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add isl_map_neg
[isl.git] / isl_tab.c
blob3adb11dd132e9196c7d331005dc9bfd988e73b05
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->mat->n_col);
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
185 if (!tab)
186 return NULL;
187
188 dup = isl_calloc_type(tab->ctx, struct isl_tab);
189 if (!dup)
190 return NULL;
191 dup->mat = isl_mat_dup(tab->mat);
192 if (!dup->mat)
193 goto error;
194 dup->var = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_var);
195 if (!dup->var)
196 goto error;
197 for (i = 0; i < tab->n_var; ++i)
198 dup->var[i] = tab->var[i];
199 dup->con = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_con);
200 if (!dup->con)
201 goto error;
202 for (i = 0; i < tab->n_con; ++i)
203 dup->con[i] = tab->con[i];
204 dup->col_var = isl_alloc_array(tab->ctx, int, tab->mat->n_col);
205 if (!dup->col_var)
206 goto error;
207 for (i = 0; i < tab->n_var; ++i)
208 dup->col_var[i] = tab->col_var[i];
209 dup->row_var = isl_alloc_array(tab->ctx, int, tab->mat->n_row);
210 if (!dup->row_var)
211 goto error;
212 for (i = 0; i < tab->n_row; ++i)
213 dup->row_var[i] = tab->row_var[i];
214 if (tab->row_sign) {
215 dup->row_sign = isl_alloc_array(tab->ctx, enum isl_tab_row_sign,
216 tab->mat->n_row);
217 if (!dup->row_sign)
218 goto error;
219 for (i = 0; i < tab->n_row; ++i)
220 dup->row_sign[i] = tab->row_sign[i];
221 }
222 if (tab->samples) {
223 dup->samples = isl_mat_dup(tab->samples);
224 if (!dup->samples)
225 goto error;
226 dup->n_sample = tab->n_sample;
227 dup->n_outside = tab->n_outside;
228 }
229 dup->n_row = tab->n_row;
230 dup->n_con = tab->n_con;
231 dup->n_eq = tab->n_eq;
232 dup->max_con = tab->max_con;
233 dup->n_col = tab->n_col;
234 dup->n_var = tab->n_var;
235 dup->max_var = tab->max_var;
236 dup->n_param = tab->n_param;
237 dup->n_div = tab->n_div;
238 dup->n_dead = tab->n_dead;
239 dup->n_redundant = tab->n_redundant;
240 dup->rational = tab->rational;
241 dup->empty = tab->empty;
242 dup->need_undo = 0;
243 dup->in_undo = 0;
244 dup->M = tab->M;
245 dup->bottom.type = isl_tab_undo_bottom;
246 dup->bottom.next = NULL;
247 dup->top = &dup->bottom;
248 return dup;
249 error:
250 isl_tab_free(dup);
251 return NULL;
252 }
253
254 static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i)
255 {
256 if (i >= 0)
257 return &tab->var[i];
258 else
259 return &tab->con[~i];
260 }
261
262 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
263 {
264 return var_from_index(tab, tab->row_var[i]);
265 }
266
267 static struct isl_tab_var *var_from_col(struct isl_tab *tab, int i)
268 {
269 return var_from_index(tab, tab->col_var[i]);
270 }
271
272 /* Check if there are any upper bounds on column variable "var",
273 * i.e., non-negative rows where var appears with a negative coefficient.
274 * Return 1 if there are no such bounds.
275 */
276 static int max_is_manifestly_unbounded(struct isl_tab *tab,
277 struct isl_tab_var *var)
278 {
279 int i;
280 unsigned off = 2 + tab->M;
281
282 if (var->is_row)
283 return 0;
284 for (i = tab->n_redundant; i < tab->n_row; ++i) {
285 if (!isl_int_is_neg(tab->mat->row[i][off + var->index]))
286 continue;
287 if (isl_tab_var_from_row(tab, i)->is_nonneg)
288 return 0;
289 }
290 return 1;
291 }
292
293 /* Check if there are any lower bounds on column variable "var",
294 * i.e., non-negative rows where var appears with a positive coefficient.
295 * Return 1 if there are no such bounds.
296 */
297 static int min_is_manifestly_unbounded(struct isl_tab *tab,
298 struct isl_tab_var *var)
299 {
300 int i;
301 unsigned off = 2 + tab->M;
302
303 if (var->is_row)
304 return 0;
305 for (i = tab->n_redundant; i < tab->n_row; ++i) {
306 if (!isl_int_is_pos(tab->mat->row[i][off + var->index]))
307 continue;
308 if (isl_tab_var_from_row(tab, i)->is_nonneg)
309 return 0;
310 }
311 return 1;
312 }
313
314 static int row_cmp(struct isl_tab *tab, int r1, int r2, int c, isl_int t)
315 {
316 unsigned off = 2 + tab->M;
317
318 if (tab->M) {
319 int s;
320 isl_int_mul(t, tab->mat->row[r1][2], tab->mat->row[r2][off+c]);
321 isl_int_submul(t, tab->mat->row[r2][2], tab->mat->row[r1][off+c]);
322 s = isl_int_sgn(t);
323 if (s)
324 return s;
325 }
326 isl_int_mul(t, tab->mat->row[r1][1], tab->mat->row[r2][off + c]);
327 isl_int_submul(t, tab->mat->row[r2][1], tab->mat->row[r1][off + c]);
328 return isl_int_sgn(t);
329 }
330
331 /* Given the index of a column "c", return the index of a row
332 * that can be used to pivot the column in, with either an increase
333 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
334 * If "var" is not NULL, then the row returned will be different from
335 * the one associated with "var".
336 *
337 * Each row in the tableau is of the form
338 *
339 * x_r = a_r0 + \sum_i a_ri x_i
340 *
341 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
342 * impose any limit on the increase or decrease in the value of x_c
343 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
344 * for the row with the smallest (most stringent) such bound.
345 * Note that the common denominator of each row drops out of the fraction.
346 * To check if row j has a smaller bound than row r, i.e.,
347 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
348 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
349 * where -sign(a_jc) is equal to "sgn".
350 */
351 static int pivot_row(struct isl_tab *tab,
352 struct isl_tab_var *var, int sgn, int c)
353 {
354 int j, r, tsgn;
355 isl_int t;
356 unsigned off = 2 + tab->M;
357
358 isl_int_init(t);
359 r = -1;
360 for (j = tab->n_redundant; j < tab->n_row; ++j) {
361 if (var && j == var->index)
362 continue;
363 if (!isl_tab_var_from_row(tab, j)->is_nonneg)
364 continue;
365 if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
366 continue;
367 if (r < 0) {
368 r = j;
369 continue;
370 }
371 tsgn = sgn * row_cmp(tab, r, j, c, t);
372 if (tsgn < 0 || (tsgn == 0 &&
373 tab->row_var[j] < tab->row_var[r]))
374 r = j;
375 }
376 isl_int_clear(t);
377 return r;
378 }
379
380 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
381 * (sgn < 0) the value of row variable var.
382 * If not NULL, then skip_var is a row variable that should be ignored
383 * while looking for a pivot row. It is usually equal to var.
384 *
385 * As the given row in the tableau is of the form
386 *
387 * x_r = a_r0 + \sum_i a_ri x_i
388 *
389 * we need to find a column such that the sign of a_ri is equal to "sgn"
390 * (such that an increase in x_i will have the desired effect) or a
391 * column with a variable that may attain negative values.
392 * If a_ri is positive, then we need to move x_i in the same direction
393 * to obtain the desired effect. Otherwise, x_i has to move in the
394 * opposite direction.
395 */
396 static void find_pivot(struct isl_tab *tab,
397 struct isl_tab_var *var, struct isl_tab_var *skip_var,
398 int sgn, int *row, int *col)
399 {
400 int j, r, c;
401 isl_int *tr;
402
403 *row = *col = -1;
404
405 isl_assert(tab->mat->ctx, var->is_row, return);
406 tr = tab->mat->row[var->index] + 2 + tab->M;
407
408 c = -1;
409 for (j = tab->n_dead; j < tab->n_col; ++j) {
410 if (isl_int_is_zero(tr[j]))
411 continue;
412 if (isl_int_sgn(tr[j]) != sgn &&
413 var_from_col(tab, j)->is_nonneg)
414 continue;
415 if (c < 0 || tab->col_var[j] < tab->col_var[c])
416 c = j;
417 }
418 if (c < 0)
419 return;
420
421 sgn *= isl_int_sgn(tr[c]);
422 r = pivot_row(tab, skip_var, sgn, c);
423 *row = r < 0 ? var->index : r;
424 *col = c;
425 }
426
427 /* Return 1 if row "row" represents an obviously redundant inequality.
428 * This means
429 * - it represents an inequality or a variable
430 * - that is the sum of a non-negative sample value and a positive
431 * combination of zero or more non-negative variables.
432 */
433 int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
434 {
435 int i;
436 unsigned off = 2 + tab->M;
437
438 if (tab->row_var[row] < 0 && !isl_tab_var_from_row(tab, row)->is_nonneg)
439 return 0;
440
441 if (isl_int_is_neg(tab->mat->row[row][1]))
442 return 0;
443 if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
444 return 0;
445
446 for (i = tab->n_dead; i < tab->n_col; ++i) {
447 if (isl_int_is_zero(tab->mat->row[row][off + i]))
448 continue;
449 if (isl_int_is_neg(tab->mat->row[row][off + i]))
450 return 0;
451 if (!var_from_col(tab, i)->is_nonneg)
452 return 0;
453 }
454 return 1;
455 }
456
457 static void swap_rows(struct isl_tab *tab, int row1, int row2)
458 {
459 int t;
460 t = tab->row_var[row1];
461 tab->row_var[row1] = tab->row_var[row2];
462 tab->row_var[row2] = t;
463 isl_tab_var_from_row(tab, row1)->index = row1;
464 isl_tab_var_from_row(tab, row2)->index = row2;
465 tab->mat = isl_mat_swap_rows(tab->mat, row1, row2);
466
467 if (!tab->row_sign)
468 return;
469 t = tab->row_sign[row1];
470 tab->row_sign[row1] = tab->row_sign[row2];
471 tab->row_sign[row2] = t;
472 }
473
474 static void push_union(struct isl_tab *tab,
475 enum isl_tab_undo_type type, union isl_tab_undo_val u)
476 {
477 struct isl_tab_undo *undo;
478
479 if (!tab->need_undo)
480 return;
481
482 undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
483 if (!undo) {
484 free_undo(tab);
485 tab->top = NULL;
486 return;
487 }
488 undo->type = type;
489 undo->u = u;
490 undo->next = tab->top;
491 tab->top = undo;
492 }
493
494 void isl_tab_push_var(struct isl_tab *tab,
495 enum isl_tab_undo_type type, struct isl_tab_var *var)
496 {
497 union isl_tab_undo_val u;
498 if (var->is_row)
499 u.var_index = tab->row_var[var->index];
500 else
501 u.var_index = tab->col_var[var->index];
502 push_union(tab, type, u);
503 }
504
505 void isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
506 {
507 union isl_tab_undo_val u = { 0 };
508 push_union(tab, type, u);
509 }
510
511 /* Push a record on the undo stack describing the current basic
512 * variables, so that the this state can be restored during rollback.
513 */
514 void isl_tab_push_basis(struct isl_tab *tab)
515 {
516 int i;
517 union isl_tab_undo_val u;
518
519 u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
520 if (!u.col_var) {
521 free_undo(tab);
522 tab->top = NULL;
523 return;
524 }
525 for (i = 0; i < tab->n_col; ++i)
526 u.col_var[i] = tab->col_var[i];
527 push_union(tab, isl_tab_undo_saved_basis, u);
528 }
529
530 /* Mark row with index "row" as being redundant.
531 * If we may need to undo the operation or if the row represents
532 * a variable of the original problem, the row is kept,
533 * but no longer considered when looking for a pivot row.
534 * Otherwise, the row is simply removed.
535 *
536 * The row may be interchanged with some other row. If it
537 * is interchanged with a later row, return 1. Otherwise return 0.
538 * If the rows are checked in order in the calling function,
539 * then a return value of 1 means that the row with the given
540 * row number may now contain a different row that hasn't been checked yet.
541 */
542 int isl_tab_mark_redundant(struct isl_tab *tab, int row)
543 {
544 struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
545 var->is_redundant = 1;
546 isl_assert(tab->mat->ctx, row >= tab->n_redundant, return);
547 if (tab->need_undo || tab->row_var[row] >= 0) {
548 if (tab->row_var[row] >= 0 && !var->is_nonneg) {
549 var->is_nonneg = 1;
550 isl_tab_push_var(tab, isl_tab_undo_nonneg, var);
551 }
552 if (row != tab->n_redundant)
553 swap_rows(tab, row, tab->n_redundant);
554 isl_tab_push_var(tab, isl_tab_undo_redundant, var);
555 tab->n_redundant++;
556 return 0;
557 } else {
558 if (row != tab->n_row - 1)
559 swap_rows(tab, row, tab->n_row - 1);
560 isl_tab_var_from_row(tab, tab->n_row - 1)->index = -1;
561 tab->n_row--;
562 return 1;
563 }
564 }
565
566 struct isl_tab *isl_tab_mark_empty(struct isl_tab *tab)
567 {
568 if (!tab->empty && tab->need_undo)
569 isl_tab_push(tab, isl_tab_undo_empty);
570 tab->empty = 1;
571 return tab;
572 }
573
574 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
575 * the original sign of the pivot element.
576 * We only keep track of row signs during PILP solving and in this case
577 * we only pivot a row with negative sign (meaning the value is always
578 * non-positive) using a positive pivot element.
579 *
580 * For each row j, the new value of the parametric constant is equal to
581 *
582 * a_j0 - a_jc a_r0/a_rc
583 *
584 * where a_j0 is the original parametric constant, a_rc is the pivot element,
585 * a_r0 is the parametric constant of the pivot row and a_jc is the
586 * pivot column entry of the row j.
587 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
588 * remains the same if a_jc has the same sign as the row j or if
589 * a_jc is zero. In all other cases, we reset the sign to "unknown".
590 */
591 static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
592 {
593 int i;
594 struct isl_mat *mat = tab->mat;
595 unsigned off = 2 + tab->M;
596
597 if (!tab->row_sign)
598 return;
599
600 if (tab->row_sign[row] == 0)
601 return;
602 isl_assert(mat->ctx, row_sgn > 0, return);
603 isl_assert(mat->ctx, tab->row_sign[row] == isl_tab_row_neg, return);
604 tab->row_sign[row] = isl_tab_row_pos;
605 for (i = 0; i < tab->n_row; ++i) {
606 int s;
607 if (i == row)
608 continue;
609 s = isl_int_sgn(mat->row[i][off + col]);
610 if (!s)
611 continue;
612 if (!tab->row_sign[i])
613 continue;
614 if (s < 0 && tab->row_sign[i] == isl_tab_row_neg)
615 continue;
616 if (s > 0 && tab->row_sign[i] == isl_tab_row_pos)
617 continue;
618 tab->row_sign[i] = isl_tab_row_unknown;
619 }
620 }
621
622 /* Given a row number "row" and a column number "col", pivot the tableau
623 * such that the associated variables are interchanged.
624 * The given row in the tableau expresses
625 *
626 * x_r = a_r0 + \sum_i a_ri x_i
627 *
628 * or
629 *
630 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
631 *
632 * Substituting this equality into the other rows
633 *
634 * x_j = a_j0 + \sum_i a_ji x_i
635 *
636 * with a_jc \ne 0, we obtain
637 *
638 * 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
639 *
640 * The tableau
641 *
642 * n_rc/d_r n_ri/d_r
643 * n_jc/d_j n_ji/d_j
644 *
645 * where i is any other column and j is any other row,
646 * is therefore transformed into
647 *
648 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
649 * 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)
650 *
651 * The transformation is performed along the following steps
652 *
653 * d_r/n_rc n_ri/n_rc
654 * n_jc/d_j n_ji/d_j
655 *
656 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
657 * n_jc/d_j n_ji/d_j
658 *
659 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
660 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
661 *
662 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
663 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
664 *
665 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
666 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
667 *
668 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
669 * 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)
670 *
671 */
672 void isl_tab_pivot(struct isl_tab *tab, int row, int col)
673 {
674 int i, j;
675 int sgn;
676 int t;
677 struct isl_mat *mat = tab->mat;
678 struct isl_tab_var *var;
679 unsigned off = 2 + tab->M;
680
681 isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
682 sgn = isl_int_sgn(mat->row[row][0]);
683 if (sgn < 0) {
684 isl_int_neg(mat->row[row][0], mat->row[row][0]);
685 isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]);
686 } else
687 for (j = 0; j < off - 1 + tab->n_col; ++j) {
688 if (j == off - 1 + col)
689 continue;
690 isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
691 }
692 if (!isl_int_is_one(mat->row[row][0]))
693 isl_seq_normalize(mat->ctx, mat->row[row], off + tab->n_col);
694 for (i = 0; i < tab->n_row; ++i) {
695 if (i == row)
696 continue;
697 if (isl_int_is_zero(mat->row[i][off + col]))
698 continue;
699 isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
700 for (j = 0; j < off - 1 + tab->n_col; ++j) {
701 if (j == off - 1 + col)
702 continue;
703 isl_int_mul(mat->row[i][1 + j],
704 mat->row[i][1 + j], mat->row[row][0]);
705 isl_int_addmul(mat->row[i][1 + j],
706 mat->row[i][off + col], mat->row[row][1 + j]);
707 }
708 isl_int_mul(mat->row[i][off + col],
709 mat->row[i][off + col], mat->row[row][off + col]);
710 if (!isl_int_is_one(mat->row[i][0]))
711 isl_seq_normalize(mat->ctx, mat->row[i], off + tab->n_col);
712 }
713 t = tab->row_var[row];
714 tab->row_var[row] = tab->col_var[col];
715 tab->col_var[col] = t;
716 var = isl_tab_var_from_row(tab, row);
717 var->is_row = 1;
718 var->index = row;
719 var = var_from_col(tab, col);
720 var->is_row = 0;
721 var->index = col;
722 update_row_sign(tab, row, col, sgn);
723 if (tab->in_undo)
724 return;
725 for (i = tab->n_redundant; i < tab->n_row; ++i) {
726 if (isl_int_is_zero(mat->row[i][off + col]))
727 continue;
728 if (!isl_tab_var_from_row(tab, i)->frozen &&
729 isl_tab_row_is_redundant(tab, i))
730 if (isl_tab_mark_redundant(tab, i))
731 --i;
732 }
733 }
734
735 /* If "var" represents a column variable, then pivot is up (sgn > 0)
736 * or down (sgn < 0) to a row. The variable is assumed not to be
737 * unbounded in the specified direction.
738 * If sgn = 0, then the variable is unbounded in both directions,
739 * and we pivot with any row we can find.
740 */
741 static void to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
742 {
743 int r;
744 unsigned off = 2 + tab->M;
745
746 if (var->is_row)
747 return;
748
749 if (sign == 0) {
750 for (r = tab->n_redundant; r < tab->n_row; ++r)
751 if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
752 break;
753 isl_assert(tab->mat->ctx, r < tab->n_row, return);
754 } else {
755 r = pivot_row(tab, NULL, sign, var->index);
756 isl_assert(tab->mat->ctx, r >= 0, return);
757 }
758
759 isl_tab_pivot(tab, r, var->index);
760 }
761
762 static void check_table(struct isl_tab *tab)
763 {
764 int i;
765
766 if (tab->empty)
767 return;
768 for (i = 0; i < tab->n_row; ++i) {
769 if (!isl_tab_var_from_row(tab, i)->is_nonneg)
770 continue;
771 assert(!isl_int_is_neg(tab->mat->row[i][1]));
772 }
773 }
774
775 /* Return the sign of the maximal value of "var".
776 * If the sign is not negative, then on return from this function,
777 * the sample value will also be non-negative.
778 *
779 * If "var" is manifestly unbounded wrt positive values, we are done.
780 * Otherwise, we pivot the variable up to a row if needed
781 * Then we continue pivoting down until either
782 * - no more down pivots can be performed
783 * - the sample value is positive
784 * - the variable is pivoted into a manifestly unbounded column
785 */
786 static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
787 {
788 int row, col;
789
790 if (max_is_manifestly_unbounded(tab, var))
791 return 1;
792 to_row(tab, var, 1);
793 while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
794 find_pivot(tab, var, var, 1, &row, &col);
795 if (row == -1)
796 return isl_int_sgn(tab->mat->row[var->index][1]);
797 isl_tab_pivot(tab, row, col);
798 if (!var->is_row) /* manifestly unbounded */
799 return 1;
800 }
801 return 1;
802 }
803
804 static int row_is_neg(struct isl_tab *tab, int row)
805 {
806 if (!tab->M)
807 return isl_int_is_neg(tab->mat->row[row][1]);
808 if (isl_int_is_pos(tab->mat->row[row][2]))
809 return 0;
810 if (isl_int_is_neg(tab->mat->row[row][2]))
811 return 1;
812 return isl_int_is_neg(tab->mat->row[row][1]);
813 }
814
815 static int row_sgn(struct isl_tab *tab, int row)
816 {
817 if (!tab->M)
818 return isl_int_sgn(tab->mat->row[row][1]);
819 if (!isl_int_is_zero(tab->mat->row[row][2]))
820 return isl_int_sgn(tab->mat->row[row][2]);
821 else
822 return isl_int_sgn(tab->mat->row[row][1]);
823 }
824
825 /* Perform pivots until the row variable "var" has a non-negative
826 * sample value or until no more upward pivots can be performed.
827 * Return the sign of the sample value after the pivots have been
828 * performed.
829 */
830 static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
831 {
832 int row, col;
833
834 while (row_is_neg(tab, var->index)) {
835 find_pivot(tab, var, var, 1, &row, &col);
836 if (row == -1)
837 break;
838 isl_tab_pivot(tab, row, col);
839 if (!var->is_row) /* manifestly unbounded */
840 return 1;
841 }
842 return row_sgn(tab, var->index);
843 }
844
845 /* Perform pivots until we are sure that the row variable "var"
846 * can attain non-negative values. After return from this
847 * function, "var" is still a row variable, but its sample
848 * value may not be non-negative, even if the function returns 1.
849 */
850 static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
851 {
852 int row, col;
853
854 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
855 find_pivot(tab, var, var, 1, &row, &col);
856 if (row == -1)
857 break;
858 if (row == var->index) /* manifestly unbounded */
859 return 1;
860 isl_tab_pivot(tab, row, col);
861 }
862 return !isl_int_is_neg(tab->mat->row[var->index][1]);
863 }
864
865 /* Return a negative value if "var" can attain negative values.
866 * Return a non-negative value otherwise.
867 *
868 * If "var" is manifestly unbounded wrt negative values, we are done.
869 * Otherwise, if var is in a column, we can pivot it down to a row.
870 * Then we continue pivoting down until either
871 * - the pivot would result in a manifestly unbounded column
872 * => we don't perform the pivot, but simply return -1
873 * - no more down pivots can be performed
874 * - the sample value is negative
875 * If the sample value becomes negative and the variable is supposed
876 * to be nonnegative, then we undo the last pivot.
877 * However, if the last pivot has made the pivoting variable
878 * obviously redundant, then it may have moved to another row.
879 * In that case we look for upward pivots until we reach a non-negative
880 * value again.
881 */
882 static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
883 {
884 int row, col;
885 struct isl_tab_var *pivot_var;
886
887 if (min_is_manifestly_unbounded(tab, var))
888 return -1;
889 if (!var->is_row) {
890 col = var->index;
891 row = pivot_row(tab, NULL, -1, col);
892 pivot_var = var_from_col(tab, col);
893 isl_tab_pivot(tab, row, col);
894 if (var->is_redundant)
895 return 0;
896 if (isl_int_is_neg(tab->mat->row[var->index][1])) {
897 if (var->is_nonneg) {
898 if (!pivot_var->is_redundant &&
899 pivot_var->index == row)
900 isl_tab_pivot(tab, row, col);
901 else
902 restore_row(tab, var);
903 }
904 return -1;
905 }
906 }
907 if (var->is_redundant)
908 return 0;
909 while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
910 find_pivot(tab, var, var, -1, &row, &col);
911 if (row == var->index)
912 return -1;
913 if (row == -1)
914 return isl_int_sgn(tab->mat->row[var->index][1]);
915 pivot_var = var_from_col(tab, col);
916 isl_tab_pivot(tab, row, col);
917 if (var->is_redundant)
918 return 0;
919 }
920 if (var->is_nonneg) {
921 /* pivot back to non-negative value */
922 if (!pivot_var->is_redundant && pivot_var->index == row)
923 isl_tab_pivot(tab, row, col);
924 else
925 restore_row(tab, var);
926 }
927 return -1;
928 }
929
930 static int row_at_most_neg_one(struct isl_tab *tab, int row)
931 {
932 if (tab->M) {
933 if (isl_int_is_pos(tab->mat->row[row][2]))
934 return 0;
935 if (isl_int_is_neg(tab->mat->row[row][2]))
936 return 1;
937 }
938 return isl_int_is_neg(tab->mat->row[row][1]) &&
939 isl_int_abs_ge(tab->mat->row[row][1],
940 tab->mat->row[row][0]);
941 }
942
943 /* Return 1 if "var" can attain values <= -1.
944 * Return 0 otherwise.
945 *
946 * The sample value of "var" is assumed to be non-negative when the
947 * the function is called and will be made non-negative again before
948 * the function returns.
949 */
950 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
951 {
952 int row, col;
953 struct isl_tab_var *pivot_var;
954
955 if (min_is_manifestly_unbounded(tab, var))
956 return 1;
957 if (!var->is_row) {
958 col = var->index;
959 row = pivot_row(tab, NULL, -1, col);
960 pivot_var = var_from_col(tab, col);
961 isl_tab_pivot(tab, row, col);
962 if (var->is_redundant)
963 return 0;
964 if (row_at_most_neg_one(tab, var->index)) {
965 if (var->is_nonneg) {
966 if (!pivot_var->is_redundant &&
967 pivot_var->index == row)
968 isl_tab_pivot(tab, row, col);
969 else
970 restore_row(tab, var);
971 }
972 return 1;
973 }
974 }
975 if (var->is_redundant)
976 return 0;
977 do {
978 find_pivot(tab, var, var, -1, &row, &col);
979 if (row == var->index)
980 return 1;
981 if (row == -1)
982 return 0;
983 pivot_var = var_from_col(tab, col);
984 isl_tab_pivot(tab, row, col);
985 if (var->is_redundant)
986 return 0;
987 } while (!row_at_most_neg_one(tab, var->index));
988 if (var->is_nonneg) {
989 /* pivot back to non-negative value */
990 if (!pivot_var->is_redundant && pivot_var->index == row)
991 isl_tab_pivot(tab, row, col);
992 restore_row(tab, var);
993 }
994 return 1;
995 }
996
997 /* Return 1 if "var" can attain values >= 1.
998 * Return 0 otherwise.
999 */
1000 static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
1001 {
1002 int row, col;
1003 isl_int *r;
1004
1005 if (max_is_manifestly_unbounded(tab, var))
1006 return 1;
1007 to_row(tab, var, 1);
1008 r = tab->mat->row[var->index];
1009 while (isl_int_lt(r[1], r[0])) {
1010 find_pivot(tab, var, var, 1, &row, &col);
1011 if (row == -1)
1012 return isl_int_ge(r[1], r[0]);
1013 if (row == var->index) /* manifestly unbounded */
1014 return 1;
1015 isl_tab_pivot(tab, row, col);
1016 }
1017 return 1;
1018 }
1019
1020 static void swap_cols(struct isl_tab *tab, int col1, int col2)
1021 {
1022 int t;
1023 unsigned off = 2 + tab->M;
1024 t = tab->col_var[col1];
1025 tab->col_var[col1] = tab->col_var[col2];
1026 tab->col_var[col2] = t;
1027 var_from_col(tab, col1)->index = col1;
1028 var_from_col(tab, col2)->index = col2;
1029 tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2);
1030 }
1031
1032 /* Mark column with index "col" as representing a zero variable.
1033 * If we may need to undo the operation the column is kept,
1034 * but no longer considered.
1035 * Otherwise, the column is simply removed.
1036 *
1037 * The column may be interchanged with some other column. If it
1038 * is interchanged with a later column, return 1. Otherwise return 0.
1039 * If the columns are checked in order in the calling function,
1040 * then a return value of 1 means that the column with the given
1041 * column number may now contain a different column that
1042 * hasn't been checked yet.
1043 */
1044 int isl_tab_kill_col(struct isl_tab *tab, int col)
1045 {
1046 var_from_col(tab, col)->is_zero = 1;
1047 if (tab->need_undo) {
1048 isl_tab_push_var(tab, isl_tab_undo_zero, var_from_col(tab, col));
1049 if (col != tab->n_dead)
1050 swap_cols(tab, col, tab->n_dead);
1051 tab->n_dead++;
1052 return 0;
1053 } else {
1054 if (col != tab->n_col - 1)
1055 swap_cols(tab, col, tab->n_col - 1);
1056 var_from_col(tab, tab->n_col - 1)->index = -1;
1057 tab->n_col--;
1058 return 1;
1059 }
1060 }
1061
1062 /* Row variable "var" is non-negative and cannot attain any values
1063 * larger than zero. This means that the coefficients of the unrestricted
1064 * column variables are zero and that the coefficients of the non-negative
1065 * column variables are zero or negative.
1066 * Each of the non-negative variables with a negative coefficient can
1067 * then also be written as the negative sum of non-negative variables
1068 * and must therefore also be zero.
1069 */
1070 static void close_row(struct isl_tab *tab, struct isl_tab_var *var)
1071 {
1072 int j;
1073 struct isl_mat *mat = tab->mat;
1074 unsigned off = 2 + tab->M;
1075
1076 isl_assert(tab->mat->ctx, var->is_nonneg, return);
1077 var->is_zero = 1;
1078 for (j = tab->n_dead; j < tab->n_col; ++j) {
1079 if (isl_int_is_zero(mat->row[var->index][off + j]))
1080 continue;
1081 isl_assert(tab->mat->ctx,
1082 isl_int_is_neg(mat->row[var->index][off + j]), return);
1083 if (isl_tab_kill_col(tab, j))
1084 --j;
1085 }
1086 isl_tab_mark_redundant(tab, var->index);
1087 }
1088
1089 /* Add a constraint to the tableau and allocate a row for it.
1090 * Return the index into the constraint array "con".
1091 */
1092 int isl_tab_allocate_con(struct isl_tab *tab)
1093 {
1094 int r;
1095
1096 isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
1097
1098 r = tab->n_con;
1099 tab->con[r].index = tab->n_row;
1100 tab->con[r].is_row = 1;
1101 tab->con[r].is_nonneg = 0;
1102 tab->con[r].is_zero = 0;
1103 tab->con[r].is_redundant = 0;
1104 tab->con[r].frozen = 0;
1105 tab->con[r].negated = 0;
1106 tab->row_var[tab->n_row] = ~r;
1107
1108 tab->n_row++;
1109 tab->n_con++;
1110 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
1111
1112 return r;
1113 }
1114
1115 /* Add a variable to the tableau and allocate a column for it.
1116 * Return the index into the variable array "var".
1117 */
1118 int isl_tab_allocate_var(struct isl_tab *tab)
1119 {
1120 int r;
1121 int i;
1122 unsigned off = 2 + tab->M;
1123
1124 isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
1125 isl_assert(tab->mat->ctx, tab->n_var < tab->max_var, return -1);
1126
1127 r = tab->n_var;
1128 tab->var[r].index = tab->n_col;
1129 tab->var[r].is_row = 0;
1130 tab->var[r].is_nonneg = 0;
1131 tab->var[r].is_zero = 0;
1132 tab->var[r].is_redundant = 0;
1133 tab->var[r].frozen = 0;
1134 tab->var[r].negated = 0;
1135 tab->col_var[tab->n_col] = r;
1136
1137 for (i = 0; i < tab->n_row; ++i)
1138 isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
1139
1140 tab->n_var++;
1141 tab->n_col++;
1142 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]);
1143
1144 return r;
1145 }
1146
1147 /* Add a row to the tableau. The row is given as an affine combination
1148 * of the original variables and needs to be expressed in terms of the
1149 * column variables.
1150 *
1151 * We add each term in turn.
1152 * If r = n/d_r is the current sum and we need to add k x, then
1153 * if x is a column variable, we increase the numerator of
1154 * this column by k d_r
1155 * if x = f/d_x is a row variable, then the new representation of r is
1156 *
1157 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1158 * --- + --- = ------------------- = -------------------
1159 * d_r d_r d_r d_x/g m
1160 *
1161 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1162 */
1163 int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
1164 {
1165 int i;
1166 int r;
1167 isl_int *row;
1168 isl_int a, b;
1169 unsigned off = 2 + tab->M;
1170
1171 r = isl_tab_allocate_con(tab);
1172 if (r < 0)
1173 return -1;
1174
1175 isl_int_init(a);
1176 isl_int_init(b);
1177 row = tab->mat->row[tab->con[r].index];
1178 isl_int_set_si(row[0], 1);
1179 isl_int_set(row[1], line[0]);
1180 isl_seq_clr(row + 2, tab->M + tab->n_col);
1181 for (i = 0; i < tab->n_var; ++i) {
1182 if (tab->var[i].is_zero)
1183 continue;
1184 if (tab->var[i].is_row) {
1185 isl_int_lcm(a,
1186 row[0], tab->mat->row[tab->var[i].index][0]);
1187 isl_int_swap(a, row[0]);
1188 isl_int_divexact(a, row[0], a);
1189 isl_int_divexact(b,
1190 row[0], tab->mat->row[tab->var[i].index][0]);
1191 isl_int_mul(b, b, line[1 + i]);
1192 isl_seq_combine(row + 1, a, row + 1,
1193 b, tab->mat->row[tab->var[i].index] + 1,
1194 1 + tab->M + tab->n_col);
1195 } else
1196 isl_int_addmul(row[off + tab->var[i].index],
1197 line[1 + i], row[0]);
1198 if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
1199 isl_int_submul(row[2], line[1 + i], row[0]);
1200 }
1201 isl_seq_normalize(tab->mat->ctx, row, off + tab->n_col);
1202 isl_int_clear(a);
1203 isl_int_clear(b);
1204
1205 if (tab->row_sign)
1206 tab->row_sign[tab->con[r].index] = 0;
1207
1208 return r;
1209 }
1210
1211 static int drop_row(struct isl_tab *tab, int row)
1212 {
1213 isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
1214 if (row != tab->n_row - 1)
1215 swap_rows(tab, row, tab->n_row - 1);
1216 tab->n_row--;
1217 tab->n_con--;
1218 return 0;
1219 }
1220
1221 static int drop_col(struct isl_tab *tab, int col)
1222 {
1223 isl_assert(tab->mat->ctx, tab->col_var[col] == tab->n_var - 1, return -1);
1224 if (col != tab->n_col - 1)
1225 swap_cols(tab, col, tab->n_col - 1);
1226 tab->n_col--;
1227 tab->n_var--;
1228 return 0;
1229 }
1230
1231 /* Add inequality "ineq" and check if it conflicts with the
1232 * previously added constraints or if it is obviously redundant.
1233 */
1234 struct isl_tab *isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
1235 {
1236 int r;
1237 int sgn;
1238
1239 if (!tab)
1240 return NULL;
1241 r = isl_tab_add_row(tab, ineq);
1242 if (r < 0)
1243 goto error;
1244 tab->con[r].is_nonneg = 1;
1245 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1246 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1247 isl_tab_mark_redundant(tab, tab->con[r].index);
1248 return tab;
1249 }
1250
1251 sgn = restore_row(tab, &tab->con[r]);
1252 if (sgn < 0)
1253 return isl_tab_mark_empty(tab);
1254 if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
1255 isl_tab_mark_redundant(tab, tab->con[r].index);
1256 return tab;
1257 error:
1258 isl_tab_free(tab);
1259 return NULL;
1260 }
1261
1262 /* Pivot a non-negative variable down until it reaches the value zero
1263 * and then pivot the variable into a column position.
1264 */
1265 int to_col(struct isl_tab *tab, struct isl_tab_var *var)
1266 {
1267 int i;
1268 int row, col;
1269 unsigned off = 2 + tab->M;
1270
1271 if (!var->is_row)
1272 return;
1273
1274 while (isl_int_is_pos(tab->mat->row[var->index][1])) {
1275 find_pivot(tab, var, NULL, -1, &row, &col);
1276 isl_assert(tab->mat->ctx, row != -1, return -1);
1277 isl_tab_pivot(tab, row, col);
1278 if (!var->is_row)
1279 return;
1280 }
1281
1282 for (i = tab->n_dead; i < tab->n_col; ++i)
1283 if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
1284 break;
1285
1286 isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
1287 isl_tab_pivot(tab, var->index, i);
1288
1289 return 0;
1290 }
1291
1292 /* We assume Gaussian elimination has been performed on the equalities.
1293 * The equalities can therefore never conflict.
1294 * Adding the equalities is currently only really useful for a later call
1295 * to isl_tab_ineq_type.
1296 */
1297 static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
1298 {
1299 int i;
1300 int r;
1301
1302 if (!tab)
1303 return NULL;
1304 r = isl_tab_add_row(tab, eq);
1305 if (r < 0)
1306 goto error;
1307
1308 r = tab->con[r].index;
1309 i = isl_seq_first_non_zero(tab->mat->row[r] + 2 + tab->M + tab->n_dead,
1310 tab->n_col - tab->n_dead);
1311 isl_assert(tab->mat->ctx, i >= 0, goto error);
1312 i += tab->n_dead;
1313 isl_tab_pivot(tab, r, i);
1314 isl_tab_kill_col(tab, i);
1315 tab->n_eq++;
1316
1317 return tab;
1318 error:
1319 isl_tab_free(tab);
1320 return NULL;
1321 }
1322
1323 /* Add an equality that is known to be valid for the given tableau.
1324 */
1325 struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
1326 {
1327 struct isl_tab_var *var;
1328 int i;
1329 int r;
1330
1331 if (!tab)
1332 return NULL;
1333 r = isl_tab_add_row(tab, eq);
1334 if (r < 0)
1335 goto error;
1336
1337 var = &tab->con[r];
1338 r = var->index;
1339 if (isl_int_is_neg(tab->mat->row[r][1])) {
1340 isl_seq_neg(tab->mat->row[r] + 1, tab->mat->row[r] + 1,
1341 1 + tab->n_col);
1342 var->negated = 1;
1343 }
1344 var->is_nonneg = 1;
1345 if (to_col(tab, var) < 0)
1346 goto error;
1347 var->is_nonneg = 0;
1348 isl_tab_kill_col(tab, var->index);
1349
1350 return tab;
1351 error:
1352 isl_tab_free(tab);
1353 return NULL;
1354 }
1355
1356 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap)
1357 {
1358 int i;
1359 struct isl_tab *tab;
1360
1361 if (!bmap)
1362 return NULL;
1363 tab = isl_tab_alloc(bmap->ctx,
1364 isl_basic_map_total_dim(bmap) + bmap->n_ineq + 1,
1365 isl_basic_map_total_dim(bmap), 0);
1366 if (!tab)
1367 return NULL;
1368 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
1369 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1370 return isl_tab_mark_empty(tab);
1371 for (i = 0; i < bmap->n_eq; ++i) {
1372 tab = add_eq(tab, bmap->eq[i]);
1373 if (!tab)
1374 return tab;
1375 }
1376 for (i = 0; i < bmap->n_ineq; ++i) {
1377 tab = isl_tab_add_ineq(tab, bmap->ineq[i]);
1378 if (!tab || tab->empty)
1379 return tab;
1380 }
1381 return tab;
1382 }
1383
1384 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset)
1385 {
1386 return isl_tab_from_basic_map((struct isl_basic_map *)bset);
1387 }
1388
1389 /* Construct a tableau corresponding to the recession cone of "bmap".
1390 */
1391 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_map *bmap)
1392 {
1393 isl_int cst;
1394 int i;
1395 struct isl_tab *tab;
1396
1397 if (!bmap)
1398 return NULL;
1399 tab = isl_tab_alloc(bmap->ctx, bmap->n_eq + bmap->n_ineq,
1400 isl_basic_map_total_dim(bmap), 0);
1401 if (!tab)
1402 return NULL;
1403 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
1404
1405 isl_int_init(cst);
1406 for (i = 0; i < bmap->n_eq; ++i) {
1407 isl_int_swap(bmap->eq[i][0], cst);
1408 tab = add_eq(tab, bmap->eq[i]);
1409 isl_int_swap(bmap->eq[i][0], cst);
1410 if (!tab)
1411 goto done;
1412 }
1413 for (i = 0; i < bmap->n_ineq; ++i) {
1414 int r;
1415 isl_int_swap(bmap->ineq[i][0], cst);
1416 r = isl_tab_add_row(tab, bmap->ineq[i]);
1417 isl_int_swap(bmap->ineq[i][0], cst);
1418 if (r < 0)
1419 goto error;
1420 tab->con[r].is_nonneg = 1;
1421 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1422 }
1423 done:
1424 isl_int_clear(cst);
1425 return tab;
1426 error:
1427 isl_int_clear(cst);
1428 isl_tab_free(tab);
1429 return NULL;
1430 }
1431
1432 /* Assuming "tab" is the tableau of a cone, check if the cone is
1433 * bounded, i.e., if it is empty or only contains the origin.
1434 */
1435 int isl_tab_cone_is_bounded(struct isl_tab *tab)
1436 {
1437 int i;
1438
1439 if (!tab)
1440 return -1;
1441 if (tab->empty)
1442 return 1;
1443 if (tab->n_dead == tab->n_col)
1444 return 1;
1445
1446 for (;;) {
1447 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1448 struct isl_tab_var *var;
1449 var = isl_tab_var_from_row(tab, i);
1450 if (!var->is_nonneg)
1451 continue;
1452 if (sign_of_max(tab, var) != 0)
1453 return 0;
1454 close_row(tab, var);
1455 break;
1456 }
1457 if (tab->n_dead == tab->n_col)
1458 return 1;
1459 if (i == tab->n_row)
1460 return 0;
1461 }
1462 }
1463
1464 int isl_tab_sample_is_integer(struct isl_tab *tab)
1465 {
1466 int i;
1467
1468 if (!tab)
1469 return -1;
1470
1471 for (i = 0; i < tab->n_var; ++i) {
1472 int row;
1473 if (!tab->var[i].is_row)
1474 continue;
1475 row = tab->var[i].index;
1476 if (!isl_int_is_divisible_by(tab->mat->row[row][1],
1477 tab->mat->row[row][0]))
1478 return 0;
1479 }
1480 return 1;
1481 }
1482
1483 static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
1484 {
1485 int i;
1486 struct isl_vec *vec;
1487
1488 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
1489 if (!vec)
1490 return NULL;
1491
1492 isl_int_set_si(vec->block.data[0], 1);
1493 for (i = 0; i < tab->n_var; ++i) {
1494 if (!tab->var[i].is_row)
1495 isl_int_set_si(vec->block.data[1 + i], 0);
1496 else {
1497 int row = tab->var[i].index;
1498 isl_int_divexact(vec->block.data[1 + i],
1499 tab->mat->row[row][1], tab->mat->row[row][0]);
1500 }
1501 }
1502
1503 return vec;
1504 }
1505
1506 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
1507 {
1508 int i;
1509 struct isl_vec *vec;
1510 isl_int m;
1511
1512 if (!tab)
1513 return NULL;
1514
1515 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
1516 if (!vec)
1517 return NULL;
1518
1519 isl_int_init(m);
1520
1521 isl_int_set_si(vec->block.data[0], 1);
1522 for (i = 0; i < tab->n_var; ++i) {
1523 int row;
1524 if (!tab->var[i].is_row) {
1525 isl_int_set_si(vec->block.data[1 + i], 0);
1526 continue;
1527 }
1528 row = tab->var[i].index;
1529 isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
1530 isl_int_divexact(m, tab->mat->row[row][0], m);
1531 isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
1532 isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
1533 isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
1534 }
1535 vec = isl_vec_normalize(vec);
1536
1537 isl_int_clear(m);
1538 return vec;
1539 }
1540
1541 /* Update "bmap" based on the results of the tableau "tab".
1542 * In particular, implicit equalities are made explicit, redundant constraints
1543 * are removed and if the sample value happens to be integer, it is stored
1544 * in "bmap" (unless "bmap" already had an integer sample).
1545 *
1546 * The tableau is assumed to have been created from "bmap" using
1547 * isl_tab_from_basic_map.
1548 */
1549 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
1550 struct isl_tab *tab)
1551 {
1552 int i;
1553 unsigned n_eq;
1554
1555 if (!bmap)
1556 return NULL;
1557 if (!tab)
1558 return bmap;
1559
1560 n_eq = tab->n_eq;
1561 if (tab->empty)
1562 bmap = isl_basic_map_set_to_empty(bmap);
1563 else
1564 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1565 if (isl_tab_is_equality(tab, n_eq + i))
1566 isl_basic_map_inequality_to_equality(bmap, i);
1567 else if (isl_tab_is_redundant(tab, n_eq + i))
1568 isl_basic_map_drop_inequality(bmap, i);
1569 }
1570 if (!tab->rational &&
1571 !bmap->sample && isl_tab_sample_is_integer(tab))
1572 bmap->sample = extract_integer_sample(tab);
1573 return bmap;
1574 }
1575
1576 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
1577 struct isl_tab *tab)
1578 {
1579 return (struct isl_basic_set *)isl_basic_map_update_from_tab(
1580 (struct isl_basic_map *)bset, tab);
1581 }
1582
1583 /* Given a non-negative variable "var", add a new non-negative variable
1584 * that is the opposite of "var", ensuring that var can only attain the
1585 * value zero.
1586 * If var = n/d is a row variable, then the new variable = -n/d.
1587 * If var is a column variables, then the new variable = -var.
1588 * If the new variable cannot attain non-negative values, then
1589 * the resulting tableau is empty.
1590 * Otherwise, we know the value will be zero and we close the row.
1591 */
1592 static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab,
1593 struct isl_tab_var *var)
1594 {
1595 unsigned r;
1596 isl_int *row;
1597 int sgn;
1598 unsigned off = 2 + tab->M;
1599
1600 if (isl_tab_extend_cons(tab, 1) < 0)
1601 goto error;
1602
1603 r = tab->n_con;
1604 tab->con[r].index = tab->n_row;
1605 tab->con[r].is_row = 1;
1606 tab->con[r].is_nonneg = 0;
1607 tab->con[r].is_zero = 0;
1608 tab->con[r].is_redundant = 0;
1609 tab->con[r].frozen = 0;
1610 tab->con[r].negated = 0;
1611 tab->row_var[tab->n_row] = ~r;
1612 row = tab->mat->row[tab->n_row];
1613
1614 if (var->is_row) {
1615 isl_int_set(row[0], tab->mat->row[var->index][0]);
1616 isl_seq_neg(row + 1,
1617 tab->mat->row[var->index] + 1, 1 + tab->n_col);
1618 } else {
1619 isl_int_set_si(row[0], 1);
1620 isl_seq_clr(row + 1, 1 + tab->n_col);
1621 isl_int_set_si(row[off + var->index], -1);
1622 }
1623
1624 tab->n_row++;
1625 tab->n_con++;
1626 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
1627
1628 sgn = sign_of_max(tab, &tab->con[r]);
1629 if (sgn < 0)
1630 return isl_tab_mark_empty(tab);
1631 tab->con[r].is_nonneg = 1;
1632 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1633 /* sgn == 0 */
1634 close_row(tab, &tab->con[r]);
1635
1636 return tab;
1637 error:
1638 isl_tab_free(tab);
1639 return NULL;
1640 }
1641
1642 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
1643 * relax the inequality by one. That is, the inequality r >= 0 is replaced
1644 * by r' = r + 1 >= 0.
1645 * If r is a row variable, we simply increase the constant term by one
1646 * (taking into account the denominator).
1647 * If r is a column variable, then we need to modify each row that
1648 * refers to r = r' - 1 by substituting this equality, effectively
1649 * subtracting the coefficient of the column from the constant.
1650 */
1651 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
1652 {
1653 struct isl_tab_var *var;
1654 unsigned off = 2 + tab->M;
1655
1656 if (!tab)
1657 return NULL;
1658
1659 var = &tab->con[con];
1660
1661 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
1662 to_row(tab, var, 1);
1663
1664 if (var->is_row)
1665 isl_int_add(tab->mat->row[var->index][1],
1666 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
1667 else {
1668 int i;
1669
1670 for (i = 0; i < tab->n_row; ++i) {
1671 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
1672 continue;
1673 isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
1674 tab->mat->row[i][off + var->index]);
1675 }
1676
1677 }
1678
1679 isl_tab_push_var(tab, isl_tab_undo_relax, var);
1680
1681 return tab;
1682 }
1683
1684 struct isl_tab *isl_tab_select_facet(struct isl_tab *tab, int con)
1685 {
1686 if (!tab)
1687 return NULL;
1688
1689 return cut_to_hyperplane(tab, &tab->con[con]);
1690 }
1691
1692 static int may_be_equality(struct isl_tab *tab, int row)
1693 {
1694 unsigned off = 2 + tab->M;
1695 return (tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
1696 : isl_int_lt(tab->mat->row[row][1],
1697 tab->mat->row[row][0])) &&
1698 isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1699 tab->n_col - tab->n_dead) != -1;
1700 }
1701
1702 /* Check for (near) equalities among the constraints.
1703 * A constraint is an equality if it is non-negative and if
1704 * its maximal value is either
1705 * - zero (in case of rational tableaus), or
1706 * - strictly less than 1 (in case of integer tableaus)
1707 *
1708 * We first mark all non-redundant and non-dead variables that
1709 * are not frozen and not obviously not an equality.
1710 * Then we iterate over all marked variables if they can attain
1711 * any values larger than zero or at least one.
1712 * If the maximal value is zero, we mark any column variables
1713 * that appear in the row as being zero and mark the row as being redundant.
1714 * Otherwise, if the maximal value is strictly less than one (and the
1715 * tableau is integer), then we restrict the value to being zero
1716 * by adding an opposite non-negative variable.
1717 */
1718 struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab)
1719 {
1720 int i;
1721 unsigned n_marked;
1722
1723 if (!tab)
1724 return NULL;
1725 if (tab->empty)
1726 return tab;
1727 if (tab->n_dead == tab->n_col)
1728 return tab;
1729
1730 n_marked = 0;
1731 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1732 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
1733 var->marked = !var->frozen && var->is_nonneg &&
1734 may_be_equality(tab, i);
1735 if (var->marked)
1736 n_marked++;
1737 }
1738 for (i = tab->n_dead; i < tab->n_col; ++i) {
1739 struct isl_tab_var *var = var_from_col(tab, i);
1740 var->marked = !var->frozen && var->is_nonneg;
1741 if (var->marked)
1742 n_marked++;
1743 }
1744 while (n_marked) {
1745 struct isl_tab_var *var;
1746 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1747 var = isl_tab_var_from_row(tab, i);
1748 if (var->marked)
1749 break;
1750 }
1751 if (i == tab->n_row) {
1752 for (i = tab->n_dead; i < tab->n_col; ++i) {
1753 var = var_from_col(tab, i);
1754 if (var->marked)
1755 break;
1756 }
1757 if (i == tab->n_col)
1758 break;
1759 }
1760 var->marked = 0;
1761 n_marked--;
1762 if (sign_of_max(tab, var) == 0)
1763 close_row(tab, var);
1764 else if (!tab->rational && !at_least_one(tab, var)) {
1765 tab = cut_to_hyperplane(tab, var);
1766 return isl_tab_detect_equalities(tab);
1767 }
1768 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1769 var = isl_tab_var_from_row(tab, i);
1770 if (!var->marked)
1771 continue;
1772 if (may_be_equality(tab, i))
1773 continue;
1774 var->marked = 0;
1775 n_marked--;
1776 }
1777 }
1778
1779 return tab;
1780 }
1781
1782 /* Check for (near) redundant constraints.
1783 * A constraint is redundant if it is non-negative and if
1784 * its minimal value (temporarily ignoring the non-negativity) is either
1785 * - zero (in case of rational tableaus), or
1786 * - strictly larger than -1 (in case of integer tableaus)
1787 *
1788 * We first mark all non-redundant and non-dead variables that
1789 * are not frozen and not obviously negatively unbounded.
1790 * Then we iterate over all marked variables if they can attain
1791 * any values smaller than zero or at most negative one.
1792 * If not, we mark the row as being redundant (assuming it hasn't
1793 * been detected as being obviously redundant in the mean time).
1794 */
1795 struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab)
1796 {
1797 int i;
1798 unsigned n_marked;
1799
1800 if (!tab)
1801 return NULL;
1802 if (tab->empty)
1803 return tab;
1804 if (tab->n_redundant == tab->n_row)
1805 return tab;
1806
1807 n_marked = 0;
1808 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1809 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
1810 var->marked = !var->frozen && var->is_nonneg;
1811 if (var->marked)
1812 n_marked++;
1813 }
1814 for (i = tab->n_dead; i < tab->n_col; ++i) {
1815 struct isl_tab_var *var = var_from_col(tab, i);
1816 var->marked = !var->frozen && var->is_nonneg &&
1817 !min_is_manifestly_unbounded(tab, var);
1818 if (var->marked)
1819 n_marked++;
1820 }
1821 while (n_marked) {
1822 struct isl_tab_var *var;
1823 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1824 var = isl_tab_var_from_row(tab, i);
1825 if (var->marked)
1826 break;
1827 }
1828 if (i == tab->n_row) {
1829 for (i = tab->n_dead; i < tab->n_col; ++i) {
1830 var = var_from_col(tab, i);
1831 if (var->marked)
1832 break;
1833 }
1834 if (i == tab->n_col)
1835 break;
1836 }
1837 var->marked = 0;
1838 n_marked--;
1839 if ((tab->rational ? (sign_of_min(tab, var) >= 0)
1840 : !isl_tab_min_at_most_neg_one(tab, var)) &&
1841 !var->is_redundant)
1842 isl_tab_mark_redundant(tab, var->index);
1843 for (i = tab->n_dead; i < tab->n_col; ++i) {
1844 var = var_from_col(tab, i);
1845 if (!var->marked)
1846 continue;
1847 if (!min_is_manifestly_unbounded(tab, var))
1848 continue;
1849 var->marked = 0;
1850 n_marked--;
1851 }
1852 }
1853
1854 return tab;
1855 }
1856
1857 int isl_tab_is_equality(struct isl_tab *tab, int con)
1858 {
1859 int row;
1860 unsigned off;
1861
1862 if (!tab)
1863 return -1;
1864 if (tab->con[con].is_zero)
1865 return 1;
1866 if (tab->con[con].is_redundant)
1867 return 0;
1868 if (!tab->con[con].is_row)
1869 return tab->con[con].index < tab->n_dead;
1870
1871 row = tab->con[con].index;
1872
1873 off = 2 + tab->M;
1874 return isl_int_is_zero(tab->mat->row[row][1]) &&
1875 isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
1876 tab->n_col - tab->n_dead) == -1;
1877 }
1878
1879 /* Return the minimial value of the affine expression "f" with denominator
1880 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
1881 * the expression cannot attain arbitrarily small values.
1882 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
1883 * The return value reflects the nature of the result (empty, unbounded,
1884 * minmimal value returned in *opt).
1885 */
1886 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
1887 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
1888 unsigned flags)
1889 {
1890 int r;
1891 enum isl_lp_result res = isl_lp_ok;
1892 struct isl_tab_var *var;
1893 struct isl_tab_undo *snap;
1894
1895 if (tab->empty)
1896 return isl_lp_empty;
1897
1898 snap = isl_tab_snap(tab);
1899 r = isl_tab_add_row(tab, f);
1900 if (r < 0)
1901 return isl_lp_error;
1902 var = &tab->con[r];
1903 isl_int_mul(tab->mat->row[var->index][0],
1904 tab->mat->row[var->index][0], denom);
1905 for (;;) {
1906 int row, col;
1907 find_pivot(tab, var, var, -1, &row, &col);
1908 if (row == var->index) {
1909 res = isl_lp_unbounded;
1910 break;
1911 }
1912 if (row == -1)
1913 break;
1914 isl_tab_pivot(tab, row, col);
1915 }
1916 if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
1917 int i;
1918
1919 isl_vec_free(tab->dual);
1920 tab->dual = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_con);
1921 if (!tab->dual)
1922 return isl_lp_error;
1923 isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
1924 for (i = 0; i < tab->n_con; ++i) {
1925 int pos;
1926 if (tab->con[i].is_row) {
1927 isl_int_set_si(tab->dual->el[1 + i], 0);
1928 continue;
1929 }
1930 pos = 2 + tab->M + tab->con[i].index;
1931 if (tab->con[i].negated)
1932 isl_int_neg(tab->dual->el[1 + i],
1933 tab->mat->row[var->index][pos]);
1934 else
1935 isl_int_set(tab->dual->el[1 + i],
1936 tab->mat->row[var->index][pos]);
1937 }
1938 }
1939 if (opt && res == isl_lp_ok) {
1940 if (opt_denom) {
1941 isl_int_set(*opt, tab->mat->row[var->index][1]);
1942 isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
1943 } else
1944 isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
1945 tab->mat->row[var->index][0]);
1946 }
1947 if (isl_tab_rollback(tab, snap) < 0)
1948 return isl_lp_error;
1949 return res;
1950 }
1951
1952 int isl_tab_is_redundant(struct isl_tab *tab, int con)
1953 {
1954 int row;
1955 unsigned n_col;
1956
1957 if (!tab)
1958 return -1;
1959 if (tab->con[con].is_zero)
1960 return 0;
1961 if (tab->con[con].is_redundant)
1962 return 1;
1963 return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
1964 }
1965
1966 /* Take a snapshot of the tableau that can be restored by s call to
1967 * isl_tab_rollback.
1968 */
1969 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
1970 {
1971 if (!tab)
1972 return NULL;
1973 tab->need_undo = 1;
1974 return tab->top;
1975 }
1976
1977 /* Undo the operation performed by isl_tab_relax.
1978 */
1979 static void unrelax(struct isl_tab *tab, struct isl_tab_var *var)
1980 {
1981 unsigned off = 2 + tab->M;
1982
1983 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
1984 to_row(tab, var, 1);
1985
1986 if (var->is_row)
1987 isl_int_sub(tab->mat->row[var->index][1],
1988 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
1989 else {
1990 int i;
1991
1992 for (i = 0; i < tab->n_row; ++i) {
1993 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
1994 continue;
1995 isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
1996 tab->mat->row[i][off + var->index]);
1997 }
1998
1999 }
2000 }
2001
2002 static void perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
2003 {
2004 struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
2005 switch(undo->type) {
2006 case isl_tab_undo_nonneg:
2007 var->is_nonneg = 0;
2008 break;
2009 case isl_tab_undo_redundant:
2010 var->is_redundant = 0;
2011 tab->n_redundant--;
2012 break;
2013 case isl_tab_undo_zero:
2014 var->is_zero = 0;
2015 tab->n_dead--;
2016 break;
2017 case isl_tab_undo_allocate:
2018 if (undo->u.var_index >= 0) {
2019 isl_assert(tab->mat->ctx, !var->is_row, return);
2020 drop_col(tab, var->index);
2021 break;
2022 }
2023 if (!var->is_row) {
2024 if (!max_is_manifestly_unbounded(tab, var))
2025 to_row(tab, var, 1);
2026 else if (!min_is_manifestly_unbounded(tab, var))
2027 to_row(tab, var, -1);
2028 else
2029 to_row(tab, var, 0);
2030 }
2031 drop_row(tab, var->index);
2032 break;
2033 case isl_tab_undo_relax:
2034 unrelax(tab, var);
2035 break;
2036 }
2037 }
2038
2039 /* Restore the tableau to the state where the basic variables
2040 * are those in "col_var".
2041 * We first construct a list of variables that are currently in
2042 * the basis, but shouldn't. Then we iterate over all variables
2043 * that should be in the basis and for each one that is currently
2044 * not in the basis, we exchange it with one of the elements of the
2045 * list constructed before.
2046 * We can always find an appropriate variable to pivot with because
2047 * the current basis is mapped to the old basis by a non-singular
2048 * matrix and so we can never end up with a zero row.
2049 */
2050 static int restore_basis(struct isl_tab *tab, int *col_var)
2051 {
2052 int i, j;
2053 int n_extra = 0;
2054 int *extra = NULL; /* current columns that contain bad stuff */
2055 unsigned off = 2 + tab->M;
2056
2057 extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
2058 if (!extra)
2059 goto error;
2060 for (i = 0; i < tab->n_col; ++i) {
2061 for (j = 0; j < tab->n_col; ++j)
2062 if (tab->col_var[i] == col_var[j])
2063 break;
2064 if (j < tab->n_col)
2065 continue;
2066 extra[n_extra++] = i;
2067 }
2068 for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
2069 struct isl_tab_var *var;
2070 int row;
2071
2072 for (j = 0; j < tab->n_col; ++j)
2073 if (col_var[i] == tab->col_var[j])
2074 break;
2075 if (j < tab->n_col)
2076 continue;
2077 var = var_from_index(tab, col_var[i]);
2078 row = var->index;
2079 for (j = 0; j < n_extra; ++j)
2080 if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
2081 break;
2082 isl_assert(tab->mat->ctx, j < n_extra, goto error);
2083 isl_tab_pivot(tab, row, extra[j]);
2084 extra[j] = extra[--n_extra];
2085 }
2086
2087 free(extra);
2088 free(col_var);
2089 return 0;
2090 error:
2091 free(extra);
2092 free(col_var);
2093 return -1;
2094 }
2095
2096 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
2097 {
2098 switch (undo->type) {
2099 case isl_tab_undo_empty:
2100 tab->empty = 0;
2101 break;
2102 case isl_tab_undo_nonneg:
2103 case isl_tab_undo_redundant:
2104 case isl_tab_undo_zero:
2105 case isl_tab_undo_allocate:
2106 case isl_tab_undo_relax:
2107 perform_undo_var(tab, undo);
2108 break;
2109 case isl_tab_undo_bset_eq:
2110 isl_basic_set_free_equality(tab->bset, 1);
2111 break;
2112 case isl_tab_undo_bset_ineq:
2113 isl_basic_set_free_inequality(tab->bset, 1);
2114 break;
2115 case isl_tab_undo_bset_div:
2116 isl_basic_set_free_div(tab->bset, 1);
2117 if (tab->samples)
2118 tab->samples->n_col--;
2119 break;
2120 case isl_tab_undo_saved_basis:
2121 if (restore_basis(tab, undo->u.col_var) < 0)
2122 return -1;
2123 break;
2124 case isl_tab_undo_drop_sample:
2125 tab->n_outside--;
2126 break;
2127 default:
2128 isl_assert(tab->mat->ctx, 0, return -1);
2129 }
2130 return 0;
2131 }
2132
2133 /* Return the tableau to the state it was in when the snapshot "snap"
2134 * was taken.
2135 */
2136 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
2137 {
2138 struct isl_tab_undo *undo, *next;
2139
2140 if (!tab)
2141 return -1;
2142
2143 tab->in_undo = 1;
2144 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
2145 next = undo->next;
2146 if (undo == snap)
2147 break;
2148 if (perform_undo(tab, undo) < 0) {
2149 free_undo(tab);
2150 tab->in_undo = 0;
2151 return -1;
2152 }
2153 free(undo);
2154 }
2155 tab->in_undo = 0;
2156 tab->top = undo;
2157 if (!undo)
2158 return -1;
2159 return 0;
2160 }
2161
2162 /* The given row "row" represents an inequality violated by all
2163 * points in the tableau. Check for some special cases of such
2164 * separating constraints.
2165 * In particular, if the row has been reduced to the constant -1,
2166 * then we know the inequality is adjacent (but opposite) to
2167 * an equality in the tableau.
2168 * If the row has been reduced to r = -1 -r', with r' an inequality
2169 * of the tableau, then the inequality is adjacent (but opposite)
2170 * to the inequality r'.
2171 */
2172 static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
2173 {
2174 int pos;
2175 unsigned off = 2 + tab->M;
2176
2177 if (tab->rational)
2178 return isl_ineq_separate;
2179
2180 if (!isl_int_is_one(tab->mat->row[row][0]))
2181 return isl_ineq_separate;
2182 if (!isl_int_is_negone(tab->mat->row[row][1]))
2183 return isl_ineq_separate;
2184
2185 pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
2186 tab->n_col - tab->n_dead);
2187 if (pos == -1)
2188 return isl_ineq_adj_eq;
2189
2190 if (!isl_int_is_negone(tab->mat->row[row][off + tab->n_dead + pos]))
2191 return isl_ineq_separate;
2192
2193 pos = isl_seq_first_non_zero(
2194 tab->mat->row[row] + off + tab->n_dead + pos + 1,
2195 tab->n_col - tab->n_dead - pos - 1);
2196
2197 return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
2198 }
2199
2200 /* Check the effect of inequality "ineq" on the tableau "tab".
2201 * The result may be
2202 * isl_ineq_redundant: satisfied by all points in the tableau
2203 * isl_ineq_separate: satisfied by no point in the tableau
2204 * isl_ineq_cut: satisfied by some by not all points
2205 * isl_ineq_adj_eq: adjacent to an equality
2206 * isl_ineq_adj_ineq: adjacent to an inequality.
2207 */
2208 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
2209 {
2210 enum isl_ineq_type type = isl_ineq_error;
2211 struct isl_tab_undo *snap = NULL;
2212 int con;
2213 int row;
2214
2215 if (!tab)
2216 return isl_ineq_error;
2217
2218 if (isl_tab_extend_cons(tab, 1) < 0)
2219 return isl_ineq_error;
2220
2221 snap = isl_tab_snap(tab);
2222
2223 con = isl_tab_add_row(tab, ineq);
2224 if (con < 0)
2225 goto error;
2226
2227 row = tab->con[con].index;
2228 if (isl_tab_row_is_redundant(tab, row))
2229 type = isl_ineq_redundant;
2230 else if (isl_int_is_neg(tab->mat->row[row][1]) &&
2231 (tab->rational ||
2232 isl_int_abs_ge(tab->mat->row[row][1],
2233 tab->mat->row[row][0]))) {
2234 if (at_least_zero(tab, &tab->con[con]))
2235 type = isl_ineq_cut;
2236 else
2237 type = separation_type(tab, row);
2238 } else if (tab->rational ? (sign_of_min(tab, &tab->con[con]) < 0)
2239 : isl_tab_min_at_most_neg_one(tab, &tab->con[con]))
2240 type = isl_ineq_cut;
2241 else
2242 type = isl_ineq_redundant;
2243
2244 if (isl_tab_rollback(tab, snap))
2245 return isl_ineq_error;
2246 return type;
2247 error:
2248 isl_tab_rollback(tab, snap);
2249 return isl_ineq_error;
2250 }
2251
2252 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent)
2253 {
2254 unsigned r, c;
2255 int i;
2256
2257 if (!tab) {
2258 fprintf(out, "%*snull tab\n", indent, "");
2259 return;
2260 }
2261 fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
2262 tab->n_redundant, tab->n_dead);
2263 if (tab->rational)
2264 fprintf(out, ", rational");
2265 if (tab->empty)
2266 fprintf(out, ", empty");
2267 fprintf(out, "\n");
2268 fprintf(out, "%*s[", indent, "");
2269 for (i = 0; i < tab->n_var; ++i) {
2270 if (i)
2271 fprintf(out, (i == tab->n_param ||
2272 i == tab->n_var - tab->n_div) ? "; "
2273 : ", ");
2274 fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
2275 tab->var[i].index,
2276 tab->var[i].is_zero ? " [=0]" :
2277 tab->var[i].is_redundant ? " [R]" : "");
2278 }
2279 fprintf(out, "]\n");
2280 fprintf(out, "%*s[", indent, "");
2281 for (i = 0; i < tab->n_con; ++i) {
2282 if (i)
2283 fprintf(out, ", ");
2284 fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
2285 tab->con[i].index,
2286 tab->con[i].is_zero ? " [=0]" :
2287 tab->con[i].is_redundant ? " [R]" : "");
2288 }
2289 fprintf(out, "]\n");
2290 fprintf(out, "%*s[", indent, "");
2291 for (i = 0; i < tab->n_row; ++i) {
2292 const char *sign = "";
2293 if (i)
2294 fprintf(out, ", ");
2295 if (tab->row_sign) {
2296 if (tab->row_sign[i] == isl_tab_row_unknown)
2297 sign = "?";
2298 else if (tab->row_sign[i] == isl_tab_row_neg)
2299 sign = "-";
2300 else if (tab->row_sign[i] == isl_tab_row_pos)
2301 sign = "+";
2302 else
2303 sign = "+-";
2304 }
2305 fprintf(out, "r%d: %d%s%s", i, tab->row_var[i],
2306 isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
2307 }
2308 fprintf(out, "]\n");
2309 fprintf(out, "%*s[", indent, "");
2310 for (i = 0; i < tab->n_col; ++i) {
2311 if (i)
2312 fprintf(out, ", ");
2313 fprintf(out, "c%d: %d%s", i, tab->col_var[i],
2314 var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
2315 }
2316 fprintf(out, "]\n");
2317 r = tab->mat->n_row;
2318 tab->mat->n_row = tab->n_row;
2319 c = tab->mat->n_col;
2320 tab->mat->n_col = 2 + tab->M + tab->n_col;
2321 isl_mat_dump(tab->mat, out, indent);
2322 tab->mat->n_row = r;
2323 tab->mat->n_col = c;
2324 if (tab->bset)
2325 isl_basic_set_dump(tab->bset, out, indent);
2326 }
Integer set library