1/*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2013 Ecole Normale Superieure
4 * Copyright 2014 INRIA Rocquencourt
5 * Copyright 2016 Sven Verdoolaege
6 *
7 * Use of this software is governed by the MIT license
8 *
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
12 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
13 * B.P. 105 - 78153 Le Chesnay, France
14 */
15
16#include <isl_ctx_private.h>
17#include <isl_mat_private.h>
18#include <isl_vec_private.h>
19#include "isl_map_private.h"
20#include "isl_tab.h"
21#include <isl_seq.h>
22#include <isl_config.h>
23
24#include <bset_to_bmap.c>
25#include <bset_from_bmap.c>
26
27/*
28 * The implementation of tableaus in this file was inspired by Section 8
29 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
30 * prover for program checking".
31 */
32
33struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
34 unsigned n_row, unsigned n_var, unsigned M)
35{
36 int i;
37 struct isl_tab *tab;
38 unsigned off = 2 + M;
39
40 tab = isl_calloc_type(ctx, struct isl_tab);
41 if (!tab)
42 return NULL;
43 tab->mat = isl_mat_alloc(ctx, n_row, n_col: off + n_var);
44 if (!tab->mat)
45 goto error;
46 tab->var = isl_alloc_array(ctx, struct isl_tab_var, n_var);
47 if (n_var && !tab->var)
48 goto error;
49 tab->con = isl_alloc_array(ctx, struct isl_tab_var, n_row);
50 if (n_row && !tab->con)
51 goto error;
52 tab->col_var = isl_alloc_array(ctx, int, n_var);
53 if (n_var && !tab->col_var)
54 goto error;
55 tab->row_var = isl_alloc_array(ctx, int, n_row);
56 if (n_row && !tab->row_var)
57 goto error;
58 for (i = 0; i < n_var; ++i) {
59 tab->var[i].index = i;
60 tab->var[i].is_row = 0;
61 tab->var[i].is_nonneg = 0;
62 tab->var[i].is_zero = 0;
63 tab->var[i].is_redundant = 0;
64 tab->var[i].frozen = 0;
65 tab->var[i].negated = 0;
66 tab->col_var[i] = i;
67 }
68 tab->n_row = 0;
69 tab->n_con = 0;
70 tab->n_eq = 0;
71 tab->max_con = n_row;
72 tab->n_col = n_var;
73 tab->n_var = n_var;
74 tab->max_var = n_var;
75 tab->n_param = 0;
76 tab->n_div = 0;
77 tab->n_dead = 0;
78 tab->n_redundant = 0;
79 tab->strict_redundant = 0;
80 tab->need_undo = 0;
81 tab->rational = 0;
82 tab->empty = 0;
83 tab->in_undo = 0;
84 tab->M = M;
85 tab->cone = 0;
86 tab->bottom.type = isl_tab_undo_bottom;
87 tab->bottom.next = NULL;
88 tab->top = &tab->bottom;
89
90 tab->n_zero = 0;
91 tab->n_unbounded = 0;
92 tab->basis = NULL;
93
94 return tab;
95error:
96 isl_tab_free(tab);
97 return NULL;
98}
99
100isl_ctx *isl_tab_get_ctx(struct isl_tab *tab)
101{
102 return tab ? isl_mat_get_ctx(mat: tab->mat) : NULL;
103}
104
105int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new)
106{
107 unsigned off;
108
109 if (!tab)
110 return -1;
111
112 off = 2 + tab->M;
113
114 if (tab->max_con < tab->n_con + n_new) {
115 struct isl_tab_var *con;
116
117 con = isl_realloc_array(tab->mat->ctx, tab->con,
118 struct isl_tab_var, tab->max_con + n_new);
119 if (!con)
120 return -1;
121 tab->con = con;
122 tab->max_con += n_new;
123 }
124 if (tab->mat->n_row < tab->n_row + n_new) {
125 int *row_var;
126
127 tab->mat = isl_mat_extend(mat: tab->mat,
128 n_row: tab->n_row + n_new, n_col: off + tab->n_col);
129 if (!tab->mat)
130 return -1;
131 row_var = isl_realloc_array(tab->mat->ctx, tab->row_var,
132 int, tab->mat->n_row);
133 if (!row_var)
134 return -1;
135 tab->row_var = row_var;
136 if (tab->row_sign) {
137 enum isl_tab_row_sign *s;
138 s = isl_realloc_array(tab->mat->ctx, tab->row_sign,
139 enum isl_tab_row_sign, tab->mat->n_row);
140 if (!s)
141 return -1;
142 tab->row_sign = s;
143 }
144 }
145 return 0;
146}
147
148/* Make room for at least n_new extra variables.
149 * Return -1 if anything went wrong.
150 */
151int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new)
152{
153 struct isl_tab_var *var;
154 unsigned off = 2 + tab->M;
155
156 if (tab->max_var < tab->n_var + n_new) {
157 var = isl_realloc_array(tab->mat->ctx, tab->var,
158 struct isl_tab_var, tab->n_var + n_new);
159 if (!var)
160 return -1;
161 tab->var = var;
162 tab->max_var = tab->n_var + n_new;
163 }
164
165 if (tab->mat->n_col < off + tab->n_col + n_new) {
166 int *p;
167
168 tab->mat = isl_mat_extend(mat: tab->mat,
169 n_row: tab->mat->n_row, n_col: off + tab->n_col + n_new);
170 if (!tab->mat)
171 return -1;
172 p = isl_realloc_array(tab->mat->ctx, tab->col_var,
173 int, tab->n_col + n_new);
174 if (!p)
175 return -1;
176 tab->col_var = p;
177 }
178
179 return 0;
180}
181
182static void free_undo_record(struct isl_tab_undo *undo)
183{
184 switch (undo->type) {
185 case isl_tab_undo_saved_basis:
186 free(ptr: undo->u.col_var);
187 break;
188 default:;
189 }
190 free(ptr: undo);
191}
192
193static void free_undo(struct isl_tab *tab)
194{
195 struct isl_tab_undo *undo, *next;
196
197 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
198 next = undo->next;
199 free_undo_record(undo);
200 }
201 tab->top = undo;
202}
203
204void isl_tab_free(struct isl_tab *tab)
205{
206 if (!tab)
207 return;
208 free_undo(tab);
209 isl_mat_free(mat: tab->mat);
210 isl_vec_free(vec: tab->dual);
211 isl_basic_map_free(bmap: tab->bmap);
212 free(ptr: tab->var);
213 free(ptr: tab->con);
214 free(ptr: tab->row_var);
215 free(ptr: tab->col_var);
216 free(ptr: tab->row_sign);
217 isl_mat_free(mat: tab->samples);
218 free(ptr: tab->sample_index);
219 isl_mat_free(mat: tab->basis);
220 free(ptr: tab);
221}
222
223struct isl_tab *isl_tab_dup(struct isl_tab *tab)
224{
225 int i;
226 struct isl_tab *dup;
227 unsigned off;
228
229 if (!tab)
230 return NULL;
231
232 off = 2 + tab->M;
233 dup = isl_calloc_type(tab->mat->ctx, struct isl_tab);
234 if (!dup)
235 return NULL;
236 dup->mat = isl_mat_dup(mat: tab->mat);
237 if (!dup->mat)
238 goto error;
239 dup->var = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_var);
240 if (tab->max_var && !dup->var)
241 goto error;
242 for (i = 0; i < tab->n_var; ++i)
243 dup->var[i] = tab->var[i];
244 dup->con = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_con);
245 if (tab->max_con && !dup->con)
246 goto error;
247 for (i = 0; i < tab->n_con; ++i)
248 dup->con[i] = tab->con[i];
249 dup->col_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_col - off);
250 if ((tab->mat->n_col - off) && !dup->col_var)
251 goto error;
252 for (i = 0; i < tab->n_col; ++i)
253 dup->col_var[i] = tab->col_var[i];
254 dup->row_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_row);
255 if (tab->mat->n_row && !dup->row_var)
256 goto error;
257 for (i = 0; i < tab->n_row; ++i)
258 dup->row_var[i] = tab->row_var[i];
259 if (tab->row_sign) {
260 dup->row_sign = isl_alloc_array(tab->mat->ctx, enum isl_tab_row_sign,
261 tab->mat->n_row);
262 if (tab->mat->n_row && !dup->row_sign)
263 goto error;
264 for (i = 0; i < tab->n_row; ++i)
265 dup->row_sign[i] = tab->row_sign[i];
266 }
267 if (tab->samples) {
268 dup->samples = isl_mat_dup(mat: tab->samples);
269 if (!dup->samples)
270 goto error;
271 dup->sample_index = isl_alloc_array(tab->mat->ctx, int,
272 tab->samples->n_row);
273 if (tab->samples->n_row && !dup->sample_index)
274 goto error;
275 dup->n_sample = tab->n_sample;
276 dup->n_outside = tab->n_outside;
277 }
278 dup->n_row = tab->n_row;
279 dup->n_con = tab->n_con;
280 dup->n_eq = tab->n_eq;
281 dup->max_con = tab->max_con;
282 dup->n_col = tab->n_col;
283 dup->n_var = tab->n_var;
284 dup->max_var = tab->max_var;
285 dup->n_param = tab->n_param;
286 dup->n_div = tab->n_div;
287 dup->n_dead = tab->n_dead;
288 dup->n_redundant = tab->n_redundant;
289 dup->rational = tab->rational;
290 dup->empty = tab->empty;
291 dup->strict_redundant = 0;
292 dup->need_undo = 0;
293 dup->in_undo = 0;
294 dup->M = tab->M;
295 dup->cone = tab->cone;
296 dup->bottom.type = isl_tab_undo_bottom;
297 dup->bottom.next = NULL;
298 dup->top = &dup->bottom;
299
300 dup->n_zero = tab->n_zero;
301 dup->n_unbounded = tab->n_unbounded;
302 dup->basis = isl_mat_dup(mat: tab->basis);
303
304 return dup;
305error:
306 isl_tab_free(tab: dup);
307 return NULL;
308}
309
310/* Construct the coefficient matrix of the product tableau
311 * of two tableaus.
312 * mat{1,2} is the coefficient matrix of tableau {1,2}
313 * row{1,2} is the number of rows in tableau {1,2}
314 * col{1,2} is the number of columns in tableau {1,2}
315 * off is the offset to the coefficient column (skipping the
316 * denominator, the constant term and the big parameter if any)
317 * r{1,2} is the number of redundant rows in tableau {1,2}
318 * d{1,2} is the number of dead columns in tableau {1,2}
319 *
320 * The order of the rows and columns in the result is as explained
321 * in isl_tab_product.
322 */
323static __isl_give isl_mat *tab_mat_product(__isl_keep isl_mat *mat1,
324 __isl_keep isl_mat *mat2, unsigned row1, unsigned row2,
325 unsigned col1, unsigned col2,
326 unsigned off, unsigned r1, unsigned r2, unsigned d1, unsigned d2)
327{
328 int i;
329 struct isl_mat *prod;
330 unsigned n;
331
332 prod = isl_mat_alloc(ctx: mat1->ctx, n_row: mat1->n_row + mat2->n_row,
333 n_col: off + col1 + col2);
334 if (!prod)
335 return NULL;
336
337 n = 0;
338 for (i = 0; i < r1; ++i) {
339 isl_seq_cpy(dst: prod->row[n + i], src: mat1->row[i], len: off + d1);
340 isl_seq_clr(p: prod->row[n + i] + off + d1, len: d2);
341 isl_seq_cpy(dst: prod->row[n + i] + off + d1 + d2,
342 src: mat1->row[i] + off + d1, len: col1 - d1);
343 isl_seq_clr(p: prod->row[n + i] + off + col1 + d1, len: col2 - d2);
344 }
345
346 n += r1;
347 for (i = 0; i < r2; ++i) {
348 isl_seq_cpy(dst: prod->row[n + i], src: mat2->row[i], len: off);
349 isl_seq_clr(p: prod->row[n + i] + off, len: d1);
350 isl_seq_cpy(dst: prod->row[n + i] + off + d1,
351 src: mat2->row[i] + off, len: d2);
352 isl_seq_clr(p: prod->row[n + i] + off + d1 + d2, len: col1 - d1);
353 isl_seq_cpy(dst: prod->row[n + i] + off + col1 + d1,
354 src: mat2->row[i] + off + d2, len: col2 - d2);
355 }
356
357 n += r2;
358 for (i = 0; i < row1 - r1; ++i) {
359 isl_seq_cpy(dst: prod->row[n + i], src: mat1->row[r1 + i], len: off + d1);
360 isl_seq_clr(p: prod->row[n + i] + off + d1, len: d2);
361 isl_seq_cpy(dst: prod->row[n + i] + off + d1 + d2,
362 src: mat1->row[r1 + i] + off + d1, len: col1 - d1);
363 isl_seq_clr(p: prod->row[n + i] + off + col1 + d1, len: col2 - d2);
364 }
365
366 n += row1 - r1;
367 for (i = 0; i < row2 - r2; ++i) {
368 isl_seq_cpy(dst: prod->row[n + i], src: mat2->row[r2 + i], len: off);
369 isl_seq_clr(p: prod->row[n + i] + off, len: d1);
370 isl_seq_cpy(dst: prod->row[n + i] + off + d1,
371 src: mat2->row[r2 + i] + off, len: d2);
372 isl_seq_clr(p: prod->row[n + i] + off + d1 + d2, len: col1 - d1);
373 isl_seq_cpy(dst: prod->row[n + i] + off + col1 + d1,
374 src: mat2->row[r2 + i] + off + d2, len: col2 - d2);
375 }
376
377 return prod;
378}
379
380/* Update the row or column index of a variable that corresponds
381 * to a variable in the first input tableau.
382 */
383static void update_index1(struct isl_tab_var *var,
384 unsigned r1, unsigned r2, unsigned d1, unsigned d2)
385{
386 if (var->index == -1)
387 return;
388 if (var->is_row && var->index >= r1)
389 var->index += r2;
390 if (!var->is_row && var->index >= d1)
391 var->index += d2;
392}
393
394/* Update the row or column index of a variable that corresponds
395 * to a variable in the second input tableau.
396 */
397static void update_index2(struct isl_tab_var *var,
398 unsigned row1, unsigned col1,
399 unsigned r1, unsigned r2, unsigned d1, unsigned d2)
400{
401 if (var->index == -1)
402 return;
403 if (var->is_row) {
404 if (var->index < r2)
405 var->index += r1;
406 else
407 var->index += row1;
408 } else {
409 if (var->index < d2)
410 var->index += d1;
411 else
412 var->index += col1;
413 }
414}
415
416/* Create a tableau that represents the Cartesian product of the sets
417 * represented by tableaus tab1 and tab2.
418 * The order of the rows in the product is
419 * - redundant rows of tab1
420 * - redundant rows of tab2
421 * - non-redundant rows of tab1
422 * - non-redundant rows of tab2
423 * The order of the columns is
424 * - denominator
425 * - constant term
426 * - coefficient of big parameter, if any
427 * - dead columns of tab1
428 * - dead columns of tab2
429 * - live columns of tab1
430 * - live columns of tab2
431 * The order of the variables and the constraints is a concatenation
432 * of order in the two input tableaus.
433 */
434struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2)
435{
436 int i;
437 struct isl_tab *prod;
438 unsigned off;
439 unsigned r1, r2, d1, d2;
440
441 if (!tab1 || !tab2)
442 return NULL;
443
444 isl_assert(tab1->mat->ctx, tab1->M == tab2->M, return NULL);
445 isl_assert(tab1->mat->ctx, tab1->rational == tab2->rational, return NULL);
446 isl_assert(tab1->mat->ctx, tab1->cone == tab2->cone, return NULL);
447 isl_assert(tab1->mat->ctx, !tab1->row_sign, return NULL);
448 isl_assert(tab1->mat->ctx, !tab2->row_sign, return NULL);
449 isl_assert(tab1->mat->ctx, tab1->n_param == 0, return NULL);
450 isl_assert(tab1->mat->ctx, tab2->n_param == 0, return NULL);
451 isl_assert(tab1->mat->ctx, tab1->n_div == 0, return NULL);
452 isl_assert(tab1->mat->ctx, tab2->n_div == 0, return NULL);
453
454 off = 2 + tab1->M;
455 r1 = tab1->n_redundant;
456 r2 = tab2->n_redundant;
457 d1 = tab1->n_dead;
458 d2 = tab2->n_dead;
459 prod = isl_calloc_type(tab1->mat->ctx, struct isl_tab);
460 if (!prod)
461 return NULL;
462 prod->mat = tab_mat_product(mat1: tab1->mat, mat2: tab2->mat,
463 row1: tab1->n_row, row2: tab2->n_row,
464 col1: tab1->n_col, col2: tab2->n_col, off, r1, r2, d1, d2);
465 if (!prod->mat)
466 goto error;
467 prod->var = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
468 tab1->max_var + tab2->max_var);
469 if ((tab1->max_var + tab2->max_var) && !prod->var)
470 goto error;
471 for (i = 0; i < tab1->n_var; ++i) {
472 prod->var[i] = tab1->var[i];
473 update_index1(var: &prod->var[i], r1, r2, d1, d2);
474 }
475 for (i = 0; i < tab2->n_var; ++i) {
476 prod->var[tab1->n_var + i] = tab2->var[i];
477 update_index2(var: &prod->var[tab1->n_var + i],
478 row1: tab1->n_row, col1: tab1->n_col,
479 r1, r2, d1, d2);
480 }
481 prod->con = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
482 tab1->max_con + tab2->max_con);
483 if ((tab1->max_con + tab2->max_con) && !prod->con)
484 goto error;
485 for (i = 0; i < tab1->n_con; ++i) {
486 prod->con[i] = tab1->con[i];
487 update_index1(var: &prod->con[i], r1, r2, d1, d2);
488 }
489 for (i = 0; i < tab2->n_con; ++i) {
490 prod->con[tab1->n_con + i] = tab2->con[i];
491 update_index2(var: &prod->con[tab1->n_con + i],
492 row1: tab1->n_row, col1: tab1->n_col,
493 r1, r2, d1, d2);
494 }
495 prod->col_var = isl_alloc_array(tab1->mat->ctx, int,
496 tab1->n_col + tab2->n_col);
497 if ((tab1->n_col + tab2->n_col) && !prod->col_var)
498 goto error;
499 for (i = 0; i < tab1->n_col; ++i) {
500 int pos = i < d1 ? i : i + d2;
501 prod->col_var[pos] = tab1->col_var[i];
502 }
503 for (i = 0; i < tab2->n_col; ++i) {
504 int pos = i < d2 ? d1 + i : tab1->n_col + i;
505 int t = tab2->col_var[i];
506 if (t >= 0)
507 t += tab1->n_var;
508 else
509 t -= tab1->n_con;
510 prod->col_var[pos] = t;
511 }
512 prod->row_var = isl_alloc_array(tab1->mat->ctx, int,
513 tab1->mat->n_row + tab2->mat->n_row);
514 if ((tab1->mat->n_row + tab2->mat->n_row) && !prod->row_var)
515 goto error;
516 for (i = 0; i < tab1->n_row; ++i) {
517 int pos = i < r1 ? i : i + r2;
518 prod->row_var[pos] = tab1->row_var[i];
519 }
520 for (i = 0; i < tab2->n_row; ++i) {
521 int pos = i < r2 ? r1 + i : tab1->n_row + i;
522 int t = tab2->row_var[i];
523 if (t >= 0)
524 t += tab1->n_var;
525 else
526 t -= tab1->n_con;
527 prod->row_var[pos] = t;
528 }
529 prod->samples = NULL;
530 prod->sample_index = NULL;
531 prod->n_row = tab1->n_row + tab2->n_row;
532 prod->n_con = tab1->n_con + tab2->n_con;
533 prod->n_eq = 0;
534 prod->max_con = tab1->max_con + tab2->max_con;
535 prod->n_col = tab1->n_col + tab2->n_col;
536 prod->n_var = tab1->n_var + tab2->n_var;
537 prod->max_var = tab1->max_var + tab2->max_var;
538 prod->n_param = 0;
539 prod->n_div = 0;
540 prod->n_dead = tab1->n_dead + tab2->n_dead;
541 prod->n_redundant = tab1->n_redundant + tab2->n_redundant;
542 prod->rational = tab1->rational;
543 prod->empty = tab1->empty || tab2->empty;
544 prod->strict_redundant = tab1->strict_redundant || tab2->strict_redundant;
545 prod->need_undo = 0;
546 prod->in_undo = 0;
547 prod->M = tab1->M;
548 prod->cone = tab1->cone;
549 prod->bottom.type = isl_tab_undo_bottom;
550 prod->bottom.next = NULL;
551 prod->top = &prod->bottom;
552
553 prod->n_zero = 0;
554 prod->n_unbounded = 0;
555 prod->basis = NULL;
556
557 return prod;
558error:
559 isl_tab_free(tab: prod);
560 return NULL;
561}
562
563static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i)
564{
565 if (i >= 0)
566 return &tab->var[i];
567 else
568 return &tab->con[~i];
569}
570
571struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
572{
573 return var_from_index(tab, i: tab->row_var[i]);
574}
575
576static struct isl_tab_var *var_from_col(struct isl_tab *tab, int i)
577{
578 return var_from_index(tab, i: tab->col_var[i]);
579}
580
581/* Check if there are any upper bounds on column variable "var",
582 * i.e., non-negative rows where var appears with a negative coefficient.
583 * Return 1 if there are no such bounds.
584 */
585static int max_is_manifestly_unbounded(struct isl_tab *tab,
586 struct isl_tab_var *var)
587{
588 int i;
589 unsigned off = 2 + tab->M;
590
591 if (var->is_row)
592 return 0;
593 for (i = tab->n_redundant; i < tab->n_row; ++i) {
594 if (!isl_int_is_neg(tab->mat->row[i][off + var->index]))
595 continue;
596 if (isl_tab_var_from_row(tab, i)->is_nonneg)
597 return 0;
598 }
599 return 1;
600}
601
602/* Check if there are any lower bounds on column variable "var",
603 * i.e., non-negative rows where var appears with a positive coefficient.
604 * Return 1 if there are no such bounds.
605 */
606static int min_is_manifestly_unbounded(struct isl_tab *tab,
607 struct isl_tab_var *var)
608{
609 int i;
610 unsigned off = 2 + tab->M;
611
612 if (var->is_row)
613 return 0;
614 for (i = tab->n_redundant; i < tab->n_row; ++i) {
615 if (!isl_int_is_pos(tab->mat->row[i][off + var->index]))
616 continue;
617 if (isl_tab_var_from_row(tab, i)->is_nonneg)
618 return 0;
619 }
620 return 1;
621}
622
623static int row_cmp(struct isl_tab *tab, int r1, int r2, int c, isl_int *t)
624{
625 unsigned off = 2 + tab->M;
626
627 if (tab->M) {
628 int s;
629 isl_int_mul(*t, tab->mat->row[r1][2], tab->mat->row[r2][off+c]);
630 isl_int_submul(*t, tab->mat->row[r2][2], tab->mat->row[r1][off+c]);
631 s = isl_int_sgn(*t);
632 if (s)
633 return s;
634 }
635 isl_int_mul(*t, tab->mat->row[r1][1], tab->mat->row[r2][off + c]);
636 isl_int_submul(*t, tab->mat->row[r2][1], tab->mat->row[r1][off + c]);
637 return isl_int_sgn(*t);
638}
639
640/* Given the index of a column "c", return the index of a row
641 * that can be used to pivot the column in, with either an increase
642 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
643 * If "var" is not NULL, then the row returned will be different from
644 * the one associated with "var".
645 *
646 * Each row in the tableau is of the form
647 *
648 * x_r = a_r0 + \sum_i a_ri x_i
649 *
650 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
651 * impose any limit on the increase or decrease in the value of x_c
652 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
653 * for the row with the smallest (most stringent) such bound.
654 * Note that the common denominator of each row drops out of the fraction.
655 * To check if row j has a smaller bound than row r, i.e.,
656 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
657 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
658 * where -sign(a_jc) is equal to "sgn".
659 */
660static int pivot_row(struct isl_tab *tab,
661 struct isl_tab_var *var, int sgn, int c)
662{
663 int j, r, tsgn;
664 isl_int t;
665 unsigned off = 2 + tab->M;
666
667 isl_int_init(t);
668 r = -1;
669 for (j = tab->n_redundant; j < tab->n_row; ++j) {
670 if (var && j == var->index)
671 continue;
672 if (!isl_tab_var_from_row(tab, i: j)->is_nonneg)
673 continue;
674 if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
675 continue;
676 if (r < 0) {
677 r = j;
678 continue;
679 }
680 tsgn = sgn * row_cmp(tab, r1: r, r2: j, c, t: &t);
681 if (tsgn < 0 || (tsgn == 0 &&
682 tab->row_var[j] < tab->row_var[r]))
683 r = j;
684 }
685 isl_int_clear(t);
686 return r;
687}
688
689/* Find a pivot (row and col) that will increase (sgn > 0) or decrease
690 * (sgn < 0) the value of row variable var.
691 * If not NULL, then skip_var is a row variable that should be ignored
692 * while looking for a pivot row. It is usually equal to var.
693 *
694 * As the given row in the tableau is of the form
695 *
696 * x_r = a_r0 + \sum_i a_ri x_i
697 *
698 * we need to find a column such that the sign of a_ri is equal to "sgn"
699 * (such that an increase in x_i will have the desired effect) or a
700 * column with a variable that may attain negative values.
701 * If a_ri is positive, then we need to move x_i in the same direction
702 * to obtain the desired effect. Otherwise, x_i has to move in the
703 * opposite direction.
704 */
705static void find_pivot(struct isl_tab *tab,
706 struct isl_tab_var *var, struct isl_tab_var *skip_var,
707 int sgn, int *row, int *col)
708{
709 int j, r, c;
710 isl_int *tr;
711
712 *row = *col = -1;
713
714 isl_assert(tab->mat->ctx, var->is_row, return);
715 tr = tab->mat->row[var->index] + 2 + tab->M;
716
717 c = -1;
718 for (j = tab->n_dead; j < tab->n_col; ++j) {
719 if (isl_int_is_zero(tr[j]))
720 continue;
721 if (isl_int_sgn(tr[j]) != sgn &&
722 var_from_col(tab, i: j)->is_nonneg)
723 continue;
724 if (c < 0 || tab->col_var[j] < tab->col_var[c])
725 c = j;
726 }
727 if (c < 0)
728 return;
729
730 sgn *= isl_int_sgn(tr[c]);
731 r = pivot_row(tab, var: skip_var, sgn, c);
732 *row = r < 0 ? var->index : r;
733 *col = c;
734}
735
736/* Return 1 if row "row" represents an obviously redundant inequality.
737 * This means
738 * - it represents an inequality or a variable
739 * - that is the sum of a non-negative sample value and a positive
740 * combination of zero or more non-negative constraints.
741 */
742int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
743{
744 int i;
745 unsigned off = 2 + tab->M;
746
747 if (tab->row_var[row] < 0 && !isl_tab_var_from_row(tab, i: row)->is_nonneg)
748 return 0;
749
750 if (isl_int_is_neg(tab->mat->row[row][1]))
751 return 0;
752 if (tab->strict_redundant && isl_int_is_zero(tab->mat->row[row][1]))
753 return 0;
754 if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
755 return 0;
756
757 for (i = tab->n_dead; i < tab->n_col; ++i) {
758 if (isl_int_is_zero(tab->mat->row[row][off + i]))
759 continue;
760 if (tab->col_var[i] >= 0)
761 return 0;
762 if (isl_int_is_neg(tab->mat->row[row][off + i]))
763 return 0;
764 if (!var_from_col(tab, i)->is_nonneg)
765 return 0;
766 }
767 return 1;
768}
769
770static void swap_rows(struct isl_tab *tab, int row1, int row2)
771{
772 int t;
773 enum isl_tab_row_sign s;
774
775 t = tab->row_var[row1];
776 tab->row_var[row1] = tab->row_var[row2];
777 tab->row_var[row2] = t;
778 isl_tab_var_from_row(tab, i: row1)->index = row1;
779 isl_tab_var_from_row(tab, i: row2)->index = row2;
780 tab->mat = isl_mat_swap_rows(mat: tab->mat, i: row1, j: row2);
781
782 if (!tab->row_sign)
783 return;
784 s = tab->row_sign[row1];
785 tab->row_sign[row1] = tab->row_sign[row2];
786 tab->row_sign[row2] = s;
787}
788
789static isl_stat push_union(struct isl_tab *tab,
790 enum isl_tab_undo_type type, union isl_tab_undo_val u) WARN_UNUSED;
791
792/* Push record "u" onto the undo stack of "tab", provided "tab"
793 * keeps track of undo information.
794 *
795 * If the record cannot be pushed, then mark the undo stack as invalid
796 * such that a later rollback attempt will not try to undo earlier
797 * records without having been able to undo the current record.
798 */
799static isl_stat push_union(struct isl_tab *tab,
800 enum isl_tab_undo_type type, union isl_tab_undo_val u)
801{
802 struct isl_tab_undo *undo;
803
804 if (!tab)
805 return isl_stat_error;
806 if (!tab->need_undo)
807 return isl_stat_ok;
808
809 undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
810 if (!undo)
811 goto error;
812 undo->type = type;
813 undo->u = u;
814 undo->next = tab->top;
815 tab->top = undo;
816
817 return isl_stat_ok;
818error:
819 free_undo(tab);
820 tab->top = NULL;
821 return isl_stat_error;
822}
823
824isl_stat isl_tab_push_var(struct isl_tab *tab,
825 enum isl_tab_undo_type type, struct isl_tab_var *var)
826{
827 union isl_tab_undo_val u;
828 if (var->is_row)
829 u.var_index = tab->row_var[var->index];
830 else
831 u.var_index = tab->col_var[var->index];
832 return push_union(tab, type, u);
833}
834
835isl_stat isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
836{
837 union isl_tab_undo_val u = { 0 };
838 return push_union(tab, type, u);
839}
840
841/* Push a record on the undo stack describing the current basic
842 * variables, so that the this state can be restored during rollback.
843 */
844isl_stat isl_tab_push_basis(struct isl_tab *tab)
845{
846 int i;
847 union isl_tab_undo_val u;
848
849 u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
850 if (tab->n_col && !u.col_var)
851 return isl_stat_error;
852 for (i = 0; i < tab->n_col; ++i)
853 u.col_var[i] = tab->col_var[i];
854 return push_union(tab, type: isl_tab_undo_saved_basis, u);
855}
856
857isl_stat isl_tab_push_callback(struct isl_tab *tab,
858 struct isl_tab_callback *callback)
859{
860 union isl_tab_undo_val u;
861 u.callback = callback;
862 return push_union(tab, type: isl_tab_undo_callback, u);
863}
864
865struct isl_tab *isl_tab_init_samples(struct isl_tab *tab)
866{
867 if (!tab)
868 return NULL;
869
870 tab->n_sample = 0;
871 tab->n_outside = 0;
872 tab->samples = isl_mat_alloc(ctx: tab->mat->ctx, n_row: 1, n_col: 1 + tab->n_var);
873 if (!tab->samples)
874 goto error;
875 tab->sample_index = isl_alloc_array(tab->mat->ctx, int, 1);
876 if (!tab->sample_index)
877 goto error;
878 return tab;
879error:
880 isl_tab_free(tab);
881 return NULL;
882}
883
884int isl_tab_add_sample(struct isl_tab *tab, __isl_take isl_vec *sample)
885{
886 if (!tab || !sample)
887 goto error;
888
889 if (tab->n_sample + 1 > tab->samples->n_row) {
890 int *t = isl_realloc_array(tab->mat->ctx,
891 tab->sample_index, int, tab->n_sample + 1);
892 if (!t)
893 goto error;
894 tab->sample_index = t;
895 }
896
897 tab->samples = isl_mat_extend(mat: tab->samples,
898 n_row: tab->n_sample + 1, n_col: tab->samples->n_col);
899 if (!tab->samples)
900 goto error;
901
902 isl_seq_cpy(dst: tab->samples->row[tab->n_sample], src: sample->el, len: sample->size);
903 isl_vec_free(vec: sample);
904 tab->sample_index[tab->n_sample] = tab->n_sample;
905 tab->n_sample++;
906
907 return 0;
908error:
909 isl_vec_free(vec: sample);
910 return -1;
911}
912
913struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s)
914{
915 if (s != tab->n_outside) {
916 int t = tab->sample_index[tab->n_outside];
917 tab->sample_index[tab->n_outside] = tab->sample_index[s];
918 tab->sample_index[s] = t;
919 isl_mat_swap_rows(mat: tab->samples, i: tab->n_outside, j: s);
920 }
921 tab->n_outside++;
922 if (isl_tab_push(tab, type: isl_tab_undo_drop_sample) < 0) {
923 isl_tab_free(tab);
924 return NULL;
925 }
926
927 return tab;
928}
929
930/* Record the current number of samples so that we can remove newer
931 * samples during a rollback.
932 */
933isl_stat isl_tab_save_samples(struct isl_tab *tab)
934{
935 union isl_tab_undo_val u;
936
937 if (!tab)
938 return isl_stat_error;
939
940 u.n = tab->n_sample;
941 return push_union(tab, type: isl_tab_undo_saved_samples, u);
942}
943
944/* Mark row with index "row" as being redundant.
945 * If we may need to undo the operation or if the row represents
946 * a variable of the original problem, the row is kept,
947 * but no longer considered when looking for a pivot row.
948 * Otherwise, the row is simply removed.
949 *
950 * The row may be interchanged with some other row. If it
951 * is interchanged with a later row, return 1. Otherwise return 0.
952 * If the rows are checked in order in the calling function,
953 * then a return value of 1 means that the row with the given
954 * row number may now contain a different row that hasn't been checked yet.
955 */
956int isl_tab_mark_redundant(struct isl_tab *tab, int row)
957{
958 struct isl_tab_var *var = isl_tab_var_from_row(tab, i: row);
959 var->is_redundant = 1;
960 isl_assert(tab->mat->ctx, row >= tab->n_redundant, return -1);
961 if (tab->preserve || tab->need_undo || tab->row_var[row] >= 0) {
962 if (tab->row_var[row] >= 0 && !var->is_nonneg) {
963 var->is_nonneg = 1;
964 if (isl_tab_push_var(tab, type: isl_tab_undo_nonneg, var) < 0)
965 return -1;
966 }
967 if (row != tab->n_redundant)
968 swap_rows(tab, row1: row, row2: tab->n_redundant);
969 tab->n_redundant++;
970 return isl_tab_push_var(tab, type: isl_tab_undo_redundant, var);
971 } else {
972 if (row != tab->n_row - 1)
973 swap_rows(tab, row1: row, row2: tab->n_row - 1);
974 isl_tab_var_from_row(tab, i: tab->n_row - 1)->index = -1;
975 tab->n_row--;
976 return 1;
977 }
978}
979
980/* Mark "tab" as a rational tableau.
981 * If it wasn't marked as a rational tableau already and if we may
982 * need to undo changes, then arrange for the marking to be undone
983 * during the undo.
984 */
985int isl_tab_mark_rational(struct isl_tab *tab)
986{
987 if (!tab)
988 return -1;
989 if (!tab->rational && tab->need_undo)
990 if (isl_tab_push(tab, type: isl_tab_undo_rational) < 0)
991 return -1;
992 tab->rational = 1;
993 return 0;
994}
995
996isl_stat isl_tab_mark_empty(struct isl_tab *tab)
997{
998 if (!tab)
999 return isl_stat_error;
1000 if (!tab->empty && tab->need_undo)
1001 if (isl_tab_push(tab, type: isl_tab_undo_empty) < 0)
1002 return isl_stat_error;
1003 tab->empty = 1;
1004 return isl_stat_ok;
1005}
1006
1007int isl_tab_freeze_constraint(struct isl_tab *tab, int con)
1008{
1009 struct isl_tab_var *var;
1010
1011 if (!tab)
1012 return -1;
1013
1014 var = &tab->con[con];
1015 if (var->frozen)
1016 return 0;
1017 if (var->index < 0)
1018 return 0;
1019 var->frozen = 1;
1020
1021 if (tab->need_undo)
1022 return isl_tab_push_var(tab, type: isl_tab_undo_freeze, var);
1023
1024 return 0;
1025}
1026
1027/* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
1028 * the original sign of the pivot element.
1029 * We only keep track of row signs during PILP solving and in this case
1030 * we only pivot a row with negative sign (meaning the value is always
1031 * non-positive) using a positive pivot element.
1032 *
1033 * For each row j, the new value of the parametric constant is equal to
1034 *
1035 * a_j0 - a_jc a_r0/a_rc
1036 *
1037 * where a_j0 is the original parametric constant, a_rc is the pivot element,
1038 * a_r0 is the parametric constant of the pivot row and a_jc is the
1039 * pivot column entry of the row j.
1040 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
1041 * remains the same if a_jc has the same sign as the row j or if
1042 * a_jc is zero. In all other cases, we reset the sign to "unknown".
1043 */
1044static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
1045{
1046 int i;
1047 struct isl_mat *mat = tab->mat;
1048 unsigned off = 2 + tab->M;
1049
1050 if (!tab->row_sign)
1051 return;
1052
1053 if (tab->row_sign[row] == 0)
1054 return;
1055 isl_assert(mat->ctx, row_sgn > 0, return);
1056 isl_assert(mat->ctx, tab->row_sign[row] == isl_tab_row_neg, return);
1057 tab->row_sign[row] = isl_tab_row_pos;
1058 for (i = 0; i < tab->n_row; ++i) {
1059 int s;
1060 if (i == row)
1061 continue;
1062 s = isl_int_sgn(mat->row[i][off + col]);
1063 if (!s)
1064 continue;
1065 if (!tab->row_sign[i])
1066 continue;
1067 if (s < 0 && tab->row_sign[i] == isl_tab_row_neg)
1068 continue;
1069 if (s > 0 && tab->row_sign[i] == isl_tab_row_pos)
1070 continue;
1071 tab->row_sign[i] = isl_tab_row_unknown;
1072 }
1073}
1074
1075/* Given a row number "row" and a column number "col", pivot the tableau
1076 * such that the associated variables are interchanged.
1077 * The given row in the tableau expresses
1078 *
1079 * x_r = a_r0 + \sum_i a_ri x_i
1080 *
1081 * or
1082 *
1083 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
1084 *
1085 * Substituting this equality into the other rows
1086 *
1087 * x_j = a_j0 + \sum_i a_ji x_i
1088 *
1089 * with a_jc \ne 0, we obtain
1090 *
1091 * 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
1092 *
1093 * The tableau
1094 *
1095 * n_rc/d_r n_ri/d_r
1096 * n_jc/d_j n_ji/d_j
1097 *
1098 * where i is any other column and j is any other row,
1099 * is therefore transformed into
1100 *
1101 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1102 * 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)
1103 *
1104 * The transformation is performed along the following steps
1105 *
1106 * d_r/n_rc n_ri/n_rc
1107 * n_jc/d_j n_ji/d_j
1108 *
1109 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1110 * n_jc/d_j n_ji/d_j
1111 *
1112 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1113 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
1114 *
1115 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1116 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
1117 *
1118 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1119 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
1120 *
1121 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1122 * 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)
1123 *
1124 */
1125int isl_tab_pivot(struct isl_tab *tab, int row, int col)
1126{
1127 int i, j;
1128 int sgn;
1129 int t;
1130 isl_ctx *ctx;
1131 struct isl_mat *mat = tab->mat;
1132 struct isl_tab_var *var;
1133 unsigned off = 2 + tab->M;
1134
1135 ctx = isl_tab_get_ctx(tab);
1136 if (isl_ctx_next_operation(ctx) < 0)
1137 return -1;
1138
1139 isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
1140 sgn = isl_int_sgn(mat->row[row][0]);
1141 if (sgn < 0) {
1142 isl_int_neg(mat->row[row][0], mat->row[row][0]);
1143 isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]);
1144 } else
1145 for (j = 0; j < off - 1 + tab->n_col; ++j) {
1146 if (j == off - 1 + col)
1147 continue;
1148 isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
1149 }
1150 if (!isl_int_is_one(mat->row[row][0]))
1151 isl_seq_normalize(ctx: mat->ctx, p: mat->row[row], len: off + tab->n_col);
1152 for (i = 0; i < tab->n_row; ++i) {
1153 if (i == row)
1154 continue;
1155 if (isl_int_is_zero(mat->row[i][off + col]))
1156 continue;
1157 isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
1158 for (j = 0; j < off - 1 + tab->n_col; ++j) {
1159 if (j == off - 1 + col)
1160 continue;
1161 isl_int_mul(mat->row[i][1 + j],
1162 mat->row[i][1 + j], mat->row[row][0]);
1163 isl_int_addmul(mat->row[i][1 + j],
1164 mat->row[i][off + col], mat->row[row][1 + j]);
1165 }
1166 isl_int_mul(mat->row[i][off + col],
1167 mat->row[i][off + col], mat->row[row][off + col]);
1168 if (!isl_int_is_one(mat->row[i][0]))
1169 isl_seq_normalize(ctx: mat->ctx, p: mat->row[i], len: off + tab->n_col);
1170 }
1171 t = tab->row_var[row];
1172 tab->row_var[row] = tab->col_var[col];
1173 tab->col_var[col] = t;
1174 var = isl_tab_var_from_row(tab, i: row);
1175 var->is_row = 1;
1176 var->index = row;
1177 var = var_from_col(tab, i: col);
1178 var->is_row = 0;
1179 var->index = col;
1180 update_row_sign(tab, row, col, row_sgn: sgn);
1181 if (tab->in_undo)
1182 return 0;
1183 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1184 if (isl_int_is_zero(mat->row[i][off + col]))
1185 continue;
1186 if (!isl_tab_var_from_row(tab, i)->frozen &&
1187 isl_tab_row_is_redundant(tab, row: i)) {
1188 int redo = isl_tab_mark_redundant(tab, row: i);
1189 if (redo < 0)
1190 return -1;
1191 if (redo)
1192 --i;
1193 }
1194 }
1195 return 0;
1196}
1197
1198/* If "var" represents a column variable, then pivot is up (sgn > 0)
1199 * or down (sgn < 0) to a row. The variable is assumed not to be
1200 * unbounded in the specified direction.
1201 * If sgn = 0, then the variable is unbounded in both directions,
1202 * and we pivot with any row we can find.
1203 */
1204static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign) WARN_UNUSED;
1205static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
1206{
1207 int r;
1208 unsigned off = 2 + tab->M;
1209
1210 if (var->is_row)
1211 return 0;
1212
1213 if (sign == 0) {
1214 for (r = tab->n_redundant; r < tab->n_row; ++r)
1215 if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
1216 break;
1217 isl_assert(tab->mat->ctx, r < tab->n_row, return -1);
1218 } else {
1219 r = pivot_row(tab, NULL, sgn: sign, c: var->index);
1220 isl_assert(tab->mat->ctx, r >= 0, return -1);
1221 }
1222
1223 return isl_tab_pivot(tab, row: r, col: var->index);
1224}
1225
1226/* Check whether all variables that are marked as non-negative
1227 * also have a non-negative sample value. This function is not
1228 * called from the current code but is useful during debugging.
1229 */
1230static void check_table(struct isl_tab *tab) __attribute__ ((unused));
1231static void check_table(struct isl_tab *tab)
1232{
1233 int i;
1234
1235 if (tab->empty)
1236 return;
1237 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1238 struct isl_tab_var *var;
1239 var = isl_tab_var_from_row(tab, i);
1240 if (!var->is_nonneg)
1241 continue;
1242 if (tab->M) {
1243 isl_assert(tab->mat->ctx,
1244 !isl_int_is_neg(tab->mat->row[i][2]), abort());
1245 if (isl_int_is_pos(tab->mat->row[i][2]))
1246 continue;
1247 }
1248 isl_assert(tab->mat->ctx, !isl_int_is_neg(tab->mat->row[i][1]),
1249 abort());
1250 }
1251}
1252
1253/* Return the sign of the maximal value of "var".
1254 * If the sign is not negative, then on return from this function,
1255 * the sample value will also be non-negative.
1256 *
1257 * If "var" is manifestly unbounded wrt positive values, we are done.
1258 * Otherwise, we pivot the variable up to a row if needed.
1259 * Then we continue pivoting up until either
1260 * - no more up pivots can be performed
1261 * - the sample value is positive
1262 * - the variable is pivoted into a manifestly unbounded column
1263 */
1264static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
1265{
1266 int row, col;
1267
1268 if (max_is_manifestly_unbounded(tab, var))
1269 return 1;
1270 if (to_row(tab, var, sign: 1) < 0)
1271 return -2;
1272 while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
1273 find_pivot(tab, var, skip_var: var, sgn: 1, row: &row, col: &col);
1274 if (row == -1)
1275 return isl_int_sgn(tab->mat->row[var->index][1]);
1276 if (isl_tab_pivot(tab, row, col) < 0)
1277 return -2;
1278 if (!var->is_row) /* manifestly unbounded */
1279 return 1;
1280 }
1281 return 1;
1282}
1283
1284int isl_tab_sign_of_max(struct isl_tab *tab, int con)
1285{
1286 struct isl_tab_var *var;
1287
1288 if (!tab)
1289 return -2;
1290
1291 var = &tab->con[con];
1292 isl_assert(tab->mat->ctx, !var->is_redundant, return -2);
1293 isl_assert(tab->mat->ctx, !var->is_zero, return -2);
1294
1295 return sign_of_max(tab, var);
1296}
1297
1298static int row_is_neg(struct isl_tab *tab, int row)
1299{
1300 if (!tab->M)
1301 return isl_int_is_neg(tab->mat->row[row][1]);
1302 if (isl_int_is_pos(tab->mat->row[row][2]))
1303 return 0;
1304 if (isl_int_is_neg(tab->mat->row[row][2]))
1305 return 1;
1306 return isl_int_is_neg(tab->mat->row[row][1]);
1307}
1308
1309static int row_sgn(struct isl_tab *tab, int row)
1310{
1311 if (!tab->M)
1312 return isl_int_sgn(tab->mat->row[row][1]);
1313 if (!isl_int_is_zero(tab->mat->row[row][2]))
1314 return isl_int_sgn(tab->mat->row[row][2]);
1315 else
1316 return isl_int_sgn(tab->mat->row[row][1]);
1317}
1318
1319/* Perform pivots until the row variable "var" has a non-negative
1320 * sample value or until no more upward pivots can be performed.
1321 * Return the sign of the sample value after the pivots have been
1322 * performed.
1323 */
1324static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
1325{
1326 int row, col;
1327
1328 while (row_is_neg(tab, row: var->index)) {
1329 find_pivot(tab, var, skip_var: var, sgn: 1, row: &row, col: &col);
1330 if (row == -1)
1331 break;
1332 if (isl_tab_pivot(tab, row, col) < 0)
1333 return -2;
1334 if (!var->is_row) /* manifestly unbounded */
1335 return 1;
1336 }
1337 return row_sgn(tab, row: var->index);
1338}
1339
1340/* Perform pivots until we are sure that the row variable "var"
1341 * can attain non-negative values. After return from this
1342 * function, "var" is still a row variable, but its sample
1343 * value may not be non-negative, even if the function returns 1.
1344 */
1345static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
1346{
1347 int row, col;
1348
1349 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
1350 find_pivot(tab, var, skip_var: var, sgn: 1, row: &row, col: &col);
1351 if (row == -1)
1352 break;
1353 if (row == var->index) /* manifestly unbounded */
1354 return 1;
1355 if (isl_tab_pivot(tab, row, col) < 0)
1356 return -1;
1357 }
1358 return !isl_int_is_neg(tab->mat->row[var->index][1]);
1359}
1360
1361/* Return a negative value if "var" can attain negative values.
1362 * Return a non-negative value otherwise.
1363 *
1364 * If "var" is manifestly unbounded wrt negative values, we are done.
1365 * Otherwise, if var is in a column, we can pivot it down to a row.
1366 * Then we continue pivoting down until either
1367 * - the pivot would result in a manifestly unbounded column
1368 * => we don't perform the pivot, but simply return -1
1369 * - no more down pivots can be performed
1370 * - the sample value is negative
1371 * If the sample value becomes negative and the variable is supposed
1372 * to be nonnegative, then we undo the last pivot.
1373 * However, if the last pivot has made the pivoting variable
1374 * obviously redundant, then it may have moved to another row.
1375 * In that case we look for upward pivots until we reach a non-negative
1376 * value again.
1377 */
1378static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
1379{
1380 int row, col;
1381 struct isl_tab_var *pivot_var = NULL;
1382
1383 if (min_is_manifestly_unbounded(tab, var))
1384 return -1;
1385 if (!var->is_row) {
1386 col = var->index;
1387 row = pivot_row(tab, NULL, sgn: -1, c: col);
1388 pivot_var = var_from_col(tab, i: col);
1389 if (isl_tab_pivot(tab, row, col) < 0)
1390 return -2;
1391 if (var->is_redundant)
1392 return 0;
1393 if (isl_int_is_neg(tab->mat->row[var->index][1])) {
1394 if (var->is_nonneg) {
1395 if (!pivot_var->is_redundant &&
1396 pivot_var->index == row) {
1397 if (isl_tab_pivot(tab, row, col) < 0)
1398 return -2;
1399 } else
1400 if (restore_row(tab, var) < -1)
1401 return -2;
1402 }
1403 return -1;
1404 }
1405 }
1406 if (var->is_redundant)
1407 return 0;
1408 while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
1409 find_pivot(tab, var, skip_var: var, sgn: -1, row: &row, col: &col);
1410 if (row == var->index)
1411 return -1;
1412 if (row == -1)
1413 return isl_int_sgn(tab->mat->row[var->index][1]);
1414 pivot_var = var_from_col(tab, i: col);
1415 if (isl_tab_pivot(tab, row, col) < 0)
1416 return -2;
1417 if (var->is_redundant)
1418 return 0;
1419 }
1420 if (pivot_var && var->is_nonneg) {
1421 /* pivot back to non-negative value */
1422 if (!pivot_var->is_redundant && pivot_var->index == row) {
1423 if (isl_tab_pivot(tab, row, col) < 0)
1424 return -2;
1425 } else
1426 if (restore_row(tab, var) < -1)
1427 return -2;
1428 }
1429 return -1;
1430}
1431
1432static int row_at_most_neg_one(struct isl_tab *tab, int row)
1433{
1434 if (tab->M) {
1435 if (isl_int_is_pos(tab->mat->row[row][2]))
1436 return 0;
1437 if (isl_int_is_neg(tab->mat->row[row][2]))
1438 return 1;
1439 }
1440 return isl_int_is_neg(tab->mat->row[row][1]) &&
1441 isl_int_abs_ge(tab->mat->row[row][1],
1442 tab->mat->row[row][0]);
1443}
1444
1445/* Return 1 if "var" can attain values <= -1.
1446 * Return 0 otherwise.
1447 *
1448 * If the variable "var" is supposed to be non-negative (is_nonneg is set),
1449 * then the sample value of "var" is assumed to be non-negative when the
1450 * the function is called. If 1 is returned then the constraint
1451 * is not redundant and the sample value is made non-negative again before
1452 * the function returns.
1453 */
1454int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
1455{
1456 int row, col;
1457 struct isl_tab_var *pivot_var;
1458
1459 if (min_is_manifestly_unbounded(tab, var))
1460 return 1;
1461 if (!var->is_row) {
1462 col = var->index;
1463 row = pivot_row(tab, NULL, sgn: -1, c: col);
1464 pivot_var = var_from_col(tab, i: col);
1465 if (isl_tab_pivot(tab, row, col) < 0)
1466 return -1;
1467 if (var->is_redundant)
1468 return 0;
1469 if (row_at_most_neg_one(tab, row: var->index)) {
1470 if (var->is_nonneg) {
1471 if (!pivot_var->is_redundant &&
1472 pivot_var->index == row) {
1473 if (isl_tab_pivot(tab, row, col) < 0)
1474 return -1;
1475 } else
1476 if (restore_row(tab, var) < -1)
1477 return -1;
1478 }
1479 return 1;
1480 }
1481 }
1482 if (var->is_redundant)
1483 return 0;
1484 do {
1485 find_pivot(tab, var, skip_var: var, sgn: -1, row: &row, col: &col);
1486 if (row == var->index) {
1487 if (var->is_nonneg && restore_row(tab, var) < -1)
1488 return -1;
1489 return 1;
1490 }
1491 if (row == -1)
1492 return 0;
1493 pivot_var = var_from_col(tab, i: col);
1494 if (isl_tab_pivot(tab, row, col) < 0)
1495 return -1;
1496 if (var->is_redundant)
1497 return 0;
1498 } while (!row_at_most_neg_one(tab, row: var->index));
1499 if (var->is_nonneg) {
1500 /* pivot back to non-negative value */
1501 if (!pivot_var->is_redundant && pivot_var->index == row)
1502 if (isl_tab_pivot(tab, row, col) < 0)
1503 return -1;
1504 if (restore_row(tab, var) < -1)
1505 return -1;
1506 }
1507 return 1;
1508}
1509
1510/* Return 1 if "var" can attain values >= 1.
1511 * Return 0 otherwise.
1512 */
1513static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
1514{
1515 int row, col;
1516 isl_int *r;
1517
1518 if (max_is_manifestly_unbounded(tab, var))
1519 return 1;
1520 if (to_row(tab, var, sign: 1) < 0)
1521 return -1;
1522 r = tab->mat->row[var->index];
1523 while (isl_int_lt(r[1], r[0])) {
1524 find_pivot(tab, var, skip_var: var, sgn: 1, row: &row, col: &col);
1525 if (row == -1)
1526 return isl_int_ge(r[1], r[0]);
1527 if (row == var->index) /* manifestly unbounded */
1528 return 1;
1529 if (isl_tab_pivot(tab, row, col) < 0)
1530 return -1;
1531 }
1532 return 1;
1533}
1534
1535static void swap_cols(struct isl_tab *tab, int col1, int col2)
1536{
1537 int t;
1538 unsigned off = 2 + tab->M;
1539 t = tab->col_var[col1];
1540 tab->col_var[col1] = tab->col_var[col2];
1541 tab->col_var[col2] = t;
1542 var_from_col(tab, i: col1)->index = col1;
1543 var_from_col(tab, i: col2)->index = col2;
1544 tab->mat = isl_mat_swap_cols(mat: tab->mat, i: off + col1, j: off + col2);
1545}
1546
1547/* Mark column with index "col" as representing a zero variable.
1548 * If we may need to undo the operation the column is kept,
1549 * but no longer considered.
1550 * Otherwise, the column is simply removed.
1551 *
1552 * The column may be interchanged with some other column. If it
1553 * is interchanged with a later column, return 1. Otherwise return 0.
1554 * If the columns are checked in order in the calling function,
1555 * then a return value of 1 means that the column with the given
1556 * column number may now contain a different column that
1557 * hasn't been checked yet.
1558 */
1559int isl_tab_kill_col(struct isl_tab *tab, int col)
1560{
1561 var_from_col(tab, i: col)->is_zero = 1;
1562 if (tab->need_undo) {
1563 if (isl_tab_push_var(tab, type: isl_tab_undo_zero,
1564 var: var_from_col(tab, i: col)) < 0)
1565 return -1;
1566 if (col != tab->n_dead)
1567 swap_cols(tab, col1: col, col2: tab->n_dead);
1568 tab->n_dead++;
1569 return 0;
1570 } else {
1571 if (col != tab->n_col - 1)
1572 swap_cols(tab, col1: col, col2: tab->n_col - 1);
1573 var_from_col(tab, i: tab->n_col - 1)->index = -1;
1574 tab->n_col--;
1575 return 1;
1576 }
1577}
1578
1579static int row_is_manifestly_non_integral(struct isl_tab *tab, int row)
1580{
1581 unsigned off = 2 + tab->M;
1582
1583 if (tab->M && !isl_int_eq(tab->mat->row[row][2],
1584 tab->mat->row[row][0]))
1585 return 0;
1586 if (isl_seq_first_non_zero(p: tab->mat->row[row] + off + tab->n_dead,
1587 len: tab->n_col - tab->n_dead) != -1)
1588 return 0;
1589
1590 return !isl_int_is_divisible_by(tab->mat->row[row][1],
1591 tab->mat->row[row][0]);
1592}
1593
1594/* For integer tableaus, check if any of the coordinates are stuck
1595 * at a non-integral value.
1596 */
1597static int tab_is_manifestly_empty(struct isl_tab *tab)
1598{
1599 int i;
1600
1601 if (tab->empty)
1602 return 1;
1603 if (tab->rational)
1604 return 0;
1605
1606 for (i = 0; i < tab->n_var; ++i) {
1607 if (!tab->var[i].is_row)
1608 continue;
1609 if (row_is_manifestly_non_integral(tab, row: tab->var[i].index))
1610 return 1;
1611 }
1612
1613 return 0;
1614}
1615
1616/* Row variable "var" is non-negative and cannot attain any values
1617 * larger than zero. This means that the coefficients of the unrestricted
1618 * column variables are zero and that the coefficients of the non-negative
1619 * column variables are zero or negative.
1620 * Each of the non-negative variables with a negative coefficient can
1621 * then also be written as the negative sum of non-negative variables
1622 * and must therefore also be zero.
1623 *
1624 * If "temp_var" is set, then "var" is a temporary variable that
1625 * will be removed after this function returns and for which
1626 * no information is recorded on the undo stack.
1627 * Do not add any undo records involving this variable in this case
1628 * since the variable will have been removed before any future undo
1629 * operations. Also avoid marking the variable as redundant,
1630 * since that either adds an undo record or needlessly removes the row
1631 * (the caller will take care of removing the row).
1632 */
1633static isl_stat close_row(struct isl_tab *tab, struct isl_tab_var *var,
1634 int temp_var) WARN_UNUSED;
1635static isl_stat close_row(struct isl_tab *tab, struct isl_tab_var *var,
1636 int temp_var)
1637{
1638 int j;
1639 struct isl_mat *mat = tab->mat;
1640 unsigned off = 2 + tab->M;
1641
1642 if (!var->is_nonneg)
1643 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
1644 "expecting non-negative variable",
1645 return isl_stat_error);
1646 var->is_zero = 1;
1647 if (!temp_var && tab->need_undo)
1648 if (isl_tab_push_var(tab, type: isl_tab_undo_zero, var) < 0)
1649 return isl_stat_error;
1650 for (j = tab->n_dead; j < tab->n_col; ++j) {
1651 int recheck;
1652 if (isl_int_is_zero(mat->row[var->index][off + j]))
1653 continue;
1654 if (isl_int_is_pos(mat->row[var->index][off + j]))
1655 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
1656 "row cannot have positive coefficients",
1657 return isl_stat_error);
1658 recheck = isl_tab_kill_col(tab, col: j);
1659 if (recheck < 0)
1660 return isl_stat_error;
1661 if (recheck)
1662 --j;
1663 }
1664 if (!temp_var && isl_tab_mark_redundant(tab, row: var->index) < 0)
1665 return isl_stat_error;
1666 if (tab_is_manifestly_empty(tab) && isl_tab_mark_empty(tab) < 0)
1667 return isl_stat_error;
1668 return isl_stat_ok;
1669}
1670
1671/* Add a constraint to the tableau and allocate a row for it.
1672 * Return the index into the constraint array "con".
1673 *
1674 * This function assumes that at least one more row and at least
1675 * one more element in the constraint array are available in the tableau.
1676 */
1677int isl_tab_allocate_con(struct isl_tab *tab)
1678{
1679 int r;
1680
1681 isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
1682 isl_assert(tab->mat->ctx, tab->n_con < tab->max_con, return -1);
1683
1684 r = tab->n_con;
1685 tab->con[r].index = tab->n_row;
1686 tab->con[r].is_row = 1;
1687 tab->con[r].is_nonneg = 0;
1688 tab->con[r].is_zero = 0;
1689 tab->con[r].is_redundant = 0;
1690 tab->con[r].frozen = 0;
1691 tab->con[r].negated = 0;
1692 tab->row_var[tab->n_row] = ~r;
1693
1694 tab->n_row++;
1695 tab->n_con++;
1696 if (isl_tab_push_var(tab, type: isl_tab_undo_allocate, var: &tab->con[r]) < 0)
1697 return -1;
1698
1699 return r;
1700}
1701
1702/* Move the entries in tab->var up one position, starting at "first",
1703 * creating room for an extra entry at position "first".
1704 * Since some of the entries of tab->row_var and tab->col_var contain
1705 * indices into this array, they have to be updated accordingly.
1706 */
1707static int var_insert_entry(struct isl_tab *tab, int first)
1708{
1709 int i;
1710
1711 if (tab->n_var >= tab->max_var)
1712 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
1713 "not enough room for new variable", return -1);
1714 if (first > tab->n_var)
1715 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
1716 "invalid initial position", return -1);
1717
1718 for (i = tab->n_var - 1; i >= first; --i) {
1719 tab->var[i + 1] = tab->var[i];
1720 if (tab->var[i + 1].is_row)
1721 tab->row_var[tab->var[i + 1].index]++;
1722 else
1723 tab->col_var[tab->var[i + 1].index]++;
1724 }
1725
1726 tab->n_var++;
1727
1728 return 0;
1729}
1730
1731/* Drop the entry at position "first" in tab->var, moving all
1732 * subsequent entries down.
1733 * Since some of the entries of tab->row_var and tab->col_var contain
1734 * indices into this array, they have to be updated accordingly.
1735 */
1736static int var_drop_entry(struct isl_tab *tab, int first)
1737{
1738 int i;
1739
1740 if (first >= tab->n_var)
1741 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
1742 "invalid initial position", return -1);
1743
1744 tab->n_var--;
1745
1746 for (i = first; i < tab->n_var; ++i) {
1747 tab->var[i] = tab->var[i + 1];
1748 if (tab->var[i + 1].is_row)
1749 tab->row_var[tab->var[i].index]--;
1750 else
1751 tab->col_var[tab->var[i].index]--;
1752 }
1753
1754 return 0;
1755}
1756
1757/* Add a variable to the tableau at position "r" and allocate a column for it.
1758 * Return the index into the variable array "var", i.e., "r",
1759 * or -1 on error.
1760 */
1761int isl_tab_insert_var(struct isl_tab *tab, int r)
1762{
1763 int i;
1764 unsigned off = 2 + tab->M;
1765
1766 isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
1767
1768 if (var_insert_entry(tab, first: r) < 0)
1769 return -1;
1770
1771 tab->var[r].index = tab->n_col;
1772 tab->var[r].is_row = 0;
1773 tab->var[r].is_nonneg = 0;
1774 tab->var[r].is_zero = 0;
1775 tab->var[r].is_redundant = 0;
1776 tab->var[r].frozen = 0;
1777 tab->var[r].negated = 0;
1778 tab->col_var[tab->n_col] = r;
1779
1780 for (i = 0; i < tab->n_row; ++i)
1781 isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
1782
1783 tab->n_col++;
1784 if (isl_tab_push_var(tab, type: isl_tab_undo_allocate, var: &tab->var[r]) < 0)
1785 return -1;
1786
1787 return r;
1788}
1789
1790/* Add a row to the tableau. The row is given as an affine combination
1791 * of the original variables and needs to be expressed in terms of the
1792 * column variables.
1793 *
1794 * This function assumes that at least one more row and at least
1795 * one more element in the constraint array are available in the tableau.
1796 *
1797 * We add each term in turn.
1798 * If r = n/d_r is the current sum and we need to add k x, then
1799 * if x is a column variable, we increase the numerator of
1800 * this column by k d_r
1801 * if x = f/d_x is a row variable, then the new representation of r is
1802 *
1803 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1804 * --- + --- = ------------------- = -------------------
1805 * d_r d_r d_r d_x/g m
1806 *
1807 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1808 *
1809 * If tab->M is set, then, internally, each variable x is represented
1810 * as x' - M. We then also need no subtract k d_r from the coefficient of M.
1811 */
1812int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
1813{
1814 int i;
1815 int r;
1816 isl_int *row;
1817 isl_int a, b;
1818 unsigned off = 2 + tab->M;
1819
1820 r = isl_tab_allocate_con(tab);
1821 if (r < 0)
1822 return -1;
1823
1824 isl_int_init(a);
1825 isl_int_init(b);
1826 row = tab->mat->row[tab->con[r].index];
1827 isl_int_set_si(row[0], 1);
1828 isl_int_set(row[1], line[0]);
1829 isl_seq_clr(p: row + 2, len: tab->M + tab->n_col);
1830 for (i = 0; i < tab->n_var; ++i) {
1831 if (tab->var[i].is_zero)
1832 continue;
1833 if (tab->var[i].is_row) {
1834 isl_int_lcm(a,
1835 row[0], tab->mat->row[tab->var[i].index][0]);
1836 isl_int_swap(a, row[0]);
1837 isl_int_divexact(a, row[0], a);
1838 isl_int_divexact(b,
1839 row[0], tab->mat->row[tab->var[i].index][0]);
1840 isl_int_mul(b, b, line[1 + i]);
1841 isl_seq_combine(dst: row + 1, m1: a, src1: row + 1,
1842 m2: b, src2: tab->mat->row[tab->var[i].index] + 1,
1843 len: 1 + tab->M + tab->n_col);
1844 } else
1845 isl_int_addmul(row[off + tab->var[i].index],
1846 line[1 + i], row[0]);
1847 if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
1848 isl_int_submul(row[2], line[1 + i], row[0]);
1849 }
1850 isl_seq_normalize(ctx: tab->mat->ctx, p: row, len: off + tab->n_col);
1851 isl_int_clear(a);
1852 isl_int_clear(b);
1853
1854 if (tab->row_sign)
1855 tab->row_sign[tab->con[r].index] = isl_tab_row_unknown;
1856
1857 return r;
1858}
1859
1860static isl_stat drop_row(struct isl_tab *tab, int row)
1861{
1862 isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1,
1863 return isl_stat_error);
1864 if (row != tab->n_row - 1)
1865 swap_rows(tab, row1: row, row2: tab->n_row - 1);
1866 tab->n_row--;
1867 tab->n_con--;
1868 return isl_stat_ok;
1869}
1870
1871/* Drop the variable in column "col" along with the column.
1872 * The column is removed first because it may need to be moved
1873 * into the last position and this process requires
1874 * the contents of the col_var array in a state
1875 * before the removal of the variable.
1876 */
1877static isl_stat drop_col(struct isl_tab *tab, int col)
1878{
1879 int var;
1880
1881 var = tab->col_var[col];
1882 if (col != tab->n_col - 1)
1883 swap_cols(tab, col1: col, col2: tab->n_col - 1);
1884 tab->n_col--;
1885 if (var_drop_entry(tab, first: var) < 0)
1886 return isl_stat_error;
1887 return isl_stat_ok;
1888}
1889
1890/* Add inequality "ineq" and check if it conflicts with the
1891 * previously added constraints or if it is obviously redundant.
1892 *
1893 * This function assumes that at least one more row and at least
1894 * one more element in the constraint array are available in the tableau.
1895 */
1896isl_stat isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
1897{
1898 int r;
1899 int sgn;
1900 isl_int cst;
1901
1902 if (!tab)
1903 return isl_stat_error;
1904 if (tab->bmap) {
1905 struct isl_basic_map *bmap = tab->bmap;
1906
1907 isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq,
1908 return isl_stat_error);
1909 isl_assert(tab->mat->ctx,
1910 tab->n_con == bmap->n_eq + bmap->n_ineq,
1911 return isl_stat_error);
1912 tab->bmap = isl_basic_map_add_ineq(bmap: tab->bmap, ineq);
1913 if (isl_tab_push(tab, type: isl_tab_undo_bmap_ineq) < 0)
1914 return isl_stat_error;
1915 if (!tab->bmap)
1916 return isl_stat_error;
1917 }
1918 if (tab->cone) {
1919 isl_int_init(cst);
1920 isl_int_set_si(cst, 0);
1921 isl_int_swap(ineq[0], cst);
1922 }
1923 r = isl_tab_add_row(tab, line: ineq);
1924 if (tab->cone) {
1925 isl_int_swap(ineq[0], cst);
1926 isl_int_clear(cst);
1927 }
1928 if (r < 0)
1929 return isl_stat_error;
1930 tab->con[r].is_nonneg = 1;
1931 if (isl_tab_push_var(tab, type: isl_tab_undo_nonneg, var: &tab->con[r]) < 0)
1932 return isl_stat_error;
1933 if (isl_tab_row_is_redundant(tab, row: tab->con[r].index)) {
1934 if (isl_tab_mark_redundant(tab, row: tab->con[r].index) < 0)
1935 return isl_stat_error;
1936 return isl_stat_ok;
1937 }
1938
1939 sgn = restore_row(tab, var: &tab->con[r]);
1940 if (sgn < -1)
1941 return isl_stat_error;
1942 if (sgn < 0)
1943 return isl_tab_mark_empty(tab);
1944 if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, row: tab->con[r].index))
1945 if (isl_tab_mark_redundant(tab, row: tab->con[r].index) < 0)
1946 return isl_stat_error;
1947 return isl_stat_ok;
1948}
1949
1950/* Pivot a non-negative variable down until it reaches the value zero
1951 * and then pivot the variable into a column position.
1952 */
1953static int to_col(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
1954static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
1955{
1956 int i;
1957 int row, col;
1958 unsigned off = 2 + tab->M;
1959
1960 if (!var->is_row)
1961 return 0;
1962
1963 while (isl_int_is_pos(tab->mat->row[var->index][1])) {
1964 find_pivot(tab, var, NULL, sgn: -1, row: &row, col: &col);
1965 isl_assert(tab->mat->ctx, row != -1, return -1);
1966 if (isl_tab_pivot(tab, row, col) < 0)
1967 return -1;
1968 if (!var->is_row)
1969 return 0;
1970 }
1971
1972 for (i = tab->n_dead; i < tab->n_col; ++i)
1973 if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
1974 break;
1975
1976 isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
1977 if (isl_tab_pivot(tab, row: var->index, col: i) < 0)
1978 return -1;
1979
1980 return 0;
1981}
1982
1983/* We assume Gaussian elimination has been performed on the equalities.
1984 * The equalities can therefore never conflict.
1985 * Adding the equalities is currently only really useful for a later call
1986 * to isl_tab_ineq_type.
1987 *
1988 * This function assumes that at least one more row and at least
1989 * one more element in the constraint array are available in the tableau.
1990 */
1991static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
1992{
1993 int i;
1994 int r;
1995
1996 if (!tab)
1997 return NULL;
1998 r = isl_tab_add_row(tab, line: eq);
1999 if (r < 0)
2000 goto error;
2001
2002 r = tab->con[r].index;
2003 i = isl_seq_first_non_zero(p: tab->mat->row[r] + 2 + tab->M + tab->n_dead,
2004 len: tab->n_col - tab->n_dead);
2005 isl_assert(tab->mat->ctx, i >= 0, goto error);
2006 i += tab->n_dead;
2007 if (isl_tab_pivot(tab, row: r, col: i) < 0)
2008 goto error;
2009 if (isl_tab_kill_col(tab, col: i) < 0)
2010 goto error;
2011 tab->n_eq++;
2012
2013 return tab;
2014error:
2015 isl_tab_free(tab);
2016 return NULL;
2017}
2018
2019/* Does the sample value of row "row" of "tab" involve the big parameter,
2020 * if any?
2021 */
2022static int row_is_big(struct isl_tab *tab, int row)
2023{
2024 return tab->M && !isl_int_is_zero(tab->mat->row[row][2]);
2025}
2026
2027static int row_is_manifestly_zero(struct isl_tab *tab, int row)
2028{
2029 unsigned off = 2 + tab->M;
2030
2031 if (!isl_int_is_zero(tab->mat->row[row][1]))
2032 return 0;
2033 if (row_is_big(tab, row))
2034 return 0;
2035 return isl_seq_first_non_zero(p: tab->mat->row[row] + off + tab->n_dead,
2036 len: tab->n_col - tab->n_dead) == -1;
2037}
2038
2039/* Add an equality that is known to be valid for the given tableau.
2040 *
2041 * This function assumes that at least one more row and at least
2042 * one more element in the constraint array are available in the tableau.
2043 */
2044int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
2045{
2046 struct isl_tab_var *var;
2047 int r;
2048
2049 if (!tab)
2050 return -1;
2051 r = isl_tab_add_row(tab, line: eq);
2052 if (r < 0)
2053 return -1;
2054
2055 var = &tab->con[r];
2056 r = var->index;
2057 if (row_is_manifestly_zero(tab, row: r)) {
2058 var->is_zero = 1;
2059 if (isl_tab_mark_redundant(tab, row: r) < 0)
2060 return -1;
2061 return 0;
2062 }
2063
2064 if (isl_int_is_neg(tab->mat->row[r][1])) {
2065 isl_seq_neg(dst: tab->mat->row[r] + 1, src: tab->mat->row[r] + 1,
2066 len: 1 + tab->n_col);
2067 var->negated = 1;
2068 }
2069 var->is_nonneg = 1;
2070 if (to_col(tab, var) < 0)
2071 return -1;
2072 var->is_nonneg = 0;
2073 if (isl_tab_kill_col(tab, col: var->index) < 0)
2074 return -1;
2075
2076 return 0;
2077}
2078
2079/* Add a zero row to "tab" and return the corresponding index
2080 * in the constraint array.
2081 *
2082 * This function assumes that at least one more row and at least
2083 * one more element in the constraint array are available in the tableau.
2084 */
2085static int add_zero_row(struct isl_tab *tab)
2086{
2087 int r;
2088 isl_int *row;
2089
2090 r = isl_tab_allocate_con(tab);
2091 if (r < 0)
2092 return -1;
2093
2094 row = tab->mat->row[tab->con[r].index];
2095 isl_seq_clr(p: row + 1, len: 1 + tab->M + tab->n_col);
2096 isl_int_set_si(row[0], 1);
2097
2098 return r;
2099}
2100
2101/* Add equality "eq" and check if it conflicts with the
2102 * previously added constraints or if it is obviously redundant.
2103 *
2104 * This function assumes that at least one more row and at least
2105 * one more element in the constraint array are available in the tableau.
2106 * If tab->bmap is set, then two rows are needed instead of one.
2107 */
2108isl_stat isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
2109{
2110 struct isl_tab_undo *snap = NULL;
2111 struct isl_tab_var *var;
2112 int r;
2113 int row;
2114 int sgn;
2115 isl_int cst;
2116
2117 if (!tab)
2118 return isl_stat_error;
2119 isl_assert(tab->mat->ctx, !tab->M, return isl_stat_error);
2120
2121 if (tab->need_undo)
2122 snap = isl_tab_snap(tab);
2123
2124 if (tab->cone) {
2125 isl_int_init(cst);
2126 isl_int_set_si(cst, 0);
2127 isl_int_swap(eq[0], cst);
2128 }
2129 r = isl_tab_add_row(tab, line: eq);
2130 if (tab->cone) {
2131 isl_int_swap(eq[0], cst);
2132 isl_int_clear(cst);
2133 }
2134 if (r < 0)
2135 return isl_stat_error;
2136
2137 var = &tab->con[r];
2138 row = var->index;
2139 if (row_is_manifestly_zero(tab, row)) {
2140 if (snap)
2141 return isl_tab_rollback(tab, snap);
2142 return drop_row(tab, row);
2143 }
2144
2145 if (tab->bmap) {
2146 tab->bmap = isl_basic_map_add_ineq(bmap: tab->bmap, ineq: eq);
2147 if (isl_tab_push(tab, type: isl_tab_undo_bmap_ineq) < 0)
2148 return isl_stat_error;
2149 isl_seq_neg(dst: eq, src: eq, len: 1 + tab->n_var);
2150 tab->bmap = isl_basic_map_add_ineq(bmap: tab->bmap, ineq: eq);
2151 isl_seq_neg(dst: eq, src: eq, len: 1 + tab->n_var);
2152 if (isl_tab_push(tab, type: isl_tab_undo_bmap_ineq) < 0)
2153 return isl_stat_error;
2154 if (!tab->bmap)
2155 return isl_stat_error;
2156 if (add_zero_row(tab) < 0)
2157 return isl_stat_error;
2158 }
2159
2160 sgn = isl_int_sgn(tab->mat->row[row][1]);
2161
2162 if (sgn > 0) {
2163 isl_seq_neg(dst: tab->mat->row[row] + 1, src: tab->mat->row[row] + 1,
2164 len: 1 + tab->n_col);
2165 var->negated = 1;
2166 sgn = -1;
2167 }
2168
2169 if (sgn < 0) {
2170 sgn = sign_of_max(tab, var);
2171 if (sgn < -1)
2172 return isl_stat_error;
2173 if (sgn < 0) {
2174 if (isl_tab_mark_empty(tab) < 0)
2175 return isl_stat_error;
2176 return isl_stat_ok;
2177 }
2178 }
2179
2180 var->is_nonneg = 1;
2181 if (to_col(tab, var) < 0)
2182 return isl_stat_error;
2183 var->is_nonneg = 0;
2184 if (isl_tab_kill_col(tab, col: var->index) < 0)
2185 return isl_stat_error;
2186
2187 return isl_stat_ok;
2188}
2189
2190/* Construct and return an inequality that expresses an upper bound
2191 * on the given div.
2192 * In particular, if the div is given by
2193 *
2194 * d = floor(e/m)
2195 *
2196 * then the inequality expresses
2197 *
2198 * m d <= e
2199 */
2200static __isl_give isl_vec *ineq_for_div(__isl_keep isl_basic_map *bmap,
2201 unsigned div)
2202{
2203 isl_size total;
2204 unsigned div_pos;
2205 struct isl_vec *ineq;
2206
2207 total = isl_basic_map_dim(bmap, type: isl_dim_all);
2208 if (total < 0)
2209 return NULL;
2210
2211 div_pos = 1 + total - bmap->n_div + div;
2212
2213 ineq = isl_vec_alloc(ctx: bmap->ctx, size: 1 + total);
2214 if (!ineq)
2215 return NULL;
2216
2217 isl_seq_cpy(dst: ineq->el, src: bmap->div[div] + 1, len: 1 + total);
2218 isl_int_neg(ineq->el[div_pos], bmap->div[div][0]);
2219 return ineq;
2220}
2221
2222/* For a div d = floor(f/m), add the constraints
2223 *
2224 * f - m d >= 0
2225 * -(f-(m-1)) + m d >= 0
2226 *
2227 * Note that the second constraint is the negation of
2228 *
2229 * f - m d >= m
2230 *
2231 * If add_ineq is not NULL, then this function is used
2232 * instead of isl_tab_add_ineq to effectively add the inequalities.
2233 *
2234 * This function assumes that at least two more rows and at least
2235 * two more elements in the constraint array are available in the tableau.
2236 */
2237static isl_stat add_div_constraints(struct isl_tab *tab, unsigned div,
2238 isl_stat (*add_ineq)(void *user, isl_int *), void *user)
2239{
2240 isl_size total;
2241 unsigned div_pos;
2242 struct isl_vec *ineq;
2243
2244 total = isl_basic_map_dim(bmap: tab->bmap, type: isl_dim_all);
2245 if (total < 0)
2246 return isl_stat_error;
2247 div_pos = 1 + total - tab->bmap->n_div + div;
2248
2249 ineq = ineq_for_div(bmap: tab->bmap, div);
2250 if (!ineq)
2251 goto error;
2252
2253 if (add_ineq) {
2254 if (add_ineq(user, ineq->el) < 0)
2255 goto error;
2256 } else {
2257 if (isl_tab_add_ineq(tab, ineq: ineq->el) < 0)
2258 goto error;
2259 }
2260
2261 isl_seq_neg(dst: ineq->el, src: tab->bmap->div[div] + 1, len: 1 + total);
2262 isl_int_set(ineq->el[div_pos], tab->bmap->div[div][0]);
2263 isl_int_add(ineq->el[0], ineq->el[0], ineq->el[div_pos]);
2264 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
2265
2266 if (add_ineq) {
2267 if (add_ineq(user, ineq->el) < 0)
2268 goto error;
2269 } else {
2270 if (isl_tab_add_ineq(tab, ineq: ineq->el) < 0)
2271 goto error;
2272 }
2273
2274 isl_vec_free(vec: ineq);
2275
2276 return isl_stat_ok;
2277error:
2278 isl_vec_free(vec: ineq);
2279 return isl_stat_error;
2280}
2281
2282/* Check whether the div described by "div" is obviously non-negative.
2283 * If we are using a big parameter, then we will encode the div
2284 * as div' = M + div, which is always non-negative.
2285 * Otherwise, we check whether div is a non-negative affine combination
2286 * of non-negative variables.
2287 */
2288static int div_is_nonneg(struct isl_tab *tab, __isl_keep isl_vec *div)
2289{
2290 int i;
2291
2292 if (tab->M)
2293 return 1;
2294
2295 if (isl_int_is_neg(div->el[1]))
2296 return 0;
2297
2298 for (i = 0; i < tab->n_var; ++i) {
2299 if (isl_int_is_neg(div->el[2 + i]))
2300 return 0;
2301 if (isl_int_is_zero(div->el[2 + i]))
2302 continue;
2303 if (!tab->var[i].is_nonneg)
2304 return 0;
2305 }
2306
2307 return 1;
2308}
2309
2310/* Insert an extra div, prescribed by "div", to the tableau and
2311 * the associated bmap (which is assumed to be non-NULL).
2312 * The extra integer division is inserted at (tableau) position "pos".
2313 * Return "pos" or -1 if an error occurred.
2314 *
2315 * If add_ineq is not NULL, then this function is used instead
2316 * of isl_tab_add_ineq to add the div constraints.
2317 * This complication is needed because the code in isl_tab_pip
2318 * wants to perform some extra processing when an inequality
2319 * is added to the tableau.
2320 */
2321int isl_tab_insert_div(struct isl_tab *tab, int pos, __isl_keep isl_vec *div,
2322 isl_stat (*add_ineq)(void *user, isl_int *), void *user)
2323{
2324 int r;
2325 int nonneg;
2326 isl_size n_div;
2327 int o_div;
2328
2329 if (!tab || !div)
2330 return -1;
2331
2332 if (div->size != 1 + 1 + tab->n_var)
2333 isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
2334 "unexpected size", return -1);
2335
2336 n_div = isl_basic_map_dim(bmap: tab->bmap, type: isl_dim_div);
2337 if (n_div < 0)
2338 return -1;
2339 o_div = tab->n_var - n_div;
2340 if (pos < o_div || pos > tab->n_var)
2341 isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
2342 "invalid position", return -1);
2343
2344 nonneg = div_is_nonneg(tab, div);
2345
2346 if (isl_tab_extend_cons(tab, n_new: 3) < 0)
2347 return -1;
2348 if (isl_tab_extend_vars(tab, n_new: 1) < 0)
2349 return -1;
2350 r = isl_tab_insert_var(tab, r: pos);
2351 if (r < 0)
2352 return -1;
2353
2354 if (nonneg)
2355 tab->var[r].is_nonneg = 1;
2356
2357 tab->bmap = isl_basic_map_insert_div(bmap: tab->bmap, pos: pos - o_div, div);
2358 if (!tab->bmap)
2359 return -1;
2360 if (isl_tab_push_var(tab, type: isl_tab_undo_bmap_div, var: &tab->var[r]) < 0)
2361 return -1;
2362
2363 if (add_div_constraints(tab, div: pos - o_div, add_ineq, user) < 0)
2364 return -1;
2365
2366 return r;
2367}
2368
2369/* Add an extra div, prescribed by "div", to the tableau and
2370 * the associated bmap (which is assumed to be non-NULL).
2371 */
2372int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div)
2373{
2374 if (!tab)
2375 return -1;
2376 return isl_tab_insert_div(tab, pos: tab->n_var, div, NULL, NULL);
2377}
2378
2379/* If "track" is set, then we want to keep track of all constraints in tab
2380 * in its bmap field. This field is initialized from a copy of "bmap",
2381 * so we need to make sure that all constraints in "bmap" also appear
2382 * in the constructed tab.
2383 */
2384__isl_give struct isl_tab *isl_tab_from_basic_map(
2385 __isl_keep isl_basic_map *bmap, int track)
2386{
2387 int i;
2388 struct isl_tab *tab;
2389 isl_size total;
2390
2391 total = isl_basic_map_dim(bmap, type: isl_dim_all);
2392 if (total < 0)
2393 return NULL;
2394 tab = isl_tab_alloc(ctx: bmap->ctx, n_row: total + bmap->n_ineq + 1, n_var: total, M: 0);
2395 if (!tab)
2396 return NULL;
2397 tab->preserve = track;
2398 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
2399 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
2400 if (isl_tab_mark_empty(tab) < 0)
2401 goto error;
2402 goto done;
2403 }
2404 for (i = 0; i < bmap->n_eq; ++i) {
2405 tab = add_eq(tab, eq: bmap->eq[i]);
2406 if (!tab)
2407 return tab;
2408 }
2409 for (i = 0; i < bmap->n_ineq; ++i) {
2410 if (isl_tab_add_ineq(tab, ineq: bmap->ineq[i]) < 0)
2411 goto error;
2412 if (tab->empty)
2413 goto done;
2414 }
2415done:
2416 if (track && isl_tab_track_bmap(tab, bmap: isl_basic_map_copy(bmap)) < 0)
2417 goto error;
2418 return tab;
2419error:
2420 isl_tab_free(tab);
2421 return NULL;
2422}
2423
2424__isl_give struct isl_tab *isl_tab_from_basic_set(
2425 __isl_keep isl_basic_set *bset, int track)
2426{
2427 return isl_tab_from_basic_map(bmap: bset, track);
2428}
2429
2430/* Construct a tableau corresponding to the recession cone of "bset".
2431 */
2432struct isl_tab *isl_tab_from_recession_cone(__isl_keep isl_basic_set *bset,
2433 int parametric)
2434{
2435 isl_int cst;
2436 int i;
2437 struct isl_tab *tab;
2438 isl_size offset = 0;
2439 isl_size total;
2440
2441 total = isl_basic_set_dim(bset, type: isl_dim_all);
2442 if (parametric)
2443 offset = isl_basic_set_dim(bset, type: isl_dim_param);
2444 if (total < 0 || offset < 0)
2445 return NULL;
2446 tab = isl_tab_alloc(ctx: bset->ctx, n_row: bset->n_eq + bset->n_ineq,
2447 n_var: total - offset, M: 0);
2448 if (!tab)
2449 return NULL;
2450 tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
2451 tab->cone = 1;
2452
2453 isl_int_init(cst);
2454 isl_int_set_si(cst, 0);
2455 for (i = 0; i < bset->n_eq; ++i) {
2456 isl_int_swap(bset->eq[i][offset], cst);
2457 if (offset > 0) {
2458 if (isl_tab_add_eq(tab, eq: bset->eq[i] + offset) < 0)
2459 goto error;
2460 } else
2461 tab = add_eq(tab, eq: bset->eq[i]);
2462 isl_int_swap(bset->eq[i][offset], cst);
2463 if (!tab)
2464 goto done;
2465 }
2466 for (i = 0; i < bset->n_ineq; ++i) {
2467 int r;
2468 isl_int_swap(bset->ineq[i][offset], cst);
2469 r = isl_tab_add_row(tab, line: bset->ineq[i] + offset);
2470 isl_int_swap(bset->ineq[i][offset], cst);
2471 if (r < 0)
2472 goto error;
2473 tab->con[r].is_nonneg = 1;
2474 if (isl_tab_push_var(tab, type: isl_tab_undo_nonneg, var: &tab->con[r]) < 0)
2475 goto error;
2476 }
2477done:
2478 isl_int_clear(cst);
2479 return tab;
2480error:
2481 isl_int_clear(cst);
2482 isl_tab_free(tab);
2483 return NULL;
2484}
2485
2486/* Assuming "tab" is the tableau of a cone, check if the cone is
2487 * bounded, i.e., if it is empty or only contains the origin.
2488 */
2489isl_bool isl_tab_cone_is_bounded(struct isl_tab *tab)
2490{
2491 int i;
2492
2493 if (!tab)
2494 return isl_bool_error;
2495 if (tab->empty)
2496 return isl_bool_true;
2497 if (tab->n_dead == tab->n_col)
2498 return isl_bool_true;
2499
2500 for (;;) {
2501 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2502 struct isl_tab_var *var;
2503 int sgn;
2504 var = isl_tab_var_from_row(tab, i);
2505 if (!var->is_nonneg)
2506 continue;
2507 sgn = sign_of_max(tab, var);
2508 if (sgn < -1)
2509 return isl_bool_error;
2510 if (sgn != 0)
2511 return isl_bool_false;
2512 if (close_row(tab, var, temp_var: 0) < 0)
2513 return isl_bool_error;
2514 break;
2515 }
2516 if (tab->n_dead == tab->n_col)
2517 return isl_bool_true;
2518 if (i == tab->n_row)
2519 return isl_bool_false;
2520 }
2521}
2522
2523int isl_tab_sample_is_integer(struct isl_tab *tab)
2524{
2525 int i;
2526
2527 if (!tab)
2528 return -1;
2529
2530 for (i = 0; i < tab->n_var; ++i) {
2531 int row;
2532 if (!tab->var[i].is_row)
2533 continue;
2534 row = tab->var[i].index;
2535 if (!isl_int_is_divisible_by(tab->mat->row[row][1],
2536 tab->mat->row[row][0]))
2537 return 0;
2538 }
2539 return 1;
2540}
2541
2542static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
2543{
2544 int i;
2545 struct isl_vec *vec;
2546
2547 vec = isl_vec_alloc(ctx: tab->mat->ctx, size: 1 + tab->n_var);
2548 if (!vec)
2549 return NULL;
2550
2551 isl_int_set_si(vec->block.data[0], 1);
2552 for (i = 0; i < tab->n_var; ++i) {
2553 if (!tab->var[i].is_row)
2554 isl_int_set_si(vec->block.data[1 + i], 0);
2555 else {
2556 int row = tab->var[i].index;
2557 isl_int_divexact(vec->block.data[1 + i],
2558 tab->mat->row[row][1], tab->mat->row[row][0]);
2559 }
2560 }
2561
2562 return vec;
2563}
2564
2565__isl_give isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
2566{
2567 int i;
2568 struct isl_vec *vec;
2569 isl_int m;
2570
2571 if (!tab)
2572 return NULL;
2573
2574 vec = isl_vec_alloc(ctx: tab->mat->ctx, size: 1 + tab->n_var);
2575 if (!vec)
2576 return NULL;
2577
2578 isl_int_init(m);
2579
2580 isl_int_set_si(vec->block.data[0], 1);
2581 for (i = 0; i < tab->n_var; ++i) {
2582 int row;
2583 if (!tab->var[i].is_row) {
2584 isl_int_set_si(vec->block.data[1 + i], 0);
2585 continue;
2586 }
2587 row = tab->var[i].index;
2588 isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
2589 isl_int_divexact(m, tab->mat->row[row][0], m);
2590 isl_seq_scale(dst: vec->block.data, src: vec->block.data, f: m, len: 1 + i);
2591 isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
2592 isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
2593 }
2594 vec = isl_vec_normalize(vec);
2595
2596 isl_int_clear(m);
2597 return vec;
2598}
2599
2600/* Store the sample value of "var" of "tab" rounded up (if sgn > 0)
2601 * or down (if sgn < 0) to the nearest integer in *v.
2602 */
2603static void get_rounded_sample_value(struct isl_tab *tab,
2604 struct isl_tab_var *var, int sgn, isl_int *v)
2605{
2606 if (!var->is_row)
2607 isl_int_set_si(*v, 0);
2608 else if (sgn > 0)
2609 isl_int_cdiv_q(*v, tab->mat->row[var->index][1],
2610 tab->mat->row[var->index][0]);
2611 else
2612 isl_int_fdiv_q(*v, tab->mat->row[var->index][1],
2613 tab->mat->row[var->index][0]);
2614}
2615
2616/* Update "bmap" based on the results of the tableau "tab".
2617 * In particular, implicit equalities are made explicit, redundant constraints
2618 * are removed and if the sample value happens to be integer, it is stored
2619 * in "bmap" (unless "bmap" already had an integer sample).
2620 *
2621 * The tableau is assumed to have been created from "bmap" using
2622 * isl_tab_from_basic_map.
2623 */
2624__isl_give isl_basic_map *isl_basic_map_update_from_tab(
2625 __isl_take isl_basic_map *bmap, struct isl_tab *tab)
2626{
2627 int i;
2628 unsigned n_eq;
2629
2630 if (!bmap)
2631 return NULL;
2632 if (!tab)
2633 return bmap;
2634
2635 n_eq = tab->n_eq;
2636 if (tab->empty)
2637 bmap = isl_basic_map_set_to_empty(bmap);
2638 else
2639 for (i = bmap->n_ineq - 1; i >= 0; --i) {
2640 if (isl_tab_is_equality(tab, con: n_eq + i))
2641 isl_basic_map_inequality_to_equality(bmap, pos: i);
2642 else if (isl_tab_is_redundant(tab, con: n_eq + i))
2643 isl_basic_map_drop_inequality(bmap, pos: i);
2644 }
2645 if (bmap->n_eq != n_eq)
2646 bmap = isl_basic_map_gauss(bmap, NULL);
2647 if (!tab->rational &&
2648 bmap && !bmap->sample && isl_tab_sample_is_integer(tab))
2649 bmap->sample = extract_integer_sample(tab);
2650 return bmap;
2651}
2652
2653__isl_give isl_basic_set *isl_basic_set_update_from_tab(
2654 __isl_take isl_basic_set *bset, struct isl_tab *tab)
2655{
2656 return bset_from_bmap(bmap: isl_basic_map_update_from_tab(bmap: bset_to_bmap(bset),
2657 tab));
2658}
2659
2660/* Drop the last constraint added to "tab" in position "r".
2661 * The constraint is expected to have remained in a row.
2662 */
2663static isl_stat drop_last_con_in_row(struct isl_tab *tab, int r)
2664{
2665 if (!tab->con[r].is_row)
2666 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
2667 "row unexpectedly moved to column",
2668 return isl_stat_error);
2669 if (r + 1 != tab->n_con)
2670 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
2671 "additional constraints added", return isl_stat_error);
2672 if (drop_row(tab, row: tab->con[r].index) < 0)
2673 return isl_stat_error;
2674
2675 return isl_stat_ok;
2676}
2677
2678/* Given a non-negative variable "var", temporarily add a new non-negative
2679 * variable that is the opposite of "var", ensuring that "var" can only attain
2680 * the value zero. The new variable is removed again before this function
2681 * returns. However, the effect of forcing "var" to be zero remains.
2682 * If var = n/d is a row variable, then the new variable = -n/d.
2683 * If var is a column variables, then the new variable = -var.
2684 * If the new variable cannot attain non-negative values, then
2685 * the resulting tableau is empty.
2686 * Otherwise, we know the value will be zero and we close the row.
2687 */
2688static isl_stat cut_to_hyperplane(struct isl_tab *tab, struct isl_tab_var *var)
2689{
2690 unsigned r;
2691 isl_int *row;
2692 int sgn;
2693 unsigned off = 2 + tab->M;
2694
2695 if (var->is_zero)
2696 return isl_stat_ok;
2697 if (var->is_redundant || !var->is_nonneg)
2698 isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
2699 "expecting non-redundant non-negative variable",
2700 return isl_stat_error);
2701
2702 if (isl_tab_extend_cons(tab, n_new: 1) < 0)
2703 return isl_stat_error;
2704
2705 r = tab->n_con;
2706 tab->con[r].index = tab->n_row;
2707 tab->con[r].is_row = 1;
2708 tab->con[r].is_nonneg = 0;
2709 tab->con[r].is_zero = 0;
2710 tab->con[r].is_redundant = 0;
2711 tab->con[r].frozen = 0;
2712 tab->con[r].negated = 0;
2713 tab->row_var[tab->n_row] = ~r;
2714 row = tab->mat->row[tab->n_row];
2715
2716 if (var->is_row) {
2717 isl_int_set(row[0], tab->mat->row[var->index][0]);
2718 isl_seq_neg(dst: row + 1,
2719 src: tab->mat->row[var->index] + 1, len: 1 + tab->n_col);
2720 } else {
2721 isl_int_set_si(row[0], 1);
2722 isl_seq_clr(p: row + 1, len: 1 + tab->n_col);
2723 isl_int_set_si(row[off + var->index], -1);
2724 }
2725
2726 tab->n_row++;
2727 tab->n_con++;
2728
2729 sgn = sign_of_max(tab, var: &tab->con[r]);
2730 if (sgn < -1)
2731 return isl_stat_error;
2732 if (sgn < 0) {
2733 if (drop_last_con_in_row(tab, r) < 0)
2734 return isl_stat_error;
2735 if (isl_tab_mark_empty(tab) < 0)
2736 return isl_stat_error;
2737 return isl_stat_ok;
2738 }
2739 tab->con[r].is_nonneg = 1;
2740 /* sgn == 0 */
2741 if (close_row(tab, var: &tab->con[r], temp_var: 1) < 0)
2742 return isl_stat_error;
2743 if (drop_last_con_in_row(tab, r) < 0)
2744 return isl_stat_error;
2745
2746 return isl_stat_ok;
2747}
2748
2749/* Check that "con" is a valid constraint position for "tab".
2750 */
2751static isl_stat isl_tab_check_con(struct isl_tab *tab, int con)
2752{
2753 if (!tab)
2754 return isl_stat_error;
2755 if (con < 0 || con >= tab->n_con)
2756 isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
2757 "position out of bounds", return isl_stat_error);
2758 return isl_stat_ok;
2759}
2760
2761/* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2762 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2763 * by r' = r + 1 >= 0.
2764 * If r is a row variable, we simply increase the constant term by one
2765 * (taking into account the denominator).
2766 * If r is a column variable, then we need to modify each row that
2767 * refers to r = r' - 1 by substituting this equality, effectively
2768 * subtracting the coefficient of the column from the constant.
2769 * We should only do this if the minimum is manifestly unbounded,
2770 * however. Otherwise, we may end up with negative sample values
2771 * for non-negative variables.
2772 * So, if r is a column variable with a minimum that is not
2773 * manifestly unbounded, then we need to move it to a row.
2774 * However, the sample value of this row may be negative,
2775 * even after the relaxation, so we need to restore it.
2776 * We therefore prefer to pivot a column up to a row, if possible.
2777 */
2778int isl_tab_relax(struct isl_tab *tab, int con)
2779{
2780 struct isl_tab_var *var;
2781
2782 if (!tab)
2783 return -1;
2784
2785 var = &tab->con[con];
2786
2787 if (var->is_row && (var->index < 0 || var->index < tab->n_redundant))
2788 isl_die(tab->mat->ctx, isl_error_invalid,
2789 "cannot relax redundant constraint", return -1);
2790 if (!var->is_row && (var->index < 0 || var->index < tab->n_dead))
2791 isl_die(tab->mat->ctx, isl_error_invalid,
2792 "cannot relax dead constraint", return -1);
2793
2794 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
2795 if (to_row(tab, var, sign: 1) < 0)
2796 return -1;
2797 if (!var->is_row && !min_is_manifestly_unbounded(tab, var))
2798 if (to_row(tab, var, sign: -1) < 0)
2799 return -1;
2800
2801 if (var->is_row) {
2802 isl_int_add(tab->mat->row[var->index][1],
2803 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
2804 if (restore_row(tab, var) < 0)
2805 return -1;
2806 } else {
2807 int i;
2808 unsigned off = 2 + tab->M;
2809
2810 for (i = 0; i < tab->n_row; ++i) {
2811 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2812 continue;
2813 isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
2814 tab->mat->row[i][off + var->index]);
2815 }
2816
2817 }
2818
2819 if (isl_tab_push_var(tab, type: isl_tab_undo_relax, var) < 0)
2820 return -1;
2821
2822 return 0;
2823}
2824
2825/* Replace the variable v at position "pos" in the tableau "tab"
2826 * by v' = v + shift.
2827 *
2828 * If the variable is in a column, then we first check if we can
2829 * simply plug in v = v' - shift. The effect on a row with
2830 * coefficient f/d for variable v is that the constant term c/d
2831 * is replaced by (c - f * shift)/d. If shift is positive and
2832 * f is negative for each row that needs to remain non-negative,
2833 * then this is clearly safe. In other words, if the minimum of v
2834 * is manifestly unbounded, then we can keep v in a column position.
2835 * Otherwise, we can pivot it down to a row.
2836 * Similarly, if shift is negative, we need to check if the maximum
2837 * of is manifestly unbounded.
2838 *
2839 * If the variable is in a row (from the start or after pivoting),
2840 * then the constant term c/d is replaced by (c + d * shift)/d.
2841 */
2842int isl_tab_shift_var(struct isl_tab *tab, int pos, isl_int shift)
2843{
2844 struct isl_tab_var *var;
2845
2846 if (!tab)
2847 return -1;
2848 if (isl_int_is_zero(shift))
2849 return 0;
2850
2851 var = &tab->var[pos];
2852 if (!var->is_row) {
2853 if (isl_int_is_neg(shift)) {
2854 if (!max_is_manifestly_unbounded(tab, var))
2855 if (to_row(tab, var, sign: 1) < 0)
2856 return -1;
2857 } else {
2858 if (!min_is_manifestly_unbounded(tab, var))
2859 if (to_row(tab, var, sign: -1) < 0)
2860 return -1;
2861 }
2862 }
2863
2864 if (var->is_row) {
2865 isl_int_addmul(tab->mat->row[var->index][1],
2866 shift, tab->mat->row[var->index][0]);
2867 } else {
2868 int i;
2869 unsigned off = 2 + tab->M;
2870
2871 for (i = 0; i < tab->n_row; ++i) {
2872 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2873 continue;
2874 isl_int_submul(tab->mat->row[i][1],
2875 shift, tab->mat->row[i][off + var->index]);
2876 }
2877
2878 }
2879
2880 return 0;
2881}
2882
2883/* Remove the sign constraint from constraint "con".
2884 *
2885 * If the constraint variable was originally marked non-negative,
2886 * then we make sure we mark it non-negative again during rollback.
2887 */
2888int isl_tab_unrestrict(struct isl_tab *tab, int con)
2889{
2890 struct isl_tab_var *var;
2891
2892 if (!tab)
2893 return -1;
2894
2895 var = &tab->con[con];
2896 if (!var->is_nonneg)
2897 return 0;
2898
2899 var->is_nonneg = 0;
2900 if (isl_tab_push_var(tab, type: isl_tab_undo_unrestrict, var) < 0)
2901 return -1;
2902
2903 return 0;
2904}
2905
2906int isl_tab_select_facet(struct isl_tab *tab, int con)
2907{
2908 if (!tab)
2909 return -1;
2910
2911 return cut_to_hyperplane(tab, var: &tab->con[con]);
2912}
2913
2914static int may_be_equality(struct isl_tab *tab, int row)
2915{
2916 return tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
2917 : isl_int_lt(tab->mat->row[row][1],
2918 tab->mat->row[row][0]);
2919}
2920
2921/* Return an isl_tab_var that has been marked or NULL if no such
2922 * variable can be found.
2923 * The marked field has only been set for variables that
2924 * appear in non-redundant rows or non-dead columns.
2925 *
2926 * Pick the last constraint variable that is marked and
2927 * that appears in either a non-redundant row or a non-dead columns.
2928 * Since the returned variable is tested for being a redundant constraint or
2929 * an implicit equality, there is no need to return any tab variable that
2930 * corresponds to a variable.
2931 */
2932static struct isl_tab_var *select_marked(struct isl_tab *tab)
2933{
2934 int i;
2935 struct isl_tab_var *var;
2936
2937 for (i = tab->n_con - 1; i >= 0; --i) {
2938 var = &tab->con[i];
2939 if (var->index < 0)
2940 continue;
2941 if (var->is_row && var->index < tab->n_redundant)
2942 continue;
2943 if (!var->is_row && var->index < tab->n_dead)
2944 continue;
2945 if (var->marked)
2946 return var;
2947 }
2948
2949 return NULL;
2950}
2951
2952/* Check for (near) equalities among the constraints.
2953 * A constraint is an equality if it is non-negative and if
2954 * its maximal value is either
2955 * - zero (in case of rational tableaus), or
2956 * - strictly less than 1 (in case of integer tableaus)
2957 *
2958 * We first mark all non-redundant and non-dead variables that
2959 * are not frozen and not obviously not an equality.
2960 * Then we iterate over all marked variables if they can attain
2961 * any values larger than zero or at least one.
2962 * If the maximal value is zero, we mark any column variables
2963 * that appear in the row as being zero and mark the row as being redundant.
2964 * Otherwise, if the maximal value is strictly less than one (and the
2965 * tableau is integer), then we restrict the value to being zero
2966 * by adding an opposite non-negative variable.
2967 * The order in which the variables are considered is not important.
2968 */
2969int isl_tab_detect_implicit_equalities(struct isl_tab *tab)
2970{
2971 int i;
2972 unsigned n_marked;
2973
2974 if (!tab)
2975 return -1;
2976 if (tab->empty)
2977 return 0;
2978 if (tab->n_dead == tab->n_col)
2979 return 0;
2980
2981 n_marked = 0;
2982 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2983 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
2984 var->marked = !var->frozen && var->is_nonneg &&
2985 may_be_equality(tab, row: i);
2986 if (var->marked)
2987 n_marked++;
2988 }
2989 for (i = tab->n_dead; i < tab->n_col; ++i) {
2990 struct isl_tab_var *var = var_from_col(tab, i);
2991 var->marked = !var->frozen && var->is_nonneg;
2992 if (var->marked)
2993 n_marked++;
2994 }
2995 while (n_marked) {
2996 struct isl_tab_var *var;
2997 int sgn;
2998 var = select_marked(tab);
2999 if (!var)
3000 break;
3001 var->marked = 0;
3002 n_marked--;
3003 sgn = sign_of_max(tab, var);
3004 if (sgn < 0)
3005 return -1;
3006 if (sgn == 0) {
3007 if (close_row(tab, var, temp_var: 0) < 0)
3008 return -1;
3009 } else if (!tab->rational && !at_least_one(tab, var)) {
3010 if (cut_to_hyperplane(tab, var) < 0)
3011 return -1;
3012 return isl_tab_detect_implicit_equalities(tab);
3013 }
3014 for (i = tab->n_redundant; i < tab->n_row; ++i) {
3015 var = isl_tab_var_from_row(tab, i);
3016 if (!var->marked)
3017 continue;
3018 if (may_be_equality(tab, row: i))
3019 continue;
3020 var->marked = 0;
3021 n_marked--;
3022 }
3023 }
3024
3025 return 0;
3026}
3027
3028/* Update the element of row_var or col_var that corresponds to
3029 * constraint tab->con[i] to a move from position "old" to position "i".
3030 */
3031static int update_con_after_move(struct isl_tab *tab, int i, int old)
3032{
3033 int *p;
3034 int index;
3035
3036 index = tab->con[i].index;
3037 if (index == -1)
3038 return 0;
3039 p = tab->con[i].is_row ? tab->row_var : tab->col_var;
3040 if (p[index] != ~old)
3041 isl_die(tab->mat->ctx, isl_error_internal,
3042 "broken internal state", return -1);
3043 p[index] = ~i;
3044
3045 return 0;
3046}
3047
3048/* Interchange constraints "con1" and "con2" in "tab".
3049 * In particular, interchange the contents of these entries in tab->con.
3050 * Since tab->col_var and tab->row_var point back into this array,
3051 * they need to be updated accordingly.
3052 */
3053isl_stat isl_tab_swap_constraints(struct isl_tab *tab, int con1, int con2)
3054{
3055 struct isl_tab_var var;
3056
3057 if (isl_tab_check_con(tab, con: con1) < 0 ||
3058 isl_tab_check_con(tab, con: con2) < 0)
3059 return isl_stat_error;
3060
3061 var = tab->con[con1];
3062 tab->con[con1] = tab->con[con2];
3063 if (update_con_after_move(tab, i: con1, old: con2) < 0)
3064 return isl_stat_error;
3065 tab->con[con2] = var;
3066 if (update_con_after_move(tab, i: con2, old: con1) < 0)
3067 return isl_stat_error;
3068
3069 return isl_stat_ok;
3070}
3071
3072/* Rotate the "n" constraints starting at "first" to the right,
3073 * putting the last constraint in the position of the first constraint.
3074 */
3075static int rotate_constraints(struct isl_tab *tab, int first, int n)
3076{
3077 int i, last;
3078 struct isl_tab_var var;
3079
3080 if (n <= 1)
3081 return 0;
3082
3083 last = first + n - 1;
3084 var = tab->con[last];
3085 for (i = last; i > first; --i) {
3086 tab->con[i] = tab->con[i - 1];
3087 if (update_con_after_move(tab, i, old: i - 1) < 0)
3088 return -1;
3089 }
3090 tab->con[first] = var;
3091 if (update_con_after_move(tab, i: first, old: last) < 0)
3092 return -1;
3093
3094 return 0;
3095}
3096
3097/* Drop the "n" entries starting at position "first" in tab->con, moving all
3098 * subsequent entries down.
3099 * Since some of the entries of tab->row_var and tab->col_var contain
3100 * indices into this array, they have to be updated accordingly.
3101 */
3102static isl_stat con_drop_entries(struct isl_tab *tab,
3103 unsigned first, unsigned n)
3104{
3105 int i;
3106
3107 if (first + n > tab->n_con || first + n < first)
3108 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
3109 "invalid range", return isl_stat_error);
3110
3111 tab->n_con -= n;
3112
3113 for (i = first; i < tab->n_con; ++i) {
3114 tab->con[i] = tab->con[i + n];
3115 if (update_con_after_move(tab, i, old: i + n) < 0)
3116 return isl_stat_error;
3117 }
3118
3119 return isl_stat_ok;
3120}
3121
3122/* isl_basic_map_gauss5 callback that gets called when
3123 * two (equality) constraints "a" and "b" get interchanged
3124 * in the basic map. Perform the same interchange in "tab".
3125 */
3126static isl_stat swap_eq(unsigned a, unsigned b, void *user)
3127{
3128 struct isl_tab *tab = user;
3129
3130 return isl_tab_swap_constraints(tab, con1: a, con2: b);
3131}
3132
3133/* isl_basic_map_gauss5 callback that gets called when
3134 * the final "n" equality constraints get removed.
3135 * As a special case, if "n" is equal to the total number
3136 * of equality constraints, then this means the basic map
3137 * turned out to be empty.
3138 * Drop the same number of equality constraints from "tab" or
3139 * mark it empty in the special case.
3140 */
3141static isl_stat drop_eq(unsigned n, void *user)
3142{
3143 struct isl_tab *tab = user;
3144
3145 if (tab->n_eq == n)
3146 return isl_tab_mark_empty(tab);
3147
3148 tab->n_eq -= n;
3149 return con_drop_entries(tab, first: tab->n_eq, n);
3150}
3151
3152/* If "bmap" has more than a single reference, then call
3153 * isl_basic_map_gauss on it, updating "tab" accordingly.
3154 */
3155static __isl_give isl_basic_map *gauss_if_shared(__isl_take isl_basic_map *bmap,
3156 struct isl_tab *tab)
3157{
3158 isl_bool single;
3159
3160 single = isl_basic_map_has_single_reference(bmap);
3161 if (single < 0)
3162 return isl_basic_map_free(bmap);
3163 if (single)
3164 return bmap;
3165 return isl_basic_map_gauss5(bmap, NULL, swap: &swap_eq, drop: &drop_eq, user: tab);
3166}
3167
3168/* Make the equalities that are implicit in "bmap" but that have been
3169 * detected in the corresponding "tab" explicit in "bmap" and update
3170 * "tab" to reflect the new order of the constraints.
3171 *
3172 * In particular, if inequality i is an implicit equality then
3173 * isl_basic_map_inequality_to_equality will move the inequality
3174 * in front of the other equality and it will move the last inequality
3175 * in the position of inequality i.
3176 * In the tableau, the inequalities of "bmap" are stored after the equalities
3177 * and so the original order
3178 *
3179 * E E E E E A A A I B B B B L
3180 *
3181 * is changed into
3182 *
3183 * I E E E E E A A A L B B B B
3184 *
3185 * where I is the implicit equality, the E are equalities,
3186 * the A inequalities before I, the B inequalities after I and
3187 * L the last inequality.
3188 * We therefore need to rotate to the right two sets of constraints,
3189 * those up to and including I and those after I.
3190 *
3191 * If "tab" contains any constraints that are not in "bmap" then they
3192 * appear after those in "bmap" and they should be left untouched.
3193 *
3194 * Note that this function only calls isl_basic_map_gauss
3195 * (in case some equality constraints got detected)
3196 * if "bmap" has more than one reference.
3197 * If it only has a single reference, then it is left in a temporary state,
3198 * because the caller may require this state.
3199 * Calling isl_basic_map_gauss is then the responsibility of the caller.
3200 */
3201__isl_give isl_basic_map *isl_tab_make_equalities_explicit(struct isl_tab *tab,
3202 __isl_take isl_basic_map *bmap)
3203{
3204 int i;
3205 unsigned n_eq;
3206
3207 if (!tab || !bmap)
3208 return isl_basic_map_free(bmap);
3209 if (tab->empty)
3210 return bmap;
3211
3212 n_eq = tab->n_eq;
3213 for (i = bmap->n_ineq - 1; i >= 0; --i) {
3214 if (!isl_tab_is_equality(tab, con: bmap->n_eq + i))
3215 continue;
3216 isl_basic_map_inequality_to_equality(bmap, pos: i);
3217 if (rotate_constraints(tab, first: 0, n: tab->n_eq + i + 1) < 0)
3218 return isl_basic_map_free(bmap);
3219 if (rotate_constraints(tab, first: tab->n_eq + i + 1,
3220 n: bmap->n_ineq - i) < 0)
3221 return isl_basic_map_free(bmap);
3222 tab->n_eq++;
3223 }
3224
3225 if (n_eq != tab->n_eq)
3226 bmap = gauss_if_shared(bmap, tab);
3227
3228 return bmap;
3229}
3230
3231static int con_is_redundant(struct isl_tab *tab, struct isl_tab_var *var)
3232{
3233 if (!tab)
3234 return -1;
3235 if (tab->rational) {
3236 int sgn = sign_of_min(tab, var);
3237 if (sgn < -1)
3238 return -1;
3239 return sgn >= 0;
3240 } else {
3241 int irred = isl_tab_min_at_most_neg_one(tab, var);
3242 if (irred < 0)
3243 return -1;
3244 return !irred;
3245 }
3246}
3247
3248/* Check for (near) redundant constraints.
3249 * A constraint is redundant if it is non-negative and if
3250 * its minimal value (temporarily ignoring the non-negativity) is either
3251 * - zero (in case of rational tableaus), or
3252 * - strictly larger than -1 (in case of integer tableaus)
3253 *
3254 * We first mark all non-redundant and non-dead variables that
3255 * are not frozen and not obviously negatively unbounded.
3256 * Then we iterate over all marked variables if they can attain
3257 * any values smaller than zero or at most negative one.
3258 * If not, we mark the row as being redundant (assuming it hasn't
3259 * been detected as being obviously redundant in the mean time).
3260 */
3261int isl_tab_detect_redundant(struct isl_tab *tab)
3262{
3263 int i;
3264 unsigned n_marked;
3265
3266 if (!tab)
3267 return -1;
3268 if (tab->empty)
3269 return 0;
3270 if (tab->n_redundant == tab->n_row)
3271 return 0;
3272
3273 n_marked = 0;
3274 for (i = tab->n_redundant; i < tab->n_row; ++i) {
3275 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
3276 var->marked = !var->frozen && var->is_nonneg;
3277 if (var->marked)
3278 n_marked++;
3279 }
3280 for (i = tab->n_dead; i < tab->n_col; ++i) {
3281 struct isl_tab_var *var = var_from_col(tab, i);
3282 var->marked = !var->frozen && var->is_nonneg &&
3283 !min_is_manifestly_unbounded(tab, var);
3284 if (var->marked)
3285 n_marked++;
3286 }
3287 while (n_marked) {
3288 struct isl_tab_var *var;
3289 int red;
3290 var = select_marked(tab);
3291 if (!var)
3292 break;
3293 var->marked = 0;
3294 n_marked--;
3295 red = con_is_redundant(tab, var);
3296 if (red < 0)
3297 return -1;
3298 if (red && !var->is_redundant)
3299 if (isl_tab_mark_redundant(tab, row: var->index) < 0)
3300 return -1;
3301 for (i = tab->n_dead; i < tab->n_col; ++i) {
3302 var = var_from_col(tab, i);
3303 if (!var->marked)
3304 continue;
3305 if (!min_is_manifestly_unbounded(tab, var))
3306 continue;
3307 var->marked = 0;
3308 n_marked--;
3309 }
3310 }
3311
3312 return 0;
3313}
3314
3315int isl_tab_is_equality(struct isl_tab *tab, int con)
3316{
3317 int row;
3318 unsigned off;
3319
3320 if (!tab)
3321 return -1;
3322 if (tab->con[con].is_zero)
3323 return 1;
3324 if (tab->con[con].is_redundant)
3325 return 0;
3326 if (!tab->con[con].is_row)
3327 return tab->con[con].index < tab->n_dead;
3328
3329 row = tab->con[con].index;
3330
3331 off = 2 + tab->M;
3332 return isl_int_is_zero(tab->mat->row[row][1]) &&
3333 !row_is_big(tab, row) &&
3334 isl_seq_first_non_zero(p: tab->mat->row[row] + off + tab->n_dead,
3335 len: tab->n_col - tab->n_dead) == -1;
3336}
3337
3338/* Return the minimal value of the affine expression "f" with denominator
3339 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
3340 * the expression cannot attain arbitrarily small values.
3341 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
3342 * The return value reflects the nature of the result (empty, unbounded,
3343 * minimal value returned in *opt).
3344 *
3345 * This function assumes that at least one more row and at least
3346 * one more element in the constraint array are available in the tableau.
3347 */
3348enum isl_lp_result isl_tab_min(struct isl_tab *tab,
3349 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
3350 unsigned flags)
3351{
3352 int r;
3353 enum isl_lp_result res = isl_lp_ok;
3354 struct isl_tab_var *var;
3355 struct isl_tab_undo *snap;
3356
3357 if (!tab)
3358 return isl_lp_error;
3359
3360 if (tab->empty)
3361 return isl_lp_empty;
3362
3363 snap = isl_tab_snap(tab);
3364 r = isl_tab_add_row(tab, line: f);
3365 if (r < 0)
3366 return isl_lp_error;
3367 var = &tab->con[r];
3368 for (;;) {
3369 int row, col;
3370 find_pivot(tab, var, skip_var: var, sgn: -1, row: &row, col: &col);
3371 if (row == var->index) {
3372 res = isl_lp_unbounded;
3373 break;
3374 }
3375 if (row == -1)
3376 break;
3377 if (isl_tab_pivot(tab, row, col) < 0)
3378 return isl_lp_error;
3379 }
3380 isl_int_mul(tab->mat->row[var->index][0],
3381 tab->mat->row[var->index][0], denom);
3382 if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
3383 int i;
3384
3385 isl_vec_free(vec: tab->dual);
3386 tab->dual = isl_vec_alloc(ctx: tab->mat->ctx, size: 1 + tab->n_con);
3387 if (!tab->dual)
3388 return isl_lp_error;
3389 isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
3390 for (i = 0; i < tab->n_con; ++i) {
3391 int pos;
3392 if (tab->con[i].is_row) {
3393 isl_int_set_si(tab->dual->el[1 + i], 0);
3394 continue;
3395 }
3396 pos = 2 + tab->M + tab->con[i].index;
3397 if (tab->con[i].negated)
3398 isl_int_neg(tab->dual->el[1 + i],
3399 tab->mat->row[var->index][pos]);
3400 else
3401 isl_int_set(tab->dual->el[1 + i],
3402 tab->mat->row[var->index][pos]);
3403 }
3404 }
3405 if (opt && res == isl_lp_ok) {
3406 if (opt_denom) {
3407 isl_int_set(*opt, tab->mat->row[var->index][1]);
3408 isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
3409 } else
3410 get_rounded_sample_value(tab, var, sgn: 1, v: opt);
3411 }
3412 if (isl_tab_rollback(tab, snap) < 0)
3413 return isl_lp_error;
3414 return res;
3415}
3416
3417/* Is the constraint at position "con" marked as being redundant?
3418 * If it is marked as representing an equality, then it is not
3419 * considered to be redundant.
3420 * Note that isl_tab_mark_redundant marks both the isl_tab_var as
3421 * redundant and moves the corresponding row into the first
3422 * tab->n_redundant positions (or removes the row, assigning it index -1),
3423 * so the final test is actually redundant itself.
3424 */
3425int isl_tab_is_redundant(struct isl_tab *tab, int con)
3426{
3427 if (isl_tab_check_con(tab, con) < 0)
3428 return -1;
3429 if (tab->con[con].is_zero)
3430 return 0;
3431 if (tab->con[con].is_redundant)
3432 return 1;
3433 return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
3434}
3435
3436/* Is variable "var" of "tab" fixed to a constant value by its row
3437 * in the tableau?
3438 * If so and if "value" is not NULL, then store this constant value
3439 * in "value".
3440 *
3441 * That is, is it a row variable that only has non-zero coefficients
3442 * for dead columns?
3443 */
3444static isl_bool is_constant(struct isl_tab *tab, struct isl_tab_var *var,
3445 isl_int *value)
3446{
3447 unsigned off = 2 + tab->M;
3448 isl_mat *mat = tab->mat;
3449 int n;
3450 int row;
3451 int pos;
3452
3453 if (!var->is_row)
3454 return isl_bool_false;
3455 row = var->index;
3456 if (row_is_big(tab, row))
3457 return isl_bool_false;
3458 n = tab->n_col - tab->n_dead;
3459 pos = isl_seq_first_non_zero(p: mat->row[row] + off + tab->n_dead, len: n);
3460 if (pos != -1)
3461 return isl_bool_false;
3462 if (value)
3463 isl_int_divexact(*value, mat->row[row][1], mat->row[row][0]);
3464 return isl_bool_true;
3465}
3466
3467/* Has the variable "var' of "tab" reached a value that is greater than
3468 * or equal (if sgn > 0) or smaller than or equal (if sgn < 0) to "target"?
3469 * "tmp" has been initialized by the caller and can be used
3470 * to perform local computations.
3471 *
3472 * If the sample value involves the big parameter, then any value
3473 * is reached.
3474 * Otherwise check if n/d >= t, i.e., n >= d * t (if sgn > 0)
3475 * or n/d <= t, i.e., n <= d * t (if sgn < 0).
3476 */
3477static int reached(struct isl_tab *tab, struct isl_tab_var *var, int sgn,
3478 isl_int target, isl_int *tmp)
3479{
3480 if (row_is_big(tab, row: var->index))
3481 return 1;
3482 isl_int_mul(*tmp, tab->mat->row[var->index][0], target);
3483 if (sgn > 0)
3484 return isl_int_ge(tab->mat->row[var->index][1], *tmp);
3485 else
3486 return isl_int_le(tab->mat->row[var->index][1], *tmp);
3487}
3488
3489/* Can variable "var" of "tab" attain the value "target" by
3490 * pivoting up (if sgn > 0) or down (if sgn < 0)?
3491 * If not, then pivot up [down] to the greatest [smallest]
3492 * rational value.
3493 * "tmp" has been initialized by the caller and can be used
3494 * to perform local computations.
3495 *
3496 * If the variable is manifestly unbounded in the desired direction,
3497 * then it can attain any value.
3498 * Otherwise, it can be moved to a row.
3499 * Continue pivoting until the target is reached.
3500 * If no more pivoting can be performed, the maximal [minimal]
3501 * rational value has been reached and the target cannot be reached.
3502 * If the variable would be pivoted into a manifestly unbounded column,
3503 * then the target can be reached.
3504 */
3505static isl_bool var_reaches(struct isl_tab *tab, struct isl_tab_var *var,
3506 int sgn, isl_int target, isl_int *tmp)
3507{
3508 int row, col;
3509
3510 if (sgn < 0 && min_is_manifestly_unbounded(tab, var))
3511 return isl_bool_true;
3512 if (sgn > 0 && max_is_manifestly_unbounded(tab, var))
3513 return isl_bool_true;
3514 if (to_row(tab, var, sign: sgn) < 0)
3515 return isl_bool_error;
3516 while (!reached(tab, var, sgn, target, tmp)) {
3517 find_pivot(tab, var, skip_var: var, sgn, row: &row, col: &col);
3518 if (row == -1)
3519 return isl_bool_false;
3520 if (row == var->index)
3521 return isl_bool_true;
3522 if (isl_tab_pivot(tab, row, col) < 0)
3523 return isl_bool_error;
3524 }
3525
3526 return isl_bool_true;
3527}
3528
3529/* Check if variable "var" of "tab" can only attain a single (integer)
3530 * value, and, if so, add an equality constraint to fix the variable
3531 * to this single value and store the result in "target".
3532 * "target" and "tmp" have been initialized by the caller.
3533 *
3534 * Given the current sample value, round it down and check
3535 * whether it is possible to attain a strictly smaller integer value.
3536 * If so, the variable is not restricted to a single integer value.
3537 * Otherwise, the search stops at the smallest rational value.
3538 * Round up this value and check whether it is possible to attain
3539 * a strictly greater integer value.
3540 * If so, the variable is not restricted to a single integer value.
3541 * Otherwise, the search stops at the greatest rational value.
3542 * If rounding down this value yields a value that is different
3543 * from rounding up the smallest rational value, then the variable
3544 * cannot attain any integer value. Mark the tableau empty.
3545 * Otherwise, add an equality constraint that fixes the variable
3546 * to the single integer value found.
3547 */
3548static isl_bool detect_constant_with_tmp(struct isl_tab *tab,
3549 struct isl_tab_var *var, isl_int *target, isl_int *tmp)
3550{
3551 isl_bool reached;
3552 isl_vec *eq;
3553 int pos;
3554 isl_stat r;
3555
3556 get_rounded_sample_value(tab, var, sgn: -1, v: target);
3557 isl_int_sub_ui(*target, *target, 1);
3558 reached = var_reaches(tab, var, sgn: -1, target: *target, tmp);
3559 if (reached < 0 || reached)
3560 return isl_bool_not(b: reached);
3561 get_rounded_sample_value(tab, var, sgn: 1, v: target);
3562 isl_int_add_ui(*target, *target, 1);
3563 reached = var_reaches(tab, var, sgn: 1, target: *target, tmp);
3564 if (reached < 0 || reached)
3565 return isl_bool_not(b: reached);
3566 get_rounded_sample_value(tab, var, sgn: -1, v: tmp);
3567 isl_int_sub_ui(*target, *target, 1);
3568 if (isl_int_ne(*target, *tmp)) {
3569 if (isl_tab_mark_empty(tab) < 0)
3570 return isl_bool_error;
3571 return isl_bool_false;
3572 }
3573
3574 if (isl_tab_extend_cons(tab, n_new: 1) < 0)
3575 return isl_bool_error;
3576 eq = isl_vec_alloc(ctx: isl_tab_get_ctx(tab), size: 1 + tab->n_var);
3577 if (!eq)
3578 return isl_bool_error;
3579 pos = var - tab->var;
3580 isl_seq_clr(p: eq->el + 1, len: tab->n_var);
3581 isl_int_set_si(eq->el[1 + pos], -1);
3582 isl_int_set(eq->el[0], *target);
3583 r = isl_tab_add_eq(tab, eq: eq->el);
3584 isl_vec_free(vec: eq);
3585
3586 return r < 0 ? isl_bool_error : isl_bool_true;
3587}
3588
3589/* Check if variable "var" of "tab" can only attain a single (integer)
3590 * value, and, if so, add an equality constraint to fix the variable
3591 * to this single value and store the result in "value" (if "value"
3592 * is not NULL).
3593 *
3594 * If the current sample value involves the big parameter,
3595 * then the variable cannot have a fixed integer value.
3596 * If the variable is already fixed to a single value by its row, then
3597 * there is no need to add another equality constraint.
3598 *
3599 * Otherwise, allocate some temporary variables and continue
3600 * with detect_constant_with_tmp.
3601 */
3602static isl_bool get_constant(struct isl_tab *tab, struct isl_tab_var *var,
3603 isl_int *value)
3604{
3605 isl_int target, tmp;
3606 isl_bool is_cst;
3607
3608 if (var->is_row && row_is_big(tab, row: var->index))
3609 return isl_bool_false;
3610 is_cst = is_constant(tab, var, value);
3611 if (is_cst < 0 || is_cst)
3612 return is_cst;
3613
3614 if (!value)
3615 isl_int_init(target);
3616 isl_int_init(tmp);
3617
3618 is_cst = detect_constant_with_tmp(tab, var,
3619 target: value ? value : &target, tmp: &tmp);
3620
3621 isl_int_clear(tmp);
3622 if (!value)
3623 isl_int_clear(target);
3624
3625 return is_cst;
3626}
3627
3628/* Check if variable "var" of "tab" can only attain a single (integer)
3629 * value, and, if so, add an equality constraint to fix the variable
3630 * to this single value and store the result in "value" (if "value"
3631 * is not NULL).
3632 *
3633 * For rational tableaus, nothing needs to be done.
3634 */
3635isl_bool isl_tab_is_constant(struct isl_tab *tab, int var, isl_int *value)
3636{
3637 if (!tab)
3638 return isl_bool_error;
3639 if (var < 0 || var >= tab->n_var)
3640 isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
3641 "position out of bounds", return isl_bool_error);
3642 if (tab->rational)
3643 return isl_bool_false;
3644
3645 return get_constant(tab, var: &tab->var[var], value);
3646}
3647
3648/* Check if any of the variables of "tab" can only attain a single (integer)
3649 * value, and, if so, add equality constraints to fix those variables
3650 * to these single values.
3651 *
3652 * For rational tableaus, nothing needs to be done.
3653 */
3654isl_stat isl_tab_detect_constants(struct isl_tab *tab)
3655{
3656 int i;
3657
3658 if (!tab)
3659 return isl_stat_error;
3660 if (tab->rational)
3661 return isl_stat_ok;
3662
3663 for (i = 0; i < tab->n_var; ++i) {
3664 if (get_constant(tab, var: &tab->var[i], NULL) < 0)
3665 return isl_stat_error;
3666 }
3667
3668 return isl_stat_ok;
3669}
3670
3671/* Take a snapshot of the tableau that can be restored by a call to
3672 * isl_tab_rollback.
3673 */
3674struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
3675{
3676 if (!tab)
3677 return NULL;
3678 tab->need_undo = 1;
3679 return tab->top;
3680}
3681
3682/* Does "tab" need to keep track of undo information?
3683 * That is, was a snapshot taken that may need to be restored?
3684 */
3685isl_bool isl_tab_need_undo(struct isl_tab *tab)
3686{
3687 if (!tab)
3688 return isl_bool_error;
3689
3690 return isl_bool_ok(b: tab->need_undo);
3691}
3692
3693/* Remove all tracking of undo information from "tab", invalidating
3694 * any snapshots that may have been taken of the tableau.
3695 * Since all snapshots have been invalidated, there is also
3696 * no need to start keeping track of undo information again.
3697 */
3698void isl_tab_clear_undo(struct isl_tab *tab)
3699{
3700 if (!tab)
3701 return;
3702
3703 free_undo(tab);
3704 tab->need_undo = 0;
3705}
3706
3707/* Undo the operation performed by isl_tab_relax.
3708 */
3709static isl_stat unrelax(struct isl_tab *tab, struct isl_tab_var *var)
3710 WARN_UNUSED;
3711static isl_stat unrelax(struct isl_tab *tab, struct isl_tab_var *var)
3712{
3713 unsigned off = 2 + tab->M;
3714
3715 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
3716 if (to_row(tab, var, sign: 1) < 0)
3717 return isl_stat_error;
3718
3719 if (var->is_row) {
3720 isl_int_sub(tab->mat->row[var->index][1],
3721 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
3722 if (var->is_nonneg) {
3723 int sgn = restore_row(tab, var);
3724 isl_assert(tab->mat->ctx, sgn >= 0,
3725 return isl_stat_error);
3726 }
3727 } else {
3728 int i;
3729
3730 for (i = 0; i < tab->n_row; ++i) {
3731 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
3732 continue;
3733 isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
3734 tab->mat->row[i][off + var->index]);
3735 }
3736
3737 }
3738
3739 return isl_stat_ok;
3740}
3741
3742/* Undo the operation performed by isl_tab_unrestrict.
3743 *
3744 * In particular, mark the variable as being non-negative and make
3745 * sure the sample value respects this constraint.
3746 */
3747static isl_stat ununrestrict(struct isl_tab *tab, struct isl_tab_var *var)
3748{
3749 var->is_nonneg = 1;
3750
3751 if (var->is_row && restore_row(tab, var) < -1)
3752 return isl_stat_error;
3753
3754 return isl_stat_ok;
3755}
3756
3757/* Unmark the last redundant row in "tab" as being redundant.
3758 * This undoes part of the modifications performed by isl_tab_mark_redundant.
3759 * In particular, remove the redundant mark and make
3760 * sure the sample value respects the constraint again.
3761 * A variable that is marked non-negative by isl_tab_mark_redundant
3762 * is covered by a separate undo record.
3763 */
3764static isl_stat restore_last_redundant(struct isl_tab *tab)
3765{
3766 struct isl_tab_var *var;
3767
3768 if (tab->n_redundant < 1)
3769 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
3770 "no redundant rows", return isl_stat_error);
3771
3772 var = isl_tab_var_from_row(tab, i: tab->n_redundant - 1);
3773 var->is_redundant = 0;
3774 tab->n_redundant--;
3775 restore_row(tab, var);
3776
3777 return isl_stat_ok;
3778}
3779
3780static isl_stat perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
3781 WARN_UNUSED;
3782static isl_stat perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
3783{
3784 struct isl_tab_var *var = var_from_index(tab, i: undo->u.var_index);
3785 switch (undo->type) {
3786 case isl_tab_undo_nonneg:
3787 var->is_nonneg = 0;
3788 break;
3789 case isl_tab_undo_redundant:
3790 if (!var->is_row || var->index != tab->n_redundant - 1)
3791 isl_die(isl_tab_get_ctx(tab), isl_error_internal,
3792 "not undoing last redundant row",
3793 return isl_stat_error);
3794 return restore_last_redundant(tab);
3795 case isl_tab_undo_freeze:
3796 var->frozen = 0;
3797 break;
3798 case isl_tab_undo_zero:
3799 var->is_zero = 0;
3800 if (!var->is_row)
3801 tab->n_dead--;
3802 break;
3803 case isl_tab_undo_allocate:
3804 if (undo->u.var_index >= 0) {
3805 isl_assert(tab->mat->ctx, !var->is_row,
3806 return isl_stat_error);
3807 return drop_col(tab, col: var->index);
3808 }
3809 if (!var->is_row) {
3810 if (!max_is_manifestly_unbounded(tab, var)) {
3811 if (to_row(tab, var, sign: 1) < 0)
3812 return isl_stat_error;
3813 } else if (!min_is_manifestly_unbounded(tab, var)) {
3814 if (to_row(tab, var, sign: -1) < 0)
3815 return isl_stat_error;
3816 } else
3817 if (to_row(tab, var, sign: 0) < 0)
3818 return isl_stat_error;
3819 }
3820 return drop_row(tab, row: var->index);
3821 case isl_tab_undo_relax:
3822 return unrelax(tab, var);
3823 case isl_tab_undo_unrestrict:
3824 return ununrestrict(tab, var);
3825 default:
3826 isl_die(tab->mat->ctx, isl_error_internal,
3827 "perform_undo_var called on invalid undo record",
3828 return isl_stat_error);
3829 }
3830
3831 return isl_stat_ok;
3832}
3833
3834/* Restore all rows that have been marked redundant by isl_tab_mark_redundant
3835 * and that have been preserved in the tableau.
3836 * Note that isl_tab_mark_redundant may also have marked some variables
3837 * as being non-negative before marking them redundant. These need
3838 * to be removed as well as otherwise some constraints could end up
3839 * getting marked redundant with respect to the variable.
3840 */
3841isl_stat isl_tab_restore_redundant(struct isl_tab *tab)
3842{
3843 if (!tab)
3844 return isl_stat_error;
3845
3846 if (tab->need_undo)
3847 isl_die(isl_tab_get_ctx(tab), isl_error_invalid,
3848 "manually restoring redundant constraints "
3849 "interferes with undo history",
3850 return isl_stat_error);
3851
3852 while (tab->n_redundant > 0) {
3853 if (tab->row_var[tab->n_redundant - 1] >= 0) {
3854 struct isl_tab_var *var;
3855
3856 var = isl_tab_var_from_row(tab, i: tab->n_redundant - 1);
3857 var->is_nonneg = 0;
3858 }
3859 restore_last_redundant(tab);
3860 }
3861 return isl_stat_ok;
3862}
3863
3864/* Undo the addition of an integer division to the basic map representation
3865 * of "tab" in position "pos".
3866 */
3867static isl_stat drop_bmap_div(struct isl_tab *tab, int pos)
3868{
3869 int off;
3870 isl_size n_div;
3871
3872 n_div = isl_basic_map_dim(bmap: tab->bmap, type: isl_dim_div);
3873 if (n_div < 0)
3874 return isl_stat_error;
3875 off = tab->n_var - n_div;
3876 tab->bmap = isl_basic_map_drop_div(bmap: tab->bmap, div: pos - off);
3877 if (!tab->bmap)
3878 return isl_stat_error;
3879 if (tab->samples) {
3880 tab->samples = isl_mat_drop_cols(mat: tab->samples, col: 1 + pos, n: 1);
3881 if (!tab->samples)
3882 return isl_stat_error;
3883 }
3884
3885 return isl_stat_ok;
3886}
3887
3888/* Restore the tableau to the state where the basic variables
3889 * are those in "col_var".
3890 * We first construct a list of variables that are currently in
3891 * the basis, but shouldn't. Then we iterate over all variables
3892 * that should be in the basis and for each one that is currently
3893 * not in the basis, we exchange it with one of the elements of the
3894 * list constructed before.
3895 * We can always find an appropriate variable to pivot with because
3896 * the current basis is mapped to the old basis by a non-singular
3897 * matrix and so we can never end up with a zero row.
3898 */
3899static int restore_basis(struct isl_tab *tab, int *col_var)
3900{
3901 int i, j;
3902 int n_extra = 0;
3903 int *extra = NULL; /* current columns that contain bad stuff */
3904 unsigned off = 2 + tab->M;
3905
3906 extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
3907 if (tab->n_col && !extra)
3908 goto error;
3909 for (i = 0; i < tab->n_col; ++i) {
3910 for (j = 0; j < tab->n_col; ++j)
3911 if (tab->col_var[i] == col_var[j])
3912 break;
3913 if (j < tab->n_col)
3914 continue;
3915 extra[n_extra++] = i;
3916 }
3917 for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
3918 struct isl_tab_var *var;
3919 int row;
3920
3921 for (j = 0; j < tab->n_col; ++j)
3922 if (col_var[i] == tab->col_var[j])
3923 break;
3924 if (j < tab->n_col)
3925 continue;
3926 var = var_from_index(tab, i: col_var[i]);
3927 row = var->index;
3928 for (j = 0; j < n_extra; ++j)
3929 if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
3930 break;
3931 isl_assert(tab->mat->ctx, j < n_extra, goto error);
3932 if (isl_tab_pivot(tab, row, col: extra[j]) < 0)
3933 goto error;
3934 extra[j] = extra[--n_extra];
3935 }
3936
3937 free(ptr: extra);
3938 return 0;
3939error:
3940 free(ptr: extra);
3941 return -1;
3942}
3943
3944/* Remove all samples with index n or greater, i.e., those samples
3945 * that were added since we saved this number of samples in
3946 * isl_tab_save_samples.
3947 */
3948static void drop_samples_since(struct isl_tab *tab, int n)
3949{
3950 int i;
3951
3952 for (i = tab->n_sample - 1; i >= 0 && tab->n_sample > n; --i) {
3953 if (tab->sample_index[i] < n)
3954 continue;
3955
3956 if (i != tab->n_sample - 1) {
3957 int t = tab->sample_index[tab->n_sample-1];
3958 tab->sample_index[tab->n_sample-1] = tab->sample_index[i];
3959 tab->sample_index[i] = t;
3960 isl_mat_swap_rows(mat: tab->samples, i: tab->n_sample-1, j: i);
3961 }
3962 tab->n_sample--;
3963 }
3964}
3965
3966static isl_stat perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
3967 WARN_UNUSED;
3968static isl_stat perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
3969{
3970 switch (undo->type) {
3971 case isl_tab_undo_rational:
3972 tab->rational = 0;
3973 break;
3974 case isl_tab_undo_empty:
3975 tab->empty = 0;
3976 break;
3977 case isl_tab_undo_nonneg:
3978 case isl_tab_undo_redundant:
3979 case isl_tab_undo_freeze:
3980 case isl_tab_undo_zero:
3981 case isl_tab_undo_allocate:
3982 case isl_tab_undo_relax:
3983 case isl_tab_undo_unrestrict:
3984 return perform_undo_var(tab, undo);
3985 case isl_tab_undo_bmap_eq:
3986 tab->bmap = isl_basic_map_free_equality(bmap: tab->bmap, n: 1);
3987 return tab->bmap ? isl_stat_ok : isl_stat_error;
3988 case isl_tab_undo_bmap_ineq:
3989 tab->bmap = isl_basic_map_free_inequality(bmap: tab->bmap, n: 1);
3990 return tab->bmap ? isl_stat_ok : isl_stat_error;
3991 case isl_tab_undo_bmap_div:
3992 return drop_bmap_div(tab, pos: undo->u.var_index);
3993 case isl_tab_undo_saved_basis:
3994 if (restore_basis(tab, col_var: undo->u.col_var) < 0)
3995 return isl_stat_error;
3996 break;
3997 case isl_tab_undo_drop_sample:
3998 tab->n_outside--;
3999 break;
4000 case isl_tab_undo_saved_samples:
4001 drop_samples_since(tab, n: undo->u.n);
4002 break;
4003 case isl_tab_undo_callback:
4004 return undo->u.callback->run(undo->u.callback);
4005 default:
4006 isl_assert(tab->mat->ctx, 0, return isl_stat_error);
4007 }
4008 return isl_stat_ok;
4009}
4010
4011/* Return the tableau to the state it was in when the snapshot "snap"
4012 * was taken.
4013 */
4014isl_stat isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
4015{
4016 struct isl_tab_undo *undo, *next;
4017
4018 if (!tab)
4019 return isl_stat_error;
4020
4021 tab->in_undo = 1;
4022 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
4023 next = undo->next;
4024 if (undo == snap)
4025 break;
4026 if (perform_undo(tab, undo) < 0) {
4027 tab->top = undo;
4028 free_undo(tab);
4029 tab->in_undo = 0;
4030 return isl_stat_error;
4031 }
4032 free_undo_record(undo);
4033 }
4034 tab->in_undo = 0;
4035 tab->top = undo;
4036 if (!undo)
4037 return isl_stat_error;
4038 return isl_stat_ok;
4039}
4040
4041/* The given row "row" represents an inequality violated by all
4042 * points in the tableau. Check for some special cases of such
4043 * separating constraints.
4044 * In particular, if the row has been reduced to the constant -1,
4045 * then we know the inequality is adjacent (but opposite) to
4046 * an equality in the tableau.
4047 * If the row has been reduced to r = c*(-1 -r'), with r' an inequality
4048 * of the tableau and c a positive constant, then the inequality
4049 * is adjacent (but opposite) to the inequality r'.
4050 */
4051static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
4052{
4053 int pos;
4054 unsigned off = 2 + tab->M;
4055
4056 if (tab->rational)
4057 return isl_ineq_separate;
4058
4059 if (!isl_int_is_one(tab->mat->row[row][0]))
4060 return isl_ineq_separate;
4061
4062 pos = isl_seq_first_non_zero(p: tab->mat->row[row] + off + tab->n_dead,
4063 len: tab->n_col - tab->n_dead);
4064 if (pos == -1) {
4065 if (isl_int_is_negone(tab->mat->row[row][1]))
4066 return isl_ineq_adj_eq;
4067 else
4068 return isl_ineq_separate;
4069 }
4070
4071 if (!isl_int_eq(tab->mat->row[row][1],
4072 tab->mat->row[row][off + tab->n_dead + pos]))
4073 return isl_ineq_separate;
4074
4075 pos = isl_seq_first_non_zero(
4076 p: tab->mat->row[row] + off + tab->n_dead + pos + 1,
4077 len: tab->n_col - tab->n_dead - pos - 1);
4078
4079 return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
4080}
4081
4082/* Check the effect of inequality "ineq" on the tableau "tab".
4083 * The result may be
4084 * isl_ineq_redundant: satisfied by all points in the tableau
4085 * isl_ineq_separate: satisfied by no point in the tableau
4086 * isl_ineq_cut: satisfied by some by not all points
4087 * isl_ineq_adj_eq: adjacent to an equality
4088 * isl_ineq_adj_ineq: adjacent to an inequality.
4089 */
4090enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
4091{
4092 enum isl_ineq_type type = isl_ineq_error;
4093 struct isl_tab_undo *snap = NULL;
4094 int con;
4095 int row;
4096
4097 if (!tab)
4098 return isl_ineq_error;
4099
4100 if (isl_tab_extend_cons(tab, n_new: 1) < 0)
4101 return isl_ineq_error;
4102
4103 snap = isl_tab_snap(tab);
4104
4105 con = isl_tab_add_row(tab, line: ineq);
4106 if (con < 0)
4107 goto error;
4108
4109 row = tab->con[con].index;
4110 if (isl_tab_row_is_redundant(tab, row))
4111 type = isl_ineq_redundant;
4112 else if (isl_int_is_neg(tab->mat->row[row][1]) &&
4113 (tab->rational ||
4114 isl_int_abs_ge(tab->mat->row[row][1],
4115 tab->mat->row[row][0]))) {
4116 int nonneg = at_least_zero(tab, var: &tab->con[con]);
4117 if (nonneg < 0)
4118 goto error;
4119 if (nonneg)
4120 type = isl_ineq_cut;
4121 else
4122 type = separation_type(tab, row);
4123 } else {
4124 int red = con_is_redundant(tab, var: &tab->con[con]);
4125 if (red < 0)
4126 goto error;
4127 if (!red)
4128 type = isl_ineq_cut;
4129 else
4130 type = isl_ineq_redundant;
4131 }
4132
4133 if (isl_tab_rollback(tab, snap))
4134 return isl_ineq_error;
4135 return type;
4136error:
4137 return isl_ineq_error;
4138}
4139
4140isl_stat isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap)
4141{
4142 bmap = isl_basic_map_cow(bmap);
4143 if (!tab || !bmap)
4144 goto error;
4145
4146 if (tab->empty) {
4147 bmap = isl_basic_map_set_to_empty(bmap);
4148 if (!bmap)
4149 goto error;
4150 tab->bmap = bmap;
4151 return isl_stat_ok;
4152 }
4153
4154 isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, goto error);
4155 isl_assert(tab->mat->ctx,
4156 tab->n_con == bmap->n_eq + bmap->n_ineq, goto error);
4157
4158 tab->bmap = bmap;
4159
4160 return isl_stat_ok;
4161error:
4162 isl_basic_map_free(bmap);
4163 return isl_stat_error;
4164}
4165
4166isl_stat isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset)
4167{
4168 return isl_tab_track_bmap(tab, bmap: bset_to_bmap(bset));
4169}
4170
4171__isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab)
4172{
4173 if (!tab)
4174 return NULL;
4175
4176 return bset_from_bmap(bmap: tab->bmap);
4177}
4178
4179static void isl_tab_print_internal(__isl_keep struct isl_tab *tab,
4180 FILE *out, int indent)
4181{
4182 unsigned r, c;
4183 int i;
4184
4185 if (!tab) {
4186 fprintf(stream: out, format: "%*snull tab\n", indent, "");
4187 return;
4188 }
4189 fprintf(stream: out, format: "%*sn_redundant: %d, n_dead: %d", indent, "",
4190 tab->n_redundant, tab->n_dead);
4191 if (tab->rational)
4192 fprintf(stream: out, format: ", rational");
4193 if (tab->empty)
4194 fprintf(stream: out, format: ", empty");
4195 fprintf(stream: out, format: "\n");
4196 fprintf(stream: out, format: "%*s[", indent, "");
4197 for (i = 0; i < tab->n_var; ++i) {
4198 if (i)
4199 fprintf(stream: out, format: (i == tab->n_param ||
4200 i == tab->n_var - tab->n_div) ? "; "
4201 : ", ");
4202 fprintf(stream: out, format: "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
4203 tab->var[i].index,
4204 tab->var[i].is_zero ? " [=0]" :
4205 tab->var[i].is_redundant ? " [R]" : "");
4206 }
4207 fprintf(stream: out, format: "]\n");
4208 fprintf(stream: out, format: "%*s[", indent, "");
4209 for (i = 0; i < tab->n_con; ++i) {
4210 if (i)
4211 fprintf(stream: out, format: ", ");
4212 fprintf(stream: out, format: "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
4213 tab->con[i].index,
4214 tab->con[i].is_zero ? " [=0]" :
4215 tab->con[i].is_redundant ? " [R]" : "");
4216 }
4217 fprintf(stream: out, format: "]\n");
4218 fprintf(stream: out, format: "%*s[", indent, "");
4219 for (i = 0; i < tab->n_row; ++i) {
4220 const char *sign = "";
4221 if (i)
4222 fprintf(stream: out, format: ", ");
4223 if (tab->row_sign) {
4224 if (tab->row_sign[i] == isl_tab_row_unknown)
4225 sign = "?";
4226 else if (tab->row_sign[i] == isl_tab_row_neg)
4227 sign = "-";
4228 else if (tab->row_sign[i] == isl_tab_row_pos)
4229 sign = "+";
4230 else
4231 sign = "+-";
4232 }
4233 fprintf(stream: out, format: "r%d: %d%s%s", i, tab->row_var[i],
4234 isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
4235 }
4236 fprintf(stream: out, format: "]\n");
4237 fprintf(stream: out, format: "%*s[", indent, "");
4238 for (i = 0; i < tab->n_col; ++i) {
4239 if (i)
4240 fprintf(stream: out, format: ", ");
4241 fprintf(stream: out, format: "c%d: %d%s", i, tab->col_var[i],
4242 var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
4243 }
4244 fprintf(stream: out, format: "]\n");
4245 r = tab->mat->n_row;
4246 tab->mat->n_row = tab->n_row;
4247 c = tab->mat->n_col;
4248 tab->mat->n_col = 2 + tab->M + tab->n_col;
4249 isl_mat_print_internal(mat: tab->mat, out, indent);
4250 tab->mat->n_row = r;
4251 tab->mat->n_col = c;
4252 if (tab->bmap)
4253 isl_basic_map_print_internal(bmap: tab->bmap, out, indent);
4254}
4255
4256void isl_tab_dump(__isl_keep struct isl_tab *tab)
4257{
4258 isl_tab_print_internal(tab, stderr, indent: 0);
4259}
4260

source code of polly/lib/External/isl/isl_tab.c