (struct isl_tab_undo *)save) < 0) {
2326 isl_tab_free(clex->tab);
2327 clex->tab = NULL;
2331 static int context_lex_is_ok(struct isl_context *context)
2333 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2334 return !!clex->tab;
2337 /* For each variable in the context tableau, check if the variable can
2338 * only attain non-negative values. If so, mark the parameter as non-negative
2339 * in the main tableau. This allows for a more direct identification of some
2340 * cases of violated constraints.
2342 static struct isl_tab *tab_detect_nonnegative_parameters(struct isl_tab *tab,
2343 struct isl_tab *context_tab)
2345 int i;
2346 struct isl_tab_undo *snap;
2347 struct isl_vec *ineq = NULL;
2348 struct isl_tab_var *var;
2349 int n;
2351 if (context_tab->n_var == 0)
2352 return tab;
2354 ineq = isl_vec_alloc(tab->mat->ctx, 1 + context_tab->n_var);
2355 if (!ineq)
2356 goto error;
2358 if (isl_tab_extend_cons(context_tab, 1) < 0)
2359 goto error;
2361 snap = isl_tab_snap(context_tab);
2363 n = 0;
2364 isl_seq_clr(ineq->el, ineq->size);
2365 for (i = 0; i < context_tab->n_var; ++i) {
2366 isl_int_set_si(ineq->el[1 + i], 1);
2367 if (isl_tab_add_ineq(context_tab, ineq->el) < 0)
2368 goto error;
2369 var = &context_tab->con[context_tab->n_con - 1];
2370 if (!context_tab->empty &&
2371 !isl_tab_min_at_most_neg_one(context_tab, var)) {
2372 int j = i;
2373 if (i >= tab->n_param)
2374 j = i - tab->n_param + tab->n_var - tab->n_div;
2375 tab->var[j].is_nonneg = 1;
2376 n++;
2378 isl_int_set_si(ineq->el[1 + i], 0);
2379 if (isl_tab_rollback(context_tab, snap) < 0)
2380 goto error;
2383 if (context_tab->M && n == context_tab->n_var) {
2384 context_tab->mat = isl_mat_drop_cols(context_tab->mat, 2, 1);
2385 context_tab->M = 0;
2388 isl_vec_free(ineq);
2389 return tab;
2390 error:
2391 isl_vec_free(ineq);
2392 isl_tab_free(tab);
2393 return NULL;
2396 static struct isl_tab *context_lex_detect_nonnegative_parameters(
2397 struct isl_context *context, struct isl_tab *tab)
2399 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2400 struct isl_tab_undo *snap;
2402 snap = isl_tab_snap(clex->tab);
2403 if (isl_tab_push_basis(clex->tab) < 0)
2404 goto error;
2406 tab = tab_detect_nonnegative_parameters(tab, clex->tab);
2408 if (isl_tab_rollback(clex->tab, snap) < 0)
2409 goto error;
2411 return tab;
2412 error:
2413 isl_tab_free(tab);
2414 return NULL;
2417 static void context_lex_invalidate(struct isl_context *context)
2419 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2420 isl_tab_free(clex->tab);
2421 clex->tab = NULL;
2424 static void context_lex_free(struct isl_context *context)
2426 struct isl_context_lex *clex = (struct isl_context_lex *)context;
2427 isl_tab_free(clex->tab);
2428 free(clex);
2431 struct isl_context_op isl_context_lex_op = {
2432 context_lex_detect_nonnegative_parameters,
2433 context_lex_peek_basic_set,
2434 context_lex_peek_tab,
2435 context_lex_add_eq,
2436 context_lex_add_ineq,
2437 context_lex_ineq_sign,
2438 context_lex_test_ineq,
2439 context_lex_get_div,
2440 context_lex_add_div,
2441 context_lex_detect_equalities,
2442 context_lex_best_split,
2443 context_lex_is_empty,
2444 context_lex_is_ok,
2445 context_lex_save,
2446 context_lex_restore,
2447 context_lex_invalidate,
2448 context_lex_free,
2451 static struct isl_tab *context_tab_for_lexmin(struct isl_basic_set *bset)
2453 struct isl_tab *tab;
2455 bset = isl_basic_set_cow(bset);
2456 if (!bset)
2457 return NULL;
2458 tab = tab_for_lexmin((struct isl_basic_map *)bset, NULL, 1, 0);
2459 if (!tab)
2460 goto error;
2461 tab->bset = bset;
2462 tab = isl_tab_init_samples(tab);
2463 return tab;
2464 error:
2465 isl_basic_set_free(bset);
2466 return NULL;
2469 static struct isl_context *isl_context_lex_alloc(struct isl_basic_set *dom)
2471 struct isl_context_lex *clex;
2473 if (!dom)
2474 return NULL;
2476 clex = isl_alloc_type(dom->ctx, struct isl_context_lex);
2477 if (!clex)
2478 return NULL;
2480 clex->context.op = &isl_context_lex_op;
2482 clex->tab = context_tab_for_lexmin(isl_basic_set_copy(dom));
2483 clex->tab = restore_lexmin(clex->tab);
2484 clex->tab = check_integer_feasible(clex->tab);
2485 if (!clex->tab)
2486 goto error;
2488 return &clex->context;
2489 error:
2490 clex->context.op->free(&clex->context);
2491 return NULL;
2494 struct isl_context_gbr {
2495 struct isl_context context;
2496 struct isl_tab *tab;
2497 struct isl_tab *shifted;
2498 struct isl_tab *cone;
2501 static struct isl_tab *context_gbr_detect_nonnegative_parameters(
2502 struct isl_context *context, struct isl_tab *tab)
2504 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2505 return tab_detect_nonnegative_parameters(tab, cgbr->tab);
2508 static struct isl_basic_set *context_gbr_peek_basic_set(
2509 struct isl_context *context)
2511 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2512 if (!cgbr->tab)
2513 return NULL;
2514 return cgbr->tab->bset;
2517 static struct isl_tab *context_gbr_peek_tab(struct isl_context *context)
2519 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2520 return cgbr->tab;
2523 /* Initialize the "shifted" tableau of the context, which
2524 * contains the constraints of the original tableau shifted
2525 * by the sum of all negative coefficients. This ensures
2526 * that any rational point in the shifted tableau can
2527 * be rounded up to yield an integer point in the original tableau.
2529 static void gbr_init_shifted(struct isl_context_gbr *cgbr)
2531 int i, j;
2532 struct isl_vec *cst;
2533 struct isl_basic_set *bset = cgbr->tab->bset;
2534 unsigned dim = isl_basic_set_total_dim(bset);
2536 cst = isl_vec_alloc(cgbr->tab->mat->ctx, bset->n_ineq);
2537 if (!cst)
2538 return;
2540 for (i = 0; i < bset->n_ineq; ++i) {
2541 isl_int_set(cst->el[i], bset->ineq[i][0]);
2542 for (j = 0; j < dim; ++j) {
2543 if (!isl_int_is_neg(bset->ineq[i][1 + j]))
2544 continue;
2545 isl_int_add(bset->ineq[i][0], bset->ineq[i][0],
2546 bset->ineq[i][1 + j]);
2550 cgbr->shifted = isl_tab_from_basic_set(bset);
2552 for (i = 0; i < bset->n_ineq; ++i)
2553 isl_int_set(bset->ineq[i][0], cst->el[i]);
2555 isl_vec_free(cst);
2558 /* Check if the shifted tableau is non-empty, and if so
2559 * use the sample point to construct an integer point
2560 * of the context tableau.
2562 static struct isl_vec *gbr_get_shifted_sample(struct isl_context_gbr *cgbr)
2564 struct isl_vec *sample;
2566 if (!cgbr->shifted)
2567 gbr_init_shifted(cgbr);
2568 if (!cgbr->shifted)
2569 return NULL;
2570 if (cgbr->shifted->empty)
2571 return isl_vec_alloc(cgbr->tab->mat->ctx, 0);
2573 sample = isl_tab_get_sample_value(cgbr->shifted);
2574 sample = isl_vec_ceil(sample);
2576 return sample;
2579 static struct isl_basic_set *drop_constant_terms(struct isl_basic_set *bset)
2581 int i;
2583 if (!bset)
2584 return NULL;
2586 for (i = 0; i < bset->n_eq; ++i)
2587 isl_int_set_si(bset->eq[i][0], 0);
2589 for (i = 0; i < bset->n_ineq; ++i)
2590 isl_int_set_si(bset->ineq[i][0], 0);
2592 return bset;
2595 static int use_shifted(struct isl_context_gbr *cgbr)
2597 return cgbr->tab->bset->n_eq == 0 && cgbr->tab->bset->n_div == 0;
2600 static struct isl_vec *gbr_get_sample(struct isl_context_gbr *cgbr)
2602 struct isl_basic_set *bset;
2603 struct isl_basic_set *cone;
2605 if (isl_tab_sample_is_integer(cgbr->tab))
2606 return isl_tab_get_sample_value(cgbr->tab);
2608 if (use_shifted(cgbr)) {
2609 struct isl_vec *sample;
2611 sample = gbr_get_shifted_sample(cgbr);
2612 if (!sample || sample->size > 0)
2613 return sample;
2615 isl_vec_free(sample);
2618 if (!cgbr->cone) {
2619 cgbr->cone = isl_tab_from_recession_cone(cgbr->tab->bset);
2620 if (!cgbr->cone)
2621 return NULL;
2622 cgbr->cone->bset = isl_basic_set_dup(cgbr->tab->bset);
2624 cgbr->cone = isl_tab_detect_implicit_equalities(cgbr->cone);
2625 if (!cgbr->cone)
2626 return NULL;
2628 if (cgbr->cone->n_dead == cgbr->cone->n_col) {
2629 struct isl_vec *sample;
2630 struct isl_tab_undo *snap;
2632 if (cgbr->tab->basis) {
2633 if (cgbr->tab->basis->n_col != 1 + cgbr->tab->n_var) {
2634 isl_mat_free(cgbr->tab->basis);
2635 cgbr->tab->basis = NULL;
2636 } else {
2637 cgbr->tab->n_zero = 0;
2638 cgbr->tab->n_unbounded = 0;
2642 snap = isl_tab_snap(cgbr->tab);
2644 sample = isl_tab_sample(cgbr->tab);
2646 if (isl_tab_rollback(cgbr->tab, snap) < 0) {
2647 isl_vec_free(sample);
2648 return NULL;
2651 return sample;
2654 cone = isl_basic_set_dup(cgbr->cone->bset);
2655 cone = drop_constant_terms(cone);
2656 cone = isl_basic_set_update_from_tab(cone, cgbr->cone);
2657 cone = isl_basic_set_underlying_set(cone);
2658 cone = isl_basic_set_gauss(cone, NULL);
2660 bset = isl_basic_set_dup(cgbr->tab->bset);
2661 bset = isl_basic_set_update_from_tab(bset, cgbr->tab);
2662 bset = isl_basic_set_underlying_set(bset);
2663 bset = isl_basic_set_gauss(bset, NULL);
2665 return isl_basic_set_sample_with_cone(bset, cone);
2668 static void check_gbr_integer_feasible(struct isl_context_gbr *cgbr)
2670 struct isl_vec *sample;
2672 if (!cgbr->tab)
2673 return;
2675 if (cgbr->tab->empty)
2676 return;
2678 sample = gbr_get_sample(cgbr);
2679 if (!sample)
2680 goto error;
2682 if (sample->size == 0) {
2683 isl_vec_free(sample);
2684 if (isl_tab_mark_empty(cgbr->tab) < 0)
2685 goto error;
2686 return;
2689 cgbr->tab = isl_tab_add_sample(cgbr->tab, sample);
2691 return;
2692 error:
2693 isl_tab_free(cgbr->tab);
2694 cgbr->tab = NULL;
2697 static struct isl_tab *add_gbr_eq(struct isl_tab *tab, isl_int *eq)
2699 int r;
2701 if (!tab)
2702 return NULL;
2704 if (isl_tab_extend_cons(tab, 2) < 0)
2705 goto error;
2707 tab = isl_tab_add_eq(tab, eq);
2709 return tab;
2710 error:
2711 isl_tab_free(tab);
2712 return NULL;
2715 static void context_gbr_add_eq(struct isl_context *context, isl_int *eq,
2716 int check, int update)
2718 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2720 cgbr->tab = add_gbr_eq(cgbr->tab, eq);
2722 if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
2723 if (isl_tab_extend_cons(cgbr->cone, 2) < 0)
2724 goto error;
2725 cgbr->cone = isl_tab_add_eq(cgbr->cone, eq);
2728 if (check) {
2729 int v = tab_has_valid_sample(cgbr->tab, eq, 1);
2730 if (v < 0)
2731 goto error;
2732 if (!v)
2733 check_gbr_integer_feasible(cgbr);
2735 if (update)
2736 cgbr->tab = check_samples(cgbr->tab, eq, 1);
2737 return;
2738 error:
2739 isl_tab_free(cgbr->tab);
2740 cgbr->tab = NULL;
2743 static void add_gbr_ineq(struct isl_context_gbr *cgbr, isl_int *ineq)
2745 if (!cgbr->tab)
2746 return;
2748 if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
2749 goto error;
2751 if (isl_tab_add_ineq(cgbr->tab, ineq) < 0)
2752 goto error;
2754 if (cgbr->shifted && !cgbr->shifted->empty && use_shifted(cgbr)) {
2755 int i;
2756 unsigned dim;
2757 dim = isl_basic_set_total_dim(cgbr->tab->bset);
2759 if (isl_tab_extend_cons(cgbr->shifted, 1) < 0)
2760 goto error;
2762 for (i = 0; i < dim; ++i) {
2763 if (!isl_int_is_neg(ineq[1 + i]))
2764 continue;
2765 isl_int_add(ineq[0], ineq[0], ineq[1 + i]);
2768 if (isl_tab_add_ineq(cgbr->shifted, ineq) < 0)
2769 goto error;
2771 for (i = 0; i < dim; ++i) {
2772 if (!isl_int_is_neg(ineq[1 + i]))
2773 continue;
2774 isl_int_sub(ineq[0], ineq[0], ineq[1 + i]);
2778 if (cgbr->cone && cgbr->cone->n_col != cgbr->cone->n_dead) {
2779 if (isl_tab_extend_cons(cgbr->cone, 1) < 0)
2780 goto error;
2781 if (isl_tab_add_ineq(cgbr->cone, ineq) < 0)
2782 goto error;
2785 return;
2786 error:
2787 isl_tab_free(cgbr->tab);
2788 cgbr->tab = NULL;
2791 static void context_gbr_add_ineq(struct isl_context *context, isl_int *ineq,
2792 int check, int update)
2794 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2796 add_gbr_ineq(cgbr, ineq);
2797 if (!cgbr->tab)
2798 return;
2800 if (check) {
2801 int v = tab_has_valid_sample(cgbr->tab, ineq, 0);
2802 if (v < 0)
2803 goto error;
2804 if (!v)
2805 check_gbr_integer_feasible(cgbr);
2807 if (update)
2808 cgbr->tab = check_samples(cgbr->tab, ineq, 0);
2809 return;
2810 error:
2811 isl_tab_free(cgbr->tab);
2812 cgbr->tab = NULL;
2815 static enum isl_tab_row_sign context_gbr_ineq_sign(struct isl_context *context,
2816 isl_int *ineq, int strict)
2818 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2819 return tab_ineq_sign(cgbr->tab, ineq, strict);
2822 /* Check whether "ineq" can be added to the tableau without rendering
2823 * it infeasible.
2825 static int context_gbr_test_ineq(struct isl_context *context, isl_int *ineq)
2827 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2828 struct isl_tab_undo *snap;
2829 struct isl_tab_undo *shifted_snap = NULL;
2830 struct isl_tab_undo *cone_snap = NULL;
2831 int feasible;
2833 if (!cgbr->tab)
2834 return -1;
2836 if (isl_tab_extend_cons(cgbr->tab, 1) < 0)
2837 return -1;
2839 snap = isl_tab_snap(cgbr->tab);
2840 if (cgbr->shifted)
2841 shifted_snap = isl_tab_snap(cgbr->shifted);
2842 if (cgbr->cone)
2843 cone_snap = isl_tab_snap(cgbr->cone);
2844 add_gbr_ineq(cgbr, ineq);
2845 check_gbr_integer_feasible(cgbr);
2846 if (!cgbr->tab)
2847 return -1;
2848 feasible = !cgbr->tab->empty;
2849 if (isl_tab_rollback(cgbr->tab, snap) < 0)
2850 return -1;
2851 if (shifted_snap) {
2852 if (isl_tab_rollback(cgbr->shifted, shifted_snap))
2853 return -1;
2854 } else if (cgbr->shifted) {
2855 isl_tab_free(cgbr->shifted);
2856 cgbr->shifted = NULL;
2858 if (cone_snap) {
2859 if (isl_tab_rollback(cgbr->cone, cone_snap))
2860 return -1;
2861 } else if (cgbr->cone) {
2862 isl_tab_free(cgbr->cone);
2863 cgbr->cone = NULL;
2866 return feasible;
2869 /* Return the column of the last of the variables associated to
2870 * a column that has a non-zero coefficient.
2871 * This function is called in a context where only coefficients
2872 * of parameters or divs can be non-zero.
2874 static int last_non_zero_var_col(struct isl_tab *tab, isl_int *p)
2876 int i;
2877 int col;
2878 unsigned dim = tab->n_var - tab->n_param - tab->n_div;
2880 if (tab->n_var == 0)
2881 return -1;
2883 for (i = tab->n_var - 1; i >= 0; --i) {
2884 if (i >= tab->n_param && i < tab->n_var - tab->n_div)
2885 continue;
2886 if (tab->var[i].is_row)
2887 continue;
2888 col = tab->var[i].index;
2889 if (!isl_int_is_zero(p[col]))
2890 return col;
2893 return -1;
2896 /* Look through all the recently added equalities in the context
2897 * to see if we can propagate any of them to the main tableau.
2899 * The newly added equalities in the context are encoded as pairs
2900 * of inequalities starting at inequality "first".
2902 * We tentatively add each of these equalities to the main tableau
2903 * and if this happens to result in a row with a final coefficient
2904 * that is one or negative one, we use it to kill a column
2905 * in the main tableau. Otherwise, we discard the tentatively
2906 * added row.
2908 static void propagate_equalities(struct isl_context_gbr *cgbr,
2909 struct isl_tab *tab, unsigned first)
2911 int i;
2912 struct isl_vec *eq = NULL;
2914 eq = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
2915 if (!eq)
2916 goto error;
2918 if (isl_tab_extend_cons(tab, (cgbr->tab->bset->n_ineq - first)/2) < 0)
2919 goto error;
2921 isl_seq_clr(eq->el + 1 + tab->n_param,
2922 tab->n_var - tab->n_param - tab->n_div);
2923 for (i = first; i < cgbr->tab->bset->n_ineq; i += 2) {
2924 int j;
2925 int r;
2926 struct isl_tab_undo *snap;
2927 snap = isl_tab_snap(tab);
2929 isl_seq_cpy(eq->el, cgbr->tab->bset->ineq[i], 1 + tab->n_param);
2930 isl_seq_cpy(eq->el + 1 + tab->n_var - tab->n_div,
2931 cgbr->tab->bset->ineq[i] + 1 + tab->n_param,
2932 tab->n_div);
2934 r = isl_tab_add_row(tab, eq->el);
2935 if (r < 0)
2936 goto error;
2937 r = tab->con[r].index;
2938 j = last_non_zero_var_col(tab, tab->mat->row[r] + 2 + tab->M);
2939 if (j < 0 || j < tab->n_dead ||
2940 !isl_int_is_one(tab->mat->row[r][0]) ||
2941 (!isl_int_is_one(tab->mat->row[r][2 + tab->M + j]) &&
2942 !isl_int_is_negone(tab->mat->row[r][2 + tab->M + j]))) {
2943 if (isl_tab_rollback(tab, snap) < 0)
2944 goto error;
2945 continue;
2947 if (isl_tab_pivot(tab, r, j) < 0)
2948 goto error;
2949 if (isl_tab_kill_col(tab, j) < 0)
2950 goto error;
2952 tab = restore_lexmin(tab);
2955 isl_vec_free(eq);
2957 return;
2958 error:
2959 isl_vec_free(eq);
2960 isl_tab_free(cgbr->tab);
2961 cgbr->tab = NULL;
2964 static int context_gbr_detect_equalities(struct isl_context *context,
2965 struct isl_tab *tab)
2967 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
2968 struct isl_ctx *ctx;
2969 int i;
2970 enum isl_lp_result res;
2971 unsigned n_ineq;
2973 ctx = cgbr->tab->mat->ctx;
2975 if (!cgbr->cone) {
2976 cgbr->cone = isl_tab_from_recession_cone(cgbr->tab->bset);
2977 if (!cgbr->cone)
2978 goto error;
2979 cgbr->cone->bset = isl_basic_set_dup(cgbr->tab->bset);
2981 cgbr->cone = isl_tab_detect_implicit_equalities(cgbr->cone);
2983 n_ineq = cgbr->tab->bset->n_ineq;
2984 cgbr->tab = isl_tab_detect_equalities(cgbr->tab, cgbr->cone);
2985 if (cgbr->tab && cgbr->tab->bset->n_ineq > n_ineq)
2986 propagate_equalities(cgbr, tab, n_ineq);
2988 return 0;
2989 error:
2990 isl_tab_free(cgbr->tab);
2991 cgbr->tab = NULL;
2992 return -1;
2995 static int context_gbr_get_div(struct isl_context *context, struct isl_tab *tab,
2996 struct isl_vec *div)
2998 return get_div(tab, context, div);
3001 static int context_gbr_add_div(struct isl_context *context, struct isl_vec *div,
3002 int *nonneg)
3004 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3005 if (cgbr->cone) {
3006 int k;
3008 if (isl_tab_extend_cons(cgbr->cone, 3) < 0)
3009 return -1;
3010 if (isl_tab_extend_vars(cgbr->cone, 1) < 0)
3011 return -1;
3012 if (isl_tab_allocate_var(cgbr->cone) <0)
3013 return -1;
3015 cgbr->cone->bset = isl_basic_set_extend_dim(cgbr->cone->bset,
3016 isl_basic_set_get_dim(cgbr->cone->bset), 1, 0, 2);
3017 k = isl_basic_set_alloc_div(cgbr->cone->bset);
3018 if (k < 0)
3019 return -1;
3020 isl_seq_cpy(cgbr->cone->bset->div[k], div->el, div->size);
3021 if (isl_tab_push(cgbr->cone, isl_tab_undo_bset_div) < 0)
3022 return -1;
3024 return context_tab_add_div(cgbr->tab, div, nonneg);
3027 static int context_gbr_best_split(struct isl_context *context,
3028 struct isl_tab *tab)
3030 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3031 struct isl_tab_undo *snap;
3032 int r;
3034 snap = isl_tab_snap(cgbr->tab);
3035 r = best_split(tab, cgbr->tab);
3037 if (isl_tab_rollback(cgbr->tab, snap) < 0)
3038 return -1;
3040 return r;
3043 static int context_gbr_is_empty(struct isl_context *context)
3045 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3046 if (!cgbr->tab)
3047 return -1;
3048 return cgbr->tab->empty;
3051 struct isl_gbr_tab_undo {
3052 struct isl_tab_undo *tab_snap;
3053 struct isl_tab_undo *shifted_snap;
3054 struct isl_tab_undo *cone_snap;
3057 static void *context_gbr_save(struct isl_context *context)
3059 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3060 struct isl_gbr_tab_undo *snap;
3062 snap = isl_alloc_type(cgbr->tab->mat->ctx, struct isl_gbr_tab_undo);
3063 if (!snap)
3064 return NULL;
3066 snap->tab_snap = isl_tab_snap(cgbr->tab);
3067 if (isl_tab_save_samples(cgbr->tab) < 0)
3068 goto error;
3070 if (cgbr->shifted)
3071 snap->shifted_snap = isl_tab_snap(cgbr->shifted);
3072 else
3073 snap->shifted_snap = NULL;
3075 if (cgbr->cone)
3076 snap->cone_snap = isl_tab_snap(cgbr->cone);
3077 else
3078 snap->cone_snap = NULL;
3080 return snap;
3081 error:
3082 free(snap);
3083 return NULL;
3086 static void context_gbr_restore(struct isl_context *context, void *save)
3088 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3089 struct isl_gbr_tab_undo *snap = (struct isl_gbr_tab_undo *)save;
3090 if (!snap)
3091 goto error;
3092 if (isl_tab_rollback(cgbr->tab, snap->tab_snap) < 0) {
3093 isl_tab_free(cgbr->tab);
3094 cgbr->tab = NULL;
3097 if (snap->shifted_snap) {
3098 if (isl_tab_rollback(cgbr->shifted, snap->shifted_snap) < 0)
3099 goto error;
3100 } else if (cgbr->shifted) {
3101 isl_tab_free(cgbr->shifted);
3102 cgbr->shifted = NULL;
3105 if (snap->cone_snap) {
3106 if (isl_tab_rollback(cgbr->cone, snap->cone_snap) < 0)
3107 goto error;
3108 } else if (cgbr->cone) {
3109 isl_tab_free(cgbr->cone);
3110 cgbr->cone = NULL;
3113 free(snap);
3115 return;
3116 error:
3117 free(snap);
3118 isl_tab_free(cgbr->tab);
3119 cgbr->tab = NULL;
3122 static int context_gbr_is_ok(struct isl_context *context)
3124 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3125 return !!cgbr->tab;
3128 static void context_gbr_invalidate(struct isl_context *context)
3130 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3131 isl_tab_free(cgbr->tab);
3132 cgbr->tab = NULL;
3135 static void context_gbr_free(struct isl_context *context)
3137 struct isl_context_gbr *cgbr = (struct isl_context_gbr *)context;
3138 isl_tab_free(cgbr->tab);
3139 isl_tab_free(cgbr->shifted);
3140 isl_tab_free(cgbr->cone);
3141 free(cgbr);
3144 struct isl_context_op isl_context_gbr_op = {
3145 context_gbr_detect_nonnegative_parameters,
3146 context_gbr_peek_basic_set,
3147 context_gbr_peek_tab,
3148 context_gbr_add_eq,
3149 context_gbr_add_ineq,
3150 context_gbr_ineq_sign,
3151 context_gbr_test_ineq,
3152 context_gbr_get_div,
3153 context_gbr_add_div,
3154 context_gbr_detect_equalities,
3155 context_gbr_best_split,
3156 context_gbr_is_empty,
3157 context_gbr_is_ok,
3158 context_gbr_save,
3159 context_gbr_restore,
3160 context_gbr_invalidate,
3161 context_gbr_free,
3164 static struct isl_context *isl_context_gbr_alloc(struct isl_basic_set *dom)
3166 struct isl_context_gbr *cgbr;
3168 if (!dom)
3169 return NULL;
3171 cgbr = isl_calloc_type(dom->ctx, struct isl_context_gbr);
3172 if (!cgbr)
3173 return NULL;
3175 cgbr->context.op = &isl_context_gbr_op;
3177 cgbr->shifted = NULL;
3178 cgbr->cone = NULL;
3179 cgbr->tab = isl_tab_from_basic_set(dom);
3180 cgbr->tab = isl_tab_init_samples(cgbr->tab);
3181 if (!cgbr->tab)
3182 goto error;
3183 cgbr->tab->bset = isl_basic_set_cow(isl_basic_set_copy(dom));
3184 if (!cgbr->tab->bset)
3185 goto error;
3186 check_gbr_integer_feasible(cgbr);
3188 return &cgbr->context;
3189 error:
3190 cgbr->context.op->free(&cgbr->context);
3191 return NULL;
3194 static struct isl_context *isl_context_alloc(struct isl_basic_set *dom)
3196 if (!dom)
3197 return NULL;
3199 if (dom->ctx->opt->context == ISL_CONTEXT_LEXMIN)
3200 return isl_context_lex_alloc(dom);
3201 else
3202 return isl_context_gbr_alloc(dom);
3205 /* Construct an isl_sol_map structure for accumulating the solution.
3206 * If track_empty is set, then we also keep track of the parts
3207 * of the context where there is no solution.
3208 * If max is set, then we are solving a maximization, rather than
3209 * a minimization problem, which means that the variables in the
3210 * tableau have value "M - x" rather than "M + x".
3212 static struct isl_sol_map *sol_map_init(struct isl_basic_map *bmap,
3213 struct isl_basic_set *dom, int track_empty, int max)
3215 struct isl_sol_map *sol_map;
3217 sol_map = isl_calloc_type(bset->ctx, struct isl_sol_map);
3218 if (!sol_map)
3219 goto error;
3221 sol_map->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
3222 sol_map->sol.dec_level.callback.run = &sol_dec_level_wrap;
3223 sol_map->sol.dec_level.sol = &sol_map->sol;
3224 sol_map->sol.max = max;
3225 sol_map->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
3226 sol_map->sol.add = &sol_map_add_wrap;
3227 sol_map->sol.add_empty = track_empty ? &sol_map_add_empty_wrap : NULL;
3228 sol_map->sol.free = &sol_map_free_wrap;
3229 sol_map->map = isl_map_alloc_dim(isl_basic_map_get_dim(bmap), 1,
3230 ISL_MAP_DISJOINT);
3231 if (!sol_map->map)
3232 goto error;
3234 sol_map->sol.context = isl_context_alloc(dom);
3235 if (!sol_map->sol.context)
3236 goto error;
3238 if (track_empty) {
3239 sol_map->empty = isl_set_alloc_dim(isl_basic_set_get_dim(dom),
3240 1, ISL_SET_DISJOINT);
3241 if (!sol_map->empty)
3242 goto error;
3245 isl_basic_set_free(dom);
3246 return sol_map;
3247 error:
3248 isl_basic_set_free(dom);
3249 sol_map_free(sol_map);
3250 return NULL;
3253 /* Check whether all coefficients of (non-parameter) variables
3254 * are non-positive, meaning that no pivots can be performed on the row.
3256 static int is_critical(struct isl_tab *tab, int row)
3258 int j;
3259 unsigned off = 2 + tab->M;
3261 for (j = tab->n_dead; j < tab->n_col; ++j) {
3262 if (tab->col_var[j] >= 0 &&
3263 (tab->col_var[j] < tab->n_param ||
3264 tab->col_var[j] >= tab->n_var - tab->n_div))
3265 continue;
3267 if (isl_int_is_pos(tab->mat->row[row][off + j]))
3268 return 0;
3271 return 1;
3274 /* Check whether the inequality represented by vec is strict over the integers,
3275 * i.e., there are no integer values satisfying the constraint with
3276 * equality. This happens if the gcd of the coefficients is not a divisor
3277 * of the constant term. If so, scale the constraint down by the gcd
3278 * of the coefficients.
3280 static int is_strict(struct isl_vec *vec)
3282 isl_int gcd;
3283 int strict = 0;
3285 isl_int_init(gcd);
3286 isl_seq_gcd(vec->el + 1, vec->size - 1, &gcd);
3287 if (!isl_int_is_one(gcd)) {
3288 strict = !isl_int_is_divisible_by(vec->el[0], gcd);
3289 isl_int_fdiv_q(vec->el[0], vec->el[0], gcd);
3290 isl_seq_scale_down(vec->el + 1, vec->el + 1, gcd, vec->size-1);
3292 isl_int_clear(gcd);
3294 return strict;
3297 /* Determine the sign of the given row of the main tableau.
3298 * The result is one of
3299 * isl_tab_row_pos: always non-negative; no pivot needed
3300 * isl_tab_row_neg: always non-positive; pivot
3301 * isl_tab_row_any: can be both positive and negative; split
3303 * We first handle some simple cases
3304 * - the row sign may be known already
3305 * - the row may be obviously non-negative
3306 * - the parametric constant may be equal to that of another row
3307 * for which we know the sign. This sign will be either "pos" or
3308 * "any". If it had been "neg" then we would have pivoted before.
3310 * If none of these cases hold, we check the value of the row for each
3311 * of the currently active samples. Based on the signs of these values
3312 * we make an initial determination of the sign of the row.
3314 * all zero -> unk(nown)
3315 * all non-negative -> pos
3316 * all non-positive -> neg
3317 * both negative and positive -> all
3319 * If we end up with "all", we are done.
3320 * Otherwise, we perform a check for positive and/or negative
3321 * values as follows.
3323 * samples neg unk pos
3324 * <0 ? Y N Y N
3325 * pos any pos
3326 * >0 ? Y N Y N
3327 * any neg any neg
3329 * There is no special sign for "zero", because we can usually treat zero
3330 * as either non-negative or non-positive, whatever works out best.
3331 * However, if the row is "critical", meaning that pivoting is impossible
3332 * then we don't want to limp zero with the non-positive case, because
3333 * then we we would lose the solution for those values of the parameters
3334 * where the value of the row is zero. Instead, we treat 0 as non-negative
3335 * ensuring a split if the row can attain both zero and negative values.
3336 * The same happens when the original constraint was one that could not
3337 * be satisfied with equality by any integer values of the parameters.
3338 * In this case, we normalize the constraint, but then a value of zero
3339 * for the normalized constraint is actually a positive value for the
3340 * original constraint, so again we need to treat zero as non-negative.
3341 * In both these cases, we have the following decision tree instead:
3343 * all non-negative -> pos
3344 * all negative -> neg
3345 * both negative and non-negative -> all
3347 * samples neg pos
3348 * <0 ? Y N
3349 * any pos
3350 * >=0 ? Y N
3351 * any neg
3353 static enum isl_tab_row_sign row_sign(struct isl_tab *tab,
3354 struct isl_sol *sol, int row)
3356 struct isl_vec *ineq = NULL;
3357 int res = isl_tab_row_unknown;
3358 int critical;
3359 int strict;
3360 int row2;
3362 if (tab->row_sign[row] != isl_tab_row_unknown)
3363 return tab->row_sign[row];
3364 if (is_obviously_nonneg(tab, row))
3365 return isl_tab_row_pos;
3366 for (row2 = tab->n_redundant; row2 < tab->n_row; ++row2) {
3367 if (tab->row_sign[row2] == isl_tab_row_unknown)
3368 continue;
3369 if (identical_parameter_line(tab, row, row2))
3370 return tab->row_sign[row2];
3373 critical = is_critical(tab, row);
3375 ineq = get_row_parameter_ineq(tab, row);
3376 if (!ineq)
3377 goto error;
3379 strict = is_strict(ineq);
3381 res = sol->context->op->ineq_sign(sol->context, ineq->el,
3382 critical || strict);
3384 if (res == isl_tab_row_unknown || res == isl_tab_row_pos) {
3385 /* test for negative values */
3386 int feasible;
3387 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3388 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3390 feasible = sol->context->op->test_ineq(sol->context, ineq->el);
3391 if (feasible < 0)
3392 goto error;
3393 if (!feasible)
3394 res = isl_tab_row_pos;
3395 else
3396 res = (res == isl_tab_row_unknown) ? isl_tab_row_neg
3397 : isl_tab_row_any;
3398 if (res == isl_tab_row_neg) {
3399 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3400 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3404 if (res == isl_tab_row_neg) {
3405 /* test for positive values */
3406 int feasible;
3407 if (!critical && !strict)
3408 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3410 feasible = sol->context->op->test_ineq(sol->context, ineq->el);
3411 if (feasible < 0)
3412 goto error;
3413 if (feasible)
3414 res = isl_tab_row_any;
3417 isl_vec_free(ineq);
3418 return res;
3419 error:
3420 isl_vec_free(ineq);
3421 return 0;
3424 static void find_solutions(struct isl_sol *sol, struct isl_tab *tab);
3426 /* Find solutions for values of the parameters that satisfy the given
3427 * inequality.
3429 * We currently take a snapshot of the context tableau that is reset
3430 * when we return from this function, while we make a copy of the main
3431 * tableau, leaving the original main tableau untouched.
3432 * These are fairly arbitrary choices. Making a copy also of the context
3433 * tableau would obviate the need to undo any changes made to it later,
3434 * while taking a snapshot of the main tableau could reduce memory usage.
3435 * If we were to switch to taking a snapshot of the main tableau,
3436 * we would have to keep in mind that we need to save the row signs
3437 * and that we need to do this before saving the current basis
3438 * such that the basis has been restore before we restore the row signs.
3440 static void find_in_pos(struct isl_sol *sol, struct isl_tab *tab, isl_int *ineq)
3442 void *saved;
3444 if (!sol->context)
3445 goto error;
3446 saved = sol->context->op->save(sol->context);
3448 tab = isl_tab_dup(tab);
3449 if (!tab)
3450 goto error;
3452 sol->context->op->add_ineq(sol->context, ineq, 0, 1);
3454 find_solutions(sol, tab);
3456 sol->context->op->restore(sol->context, saved);
3457 return;
3458 error:
3459 sol->error = 1;
3462 /* Record the absence of solutions for those values of the parameters
3463 * that do not satisfy the given inequality with equality.
3465 static void no_sol_in_strict(struct isl_sol *sol,
3466 struct isl_tab *tab, struct isl_vec *ineq)
3468 int empty;
3469 void *saved;
3471 if (!sol->context)
3472 goto error;
3473 saved = sol->context->op->save(sol->context);
3475 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3477 sol->context->op->add_ineq(sol->context, ineq->el, 1, 0);
3478 if (!sol->context)
3479 goto error;
3481 empty = tab->empty;
3482 tab->empty = 1;
3483 sol_add(sol, tab);
3484 tab->empty = empty;
3486 isl_int_add_ui(ineq->el[0], ineq->el[0], 1);
3488 sol->context->op->restore(sol->context, saved);
3489 return;
3490 error:
3491 sol->error = 1;
3494 /* Compute the lexicographic minimum of the set represented by the main
3495 * tableau "tab" within the context "sol->context_tab".
3496 * On entry the sample value of the main tableau is lexicographically
3497 * less than or equal to this lexicographic minimum.
3498 * Pivots are performed until a feasible point is found, which is then
3499 * necessarily equal to the minimum, or until the tableau is found to
3500 * be infeasible. Some pivots may need to be performed for only some
3501 * feasible values of the context tableau. If so, the context tableau
3502 * is split into a part where the pivot is needed and a part where it is not.
3504 * Whenever we enter the main loop, the main tableau is such that no
3505 * "obvious" pivots need to be performed on it, where "obvious" means
3506 * that the given row can be seen to be negative without looking at
3507 * the context tableau. In particular, for non-parametric problems,
3508 * no pivots need to be performed on the main tableau.
3509 * The caller of find_solutions is responsible for making this property
3510 * hold prior to the first iteration of the loop, while restore_lexmin
3511 * is called before every other iteration.
3513 * Inside the main loop, we first examine the signs of the rows of
3514 * the main tableau within the context of the context tableau.
3515 * If we find a row that is always non-positive for all values of
3516 * the parameters satisfying the context tableau and negative for at
3517 * least one value of the parameters, we perform the appropriate pivot
3518 * and start over. An exception is the case where no pivot can be
3519 * performed on the row. In this case, we require that the sign of
3520 * the row is negative for all values of the parameters (rather than just
3521 * non-positive). This special case is handled inside row_sign, which
3522 * will say that the row can have any sign if it determines that it can
3523 * attain both negative and zero values.
3525 * If we can't find a row that always requires a pivot, but we can find
3526 * one or more rows that require a pivot for some values of the parameters
3527 * (i.e., the row can attain both positive and negative signs), then we split
3528 * the context tableau into two parts, one where we force the sign to be
3529 * non-negative and one where we force is to be negative.
3530 * The non-negative part is handled by a recursive call (through find_in_pos).
3531 * Upon returning from this call, we continue with the negative part and
3532 * perform the required pivot.
3534 * If no such rows can be found, all rows are non-negative and we have
3535 * found a (rational) feasible point. If we only wanted a rational point
3536 * then we are done.
3537 * Otherwise, we check if all values of the sample point of the tableau
3538 * are integral for the variables. If so, we have found the minimal
3539 * integral point and we are done.
3540 * If the sample point is not integral, then we need to make a distinction
3541 * based on whether the constant term is non-integral or the coefficients
3542 * of the parameters. Furthermore, in order to decide how to handle
3543 * the non-integrality, we also need to know whether the coefficients
3544 * of the other columns in the tableau are integral. This leads
3545 * to the following table. The first two rows do not correspond
3546 * to a non-integral sample point and are only mentioned for completeness.
3548 * constant parameters other
3550 * int int int |
3551 * int int rat | -> no problem
3553 * rat int int -> fail
3555 * rat int rat -> cut
3557 * int rat rat |
3558 * rat rat rat | -> parametric cut
3560 * int rat int |
3561 * rat rat int | -> split context
3563 * If the parametric constant is completely integral, then there is nothing
3564 * to be done. If the constant term is non-integral, but all the other
3565 * coefficient are integral, then there is nothing that can be done
3566 * and the tableau has no integral solution.
3567 * If, on the other hand, one or more of the other columns have rational
3568 * coeffcients, but the parameter coefficients are all integral, then
3569 * we can perform a regular (non-parametric) cut.
3570 * Finally, if there is any parameter coefficient that is non-integral,
3571 * then we need to involve the context tableau. There are two cases here.
3572 * If at least one other column has a rational coefficient, then we
3573 * can perform a parametric cut in the main tableau by adding a new
3574 * integer division in the context tableau.
3575 * If all other columns have integral coefficients, then we need to
3576 * enforce that the rational combination of parameters (c + \sum a_i y_i)/m
3577 * is always integral. We do this by introducing an integer division
3578 * q = floor((c + \sum a_i y_i)/m) and stipulating that its argument should
3579 * always be integral in the context tableau, i.e., m q = c + \sum a_i y_i.
3580 * Since q is expressed in the tableau as
3581 * c + \sum a_i y_i - m q >= 0
3582 * -c - \sum a_i y_i + m q + m - 1 >= 0
3583 * it is sufficient to add the inequality
3584 * -c - \sum a_i y_i + m q >= 0
3585 * In the part of the context where this inequality does not hold, the
3586 * main tableau is marked as being empty.
3588 static void find_solutions(struct isl_sol *sol, struct isl_tab *tab)
3590 struct isl_context *context;
3592 if (!tab || sol->error)
3593 goto error;
3595 context = sol->context;
3597 if (tab->empty)
3598 goto done;
3599 if (context->op->is_empty(context))
3600 goto done;
3602 for (; tab && !tab->empty; tab = restore_lexmin(tab)) {
3603 int flags;
3604 int row;
3605 int sgn;
3606 int split = -1;
3607 int n_split = 0;
3609 for (row = tab->n_redundant; row < tab->n_row; ++row) {
3610 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
3611 continue;
3612 sgn = row_sign(tab, sol, row);
3613 if (!sgn)
3614 goto error;
3615 tab->row_sign[row] = sgn;
3616 if (sgn == isl_tab_row_any)
3617 n_split++;
3618 if (sgn == isl_tab_row_any && split == -1)
3619 split = row;
3620 if (sgn == isl_tab_row_neg)
3621 break;
3623 if (row < tab->n_row)
3624 continue;
3625 if (split != -1) {
3626 struct isl_vec *ineq;
3627 if (n_split != 1)
3628 split = context->op->best_split(context, tab);
3629 if (split < 0)
3630 goto error;
3631 ineq = get_row_parameter_ineq(tab, split);
3632 if (!ineq)
3633 goto error;
3634 is_strict(ineq);
3635 for (row = tab->n_redundant; row < tab->n_row; ++row) {
3636 if (!isl_tab_var_from_row(tab, row)->is_nonneg)
3637 continue;
3638 if (tab->row_sign[row] == isl_tab_row_any)
3639 tab->row_sign[row] = isl_tab_row_unknown;
3641 tab->row_sign[split] = isl_tab_row_pos;
3642 sol_inc_level(sol);
3643 find_in_pos(sol, tab, ineq->el);
3644 tab->row_sign[split] = isl_tab_row_neg;
3645 row = split;
3646 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3647 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
3648 context->op->add_ineq(context, ineq->el, 0, 1);
3649 isl_vec_free(ineq);
3650 if (sol->error)
3651 goto error;
3652 continue;
3654 if (tab->rational)
3655 break;
3656 row = first_non_integer(tab, &flags);
3657 if (row < 0)
3658 break;
3659 if (ISL_FL_ISSET(flags, I_PAR)) {
3660 if (ISL_FL_ISSET(flags, I_VAR)) {
3661 if (isl_tab_mark_empty(tab) < 0)
3662 goto error;
3663 break;
3665 row = add_cut(tab, row);
3666 } else if (ISL_FL_ISSET(flags, I_VAR)) {
3667 struct isl_vec *div;
3668 struct isl_vec *ineq;
3669 int d;
3670 div = get_row_split_div(tab, row);
3671 if (!div)
3672 goto error;
3673 d = context->op->get_div(context, tab, div);
3674 isl_vec_free(div);
3675 if (d < 0)
3676 goto error;
3677 ineq = ineq_for_div(context->op->peek_basic_set(context), d);
3678 sol_inc_level(sol);
3679 no_sol_in_strict(sol, tab, ineq);
3680 isl_seq_neg(ineq->el, ineq->el, ineq->size);
3681 context->op->add_ineq(context, ineq->el, 1, 1);
3682 isl_vec_free(ineq);
3683 if (sol->error || !context->op->is_ok(context))
3684 goto error;
3685 tab = set_row_cst_to_div(tab, row, d);
3686 } else
3687 row = add_parametric_cut(tab, row, context);
3688 if (row < 0)
3689 goto error;
3691 done:
3692 sol_add(sol, tab);
3693 isl_tab_free(tab);
3694 return;
3695 error:
3696 isl_tab_free(tab);
3697 sol_free(sol);
3700 /* Compute the lexicographic minimum of the set represented by the main
3701 * tableau "tab" within the context "sol->context_tab".
3703 * As a preprocessing step, we first transfer all the purely parametric
3704 * equalities from the main tableau to the context tableau, i.e.,
3705 * parameters that have been pivoted to a row.
3706 * These equalities are ignored by the main algorithm, because the
3707 * corresponding rows may not be marked as being non-negative.
3708 * In parts of the context where the added equality does not hold,
3709 * the main tableau is marked as being empty.
3711 static void find_solutions_main(struct isl_sol *sol, struct isl_tab *tab)
3713 int row;
3715 sol->level = 0;
3717 for (row = tab->n_redundant; row < tab->n_row; ++row) {
3718 int p;
3719 struct isl_vec *eq;
3721 if (tab->row_var[row] < 0)
3722 continue;
3723 if (tab->row_var[row] >= tab->n_param &&
3724 tab->row_var[row] < tab->n_var - tab->n_div)
3725 continue;
3726 if (tab->row_var[row] < tab->n_param)
3727 p = tab->row_var[row];
3728 else
3729 p = tab->row_var[row]
3730 + tab->n_param - (tab->n_var - tab->n_div);
3732 eq = isl_vec_alloc(tab->mat->ctx, 1+tab->n_param+tab->n_div);
3733 get_row_parameter_line(tab, row, eq->el);
3734 isl_int_neg(eq->el[1 + p], tab->mat->row[row][0]);
3735 eq = isl_vec_normalize(eq);
3737 sol_inc_level(sol);
3738 no_sol_in_strict(sol, tab, eq);
3740 isl_seq_neg(eq->el, eq->el, eq->size);
3741 sol_inc_level(sol);
3742 no_sol_in_strict(sol, tab, eq);
3743 isl_seq_neg(eq->el, eq->el, eq->size);
3745 sol->context->op->add_eq(sol->context, eq->el, 1, 1);
3747 isl_vec_free(eq);
3749 if (isl_tab_mark_redundant(tab, row) < 0)
3750 goto error;
3752 if (sol->context->op->is_empty(sol->context))
3753 break;
3755 row = tab->n_redundant - 1;
3758 find_solutions(sol, tab);
3760 sol->level = 0;
3761 sol_pop(sol);
3763 return;
3764 error:
3765 isl_tab_free(tab);
3766 sol_free(sol);
3769 static void sol_map_find_solutions(struct isl_sol_map *sol_map,
3770 struct isl_tab *tab)
3772 find_solutions_main(&sol_map->sol, tab);
3775 /* Check if integer division "div" of "dom" also occurs in "bmap".
3776 * If so, return its position within the divs.
3777 * If not, return -1.
3779 static int find_context_div(struct isl_basic_map *bmap,
3780 struct isl_basic_set *dom, unsigned div)
3782 int i;
3783 unsigned b_dim = isl_dim_total(bmap->dim);
3784 unsigned d_dim = isl_dim_total(dom->dim);
3786 if (isl_int_is_zero(dom->div[div][0]))
3787 return -1;
3788 if (isl_seq_first_non_zero(dom->div[div] + 2 + d_dim, dom->n_div) != -1)
3789 return -1;
3791 for (i = 0; i < bmap->n_div; ++i) {
3792 if (isl_int_is_zero(bmap->div[i][0]))
3793 continue;
3794 if (isl_seq_first_non_zero(bmap->div[i] + 2 + d_dim,
3795 (b_dim - d_dim) + bmap->n_div) != -1)
3796 continue;
3797 if (isl_seq_eq(bmap->div[i], dom->div[div], 2 + d_dim))
3798 return i;
3800 return -1;
3803 /* The correspondence between the variables in the main tableau,
3804 * the context tableau, and the input map and domain is as follows.
3805 * The first n_param and the last n_div variables of the main tableau
3806 * form the variables of the context tableau.
3807 * In the basic map, these n_param variables correspond to the
3808 * parameters and the input dimensions. In the domain, they correspond
3809 * to the parameters and the set dimensions.
3810 * The n_div variables correspond to the integer divisions in the domain.
3811 * To ensure that everything lines up, we may need to copy some of the
3812 * integer divisions of the domain to the map. These have to be placed
3813 * in the same order as those in the context and they have to be placed
3814 * after any other integer divisions that the map may have.
3815 * This function performs the required reordering.
3817 static struct isl_basic_map *align_context_divs(struct isl_basic_map *bmap,
3818 struct isl_basic_set *dom)
3820 int i;
3821 int common = 0;
3822 int other;
3824 for (i = 0; i < dom->n_div; ++i)
3825 if (find_context_div(bmap, dom, i) != -1)
3826 common++;
3827 other = bmap->n_div - common;
3828 if (dom->n_div - common > 0) {
3829 bmap = isl_basic_map_extend_dim(bmap, isl_dim_copy(bmap->dim),
3830 dom->n_div - common, 0, 0);
3831 if (!bmap)
3832 return NULL;
3834 for (i = 0; i < dom->n_div; ++i) {
3835 int pos = find_context_div(bmap, dom, i);
3836 if (pos < 0) {
3837 pos = isl_basic_map_alloc_div(bmap);
3838 if (pos < 0)
3839 goto error;
3840 isl_int_set_si(bmap->div[pos][0], 0);
3842 if (pos != other + i)
3843 isl_basic_map_swap_div(bmap, pos, other + i);
3845 return bmap;
3846 error:
3847 isl_basic_map_free(bmap);
3848 return NULL;
3851 /* Compute the lexicographic minimum (or maximum if "max" is set)
3852 * of "bmap" over the domain "dom" and return the result as a map.
3853 * If "empty" is not NULL, then *empty is assigned a set that
3854 * contains those parts of the domain where there is no solution.
3855 * If "bmap" is marked as rational (ISL_BASIC_MAP_RATIONAL),
3856 * then we compute the rational optimum. Otherwise, we compute
3857 * the integral optimum.
3859 * We perform some preprocessing. As the PILP solver does not
3860 * handle implicit equalities very well, we first make sure all
3861 * the equalities are explicitly available.
3862 * We also make sure the divs in the domain are properly order,
3863 * because they will be added one by one in the given order
3864 * during the construction of the solution map.
3866 struct isl_map *isl_tab_basic_map_partial_lexopt(
3867 struct isl_basic_map *bmap, struct isl_basic_set *dom,
3868 struct isl_set **empty, int max)
3870 struct isl_tab *tab;
3871 struct isl_map *result = NULL;
3872 struct isl_sol_map *sol_map = NULL;
3873 struct isl_context *context;
3874 struct isl_basic_map *eq;
3876 if (empty)
3877 *empty = NULL;
3878 if (!bmap || !dom)
3879 goto error;
3881 isl_assert(bmap->ctx,
3882 isl_basic_map_compatible_domain(bmap, dom), goto error);
3884 eq = isl_basic_map_copy(bmap);
3885 eq = isl_basic_map_intersect_domain(eq, isl_basic_set_copy(dom));
3886 eq = isl_basic_map_affine_hull(eq);
3887 bmap = isl_basic_map_intersect(bmap, eq);
3889 if (dom->n_div) {
3890 dom = isl_basic_set_order_divs(dom);
3891 bmap = align_context_divs(bmap, dom);
3893 sol_map = sol_map_init(bmap, dom, !!empty, max);
3894 if (!sol_map)
3895 goto error;
3897 context = sol_map->sol.context;
3898 if (isl_basic_set_fast_is_empty(context->op->peek_basic_set(context)))
3899 /* nothing */;
3900 else if (isl_basic_map_fast_is_empty(bmap))
3901 sol_map_add_empty(sol_map,
3902 isl_basic_set_dup(context->op->peek_basic_set(context)));
3903 else {
3904 tab = tab_for_lexmin(bmap,
3905 context->op->peek_basic_set(context), 1, max);
3906 tab = context->op->detect_nonnegative_parameters(context, tab);
3907 sol_map_find_solutions(sol_map, tab);
3909 if (sol_map->sol.error)
3910 goto error;
3912 result = isl_map_copy(sol_map->map);
3913 if (empty)
3914 *empty = isl_set_copy(sol_map->empty);
3915 sol_free(&sol_map->sol);
3916 isl_basic_map_free(bmap);
3917 return result;
3918 error:
3919 sol_free(&sol_map->sol);
3920 isl_basic_map_free(bmap);
3921 return NULL;
3924 struct isl_sol_for {
3925 struct isl_sol sol;
3926 int (*fn)(__isl_take isl_basic_set *dom,
3927 __isl_take isl_mat *map, void *user);
3928 void *user;
3931 static void sol_for_free(struct isl_sol_for *sol_for)
3933 if (sol_for->sol.context)
3934 sol_for->sol.context->op->free(sol_for->sol.context);
3935 free(sol_for);
3938 static void sol_for_free_wrap(struct isl_sol *sol)
3940 sol_for_free((struct isl_sol_for *)sol);
3943 /* Add the solution identified by the tableau and the context tableau.
3945 * See documentation of sol_add for more details.
3947 * Instead of constructing a basic map, this function calls a user
3948 * defined function with the current context as a basic set and
3949 * an affine matrix reprenting the relation between the input and output.
3950 * The number of rows in this matrix is equal to one plus the number
3951 * of output variables. The number of columns is equal to one plus
3952 * the total dimension of the context, i.e., the number of parameters,
3953 * input variables and divs. Since some of the columns in the matrix
3954 * may refer to the divs, the basic set is not simplified.
3955 * (Simplification may reorder or remove divs.)
3957 static void sol_for_add(struct isl_sol_for *sol,
3958 struct isl_basic_set *dom, struct isl_mat *M)
3960 if (sol->sol.error || !dom || !M)
3961 goto error;
3963 dom = isl_basic_set_simplify(dom);
3964 dom = isl_basic_set_finalize(dom);
3966 if (sol->fn(isl_basic_set_copy(dom), isl_mat_copy(M), sol->user) < 0)
3967 goto error;
3969 isl_basic_set_free(dom);
3970 isl_mat_free(M);
3971 return;
3972 error:
3973 isl_basic_set_free(dom);
3974 isl_mat_free(M);
3975 sol->sol.error = 1;
3978 static void sol_for_add_wrap(struct isl_sol *sol,
3979 struct isl_basic_set *dom, struct isl_mat *M)
3981 sol_for_add((struct isl_sol_for *)sol, dom, M);
3984 static struct isl_sol_for *sol_for_init(struct isl_basic_map *bmap, int max,
3985 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
3986 void *user),
3987 void *user)
3989 struct isl_sol_for *sol_for = NULL;
3990 struct isl_dim *dom_dim;
3991 struct isl_basic_set *dom = NULL;
3993 sol_for = isl_calloc_type(bset->ctx, struct isl_sol_for);
3994 if (!sol_for)
3995 goto error;
3997 dom_dim = isl_dim_domain(isl_dim_copy(bmap->dim));
3998 dom = isl_basic_set_universe(dom_dim);
4000 sol_for->sol.rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
4001 sol_for->sol.dec_level.callback.run = &sol_dec_level_wrap;
4002 sol_for->sol.dec_level.sol = &sol_for->sol;
4003 sol_for->fn = fn;
4004 sol_for->user = user;
4005 sol_for->sol.max = max;
4006 sol_for->sol.n_out = isl_basic_map_dim(bmap, isl_dim_out);
4007 sol_for->sol.add = &sol_for_add_wrap;
4008 sol_for->sol.add_empty = NULL;
4009 sol_for->sol.free = &sol_for_free_wrap;
4011 sol_for->sol.context = isl_context_alloc(dom);
4012 if (!sol_for->sol.context)
4013 goto error;
4015 isl_basic_set_free(dom);
4016 return sol_for;
4017 error:
4018 isl_basic_set_free(dom);
4019 sol_for_free(sol_for);
4020 return NULL;
4023 static void sol_for_find_solutions(struct isl_sol_for *sol_for,
4024 struct isl_tab *tab)
4026 find_solutions_main(&sol_for->sol, tab);
4029 int isl_basic_map_foreach_lexopt(__isl_keep isl_basic_map *bmap, int max,
4030 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
4031 void *user),
4032 void *user)
4034 struct isl_sol_for *sol_for = NULL;
4036 bmap = isl_basic_map_copy(bmap);
4037 if (!bmap)
4038 return -1;
4040 bmap = isl_basic_map_detect_equalities(bmap);
4041 sol_for = sol_for_init(bmap, max, fn, user);
4043 if (isl_basic_map_fast_is_empty(bmap))
4044 /* nothing */;
4045 else {
4046 struct isl_tab *tab;
4047 struct isl_context *context = sol_for->sol.context;
4048 tab = tab_for_lexmin(bmap,
4049 context->op->peek_basic_set(context), 1, max);
4050 tab = context->op->detect_nonnegative_parameters(context, tab);
4051 sol_for_find_solutions(sol_for, tab);
4052 if (sol_for->sol.error)
4053 goto error;
4056 sol_free(&sol_for->sol);
4057 isl_basic_map_free(bmap);
4058 return 0;
4059 error:
4060 sol_free(&sol_for->sol);
4061 isl_basic_map_free(bmap);
4062 return -1;
4065 int isl_basic_map_foreach_lexmin(__isl_keep isl_basic_map *bmap,
4066 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
4067 void *user),
4068 void *user)
4070 return isl_basic_map_foreach_lexopt(bmap, 0, fn, user);
4073 int isl_basic_map_foreach_lexmax(__isl_keep isl_basic_map *bmap,
4074 int (*fn)(__isl_take isl_basic_set *dom, __isl_take isl_mat *map,
4075 void *user),
4076 void *user)
4078 return isl_basic_map_foreach_lexopt(bmap, 1, fn, user);