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isl_tab: optionally keep track of row signs
[isl.git] / isl_tab.c
blobbbe040419bf7aded35b1ff209d065d9a00b76324
1 #include "isl_mat.h"
2 #include "isl_map_private.h"
3 #include "isl_tab.h"
4
5 /*
6 * The implementation of tableaus in this file was inspired by Section 8
7 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
8 * prover for program checking".
9 */
10
11 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
12 unsigned n_row, unsigned n_var, unsigned M)
13 {
14 int i;
15 struct isl_tab *tab;
16 unsigned off = 2 + M;
17
18 tab = isl_calloc_type(ctx, struct isl_tab);
19 if (!tab)
20 return NULL;
21 tab->mat = isl_mat_alloc(ctx, n_row, off + n_var);
22 if (!tab->mat)
23 goto error;
24 tab->var = isl_alloc_array(ctx, struct isl_tab_var, n_var);
25 if (!tab->var)
26 goto error;
27 tab->con = isl_alloc_array(ctx, struct isl_tab_var, n_row);
28 if (!tab->con)
29 goto error;
30 tab->col_var = isl_alloc_array(ctx, int, n_var);
31 if (!tab->col_var)
32 goto error;
33 tab->row_var = isl_alloc_array(ctx, int, n_row);
34 if (!tab->row_var)
35 goto error;
36 for (i = 0; i < n_var; ++i) {
37 tab->var[i].index = i;
38 tab->var[i].is_row = 0;
39 tab->var[i].is_nonneg = 0;
40 tab->var[i].is_zero = 0;
41 tab->var[i].is_redundant = 0;
42 tab->var[i].frozen = 0;
43 tab->col_var[i] = i;
44 }
45 tab->n_row = 0;
46 tab->n_con = 0;
47 tab->n_eq = 0;
48 tab->max_con = n_row;
49 tab->n_col = n_var;
50 tab->n_var = n_var;
51 tab->max_var = n_var;
52 tab->n_param = 0;
53 tab->n_div = 0;
54 tab->n_dead = 0;
55 tab->n_redundant = 0;
56 tab->need_undo = 0;
57 tab->rational = 0;
58 tab->empty = 0;
59 tab->in_undo = 0;
60 tab->M = M;
61 tab->bottom.type = isl_tab_undo_bottom;
62 tab->bottom.next = NULL;
63 tab->top = &tab->bottom;
64 return tab;
65 error:
66 isl_tab_free(tab);
67 return NULL;
68 }
69
70 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new)
71 {
72 unsigned off = 2 + tab->M;
73 if (tab->max_con < tab->n_con + n_new) {
74 struct isl_tab_var *con;
75
76 con = isl_realloc_array(tab->mat->ctx, tab->con,
77 struct isl_tab_var, tab->max_con + n_new);
78 if (!con)
79 return -1;
80 tab->con = con;
81 tab->max_con += n_new;
82 }
83 if (tab->mat->n_row < tab->n_row + n_new) {
84 int *row_var;
85
86 tab->mat = isl_mat_extend(tab->mat,
87 tab->n_row + n_new, off + tab->n_col);
88 if (!tab->mat)
89 return -1;
90 row_var = isl_realloc_array(tab->mat->ctx, tab->row_var,
91 int, tab->mat->n_row);
92 if (!row_var)
93 return -1;
94 tab->row_var = row_var;
95 if (tab->row_sign) {
96 enum isl_tab_row_sign *s;
97 s = isl_realloc_array(tab->mat->ctx, tab->row_sign,
98 enum isl_tab_row_sign, tab->mat->n_row);
99 if (!s)
100 return -1;
101 tab->row_sign = s;
102 }
103 }
104 return 0;
105 }
106
107 /* Make room for at least n_new extra variables.
108 * Return -1 if anything went wrong.
109 */
110 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new)
111 {
112 struct isl_tab_var *var;
113 unsigned off = 2 + tab->M;
114
115 if (tab->max_var < tab->n_var + n_new) {
116 var = isl_realloc_array(tab->mat->ctx, tab->var,
117 struct isl_tab_var, tab->n_var + n_new);
118 if (!var)
119 return -1;
120 tab->var = var;
121 tab->max_var += n_new;
122 }
123
124 if (tab->mat->n_col < off + tab->n_col + n_new) {
125 int *p;
126
127 tab->mat = isl_mat_extend(tab->mat,
128 tab->mat->n_row, off + tab->n_col + n_new);
129 if (!tab->mat)
130 return -1;
131 p = isl_realloc_array(tab->mat->ctx, tab->col_var,
132 int, tab->mat->n_col);
133 if (!p)
134 return -1;
135 tab->col_var = p;
136 }
137
138 return 0;
139 }
140
141 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new)
142 {
143 if (isl_tab_extend_cons(tab, n_new) >= 0)
144 return tab;
145
146 isl_tab_free(tab);
147 return NULL;
148 }
149
150 static void free_undo(struct isl_tab *tab)
151 {
152 struct isl_tab_undo *undo, *next;
153
154 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
155 next = undo->next;
156 free(undo);
157 }
158 tab->top = undo;
159 }
160
161 void isl_tab_free(struct isl_tab *tab)
162 {
163 if (!tab)
164 return;
165 free_undo(tab);
166 isl_mat_free(tab->mat);
167 isl_vec_free(tab->dual);
168 isl_basic_set_free(tab->bset);
169 free(tab->var);
170 free(tab->con);
171 free(tab->row_var);
172 free(tab->col_var);
173 free(tab->row_sign);
174 free(tab);
175 }
176
177 struct isl_tab *isl_tab_dup(struct isl_tab *tab)
178 {
179 int i;
180 struct isl_tab *dup;
181
182 if (!tab)
183 return NULL;
184
185 dup = isl_calloc_type(tab->ctx, struct isl_tab);
186 if (!dup)
187 return NULL;
188 dup->mat = isl_mat_dup(tab->mat);
189 if (!dup->mat)
190 goto error;
191 dup->var = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_var);
192 if (!dup->var)
193 goto error;
194 for (i = 0; i < tab->n_var; ++i)
195 dup->var[i] = tab->var[i];
196 dup->con = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_con);
197 if (!dup->con)
198 goto error;
199 for (i = 0; i < tab->n_con; ++i)
200 dup->con[i] = tab->con[i];
201 dup->col_var = isl_alloc_array(tab->ctx, int, tab->mat->n_col);
202 if (!dup->col_var)
203 goto error;
204 for (i = 0; i < tab->n_var; ++i)
205 dup->col_var[i] = tab->col_var[i];
206 dup->row_var = isl_alloc_array(tab->ctx, int, tab->mat->n_row);
207 if (!dup->row_var)
208 goto error;
209 for (i = 0; i < tab->n_row; ++i)
210 dup->row_var[i] = tab->row_var[i];
211 if (tab->row_sign) {
212 dup->row_sign = isl_alloc_array(tab->ctx, enum isl_tab_row_sign,
213 tab->mat->n_row);
214 if (!dup->row_sign)
215 goto error;
216 for (i = 0; i < tab->n_row; ++i)
217 dup->row_sign[i] = tab->row_sign[i];
218 }
219 dup->n_row = tab->n_row;
220 dup->n_con = tab->n_con;
221 dup->n_eq = tab->n_eq;
222 dup->max_con = tab->max_con;
223 dup->n_col = tab->n_col;
224 dup->n_var = tab->n_var;
225 dup->max_var = tab->max_var;
226 dup->n_param = tab->n_param;
227 dup->n_div = tab->n_div;
228 dup->n_dead = tab->n_dead;
229 dup->n_redundant = tab->n_redundant;
230 dup->rational = tab->rational;
231 dup->empty = tab->empty;
232 dup->need_undo = 0;
233 dup->in_undo = 0;
234 dup->M = tab->M;
235 dup->bottom.type = isl_tab_undo_bottom;
236 dup->bottom.next = NULL;
237 dup->top = &dup->bottom;
238 return dup;
239 error:
240 isl_tab_free(dup);
241 return NULL;
242 }
243
244 static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i)
245 {
246 if (i >= 0)
247 return &tab->var[i];
248 else
249 return &tab->con[~i];
250 }
251
252 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
253 {
254 return var_from_index(tab, tab->row_var[i]);
255 }
256
257 static struct isl_tab_var *var_from_col(struct isl_tab *tab, int i)
258 {
259 return var_from_index(tab, tab->col_var[i]);
260 }
261
262 /* Check if there are any upper bounds on column variable "var",
263 * i.e., non-negative rows where var appears with a negative coefficient.
264 * Return 1 if there are no such bounds.
265 */
266 static int max_is_manifestly_unbounded(struct isl_tab *tab,
267 struct isl_tab_var *var)
268 {
269 int i;
270 unsigned off = 2 + tab->M;
271
272 if (var->is_row)
273 return 0;
274 for (i = tab->n_redundant; i < tab->n_row; ++i) {
275 if (!isl_int_is_neg(tab->mat->row[i][off + var->index]))
276 continue;
277 if (isl_tab_var_from_row(tab, i)->is_nonneg)
278 return 0;
279 }
280 return 1;
281 }
282
283 /* Check if there are any lower bounds on column variable "var",
284 * i.e., non-negative rows where var appears with a positive coefficient.
285 * Return 1 if there are no such bounds.
286 */
287 static int min_is_manifestly_unbounded(struct isl_tab *tab,
288 struct isl_tab_var *var)
289 {
290 int i;
291 unsigned off = 2 + tab->M;
292
293 if (var->is_row)
294 return 0;
295 for (i = tab->n_redundant; i < tab->n_row; ++i) {
296 if (!isl_int_is_pos(tab->mat->row[i][off + var->index]))
297 continue;
298 if (isl_tab_var_from_row(tab, i)->is_nonneg)
299 return 0;
300 }
301 return 1;
302 }
303
304 static int row_cmp(struct isl_tab *tab, int r1, int r2, int c, isl_int t)
305 {
306 unsigned off = 2 + tab->M;
307
308 if (tab->M) {
309 int s;
310 isl_int_mul(t, tab->mat->row[r1][2], tab->mat->row[r2][off+c]);
311 isl_int_submul(t, tab->mat->row[r2][2], tab->mat->row[r1][off+c]);
312 s = isl_int_sgn(t);
313 if (s)
314 return s;
315 }
316 isl_int_mul(t, tab->mat->row[r1][1], tab->mat->row[r2][off + c]);
317 isl_int_submul(t, tab->mat->row[r2][1], tab->mat->row[r1][off + c]);
318 return isl_int_sgn(t);
319 }
320
321 /* Given the index of a column "c", return the index of a row
322 * that can be used to pivot the column in, with either an increase
323 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
324 * If "var" is not NULL, then the row returned will be different from
325 * the one associated with "var".
326 *
327 * Each row in the tableau is of the form
328 *
329 * x_r = a_r0 + \sum_i a_ri x_i
330 *
331 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
332 * impose any limit on the increase or decrease in the value of x_c
333 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
334 * for the row with the smallest (most stringent) such bound.
335 * Note that the common denominator of each row drops out of the fraction.
336 * To check if row j has a smaller bound than row r, i.e.,
337 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
338 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
339 * where -sign(a_jc) is equal to "sgn".
340 */
341 static int pivot_row(struct isl_tab *tab,
342 struct isl_tab_var *var, int sgn, int c)
343 {
344 int j, r, tsgn;
345 isl_int t;
346 unsigned off = 2 + tab->M;
347
348 isl_int_init(t);
349 r = -1;
350 for (j = tab->n_redundant; j < tab->n_row; ++j) {
351 if (var && j == var->index)
352 continue;
353 if (!isl_tab_var_from_row(tab, j)->is_nonneg)
354 continue;
355 if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
356 continue;
357 if (r < 0) {
358 r = j;
359 continue;
360 }
361 tsgn = sgn * row_cmp(tab, r, j, c, t);
362 if (tsgn < 0 || (tsgn == 0 &&
363 tab->row_var[j] < tab->row_var[r]))
364 r = j;
365 }
366 isl_int_clear(t);
367 return r;
368 }
369
370 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
371 * (sgn < 0) the value of row variable var.
372 * If not NULL, then skip_var is a row variable that should be ignored
373 * while looking for a pivot row. It is usually equal to var.
374 *
375 * As the given row in the tableau is of the form
376 *
377 * x_r = a_r0 + \sum_i a_ri x_i
378 *
379 * we need to find a column such that the sign of a_ri is equal to "sgn"
380 * (such that an increase in x_i will have the desired effect) or a
381 * column with a variable that may attain negative values.
382 * If a_ri is positive, then we need to move x_i in the same direction
383 * to obtain the desired effect. Otherwise, x_i has to move in the
384 * opposite direction.
385 */
386 static void find_pivot(struct isl_tab *tab,
387 struct isl_tab_var *var, struct isl_tab_var *skip_var,
388 int sgn, int *row, int *col)
389 {
390 int j, r, c;
391 isl_int *tr;
392
393 *row = *col = -1;
394
395 isl_assert(tab->mat->ctx, var->is_row, return);
396 tr = tab->mat->row[var->index] + 2 + tab->M;
397
398 c = -1;
399 for (j = tab->n_dead; j < tab->n_col; ++j) {
400 if (isl_int_is_zero(tr[j]))
401 continue;
402 if (isl_int_sgn(tr[j]) != sgn &&
403 var_from_col(tab, j)->is_nonneg)
404 continue;
405 if (c < 0 || tab->col_var[j] < tab->col_var[c])
406 c = j;
407 }
408 if (c < 0)
409 return;
410
411 sgn *= isl_int_sgn(tr[c]);
412 r = pivot_row(tab, skip_var, sgn, c);
413 *row = r < 0 ? var->index : r;
414 *col = c;
415 }
416
417 /* Return 1 if row "row" represents an obviously redundant inequality.
418 * This means
419 * - it represents an inequality or a variable
420 * - that is the sum of a non-negative sample value and a positive
421 * combination of zero or more non-negative variables.
422 */
423 int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
424 {
425 int i;
426 unsigned off = 2 + tab->M;
427
428 if (tab->row_var[row] < 0 && !isl_tab_var_from_row(tab, row)->is_nonneg)
429 return 0;
430
431 if (isl_int_is_neg(tab->mat->row[row][1]))
432 return 0;
433 if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
434 return 0;
435
436 for (i = tab->n_dead; i < tab->n_col; ++i) {
437 if (isl_int_is_zero(tab->mat->row[row][off + i]))
438 continue;
439 if (isl_int_is_neg(tab->mat->row[row][off + i]))
440 return 0;
441 if (!var_from_col(tab, i)->is_nonneg)
442 return 0;
443 }
444 return 1;
445 }
446
447 static void swap_rows(struct isl_tab *tab, int row1, int row2)
448 {
449 int t;
450 t = tab->row_var[row1];
451 tab->row_var[row1] = tab->row_var[row2];
452 tab->row_var[row2] = t;
453 isl_tab_var_from_row(tab, row1)->index = row1;
454 isl_tab_var_from_row(tab, row2)->index = row2;
455 tab->mat = isl_mat_swap_rows(tab->mat, row1, row2);
456
457 if (!tab->row_sign)
458 return;
459 t = tab->row_sign[row1];
460 tab->row_sign[row1] = tab->row_sign[row2];
461 tab->row_sign[row2] = t;
462 }
463
464 static void push_union(struct isl_tab *tab,
465 enum isl_tab_undo_type type, union isl_tab_undo_val u)
466 {
467 struct isl_tab_undo *undo;
468
469 if (!tab->need_undo)
470 return;
471
472 undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
473 if (!undo) {
474 free_undo(tab);
475 tab->top = NULL;
476 return;
477 }
478 undo->type = type;
479 undo->u = u;
480 undo->next = tab->top;
481 tab->top = undo;
482 }
483
484 void isl_tab_push_var(struct isl_tab *tab,
485 enum isl_tab_undo_type type, struct isl_tab_var *var)
486 {
487 union isl_tab_undo_val u;
488 if (var->is_row)
489 u.var_index = tab->row_var[var->index];
490 else
491 u.var_index = tab->col_var[var->index];
492 push_union(tab, type, u);
493 }
494
495 void isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
496 {
497 union isl_tab_undo_val u = { 0 };
498 push_union(tab, type, u);
499 }
500
501 /* Push a record on the undo stack describing the current basic
502 * variables, so that the this state can be restored during rollback.
503 */
504 void isl_tab_push_basis(struct isl_tab *tab)
505 {
506 int i;
507 union isl_tab_undo_val u;
508
509 u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
510 if (!u.col_var) {
511 free_undo(tab);
512 tab->top = NULL;
513 return;
514 }
515 for (i = 0; i < tab->n_col; ++i)
516 u.col_var[i] = tab->col_var[i];
517 push_union(tab, isl_tab_undo_saved_basis, u);
518 }
519
520 /* Mark row with index "row" as being redundant.
521 * If we may need to undo the operation or if the row represents
522 * a variable of the original problem, the row is kept,
523 * but no longer considered when looking for a pivot row.
524 * Otherwise, the row is simply removed.
525 *
526 * The row may be interchanged with some other row. If it
527 * is interchanged with a later row, return 1. Otherwise return 0.
528 * If the rows are checked in order in the calling function,
529 * then a return value of 1 means that the row with the given
530 * row number may now contain a different row that hasn't been checked yet.
531 */
532 int isl_tab_mark_redundant(struct isl_tab *tab, int row)
533 {
534 struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
535 var->is_redundant = 1;
536 isl_assert(tab->mat->ctx, row >= tab->n_redundant, return);
537 if (tab->need_undo || tab->row_var[row] >= 0) {
538 if (tab->row_var[row] >= 0 && !var->is_nonneg) {
539 var->is_nonneg = 1;
540 isl_tab_push_var(tab, isl_tab_undo_nonneg, var);
541 }
542 if (row != tab->n_redundant)
543 swap_rows(tab, row, tab->n_redundant);
544 isl_tab_push_var(tab, isl_tab_undo_redundant, var);
545 tab->n_redundant++;
546 return 0;
547 } else {
548 if (row != tab->n_row - 1)
549 swap_rows(tab, row, tab->n_row - 1);
550 isl_tab_var_from_row(tab, tab->n_row - 1)->index = -1;
551 tab->n_row--;
552 return 1;
553 }
554 }
555
556 struct isl_tab *isl_tab_mark_empty(struct isl_tab *tab)
557 {
558 if (!tab->empty && tab->need_undo)
559 isl_tab_push(tab, isl_tab_undo_empty);
560 tab->empty = 1;
561 return tab;
562 }
563
564 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
565 * the original sign of the pivot element.
566 * We only keep track of row signs during PILP solving and in this case
567 * we only pivot a row with negative sign (meaning the value is always
568 * non-positive) using a positive pivot element.
569 *
570 * For each row j, the new value of the parametric constant is equal to
571 *
572 * a_j0 - a_jc a_r0/a_rc
573 *
574 * where a_j0 is the original parametric constant, a_rc is the pivot element,
575 * a_r0 is the parametric constant of the pivot row and a_jc is the
576 * pivot column entry of the row j.
577 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
578 * remains the same if a_jc has the same sign as the row j or if
579 * a_jc is zero. In all other cases, we reset the sign to "unknown".
580 */
581 static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
582 {
583 int i;
584 struct isl_mat *mat = tab->mat;
585 unsigned off = 2 + tab->M;
586
587 if (!tab->row_sign)
588 return;
589
590 if (tab->row_sign[row] == 0)
591 return;
592 isl_assert(mat->ctx, row_sgn > 0, return);
593 isl_assert(mat->ctx, tab->row_sign[row] == isl_tab_row_neg, return);
594 tab->row_sign[row] = isl_tab_row_pos;
595 for (i = 0; i < tab->n_row; ++i) {
596 int s;
597 if (i == row)
598 continue;
599 s = isl_int_sgn(mat->row[i][off + col]);
600 if (!s)
601 continue;
602 if (!tab->row_sign[i])
603 continue;
604 if (s < 0 && tab->row_sign[i] == isl_tab_row_neg)
605 continue;
606 if (s > 0 && tab->row_sign[i] == isl_tab_row_pos)
607 continue;
608 tab->row_sign[i] = isl_tab_row_unknown;
609 }
610 }
611
612 /* Given a row number "row" and a column number "col", pivot the tableau
613 * such that the associated variables are interchanged.
614 * The given row in the tableau expresses
615 *
616 * x_r = a_r0 + \sum_i a_ri x_i
617 *
618 * or
619 *
620 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
621 *
622 * Substituting this equality into the other rows
623 *
624 * x_j = a_j0 + \sum_i a_ji x_i
625 *
626 * with a_jc \ne 0, we obtain
627 *
628 * x_j = a_jc/a_rc x_r + a_j0 - a_jc a_r0/a_rc + sum a_ji - a_jc a_ri/a_rc
629 *
630 * The tableau
631 *
632 * n_rc/d_r n_ri/d_r
633 * n_jc/d_j n_ji/d_j
634 *
635 * where i is any other column and j is any other row,
636 * is therefore transformed into
637 *
638 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
639 * s(n_rc)d_r n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
640 *
641 * The transformation is performed along the following steps
642 *
643 * d_r/n_rc n_ri/n_rc
644 * n_jc/d_j n_ji/d_j
645 *
646 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
647 * n_jc/d_j n_ji/d_j
648 *
649 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
650 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
651 *
652 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
653 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
654 *
655 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
656 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
657 *
658 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
659 * s(n_rc)d_r n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
660 *
661 */
662 void isl_tab_pivot(struct isl_tab *tab, int row, int col)
663 {
664 int i, j;
665 int sgn;
666 int t;
667 struct isl_mat *mat = tab->mat;
668 struct isl_tab_var *var;
669 unsigned off = 2 + tab->M;
670
671 isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
672 sgn = isl_int_sgn(mat->row[row][0]);
673 if (sgn < 0) {
674 isl_int_neg(mat->row[row][0], mat->row[row][0]);
675 isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]);
676 } else
677 for (j = 0; j < off - 1 + tab->n_col; ++j) {
678 if (j == off - 1 + col)
679 continue;
680 isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
681 }
682 if (!isl_int_is_one(mat->row[row][0]))
683 isl_seq_normalize(mat->row[row], off + tab->n_col);
684 for (i = 0; i < tab->n_row; ++i) {
685 if (i == row)
686 continue;
687 if (isl_int_is_zero(mat->row[i][off + col]))
688 continue;
689 isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
690 for (j = 0; j < off - 1 + tab->n_col; ++j) {
691 if (j == off - 1 + col)
692 continue;
693 isl_int_mul(mat->row[i][1 + j],
694 mat->row[i][1 + j], mat->row[row][0]);
695 isl_int_addmul(mat->row[i][1 + j],
696 mat->row[i][off + col], mat->row[row][1 + j]);
697 }
698 isl_int_mul(mat->row[i][off + col],
699 mat->row[i][off + col], mat->row[row][off + col]);
700 if (!isl_int_is_one(mat->row[i][0]))
701 isl_seq_normalize(mat->row[i], off + tab->n_col);
702 }
703 t = tab->row_var[row];
704 tab->row_var[row] = tab->col_var[col];
705 tab->col_var[col] = t;
706 var = isl_tab_var_from_row(tab, row);
707 var->is_row = 1;
708 var->index = row;
709 var = var_from_col(tab, col);
710 var->is_row = 0;
711 var->index = col;
712 update_row_sign(tab, row, col, sgn);
713 if (tab->in_undo)
714 return;
715 for (i = tab->n_redundant; i < tab->n_row; ++i) {
716 if (isl_int_is_zero(mat->row[i][off + col]))
717 continue;
718 if (!isl_tab_var_from_row(tab, i)->frozen &&
719 isl_tab_row_is_redundant(tab, i))
720 if (isl_tab_mark_redundant(tab, i))
721 --i;
722 }
723 }
724
725 /* If "var" represents a column variable, then pivot is up (sgn > 0)
726 * or down (sgn < 0) to a row. The variable is assumed not to be
727 * unbounded in the specified direction.
728 * If sgn = 0, then the variable is unbounded in both directions,
729 * and we pivot with any row we can find.
730 */
731 static void to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
732 {
733 int r;
734 unsigned off = 2 + tab->M;
735
736 if (var->is_row)
737 return;
738
739 if (sign == 0) {
740 for (r = tab->n_redundant; r < tab->n_row; ++r)
741 if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
742 break;
743 isl_assert(tab->mat->ctx, r < tab->n_row, return);
744 } else {
745 r = pivot_row(tab, NULL, sign, var->index);
746 isl_assert(tab->mat->ctx, r >= 0, return);
747 }
748
749 isl_tab_pivot(tab, r, var->index);
750 }
751
752 static void check_table(struct isl_tab *tab)
753 {
754 int i;
755
756 if (tab->empty)
757 return;
758 for (i = 0; i < tab->n_row; ++i) {
759 if (!isl_tab_var_from_row(tab, i)->is_nonneg)
760 continue;
761 assert(!isl_int_is_neg(tab->mat->row[i][1]));
762 }
763 }
764
765 /* Return the sign of the maximal value of "var".
766 * If the sign is not negative, then on return from this function,
767 * the sample value will also be non-negative.
768 *
769 * If "var" is manifestly unbounded wrt positive values, we are done.
770 * Otherwise, we pivot the variable up to a row if needed
771 * Then we continue pivoting down until either
772 * - no more down pivots can be performed
773 * - the sample value is positive
774 * - the variable is pivoted into a manifestly unbounded column
775 */
776 static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
777 {
778 int row, col;
779
780 if (max_is_manifestly_unbounded(tab, var))
781 return 1;
782 to_row(tab, var, 1);
783 while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
784 find_pivot(tab, var, var, 1, &row, &col);
785 if (row == -1)
786 return isl_int_sgn(tab->mat->row[var->index][1]);
787 isl_tab_pivot(tab, row, col);
788 if (!var->is_row) /* manifestly unbounded */
789 return 1;
790 }
791 return 1;
792 }
793
794 static int row_is_neg(struct isl_tab *tab, int row)
795 {
796 if (!tab->M)
797 return isl_int_is_neg(tab->mat->row[row][1]);
798 if (isl_int_is_pos(tab->mat->row[row][2]))
799 return 0;
800 if (isl_int_is_neg(tab->mat->row[row][2]))
801 return 1;
802 return isl_int_is_neg(tab->mat->row[row][1]);
803 }
804
805 static int row_sgn(struct isl_tab *tab, int row)
806 {
807 if (!tab->M)
808 return isl_int_sgn(tab->mat->row[row][1]);
809 if (!isl_int_is_zero(tab->mat->row[row][2]))
810 return isl_int_sgn(tab->mat->row[row][2]);
811 else
812 return isl_int_sgn(tab->mat->row[row][1]);
813 }
814
815 /* Perform pivots until the row variable "var" has a non-negative
816 * sample value or until no more upward pivots can be performed.
817 * Return the sign of the sample value after the pivots have been
818 * performed.
819 */
820 static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
821 {
822 int row, col;
823
824 while (row_is_neg(tab, var->index)) {
825 find_pivot(tab, var, var, 1, &row, &col);
826 if (row == -1)
827 break;
828 isl_tab_pivot(tab, row, col);
829 if (!var->is_row) /* manifestly unbounded */
830 return 1;
831 }
832 return row_sgn(tab, var->index);
833 }
834
835 /* Perform pivots until we are sure that the row variable "var"
836 * can attain non-negative values. After return from this
837 * function, "var" is still a row variable, but its sample
838 * value may not be non-negative, even if the function returns 1.
839 */
840 static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
841 {
842 int row, col;
843
844 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
845 find_pivot(tab, var, var, 1, &row, &col);
846 if (row == -1)
847 break;
848 if (row == var->index) /* manifestly unbounded */
849 return 1;
850 isl_tab_pivot(tab, row, col);
851 }
852 return !isl_int_is_neg(tab->mat->row[var->index][1]);
853 }
854
855 /* Return a negative value if "var" can attain negative values.
856 * Return a non-negative value otherwise.
857 *
858 * If "var" is manifestly unbounded wrt negative values, we are done.
859 * Otherwise, if var is in a column, we can pivot it down to a row.
860 * Then we continue pivoting down until either
861 * - the pivot would result in a manifestly unbounded column
862 * => we don't perform the pivot, but simply return -1
863 * - no more down pivots can be performed
864 * - the sample value is negative
865 * If the sample value becomes negative and the variable is supposed
866 * to be nonnegative, then we undo the last pivot.
867 * However, if the last pivot has made the pivoting variable
868 * obviously redundant, then it may have moved to another row.
869 * In that case we look for upward pivots until we reach a non-negative
870 * value again.
871 */
872 static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
873 {
874 int row, col;
875 struct isl_tab_var *pivot_var;
876
877 if (min_is_manifestly_unbounded(tab, var))
878 return -1;
879 if (!var->is_row) {
880 col = var->index;
881 row = pivot_row(tab, NULL, -1, col);
882 pivot_var = var_from_col(tab, col);
883 isl_tab_pivot(tab, row, col);
884 if (var->is_redundant)
885 return 0;
886 if (isl_int_is_neg(tab->mat->row[var->index][1])) {
887 if (var->is_nonneg) {
888 if (!pivot_var->is_redundant &&
889 pivot_var->index == row)
890 isl_tab_pivot(tab, row, col);
891 else
892 restore_row(tab, var);
893 }
894 return -1;
895 }
896 }
897 if (var->is_redundant)
898 return 0;
899 while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
900 find_pivot(tab, var, var, -1, &row, &col);
901 if (row == var->index)
902 return -1;
903 if (row == -1)
904 return isl_int_sgn(tab->mat->row[var->index][1]);
905 pivot_var = var_from_col(tab, col);
906 isl_tab_pivot(tab, row, col);
907 if (var->is_redundant)
908 return 0;
909 }
910 if (var->is_nonneg) {
911 /* pivot back to non-negative value */
912 if (!pivot_var->is_redundant && pivot_var->index == row)
913 isl_tab_pivot(tab, row, col);
914 else
915 restore_row(tab, var);
916 }
917 return -1;
918 }
919
920 static int row_at_most_neg_one(struct isl_tab *tab, int row)
921 {
922 if (tab->M) {
923 if (isl_int_is_pos(tab->mat->row[row][2]))
924 return 0;
925 if (isl_int_is_neg(tab->mat->row[row][2]))
926 return 1;
927 }
928 return isl_int_is_neg(tab->mat->row[row][1]) &&
929 isl_int_abs_ge(tab->mat->row[row][1],
930 tab->mat->row[row][0]);
931 }
932
933 /* Return 1 if "var" can attain values <= -1.
934 * Return 0 otherwise.
935 *
936 * The sample value of "var" is assumed to be non-negative when the
937 * the function is called and will be made non-negative again before
938 * the function returns.
939 */
940 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
941 {
942 int row, col;
943 struct isl_tab_var *pivot_var;
944
945 if (min_is_manifestly_unbounded(tab, var))
946 return 1;
947 if (!var->is_row) {
948 col = var->index;
949 row = pivot_row(tab, NULL, -1, col);
950 pivot_var = var_from_col(tab, col);
951 isl_tab_pivot(tab, row, col);
952 if (var->is_redundant)
953 return 0;
954 if (row_at_most_neg_one(tab, var->index)) {
955 if (var->is_nonneg) {
956 if (!pivot_var->is_redundant &&
957 pivot_var->index == row)
958 isl_tab_pivot(tab, row, col);
959 else
960 restore_row(tab, var);
961 }
962 return 1;
963 }
964 }
965 if (var->is_redundant)
966 return 0;
967 do {
968 find_pivot(tab, var, var, -1, &row, &col);
969 if (row == var->index)
970 return 1;
971 if (row == -1)
972 return 0;
973 pivot_var = var_from_col(tab, col);
974 isl_tab_pivot(tab, row, col);
975 if (var->is_redundant)
976 return 0;
977 } while (!row_at_most_neg_one(tab, var->index));
978 if (var->is_nonneg) {
979 /* pivot back to non-negative value */
980 if (!pivot_var->is_redundant && pivot_var->index == row)
981 isl_tab_pivot(tab, row, col);
982 restore_row(tab, var);
983 }
984 return 1;
985 }
986
987 /* Return 1 if "var" can attain values >= 1.
988 * Return 0 otherwise.
989 */
990 static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
991 {
992 int row, col;
993 isl_int *r;
994
995 if (max_is_manifestly_unbounded(tab, var))
996 return 1;
997 to_row(tab, var, 1);
998 r = tab->mat->row[var->index];
999 while (isl_int_lt(r[1], r[0])) {
1000 find_pivot(tab, var, var, 1, &row, &col);
1001 if (row == -1)
1002 return isl_int_ge(r[1], r[0]);
1003 if (row == var->index) /* manifestly unbounded */
1004 return 1;
1005 isl_tab_pivot(tab, row, col);
1006 }
1007 return 1;
1008 }
1009
1010 static void swap_cols(struct isl_tab *tab, int col1, int col2)
1011 {
1012 int t;
1013 unsigned off = 2 + tab->M;
1014 t = tab->col_var[col1];
1015 tab->col_var[col1] = tab->col_var[col2];
1016 tab->col_var[col2] = t;
1017 var_from_col(tab, col1)->index = col1;
1018 var_from_col(tab, col2)->index = col2;
1019 tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2);
1020 }
1021
1022 /* Mark column with index "col" as representing a zero variable.
1023 * If we may need to undo the operation the column is kept,
1024 * but no longer considered.
1025 * Otherwise, the column is simply removed.
1026 *
1027 * The column may be interchanged with some other column. If it
1028 * is interchanged with a later column, return 1. Otherwise return 0.
1029 * If the columns are checked in order in the calling function,
1030 * then a return value of 1 means that the column with the given
1031 * column number may now contain a different column that
1032 * hasn't been checked yet.
1033 */
1034 int isl_tab_kill_col(struct isl_tab *tab, int col)
1035 {
1036 var_from_col(tab, col)->is_zero = 1;
1037 if (tab->need_undo) {
1038 isl_tab_push_var(tab, isl_tab_undo_zero, var_from_col(tab, col));
1039 if (col != tab->n_dead)
1040 swap_cols(tab, col, tab->n_dead);
1041 tab->n_dead++;
1042 return 0;
1043 } else {
1044 if (col != tab->n_col - 1)
1045 swap_cols(tab, col, tab->n_col - 1);
1046 var_from_col(tab, tab->n_col - 1)->index = -1;
1047 tab->n_col--;
1048 return 1;
1049 }
1050 }
1051
1052 /* Row variable "var" is non-negative and cannot attain any values
1053 * larger than zero. This means that the coefficients of the unrestricted
1054 * column variables are zero and that the coefficients of the non-negative
1055 * column variables are zero or negative.
1056 * Each of the non-negative variables with a negative coefficient can
1057 * then also be written as the negative sum of non-negative variables
1058 * and must therefore also be zero.
1059 */
1060 static void close_row(struct isl_tab *tab, struct isl_tab_var *var)
1061 {
1062 int j;
1063 struct isl_mat *mat = tab->mat;
1064 unsigned off = 2 + tab->M;
1065
1066 isl_assert(tab->mat->ctx, var->is_nonneg, return);
1067 var->is_zero = 1;
1068 for (j = tab->n_dead; j < tab->n_col; ++j) {
1069 if (isl_int_is_zero(mat->row[var->index][off + j]))
1070 continue;
1071 isl_assert(tab->mat->ctx,
1072 isl_int_is_neg(mat->row[var->index][off + j]), return);
1073 if (isl_tab_kill_col(tab, j))
1074 --j;
1075 }
1076 isl_tab_mark_redundant(tab, var->index);
1077 }
1078
1079 /* Add a constraint to the tableau and allocate a row for it.
1080 * Return the index into the constraint array "con".
1081 */
1082 int isl_tab_allocate_con(struct isl_tab *tab)
1083 {
1084 int r;
1085
1086 isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
1087
1088 r = tab->n_con;
1089 tab->con[r].index = tab->n_row;
1090 tab->con[r].is_row = 1;
1091 tab->con[r].is_nonneg = 0;
1092 tab->con[r].is_zero = 0;
1093 tab->con[r].is_redundant = 0;
1094 tab->con[r].frozen = 0;
1095 tab->row_var[tab->n_row] = ~r;
1096
1097 tab->n_row++;
1098 tab->n_con++;
1099 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
1100
1101 return r;
1102 }
1103
1104 /* Add a variable to the tableau and allocate a column for it.
1105 * Return the index into the variable array "var".
1106 */
1107 int isl_tab_allocate_var(struct isl_tab *tab)
1108 {
1109 int r;
1110 int i;
1111 unsigned off = 2 + tab->M;
1112
1113 isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
1114 isl_assert(tab->mat->ctx, tab->n_var < tab->max_var, return -1);
1115
1116 r = tab->n_var;
1117 tab->var[r].index = tab->n_col;
1118 tab->var[r].is_row = 0;
1119 tab->var[r].is_nonneg = 0;
1120 tab->var[r].is_zero = 0;
1121 tab->var[r].is_redundant = 0;
1122 tab->var[r].frozen = 0;
1123 tab->col_var[tab->n_col] = r;
1124
1125 for (i = 0; i < tab->n_row; ++i)
1126 isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
1127
1128 tab->n_var++;
1129 tab->n_col++;
1130 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]);
1131
1132 return r;
1133 }
1134
1135 /* Add a row to the tableau. The row is given as an affine combination
1136 * of the original variables and needs to be expressed in terms of the
1137 * column variables.
1138 *
1139 * We add each term in turn.
1140 * If r = n/d_r is the current sum and we need to add k x, then
1141 * if x is a column variable, we increase the numerator of
1142 * this column by k d_r
1143 * if x = f/d_x is a row variable, then the new representation of r is
1144 *
1145 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1146 * --- + --- = ------------------- = -------------------
1147 * d_r d_r d_r d_x/g m
1148 *
1149 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1150 */
1151 int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
1152 {
1153 int i;
1154 int r;
1155 isl_int *row;
1156 isl_int a, b;
1157 unsigned off = 2 + tab->M;
1158
1159 r = isl_tab_allocate_con(tab);
1160 if (r < 0)
1161 return -1;
1162
1163 isl_int_init(a);
1164 isl_int_init(b);
1165 row = tab->mat->row[tab->con[r].index];
1166 isl_int_set_si(row[0], 1);
1167 isl_int_set(row[1], line[0]);
1168 isl_seq_clr(row + 2, tab->M + tab->n_col);
1169 for (i = 0; i < tab->n_var; ++i) {
1170 if (tab->var[i].is_zero)
1171 continue;
1172 if (tab->var[i].is_row) {
1173 isl_int_lcm(a,
1174 row[0], tab->mat->row[tab->var[i].index][0]);
1175 isl_int_swap(a, row[0]);
1176 isl_int_divexact(a, row[0], a);
1177 isl_int_divexact(b,
1178 row[0], tab->mat->row[tab->var[i].index][0]);
1179 isl_int_mul(b, b, line[1 + i]);
1180 isl_seq_combine(row + 1, a, row + 1,
1181 b, tab->mat->row[tab->var[i].index] + 1,
1182 1 + tab->M + tab->n_col);
1183 } else
1184 isl_int_addmul(row[off + tab->var[i].index],
1185 line[1 + i], row[0]);
1186 if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
1187 isl_int_submul(row[2], line[1 + i], row[0]);
1188 }
1189 isl_seq_normalize(row, off + tab->n_col);
1190 isl_int_clear(a);
1191 isl_int_clear(b);
1192
1193 if (tab->row_sign)
1194 tab->row_sign[tab->con[r].index] = 0;
1195
1196 return r;
1197 }
1198
1199 static int drop_row(struct isl_tab *tab, int row)
1200 {
1201 isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
1202 if (row != tab->n_row - 1)
1203 swap_rows(tab, row, tab->n_row - 1);
1204 tab->n_row--;
1205 tab->n_con--;
1206 return 0;
1207 }
1208
1209 static int drop_col(struct isl_tab *tab, int col)
1210 {
1211 isl_assert(tab->mat->ctx, tab->col_var[col] == tab->n_var - 1, return -1);
1212 if (col != tab->n_col - 1)
1213 swap_cols(tab, col, tab->n_col - 1);
1214 tab->n_col--;
1215 tab->n_var--;
1216 return 0;
1217 }
1218
1219 /* Add inequality "ineq" and check if it conflicts with the
1220 * previously added constraints or if it is obviously redundant.
1221 */
1222 struct isl_tab *isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
1223 {
1224 int r;
1225 int sgn;
1226
1227 if (!tab)
1228 return NULL;
1229 r = isl_tab_add_row(tab, ineq);
1230 if (r < 0)
1231 goto error;
1232 tab->con[r].is_nonneg = 1;
1233 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1234 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1235 isl_tab_mark_redundant(tab, tab->con[r].index);
1236 return tab;
1237 }
1238
1239 sgn = restore_row(tab, &tab->con[r]);
1240 if (sgn < 0)
1241 return isl_tab_mark_empty(tab);
1242 if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
1243 isl_tab_mark_redundant(tab, tab->con[r].index);
1244 return tab;
1245 error:
1246 isl_tab_free(tab);
1247 return NULL;
1248 }
1249
1250 /* Pivot a non-negative variable down until it reaches the value zero
1251 * and then pivot the variable into a column position.
1252 */
1253 int to_col(struct isl_tab *tab, struct isl_tab_var *var)
1254 {
1255 int i;
1256 int row, col;
1257 unsigned off = 2 + tab->M;
1258
1259 if (!var->is_row)
1260 return;
1261
1262 while (isl_int_is_pos(tab->mat->row[var->index][1])) {
1263 find_pivot(tab, var, NULL, -1, &row, &col);
1264 isl_assert(tab->mat->ctx, row != -1, return -1);
1265 isl_tab_pivot(tab, row, col);
1266 if (!var->is_row)
1267 return;
1268 }
1269
1270 for (i = tab->n_dead; i < tab->n_col; ++i)
1271 if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
1272 break;
1273
1274 isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
1275 isl_tab_pivot(tab, var->index, i);
1276
1277 return 0;
1278 }
1279
1280 /* We assume Gaussian elimination has been performed on the equalities.
1281 * The equalities can therefore never conflict.
1282 * Adding the equalities is currently only really useful for a later call
1283 * to isl_tab_ineq_type.
1284 */
1285 static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
1286 {
1287 int i;
1288 int r;
1289
1290 if (!tab)
1291 return NULL;
1292 r = isl_tab_add_row(tab, eq);
1293 if (r < 0)
1294 goto error;
1295
1296 r = tab->con[r].index;
1297 i = isl_seq_first_non_zero(tab->mat->row[r] + 2 + tab->M + tab->n_dead,
1298 tab->n_col - tab->n_dead);
1299 isl_assert(tab->mat->ctx, i >= 0, goto error);
1300 i += tab->n_dead;
1301 isl_tab_pivot(tab, r, i);
1302 isl_tab_kill_col(tab, i);
1303 tab->n_eq++;
1304
1305 return tab;
1306 error:
1307 isl_tab_free(tab);
1308 return NULL;
1309 }
1310
1311 /* Add an equality that is known to be valid for the given tableau.
1312 */
1313 struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
1314 {
1315 struct isl_tab_var *var;
1316 int i;
1317 int r;
1318
1319 if (!tab)
1320 return NULL;
1321 r = isl_tab_add_row(tab, eq);
1322 if (r < 0)
1323 goto error;
1324
1325 var = &tab->con[r];
1326 r = var->index;
1327 if (isl_int_is_neg(tab->mat->row[r][1]))
1328 isl_seq_neg(tab->mat->row[r] + 1, tab->mat->row[r] + 1,
1329 1 + tab->n_col);
1330 var->is_nonneg = 1;
1331 if (to_col(tab, var) < 0)
1332 goto error;
1333 var->is_nonneg = 0;
1334 isl_tab_kill_col(tab, var->index);
1335
1336 return tab;
1337 error:
1338 isl_tab_free(tab);
1339 return NULL;
1340 }
1341
1342 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap)
1343 {
1344 int i;
1345 struct isl_tab *tab;
1346
1347 if (!bmap)
1348 return NULL;
1349 tab = isl_tab_alloc(bmap->ctx,
1350 isl_basic_map_total_dim(bmap) + bmap->n_ineq + 1,
1351 isl_basic_map_total_dim(bmap), 0);
1352 if (!tab)
1353 return NULL;
1354 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
1355 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1356 return isl_tab_mark_empty(tab);
1357 for (i = 0; i < bmap->n_eq; ++i) {
1358 tab = add_eq(tab, bmap->eq[i]);
1359 if (!tab)
1360 return tab;
1361 }
1362 for (i = 0; i < bmap->n_ineq; ++i) {
1363 tab = isl_tab_add_ineq(tab, bmap->ineq[i]);
1364 if (!tab || tab->empty)
1365 return tab;
1366 }
1367 return tab;
1368 }
1369
1370 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset)
1371 {
1372 return isl_tab_from_basic_map((struct isl_basic_map *)bset);
1373 }
1374
1375 /* Construct a tableau corresponding to the recession cone of "bmap".
1376 */
1377 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_map *bmap)
1378 {
1379 isl_int cst;
1380 int i;
1381 struct isl_tab *tab;
1382
1383 if (!bmap)
1384 return NULL;
1385 tab = isl_tab_alloc(bmap->ctx, bmap->n_eq + bmap->n_ineq,
1386 isl_basic_map_total_dim(bmap), 0);
1387 if (!tab)
1388 return NULL;
1389 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
1390
1391 isl_int_init(cst);
1392 for (i = 0; i < bmap->n_eq; ++i) {
1393 isl_int_swap(bmap->eq[i][0], cst);
1394 tab = add_eq(tab, bmap->eq[i]);
1395 isl_int_swap(bmap->eq[i][0], cst);
1396 if (!tab)
1397 goto done;
1398 }
1399 for (i = 0; i < bmap->n_ineq; ++i) {
1400 int r;
1401 isl_int_swap(bmap->ineq[i][0], cst);
1402 r = isl_tab_add_row(tab, bmap->ineq[i]);
1403 isl_int_swap(bmap->ineq[i][0], cst);
1404 if (r < 0)
1405 goto error;
1406 tab->con[r].is_nonneg = 1;
1407 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1408 }
1409 done:
1410 isl_int_clear(cst);
1411 return tab;
1412 error:
1413 isl_int_clear(cst);
1414 isl_tab_free(tab);
1415 return NULL;
1416 }
1417
1418 /* Assuming "tab" is the tableau of a cone, check if the cone is
1419 * bounded, i.e., if it is empty or only contains the origin.
1420 */
1421 int isl_tab_cone_is_bounded(struct isl_tab *tab)
1422 {
1423 int i;
1424
1425 if (!tab)
1426 return -1;
1427 if (tab->empty)
1428 return 1;
1429 if (tab->n_dead == tab->n_col)
1430 return 1;
1431
1432 for (;;) {
1433 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1434 struct isl_tab_var *var;
1435 var = isl_tab_var_from_row(tab, i);
1436 if (!var->is_nonneg)
1437 continue;
1438 if (sign_of_max(tab, var) != 0)
1439 return 0;
1440 close_row(tab, var);
1441 break;
1442 }
1443 if (tab->n_dead == tab->n_col)
1444 return 1;
1445 if (i == tab->n_row)
1446 return 0;
1447 }
1448 }
1449
1450 int isl_tab_sample_is_integer(struct isl_tab *tab)
1451 {
1452 int i;
1453
1454 if (!tab)
1455 return -1;
1456
1457 for (i = 0; i < tab->n_var; ++i) {
1458 int row;
1459 if (!tab->var[i].is_row)
1460 continue;
1461 row = tab->var[i].index;
1462 if (!isl_int_is_divisible_by(tab->mat->row[row][1],
1463 tab->mat->row[row][0]))
1464 return 0;
1465 }
1466 return 1;
1467 }
1468
1469 static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
1470 {
1471 int i;
1472 struct isl_vec *vec;
1473
1474 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
1475 if (!vec)
1476 return NULL;
1477
1478 isl_int_set_si(vec->block.data[0], 1);
1479 for (i = 0; i < tab->n_var; ++i) {
1480 if (!tab->var[i].is_row)
1481 isl_int_set_si(vec->block.data[1 + i], 0);
1482 else {
1483 int row = tab->var[i].index;
1484 isl_int_divexact(vec->block.data[1 + i],
1485 tab->mat->row[row][1], tab->mat->row[row][0]);
1486 }
1487 }
1488
1489 return vec;
1490 }
1491
1492 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
1493 {
1494 int i;
1495 struct isl_vec *vec;
1496 isl_int m;
1497
1498 if (!tab)
1499 return NULL;
1500
1501 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
1502 if (!vec)
1503 return NULL;
1504
1505 isl_int_init(m);
1506
1507 isl_int_set_si(vec->block.data[0], 1);
1508 for (i = 0; i < tab->n_var; ++i) {
1509 int row;
1510 if (!tab->var[i].is_row) {
1511 isl_int_set_si(vec->block.data[1 + i], 0);
1512 continue;
1513 }
1514 row = tab->var[i].index;
1515 isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
1516 isl_int_divexact(m, tab->mat->row[row][0], m);
1517 isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
1518 isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
1519 isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
1520 }
1521 isl_seq_normalize(vec->block.data, vec->size);
1522
1523 isl_int_clear(m);
1524 return vec;
1525 }
1526
1527 /* Update "bmap" based on the results of the tableau "tab".
1528 * In particular, implicit equalities are made explicit, redundant constraints
1529 * are removed and if the sample value happens to be integer, it is stored
1530 * in "bmap" (unless "bmap" already had an integer sample).
1531 *
1532 * The tableau is assumed to have been created from "bmap" using
1533 * isl_tab_from_basic_map.
1534 */
1535 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
1536 struct isl_tab *tab)
1537 {
1538 int i;
1539 unsigned n_eq;
1540
1541 if (!bmap)
1542 return NULL;
1543 if (!tab)
1544 return bmap;
1545
1546 n_eq = tab->n_eq;
1547 if (tab->empty)
1548 bmap = isl_basic_map_set_to_empty(bmap);
1549 else
1550 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1551 if (isl_tab_is_equality(tab, n_eq + i))
1552 isl_basic_map_inequality_to_equality(bmap, i);
1553 else if (isl_tab_is_redundant(tab, n_eq + i))
1554 isl_basic_map_drop_inequality(bmap, i);
1555 }
1556 if (!tab->rational &&
1557 !bmap->sample && isl_tab_sample_is_integer(tab))
1558 bmap->sample = extract_integer_sample(tab);
1559 return bmap;
1560 }
1561
1562 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
1563 struct isl_tab *tab)
1564 {
1565 return (struct isl_basic_set *)isl_basic_map_update_from_tab(
1566 (struct isl_basic_map *)bset, tab);
1567 }
1568
1569 /* Given a non-negative variable "var", add a new non-negative variable
1570 * that is the opposite of "var", ensuring that var can only attain the
1571 * value zero.
1572 * If var = n/d is a row variable, then the new variable = -n/d.
1573 * If var is a column variables, then the new variable = -var.
1574 * If the new variable cannot attain non-negative values, then
1575 * the resulting tableau is empty.
1576 * Otherwise, we know the value will be zero and we close the row.
1577 */
1578 static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab,
1579 struct isl_tab_var *var)
1580 {
1581 unsigned r;
1582 isl_int *row;
1583 int sgn;
1584 unsigned off = 2 + tab->M;
1585
1586 if (isl_tab_extend_cons(tab, 1) < 0)
1587 goto error;
1588
1589 r = tab->n_con;
1590 tab->con[r].index = tab->n_row;
1591 tab->con[r].is_row = 1;
1592 tab->con[r].is_nonneg = 0;
1593 tab->con[r].is_zero = 0;
1594 tab->con[r].is_redundant = 0;
1595 tab->con[r].frozen = 0;
1596 tab->row_var[tab->n_row] = ~r;
1597 row = tab->mat->row[tab->n_row];
1598
1599 if (var->is_row) {
1600 isl_int_set(row[0], tab->mat->row[var->index][0]);
1601 isl_seq_neg(row + 1,
1602 tab->mat->row[var->index] + 1, 1 + tab->n_col);
1603 } else {
1604 isl_int_set_si(row[0], 1);
1605 isl_seq_clr(row + 1, 1 + tab->n_col);
1606 isl_int_set_si(row[off + var->index], -1);
1607 }
1608
1609 tab->n_row++;
1610 tab->n_con++;
1611 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
1612
1613 sgn = sign_of_max(tab, &tab->con[r]);
1614 if (sgn < 0)
1615 return isl_tab_mark_empty(tab);
1616 tab->con[r].is_nonneg = 1;
1617 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1618 /* sgn == 0 */
1619 close_row(tab, &tab->con[r]);
1620
1621 return tab;
1622 error:
1623 isl_tab_free(tab);
1624 return NULL;
1625 }
1626
1627 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
1628 * relax the inequality by one. That is, the inequality r >= 0 is replaced
1629 * by r' = r + 1 >= 0.
1630 * If r is a row variable, we simply increase the constant term by one
1631 * (taking into account the denominator).
1632 * If r is a column variable, then we need to modify each row that
1633 * refers to r = r' - 1 by substituting this equality, effectively
1634 * subtracting the coefficient of the column from the constant.
1635 */
1636 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
1637 {
1638 struct isl_tab_var *var;
1639 unsigned off = 2 + tab->M;
1640
1641 if (!tab)
1642 return NULL;
1643
1644 var = &tab->con[con];
1645
1646 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
1647 to_row(tab, var, 1);
1648
1649 if (var->is_row)
1650 isl_int_add(tab->mat->row[var->index][1],
1651 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
1652 else {
1653 int i;
1654
1655 for (i = 0; i < tab->n_row; ++i) {
1656 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
1657 continue;
1658 isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
1659 tab->mat->row[i][off + var->index]);
1660 }
1661
1662 }
1663
1664 isl_tab_push_var(tab, isl_tab_undo_relax, var);
1665
1666 return tab;
1667 }
1668
1669 struct isl_tab *isl_tab_select_facet(struct isl_tab *tab, int con)
1670 {
1671 if (!tab)
1672 return NULL;
1673
1674 return cut_to_hyperplane(tab, &tab->con[con]);
1675 }
1676
1677 static int may_be_equality(struct isl_tab *tab, int row)
1678 {
1679 unsigned off = 2 + tab->M;
1680 return (tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
1681 : isl_int_lt(tab->mat->row[row][1],
1682 tab->mat->row[row][0])) &&
1683 isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1684 tab->n_col - tab->n_dead) != -1;
1685 }
1686
1687 /* Check for (near) equalities among the constraints.
1688 * A constraint is an equality if it is non-negative and if
1689 * its maximal value is either
1690 * - zero (in case of rational tableaus), or
1691 * - strictly less than 1 (in case of integer tableaus)
1692 *
1693 * We first mark all non-redundant and non-dead variables that
1694 * are not frozen and not obviously not an equality.
1695 * Then we iterate over all marked variables if they can attain
1696 * any values larger than zero or at least one.
1697 * If the maximal value is zero, we mark any column variables
1698 * that appear in the row as being zero and mark the row as being redundant.
1699 * Otherwise, if the maximal value is strictly less than one (and the
1700 * tableau is integer), then we restrict the value to being zero
1701 * by adding an opposite non-negative variable.
1702 */
1703 struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab)
1704 {
1705 int i;
1706 unsigned n_marked;
1707
1708 if (!tab)
1709 return NULL;
1710 if (tab->empty)
1711 return tab;
1712 if (tab->n_dead == tab->n_col)
1713 return tab;
1714
1715 n_marked = 0;
1716 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1717 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
1718 var->marked = !var->frozen && var->is_nonneg &&
1719 may_be_equality(tab, i);
1720 if (var->marked)
1721 n_marked++;
1722 }
1723 for (i = tab->n_dead; i < tab->n_col; ++i) {
1724 struct isl_tab_var *var = var_from_col(tab, i);
1725 var->marked = !var->frozen && var->is_nonneg;
1726 if (var->marked)
1727 n_marked++;
1728 }
1729 while (n_marked) {
1730 struct isl_tab_var *var;
1731 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1732 var = isl_tab_var_from_row(tab, i);
1733 if (var->marked)
1734 break;
1735 }
1736 if (i == tab->n_row) {
1737 for (i = tab->n_dead; i < tab->n_col; ++i) {
1738 var = var_from_col(tab, i);
1739 if (var->marked)
1740 break;
1741 }
1742 if (i == tab->n_col)
1743 break;
1744 }
1745 var->marked = 0;
1746 n_marked--;
1747 if (sign_of_max(tab, var) == 0)
1748 close_row(tab, var);
1749 else if (!tab->rational && !at_least_one(tab, var)) {
1750 tab = cut_to_hyperplane(tab, var);
1751 return isl_tab_detect_equalities(tab);
1752 }
1753 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1754 var = isl_tab_var_from_row(tab, i);
1755 if (!var->marked)
1756 continue;
1757 if (may_be_equality(tab, i))
1758 continue;
1759 var->marked = 0;
1760 n_marked--;
1761 }
1762 }
1763
1764 return tab;
1765 }
1766
1767 /* Check for (near) redundant constraints.
1768 * A constraint is redundant if it is non-negative and if
1769 * its minimal value (temporarily ignoring the non-negativity) is either
1770 * - zero (in case of rational tableaus), or
1771 * - strictly larger than -1 (in case of integer tableaus)
1772 *
1773 * We first mark all non-redundant and non-dead variables that
1774 * are not frozen and not obviously negatively unbounded.
1775 * Then we iterate over all marked variables if they can attain
1776 * any values smaller than zero or at most negative one.
1777 * If not, we mark the row as being redundant (assuming it hasn't
1778 * been detected as being obviously redundant in the mean time).
1779 */
1780 struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab)
1781 {
1782 int i;
1783 unsigned n_marked;
1784
1785 if (!tab)
1786 return NULL;
1787 if (tab->empty)
1788 return tab;
1789 if (tab->n_redundant == tab->n_row)
1790 return tab;
1791
1792 n_marked = 0;
1793 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1794 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
1795 var->marked = !var->frozen && var->is_nonneg;
1796 if (var->marked)
1797 n_marked++;
1798 }
1799 for (i = tab->n_dead; i < tab->n_col; ++i) {
1800 struct isl_tab_var *var = var_from_col(tab, i);
1801 var->marked = !var->frozen && var->is_nonneg &&
1802 !min_is_manifestly_unbounded(tab, var);
1803 if (var->marked)
1804 n_marked++;
1805 }
1806 while (n_marked) {
1807 struct isl_tab_var *var;
1808 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1809 var = isl_tab_var_from_row(tab, i);
1810 if (var->marked)
1811 break;
1812 }
1813 if (i == tab->n_row) {
1814 for (i = tab->n_dead; i < tab->n_col; ++i) {
1815 var = var_from_col(tab, i);
1816 if (var->marked)
1817 break;
1818 }
1819 if (i == tab->n_col)
1820 break;
1821 }
1822 var->marked = 0;
1823 n_marked--;
1824 if ((tab->rational ? (sign_of_min(tab, var) >= 0)
1825 : !isl_tab_min_at_most_neg_one(tab, var)) &&
1826 !var->is_redundant)
1827 isl_tab_mark_redundant(tab, var->index);
1828 for (i = tab->n_dead; i < tab->n_col; ++i) {
1829 var = var_from_col(tab, i);
1830 if (!var->marked)
1831 continue;
1832 if (!min_is_manifestly_unbounded(tab, var))
1833 continue;
1834 var->marked = 0;
1835 n_marked--;
1836 }
1837 }
1838
1839 return tab;
1840 }
1841
1842 int isl_tab_is_equality(struct isl_tab *tab, int con)
1843 {
1844 int row;
1845 unsigned off;
1846
1847 if (!tab)
1848 return -1;
1849 if (tab->con[con].is_zero)
1850 return 1;
1851 if (tab->con[con].is_redundant)
1852 return 0;
1853 if (!tab->con[con].is_row)
1854 return tab->con[con].index < tab->n_dead;
1855
1856 row = tab->con[con].index;
1857
1858 off = 2 + tab->M;
1859 return isl_int_is_zero(tab->mat->row[row][1]) &&
1860 isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
1861 tab->n_col - tab->n_dead) == -1;
1862 }
1863
1864 /* Return the minimial value of the affine expression "f" with denominator
1865 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
1866 * the expression cannot attain arbitrarily small values.
1867 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
1868 * The return value reflects the nature of the result (empty, unbounded,
1869 * minmimal value returned in *opt).
1870 */
1871 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
1872 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
1873 unsigned flags)
1874 {
1875 int r;
1876 enum isl_lp_result res = isl_lp_ok;
1877 struct isl_tab_var *var;
1878 struct isl_tab_undo *snap;
1879
1880 if (tab->empty)
1881 return isl_lp_empty;
1882
1883 snap = isl_tab_snap(tab);
1884 r = isl_tab_add_row(tab, f);
1885 if (r < 0)
1886 return isl_lp_error;
1887 var = &tab->con[r];
1888 isl_int_mul(tab->mat->row[var->index][0],
1889 tab->mat->row[var->index][0], denom);
1890 for (;;) {
1891 int row, col;
1892 find_pivot(tab, var, var, -1, &row, &col);
1893 if (row == var->index) {
1894 res = isl_lp_unbounded;
1895 break;
1896 }
1897 if (row == -1)
1898 break;
1899 isl_tab_pivot(tab, row, col);
1900 }
1901 if (isl_tab_rollback(tab, snap) < 0)
1902 return isl_lp_error;
1903 if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
1904 int i;
1905
1906 isl_vec_free(tab->dual);
1907 tab->dual = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_con);
1908 if (!tab->dual)
1909 return isl_lp_error;
1910 isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
1911 for (i = 0; i < tab->n_con; ++i) {
1912 if (tab->con[i].is_row)
1913 isl_int_set_si(tab->dual->el[1 + i], 0);
1914 else {
1915 int pos = 2 + tab->con[i].index;
1916 isl_int_set(tab->dual->el[1 + i],
1917 tab->mat->row[var->index][pos]);
1918 }
1919 }
1920 }
1921 if (res == isl_lp_ok) {
1922 if (opt_denom) {
1923 isl_int_set(*opt, tab->mat->row[var->index][1]);
1924 isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
1925 } else
1926 isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
1927 tab->mat->row[var->index][0]);
1928 }
1929 return res;
1930 }
1931
1932 int isl_tab_is_redundant(struct isl_tab *tab, int con)
1933 {
1934 int row;
1935 unsigned n_col;
1936
1937 if (!tab)
1938 return -1;
1939 if (tab->con[con].is_zero)
1940 return 0;
1941 if (tab->con[con].is_redundant)
1942 return 1;
1943 return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
1944 }
1945
1946 /* Take a snapshot of the tableau that can be restored by s call to
1947 * isl_tab_rollback.
1948 */
1949 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
1950 {
1951 if (!tab)
1952 return NULL;
1953 tab->need_undo = 1;
1954 return tab->top;
1955 }
1956
1957 /* Undo the operation performed by isl_tab_relax.
1958 */
1959 static void unrelax(struct isl_tab *tab, struct isl_tab_var *var)
1960 {
1961 unsigned off = 2 + tab->M;
1962
1963 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
1964 to_row(tab, var, 1);
1965
1966 if (var->is_row)
1967 isl_int_sub(tab->mat->row[var->index][1],
1968 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
1969 else {
1970 int i;
1971
1972 for (i = 0; i < tab->n_row; ++i) {
1973 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
1974 continue;
1975 isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
1976 tab->mat->row[i][off + var->index]);
1977 }
1978
1979 }
1980 }
1981
1982 static void perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
1983 {
1984 struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
1985 switch(undo->type) {
1986 case isl_tab_undo_nonneg:
1987 var->is_nonneg = 0;
1988 break;
1989 case isl_tab_undo_redundant:
1990 var->is_redundant = 0;
1991 tab->n_redundant--;
1992 break;
1993 case isl_tab_undo_zero:
1994 var->is_zero = 0;
1995 tab->n_dead--;
1996 break;
1997 case isl_tab_undo_allocate:
1998 if (undo->u.var_index >= 0) {
1999 isl_assert(tab->mat->ctx, !var->is_row, return);
2000 drop_col(tab, var->index);
2001 break;
2002 }
2003 if (!var->is_row) {
2004 if (!max_is_manifestly_unbounded(tab, var))
2005 to_row(tab, var, 1);
2006 else if (!min_is_manifestly_unbounded(tab, var))
2007 to_row(tab, var, -1);
2008 else
2009 to_row(tab, var, 0);
2010 }
2011 drop_row(tab, var->index);
2012 break;
2013 case isl_tab_undo_relax:
2014 unrelax(tab, var);
2015 break;
2016 }
2017 }
2018
2019 /* Restore the tableau to the state where the basic variables
2020 * are those in "col_var".
2021 * We first construct a list of variables that are currently in
2022 * the basis, but shouldn't. Then we iterate over all variables
2023 * that should be in the basis and for each one that is currently
2024 * not in the basis, we exchange it with one of the elements of the
2025 * list constructed before.
2026 * We can always find an appropriate variable to pivot with because
2027 * the current basis is mapped to the old basis by a non-singular
2028 * matrix and so we can never end up with a zero row.
2029 */
2030 static int restore_basis(struct isl_tab *tab, int *col_var)
2031 {
2032 int i, j;
2033 int n_extra = 0;
2034 int *extra = NULL; /* current columns that contain bad stuff */
2035 unsigned off = 2 + tab->M;
2036
2037 extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
2038 if (!extra)
2039 goto error;
2040 for (i = 0; i < tab->n_col; ++i) {
2041 for (j = 0; j < tab->n_col; ++j)
2042 if (tab->col_var[i] == col_var[j])
2043 break;
2044 if (j < tab->n_col)
2045 continue;
2046 extra[n_extra++] = i;
2047 }
2048 for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
2049 struct isl_tab_var *var;
2050 int row;
2051
2052 for (j = 0; j < tab->n_col; ++j)
2053 if (col_var[i] == tab->col_var[j])
2054 break;
2055 if (j < tab->n_col)
2056 continue;
2057 var = var_from_index(tab, col_var[i]);
2058 row = var->index;
2059 for (j = 0; j < n_extra; ++j)
2060 if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
2061 break;
2062 isl_assert(tab->mat->ctx, j < n_extra, goto error);
2063 isl_tab_pivot(tab, row, extra[j]);
2064 extra[j] = extra[--n_extra];
2065 }
2066
2067 free(extra);
2068 free(col_var);
2069 return 0;
2070 error:
2071 free(extra);
2072 free(col_var);
2073 return -1;
2074 }
2075
2076 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
2077 {
2078 switch (undo->type) {
2079 case isl_tab_undo_empty:
2080 tab->empty = 0;
2081 break;
2082 case isl_tab_undo_nonneg:
2083 case isl_tab_undo_redundant:
2084 case isl_tab_undo_zero:
2085 case isl_tab_undo_allocate:
2086 case isl_tab_undo_relax:
2087 perform_undo_var(tab, undo);
2088 break;
2089 case isl_tab_undo_bset_eq:
2090 isl_basic_set_free_equality(tab->bset, 1);
2091 break;
2092 case isl_tab_undo_bset_ineq:
2093 isl_basic_set_free_inequality(tab->bset, 1);
2094 break;
2095 case isl_tab_undo_bset_div:
2096 isl_basic_set_free_div(tab->bset, 1);
2097 break;
2098 case isl_tab_undo_saved_basis:
2099 if (restore_basis(tab, undo->u.col_var) < 0)
2100 return -1;
2101 break;
2102 default:
2103 isl_assert(tab->mat->ctx, 0, return -1);
2104 }
2105 return 0;
2106 }
2107
2108 /* Return the tableau to the state it was in when the snapshot "snap"
2109 * was taken.
2110 */
2111 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
2112 {
2113 struct isl_tab_undo *undo, *next;
2114
2115 if (!tab)
2116 return -1;
2117
2118 tab->in_undo = 1;
2119 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
2120 next = undo->next;
2121 if (undo == snap)
2122 break;
2123 if (perform_undo(tab, undo) < 0) {
2124 free_undo(tab);
2125 tab->in_undo = 0;
2126 return -1;
2127 }
2128 free(undo);
2129 }
2130 tab->in_undo = 0;
2131 tab->top = undo;
2132 if (!undo)
2133 return -1;
2134 return 0;
2135 }
2136
2137 /* The given row "row" represents an inequality violated by all
2138 * points in the tableau. Check for some special cases of such
2139 * separating constraints.
2140 * In particular, if the row has been reduced to the constant -1,
2141 * then we know the inequality is adjacent (but opposite) to
2142 * an equality in the tableau.
2143 * If the row has been reduced to r = -1 -r', with r' an inequality
2144 * of the tableau, then the inequality is adjacent (but opposite)
2145 * to the inequality r'.
2146 */
2147 static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
2148 {
2149 int pos;
2150 unsigned off = 2 + tab->M;
2151
2152 if (tab->rational)
2153 return isl_ineq_separate;
2154
2155 if (!isl_int_is_one(tab->mat->row[row][0]))
2156 return isl_ineq_separate;
2157 if (!isl_int_is_negone(tab->mat->row[row][1]))
2158 return isl_ineq_separate;
2159
2160 pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
2161 tab->n_col - tab->n_dead);
2162 if (pos == -1)
2163 return isl_ineq_adj_eq;
2164
2165 if (!isl_int_is_negone(tab->mat->row[row][off + tab->n_dead + pos]))
2166 return isl_ineq_separate;
2167
2168 pos = isl_seq_first_non_zero(
2169 tab->mat->row[row] + off + tab->n_dead + pos + 1,
2170 tab->n_col - tab->n_dead - pos - 1);
2171
2172 return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
2173 }
2174
2175 /* Check the effect of inequality "ineq" on the tableau "tab".
2176 * The result may be
2177 * isl_ineq_redundant: satisfied by all points in the tableau
2178 * isl_ineq_separate: satisfied by no point in the tableau
2179 * isl_ineq_cut: satisfied by some by not all points
2180 * isl_ineq_adj_eq: adjacent to an equality
2181 * isl_ineq_adj_ineq: adjacent to an inequality.
2182 */
2183 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
2184 {
2185 enum isl_ineq_type type = isl_ineq_error;
2186 struct isl_tab_undo *snap = NULL;
2187 int con;
2188 int row;
2189
2190 if (!tab)
2191 return isl_ineq_error;
2192
2193 if (isl_tab_extend_cons(tab, 1) < 0)
2194 return isl_ineq_error;
2195
2196 snap = isl_tab_snap(tab);
2197
2198 con = isl_tab_add_row(tab, ineq);
2199 if (con < 0)
2200 goto error;
2201
2202 row = tab->con[con].index;
2203 if (isl_tab_row_is_redundant(tab, row))
2204 type = isl_ineq_redundant;
2205 else if (isl_int_is_neg(tab->mat->row[row][1]) &&
2206 (tab->rational ||
2207 isl_int_abs_ge(tab->mat->row[row][1],
2208 tab->mat->row[row][0]))) {
2209 if (at_least_zero(tab, &tab->con[con]))
2210 type = isl_ineq_cut;
2211 else
2212 type = separation_type(tab, row);
2213 } else if (tab->rational ? (sign_of_min(tab, &tab->con[con]) < 0)
2214 : isl_tab_min_at_most_neg_one(tab, &tab->con[con]))
2215 type = isl_ineq_cut;
2216 else
2217 type = isl_ineq_redundant;
2218
2219 if (isl_tab_rollback(tab, snap))
2220 return isl_ineq_error;
2221 return type;
2222 error:
2223 isl_tab_rollback(tab, snap);
2224 return isl_ineq_error;
2225 }
2226
2227 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent)
2228 {
2229 unsigned r, c;
2230 int i;
2231
2232 if (!tab) {
2233 fprintf(out, "%*snull tab\n", indent, "");
2234 return;
2235 }
2236 fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
2237 tab->n_redundant, tab->n_dead);
2238 if (tab->rational)
2239 fprintf(out, ", rational");
2240 if (tab->empty)
2241 fprintf(out, ", empty");
2242 fprintf(out, "\n");
2243 fprintf(out, "%*s[", indent, "");
2244 for (i = 0; i < tab->n_var; ++i) {
2245 if (i)
2246 fprintf(out, (i == tab->n_param ||
2247 i == tab->n_var - tab->n_div) ? "; "
2248 : ", ");
2249 fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
2250 tab->var[i].index,
2251 tab->var[i].is_zero ? " [=0]" :
2252 tab->var[i].is_redundant ? " [R]" : "");
2253 }
2254 fprintf(out, "]\n");
2255 fprintf(out, "%*s[", indent, "");
2256 for (i = 0; i < tab->n_con; ++i) {
2257 if (i)
2258 fprintf(out, ", ");
2259 fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
2260 tab->con[i].index,
2261 tab->con[i].is_zero ? " [=0]" :
2262 tab->con[i].is_redundant ? " [R]" : "");
2263 }
2264 fprintf(out, "]\n");
2265 fprintf(out, "%*s[", indent, "");
2266 for (i = 0; i < tab->n_row; ++i) {
2267 const char *sign = "";
2268 if (i)
2269 fprintf(out, ", ");
2270 if (tab->row_sign) {
2271 if (tab->row_sign[i] == isl_tab_row_unknown)
2272 sign = "?";
2273 else if (tab->row_sign[i] == isl_tab_row_neg)
2274 sign = "-";
2275 else if (tab->row_sign[i] == isl_tab_row_pos)
2276 sign = "+";
2277 else
2278 sign = "+-";
2279 }
2280 fprintf(out, "r%d: %d%s%s", i, tab->row_var[i],
2281 isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
2282 }
2283 fprintf(out, "]\n");
2284 fprintf(out, "%*s[", indent, "");
2285 for (i = 0; i < tab->n_col; ++i) {
2286 if (i)
2287 fprintf(out, ", ");
2288 fprintf(out, "c%d: %d%s", i, tab->col_var[i],
2289 var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
2290 }
2291 fprintf(out, "]\n");
2292 r = tab->mat->n_row;
2293 tab->mat->n_row = tab->n_row;
2294 c = tab->mat->n_col;
2295 tab->mat->n_col = 2 + tab->M + tab->n_col;
2296 isl_mat_dump(tab->mat, out, indent);
2297 tab->mat->n_row = r;
2298 tab->mat->n_col = c;
2299 if (tab->bset)
2300 isl_basic_set_dump(tab->bset, out, indent);
2301 }
Integer set library