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export isl_set_sample
[isl.git] / isl_tab.c
blob258a7c16081b557ddebe11fb0875706897534b8c
1 #include "isl_mat.h"
2 #include "isl_map_private.h"
3 #include "isl_tab.h"
4 #include "isl_seq.h"
5
6 /*
7 * The implementation of tableaus in this file was inspired by Section 8
8 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
9 * prover for program checking".
10 */
11
12 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
13 unsigned n_row, unsigned n_var, unsigned M)
14 {
15 int i;
16 struct isl_tab *tab;
17 unsigned off = 2 + M;
18
19 tab = isl_calloc_type(ctx, struct isl_tab);
20 if (!tab)
21 return NULL;
22 tab->mat = isl_mat_alloc(ctx, n_row, off + n_var);
23 if (!tab->mat)
24 goto error;
25 tab->var = isl_alloc_array(ctx, struct isl_tab_var, n_var);
26 if (!tab->var)
27 goto error;
28 tab->con = isl_alloc_array(ctx, struct isl_tab_var, n_row);
29 if (!tab->con)
30 goto error;
31 tab->col_var = isl_alloc_array(ctx, int, n_var);
32 if (!tab->col_var)
33 goto error;
34 tab->row_var = isl_alloc_array(ctx, int, n_row);
35 if (!tab->row_var)
36 goto error;
37 for (i = 0; i < n_var; ++i) {
38 tab->var[i].index = i;
39 tab->var[i].is_row = 0;
40 tab->var[i].is_nonneg = 0;
41 tab->var[i].is_zero = 0;
42 tab->var[i].is_redundant = 0;
43 tab->var[i].frozen = 0;
44 tab->var[i].negated = 0;
45 tab->col_var[i] = i;
46 }
47 tab->n_row = 0;
48 tab->n_con = 0;
49 tab->n_eq = 0;
50 tab->max_con = n_row;
51 tab->n_col = n_var;
52 tab->n_var = n_var;
53 tab->max_var = n_var;
54 tab->n_param = 0;
55 tab->n_div = 0;
56 tab->n_dead = 0;
57 tab->n_redundant = 0;
58 tab->need_undo = 0;
59 tab->rational = 0;
60 tab->empty = 0;
61 tab->in_undo = 0;
62 tab->M = M;
63 tab->bottom.type = isl_tab_undo_bottom;
64 tab->bottom.next = NULL;
65 tab->top = &tab->bottom;
66 return tab;
67 error:
68 isl_tab_free(tab);
69 return NULL;
70 }
71
72 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new)
73 {
74 unsigned off = 2 + tab->M;
75 if (tab->max_con < tab->n_con + n_new) {
76 struct isl_tab_var *con;
77
78 con = isl_realloc_array(tab->mat->ctx, tab->con,
79 struct isl_tab_var, tab->max_con + n_new);
80 if (!con)
81 return -1;
82 tab->con = con;
83 tab->max_con += n_new;
84 }
85 if (tab->mat->n_row < tab->n_row + n_new) {
86 int *row_var;
87
88 tab->mat = isl_mat_extend(tab->mat,
89 tab->n_row + n_new, off + tab->n_col);
90 if (!tab->mat)
91 return -1;
92 row_var = isl_realloc_array(tab->mat->ctx, tab->row_var,
93 int, tab->mat->n_row);
94 if (!row_var)
95 return -1;
96 tab->row_var = row_var;
97 if (tab->row_sign) {
98 enum isl_tab_row_sign *s;
99 s = isl_realloc_array(tab->mat->ctx, tab->row_sign,
100 enum isl_tab_row_sign, tab->mat->n_row);
101 if (!s)
102 return -1;
103 tab->row_sign = s;
104 }
105 }
106 return 0;
107 }
108
109 /* Make room for at least n_new extra variables.
110 * Return -1 if anything went wrong.
111 */
112 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new)
113 {
114 struct isl_tab_var *var;
115 unsigned off = 2 + tab->M;
116
117 if (tab->max_var < tab->n_var + n_new) {
118 var = isl_realloc_array(tab->mat->ctx, tab->var,
119 struct isl_tab_var, tab->n_var + n_new);
120 if (!var)
121 return -1;
122 tab->var = var;
123 tab->max_var += n_new;
124 }
125
126 if (tab->mat->n_col < off + tab->n_col + n_new) {
127 int *p;
128
129 tab->mat = isl_mat_extend(tab->mat,
130 tab->mat->n_row, off + tab->n_col + n_new);
131 if (!tab->mat)
132 return -1;
133 p = isl_realloc_array(tab->mat->ctx, tab->col_var,
134 int, tab->n_col + n_new);
135 if (!p)
136 return -1;
137 tab->col_var = p;
138 }
139
140 return 0;
141 }
142
143 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new)
144 {
145 if (isl_tab_extend_cons(tab, n_new) >= 0)
146 return tab;
147
148 isl_tab_free(tab);
149 return NULL;
150 }
151
152 static void free_undo(struct isl_tab *tab)
153 {
154 struct isl_tab_undo *undo, *next;
155
156 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
157 next = undo->next;
158 free(undo);
159 }
160 tab->top = undo;
161 }
162
163 void isl_tab_free(struct isl_tab *tab)
164 {
165 if (!tab)
166 return;
167 free_undo(tab);
168 isl_mat_free(tab->mat);
169 isl_vec_free(tab->dual);
170 isl_basic_set_free(tab->bset);
171 free(tab->var);
172 free(tab->con);
173 free(tab->row_var);
174 free(tab->col_var);
175 free(tab->row_sign);
176 isl_mat_free(tab->samples);
177 free(tab);
178 }
179
180 struct isl_tab *isl_tab_dup(struct isl_tab *tab)
181 {
182 int i;
183 struct isl_tab *dup;
184 unsigned off;
185
186 if (!tab)
187 return NULL;
188
189 off = 2 + tab->M;
190 dup = isl_calloc_type(tab->ctx, struct isl_tab);
191 if (!dup)
192 return NULL;
193 dup->mat = isl_mat_dup(tab->mat);
194 if (!dup->mat)
195 goto error;
196 dup->var = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_var);
197 if (!dup->var)
198 goto error;
199 for (i = 0; i < tab->n_var; ++i)
200 dup->var[i] = tab->var[i];
201 dup->con = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_con);
202 if (!dup->con)
203 goto error;
204 for (i = 0; i < tab->n_con; ++i)
205 dup->con[i] = tab->con[i];
206 dup->col_var = isl_alloc_array(tab->ctx, int, tab->mat->n_col - off);
207 if (!dup->col_var)
208 goto error;
209 for (i = 0; i < tab->n_col; ++i)
210 dup->col_var[i] = tab->col_var[i];
211 dup->row_var = isl_alloc_array(tab->ctx, int, tab->mat->n_row);
212 if (!dup->row_var)
213 goto error;
214 for (i = 0; i < tab->n_row; ++i)
215 dup->row_var[i] = tab->row_var[i];
216 if (tab->row_sign) {
217 dup->row_sign = isl_alloc_array(tab->ctx, enum isl_tab_row_sign,
218 tab->mat->n_row);
219 if (!dup->row_sign)
220 goto error;
221 for (i = 0; i < tab->n_row; ++i)
222 dup->row_sign[i] = tab->row_sign[i];
223 }
224 if (tab->samples) {
225 dup->samples = isl_mat_dup(tab->samples);
226 if (!dup->samples)
227 goto error;
228 dup->n_sample = tab->n_sample;
229 dup->n_outside = tab->n_outside;
230 }
231 dup->n_row = tab->n_row;
232 dup->n_con = tab->n_con;
233 dup->n_eq = tab->n_eq;
234 dup->max_con = tab->max_con;
235 dup->n_col = tab->n_col;
236 dup->n_var = tab->n_var;
237 dup->max_var = tab->max_var;
238 dup->n_param = tab->n_param;
239 dup->n_div = tab->n_div;
240 dup->n_dead = tab->n_dead;
241 dup->n_redundant = tab->n_redundant;
242 dup->rational = tab->rational;
243 dup->empty = tab->empty;
244 dup->need_undo = 0;
245 dup->in_undo = 0;
246 dup->M = tab->M;
247 dup->bottom.type = isl_tab_undo_bottom;
248 dup->bottom.next = NULL;
249 dup->top = &dup->bottom;
250 return dup;
251 error:
252 isl_tab_free(dup);
253 return NULL;
254 }
255
256 static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i)
257 {
258 if (i >= 0)
259 return &tab->var[i];
260 else
261 return &tab->con[~i];
262 }
263
264 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
265 {
266 return var_from_index(tab, tab->row_var[i]);
267 }
268
269 static struct isl_tab_var *var_from_col(struct isl_tab *tab, int i)
270 {
271 return var_from_index(tab, tab->col_var[i]);
272 }
273
274 /* Check if there are any upper bounds on column variable "var",
275 * i.e., non-negative rows where var appears with a negative coefficient.
276 * Return 1 if there are no such bounds.
277 */
278 static int max_is_manifestly_unbounded(struct isl_tab *tab,
279 struct isl_tab_var *var)
280 {
281 int i;
282 unsigned off = 2 + tab->M;
283
284 if (var->is_row)
285 return 0;
286 for (i = tab->n_redundant; i < tab->n_row; ++i) {
287 if (!isl_int_is_neg(tab->mat->row[i][off + var->index]))
288 continue;
289 if (isl_tab_var_from_row(tab, i)->is_nonneg)
290 return 0;
291 }
292 return 1;
293 }
294
295 /* Check if there are any lower bounds on column variable "var",
296 * i.e., non-negative rows where var appears with a positive coefficient.
297 * Return 1 if there are no such bounds.
298 */
299 static int min_is_manifestly_unbounded(struct isl_tab *tab,
300 struct isl_tab_var *var)
301 {
302 int i;
303 unsigned off = 2 + tab->M;
304
305 if (var->is_row)
306 return 0;
307 for (i = tab->n_redundant; i < tab->n_row; ++i) {
308 if (!isl_int_is_pos(tab->mat->row[i][off + var->index]))
309 continue;
310 if (isl_tab_var_from_row(tab, i)->is_nonneg)
311 return 0;
312 }
313 return 1;
314 }
315
316 static int row_cmp(struct isl_tab *tab, int r1, int r2, int c, isl_int t)
317 {
318 unsigned off = 2 + tab->M;
319
320 if (tab->M) {
321 int s;
322 isl_int_mul(t, tab->mat->row[r1][2], tab->mat->row[r2][off+c]);
323 isl_int_submul(t, tab->mat->row[r2][2], tab->mat->row[r1][off+c]);
324 s = isl_int_sgn(t);
325 if (s)
326 return s;
327 }
328 isl_int_mul(t, tab->mat->row[r1][1], tab->mat->row[r2][off + c]);
329 isl_int_submul(t, tab->mat->row[r2][1], tab->mat->row[r1][off + c]);
330 return isl_int_sgn(t);
331 }
332
333 /* Given the index of a column "c", return the index of a row
334 * that can be used to pivot the column in, with either an increase
335 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
336 * If "var" is not NULL, then the row returned will be different from
337 * the one associated with "var".
338 *
339 * Each row in the tableau is of the form
340 *
341 * x_r = a_r0 + \sum_i a_ri x_i
342 *
343 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
344 * impose any limit on the increase or decrease in the value of x_c
345 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
346 * for the row with the smallest (most stringent) such bound.
347 * Note that the common denominator of each row drops out of the fraction.
348 * To check if row j has a smaller bound than row r, i.e.,
349 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
350 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
351 * where -sign(a_jc) is equal to "sgn".
352 */
353 static int pivot_row(struct isl_tab *tab,
354 struct isl_tab_var *var, int sgn, int c)
355 {
356 int j, r, tsgn;
357 isl_int t;
358 unsigned off = 2 + tab->M;
359
360 isl_int_init(t);
361 r = -1;
362 for (j = tab->n_redundant; j < tab->n_row; ++j) {
363 if (var && j == var->index)
364 continue;
365 if (!isl_tab_var_from_row(tab, j)->is_nonneg)
366 continue;
367 if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
368 continue;
369 if (r < 0) {
370 r = j;
371 continue;
372 }
373 tsgn = sgn * row_cmp(tab, r, j, c, t);
374 if (tsgn < 0 || (tsgn == 0 &&
375 tab->row_var[j] < tab->row_var[r]))
376 r = j;
377 }
378 isl_int_clear(t);
379 return r;
380 }
381
382 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
383 * (sgn < 0) the value of row variable var.
384 * If not NULL, then skip_var is a row variable that should be ignored
385 * while looking for a pivot row. It is usually equal to var.
386 *
387 * As the given row in the tableau is of the form
388 *
389 * x_r = a_r0 + \sum_i a_ri x_i
390 *
391 * we need to find a column such that the sign of a_ri is equal to "sgn"
392 * (such that an increase in x_i will have the desired effect) or a
393 * column with a variable that may attain negative values.
394 * If a_ri is positive, then we need to move x_i in the same direction
395 * to obtain the desired effect. Otherwise, x_i has to move in the
396 * opposite direction.
397 */
398 static void find_pivot(struct isl_tab *tab,
399 struct isl_tab_var *var, struct isl_tab_var *skip_var,
400 int sgn, int *row, int *col)
401 {
402 int j, r, c;
403 isl_int *tr;
404
405 *row = *col = -1;
406
407 isl_assert(tab->mat->ctx, var->is_row, return);
408 tr = tab->mat->row[var->index] + 2 + tab->M;
409
410 c = -1;
411 for (j = tab->n_dead; j < tab->n_col; ++j) {
412 if (isl_int_is_zero(tr[j]))
413 continue;
414 if (isl_int_sgn(tr[j]) != sgn &&
415 var_from_col(tab, j)->is_nonneg)
416 continue;
417 if (c < 0 || tab->col_var[j] < tab->col_var[c])
418 c = j;
419 }
420 if (c < 0)
421 return;
422
423 sgn *= isl_int_sgn(tr[c]);
424 r = pivot_row(tab, skip_var, sgn, c);
425 *row = r < 0 ? var->index : r;
426 *col = c;
427 }
428
429 /* Return 1 if row "row" represents an obviously redundant inequality.
430 * This means
431 * - it represents an inequality or a variable
432 * - that is the sum of a non-negative sample value and a positive
433 * combination of zero or more non-negative variables.
434 */
435 int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
436 {
437 int i;
438 unsigned off = 2 + tab->M;
439
440 if (tab->row_var[row] < 0 && !isl_tab_var_from_row(tab, row)->is_nonneg)
441 return 0;
442
443 if (isl_int_is_neg(tab->mat->row[row][1]))
444 return 0;
445 if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
446 return 0;
447
448 for (i = tab->n_dead; i < tab->n_col; ++i) {
449 if (isl_int_is_zero(tab->mat->row[row][off + i]))
450 continue;
451 if (isl_int_is_neg(tab->mat->row[row][off + i]))
452 return 0;
453 if (!var_from_col(tab, i)->is_nonneg)
454 return 0;
455 }
456 return 1;
457 }
458
459 static void swap_rows(struct isl_tab *tab, int row1, int row2)
460 {
461 int t;
462 t = tab->row_var[row1];
463 tab->row_var[row1] = tab->row_var[row2];
464 tab->row_var[row2] = t;
465 isl_tab_var_from_row(tab, row1)->index = row1;
466 isl_tab_var_from_row(tab, row2)->index = row2;
467 tab->mat = isl_mat_swap_rows(tab->mat, row1, row2);
468
469 if (!tab->row_sign)
470 return;
471 t = tab->row_sign[row1];
472 tab->row_sign[row1] = tab->row_sign[row2];
473 tab->row_sign[row2] = t;
474 }
475
476 static void push_union(struct isl_tab *tab,
477 enum isl_tab_undo_type type, union isl_tab_undo_val u)
478 {
479 struct isl_tab_undo *undo;
480
481 if (!tab->need_undo)
482 return;
483
484 undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
485 if (!undo) {
486 free_undo(tab);
487 tab->top = NULL;
488 return;
489 }
490 undo->type = type;
491 undo->u = u;
492 undo->next = tab->top;
493 tab->top = undo;
494 }
495
496 void isl_tab_push_var(struct isl_tab *tab,
497 enum isl_tab_undo_type type, struct isl_tab_var *var)
498 {
499 union isl_tab_undo_val u;
500 if (var->is_row)
501 u.var_index = tab->row_var[var->index];
502 else
503 u.var_index = tab->col_var[var->index];
504 push_union(tab, type, u);
505 }
506
507 void isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
508 {
509 union isl_tab_undo_val u = { 0 };
510 push_union(tab, type, u);
511 }
512
513 /* Push a record on the undo stack describing the current basic
514 * variables, so that the this state can be restored during rollback.
515 */
516 void isl_tab_push_basis(struct isl_tab *tab)
517 {
518 int i;
519 union isl_tab_undo_val u;
520
521 u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
522 if (!u.col_var) {
523 free_undo(tab);
524 tab->top = NULL;
525 return;
526 }
527 for (i = 0; i < tab->n_col; ++i)
528 u.col_var[i] = tab->col_var[i];
529 push_union(tab, isl_tab_undo_saved_basis, u);
530 }
531
532 /* Mark row with index "row" as being redundant.
533 * If we may need to undo the operation or if the row represents
534 * a variable of the original problem, the row is kept,
535 * but no longer considered when looking for a pivot row.
536 * Otherwise, the row is simply removed.
537 *
538 * The row may be interchanged with some other row. If it
539 * is interchanged with a later row, return 1. Otherwise return 0.
540 * If the rows are checked in order in the calling function,
541 * then a return value of 1 means that the row with the given
542 * row number may now contain a different row that hasn't been checked yet.
543 */
544 int isl_tab_mark_redundant(struct isl_tab *tab, int row)
545 {
546 struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
547 var->is_redundant = 1;
548 isl_assert(tab->mat->ctx, row >= tab->n_redundant, return -1);
549 if (tab->need_undo || tab->row_var[row] >= 0) {
550 if (tab->row_var[row] >= 0 && !var->is_nonneg) {
551 var->is_nonneg = 1;
552 isl_tab_push_var(tab, isl_tab_undo_nonneg, var);
553 }
554 if (row != tab->n_redundant)
555 swap_rows(tab, row, tab->n_redundant);
556 isl_tab_push_var(tab, isl_tab_undo_redundant, var);
557 tab->n_redundant++;
558 return 0;
559 } else {
560 if (row != tab->n_row - 1)
561 swap_rows(tab, row, tab->n_row - 1);
562 isl_tab_var_from_row(tab, tab->n_row - 1)->index = -1;
563 tab->n_row--;
564 return 1;
565 }
566 }
567
568 struct isl_tab *isl_tab_mark_empty(struct isl_tab *tab)
569 {
570 if (!tab->empty && tab->need_undo)
571 isl_tab_push(tab, isl_tab_undo_empty);
572 tab->empty = 1;
573 return tab;
574 }
575
576 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
577 * the original sign of the pivot element.
578 * We only keep track of row signs during PILP solving and in this case
579 * we only pivot a row with negative sign (meaning the value is always
580 * non-positive) using a positive pivot element.
581 *
582 * For each row j, the new value of the parametric constant is equal to
583 *
584 * a_j0 - a_jc a_r0/a_rc
585 *
586 * where a_j0 is the original parametric constant, a_rc is the pivot element,
587 * a_r0 is the parametric constant of the pivot row and a_jc is the
588 * pivot column entry of the row j.
589 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
590 * remains the same if a_jc has the same sign as the row j or if
591 * a_jc is zero. In all other cases, we reset the sign to "unknown".
592 */
593 static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
594 {
595 int i;
596 struct isl_mat *mat = tab->mat;
597 unsigned off = 2 + tab->M;
598
599 if (!tab->row_sign)
600 return;
601
602 if (tab->row_sign[row] == 0)
603 return;
604 isl_assert(mat->ctx, row_sgn > 0, return);
605 isl_assert(mat->ctx, tab->row_sign[row] == isl_tab_row_neg, return);
606 tab->row_sign[row] = isl_tab_row_pos;
607 for (i = 0; i < tab->n_row; ++i) {
608 int s;
609 if (i == row)
610 continue;
611 s = isl_int_sgn(mat->row[i][off + col]);
612 if (!s)
613 continue;
614 if (!tab->row_sign[i])
615 continue;
616 if (s < 0 && tab->row_sign[i] == isl_tab_row_neg)
617 continue;
618 if (s > 0 && tab->row_sign[i] == isl_tab_row_pos)
619 continue;
620 tab->row_sign[i] = isl_tab_row_unknown;
621 }
622 }
623
624 /* Given a row number "row" and a column number "col", pivot the tableau
625 * such that the associated variables are interchanged.
626 * The given row in the tableau expresses
627 *
628 * x_r = a_r0 + \sum_i a_ri x_i
629 *
630 * or
631 *
632 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
633 *
634 * Substituting this equality into the other rows
635 *
636 * x_j = a_j0 + \sum_i a_ji x_i
637 *
638 * with a_jc \ne 0, we obtain
639 *
640 * 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
641 *
642 * The tableau
643 *
644 * n_rc/d_r n_ri/d_r
645 * n_jc/d_j n_ji/d_j
646 *
647 * where i is any other column and j is any other row,
648 * is therefore transformed into
649 *
650 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
651 * 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)
652 *
653 * The transformation is performed along the following steps
654 *
655 * d_r/n_rc n_ri/n_rc
656 * n_jc/d_j n_ji/d_j
657 *
658 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
659 * n_jc/d_j n_ji/d_j
660 *
661 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
662 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
663 *
664 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
665 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
666 *
667 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
668 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
669 *
670 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
671 * 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)
672 *
673 */
674 void isl_tab_pivot(struct isl_tab *tab, int row, int col)
675 {
676 int i, j;
677 int sgn;
678 int t;
679 struct isl_mat *mat = tab->mat;
680 struct isl_tab_var *var;
681 unsigned off = 2 + tab->M;
682
683 isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
684 sgn = isl_int_sgn(mat->row[row][0]);
685 if (sgn < 0) {
686 isl_int_neg(mat->row[row][0], mat->row[row][0]);
687 isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]);
688 } else
689 for (j = 0; j < off - 1 + tab->n_col; ++j) {
690 if (j == off - 1 + col)
691 continue;
692 isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
693 }
694 if (!isl_int_is_one(mat->row[row][0]))
695 isl_seq_normalize(mat->ctx, mat->row[row], off + tab->n_col);
696 for (i = 0; i < tab->n_row; ++i) {
697 if (i == row)
698 continue;
699 if (isl_int_is_zero(mat->row[i][off + col]))
700 continue;
701 isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
702 for (j = 0; j < off - 1 + tab->n_col; ++j) {
703 if (j == off - 1 + col)
704 continue;
705 isl_int_mul(mat->row[i][1 + j],
706 mat->row[i][1 + j], mat->row[row][0]);
707 isl_int_addmul(mat->row[i][1 + j],
708 mat->row[i][off + col], mat->row[row][1 + j]);
709 }
710 isl_int_mul(mat->row[i][off + col],
711 mat->row[i][off + col], mat->row[row][off + col]);
712 if (!isl_int_is_one(mat->row[i][0]))
713 isl_seq_normalize(mat->ctx, mat->row[i], off + tab->n_col);
714 }
715 t = tab->row_var[row];
716 tab->row_var[row] = tab->col_var[col];
717 tab->col_var[col] = t;
718 var = isl_tab_var_from_row(tab, row);
719 var->is_row = 1;
720 var->index = row;
721 var = var_from_col(tab, col);
722 var->is_row = 0;
723 var->index = col;
724 update_row_sign(tab, row, col, sgn);
725 if (tab->in_undo)
726 return;
727 for (i = tab->n_redundant; i < tab->n_row; ++i) {
728 if (isl_int_is_zero(mat->row[i][off + col]))
729 continue;
730 if (!isl_tab_var_from_row(tab, i)->frozen &&
731 isl_tab_row_is_redundant(tab, i))
732 if (isl_tab_mark_redundant(tab, i))
733 --i;
734 }
735 }
736
737 /* If "var" represents a column variable, then pivot is up (sgn > 0)
738 * or down (sgn < 0) to a row. The variable is assumed not to be
739 * unbounded in the specified direction.
740 * If sgn = 0, then the variable is unbounded in both directions,
741 * and we pivot with any row we can find.
742 */
743 static void to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
744 {
745 int r;
746 unsigned off = 2 + tab->M;
747
748 if (var->is_row)
749 return;
750
751 if (sign == 0) {
752 for (r = tab->n_redundant; r < tab->n_row; ++r)
753 if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
754 break;
755 isl_assert(tab->mat->ctx, r < tab->n_row, return);
756 } else {
757 r = pivot_row(tab, NULL, sign, var->index);
758 isl_assert(tab->mat->ctx, r >= 0, return);
759 }
760
761 isl_tab_pivot(tab, r, var->index);
762 }
763
764 static void check_table(struct isl_tab *tab)
765 {
766 int i;
767
768 if (tab->empty)
769 return;
770 for (i = 0; i < tab->n_row; ++i) {
771 if (!isl_tab_var_from_row(tab, i)->is_nonneg)
772 continue;
773 assert(!isl_int_is_neg(tab->mat->row[i][1]));
774 }
775 }
776
777 /* Return the sign of the maximal value of "var".
778 * If the sign is not negative, then on return from this function,
779 * the sample value will also be non-negative.
780 *
781 * If "var" is manifestly unbounded wrt positive values, we are done.
782 * Otherwise, we pivot the variable up to a row if needed
783 * Then we continue pivoting down until either
784 * - no more down pivots can be performed
785 * - the sample value is positive
786 * - the variable is pivoted into a manifestly unbounded column
787 */
788 static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
789 {
790 int row, col;
791
792 if (max_is_manifestly_unbounded(tab, var))
793 return 1;
794 to_row(tab, var, 1);
795 while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
796 find_pivot(tab, var, var, 1, &row, &col);
797 if (row == -1)
798 return isl_int_sgn(tab->mat->row[var->index][1]);
799 isl_tab_pivot(tab, row, col);
800 if (!var->is_row) /* manifestly unbounded */
801 return 1;
802 }
803 return 1;
804 }
805
806 static int row_is_neg(struct isl_tab *tab, int row)
807 {
808 if (!tab->M)
809 return isl_int_is_neg(tab->mat->row[row][1]);
810 if (isl_int_is_pos(tab->mat->row[row][2]))
811 return 0;
812 if (isl_int_is_neg(tab->mat->row[row][2]))
813 return 1;
814 return isl_int_is_neg(tab->mat->row[row][1]);
815 }
816
817 static int row_sgn(struct isl_tab *tab, int row)
818 {
819 if (!tab->M)
820 return isl_int_sgn(tab->mat->row[row][1]);
821 if (!isl_int_is_zero(tab->mat->row[row][2]))
822 return isl_int_sgn(tab->mat->row[row][2]);
823 else
824 return isl_int_sgn(tab->mat->row[row][1]);
825 }
826
827 /* Perform pivots until the row variable "var" has a non-negative
828 * sample value or until no more upward pivots can be performed.
829 * Return the sign of the sample value after the pivots have been
830 * performed.
831 */
832 static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
833 {
834 int row, col;
835
836 while (row_is_neg(tab, var->index)) {
837 find_pivot(tab, var, var, 1, &row, &col);
838 if (row == -1)
839 break;
840 isl_tab_pivot(tab, row, col);
841 if (!var->is_row) /* manifestly unbounded */
842 return 1;
843 }
844 return row_sgn(tab, var->index);
845 }
846
847 /* Perform pivots until we are sure that the row variable "var"
848 * can attain non-negative values. After return from this
849 * function, "var" is still a row variable, but its sample
850 * value may not be non-negative, even if the function returns 1.
851 */
852 static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
853 {
854 int row, col;
855
856 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
857 find_pivot(tab, var, var, 1, &row, &col);
858 if (row == -1)
859 break;
860 if (row == var->index) /* manifestly unbounded */
861 return 1;
862 isl_tab_pivot(tab, row, col);
863 }
864 return !isl_int_is_neg(tab->mat->row[var->index][1]);
865 }
866
867 /* Return a negative value if "var" can attain negative values.
868 * Return a non-negative value otherwise.
869 *
870 * If "var" is manifestly unbounded wrt negative values, we are done.
871 * Otherwise, if var is in a column, we can pivot it down to a row.
872 * Then we continue pivoting down until either
873 * - the pivot would result in a manifestly unbounded column
874 * => we don't perform the pivot, but simply return -1
875 * - no more down pivots can be performed
876 * - the sample value is negative
877 * If the sample value becomes negative and the variable is supposed
878 * to be nonnegative, then we undo the last pivot.
879 * However, if the last pivot has made the pivoting variable
880 * obviously redundant, then it may have moved to another row.
881 * In that case we look for upward pivots until we reach a non-negative
882 * value again.
883 */
884 static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
885 {
886 int row, col;
887 struct isl_tab_var *pivot_var = NULL;
888
889 if (min_is_manifestly_unbounded(tab, var))
890 return -1;
891 if (!var->is_row) {
892 col = var->index;
893 row = pivot_row(tab, NULL, -1, col);
894 pivot_var = var_from_col(tab, col);
895 isl_tab_pivot(tab, row, col);
896 if (var->is_redundant)
897 return 0;
898 if (isl_int_is_neg(tab->mat->row[var->index][1])) {
899 if (var->is_nonneg) {
900 if (!pivot_var->is_redundant &&
901 pivot_var->index == row)
902 isl_tab_pivot(tab, row, col);
903 else
904 restore_row(tab, var);
905 }
906 return -1;
907 }
908 }
909 if (var->is_redundant)
910 return 0;
911 while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
912 find_pivot(tab, var, var, -1, &row, &col);
913 if (row == var->index)
914 return -1;
915 if (row == -1)
916 return isl_int_sgn(tab->mat->row[var->index][1]);
917 pivot_var = var_from_col(tab, col);
918 isl_tab_pivot(tab, row, col);
919 if (var->is_redundant)
920 return 0;
921 }
922 if (pivot_var && var->is_nonneg) {
923 /* pivot back to non-negative value */
924 if (!pivot_var->is_redundant && pivot_var->index == row)
925 isl_tab_pivot(tab, row, col);
926 else
927 restore_row(tab, var);
928 }
929 return -1;
930 }
931
932 static int row_at_most_neg_one(struct isl_tab *tab, int row)
933 {
934 if (tab->M) {
935 if (isl_int_is_pos(tab->mat->row[row][2]))
936 return 0;
937 if (isl_int_is_neg(tab->mat->row[row][2]))
938 return 1;
939 }
940 return isl_int_is_neg(tab->mat->row[row][1]) &&
941 isl_int_abs_ge(tab->mat->row[row][1],
942 tab->mat->row[row][0]);
943 }
944
945 /* Return 1 if "var" can attain values <= -1.
946 * Return 0 otherwise.
947 *
948 * The sample value of "var" is assumed to be non-negative when the
949 * the function is called and will be made non-negative again before
950 * the function returns.
951 */
952 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
953 {
954 int row, col;
955 struct isl_tab_var *pivot_var;
956
957 if (min_is_manifestly_unbounded(tab, var))
958 return 1;
959 if (!var->is_row) {
960 col = var->index;
961 row = pivot_row(tab, NULL, -1, col);
962 pivot_var = var_from_col(tab, col);
963 isl_tab_pivot(tab, row, col);
964 if (var->is_redundant)
965 return 0;
966 if (row_at_most_neg_one(tab, var->index)) {
967 if (var->is_nonneg) {
968 if (!pivot_var->is_redundant &&
969 pivot_var->index == row)
970 isl_tab_pivot(tab, row, col);
971 else
972 restore_row(tab, var);
973 }
974 return 1;
975 }
976 }
977 if (var->is_redundant)
978 return 0;
979 do {
980 find_pivot(tab, var, var, -1, &row, &col);
981 if (row == var->index)
982 return 1;
983 if (row == -1)
984 return 0;
985 pivot_var = var_from_col(tab, col);
986 isl_tab_pivot(tab, row, col);
987 if (var->is_redundant)
988 return 0;
989 } while (!row_at_most_neg_one(tab, var->index));
990 if (var->is_nonneg) {
991 /* pivot back to non-negative value */
992 if (!pivot_var->is_redundant && pivot_var->index == row)
993 isl_tab_pivot(tab, row, col);
994 restore_row(tab, var);
995 }
996 return 1;
997 }
998
999 /* Return 1 if "var" can attain values >= 1.
1000 * Return 0 otherwise.
1001 */
1002 static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
1003 {
1004 int row, col;
1005 isl_int *r;
1006
1007 if (max_is_manifestly_unbounded(tab, var))
1008 return 1;
1009 to_row(tab, var, 1);
1010 r = tab->mat->row[var->index];
1011 while (isl_int_lt(r[1], r[0])) {
1012 find_pivot(tab, var, var, 1, &row, &col);
1013 if (row == -1)
1014 return isl_int_ge(r[1], r[0]);
1015 if (row == var->index) /* manifestly unbounded */
1016 return 1;
1017 isl_tab_pivot(tab, row, col);
1018 }
1019 return 1;
1020 }
1021
1022 static void swap_cols(struct isl_tab *tab, int col1, int col2)
1023 {
1024 int t;
1025 unsigned off = 2 + tab->M;
1026 t = tab->col_var[col1];
1027 tab->col_var[col1] = tab->col_var[col2];
1028 tab->col_var[col2] = t;
1029 var_from_col(tab, col1)->index = col1;
1030 var_from_col(tab, col2)->index = col2;
1031 tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2);
1032 }
1033
1034 /* Mark column with index "col" as representing a zero variable.
1035 * If we may need to undo the operation the column is kept,
1036 * but no longer considered.
1037 * Otherwise, the column is simply removed.
1038 *
1039 * The column may be interchanged with some other column. If it
1040 * is interchanged with a later column, return 1. Otherwise return 0.
1041 * If the columns are checked in order in the calling function,
1042 * then a return value of 1 means that the column with the given
1043 * column number may now contain a different column that
1044 * hasn't been checked yet.
1045 */
1046 int isl_tab_kill_col(struct isl_tab *tab, int col)
1047 {
1048 var_from_col(tab, col)->is_zero = 1;
1049 if (tab->need_undo) {
1050 isl_tab_push_var(tab, isl_tab_undo_zero, var_from_col(tab, col));
1051 if (col != tab->n_dead)
1052 swap_cols(tab, col, tab->n_dead);
1053 tab->n_dead++;
1054 return 0;
1055 } else {
1056 if (col != tab->n_col - 1)
1057 swap_cols(tab, col, tab->n_col - 1);
1058 var_from_col(tab, tab->n_col - 1)->index = -1;
1059 tab->n_col--;
1060 return 1;
1061 }
1062 }
1063
1064 /* Row variable "var" is non-negative and cannot attain any values
1065 * larger than zero. This means that the coefficients of the unrestricted
1066 * column variables are zero and that the coefficients of the non-negative
1067 * column variables are zero or negative.
1068 * Each of the non-negative variables with a negative coefficient can
1069 * then also be written as the negative sum of non-negative variables
1070 * and must therefore also be zero.
1071 */
1072 static void close_row(struct isl_tab *tab, struct isl_tab_var *var)
1073 {
1074 int j;
1075 struct isl_mat *mat = tab->mat;
1076 unsigned off = 2 + tab->M;
1077
1078 isl_assert(tab->mat->ctx, var->is_nonneg, return);
1079 var->is_zero = 1;
1080 for (j = tab->n_dead; j < tab->n_col; ++j) {
1081 if (isl_int_is_zero(mat->row[var->index][off + j]))
1082 continue;
1083 isl_assert(tab->mat->ctx,
1084 isl_int_is_neg(mat->row[var->index][off + j]), return);
1085 if (isl_tab_kill_col(tab, j))
1086 --j;
1087 }
1088 isl_tab_mark_redundant(tab, var->index);
1089 }
1090
1091 /* Add a constraint to the tableau and allocate a row for it.
1092 * Return the index into the constraint array "con".
1093 */
1094 int isl_tab_allocate_con(struct isl_tab *tab)
1095 {
1096 int r;
1097
1098 isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
1099
1100 r = tab->n_con;
1101 tab->con[r].index = tab->n_row;
1102 tab->con[r].is_row = 1;
1103 tab->con[r].is_nonneg = 0;
1104 tab->con[r].is_zero = 0;
1105 tab->con[r].is_redundant = 0;
1106 tab->con[r].frozen = 0;
1107 tab->con[r].negated = 0;
1108 tab->row_var[tab->n_row] = ~r;
1109
1110 tab->n_row++;
1111 tab->n_con++;
1112 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
1113
1114 return r;
1115 }
1116
1117 /* Add a variable to the tableau and allocate a column for it.
1118 * Return the index into the variable array "var".
1119 */
1120 int isl_tab_allocate_var(struct isl_tab *tab)
1121 {
1122 int r;
1123 int i;
1124 unsigned off = 2 + tab->M;
1125
1126 isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
1127 isl_assert(tab->mat->ctx, tab->n_var < tab->max_var, return -1);
1128
1129 r = tab->n_var;
1130 tab->var[r].index = tab->n_col;
1131 tab->var[r].is_row = 0;
1132 tab->var[r].is_nonneg = 0;
1133 tab->var[r].is_zero = 0;
1134 tab->var[r].is_redundant = 0;
1135 tab->var[r].frozen = 0;
1136 tab->var[r].negated = 0;
1137 tab->col_var[tab->n_col] = r;
1138
1139 for (i = 0; i < tab->n_row; ++i)
1140 isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
1141
1142 tab->n_var++;
1143 tab->n_col++;
1144 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]);
1145
1146 return r;
1147 }
1148
1149 /* Add a row to the tableau. The row is given as an affine combination
1150 * of the original variables and needs to be expressed in terms of the
1151 * column variables.
1152 *
1153 * We add each term in turn.
1154 * If r = n/d_r is the current sum and we need to add k x, then
1155 * if x is a column variable, we increase the numerator of
1156 * this column by k d_r
1157 * if x = f/d_x is a row variable, then the new representation of r is
1158 *
1159 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1160 * --- + --- = ------------------- = -------------------
1161 * d_r d_r d_r d_x/g m
1162 *
1163 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1164 */
1165 int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
1166 {
1167 int i;
1168 int r;
1169 isl_int *row;
1170 isl_int a, b;
1171 unsigned off = 2 + tab->M;
1172
1173 r = isl_tab_allocate_con(tab);
1174 if (r < 0)
1175 return -1;
1176
1177 isl_int_init(a);
1178 isl_int_init(b);
1179 row = tab->mat->row[tab->con[r].index];
1180 isl_int_set_si(row[0], 1);
1181 isl_int_set(row[1], line[0]);
1182 isl_seq_clr(row + 2, tab->M + tab->n_col);
1183 for (i = 0; i < tab->n_var; ++i) {
1184 if (tab->var[i].is_zero)
1185 continue;
1186 if (tab->var[i].is_row) {
1187 isl_int_lcm(a,
1188 row[0], tab->mat->row[tab->var[i].index][0]);
1189 isl_int_swap(a, row[0]);
1190 isl_int_divexact(a, row[0], a);
1191 isl_int_divexact(b,
1192 row[0], tab->mat->row[tab->var[i].index][0]);
1193 isl_int_mul(b, b, line[1 + i]);
1194 isl_seq_combine(row + 1, a, row + 1,
1195 b, tab->mat->row[tab->var[i].index] + 1,
1196 1 + tab->M + tab->n_col);
1197 } else
1198 isl_int_addmul(row[off + tab->var[i].index],
1199 line[1 + i], row[0]);
1200 if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
1201 isl_int_submul(row[2], line[1 + i], row[0]);
1202 }
1203 isl_seq_normalize(tab->mat->ctx, row, off + tab->n_col);
1204 isl_int_clear(a);
1205 isl_int_clear(b);
1206
1207 if (tab->row_sign)
1208 tab->row_sign[tab->con[r].index] = 0;
1209
1210 return r;
1211 }
1212
1213 static int drop_row(struct isl_tab *tab, int row)
1214 {
1215 isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
1216 if (row != tab->n_row - 1)
1217 swap_rows(tab, row, tab->n_row - 1);
1218 tab->n_row--;
1219 tab->n_con--;
1220 return 0;
1221 }
1222
1223 static int drop_col(struct isl_tab *tab, int col)
1224 {
1225 isl_assert(tab->mat->ctx, tab->col_var[col] == tab->n_var - 1, return -1);
1226 if (col != tab->n_col - 1)
1227 swap_cols(tab, col, tab->n_col - 1);
1228 tab->n_col--;
1229 tab->n_var--;
1230 return 0;
1231 }
1232
1233 /* Add inequality "ineq" and check if it conflicts with the
1234 * previously added constraints or if it is obviously redundant.
1235 */
1236 struct isl_tab *isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
1237 {
1238 int r;
1239 int sgn;
1240
1241 if (!tab)
1242 return NULL;
1243 r = isl_tab_add_row(tab, ineq);
1244 if (r < 0)
1245 goto error;
1246 tab->con[r].is_nonneg = 1;
1247 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1248 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1249 isl_tab_mark_redundant(tab, tab->con[r].index);
1250 return tab;
1251 }
1252
1253 sgn = restore_row(tab, &tab->con[r]);
1254 if (sgn < 0)
1255 return isl_tab_mark_empty(tab);
1256 if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
1257 isl_tab_mark_redundant(tab, tab->con[r].index);
1258 return tab;
1259 error:
1260 isl_tab_free(tab);
1261 return NULL;
1262 }
1263
1264 /* Pivot a non-negative variable down until it reaches the value zero
1265 * and then pivot the variable into a column position.
1266 */
1267 static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
1268 {
1269 int i;
1270 int row, col;
1271 unsigned off = 2 + tab->M;
1272
1273 if (!var->is_row)
1274 return 0;
1275
1276 while (isl_int_is_pos(tab->mat->row[var->index][1])) {
1277 find_pivot(tab, var, NULL, -1, &row, &col);
1278 isl_assert(tab->mat->ctx, row != -1, return -1);
1279 isl_tab_pivot(tab, row, col);
1280 if (!var->is_row)
1281 return 0;
1282 }
1283
1284 for (i = tab->n_dead; i < tab->n_col; ++i)
1285 if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
1286 break;
1287
1288 isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
1289 isl_tab_pivot(tab, var->index, i);
1290
1291 return 0;
1292 }
1293
1294 /* We assume Gaussian elimination has been performed on the equalities.
1295 * The equalities can therefore never conflict.
1296 * Adding the equalities is currently only really useful for a later call
1297 * to isl_tab_ineq_type.
1298 */
1299 static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
1300 {
1301 int i;
1302 int r;
1303
1304 if (!tab)
1305 return NULL;
1306 r = isl_tab_add_row(tab, eq);
1307 if (r < 0)
1308 goto error;
1309
1310 r = tab->con[r].index;
1311 i = isl_seq_first_non_zero(tab->mat->row[r] + 2 + tab->M + tab->n_dead,
1312 tab->n_col - tab->n_dead);
1313 isl_assert(tab->mat->ctx, i >= 0, goto error);
1314 i += tab->n_dead;
1315 isl_tab_pivot(tab, r, i);
1316 isl_tab_kill_col(tab, i);
1317 tab->n_eq++;
1318
1319 return tab;
1320 error:
1321 isl_tab_free(tab);
1322 return NULL;
1323 }
1324
1325 /* Add an equality that is known to be valid for the given tableau.
1326 */
1327 struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
1328 {
1329 struct isl_tab_var *var;
1330 int r;
1331
1332 if (!tab)
1333 return NULL;
1334 r = isl_tab_add_row(tab, eq);
1335 if (r < 0)
1336 goto error;
1337
1338 var = &tab->con[r];
1339 r = var->index;
1340 if (isl_int_is_neg(tab->mat->row[r][1])) {
1341 isl_seq_neg(tab->mat->row[r] + 1, tab->mat->row[r] + 1,
1342 1 + tab->n_col);
1343 var->negated = 1;
1344 }
1345 var->is_nonneg = 1;
1346 if (to_col(tab, var) < 0)
1347 goto error;
1348 var->is_nonneg = 0;
1349 isl_tab_kill_col(tab, var->index);
1350
1351 return tab;
1352 error:
1353 isl_tab_free(tab);
1354 return NULL;
1355 }
1356
1357 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap)
1358 {
1359 int i;
1360 struct isl_tab *tab;
1361
1362 if (!bmap)
1363 return NULL;
1364 tab = isl_tab_alloc(bmap->ctx,
1365 isl_basic_map_total_dim(bmap) + bmap->n_ineq + 1,
1366 isl_basic_map_total_dim(bmap), 0);
1367 if (!tab)
1368 return NULL;
1369 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
1370 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1371 return isl_tab_mark_empty(tab);
1372 for (i = 0; i < bmap->n_eq; ++i) {
1373 tab = add_eq(tab, bmap->eq[i]);
1374 if (!tab)
1375 return tab;
1376 }
1377 for (i = 0; i < bmap->n_ineq; ++i) {
1378 tab = isl_tab_add_ineq(tab, bmap->ineq[i]);
1379 if (!tab || tab->empty)
1380 return tab;
1381 }
1382 return tab;
1383 }
1384
1385 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset)
1386 {
1387 return isl_tab_from_basic_map((struct isl_basic_map *)bset);
1388 }
1389
1390 /* Construct a tableau corresponding to the recession cone of "bmap".
1391 */
1392 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_map *bmap)
1393 {
1394 isl_int cst;
1395 int i;
1396 struct isl_tab *tab;
1397
1398 if (!bmap)
1399 return NULL;
1400 tab = isl_tab_alloc(bmap->ctx, bmap->n_eq + bmap->n_ineq,
1401 isl_basic_map_total_dim(bmap), 0);
1402 if (!tab)
1403 return NULL;
1404 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
1405
1406 isl_int_init(cst);
1407 for (i = 0; i < bmap->n_eq; ++i) {
1408 isl_int_swap(bmap->eq[i][0], cst);
1409 tab = add_eq(tab, bmap->eq[i]);
1410 isl_int_swap(bmap->eq[i][0], cst);
1411 if (!tab)
1412 goto done;
1413 }
1414 for (i = 0; i < bmap->n_ineq; ++i) {
1415 int r;
1416 isl_int_swap(bmap->ineq[i][0], cst);
1417 r = isl_tab_add_row(tab, bmap->ineq[i]);
1418 isl_int_swap(bmap->ineq[i][0], cst);
1419 if (r < 0)
1420 goto error;
1421 tab->con[r].is_nonneg = 1;
1422 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1423 }
1424 done:
1425 isl_int_clear(cst);
1426 return tab;
1427 error:
1428 isl_int_clear(cst);
1429 isl_tab_free(tab);
1430 return NULL;
1431 }
1432
1433 /* Assuming "tab" is the tableau of a cone, check if the cone is
1434 * bounded, i.e., if it is empty or only contains the origin.
1435 */
1436 int isl_tab_cone_is_bounded(struct isl_tab *tab)
1437 {
1438 int i;
1439
1440 if (!tab)
1441 return -1;
1442 if (tab->empty)
1443 return 1;
1444 if (tab->n_dead == tab->n_col)
1445 return 1;
1446
1447 for (;;) {
1448 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1449 struct isl_tab_var *var;
1450 var = isl_tab_var_from_row(tab, i);
1451 if (!var->is_nonneg)
1452 continue;
1453 if (sign_of_max(tab, var) != 0)
1454 return 0;
1455 close_row(tab, var);
1456 break;
1457 }
1458 if (tab->n_dead == tab->n_col)
1459 return 1;
1460 if (i == tab->n_row)
1461 return 0;
1462 }
1463 }
1464
1465 int isl_tab_sample_is_integer(struct isl_tab *tab)
1466 {
1467 int i;
1468
1469 if (!tab)
1470 return -1;
1471
1472 for (i = 0; i < tab->n_var; ++i) {
1473 int row;
1474 if (!tab->var[i].is_row)
1475 continue;
1476 row = tab->var[i].index;
1477 if (!isl_int_is_divisible_by(tab->mat->row[row][1],
1478 tab->mat->row[row][0]))
1479 return 0;
1480 }
1481 return 1;
1482 }
1483
1484 static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
1485 {
1486 int i;
1487 struct isl_vec *vec;
1488
1489 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
1490 if (!vec)
1491 return NULL;
1492
1493 isl_int_set_si(vec->block.data[0], 1);
1494 for (i = 0; i < tab->n_var; ++i) {
1495 if (!tab->var[i].is_row)
1496 isl_int_set_si(vec->block.data[1 + i], 0);
1497 else {
1498 int row = tab->var[i].index;
1499 isl_int_divexact(vec->block.data[1 + i],
1500 tab->mat->row[row][1], tab->mat->row[row][0]);
1501 }
1502 }
1503
1504 return vec;
1505 }
1506
1507 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
1508 {
1509 int i;
1510 struct isl_vec *vec;
1511 isl_int m;
1512
1513 if (!tab)
1514 return NULL;
1515
1516 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
1517 if (!vec)
1518 return NULL;
1519
1520 isl_int_init(m);
1521
1522 isl_int_set_si(vec->block.data[0], 1);
1523 for (i = 0; i < tab->n_var; ++i) {
1524 int row;
1525 if (!tab->var[i].is_row) {
1526 isl_int_set_si(vec->block.data[1 + i], 0);
1527 continue;
1528 }
1529 row = tab->var[i].index;
1530 isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
1531 isl_int_divexact(m, tab->mat->row[row][0], m);
1532 isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
1533 isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
1534 isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
1535 }
1536 vec = isl_vec_normalize(vec);
1537
1538 isl_int_clear(m);
1539 return vec;
1540 }
1541
1542 /* Update "bmap" based on the results of the tableau "tab".
1543 * In particular, implicit equalities are made explicit, redundant constraints
1544 * are removed and if the sample value happens to be integer, it is stored
1545 * in "bmap" (unless "bmap" already had an integer sample).
1546 *
1547 * The tableau is assumed to have been created from "bmap" using
1548 * isl_tab_from_basic_map.
1549 */
1550 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
1551 struct isl_tab *tab)
1552 {
1553 int i;
1554 unsigned n_eq;
1555
1556 if (!bmap)
1557 return NULL;
1558 if (!tab)
1559 return bmap;
1560
1561 n_eq = tab->n_eq;
1562 if (tab->empty)
1563 bmap = isl_basic_map_set_to_empty(bmap);
1564 else
1565 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1566 if (isl_tab_is_equality(tab, n_eq + i))
1567 isl_basic_map_inequality_to_equality(bmap, i);
1568 else if (isl_tab_is_redundant(tab, n_eq + i))
1569 isl_basic_map_drop_inequality(bmap, i);
1570 }
1571 if (!tab->rational &&
1572 !bmap->sample && isl_tab_sample_is_integer(tab))
1573 bmap->sample = extract_integer_sample(tab);
1574 return bmap;
1575 }
1576
1577 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
1578 struct isl_tab *tab)
1579 {
1580 return (struct isl_basic_set *)isl_basic_map_update_from_tab(
1581 (struct isl_basic_map *)bset, tab);
1582 }
1583
1584 /* Given a non-negative variable "var", add a new non-negative variable
1585 * that is the opposite of "var", ensuring that var can only attain the
1586 * value zero.
1587 * If var = n/d is a row variable, then the new variable = -n/d.
1588 * If var is a column variables, then the new variable = -var.
1589 * If the new variable cannot attain non-negative values, then
1590 * the resulting tableau is empty.
1591 * Otherwise, we know the value will be zero and we close the row.
1592 */
1593 static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab,
1594 struct isl_tab_var *var)
1595 {
1596 unsigned r;
1597 isl_int *row;
1598 int sgn;
1599 unsigned off = 2 + tab->M;
1600
1601 if (var->is_zero)
1602 return tab;
1603 isl_assert(tab->mat->ctx, !var->is_redundant, goto error);
1604
1605 if (isl_tab_extend_cons(tab, 1) < 0)
1606 goto error;
1607
1608 r = tab->n_con;
1609 tab->con[r].index = tab->n_row;
1610 tab->con[r].is_row = 1;
1611 tab->con[r].is_nonneg = 0;
1612 tab->con[r].is_zero = 0;
1613 tab->con[r].is_redundant = 0;
1614 tab->con[r].frozen = 0;
1615 tab->con[r].negated = 0;
1616 tab->row_var[tab->n_row] = ~r;
1617 row = tab->mat->row[tab->n_row];
1618
1619 if (var->is_row) {
1620 isl_int_set(row[0], tab->mat->row[var->index][0]);
1621 isl_seq_neg(row + 1,
1622 tab->mat->row[var->index] + 1, 1 + tab->n_col);
1623 } else {
1624 isl_int_set_si(row[0], 1);
1625 isl_seq_clr(row + 1, 1 + tab->n_col);
1626 isl_int_set_si(row[off + var->index], -1);
1627 }
1628
1629 tab->n_row++;
1630 tab->n_con++;
1631 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
1632
1633 sgn = sign_of_max(tab, &tab->con[r]);
1634 if (sgn < 0)
1635 return isl_tab_mark_empty(tab);
1636 tab->con[r].is_nonneg = 1;
1637 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1638 /* sgn == 0 */
1639 close_row(tab, &tab->con[r]);
1640
1641 return tab;
1642 error:
1643 isl_tab_free(tab);
1644 return NULL;
1645 }
1646
1647 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
1648 * relax the inequality by one. That is, the inequality r >= 0 is replaced
1649 * by r' = r + 1 >= 0.
1650 * If r is a row variable, we simply increase the constant term by one
1651 * (taking into account the denominator).
1652 * If r is a column variable, then we need to modify each row that
1653 * refers to r = r' - 1 by substituting this equality, effectively
1654 * subtracting the coefficient of the column from the constant.
1655 */
1656 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
1657 {
1658 struct isl_tab_var *var;
1659 unsigned off = 2 + tab->M;
1660
1661 if (!tab)
1662 return NULL;
1663
1664 var = &tab->con[con];
1665
1666 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
1667 to_row(tab, var, 1);
1668
1669 if (var->is_row)
1670 isl_int_add(tab->mat->row[var->index][1],
1671 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
1672 else {
1673 int i;
1674
1675 for (i = 0; i < tab->n_row; ++i) {
1676 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
1677 continue;
1678 isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
1679 tab->mat->row[i][off + var->index]);
1680 }
1681
1682 }
1683
1684 isl_tab_push_var(tab, isl_tab_undo_relax, var);
1685
1686 return tab;
1687 }
1688
1689 struct isl_tab *isl_tab_select_facet(struct isl_tab *tab, int con)
1690 {
1691 if (!tab)
1692 return NULL;
1693
1694 return cut_to_hyperplane(tab, &tab->con[con]);
1695 }
1696
1697 static int may_be_equality(struct isl_tab *tab, int row)
1698 {
1699 unsigned off = 2 + tab->M;
1700 return (tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
1701 : isl_int_lt(tab->mat->row[row][1],
1702 tab->mat->row[row][0])) &&
1703 isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1704 tab->n_col - tab->n_dead) != -1;
1705 }
1706
1707 /* Check for (near) equalities among the constraints.
1708 * A constraint is an equality if it is non-negative and if
1709 * its maximal value is either
1710 * - zero (in case of rational tableaus), or
1711 * - strictly less than 1 (in case of integer tableaus)
1712 *
1713 * We first mark all non-redundant and non-dead variables that
1714 * are not frozen and not obviously not an equality.
1715 * Then we iterate over all marked variables if they can attain
1716 * any values larger than zero or at least one.
1717 * If the maximal value is zero, we mark any column variables
1718 * that appear in the row as being zero and mark the row as being redundant.
1719 * Otherwise, if the maximal value is strictly less than one (and the
1720 * tableau is integer), then we restrict the value to being zero
1721 * by adding an opposite non-negative variable.
1722 */
1723 struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab)
1724 {
1725 int i;
1726 unsigned n_marked;
1727
1728 if (!tab)
1729 return NULL;
1730 if (tab->empty)
1731 return tab;
1732 if (tab->n_dead == tab->n_col)
1733 return tab;
1734
1735 n_marked = 0;
1736 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1737 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
1738 var->marked = !var->frozen && var->is_nonneg &&
1739 may_be_equality(tab, i);
1740 if (var->marked)
1741 n_marked++;
1742 }
1743 for (i = tab->n_dead; i < tab->n_col; ++i) {
1744 struct isl_tab_var *var = var_from_col(tab, i);
1745 var->marked = !var->frozen && var->is_nonneg;
1746 if (var->marked)
1747 n_marked++;
1748 }
1749 while (n_marked) {
1750 struct isl_tab_var *var;
1751 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1752 var = isl_tab_var_from_row(tab, i);
1753 if (var->marked)
1754 break;
1755 }
1756 if (i == tab->n_row) {
1757 for (i = tab->n_dead; i < tab->n_col; ++i) {
1758 var = var_from_col(tab, i);
1759 if (var->marked)
1760 break;
1761 }
1762 if (i == tab->n_col)
1763 break;
1764 }
1765 var->marked = 0;
1766 n_marked--;
1767 if (sign_of_max(tab, var) == 0)
1768 close_row(tab, var);
1769 else if (!tab->rational && !at_least_one(tab, var)) {
1770 tab = cut_to_hyperplane(tab, var);
1771 return isl_tab_detect_equalities(tab);
1772 }
1773 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1774 var = isl_tab_var_from_row(tab, i);
1775 if (!var->marked)
1776 continue;
1777 if (may_be_equality(tab, i))
1778 continue;
1779 var->marked = 0;
1780 n_marked--;
1781 }
1782 }
1783
1784 return tab;
1785 }
1786
1787 /* Check for (near) redundant constraints.
1788 * A constraint is redundant if it is non-negative and if
1789 * its minimal value (temporarily ignoring the non-negativity) is either
1790 * - zero (in case of rational tableaus), or
1791 * - strictly larger than -1 (in case of integer tableaus)
1792 *
1793 * We first mark all non-redundant and non-dead variables that
1794 * are not frozen and not obviously negatively unbounded.
1795 * Then we iterate over all marked variables if they can attain
1796 * any values smaller than zero or at most negative one.
1797 * If not, we mark the row as being redundant (assuming it hasn't
1798 * been detected as being obviously redundant in the mean time).
1799 */
1800 struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab)
1801 {
1802 int i;
1803 unsigned n_marked;
1804
1805 if (!tab)
1806 return NULL;
1807 if (tab->empty)
1808 return tab;
1809 if (tab->n_redundant == tab->n_row)
1810 return tab;
1811
1812 n_marked = 0;
1813 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1814 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
1815 var->marked = !var->frozen && var->is_nonneg;
1816 if (var->marked)
1817 n_marked++;
1818 }
1819 for (i = tab->n_dead; i < tab->n_col; ++i) {
1820 struct isl_tab_var *var = var_from_col(tab, i);
1821 var->marked = !var->frozen && var->is_nonneg &&
1822 !min_is_manifestly_unbounded(tab, var);
1823 if (var->marked)
1824 n_marked++;
1825 }
1826 while (n_marked) {
1827 struct isl_tab_var *var;
1828 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1829 var = isl_tab_var_from_row(tab, i);
1830 if (var->marked)
1831 break;
1832 }
1833 if (i == tab->n_row) {
1834 for (i = tab->n_dead; i < tab->n_col; ++i) {
1835 var = var_from_col(tab, i);
1836 if (var->marked)
1837 break;
1838 }
1839 if (i == tab->n_col)
1840 break;
1841 }
1842 var->marked = 0;
1843 n_marked--;
1844 if ((tab->rational ? (sign_of_min(tab, var) >= 0)
1845 : !isl_tab_min_at_most_neg_one(tab, var)) &&
1846 !var->is_redundant)
1847 isl_tab_mark_redundant(tab, var->index);
1848 for (i = tab->n_dead; i < tab->n_col; ++i) {
1849 var = var_from_col(tab, i);
1850 if (!var->marked)
1851 continue;
1852 if (!min_is_manifestly_unbounded(tab, var))
1853 continue;
1854 var->marked = 0;
1855 n_marked--;
1856 }
1857 }
1858
1859 return tab;
1860 }
1861
1862 int isl_tab_is_equality(struct isl_tab *tab, int con)
1863 {
1864 int row;
1865 unsigned off;
1866
1867 if (!tab)
1868 return -1;
1869 if (tab->con[con].is_zero)
1870 return 1;
1871 if (tab->con[con].is_redundant)
1872 return 0;
1873 if (!tab->con[con].is_row)
1874 return tab->con[con].index < tab->n_dead;
1875
1876 row = tab->con[con].index;
1877
1878 off = 2 + tab->M;
1879 return isl_int_is_zero(tab->mat->row[row][1]) &&
1880 isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
1881 tab->n_col - tab->n_dead) == -1;
1882 }
1883
1884 /* Return the minimial value of the affine expression "f" with denominator
1885 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
1886 * the expression cannot attain arbitrarily small values.
1887 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
1888 * The return value reflects the nature of the result (empty, unbounded,
1889 * minmimal value returned in *opt).
1890 */
1891 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
1892 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
1893 unsigned flags)
1894 {
1895 int r;
1896 enum isl_lp_result res = isl_lp_ok;
1897 struct isl_tab_var *var;
1898 struct isl_tab_undo *snap;
1899
1900 if (tab->empty)
1901 return isl_lp_empty;
1902
1903 snap = isl_tab_snap(tab);
1904 r = isl_tab_add_row(tab, f);
1905 if (r < 0)
1906 return isl_lp_error;
1907 var = &tab->con[r];
1908 isl_int_mul(tab->mat->row[var->index][0],
1909 tab->mat->row[var->index][0], denom);
1910 for (;;) {
1911 int row, col;
1912 find_pivot(tab, var, var, -1, &row, &col);
1913 if (row == var->index) {
1914 res = isl_lp_unbounded;
1915 break;
1916 }
1917 if (row == -1)
1918 break;
1919 isl_tab_pivot(tab, row, col);
1920 }
1921 if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
1922 int i;
1923
1924 isl_vec_free(tab->dual);
1925 tab->dual = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_con);
1926 if (!tab->dual)
1927 return isl_lp_error;
1928 isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
1929 for (i = 0; i < tab->n_con; ++i) {
1930 int pos;
1931 if (tab->con[i].is_row) {
1932 isl_int_set_si(tab->dual->el[1 + i], 0);
1933 continue;
1934 }
1935 pos = 2 + tab->M + tab->con[i].index;
1936 if (tab->con[i].negated)
1937 isl_int_neg(tab->dual->el[1 + i],
1938 tab->mat->row[var->index][pos]);
1939 else
1940 isl_int_set(tab->dual->el[1 + i],
1941 tab->mat->row[var->index][pos]);
1942 }
1943 }
1944 if (opt && res == isl_lp_ok) {
1945 if (opt_denom) {
1946 isl_int_set(*opt, tab->mat->row[var->index][1]);
1947 isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
1948 } else
1949 isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
1950 tab->mat->row[var->index][0]);
1951 }
1952 if (isl_tab_rollback(tab, snap) < 0)
1953 return isl_lp_error;
1954 return res;
1955 }
1956
1957 int isl_tab_is_redundant(struct isl_tab *tab, int con)
1958 {
1959 if (!tab)
1960 return -1;
1961 if (tab->con[con].is_zero)
1962 return 0;
1963 if (tab->con[con].is_redundant)
1964 return 1;
1965 return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
1966 }
1967
1968 /* Take a snapshot of the tableau that can be restored by s call to
1969 * isl_tab_rollback.
1970 */
1971 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
1972 {
1973 if (!tab)
1974 return NULL;
1975 tab->need_undo = 1;
1976 return tab->top;
1977 }
1978
1979 /* Undo the operation performed by isl_tab_relax.
1980 */
1981 static void unrelax(struct isl_tab *tab, struct isl_tab_var *var)
1982 {
1983 unsigned off = 2 + tab->M;
1984
1985 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
1986 to_row(tab, var, 1);
1987
1988 if (var->is_row)
1989 isl_int_sub(tab->mat->row[var->index][1],
1990 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
1991 else {
1992 int i;
1993
1994 for (i = 0; i < tab->n_row; ++i) {
1995 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
1996 continue;
1997 isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
1998 tab->mat->row[i][off + var->index]);
1999 }
2000
2001 }
2002 }
2003
2004 static void perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
2005 {
2006 struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
2007 switch(undo->type) {
2008 case isl_tab_undo_nonneg:
2009 var->is_nonneg = 0;
2010 break;
2011 case isl_tab_undo_redundant:
2012 var->is_redundant = 0;
2013 tab->n_redundant--;
2014 break;
2015 case isl_tab_undo_zero:
2016 var->is_zero = 0;
2017 tab->n_dead--;
2018 break;
2019 case isl_tab_undo_allocate:
2020 if (undo->u.var_index >= 0) {
2021 isl_assert(tab->mat->ctx, !var->is_row, return);
2022 drop_col(tab, var->index);
2023 break;
2024 }
2025 if (!var->is_row) {
2026 if (!max_is_manifestly_unbounded(tab, var))
2027 to_row(tab, var, 1);
2028 else if (!min_is_manifestly_unbounded(tab, var))
2029 to_row(tab, var, -1);
2030 else
2031 to_row(tab, var, 0);
2032 }
2033 drop_row(tab, var->index);
2034 break;
2035 case isl_tab_undo_relax:
2036 unrelax(tab, var);
2037 break;
2038 }
2039 }
2040
2041 /* Restore the tableau to the state where the basic variables
2042 * are those in "col_var".
2043 * We first construct a list of variables that are currently in
2044 * the basis, but shouldn't. Then we iterate over all variables
2045 * that should be in the basis and for each one that is currently
2046 * not in the basis, we exchange it with one of the elements of the
2047 * list constructed before.
2048 * We can always find an appropriate variable to pivot with because
2049 * the current basis is mapped to the old basis by a non-singular
2050 * matrix and so we can never end up with a zero row.
2051 */
2052 static int restore_basis(struct isl_tab *tab, int *col_var)
2053 {
2054 int i, j;
2055 int n_extra = 0;
2056 int *extra = NULL; /* current columns that contain bad stuff */
2057 unsigned off = 2 + tab->M;
2058
2059 extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
2060 if (!extra)
2061 goto error;
2062 for (i = 0; i < tab->n_col; ++i) {
2063 for (j = 0; j < tab->n_col; ++j)
2064 if (tab->col_var[i] == col_var[j])
2065 break;
2066 if (j < tab->n_col)
2067 continue;
2068 extra[n_extra++] = i;
2069 }
2070 for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
2071 struct isl_tab_var *var;
2072 int row;
2073
2074 for (j = 0; j < tab->n_col; ++j)
2075 if (col_var[i] == tab->col_var[j])
2076 break;
2077 if (j < tab->n_col)
2078 continue;
2079 var = var_from_index(tab, col_var[i]);
2080 row = var->index;
2081 for (j = 0; j < n_extra; ++j)
2082 if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
2083 break;
2084 isl_assert(tab->mat->ctx, j < n_extra, goto error);
2085 isl_tab_pivot(tab, row, extra[j]);
2086 extra[j] = extra[--n_extra];
2087 }
2088
2089 free(extra);
2090 free(col_var);
2091 return 0;
2092 error:
2093 free(extra);
2094 free(col_var);
2095 return -1;
2096 }
2097
2098 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
2099 {
2100 switch (undo->type) {
2101 case isl_tab_undo_empty:
2102 tab->empty = 0;
2103 break;
2104 case isl_tab_undo_nonneg:
2105 case isl_tab_undo_redundant:
2106 case isl_tab_undo_zero:
2107 case isl_tab_undo_allocate:
2108 case isl_tab_undo_relax:
2109 perform_undo_var(tab, undo);
2110 break;
2111 case isl_tab_undo_bset_eq:
2112 isl_basic_set_free_equality(tab->bset, 1);
2113 break;
2114 case isl_tab_undo_bset_ineq:
2115 isl_basic_set_free_inequality(tab->bset, 1);
2116 break;
2117 case isl_tab_undo_bset_div:
2118 isl_basic_set_free_div(tab->bset, 1);
2119 if (tab->samples)
2120 tab->samples->n_col--;
2121 break;
2122 case isl_tab_undo_saved_basis:
2123 if (restore_basis(tab, undo->u.col_var) < 0)
2124 return -1;
2125 break;
2126 case isl_tab_undo_drop_sample:
2127 tab->n_outside--;
2128 break;
2129 default:
2130 isl_assert(tab->mat->ctx, 0, return -1);
2131 }
2132 return 0;
2133 }
2134
2135 /* Return the tableau to the state it was in when the snapshot "snap"
2136 * was taken.
2137 */
2138 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
2139 {
2140 struct isl_tab_undo *undo, *next;
2141
2142 if (!tab)
2143 return -1;
2144
2145 tab->in_undo = 1;
2146 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
2147 next = undo->next;
2148 if (undo == snap)
2149 break;
2150 if (perform_undo(tab, undo) < 0) {
2151 free_undo(tab);
2152 tab->in_undo = 0;
2153 return -1;
2154 }
2155 free(undo);
2156 }
2157 tab->in_undo = 0;
2158 tab->top = undo;
2159 if (!undo)
2160 return -1;
2161 return 0;
2162 }
2163
2164 /* The given row "row" represents an inequality violated by all
2165 * points in the tableau. Check for some special cases of such
2166 * separating constraints.
2167 * In particular, if the row has been reduced to the constant -1,
2168 * then we know the inequality is adjacent (but opposite) to
2169 * an equality in the tableau.
2170 * If the row has been reduced to r = -1 -r', with r' an inequality
2171 * of the tableau, then the inequality is adjacent (but opposite)
2172 * to the inequality r'.
2173 */
2174 static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
2175 {
2176 int pos;
2177 unsigned off = 2 + tab->M;
2178
2179 if (tab->rational)
2180 return isl_ineq_separate;
2181
2182 if (!isl_int_is_one(tab->mat->row[row][0]))
2183 return isl_ineq_separate;
2184 if (!isl_int_is_negone(tab->mat->row[row][1]))
2185 return isl_ineq_separate;
2186
2187 pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
2188 tab->n_col - tab->n_dead);
2189 if (pos == -1)
2190 return isl_ineq_adj_eq;
2191
2192 if (!isl_int_is_negone(tab->mat->row[row][off + tab->n_dead + pos]))
2193 return isl_ineq_separate;
2194
2195 pos = isl_seq_first_non_zero(
2196 tab->mat->row[row] + off + tab->n_dead + pos + 1,
2197 tab->n_col - tab->n_dead - pos - 1);
2198
2199 return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
2200 }
2201
2202 /* Check the effect of inequality "ineq" on the tableau "tab".
2203 * The result may be
2204 * isl_ineq_redundant: satisfied by all points in the tableau
2205 * isl_ineq_separate: satisfied by no point in the tableau
2206 * isl_ineq_cut: satisfied by some by not all points
2207 * isl_ineq_adj_eq: adjacent to an equality
2208 * isl_ineq_adj_ineq: adjacent to an inequality.
2209 */
2210 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
2211 {
2212 enum isl_ineq_type type = isl_ineq_error;
2213 struct isl_tab_undo *snap = NULL;
2214 int con;
2215 int row;
2216
2217 if (!tab)
2218 return isl_ineq_error;
2219
2220 if (isl_tab_extend_cons(tab, 1) < 0)
2221 return isl_ineq_error;
2222
2223 snap = isl_tab_snap(tab);
2224
2225 con = isl_tab_add_row(tab, ineq);
2226 if (con < 0)
2227 goto error;
2228
2229 row = tab->con[con].index;
2230 if (isl_tab_row_is_redundant(tab, row))
2231 type = isl_ineq_redundant;
2232 else if (isl_int_is_neg(tab->mat->row[row][1]) &&
2233 (tab->rational ||
2234 isl_int_abs_ge(tab->mat->row[row][1],
2235 tab->mat->row[row][0]))) {
2236 if (at_least_zero(tab, &tab->con[con]))
2237 type = isl_ineq_cut;
2238 else
2239 type = separation_type(tab, row);
2240 } else if (tab->rational ? (sign_of_min(tab, &tab->con[con]) < 0)
2241 : isl_tab_min_at_most_neg_one(tab, &tab->con[con]))
2242 type = isl_ineq_cut;
2243 else
2244 type = isl_ineq_redundant;
2245
2246 if (isl_tab_rollback(tab, snap))
2247 return isl_ineq_error;
2248 return type;
2249 error:
2250 isl_tab_rollback(tab, snap);
2251 return isl_ineq_error;
2252 }
2253
2254 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent)
2255 {
2256 unsigned r, c;
2257 int i;
2258
2259 if (!tab) {
2260 fprintf(out, "%*snull tab\n", indent, "");
2261 return;
2262 }
2263 fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
2264 tab->n_redundant, tab->n_dead);
2265 if (tab->rational)
2266 fprintf(out, ", rational");
2267 if (tab->empty)
2268 fprintf(out, ", empty");
2269 fprintf(out, "\n");
2270 fprintf(out, "%*s[", indent, "");
2271 for (i = 0; i < tab->n_var; ++i) {
2272 if (i)
2273 fprintf(out, (i == tab->n_param ||
2274 i == tab->n_var - tab->n_div) ? "; "
2275 : ", ");
2276 fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
2277 tab->var[i].index,
2278 tab->var[i].is_zero ? " [=0]" :
2279 tab->var[i].is_redundant ? " [R]" : "");
2280 }
2281 fprintf(out, "]\n");
2282 fprintf(out, "%*s[", indent, "");
2283 for (i = 0; i < tab->n_con; ++i) {
2284 if (i)
2285 fprintf(out, ", ");
2286 fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
2287 tab->con[i].index,
2288 tab->con[i].is_zero ? " [=0]" :
2289 tab->con[i].is_redundant ? " [R]" : "");
2290 }
2291 fprintf(out, "]\n");
2292 fprintf(out, "%*s[", indent, "");
2293 for (i = 0; i < tab->n_row; ++i) {
2294 const char *sign = "";
2295 if (i)
2296 fprintf(out, ", ");
2297 if (tab->row_sign) {
2298 if (tab->row_sign[i] == isl_tab_row_unknown)
2299 sign = "?";
2300 else if (tab->row_sign[i] == isl_tab_row_neg)
2301 sign = "-";
2302 else if (tab->row_sign[i] == isl_tab_row_pos)
2303 sign = "+";
2304 else
2305 sign = "+-";
2306 }
2307 fprintf(out, "r%d: %d%s%s", i, tab->row_var[i],
2308 isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
2309 }
2310 fprintf(out, "]\n");
2311 fprintf(out, "%*s[", indent, "");
2312 for (i = 0; i < tab->n_col; ++i) {
2313 if (i)
2314 fprintf(out, ", ");
2315 fprintf(out, "c%d: %d%s", i, tab->col_var[i],
2316 var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
2317 }
2318 fprintf(out, "]\n");
2319 r = tab->mat->n_row;
2320 tab->mat->n_row = tab->n_row;
2321 c = tab->mat->n_col;
2322 tab->mat->n_col = 2 + tab->M + tab->n_col;
2323 isl_mat_dump(tab->mat, out, indent);
2324 tab->mat->n_row = r;
2325 tab->mat->n_col = c;
2326 if (tab->bset)
2327 isl_basic_set_dump(tab->bset, out, indent);
2328 }
Integer set library