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isl_tab_compute_reduced_basis: work with affine basis instead of linear basis
[isl.git] / isl_tab.c
blob84345e0cf6d5b2e70bfb2f953a400e721784c39d
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
67 tab->n_zero = 0;
68 tab->basis = NULL;
69
70 return tab;
71 error:
72 isl_tab_free(tab);
73 return NULL;
74 }
75
76 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new)
77 {
78 unsigned off = 2 + tab->M;
79
80 if (!tab)
81 return -1;
82
83 if (tab->max_con < tab->n_con + n_new) {
84 struct isl_tab_var *con;
85
86 con = isl_realloc_array(tab->mat->ctx, tab->con,
87 struct isl_tab_var, tab->max_con + n_new);
88 if (!con)
89 return -1;
90 tab->con = con;
91 tab->max_con += n_new;
92 }
93 if (tab->mat->n_row < tab->n_row + n_new) {
94 int *row_var;
95
96 tab->mat = isl_mat_extend(tab->mat,
97 tab->n_row + n_new, off + tab->n_col);
98 if (!tab->mat)
99 return -1;
100 row_var = isl_realloc_array(tab->mat->ctx, tab->row_var,
101 int, tab->mat->n_row);
102 if (!row_var)
103 return -1;
104 tab->row_var = row_var;
105 if (tab->row_sign) {
106 enum isl_tab_row_sign *s;
107 s = isl_realloc_array(tab->mat->ctx, tab->row_sign,
108 enum isl_tab_row_sign, tab->mat->n_row);
109 if (!s)
110 return -1;
111 tab->row_sign = s;
112 }
113 }
114 return 0;
115 }
116
117 /* Make room for at least n_new extra variables.
118 * Return -1 if anything went wrong.
119 */
120 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new)
121 {
122 struct isl_tab_var *var;
123 unsigned off = 2 + tab->M;
124
125 if (tab->max_var < tab->n_var + n_new) {
126 var = isl_realloc_array(tab->mat->ctx, tab->var,
127 struct isl_tab_var, tab->n_var + n_new);
128 if (!var)
129 return -1;
130 tab->var = var;
131 tab->max_var += n_new;
132 }
133
134 if (tab->mat->n_col < off + tab->n_col + n_new) {
135 int *p;
136
137 tab->mat = isl_mat_extend(tab->mat,
138 tab->mat->n_row, off + tab->n_col + n_new);
139 if (!tab->mat)
140 return -1;
141 p = isl_realloc_array(tab->mat->ctx, tab->col_var,
142 int, tab->n_col + n_new);
143 if (!p)
144 return -1;
145 tab->col_var = p;
146 }
147
148 return 0;
149 }
150
151 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new)
152 {
153 if (isl_tab_extend_cons(tab, n_new) >= 0)
154 return tab;
155
156 isl_tab_free(tab);
157 return NULL;
158 }
159
160 static void free_undo(struct isl_tab *tab)
161 {
162 struct isl_tab_undo *undo, *next;
163
164 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
165 next = undo->next;
166 free(undo);
167 }
168 tab->top = undo;
169 }
170
171 void isl_tab_free(struct isl_tab *tab)
172 {
173 if (!tab)
174 return;
175 free_undo(tab);
176 isl_mat_free(tab->mat);
177 isl_vec_free(tab->dual);
178 isl_basic_set_free(tab->bset);
179 free(tab->var);
180 free(tab->con);
181 free(tab->row_var);
182 free(tab->col_var);
183 free(tab->row_sign);
184 isl_mat_free(tab->samples);
185 isl_mat_free(tab->basis);
186 free(tab);
187 }
188
189 struct isl_tab *isl_tab_dup(struct isl_tab *tab)
190 {
191 int i;
192 struct isl_tab *dup;
193 unsigned off;
194
195 if (!tab)
196 return NULL;
197
198 off = 2 + tab->M;
199 dup = isl_calloc_type(tab->ctx, struct isl_tab);
200 if (!dup)
201 return NULL;
202 dup->mat = isl_mat_dup(tab->mat);
203 if (!dup->mat)
204 goto error;
205 dup->var = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_var);
206 if (!dup->var)
207 goto error;
208 for (i = 0; i < tab->n_var; ++i)
209 dup->var[i] = tab->var[i];
210 dup->con = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_con);
211 if (!dup->con)
212 goto error;
213 for (i = 0; i < tab->n_con; ++i)
214 dup->con[i] = tab->con[i];
215 dup->col_var = isl_alloc_array(tab->ctx, int, tab->mat->n_col - off);
216 if (!dup->col_var)
217 goto error;
218 for (i = 0; i < tab->n_col; ++i)
219 dup->col_var[i] = tab->col_var[i];
220 dup->row_var = isl_alloc_array(tab->ctx, int, tab->mat->n_row);
221 if (!dup->row_var)
222 goto error;
223 for (i = 0; i < tab->n_row; ++i)
224 dup->row_var[i] = tab->row_var[i];
225 if (tab->row_sign) {
226 dup->row_sign = isl_alloc_array(tab->ctx, enum isl_tab_row_sign,
227 tab->mat->n_row);
228 if (!dup->row_sign)
229 goto error;
230 for (i = 0; i < tab->n_row; ++i)
231 dup->row_sign[i] = tab->row_sign[i];
232 }
233 if (tab->samples) {
234 dup->samples = isl_mat_dup(tab->samples);
235 if (!dup->samples)
236 goto error;
237 dup->n_sample = tab->n_sample;
238 dup->n_outside = tab->n_outside;
239 }
240 dup->n_row = tab->n_row;
241 dup->n_con = tab->n_con;
242 dup->n_eq = tab->n_eq;
243 dup->max_con = tab->max_con;
244 dup->n_col = tab->n_col;
245 dup->n_var = tab->n_var;
246 dup->max_var = tab->max_var;
247 dup->n_param = tab->n_param;
248 dup->n_div = tab->n_div;
249 dup->n_dead = tab->n_dead;
250 dup->n_redundant = tab->n_redundant;
251 dup->rational = tab->rational;
252 dup->empty = tab->empty;
253 dup->need_undo = 0;
254 dup->in_undo = 0;
255 dup->M = tab->M;
256 dup->bottom.type = isl_tab_undo_bottom;
257 dup->bottom.next = NULL;
258 dup->top = &dup->bottom;
259
260 dup->n_zero = tab->n_zero;
261 dup->basis = isl_mat_dup(tab->basis);
262
263 return dup;
264 error:
265 isl_tab_free(dup);
266 return NULL;
267 }
268
269 /* Construct the coefficient matrix of the product tableau
270 * of two tableaus.
271 * mat{1,2} is the coefficient matrix of tableau {1,2}
272 * row{1,2} is the number of rows in tableau {1,2}
273 * col{1,2} is the number of columns in tableau {1,2}
274 * off is the offset to the coefficient column (skipping the
275 * denominator, the constant term and the big parameter if any)
276 * r{1,2} is the number of redundant rows in tableau {1,2}
277 * d{1,2} is the number of dead columns in tableau {1,2}
278 *
279 * The order of the rows and columns in the result is as explained
280 * in isl_tab_product.
281 */
282 static struct isl_mat *tab_mat_product(struct isl_mat *mat1,
283 struct isl_mat *mat2, unsigned row1, unsigned row2,
284 unsigned col1, unsigned col2,
285 unsigned off, unsigned r1, unsigned r2, unsigned d1, unsigned d2)
286 {
287 int i;
288 struct isl_mat *prod;
289 unsigned n;
290
291 prod = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
292 off + col1 + col2);
293
294 n = 0;
295 for (i = 0; i < r1; ++i) {
296 isl_seq_cpy(prod->row[n + i], mat1->row[i], off + d1);
297 isl_seq_clr(prod->row[n + i] + off + d1, d2);
298 isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
299 mat1->row[i] + off + d1, col1 - d1);
300 isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
301 }
302
303 n += r1;
304 for (i = 0; i < r2; ++i) {
305 isl_seq_cpy(prod->row[n + i], mat2->row[i], off);
306 isl_seq_clr(prod->row[n + i] + off, d1);
307 isl_seq_cpy(prod->row[n + i] + off + d1,
308 mat2->row[i] + off, d2);
309 isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
310 isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
311 mat2->row[i] + off + d2, col2 - d2);
312 }
313
314 n += r2;
315 for (i = 0; i < row1 - r1; ++i) {
316 isl_seq_cpy(prod->row[n + i], mat1->row[r1 + i], off + d1);
317 isl_seq_clr(prod->row[n + i] + off + d1, d2);
318 isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
319 mat1->row[r1 + i] + off + d1, col1 - d1);
320 isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
321 }
322
323 n += row1 - r1;
324 for (i = 0; i < row2 - r2; ++i) {
325 isl_seq_cpy(prod->row[n + i], mat2->row[r2 + i], off);
326 isl_seq_clr(prod->row[n + i] + off, d1);
327 isl_seq_cpy(prod->row[n + i] + off + d1,
328 mat2->row[r2 + i] + off, d2);
329 isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
330 isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
331 mat2->row[r2 + i] + off + d2, col2 - d2);
332 }
333
334 return prod;
335 }
336
337 /* Update the row or column index of a variable that corresponds
338 * to a variable in the first input tableau.
339 */
340 static void update_index1(struct isl_tab_var *var,
341 unsigned r1, unsigned r2, unsigned d1, unsigned d2)
342 {
343 if (var->index == -1)
344 return;
345 if (var->is_row && var->index >= r1)
346 var->index += r2;
347 if (!var->is_row && var->index >= d1)
348 var->index += d2;
349 }
350
351 /* Update the row or column index of a variable that corresponds
352 * to a variable in the second input tableau.
353 */
354 static void update_index2(struct isl_tab_var *var,
355 unsigned row1, unsigned col1,
356 unsigned r1, unsigned r2, unsigned d1, unsigned d2)
357 {
358 if (var->index == -1)
359 return;
360 if (var->is_row) {
361 if (var->index < r2)
362 var->index += r1;
363 else
364 var->index += row1;
365 } else {
366 if (var->index < d2)
367 var->index += d1;
368 else
369 var->index += col1;
370 }
371 }
372
373 /* Create a tableau that represents the Cartesian product of the sets
374 * represented by tableaus tab1 and tab2.
375 * The order of the rows in the product is
376 * - redundant rows of tab1
377 * - redundant rows of tab2
378 * - non-redundant rows of tab1
379 * - non-redundant rows of tab2
380 * The order of the columns is
381 * - denominator
382 * - constant term
383 * - coefficient of big parameter, if any
384 * - dead columns of tab1
385 * - dead columns of tab2
386 * - live columns of tab1
387 * - live columns of tab2
388 * The order of the variables and the constraints is a concatenation
389 * of order in the two input tableaus.
390 */
391 struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2)
392 {
393 int i;
394 struct isl_tab *prod;
395 unsigned off;
396 unsigned r1, r2, d1, d2;
397
398 if (!tab1 || !tab2)
399 return NULL;
400
401 isl_assert(tab1->mat->ctx, tab1->M == tab2->M, return NULL);
402 isl_assert(tab1->mat->ctx, tab1->rational == tab2->rational, return NULL);
403 isl_assert(tab1->mat->ctx, !tab1->row_sign, return NULL);
404 isl_assert(tab1->mat->ctx, !tab2->row_sign, return NULL);
405 isl_assert(tab1->mat->ctx, tab1->n_param == 0, return NULL);
406 isl_assert(tab1->mat->ctx, tab2->n_param == 0, return NULL);
407 isl_assert(tab1->mat->ctx, tab1->n_div == 0, return NULL);
408 isl_assert(tab1->mat->ctx, tab2->n_div == 0, return NULL);
409
410 off = 2 + tab1->M;
411 r1 = tab1->n_redundant;
412 r2 = tab2->n_redundant;
413 d1 = tab1->n_dead;
414 d2 = tab2->n_dead;
415 prod = isl_calloc_type(tab1->mat->ctx, struct isl_tab);
416 if (!prod)
417 return NULL;
418 prod->mat = tab_mat_product(tab1->mat, tab2->mat,
419 tab1->n_row, tab2->n_row,
420 tab1->n_col, tab2->n_col, off, r1, r2, d1, d2);
421 if (!prod->mat)
422 goto error;
423 prod->var = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
424 tab1->max_var + tab2->max_var);
425 if (!prod->var)
426 goto error;
427 for (i = 0; i < tab1->n_var; ++i) {
428 prod->var[i] = tab1->var[i];
429 update_index1(&prod->var[i], r1, r2, d1, d2);
430 }
431 for (i = 0; i < tab2->n_var; ++i) {
432 prod->var[tab1->n_var + i] = tab2->var[i];
433 update_index2(&prod->var[tab1->n_var + i],
434 tab1->n_row, tab1->n_col,
435 r1, r2, d1, d2);
436 }
437 prod->con = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
438 tab1->max_con + tab2->max_con);
439 if (!prod->con)
440 goto error;
441 for (i = 0; i < tab1->n_con; ++i) {
442 prod->con[i] = tab1->con[i];
443 update_index1(&prod->con[i], r1, r2, d1, d2);
444 }
445 for (i = 0; i < tab2->n_con; ++i) {
446 prod->con[tab1->n_con + i] = tab2->con[i];
447 update_index2(&prod->con[tab1->n_con + i],
448 tab1->n_row, tab1->n_col,
449 r1, r2, d1, d2);
450 }
451 prod->col_var = isl_alloc_array(tab1->mat->ctx, int,
452 tab1->n_col + tab2->n_col);
453 if (!prod->col_var)
454 goto error;
455 for (i = 0; i < tab1->n_col; ++i) {
456 int pos = i < d1 ? i : i + d2;
457 prod->col_var[pos] = tab1->col_var[i];
458 }
459 for (i = 0; i < tab2->n_col; ++i) {
460 int pos = i < d2 ? d1 + i : tab1->n_col + i;
461 int t = tab2->col_var[i];
462 if (t >= 0)
463 t += tab1->n_var;
464 else
465 t -= tab1->n_con;
466 prod->col_var[pos] = t;
467 }
468 prod->row_var = isl_alloc_array(tab1->mat->ctx, int,
469 tab1->mat->n_row + tab2->mat->n_row);
470 if (!prod->row_var)
471 goto error;
472 for (i = 0; i < tab1->n_row; ++i) {
473 int pos = i < r1 ? i : i + r2;
474 prod->row_var[pos] = tab1->row_var[i];
475 }
476 for (i = 0; i < tab2->n_row; ++i) {
477 int pos = i < r2 ? r1 + i : tab1->n_row + i;
478 int t = tab2->row_var[i];
479 if (t >= 0)
480 t += tab1->n_var;
481 else
482 t -= tab1->n_con;
483 prod->row_var[pos] = t;
484 }
485 prod->samples = NULL;
486 prod->n_row = tab1->n_row + tab2->n_row;
487 prod->n_con = tab1->n_con + tab2->n_con;
488 prod->n_eq = 0;
489 prod->max_con = tab1->max_con + tab2->max_con;
490 prod->n_col = tab1->n_col + tab2->n_col;
491 prod->n_var = tab1->n_var + tab2->n_var;
492 prod->max_var = tab1->max_var + tab2->max_var;
493 prod->n_param = 0;
494 prod->n_div = 0;
495 prod->n_dead = tab1->n_dead + tab2->n_dead;
496 prod->n_redundant = tab1->n_redundant + tab2->n_redundant;
497 prod->rational = tab1->rational;
498 prod->empty = tab1->empty || tab2->empty;
499 prod->need_undo = 0;
500 prod->in_undo = 0;
501 prod->M = tab1->M;
502 prod->bottom.type = isl_tab_undo_bottom;
503 prod->bottom.next = NULL;
504 prod->top = &prod->bottom;
505
506 prod->n_zero = 0;
507 prod->basis = NULL;
508
509 return prod;
510 error:
511 isl_tab_free(prod);
512 return NULL;
513 }
514
515 static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i)
516 {
517 if (i >= 0)
518 return &tab->var[i];
519 else
520 return &tab->con[~i];
521 }
522
523 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
524 {
525 return var_from_index(tab, tab->row_var[i]);
526 }
527
528 static struct isl_tab_var *var_from_col(struct isl_tab *tab, int i)
529 {
530 return var_from_index(tab, tab->col_var[i]);
531 }
532
533 /* Check if there are any upper bounds on column variable "var",
534 * i.e., non-negative rows where var appears with a negative coefficient.
535 * Return 1 if there are no such bounds.
536 */
537 static int max_is_manifestly_unbounded(struct isl_tab *tab,
538 struct isl_tab_var *var)
539 {
540 int i;
541 unsigned off = 2 + tab->M;
542
543 if (var->is_row)
544 return 0;
545 for (i = tab->n_redundant; i < tab->n_row; ++i) {
546 if (!isl_int_is_neg(tab->mat->row[i][off + var->index]))
547 continue;
548 if (isl_tab_var_from_row(tab, i)->is_nonneg)
549 return 0;
550 }
551 return 1;
552 }
553
554 /* Check if there are any lower bounds on column variable "var",
555 * i.e., non-negative rows where var appears with a positive coefficient.
556 * Return 1 if there are no such bounds.
557 */
558 static int min_is_manifestly_unbounded(struct isl_tab *tab,
559 struct isl_tab_var *var)
560 {
561 int i;
562 unsigned off = 2 + tab->M;
563
564 if (var->is_row)
565 return 0;
566 for (i = tab->n_redundant; i < tab->n_row; ++i) {
567 if (!isl_int_is_pos(tab->mat->row[i][off + var->index]))
568 continue;
569 if (isl_tab_var_from_row(tab, i)->is_nonneg)
570 return 0;
571 }
572 return 1;
573 }
574
575 static int row_cmp(struct isl_tab *tab, int r1, int r2, int c, isl_int t)
576 {
577 unsigned off = 2 + tab->M;
578
579 if (tab->M) {
580 int s;
581 isl_int_mul(t, tab->mat->row[r1][2], tab->mat->row[r2][off+c]);
582 isl_int_submul(t, tab->mat->row[r2][2], tab->mat->row[r1][off+c]);
583 s = isl_int_sgn(t);
584 if (s)
585 return s;
586 }
587 isl_int_mul(t, tab->mat->row[r1][1], tab->mat->row[r2][off + c]);
588 isl_int_submul(t, tab->mat->row[r2][1], tab->mat->row[r1][off + c]);
589 return isl_int_sgn(t);
590 }
591
592 /* Given the index of a column "c", return the index of a row
593 * that can be used to pivot the column in, with either an increase
594 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
595 * If "var" is not NULL, then the row returned will be different from
596 * the one associated with "var".
597 *
598 * Each row in the tableau is of the form
599 *
600 * x_r = a_r0 + \sum_i a_ri x_i
601 *
602 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
603 * impose any limit on the increase or decrease in the value of x_c
604 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
605 * for the row with the smallest (most stringent) such bound.
606 * Note that the common denominator of each row drops out of the fraction.
607 * To check if row j has a smaller bound than row r, i.e.,
608 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
609 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
610 * where -sign(a_jc) is equal to "sgn".
611 */
612 static int pivot_row(struct isl_tab *tab,
613 struct isl_tab_var *var, int sgn, int c)
614 {
615 int j, r, tsgn;
616 isl_int t;
617 unsigned off = 2 + tab->M;
618
619 isl_int_init(t);
620 r = -1;
621 for (j = tab->n_redundant; j < tab->n_row; ++j) {
622 if (var && j == var->index)
623 continue;
624 if (!isl_tab_var_from_row(tab, j)->is_nonneg)
625 continue;
626 if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
627 continue;
628 if (r < 0) {
629 r = j;
630 continue;
631 }
632 tsgn = sgn * row_cmp(tab, r, j, c, t);
633 if (tsgn < 0 || (tsgn == 0 &&
634 tab->row_var[j] < tab->row_var[r]))
635 r = j;
636 }
637 isl_int_clear(t);
638 return r;
639 }
640
641 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
642 * (sgn < 0) the value of row variable var.
643 * If not NULL, then skip_var is a row variable that should be ignored
644 * while looking for a pivot row. It is usually equal to var.
645 *
646 * As the given row in the tableau is of the form
647 *
648 * x_r = a_r0 + \sum_i a_ri x_i
649 *
650 * we need to find a column such that the sign of a_ri is equal to "sgn"
651 * (such that an increase in x_i will have the desired effect) or a
652 * column with a variable that may attain negative values.
653 * If a_ri is positive, then we need to move x_i in the same direction
654 * to obtain the desired effect. Otherwise, x_i has to move in the
655 * opposite direction.
656 */
657 static void find_pivot(struct isl_tab *tab,
658 struct isl_tab_var *var, struct isl_tab_var *skip_var,
659 int sgn, int *row, int *col)
660 {
661 int j, r, c;
662 isl_int *tr;
663
664 *row = *col = -1;
665
666 isl_assert(tab->mat->ctx, var->is_row, return);
667 tr = tab->mat->row[var->index] + 2 + tab->M;
668
669 c = -1;
670 for (j = tab->n_dead; j < tab->n_col; ++j) {
671 if (isl_int_is_zero(tr[j]))
672 continue;
673 if (isl_int_sgn(tr[j]) != sgn &&
674 var_from_col(tab, j)->is_nonneg)
675 continue;
676 if (c < 0 || tab->col_var[j] < tab->col_var[c])
677 c = j;
678 }
679 if (c < 0)
680 return;
681
682 sgn *= isl_int_sgn(tr[c]);
683 r = pivot_row(tab, skip_var, sgn, c);
684 *row = r < 0 ? var->index : r;
685 *col = c;
686 }
687
688 /* Return 1 if row "row" represents an obviously redundant inequality.
689 * This means
690 * - it represents an inequality or a variable
691 * - that is the sum of a non-negative sample value and a positive
692 * combination of zero or more non-negative variables.
693 */
694 int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
695 {
696 int i;
697 unsigned off = 2 + tab->M;
698
699 if (tab->row_var[row] < 0 && !isl_tab_var_from_row(tab, row)->is_nonneg)
700 return 0;
701
702 if (isl_int_is_neg(tab->mat->row[row][1]))
703 return 0;
704 if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
705 return 0;
706
707 for (i = tab->n_dead; i < tab->n_col; ++i) {
708 if (isl_int_is_zero(tab->mat->row[row][off + i]))
709 continue;
710 if (isl_int_is_neg(tab->mat->row[row][off + i]))
711 return 0;
712 if (!var_from_col(tab, i)->is_nonneg)
713 return 0;
714 }
715 return 1;
716 }
717
718 static void swap_rows(struct isl_tab *tab, int row1, int row2)
719 {
720 int t;
721 t = tab->row_var[row1];
722 tab->row_var[row1] = tab->row_var[row2];
723 tab->row_var[row2] = t;
724 isl_tab_var_from_row(tab, row1)->index = row1;
725 isl_tab_var_from_row(tab, row2)->index = row2;
726 tab->mat = isl_mat_swap_rows(tab->mat, row1, row2);
727
728 if (!tab->row_sign)
729 return;
730 t = tab->row_sign[row1];
731 tab->row_sign[row1] = tab->row_sign[row2];
732 tab->row_sign[row2] = t;
733 }
734
735 static void push_union(struct isl_tab *tab,
736 enum isl_tab_undo_type type, union isl_tab_undo_val u)
737 {
738 struct isl_tab_undo *undo;
739
740 if (!tab->need_undo)
741 return;
742
743 undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
744 if (!undo) {
745 free_undo(tab);
746 tab->top = NULL;
747 return;
748 }
749 undo->type = type;
750 undo->u = u;
751 undo->next = tab->top;
752 tab->top = undo;
753 }
754
755 void isl_tab_push_var(struct isl_tab *tab,
756 enum isl_tab_undo_type type, struct isl_tab_var *var)
757 {
758 union isl_tab_undo_val u;
759 if (var->is_row)
760 u.var_index = tab->row_var[var->index];
761 else
762 u.var_index = tab->col_var[var->index];
763 push_union(tab, type, u);
764 }
765
766 void isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
767 {
768 union isl_tab_undo_val u = { 0 };
769 push_union(tab, type, u);
770 }
771
772 /* Push a record on the undo stack describing the current basic
773 * variables, so that the this state can be restored during rollback.
774 */
775 void isl_tab_push_basis(struct isl_tab *tab)
776 {
777 int i;
778 union isl_tab_undo_val u;
779
780 u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
781 if (!u.col_var) {
782 free_undo(tab);
783 tab->top = NULL;
784 return;
785 }
786 for (i = 0; i < tab->n_col; ++i)
787 u.col_var[i] = tab->col_var[i];
788 push_union(tab, isl_tab_undo_saved_basis, u);
789 }
790
791 /* Mark row with index "row" as being redundant.
792 * If we may need to undo the operation or if the row represents
793 * a variable of the original problem, the row is kept,
794 * but no longer considered when looking for a pivot row.
795 * Otherwise, the row is simply removed.
796 *
797 * The row may be interchanged with some other row. If it
798 * is interchanged with a later row, return 1. Otherwise return 0.
799 * If the rows are checked in order in the calling function,
800 * then a return value of 1 means that the row with the given
801 * row number may now contain a different row that hasn't been checked yet.
802 */
803 int isl_tab_mark_redundant(struct isl_tab *tab, int row)
804 {
805 struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
806 var->is_redundant = 1;
807 isl_assert(tab->mat->ctx, row >= tab->n_redundant, return -1);
808 if (tab->need_undo || tab->row_var[row] >= 0) {
809 if (tab->row_var[row] >= 0 && !var->is_nonneg) {
810 var->is_nonneg = 1;
811 isl_tab_push_var(tab, isl_tab_undo_nonneg, var);
812 }
813 if (row != tab->n_redundant)
814 swap_rows(tab, row, tab->n_redundant);
815 isl_tab_push_var(tab, isl_tab_undo_redundant, var);
816 tab->n_redundant++;
817 return 0;
818 } else {
819 if (row != tab->n_row - 1)
820 swap_rows(tab, row, tab->n_row - 1);
821 isl_tab_var_from_row(tab, tab->n_row - 1)->index = -1;
822 tab->n_row--;
823 return 1;
824 }
825 }
826
827 struct isl_tab *isl_tab_mark_empty(struct isl_tab *tab)
828 {
829 if (!tab->empty && tab->need_undo)
830 isl_tab_push(tab, isl_tab_undo_empty);
831 tab->empty = 1;
832 return tab;
833 }
834
835 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
836 * the original sign of the pivot element.
837 * We only keep track of row signs during PILP solving and in this case
838 * we only pivot a row with negative sign (meaning the value is always
839 * non-positive) using a positive pivot element.
840 *
841 * For each row j, the new value of the parametric constant is equal to
842 *
843 * a_j0 - a_jc a_r0/a_rc
844 *
845 * where a_j0 is the original parametric constant, a_rc is the pivot element,
846 * a_r0 is the parametric constant of the pivot row and a_jc is the
847 * pivot column entry of the row j.
848 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
849 * remains the same if a_jc has the same sign as the row j or if
850 * a_jc is zero. In all other cases, we reset the sign to "unknown".
851 */
852 static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
853 {
854 int i;
855 struct isl_mat *mat = tab->mat;
856 unsigned off = 2 + tab->M;
857
858 if (!tab->row_sign)
859 return;
860
861 if (tab->row_sign[row] == 0)
862 return;
863 isl_assert(mat->ctx, row_sgn > 0, return);
864 isl_assert(mat->ctx, tab->row_sign[row] == isl_tab_row_neg, return);
865 tab->row_sign[row] = isl_tab_row_pos;
866 for (i = 0; i < tab->n_row; ++i) {
867 int s;
868 if (i == row)
869 continue;
870 s = isl_int_sgn(mat->row[i][off + col]);
871 if (!s)
872 continue;
873 if (!tab->row_sign[i])
874 continue;
875 if (s < 0 && tab->row_sign[i] == isl_tab_row_neg)
876 continue;
877 if (s > 0 && tab->row_sign[i] == isl_tab_row_pos)
878 continue;
879 tab->row_sign[i] = isl_tab_row_unknown;
880 }
881 }
882
883 /* Given a row number "row" and a column number "col", pivot the tableau
884 * such that the associated variables are interchanged.
885 * The given row in the tableau expresses
886 *
887 * x_r = a_r0 + \sum_i a_ri x_i
888 *
889 * or
890 *
891 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
892 *
893 * Substituting this equality into the other rows
894 *
895 * x_j = a_j0 + \sum_i a_ji x_i
896 *
897 * with a_jc \ne 0, we obtain
898 *
899 * 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
900 *
901 * The tableau
902 *
903 * n_rc/d_r n_ri/d_r
904 * n_jc/d_j n_ji/d_j
905 *
906 * where i is any other column and j is any other row,
907 * is therefore transformed into
908 *
909 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
910 * 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)
911 *
912 * The transformation is performed along the following steps
913 *
914 * d_r/n_rc n_ri/n_rc
915 * n_jc/d_j n_ji/d_j
916 *
917 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
918 * n_jc/d_j n_ji/d_j
919 *
920 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
921 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
922 *
923 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
924 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
925 *
926 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
927 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
928 *
929 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
930 * 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)
931 *
932 */
933 void isl_tab_pivot(struct isl_tab *tab, int row, int col)
934 {
935 int i, j;
936 int sgn;
937 int t;
938 struct isl_mat *mat = tab->mat;
939 struct isl_tab_var *var;
940 unsigned off = 2 + tab->M;
941
942 isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
943 sgn = isl_int_sgn(mat->row[row][0]);
944 if (sgn < 0) {
945 isl_int_neg(mat->row[row][0], mat->row[row][0]);
946 isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]);
947 } else
948 for (j = 0; j < off - 1 + tab->n_col; ++j) {
949 if (j == off - 1 + col)
950 continue;
951 isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
952 }
953 if (!isl_int_is_one(mat->row[row][0]))
954 isl_seq_normalize(mat->ctx, mat->row[row], off + tab->n_col);
955 for (i = 0; i < tab->n_row; ++i) {
956 if (i == row)
957 continue;
958 if (isl_int_is_zero(mat->row[i][off + col]))
959 continue;
960 isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
961 for (j = 0; j < off - 1 + tab->n_col; ++j) {
962 if (j == off - 1 + col)
963 continue;
964 isl_int_mul(mat->row[i][1 + j],
965 mat->row[i][1 + j], mat->row[row][0]);
966 isl_int_addmul(mat->row[i][1 + j],
967 mat->row[i][off + col], mat->row[row][1 + j]);
968 }
969 isl_int_mul(mat->row[i][off + col],
970 mat->row[i][off + col], mat->row[row][off + col]);
971 if (!isl_int_is_one(mat->row[i][0]))
972 isl_seq_normalize(mat->ctx, mat->row[i], off + tab->n_col);
973 }
974 t = tab->row_var[row];
975 tab->row_var[row] = tab->col_var[col];
976 tab->col_var[col] = t;
977 var = isl_tab_var_from_row(tab, row);
978 var->is_row = 1;
979 var->index = row;
980 var = var_from_col(tab, col);
981 var->is_row = 0;
982 var->index = col;
983 update_row_sign(tab, row, col, sgn);
984 if (tab->in_undo)
985 return;
986 for (i = tab->n_redundant; i < tab->n_row; ++i) {
987 if (isl_int_is_zero(mat->row[i][off + col]))
988 continue;
989 if (!isl_tab_var_from_row(tab, i)->frozen &&
990 isl_tab_row_is_redundant(tab, i))
991 if (isl_tab_mark_redundant(tab, i))
992 --i;
993 }
994 }
995
996 /* If "var" represents a column variable, then pivot is up (sgn > 0)
997 * or down (sgn < 0) to a row. The variable is assumed not to be
998 * unbounded in the specified direction.
999 * If sgn = 0, then the variable is unbounded in both directions,
1000 * and we pivot with any row we can find.
1001 */
1002 static void to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
1003 {
1004 int r;
1005 unsigned off = 2 + tab->M;
1006
1007 if (var->is_row)
1008 return;
1009
1010 if (sign == 0) {
1011 for (r = tab->n_redundant; r < tab->n_row; ++r)
1012 if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
1013 break;
1014 isl_assert(tab->mat->ctx, r < tab->n_row, return);
1015 } else {
1016 r = pivot_row(tab, NULL, sign, var->index);
1017 isl_assert(tab->mat->ctx, r >= 0, return);
1018 }
1019
1020 isl_tab_pivot(tab, r, var->index);
1021 }
1022
1023 static void check_table(struct isl_tab *tab)
1024 {
1025 int i;
1026
1027 if (tab->empty)
1028 return;
1029 for (i = 0; i < tab->n_row; ++i) {
1030 if (!isl_tab_var_from_row(tab, i)->is_nonneg)
1031 continue;
1032 assert(!isl_int_is_neg(tab->mat->row[i][1]));
1033 }
1034 }
1035
1036 /* Return the sign of the maximal value of "var".
1037 * If the sign is not negative, then on return from this function,
1038 * the sample value will also be non-negative.
1039 *
1040 * If "var" is manifestly unbounded wrt positive values, we are done.
1041 * Otherwise, we pivot the variable up to a row if needed
1042 * Then we continue pivoting down until either
1043 * - no more down pivots can be performed
1044 * - the sample value is positive
1045 * - the variable is pivoted into a manifestly unbounded column
1046 */
1047 static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
1048 {
1049 int row, col;
1050
1051 if (max_is_manifestly_unbounded(tab, var))
1052 return 1;
1053 to_row(tab, var, 1);
1054 while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
1055 find_pivot(tab, var, var, 1, &row, &col);
1056 if (row == -1)
1057 return isl_int_sgn(tab->mat->row[var->index][1]);
1058 isl_tab_pivot(tab, row, col);
1059 if (!var->is_row) /* manifestly unbounded */
1060 return 1;
1061 }
1062 return 1;
1063 }
1064
1065 static int row_is_neg(struct isl_tab *tab, int row)
1066 {
1067 if (!tab->M)
1068 return isl_int_is_neg(tab->mat->row[row][1]);
1069 if (isl_int_is_pos(tab->mat->row[row][2]))
1070 return 0;
1071 if (isl_int_is_neg(tab->mat->row[row][2]))
1072 return 1;
1073 return isl_int_is_neg(tab->mat->row[row][1]);
1074 }
1075
1076 static int row_sgn(struct isl_tab *tab, int row)
1077 {
1078 if (!tab->M)
1079 return isl_int_sgn(tab->mat->row[row][1]);
1080 if (!isl_int_is_zero(tab->mat->row[row][2]))
1081 return isl_int_sgn(tab->mat->row[row][2]);
1082 else
1083 return isl_int_sgn(tab->mat->row[row][1]);
1084 }
1085
1086 /* Perform pivots until the row variable "var" has a non-negative
1087 * sample value or until no more upward pivots can be performed.
1088 * Return the sign of the sample value after the pivots have been
1089 * performed.
1090 */
1091 static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
1092 {
1093 int row, col;
1094
1095 while (row_is_neg(tab, var->index)) {
1096 find_pivot(tab, var, var, 1, &row, &col);
1097 if (row == -1)
1098 break;
1099 isl_tab_pivot(tab, row, col);
1100 if (!var->is_row) /* manifestly unbounded */
1101 return 1;
1102 }
1103 return row_sgn(tab, var->index);
1104 }
1105
1106 /* Perform pivots until we are sure that the row variable "var"
1107 * can attain non-negative values. After return from this
1108 * function, "var" is still a row variable, but its sample
1109 * value may not be non-negative, even if the function returns 1.
1110 */
1111 static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
1112 {
1113 int row, col;
1114
1115 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
1116 find_pivot(tab, var, var, 1, &row, &col);
1117 if (row == -1)
1118 break;
1119 if (row == var->index) /* manifestly unbounded */
1120 return 1;
1121 isl_tab_pivot(tab, row, col);
1122 }
1123 return !isl_int_is_neg(tab->mat->row[var->index][1]);
1124 }
1125
1126 /* Return a negative value if "var" can attain negative values.
1127 * Return a non-negative value otherwise.
1128 *
1129 * If "var" is manifestly unbounded wrt negative values, we are done.
1130 * Otherwise, if var is in a column, we can pivot it down to a row.
1131 * Then we continue pivoting down until either
1132 * - the pivot would result in a manifestly unbounded column
1133 * => we don't perform the pivot, but simply return -1
1134 * - no more down pivots can be performed
1135 * - the sample value is negative
1136 * If the sample value becomes negative and the variable is supposed
1137 * to be nonnegative, then we undo the last pivot.
1138 * However, if the last pivot has made the pivoting variable
1139 * obviously redundant, then it may have moved to another row.
1140 * In that case we look for upward pivots until we reach a non-negative
1141 * value again.
1142 */
1143 static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
1144 {
1145 int row, col;
1146 struct isl_tab_var *pivot_var = NULL;
1147
1148 if (min_is_manifestly_unbounded(tab, var))
1149 return -1;
1150 if (!var->is_row) {
1151 col = var->index;
1152 row = pivot_row(tab, NULL, -1, col);
1153 pivot_var = var_from_col(tab, col);
1154 isl_tab_pivot(tab, row, col);
1155 if (var->is_redundant)
1156 return 0;
1157 if (isl_int_is_neg(tab->mat->row[var->index][1])) {
1158 if (var->is_nonneg) {
1159 if (!pivot_var->is_redundant &&
1160 pivot_var->index == row)
1161 isl_tab_pivot(tab, row, col);
1162 else
1163 restore_row(tab, var);
1164 }
1165 return -1;
1166 }
1167 }
1168 if (var->is_redundant)
1169 return 0;
1170 while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
1171 find_pivot(tab, var, var, -1, &row, &col);
1172 if (row == var->index)
1173 return -1;
1174 if (row == -1)
1175 return isl_int_sgn(tab->mat->row[var->index][1]);
1176 pivot_var = var_from_col(tab, col);
1177 isl_tab_pivot(tab, row, col);
1178 if (var->is_redundant)
1179 return 0;
1180 }
1181 if (pivot_var && var->is_nonneg) {
1182 /* pivot back to non-negative value */
1183 if (!pivot_var->is_redundant && pivot_var->index == row)
1184 isl_tab_pivot(tab, row, col);
1185 else
1186 restore_row(tab, var);
1187 }
1188 return -1;
1189 }
1190
1191 static int row_at_most_neg_one(struct isl_tab *tab, int row)
1192 {
1193 if (tab->M) {
1194 if (isl_int_is_pos(tab->mat->row[row][2]))
1195 return 0;
1196 if (isl_int_is_neg(tab->mat->row[row][2]))
1197 return 1;
1198 }
1199 return isl_int_is_neg(tab->mat->row[row][1]) &&
1200 isl_int_abs_ge(tab->mat->row[row][1],
1201 tab->mat->row[row][0]);
1202 }
1203
1204 /* Return 1 if "var" can attain values <= -1.
1205 * Return 0 otherwise.
1206 *
1207 * The sample value of "var" is assumed to be non-negative when the
1208 * the function is called and will be made non-negative again before
1209 * the function returns.
1210 */
1211 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
1212 {
1213 int row, col;
1214 struct isl_tab_var *pivot_var;
1215
1216 if (min_is_manifestly_unbounded(tab, var))
1217 return 1;
1218 if (!var->is_row) {
1219 col = var->index;
1220 row = pivot_row(tab, NULL, -1, col);
1221 pivot_var = var_from_col(tab, col);
1222 isl_tab_pivot(tab, row, col);
1223 if (var->is_redundant)
1224 return 0;
1225 if (row_at_most_neg_one(tab, var->index)) {
1226 if (var->is_nonneg) {
1227 if (!pivot_var->is_redundant &&
1228 pivot_var->index == row)
1229 isl_tab_pivot(tab, row, col);
1230 else
1231 restore_row(tab, var);
1232 }
1233 return 1;
1234 }
1235 }
1236 if (var->is_redundant)
1237 return 0;
1238 do {
1239 find_pivot(tab, var, var, -1, &row, &col);
1240 if (row == var->index)
1241 return 1;
1242 if (row == -1)
1243 return 0;
1244 pivot_var = var_from_col(tab, col);
1245 isl_tab_pivot(tab, row, col);
1246 if (var->is_redundant)
1247 return 0;
1248 } while (!row_at_most_neg_one(tab, var->index));
1249 if (var->is_nonneg) {
1250 /* pivot back to non-negative value */
1251 if (!pivot_var->is_redundant && pivot_var->index == row)
1252 isl_tab_pivot(tab, row, col);
1253 restore_row(tab, var);
1254 }
1255 return 1;
1256 }
1257
1258 /* Return 1 if "var" can attain values >= 1.
1259 * Return 0 otherwise.
1260 */
1261 static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
1262 {
1263 int row, col;
1264 isl_int *r;
1265
1266 if (max_is_manifestly_unbounded(tab, var))
1267 return 1;
1268 to_row(tab, var, 1);
1269 r = tab->mat->row[var->index];
1270 while (isl_int_lt(r[1], r[0])) {
1271 find_pivot(tab, var, var, 1, &row, &col);
1272 if (row == -1)
1273 return isl_int_ge(r[1], r[0]);
1274 if (row == var->index) /* manifestly unbounded */
1275 return 1;
1276 isl_tab_pivot(tab, row, col);
1277 }
1278 return 1;
1279 }
1280
1281 static void swap_cols(struct isl_tab *tab, int col1, int col2)
1282 {
1283 int t;
1284 unsigned off = 2 + tab->M;
1285 t = tab->col_var[col1];
1286 tab->col_var[col1] = tab->col_var[col2];
1287 tab->col_var[col2] = t;
1288 var_from_col(tab, col1)->index = col1;
1289 var_from_col(tab, col2)->index = col2;
1290 tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2);
1291 }
1292
1293 /* Mark column with index "col" as representing a zero variable.
1294 * If we may need to undo the operation the column is kept,
1295 * but no longer considered.
1296 * Otherwise, the column is simply removed.
1297 *
1298 * The column may be interchanged with some other column. If it
1299 * is interchanged with a later column, return 1. Otherwise return 0.
1300 * If the columns are checked in order in the calling function,
1301 * then a return value of 1 means that the column with the given
1302 * column number may now contain a different column that
1303 * hasn't been checked yet.
1304 */
1305 int isl_tab_kill_col(struct isl_tab *tab, int col)
1306 {
1307 var_from_col(tab, col)->is_zero = 1;
1308 if (tab->need_undo) {
1309 isl_tab_push_var(tab, isl_tab_undo_zero, var_from_col(tab, col));
1310 if (col != tab->n_dead)
1311 swap_cols(tab, col, tab->n_dead);
1312 tab->n_dead++;
1313 return 0;
1314 } else {
1315 if (col != tab->n_col - 1)
1316 swap_cols(tab, col, tab->n_col - 1);
1317 var_from_col(tab, tab->n_col - 1)->index = -1;
1318 tab->n_col--;
1319 return 1;
1320 }
1321 }
1322
1323 /* Row variable "var" is non-negative and cannot attain any values
1324 * larger than zero. This means that the coefficients of the unrestricted
1325 * column variables are zero and that the coefficients of the non-negative
1326 * column variables are zero or negative.
1327 * Each of the non-negative variables with a negative coefficient can
1328 * then also be written as the negative sum of non-negative variables
1329 * and must therefore also be zero.
1330 */
1331 static void close_row(struct isl_tab *tab, struct isl_tab_var *var)
1332 {
1333 int j;
1334 struct isl_mat *mat = tab->mat;
1335 unsigned off = 2 + tab->M;
1336
1337 isl_assert(tab->mat->ctx, var->is_nonneg, return);
1338 var->is_zero = 1;
1339 if (tab->need_undo)
1340 isl_tab_push_var(tab, isl_tab_undo_zero, var);
1341 for (j = tab->n_dead; j < tab->n_col; ++j) {
1342 if (isl_int_is_zero(mat->row[var->index][off + j]))
1343 continue;
1344 isl_assert(tab->mat->ctx,
1345 isl_int_is_neg(mat->row[var->index][off + j]), return);
1346 if (isl_tab_kill_col(tab, j))
1347 --j;
1348 }
1349 isl_tab_mark_redundant(tab, var->index);
1350 }
1351
1352 /* Add a constraint to the tableau and allocate a row for it.
1353 * Return the index into the constraint array "con".
1354 */
1355 int isl_tab_allocate_con(struct isl_tab *tab)
1356 {
1357 int r;
1358
1359 isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
1360 isl_assert(tab->mat->ctx, tab->n_con < tab->max_con, return -1);
1361
1362 r = tab->n_con;
1363 tab->con[r].index = tab->n_row;
1364 tab->con[r].is_row = 1;
1365 tab->con[r].is_nonneg = 0;
1366 tab->con[r].is_zero = 0;
1367 tab->con[r].is_redundant = 0;
1368 tab->con[r].frozen = 0;
1369 tab->con[r].negated = 0;
1370 tab->row_var[tab->n_row] = ~r;
1371
1372 tab->n_row++;
1373 tab->n_con++;
1374 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
1375
1376 return r;
1377 }
1378
1379 /* Add a variable to the tableau and allocate a column for it.
1380 * Return the index into the variable array "var".
1381 */
1382 int isl_tab_allocate_var(struct isl_tab *tab)
1383 {
1384 int r;
1385 int i;
1386 unsigned off = 2 + tab->M;
1387
1388 isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
1389 isl_assert(tab->mat->ctx, tab->n_var < tab->max_var, return -1);
1390
1391 r = tab->n_var;
1392 tab->var[r].index = tab->n_col;
1393 tab->var[r].is_row = 0;
1394 tab->var[r].is_nonneg = 0;
1395 tab->var[r].is_zero = 0;
1396 tab->var[r].is_redundant = 0;
1397 tab->var[r].frozen = 0;
1398 tab->var[r].negated = 0;
1399 tab->col_var[tab->n_col] = r;
1400
1401 for (i = 0; i < tab->n_row; ++i)
1402 isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
1403
1404 tab->n_var++;
1405 tab->n_col++;
1406 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]);
1407
1408 return r;
1409 }
1410
1411 /* Add a row to the tableau. The row is given as an affine combination
1412 * of the original variables and needs to be expressed in terms of the
1413 * column variables.
1414 *
1415 * We add each term in turn.
1416 * If r = n/d_r is the current sum and we need to add k x, then
1417 * if x is a column variable, we increase the numerator of
1418 * this column by k d_r
1419 * if x = f/d_x is a row variable, then the new representation of r is
1420 *
1421 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1422 * --- + --- = ------------------- = -------------------
1423 * d_r d_r d_r d_x/g m
1424 *
1425 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1426 */
1427 int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
1428 {
1429 int i;
1430 int r;
1431 isl_int *row;
1432 isl_int a, b;
1433 unsigned off = 2 + tab->M;
1434
1435 r = isl_tab_allocate_con(tab);
1436 if (r < 0)
1437 return -1;
1438
1439 isl_int_init(a);
1440 isl_int_init(b);
1441 row = tab->mat->row[tab->con[r].index];
1442 isl_int_set_si(row[0], 1);
1443 isl_int_set(row[1], line[0]);
1444 isl_seq_clr(row + 2, tab->M + tab->n_col);
1445 for (i = 0; i < tab->n_var; ++i) {
1446 if (tab->var[i].is_zero)
1447 continue;
1448 if (tab->var[i].is_row) {
1449 isl_int_lcm(a,
1450 row[0], tab->mat->row[tab->var[i].index][0]);
1451 isl_int_swap(a, row[0]);
1452 isl_int_divexact(a, row[0], a);
1453 isl_int_divexact(b,
1454 row[0], tab->mat->row[tab->var[i].index][0]);
1455 isl_int_mul(b, b, line[1 + i]);
1456 isl_seq_combine(row + 1, a, row + 1,
1457 b, tab->mat->row[tab->var[i].index] + 1,
1458 1 + tab->M + tab->n_col);
1459 } else
1460 isl_int_addmul(row[off + tab->var[i].index],
1461 line[1 + i], row[0]);
1462 if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
1463 isl_int_submul(row[2], line[1 + i], row[0]);
1464 }
1465 isl_seq_normalize(tab->mat->ctx, row, off + tab->n_col);
1466 isl_int_clear(a);
1467 isl_int_clear(b);
1468
1469 if (tab->row_sign)
1470 tab->row_sign[tab->con[r].index] = 0;
1471
1472 return r;
1473 }
1474
1475 static int drop_row(struct isl_tab *tab, int row)
1476 {
1477 isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
1478 if (row != tab->n_row - 1)
1479 swap_rows(tab, row, tab->n_row - 1);
1480 tab->n_row--;
1481 tab->n_con--;
1482 return 0;
1483 }
1484
1485 static int drop_col(struct isl_tab *tab, int col)
1486 {
1487 isl_assert(tab->mat->ctx, tab->col_var[col] == tab->n_var - 1, return -1);
1488 if (col != tab->n_col - 1)
1489 swap_cols(tab, col, tab->n_col - 1);
1490 tab->n_col--;
1491 tab->n_var--;
1492 return 0;
1493 }
1494
1495 /* Add inequality "ineq" and check if it conflicts with the
1496 * previously added constraints or if it is obviously redundant.
1497 */
1498 struct isl_tab *isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
1499 {
1500 int r;
1501 int sgn;
1502
1503 if (!tab)
1504 return NULL;
1505 r = isl_tab_add_row(tab, ineq);
1506 if (r < 0)
1507 goto error;
1508 tab->con[r].is_nonneg = 1;
1509 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1510 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1511 isl_tab_mark_redundant(tab, tab->con[r].index);
1512 return tab;
1513 }
1514
1515 sgn = restore_row(tab, &tab->con[r]);
1516 if (sgn < 0)
1517 return isl_tab_mark_empty(tab);
1518 if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
1519 isl_tab_mark_redundant(tab, tab->con[r].index);
1520 return tab;
1521 error:
1522 isl_tab_free(tab);
1523 return NULL;
1524 }
1525
1526 /* Pivot a non-negative variable down until it reaches the value zero
1527 * and then pivot the variable into a column position.
1528 */
1529 static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
1530 {
1531 int i;
1532 int row, col;
1533 unsigned off = 2 + tab->M;
1534
1535 if (!var->is_row)
1536 return 0;
1537
1538 while (isl_int_is_pos(tab->mat->row[var->index][1])) {
1539 find_pivot(tab, var, NULL, -1, &row, &col);
1540 isl_assert(tab->mat->ctx, row != -1, return -1);
1541 isl_tab_pivot(tab, row, col);
1542 if (!var->is_row)
1543 return 0;
1544 }
1545
1546 for (i = tab->n_dead; i < tab->n_col; ++i)
1547 if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
1548 break;
1549
1550 isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
1551 isl_tab_pivot(tab, var->index, i);
1552
1553 return 0;
1554 }
1555
1556 /* We assume Gaussian elimination has been performed on the equalities.
1557 * The equalities can therefore never conflict.
1558 * Adding the equalities is currently only really useful for a later call
1559 * to isl_tab_ineq_type.
1560 */
1561 static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
1562 {
1563 int i;
1564 int r;
1565
1566 if (!tab)
1567 return NULL;
1568 r = isl_tab_add_row(tab, eq);
1569 if (r < 0)
1570 goto error;
1571
1572 r = tab->con[r].index;
1573 i = isl_seq_first_non_zero(tab->mat->row[r] + 2 + tab->M + tab->n_dead,
1574 tab->n_col - tab->n_dead);
1575 isl_assert(tab->mat->ctx, i >= 0, goto error);
1576 i += tab->n_dead;
1577 isl_tab_pivot(tab, r, i);
1578 isl_tab_kill_col(tab, i);
1579 tab->n_eq++;
1580
1581 return tab;
1582 error:
1583 isl_tab_free(tab);
1584 return NULL;
1585 }
1586
1587 static int row_is_manifestly_zero(struct isl_tab *tab, int row)
1588 {
1589 unsigned off = 2 + tab->M;
1590
1591 if (!isl_int_is_zero(tab->mat->row[row][1]))
1592 return 0;
1593 if (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))
1594 return 0;
1595 return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1596 tab->n_col - tab->n_dead) == -1;
1597 }
1598
1599 /* Add an equality that is known to be valid for the given tableau.
1600 */
1601 struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
1602 {
1603 struct isl_tab_var *var;
1604 int r;
1605
1606 if (!tab)
1607 return NULL;
1608 r = isl_tab_add_row(tab, eq);
1609 if (r < 0)
1610 goto error;
1611
1612 var = &tab->con[r];
1613 r = var->index;
1614 if (row_is_manifestly_zero(tab, r)) {
1615 var->is_zero = 1;
1616 isl_tab_mark_redundant(tab, r);
1617 return tab;
1618 }
1619
1620 if (isl_int_is_neg(tab->mat->row[r][1])) {
1621 isl_seq_neg(tab->mat->row[r] + 1, tab->mat->row[r] + 1,
1622 1 + tab->n_col);
1623 var->negated = 1;
1624 }
1625 var->is_nonneg = 1;
1626 if (to_col(tab, var) < 0)
1627 goto error;
1628 var->is_nonneg = 0;
1629 isl_tab_kill_col(tab, var->index);
1630
1631 return tab;
1632 error:
1633 isl_tab_free(tab);
1634 return NULL;
1635 }
1636
1637 /* Add equality "eq" and check if it conflicts with the
1638 * previously added constraints or if it is obviously redundant.
1639 */
1640 struct isl_tab *isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
1641 {
1642 struct isl_tab_undo *snap = NULL;
1643 struct isl_tab_var *var;
1644 int r;
1645 int row;
1646 int sgn;
1647
1648 if (!tab)
1649 return NULL;
1650 isl_assert(tab->mat->ctx, !tab->M, goto error);
1651
1652 if (tab->need_undo)
1653 snap = isl_tab_snap(tab);
1654
1655 r = isl_tab_add_row(tab, eq);
1656 if (r < 0)
1657 goto error;
1658
1659 var = &tab->con[r];
1660 row = var->index;
1661 if (row_is_manifestly_zero(tab, row)) {
1662 if (snap) {
1663 if (isl_tab_rollback(tab, snap) < 0)
1664 goto error;
1665 } else
1666 drop_row(tab, row);
1667 return tab;
1668 }
1669
1670 sgn = isl_int_sgn(tab->mat->row[row][1]);
1671
1672 if (sgn > 0) {
1673 isl_seq_neg(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
1674 1 + tab->n_col);
1675 var->negated = 1;
1676 sgn = -1;
1677 }
1678
1679 if (sgn < 0 && sign_of_max(tab, var) < 0)
1680 return isl_tab_mark_empty(tab);
1681
1682 var->is_nonneg = 1;
1683 if (to_col(tab, var) < 0)
1684 goto error;
1685 var->is_nonneg = 0;
1686 isl_tab_kill_col(tab, var->index);
1687
1688 return tab;
1689 error:
1690 isl_tab_free(tab);
1691 return NULL;
1692 }
1693
1694 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap)
1695 {
1696 int i;
1697 struct isl_tab *tab;
1698
1699 if (!bmap)
1700 return NULL;
1701 tab = isl_tab_alloc(bmap->ctx,
1702 isl_basic_map_total_dim(bmap) + bmap->n_ineq + 1,
1703 isl_basic_map_total_dim(bmap), 0);
1704 if (!tab)
1705 return NULL;
1706 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
1707 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1708 return isl_tab_mark_empty(tab);
1709 for (i = 0; i < bmap->n_eq; ++i) {
1710 tab = add_eq(tab, bmap->eq[i]);
1711 if (!tab)
1712 return tab;
1713 }
1714 for (i = 0; i < bmap->n_ineq; ++i) {
1715 tab = isl_tab_add_ineq(tab, bmap->ineq[i]);
1716 if (!tab || tab->empty)
1717 return tab;
1718 }
1719 return tab;
1720 }
1721
1722 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset)
1723 {
1724 return isl_tab_from_basic_map((struct isl_basic_map *)bset);
1725 }
1726
1727 /* Construct a tableau corresponding to the recession cone of "bset".
1728 */
1729 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_set *bset)
1730 {
1731 isl_int cst;
1732 int i;
1733 struct isl_tab *tab;
1734
1735 if (!bset)
1736 return NULL;
1737 tab = isl_tab_alloc(bset->ctx, bset->n_eq + bset->n_ineq,
1738 isl_basic_set_total_dim(bset), 0);
1739 if (!tab)
1740 return NULL;
1741 tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
1742
1743 isl_int_init(cst);
1744 for (i = 0; i < bset->n_eq; ++i) {
1745 isl_int_swap(bset->eq[i][0], cst);
1746 tab = add_eq(tab, bset->eq[i]);
1747 isl_int_swap(bset->eq[i][0], cst);
1748 if (!tab)
1749 goto done;
1750 }
1751 for (i = 0; i < bset->n_ineq; ++i) {
1752 int r;
1753 isl_int_swap(bset->ineq[i][0], cst);
1754 r = isl_tab_add_row(tab, bset->ineq[i]);
1755 isl_int_swap(bset->ineq[i][0], cst);
1756 if (r < 0)
1757 goto error;
1758 tab->con[r].is_nonneg = 1;
1759 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1760 }
1761 done:
1762 isl_int_clear(cst);
1763 return tab;
1764 error:
1765 isl_int_clear(cst);
1766 isl_tab_free(tab);
1767 return NULL;
1768 }
1769
1770 /* Assuming "tab" is the tableau of a cone, check if the cone is
1771 * bounded, i.e., if it is empty or only contains the origin.
1772 */
1773 int isl_tab_cone_is_bounded(struct isl_tab *tab)
1774 {
1775 int i;
1776
1777 if (!tab)
1778 return -1;
1779 if (tab->empty)
1780 return 1;
1781 if (tab->n_dead == tab->n_col)
1782 return 1;
1783
1784 for (;;) {
1785 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1786 struct isl_tab_var *var;
1787 var = isl_tab_var_from_row(tab, i);
1788 if (!var->is_nonneg)
1789 continue;
1790 if (sign_of_max(tab, var) != 0)
1791 return 0;
1792 close_row(tab, var);
1793 break;
1794 }
1795 if (tab->n_dead == tab->n_col)
1796 return 1;
1797 if (i == tab->n_row)
1798 return 0;
1799 }
1800 }
1801
1802 int isl_tab_sample_is_integer(struct isl_tab *tab)
1803 {
1804 int i;
1805
1806 if (!tab)
1807 return -1;
1808
1809 for (i = 0; i < tab->n_var; ++i) {
1810 int row;
1811 if (!tab->var[i].is_row)
1812 continue;
1813 row = tab->var[i].index;
1814 if (!isl_int_is_divisible_by(tab->mat->row[row][1],
1815 tab->mat->row[row][0]))
1816 return 0;
1817 }
1818 return 1;
1819 }
1820
1821 static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
1822 {
1823 int i;
1824 struct isl_vec *vec;
1825
1826 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
1827 if (!vec)
1828 return NULL;
1829
1830 isl_int_set_si(vec->block.data[0], 1);
1831 for (i = 0; i < tab->n_var; ++i) {
1832 if (!tab->var[i].is_row)
1833 isl_int_set_si(vec->block.data[1 + i], 0);
1834 else {
1835 int row = tab->var[i].index;
1836 isl_int_divexact(vec->block.data[1 + i],
1837 tab->mat->row[row][1], tab->mat->row[row][0]);
1838 }
1839 }
1840
1841 return vec;
1842 }
1843
1844 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
1845 {
1846 int i;
1847 struct isl_vec *vec;
1848 isl_int m;
1849
1850 if (!tab)
1851 return NULL;
1852
1853 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
1854 if (!vec)
1855 return NULL;
1856
1857 isl_int_init(m);
1858
1859 isl_int_set_si(vec->block.data[0], 1);
1860 for (i = 0; i < tab->n_var; ++i) {
1861 int row;
1862 if (!tab->var[i].is_row) {
1863 isl_int_set_si(vec->block.data[1 + i], 0);
1864 continue;
1865 }
1866 row = tab->var[i].index;
1867 isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
1868 isl_int_divexact(m, tab->mat->row[row][0], m);
1869 isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
1870 isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
1871 isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
1872 }
1873 vec = isl_vec_normalize(vec);
1874
1875 isl_int_clear(m);
1876 return vec;
1877 }
1878
1879 /* Update "bmap" based on the results of the tableau "tab".
1880 * In particular, implicit equalities are made explicit, redundant constraints
1881 * are removed and if the sample value happens to be integer, it is stored
1882 * in "bmap" (unless "bmap" already had an integer sample).
1883 *
1884 * The tableau is assumed to have been created from "bmap" using
1885 * isl_tab_from_basic_map.
1886 */
1887 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
1888 struct isl_tab *tab)
1889 {
1890 int i;
1891 unsigned n_eq;
1892
1893 if (!bmap)
1894 return NULL;
1895 if (!tab)
1896 return bmap;
1897
1898 n_eq = tab->n_eq;
1899 if (tab->empty)
1900 bmap = isl_basic_map_set_to_empty(bmap);
1901 else
1902 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1903 if (isl_tab_is_equality(tab, n_eq + i))
1904 isl_basic_map_inequality_to_equality(bmap, i);
1905 else if (isl_tab_is_redundant(tab, n_eq + i))
1906 isl_basic_map_drop_inequality(bmap, i);
1907 }
1908 if (!tab->rational &&
1909 !bmap->sample && isl_tab_sample_is_integer(tab))
1910 bmap->sample = extract_integer_sample(tab);
1911 return bmap;
1912 }
1913
1914 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
1915 struct isl_tab *tab)
1916 {
1917 return (struct isl_basic_set *)isl_basic_map_update_from_tab(
1918 (struct isl_basic_map *)bset, tab);
1919 }
1920
1921 /* Given a non-negative variable "var", add a new non-negative variable
1922 * that is the opposite of "var", ensuring that var can only attain the
1923 * value zero.
1924 * If var = n/d is a row variable, then the new variable = -n/d.
1925 * If var is a column variables, then the new variable = -var.
1926 * If the new variable cannot attain non-negative values, then
1927 * the resulting tableau is empty.
1928 * Otherwise, we know the value will be zero and we close the row.
1929 */
1930 static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab,
1931 struct isl_tab_var *var)
1932 {
1933 unsigned r;
1934 isl_int *row;
1935 int sgn;
1936 unsigned off = 2 + tab->M;
1937
1938 if (var->is_zero)
1939 return tab;
1940 isl_assert(tab->mat->ctx, !var->is_redundant, goto error);
1941
1942 if (isl_tab_extend_cons(tab, 1) < 0)
1943 goto error;
1944
1945 r = tab->n_con;
1946 tab->con[r].index = tab->n_row;
1947 tab->con[r].is_row = 1;
1948 tab->con[r].is_nonneg = 0;
1949 tab->con[r].is_zero = 0;
1950 tab->con[r].is_redundant = 0;
1951 tab->con[r].frozen = 0;
1952 tab->con[r].negated = 0;
1953 tab->row_var[tab->n_row] = ~r;
1954 row = tab->mat->row[tab->n_row];
1955
1956 if (var->is_row) {
1957 isl_int_set(row[0], tab->mat->row[var->index][0]);
1958 isl_seq_neg(row + 1,
1959 tab->mat->row[var->index] + 1, 1 + tab->n_col);
1960 } else {
1961 isl_int_set_si(row[0], 1);
1962 isl_seq_clr(row + 1, 1 + tab->n_col);
1963 isl_int_set_si(row[off + var->index], -1);
1964 }
1965
1966 tab->n_row++;
1967 tab->n_con++;
1968 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
1969
1970 sgn = sign_of_max(tab, &tab->con[r]);
1971 if (sgn < 0)
1972 return isl_tab_mark_empty(tab);
1973 tab->con[r].is_nonneg = 1;
1974 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1975 /* sgn == 0 */
1976 close_row(tab, &tab->con[r]);
1977
1978 return tab;
1979 error:
1980 isl_tab_free(tab);
1981 return NULL;
1982 }
1983
1984 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
1985 * relax the inequality by one. That is, the inequality r >= 0 is replaced
1986 * by r' = r + 1 >= 0.
1987 * If r is a row variable, we simply increase the constant term by one
1988 * (taking into account the denominator).
1989 * If r is a column variable, then we need to modify each row that
1990 * refers to r = r' - 1 by substituting this equality, effectively
1991 * subtracting the coefficient of the column from the constant.
1992 */
1993 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
1994 {
1995 struct isl_tab_var *var;
1996 unsigned off = 2 + tab->M;
1997
1998 if (!tab)
1999 return NULL;
2000
2001 var = &tab->con[con];
2002
2003 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
2004 to_row(tab, var, 1);
2005
2006 if (var->is_row)
2007 isl_int_add(tab->mat->row[var->index][1],
2008 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
2009 else {
2010 int i;
2011
2012 for (i = 0; i < tab->n_row; ++i) {
2013 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2014 continue;
2015 isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
2016 tab->mat->row[i][off + var->index]);
2017 }
2018
2019 }
2020
2021 isl_tab_push_var(tab, isl_tab_undo_relax, var);
2022
2023 return tab;
2024 }
2025
2026 struct isl_tab *isl_tab_select_facet(struct isl_tab *tab, int con)
2027 {
2028 if (!tab)
2029 return NULL;
2030
2031 return cut_to_hyperplane(tab, &tab->con[con]);
2032 }
2033
2034 static int may_be_equality(struct isl_tab *tab, int row)
2035 {
2036 unsigned off = 2 + tab->M;
2037 return (tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
2038 : isl_int_lt(tab->mat->row[row][1],
2039 tab->mat->row[row][0])) &&
2040 isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
2041 tab->n_col - tab->n_dead) != -1;
2042 }
2043
2044 /* Check for (near) equalities among the constraints.
2045 * A constraint is an equality if it is non-negative and if
2046 * its maximal value is either
2047 * - zero (in case of rational tableaus), or
2048 * - strictly less than 1 (in case of integer tableaus)
2049 *
2050 * We first mark all non-redundant and non-dead variables that
2051 * are not frozen and not obviously not an equality.
2052 * Then we iterate over all marked variables if they can attain
2053 * any values larger than zero or at least one.
2054 * If the maximal value is zero, we mark any column variables
2055 * that appear in the row as being zero and mark the row as being redundant.
2056 * Otherwise, if the maximal value is strictly less than one (and the
2057 * tableau is integer), then we restrict the value to being zero
2058 * by adding an opposite non-negative variable.
2059 */
2060 struct isl_tab *isl_tab_detect_implicit_equalities(struct isl_tab *tab)
2061 {
2062 int i;
2063 unsigned n_marked;
2064
2065 if (!tab)
2066 return NULL;
2067 if (tab->empty)
2068 return tab;
2069 if (tab->n_dead == tab->n_col)
2070 return tab;
2071
2072 n_marked = 0;
2073 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2074 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
2075 var->marked = !var->frozen && var->is_nonneg &&
2076 may_be_equality(tab, i);
2077 if (var->marked)
2078 n_marked++;
2079 }
2080 for (i = tab->n_dead; i < tab->n_col; ++i) {
2081 struct isl_tab_var *var = var_from_col(tab, i);
2082 var->marked = !var->frozen && var->is_nonneg;
2083 if (var->marked)
2084 n_marked++;
2085 }
2086 while (n_marked) {
2087 struct isl_tab_var *var;
2088 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2089 var = isl_tab_var_from_row(tab, i);
2090 if (var->marked)
2091 break;
2092 }
2093 if (i == tab->n_row) {
2094 for (i = tab->n_dead; i < tab->n_col; ++i) {
2095 var = var_from_col(tab, i);
2096 if (var->marked)
2097 break;
2098 }
2099 if (i == tab->n_col)
2100 break;
2101 }
2102 var->marked = 0;
2103 n_marked--;
2104 if (sign_of_max(tab, var) == 0)
2105 close_row(tab, var);
2106 else if (!tab->rational && !at_least_one(tab, var)) {
2107 tab = cut_to_hyperplane(tab, var);
2108 return isl_tab_detect_implicit_equalities(tab);
2109 }
2110 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2111 var = isl_tab_var_from_row(tab, i);
2112 if (!var->marked)
2113 continue;
2114 if (may_be_equality(tab, i))
2115 continue;
2116 var->marked = 0;
2117 n_marked--;
2118 }
2119 }
2120
2121 return tab;
2122 }
2123
2124 /* Check for (near) redundant constraints.
2125 * A constraint is redundant if it is non-negative and if
2126 * its minimal value (temporarily ignoring the non-negativity) is either
2127 * - zero (in case of rational tableaus), or
2128 * - strictly larger than -1 (in case of integer tableaus)
2129 *
2130 * We first mark all non-redundant and non-dead variables that
2131 * are not frozen and not obviously negatively unbounded.
2132 * Then we iterate over all marked variables if they can attain
2133 * any values smaller than zero or at most negative one.
2134 * If not, we mark the row as being redundant (assuming it hasn't
2135 * been detected as being obviously redundant in the mean time).
2136 */
2137 struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab)
2138 {
2139 int i;
2140 unsigned n_marked;
2141
2142 if (!tab)
2143 return NULL;
2144 if (tab->empty)
2145 return tab;
2146 if (tab->n_redundant == tab->n_row)
2147 return tab;
2148
2149 n_marked = 0;
2150 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2151 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
2152 var->marked = !var->frozen && var->is_nonneg;
2153 if (var->marked)
2154 n_marked++;
2155 }
2156 for (i = tab->n_dead; i < tab->n_col; ++i) {
2157 struct isl_tab_var *var = var_from_col(tab, i);
2158 var->marked = !var->frozen && var->is_nonneg &&
2159 !min_is_manifestly_unbounded(tab, var);
2160 if (var->marked)
2161 n_marked++;
2162 }
2163 while (n_marked) {
2164 struct isl_tab_var *var;
2165 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2166 var = isl_tab_var_from_row(tab, i);
2167 if (var->marked)
2168 break;
2169 }
2170 if (i == tab->n_row) {
2171 for (i = tab->n_dead; i < tab->n_col; ++i) {
2172 var = var_from_col(tab, i);
2173 if (var->marked)
2174 break;
2175 }
2176 if (i == tab->n_col)
2177 break;
2178 }
2179 var->marked = 0;
2180 n_marked--;
2181 if ((tab->rational ? (sign_of_min(tab, var) >= 0)
2182 : !isl_tab_min_at_most_neg_one(tab, var)) &&
2183 !var->is_redundant)
2184 isl_tab_mark_redundant(tab, var->index);
2185 for (i = tab->n_dead; i < tab->n_col; ++i) {
2186 var = var_from_col(tab, i);
2187 if (!var->marked)
2188 continue;
2189 if (!min_is_manifestly_unbounded(tab, var))
2190 continue;
2191 var->marked = 0;
2192 n_marked--;
2193 }
2194 }
2195
2196 return tab;
2197 }
2198
2199 int isl_tab_is_equality(struct isl_tab *tab, int con)
2200 {
2201 int row;
2202 unsigned off;
2203
2204 if (!tab)
2205 return -1;
2206 if (tab->con[con].is_zero)
2207 return 1;
2208 if (tab->con[con].is_redundant)
2209 return 0;
2210 if (!tab->con[con].is_row)
2211 return tab->con[con].index < tab->n_dead;
2212
2213 row = tab->con[con].index;
2214
2215 off = 2 + tab->M;
2216 return isl_int_is_zero(tab->mat->row[row][1]) &&
2217 isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
2218 tab->n_col - tab->n_dead) == -1;
2219 }
2220
2221 /* Return the minimial value of the affine expression "f" with denominator
2222 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
2223 * the expression cannot attain arbitrarily small values.
2224 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
2225 * The return value reflects the nature of the result (empty, unbounded,
2226 * minmimal value returned in *opt).
2227 */
2228 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
2229 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
2230 unsigned flags)
2231 {
2232 int r;
2233 enum isl_lp_result res = isl_lp_ok;
2234 struct isl_tab_var *var;
2235 struct isl_tab_undo *snap;
2236
2237 if (tab->empty)
2238 return isl_lp_empty;
2239
2240 snap = isl_tab_snap(tab);
2241 r = isl_tab_add_row(tab, f);
2242 if (r < 0)
2243 return isl_lp_error;
2244 var = &tab->con[r];
2245 isl_int_mul(tab->mat->row[var->index][0],
2246 tab->mat->row[var->index][0], denom);
2247 for (;;) {
2248 int row, col;
2249 find_pivot(tab, var, var, -1, &row, &col);
2250 if (row == var->index) {
2251 res = isl_lp_unbounded;
2252 break;
2253 }
2254 if (row == -1)
2255 break;
2256 isl_tab_pivot(tab, row, col);
2257 }
2258 if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
2259 int i;
2260
2261 isl_vec_free(tab->dual);
2262 tab->dual = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_con);
2263 if (!tab->dual)
2264 return isl_lp_error;
2265 isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
2266 for (i = 0; i < tab->n_con; ++i) {
2267 int pos;
2268 if (tab->con[i].is_row) {
2269 isl_int_set_si(tab->dual->el[1 + i], 0);
2270 continue;
2271 }
2272 pos = 2 + tab->M + tab->con[i].index;
2273 if (tab->con[i].negated)
2274 isl_int_neg(tab->dual->el[1 + i],
2275 tab->mat->row[var->index][pos]);
2276 else
2277 isl_int_set(tab->dual->el[1 + i],
2278 tab->mat->row[var->index][pos]);
2279 }
2280 }
2281 if (opt && res == isl_lp_ok) {
2282 if (opt_denom) {
2283 isl_int_set(*opt, tab->mat->row[var->index][1]);
2284 isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
2285 } else
2286 isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
2287 tab->mat->row[var->index][0]);
2288 }
2289 if (isl_tab_rollback(tab, snap) < 0)
2290 return isl_lp_error;
2291 return res;
2292 }
2293
2294 int isl_tab_is_redundant(struct isl_tab *tab, int con)
2295 {
2296 if (!tab)
2297 return -1;
2298 if (tab->con[con].is_zero)
2299 return 0;
2300 if (tab->con[con].is_redundant)
2301 return 1;
2302 return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
2303 }
2304
2305 /* Take a snapshot of the tableau that can be restored by s call to
2306 * isl_tab_rollback.
2307 */
2308 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
2309 {
2310 if (!tab)
2311 return NULL;
2312 tab->need_undo = 1;
2313 return tab->top;
2314 }
2315
2316 /* Undo the operation performed by isl_tab_relax.
2317 */
2318 static void unrelax(struct isl_tab *tab, struct isl_tab_var *var)
2319 {
2320 unsigned off = 2 + tab->M;
2321
2322 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
2323 to_row(tab, var, 1);
2324
2325 if (var->is_row)
2326 isl_int_sub(tab->mat->row[var->index][1],
2327 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
2328 else {
2329 int i;
2330
2331 for (i = 0; i < tab->n_row; ++i) {
2332 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2333 continue;
2334 isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
2335 tab->mat->row[i][off + var->index]);
2336 }
2337
2338 }
2339 }
2340
2341 static void perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
2342 {
2343 struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
2344 switch(undo->type) {
2345 case isl_tab_undo_nonneg:
2346 var->is_nonneg = 0;
2347 break;
2348 case isl_tab_undo_redundant:
2349 var->is_redundant = 0;
2350 tab->n_redundant--;
2351 break;
2352 case isl_tab_undo_zero:
2353 var->is_zero = 0;
2354 if (!var->is_row)
2355 tab->n_dead--;
2356 break;
2357 case isl_tab_undo_allocate:
2358 if (undo->u.var_index >= 0) {
2359 isl_assert(tab->mat->ctx, !var->is_row, return);
2360 drop_col(tab, var->index);
2361 break;
2362 }
2363 if (!var->is_row) {
2364 if (!max_is_manifestly_unbounded(tab, var))
2365 to_row(tab, var, 1);
2366 else if (!min_is_manifestly_unbounded(tab, var))
2367 to_row(tab, var, -1);
2368 else
2369 to_row(tab, var, 0);
2370 }
2371 drop_row(tab, var->index);
2372 break;
2373 case isl_tab_undo_relax:
2374 unrelax(tab, var);
2375 break;
2376 }
2377 }
2378
2379 /* Restore the tableau to the state where the basic variables
2380 * are those in "col_var".
2381 * We first construct a list of variables that are currently in
2382 * the basis, but shouldn't. Then we iterate over all variables
2383 * that should be in the basis and for each one that is currently
2384 * not in the basis, we exchange it with one of the elements of the
2385 * list constructed before.
2386 * We can always find an appropriate variable to pivot with because
2387 * the current basis is mapped to the old basis by a non-singular
2388 * matrix and so we can never end up with a zero row.
2389 */
2390 static int restore_basis(struct isl_tab *tab, int *col_var)
2391 {
2392 int i, j;
2393 int n_extra = 0;
2394 int *extra = NULL; /* current columns that contain bad stuff */
2395 unsigned off = 2 + tab->M;
2396
2397 extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
2398 if (!extra)
2399 goto error;
2400 for (i = 0; i < tab->n_col; ++i) {
2401 for (j = 0; j < tab->n_col; ++j)
2402 if (tab->col_var[i] == col_var[j])
2403 break;
2404 if (j < tab->n_col)
2405 continue;
2406 extra[n_extra++] = i;
2407 }
2408 for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
2409 struct isl_tab_var *var;
2410 int row;
2411
2412 for (j = 0; j < tab->n_col; ++j)
2413 if (col_var[i] == tab->col_var[j])
2414 break;
2415 if (j < tab->n_col)
2416 continue;
2417 var = var_from_index(tab, col_var[i]);
2418 row = var->index;
2419 for (j = 0; j < n_extra; ++j)
2420 if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
2421 break;
2422 isl_assert(tab->mat->ctx, j < n_extra, goto error);
2423 isl_tab_pivot(tab, row, extra[j]);
2424 extra[j] = extra[--n_extra];
2425 }
2426
2427 free(extra);
2428 free(col_var);
2429 return 0;
2430 error:
2431 free(extra);
2432 free(col_var);
2433 return -1;
2434 }
2435
2436 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
2437 {
2438 switch (undo->type) {
2439 case isl_tab_undo_empty:
2440 tab->empty = 0;
2441 break;
2442 case isl_tab_undo_nonneg:
2443 case isl_tab_undo_redundant:
2444 case isl_tab_undo_zero:
2445 case isl_tab_undo_allocate:
2446 case isl_tab_undo_relax:
2447 perform_undo_var(tab, undo);
2448 break;
2449 case isl_tab_undo_bset_eq:
2450 isl_basic_set_free_equality(tab->bset, 1);
2451 break;
2452 case isl_tab_undo_bset_ineq:
2453 isl_basic_set_free_inequality(tab->bset, 1);
2454 break;
2455 case isl_tab_undo_bset_div:
2456 isl_basic_set_free_div(tab->bset, 1);
2457 if (tab->samples)
2458 tab->samples->n_col--;
2459 break;
2460 case isl_tab_undo_saved_basis:
2461 if (restore_basis(tab, undo->u.col_var) < 0)
2462 return -1;
2463 break;
2464 case isl_tab_undo_drop_sample:
2465 tab->n_outside--;
2466 break;
2467 default:
2468 isl_assert(tab->mat->ctx, 0, return -1);
2469 }
2470 return 0;
2471 }
2472
2473 /* Return the tableau to the state it was in when the snapshot "snap"
2474 * was taken.
2475 */
2476 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
2477 {
2478 struct isl_tab_undo *undo, *next;
2479
2480 if (!tab)
2481 return -1;
2482
2483 tab->in_undo = 1;
2484 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
2485 next = undo->next;
2486 if (undo == snap)
2487 break;
2488 if (perform_undo(tab, undo) < 0) {
2489 free_undo(tab);
2490 tab->in_undo = 0;
2491 return -1;
2492 }
2493 free(undo);
2494 }
2495 tab->in_undo = 0;
2496 tab->top = undo;
2497 if (!undo)
2498 return -1;
2499 return 0;
2500 }
2501
2502 /* The given row "row" represents an inequality violated by all
2503 * points in the tableau. Check for some special cases of such
2504 * separating constraints.
2505 * In particular, if the row has been reduced to the constant -1,
2506 * then we know the inequality is adjacent (but opposite) to
2507 * an equality in the tableau.
2508 * If the row has been reduced to r = -1 -r', with r' an inequality
2509 * of the tableau, then the inequality is adjacent (but opposite)
2510 * to the inequality r'.
2511 */
2512 static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
2513 {
2514 int pos;
2515 unsigned off = 2 + tab->M;
2516
2517 if (tab->rational)
2518 return isl_ineq_separate;
2519
2520 if (!isl_int_is_one(tab->mat->row[row][0]))
2521 return isl_ineq_separate;
2522 if (!isl_int_is_negone(tab->mat->row[row][1]))
2523 return isl_ineq_separate;
2524
2525 pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
2526 tab->n_col - tab->n_dead);
2527 if (pos == -1)
2528 return isl_ineq_adj_eq;
2529
2530 if (!isl_int_is_negone(tab->mat->row[row][off + tab->n_dead + pos]))
2531 return isl_ineq_separate;
2532
2533 pos = isl_seq_first_non_zero(
2534 tab->mat->row[row] + off + tab->n_dead + pos + 1,
2535 tab->n_col - tab->n_dead - pos - 1);
2536
2537 return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
2538 }
2539
2540 /* Check the effect of inequality "ineq" on the tableau "tab".
2541 * The result may be
2542 * isl_ineq_redundant: satisfied by all points in the tableau
2543 * isl_ineq_separate: satisfied by no point in the tableau
2544 * isl_ineq_cut: satisfied by some by not all points
2545 * isl_ineq_adj_eq: adjacent to an equality
2546 * isl_ineq_adj_ineq: adjacent to an inequality.
2547 */
2548 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
2549 {
2550 enum isl_ineq_type type = isl_ineq_error;
2551 struct isl_tab_undo *snap = NULL;
2552 int con;
2553 int row;
2554
2555 if (!tab)
2556 return isl_ineq_error;
2557
2558 if (isl_tab_extend_cons(tab, 1) < 0)
2559 return isl_ineq_error;
2560
2561 snap = isl_tab_snap(tab);
2562
2563 con = isl_tab_add_row(tab, ineq);
2564 if (con < 0)
2565 goto error;
2566
2567 row = tab->con[con].index;
2568 if (isl_tab_row_is_redundant(tab, row))
2569 type = isl_ineq_redundant;
2570 else if (isl_int_is_neg(tab->mat->row[row][1]) &&
2571 (tab->rational ||
2572 isl_int_abs_ge(tab->mat->row[row][1],
2573 tab->mat->row[row][0]))) {
2574 if (at_least_zero(tab, &tab->con[con]))
2575 type = isl_ineq_cut;
2576 else
2577 type = separation_type(tab, row);
2578 } else if (tab->rational ? (sign_of_min(tab, &tab->con[con]) < 0)
2579 : isl_tab_min_at_most_neg_one(tab, &tab->con[con]))
2580 type = isl_ineq_cut;
2581 else
2582 type = isl_ineq_redundant;
2583
2584 if (isl_tab_rollback(tab, snap))
2585 return isl_ineq_error;
2586 return type;
2587 error:
2588 isl_tab_rollback(tab, snap);
2589 return isl_ineq_error;
2590 }
2591
2592 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent)
2593 {
2594 unsigned r, c;
2595 int i;
2596
2597 if (!tab) {
2598 fprintf(out, "%*snull tab\n", indent, "");
2599 return;
2600 }
2601 fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
2602 tab->n_redundant, tab->n_dead);
2603 if (tab->rational)
2604 fprintf(out, ", rational");
2605 if (tab->empty)
2606 fprintf(out, ", empty");
2607 fprintf(out, "\n");
2608 fprintf(out, "%*s[", indent, "");
2609 for (i = 0; i < tab->n_var; ++i) {
2610 if (i)
2611 fprintf(out, (i == tab->n_param ||
2612 i == tab->n_var - tab->n_div) ? "; "
2613 : ", ");
2614 fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
2615 tab->var[i].index,
2616 tab->var[i].is_zero ? " [=0]" :
2617 tab->var[i].is_redundant ? " [R]" : "");
2618 }
2619 fprintf(out, "]\n");
2620 fprintf(out, "%*s[", indent, "");
2621 for (i = 0; i < tab->n_con; ++i) {
2622 if (i)
2623 fprintf(out, ", ");
2624 fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
2625 tab->con[i].index,
2626 tab->con[i].is_zero ? " [=0]" :
2627 tab->con[i].is_redundant ? " [R]" : "");
2628 }
2629 fprintf(out, "]\n");
2630 fprintf(out, "%*s[", indent, "");
2631 for (i = 0; i < tab->n_row; ++i) {
2632 const char *sign = "";
2633 if (i)
2634 fprintf(out, ", ");
2635 if (tab->row_sign) {
2636 if (tab->row_sign[i] == isl_tab_row_unknown)
2637 sign = "?";
2638 else if (tab->row_sign[i] == isl_tab_row_neg)
2639 sign = "-";
2640 else if (tab->row_sign[i] == isl_tab_row_pos)
2641 sign = "+";
2642 else
2643 sign = "+-";
2644 }
2645 fprintf(out, "r%d: %d%s%s", i, tab->row_var[i],
2646 isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
2647 }
2648 fprintf(out, "]\n");
2649 fprintf(out, "%*s[", indent, "");
2650 for (i = 0; i < tab->n_col; ++i) {
2651 if (i)
2652 fprintf(out, ", ");
2653 fprintf(out, "c%d: %d%s", i, tab->col_var[i],
2654 var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
2655 }
2656 fprintf(out, "]\n");
2657 r = tab->mat->n_row;
2658 tab->mat->n_row = tab->n_row;
2659 c = tab->mat->n_col;
2660 tab->mat->n_col = 2 + tab->M + tab->n_col;
2661 isl_mat_dump(tab->mat, out, indent);
2662 tab->mat->n_row = r;
2663 tab->mat->n_col = c;
2664 if (tab->bset)
2665 isl_basic_set_dump(tab->bset, out, indent);
2666 }
Integer set library