?  search:
summary | log | graphiclog1 | graphiclog2 | commit | commitdiff | tree | refs | edit | fork
blame | history | raw | HEAD
isl_basic_map_apply_{domain,range}: drop redundant divs in result
[isl.git] / isl_tab.c
blobff6ed85e65a47b8950350fdaba21a4679e6f8859
1 #include "isl_mat.h"
2 #include "isl_map_private.h"
3 #include "isl_tab.h"
4
5 /*
6 * The implementation of tableaus in this file was inspired by Section 8
7 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
8 * prover for program checking".
9 */
10
11 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
12 unsigned n_row, unsigned n_var, unsigned M)
13 {
14 int i;
15 struct isl_tab *tab;
16 unsigned off = 2 + M;
17
18 tab = isl_calloc_type(ctx, struct isl_tab);
19 if (!tab)
20 return NULL;
21 tab->mat = isl_mat_alloc(ctx, n_row, off + n_var);
22 if (!tab->mat)
23 goto error;
24 tab->var = isl_alloc_array(ctx, struct isl_tab_var, n_var);
25 if (!tab->var)
26 goto error;
27 tab->con = isl_alloc_array(ctx, struct isl_tab_var, n_row);
28 if (!tab->con)
29 goto error;
30 tab->col_var = isl_alloc_array(ctx, int, n_var);
31 if (!tab->col_var)
32 goto error;
33 tab->row_var = isl_alloc_array(ctx, int, n_row);
34 if (!tab->row_var)
35 goto error;
36 for (i = 0; i < n_var; ++i) {
37 tab->var[i].index = i;
38 tab->var[i].is_row = 0;
39 tab->var[i].is_nonneg = 0;
40 tab->var[i].is_zero = 0;
41 tab->var[i].is_redundant = 0;
42 tab->var[i].frozen = 0;
43 tab->var[i].negated = 0;
44 tab->col_var[i] = i;
45 }
46 tab->n_row = 0;
47 tab->n_con = 0;
48 tab->n_eq = 0;
49 tab->max_con = n_row;
50 tab->n_col = n_var;
51 tab->n_var = n_var;
52 tab->max_var = n_var;
53 tab->n_param = 0;
54 tab->n_div = 0;
55 tab->n_dead = 0;
56 tab->n_redundant = 0;
57 tab->need_undo = 0;
58 tab->rational = 0;
59 tab->empty = 0;
60 tab->in_undo = 0;
61 tab->M = M;
62 tab->bottom.type = isl_tab_undo_bottom;
63 tab->bottom.next = NULL;
64 tab->top = &tab->bottom;
65 return tab;
66 error:
67 isl_tab_free(tab);
68 return NULL;
69 }
70
71 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new)
72 {
73 unsigned off = 2 + tab->M;
74 if (tab->max_con < tab->n_con + n_new) {
75 struct isl_tab_var *con;
76
77 con = isl_realloc_array(tab->mat->ctx, tab->con,
78 struct isl_tab_var, tab->max_con + n_new);
79 if (!con)
80 return -1;
81 tab->con = con;
82 tab->max_con += n_new;
83 }
84 if (tab->mat->n_row < tab->n_row + n_new) {
85 int *row_var;
86
87 tab->mat = isl_mat_extend(tab->mat,
88 tab->n_row + n_new, off + tab->n_col);
89 if (!tab->mat)
90 return -1;
91 row_var = isl_realloc_array(tab->mat->ctx, tab->row_var,
92 int, tab->mat->n_row);
93 if (!row_var)
94 return -1;
95 tab->row_var = row_var;
96 if (tab->row_sign) {
97 enum isl_tab_row_sign *s;
98 s = isl_realloc_array(tab->mat->ctx, tab->row_sign,
99 enum isl_tab_row_sign, tab->mat->n_row);
100 if (!s)
101 return -1;
102 tab->row_sign = s;
103 }
104 }
105 return 0;
106 }
107
108 /* Make room for at least n_new extra variables.
109 * Return -1 if anything went wrong.
110 */
111 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new)
112 {
113 struct isl_tab_var *var;
114 unsigned off = 2 + tab->M;
115
116 if (tab->max_var < tab->n_var + n_new) {
117 var = isl_realloc_array(tab->mat->ctx, tab->var,
118 struct isl_tab_var, tab->n_var + n_new);
119 if (!var)
120 return -1;
121 tab->var = var;
122 tab->max_var += n_new;
123 }
124
125 if (tab->mat->n_col < off + tab->n_col + n_new) {
126 int *p;
127
128 tab->mat = isl_mat_extend(tab->mat,
129 tab->mat->n_row, off + tab->n_col + n_new);
130 if (!tab->mat)
131 return -1;
132 p = isl_realloc_array(tab->mat->ctx, tab->col_var,
133 int, tab->mat->n_col);
134 if (!p)
135 return -1;
136 tab->col_var = p;
137 }
138
139 return 0;
140 }
141
142 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new)
143 {
144 if (isl_tab_extend_cons(tab, n_new) >= 0)
145 return tab;
146
147 isl_tab_free(tab);
148 return NULL;
149 }
150
151 static void free_undo(struct isl_tab *tab)
152 {
153 struct isl_tab_undo *undo, *next;
154
155 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
156 next = undo->next;
157 free(undo);
158 }
159 tab->top = undo;
160 }
161
162 void isl_tab_free(struct isl_tab *tab)
163 {
164 if (!tab)
165 return;
166 free_undo(tab);
167 isl_mat_free(tab->mat);
168 isl_vec_free(tab->dual);
169 isl_basic_set_free(tab->bset);
170 free(tab->var);
171 free(tab->con);
172 free(tab->row_var);
173 free(tab->col_var);
174 free(tab->row_sign);
175 isl_mat_free(tab->samples);
176 free(tab);
177 }
178
179 struct isl_tab *isl_tab_dup(struct isl_tab *tab)
180 {
181 int i;
182 struct isl_tab *dup;
183
184 if (!tab)
185 return NULL;
186
187 dup = isl_calloc_type(tab->ctx, struct isl_tab);
188 if (!dup)
189 return NULL;
190 dup->mat = isl_mat_dup(tab->mat);
191 if (!dup->mat)
192 goto error;
193 dup->var = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_var);
194 if (!dup->var)
195 goto error;
196 for (i = 0; i < tab->n_var; ++i)
197 dup->var[i] = tab->var[i];
198 dup->con = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_con);
199 if (!dup->con)
200 goto error;
201 for (i = 0; i < tab->n_con; ++i)
202 dup->con[i] = tab->con[i];
203 dup->col_var = isl_alloc_array(tab->ctx, int, tab->mat->n_col);
204 if (!dup->col_var)
205 goto error;
206 for (i = 0; i < tab->n_var; ++i)
207 dup->col_var[i] = tab->col_var[i];
208 dup->row_var = isl_alloc_array(tab->ctx, int, tab->mat->n_row);
209 if (!dup->row_var)
210 goto error;
211 for (i = 0; i < tab->n_row; ++i)
212 dup->row_var[i] = tab->row_var[i];
213 if (tab->row_sign) {
214 dup->row_sign = isl_alloc_array(tab->ctx, enum isl_tab_row_sign,
215 tab->mat->n_row);
216 if (!dup->row_sign)
217 goto error;
218 for (i = 0; i < tab->n_row; ++i)
219 dup->row_sign[i] = tab->row_sign[i];
220 }
221 if (tab->samples) {
222 dup->samples = isl_mat_dup(tab->samples);
223 if (!dup->samples)
224 goto error;
225 dup->n_sample = tab->n_sample;
226 dup->n_outside = tab->n_outside;
227 }
228 dup->n_row = tab->n_row;
229 dup->n_con = tab->n_con;
230 dup->n_eq = tab->n_eq;
231 dup->max_con = tab->max_con;
232 dup->n_col = tab->n_col;
233 dup->n_var = tab->n_var;
234 dup->max_var = tab->max_var;
235 dup->n_param = tab->n_param;
236 dup->n_div = tab->n_div;
237 dup->n_dead = tab->n_dead;
238 dup->n_redundant = tab->n_redundant;
239 dup->rational = tab->rational;
240 dup->empty = tab->empty;
241 dup->need_undo = 0;
242 dup->in_undo = 0;
243 dup->M = tab->M;
244 dup->bottom.type = isl_tab_undo_bottom;
245 dup->bottom.next = NULL;
246 dup->top = &dup->bottom;
247 return dup;
248 error:
249 isl_tab_free(dup);
250 return NULL;
251 }
252
253 static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i)
254 {
255 if (i >= 0)
256 return &tab->var[i];
257 else
258 return &tab->con[~i];
259 }
260
261 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
262 {
263 return var_from_index(tab, tab->row_var[i]);
264 }
265
266 static struct isl_tab_var *var_from_col(struct isl_tab *tab, int i)
267 {
268 return var_from_index(tab, tab->col_var[i]);
269 }
270
271 /* Check if there are any upper bounds on column variable "var",
272 * i.e., non-negative rows where var appears with a negative coefficient.
273 * Return 1 if there are no such bounds.
274 */
275 static int max_is_manifestly_unbounded(struct isl_tab *tab,
276 struct isl_tab_var *var)
277 {
278 int i;
279 unsigned off = 2 + tab->M;
280
281 if (var->is_row)
282 return 0;
283 for (i = tab->n_redundant; i < tab->n_row; ++i) {
284 if (!isl_int_is_neg(tab->mat->row[i][off + var->index]))
285 continue;
286 if (isl_tab_var_from_row(tab, i)->is_nonneg)
287 return 0;
288 }
289 return 1;
290 }
291
292 /* Check if there are any lower bounds on column variable "var",
293 * i.e., non-negative rows where var appears with a positive coefficient.
294 * Return 1 if there are no such bounds.
295 */
296 static int min_is_manifestly_unbounded(struct isl_tab *tab,
297 struct isl_tab_var *var)
298 {
299 int i;
300 unsigned off = 2 + tab->M;
301
302 if (var->is_row)
303 return 0;
304 for (i = tab->n_redundant; i < tab->n_row; ++i) {
305 if (!isl_int_is_pos(tab->mat->row[i][off + var->index]))
306 continue;
307 if (isl_tab_var_from_row(tab, i)->is_nonneg)
308 return 0;
309 }
310 return 1;
311 }
312
313 static int row_cmp(struct isl_tab *tab, int r1, int r2, int c, isl_int t)
314 {
315 unsigned off = 2 + tab->M;
316
317 if (tab->M) {
318 int s;
319 isl_int_mul(t, tab->mat->row[r1][2], tab->mat->row[r2][off+c]);
320 isl_int_submul(t, tab->mat->row[r2][2], tab->mat->row[r1][off+c]);
321 s = isl_int_sgn(t);
322 if (s)
323 return s;
324 }
325 isl_int_mul(t, tab->mat->row[r1][1], tab->mat->row[r2][off + c]);
326 isl_int_submul(t, tab->mat->row[r2][1], tab->mat->row[r1][off + c]);
327 return isl_int_sgn(t);
328 }
329
330 /* Given the index of a column "c", return the index of a row
331 * that can be used to pivot the column in, with either an increase
332 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
333 * If "var" is not NULL, then the row returned will be different from
334 * the one associated with "var".
335 *
336 * Each row in the tableau is of the form
337 *
338 * x_r = a_r0 + \sum_i a_ri x_i
339 *
340 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
341 * impose any limit on the increase or decrease in the value of x_c
342 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
343 * for the row with the smallest (most stringent) such bound.
344 * Note that the common denominator of each row drops out of the fraction.
345 * To check if row j has a smaller bound than row r, i.e.,
346 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
347 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
348 * where -sign(a_jc) is equal to "sgn".
349 */
350 static int pivot_row(struct isl_tab *tab,
351 struct isl_tab_var *var, int sgn, int c)
352 {
353 int j, r, tsgn;
354 isl_int t;
355 unsigned off = 2 + tab->M;
356
357 isl_int_init(t);
358 r = -1;
359 for (j = tab->n_redundant; j < tab->n_row; ++j) {
360 if (var && j == var->index)
361 continue;
362 if (!isl_tab_var_from_row(tab, j)->is_nonneg)
363 continue;
364 if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
365 continue;
366 if (r < 0) {
367 r = j;
368 continue;
369 }
370 tsgn = sgn * row_cmp(tab, r, j, c, t);
371 if (tsgn < 0 || (tsgn == 0 &&
372 tab->row_var[j] < tab->row_var[r]))
373 r = j;
374 }
375 isl_int_clear(t);
376 return r;
377 }
378
379 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
380 * (sgn < 0) the value of row variable var.
381 * If not NULL, then skip_var is a row variable that should be ignored
382 * while looking for a pivot row. It is usually equal to var.
383 *
384 * As the given row in the tableau is of the form
385 *
386 * x_r = a_r0 + \sum_i a_ri x_i
387 *
388 * we need to find a column such that the sign of a_ri is equal to "sgn"
389 * (such that an increase in x_i will have the desired effect) or a
390 * column with a variable that may attain negative values.
391 * If a_ri is positive, then we need to move x_i in the same direction
392 * to obtain the desired effect. Otherwise, x_i has to move in the
393 * opposite direction.
394 */
395 static void find_pivot(struct isl_tab *tab,
396 struct isl_tab_var *var, struct isl_tab_var *skip_var,
397 int sgn, int *row, int *col)
398 {
399 int j, r, c;
400 isl_int *tr;
401
402 *row = *col = -1;
403
404 isl_assert(tab->mat->ctx, var->is_row, return);
405 tr = tab->mat->row[var->index] + 2 + tab->M;
406
407 c = -1;
408 for (j = tab->n_dead; j < tab->n_col; ++j) {
409 if (isl_int_is_zero(tr[j]))
410 continue;
411 if (isl_int_sgn(tr[j]) != sgn &&
412 var_from_col(tab, j)->is_nonneg)
413 continue;
414 if (c < 0 || tab->col_var[j] < tab->col_var[c])
415 c = j;
416 }
417 if (c < 0)
418 return;
419
420 sgn *= isl_int_sgn(tr[c]);
421 r = pivot_row(tab, skip_var, sgn, c);
422 *row = r < 0 ? var->index : r;
423 *col = c;
424 }
425
426 /* Return 1 if row "row" represents an obviously redundant inequality.
427 * This means
428 * - it represents an inequality or a variable
429 * - that is the sum of a non-negative sample value and a positive
430 * combination of zero or more non-negative variables.
431 */
432 int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
433 {
434 int i;
435 unsigned off = 2 + tab->M;
436
437 if (tab->row_var[row] < 0 && !isl_tab_var_from_row(tab, row)->is_nonneg)
438 return 0;
439
440 if (isl_int_is_neg(tab->mat->row[row][1]))
441 return 0;
442 if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
443 return 0;
444
445 for (i = tab->n_dead; i < tab->n_col; ++i) {
446 if (isl_int_is_zero(tab->mat->row[row][off + i]))
447 continue;
448 if (isl_int_is_neg(tab->mat->row[row][off + i]))
449 return 0;
450 if (!var_from_col(tab, i)->is_nonneg)
451 return 0;
452 }
453 return 1;
454 }
455
456 static void swap_rows(struct isl_tab *tab, int row1, int row2)
457 {
458 int t;
459 t = tab->row_var[row1];
460 tab->row_var[row1] = tab->row_var[row2];
461 tab->row_var[row2] = t;
462 isl_tab_var_from_row(tab, row1)->index = row1;
463 isl_tab_var_from_row(tab, row2)->index = row2;
464 tab->mat = isl_mat_swap_rows(tab->mat, row1, row2);
465
466 if (!tab->row_sign)
467 return;
468 t = tab->row_sign[row1];
469 tab->row_sign[row1] = tab->row_sign[row2];
470 tab->row_sign[row2] = t;
471 }
472
473 static void push_union(struct isl_tab *tab,
474 enum isl_tab_undo_type type, union isl_tab_undo_val u)
475 {
476 struct isl_tab_undo *undo;
477
478 if (!tab->need_undo)
479 return;
480
481 undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
482 if (!undo) {
483 free_undo(tab);
484 tab->top = NULL;
485 return;
486 }
487 undo->type = type;
488 undo->u = u;
489 undo->next = tab->top;
490 tab->top = undo;
491 }
492
493 void isl_tab_push_var(struct isl_tab *tab,
494 enum isl_tab_undo_type type, struct isl_tab_var *var)
495 {
496 union isl_tab_undo_val u;
497 if (var->is_row)
498 u.var_index = tab->row_var[var->index];
499 else
500 u.var_index = tab->col_var[var->index];
501 push_union(tab, type, u);
502 }
503
504 void isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
505 {
506 union isl_tab_undo_val u = { 0 };
507 push_union(tab, type, u);
508 }
509
510 /* Push a record on the undo stack describing the current basic
511 * variables, so that the this state can be restored during rollback.
512 */
513 void isl_tab_push_basis(struct isl_tab *tab)
514 {
515 int i;
516 union isl_tab_undo_val u;
517
518 u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
519 if (!u.col_var) {
520 free_undo(tab);
521 tab->top = NULL;
522 return;
523 }
524 for (i = 0; i < tab->n_col; ++i)
525 u.col_var[i] = tab->col_var[i];
526 push_union(tab, isl_tab_undo_saved_basis, u);
527 }
528
529 /* Mark row with index "row" as being redundant.
530 * If we may need to undo the operation or if the row represents
531 * a variable of the original problem, the row is kept,
532 * but no longer considered when looking for a pivot row.
533 * Otherwise, the row is simply removed.
534 *
535 * The row may be interchanged with some other row. If it
536 * is interchanged with a later row, return 1. Otherwise return 0.
537 * If the rows are checked in order in the calling function,
538 * then a return value of 1 means that the row with the given
539 * row number may now contain a different row that hasn't been checked yet.
540 */
541 int isl_tab_mark_redundant(struct isl_tab *tab, int row)
542 {
543 struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
544 var->is_redundant = 1;
545 isl_assert(tab->mat->ctx, row >= tab->n_redundant, return);
546 if (tab->need_undo || tab->row_var[row] >= 0) {
547 if (tab->row_var[row] >= 0 && !var->is_nonneg) {
548 var->is_nonneg = 1;
549 isl_tab_push_var(tab, isl_tab_undo_nonneg, var);
550 }
551 if (row != tab->n_redundant)
552 swap_rows(tab, row, tab->n_redundant);
553 isl_tab_push_var(tab, isl_tab_undo_redundant, var);
554 tab->n_redundant++;
555 return 0;
556 } else {
557 if (row != tab->n_row - 1)
558 swap_rows(tab, row, tab->n_row - 1);
559 isl_tab_var_from_row(tab, tab->n_row - 1)->index = -1;
560 tab->n_row--;
561 return 1;
562 }
563 }
564
565 struct isl_tab *isl_tab_mark_empty(struct isl_tab *tab)
566 {
567 if (!tab->empty && tab->need_undo)
568 isl_tab_push(tab, isl_tab_undo_empty);
569 tab->empty = 1;
570 return tab;
571 }
572
573 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
574 * the original sign of the pivot element.
575 * We only keep track of row signs during PILP solving and in this case
576 * we only pivot a row with negative sign (meaning the value is always
577 * non-positive) using a positive pivot element.
578 *
579 * For each row j, the new value of the parametric constant is equal to
580 *
581 * a_j0 - a_jc a_r0/a_rc
582 *
583 * where a_j0 is the original parametric constant, a_rc is the pivot element,
584 * a_r0 is the parametric constant of the pivot row and a_jc is the
585 * pivot column entry of the row j.
586 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
587 * remains the same if a_jc has the same sign as the row j or if
588 * a_jc is zero. In all other cases, we reset the sign to "unknown".
589 */
590 static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
591 {
592 int i;
593 struct isl_mat *mat = tab->mat;
594 unsigned off = 2 + tab->M;
595
596 if (!tab->row_sign)
597 return;
598
599 if (tab->row_sign[row] == 0)
600 return;
601 isl_assert(mat->ctx, row_sgn > 0, return);
602 isl_assert(mat->ctx, tab->row_sign[row] == isl_tab_row_neg, return);
603 tab->row_sign[row] = isl_tab_row_pos;
604 for (i = 0; i < tab->n_row; ++i) {
605 int s;
606 if (i == row)
607 continue;
608 s = isl_int_sgn(mat->row[i][off + col]);
609 if (!s)
610 continue;
611 if (!tab->row_sign[i])
612 continue;
613 if (s < 0 && tab->row_sign[i] == isl_tab_row_neg)
614 continue;
615 if (s > 0 && tab->row_sign[i] == isl_tab_row_pos)
616 continue;
617 tab->row_sign[i] = isl_tab_row_unknown;
618 }
619 }
620
621 /* Given a row number "row" and a column number "col", pivot the tableau
622 * such that the associated variables are interchanged.
623 * The given row in the tableau expresses
624 *
625 * x_r = a_r0 + \sum_i a_ri x_i
626 *
627 * or
628 *
629 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
630 *
631 * Substituting this equality into the other rows
632 *
633 * x_j = a_j0 + \sum_i a_ji x_i
634 *
635 * with a_jc \ne 0, we obtain
636 *
637 * 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
638 *
639 * The tableau
640 *
641 * n_rc/d_r n_ri/d_r
642 * n_jc/d_j n_ji/d_j
643 *
644 * where i is any other column and j is any other row,
645 * is therefore transformed into
646 *
647 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
648 * 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)
649 *
650 * The transformation is performed along the following steps
651 *
652 * d_r/n_rc n_ri/n_rc
653 * n_jc/d_j n_ji/d_j
654 *
655 * s(n_rc)d_r/|n_rc| -s(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/(|n_rc| d_j) n_ji/(|n_rc| 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|)/(|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| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
666 *
667 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
668 * 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)
669 *
670 */
671 void isl_tab_pivot(struct isl_tab *tab, int row, int col)
672 {
673 int i, j;
674 int sgn;
675 int t;
676 struct isl_mat *mat = tab->mat;
677 struct isl_tab_var *var;
678 unsigned off = 2 + tab->M;
679
680 isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
681 sgn = isl_int_sgn(mat->row[row][0]);
682 if (sgn < 0) {
683 isl_int_neg(mat->row[row][0], mat->row[row][0]);
684 isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]);
685 } else
686 for (j = 0; j < off - 1 + tab->n_col; ++j) {
687 if (j == off - 1 + col)
688 continue;
689 isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
690 }
691 if (!isl_int_is_one(mat->row[row][0]))
692 isl_seq_normalize(mat->row[row], off + tab->n_col);
693 for (i = 0; i < tab->n_row; ++i) {
694 if (i == row)
695 continue;
696 if (isl_int_is_zero(mat->row[i][off + col]))
697 continue;
698 isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
699 for (j = 0; j < off - 1 + tab->n_col; ++j) {
700 if (j == off - 1 + col)
701 continue;
702 isl_int_mul(mat->row[i][1 + j],
703 mat->row[i][1 + j], mat->row[row][0]);
704 isl_int_addmul(mat->row[i][1 + j],
705 mat->row[i][off + col], mat->row[row][1 + j]);
706 }
707 isl_int_mul(mat->row[i][off + col],
708 mat->row[i][off + col], mat->row[row][off + col]);
709 if (!isl_int_is_one(mat->row[i][0]))
710 isl_seq_normalize(mat->row[i], off + tab->n_col);
711 }
712 t = tab->row_var[row];
713 tab->row_var[row] = tab->col_var[col];
714 tab->col_var[col] = t;
715 var = isl_tab_var_from_row(tab, row);
716 var->is_row = 1;
717 var->index = row;
718 var = var_from_col(tab, col);
719 var->is_row = 0;
720 var->index = col;
721 update_row_sign(tab, row, col, sgn);
722 if (tab->in_undo)
723 return;
724 for (i = tab->n_redundant; i < tab->n_row; ++i) {
725 if (isl_int_is_zero(mat->row[i][off + col]))
726 continue;
727 if (!isl_tab_var_from_row(tab, i)->frozen &&
728 isl_tab_row_is_redundant(tab, i))
729 if (isl_tab_mark_redundant(tab, i))
730 --i;
731 }
732 }
733
734 /* If "var" represents a column variable, then pivot is up (sgn > 0)
735 * or down (sgn < 0) to a row. The variable is assumed not to be
736 * unbounded in the specified direction.
737 * If sgn = 0, then the variable is unbounded in both directions,
738 * and we pivot with any row we can find.
739 */
740 static void to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
741 {
742 int r;
743 unsigned off = 2 + tab->M;
744
745 if (var->is_row)
746 return;
747
748 if (sign == 0) {
749 for (r = tab->n_redundant; r < tab->n_row; ++r)
750 if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
751 break;
752 isl_assert(tab->mat->ctx, r < tab->n_row, return);
753 } else {
754 r = pivot_row(tab, NULL, sign, var->index);
755 isl_assert(tab->mat->ctx, r >= 0, return);
756 }
757
758 isl_tab_pivot(tab, r, var->index);
759 }
760
761 static void check_table(struct isl_tab *tab)
762 {
763 int i;
764
765 if (tab->empty)
766 return;
767 for (i = 0; i < tab->n_row; ++i) {
768 if (!isl_tab_var_from_row(tab, i)->is_nonneg)
769 continue;
770 assert(!isl_int_is_neg(tab->mat->row[i][1]));
771 }
772 }
773
774 /* Return the sign of the maximal value of "var".
775 * If the sign is not negative, then on return from this function,
776 * the sample value will also be non-negative.
777 *
778 * If "var" is manifestly unbounded wrt positive values, we are done.
779 * Otherwise, we pivot the variable up to a row if needed
780 * Then we continue pivoting down until either
781 * - no more down pivots can be performed
782 * - the sample value is positive
783 * - the variable is pivoted into a manifestly unbounded column
784 */
785 static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
786 {
787 int row, col;
788
789 if (max_is_manifestly_unbounded(tab, var))
790 return 1;
791 to_row(tab, var, 1);
792 while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
793 find_pivot(tab, var, var, 1, &row, &col);
794 if (row == -1)
795 return isl_int_sgn(tab->mat->row[var->index][1]);
796 isl_tab_pivot(tab, row, col);
797 if (!var->is_row) /* manifestly unbounded */
798 return 1;
799 }
800 return 1;
801 }
802
803 static int row_is_neg(struct isl_tab *tab, int row)
804 {
805 if (!tab->M)
806 return isl_int_is_neg(tab->mat->row[row][1]);
807 if (isl_int_is_pos(tab->mat->row[row][2]))
808 return 0;
809 if (isl_int_is_neg(tab->mat->row[row][2]))
810 return 1;
811 return isl_int_is_neg(tab->mat->row[row][1]);
812 }
813
814 static int row_sgn(struct isl_tab *tab, int row)
815 {
816 if (!tab->M)
817 return isl_int_sgn(tab->mat->row[row][1]);
818 if (!isl_int_is_zero(tab->mat->row[row][2]))
819 return isl_int_sgn(tab->mat->row[row][2]);
820 else
821 return isl_int_sgn(tab->mat->row[row][1]);
822 }
823
824 /* Perform pivots until the row variable "var" has a non-negative
825 * sample value or until no more upward pivots can be performed.
826 * Return the sign of the sample value after the pivots have been
827 * performed.
828 */
829 static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
830 {
831 int row, col;
832
833 while (row_is_neg(tab, var->index)) {
834 find_pivot(tab, var, var, 1, &row, &col);
835 if (row == -1)
836 break;
837 isl_tab_pivot(tab, row, col);
838 if (!var->is_row) /* manifestly unbounded */
839 return 1;
840 }
841 return row_sgn(tab, var->index);
842 }
843
844 /* Perform pivots until we are sure that the row variable "var"
845 * can attain non-negative values. After return from this
846 * function, "var" is still a row variable, but its sample
847 * value may not be non-negative, even if the function returns 1.
848 */
849 static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
850 {
851 int row, col;
852
853 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
854 find_pivot(tab, var, var, 1, &row, &col);
855 if (row == -1)
856 break;
857 if (row == var->index) /* manifestly unbounded */
858 return 1;
859 isl_tab_pivot(tab, row, col);
860 }
861 return !isl_int_is_neg(tab->mat->row[var->index][1]);
862 }
863
864 /* Return a negative value if "var" can attain negative values.
865 * Return a non-negative value otherwise.
866 *
867 * If "var" is manifestly unbounded wrt negative values, we are done.
868 * Otherwise, if var is in a column, we can pivot it down to a row.
869 * Then we continue pivoting down until either
870 * - the pivot would result in a manifestly unbounded column
871 * => we don't perform the pivot, but simply return -1
872 * - no more down pivots can be performed
873 * - the sample value is negative
874 * If the sample value becomes negative and the variable is supposed
875 * to be nonnegative, then we undo the last pivot.
876 * However, if the last pivot has made the pivoting variable
877 * obviously redundant, then it may have moved to another row.
878 * In that case we look for upward pivots until we reach a non-negative
879 * value again.
880 */
881 static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
882 {
883 int row, col;
884 struct isl_tab_var *pivot_var;
885
886 if (min_is_manifestly_unbounded(tab, var))
887 return -1;
888 if (!var->is_row) {
889 col = var->index;
890 row = pivot_row(tab, NULL, -1, col);
891 pivot_var = var_from_col(tab, col);
892 isl_tab_pivot(tab, row, col);
893 if (var->is_redundant)
894 return 0;
895 if (isl_int_is_neg(tab->mat->row[var->index][1])) {
896 if (var->is_nonneg) {
897 if (!pivot_var->is_redundant &&
898 pivot_var->index == row)
899 isl_tab_pivot(tab, row, col);
900 else
901 restore_row(tab, var);
902 }
903 return -1;
904 }
905 }
906 if (var->is_redundant)
907 return 0;
908 while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
909 find_pivot(tab, var, var, -1, &row, &col);
910 if (row == var->index)
911 return -1;
912 if (row == -1)
913 return isl_int_sgn(tab->mat->row[var->index][1]);
914 pivot_var = var_from_col(tab, col);
915 isl_tab_pivot(tab, row, col);
916 if (var->is_redundant)
917 return 0;
918 }
919 if (var->is_nonneg) {
920 /* pivot back to non-negative value */
921 if (!pivot_var->is_redundant && pivot_var->index == row)
922 isl_tab_pivot(tab, row, col);
923 else
924 restore_row(tab, var);
925 }
926 return -1;
927 }
928
929 static int row_at_most_neg_one(struct isl_tab *tab, int row)
930 {
931 if (tab->M) {
932 if (isl_int_is_pos(tab->mat->row[row][2]))
933 return 0;
934 if (isl_int_is_neg(tab->mat->row[row][2]))
935 return 1;
936 }
937 return isl_int_is_neg(tab->mat->row[row][1]) &&
938 isl_int_abs_ge(tab->mat->row[row][1],
939 tab->mat->row[row][0]);
940 }
941
942 /* Return 1 if "var" can attain values <= -1.
943 * Return 0 otherwise.
944 *
945 * The sample value of "var" is assumed to be non-negative when the
946 * the function is called and will be made non-negative again before
947 * the function returns.
948 */
949 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
950 {
951 int row, col;
952 struct isl_tab_var *pivot_var;
953
954 if (min_is_manifestly_unbounded(tab, var))
955 return 1;
956 if (!var->is_row) {
957 col = var->index;
958 row = pivot_row(tab, NULL, -1, col);
959 pivot_var = var_from_col(tab, col);
960 isl_tab_pivot(tab, row, col);
961 if (var->is_redundant)
962 return 0;
963 if (row_at_most_neg_one(tab, var->index)) {
964 if (var->is_nonneg) {
965 if (!pivot_var->is_redundant &&
966 pivot_var->index == row)
967 isl_tab_pivot(tab, row, col);
968 else
969 restore_row(tab, var);
970 }
971 return 1;
972 }
973 }
974 if (var->is_redundant)
975 return 0;
976 do {
977 find_pivot(tab, var, var, -1, &row, &col);
978 if (row == var->index)
979 return 1;
980 if (row == -1)
981 return 0;
982 pivot_var = var_from_col(tab, col);
983 isl_tab_pivot(tab, row, col);
984 if (var->is_redundant)
985 return 0;
986 } while (!row_at_most_neg_one(tab, var->index));
987 if (var->is_nonneg) {
988 /* pivot back to non-negative value */
989 if (!pivot_var->is_redundant && pivot_var->index == row)
990 isl_tab_pivot(tab, row, col);
991 restore_row(tab, var);
992 }
993 return 1;
994 }
995
996 /* Return 1 if "var" can attain values >= 1.
997 * Return 0 otherwise.
998 */
999 static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
1000 {
1001 int row, col;
1002 isl_int *r;
1003
1004 if (max_is_manifestly_unbounded(tab, var))
1005 return 1;
1006 to_row(tab, var, 1);
1007 r = tab->mat->row[var->index];
1008 while (isl_int_lt(r[1], r[0])) {
1009 find_pivot(tab, var, var, 1, &row, &col);
1010 if (row == -1)
1011 return isl_int_ge(r[1], r[0]);
1012 if (row == var->index) /* manifestly unbounded */
1013 return 1;
1014 isl_tab_pivot(tab, row, col);
1015 }
1016 return 1;
1017 }
1018
1019 static void swap_cols(struct isl_tab *tab, int col1, int col2)
1020 {
1021 int t;
1022 unsigned off = 2 + tab->M;
1023 t = tab->col_var[col1];
1024 tab->col_var[col1] = tab->col_var[col2];
1025 tab->col_var[col2] = t;
1026 var_from_col(tab, col1)->index = col1;
1027 var_from_col(tab, col2)->index = col2;
1028 tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2);
1029 }
1030
1031 /* Mark column with index "col" as representing a zero variable.
1032 * If we may need to undo the operation the column is kept,
1033 * but no longer considered.
1034 * Otherwise, the column is simply removed.
1035 *
1036 * The column may be interchanged with some other column. If it
1037 * is interchanged with a later column, return 1. Otherwise return 0.
1038 * If the columns are checked in order in the calling function,
1039 * then a return value of 1 means that the column with the given
1040 * column number may now contain a different column that
1041 * hasn't been checked yet.
1042 */
1043 int isl_tab_kill_col(struct isl_tab *tab, int col)
1044 {
1045 var_from_col(tab, col)->is_zero = 1;
1046 if (tab->need_undo) {
1047 isl_tab_push_var(tab, isl_tab_undo_zero, var_from_col(tab, col));
1048 if (col != tab->n_dead)
1049 swap_cols(tab, col, tab->n_dead);
1050 tab->n_dead++;
1051 return 0;
1052 } else {
1053 if (col != tab->n_col - 1)
1054 swap_cols(tab, col, tab->n_col - 1);
1055 var_from_col(tab, tab->n_col - 1)->index = -1;
1056 tab->n_col--;
1057 return 1;
1058 }
1059 }
1060
1061 /* Row variable "var" is non-negative and cannot attain any values
1062 * larger than zero. This means that the coefficients of the unrestricted
1063 * column variables are zero and that the coefficients of the non-negative
1064 * column variables are zero or negative.
1065 * Each of the non-negative variables with a negative coefficient can
1066 * then also be written as the negative sum of non-negative variables
1067 * and must therefore also be zero.
1068 */
1069 static void close_row(struct isl_tab *tab, struct isl_tab_var *var)
1070 {
1071 int j;
1072 struct isl_mat *mat = tab->mat;
1073 unsigned off = 2 + tab->M;
1074
1075 isl_assert(tab->mat->ctx, var->is_nonneg, return);
1076 var->is_zero = 1;
1077 for (j = tab->n_dead; j < tab->n_col; ++j) {
1078 if (isl_int_is_zero(mat->row[var->index][off + j]))
1079 continue;
1080 isl_assert(tab->mat->ctx,
1081 isl_int_is_neg(mat->row[var->index][off + j]), return);
1082 if (isl_tab_kill_col(tab, j))
1083 --j;
1084 }
1085 isl_tab_mark_redundant(tab, var->index);
1086 }
1087
1088 /* Add a constraint to the tableau and allocate a row for it.
1089 * Return the index into the constraint array "con".
1090 */
1091 int isl_tab_allocate_con(struct isl_tab *tab)
1092 {
1093 int r;
1094
1095 isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
1096
1097 r = tab->n_con;
1098 tab->con[r].index = tab->n_row;
1099 tab->con[r].is_row = 1;
1100 tab->con[r].is_nonneg = 0;
1101 tab->con[r].is_zero = 0;
1102 tab->con[r].is_redundant = 0;
1103 tab->con[r].frozen = 0;
1104 tab->con[r].negated = 0;
1105 tab->row_var[tab->n_row] = ~r;
1106
1107 tab->n_row++;
1108 tab->n_con++;
1109 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
1110
1111 return r;
1112 }
1113
1114 /* Add a variable to the tableau and allocate a column for it.
1115 * Return the index into the variable array "var".
1116 */
1117 int isl_tab_allocate_var(struct isl_tab *tab)
1118 {
1119 int r;
1120 int i;
1121 unsigned off = 2 + tab->M;
1122
1123 isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
1124 isl_assert(tab->mat->ctx, tab->n_var < tab->max_var, return -1);
1125
1126 r = tab->n_var;
1127 tab->var[r].index = tab->n_col;
1128 tab->var[r].is_row = 0;
1129 tab->var[r].is_nonneg = 0;
1130 tab->var[r].is_zero = 0;
1131 tab->var[r].is_redundant = 0;
1132 tab->var[r].frozen = 0;
1133 tab->var[r].negated = 0;
1134 tab->col_var[tab->n_col] = r;
1135
1136 for (i = 0; i < tab->n_row; ++i)
1137 isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
1138
1139 tab->n_var++;
1140 tab->n_col++;
1141 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]);
1142
1143 return r;
1144 }
1145
1146 /* Add a row to the tableau. The row is given as an affine combination
1147 * of the original variables and needs to be expressed in terms of the
1148 * column variables.
1149 *
1150 * We add each term in turn.
1151 * If r = n/d_r is the current sum and we need to add k x, then
1152 * if x is a column variable, we increase the numerator of
1153 * this column by k d_r
1154 * if x = f/d_x is a row variable, then the new representation of r is
1155 *
1156 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1157 * --- + --- = ------------------- = -------------------
1158 * d_r d_r d_r d_x/g m
1159 *
1160 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1161 */
1162 int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
1163 {
1164 int i;
1165 int r;
1166 isl_int *row;
1167 isl_int a, b;
1168 unsigned off = 2 + tab->M;
1169
1170 r = isl_tab_allocate_con(tab);
1171 if (r < 0)
1172 return -1;
1173
1174 isl_int_init(a);
1175 isl_int_init(b);
1176 row = tab->mat->row[tab->con[r].index];
1177 isl_int_set_si(row[0], 1);
1178 isl_int_set(row[1], line[0]);
1179 isl_seq_clr(row + 2, tab->M + tab->n_col);
1180 for (i = 0; i < tab->n_var; ++i) {
1181 if (tab->var[i].is_zero)
1182 continue;
1183 if (tab->var[i].is_row) {
1184 isl_int_lcm(a,
1185 row[0], tab->mat->row[tab->var[i].index][0]);
1186 isl_int_swap(a, row[0]);
1187 isl_int_divexact(a, row[0], a);
1188 isl_int_divexact(b,
1189 row[0], tab->mat->row[tab->var[i].index][0]);
1190 isl_int_mul(b, b, line[1 + i]);
1191 isl_seq_combine(row + 1, a, row + 1,
1192 b, tab->mat->row[tab->var[i].index] + 1,
1193 1 + tab->M + tab->n_col);
1194 } else
1195 isl_int_addmul(row[off + tab->var[i].index],
1196 line[1 + i], row[0]);
1197 if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
1198 isl_int_submul(row[2], line[1 + i], row[0]);
1199 }
1200 isl_seq_normalize(row, off + tab->n_col);
1201 isl_int_clear(a);
1202 isl_int_clear(b);
1203
1204 if (tab->row_sign)
1205 tab->row_sign[tab->con[r].index] = 0;
1206
1207 return r;
1208 }
1209
1210 static int drop_row(struct isl_tab *tab, int row)
1211 {
1212 isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
1213 if (row != tab->n_row - 1)
1214 swap_rows(tab, row, tab->n_row - 1);
1215 tab->n_row--;
1216 tab->n_con--;
1217 return 0;
1218 }
1219
1220 static int drop_col(struct isl_tab *tab, int col)
1221 {
1222 isl_assert(tab->mat->ctx, tab->col_var[col] == tab->n_var - 1, return -1);
1223 if (col != tab->n_col - 1)
1224 swap_cols(tab, col, tab->n_col - 1);
1225 tab->n_col--;
1226 tab->n_var--;
1227 return 0;
1228 }
1229
1230 /* Add inequality "ineq" and check if it conflicts with the
1231 * previously added constraints or if it is obviously redundant.
1232 */
1233 struct isl_tab *isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
1234 {
1235 int r;
1236 int sgn;
1237
1238 if (!tab)
1239 return NULL;
1240 r = isl_tab_add_row(tab, ineq);
1241 if (r < 0)
1242 goto error;
1243 tab->con[r].is_nonneg = 1;
1244 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1245 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1246 isl_tab_mark_redundant(tab, tab->con[r].index);
1247 return tab;
1248 }
1249
1250 sgn = restore_row(tab, &tab->con[r]);
1251 if (sgn < 0)
1252 return isl_tab_mark_empty(tab);
1253 if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
1254 isl_tab_mark_redundant(tab, tab->con[r].index);
1255 return tab;
1256 error:
1257 isl_tab_free(tab);
1258 return NULL;
1259 }
1260
1261 /* Pivot a non-negative variable down until it reaches the value zero
1262 * and then pivot the variable into a column position.
1263 */
1264 int to_col(struct isl_tab *tab, struct isl_tab_var *var)
1265 {
1266 int i;
1267 int row, col;
1268 unsigned off = 2 + tab->M;
1269
1270 if (!var->is_row)
1271 return;
1272
1273 while (isl_int_is_pos(tab->mat->row[var->index][1])) {
1274 find_pivot(tab, var, NULL, -1, &row, &col);
1275 isl_assert(tab->mat->ctx, row != -1, return -1);
1276 isl_tab_pivot(tab, row, col);
1277 if (!var->is_row)
1278 return;
1279 }
1280
1281 for (i = tab->n_dead; i < tab->n_col; ++i)
1282 if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
1283 break;
1284
1285 isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
1286 isl_tab_pivot(tab, var->index, i);
1287
1288 return 0;
1289 }
1290
1291 /* We assume Gaussian elimination has been performed on the equalities.
1292 * The equalities can therefore never conflict.
1293 * Adding the equalities is currently only really useful for a later call
1294 * to isl_tab_ineq_type.
1295 */
1296 static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
1297 {
1298 int i;
1299 int r;
1300
1301 if (!tab)
1302 return NULL;
1303 r = isl_tab_add_row(tab, eq);
1304 if (r < 0)
1305 goto error;
1306
1307 r = tab->con[r].index;
1308 i = isl_seq_first_non_zero(tab->mat->row[r] + 2 + tab->M + tab->n_dead,
1309 tab->n_col - tab->n_dead);
1310 isl_assert(tab->mat->ctx, i >= 0, goto error);
1311 i += tab->n_dead;
1312 isl_tab_pivot(tab, r, i);
1313 isl_tab_kill_col(tab, i);
1314 tab->n_eq++;
1315
1316 return tab;
1317 error:
1318 isl_tab_free(tab);
1319 return NULL;
1320 }
1321
1322 /* Add an equality that is known to be valid for the given tableau.
1323 */
1324 struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
1325 {
1326 struct isl_tab_var *var;
1327 int i;
1328 int r;
1329
1330 if (!tab)
1331 return NULL;
1332 r = isl_tab_add_row(tab, eq);
1333 if (r < 0)
1334 goto error;
1335
1336 var = &tab->con[r];
1337 r = var->index;
1338 if (isl_int_is_neg(tab->mat->row[r][1])) {
1339 isl_seq_neg(tab->mat->row[r] + 1, tab->mat->row[r] + 1,
1340 1 + tab->n_col);
1341 var->negated = 1;
1342 }
1343 var->is_nonneg = 1;
1344 if (to_col(tab, var) < 0)
1345 goto error;
1346 var->is_nonneg = 0;
1347 isl_tab_kill_col(tab, var->index);
1348
1349 return tab;
1350 error:
1351 isl_tab_free(tab);
1352 return NULL;
1353 }
1354
1355 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap)
1356 {
1357 int i;
1358 struct isl_tab *tab;
1359
1360 if (!bmap)
1361 return NULL;
1362 tab = isl_tab_alloc(bmap->ctx,
1363 isl_basic_map_total_dim(bmap) + bmap->n_ineq + 1,
1364 isl_basic_map_total_dim(bmap), 0);
1365 if (!tab)
1366 return NULL;
1367 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
1368 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1369 return isl_tab_mark_empty(tab);
1370 for (i = 0; i < bmap->n_eq; ++i) {
1371 tab = add_eq(tab, bmap->eq[i]);
1372 if (!tab)
1373 return tab;
1374 }
1375 for (i = 0; i < bmap->n_ineq; ++i) {
1376 tab = isl_tab_add_ineq(tab, bmap->ineq[i]);
1377 if (!tab || tab->empty)
1378 return tab;
1379 }
1380 return tab;
1381 }
1382
1383 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset)
1384 {
1385 return isl_tab_from_basic_map((struct isl_basic_map *)bset);
1386 }
1387
1388 /* Construct a tableau corresponding to the recession cone of "bmap".
1389 */
1390 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_map *bmap)
1391 {
1392 isl_int cst;
1393 int i;
1394 struct isl_tab *tab;
1395
1396 if (!bmap)
1397 return NULL;
1398 tab = isl_tab_alloc(bmap->ctx, bmap->n_eq + bmap->n_ineq,
1399 isl_basic_map_total_dim(bmap), 0);
1400 if (!tab)
1401 return NULL;
1402 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
1403
1404 isl_int_init(cst);
1405 for (i = 0; i < bmap->n_eq; ++i) {
1406 isl_int_swap(bmap->eq[i][0], cst);
1407 tab = add_eq(tab, bmap->eq[i]);
1408 isl_int_swap(bmap->eq[i][0], cst);
1409 if (!tab)
1410 goto done;
1411 }
1412 for (i = 0; i < bmap->n_ineq; ++i) {
1413 int r;
1414 isl_int_swap(bmap->ineq[i][0], cst);
1415 r = isl_tab_add_row(tab, bmap->ineq[i]);
1416 isl_int_swap(bmap->ineq[i][0], cst);
1417 if (r < 0)
1418 goto error;
1419 tab->con[r].is_nonneg = 1;
1420 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1421 }
1422 done:
1423 isl_int_clear(cst);
1424 return tab;
1425 error:
1426 isl_int_clear(cst);
1427 isl_tab_free(tab);
1428 return NULL;
1429 }
1430
1431 /* Assuming "tab" is the tableau of a cone, check if the cone is
1432 * bounded, i.e., if it is empty or only contains the origin.
1433 */
1434 int isl_tab_cone_is_bounded(struct isl_tab *tab)
1435 {
1436 int i;
1437
1438 if (!tab)
1439 return -1;
1440 if (tab->empty)
1441 return 1;
1442 if (tab->n_dead == tab->n_col)
1443 return 1;
1444
1445 for (;;) {
1446 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1447 struct isl_tab_var *var;
1448 var = isl_tab_var_from_row(tab, i);
1449 if (!var->is_nonneg)
1450 continue;
1451 if (sign_of_max(tab, var) != 0)
1452 return 0;
1453 close_row(tab, var);
1454 break;
1455 }
1456 if (tab->n_dead == tab->n_col)
1457 return 1;
1458 if (i == tab->n_row)
1459 return 0;
1460 }
1461 }
1462
1463 int isl_tab_sample_is_integer(struct isl_tab *tab)
1464 {
1465 int i;
1466
1467 if (!tab)
1468 return -1;
1469
1470 for (i = 0; i < tab->n_var; ++i) {
1471 int row;
1472 if (!tab->var[i].is_row)
1473 continue;
1474 row = tab->var[i].index;
1475 if (!isl_int_is_divisible_by(tab->mat->row[row][1],
1476 tab->mat->row[row][0]))
1477 return 0;
1478 }
1479 return 1;
1480 }
1481
1482 static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
1483 {
1484 int i;
1485 struct isl_vec *vec;
1486
1487 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
1488 if (!vec)
1489 return NULL;
1490
1491 isl_int_set_si(vec->block.data[0], 1);
1492 for (i = 0; i < tab->n_var; ++i) {
1493 if (!tab->var[i].is_row)
1494 isl_int_set_si(vec->block.data[1 + i], 0);
1495 else {
1496 int row = tab->var[i].index;
1497 isl_int_divexact(vec->block.data[1 + i],
1498 tab->mat->row[row][1], tab->mat->row[row][0]);
1499 }
1500 }
1501
1502 return vec;
1503 }
1504
1505 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
1506 {
1507 int i;
1508 struct isl_vec *vec;
1509 isl_int m;
1510
1511 if (!tab)
1512 return NULL;
1513
1514 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
1515 if (!vec)
1516 return NULL;
1517
1518 isl_int_init(m);
1519
1520 isl_int_set_si(vec->block.data[0], 1);
1521 for (i = 0; i < tab->n_var; ++i) {
1522 int row;
1523 if (!tab->var[i].is_row) {
1524 isl_int_set_si(vec->block.data[1 + i], 0);
1525 continue;
1526 }
1527 row = tab->var[i].index;
1528 isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
1529 isl_int_divexact(m, tab->mat->row[row][0], m);
1530 isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
1531 isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
1532 isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
1533 }
1534 isl_seq_normalize(vec->block.data, vec->size);
1535
1536 isl_int_clear(m);
1537 return vec;
1538 }
1539
1540 /* Update "bmap" based on the results of the tableau "tab".
1541 * In particular, implicit equalities are made explicit, redundant constraints
1542 * are removed and if the sample value happens to be integer, it is stored
1543 * in "bmap" (unless "bmap" already had an integer sample).
1544 *
1545 * The tableau is assumed to have been created from "bmap" using
1546 * isl_tab_from_basic_map.
1547 */
1548 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
1549 struct isl_tab *tab)
1550 {
1551 int i;
1552 unsigned n_eq;
1553
1554 if (!bmap)
1555 return NULL;
1556 if (!tab)
1557 return bmap;
1558
1559 n_eq = tab->n_eq;
1560 if (tab->empty)
1561 bmap = isl_basic_map_set_to_empty(bmap);
1562 else
1563 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1564 if (isl_tab_is_equality(tab, n_eq + i))
1565 isl_basic_map_inequality_to_equality(bmap, i);
1566 else if (isl_tab_is_redundant(tab, n_eq + i))
1567 isl_basic_map_drop_inequality(bmap, i);
1568 }
1569 if (!tab->rational &&
1570 !bmap->sample && isl_tab_sample_is_integer(tab))
1571 bmap->sample = extract_integer_sample(tab);
1572 return bmap;
1573 }
1574
1575 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
1576 struct isl_tab *tab)
1577 {
1578 return (struct isl_basic_set *)isl_basic_map_update_from_tab(
1579 (struct isl_basic_map *)bset, tab);
1580 }
1581
1582 /* Given a non-negative variable "var", add a new non-negative variable
1583 * that is the opposite of "var", ensuring that var can only attain the
1584 * value zero.
1585 * If var = n/d is a row variable, then the new variable = -n/d.
1586 * If var is a column variables, then the new variable = -var.
1587 * If the new variable cannot attain non-negative values, then
1588 * the resulting tableau is empty.
1589 * Otherwise, we know the value will be zero and we close the row.
1590 */
1591 static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab,
1592 struct isl_tab_var *var)
1593 {
1594 unsigned r;
1595 isl_int *row;
1596 int sgn;
1597 unsigned off = 2 + tab->M;
1598
1599 if (isl_tab_extend_cons(tab, 1) < 0)
1600 goto error;
1601
1602 r = tab->n_con;
1603 tab->con[r].index = tab->n_row;
1604 tab->con[r].is_row = 1;
1605 tab->con[r].is_nonneg = 0;
1606 tab->con[r].is_zero = 0;
1607 tab->con[r].is_redundant = 0;
1608 tab->con[r].frozen = 0;
1609 tab->con[r].negated = 0;
1610 tab->row_var[tab->n_row] = ~r;
1611 row = tab->mat->row[tab->n_row];
1612
1613 if (var->is_row) {
1614 isl_int_set(row[0], tab->mat->row[var->index][0]);
1615 isl_seq_neg(row + 1,
1616 tab->mat->row[var->index] + 1, 1 + tab->n_col);
1617 } else {
1618 isl_int_set_si(row[0], 1);
1619 isl_seq_clr(row + 1, 1 + tab->n_col);
1620 isl_int_set_si(row[off + var->index], -1);
1621 }
1622
1623 tab->n_row++;
1624 tab->n_con++;
1625 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
1626
1627 sgn = sign_of_max(tab, &tab->con[r]);
1628 if (sgn < 0)
1629 return isl_tab_mark_empty(tab);
1630 tab->con[r].is_nonneg = 1;
1631 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1632 /* sgn == 0 */
1633 close_row(tab, &tab->con[r]);
1634
1635 return tab;
1636 error:
1637 isl_tab_free(tab);
1638 return NULL;
1639 }
1640
1641 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
1642 * relax the inequality by one. That is, the inequality r >= 0 is replaced
1643 * by r' = r + 1 >= 0.
1644 * If r is a row variable, we simply increase the constant term by one
1645 * (taking into account the denominator).
1646 * If r is a column variable, then we need to modify each row that
1647 * refers to r = r' - 1 by substituting this equality, effectively
1648 * subtracting the coefficient of the column from the constant.
1649 */
1650 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
1651 {
1652 struct isl_tab_var *var;
1653 unsigned off = 2 + tab->M;
1654
1655 if (!tab)
1656 return NULL;
1657
1658 var = &tab->con[con];
1659
1660 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
1661 to_row(tab, var, 1);
1662
1663 if (var->is_row)
1664 isl_int_add(tab->mat->row[var->index][1],
1665 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
1666 else {
1667 int i;
1668
1669 for (i = 0; i < tab->n_row; ++i) {
1670 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
1671 continue;
1672 isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
1673 tab->mat->row[i][off + var->index]);
1674 }
1675
1676 }
1677
1678 isl_tab_push_var(tab, isl_tab_undo_relax, var);
1679
1680 return tab;
1681 }
1682
1683 struct isl_tab *isl_tab_select_facet(struct isl_tab *tab, int con)
1684 {
1685 if (!tab)
1686 return NULL;
1687
1688 return cut_to_hyperplane(tab, &tab->con[con]);
1689 }
1690
1691 static int may_be_equality(struct isl_tab *tab, int row)
1692 {
1693 unsigned off = 2 + tab->M;
1694 return (tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
1695 : isl_int_lt(tab->mat->row[row][1],
1696 tab->mat->row[row][0])) &&
1697 isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1698 tab->n_col - tab->n_dead) != -1;
1699 }
1700
1701 /* Check for (near) equalities among the constraints.
1702 * A constraint is an equality if it is non-negative and if
1703 * its maximal value is either
1704 * - zero (in case of rational tableaus), or
1705 * - strictly less than 1 (in case of integer tableaus)
1706 *
1707 * We first mark all non-redundant and non-dead variables that
1708 * are not frozen and not obviously not an equality.
1709 * Then we iterate over all marked variables if they can attain
1710 * any values larger than zero or at least one.
1711 * If the maximal value is zero, we mark any column variables
1712 * that appear in the row as being zero and mark the row as being redundant.
1713 * Otherwise, if the maximal value is strictly less than one (and the
1714 * tableau is integer), then we restrict the value to being zero
1715 * by adding an opposite non-negative variable.
1716 */
1717 struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab)
1718 {
1719 int i;
1720 unsigned n_marked;
1721
1722 if (!tab)
1723 return NULL;
1724 if (tab->empty)
1725 return tab;
1726 if (tab->n_dead == tab->n_col)
1727 return tab;
1728
1729 n_marked = 0;
1730 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1731 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
1732 var->marked = !var->frozen && var->is_nonneg &&
1733 may_be_equality(tab, i);
1734 if (var->marked)
1735 n_marked++;
1736 }
1737 for (i = tab->n_dead; i < tab->n_col; ++i) {
1738 struct isl_tab_var *var = var_from_col(tab, i);
1739 var->marked = !var->frozen && var->is_nonneg;
1740 if (var->marked)
1741 n_marked++;
1742 }
1743 while (n_marked) {
1744 struct isl_tab_var *var;
1745 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1746 var = isl_tab_var_from_row(tab, i);
1747 if (var->marked)
1748 break;
1749 }
1750 if (i == tab->n_row) {
1751 for (i = tab->n_dead; i < tab->n_col; ++i) {
1752 var = var_from_col(tab, i);
1753 if (var->marked)
1754 break;
1755 }
1756 if (i == tab->n_col)
1757 break;
1758 }
1759 var->marked = 0;
1760 n_marked--;
1761 if (sign_of_max(tab, var) == 0)
1762 close_row(tab, var);
1763 else if (!tab->rational && !at_least_one(tab, var)) {
1764 tab = cut_to_hyperplane(tab, var);
1765 return isl_tab_detect_equalities(tab);
1766 }
1767 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1768 var = isl_tab_var_from_row(tab, i);
1769 if (!var->marked)
1770 continue;
1771 if (may_be_equality(tab, i))
1772 continue;
1773 var->marked = 0;
1774 n_marked--;
1775 }
1776 }
1777
1778 return tab;
1779 }
1780
1781 /* Check for (near) redundant constraints.
1782 * A constraint is redundant if it is non-negative and if
1783 * its minimal value (temporarily ignoring the non-negativity) is either
1784 * - zero (in case of rational tableaus), or
1785 * - strictly larger than -1 (in case of integer tableaus)
1786 *
1787 * We first mark all non-redundant and non-dead variables that
1788 * are not frozen and not obviously negatively unbounded.
1789 * Then we iterate over all marked variables if they can attain
1790 * any values smaller than zero or at most negative one.
1791 * If not, we mark the row as being redundant (assuming it hasn't
1792 * been detected as being obviously redundant in the mean time).
1793 */
1794 struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab)
1795 {
1796 int i;
1797 unsigned n_marked;
1798
1799 if (!tab)
1800 return NULL;
1801 if (tab->empty)
1802 return tab;
1803 if (tab->n_redundant == tab->n_row)
1804 return tab;
1805
1806 n_marked = 0;
1807 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1808 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
1809 var->marked = !var->frozen && var->is_nonneg;
1810 if (var->marked)
1811 n_marked++;
1812 }
1813 for (i = tab->n_dead; i < tab->n_col; ++i) {
1814 struct isl_tab_var *var = var_from_col(tab, i);
1815 var->marked = !var->frozen && var->is_nonneg &&
1816 !min_is_manifestly_unbounded(tab, var);
1817 if (var->marked)
1818 n_marked++;
1819 }
1820 while (n_marked) {
1821 struct isl_tab_var *var;
1822 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1823 var = isl_tab_var_from_row(tab, i);
1824 if (var->marked)
1825 break;
1826 }
1827 if (i == tab->n_row) {
1828 for (i = tab->n_dead; i < tab->n_col; ++i) {
1829 var = var_from_col(tab, i);
1830 if (var->marked)
1831 break;
1832 }
1833 if (i == tab->n_col)
1834 break;
1835 }
1836 var->marked = 0;
1837 n_marked--;
1838 if ((tab->rational ? (sign_of_min(tab, var) >= 0)
1839 : !isl_tab_min_at_most_neg_one(tab, var)) &&
1840 !var->is_redundant)
1841 isl_tab_mark_redundant(tab, var->index);
1842 for (i = tab->n_dead; i < tab->n_col; ++i) {
1843 var = var_from_col(tab, i);
1844 if (!var->marked)
1845 continue;
1846 if (!min_is_manifestly_unbounded(tab, var))
1847 continue;
1848 var->marked = 0;
1849 n_marked--;
1850 }
1851 }
1852
1853 return tab;
1854 }
1855
1856 int isl_tab_is_equality(struct isl_tab *tab, int con)
1857 {
1858 int row;
1859 unsigned off;
1860
1861 if (!tab)
1862 return -1;
1863 if (tab->con[con].is_zero)
1864 return 1;
1865 if (tab->con[con].is_redundant)
1866 return 0;
1867 if (!tab->con[con].is_row)
1868 return tab->con[con].index < tab->n_dead;
1869
1870 row = tab->con[con].index;
1871
1872 off = 2 + tab->M;
1873 return isl_int_is_zero(tab->mat->row[row][1]) &&
1874 isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
1875 tab->n_col - tab->n_dead) == -1;
1876 }
1877
1878 /* Return the minimial value of the affine expression "f" with denominator
1879 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
1880 * the expression cannot attain arbitrarily small values.
1881 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
1882 * The return value reflects the nature of the result (empty, unbounded,
1883 * minmimal value returned in *opt).
1884 */
1885 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
1886 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
1887 unsigned flags)
1888 {
1889 int r;
1890 enum isl_lp_result res = isl_lp_ok;
1891 struct isl_tab_var *var;
1892 struct isl_tab_undo *snap;
1893
1894 if (tab->empty)
1895 return isl_lp_empty;
1896
1897 snap = isl_tab_snap(tab);
1898 r = isl_tab_add_row(tab, f);
1899 if (r < 0)
1900 return isl_lp_error;
1901 var = &tab->con[r];
1902 isl_int_mul(tab->mat->row[var->index][0],
1903 tab->mat->row[var->index][0], denom);
1904 for (;;) {
1905 int row, col;
1906 find_pivot(tab, var, var, -1, &row, &col);
1907 if (row == var->index) {
1908 res = isl_lp_unbounded;
1909 break;
1910 }
1911 if (row == -1)
1912 break;
1913 isl_tab_pivot(tab, row, col);
1914 }
1915 if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
1916 int i;
1917
1918 isl_vec_free(tab->dual);
1919 tab->dual = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_con);
1920 if (!tab->dual)
1921 return isl_lp_error;
1922 isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
1923 for (i = 0; i < tab->n_con; ++i) {
1924 int pos;
1925 if (tab->con[i].is_row) {
1926 isl_int_set_si(tab->dual->el[1 + i], 0);
1927 continue;
1928 }
1929 pos = 2 + tab->M + tab->con[i].index;
1930 if (tab->con[i].negated)
1931 isl_int_neg(tab->dual->el[1 + i],
1932 tab->mat->row[var->index][pos]);
1933 else
1934 isl_int_set(tab->dual->el[1 + i],
1935 tab->mat->row[var->index][pos]);
1936 }
1937 }
1938 if (res == isl_lp_ok) {
1939 if (opt_denom) {
1940 isl_int_set(*opt, tab->mat->row[var->index][1]);
1941 isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
1942 } else
1943 isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
1944 tab->mat->row[var->index][0]);
1945 }
1946 if (isl_tab_rollback(tab, snap) < 0)
1947 return isl_lp_error;
1948 return res;
1949 }
1950
1951 int isl_tab_is_redundant(struct isl_tab *tab, int con)
1952 {
1953 int row;
1954 unsigned n_col;
1955
1956 if (!tab)
1957 return -1;
1958 if (tab->con[con].is_zero)
1959 return 0;
1960 if (tab->con[con].is_redundant)
1961 return 1;
1962 return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
1963 }
1964
1965 /* Take a snapshot of the tableau that can be restored by s call to
1966 * isl_tab_rollback.
1967 */
1968 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
1969 {
1970 if (!tab)
1971 return NULL;
1972 tab->need_undo = 1;
1973 return tab->top;
1974 }
1975
1976 /* Undo the operation performed by isl_tab_relax.
1977 */
1978 static void unrelax(struct isl_tab *tab, struct isl_tab_var *var)
1979 {
1980 unsigned off = 2 + tab->M;
1981
1982 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
1983 to_row(tab, var, 1);
1984
1985 if (var->is_row)
1986 isl_int_sub(tab->mat->row[var->index][1],
1987 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
1988 else {
1989 int i;
1990
1991 for (i = 0; i < tab->n_row; ++i) {
1992 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
1993 continue;
1994 isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
1995 tab->mat->row[i][off + var->index]);
1996 }
1997
1998 }
1999 }
2000
2001 static void perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
2002 {
2003 struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
2004 switch(undo->type) {
2005 case isl_tab_undo_nonneg:
2006 var->is_nonneg = 0;
2007 break;
2008 case isl_tab_undo_redundant:
2009 var->is_redundant = 0;
2010 tab->n_redundant--;
2011 break;
2012 case isl_tab_undo_zero:
2013 var->is_zero = 0;
2014 tab->n_dead--;
2015 break;
2016 case isl_tab_undo_allocate:
2017 if (undo->u.var_index >= 0) {
2018 isl_assert(tab->mat->ctx, !var->is_row, return);
2019 drop_col(tab, var->index);
2020 break;
2021 }
2022 if (!var->is_row) {
2023 if (!max_is_manifestly_unbounded(tab, var))
2024 to_row(tab, var, 1);
2025 else if (!min_is_manifestly_unbounded(tab, var))
2026 to_row(tab, var, -1);
2027 else
2028 to_row(tab, var, 0);
2029 }
2030 drop_row(tab, var->index);
2031 break;
2032 case isl_tab_undo_relax:
2033 unrelax(tab, var);
2034 break;
2035 }
2036 }
2037
2038 /* Restore the tableau to the state where the basic variables
2039 * are those in "col_var".
2040 * We first construct a list of variables that are currently in
2041 * the basis, but shouldn't. Then we iterate over all variables
2042 * that should be in the basis and for each one that is currently
2043 * not in the basis, we exchange it with one of the elements of the
2044 * list constructed before.
2045 * We can always find an appropriate variable to pivot with because
2046 * the current basis is mapped to the old basis by a non-singular
2047 * matrix and so we can never end up with a zero row.
2048 */
2049 static int restore_basis(struct isl_tab *tab, int *col_var)
2050 {
2051 int i, j;
2052 int n_extra = 0;
2053 int *extra = NULL; /* current columns that contain bad stuff */
2054 unsigned off = 2 + tab->M;
2055
2056 extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
2057 if (!extra)
2058 goto error;
2059 for (i = 0; i < tab->n_col; ++i) {
2060 for (j = 0; j < tab->n_col; ++j)
2061 if (tab->col_var[i] == col_var[j])
2062 break;
2063 if (j < tab->n_col)
2064 continue;
2065 extra[n_extra++] = i;
2066 }
2067 for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
2068 struct isl_tab_var *var;
2069 int row;
2070
2071 for (j = 0; j < tab->n_col; ++j)
2072 if (col_var[i] == tab->col_var[j])
2073 break;
2074 if (j < tab->n_col)
2075 continue;
2076 var = var_from_index(tab, col_var[i]);
2077 row = var->index;
2078 for (j = 0; j < n_extra; ++j)
2079 if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
2080 break;
2081 isl_assert(tab->mat->ctx, j < n_extra, goto error);
2082 isl_tab_pivot(tab, row, extra[j]);
2083 extra[j] = extra[--n_extra];
2084 }
2085
2086 free(extra);
2087 free(col_var);
2088 return 0;
2089 error:
2090 free(extra);
2091 free(col_var);
2092 return -1;
2093 }
2094
2095 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
2096 {
2097 switch (undo->type) {
2098 case isl_tab_undo_empty:
2099 tab->empty = 0;
2100 break;
2101 case isl_tab_undo_nonneg:
2102 case isl_tab_undo_redundant:
2103 case isl_tab_undo_zero:
2104 case isl_tab_undo_allocate:
2105 case isl_tab_undo_relax:
2106 perform_undo_var(tab, undo);
2107 break;
2108 case isl_tab_undo_bset_eq:
2109 isl_basic_set_free_equality(tab->bset, 1);
2110 break;
2111 case isl_tab_undo_bset_ineq:
2112 isl_basic_set_free_inequality(tab->bset, 1);
2113 break;
2114 case isl_tab_undo_bset_div:
2115 isl_basic_set_free_div(tab->bset, 1);
2116 if (tab->samples)
2117 tab->samples->n_col--;
2118 break;
2119 case isl_tab_undo_saved_basis:
2120 if (restore_basis(tab, undo->u.col_var) < 0)
2121 return -1;
2122 break;
2123 case isl_tab_undo_drop_sample:
2124 tab->n_outside--;
2125 break;
2126 default:
2127 isl_assert(tab->mat->ctx, 0, return -1);
2128 }
2129 return 0;
2130 }
2131
2132 /* Return the tableau to the state it was in when the snapshot "snap"
2133 * was taken.
2134 */
2135 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
2136 {
2137 struct isl_tab_undo *undo, *next;
2138
2139 if (!tab)
2140 return -1;
2141
2142 tab->in_undo = 1;
2143 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
2144 next = undo->next;
2145 if (undo == snap)
2146 break;
2147 if (perform_undo(tab, undo) < 0) {
2148 free_undo(tab);
2149 tab->in_undo = 0;
2150 return -1;
2151 }
2152 free(undo);
2153 }
2154 tab->in_undo = 0;
2155 tab->top = undo;
2156 if (!undo)
2157 return -1;
2158 return 0;
2159 }
2160
2161 /* The given row "row" represents an inequality violated by all
2162 * points in the tableau. Check for some special cases of such
2163 * separating constraints.
2164 * In particular, if the row has been reduced to the constant -1,
2165 * then we know the inequality is adjacent (but opposite) to
2166 * an equality in the tableau.
2167 * If the row has been reduced to r = -1 -r', with r' an inequality
2168 * of the tableau, then the inequality is adjacent (but opposite)
2169 * to the inequality r'.
2170 */
2171 static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
2172 {
2173 int pos;
2174 unsigned off = 2 + tab->M;
2175
2176 if (tab->rational)
2177 return isl_ineq_separate;
2178
2179 if (!isl_int_is_one(tab->mat->row[row][0]))
2180 return isl_ineq_separate;
2181 if (!isl_int_is_negone(tab->mat->row[row][1]))
2182 return isl_ineq_separate;
2183
2184 pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
2185 tab->n_col - tab->n_dead);
2186 if (pos == -1)
2187 return isl_ineq_adj_eq;
2188
2189 if (!isl_int_is_negone(tab->mat->row[row][off + tab->n_dead + pos]))
2190 return isl_ineq_separate;
2191
2192 pos = isl_seq_first_non_zero(
2193 tab->mat->row[row] + off + tab->n_dead + pos + 1,
2194 tab->n_col - tab->n_dead - pos - 1);
2195
2196 return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
2197 }
2198
2199 /* Check the effect of inequality "ineq" on the tableau "tab".
2200 * The result may be
2201 * isl_ineq_redundant: satisfied by all points in the tableau
2202 * isl_ineq_separate: satisfied by no point in the tableau
2203 * isl_ineq_cut: satisfied by some by not all points
2204 * isl_ineq_adj_eq: adjacent to an equality
2205 * isl_ineq_adj_ineq: adjacent to an inequality.
2206 */
2207 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
2208 {
2209 enum isl_ineq_type type = isl_ineq_error;
2210 struct isl_tab_undo *snap = NULL;
2211 int con;
2212 int row;
2213
2214 if (!tab)
2215 return isl_ineq_error;
2216
2217 if (isl_tab_extend_cons(tab, 1) < 0)
2218 return isl_ineq_error;
2219
2220 snap = isl_tab_snap(tab);
2221
2222 con = isl_tab_add_row(tab, ineq);
2223 if (con < 0)
2224 goto error;
2225
2226 row = tab->con[con].index;
2227 if (isl_tab_row_is_redundant(tab, row))
2228 type = isl_ineq_redundant;
2229 else if (isl_int_is_neg(tab->mat->row[row][1]) &&
2230 (tab->rational ||
2231 isl_int_abs_ge(tab->mat->row[row][1],
2232 tab->mat->row[row][0]))) {
2233 if (at_least_zero(tab, &tab->con[con]))
2234 type = isl_ineq_cut;
2235 else
2236 type = separation_type(tab, row);
2237 } else if (tab->rational ? (sign_of_min(tab, &tab->con[con]) < 0)
2238 : isl_tab_min_at_most_neg_one(tab, &tab->con[con]))
2239 type = isl_ineq_cut;
2240 else
2241 type = isl_ineq_redundant;
2242
2243 if (isl_tab_rollback(tab, snap))
2244 return isl_ineq_error;
2245 return type;
2246 error:
2247 isl_tab_rollback(tab, snap);
2248 return isl_ineq_error;
2249 }
2250
2251 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent)
2252 {
2253 unsigned r, c;
2254 int i;
2255
2256 if (!tab) {
2257 fprintf(out, "%*snull tab\n", indent, "");
2258 return;
2259 }
2260 fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
2261 tab->n_redundant, tab->n_dead);
2262 if (tab->rational)
2263 fprintf(out, ", rational");
2264 if (tab->empty)
2265 fprintf(out, ", empty");
2266 fprintf(out, "\n");
2267 fprintf(out, "%*s[", indent, "");
2268 for (i = 0; i < tab->n_var; ++i) {
2269 if (i)
2270 fprintf(out, (i == tab->n_param ||
2271 i == tab->n_var - tab->n_div) ? "; "
2272 : ", ");
2273 fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
2274 tab->var[i].index,
2275 tab->var[i].is_zero ? " [=0]" :
2276 tab->var[i].is_redundant ? " [R]" : "");
2277 }
2278 fprintf(out, "]\n");
2279 fprintf(out, "%*s[", indent, "");
2280 for (i = 0; i < tab->n_con; ++i) {
2281 if (i)
2282 fprintf(out, ", ");
2283 fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
2284 tab->con[i].index,
2285 tab->con[i].is_zero ? " [=0]" :
2286 tab->con[i].is_redundant ? " [R]" : "");
2287 }
2288 fprintf(out, "]\n");
2289 fprintf(out, "%*s[", indent, "");
2290 for (i = 0; i < tab->n_row; ++i) {
2291 const char *sign = "";
2292 if (i)
2293 fprintf(out, ", ");
2294 if (tab->row_sign) {
2295 if (tab->row_sign[i] == isl_tab_row_unknown)
2296 sign = "?";
2297 else if (tab->row_sign[i] == isl_tab_row_neg)
2298 sign = "-";
2299 else if (tab->row_sign[i] == isl_tab_row_pos)
2300 sign = "+";
2301 else
2302 sign = "+-";
2303 }
2304 fprintf(out, "r%d: %d%s%s", i, tab->row_var[i],
2305 isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
2306 }
2307 fprintf(out, "]\n");
2308 fprintf(out, "%*s[", indent, "");
2309 for (i = 0; i < tab->n_col; ++i) {
2310 if (i)
2311 fprintf(out, ", ");
2312 fprintf(out, "c%d: %d%s", i, tab->col_var[i],
2313 var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
2314 }
2315 fprintf(out, "]\n");
2316 r = tab->mat->n_row;
2317 tab->mat->n_row = tab->n_row;
2318 c = tab->mat->n_col;
2319 tab->mat->n_col = 2 + tab->M + tab->n_col;
2320 isl_mat_dump(tab->mat, out, indent);
2321 tab->mat->n_row = r;
2322 tab->mat->n_col = c;
2323 if (tab->bset)
2324 isl_basic_set_dump(tab->bset, out, indent);
2325 }
Integer set library