isl_scheduler.c: graph_init: use isl_schedule_constraints_get_context
[isl.git] / isl_tab.c
blob4985f49e747b46d869394b985f5df95d9e39e927
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2013 Ecole Normale Superieure
4 * Copyright 2014 INRIA Rocquencourt
6 * Use of this software is governed by the MIT license
8 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
11 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
12 * B.P. 105 - 78153 Le Chesnay, France
15 #include <isl_ctx_private.h>
16 #include <isl_mat_private.h>
17 #include <isl_vec_private.h>
18 #include "isl_map_private.h"
19 #include "isl_tab.h"
20 #include <isl_seq.h>
21 #include <isl_config.h>
24 * The implementation of tableaus in this file was inspired by Section 8
25 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
26 * prover for program checking".
29 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
30 unsigned n_row, unsigned n_var, unsigned M)
32 int i;
33 struct isl_tab *tab;
34 unsigned off = 2 + M;
36 tab = isl_calloc_type(ctx, struct isl_tab);
37 if (!tab)
38 return NULL;
39 tab->mat = isl_mat_alloc(ctx, n_row, off + n_var);
40 if (!tab->mat)
41 goto error;
42 tab->var = isl_alloc_array(ctx, struct isl_tab_var, n_var);
43 if (n_var && !tab->var)
44 goto error;
45 tab->con = isl_alloc_array(ctx, struct isl_tab_var, n_row);
46 if (n_row && !tab->con)
47 goto error;
48 tab->col_var = isl_alloc_array(ctx, int, n_var);
49 if (n_var && !tab->col_var)
50 goto error;
51 tab->row_var = isl_alloc_array(ctx, int, n_row);
52 if (n_row && !tab->row_var)
53 goto error;
54 for (i = 0; i < n_var; ++i) {
55 tab->var[i].index = i;
56 tab->var[i].is_row = 0;
57 tab->var[i].is_nonneg = 0;
58 tab->var[i].is_zero = 0;
59 tab->var[i].is_redundant = 0;
60 tab->var[i].frozen = 0;
61 tab->var[i].negated = 0;
62 tab->col_var[i] = i;
64 tab->n_row = 0;
65 tab->n_con = 0;
66 tab->n_eq = 0;
67 tab->max_con = n_row;
68 tab->n_col = n_var;
69 tab->n_var = n_var;
70 tab->max_var = n_var;
71 tab->n_param = 0;
72 tab->n_div = 0;
73 tab->n_dead = 0;
74 tab->n_redundant = 0;
75 tab->strict_redundant = 0;
76 tab->need_undo = 0;
77 tab->rational = 0;
78 tab->empty = 0;
79 tab->in_undo = 0;
80 tab->M = M;
81 tab->cone = 0;
82 tab->bottom.type = isl_tab_undo_bottom;
83 tab->bottom.next = NULL;
84 tab->top = &tab->bottom;
86 tab->n_zero = 0;
87 tab->n_unbounded = 0;
88 tab->basis = NULL;
90 return tab;
91 error:
92 isl_tab_free(tab);
93 return NULL;
96 isl_ctx *isl_tab_get_ctx(struct isl_tab *tab)
98 return tab ? isl_mat_get_ctx(tab->mat) : NULL;
101 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new)
103 unsigned off;
105 if (!tab)
106 return -1;
108 off = 2 + tab->M;
110 if (tab->max_con < tab->n_con + n_new) {
111 struct isl_tab_var *con;
113 con = isl_realloc_array(tab->mat->ctx, tab->con,
114 struct isl_tab_var, tab->max_con + n_new);
115 if (!con)
116 return -1;
117 tab->con = con;
118 tab->max_con += n_new;
120 if (tab->mat->n_row < tab->n_row + n_new) {
121 int *row_var;
123 tab->mat = isl_mat_extend(tab->mat,
124 tab->n_row + n_new, off + tab->n_col);
125 if (!tab->mat)
126 return -1;
127 row_var = isl_realloc_array(tab->mat->ctx, tab->row_var,
128 int, tab->mat->n_row);
129 if (!row_var)
130 return -1;
131 tab->row_var = row_var;
132 if (tab->row_sign) {
133 enum isl_tab_row_sign *s;
134 s = isl_realloc_array(tab->mat->ctx, tab->row_sign,
135 enum isl_tab_row_sign, tab->mat->n_row);
136 if (!s)
137 return -1;
138 tab->row_sign = s;
141 return 0;
144 /* Make room for at least n_new extra variables.
145 * Return -1 if anything went wrong.
147 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new)
149 struct isl_tab_var *var;
150 unsigned off = 2 + tab->M;
152 if (tab->max_var < tab->n_var + n_new) {
153 var = isl_realloc_array(tab->mat->ctx, tab->var,
154 struct isl_tab_var, tab->n_var + n_new);
155 if (!var)
156 return -1;
157 tab->var = var;
158 tab->max_var = tab->n_var + n_new;
161 if (tab->mat->n_col < off + tab->n_col + n_new) {
162 int *p;
164 tab->mat = isl_mat_extend(tab->mat,
165 tab->mat->n_row, off + tab->n_col + n_new);
166 if (!tab->mat)
167 return -1;
168 p = isl_realloc_array(tab->mat->ctx, tab->col_var,
169 int, tab->n_col + n_new);
170 if (!p)
171 return -1;
172 tab->col_var = p;
175 return 0;
178 static void free_undo_record(struct isl_tab_undo *undo)
180 switch (undo->type) {
181 case isl_tab_undo_saved_basis:
182 free(undo->u.col_var);
183 break;
184 default:;
186 free(undo);
189 static void free_undo(struct isl_tab *tab)
191 struct isl_tab_undo *undo, *next;
193 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
194 next = undo->next;
195 free_undo_record(undo);
197 tab->top = undo;
200 void isl_tab_free(struct isl_tab *tab)
202 if (!tab)
203 return;
204 free_undo(tab);
205 isl_mat_free(tab->mat);
206 isl_vec_free(tab->dual);
207 isl_basic_map_free(tab->bmap);
208 free(tab->var);
209 free(tab->con);
210 free(tab->row_var);
211 free(tab->col_var);
212 free(tab->row_sign);
213 isl_mat_free(tab->samples);
214 free(tab->sample_index);
215 isl_mat_free(tab->basis);
216 free(tab);
219 struct isl_tab *isl_tab_dup(struct isl_tab *tab)
221 int i;
222 struct isl_tab *dup;
223 unsigned off;
225 if (!tab)
226 return NULL;
228 off = 2 + tab->M;
229 dup = isl_calloc_type(tab->mat->ctx, struct isl_tab);
230 if (!dup)
231 return NULL;
232 dup->mat = isl_mat_dup(tab->mat);
233 if (!dup->mat)
234 goto error;
235 dup->var = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_var);
236 if (tab->max_var && !dup->var)
237 goto error;
238 for (i = 0; i < tab->n_var; ++i)
239 dup->var[i] = tab->var[i];
240 dup->con = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_con);
241 if (tab->max_con && !dup->con)
242 goto error;
243 for (i = 0; i < tab->n_con; ++i)
244 dup->con[i] = tab->con[i];
245 dup->col_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_col - off);
246 if ((tab->mat->n_col - off) && !dup->col_var)
247 goto error;
248 for (i = 0; i < tab->n_col; ++i)
249 dup->col_var[i] = tab->col_var[i];
250 dup->row_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_row);
251 if (tab->mat->n_row && !dup->row_var)
252 goto error;
253 for (i = 0; i < tab->n_row; ++i)
254 dup->row_var[i] = tab->row_var[i];
255 if (tab->row_sign) {
256 dup->row_sign = isl_alloc_array(tab->mat->ctx, enum isl_tab_row_sign,
257 tab->mat->n_row);
258 if (tab->mat->n_row && !dup->row_sign)
259 goto error;
260 for (i = 0; i < tab->n_row; ++i)
261 dup->row_sign[i] = tab->row_sign[i];
263 if (tab->samples) {
264 dup->samples = isl_mat_dup(tab->samples);
265 if (!dup->samples)
266 goto error;
267 dup->sample_index = isl_alloc_array(tab->mat->ctx, int,
268 tab->samples->n_row);
269 if (tab->samples->n_row && !dup->sample_index)
270 goto error;
271 dup->n_sample = tab->n_sample;
272 dup->n_outside = tab->n_outside;
274 dup->n_row = tab->n_row;
275 dup->n_con = tab->n_con;
276 dup->n_eq = tab->n_eq;
277 dup->max_con = tab->max_con;
278 dup->n_col = tab->n_col;
279 dup->n_var = tab->n_var;
280 dup->max_var = tab->max_var;
281 dup->n_param = tab->n_param;
282 dup->n_div = tab->n_div;
283 dup->n_dead = tab->n_dead;
284 dup->n_redundant = tab->n_redundant;
285 dup->rational = tab->rational;
286 dup->empty = tab->empty;
287 dup->strict_redundant = 0;
288 dup->need_undo = 0;
289 dup->in_undo = 0;
290 dup->M = tab->M;
291 tab->cone = tab->cone;
292 dup->bottom.type = isl_tab_undo_bottom;
293 dup->bottom.next = NULL;
294 dup->top = &dup->bottom;
296 dup->n_zero = tab->n_zero;
297 dup->n_unbounded = tab->n_unbounded;
298 dup->basis = isl_mat_dup(tab->basis);
300 return dup;
301 error:
302 isl_tab_free(dup);
303 return NULL;
306 /* Construct the coefficient matrix of the product tableau
307 * of two tableaus.
308 * mat{1,2} is the coefficient matrix of tableau {1,2}
309 * row{1,2} is the number of rows in tableau {1,2}
310 * col{1,2} is the number of columns in tableau {1,2}
311 * off is the offset to the coefficient column (skipping the
312 * denominator, the constant term and the big parameter if any)
313 * r{1,2} is the number of redundant rows in tableau {1,2}
314 * d{1,2} is the number of dead columns in tableau {1,2}
316 * The order of the rows and columns in the result is as explained
317 * in isl_tab_product.
319 static struct isl_mat *tab_mat_product(struct isl_mat *mat1,
320 struct isl_mat *mat2, unsigned row1, unsigned row2,
321 unsigned col1, unsigned col2,
322 unsigned off, unsigned r1, unsigned r2, unsigned d1, unsigned d2)
324 int i;
325 struct isl_mat *prod;
326 unsigned n;
328 prod = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
329 off + col1 + col2);
330 if (!prod)
331 return NULL;
333 n = 0;
334 for (i = 0; i < r1; ++i) {
335 isl_seq_cpy(prod->row[n + i], mat1->row[i], off + d1);
336 isl_seq_clr(prod->row[n + i] + off + d1, d2);
337 isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
338 mat1->row[i] + off + d1, col1 - d1);
339 isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
342 n += r1;
343 for (i = 0; i < r2; ++i) {
344 isl_seq_cpy(prod->row[n + i], mat2->row[i], off);
345 isl_seq_clr(prod->row[n + i] + off, d1);
346 isl_seq_cpy(prod->row[n + i] + off + d1,
347 mat2->row[i] + off, d2);
348 isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
349 isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
350 mat2->row[i] + off + d2, col2 - d2);
353 n += r2;
354 for (i = 0; i < row1 - r1; ++i) {
355 isl_seq_cpy(prod->row[n + i], mat1->row[r1 + i], off + d1);
356 isl_seq_clr(prod->row[n + i] + off + d1, d2);
357 isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
358 mat1->row[r1 + i] + off + d1, col1 - d1);
359 isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
362 n += row1 - r1;
363 for (i = 0; i < row2 - r2; ++i) {
364 isl_seq_cpy(prod->row[n + i], mat2->row[r2 + i], off);
365 isl_seq_clr(prod->row[n + i] + off, d1);
366 isl_seq_cpy(prod->row[n + i] + off + d1,
367 mat2->row[r2 + i] + off, d2);
368 isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
369 isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
370 mat2->row[r2 + i] + off + d2, col2 - d2);
373 return prod;
376 /* Update the row or column index of a variable that corresponds
377 * to a variable in the first input tableau.
379 static void update_index1(struct isl_tab_var *var,
380 unsigned r1, unsigned r2, unsigned d1, unsigned d2)
382 if (var->index == -1)
383 return;
384 if (var->is_row && var->index >= r1)
385 var->index += r2;
386 if (!var->is_row && var->index >= d1)
387 var->index += d2;
390 /* Update the row or column index of a variable that corresponds
391 * to a variable in the second input tableau.
393 static void update_index2(struct isl_tab_var *var,
394 unsigned row1, unsigned col1,
395 unsigned r1, unsigned r2, unsigned d1, unsigned d2)
397 if (var->index == -1)
398 return;
399 if (var->is_row) {
400 if (var->index < r2)
401 var->index += r1;
402 else
403 var->index += row1;
404 } else {
405 if (var->index < d2)
406 var->index += d1;
407 else
408 var->index += col1;
412 /* Create a tableau that represents the Cartesian product of the sets
413 * represented by tableaus tab1 and tab2.
414 * The order of the rows in the product is
415 * - redundant rows of tab1
416 * - redundant rows of tab2
417 * - non-redundant rows of tab1
418 * - non-redundant rows of tab2
419 * The order of the columns is
420 * - denominator
421 * - constant term
422 * - coefficient of big parameter, if any
423 * - dead columns of tab1
424 * - dead columns of tab2
425 * - live columns of tab1
426 * - live columns of tab2
427 * The order of the variables and the constraints is a concatenation
428 * of order in the two input tableaus.
430 struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2)
432 int i;
433 struct isl_tab *prod;
434 unsigned off;
435 unsigned r1, r2, d1, d2;
437 if (!tab1 || !tab2)
438 return NULL;
440 isl_assert(tab1->mat->ctx, tab1->M == tab2->M, return NULL);
441 isl_assert(tab1->mat->ctx, tab1->rational == tab2->rational, return NULL);
442 isl_assert(tab1->mat->ctx, tab1->cone == tab2->cone, return NULL);
443 isl_assert(tab1->mat->ctx, !tab1->row_sign, return NULL);
444 isl_assert(tab1->mat->ctx, !tab2->row_sign, return NULL);
445 isl_assert(tab1->mat->ctx, tab1->n_param == 0, return NULL);
446 isl_assert(tab1->mat->ctx, tab2->n_param == 0, return NULL);
447 isl_assert(tab1->mat->ctx, tab1->n_div == 0, return NULL);
448 isl_assert(tab1->mat->ctx, tab2->n_div == 0, return NULL);
450 off = 2 + tab1->M;
451 r1 = tab1->n_redundant;
452 r2 = tab2->n_redundant;
453 d1 = tab1->n_dead;
454 d2 = tab2->n_dead;
455 prod = isl_calloc_type(tab1->mat->ctx, struct isl_tab);
456 if (!prod)
457 return NULL;
458 prod->mat = tab_mat_product(tab1->mat, tab2->mat,
459 tab1->n_row, tab2->n_row,
460 tab1->n_col, tab2->n_col, off, r1, r2, d1, d2);
461 if (!prod->mat)
462 goto error;
463 prod->var = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
464 tab1->max_var + tab2->max_var);
465 if ((tab1->max_var + tab2->max_var) && !prod->var)
466 goto error;
467 for (i = 0; i < tab1->n_var; ++i) {
468 prod->var[i] = tab1->var[i];
469 update_index1(&prod->var[i], r1, r2, d1, d2);
471 for (i = 0; i < tab2->n_var; ++i) {
472 prod->var[tab1->n_var + i] = tab2->var[i];
473 update_index2(&prod->var[tab1->n_var + i],
474 tab1->n_row, tab1->n_col,
475 r1, r2, d1, d2);
477 prod->con = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
478 tab1->max_con + tab2->max_con);
479 if ((tab1->max_con + tab2->max_con) && !prod->con)
480 goto error;
481 for (i = 0; i < tab1->n_con; ++i) {
482 prod->con[i] = tab1->con[i];
483 update_index1(&prod->con[i], r1, r2, d1, d2);
485 for (i = 0; i < tab2->n_con; ++i) {
486 prod->con[tab1->n_con + i] = tab2->con[i];
487 update_index2(&prod->con[tab1->n_con + i],
488 tab1->n_row, tab1->n_col,
489 r1, r2, d1, d2);
491 prod->col_var = isl_alloc_array(tab1->mat->ctx, int,
492 tab1->n_col + tab2->n_col);
493 if ((tab1->n_col + tab2->n_col) && !prod->col_var)
494 goto error;
495 for (i = 0; i < tab1->n_col; ++i) {
496 int pos = i < d1 ? i : i + d2;
497 prod->col_var[pos] = tab1->col_var[i];
499 for (i = 0; i < tab2->n_col; ++i) {
500 int pos = i < d2 ? d1 + i : tab1->n_col + i;
501 int t = tab2->col_var[i];
502 if (t >= 0)
503 t += tab1->n_var;
504 else
505 t -= tab1->n_con;
506 prod->col_var[pos] = t;
508 prod->row_var = isl_alloc_array(tab1->mat->ctx, int,
509 tab1->mat->n_row + tab2->mat->n_row);
510 if ((tab1->mat->n_row + tab2->mat->n_row) && !prod->row_var)
511 goto error;
512 for (i = 0; i < tab1->n_row; ++i) {
513 int pos = i < r1 ? i : i + r2;
514 prod->row_var[pos] = tab1->row_var[i];
516 for (i = 0; i < tab2->n_row; ++i) {
517 int pos = i < r2 ? r1 + i : tab1->n_row + i;
518 int t = tab2->row_var[i];
519 if (t >= 0)
520 t += tab1->n_var;
521 else
522 t -= tab1->n_con;
523 prod->row_var[pos] = t;
525 prod->samples = NULL;
526 prod->sample_index = NULL;
527 prod->n_row = tab1->n_row + tab2->n_row;
528 prod->n_con = tab1->n_con + tab2->n_con;
529 prod->n_eq = 0;
530 prod->max_con = tab1->max_con + tab2->max_con;
531 prod->n_col = tab1->n_col + tab2->n_col;
532 prod->n_var = tab1->n_var + tab2->n_var;
533 prod->max_var = tab1->max_var + tab2->max_var;
534 prod->n_param = 0;
535 prod->n_div = 0;
536 prod->n_dead = tab1->n_dead + tab2->n_dead;
537 prod->n_redundant = tab1->n_redundant + tab2->n_redundant;
538 prod->rational = tab1->rational;
539 prod->empty = tab1->empty || tab2->empty;
540 prod->strict_redundant = tab1->strict_redundant || tab2->strict_redundant;
541 prod->need_undo = 0;
542 prod->in_undo = 0;
543 prod->M = tab1->M;
544 prod->cone = tab1->cone;
545 prod->bottom.type = isl_tab_undo_bottom;
546 prod->bottom.next = NULL;
547 prod->top = &prod->bottom;
549 prod->n_zero = 0;
550 prod->n_unbounded = 0;
551 prod->basis = NULL;
553 return prod;
554 error:
555 isl_tab_free(prod);
556 return NULL;
559 static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i)
561 if (i >= 0)
562 return &tab->var[i];
563 else
564 return &tab->con[~i];
567 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
569 return var_from_index(tab, tab->row_var[i]);
572 static struct isl_tab_var *var_from_col(struct isl_tab *tab, int i)
574 return var_from_index(tab, tab->col_var[i]);
577 /* Check if there are any upper bounds on column variable "var",
578 * i.e., non-negative rows where var appears with a negative coefficient.
579 * Return 1 if there are no such bounds.
581 static int max_is_manifestly_unbounded(struct isl_tab *tab,
582 struct isl_tab_var *var)
584 int i;
585 unsigned off = 2 + tab->M;
587 if (var->is_row)
588 return 0;
589 for (i = tab->n_redundant; i < tab->n_row; ++i) {
590 if (!isl_int_is_neg(tab->mat->row[i][off + var->index]))
591 continue;
592 if (isl_tab_var_from_row(tab, i)->is_nonneg)
593 return 0;
595 return 1;
598 /* Check if there are any lower bounds on column variable "var",
599 * i.e., non-negative rows where var appears with a positive coefficient.
600 * Return 1 if there are no such bounds.
602 static int min_is_manifestly_unbounded(struct isl_tab *tab,
603 struct isl_tab_var *var)
605 int i;
606 unsigned off = 2 + tab->M;
608 if (var->is_row)
609 return 0;
610 for (i = tab->n_redundant; i < tab->n_row; ++i) {
611 if (!isl_int_is_pos(tab->mat->row[i][off + var->index]))
612 continue;
613 if (isl_tab_var_from_row(tab, i)->is_nonneg)
614 return 0;
616 return 1;
619 static int row_cmp(struct isl_tab *tab, int r1, int r2, int c, isl_int *t)
621 unsigned off = 2 + tab->M;
623 if (tab->M) {
624 int s;
625 isl_int_mul(*t, tab->mat->row[r1][2], tab->mat->row[r2][off+c]);
626 isl_int_submul(*t, tab->mat->row[r2][2], tab->mat->row[r1][off+c]);
627 s = isl_int_sgn(*t);
628 if (s)
629 return s;
631 isl_int_mul(*t, tab->mat->row[r1][1], tab->mat->row[r2][off + c]);
632 isl_int_submul(*t, tab->mat->row[r2][1], tab->mat->row[r1][off + c]);
633 return isl_int_sgn(*t);
636 /* Given the index of a column "c", return the index of a row
637 * that can be used to pivot the column in, with either an increase
638 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
639 * If "var" is not NULL, then the row returned will be different from
640 * the one associated with "var".
642 * Each row in the tableau is of the form
644 * x_r = a_r0 + \sum_i a_ri x_i
646 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
647 * impose any limit on the increase or decrease in the value of x_c
648 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
649 * for the row with the smallest (most stringent) such bound.
650 * Note that the common denominator of each row drops out of the fraction.
651 * To check if row j has a smaller bound than row r, i.e.,
652 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
653 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
654 * where -sign(a_jc) is equal to "sgn".
656 static int pivot_row(struct isl_tab *tab,
657 struct isl_tab_var *var, int sgn, int c)
659 int j, r, tsgn;
660 isl_int t;
661 unsigned off = 2 + tab->M;
663 isl_int_init(t);
664 r = -1;
665 for (j = tab->n_redundant; j < tab->n_row; ++j) {
666 if (var && j == var->index)
667 continue;
668 if (!isl_tab_var_from_row(tab, j)->is_nonneg)
669 continue;
670 if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
671 continue;
672 if (r < 0) {
673 r = j;
674 continue;
676 tsgn = sgn * row_cmp(tab, r, j, c, &t);
677 if (tsgn < 0 || (tsgn == 0 &&
678 tab->row_var[j] < tab->row_var[r]))
679 r = j;
681 isl_int_clear(t);
682 return r;
685 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
686 * (sgn < 0) the value of row variable var.
687 * If not NULL, then skip_var is a row variable that should be ignored
688 * while looking for a pivot row. It is usually equal to var.
690 * As the given row in the tableau is of the form
692 * x_r = a_r0 + \sum_i a_ri x_i
694 * we need to find a column such that the sign of a_ri is equal to "sgn"
695 * (such that an increase in x_i will have the desired effect) or a
696 * column with a variable that may attain negative values.
697 * If a_ri is positive, then we need to move x_i in the same direction
698 * to obtain the desired effect. Otherwise, x_i has to move in the
699 * opposite direction.
701 static void find_pivot(struct isl_tab *tab,
702 struct isl_tab_var *var, struct isl_tab_var *skip_var,
703 int sgn, int *row, int *col)
705 int j, r, c;
706 isl_int *tr;
708 *row = *col = -1;
710 isl_assert(tab->mat->ctx, var->is_row, return);
711 tr = tab->mat->row[var->index] + 2 + tab->M;
713 c = -1;
714 for (j = tab->n_dead; j < tab->n_col; ++j) {
715 if (isl_int_is_zero(tr[j]))
716 continue;
717 if (isl_int_sgn(tr[j]) != sgn &&
718 var_from_col(tab, j)->is_nonneg)
719 continue;
720 if (c < 0 || tab->col_var[j] < tab->col_var[c])
721 c = j;
723 if (c < 0)
724 return;
726 sgn *= isl_int_sgn(tr[c]);
727 r = pivot_row(tab, skip_var, sgn, c);
728 *row = r < 0 ? var->index : r;
729 *col = c;
732 /* Return 1 if row "row" represents an obviously redundant inequality.
733 * This means
734 * - it represents an inequality or a variable
735 * - that is the sum of a non-negative sample value and a positive
736 * combination of zero or more non-negative constraints.
738 int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
740 int i;
741 unsigned off = 2 + tab->M;
743 if (tab->row_var[row] < 0 && !isl_tab_var_from_row(tab, row)->is_nonneg)
744 return 0;
746 if (isl_int_is_neg(tab->mat->row[row][1]))
747 return 0;
748 if (tab->strict_redundant && isl_int_is_zero(tab->mat->row[row][1]))
749 return 0;
750 if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
751 return 0;
753 for (i = tab->n_dead; i < tab->n_col; ++i) {
754 if (isl_int_is_zero(tab->mat->row[row][off + i]))
755 continue;
756 if (tab->col_var[i] >= 0)
757 return 0;
758 if (isl_int_is_neg(tab->mat->row[row][off + i]))
759 return 0;
760 if (!var_from_col(tab, i)->is_nonneg)
761 return 0;
763 return 1;
766 static void swap_rows(struct isl_tab *tab, int row1, int row2)
768 int t;
769 enum isl_tab_row_sign s;
771 t = tab->row_var[row1];
772 tab->row_var[row1] = tab->row_var[row2];
773 tab->row_var[row2] = t;
774 isl_tab_var_from_row(tab, row1)->index = row1;
775 isl_tab_var_from_row(tab, row2)->index = row2;
776 tab->mat = isl_mat_swap_rows(tab->mat, row1, row2);
778 if (!tab->row_sign)
779 return;
780 s = tab->row_sign[row1];
781 tab->row_sign[row1] = tab->row_sign[row2];
782 tab->row_sign[row2] = s;
785 static int push_union(struct isl_tab *tab,
786 enum isl_tab_undo_type type, union isl_tab_undo_val u) WARN_UNUSED;
787 static int push_union(struct isl_tab *tab,
788 enum isl_tab_undo_type type, union isl_tab_undo_val u)
790 struct isl_tab_undo *undo;
792 if (!tab)
793 return -1;
794 if (!tab->need_undo)
795 return 0;
797 undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
798 if (!undo)
799 return -1;
800 undo->type = type;
801 undo->u = u;
802 undo->next = tab->top;
803 tab->top = undo;
805 return 0;
808 int isl_tab_push_var(struct isl_tab *tab,
809 enum isl_tab_undo_type type, struct isl_tab_var *var)
811 union isl_tab_undo_val u;
812 if (var->is_row)
813 u.var_index = tab->row_var[var->index];
814 else
815 u.var_index = tab->col_var[var->index];
816 return push_union(tab, type, u);
819 int isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
821 union isl_tab_undo_val u = { 0 };
822 return push_union(tab, type, u);
825 /* Push a record on the undo stack describing the current basic
826 * variables, so that the this state can be restored during rollback.
828 int isl_tab_push_basis(struct isl_tab *tab)
830 int i;
831 union isl_tab_undo_val u;
833 u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
834 if (tab->n_col && !u.col_var)
835 return -1;
836 for (i = 0; i < tab->n_col; ++i)
837 u.col_var[i] = tab->col_var[i];
838 return push_union(tab, isl_tab_undo_saved_basis, u);
841 int isl_tab_push_callback(struct isl_tab *tab, struct isl_tab_callback *callback)
843 union isl_tab_undo_val u;
844 u.callback = callback;
845 return push_union(tab, isl_tab_undo_callback, u);
848 struct isl_tab *isl_tab_init_samples(struct isl_tab *tab)
850 if (!tab)
851 return NULL;
853 tab->n_sample = 0;
854 tab->n_outside = 0;
855 tab->samples = isl_mat_alloc(tab->mat->ctx, 1, 1 + tab->n_var);
856 if (!tab->samples)
857 goto error;
858 tab->sample_index = isl_alloc_array(tab->mat->ctx, int, 1);
859 if (!tab->sample_index)
860 goto error;
861 return tab;
862 error:
863 isl_tab_free(tab);
864 return NULL;
867 int isl_tab_add_sample(struct isl_tab *tab, __isl_take isl_vec *sample)
869 if (!tab || !sample)
870 goto error;
872 if (tab->n_sample + 1 > tab->samples->n_row) {
873 int *t = isl_realloc_array(tab->mat->ctx,
874 tab->sample_index, int, tab->n_sample + 1);
875 if (!t)
876 goto error;
877 tab->sample_index = t;
880 tab->samples = isl_mat_extend(tab->samples,
881 tab->n_sample + 1, tab->samples->n_col);
882 if (!tab->samples)
883 goto error;
885 isl_seq_cpy(tab->samples->row[tab->n_sample], sample->el, sample->size);
886 isl_vec_free(sample);
887 tab->sample_index[tab->n_sample] = tab->n_sample;
888 tab->n_sample++;
890 return 0;
891 error:
892 isl_vec_free(sample);
893 return -1;
896 struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s)
898 if (s != tab->n_outside) {
899 int t = tab->sample_index[tab->n_outside];
900 tab->sample_index[tab->n_outside] = tab->sample_index[s];
901 tab->sample_index[s] = t;
902 isl_mat_swap_rows(tab->samples, tab->n_outside, s);
904 tab->n_outside++;
905 if (isl_tab_push(tab, isl_tab_undo_drop_sample) < 0) {
906 isl_tab_free(tab);
907 return NULL;
910 return tab;
913 /* Record the current number of samples so that we can remove newer
914 * samples during a rollback.
916 int isl_tab_save_samples(struct isl_tab *tab)
918 union isl_tab_undo_val u;
920 if (!tab)
921 return -1;
923 u.n = tab->n_sample;
924 return push_union(tab, isl_tab_undo_saved_samples, u);
927 /* Mark row with index "row" as being redundant.
928 * If we may need to undo the operation or if the row represents
929 * a variable of the original problem, the row is kept,
930 * but no longer considered when looking for a pivot row.
931 * Otherwise, the row is simply removed.
933 * The row may be interchanged with some other row. If it
934 * is interchanged with a later row, return 1. Otherwise return 0.
935 * If the rows are checked in order in the calling function,
936 * then a return value of 1 means that the row with the given
937 * row number may now contain a different row that hasn't been checked yet.
939 int isl_tab_mark_redundant(struct isl_tab *tab, int row)
941 struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
942 var->is_redundant = 1;
943 isl_assert(tab->mat->ctx, row >= tab->n_redundant, return -1);
944 if (tab->preserve || tab->need_undo || tab->row_var[row] >= 0) {
945 if (tab->row_var[row] >= 0 && !var->is_nonneg) {
946 var->is_nonneg = 1;
947 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, var) < 0)
948 return -1;
950 if (row != tab->n_redundant)
951 swap_rows(tab, row, tab->n_redundant);
952 tab->n_redundant++;
953 return isl_tab_push_var(tab, isl_tab_undo_redundant, var);
954 } else {
955 if (row != tab->n_row - 1)
956 swap_rows(tab, row, tab->n_row - 1);
957 isl_tab_var_from_row(tab, tab->n_row - 1)->index = -1;
958 tab->n_row--;
959 return 1;
963 /* Mark "tab" as a rational tableau.
964 * If it wasn't marked as a rational tableau already and if we may
965 * need to undo changes, then arrange for the marking to be undone
966 * during the undo.
968 int isl_tab_mark_rational(struct isl_tab *tab)
970 if (!tab)
971 return -1;
972 if (!tab->rational && tab->need_undo)
973 if (isl_tab_push(tab, isl_tab_undo_rational) < 0)
974 return -1;
975 tab->rational = 1;
976 return 0;
979 int isl_tab_mark_empty(struct isl_tab *tab)
981 if (!tab)
982 return -1;
983 if (!tab->empty && tab->need_undo)
984 if (isl_tab_push(tab, isl_tab_undo_empty) < 0)
985 return -1;
986 tab->empty = 1;
987 return 0;
990 int isl_tab_freeze_constraint(struct isl_tab *tab, int con)
992 struct isl_tab_var *var;
994 if (!tab)
995 return -1;
997 var = &tab->con[con];
998 if (var->frozen)
999 return 0;
1000 if (var->index < 0)
1001 return 0;
1002 var->frozen = 1;
1004 if (tab->need_undo)
1005 return isl_tab_push_var(tab, isl_tab_undo_freeze, var);
1007 return 0;
1010 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
1011 * the original sign of the pivot element.
1012 * We only keep track of row signs during PILP solving and in this case
1013 * we only pivot a row with negative sign (meaning the value is always
1014 * non-positive) using a positive pivot element.
1016 * For each row j, the new value of the parametric constant is equal to
1018 * a_j0 - a_jc a_r0/a_rc
1020 * where a_j0 is the original parametric constant, a_rc is the pivot element,
1021 * a_r0 is the parametric constant of the pivot row and a_jc is the
1022 * pivot column entry of the row j.
1023 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
1024 * remains the same if a_jc has the same sign as the row j or if
1025 * a_jc is zero. In all other cases, we reset the sign to "unknown".
1027 static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
1029 int i;
1030 struct isl_mat *mat = tab->mat;
1031 unsigned off = 2 + tab->M;
1033 if (!tab->row_sign)
1034 return;
1036 if (tab->row_sign[row] == 0)
1037 return;
1038 isl_assert(mat->ctx, row_sgn > 0, return);
1039 isl_assert(mat->ctx, tab->row_sign[row] == isl_tab_row_neg, return);
1040 tab->row_sign[row] = isl_tab_row_pos;
1041 for (i = 0; i < tab->n_row; ++i) {
1042 int s;
1043 if (i == row)
1044 continue;
1045 s = isl_int_sgn(mat->row[i][off + col]);
1046 if (!s)
1047 continue;
1048 if (!tab->row_sign[i])
1049 continue;
1050 if (s < 0 && tab->row_sign[i] == isl_tab_row_neg)
1051 continue;
1052 if (s > 0 && tab->row_sign[i] == isl_tab_row_pos)
1053 continue;
1054 tab->row_sign[i] = isl_tab_row_unknown;
1058 /* Given a row number "row" and a column number "col", pivot the tableau
1059 * such that the associated variables are interchanged.
1060 * The given row in the tableau expresses
1062 * x_r = a_r0 + \sum_i a_ri x_i
1064 * or
1066 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
1068 * Substituting this equality into the other rows
1070 * x_j = a_j0 + \sum_i a_ji x_i
1072 * with a_jc \ne 0, we obtain
1074 * 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
1076 * The tableau
1078 * n_rc/d_r n_ri/d_r
1079 * n_jc/d_j n_ji/d_j
1081 * where i is any other column and j is any other row,
1082 * is therefore transformed into
1084 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1085 * 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)
1087 * The transformation is performed along the following steps
1089 * d_r/n_rc n_ri/n_rc
1090 * n_jc/d_j n_ji/d_j
1092 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1093 * n_jc/d_j n_ji/d_j
1095 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1096 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
1098 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1099 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
1101 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1102 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
1104 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1105 * 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)
1108 int isl_tab_pivot(struct isl_tab *tab, int row, int col)
1110 int i, j;
1111 int sgn;
1112 int t;
1113 isl_ctx *ctx;
1114 struct isl_mat *mat = tab->mat;
1115 struct isl_tab_var *var;
1116 unsigned off = 2 + tab->M;
1118 ctx = isl_tab_get_ctx(tab);
1119 if (isl_ctx_next_operation(ctx) < 0)
1120 return -1;
1122 isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
1123 sgn = isl_int_sgn(mat->row[row][0]);
1124 if (sgn < 0) {
1125 isl_int_neg(mat->row[row][0], mat->row[row][0]);
1126 isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]);
1127 } else
1128 for (j = 0; j < off - 1 + tab->n_col; ++j) {
1129 if (j == off - 1 + col)
1130 continue;
1131 isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
1133 if (!isl_int_is_one(mat->row[row][0]))
1134 isl_seq_normalize(mat->ctx, mat->row[row], off + tab->n_col);
1135 for (i = 0; i < tab->n_row; ++i) {
1136 if (i == row)
1137 continue;
1138 if (isl_int_is_zero(mat->row[i][off + col]))
1139 continue;
1140 isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
1141 for (j = 0; j < off - 1 + tab->n_col; ++j) {
1142 if (j == off - 1 + col)
1143 continue;
1144 isl_int_mul(mat->row[i][1 + j],
1145 mat->row[i][1 + j], mat->row[row][0]);
1146 isl_int_addmul(mat->row[i][1 + j],
1147 mat->row[i][off + col], mat->row[row][1 + j]);
1149 isl_int_mul(mat->row[i][off + col],
1150 mat->row[i][off + col], mat->row[row][off + col]);
1151 if (!isl_int_is_one(mat->row[i][0]))
1152 isl_seq_normalize(mat->ctx, mat->row[i], off + tab->n_col);
1154 t = tab->row_var[row];
1155 tab->row_var[row] = tab->col_var[col];
1156 tab->col_var[col] = t;
1157 var = isl_tab_var_from_row(tab, row);
1158 var->is_row = 1;
1159 var->index = row;
1160 var = var_from_col(tab, col);
1161 var->is_row = 0;
1162 var->index = col;
1163 update_row_sign(tab, row, col, sgn);
1164 if (tab->in_undo)
1165 return 0;
1166 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1167 if (isl_int_is_zero(mat->row[i][off + col]))
1168 continue;
1169 if (!isl_tab_var_from_row(tab, i)->frozen &&
1170 isl_tab_row_is_redundant(tab, i)) {
1171 int redo = isl_tab_mark_redundant(tab, i);
1172 if (redo < 0)
1173 return -1;
1174 if (redo)
1175 --i;
1178 return 0;
1181 /* If "var" represents a column variable, then pivot is up (sgn > 0)
1182 * or down (sgn < 0) to a row. The variable is assumed not to be
1183 * unbounded in the specified direction.
1184 * If sgn = 0, then the variable is unbounded in both directions,
1185 * and we pivot with any row we can find.
1187 static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign) WARN_UNUSED;
1188 static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
1190 int r;
1191 unsigned off = 2 + tab->M;
1193 if (var->is_row)
1194 return 0;
1196 if (sign == 0) {
1197 for (r = tab->n_redundant; r < tab->n_row; ++r)
1198 if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
1199 break;
1200 isl_assert(tab->mat->ctx, r < tab->n_row, return -1);
1201 } else {
1202 r = pivot_row(tab, NULL, sign, var->index);
1203 isl_assert(tab->mat->ctx, r >= 0, return -1);
1206 return isl_tab_pivot(tab, r, var->index);
1209 /* Check whether all variables that are marked as non-negative
1210 * also have a non-negative sample value. This function is not
1211 * called from the current code but is useful during debugging.
1213 static void check_table(struct isl_tab *tab) __attribute__ ((unused));
1214 static void check_table(struct isl_tab *tab)
1216 int i;
1218 if (tab->empty)
1219 return;
1220 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1221 struct isl_tab_var *var;
1222 var = isl_tab_var_from_row(tab, i);
1223 if (!var->is_nonneg)
1224 continue;
1225 if (tab->M) {
1226 isl_assert(tab->mat->ctx,
1227 !isl_int_is_neg(tab->mat->row[i][2]), abort());
1228 if (isl_int_is_pos(tab->mat->row[i][2]))
1229 continue;
1231 isl_assert(tab->mat->ctx, !isl_int_is_neg(tab->mat->row[i][1]),
1232 abort());
1236 /* Return the sign of the maximal value of "var".
1237 * If the sign is not negative, then on return from this function,
1238 * the sample value will also be non-negative.
1240 * If "var" is manifestly unbounded wrt positive values, we are done.
1241 * Otherwise, we pivot the variable up to a row if needed
1242 * Then we continue pivoting down until either
1243 * - no more down pivots can be performed
1244 * - the sample value is positive
1245 * - the variable is pivoted into a manifestly unbounded column
1247 static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
1249 int row, col;
1251 if (max_is_manifestly_unbounded(tab, var))
1252 return 1;
1253 if (to_row(tab, var, 1) < 0)
1254 return -2;
1255 while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
1256 find_pivot(tab, var, var, 1, &row, &col);
1257 if (row == -1)
1258 return isl_int_sgn(tab->mat->row[var->index][1]);
1259 if (isl_tab_pivot(tab, row, col) < 0)
1260 return -2;
1261 if (!var->is_row) /* manifestly unbounded */
1262 return 1;
1264 return 1;
1267 int isl_tab_sign_of_max(struct isl_tab *tab, int con)
1269 struct isl_tab_var *var;
1271 if (!tab)
1272 return -2;
1274 var = &tab->con[con];
1275 isl_assert(tab->mat->ctx, !var->is_redundant, return -2);
1276 isl_assert(tab->mat->ctx, !var->is_zero, return -2);
1278 return sign_of_max(tab, var);
1281 static int row_is_neg(struct isl_tab *tab, int row)
1283 if (!tab->M)
1284 return isl_int_is_neg(tab->mat->row[row][1]);
1285 if (isl_int_is_pos(tab->mat->row[row][2]))
1286 return 0;
1287 if (isl_int_is_neg(tab->mat->row[row][2]))
1288 return 1;
1289 return isl_int_is_neg(tab->mat->row[row][1]);
1292 static int row_sgn(struct isl_tab *tab, int row)
1294 if (!tab->M)
1295 return isl_int_sgn(tab->mat->row[row][1]);
1296 if (!isl_int_is_zero(tab->mat->row[row][2]))
1297 return isl_int_sgn(tab->mat->row[row][2]);
1298 else
1299 return isl_int_sgn(tab->mat->row[row][1]);
1302 /* Perform pivots until the row variable "var" has a non-negative
1303 * sample value or until no more upward pivots can be performed.
1304 * Return the sign of the sample value after the pivots have been
1305 * performed.
1307 static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
1309 int row, col;
1311 while (row_is_neg(tab, var->index)) {
1312 find_pivot(tab, var, var, 1, &row, &col);
1313 if (row == -1)
1314 break;
1315 if (isl_tab_pivot(tab, row, col) < 0)
1316 return -2;
1317 if (!var->is_row) /* manifestly unbounded */
1318 return 1;
1320 return row_sgn(tab, var->index);
1323 /* Perform pivots until we are sure that the row variable "var"
1324 * can attain non-negative values. After return from this
1325 * function, "var" is still a row variable, but its sample
1326 * value may not be non-negative, even if the function returns 1.
1328 static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
1330 int row, col;
1332 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
1333 find_pivot(tab, var, var, 1, &row, &col);
1334 if (row == -1)
1335 break;
1336 if (row == var->index) /* manifestly unbounded */
1337 return 1;
1338 if (isl_tab_pivot(tab, row, col) < 0)
1339 return -1;
1341 return !isl_int_is_neg(tab->mat->row[var->index][1]);
1344 /* Return a negative value if "var" can attain negative values.
1345 * Return a non-negative value otherwise.
1347 * If "var" is manifestly unbounded wrt negative values, we are done.
1348 * Otherwise, if var is in a column, we can pivot it down to a row.
1349 * Then we continue pivoting down until either
1350 * - the pivot would result in a manifestly unbounded column
1351 * => we don't perform the pivot, but simply return -1
1352 * - no more down pivots can be performed
1353 * - the sample value is negative
1354 * If the sample value becomes negative and the variable is supposed
1355 * to be nonnegative, then we undo the last pivot.
1356 * However, if the last pivot has made the pivoting variable
1357 * obviously redundant, then it may have moved to another row.
1358 * In that case we look for upward pivots until we reach a non-negative
1359 * value again.
1361 static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
1363 int row, col;
1364 struct isl_tab_var *pivot_var = NULL;
1366 if (min_is_manifestly_unbounded(tab, var))
1367 return -1;
1368 if (!var->is_row) {
1369 col = var->index;
1370 row = pivot_row(tab, NULL, -1, col);
1371 pivot_var = var_from_col(tab, col);
1372 if (isl_tab_pivot(tab, row, col) < 0)
1373 return -2;
1374 if (var->is_redundant)
1375 return 0;
1376 if (isl_int_is_neg(tab->mat->row[var->index][1])) {
1377 if (var->is_nonneg) {
1378 if (!pivot_var->is_redundant &&
1379 pivot_var->index == row) {
1380 if (isl_tab_pivot(tab, row, col) < 0)
1381 return -2;
1382 } else
1383 if (restore_row(tab, var) < -1)
1384 return -2;
1386 return -1;
1389 if (var->is_redundant)
1390 return 0;
1391 while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
1392 find_pivot(tab, var, var, -1, &row, &col);
1393 if (row == var->index)
1394 return -1;
1395 if (row == -1)
1396 return isl_int_sgn(tab->mat->row[var->index][1]);
1397 pivot_var = var_from_col(tab, col);
1398 if (isl_tab_pivot(tab, row, col) < 0)
1399 return -2;
1400 if (var->is_redundant)
1401 return 0;
1403 if (pivot_var && var->is_nonneg) {
1404 /* pivot back to non-negative value */
1405 if (!pivot_var->is_redundant && pivot_var->index == row) {
1406 if (isl_tab_pivot(tab, row, col) < 0)
1407 return -2;
1408 } else
1409 if (restore_row(tab, var) < -1)
1410 return -2;
1412 return -1;
1415 static int row_at_most_neg_one(struct isl_tab *tab, int row)
1417 if (tab->M) {
1418 if (isl_int_is_pos(tab->mat->row[row][2]))
1419 return 0;
1420 if (isl_int_is_neg(tab->mat->row[row][2]))
1421 return 1;
1423 return isl_int_is_neg(tab->mat->row[row][1]) &&
1424 isl_int_abs_ge(tab->mat->row[row][1],
1425 tab->mat->row[row][0]);
1428 /* Return 1 if "var" can attain values <= -1.
1429 * Return 0 otherwise.
1431 * If the variable "var" is supposed to be non-negative (is_nonneg is set),
1432 * then the sample value of "var" is assumed to be non-negative when the
1433 * the function is called. If 1 is returned then the constraint
1434 * is not redundant and the sample value is made non-negative again before
1435 * the function returns.
1437 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
1439 int row, col;
1440 struct isl_tab_var *pivot_var;
1442 if (min_is_manifestly_unbounded(tab, var))
1443 return 1;
1444 if (!var->is_row) {
1445 col = var->index;
1446 row = pivot_row(tab, NULL, -1, col);
1447 pivot_var = var_from_col(tab, col);
1448 if (isl_tab_pivot(tab, row, col) < 0)
1449 return -1;
1450 if (var->is_redundant)
1451 return 0;
1452 if (row_at_most_neg_one(tab, var->index)) {
1453 if (var->is_nonneg) {
1454 if (!pivot_var->is_redundant &&
1455 pivot_var->index == row) {
1456 if (isl_tab_pivot(tab, row, col) < 0)
1457 return -1;
1458 } else
1459 if (restore_row(tab, var) < -1)
1460 return -1;
1462 return 1;
1465 if (var->is_redundant)
1466 return 0;
1467 do {
1468 find_pivot(tab, var, var, -1, &row, &col);
1469 if (row == var->index) {
1470 if (var->is_nonneg && restore_row(tab, var) < -1)
1471 return -1;
1472 return 1;
1474 if (row == -1)
1475 return 0;
1476 pivot_var = var_from_col(tab, col);
1477 if (isl_tab_pivot(tab, row, col) < 0)
1478 return -1;
1479 if (var->is_redundant)
1480 return 0;
1481 } while (!row_at_most_neg_one(tab, var->index));
1482 if (var->is_nonneg) {
1483 /* pivot back to non-negative value */
1484 if (!pivot_var->is_redundant && pivot_var->index == row)
1485 if (isl_tab_pivot(tab, row, col) < 0)
1486 return -1;
1487 if (restore_row(tab, var) < -1)
1488 return -1;
1490 return 1;
1493 /* Return 1 if "var" can attain values >= 1.
1494 * Return 0 otherwise.
1496 static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
1498 int row, col;
1499 isl_int *r;
1501 if (max_is_manifestly_unbounded(tab, var))
1502 return 1;
1503 if (to_row(tab, var, 1) < 0)
1504 return -1;
1505 r = tab->mat->row[var->index];
1506 while (isl_int_lt(r[1], r[0])) {
1507 find_pivot(tab, var, var, 1, &row, &col);
1508 if (row == -1)
1509 return isl_int_ge(r[1], r[0]);
1510 if (row == var->index) /* manifestly unbounded */
1511 return 1;
1512 if (isl_tab_pivot(tab, row, col) < 0)
1513 return -1;
1515 return 1;
1518 static void swap_cols(struct isl_tab *tab, int col1, int col2)
1520 int t;
1521 unsigned off = 2 + tab->M;
1522 t = tab->col_var[col1];
1523 tab->col_var[col1] = tab->col_var[col2];
1524 tab->col_var[col2] = t;
1525 var_from_col(tab, col1)->index = col1;
1526 var_from_col(tab, col2)->index = col2;
1527 tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2);
1530 /* Mark column with index "col" as representing a zero variable.
1531 * If we may need to undo the operation the column is kept,
1532 * but no longer considered.
1533 * Otherwise, the column is simply removed.
1535 * The column may be interchanged with some other column. If it
1536 * is interchanged with a later column, return 1. Otherwise return 0.
1537 * If the columns are checked in order in the calling function,
1538 * then a return value of 1 means that the column with the given
1539 * column number may now contain a different column that
1540 * hasn't been checked yet.
1542 int isl_tab_kill_col(struct isl_tab *tab, int col)
1544 var_from_col(tab, col)->is_zero = 1;
1545 if (tab->need_undo) {
1546 if (isl_tab_push_var(tab, isl_tab_undo_zero,
1547 var_from_col(tab, col)) < 0)
1548 return -1;
1549 if (col != tab->n_dead)
1550 swap_cols(tab, col, tab->n_dead);
1551 tab->n_dead++;
1552 return 0;
1553 } else {
1554 if (col != tab->n_col - 1)
1555 swap_cols(tab, col, tab->n_col - 1);
1556 var_from_col(tab, tab->n_col - 1)->index = -1;
1557 tab->n_col--;
1558 return 1;
1562 static int row_is_manifestly_non_integral(struct isl_tab *tab, int row)
1564 unsigned off = 2 + tab->M;
1566 if (tab->M && !isl_int_eq(tab->mat->row[row][2],
1567 tab->mat->row[row][0]))
1568 return 0;
1569 if (isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1570 tab->n_col - tab->n_dead) != -1)
1571 return 0;
1573 return !isl_int_is_divisible_by(tab->mat->row[row][1],
1574 tab->mat->row[row][0]);
1577 /* For integer tableaus, check if any of the coordinates are stuck
1578 * at a non-integral value.
1580 static int tab_is_manifestly_empty(struct isl_tab *tab)
1582 int i;
1584 if (tab->empty)
1585 return 1;
1586 if (tab->rational)
1587 return 0;
1589 for (i = 0; i < tab->n_var; ++i) {
1590 if (!tab->var[i].is_row)
1591 continue;
1592 if (row_is_manifestly_non_integral(tab, tab->var[i].index))
1593 return 1;
1596 return 0;
1599 /* Row variable "var" is non-negative and cannot attain any values
1600 * larger than zero. This means that the coefficients of the unrestricted
1601 * column variables are zero and that the coefficients of the non-negative
1602 * column variables are zero or negative.
1603 * Each of the non-negative variables with a negative coefficient can
1604 * then also be written as the negative sum of non-negative variables
1605 * and must therefore also be zero.
1607 * If "temp_var" is set, then "var" is a temporary variable that
1608 * will be removed after this function returns and for which
1609 * no information is recorded on the undo stack.
1610 * Do not add any undo records involving this variable in this case
1611 * since the variable will have been removed before any future undo
1612 * operations. Also avoid marking the variable as redundant,
1613 * since that either adds an undo record or needlessly removes the row
1614 * (the caller will take care of removing the row).
1616 static isl_stat close_row(struct isl_tab *tab, struct isl_tab_var *var,
1617 int temp_var) WARN_UNUSED;
1618 static isl_stat close_row(struct isl_tab *tab, struct isl_tab_var *var,
1619 int temp_var)
1621 int j;
1622 struct isl_mat *mat = tab->mat;
1623 unsigned off = 2 + tab->M;
1625 if (!var->is_nonneg)
1626 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
1627 "expecting non-negative variable",
1628 return isl_stat_error);
1629 var->is_zero = 1;
1630 if (!temp_var && tab->need_undo)
1631 if (isl_tab_push_var(tab, isl_tab_undo_zero, var) < 0)
1632 return isl_stat_error;
1633 for (j = tab->n_dead; j < tab->n_col; ++j) {
1634 int recheck;
1635 if (isl_int_is_zero(mat->row[var->index][off + j]))
1636 continue;
1637 if (isl_int_is_pos(mat->row[var->index][off + j]))
1638 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
1639 "row cannot have positive coefficients",
1640 return isl_stat_error);
1641 recheck = isl_tab_kill_col(tab, j);
1642 if (recheck < 0)
1643 return isl_stat_error;
1644 if (recheck)
1645 --j;
1647 if (!temp_var && isl_tab_mark_redundant(tab, var->index) < 0)
1648 return isl_stat_error;
1649 if (tab_is_manifestly_empty(tab) && isl_tab_mark_empty(tab) < 0)
1650 return isl_stat_error;
1651 return isl_stat_ok;
1654 /* Add a constraint to the tableau and allocate a row for it.
1655 * Return the index into the constraint array "con".
1657 * This function assumes that at least one more row and at least
1658 * one more element in the constraint array are available in the tableau.
1660 int isl_tab_allocate_con(struct isl_tab *tab)
1662 int r;
1664 isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
1665 isl_assert(tab->mat->ctx, tab->n_con < tab->max_con, return -1);
1667 r = tab->n_con;
1668 tab->con[r].index = tab->n_row;
1669 tab->con[r].is_row = 1;
1670 tab->con[r].is_nonneg = 0;
1671 tab->con[r].is_zero = 0;
1672 tab->con[r].is_redundant = 0;
1673 tab->con[r].frozen = 0;
1674 tab->con[r].negated = 0;
1675 tab->row_var[tab->n_row] = ~r;
1677 tab->n_row++;
1678 tab->n_con++;
1679 if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
1680 return -1;
1682 return r;
1685 /* Move the entries in tab->var up one position, starting at "first",
1686 * creating room for an extra entry at position "first".
1687 * Since some of the entries of tab->row_var and tab->col_var contain
1688 * indices into this array, they have to be updated accordingly.
1690 static int var_insert_entry(struct isl_tab *tab, int first)
1692 int i;
1694 if (tab->n_var >= tab->max_var)
1695 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
1696 "not enough room for new variable", return -1);
1697 if (first > tab->n_var)
1698 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
1699 "invalid initial position", return -1);
1701 for (i = tab->n_var - 1; i >= first; --i) {
1702 tab->var[i + 1] = tab->var[i];
1703 if (tab->var[i + 1].is_row)
1704 tab->row_var[tab->var[i + 1].index]++;
1705 else
1706 tab->col_var[tab->var[i + 1].index]++;
1709 tab->n_var++;
1711 return 0;
1714 /* Drop the entry at position "first" in tab->var, moving all
1715 * subsequent entries down.
1716 * Since some of the entries of tab->row_var and tab->col_var contain
1717 * indices into this array, they have to be updated accordingly.
1719 static int var_drop_entry(struct isl_tab *tab, int first)
1721 int i;
1723 if (first >= tab->n_var)
1724 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
1725 "invalid initial position", return -1);
1727 tab->n_var--;
1729 for (i = first; i < tab->n_var; ++i) {
1730 tab->var[i] = tab->var[i + 1];
1731 if (tab->var[i + 1].is_row)
1732 tab->row_var[tab->var[i].index]--;
1733 else
1734 tab->col_var[tab->var[i].index]--;
1737 return 0;
1740 /* Add a variable to the tableau at position "r" and allocate a column for it.
1741 * Return the index into the variable array "var", i.e., "r",
1742 * or -1 on error.
1744 int isl_tab_insert_var(struct isl_tab *tab, int r)
1746 int i;
1747 unsigned off = 2 + tab->M;
1749 isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
1751 if (var_insert_entry(tab, r) < 0)
1752 return -1;
1754 tab->var[r].index = tab->n_col;
1755 tab->var[r].is_row = 0;
1756 tab->var[r].is_nonneg = 0;
1757 tab->var[r].is_zero = 0;
1758 tab->var[r].is_redundant = 0;
1759 tab->var[r].frozen = 0;
1760 tab->var[r].negated = 0;
1761 tab->col_var[tab->n_col] = r;
1763 for (i = 0; i < tab->n_row; ++i)
1764 isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
1766 tab->n_col++;
1767 if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]) < 0)
1768 return -1;
1770 return r;
1773 /* Add a variable to the tableau and allocate a column for it.
1774 * Return the index into the variable array "var".
1776 int isl_tab_allocate_var(struct isl_tab *tab)
1778 if (!tab)
1779 return -1;
1781 return isl_tab_insert_var(tab, tab->n_var);
1784 /* Add a row to the tableau. The row is given as an affine combination
1785 * of the original variables and needs to be expressed in terms of the
1786 * column variables.
1788 * This function assumes that at least one more row and at least
1789 * one more element in the constraint array are available in the tableau.
1791 * We add each term in turn.
1792 * If r = n/d_r is the current sum and we need to add k x, then
1793 * if x is a column variable, we increase the numerator of
1794 * this column by k d_r
1795 * if x = f/d_x is a row variable, then the new representation of r is
1797 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1798 * --- + --- = ------------------- = -------------------
1799 * d_r d_r d_r d_x/g m
1801 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1803 * If tab->M is set, then, internally, each variable x is represented
1804 * as x' - M. We then also need no subtract k d_r from the coefficient of M.
1806 int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
1808 int i;
1809 int r;
1810 isl_int *row;
1811 isl_int a, b;
1812 unsigned off = 2 + tab->M;
1814 r = isl_tab_allocate_con(tab);
1815 if (r < 0)
1816 return -1;
1818 isl_int_init(a);
1819 isl_int_init(b);
1820 row = tab->mat->row[tab->con[r].index];
1821 isl_int_set_si(row[0], 1);
1822 isl_int_set(row[1], line[0]);
1823 isl_seq_clr(row + 2, tab->M + tab->n_col);
1824 for (i = 0; i < tab->n_var; ++i) {
1825 if (tab->var[i].is_zero)
1826 continue;
1827 if (tab->var[i].is_row) {
1828 isl_int_lcm(a,
1829 row[0], tab->mat->row[tab->var[i].index][0]);
1830 isl_int_swap(a, row[0]);
1831 isl_int_divexact(a, row[0], a);
1832 isl_int_divexact(b,
1833 row[0], tab->mat->row[tab->var[i].index][0]);
1834 isl_int_mul(b, b, line[1 + i]);
1835 isl_seq_combine(row + 1, a, row + 1,
1836 b, tab->mat->row[tab->var[i].index] + 1,
1837 1 + tab->M + tab->n_col);
1838 } else
1839 isl_int_addmul(row[off + tab->var[i].index],
1840 line[1 + i], row[0]);
1841 if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
1842 isl_int_submul(row[2], line[1 + i], row[0]);
1844 isl_seq_normalize(tab->mat->ctx, row, off + tab->n_col);
1845 isl_int_clear(a);
1846 isl_int_clear(b);
1848 if (tab->row_sign)
1849 tab->row_sign[tab->con[r].index] = isl_tab_row_unknown;
1851 return r;
1854 static int drop_row(struct isl_tab *tab, int row)
1856 isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
1857 if (row != tab->n_row - 1)
1858 swap_rows(tab, row, tab->n_row - 1);
1859 tab->n_row--;
1860 tab->n_con--;
1861 return 0;
1864 /* Drop the variable in column "col" along with the column.
1865 * The column is removed first because it may need to be moved
1866 * into the last position and this process requires
1867 * the contents of the col_var array in a state
1868 * before the removal of the variable.
1870 static int drop_col(struct isl_tab *tab, int col)
1872 int var;
1874 var = tab->col_var[col];
1875 if (col != tab->n_col - 1)
1876 swap_cols(tab, col, tab->n_col - 1);
1877 tab->n_col--;
1878 if (var_drop_entry(tab, var) < 0)
1879 return -1;
1880 return 0;
1883 /* Add inequality "ineq" and check if it conflicts with the
1884 * previously added constraints or if it is obviously redundant.
1886 * This function assumes that at least one more row and at least
1887 * one more element in the constraint array are available in the tableau.
1889 int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
1891 int r;
1892 int sgn;
1893 isl_int cst;
1895 if (!tab)
1896 return -1;
1897 if (tab->bmap) {
1898 struct isl_basic_map *bmap = tab->bmap;
1900 isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, return -1);
1901 isl_assert(tab->mat->ctx,
1902 tab->n_con == bmap->n_eq + bmap->n_ineq, return -1);
1903 tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
1904 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1905 return -1;
1906 if (!tab->bmap)
1907 return -1;
1909 if (tab->cone) {
1910 isl_int_init(cst);
1911 isl_int_set_si(cst, 0);
1912 isl_int_swap(ineq[0], cst);
1914 r = isl_tab_add_row(tab, ineq);
1915 if (tab->cone) {
1916 isl_int_swap(ineq[0], cst);
1917 isl_int_clear(cst);
1919 if (r < 0)
1920 return -1;
1921 tab->con[r].is_nonneg = 1;
1922 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1923 return -1;
1924 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1925 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1926 return -1;
1927 return 0;
1930 sgn = restore_row(tab, &tab->con[r]);
1931 if (sgn < -1)
1932 return -1;
1933 if (sgn < 0)
1934 return isl_tab_mark_empty(tab);
1935 if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
1936 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1937 return -1;
1938 return 0;
1941 /* Pivot a non-negative variable down until it reaches the value zero
1942 * and then pivot the variable into a column position.
1944 static int to_col(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
1945 static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
1947 int i;
1948 int row, col;
1949 unsigned off = 2 + tab->M;
1951 if (!var->is_row)
1952 return 0;
1954 while (isl_int_is_pos(tab->mat->row[var->index][1])) {
1955 find_pivot(tab, var, NULL, -1, &row, &col);
1956 isl_assert(tab->mat->ctx, row != -1, return -1);
1957 if (isl_tab_pivot(tab, row, col) < 0)
1958 return -1;
1959 if (!var->is_row)
1960 return 0;
1963 for (i = tab->n_dead; i < tab->n_col; ++i)
1964 if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
1965 break;
1967 isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
1968 if (isl_tab_pivot(tab, var->index, i) < 0)
1969 return -1;
1971 return 0;
1974 /* We assume Gaussian elimination has been performed on the equalities.
1975 * The equalities can therefore never conflict.
1976 * Adding the equalities is currently only really useful for a later call
1977 * to isl_tab_ineq_type.
1979 * This function assumes that at least one more row and at least
1980 * one more element in the constraint array are available in the tableau.
1982 static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
1984 int i;
1985 int r;
1987 if (!tab)
1988 return NULL;
1989 r = isl_tab_add_row(tab, eq);
1990 if (r < 0)
1991 goto error;
1993 r = tab->con[r].index;
1994 i = isl_seq_first_non_zero(tab->mat->row[r] + 2 + tab->M + tab->n_dead,
1995 tab->n_col - tab->n_dead);
1996 isl_assert(tab->mat->ctx, i >= 0, goto error);
1997 i += tab->n_dead;
1998 if (isl_tab_pivot(tab, r, i) < 0)
1999 goto error;
2000 if (isl_tab_kill_col(tab, i) < 0)
2001 goto error;
2002 tab->n_eq++;
2004 return tab;
2005 error:
2006 isl_tab_free(tab);
2007 return NULL;
2010 static int row_is_manifestly_zero(struct isl_tab *tab, int row)
2012 unsigned off = 2 + tab->M;
2014 if (!isl_int_is_zero(tab->mat->row[row][1]))
2015 return 0;
2016 if (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))
2017 return 0;
2018 return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
2019 tab->n_col - tab->n_dead) == -1;
2022 /* Add an equality that is known to be valid for the given tableau.
2024 * This function assumes that at least one more row and at least
2025 * one more element in the constraint array are available in the tableau.
2027 int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
2029 struct isl_tab_var *var;
2030 int r;
2032 if (!tab)
2033 return -1;
2034 r = isl_tab_add_row(tab, eq);
2035 if (r < 0)
2036 return -1;
2038 var = &tab->con[r];
2039 r = var->index;
2040 if (row_is_manifestly_zero(tab, r)) {
2041 var->is_zero = 1;
2042 if (isl_tab_mark_redundant(tab, r) < 0)
2043 return -1;
2044 return 0;
2047 if (isl_int_is_neg(tab->mat->row[r][1])) {
2048 isl_seq_neg(tab->mat->row[r] + 1, tab->mat->row[r] + 1,
2049 1 + tab->n_col);
2050 var->negated = 1;
2052 var->is_nonneg = 1;
2053 if (to_col(tab, var) < 0)
2054 return -1;
2055 var->is_nonneg = 0;
2056 if (isl_tab_kill_col(tab, var->index) < 0)
2057 return -1;
2059 return 0;
2062 /* Add a zero row to "tab" and return the corresponding index
2063 * in the constraint array.
2065 * This function assumes that at least one more row and at least
2066 * one more element in the constraint array are available in the tableau.
2068 static int add_zero_row(struct isl_tab *tab)
2070 int r;
2071 isl_int *row;
2073 r = isl_tab_allocate_con(tab);
2074 if (r < 0)
2075 return -1;
2077 row = tab->mat->row[tab->con[r].index];
2078 isl_seq_clr(row + 1, 1 + tab->M + tab->n_col);
2079 isl_int_set_si(row[0], 1);
2081 return r;
2084 /* Add equality "eq" and check if it conflicts with the
2085 * previously added constraints or if it is obviously redundant.
2087 * This function assumes that at least one more row and at least
2088 * one more element in the constraint array are available in the tableau.
2089 * If tab->bmap is set, then two rows are needed instead of one.
2091 int isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
2093 struct isl_tab_undo *snap = NULL;
2094 struct isl_tab_var *var;
2095 int r;
2096 int row;
2097 int sgn;
2098 isl_int cst;
2100 if (!tab)
2101 return -1;
2102 isl_assert(tab->mat->ctx, !tab->M, return -1);
2104 if (tab->need_undo)
2105 snap = isl_tab_snap(tab);
2107 if (tab->cone) {
2108 isl_int_init(cst);
2109 isl_int_set_si(cst, 0);
2110 isl_int_swap(eq[0], cst);
2112 r = isl_tab_add_row(tab, eq);
2113 if (tab->cone) {
2114 isl_int_swap(eq[0], cst);
2115 isl_int_clear(cst);
2117 if (r < 0)
2118 return -1;
2120 var = &tab->con[r];
2121 row = var->index;
2122 if (row_is_manifestly_zero(tab, row)) {
2123 if (snap)
2124 return isl_tab_rollback(tab, snap);
2125 return drop_row(tab, row);
2128 if (tab->bmap) {
2129 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
2130 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
2131 return -1;
2132 isl_seq_neg(eq, eq, 1 + tab->n_var);
2133 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
2134 isl_seq_neg(eq, eq, 1 + tab->n_var);
2135 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
2136 return -1;
2137 if (!tab->bmap)
2138 return -1;
2139 if (add_zero_row(tab) < 0)
2140 return -1;
2143 sgn = isl_int_sgn(tab->mat->row[row][1]);
2145 if (sgn > 0) {
2146 isl_seq_neg(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
2147 1 + tab->n_col);
2148 var->negated = 1;
2149 sgn = -1;
2152 if (sgn < 0) {
2153 sgn = sign_of_max(tab, var);
2154 if (sgn < -1)
2155 return -1;
2156 if (sgn < 0) {
2157 if (isl_tab_mark_empty(tab) < 0)
2158 return -1;
2159 return 0;
2163 var->is_nonneg = 1;
2164 if (to_col(tab, var) < 0)
2165 return -1;
2166 var->is_nonneg = 0;
2167 if (isl_tab_kill_col(tab, var->index) < 0)
2168 return -1;
2170 return 0;
2173 /* Construct and return an inequality that expresses an upper bound
2174 * on the given div.
2175 * In particular, if the div is given by
2177 * d = floor(e/m)
2179 * then the inequality expresses
2181 * m d <= e
2183 static struct isl_vec *ineq_for_div(struct isl_basic_map *bmap, unsigned div)
2185 unsigned total;
2186 unsigned div_pos;
2187 struct isl_vec *ineq;
2189 if (!bmap)
2190 return NULL;
2192 total = isl_basic_map_total_dim(bmap);
2193 div_pos = 1 + total - bmap->n_div + div;
2195 ineq = isl_vec_alloc(bmap->ctx, 1 + total);
2196 if (!ineq)
2197 return NULL;
2199 isl_seq_cpy(ineq->el, bmap->div[div] + 1, 1 + total);
2200 isl_int_neg(ineq->el[div_pos], bmap->div[div][0]);
2201 return ineq;
2204 /* For a div d = floor(f/m), add the constraints
2206 * f - m d >= 0
2207 * -(f-(m-1)) + m d >= 0
2209 * Note that the second constraint is the negation of
2211 * f - m d >= m
2213 * If add_ineq is not NULL, then this function is used
2214 * instead of isl_tab_add_ineq to effectively add the inequalities.
2216 * This function assumes that at least two more rows and at least
2217 * two more elements in the constraint array are available in the tableau.
2219 static int add_div_constraints(struct isl_tab *tab, unsigned div,
2220 int (*add_ineq)(void *user, isl_int *), void *user)
2222 unsigned total;
2223 unsigned div_pos;
2224 struct isl_vec *ineq;
2226 total = isl_basic_map_total_dim(tab->bmap);
2227 div_pos = 1 + total - tab->bmap->n_div + div;
2229 ineq = ineq_for_div(tab->bmap, div);
2230 if (!ineq)
2231 goto error;
2233 if (add_ineq) {
2234 if (add_ineq(user, ineq->el) < 0)
2235 goto error;
2236 } else {
2237 if (isl_tab_add_ineq(tab, ineq->el) < 0)
2238 goto error;
2241 isl_seq_neg(ineq->el, tab->bmap->div[div] + 1, 1 + total);
2242 isl_int_set(ineq->el[div_pos], tab->bmap->div[div][0]);
2243 isl_int_add(ineq->el[0], ineq->el[0], ineq->el[div_pos]);
2244 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
2246 if (add_ineq) {
2247 if (add_ineq(user, ineq->el) < 0)
2248 goto error;
2249 } else {
2250 if (isl_tab_add_ineq(tab, ineq->el) < 0)
2251 goto error;
2254 isl_vec_free(ineq);
2256 return 0;
2257 error:
2258 isl_vec_free(ineq);
2259 return -1;
2262 /* Check whether the div described by "div" is obviously non-negative.
2263 * If we are using a big parameter, then we will encode the div
2264 * as div' = M + div, which is always non-negative.
2265 * Otherwise, we check whether div is a non-negative affine combination
2266 * of non-negative variables.
2268 static int div_is_nonneg(struct isl_tab *tab, __isl_keep isl_vec *div)
2270 int i;
2272 if (tab->M)
2273 return 1;
2275 if (isl_int_is_neg(div->el[1]))
2276 return 0;
2278 for (i = 0; i < tab->n_var; ++i) {
2279 if (isl_int_is_neg(div->el[2 + i]))
2280 return 0;
2281 if (isl_int_is_zero(div->el[2 + i]))
2282 continue;
2283 if (!tab->var[i].is_nonneg)
2284 return 0;
2287 return 1;
2290 /* Insert an extra div, prescribed by "div", to the tableau and
2291 * the associated bmap (which is assumed to be non-NULL).
2292 * The extra integer division is inserted at (tableau) position "pos".
2293 * Return "pos" or -1 if an error occurred.
2295 * If add_ineq is not NULL, then this function is used instead
2296 * of isl_tab_add_ineq to add the div constraints.
2297 * This complication is needed because the code in isl_tab_pip
2298 * wants to perform some extra processing when an inequality
2299 * is added to the tableau.
2301 int isl_tab_insert_div(struct isl_tab *tab, int pos, __isl_keep isl_vec *div,
2302 int (*add_ineq)(void *user, isl_int *), void *user)
2304 int r;
2305 int nonneg;
2306 int n_div, o_div;
2308 if (!tab || !div)
2309 return -1;
2311 if (div->size != 1 + 1 + tab->n_var)
2312 isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
2313 "unexpected size", return -1);
2315 isl_assert(tab->mat->ctx, tab->bmap, return -1);
2316 n_div = isl_basic_map_dim(tab->bmap, isl_dim_div);
2317 o_div = tab->n_var - n_div;
2318 if (pos < o_div || pos > tab->n_var)
2319 isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
2320 "invalid position", return -1);
2322 nonneg = div_is_nonneg(tab, div);
2324 if (isl_tab_extend_cons(tab, 3) < 0)
2325 return -1;
2326 if (isl_tab_extend_vars(tab, 1) < 0)
2327 return -1;
2328 r = isl_tab_insert_var(tab, pos);
2329 if (r < 0)
2330 return -1;
2332 if (nonneg)
2333 tab->var[r].is_nonneg = 1;
2335 tab->bmap = isl_basic_map_insert_div(tab->bmap, pos - o_div, div);
2336 if (!tab->bmap)
2337 return -1;
2338 if (isl_tab_push_var(tab, isl_tab_undo_bmap_div, &tab->var[r]) < 0)
2339 return -1;
2341 if (add_div_constraints(tab, pos - o_div, add_ineq, user) < 0)
2342 return -1;
2344 return r;
2347 /* Add an extra div, prescribed by "div", to the tableau and
2348 * the associated bmap (which is assumed to be non-NULL).
2350 int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div)
2352 if (!tab)
2353 return -1;
2354 return isl_tab_insert_div(tab, tab->n_var, div, NULL, NULL);
2357 /* If "track" is set, then we want to keep track of all constraints in tab
2358 * in its bmap field. This field is initialized from a copy of "bmap",
2359 * so we need to make sure that all constraints in "bmap" also appear
2360 * in the constructed tab.
2362 __isl_give struct isl_tab *isl_tab_from_basic_map(
2363 __isl_keep isl_basic_map *bmap, int track)
2365 int i;
2366 struct isl_tab *tab;
2368 if (!bmap)
2369 return NULL;
2370 tab = isl_tab_alloc(bmap->ctx,
2371 isl_basic_map_total_dim(bmap) + bmap->n_ineq + 1,
2372 isl_basic_map_total_dim(bmap), 0);
2373 if (!tab)
2374 return NULL;
2375 tab->preserve = track;
2376 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
2377 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
2378 if (isl_tab_mark_empty(tab) < 0)
2379 goto error;
2380 goto done;
2382 for (i = 0; i < bmap->n_eq; ++i) {
2383 tab = add_eq(tab, bmap->eq[i]);
2384 if (!tab)
2385 return tab;
2387 for (i = 0; i < bmap->n_ineq; ++i) {
2388 if (isl_tab_add_ineq(tab, bmap->ineq[i]) < 0)
2389 goto error;
2390 if (tab->empty)
2391 goto done;
2393 done:
2394 if (track && isl_tab_track_bmap(tab, isl_basic_map_copy(bmap)) < 0)
2395 goto error;
2396 return tab;
2397 error:
2398 isl_tab_free(tab);
2399 return NULL;
2402 __isl_give struct isl_tab *isl_tab_from_basic_set(
2403 __isl_keep isl_basic_set *bset, int track)
2405 return isl_tab_from_basic_map(bset, track);
2408 /* Construct a tableau corresponding to the recession cone of "bset".
2410 struct isl_tab *isl_tab_from_recession_cone(__isl_keep isl_basic_set *bset,
2411 int parametric)
2413 isl_int cst;
2414 int i;
2415 struct isl_tab *tab;
2416 unsigned offset = 0;
2418 if (!bset)
2419 return NULL;
2420 if (parametric)
2421 offset = isl_basic_set_dim(bset, isl_dim_param);
2422 tab = isl_tab_alloc(bset->ctx, bset->n_eq + bset->n_ineq,
2423 isl_basic_set_total_dim(bset) - offset, 0);
2424 if (!tab)
2425 return NULL;
2426 tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
2427 tab->cone = 1;
2429 isl_int_init(cst);
2430 isl_int_set_si(cst, 0);
2431 for (i = 0; i < bset->n_eq; ++i) {
2432 isl_int_swap(bset->eq[i][offset], cst);
2433 if (offset > 0) {
2434 if (isl_tab_add_eq(tab, bset->eq[i] + offset) < 0)
2435 goto error;
2436 } else
2437 tab = add_eq(tab, bset->eq[i]);
2438 isl_int_swap(bset->eq[i][offset], cst);
2439 if (!tab)
2440 goto done;
2442 for (i = 0; i < bset->n_ineq; ++i) {
2443 int r;
2444 isl_int_swap(bset->ineq[i][offset], cst);
2445 r = isl_tab_add_row(tab, bset->ineq[i] + offset);
2446 isl_int_swap(bset->ineq[i][offset], cst);
2447 if (r < 0)
2448 goto error;
2449 tab->con[r].is_nonneg = 1;
2450 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
2451 goto error;
2453 done:
2454 isl_int_clear(cst);
2455 return tab;
2456 error:
2457 isl_int_clear(cst);
2458 isl_tab_free(tab);
2459 return NULL;
2462 /* Assuming "tab" is the tableau of a cone, check if the cone is
2463 * bounded, i.e., if it is empty or only contains the origin.
2465 int isl_tab_cone_is_bounded(struct isl_tab *tab)
2467 int i;
2469 if (!tab)
2470 return -1;
2471 if (tab->empty)
2472 return 1;
2473 if (tab->n_dead == tab->n_col)
2474 return 1;
2476 for (;;) {
2477 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2478 struct isl_tab_var *var;
2479 int sgn;
2480 var = isl_tab_var_from_row(tab, i);
2481 if (!var->is_nonneg)
2482 continue;
2483 sgn = sign_of_max(tab, var);
2484 if (sgn < -1)
2485 return -1;
2486 if (sgn != 0)
2487 return 0;
2488 if (close_row(tab, var, 0) < 0)
2489 return -1;
2490 break;
2492 if (tab->n_dead == tab->n_col)
2493 return 1;
2494 if (i == tab->n_row)
2495 return 0;
2499 int isl_tab_sample_is_integer(struct isl_tab *tab)
2501 int i;
2503 if (!tab)
2504 return -1;
2506 for (i = 0; i < tab->n_var; ++i) {
2507 int row;
2508 if (!tab->var[i].is_row)
2509 continue;
2510 row = tab->var[i].index;
2511 if (!isl_int_is_divisible_by(tab->mat->row[row][1],
2512 tab->mat->row[row][0]))
2513 return 0;
2515 return 1;
2518 static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
2520 int i;
2521 struct isl_vec *vec;
2523 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
2524 if (!vec)
2525 return NULL;
2527 isl_int_set_si(vec->block.data[0], 1);
2528 for (i = 0; i < tab->n_var; ++i) {
2529 if (!tab->var[i].is_row)
2530 isl_int_set_si(vec->block.data[1 + i], 0);
2531 else {
2532 int row = tab->var[i].index;
2533 isl_int_divexact(vec->block.data[1 + i],
2534 tab->mat->row[row][1], tab->mat->row[row][0]);
2538 return vec;
2541 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
2543 int i;
2544 struct isl_vec *vec;
2545 isl_int m;
2547 if (!tab)
2548 return NULL;
2550 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
2551 if (!vec)
2552 return NULL;
2554 isl_int_init(m);
2556 isl_int_set_si(vec->block.data[0], 1);
2557 for (i = 0; i < tab->n_var; ++i) {
2558 int row;
2559 if (!tab->var[i].is_row) {
2560 isl_int_set_si(vec->block.data[1 + i], 0);
2561 continue;
2563 row = tab->var[i].index;
2564 isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
2565 isl_int_divexact(m, tab->mat->row[row][0], m);
2566 isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
2567 isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
2568 isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
2570 vec = isl_vec_normalize(vec);
2572 isl_int_clear(m);
2573 return vec;
2576 /* Update "bmap" based on the results of the tableau "tab".
2577 * In particular, implicit equalities are made explicit, redundant constraints
2578 * are removed and if the sample value happens to be integer, it is stored
2579 * in "bmap" (unless "bmap" already had an integer sample).
2581 * The tableau is assumed to have been created from "bmap" using
2582 * isl_tab_from_basic_map.
2584 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
2585 struct isl_tab *tab)
2587 int i;
2588 unsigned n_eq;
2590 if (!bmap)
2591 return NULL;
2592 if (!tab)
2593 return bmap;
2595 n_eq = tab->n_eq;
2596 if (tab->empty)
2597 bmap = isl_basic_map_set_to_empty(bmap);
2598 else
2599 for (i = bmap->n_ineq - 1; i >= 0; --i) {
2600 if (isl_tab_is_equality(tab, n_eq + i))
2601 isl_basic_map_inequality_to_equality(bmap, i);
2602 else if (isl_tab_is_redundant(tab, n_eq + i))
2603 isl_basic_map_drop_inequality(bmap, i);
2605 if (bmap->n_eq != n_eq)
2606 bmap = isl_basic_map_gauss(bmap, NULL);
2607 if (!tab->rational &&
2608 bmap && !bmap->sample && isl_tab_sample_is_integer(tab))
2609 bmap->sample = extract_integer_sample(tab);
2610 return bmap;
2613 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
2614 struct isl_tab *tab)
2616 return (struct isl_basic_set *)isl_basic_map_update_from_tab(
2617 (struct isl_basic_map *)bset, tab);
2620 /* Drop the last constraint added to "tab" in position "r".
2621 * The constraint is expected to have remained in a row.
2623 static isl_stat drop_last_con_in_row(struct isl_tab *tab, int r)
2625 if (!tab->con[r].is_row)
2626 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
2627 "row unexpectedly moved to column",
2628 return isl_stat_error);
2629 if (r + 1 != tab->n_con)
2630 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
2631 "additional constraints added", return isl_stat_error);
2632 if (drop_row(tab, tab->con[r].index) < 0)
2633 return isl_stat_error;
2635 return isl_stat_ok;
2638 /* Given a non-negative variable "var", temporarily add a new non-negative
2639 * variable that is the opposite of "var", ensuring that "var" can only attain
2640 * the value zero. The new variable is removed again before this function
2641 * returns. However, the effect of forcing "var" to be zero remains.
2642 * If var = n/d is a row variable, then the new variable = -n/d.
2643 * If var is a column variables, then the new variable = -var.
2644 * If the new variable cannot attain non-negative values, then
2645 * the resulting tableau is empty.
2646 * Otherwise, we know the value will be zero and we close the row.
2648 static isl_stat cut_to_hyperplane(struct isl_tab *tab, struct isl_tab_var *var)
2650 unsigned r;
2651 isl_int *row;
2652 int sgn;
2653 unsigned off = 2 + tab->M;
2655 if (var->is_zero)
2656 return isl_stat_ok;
2657 if (var->is_redundant || !var->is_nonneg)
2658 isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
2659 "expecting non-redundant non-negative variable",
2660 return isl_stat_error);
2662 if (isl_tab_extend_cons(tab, 1) < 0)
2663 return isl_stat_error;
2665 r = tab->n_con;
2666 tab->con[r].index = tab->n_row;
2667 tab->con[r].is_row = 1;
2668 tab->con[r].is_nonneg = 0;
2669 tab->con[r].is_zero = 0;
2670 tab->con[r].is_redundant = 0;
2671 tab->con[r].frozen = 0;
2672 tab->con[r].negated = 0;
2673 tab->row_var[tab->n_row] = ~r;
2674 row = tab->mat->row[tab->n_row];
2676 if (var->is_row) {
2677 isl_int_set(row[0], tab->mat->row[var->index][0]);
2678 isl_seq_neg(row + 1,
2679 tab->mat->row[var->index] + 1, 1 + tab->n_col);
2680 } else {
2681 isl_int_set_si(row[0], 1);
2682 isl_seq_clr(row + 1, 1 + tab->n_col);
2683 isl_int_set_si(row[off + var->index], -1);
2686 tab->n_row++;
2687 tab->n_con++;
2689 sgn = sign_of_max(tab, &tab->con[r]);
2690 if (sgn < -1)
2691 return isl_stat_error;
2692 if (sgn < 0) {
2693 if (drop_last_con_in_row(tab, r) < 0)
2694 return isl_stat_error;
2695 if (isl_tab_mark_empty(tab) < 0)
2696 return isl_stat_error;
2697 return isl_stat_ok;
2699 tab->con[r].is_nonneg = 1;
2700 /* sgn == 0 */
2701 if (close_row(tab, &tab->con[r], 1) < 0)
2702 return isl_stat_error;
2703 if (drop_last_con_in_row(tab, r) < 0)
2704 return isl_stat_error;
2706 return isl_stat_ok;
2709 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2710 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2711 * by r' = r + 1 >= 0.
2712 * If r is a row variable, we simply increase the constant term by one
2713 * (taking into account the denominator).
2714 * If r is a column variable, then we need to modify each row that
2715 * refers to r = r' - 1 by substituting this equality, effectively
2716 * subtracting the coefficient of the column from the constant.
2717 * We should only do this if the minimum is manifestly unbounded,
2718 * however. Otherwise, we may end up with negative sample values
2719 * for non-negative variables.
2720 * So, if r is a column variable with a minimum that is not
2721 * manifestly unbounded, then we need to move it to a row.
2722 * However, the sample value of this row may be negative,
2723 * even after the relaxation, so we need to restore it.
2724 * We therefore prefer to pivot a column up to a row, if possible.
2726 int isl_tab_relax(struct isl_tab *tab, int con)
2728 struct isl_tab_var *var;
2730 if (!tab)
2731 return -1;
2733 var = &tab->con[con];
2735 if (var->is_row && (var->index < 0 || var->index < tab->n_redundant))
2736 isl_die(tab->mat->ctx, isl_error_invalid,
2737 "cannot relax redundant constraint", return -1);
2738 if (!var->is_row && (var->index < 0 || var->index < tab->n_dead))
2739 isl_die(tab->mat->ctx, isl_error_invalid,
2740 "cannot relax dead constraint", return -1);
2742 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
2743 if (to_row(tab, var, 1) < 0)
2744 return -1;
2745 if (!var->is_row && !min_is_manifestly_unbounded(tab, var))
2746 if (to_row(tab, var, -1) < 0)
2747 return -1;
2749 if (var->is_row) {
2750 isl_int_add(tab->mat->row[var->index][1],
2751 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
2752 if (restore_row(tab, var) < 0)
2753 return -1;
2754 } else {
2755 int i;
2756 unsigned off = 2 + tab->M;
2758 for (i = 0; i < tab->n_row; ++i) {
2759 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2760 continue;
2761 isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
2762 tab->mat->row[i][off + var->index]);
2767 if (isl_tab_push_var(tab, isl_tab_undo_relax, var) < 0)
2768 return -1;
2770 return 0;
2773 /* Replace the variable v at position "pos" in the tableau "tab"
2774 * by v' = v + shift.
2776 * If the variable is in a column, then we first check if we can
2777 * simply plug in v = v' - shift. The effect on a row with
2778 * coefficient f/d for variable v is that the constant term c/d
2779 * is replaced by (c - f * shift)/d. If shift is positive and
2780 * f is negative for each row that needs to remain non-negative,
2781 * then this is clearly safe. In other words, if the minimum of v
2782 * is manifestly unbounded, then we can keep v in a column position.
2783 * Otherwise, we can pivot it down to a row.
2784 * Similarly, if shift is negative, we need to check if the maximum
2785 * of is manifestly unbounded.
2787 * If the variable is in a row (from the start or after pivoting),
2788 * then the constant term c/d is replaced by (c + d * shift)/d.
2790 int isl_tab_shift_var(struct isl_tab *tab, int pos, isl_int shift)
2792 struct isl_tab_var *var;
2794 if (!tab)
2795 return -1;
2796 if (isl_int_is_zero(shift))
2797 return 0;
2799 var = &tab->var[pos];
2800 if (!var->is_row) {
2801 if (isl_int_is_neg(shift)) {
2802 if (!max_is_manifestly_unbounded(tab, var))
2803 if (to_row(tab, var, 1) < 0)
2804 return -1;
2805 } else {
2806 if (!min_is_manifestly_unbounded(tab, var))
2807 if (to_row(tab, var, -1) < 0)
2808 return -1;
2812 if (var->is_row) {
2813 isl_int_addmul(tab->mat->row[var->index][1],
2814 shift, tab->mat->row[var->index][0]);
2815 } else {
2816 int i;
2817 unsigned off = 2 + tab->M;
2819 for (i = 0; i < tab->n_row; ++i) {
2820 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2821 continue;
2822 isl_int_submul(tab->mat->row[i][1],
2823 shift, tab->mat->row[i][off + var->index]);
2828 return 0;
2831 /* Remove the sign constraint from constraint "con".
2833 * If the constraint variable was originally marked non-negative,
2834 * then we make sure we mark it non-negative again during rollback.
2836 int isl_tab_unrestrict(struct isl_tab *tab, int con)
2838 struct isl_tab_var *var;
2840 if (!tab)
2841 return -1;
2843 var = &tab->con[con];
2844 if (!var->is_nonneg)
2845 return 0;
2847 var->is_nonneg = 0;
2848 if (isl_tab_push_var(tab, isl_tab_undo_unrestrict, var) < 0)
2849 return -1;
2851 return 0;
2854 int isl_tab_select_facet(struct isl_tab *tab, int con)
2856 if (!tab)
2857 return -1;
2859 return cut_to_hyperplane(tab, &tab->con[con]);
2862 static int may_be_equality(struct isl_tab *tab, int row)
2864 return tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
2865 : isl_int_lt(tab->mat->row[row][1],
2866 tab->mat->row[row][0]);
2869 /* Check for (near) equalities among the constraints.
2870 * A constraint is an equality if it is non-negative and if
2871 * its maximal value is either
2872 * - zero (in case of rational tableaus), or
2873 * - strictly less than 1 (in case of integer tableaus)
2875 * We first mark all non-redundant and non-dead variables that
2876 * are not frozen and not obviously not an equality.
2877 * Then we iterate over all marked variables if they can attain
2878 * any values larger than zero or at least one.
2879 * If the maximal value is zero, we mark any column variables
2880 * that appear in the row as being zero and mark the row as being redundant.
2881 * Otherwise, if the maximal value is strictly less than one (and the
2882 * tableau is integer), then we restrict the value to being zero
2883 * by adding an opposite non-negative variable.
2885 int isl_tab_detect_implicit_equalities(struct isl_tab *tab)
2887 int i;
2888 unsigned n_marked;
2890 if (!tab)
2891 return -1;
2892 if (tab->empty)
2893 return 0;
2894 if (tab->n_dead == tab->n_col)
2895 return 0;
2897 n_marked = 0;
2898 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2899 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
2900 var->marked = !var->frozen && var->is_nonneg &&
2901 may_be_equality(tab, i);
2902 if (var->marked)
2903 n_marked++;
2905 for (i = tab->n_dead; i < tab->n_col; ++i) {
2906 struct isl_tab_var *var = var_from_col(tab, i);
2907 var->marked = !var->frozen && var->is_nonneg;
2908 if (var->marked)
2909 n_marked++;
2911 while (n_marked) {
2912 struct isl_tab_var *var;
2913 int sgn;
2914 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2915 var = isl_tab_var_from_row(tab, i);
2916 if (var->marked)
2917 break;
2919 if (i == tab->n_row) {
2920 for (i = tab->n_dead; i < tab->n_col; ++i) {
2921 var = var_from_col(tab, i);
2922 if (var->marked)
2923 break;
2925 if (i == tab->n_col)
2926 break;
2928 var->marked = 0;
2929 n_marked--;
2930 sgn = sign_of_max(tab, var);
2931 if (sgn < 0)
2932 return -1;
2933 if (sgn == 0) {
2934 if (close_row(tab, var, 0) < 0)
2935 return -1;
2936 } else if (!tab->rational && !at_least_one(tab, var)) {
2937 if (cut_to_hyperplane(tab, var) < 0)
2938 return -1;
2939 return isl_tab_detect_implicit_equalities(tab);
2941 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2942 var = isl_tab_var_from_row(tab, i);
2943 if (!var->marked)
2944 continue;
2945 if (may_be_equality(tab, i))
2946 continue;
2947 var->marked = 0;
2948 n_marked--;
2952 return 0;
2955 /* Update the element of row_var or col_var that corresponds to
2956 * constraint tab->con[i] to a move from position "old" to position "i".
2958 static int update_con_after_move(struct isl_tab *tab, int i, int old)
2960 int *p;
2961 int index;
2963 index = tab->con[i].index;
2964 if (index == -1)
2965 return 0;
2966 p = tab->con[i].is_row ? tab->row_var : tab->col_var;
2967 if (p[index] != ~old)
2968 isl_die(tab->mat->ctx, isl_error_internal,
2969 "broken internal state", return -1);
2970 p[index] = ~i;
2972 return 0;
2975 /* Rotate the "n" constraints starting at "first" to the right,
2976 * putting the last constraint in the position of the first constraint.
2978 static int rotate_constraints(struct isl_tab *tab, int first, int n)
2980 int i, last;
2981 struct isl_tab_var var;
2983 if (n <= 1)
2984 return 0;
2986 last = first + n - 1;
2987 var = tab->con[last];
2988 for (i = last; i > first; --i) {
2989 tab->con[i] = tab->con[i - 1];
2990 if (update_con_after_move(tab, i, i - 1) < 0)
2991 return -1;
2993 tab->con[first] = var;
2994 if (update_con_after_move(tab, first, last) < 0)
2995 return -1;
2997 return 0;
3000 /* Make the equalities that are implicit in "bmap" but that have been
3001 * detected in the corresponding "tab" explicit in "bmap" and update
3002 * "tab" to reflect the new order of the constraints.
3004 * In particular, if inequality i is an implicit equality then
3005 * isl_basic_map_inequality_to_equality will move the inequality
3006 * in front of the other equality and it will move the last inequality
3007 * in the position of inequality i.
3008 * In the tableau, the inequalities of "bmap" are stored after the equalities
3009 * and so the original order
3011 * E E E E E A A A I B B B B L
3013 * is changed into
3015 * I E E E E E A A A L B B B B
3017 * where I is the implicit equality, the E are equalities,
3018 * the A inequalities before I, the B inequalities after I and
3019 * L the last inequality.
3020 * We therefore need to rotate to the right two sets of constraints,
3021 * those up to and including I and those after I.
3023 * If "tab" contains any constraints that are not in "bmap" then they
3024 * appear after those in "bmap" and they should be left untouched.
3026 * Note that this function leaves "bmap" in a temporary state
3027 * as it does not call isl_basic_map_gauss. Calling this function
3028 * is the responsibility of the caller.
3030 __isl_give isl_basic_map *isl_tab_make_equalities_explicit(struct isl_tab *tab,
3031 __isl_take isl_basic_map *bmap)
3033 int i;
3035 if (!tab || !bmap)
3036 return isl_basic_map_free(bmap);
3037 if (tab->empty)
3038 return bmap;
3040 for (i = bmap->n_ineq - 1; i >= 0; --i) {
3041 if (!isl_tab_is_equality(tab, bmap->n_eq + i))
3042 continue;
3043 isl_basic_map_inequality_to_equality(bmap, i);
3044 if (rotate_constraints(tab, 0, tab->n_eq + i + 1) < 0)
3045 return isl_basic_map_free(bmap);
3046 if (rotate_constraints(tab, tab->n_eq + i + 1,
3047 bmap->n_ineq - i) < 0)
3048 return isl_basic_map_free(bmap);
3049 tab->n_eq++;
3052 return bmap;
3055 static int con_is_redundant(struct isl_tab *tab, struct isl_tab_var *var)
3057 if (!tab)
3058 return -1;
3059 if (tab->rational) {
3060 int sgn = sign_of_min(tab, var);
3061 if (sgn < -1)
3062 return -1;
3063 return sgn >= 0;
3064 } else {
3065 int irred = isl_tab_min_at_most_neg_one(tab, var);
3066 if (irred < 0)
3067 return -1;
3068 return !irred;
3072 /* Return an isl_tab_var that has been marked or NULL if no such
3073 * variable can be found.
3074 * The marked field has only been set for variables that
3075 * appear in non-redundant rows or non-dead columns.
3077 * Pick the last constraint variable that is marked and
3078 * that appears in either a non-redundant row or a non-dead columns.
3079 * Since the returned variable is tested for being a redundant constraint,
3080 * there is no need to return any tab variable that corresponds to a variable.
3082 static struct isl_tab_var *select_marked(struct isl_tab *tab)
3084 int i;
3085 struct isl_tab_var *var;
3087 for (i = tab->n_con - 1; i >= 0; --i) {
3088 var = &tab->con[i];
3089 if (var->index < 0)
3090 continue;
3091 if (var->is_row && var->index < tab->n_redundant)
3092 continue;
3093 if (!var->is_row && var->index < tab->n_dead)
3094 continue;
3095 if (var->marked)
3096 return var;
3099 return NULL;
3102 /* Check for (near) redundant constraints.
3103 * A constraint is redundant if it is non-negative and if
3104 * its minimal value (temporarily ignoring the non-negativity) is either
3105 * - zero (in case of rational tableaus), or
3106 * - strictly larger than -1 (in case of integer tableaus)
3108 * We first mark all non-redundant and non-dead variables that
3109 * are not frozen and not obviously negatively unbounded.
3110 * Then we iterate over all marked variables if they can attain
3111 * any values smaller than zero or at most negative one.
3112 * If not, we mark the row as being redundant (assuming it hasn't
3113 * been detected as being obviously redundant in the mean time).
3115 int isl_tab_detect_redundant(struct isl_tab *tab)
3117 int i;
3118 unsigned n_marked;
3120 if (!tab)
3121 return -1;
3122 if (tab->empty)
3123 return 0;
3124 if (tab->n_redundant == tab->n_row)
3125 return 0;
3127 n_marked = 0;
3128 for (i = tab->n_redundant; i < tab->n_row; ++i) {
3129 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
3130 var->marked = !var->frozen && var->is_nonneg;
3131 if (var->marked)
3132 n_marked++;
3134 for (i = tab->n_dead; i < tab->n_col; ++i) {
3135 struct isl_tab_var *var = var_from_col(tab, i);
3136 var->marked = !var->frozen && var->is_nonneg &&
3137 !min_is_manifestly_unbounded(tab, var);
3138 if (var->marked)
3139 n_marked++;
3141 while (n_marked) {
3142 struct isl_tab_var *var;
3143 int red;
3144 var = select_marked(tab);
3145 if (!var)
3146 break;
3147 var->marked = 0;
3148 n_marked--;
3149 red = con_is_redundant(tab, var);
3150 if (red < 0)
3151 return -1;
3152 if (red && !var->is_redundant)
3153 if (isl_tab_mark_redundant(tab, var->index) < 0)
3154 return -1;
3155 for (i = tab->n_dead; i < tab->n_col; ++i) {
3156 var = var_from_col(tab, i);
3157 if (!var->marked)
3158 continue;
3159 if (!min_is_manifestly_unbounded(tab, var))
3160 continue;
3161 var->marked = 0;
3162 n_marked--;
3166 return 0;
3169 int isl_tab_is_equality(struct isl_tab *tab, int con)
3171 int row;
3172 unsigned off;
3174 if (!tab)
3175 return -1;
3176 if (tab->con[con].is_zero)
3177 return 1;
3178 if (tab->con[con].is_redundant)
3179 return 0;
3180 if (!tab->con[con].is_row)
3181 return tab->con[con].index < tab->n_dead;
3183 row = tab->con[con].index;
3185 off = 2 + tab->M;
3186 return isl_int_is_zero(tab->mat->row[row][1]) &&
3187 (!tab->M || isl_int_is_zero(tab->mat->row[row][2])) &&
3188 isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
3189 tab->n_col - tab->n_dead) == -1;
3192 /* Return the minimal value of the affine expression "f" with denominator
3193 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
3194 * the expression cannot attain arbitrarily small values.
3195 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
3196 * The return value reflects the nature of the result (empty, unbounded,
3197 * minimal value returned in *opt).
3199 * This function assumes that at least one more row and at least
3200 * one more element in the constraint array are available in the tableau.
3202 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
3203 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
3204 unsigned flags)
3206 int r;
3207 enum isl_lp_result res = isl_lp_ok;
3208 struct isl_tab_var *var;
3209 struct isl_tab_undo *snap;
3211 if (!tab)
3212 return isl_lp_error;
3214 if (tab->empty)
3215 return isl_lp_empty;
3217 snap = isl_tab_snap(tab);
3218 r = isl_tab_add_row(tab, f);
3219 if (r < 0)
3220 return isl_lp_error;
3221 var = &tab->con[r];
3222 for (;;) {
3223 int row, col;
3224 find_pivot(tab, var, var, -1, &row, &col);
3225 if (row == var->index) {
3226 res = isl_lp_unbounded;
3227 break;
3229 if (row == -1)
3230 break;
3231 if (isl_tab_pivot(tab, row, col) < 0)
3232 return isl_lp_error;
3234 isl_int_mul(tab->mat->row[var->index][0],
3235 tab->mat->row[var->index][0], denom);
3236 if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
3237 int i;
3239 isl_vec_free(tab->dual);
3240 tab->dual = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_con);
3241 if (!tab->dual)
3242 return isl_lp_error;
3243 isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
3244 for (i = 0; i < tab->n_con; ++i) {
3245 int pos;
3246 if (tab->con[i].is_row) {
3247 isl_int_set_si(tab->dual->el[1 + i], 0);
3248 continue;
3250 pos = 2 + tab->M + tab->con[i].index;
3251 if (tab->con[i].negated)
3252 isl_int_neg(tab->dual->el[1 + i],
3253 tab->mat->row[var->index][pos]);
3254 else
3255 isl_int_set(tab->dual->el[1 + i],
3256 tab->mat->row[var->index][pos]);
3259 if (opt && res == isl_lp_ok) {
3260 if (opt_denom) {
3261 isl_int_set(*opt, tab->mat->row[var->index][1]);
3262 isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
3263 } else
3264 isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
3265 tab->mat->row[var->index][0]);
3267 if (isl_tab_rollback(tab, snap) < 0)
3268 return isl_lp_error;
3269 return res;
3272 /* Is the constraint at position "con" marked as being redundant?
3273 * If it is marked as representing an equality, then it is not
3274 * considered to be redundant.
3275 * Note that isl_tab_mark_redundant marks both the isl_tab_var as
3276 * redundant and moves the corresponding row into the first
3277 * tab->n_redundant positions (or removes the row, assigning it index -1),
3278 * so the final test is actually redundant itself.
3280 int isl_tab_is_redundant(struct isl_tab *tab, int con)
3282 if (!tab)
3283 return -1;
3284 if (con < 0 || con >= tab->n_con)
3285 isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
3286 "position out of bounds", return -1);
3287 if (tab->con[con].is_zero)
3288 return 0;
3289 if (tab->con[con].is_redundant)
3290 return 1;
3291 return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
3294 /* Take a snapshot of the tableau that can be restored by a call to
3295 * isl_tab_rollback.
3297 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
3299 if (!tab)
3300 return NULL;
3301 tab->need_undo = 1;
3302 return tab->top;
3305 /* Does "tab" need to keep track of undo information?
3306 * That is, was a snapshot taken that may need to be restored?
3308 isl_bool isl_tab_need_undo(struct isl_tab *tab)
3310 if (!tab)
3311 return isl_bool_error;
3313 return tab->need_undo;
3316 /* Remove all tracking of undo information from "tab", invalidating
3317 * any snapshots that may have been taken of the tableau.
3318 * Since all snapshots have been invalidated, there is also
3319 * no need to start keeping track of undo information again.
3321 void isl_tab_clear_undo(struct isl_tab *tab)
3323 if (!tab)
3324 return;
3326 free_undo(tab);
3327 tab->need_undo = 0;
3330 /* Undo the operation performed by isl_tab_relax.
3332 static int unrelax(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
3333 static int unrelax(struct isl_tab *tab, struct isl_tab_var *var)
3335 unsigned off = 2 + tab->M;
3337 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
3338 if (to_row(tab, var, 1) < 0)
3339 return -1;
3341 if (var->is_row) {
3342 isl_int_sub(tab->mat->row[var->index][1],
3343 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
3344 if (var->is_nonneg) {
3345 int sgn = restore_row(tab, var);
3346 isl_assert(tab->mat->ctx, sgn >= 0, return -1);
3348 } else {
3349 int i;
3351 for (i = 0; i < tab->n_row; ++i) {
3352 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
3353 continue;
3354 isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
3355 tab->mat->row[i][off + var->index]);
3360 return 0;
3363 /* Undo the operation performed by isl_tab_unrestrict.
3365 * In particular, mark the variable as being non-negative and make
3366 * sure the sample value respects this constraint.
3368 static int ununrestrict(struct isl_tab *tab, struct isl_tab_var *var)
3370 var->is_nonneg = 1;
3372 if (var->is_row && restore_row(tab, var) < -1)
3373 return -1;
3375 return 0;
3378 static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
3379 static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
3381 struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
3382 switch (undo->type) {
3383 case isl_tab_undo_nonneg:
3384 var->is_nonneg = 0;
3385 break;
3386 case isl_tab_undo_redundant:
3387 var->is_redundant = 0;
3388 tab->n_redundant--;
3389 restore_row(tab, isl_tab_var_from_row(tab, tab->n_redundant));
3390 break;
3391 case isl_tab_undo_freeze:
3392 var->frozen = 0;
3393 break;
3394 case isl_tab_undo_zero:
3395 var->is_zero = 0;
3396 if (!var->is_row)
3397 tab->n_dead--;
3398 break;
3399 case isl_tab_undo_allocate:
3400 if (undo->u.var_index >= 0) {
3401 isl_assert(tab->mat->ctx, !var->is_row, return -1);
3402 return drop_col(tab, var->index);
3404 if (!var->is_row) {
3405 if (!max_is_manifestly_unbounded(tab, var)) {
3406 if (to_row(tab, var, 1) < 0)
3407 return -1;
3408 } else if (!min_is_manifestly_unbounded(tab, var)) {
3409 if (to_row(tab, var, -1) < 0)
3410 return -1;
3411 } else
3412 if (to_row(tab, var, 0) < 0)
3413 return -1;
3415 return drop_row(tab, var->index);
3416 case isl_tab_undo_relax:
3417 return unrelax(tab, var);
3418 case isl_tab_undo_unrestrict:
3419 return ununrestrict(tab, var);
3420 default:
3421 isl_die(tab->mat->ctx, isl_error_internal,
3422 "perform_undo_var called on invalid undo record",
3423 return -1);
3426 return 0;
3429 /* Undo the addition of an integer division to the basic map representation
3430 * of "tab" in position "pos".
3432 static isl_stat drop_bmap_div(struct isl_tab *tab, int pos)
3434 int off;
3436 off = tab->n_var - isl_basic_map_dim(tab->bmap, isl_dim_div);
3437 if (isl_basic_map_drop_div(tab->bmap, pos - off) < 0)
3438 return isl_stat_error;
3439 if (tab->samples) {
3440 tab->samples = isl_mat_drop_cols(tab->samples, 1 + pos, 1);
3441 if (!tab->samples)
3442 return isl_stat_error;
3445 return isl_stat_ok;
3448 /* Restore the tableau to the state where the basic variables
3449 * are those in "col_var".
3450 * We first construct a list of variables that are currently in
3451 * the basis, but shouldn't. Then we iterate over all variables
3452 * that should be in the basis and for each one that is currently
3453 * not in the basis, we exchange it with one of the elements of the
3454 * list constructed before.
3455 * We can always find an appropriate variable to pivot with because
3456 * the current basis is mapped to the old basis by a non-singular
3457 * matrix and so we can never end up with a zero row.
3459 static int restore_basis(struct isl_tab *tab, int *col_var)
3461 int i, j;
3462 int n_extra = 0;
3463 int *extra = NULL; /* current columns that contain bad stuff */
3464 unsigned off = 2 + tab->M;
3466 extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
3467 if (tab->n_col && !extra)
3468 goto error;
3469 for (i = 0; i < tab->n_col; ++i) {
3470 for (j = 0; j < tab->n_col; ++j)
3471 if (tab->col_var[i] == col_var[j])
3472 break;
3473 if (j < tab->n_col)
3474 continue;
3475 extra[n_extra++] = i;
3477 for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
3478 struct isl_tab_var *var;
3479 int row;
3481 for (j = 0; j < tab->n_col; ++j)
3482 if (col_var[i] == tab->col_var[j])
3483 break;
3484 if (j < tab->n_col)
3485 continue;
3486 var = var_from_index(tab, col_var[i]);
3487 row = var->index;
3488 for (j = 0; j < n_extra; ++j)
3489 if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
3490 break;
3491 isl_assert(tab->mat->ctx, j < n_extra, goto error);
3492 if (isl_tab_pivot(tab, row, extra[j]) < 0)
3493 goto error;
3494 extra[j] = extra[--n_extra];
3497 free(extra);
3498 return 0;
3499 error:
3500 free(extra);
3501 return -1;
3504 /* Remove all samples with index n or greater, i.e., those samples
3505 * that were added since we saved this number of samples in
3506 * isl_tab_save_samples.
3508 static void drop_samples_since(struct isl_tab *tab, int n)
3510 int i;
3512 for (i = tab->n_sample - 1; i >= 0 && tab->n_sample > n; --i) {
3513 if (tab->sample_index[i] < n)
3514 continue;
3516 if (i != tab->n_sample - 1) {
3517 int t = tab->sample_index[tab->n_sample-1];
3518 tab->sample_index[tab->n_sample-1] = tab->sample_index[i];
3519 tab->sample_index[i] = t;
3520 isl_mat_swap_rows(tab->samples, tab->n_sample-1, i);
3522 tab->n_sample--;
3526 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
3527 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
3529 switch (undo->type) {
3530 case isl_tab_undo_rational:
3531 tab->rational = 0;
3532 break;
3533 case isl_tab_undo_empty:
3534 tab->empty = 0;
3535 break;
3536 case isl_tab_undo_nonneg:
3537 case isl_tab_undo_redundant:
3538 case isl_tab_undo_freeze:
3539 case isl_tab_undo_zero:
3540 case isl_tab_undo_allocate:
3541 case isl_tab_undo_relax:
3542 case isl_tab_undo_unrestrict:
3543 return perform_undo_var(tab, undo);
3544 case isl_tab_undo_bmap_eq:
3545 return isl_basic_map_free_equality(tab->bmap, 1);
3546 case isl_tab_undo_bmap_ineq:
3547 return isl_basic_map_free_inequality(tab->bmap, 1);
3548 case isl_tab_undo_bmap_div:
3549 return drop_bmap_div(tab, undo->u.var_index);
3550 case isl_tab_undo_saved_basis:
3551 if (restore_basis(tab, undo->u.col_var) < 0)
3552 return -1;
3553 break;
3554 case isl_tab_undo_drop_sample:
3555 tab->n_outside--;
3556 break;
3557 case isl_tab_undo_saved_samples:
3558 drop_samples_since(tab, undo->u.n);
3559 break;
3560 case isl_tab_undo_callback:
3561 return undo->u.callback->run(undo->u.callback);
3562 default:
3563 isl_assert(tab->mat->ctx, 0, return -1);
3565 return 0;
3568 /* Return the tableau to the state it was in when the snapshot "snap"
3569 * was taken.
3571 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
3573 struct isl_tab_undo *undo, *next;
3575 if (!tab)
3576 return -1;
3578 tab->in_undo = 1;
3579 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
3580 next = undo->next;
3581 if (undo == snap)
3582 break;
3583 if (perform_undo(tab, undo) < 0) {
3584 tab->top = undo;
3585 free_undo(tab);
3586 tab->in_undo = 0;
3587 return -1;
3589 free_undo_record(undo);
3591 tab->in_undo = 0;
3592 tab->top = undo;
3593 if (!undo)
3594 return -1;
3595 return 0;
3598 /* The given row "row" represents an inequality violated by all
3599 * points in the tableau. Check for some special cases of such
3600 * separating constraints.
3601 * In particular, if the row has been reduced to the constant -1,
3602 * then we know the inequality is adjacent (but opposite) to
3603 * an equality in the tableau.
3604 * If the row has been reduced to r = c*(-1 -r'), with r' an inequality
3605 * of the tableau and c a positive constant, then the inequality
3606 * is adjacent (but opposite) to the inequality r'.
3608 static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
3610 int pos;
3611 unsigned off = 2 + tab->M;
3613 if (tab->rational)
3614 return isl_ineq_separate;
3616 if (!isl_int_is_one(tab->mat->row[row][0]))
3617 return isl_ineq_separate;
3619 pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
3620 tab->n_col - tab->n_dead);
3621 if (pos == -1) {
3622 if (isl_int_is_negone(tab->mat->row[row][1]))
3623 return isl_ineq_adj_eq;
3624 else
3625 return isl_ineq_separate;
3628 if (!isl_int_eq(tab->mat->row[row][1],
3629 tab->mat->row[row][off + tab->n_dead + pos]))
3630 return isl_ineq_separate;
3632 pos = isl_seq_first_non_zero(
3633 tab->mat->row[row] + off + tab->n_dead + pos + 1,
3634 tab->n_col - tab->n_dead - pos - 1);
3636 return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
3639 /* Check the effect of inequality "ineq" on the tableau "tab".
3640 * The result may be
3641 * isl_ineq_redundant: satisfied by all points in the tableau
3642 * isl_ineq_separate: satisfied by no point in the tableau
3643 * isl_ineq_cut: satisfied by some by not all points
3644 * isl_ineq_adj_eq: adjacent to an equality
3645 * isl_ineq_adj_ineq: adjacent to an inequality.
3647 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
3649 enum isl_ineq_type type = isl_ineq_error;
3650 struct isl_tab_undo *snap = NULL;
3651 int con;
3652 int row;
3654 if (!tab)
3655 return isl_ineq_error;
3657 if (isl_tab_extend_cons(tab, 1) < 0)
3658 return isl_ineq_error;
3660 snap = isl_tab_snap(tab);
3662 con = isl_tab_add_row(tab, ineq);
3663 if (con < 0)
3664 goto error;
3666 row = tab->con[con].index;
3667 if (isl_tab_row_is_redundant(tab, row))
3668 type = isl_ineq_redundant;
3669 else if (isl_int_is_neg(tab->mat->row[row][1]) &&
3670 (tab->rational ||
3671 isl_int_abs_ge(tab->mat->row[row][1],
3672 tab->mat->row[row][0]))) {
3673 int nonneg = at_least_zero(tab, &tab->con[con]);
3674 if (nonneg < 0)
3675 goto error;
3676 if (nonneg)
3677 type = isl_ineq_cut;
3678 else
3679 type = separation_type(tab, row);
3680 } else {
3681 int red = con_is_redundant(tab, &tab->con[con]);
3682 if (red < 0)
3683 goto error;
3684 if (!red)
3685 type = isl_ineq_cut;
3686 else
3687 type = isl_ineq_redundant;
3690 if (isl_tab_rollback(tab, snap))
3691 return isl_ineq_error;
3692 return type;
3693 error:
3694 return isl_ineq_error;
3697 int isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap)
3699 bmap = isl_basic_map_cow(bmap);
3700 if (!tab || !bmap)
3701 goto error;
3703 if (tab->empty) {
3704 bmap = isl_basic_map_set_to_empty(bmap);
3705 if (!bmap)
3706 goto error;
3707 tab->bmap = bmap;
3708 return 0;
3711 isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, goto error);
3712 isl_assert(tab->mat->ctx,
3713 tab->n_con == bmap->n_eq + bmap->n_ineq, goto error);
3715 tab->bmap = bmap;
3717 return 0;
3718 error:
3719 isl_basic_map_free(bmap);
3720 return -1;
3723 int isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset)
3725 return isl_tab_track_bmap(tab, (isl_basic_map *)bset);
3728 __isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab)
3730 if (!tab)
3731 return NULL;
3733 return (isl_basic_set *)tab->bmap;
3736 static void isl_tab_print_internal(__isl_keep struct isl_tab *tab,
3737 FILE *out, int indent)
3739 unsigned r, c;
3740 int i;
3742 if (!tab) {
3743 fprintf(out, "%*snull tab\n", indent, "");
3744 return;
3746 fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
3747 tab->n_redundant, tab->n_dead);
3748 if (tab->rational)
3749 fprintf(out, ", rational");
3750 if (tab->empty)
3751 fprintf(out, ", empty");
3752 fprintf(out, "\n");
3753 fprintf(out, "%*s[", indent, "");
3754 for (i = 0; i < tab->n_var; ++i) {
3755 if (i)
3756 fprintf(out, (i == tab->n_param ||
3757 i == tab->n_var - tab->n_div) ? "; "
3758 : ", ");
3759 fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
3760 tab->var[i].index,
3761 tab->var[i].is_zero ? " [=0]" :
3762 tab->var[i].is_redundant ? " [R]" : "");
3764 fprintf(out, "]\n");
3765 fprintf(out, "%*s[", indent, "");
3766 for (i = 0; i < tab->n_con; ++i) {
3767 if (i)
3768 fprintf(out, ", ");
3769 fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
3770 tab->con[i].index,
3771 tab->con[i].is_zero ? " [=0]" :
3772 tab->con[i].is_redundant ? " [R]" : "");
3774 fprintf(out, "]\n");
3775 fprintf(out, "%*s[", indent, "");
3776 for (i = 0; i < tab->n_row; ++i) {
3777 const char *sign = "";
3778 if (i)
3779 fprintf(out, ", ");
3780 if (tab->row_sign) {
3781 if (tab->row_sign[i] == isl_tab_row_unknown)
3782 sign = "?";
3783 else if (tab->row_sign[i] == isl_tab_row_neg)
3784 sign = "-";
3785 else if (tab->row_sign[i] == isl_tab_row_pos)
3786 sign = "+";
3787 else
3788 sign = "+-";
3790 fprintf(out, "r%d: %d%s%s", i, tab->row_var[i],
3791 isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
3793 fprintf(out, "]\n");
3794 fprintf(out, "%*s[", indent, "");
3795 for (i = 0; i < tab->n_col; ++i) {
3796 if (i)
3797 fprintf(out, ", ");
3798 fprintf(out, "c%d: %d%s", i, tab->col_var[i],
3799 var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
3801 fprintf(out, "]\n");
3802 r = tab->mat->n_row;
3803 tab->mat->n_row = tab->n_row;
3804 c = tab->mat->n_col;
3805 tab->mat->n_col = 2 + tab->M + tab->n_col;
3806 isl_mat_print_internal(tab->mat, out, indent);
3807 tab->mat->n_row = r;
3808 tab->mat->n_col = c;
3809 if (tab->bmap)
3810 isl_basic_map_print_internal(tab->bmap, out, indent);
3813 void isl_tab_dump(__isl_keep struct isl_tab *tab)
3815 isl_tab_print_internal(tab, stderr, 0);