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isl_tab_from_recession_cone: take basic set instead of basic map as argument
[isl.git] / isl_tab.c
blobfd4f891b4c2da8901f6430f0ad45faa95e74c342
1 #include "isl_mat.h"
2 #include "isl_map_private.h"
3 #include "isl_tab.h"
4 #include "isl_seq.h"
5
6 /*
7 * The implementation of tableaus in this file was inspired by Section 8
8 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
9 * prover for program checking".
10 */
11
12 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
13 unsigned n_row, unsigned n_var, unsigned M)
14 {
15 int i;
16 struct isl_tab *tab;
17 unsigned off = 2 + M;
18
19 tab = isl_calloc_type(ctx, struct isl_tab);
20 if (!tab)
21 return NULL;
22 tab->mat = isl_mat_alloc(ctx, n_row, off + n_var);
23 if (!tab->mat)
24 goto error;
25 tab->var = isl_alloc_array(ctx, struct isl_tab_var, n_var);
26 if (!tab->var)
27 goto error;
28 tab->con = isl_alloc_array(ctx, struct isl_tab_var, n_row);
29 if (!tab->con)
30 goto error;
31 tab->col_var = isl_alloc_array(ctx, int, n_var);
32 if (!tab->col_var)
33 goto error;
34 tab->row_var = isl_alloc_array(ctx, int, n_row);
35 if (!tab->row_var)
36 goto error;
37 for (i = 0; i < n_var; ++i) {
38 tab->var[i].index = i;
39 tab->var[i].is_row = 0;
40 tab->var[i].is_nonneg = 0;
41 tab->var[i].is_zero = 0;
42 tab->var[i].is_redundant = 0;
43 tab->var[i].frozen = 0;
44 tab->var[i].negated = 0;
45 tab->col_var[i] = i;
46 }
47 tab->n_row = 0;
48 tab->n_con = 0;
49 tab->n_eq = 0;
50 tab->max_con = n_row;
51 tab->n_col = n_var;
52 tab->n_var = n_var;
53 tab->max_var = n_var;
54 tab->n_param = 0;
55 tab->n_div = 0;
56 tab->n_dead = 0;
57 tab->n_redundant = 0;
58 tab->need_undo = 0;
59 tab->rational = 0;
60 tab->empty = 0;
61 tab->in_undo = 0;
62 tab->M = M;
63 tab->bottom.type = isl_tab_undo_bottom;
64 tab->bottom.next = NULL;
65 tab->top = &tab->bottom;
66 return tab;
67 error:
68 isl_tab_free(tab);
69 return NULL;
70 }
71
72 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new)
73 {
74 unsigned off = 2 + tab->M;
75 if (tab->max_con < tab->n_con + n_new) {
76 struct isl_tab_var *con;
77
78 con = isl_realloc_array(tab->mat->ctx, tab->con,
79 struct isl_tab_var, tab->max_con + n_new);
80 if (!con)
81 return -1;
82 tab->con = con;
83 tab->max_con += n_new;
84 }
85 if (tab->mat->n_row < tab->n_row + n_new) {
86 int *row_var;
87
88 tab->mat = isl_mat_extend(tab->mat,
89 tab->n_row + n_new, off + tab->n_col);
90 if (!tab->mat)
91 return -1;
92 row_var = isl_realloc_array(tab->mat->ctx, tab->row_var,
93 int, tab->mat->n_row);
94 if (!row_var)
95 return -1;
96 tab->row_var = row_var;
97 if (tab->row_sign) {
98 enum isl_tab_row_sign *s;
99 s = isl_realloc_array(tab->mat->ctx, tab->row_sign,
100 enum isl_tab_row_sign, tab->mat->n_row);
101 if (!s)
102 return -1;
103 tab->row_sign = s;
104 }
105 }
106 return 0;
107 }
108
109 /* Make room for at least n_new extra variables.
110 * Return -1 if anything went wrong.
111 */
112 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new)
113 {
114 struct isl_tab_var *var;
115 unsigned off = 2 + tab->M;
116
117 if (tab->max_var < tab->n_var + n_new) {
118 var = isl_realloc_array(tab->mat->ctx, tab->var,
119 struct isl_tab_var, tab->n_var + n_new);
120 if (!var)
121 return -1;
122 tab->var = var;
123 tab->max_var += n_new;
124 }
125
126 if (tab->mat->n_col < off + tab->n_col + n_new) {
127 int *p;
128
129 tab->mat = isl_mat_extend(tab->mat,
130 tab->mat->n_row, off + tab->n_col + n_new);
131 if (!tab->mat)
132 return -1;
133 p = isl_realloc_array(tab->mat->ctx, tab->col_var,
134 int, tab->n_col + n_new);
135 if (!p)
136 return -1;
137 tab->col_var = p;
138 }
139
140 return 0;
141 }
142
143 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new)
144 {
145 if (isl_tab_extend_cons(tab, n_new) >= 0)
146 return tab;
147
148 isl_tab_free(tab);
149 return NULL;
150 }
151
152 static void free_undo(struct isl_tab *tab)
153 {
154 struct isl_tab_undo *undo, *next;
155
156 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
157 next = undo->next;
158 free(undo);
159 }
160 tab->top = undo;
161 }
162
163 void isl_tab_free(struct isl_tab *tab)
164 {
165 if (!tab)
166 return;
167 free_undo(tab);
168 isl_mat_free(tab->mat);
169 isl_vec_free(tab->dual);
170 isl_basic_set_free(tab->bset);
171 free(tab->var);
172 free(tab->con);
173 free(tab->row_var);
174 free(tab->col_var);
175 free(tab->row_sign);
176 isl_mat_free(tab->samples);
177 free(tab);
178 }
179
180 struct isl_tab *isl_tab_dup(struct isl_tab *tab)
181 {
182 int i;
183 struct isl_tab *dup;
184 unsigned off;
185
186 if (!tab)
187 return NULL;
188
189 off = 2 + tab->M;
190 dup = isl_calloc_type(tab->ctx, struct isl_tab);
191 if (!dup)
192 return NULL;
193 dup->mat = isl_mat_dup(tab->mat);
194 if (!dup->mat)
195 goto error;
196 dup->var = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_var);
197 if (!dup->var)
198 goto error;
199 for (i = 0; i < tab->n_var; ++i)
200 dup->var[i] = tab->var[i];
201 dup->con = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_con);
202 if (!dup->con)
203 goto error;
204 for (i = 0; i < tab->n_con; ++i)
205 dup->con[i] = tab->con[i];
206 dup->col_var = isl_alloc_array(tab->ctx, int, tab->mat->n_col - off);
207 if (!dup->col_var)
208 goto error;
209 for (i = 0; i < tab->n_col; ++i)
210 dup->col_var[i] = tab->col_var[i];
211 dup->row_var = isl_alloc_array(tab->ctx, int, tab->mat->n_row);
212 if (!dup->row_var)
213 goto error;
214 for (i = 0; i < tab->n_row; ++i)
215 dup->row_var[i] = tab->row_var[i];
216 if (tab->row_sign) {
217 dup->row_sign = isl_alloc_array(tab->ctx, enum isl_tab_row_sign,
218 tab->mat->n_row);
219 if (!dup->row_sign)
220 goto error;
221 for (i = 0; i < tab->n_row; ++i)
222 dup->row_sign[i] = tab->row_sign[i];
223 }
224 if (tab->samples) {
225 dup->samples = isl_mat_dup(tab->samples);
226 if (!dup->samples)
227 goto error;
228 dup->n_sample = tab->n_sample;
229 dup->n_outside = tab->n_outside;
230 }
231 dup->n_row = tab->n_row;
232 dup->n_con = tab->n_con;
233 dup->n_eq = tab->n_eq;
234 dup->max_con = tab->max_con;
235 dup->n_col = tab->n_col;
236 dup->n_var = tab->n_var;
237 dup->max_var = tab->max_var;
238 dup->n_param = tab->n_param;
239 dup->n_div = tab->n_div;
240 dup->n_dead = tab->n_dead;
241 dup->n_redundant = tab->n_redundant;
242 dup->rational = tab->rational;
243 dup->empty = tab->empty;
244 dup->need_undo = 0;
245 dup->in_undo = 0;
246 dup->M = tab->M;
247 dup->bottom.type = isl_tab_undo_bottom;
248 dup->bottom.next = NULL;
249 dup->top = &dup->bottom;
250 return dup;
251 error:
252 isl_tab_free(dup);
253 return NULL;
254 }
255
256 static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i)
257 {
258 if (i >= 0)
259 return &tab->var[i];
260 else
261 return &tab->con[~i];
262 }
263
264 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
265 {
266 return var_from_index(tab, tab->row_var[i]);
267 }
268
269 static struct isl_tab_var *var_from_col(struct isl_tab *tab, int i)
270 {
271 return var_from_index(tab, tab->col_var[i]);
272 }
273
274 /* Check if there are any upper bounds on column variable "var",
275 * i.e., non-negative rows where var appears with a negative coefficient.
276 * Return 1 if there are no such bounds.
277 */
278 static int max_is_manifestly_unbounded(struct isl_tab *tab,
279 struct isl_tab_var *var)
280 {
281 int i;
282 unsigned off = 2 + tab->M;
283
284 if (var->is_row)
285 return 0;
286 for (i = tab->n_redundant; i < tab->n_row; ++i) {
287 if (!isl_int_is_neg(tab->mat->row[i][off + var->index]))
288 continue;
289 if (isl_tab_var_from_row(tab, i)->is_nonneg)
290 return 0;
291 }
292 return 1;
293 }
294
295 /* Check if there are any lower bounds on column variable "var",
296 * i.e., non-negative rows where var appears with a positive coefficient.
297 * Return 1 if there are no such bounds.
298 */
299 static int min_is_manifestly_unbounded(struct isl_tab *tab,
300 struct isl_tab_var *var)
301 {
302 int i;
303 unsigned off = 2 + tab->M;
304
305 if (var->is_row)
306 return 0;
307 for (i = tab->n_redundant; i < tab->n_row; ++i) {
308 if (!isl_int_is_pos(tab->mat->row[i][off + var->index]))
309 continue;
310 if (isl_tab_var_from_row(tab, i)->is_nonneg)
311 return 0;
312 }
313 return 1;
314 }
315
316 static int row_cmp(struct isl_tab *tab, int r1, int r2, int c, isl_int t)
317 {
318 unsigned off = 2 + tab->M;
319
320 if (tab->M) {
321 int s;
322 isl_int_mul(t, tab->mat->row[r1][2], tab->mat->row[r2][off+c]);
323 isl_int_submul(t, tab->mat->row[r2][2], tab->mat->row[r1][off+c]);
324 s = isl_int_sgn(t);
325 if (s)
326 return s;
327 }
328 isl_int_mul(t, tab->mat->row[r1][1], tab->mat->row[r2][off + c]);
329 isl_int_submul(t, tab->mat->row[r2][1], tab->mat->row[r1][off + c]);
330 return isl_int_sgn(t);
331 }
332
333 /* Given the index of a column "c", return the index of a row
334 * that can be used to pivot the column in, with either an increase
335 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
336 * If "var" is not NULL, then the row returned will be different from
337 * the one associated with "var".
338 *
339 * Each row in the tableau is of the form
340 *
341 * x_r = a_r0 + \sum_i a_ri x_i
342 *
343 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
344 * impose any limit on the increase or decrease in the value of x_c
345 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
346 * for the row with the smallest (most stringent) such bound.
347 * Note that the common denominator of each row drops out of the fraction.
348 * To check if row j has a smaller bound than row r, i.e.,
349 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
350 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
351 * where -sign(a_jc) is equal to "sgn".
352 */
353 static int pivot_row(struct isl_tab *tab,
354 struct isl_tab_var *var, int sgn, int c)
355 {
356 int j, r, tsgn;
357 isl_int t;
358 unsigned off = 2 + tab->M;
359
360 isl_int_init(t);
361 r = -1;
362 for (j = tab->n_redundant; j < tab->n_row; ++j) {
363 if (var && j == var->index)
364 continue;
365 if (!isl_tab_var_from_row(tab, j)->is_nonneg)
366 continue;
367 if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
368 continue;
369 if (r < 0) {
370 r = j;
371 continue;
372 }
373 tsgn = sgn * row_cmp(tab, r, j, c, t);
374 if (tsgn < 0 || (tsgn == 0 &&
375 tab->row_var[j] < tab->row_var[r]))
376 r = j;
377 }
378 isl_int_clear(t);
379 return r;
380 }
381
382 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
383 * (sgn < 0) the value of row variable var.
384 * If not NULL, then skip_var is a row variable that should be ignored
385 * while looking for a pivot row. It is usually equal to var.
386 *
387 * As the given row in the tableau is of the form
388 *
389 * x_r = a_r0 + \sum_i a_ri x_i
390 *
391 * we need to find a column such that the sign of a_ri is equal to "sgn"
392 * (such that an increase in x_i will have the desired effect) or a
393 * column with a variable that may attain negative values.
394 * If a_ri is positive, then we need to move x_i in the same direction
395 * to obtain the desired effect. Otherwise, x_i has to move in the
396 * opposite direction.
397 */
398 static void find_pivot(struct isl_tab *tab,
399 struct isl_tab_var *var, struct isl_tab_var *skip_var,
400 int sgn, int *row, int *col)
401 {
402 int j, r, c;
403 isl_int *tr;
404
405 *row = *col = -1;
406
407 isl_assert(tab->mat->ctx, var->is_row, return);
408 tr = tab->mat->row[var->index] + 2 + tab->M;
409
410 c = -1;
411 for (j = tab->n_dead; j < tab->n_col; ++j) {
412 if (isl_int_is_zero(tr[j]))
413 continue;
414 if (isl_int_sgn(tr[j]) != sgn &&
415 var_from_col(tab, j)->is_nonneg)
416 continue;
417 if (c < 0 || tab->col_var[j] < tab->col_var[c])
418 c = j;
419 }
420 if (c < 0)
421 return;
422
423 sgn *= isl_int_sgn(tr[c]);
424 r = pivot_row(tab, skip_var, sgn, c);
425 *row = r < 0 ? var->index : r;
426 *col = c;
427 }
428
429 /* Return 1 if row "row" represents an obviously redundant inequality.
430 * This means
431 * - it represents an inequality or a variable
432 * - that is the sum of a non-negative sample value and a positive
433 * combination of zero or more non-negative variables.
434 */
435 int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
436 {
437 int i;
438 unsigned off = 2 + tab->M;
439
440 if (tab->row_var[row] < 0 && !isl_tab_var_from_row(tab, row)->is_nonneg)
441 return 0;
442
443 if (isl_int_is_neg(tab->mat->row[row][1]))
444 return 0;
445 if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
446 return 0;
447
448 for (i = tab->n_dead; i < tab->n_col; ++i) {
449 if (isl_int_is_zero(tab->mat->row[row][off + i]))
450 continue;
451 if (isl_int_is_neg(tab->mat->row[row][off + i]))
452 return 0;
453 if (!var_from_col(tab, i)->is_nonneg)
454 return 0;
455 }
456 return 1;
457 }
458
459 static void swap_rows(struct isl_tab *tab, int row1, int row2)
460 {
461 int t;
462 t = tab->row_var[row1];
463 tab->row_var[row1] = tab->row_var[row2];
464 tab->row_var[row2] = t;
465 isl_tab_var_from_row(tab, row1)->index = row1;
466 isl_tab_var_from_row(tab, row2)->index = row2;
467 tab->mat = isl_mat_swap_rows(tab->mat, row1, row2);
468
469 if (!tab->row_sign)
470 return;
471 t = tab->row_sign[row1];
472 tab->row_sign[row1] = tab->row_sign[row2];
473 tab->row_sign[row2] = t;
474 }
475
476 static void push_union(struct isl_tab *tab,
477 enum isl_tab_undo_type type, union isl_tab_undo_val u)
478 {
479 struct isl_tab_undo *undo;
480
481 if (!tab->need_undo)
482 return;
483
484 undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
485 if (!undo) {
486 free_undo(tab);
487 tab->top = NULL;
488 return;
489 }
490 undo->type = type;
491 undo->u = u;
492 undo->next = tab->top;
493 tab->top = undo;
494 }
495
496 void isl_tab_push_var(struct isl_tab *tab,
497 enum isl_tab_undo_type type, struct isl_tab_var *var)
498 {
499 union isl_tab_undo_val u;
500 if (var->is_row)
501 u.var_index = tab->row_var[var->index];
502 else
503 u.var_index = tab->col_var[var->index];
504 push_union(tab, type, u);
505 }
506
507 void isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
508 {
509 union isl_tab_undo_val u = { 0 };
510 push_union(tab, type, u);
511 }
512
513 /* Push a record on the undo stack describing the current basic
514 * variables, so that the this state can be restored during rollback.
515 */
516 void isl_tab_push_basis(struct isl_tab *tab)
517 {
518 int i;
519 union isl_tab_undo_val u;
520
521 u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
522 if (!u.col_var) {
523 free_undo(tab);
524 tab->top = NULL;
525 return;
526 }
527 for (i = 0; i < tab->n_col; ++i)
528 u.col_var[i] = tab->col_var[i];
529 push_union(tab, isl_tab_undo_saved_basis, u);
530 }
531
532 /* Mark row with index "row" as being redundant.
533 * If we may need to undo the operation or if the row represents
534 * a variable of the original problem, the row is kept,
535 * but no longer considered when looking for a pivot row.
536 * Otherwise, the row is simply removed.
537 *
538 * The row may be interchanged with some other row. If it
539 * is interchanged with a later row, return 1. Otherwise return 0.
540 * If the rows are checked in order in the calling function,
541 * then a return value of 1 means that the row with the given
542 * row number may now contain a different row that hasn't been checked yet.
543 */
544 int isl_tab_mark_redundant(struct isl_tab *tab, int row)
545 {
546 struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
547 var->is_redundant = 1;
548 isl_assert(tab->mat->ctx, row >= tab->n_redundant, return -1);
549 if (tab->need_undo || tab->row_var[row] >= 0) {
550 if (tab->row_var[row] >= 0 && !var->is_nonneg) {
551 var->is_nonneg = 1;
552 isl_tab_push_var(tab, isl_tab_undo_nonneg, var);
553 }
554 if (row != tab->n_redundant)
555 swap_rows(tab, row, tab->n_redundant);
556 isl_tab_push_var(tab, isl_tab_undo_redundant, var);
557 tab->n_redundant++;
558 return 0;
559 } else {
560 if (row != tab->n_row - 1)
561 swap_rows(tab, row, tab->n_row - 1);
562 isl_tab_var_from_row(tab, tab->n_row - 1)->index = -1;
563 tab->n_row--;
564 return 1;
565 }
566 }
567
568 struct isl_tab *isl_tab_mark_empty(struct isl_tab *tab)
569 {
570 if (!tab->empty && tab->need_undo)
571 isl_tab_push(tab, isl_tab_undo_empty);
572 tab->empty = 1;
573 return tab;
574 }
575
576 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
577 * the original sign of the pivot element.
578 * We only keep track of row signs during PILP solving and in this case
579 * we only pivot a row with negative sign (meaning the value is always
580 * non-positive) using a positive pivot element.
581 *
582 * For each row j, the new value of the parametric constant is equal to
583 *
584 * a_j0 - a_jc a_r0/a_rc
585 *
586 * where a_j0 is the original parametric constant, a_rc is the pivot element,
587 * a_r0 is the parametric constant of the pivot row and a_jc is the
588 * pivot column entry of the row j.
589 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
590 * remains the same if a_jc has the same sign as the row j or if
591 * a_jc is zero. In all other cases, we reset the sign to "unknown".
592 */
593 static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
594 {
595 int i;
596 struct isl_mat *mat = tab->mat;
597 unsigned off = 2 + tab->M;
598
599 if (!tab->row_sign)
600 return;
601
602 if (tab->row_sign[row] == 0)
603 return;
604 isl_assert(mat->ctx, row_sgn > 0, return);
605 isl_assert(mat->ctx, tab->row_sign[row] == isl_tab_row_neg, return);
606 tab->row_sign[row] = isl_tab_row_pos;
607 for (i = 0; i < tab->n_row; ++i) {
608 int s;
609 if (i == row)
610 continue;
611 s = isl_int_sgn(mat->row[i][off + col]);
612 if (!s)
613 continue;
614 if (!tab->row_sign[i])
615 continue;
616 if (s < 0 && tab->row_sign[i] == isl_tab_row_neg)
617 continue;
618 if (s > 0 && tab->row_sign[i] == isl_tab_row_pos)
619 continue;
620 tab->row_sign[i] = isl_tab_row_unknown;
621 }
622 }
623
624 /* Given a row number "row" and a column number "col", pivot the tableau
625 * such that the associated variables are interchanged.
626 * The given row in the tableau expresses
627 *
628 * x_r = a_r0 + \sum_i a_ri x_i
629 *
630 * or
631 *
632 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
633 *
634 * Substituting this equality into the other rows
635 *
636 * x_j = a_j0 + \sum_i a_ji x_i
637 *
638 * with a_jc \ne 0, we obtain
639 *
640 * x_j = a_jc/a_rc x_r + a_j0 - a_jc a_r0/a_rc + sum a_ji - a_jc a_ri/a_rc
641 *
642 * The tableau
643 *
644 * n_rc/d_r n_ri/d_r
645 * n_jc/d_j n_ji/d_j
646 *
647 * where i is any other column and j is any other row,
648 * is therefore transformed into
649 *
650 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
651 * s(n_rc)d_r n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
652 *
653 * The transformation is performed along the following steps
654 *
655 * d_r/n_rc n_ri/n_rc
656 * n_jc/d_j n_ji/d_j
657 *
658 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
659 * n_jc/d_j n_ji/d_j
660 *
661 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
662 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
663 *
664 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
665 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
666 *
667 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
668 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
669 *
670 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
671 * s(n_rc)d_r n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
672 *
673 */
674 void isl_tab_pivot(struct isl_tab *tab, int row, int col)
675 {
676 int i, j;
677 int sgn;
678 int t;
679 struct isl_mat *mat = tab->mat;
680 struct isl_tab_var *var;
681 unsigned off = 2 + tab->M;
682
683 isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
684 sgn = isl_int_sgn(mat->row[row][0]);
685 if (sgn < 0) {
686 isl_int_neg(mat->row[row][0], mat->row[row][0]);
687 isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]);
688 } else
689 for (j = 0; j < off - 1 + tab->n_col; ++j) {
690 if (j == off - 1 + col)
691 continue;
692 isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
693 }
694 if (!isl_int_is_one(mat->row[row][0]))
695 isl_seq_normalize(mat->ctx, mat->row[row], off + tab->n_col);
696 for (i = 0; i < tab->n_row; ++i) {
697 if (i == row)
698 continue;
699 if (isl_int_is_zero(mat->row[i][off + col]))
700 continue;
701 isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
702 for (j = 0; j < off - 1 + tab->n_col; ++j) {
703 if (j == off - 1 + col)
704 continue;
705 isl_int_mul(mat->row[i][1 + j],
706 mat->row[i][1 + j], mat->row[row][0]);
707 isl_int_addmul(mat->row[i][1 + j],
708 mat->row[i][off + col], mat->row[row][1 + j]);
709 }
710 isl_int_mul(mat->row[i][off + col],
711 mat->row[i][off + col], mat->row[row][off + col]);
712 if (!isl_int_is_one(mat->row[i][0]))
713 isl_seq_normalize(mat->ctx, mat->row[i], off + tab->n_col);
714 }
715 t = tab->row_var[row];
716 tab->row_var[row] = tab->col_var[col];
717 tab->col_var[col] = t;
718 var = isl_tab_var_from_row(tab, row);
719 var->is_row = 1;
720 var->index = row;
721 var = var_from_col(tab, col);
722 var->is_row = 0;
723 var->index = col;
724 update_row_sign(tab, row, col, sgn);
725 if (tab->in_undo)
726 return;
727 for (i = tab->n_redundant; i < tab->n_row; ++i) {
728 if (isl_int_is_zero(mat->row[i][off + col]))
729 continue;
730 if (!isl_tab_var_from_row(tab, i)->frozen &&
731 isl_tab_row_is_redundant(tab, i))
732 if (isl_tab_mark_redundant(tab, i))
733 --i;
734 }
735 }
736
737 /* If "var" represents a column variable, then pivot is up (sgn > 0)
738 * or down (sgn < 0) to a row. The variable is assumed not to be
739 * unbounded in the specified direction.
740 * If sgn = 0, then the variable is unbounded in both directions,
741 * and we pivot with any row we can find.
742 */
743 static void to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
744 {
745 int r;
746 unsigned off = 2 + tab->M;
747
748 if (var->is_row)
749 return;
750
751 if (sign == 0) {
752 for (r = tab->n_redundant; r < tab->n_row; ++r)
753 if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
754 break;
755 isl_assert(tab->mat->ctx, r < tab->n_row, return);
756 } else {
757 r = pivot_row(tab, NULL, sign, var->index);
758 isl_assert(tab->mat->ctx, r >= 0, return);
759 }
760
761 isl_tab_pivot(tab, r, var->index);
762 }
763
764 static void check_table(struct isl_tab *tab)
765 {
766 int i;
767
768 if (tab->empty)
769 return;
770 for (i = 0; i < tab->n_row; ++i) {
771 if (!isl_tab_var_from_row(tab, i)->is_nonneg)
772 continue;
773 assert(!isl_int_is_neg(tab->mat->row[i][1]));
774 }
775 }
776
777 /* Return the sign of the maximal value of "var".
778 * If the sign is not negative, then on return from this function,
779 * the sample value will also be non-negative.
780 *
781 * If "var" is manifestly unbounded wrt positive values, we are done.
782 * Otherwise, we pivot the variable up to a row if needed
783 * Then we continue pivoting down until either
784 * - no more down pivots can be performed
785 * - the sample value is positive
786 * - the variable is pivoted into a manifestly unbounded column
787 */
788 static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
789 {
790 int row, col;
791
792 if (max_is_manifestly_unbounded(tab, var))
793 return 1;
794 to_row(tab, var, 1);
795 while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
796 find_pivot(tab, var, var, 1, &row, &col);
797 if (row == -1)
798 return isl_int_sgn(tab->mat->row[var->index][1]);
799 isl_tab_pivot(tab, row, col);
800 if (!var->is_row) /* manifestly unbounded */
801 return 1;
802 }
803 return 1;
804 }
805
806 static int row_is_neg(struct isl_tab *tab, int row)
807 {
808 if (!tab->M)
809 return isl_int_is_neg(tab->mat->row[row][1]);
810 if (isl_int_is_pos(tab->mat->row[row][2]))
811 return 0;
812 if (isl_int_is_neg(tab->mat->row[row][2]))
813 return 1;
814 return isl_int_is_neg(tab->mat->row[row][1]);
815 }
816
817 static int row_sgn(struct isl_tab *tab, int row)
818 {
819 if (!tab->M)
820 return isl_int_sgn(tab->mat->row[row][1]);
821 if (!isl_int_is_zero(tab->mat->row[row][2]))
822 return isl_int_sgn(tab->mat->row[row][2]);
823 else
824 return isl_int_sgn(tab->mat->row[row][1]);
825 }
826
827 /* Perform pivots until the row variable "var" has a non-negative
828 * sample value or until no more upward pivots can be performed.
829 * Return the sign of the sample value after the pivots have been
830 * performed.
831 */
832 static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
833 {
834 int row, col;
835
836 while (row_is_neg(tab, var->index)) {
837 find_pivot(tab, var, var, 1, &row, &col);
838 if (row == -1)
839 break;
840 isl_tab_pivot(tab, row, col);
841 if (!var->is_row) /* manifestly unbounded */
842 return 1;
843 }
844 return row_sgn(tab, var->index);
845 }
846
847 /* Perform pivots until we are sure that the row variable "var"
848 * can attain non-negative values. After return from this
849 * function, "var" is still a row variable, but its sample
850 * value may not be non-negative, even if the function returns 1.
851 */
852 static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
853 {
854 int row, col;
855
856 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
857 find_pivot(tab, var, var, 1, &row, &col);
858 if (row == -1)
859 break;
860 if (row == var->index) /* manifestly unbounded */
861 return 1;
862 isl_tab_pivot(tab, row, col);
863 }
864 return !isl_int_is_neg(tab->mat->row[var->index][1]);
865 }
866
867 /* Return a negative value if "var" can attain negative values.
868 * Return a non-negative value otherwise.
869 *
870 * If "var" is manifestly unbounded wrt negative values, we are done.
871 * Otherwise, if var is in a column, we can pivot it down to a row.
872 * Then we continue pivoting down until either
873 * - the pivot would result in a manifestly unbounded column
874 * => we don't perform the pivot, but simply return -1
875 * - no more down pivots can be performed
876 * - the sample value is negative
877 * If the sample value becomes negative and the variable is supposed
878 * to be nonnegative, then we undo the last pivot.
879 * However, if the last pivot has made the pivoting variable
880 * obviously redundant, then it may have moved to another row.
881 * In that case we look for upward pivots until we reach a non-negative
882 * value again.
883 */
884 static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
885 {
886 int row, col;
887 struct isl_tab_var *pivot_var = NULL;
888
889 if (min_is_manifestly_unbounded(tab, var))
890 return -1;
891 if (!var->is_row) {
892 col = var->index;
893 row = pivot_row(tab, NULL, -1, col);
894 pivot_var = var_from_col(tab, col);
895 isl_tab_pivot(tab, row, col);
896 if (var->is_redundant)
897 return 0;
898 if (isl_int_is_neg(tab->mat->row[var->index][1])) {
899 if (var->is_nonneg) {
900 if (!pivot_var->is_redundant &&
901 pivot_var->index == row)
902 isl_tab_pivot(tab, row, col);
903 else
904 restore_row(tab, var);
905 }
906 return -1;
907 }
908 }
909 if (var->is_redundant)
910 return 0;
911 while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
912 find_pivot(tab, var, var, -1, &row, &col);
913 if (row == var->index)
914 return -1;
915 if (row == -1)
916 return isl_int_sgn(tab->mat->row[var->index][1]);
917 pivot_var = var_from_col(tab, col);
918 isl_tab_pivot(tab, row, col);
919 if (var->is_redundant)
920 return 0;
921 }
922 if (pivot_var && var->is_nonneg) {
923 /* pivot back to non-negative value */
924 if (!pivot_var->is_redundant && pivot_var->index == row)
925 isl_tab_pivot(tab, row, col);
926 else
927 restore_row(tab, var);
928 }
929 return -1;
930 }
931
932 static int row_at_most_neg_one(struct isl_tab *tab, int row)
933 {
934 if (tab->M) {
935 if (isl_int_is_pos(tab->mat->row[row][2]))
936 return 0;
937 if (isl_int_is_neg(tab->mat->row[row][2]))
938 return 1;
939 }
940 return isl_int_is_neg(tab->mat->row[row][1]) &&
941 isl_int_abs_ge(tab->mat->row[row][1],
942 tab->mat->row[row][0]);
943 }
944
945 /* Return 1 if "var" can attain values <= -1.
946 * Return 0 otherwise.
947 *
948 * The sample value of "var" is assumed to be non-negative when the
949 * the function is called and will be made non-negative again before
950 * the function returns.
951 */
952 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
953 {
954 int row, col;
955 struct isl_tab_var *pivot_var;
956
957 if (min_is_manifestly_unbounded(tab, var))
958 return 1;
959 if (!var->is_row) {
960 col = var->index;
961 row = pivot_row(tab, NULL, -1, col);
962 pivot_var = var_from_col(tab, col);
963 isl_tab_pivot(tab, row, col);
964 if (var->is_redundant)
965 return 0;
966 if (row_at_most_neg_one(tab, var->index)) {
967 if (var->is_nonneg) {
968 if (!pivot_var->is_redundant &&
969 pivot_var->index == row)
970 isl_tab_pivot(tab, row, col);
971 else
972 restore_row(tab, var);
973 }
974 return 1;
975 }
976 }
977 if (var->is_redundant)
978 return 0;
979 do {
980 find_pivot(tab, var, var, -1, &row, &col);
981 if (row == var->index)
982 return 1;
983 if (row == -1)
984 return 0;
985 pivot_var = var_from_col(tab, col);
986 isl_tab_pivot(tab, row, col);
987 if (var->is_redundant)
988 return 0;
989 } while (!row_at_most_neg_one(tab, var->index));
990 if (var->is_nonneg) {
991 /* pivot back to non-negative value */
992 if (!pivot_var->is_redundant && pivot_var->index == row)
993 isl_tab_pivot(tab, row, col);
994 restore_row(tab, var);
995 }
996 return 1;
997 }
998
999 /* Return 1 if "var" can attain values >= 1.
1000 * Return 0 otherwise.
1001 */
1002 static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
1003 {
1004 int row, col;
1005 isl_int *r;
1006
1007 if (max_is_manifestly_unbounded(tab, var))
1008 return 1;
1009 to_row(tab, var, 1);
1010 r = tab->mat->row[var->index];
1011 while (isl_int_lt(r[1], r[0])) {
1012 find_pivot(tab, var, var, 1, &row, &col);
1013 if (row == -1)
1014 return isl_int_ge(r[1], r[0]);
1015 if (row == var->index) /* manifestly unbounded */
1016 return 1;
1017 isl_tab_pivot(tab, row, col);
1018 }
1019 return 1;
1020 }
1021
1022 static void swap_cols(struct isl_tab *tab, int col1, int col2)
1023 {
1024 int t;
1025 unsigned off = 2 + tab->M;
1026 t = tab->col_var[col1];
1027 tab->col_var[col1] = tab->col_var[col2];
1028 tab->col_var[col2] = t;
1029 var_from_col(tab, col1)->index = col1;
1030 var_from_col(tab, col2)->index = col2;
1031 tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2);
1032 }
1033
1034 /* Mark column with index "col" as representing a zero variable.
1035 * If we may need to undo the operation the column is kept,
1036 * but no longer considered.
1037 * Otherwise, the column is simply removed.
1038 *
1039 * The column may be interchanged with some other column. If it
1040 * is interchanged with a later column, return 1. Otherwise return 0.
1041 * If the columns are checked in order in the calling function,
1042 * then a return value of 1 means that the column with the given
1043 * column number may now contain a different column that
1044 * hasn't been checked yet.
1045 */
1046 int isl_tab_kill_col(struct isl_tab *tab, int col)
1047 {
1048 var_from_col(tab, col)->is_zero = 1;
1049 if (tab->need_undo) {
1050 isl_tab_push_var(tab, isl_tab_undo_zero, var_from_col(tab, col));
1051 if (col != tab->n_dead)
1052 swap_cols(tab, col, tab->n_dead);
1053 tab->n_dead++;
1054 return 0;
1055 } else {
1056 if (col != tab->n_col - 1)
1057 swap_cols(tab, col, tab->n_col - 1);
1058 var_from_col(tab, tab->n_col - 1)->index = -1;
1059 tab->n_col--;
1060 return 1;
1061 }
1062 }
1063
1064 /* Row variable "var" is non-negative and cannot attain any values
1065 * larger than zero. This means that the coefficients of the unrestricted
1066 * column variables are zero and that the coefficients of the non-negative
1067 * column variables are zero or negative.
1068 * Each of the non-negative variables with a negative coefficient can
1069 * then also be written as the negative sum of non-negative variables
1070 * and must therefore also be zero.
1071 */
1072 static void close_row(struct isl_tab *tab, struct isl_tab_var *var)
1073 {
1074 int j;
1075 struct isl_mat *mat = tab->mat;
1076 unsigned off = 2 + tab->M;
1077
1078 isl_assert(tab->mat->ctx, var->is_nonneg, return);
1079 var->is_zero = 1;
1080 if (tab->need_undo)
1081 isl_tab_push_var(tab, isl_tab_undo_zero, var);
1082 for (j = tab->n_dead; j < tab->n_col; ++j) {
1083 if (isl_int_is_zero(mat->row[var->index][off + j]))
1084 continue;
1085 isl_assert(tab->mat->ctx,
1086 isl_int_is_neg(mat->row[var->index][off + j]), return);
1087 if (isl_tab_kill_col(tab, j))
1088 --j;
1089 }
1090 isl_tab_mark_redundant(tab, var->index);
1091 }
1092
1093 /* Add a constraint to the tableau and allocate a row for it.
1094 * Return the index into the constraint array "con".
1095 */
1096 int isl_tab_allocate_con(struct isl_tab *tab)
1097 {
1098 int r;
1099
1100 isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
1101 isl_assert(tab->mat->ctx, tab->n_con < tab->max_con, return -1);
1102
1103 r = tab->n_con;
1104 tab->con[r].index = tab->n_row;
1105 tab->con[r].is_row = 1;
1106 tab->con[r].is_nonneg = 0;
1107 tab->con[r].is_zero = 0;
1108 tab->con[r].is_redundant = 0;
1109 tab->con[r].frozen = 0;
1110 tab->con[r].negated = 0;
1111 tab->row_var[tab->n_row] = ~r;
1112
1113 tab->n_row++;
1114 tab->n_con++;
1115 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
1116
1117 return r;
1118 }
1119
1120 /* Add a variable to the tableau and allocate a column for it.
1121 * Return the index into the variable array "var".
1122 */
1123 int isl_tab_allocate_var(struct isl_tab *tab)
1124 {
1125 int r;
1126 int i;
1127 unsigned off = 2 + tab->M;
1128
1129 isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
1130 isl_assert(tab->mat->ctx, tab->n_var < tab->max_var, return -1);
1131
1132 r = tab->n_var;
1133 tab->var[r].index = tab->n_col;
1134 tab->var[r].is_row = 0;
1135 tab->var[r].is_nonneg = 0;
1136 tab->var[r].is_zero = 0;
1137 tab->var[r].is_redundant = 0;
1138 tab->var[r].frozen = 0;
1139 tab->var[r].negated = 0;
1140 tab->col_var[tab->n_col] = r;
1141
1142 for (i = 0; i < tab->n_row; ++i)
1143 isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
1144
1145 tab->n_var++;
1146 tab->n_col++;
1147 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]);
1148
1149 return r;
1150 }
1151
1152 /* Add a row to the tableau. The row is given as an affine combination
1153 * of the original variables and needs to be expressed in terms of the
1154 * column variables.
1155 *
1156 * We add each term in turn.
1157 * If r = n/d_r is the current sum and we need to add k x, then
1158 * if x is a column variable, we increase the numerator of
1159 * this column by k d_r
1160 * if x = f/d_x is a row variable, then the new representation of r is
1161 *
1162 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1163 * --- + --- = ------------------- = -------------------
1164 * d_r d_r d_r d_x/g m
1165 *
1166 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1167 */
1168 int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
1169 {
1170 int i;
1171 int r;
1172 isl_int *row;
1173 isl_int a, b;
1174 unsigned off = 2 + tab->M;
1175
1176 r = isl_tab_allocate_con(tab);
1177 if (r < 0)
1178 return -1;
1179
1180 isl_int_init(a);
1181 isl_int_init(b);
1182 row = tab->mat->row[tab->con[r].index];
1183 isl_int_set_si(row[0], 1);
1184 isl_int_set(row[1], line[0]);
1185 isl_seq_clr(row + 2, tab->M + tab->n_col);
1186 for (i = 0; i < tab->n_var; ++i) {
1187 if (tab->var[i].is_zero)
1188 continue;
1189 if (tab->var[i].is_row) {
1190 isl_int_lcm(a,
1191 row[0], tab->mat->row[tab->var[i].index][0]);
1192 isl_int_swap(a, row[0]);
1193 isl_int_divexact(a, row[0], a);
1194 isl_int_divexact(b,
1195 row[0], tab->mat->row[tab->var[i].index][0]);
1196 isl_int_mul(b, b, line[1 + i]);
1197 isl_seq_combine(row + 1, a, row + 1,
1198 b, tab->mat->row[tab->var[i].index] + 1,
1199 1 + tab->M + tab->n_col);
1200 } else
1201 isl_int_addmul(row[off + tab->var[i].index],
1202 line[1 + i], row[0]);
1203 if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
1204 isl_int_submul(row[2], line[1 + i], row[0]);
1205 }
1206 isl_seq_normalize(tab->mat->ctx, row, off + tab->n_col);
1207 isl_int_clear(a);
1208 isl_int_clear(b);
1209
1210 if (tab->row_sign)
1211 tab->row_sign[tab->con[r].index] = 0;
1212
1213 return r;
1214 }
1215
1216 static int drop_row(struct isl_tab *tab, int row)
1217 {
1218 isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
1219 if (row != tab->n_row - 1)
1220 swap_rows(tab, row, tab->n_row - 1);
1221 tab->n_row--;
1222 tab->n_con--;
1223 return 0;
1224 }
1225
1226 static int drop_col(struct isl_tab *tab, int col)
1227 {
1228 isl_assert(tab->mat->ctx, tab->col_var[col] == tab->n_var - 1, return -1);
1229 if (col != tab->n_col - 1)
1230 swap_cols(tab, col, tab->n_col - 1);
1231 tab->n_col--;
1232 tab->n_var--;
1233 return 0;
1234 }
1235
1236 /* Add inequality "ineq" and check if it conflicts with the
1237 * previously added constraints or if it is obviously redundant.
1238 */
1239 struct isl_tab *isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
1240 {
1241 int r;
1242 int sgn;
1243
1244 if (!tab)
1245 return NULL;
1246 r = isl_tab_add_row(tab, ineq);
1247 if (r < 0)
1248 goto error;
1249 tab->con[r].is_nonneg = 1;
1250 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1251 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1252 isl_tab_mark_redundant(tab, tab->con[r].index);
1253 return tab;
1254 }
1255
1256 sgn = restore_row(tab, &tab->con[r]);
1257 if (sgn < 0)
1258 return isl_tab_mark_empty(tab);
1259 if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
1260 isl_tab_mark_redundant(tab, tab->con[r].index);
1261 return tab;
1262 error:
1263 isl_tab_free(tab);
1264 return NULL;
1265 }
1266
1267 /* Pivot a non-negative variable down until it reaches the value zero
1268 * and then pivot the variable into a column position.
1269 */
1270 static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
1271 {
1272 int i;
1273 int row, col;
1274 unsigned off = 2 + tab->M;
1275
1276 if (!var->is_row)
1277 return 0;
1278
1279 while (isl_int_is_pos(tab->mat->row[var->index][1])) {
1280 find_pivot(tab, var, NULL, -1, &row, &col);
1281 isl_assert(tab->mat->ctx, row != -1, return -1);
1282 isl_tab_pivot(tab, row, col);
1283 if (!var->is_row)
1284 return 0;
1285 }
1286
1287 for (i = tab->n_dead; i < tab->n_col; ++i)
1288 if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
1289 break;
1290
1291 isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
1292 isl_tab_pivot(tab, var->index, i);
1293
1294 return 0;
1295 }
1296
1297 /* We assume Gaussian elimination has been performed on the equalities.
1298 * The equalities can therefore never conflict.
1299 * Adding the equalities is currently only really useful for a later call
1300 * to isl_tab_ineq_type.
1301 */
1302 static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
1303 {
1304 int i;
1305 int r;
1306
1307 if (!tab)
1308 return NULL;
1309 r = isl_tab_add_row(tab, eq);
1310 if (r < 0)
1311 goto error;
1312
1313 r = tab->con[r].index;
1314 i = isl_seq_first_non_zero(tab->mat->row[r] + 2 + tab->M + tab->n_dead,
1315 tab->n_col - tab->n_dead);
1316 isl_assert(tab->mat->ctx, i >= 0, goto error);
1317 i += tab->n_dead;
1318 isl_tab_pivot(tab, r, i);
1319 isl_tab_kill_col(tab, i);
1320 tab->n_eq++;
1321
1322 return tab;
1323 error:
1324 isl_tab_free(tab);
1325 return NULL;
1326 }
1327
1328 /* Add an equality that is known to be valid for the given tableau.
1329 */
1330 struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
1331 {
1332 struct isl_tab_var *var;
1333 int r;
1334
1335 if (!tab)
1336 return NULL;
1337 r = isl_tab_add_row(tab, eq);
1338 if (r < 0)
1339 goto error;
1340
1341 var = &tab->con[r];
1342 r = var->index;
1343 if (isl_int_is_neg(tab->mat->row[r][1])) {
1344 isl_seq_neg(tab->mat->row[r] + 1, tab->mat->row[r] + 1,
1345 1 + tab->n_col);
1346 var->negated = 1;
1347 }
1348 var->is_nonneg = 1;
1349 if (to_col(tab, var) < 0)
1350 goto error;
1351 var->is_nonneg = 0;
1352 isl_tab_kill_col(tab, var->index);
1353
1354 return tab;
1355 error:
1356 isl_tab_free(tab);
1357 return NULL;
1358 }
1359
1360 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap)
1361 {
1362 int i;
1363 struct isl_tab *tab;
1364
1365 if (!bmap)
1366 return NULL;
1367 tab = isl_tab_alloc(bmap->ctx,
1368 isl_basic_map_total_dim(bmap) + bmap->n_ineq + 1,
1369 isl_basic_map_total_dim(bmap), 0);
1370 if (!tab)
1371 return NULL;
1372 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
1373 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1374 return isl_tab_mark_empty(tab);
1375 for (i = 0; i < bmap->n_eq; ++i) {
1376 tab = add_eq(tab, bmap->eq[i]);
1377 if (!tab)
1378 return tab;
1379 }
1380 for (i = 0; i < bmap->n_ineq; ++i) {
1381 tab = isl_tab_add_ineq(tab, bmap->ineq[i]);
1382 if (!tab || tab->empty)
1383 return tab;
1384 }
1385 return tab;
1386 }
1387
1388 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset)
1389 {
1390 return isl_tab_from_basic_map((struct isl_basic_map *)bset);
1391 }
1392
1393 /* Construct a tableau corresponding to the recession cone of "bset".
1394 */
1395 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_set *bset)
1396 {
1397 isl_int cst;
1398 int i;
1399 struct isl_tab *tab;
1400
1401 if (!bset)
1402 return NULL;
1403 tab = isl_tab_alloc(bset->ctx, bset->n_eq + bset->n_ineq,
1404 isl_basic_set_total_dim(bset), 0);
1405 if (!tab)
1406 return NULL;
1407 tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
1408
1409 isl_int_init(cst);
1410 for (i = 0; i < bset->n_eq; ++i) {
1411 isl_int_swap(bset->eq[i][0], cst);
1412 tab = add_eq(tab, bset->eq[i]);
1413 isl_int_swap(bset->eq[i][0], cst);
1414 if (!tab)
1415 goto done;
1416 }
1417 for (i = 0; i < bset->n_ineq; ++i) {
1418 int r;
1419 isl_int_swap(bset->ineq[i][0], cst);
1420 r = isl_tab_add_row(tab, bset->ineq[i]);
1421 isl_int_swap(bset->ineq[i][0], cst);
1422 if (r < 0)
1423 goto error;
1424 tab->con[r].is_nonneg = 1;
1425 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1426 }
1427 done:
1428 isl_int_clear(cst);
1429 return tab;
1430 error:
1431 isl_int_clear(cst);
1432 isl_tab_free(tab);
1433 return NULL;
1434 }
1435
1436 /* Assuming "tab" is the tableau of a cone, check if the cone is
1437 * bounded, i.e., if it is empty or only contains the origin.
1438 */
1439 int isl_tab_cone_is_bounded(struct isl_tab *tab)
1440 {
1441 int i;
1442
1443 if (!tab)
1444 return -1;
1445 if (tab->empty)
1446 return 1;
1447 if (tab->n_dead == tab->n_col)
1448 return 1;
1449
1450 for (;;) {
1451 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1452 struct isl_tab_var *var;
1453 var = isl_tab_var_from_row(tab, i);
1454 if (!var->is_nonneg)
1455 continue;
1456 if (sign_of_max(tab, var) != 0)
1457 return 0;
1458 close_row(tab, var);
1459 break;
1460 }
1461 if (tab->n_dead == tab->n_col)
1462 return 1;
1463 if (i == tab->n_row)
1464 return 0;
1465 }
1466 }
1467
1468 int isl_tab_sample_is_integer(struct isl_tab *tab)
1469 {
1470 int i;
1471
1472 if (!tab)
1473 return -1;
1474
1475 for (i = 0; i < tab->n_var; ++i) {
1476 int row;
1477 if (!tab->var[i].is_row)
1478 continue;
1479 row = tab->var[i].index;
1480 if (!isl_int_is_divisible_by(tab->mat->row[row][1],
1481 tab->mat->row[row][0]))
1482 return 0;
1483 }
1484 return 1;
1485 }
1486
1487 static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
1488 {
1489 int i;
1490 struct isl_vec *vec;
1491
1492 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
1493 if (!vec)
1494 return NULL;
1495
1496 isl_int_set_si(vec->block.data[0], 1);
1497 for (i = 0; i < tab->n_var; ++i) {
1498 if (!tab->var[i].is_row)
1499 isl_int_set_si(vec->block.data[1 + i], 0);
1500 else {
1501 int row = tab->var[i].index;
1502 isl_int_divexact(vec->block.data[1 + i],
1503 tab->mat->row[row][1], tab->mat->row[row][0]);
1504 }
1505 }
1506
1507 return vec;
1508 }
1509
1510 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
1511 {
1512 int i;
1513 struct isl_vec *vec;
1514 isl_int m;
1515
1516 if (!tab)
1517 return NULL;
1518
1519 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
1520 if (!vec)
1521 return NULL;
1522
1523 isl_int_init(m);
1524
1525 isl_int_set_si(vec->block.data[0], 1);
1526 for (i = 0; i < tab->n_var; ++i) {
1527 int row;
1528 if (!tab->var[i].is_row) {
1529 isl_int_set_si(vec->block.data[1 + i], 0);
1530 continue;
1531 }
1532 row = tab->var[i].index;
1533 isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
1534 isl_int_divexact(m, tab->mat->row[row][0], m);
1535 isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
1536 isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
1537 isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
1538 }
1539 vec = isl_vec_normalize(vec);
1540
1541 isl_int_clear(m);
1542 return vec;
1543 }
1544
1545 /* Update "bmap" based on the results of the tableau "tab".
1546 * In particular, implicit equalities are made explicit, redundant constraints
1547 * are removed and if the sample value happens to be integer, it is stored
1548 * in "bmap" (unless "bmap" already had an integer sample).
1549 *
1550 * The tableau is assumed to have been created from "bmap" using
1551 * isl_tab_from_basic_map.
1552 */
1553 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
1554 struct isl_tab *tab)
1555 {
1556 int i;
1557 unsigned n_eq;
1558
1559 if (!bmap)
1560 return NULL;
1561 if (!tab)
1562 return bmap;
1563
1564 n_eq = tab->n_eq;
1565 if (tab->empty)
1566 bmap = isl_basic_map_set_to_empty(bmap);
1567 else
1568 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1569 if (isl_tab_is_equality(tab, n_eq + i))
1570 isl_basic_map_inequality_to_equality(bmap, i);
1571 else if (isl_tab_is_redundant(tab, n_eq + i))
1572 isl_basic_map_drop_inequality(bmap, i);
1573 }
1574 if (!tab->rational &&
1575 !bmap->sample && isl_tab_sample_is_integer(tab))
1576 bmap->sample = extract_integer_sample(tab);
1577 return bmap;
1578 }
1579
1580 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
1581 struct isl_tab *tab)
1582 {
1583 return (struct isl_basic_set *)isl_basic_map_update_from_tab(
1584 (struct isl_basic_map *)bset, tab);
1585 }
1586
1587 /* Given a non-negative variable "var", add a new non-negative variable
1588 * that is the opposite of "var", ensuring that var can only attain the
1589 * value zero.
1590 * If var = n/d is a row variable, then the new variable = -n/d.
1591 * If var is a column variables, then the new variable = -var.
1592 * If the new variable cannot attain non-negative values, then
1593 * the resulting tableau is empty.
1594 * Otherwise, we know the value will be zero and we close the row.
1595 */
1596 static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab,
1597 struct isl_tab_var *var)
1598 {
1599 unsigned r;
1600 isl_int *row;
1601 int sgn;
1602 unsigned off = 2 + tab->M;
1603
1604 if (var->is_zero)
1605 return tab;
1606 isl_assert(tab->mat->ctx, !var->is_redundant, goto error);
1607
1608 if (isl_tab_extend_cons(tab, 1) < 0)
1609 goto error;
1610
1611 r = tab->n_con;
1612 tab->con[r].index = tab->n_row;
1613 tab->con[r].is_row = 1;
1614 tab->con[r].is_nonneg = 0;
1615 tab->con[r].is_zero = 0;
1616 tab->con[r].is_redundant = 0;
1617 tab->con[r].frozen = 0;
1618 tab->con[r].negated = 0;
1619 tab->row_var[tab->n_row] = ~r;
1620 row = tab->mat->row[tab->n_row];
1621
1622 if (var->is_row) {
1623 isl_int_set(row[0], tab->mat->row[var->index][0]);
1624 isl_seq_neg(row + 1,
1625 tab->mat->row[var->index] + 1, 1 + tab->n_col);
1626 } else {
1627 isl_int_set_si(row[0], 1);
1628 isl_seq_clr(row + 1, 1 + tab->n_col);
1629 isl_int_set_si(row[off + var->index], -1);
1630 }
1631
1632 tab->n_row++;
1633 tab->n_con++;
1634 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
1635
1636 sgn = sign_of_max(tab, &tab->con[r]);
1637 if (sgn < 0)
1638 return isl_tab_mark_empty(tab);
1639 tab->con[r].is_nonneg = 1;
1640 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1641 /* sgn == 0 */
1642 close_row(tab, &tab->con[r]);
1643
1644 return tab;
1645 error:
1646 isl_tab_free(tab);
1647 return NULL;
1648 }
1649
1650 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
1651 * relax the inequality by one. That is, the inequality r >= 0 is replaced
1652 * by r' = r + 1 >= 0.
1653 * If r is a row variable, we simply increase the constant term by one
1654 * (taking into account the denominator).
1655 * If r is a column variable, then we need to modify each row that
1656 * refers to r = r' - 1 by substituting this equality, effectively
1657 * subtracting the coefficient of the column from the constant.
1658 */
1659 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
1660 {
1661 struct isl_tab_var *var;
1662 unsigned off = 2 + tab->M;
1663
1664 if (!tab)
1665 return NULL;
1666
1667 var = &tab->con[con];
1668
1669 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
1670 to_row(tab, var, 1);
1671
1672 if (var->is_row)
1673 isl_int_add(tab->mat->row[var->index][1],
1674 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
1675 else {
1676 int i;
1677
1678 for (i = 0; i < tab->n_row; ++i) {
1679 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
1680 continue;
1681 isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
1682 tab->mat->row[i][off + var->index]);
1683 }
1684
1685 }
1686
1687 isl_tab_push_var(tab, isl_tab_undo_relax, var);
1688
1689 return tab;
1690 }
1691
1692 struct isl_tab *isl_tab_select_facet(struct isl_tab *tab, int con)
1693 {
1694 if (!tab)
1695 return NULL;
1696
1697 return cut_to_hyperplane(tab, &tab->con[con]);
1698 }
1699
1700 static int may_be_equality(struct isl_tab *tab, int row)
1701 {
1702 unsigned off = 2 + tab->M;
1703 return (tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
1704 : isl_int_lt(tab->mat->row[row][1],
1705 tab->mat->row[row][0])) &&
1706 isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1707 tab->n_col - tab->n_dead) != -1;
1708 }
1709
1710 /* Check for (near) equalities among the constraints.
1711 * A constraint is an equality if it is non-negative and if
1712 * its maximal value is either
1713 * - zero (in case of rational tableaus), or
1714 * - strictly less than 1 (in case of integer tableaus)
1715 *
1716 * We first mark all non-redundant and non-dead variables that
1717 * are not frozen and not obviously not an equality.
1718 * Then we iterate over all marked variables if they can attain
1719 * any values larger than zero or at least one.
1720 * If the maximal value is zero, we mark any column variables
1721 * that appear in the row as being zero and mark the row as being redundant.
1722 * Otherwise, if the maximal value is strictly less than one (and the
1723 * tableau is integer), then we restrict the value to being zero
1724 * by adding an opposite non-negative variable.
1725 */
1726 struct isl_tab *isl_tab_detect_equalities(struct isl_tab *tab)
1727 {
1728 int i;
1729 unsigned n_marked;
1730
1731 if (!tab)
1732 return NULL;
1733 if (tab->empty)
1734 return tab;
1735 if (tab->n_dead == tab->n_col)
1736 return tab;
1737
1738 n_marked = 0;
1739 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1740 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
1741 var->marked = !var->frozen && var->is_nonneg &&
1742 may_be_equality(tab, i);
1743 if (var->marked)
1744 n_marked++;
1745 }
1746 for (i = tab->n_dead; i < tab->n_col; ++i) {
1747 struct isl_tab_var *var = var_from_col(tab, i);
1748 var->marked = !var->frozen && var->is_nonneg;
1749 if (var->marked)
1750 n_marked++;
1751 }
1752 while (n_marked) {
1753 struct isl_tab_var *var;
1754 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1755 var = isl_tab_var_from_row(tab, i);
1756 if (var->marked)
1757 break;
1758 }
1759 if (i == tab->n_row) {
1760 for (i = tab->n_dead; i < tab->n_col; ++i) {
1761 var = var_from_col(tab, i);
1762 if (var->marked)
1763 break;
1764 }
1765 if (i == tab->n_col)
1766 break;
1767 }
1768 var->marked = 0;
1769 n_marked--;
1770 if (sign_of_max(tab, var) == 0)
1771 close_row(tab, var);
1772 else if (!tab->rational && !at_least_one(tab, var)) {
1773 tab = cut_to_hyperplane(tab, var);
1774 return isl_tab_detect_equalities(tab);
1775 }
1776 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1777 var = isl_tab_var_from_row(tab, i);
1778 if (!var->marked)
1779 continue;
1780 if (may_be_equality(tab, i))
1781 continue;
1782 var->marked = 0;
1783 n_marked--;
1784 }
1785 }
1786
1787 return tab;
1788 }
1789
1790 /* Check for (near) redundant constraints.
1791 * A constraint is redundant if it is non-negative and if
1792 * its minimal value (temporarily ignoring the non-negativity) is either
1793 * - zero (in case of rational tableaus), or
1794 * - strictly larger than -1 (in case of integer tableaus)
1795 *
1796 * We first mark all non-redundant and non-dead variables that
1797 * are not frozen and not obviously negatively unbounded.
1798 * Then we iterate over all marked variables if they can attain
1799 * any values smaller than zero or at most negative one.
1800 * If not, we mark the row as being redundant (assuming it hasn't
1801 * been detected as being obviously redundant in the mean time).
1802 */
1803 struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab)
1804 {
1805 int i;
1806 unsigned n_marked;
1807
1808 if (!tab)
1809 return NULL;
1810 if (tab->empty)
1811 return tab;
1812 if (tab->n_redundant == tab->n_row)
1813 return tab;
1814
1815 n_marked = 0;
1816 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1817 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
1818 var->marked = !var->frozen && var->is_nonneg;
1819 if (var->marked)
1820 n_marked++;
1821 }
1822 for (i = tab->n_dead; i < tab->n_col; ++i) {
1823 struct isl_tab_var *var = var_from_col(tab, i);
1824 var->marked = !var->frozen && var->is_nonneg &&
1825 !min_is_manifestly_unbounded(tab, var);
1826 if (var->marked)
1827 n_marked++;
1828 }
1829 while (n_marked) {
1830 struct isl_tab_var *var;
1831 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1832 var = isl_tab_var_from_row(tab, i);
1833 if (var->marked)
1834 break;
1835 }
1836 if (i == tab->n_row) {
1837 for (i = tab->n_dead; i < tab->n_col; ++i) {
1838 var = var_from_col(tab, i);
1839 if (var->marked)
1840 break;
1841 }
1842 if (i == tab->n_col)
1843 break;
1844 }
1845 var->marked = 0;
1846 n_marked--;
1847 if ((tab->rational ? (sign_of_min(tab, var) >= 0)
1848 : !isl_tab_min_at_most_neg_one(tab, var)) &&
1849 !var->is_redundant)
1850 isl_tab_mark_redundant(tab, var->index);
1851 for (i = tab->n_dead; i < tab->n_col; ++i) {
1852 var = var_from_col(tab, i);
1853 if (!var->marked)
1854 continue;
1855 if (!min_is_manifestly_unbounded(tab, var))
1856 continue;
1857 var->marked = 0;
1858 n_marked--;
1859 }
1860 }
1861
1862 return tab;
1863 }
1864
1865 int isl_tab_is_equality(struct isl_tab *tab, int con)
1866 {
1867 int row;
1868 unsigned off;
1869
1870 if (!tab)
1871 return -1;
1872 if (tab->con[con].is_zero)
1873 return 1;
1874 if (tab->con[con].is_redundant)
1875 return 0;
1876 if (!tab->con[con].is_row)
1877 return tab->con[con].index < tab->n_dead;
1878
1879 row = tab->con[con].index;
1880
1881 off = 2 + tab->M;
1882 return isl_int_is_zero(tab->mat->row[row][1]) &&
1883 isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
1884 tab->n_col - tab->n_dead) == -1;
1885 }
1886
1887 /* Return the minimial value of the affine expression "f" with denominator
1888 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
1889 * the expression cannot attain arbitrarily small values.
1890 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
1891 * The return value reflects the nature of the result (empty, unbounded,
1892 * minmimal value returned in *opt).
1893 */
1894 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
1895 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
1896 unsigned flags)
1897 {
1898 int r;
1899 enum isl_lp_result res = isl_lp_ok;
1900 struct isl_tab_var *var;
1901 struct isl_tab_undo *snap;
1902
1903 if (tab->empty)
1904 return isl_lp_empty;
1905
1906 snap = isl_tab_snap(tab);
1907 r = isl_tab_add_row(tab, f);
1908 if (r < 0)
1909 return isl_lp_error;
1910 var = &tab->con[r];
1911 isl_int_mul(tab->mat->row[var->index][0],
1912 tab->mat->row[var->index][0], denom);
1913 for (;;) {
1914 int row, col;
1915 find_pivot(tab, var, var, -1, &row, &col);
1916 if (row == var->index) {
1917 res = isl_lp_unbounded;
1918 break;
1919 }
1920 if (row == -1)
1921 break;
1922 isl_tab_pivot(tab, row, col);
1923 }
1924 if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
1925 int i;
1926
1927 isl_vec_free(tab->dual);
1928 tab->dual = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_con);
1929 if (!tab->dual)
1930 return isl_lp_error;
1931 isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
1932 for (i = 0; i < tab->n_con; ++i) {
1933 int pos;
1934 if (tab->con[i].is_row) {
1935 isl_int_set_si(tab->dual->el[1 + i], 0);
1936 continue;
1937 }
1938 pos = 2 + tab->M + tab->con[i].index;
1939 if (tab->con[i].negated)
1940 isl_int_neg(tab->dual->el[1 + i],
1941 tab->mat->row[var->index][pos]);
1942 else
1943 isl_int_set(tab->dual->el[1 + i],
1944 tab->mat->row[var->index][pos]);
1945 }
1946 }
1947 if (opt && res == isl_lp_ok) {
1948 if (opt_denom) {
1949 isl_int_set(*opt, tab->mat->row[var->index][1]);
1950 isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
1951 } else
1952 isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
1953 tab->mat->row[var->index][0]);
1954 }
1955 if (isl_tab_rollback(tab, snap) < 0)
1956 return isl_lp_error;
1957 return res;
1958 }
1959
1960 int isl_tab_is_redundant(struct isl_tab *tab, int con)
1961 {
1962 if (!tab)
1963 return -1;
1964 if (tab->con[con].is_zero)
1965 return 0;
1966 if (tab->con[con].is_redundant)
1967 return 1;
1968 return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
1969 }
1970
1971 /* Take a snapshot of the tableau that can be restored by s call to
1972 * isl_tab_rollback.
1973 */
1974 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
1975 {
1976 if (!tab)
1977 return NULL;
1978 tab->need_undo = 1;
1979 return tab->top;
1980 }
1981
1982 /* Undo the operation performed by isl_tab_relax.
1983 */
1984 static void unrelax(struct isl_tab *tab, struct isl_tab_var *var)
1985 {
1986 unsigned off = 2 + tab->M;
1987
1988 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
1989 to_row(tab, var, 1);
1990
1991 if (var->is_row)
1992 isl_int_sub(tab->mat->row[var->index][1],
1993 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
1994 else {
1995 int i;
1996
1997 for (i = 0; i < tab->n_row; ++i) {
1998 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
1999 continue;
2000 isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
2001 tab->mat->row[i][off + var->index]);
2002 }
2003
2004 }
2005 }
2006
2007 static void perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
2008 {
2009 struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
2010 switch(undo->type) {
2011 case isl_tab_undo_nonneg:
2012 var->is_nonneg = 0;
2013 break;
2014 case isl_tab_undo_redundant:
2015 var->is_redundant = 0;
2016 tab->n_redundant--;
2017 break;
2018 case isl_tab_undo_zero:
2019 var->is_zero = 0;
2020 if (!var->is_row)
2021 tab->n_dead--;
2022 break;
2023 case isl_tab_undo_allocate:
2024 if (undo->u.var_index >= 0) {
2025 isl_assert(tab->mat->ctx, !var->is_row, return);
2026 drop_col(tab, var->index);
2027 break;
2028 }
2029 if (!var->is_row) {
2030 if (!max_is_manifestly_unbounded(tab, var))
2031 to_row(tab, var, 1);
2032 else if (!min_is_manifestly_unbounded(tab, var))
2033 to_row(tab, var, -1);
2034 else
2035 to_row(tab, var, 0);
2036 }
2037 drop_row(tab, var->index);
2038 break;
2039 case isl_tab_undo_relax:
2040 unrelax(tab, var);
2041 break;
2042 }
2043 }
2044
2045 /* Restore the tableau to the state where the basic variables
2046 * are those in "col_var".
2047 * We first construct a list of variables that are currently in
2048 * the basis, but shouldn't. Then we iterate over all variables
2049 * that should be in the basis and for each one that is currently
2050 * not in the basis, we exchange it with one of the elements of the
2051 * list constructed before.
2052 * We can always find an appropriate variable to pivot with because
2053 * the current basis is mapped to the old basis by a non-singular
2054 * matrix and so we can never end up with a zero row.
2055 */
2056 static int restore_basis(struct isl_tab *tab, int *col_var)
2057 {
2058 int i, j;
2059 int n_extra = 0;
2060 int *extra = NULL; /* current columns that contain bad stuff */
2061 unsigned off = 2 + tab->M;
2062
2063 extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
2064 if (!extra)
2065 goto error;
2066 for (i = 0; i < tab->n_col; ++i) {
2067 for (j = 0; j < tab->n_col; ++j)
2068 if (tab->col_var[i] == col_var[j])
2069 break;
2070 if (j < tab->n_col)
2071 continue;
2072 extra[n_extra++] = i;
2073 }
2074 for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
2075 struct isl_tab_var *var;
2076 int row;
2077
2078 for (j = 0; j < tab->n_col; ++j)
2079 if (col_var[i] == tab->col_var[j])
2080 break;
2081 if (j < tab->n_col)
2082 continue;
2083 var = var_from_index(tab, col_var[i]);
2084 row = var->index;
2085 for (j = 0; j < n_extra; ++j)
2086 if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
2087 break;
2088 isl_assert(tab->mat->ctx, j < n_extra, goto error);
2089 isl_tab_pivot(tab, row, extra[j]);
2090 extra[j] = extra[--n_extra];
2091 }
2092
2093 free(extra);
2094 free(col_var);
2095 return 0;
2096 error:
2097 free(extra);
2098 free(col_var);
2099 return -1;
2100 }
2101
2102 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
2103 {
2104 switch (undo->type) {
2105 case isl_tab_undo_empty:
2106 tab->empty = 0;
2107 break;
2108 case isl_tab_undo_nonneg:
2109 case isl_tab_undo_redundant:
2110 case isl_tab_undo_zero:
2111 case isl_tab_undo_allocate:
2112 case isl_tab_undo_relax:
2113 perform_undo_var(tab, undo);
2114 break;
2115 case isl_tab_undo_bset_eq:
2116 isl_basic_set_free_equality(tab->bset, 1);
2117 break;
2118 case isl_tab_undo_bset_ineq:
2119 isl_basic_set_free_inequality(tab->bset, 1);
2120 break;
2121 case isl_tab_undo_bset_div:
2122 isl_basic_set_free_div(tab->bset, 1);
2123 if (tab->samples)
2124 tab->samples->n_col--;
2125 break;
2126 case isl_tab_undo_saved_basis:
2127 if (restore_basis(tab, undo->u.col_var) < 0)
2128 return -1;
2129 break;
2130 case isl_tab_undo_drop_sample:
2131 tab->n_outside--;
2132 break;
2133 default:
2134 isl_assert(tab->mat->ctx, 0, return -1);
2135 }
2136 return 0;
2137 }
2138
2139 /* Return the tableau to the state it was in when the snapshot "snap"
2140 * was taken.
2141 */
2142 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
2143 {
2144 struct isl_tab_undo *undo, *next;
2145
2146 if (!tab)
2147 return -1;
2148
2149 tab->in_undo = 1;
2150 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
2151 next = undo->next;
2152 if (undo == snap)
2153 break;
2154 if (perform_undo(tab, undo) < 0) {
2155 free_undo(tab);
2156 tab->in_undo = 0;
2157 return -1;
2158 }
2159 free(undo);
2160 }
2161 tab->in_undo = 0;
2162 tab->top = undo;
2163 if (!undo)
2164 return -1;
2165 return 0;
2166 }
2167
2168 /* The given row "row" represents an inequality violated by all
2169 * points in the tableau. Check for some special cases of such
2170 * separating constraints.
2171 * In particular, if the row has been reduced to the constant -1,
2172 * then we know the inequality is adjacent (but opposite) to
2173 * an equality in the tableau.
2174 * If the row has been reduced to r = -1 -r', with r' an inequality
2175 * of the tableau, then the inequality is adjacent (but opposite)
2176 * to the inequality r'.
2177 */
2178 static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
2179 {
2180 int pos;
2181 unsigned off = 2 + tab->M;
2182
2183 if (tab->rational)
2184 return isl_ineq_separate;
2185
2186 if (!isl_int_is_one(tab->mat->row[row][0]))
2187 return isl_ineq_separate;
2188 if (!isl_int_is_negone(tab->mat->row[row][1]))
2189 return isl_ineq_separate;
2190
2191 pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
2192 tab->n_col - tab->n_dead);
2193 if (pos == -1)
2194 return isl_ineq_adj_eq;
2195
2196 if (!isl_int_is_negone(tab->mat->row[row][off + tab->n_dead + pos]))
2197 return isl_ineq_separate;
2198
2199 pos = isl_seq_first_non_zero(
2200 tab->mat->row[row] + off + tab->n_dead + pos + 1,
2201 tab->n_col - tab->n_dead - pos - 1);
2202
2203 return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
2204 }
2205
2206 /* Check the effect of inequality "ineq" on the tableau "tab".
2207 * The result may be
2208 * isl_ineq_redundant: satisfied by all points in the tableau
2209 * isl_ineq_separate: satisfied by no point in the tableau
2210 * isl_ineq_cut: satisfied by some by not all points
2211 * isl_ineq_adj_eq: adjacent to an equality
2212 * isl_ineq_adj_ineq: adjacent to an inequality.
2213 */
2214 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
2215 {
2216 enum isl_ineq_type type = isl_ineq_error;
2217 struct isl_tab_undo *snap = NULL;
2218 int con;
2219 int row;
2220
2221 if (!tab)
2222 return isl_ineq_error;
2223
2224 if (isl_tab_extend_cons(tab, 1) < 0)
2225 return isl_ineq_error;
2226
2227 snap = isl_tab_snap(tab);
2228
2229 con = isl_tab_add_row(tab, ineq);
2230 if (con < 0)
2231 goto error;
2232
2233 row = tab->con[con].index;
2234 if (isl_tab_row_is_redundant(tab, row))
2235 type = isl_ineq_redundant;
2236 else if (isl_int_is_neg(tab->mat->row[row][1]) &&
2237 (tab->rational ||
2238 isl_int_abs_ge(tab->mat->row[row][1],
2239 tab->mat->row[row][0]))) {
2240 if (at_least_zero(tab, &tab->con[con]))
2241 type = isl_ineq_cut;
2242 else
2243 type = separation_type(tab, row);
2244 } else if (tab->rational ? (sign_of_min(tab, &tab->con[con]) < 0)
2245 : isl_tab_min_at_most_neg_one(tab, &tab->con[con]))
2246 type = isl_ineq_cut;
2247 else
2248 type = isl_ineq_redundant;
2249
2250 if (isl_tab_rollback(tab, snap))
2251 return isl_ineq_error;
2252 return type;
2253 error:
2254 isl_tab_rollback(tab, snap);
2255 return isl_ineq_error;
2256 }
2257
2258 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent)
2259 {
2260 unsigned r, c;
2261 int i;
2262
2263 if (!tab) {
2264 fprintf(out, "%*snull tab\n", indent, "");
2265 return;
2266 }
2267 fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
2268 tab->n_redundant, tab->n_dead);
2269 if (tab->rational)
2270 fprintf(out, ", rational");
2271 if (tab->empty)
2272 fprintf(out, ", empty");
2273 fprintf(out, "\n");
2274 fprintf(out, "%*s[", indent, "");
2275 for (i = 0; i < tab->n_var; ++i) {
2276 if (i)
2277 fprintf(out, (i == tab->n_param ||
2278 i == tab->n_var - tab->n_div) ? "; "
2279 : ", ");
2280 fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
2281 tab->var[i].index,
2282 tab->var[i].is_zero ? " [=0]" :
2283 tab->var[i].is_redundant ? " [R]" : "");
2284 }
2285 fprintf(out, "]\n");
2286 fprintf(out, "%*s[", indent, "");
2287 for (i = 0; i < tab->n_con; ++i) {
2288 if (i)
2289 fprintf(out, ", ");
2290 fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
2291 tab->con[i].index,
2292 tab->con[i].is_zero ? " [=0]" :
2293 tab->con[i].is_redundant ? " [R]" : "");
2294 }
2295 fprintf(out, "]\n");
2296 fprintf(out, "%*s[", indent, "");
2297 for (i = 0; i < tab->n_row; ++i) {
2298 const char *sign = "";
2299 if (i)
2300 fprintf(out, ", ");
2301 if (tab->row_sign) {
2302 if (tab->row_sign[i] == isl_tab_row_unknown)
2303 sign = "?";
2304 else if (tab->row_sign[i] == isl_tab_row_neg)
2305 sign = "-";
2306 else if (tab->row_sign[i] == isl_tab_row_pos)
2307 sign = "+";
2308 else
2309 sign = "+-";
2310 }
2311 fprintf(out, "r%d: %d%s%s", i, tab->row_var[i],
2312 isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
2313 }
2314 fprintf(out, "]\n");
2315 fprintf(out, "%*s[", indent, "");
2316 for (i = 0; i < tab->n_col; ++i) {
2317 if (i)
2318 fprintf(out, ", ");
2319 fprintf(out, "c%d: %d%s", i, tab->col_var[i],
2320 var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
2321 }
2322 fprintf(out, "]\n");
2323 r = tab->mat->n_row;
2324 tab->mat->n_row = tab->n_row;
2325 c = tab->mat->n_col;
2326 tab->mat->n_col = 2 + tab->M + tab->n_col;
2327 isl_mat_dump(tab->mat, out, indent);
2328 tab->mat->n_row = r;
2329 tab->mat->n_col = c;
2330 if (tab->bset)
2331 isl_basic_set_dump(tab->bset, out, indent);
2332 }
Integer set library