deprecate isl_int
[isl.git] / isl_tab.c
blobcc71fb4ffe7588581a66995adce12025ab2a2fa1
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2013 Ecole Normale Superieure
5 * Use of this software is governed by the MIT license
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
12 #include <isl_ctx_private.h>
13 #include <isl_mat_private.h>
14 #include <isl_vec_private.h>
15 #include "isl_map_private.h"
16 #include "isl_tab.h"
17 #include <isl_seq.h>
18 #include <isl_config.h>
21 * The implementation of tableaus in this file was inspired by Section 8
22 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
23 * prover for program checking".
26 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
27 unsigned n_row, unsigned n_var, unsigned M)
29 int i;
30 struct isl_tab *tab;
31 unsigned off = 2 + M;
33 tab = isl_calloc_type(ctx, struct isl_tab);
34 if (!tab)
35 return NULL;
36 tab->mat = isl_mat_alloc(ctx, n_row, off + n_var);
37 if (!tab->mat)
38 goto error;
39 tab->var = isl_alloc_array(ctx, struct isl_tab_var, n_var);
40 if (!tab->var)
41 goto error;
42 tab->con = isl_alloc_array(ctx, struct isl_tab_var, n_row);
43 if (!tab->con)
44 goto error;
45 tab->col_var = isl_alloc_array(ctx, int, n_var);
46 if (!tab->col_var)
47 goto error;
48 tab->row_var = isl_alloc_array(ctx, int, n_row);
49 if (!tab->row_var)
50 goto error;
51 for (i = 0; i < n_var; ++i) {
52 tab->var[i].index = i;
53 tab->var[i].is_row = 0;
54 tab->var[i].is_nonneg = 0;
55 tab->var[i].is_zero = 0;
56 tab->var[i].is_redundant = 0;
57 tab->var[i].frozen = 0;
58 tab->var[i].negated = 0;
59 tab->col_var[i] = i;
61 tab->n_row = 0;
62 tab->n_con = 0;
63 tab->n_eq = 0;
64 tab->max_con = n_row;
65 tab->n_col = n_var;
66 tab->n_var = n_var;
67 tab->max_var = n_var;
68 tab->n_param = 0;
69 tab->n_div = 0;
70 tab->n_dead = 0;
71 tab->n_redundant = 0;
72 tab->strict_redundant = 0;
73 tab->need_undo = 0;
74 tab->rational = 0;
75 tab->empty = 0;
76 tab->in_undo = 0;
77 tab->M = M;
78 tab->cone = 0;
79 tab->bottom.type = isl_tab_undo_bottom;
80 tab->bottom.next = NULL;
81 tab->top = &tab->bottom;
83 tab->n_zero = 0;
84 tab->n_unbounded = 0;
85 tab->basis = NULL;
87 return tab;
88 error:
89 isl_tab_free(tab);
90 return NULL;
93 isl_ctx *isl_tab_get_ctx(struct isl_tab *tab)
95 return tab ? isl_mat_get_ctx(tab->mat) : NULL;
98 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new)
100 unsigned off;
102 if (!tab)
103 return -1;
105 off = 2 + tab->M;
107 if (tab->max_con < tab->n_con + n_new) {
108 struct isl_tab_var *con;
110 con = isl_realloc_array(tab->mat->ctx, tab->con,
111 struct isl_tab_var, tab->max_con + n_new);
112 if (!con)
113 return -1;
114 tab->con = con;
115 tab->max_con += n_new;
117 if (tab->mat->n_row < tab->n_row + n_new) {
118 int *row_var;
120 tab->mat = isl_mat_extend(tab->mat,
121 tab->n_row + n_new, off + tab->n_col);
122 if (!tab->mat)
123 return -1;
124 row_var = isl_realloc_array(tab->mat->ctx, tab->row_var,
125 int, tab->mat->n_row);
126 if (!row_var)
127 return -1;
128 tab->row_var = row_var;
129 if (tab->row_sign) {
130 enum isl_tab_row_sign *s;
131 s = isl_realloc_array(tab->mat->ctx, tab->row_sign,
132 enum isl_tab_row_sign, tab->mat->n_row);
133 if (!s)
134 return -1;
135 tab->row_sign = s;
138 return 0;
141 /* Make room for at least n_new extra variables.
142 * Return -1 if anything went wrong.
144 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new)
146 struct isl_tab_var *var;
147 unsigned off = 2 + tab->M;
149 if (tab->max_var < tab->n_var + n_new) {
150 var = isl_realloc_array(tab->mat->ctx, tab->var,
151 struct isl_tab_var, tab->n_var + n_new);
152 if (!var)
153 return -1;
154 tab->var = var;
155 tab->max_var += n_new;
158 if (tab->mat->n_col < off + tab->n_col + n_new) {
159 int *p;
161 tab->mat = isl_mat_extend(tab->mat,
162 tab->mat->n_row, off + tab->n_col + n_new);
163 if (!tab->mat)
164 return -1;
165 p = isl_realloc_array(tab->mat->ctx, tab->col_var,
166 int, tab->n_col + n_new);
167 if (!p)
168 return -1;
169 tab->col_var = p;
172 return 0;
175 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new)
177 if (isl_tab_extend_cons(tab, n_new) >= 0)
178 return tab;
180 isl_tab_free(tab);
181 return NULL;
184 static void free_undo_record(struct isl_tab_undo *undo)
186 switch (undo->type) {
187 case isl_tab_undo_saved_basis:
188 free(undo->u.col_var);
189 break;
190 default:;
192 free(undo);
195 static void free_undo(struct isl_tab *tab)
197 struct isl_tab_undo *undo, *next;
199 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
200 next = undo->next;
201 free_undo_record(undo);
203 tab->top = undo;
206 void isl_tab_free(struct isl_tab *tab)
208 if (!tab)
209 return;
210 free_undo(tab);
211 isl_mat_free(tab->mat);
212 isl_vec_free(tab->dual);
213 isl_basic_map_free(tab->bmap);
214 free(tab->var);
215 free(tab->con);
216 free(tab->row_var);
217 free(tab->col_var);
218 free(tab->row_sign);
219 isl_mat_free(tab->samples);
220 free(tab->sample_index);
221 isl_mat_free(tab->basis);
222 free(tab);
225 struct isl_tab *isl_tab_dup(struct isl_tab *tab)
227 int i;
228 struct isl_tab *dup;
229 unsigned off;
231 if (!tab)
232 return NULL;
234 off = 2 + tab->M;
235 dup = isl_calloc_type(tab->mat->ctx, struct isl_tab);
236 if (!dup)
237 return NULL;
238 dup->mat = isl_mat_dup(tab->mat);
239 if (!dup->mat)
240 goto error;
241 dup->var = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_var);
242 if (!dup->var)
243 goto error;
244 for (i = 0; i < tab->n_var; ++i)
245 dup->var[i] = tab->var[i];
246 dup->con = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_con);
247 if (!dup->con)
248 goto error;
249 for (i = 0; i < tab->n_con; ++i)
250 dup->con[i] = tab->con[i];
251 dup->col_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_col - off);
252 if (!dup->col_var)
253 goto error;
254 for (i = 0; i < tab->n_col; ++i)
255 dup->col_var[i] = tab->col_var[i];
256 dup->row_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_row);
257 if (!dup->row_var)
258 goto error;
259 for (i = 0; i < tab->n_row; ++i)
260 dup->row_var[i] = tab->row_var[i];
261 if (tab->row_sign) {
262 dup->row_sign = isl_alloc_array(tab->mat->ctx, enum isl_tab_row_sign,
263 tab->mat->n_row);
264 if (!dup->row_sign)
265 goto error;
266 for (i = 0; i < tab->n_row; ++i)
267 dup->row_sign[i] = tab->row_sign[i];
269 if (tab->samples) {
270 dup->samples = isl_mat_dup(tab->samples);
271 if (!dup->samples)
272 goto error;
273 dup->sample_index = isl_alloc_array(tab->mat->ctx, int,
274 tab->samples->n_row);
275 if (!dup->sample_index)
276 goto error;
277 dup->n_sample = tab->n_sample;
278 dup->n_outside = tab->n_outside;
280 dup->n_row = tab->n_row;
281 dup->n_con = tab->n_con;
282 dup->n_eq = tab->n_eq;
283 dup->max_con = tab->max_con;
284 dup->n_col = tab->n_col;
285 dup->n_var = tab->n_var;
286 dup->max_var = tab->max_var;
287 dup->n_param = tab->n_param;
288 dup->n_div = tab->n_div;
289 dup->n_dead = tab->n_dead;
290 dup->n_redundant = tab->n_redundant;
291 dup->rational = tab->rational;
292 dup->empty = tab->empty;
293 dup->strict_redundant = 0;
294 dup->need_undo = 0;
295 dup->in_undo = 0;
296 dup->M = tab->M;
297 tab->cone = tab->cone;
298 dup->bottom.type = isl_tab_undo_bottom;
299 dup->bottom.next = NULL;
300 dup->top = &dup->bottom;
302 dup->n_zero = tab->n_zero;
303 dup->n_unbounded = tab->n_unbounded;
304 dup->basis = isl_mat_dup(tab->basis);
306 return dup;
307 error:
308 isl_tab_free(dup);
309 return NULL;
312 /* Construct the coefficient matrix of the product tableau
313 * of two tableaus.
314 * mat{1,2} is the coefficient matrix of tableau {1,2}
315 * row{1,2} is the number of rows in tableau {1,2}
316 * col{1,2} is the number of columns in tableau {1,2}
317 * off is the offset to the coefficient column (skipping the
318 * denominator, the constant term and the big parameter if any)
319 * r{1,2} is the number of redundant rows in tableau {1,2}
320 * d{1,2} is the number of dead columns in tableau {1,2}
322 * The order of the rows and columns in the result is as explained
323 * in isl_tab_product.
325 static struct isl_mat *tab_mat_product(struct isl_mat *mat1,
326 struct isl_mat *mat2, unsigned row1, unsigned row2,
327 unsigned col1, unsigned col2,
328 unsigned off, unsigned r1, unsigned r2, unsigned d1, unsigned d2)
330 int i;
331 struct isl_mat *prod;
332 unsigned n;
334 prod = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
335 off + col1 + col2);
336 if (!prod)
337 return NULL;
339 n = 0;
340 for (i = 0; i < r1; ++i) {
341 isl_seq_cpy(prod->row[n + i], mat1->row[i], off + d1);
342 isl_seq_clr(prod->row[n + i] + off + d1, d2);
343 isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
344 mat1->row[i] + off + d1, col1 - d1);
345 isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
348 n += r1;
349 for (i = 0; i < r2; ++i) {
350 isl_seq_cpy(prod->row[n + i], mat2->row[i], off);
351 isl_seq_clr(prod->row[n + i] + off, d1);
352 isl_seq_cpy(prod->row[n + i] + off + d1,
353 mat2->row[i] + off, d2);
354 isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
355 isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
356 mat2->row[i] + off + d2, col2 - d2);
359 n += r2;
360 for (i = 0; i < row1 - r1; ++i) {
361 isl_seq_cpy(prod->row[n + i], mat1->row[r1 + i], off + d1);
362 isl_seq_clr(prod->row[n + i] + off + d1, d2);
363 isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
364 mat1->row[r1 + i] + off + d1, col1 - d1);
365 isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
368 n += row1 - r1;
369 for (i = 0; i < row2 - r2; ++i) {
370 isl_seq_cpy(prod->row[n + i], mat2->row[r2 + i], off);
371 isl_seq_clr(prod->row[n + i] + off, d1);
372 isl_seq_cpy(prod->row[n + i] + off + d1,
373 mat2->row[r2 + i] + off, d2);
374 isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
375 isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
376 mat2->row[r2 + i] + off + d2, col2 - d2);
379 return prod;
382 /* Update the row or column index of a variable that corresponds
383 * to a variable in the first input tableau.
385 static void update_index1(struct isl_tab_var *var,
386 unsigned r1, unsigned r2, unsigned d1, unsigned d2)
388 if (var->index == -1)
389 return;
390 if (var->is_row && var->index >= r1)
391 var->index += r2;
392 if (!var->is_row && var->index >= d1)
393 var->index += d2;
396 /* Update the row or column index of a variable that corresponds
397 * to a variable in the second input tableau.
399 static void update_index2(struct isl_tab_var *var,
400 unsigned row1, unsigned col1,
401 unsigned r1, unsigned r2, unsigned d1, unsigned d2)
403 if (var->index == -1)
404 return;
405 if (var->is_row) {
406 if (var->index < r2)
407 var->index += r1;
408 else
409 var->index += row1;
410 } else {
411 if (var->index < d2)
412 var->index += d1;
413 else
414 var->index += col1;
418 /* Create a tableau that represents the Cartesian product of the sets
419 * represented by tableaus tab1 and tab2.
420 * The order of the rows in the product is
421 * - redundant rows of tab1
422 * - redundant rows of tab2
423 * - non-redundant rows of tab1
424 * - non-redundant rows of tab2
425 * The order of the columns is
426 * - denominator
427 * - constant term
428 * - coefficient of big parameter, if any
429 * - dead columns of tab1
430 * - dead columns of tab2
431 * - live columns of tab1
432 * - live columns of tab2
433 * The order of the variables and the constraints is a concatenation
434 * of order in the two input tableaus.
436 struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2)
438 int i;
439 struct isl_tab *prod;
440 unsigned off;
441 unsigned r1, r2, d1, d2;
443 if (!tab1 || !tab2)
444 return NULL;
446 isl_assert(tab1->mat->ctx, tab1->M == tab2->M, return NULL);
447 isl_assert(tab1->mat->ctx, tab1->rational == tab2->rational, return NULL);
448 isl_assert(tab1->mat->ctx, tab1->cone == tab2->cone, return NULL);
449 isl_assert(tab1->mat->ctx, !tab1->row_sign, return NULL);
450 isl_assert(tab1->mat->ctx, !tab2->row_sign, return NULL);
451 isl_assert(tab1->mat->ctx, tab1->n_param == 0, return NULL);
452 isl_assert(tab1->mat->ctx, tab2->n_param == 0, return NULL);
453 isl_assert(tab1->mat->ctx, tab1->n_div == 0, return NULL);
454 isl_assert(tab1->mat->ctx, tab2->n_div == 0, return NULL);
456 off = 2 + tab1->M;
457 r1 = tab1->n_redundant;
458 r2 = tab2->n_redundant;
459 d1 = tab1->n_dead;
460 d2 = tab2->n_dead;
461 prod = isl_calloc_type(tab1->mat->ctx, struct isl_tab);
462 if (!prod)
463 return NULL;
464 prod->mat = tab_mat_product(tab1->mat, tab2->mat,
465 tab1->n_row, tab2->n_row,
466 tab1->n_col, tab2->n_col, off, r1, r2, d1, d2);
467 if (!prod->mat)
468 goto error;
469 prod->var = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
470 tab1->max_var + tab2->max_var);
471 if (!prod->var)
472 goto error;
473 for (i = 0; i < tab1->n_var; ++i) {
474 prod->var[i] = tab1->var[i];
475 update_index1(&prod->var[i], r1, r2, d1, d2);
477 for (i = 0; i < tab2->n_var; ++i) {
478 prod->var[tab1->n_var + i] = tab2->var[i];
479 update_index2(&prod->var[tab1->n_var + i],
480 tab1->n_row, tab1->n_col,
481 r1, r2, d1, d2);
483 prod->con = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
484 tab1->max_con + tab2->max_con);
485 if (!prod->con)
486 goto error;
487 for (i = 0; i < tab1->n_con; ++i) {
488 prod->con[i] = tab1->con[i];
489 update_index1(&prod->con[i], r1, r2, d1, d2);
491 for (i = 0; i < tab2->n_con; ++i) {
492 prod->con[tab1->n_con + i] = tab2->con[i];
493 update_index2(&prod->con[tab1->n_con + i],
494 tab1->n_row, tab1->n_col,
495 r1, r2, d1, d2);
497 prod->col_var = isl_alloc_array(tab1->mat->ctx, int,
498 tab1->n_col + tab2->n_col);
499 if (!prod->col_var)
500 goto error;
501 for (i = 0; i < tab1->n_col; ++i) {
502 int pos = i < d1 ? i : i + d2;
503 prod->col_var[pos] = tab1->col_var[i];
505 for (i = 0; i < tab2->n_col; ++i) {
506 int pos = i < d2 ? d1 + i : tab1->n_col + i;
507 int t = tab2->col_var[i];
508 if (t >= 0)
509 t += tab1->n_var;
510 else
511 t -= tab1->n_con;
512 prod->col_var[pos] = t;
514 prod->row_var = isl_alloc_array(tab1->mat->ctx, int,
515 tab1->mat->n_row + tab2->mat->n_row);
516 if (!prod->row_var)
517 goto error;
518 for (i = 0; i < tab1->n_row; ++i) {
519 int pos = i < r1 ? i : i + r2;
520 prod->row_var[pos] = tab1->row_var[i];
522 for (i = 0; i < tab2->n_row; ++i) {
523 int pos = i < r2 ? r1 + i : tab1->n_row + i;
524 int t = tab2->row_var[i];
525 if (t >= 0)
526 t += tab1->n_var;
527 else
528 t -= tab1->n_con;
529 prod->row_var[pos] = t;
531 prod->samples = NULL;
532 prod->sample_index = NULL;
533 prod->n_row = tab1->n_row + tab2->n_row;
534 prod->n_con = tab1->n_con + tab2->n_con;
535 prod->n_eq = 0;
536 prod->max_con = tab1->max_con + tab2->max_con;
537 prod->n_col = tab1->n_col + tab2->n_col;
538 prod->n_var = tab1->n_var + tab2->n_var;
539 prod->max_var = tab1->max_var + tab2->max_var;
540 prod->n_param = 0;
541 prod->n_div = 0;
542 prod->n_dead = tab1->n_dead + tab2->n_dead;
543 prod->n_redundant = tab1->n_redundant + tab2->n_redundant;
544 prod->rational = tab1->rational;
545 prod->empty = tab1->empty || tab2->empty;
546 prod->strict_redundant = tab1->strict_redundant || tab2->strict_redundant;
547 prod->need_undo = 0;
548 prod->in_undo = 0;
549 prod->M = tab1->M;
550 prod->cone = tab1->cone;
551 prod->bottom.type = isl_tab_undo_bottom;
552 prod->bottom.next = NULL;
553 prod->top = &prod->bottom;
555 prod->n_zero = 0;
556 prod->n_unbounded = 0;
557 prod->basis = NULL;
559 return prod;
560 error:
561 isl_tab_free(prod);
562 return NULL;
565 static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i)
567 if (i >= 0)
568 return &tab->var[i];
569 else
570 return &tab->con[~i];
573 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
575 return var_from_index(tab, tab->row_var[i]);
578 static struct isl_tab_var *var_from_col(struct isl_tab *tab, int i)
580 return var_from_index(tab, tab->col_var[i]);
583 /* Check if there are any upper bounds on column variable "var",
584 * i.e., non-negative rows where var appears with a negative coefficient.
585 * Return 1 if there are no such bounds.
587 static int max_is_manifestly_unbounded(struct isl_tab *tab,
588 struct isl_tab_var *var)
590 int i;
591 unsigned off = 2 + tab->M;
593 if (var->is_row)
594 return 0;
595 for (i = tab->n_redundant; i < tab->n_row; ++i) {
596 if (!isl_int_is_neg(tab->mat->row[i][off + var->index]))
597 continue;
598 if (isl_tab_var_from_row(tab, i)->is_nonneg)
599 return 0;
601 return 1;
604 /* Check if there are any lower bounds on column variable "var",
605 * i.e., non-negative rows where var appears with a positive coefficient.
606 * Return 1 if there are no such bounds.
608 static int min_is_manifestly_unbounded(struct isl_tab *tab,
609 struct isl_tab_var *var)
611 int i;
612 unsigned off = 2 + tab->M;
614 if (var->is_row)
615 return 0;
616 for (i = tab->n_redundant; i < tab->n_row; ++i) {
617 if (!isl_int_is_pos(tab->mat->row[i][off + var->index]))
618 continue;
619 if (isl_tab_var_from_row(tab, i)->is_nonneg)
620 return 0;
622 return 1;
625 static int row_cmp(struct isl_tab *tab, int r1, int r2, int c, isl_int t)
627 unsigned off = 2 + tab->M;
629 if (tab->M) {
630 int s;
631 isl_int_mul(t, tab->mat->row[r1][2], tab->mat->row[r2][off+c]);
632 isl_int_submul(t, tab->mat->row[r2][2], tab->mat->row[r1][off+c]);
633 s = isl_int_sgn(t);
634 if (s)
635 return s;
637 isl_int_mul(t, tab->mat->row[r1][1], tab->mat->row[r2][off + c]);
638 isl_int_submul(t, tab->mat->row[r2][1], tab->mat->row[r1][off + c]);
639 return isl_int_sgn(t);
642 /* Given the index of a column "c", return the index of a row
643 * that can be used to pivot the column in, with either an increase
644 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
645 * If "var" is not NULL, then the row returned will be different from
646 * the one associated with "var".
648 * Each row in the tableau is of the form
650 * x_r = a_r0 + \sum_i a_ri x_i
652 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
653 * impose any limit on the increase or decrease in the value of x_c
654 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
655 * for the row with the smallest (most stringent) such bound.
656 * Note that the common denominator of each row drops out of the fraction.
657 * To check if row j has a smaller bound than row r, i.e.,
658 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
659 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
660 * where -sign(a_jc) is equal to "sgn".
662 static int pivot_row(struct isl_tab *tab,
663 struct isl_tab_var *var, int sgn, int c)
665 int j, r, tsgn;
666 isl_int t;
667 unsigned off = 2 + tab->M;
669 isl_int_init(t);
670 r = -1;
671 for (j = tab->n_redundant; j < tab->n_row; ++j) {
672 if (var && j == var->index)
673 continue;
674 if (!isl_tab_var_from_row(tab, j)->is_nonneg)
675 continue;
676 if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
677 continue;
678 if (r < 0) {
679 r = j;
680 continue;
682 tsgn = sgn * row_cmp(tab, r, j, c, t);
683 if (tsgn < 0 || (tsgn == 0 &&
684 tab->row_var[j] < tab->row_var[r]))
685 r = j;
687 isl_int_clear(t);
688 return r;
691 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
692 * (sgn < 0) the value of row variable var.
693 * If not NULL, then skip_var is a row variable that should be ignored
694 * while looking for a pivot row. It is usually equal to var.
696 * As the given row in the tableau is of the form
698 * x_r = a_r0 + \sum_i a_ri x_i
700 * we need to find a column such that the sign of a_ri is equal to "sgn"
701 * (such that an increase in x_i will have the desired effect) or a
702 * column with a variable that may attain negative values.
703 * If a_ri is positive, then we need to move x_i in the same direction
704 * to obtain the desired effect. Otherwise, x_i has to move in the
705 * opposite direction.
707 static void find_pivot(struct isl_tab *tab,
708 struct isl_tab_var *var, struct isl_tab_var *skip_var,
709 int sgn, int *row, int *col)
711 int j, r, c;
712 isl_int *tr;
714 *row = *col = -1;
716 isl_assert(tab->mat->ctx, var->is_row, return);
717 tr = tab->mat->row[var->index] + 2 + tab->M;
719 c = -1;
720 for (j = tab->n_dead; j < tab->n_col; ++j) {
721 if (isl_int_is_zero(tr[j]))
722 continue;
723 if (isl_int_sgn(tr[j]) != sgn &&
724 var_from_col(tab, j)->is_nonneg)
725 continue;
726 if (c < 0 || tab->col_var[j] < tab->col_var[c])
727 c = j;
729 if (c < 0)
730 return;
732 sgn *= isl_int_sgn(tr[c]);
733 r = pivot_row(tab, skip_var, sgn, c);
734 *row = r < 0 ? var->index : r;
735 *col = c;
738 /* Return 1 if row "row" represents an obviously redundant inequality.
739 * This means
740 * - it represents an inequality or a variable
741 * - that is the sum of a non-negative sample value and a positive
742 * combination of zero or more non-negative constraints.
744 int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
746 int i;
747 unsigned off = 2 + tab->M;
749 if (tab->row_var[row] < 0 && !isl_tab_var_from_row(tab, row)->is_nonneg)
750 return 0;
752 if (isl_int_is_neg(tab->mat->row[row][1]))
753 return 0;
754 if (tab->strict_redundant && isl_int_is_zero(tab->mat->row[row][1]))
755 return 0;
756 if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
757 return 0;
759 for (i = tab->n_dead; i < tab->n_col; ++i) {
760 if (isl_int_is_zero(tab->mat->row[row][off + i]))
761 continue;
762 if (tab->col_var[i] >= 0)
763 return 0;
764 if (isl_int_is_neg(tab->mat->row[row][off + i]))
765 return 0;
766 if (!var_from_col(tab, i)->is_nonneg)
767 return 0;
769 return 1;
772 static void swap_rows(struct isl_tab *tab, int row1, int row2)
774 int t;
775 enum isl_tab_row_sign s;
777 t = tab->row_var[row1];
778 tab->row_var[row1] = tab->row_var[row2];
779 tab->row_var[row2] = t;
780 isl_tab_var_from_row(tab, row1)->index = row1;
781 isl_tab_var_from_row(tab, row2)->index = row2;
782 tab->mat = isl_mat_swap_rows(tab->mat, row1, row2);
784 if (!tab->row_sign)
785 return;
786 s = tab->row_sign[row1];
787 tab->row_sign[row1] = tab->row_sign[row2];
788 tab->row_sign[row2] = s;
791 static int push_union(struct isl_tab *tab,
792 enum isl_tab_undo_type type, union isl_tab_undo_val u) WARN_UNUSED;
793 static int push_union(struct isl_tab *tab,
794 enum isl_tab_undo_type type, union isl_tab_undo_val u)
796 struct isl_tab_undo *undo;
798 if (!tab)
799 return -1;
800 if (!tab->need_undo)
801 return 0;
803 undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
804 if (!undo)
805 return -1;
806 undo->type = type;
807 undo->u = u;
808 undo->next = tab->top;
809 tab->top = undo;
811 return 0;
814 int isl_tab_push_var(struct isl_tab *tab,
815 enum isl_tab_undo_type type, struct isl_tab_var *var)
817 union isl_tab_undo_val u;
818 if (var->is_row)
819 u.var_index = tab->row_var[var->index];
820 else
821 u.var_index = tab->col_var[var->index];
822 return push_union(tab, type, u);
825 int isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
827 union isl_tab_undo_val u = { 0 };
828 return push_union(tab, type, u);
831 /* Push a record on the undo stack describing the current basic
832 * variables, so that the this state can be restored during rollback.
834 int isl_tab_push_basis(struct isl_tab *tab)
836 int i;
837 union isl_tab_undo_val u;
839 u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
840 if (!u.col_var)
841 return -1;
842 for (i = 0; i < tab->n_col; ++i)
843 u.col_var[i] = tab->col_var[i];
844 return push_union(tab, isl_tab_undo_saved_basis, u);
847 int isl_tab_push_callback(struct isl_tab *tab, struct isl_tab_callback *callback)
849 union isl_tab_undo_val u;
850 u.callback = callback;
851 return push_union(tab, isl_tab_undo_callback, u);
854 struct isl_tab *isl_tab_init_samples(struct isl_tab *tab)
856 if (!tab)
857 return NULL;
859 tab->n_sample = 0;
860 tab->n_outside = 0;
861 tab->samples = isl_mat_alloc(tab->mat->ctx, 1, 1 + tab->n_var);
862 if (!tab->samples)
863 goto error;
864 tab->sample_index = isl_alloc_array(tab->mat->ctx, int, 1);
865 if (!tab->sample_index)
866 goto error;
867 return tab;
868 error:
869 isl_tab_free(tab);
870 return NULL;
873 struct isl_tab *isl_tab_add_sample(struct isl_tab *tab,
874 __isl_take isl_vec *sample)
876 if (!tab || !sample)
877 goto error;
879 if (tab->n_sample + 1 > tab->samples->n_row) {
880 int *t = isl_realloc_array(tab->mat->ctx,
881 tab->sample_index, int, tab->n_sample + 1);
882 if (!t)
883 goto error;
884 tab->sample_index = t;
887 tab->samples = isl_mat_extend(tab->samples,
888 tab->n_sample + 1, tab->samples->n_col);
889 if (!tab->samples)
890 goto error;
892 isl_seq_cpy(tab->samples->row[tab->n_sample], sample->el, sample->size);
893 isl_vec_free(sample);
894 tab->sample_index[tab->n_sample] = tab->n_sample;
895 tab->n_sample++;
897 return tab;
898 error:
899 isl_vec_free(sample);
900 isl_tab_free(tab);
901 return NULL;
904 struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s)
906 if (s != tab->n_outside) {
907 int t = tab->sample_index[tab->n_outside];
908 tab->sample_index[tab->n_outside] = tab->sample_index[s];
909 tab->sample_index[s] = t;
910 isl_mat_swap_rows(tab->samples, tab->n_outside, s);
912 tab->n_outside++;
913 if (isl_tab_push(tab, isl_tab_undo_drop_sample) < 0) {
914 isl_tab_free(tab);
915 return NULL;
918 return tab;
921 /* Record the current number of samples so that we can remove newer
922 * samples during a rollback.
924 int isl_tab_save_samples(struct isl_tab *tab)
926 union isl_tab_undo_val u;
928 if (!tab)
929 return -1;
931 u.n = tab->n_sample;
932 return push_union(tab, isl_tab_undo_saved_samples, u);
935 /* Mark row with index "row" as being redundant.
936 * If we may need to undo the operation or if the row represents
937 * a variable of the original problem, the row is kept,
938 * but no longer considered when looking for a pivot row.
939 * Otherwise, the row is simply removed.
941 * The row may be interchanged with some other row. If it
942 * is interchanged with a later row, return 1. Otherwise return 0.
943 * If the rows are checked in order in the calling function,
944 * then a return value of 1 means that the row with the given
945 * row number may now contain a different row that hasn't been checked yet.
947 int isl_tab_mark_redundant(struct isl_tab *tab, int row)
949 struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
950 var->is_redundant = 1;
951 isl_assert(tab->mat->ctx, row >= tab->n_redundant, return -1);
952 if (tab->preserve || tab->need_undo || tab->row_var[row] >= 0) {
953 if (tab->row_var[row] >= 0 && !var->is_nonneg) {
954 var->is_nonneg = 1;
955 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, var) < 0)
956 return -1;
958 if (row != tab->n_redundant)
959 swap_rows(tab, row, tab->n_redundant);
960 tab->n_redundant++;
961 return isl_tab_push_var(tab, isl_tab_undo_redundant, var);
962 } else {
963 if (row != tab->n_row - 1)
964 swap_rows(tab, row, tab->n_row - 1);
965 isl_tab_var_from_row(tab, tab->n_row - 1)->index = -1;
966 tab->n_row--;
967 return 1;
971 int isl_tab_mark_empty(struct isl_tab *tab)
973 if (!tab)
974 return -1;
975 if (!tab->empty && tab->need_undo)
976 if (isl_tab_push(tab, isl_tab_undo_empty) < 0)
977 return -1;
978 tab->empty = 1;
979 return 0;
982 int isl_tab_freeze_constraint(struct isl_tab *tab, int con)
984 struct isl_tab_var *var;
986 if (!tab)
987 return -1;
989 var = &tab->con[con];
990 if (var->frozen)
991 return 0;
992 if (var->index < 0)
993 return 0;
994 var->frozen = 1;
996 if (tab->need_undo)
997 return isl_tab_push_var(tab, isl_tab_undo_freeze, var);
999 return 0;
1002 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
1003 * the original sign of the pivot element.
1004 * We only keep track of row signs during PILP solving and in this case
1005 * we only pivot a row with negative sign (meaning the value is always
1006 * non-positive) using a positive pivot element.
1008 * For each row j, the new value of the parametric constant is equal to
1010 * a_j0 - a_jc a_r0/a_rc
1012 * where a_j0 is the original parametric constant, a_rc is the pivot element,
1013 * a_r0 is the parametric constant of the pivot row and a_jc is the
1014 * pivot column entry of the row j.
1015 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
1016 * remains the same if a_jc has the same sign as the row j or if
1017 * a_jc is zero. In all other cases, we reset the sign to "unknown".
1019 static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
1021 int i;
1022 struct isl_mat *mat = tab->mat;
1023 unsigned off = 2 + tab->M;
1025 if (!tab->row_sign)
1026 return;
1028 if (tab->row_sign[row] == 0)
1029 return;
1030 isl_assert(mat->ctx, row_sgn > 0, return);
1031 isl_assert(mat->ctx, tab->row_sign[row] == isl_tab_row_neg, return);
1032 tab->row_sign[row] = isl_tab_row_pos;
1033 for (i = 0; i < tab->n_row; ++i) {
1034 int s;
1035 if (i == row)
1036 continue;
1037 s = isl_int_sgn(mat->row[i][off + col]);
1038 if (!s)
1039 continue;
1040 if (!tab->row_sign[i])
1041 continue;
1042 if (s < 0 && tab->row_sign[i] == isl_tab_row_neg)
1043 continue;
1044 if (s > 0 && tab->row_sign[i] == isl_tab_row_pos)
1045 continue;
1046 tab->row_sign[i] = isl_tab_row_unknown;
1050 /* Given a row number "row" and a column number "col", pivot the tableau
1051 * such that the associated variables are interchanged.
1052 * The given row in the tableau expresses
1054 * x_r = a_r0 + \sum_i a_ri x_i
1056 * or
1058 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
1060 * Substituting this equality into the other rows
1062 * x_j = a_j0 + \sum_i a_ji x_i
1064 * with a_jc \ne 0, we obtain
1066 * 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
1068 * The tableau
1070 * n_rc/d_r n_ri/d_r
1071 * n_jc/d_j n_ji/d_j
1073 * where i is any other column and j is any other row,
1074 * is therefore transformed into
1076 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1077 * 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)
1079 * The transformation is performed along the following steps
1081 * d_r/n_rc n_ri/n_rc
1082 * n_jc/d_j n_ji/d_j
1084 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1085 * n_jc/d_j n_ji/d_j
1087 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1088 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
1090 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1091 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
1093 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1094 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
1096 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1097 * 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)
1100 int isl_tab_pivot(struct isl_tab *tab, int row, int col)
1102 int i, j;
1103 int sgn;
1104 int t;
1105 struct isl_mat *mat = tab->mat;
1106 struct isl_tab_var *var;
1107 unsigned off = 2 + tab->M;
1109 if (tab->mat->ctx->abort) {
1110 isl_ctx_set_error(tab->mat->ctx, isl_error_abort);
1111 return -1;
1114 isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
1115 sgn = isl_int_sgn(mat->row[row][0]);
1116 if (sgn < 0) {
1117 isl_int_neg(mat->row[row][0], mat->row[row][0]);
1118 isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]);
1119 } else
1120 for (j = 0; j < off - 1 + tab->n_col; ++j) {
1121 if (j == off - 1 + col)
1122 continue;
1123 isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
1125 if (!isl_int_is_one(mat->row[row][0]))
1126 isl_seq_normalize(mat->ctx, mat->row[row], off + tab->n_col);
1127 for (i = 0; i < tab->n_row; ++i) {
1128 if (i == row)
1129 continue;
1130 if (isl_int_is_zero(mat->row[i][off + col]))
1131 continue;
1132 isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
1133 for (j = 0; j < off - 1 + tab->n_col; ++j) {
1134 if (j == off - 1 + col)
1135 continue;
1136 isl_int_mul(mat->row[i][1 + j],
1137 mat->row[i][1 + j], mat->row[row][0]);
1138 isl_int_addmul(mat->row[i][1 + j],
1139 mat->row[i][off + col], mat->row[row][1 + j]);
1141 isl_int_mul(mat->row[i][off + col],
1142 mat->row[i][off + col], mat->row[row][off + col]);
1143 if (!isl_int_is_one(mat->row[i][0]))
1144 isl_seq_normalize(mat->ctx, mat->row[i], off + tab->n_col);
1146 t = tab->row_var[row];
1147 tab->row_var[row] = tab->col_var[col];
1148 tab->col_var[col] = t;
1149 var = isl_tab_var_from_row(tab, row);
1150 var->is_row = 1;
1151 var->index = row;
1152 var = var_from_col(tab, col);
1153 var->is_row = 0;
1154 var->index = col;
1155 update_row_sign(tab, row, col, sgn);
1156 if (tab->in_undo)
1157 return 0;
1158 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1159 if (isl_int_is_zero(mat->row[i][off + col]))
1160 continue;
1161 if (!isl_tab_var_from_row(tab, i)->frozen &&
1162 isl_tab_row_is_redundant(tab, i)) {
1163 int redo = isl_tab_mark_redundant(tab, i);
1164 if (redo < 0)
1165 return -1;
1166 if (redo)
1167 --i;
1170 return 0;
1173 /* If "var" represents a column variable, then pivot is up (sgn > 0)
1174 * or down (sgn < 0) to a row. The variable is assumed not to be
1175 * unbounded in the specified direction.
1176 * If sgn = 0, then the variable is unbounded in both directions,
1177 * and we pivot with any row we can find.
1179 static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign) WARN_UNUSED;
1180 static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
1182 int r;
1183 unsigned off = 2 + tab->M;
1185 if (var->is_row)
1186 return 0;
1188 if (sign == 0) {
1189 for (r = tab->n_redundant; r < tab->n_row; ++r)
1190 if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
1191 break;
1192 isl_assert(tab->mat->ctx, r < tab->n_row, return -1);
1193 } else {
1194 r = pivot_row(tab, NULL, sign, var->index);
1195 isl_assert(tab->mat->ctx, r >= 0, return -1);
1198 return isl_tab_pivot(tab, r, var->index);
1201 /* Check whether all variables that are marked as non-negative
1202 * also have a non-negative sample value. This function is not
1203 * called from the current code but is useful during debugging.
1205 static void check_table(struct isl_tab *tab) __attribute__ ((unused));
1206 static void check_table(struct isl_tab *tab)
1208 int i;
1210 if (tab->empty)
1211 return;
1212 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1213 struct isl_tab_var *var;
1214 var = isl_tab_var_from_row(tab, i);
1215 if (!var->is_nonneg)
1216 continue;
1217 if (tab->M) {
1218 isl_assert(tab->mat->ctx,
1219 !isl_int_is_neg(tab->mat->row[i][2]), abort());
1220 if (isl_int_is_pos(tab->mat->row[i][2]))
1221 continue;
1223 isl_assert(tab->mat->ctx, !isl_int_is_neg(tab->mat->row[i][1]),
1224 abort());
1228 /* Return the sign of the maximal value of "var".
1229 * If the sign is not negative, then on return from this function,
1230 * the sample value will also be non-negative.
1232 * If "var" is manifestly unbounded wrt positive values, we are done.
1233 * Otherwise, we pivot the variable up to a row if needed
1234 * Then we continue pivoting down until either
1235 * - no more down pivots can be performed
1236 * - the sample value is positive
1237 * - the variable is pivoted into a manifestly unbounded column
1239 static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
1241 int row, col;
1243 if (max_is_manifestly_unbounded(tab, var))
1244 return 1;
1245 if (to_row(tab, var, 1) < 0)
1246 return -2;
1247 while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
1248 find_pivot(tab, var, var, 1, &row, &col);
1249 if (row == -1)
1250 return isl_int_sgn(tab->mat->row[var->index][1]);
1251 if (isl_tab_pivot(tab, row, col) < 0)
1252 return -2;
1253 if (!var->is_row) /* manifestly unbounded */
1254 return 1;
1256 return 1;
1259 int isl_tab_sign_of_max(struct isl_tab *tab, int con)
1261 struct isl_tab_var *var;
1263 if (!tab)
1264 return -2;
1266 var = &tab->con[con];
1267 isl_assert(tab->mat->ctx, !var->is_redundant, return -2);
1268 isl_assert(tab->mat->ctx, !var->is_zero, return -2);
1270 return sign_of_max(tab, var);
1273 static int row_is_neg(struct isl_tab *tab, int row)
1275 if (!tab->M)
1276 return isl_int_is_neg(tab->mat->row[row][1]);
1277 if (isl_int_is_pos(tab->mat->row[row][2]))
1278 return 0;
1279 if (isl_int_is_neg(tab->mat->row[row][2]))
1280 return 1;
1281 return isl_int_is_neg(tab->mat->row[row][1]);
1284 static int row_sgn(struct isl_tab *tab, int row)
1286 if (!tab->M)
1287 return isl_int_sgn(tab->mat->row[row][1]);
1288 if (!isl_int_is_zero(tab->mat->row[row][2]))
1289 return isl_int_sgn(tab->mat->row[row][2]);
1290 else
1291 return isl_int_sgn(tab->mat->row[row][1]);
1294 /* Perform pivots until the row variable "var" has a non-negative
1295 * sample value or until no more upward pivots can be performed.
1296 * Return the sign of the sample value after the pivots have been
1297 * performed.
1299 static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
1301 int row, col;
1303 while (row_is_neg(tab, var->index)) {
1304 find_pivot(tab, var, var, 1, &row, &col);
1305 if (row == -1)
1306 break;
1307 if (isl_tab_pivot(tab, row, col) < 0)
1308 return -2;
1309 if (!var->is_row) /* manifestly unbounded */
1310 return 1;
1312 return row_sgn(tab, var->index);
1315 /* Perform pivots until we are sure that the row variable "var"
1316 * can attain non-negative values. After return from this
1317 * function, "var" is still a row variable, but its sample
1318 * value may not be non-negative, even if the function returns 1.
1320 static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
1322 int row, col;
1324 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
1325 find_pivot(tab, var, var, 1, &row, &col);
1326 if (row == -1)
1327 break;
1328 if (row == var->index) /* manifestly unbounded */
1329 return 1;
1330 if (isl_tab_pivot(tab, row, col) < 0)
1331 return -1;
1333 return !isl_int_is_neg(tab->mat->row[var->index][1]);
1336 /* Return a negative value if "var" can attain negative values.
1337 * Return a non-negative value otherwise.
1339 * If "var" is manifestly unbounded wrt negative values, we are done.
1340 * Otherwise, if var is in a column, we can pivot it down to a row.
1341 * Then we continue pivoting down until either
1342 * - the pivot would result in a manifestly unbounded column
1343 * => we don't perform the pivot, but simply return -1
1344 * - no more down pivots can be performed
1345 * - the sample value is negative
1346 * If the sample value becomes negative and the variable is supposed
1347 * to be nonnegative, then we undo the last pivot.
1348 * However, if the last pivot has made the pivoting variable
1349 * obviously redundant, then it may have moved to another row.
1350 * In that case we look for upward pivots until we reach a non-negative
1351 * value again.
1353 static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
1355 int row, col;
1356 struct isl_tab_var *pivot_var = NULL;
1358 if (min_is_manifestly_unbounded(tab, var))
1359 return -1;
1360 if (!var->is_row) {
1361 col = var->index;
1362 row = pivot_row(tab, NULL, -1, col);
1363 pivot_var = var_from_col(tab, col);
1364 if (isl_tab_pivot(tab, row, col) < 0)
1365 return -2;
1366 if (var->is_redundant)
1367 return 0;
1368 if (isl_int_is_neg(tab->mat->row[var->index][1])) {
1369 if (var->is_nonneg) {
1370 if (!pivot_var->is_redundant &&
1371 pivot_var->index == row) {
1372 if (isl_tab_pivot(tab, row, col) < 0)
1373 return -2;
1374 } else
1375 if (restore_row(tab, var) < -1)
1376 return -2;
1378 return -1;
1381 if (var->is_redundant)
1382 return 0;
1383 while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
1384 find_pivot(tab, var, var, -1, &row, &col);
1385 if (row == var->index)
1386 return -1;
1387 if (row == -1)
1388 return isl_int_sgn(tab->mat->row[var->index][1]);
1389 pivot_var = var_from_col(tab, col);
1390 if (isl_tab_pivot(tab, row, col) < 0)
1391 return -2;
1392 if (var->is_redundant)
1393 return 0;
1395 if (pivot_var && var->is_nonneg) {
1396 /* pivot back to non-negative value */
1397 if (!pivot_var->is_redundant && pivot_var->index == row) {
1398 if (isl_tab_pivot(tab, row, col) < 0)
1399 return -2;
1400 } else
1401 if (restore_row(tab, var) < -1)
1402 return -2;
1404 return -1;
1407 static int row_at_most_neg_one(struct isl_tab *tab, int row)
1409 if (tab->M) {
1410 if (isl_int_is_pos(tab->mat->row[row][2]))
1411 return 0;
1412 if (isl_int_is_neg(tab->mat->row[row][2]))
1413 return 1;
1415 return isl_int_is_neg(tab->mat->row[row][1]) &&
1416 isl_int_abs_ge(tab->mat->row[row][1],
1417 tab->mat->row[row][0]);
1420 /* Return 1 if "var" can attain values <= -1.
1421 * Return 0 otherwise.
1423 * The sample value of "var" is assumed to be non-negative when the
1424 * the function is called. If 1 is returned then the constraint
1425 * is not redundant and the sample value is made non-negative again before
1426 * the function returns.
1428 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
1430 int row, col;
1431 struct isl_tab_var *pivot_var;
1433 if (min_is_manifestly_unbounded(tab, var))
1434 return 1;
1435 if (!var->is_row) {
1436 col = var->index;
1437 row = pivot_row(tab, NULL, -1, col);
1438 pivot_var = var_from_col(tab, col);
1439 if (isl_tab_pivot(tab, row, col) < 0)
1440 return -1;
1441 if (var->is_redundant)
1442 return 0;
1443 if (row_at_most_neg_one(tab, var->index)) {
1444 if (var->is_nonneg) {
1445 if (!pivot_var->is_redundant &&
1446 pivot_var->index == row) {
1447 if (isl_tab_pivot(tab, row, col) < 0)
1448 return -1;
1449 } else
1450 if (restore_row(tab, var) < -1)
1451 return -1;
1453 return 1;
1456 if (var->is_redundant)
1457 return 0;
1458 do {
1459 find_pivot(tab, var, var, -1, &row, &col);
1460 if (row == var->index) {
1461 if (restore_row(tab, var) < -1)
1462 return -1;
1463 return 1;
1465 if (row == -1)
1466 return 0;
1467 pivot_var = var_from_col(tab, col);
1468 if (isl_tab_pivot(tab, row, col) < 0)
1469 return -1;
1470 if (var->is_redundant)
1471 return 0;
1472 } while (!row_at_most_neg_one(tab, var->index));
1473 if (var->is_nonneg) {
1474 /* pivot back to non-negative value */
1475 if (!pivot_var->is_redundant && pivot_var->index == row)
1476 if (isl_tab_pivot(tab, row, col) < 0)
1477 return -1;
1478 if (restore_row(tab, var) < -1)
1479 return -1;
1481 return 1;
1484 /* Return 1 if "var" can attain values >= 1.
1485 * Return 0 otherwise.
1487 static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
1489 int row, col;
1490 isl_int *r;
1492 if (max_is_manifestly_unbounded(tab, var))
1493 return 1;
1494 if (to_row(tab, var, 1) < 0)
1495 return -1;
1496 r = tab->mat->row[var->index];
1497 while (isl_int_lt(r[1], r[0])) {
1498 find_pivot(tab, var, var, 1, &row, &col);
1499 if (row == -1)
1500 return isl_int_ge(r[1], r[0]);
1501 if (row == var->index) /* manifestly unbounded */
1502 return 1;
1503 if (isl_tab_pivot(tab, row, col) < 0)
1504 return -1;
1506 return 1;
1509 static void swap_cols(struct isl_tab *tab, int col1, int col2)
1511 int t;
1512 unsigned off = 2 + tab->M;
1513 t = tab->col_var[col1];
1514 tab->col_var[col1] = tab->col_var[col2];
1515 tab->col_var[col2] = t;
1516 var_from_col(tab, col1)->index = col1;
1517 var_from_col(tab, col2)->index = col2;
1518 tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2);
1521 /* Mark column with index "col" as representing a zero variable.
1522 * If we may need to undo the operation the column is kept,
1523 * but no longer considered.
1524 * Otherwise, the column is simply removed.
1526 * The column may be interchanged with some other column. If it
1527 * is interchanged with a later column, return 1. Otherwise return 0.
1528 * If the columns are checked in order in the calling function,
1529 * then a return value of 1 means that the column with the given
1530 * column number may now contain a different column that
1531 * hasn't been checked yet.
1533 int isl_tab_kill_col(struct isl_tab *tab, int col)
1535 var_from_col(tab, col)->is_zero = 1;
1536 if (tab->need_undo) {
1537 if (isl_tab_push_var(tab, isl_tab_undo_zero,
1538 var_from_col(tab, col)) < 0)
1539 return -1;
1540 if (col != tab->n_dead)
1541 swap_cols(tab, col, tab->n_dead);
1542 tab->n_dead++;
1543 return 0;
1544 } else {
1545 if (col != tab->n_col - 1)
1546 swap_cols(tab, col, tab->n_col - 1);
1547 var_from_col(tab, tab->n_col - 1)->index = -1;
1548 tab->n_col--;
1549 return 1;
1553 static int row_is_manifestly_non_integral(struct isl_tab *tab, int row)
1555 unsigned off = 2 + tab->M;
1557 if (tab->M && !isl_int_eq(tab->mat->row[row][2],
1558 tab->mat->row[row][0]))
1559 return 0;
1560 if (isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1561 tab->n_col - tab->n_dead) != -1)
1562 return 0;
1564 return !isl_int_is_divisible_by(tab->mat->row[row][1],
1565 tab->mat->row[row][0]);
1568 /* For integer tableaus, check if any of the coordinates are stuck
1569 * at a non-integral value.
1571 static int tab_is_manifestly_empty(struct isl_tab *tab)
1573 int i;
1575 if (tab->empty)
1576 return 1;
1577 if (tab->rational)
1578 return 0;
1580 for (i = 0; i < tab->n_var; ++i) {
1581 if (!tab->var[i].is_row)
1582 continue;
1583 if (row_is_manifestly_non_integral(tab, tab->var[i].index))
1584 return 1;
1587 return 0;
1590 /* Row variable "var" is non-negative and cannot attain any values
1591 * larger than zero. This means that the coefficients of the unrestricted
1592 * column variables are zero and that the coefficients of the non-negative
1593 * column variables are zero or negative.
1594 * Each of the non-negative variables with a negative coefficient can
1595 * then also be written as the negative sum of non-negative variables
1596 * and must therefore also be zero.
1598 static int close_row(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
1599 static int close_row(struct isl_tab *tab, struct isl_tab_var *var)
1601 int j;
1602 struct isl_mat *mat = tab->mat;
1603 unsigned off = 2 + tab->M;
1605 isl_assert(tab->mat->ctx, var->is_nonneg, return -1);
1606 var->is_zero = 1;
1607 if (tab->need_undo)
1608 if (isl_tab_push_var(tab, isl_tab_undo_zero, var) < 0)
1609 return -1;
1610 for (j = tab->n_dead; j < tab->n_col; ++j) {
1611 int recheck;
1612 if (isl_int_is_zero(mat->row[var->index][off + j]))
1613 continue;
1614 isl_assert(tab->mat->ctx,
1615 isl_int_is_neg(mat->row[var->index][off + j]), return -1);
1616 recheck = isl_tab_kill_col(tab, j);
1617 if (recheck < 0)
1618 return -1;
1619 if (recheck)
1620 --j;
1622 if (isl_tab_mark_redundant(tab, var->index) < 0)
1623 return -1;
1624 if (tab_is_manifestly_empty(tab) && isl_tab_mark_empty(tab) < 0)
1625 return -1;
1626 return 0;
1629 /* Add a constraint to the tableau and allocate a row for it.
1630 * Return the index into the constraint array "con".
1632 int isl_tab_allocate_con(struct isl_tab *tab)
1634 int r;
1636 isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
1637 isl_assert(tab->mat->ctx, tab->n_con < tab->max_con, return -1);
1639 r = tab->n_con;
1640 tab->con[r].index = tab->n_row;
1641 tab->con[r].is_row = 1;
1642 tab->con[r].is_nonneg = 0;
1643 tab->con[r].is_zero = 0;
1644 tab->con[r].is_redundant = 0;
1645 tab->con[r].frozen = 0;
1646 tab->con[r].negated = 0;
1647 tab->row_var[tab->n_row] = ~r;
1649 tab->n_row++;
1650 tab->n_con++;
1651 if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
1652 return -1;
1654 return r;
1657 /* Add a variable to the tableau and allocate a column for it.
1658 * Return the index into the variable array "var".
1660 int isl_tab_allocate_var(struct isl_tab *tab)
1662 int r;
1663 int i;
1664 unsigned off = 2 + tab->M;
1666 isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
1667 isl_assert(tab->mat->ctx, tab->n_var < tab->max_var, return -1);
1669 r = tab->n_var;
1670 tab->var[r].index = tab->n_col;
1671 tab->var[r].is_row = 0;
1672 tab->var[r].is_nonneg = 0;
1673 tab->var[r].is_zero = 0;
1674 tab->var[r].is_redundant = 0;
1675 tab->var[r].frozen = 0;
1676 tab->var[r].negated = 0;
1677 tab->col_var[tab->n_col] = r;
1679 for (i = 0; i < tab->n_row; ++i)
1680 isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
1682 tab->n_var++;
1683 tab->n_col++;
1684 if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]) < 0)
1685 return -1;
1687 return r;
1690 /* Add a row to the tableau. The row is given as an affine combination
1691 * of the original variables and needs to be expressed in terms of the
1692 * column variables.
1694 * We add each term in turn.
1695 * If r = n/d_r is the current sum and we need to add k x, then
1696 * if x is a column variable, we increase the numerator of
1697 * this column by k d_r
1698 * if x = f/d_x is a row variable, then the new representation of r is
1700 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1701 * --- + --- = ------------------- = -------------------
1702 * d_r d_r d_r d_x/g m
1704 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1706 * If tab->M is set, then, internally, each variable x is represented
1707 * as x' - M. We then also need no subtract k d_r from the coefficient of M.
1709 int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
1711 int i;
1712 int r;
1713 isl_int *row;
1714 isl_int a, b;
1715 unsigned off = 2 + tab->M;
1717 r = isl_tab_allocate_con(tab);
1718 if (r < 0)
1719 return -1;
1721 isl_int_init(a);
1722 isl_int_init(b);
1723 row = tab->mat->row[tab->con[r].index];
1724 isl_int_set_si(row[0], 1);
1725 isl_int_set(row[1], line[0]);
1726 isl_seq_clr(row + 2, tab->M + tab->n_col);
1727 for (i = 0; i < tab->n_var; ++i) {
1728 if (tab->var[i].is_zero)
1729 continue;
1730 if (tab->var[i].is_row) {
1731 isl_int_lcm(a,
1732 row[0], tab->mat->row[tab->var[i].index][0]);
1733 isl_int_swap(a, row[0]);
1734 isl_int_divexact(a, row[0], a);
1735 isl_int_divexact(b,
1736 row[0], tab->mat->row[tab->var[i].index][0]);
1737 isl_int_mul(b, b, line[1 + i]);
1738 isl_seq_combine(row + 1, a, row + 1,
1739 b, tab->mat->row[tab->var[i].index] + 1,
1740 1 + tab->M + tab->n_col);
1741 } else
1742 isl_int_addmul(row[off + tab->var[i].index],
1743 line[1 + i], row[0]);
1744 if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
1745 isl_int_submul(row[2], line[1 + i], row[0]);
1747 isl_seq_normalize(tab->mat->ctx, row, off + tab->n_col);
1748 isl_int_clear(a);
1749 isl_int_clear(b);
1751 if (tab->row_sign)
1752 tab->row_sign[tab->con[r].index] = isl_tab_row_unknown;
1754 return r;
1757 static int drop_row(struct isl_tab *tab, int row)
1759 isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
1760 if (row != tab->n_row - 1)
1761 swap_rows(tab, row, tab->n_row - 1);
1762 tab->n_row--;
1763 tab->n_con--;
1764 return 0;
1767 static int drop_col(struct isl_tab *tab, int col)
1769 isl_assert(tab->mat->ctx, tab->col_var[col] == tab->n_var - 1, return -1);
1770 if (col != tab->n_col - 1)
1771 swap_cols(tab, col, tab->n_col - 1);
1772 tab->n_col--;
1773 tab->n_var--;
1774 return 0;
1777 /* Add inequality "ineq" and check if it conflicts with the
1778 * previously added constraints or if it is obviously redundant.
1780 int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
1782 int r;
1783 int sgn;
1784 isl_int cst;
1786 if (!tab)
1787 return -1;
1788 if (tab->bmap) {
1789 struct isl_basic_map *bmap = tab->bmap;
1791 isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, return -1);
1792 isl_assert(tab->mat->ctx,
1793 tab->n_con == bmap->n_eq + bmap->n_ineq, return -1);
1794 tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
1795 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1796 return -1;
1797 if (!tab->bmap)
1798 return -1;
1800 if (tab->cone) {
1801 isl_int_init(cst);
1802 isl_int_swap(ineq[0], cst);
1804 r = isl_tab_add_row(tab, ineq);
1805 if (tab->cone) {
1806 isl_int_swap(ineq[0], cst);
1807 isl_int_clear(cst);
1809 if (r < 0)
1810 return -1;
1811 tab->con[r].is_nonneg = 1;
1812 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1813 return -1;
1814 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1815 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1816 return -1;
1817 return 0;
1820 sgn = restore_row(tab, &tab->con[r]);
1821 if (sgn < -1)
1822 return -1;
1823 if (sgn < 0)
1824 return isl_tab_mark_empty(tab);
1825 if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
1826 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1827 return -1;
1828 return 0;
1831 /* Pivot a non-negative variable down until it reaches the value zero
1832 * and then pivot the variable into a column position.
1834 static int to_col(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
1835 static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
1837 int i;
1838 int row, col;
1839 unsigned off = 2 + tab->M;
1841 if (!var->is_row)
1842 return 0;
1844 while (isl_int_is_pos(tab->mat->row[var->index][1])) {
1845 find_pivot(tab, var, NULL, -1, &row, &col);
1846 isl_assert(tab->mat->ctx, row != -1, return -1);
1847 if (isl_tab_pivot(tab, row, col) < 0)
1848 return -1;
1849 if (!var->is_row)
1850 return 0;
1853 for (i = tab->n_dead; i < tab->n_col; ++i)
1854 if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
1855 break;
1857 isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
1858 if (isl_tab_pivot(tab, var->index, i) < 0)
1859 return -1;
1861 return 0;
1864 /* We assume Gaussian elimination has been performed on the equalities.
1865 * The equalities can therefore never conflict.
1866 * Adding the equalities is currently only really useful for a later call
1867 * to isl_tab_ineq_type.
1869 static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
1871 int i;
1872 int r;
1874 if (!tab)
1875 return NULL;
1876 r = isl_tab_add_row(tab, eq);
1877 if (r < 0)
1878 goto error;
1880 r = tab->con[r].index;
1881 i = isl_seq_first_non_zero(tab->mat->row[r] + 2 + tab->M + tab->n_dead,
1882 tab->n_col - tab->n_dead);
1883 isl_assert(tab->mat->ctx, i >= 0, goto error);
1884 i += tab->n_dead;
1885 if (isl_tab_pivot(tab, r, i) < 0)
1886 goto error;
1887 if (isl_tab_kill_col(tab, i) < 0)
1888 goto error;
1889 tab->n_eq++;
1891 return tab;
1892 error:
1893 isl_tab_free(tab);
1894 return NULL;
1897 static int row_is_manifestly_zero(struct isl_tab *tab, int row)
1899 unsigned off = 2 + tab->M;
1901 if (!isl_int_is_zero(tab->mat->row[row][1]))
1902 return 0;
1903 if (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))
1904 return 0;
1905 return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1906 tab->n_col - tab->n_dead) == -1;
1909 /* Add an equality that is known to be valid for the given tableau.
1911 int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
1913 struct isl_tab_var *var;
1914 int r;
1916 if (!tab)
1917 return -1;
1918 r = isl_tab_add_row(tab, eq);
1919 if (r < 0)
1920 return -1;
1922 var = &tab->con[r];
1923 r = var->index;
1924 if (row_is_manifestly_zero(tab, r)) {
1925 var->is_zero = 1;
1926 if (isl_tab_mark_redundant(tab, r) < 0)
1927 return -1;
1928 return 0;
1931 if (isl_int_is_neg(tab->mat->row[r][1])) {
1932 isl_seq_neg(tab->mat->row[r] + 1, tab->mat->row[r] + 1,
1933 1 + tab->n_col);
1934 var->negated = 1;
1936 var->is_nonneg = 1;
1937 if (to_col(tab, var) < 0)
1938 return -1;
1939 var->is_nonneg = 0;
1940 if (isl_tab_kill_col(tab, var->index) < 0)
1941 return -1;
1943 return 0;
1946 static int add_zero_row(struct isl_tab *tab)
1948 int r;
1949 isl_int *row;
1951 r = isl_tab_allocate_con(tab);
1952 if (r < 0)
1953 return -1;
1955 row = tab->mat->row[tab->con[r].index];
1956 isl_seq_clr(row + 1, 1 + tab->M + tab->n_col);
1957 isl_int_set_si(row[0], 1);
1959 return r;
1962 /* Add equality "eq" and check if it conflicts with the
1963 * previously added constraints or if it is obviously redundant.
1965 int isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
1967 struct isl_tab_undo *snap = NULL;
1968 struct isl_tab_var *var;
1969 int r;
1970 int row;
1971 int sgn;
1972 isl_int cst;
1974 if (!tab)
1975 return -1;
1976 isl_assert(tab->mat->ctx, !tab->M, return -1);
1978 if (tab->need_undo)
1979 snap = isl_tab_snap(tab);
1981 if (tab->cone) {
1982 isl_int_init(cst);
1983 isl_int_swap(eq[0], cst);
1985 r = isl_tab_add_row(tab, eq);
1986 if (tab->cone) {
1987 isl_int_swap(eq[0], cst);
1988 isl_int_clear(cst);
1990 if (r < 0)
1991 return -1;
1993 var = &tab->con[r];
1994 row = var->index;
1995 if (row_is_manifestly_zero(tab, row)) {
1996 if (snap) {
1997 if (isl_tab_rollback(tab, snap) < 0)
1998 return -1;
1999 } else
2000 drop_row(tab, row);
2001 return 0;
2004 if (tab->bmap) {
2005 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
2006 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
2007 return -1;
2008 isl_seq_neg(eq, eq, 1 + tab->n_var);
2009 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
2010 isl_seq_neg(eq, eq, 1 + tab->n_var);
2011 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
2012 return -1;
2013 if (!tab->bmap)
2014 return -1;
2015 if (add_zero_row(tab) < 0)
2016 return -1;
2019 sgn = isl_int_sgn(tab->mat->row[row][1]);
2021 if (sgn > 0) {
2022 isl_seq_neg(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
2023 1 + tab->n_col);
2024 var->negated = 1;
2025 sgn = -1;
2028 if (sgn < 0) {
2029 sgn = sign_of_max(tab, var);
2030 if (sgn < -1)
2031 return -1;
2032 if (sgn < 0) {
2033 if (isl_tab_mark_empty(tab) < 0)
2034 return -1;
2035 return 0;
2039 var->is_nonneg = 1;
2040 if (to_col(tab, var) < 0)
2041 return -1;
2042 var->is_nonneg = 0;
2043 if (isl_tab_kill_col(tab, var->index) < 0)
2044 return -1;
2046 return 0;
2049 /* Construct and return an inequality that expresses an upper bound
2050 * on the given div.
2051 * In particular, if the div is given by
2053 * d = floor(e/m)
2055 * then the inequality expresses
2057 * m d <= e
2059 static struct isl_vec *ineq_for_div(struct isl_basic_map *bmap, unsigned div)
2061 unsigned total;
2062 unsigned div_pos;
2063 struct isl_vec *ineq;
2065 if (!bmap)
2066 return NULL;
2068 total = isl_basic_map_total_dim(bmap);
2069 div_pos = 1 + total - bmap->n_div + div;
2071 ineq = isl_vec_alloc(bmap->ctx, 1 + total);
2072 if (!ineq)
2073 return NULL;
2075 isl_seq_cpy(ineq->el, bmap->div[div] + 1, 1 + total);
2076 isl_int_neg(ineq->el[div_pos], bmap->div[div][0]);
2077 return ineq;
2080 /* For a div d = floor(f/m), add the constraints
2082 * f - m d >= 0
2083 * -(f-(m-1)) + m d >= 0
2085 * Note that the second constraint is the negation of
2087 * f - m d >= m
2089 * If add_ineq is not NULL, then this function is used
2090 * instead of isl_tab_add_ineq to effectively add the inequalities.
2092 static int add_div_constraints(struct isl_tab *tab, unsigned div,
2093 int (*add_ineq)(void *user, isl_int *), void *user)
2095 unsigned total;
2096 unsigned div_pos;
2097 struct isl_vec *ineq;
2099 total = isl_basic_map_total_dim(tab->bmap);
2100 div_pos = 1 + total - tab->bmap->n_div + div;
2102 ineq = ineq_for_div(tab->bmap, div);
2103 if (!ineq)
2104 goto error;
2106 if (add_ineq) {
2107 if (add_ineq(user, ineq->el) < 0)
2108 goto error;
2109 } else {
2110 if (isl_tab_add_ineq(tab, ineq->el) < 0)
2111 goto error;
2114 isl_seq_neg(ineq->el, tab->bmap->div[div] + 1, 1 + total);
2115 isl_int_set(ineq->el[div_pos], tab->bmap->div[div][0]);
2116 isl_int_add(ineq->el[0], ineq->el[0], ineq->el[div_pos]);
2117 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
2119 if (add_ineq) {
2120 if (add_ineq(user, ineq->el) < 0)
2121 goto error;
2122 } else {
2123 if (isl_tab_add_ineq(tab, ineq->el) < 0)
2124 goto error;
2127 isl_vec_free(ineq);
2129 return 0;
2130 error:
2131 isl_vec_free(ineq);
2132 return -1;
2135 /* Check whether the div described by "div" is obviously non-negative.
2136 * If we are using a big parameter, then we will encode the div
2137 * as div' = M + div, which is always non-negative.
2138 * Otherwise, we check whether div is a non-negative affine combination
2139 * of non-negative variables.
2141 static int div_is_nonneg(struct isl_tab *tab, __isl_keep isl_vec *div)
2143 int i;
2145 if (tab->M)
2146 return 1;
2148 if (isl_int_is_neg(div->el[1]))
2149 return 0;
2151 for (i = 0; i < tab->n_var; ++i) {
2152 if (isl_int_is_neg(div->el[2 + i]))
2153 return 0;
2154 if (isl_int_is_zero(div->el[2 + i]))
2155 continue;
2156 if (!tab->var[i].is_nonneg)
2157 return 0;
2160 return 1;
2163 /* Add an extra div, prescribed by "div" to the tableau and
2164 * the associated bmap (which is assumed to be non-NULL).
2166 * If add_ineq is not NULL, then this function is used instead
2167 * of isl_tab_add_ineq to add the div constraints.
2168 * This complication is needed because the code in isl_tab_pip
2169 * wants to perform some extra processing when an inequality
2170 * is added to the tableau.
2172 int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
2173 int (*add_ineq)(void *user, isl_int *), void *user)
2175 int r;
2176 int k;
2177 int nonneg;
2179 if (!tab || !div)
2180 return -1;
2182 isl_assert(tab->mat->ctx, tab->bmap, return -1);
2184 nonneg = div_is_nonneg(tab, div);
2186 if (isl_tab_extend_cons(tab, 3) < 0)
2187 return -1;
2188 if (isl_tab_extend_vars(tab, 1) < 0)
2189 return -1;
2190 r = isl_tab_allocate_var(tab);
2191 if (r < 0)
2192 return -1;
2194 if (nonneg)
2195 tab->var[r].is_nonneg = 1;
2197 tab->bmap = isl_basic_map_extend_space(tab->bmap,
2198 isl_basic_map_get_space(tab->bmap), 1, 0, 2);
2199 k = isl_basic_map_alloc_div(tab->bmap);
2200 if (k < 0)
2201 return -1;
2202 isl_seq_cpy(tab->bmap->div[k], div->el, div->size);
2203 if (isl_tab_push(tab, isl_tab_undo_bmap_div) < 0)
2204 return -1;
2206 if (add_div_constraints(tab, k, add_ineq, user) < 0)
2207 return -1;
2209 return r;
2212 /* If "track" is set, then we want to keep track of all constraints in tab
2213 * in its bmap field. This field is initialized from a copy of "bmap",
2214 * so we need to make sure that all constraints in "bmap" also appear
2215 * in the constructed tab.
2217 __isl_give struct isl_tab *isl_tab_from_basic_map(
2218 __isl_keep isl_basic_map *bmap, int track)
2220 int i;
2221 struct isl_tab *tab;
2223 if (!bmap)
2224 return NULL;
2225 tab = isl_tab_alloc(bmap->ctx,
2226 isl_basic_map_total_dim(bmap) + bmap->n_ineq + 1,
2227 isl_basic_map_total_dim(bmap), 0);
2228 if (!tab)
2229 return NULL;
2230 tab->preserve = track;
2231 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
2232 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
2233 if (isl_tab_mark_empty(tab) < 0)
2234 goto error;
2235 goto done;
2237 for (i = 0; i < bmap->n_eq; ++i) {
2238 tab = add_eq(tab, bmap->eq[i]);
2239 if (!tab)
2240 return tab;
2242 for (i = 0; i < bmap->n_ineq; ++i) {
2243 if (isl_tab_add_ineq(tab, bmap->ineq[i]) < 0)
2244 goto error;
2245 if (tab->empty)
2246 goto done;
2248 done:
2249 if (track && isl_tab_track_bmap(tab, isl_basic_map_copy(bmap)) < 0)
2250 goto error;
2251 return tab;
2252 error:
2253 isl_tab_free(tab);
2254 return NULL;
2257 __isl_give struct isl_tab *isl_tab_from_basic_set(
2258 __isl_keep isl_basic_set *bset, int track)
2260 return isl_tab_from_basic_map(bset, track);
2263 /* Construct a tableau corresponding to the recession cone of "bset".
2265 struct isl_tab *isl_tab_from_recession_cone(__isl_keep isl_basic_set *bset,
2266 int parametric)
2268 isl_int cst;
2269 int i;
2270 struct isl_tab *tab;
2271 unsigned offset = 0;
2273 if (!bset)
2274 return NULL;
2275 if (parametric)
2276 offset = isl_basic_set_dim(bset, isl_dim_param);
2277 tab = isl_tab_alloc(bset->ctx, bset->n_eq + bset->n_ineq,
2278 isl_basic_set_total_dim(bset) - offset, 0);
2279 if (!tab)
2280 return NULL;
2281 tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
2282 tab->cone = 1;
2284 isl_int_init(cst);
2285 for (i = 0; i < bset->n_eq; ++i) {
2286 isl_int_swap(bset->eq[i][offset], cst);
2287 if (offset > 0) {
2288 if (isl_tab_add_eq(tab, bset->eq[i] + offset) < 0)
2289 goto error;
2290 } else
2291 tab = add_eq(tab, bset->eq[i]);
2292 isl_int_swap(bset->eq[i][offset], cst);
2293 if (!tab)
2294 goto done;
2296 for (i = 0; i < bset->n_ineq; ++i) {
2297 int r;
2298 isl_int_swap(bset->ineq[i][offset], cst);
2299 r = isl_tab_add_row(tab, bset->ineq[i] + offset);
2300 isl_int_swap(bset->ineq[i][offset], cst);
2301 if (r < 0)
2302 goto error;
2303 tab->con[r].is_nonneg = 1;
2304 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
2305 goto error;
2307 done:
2308 isl_int_clear(cst);
2309 return tab;
2310 error:
2311 isl_int_clear(cst);
2312 isl_tab_free(tab);
2313 return NULL;
2316 /* Assuming "tab" is the tableau of a cone, check if the cone is
2317 * bounded, i.e., if it is empty or only contains the origin.
2319 int isl_tab_cone_is_bounded(struct isl_tab *tab)
2321 int i;
2323 if (!tab)
2324 return -1;
2325 if (tab->empty)
2326 return 1;
2327 if (tab->n_dead == tab->n_col)
2328 return 1;
2330 for (;;) {
2331 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2332 struct isl_tab_var *var;
2333 int sgn;
2334 var = isl_tab_var_from_row(tab, i);
2335 if (!var->is_nonneg)
2336 continue;
2337 sgn = sign_of_max(tab, var);
2338 if (sgn < -1)
2339 return -1;
2340 if (sgn != 0)
2341 return 0;
2342 if (close_row(tab, var) < 0)
2343 return -1;
2344 break;
2346 if (tab->n_dead == tab->n_col)
2347 return 1;
2348 if (i == tab->n_row)
2349 return 0;
2353 int isl_tab_sample_is_integer(struct isl_tab *tab)
2355 int i;
2357 if (!tab)
2358 return -1;
2360 for (i = 0; i < tab->n_var; ++i) {
2361 int row;
2362 if (!tab->var[i].is_row)
2363 continue;
2364 row = tab->var[i].index;
2365 if (!isl_int_is_divisible_by(tab->mat->row[row][1],
2366 tab->mat->row[row][0]))
2367 return 0;
2369 return 1;
2372 static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
2374 int i;
2375 struct isl_vec *vec;
2377 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
2378 if (!vec)
2379 return NULL;
2381 isl_int_set_si(vec->block.data[0], 1);
2382 for (i = 0; i < tab->n_var; ++i) {
2383 if (!tab->var[i].is_row)
2384 isl_int_set_si(vec->block.data[1 + i], 0);
2385 else {
2386 int row = tab->var[i].index;
2387 isl_int_divexact(vec->block.data[1 + i],
2388 tab->mat->row[row][1], tab->mat->row[row][0]);
2392 return vec;
2395 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
2397 int i;
2398 struct isl_vec *vec;
2399 isl_int m;
2401 if (!tab)
2402 return NULL;
2404 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
2405 if (!vec)
2406 return NULL;
2408 isl_int_init(m);
2410 isl_int_set_si(vec->block.data[0], 1);
2411 for (i = 0; i < tab->n_var; ++i) {
2412 int row;
2413 if (!tab->var[i].is_row) {
2414 isl_int_set_si(vec->block.data[1 + i], 0);
2415 continue;
2417 row = tab->var[i].index;
2418 isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
2419 isl_int_divexact(m, tab->mat->row[row][0], m);
2420 isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
2421 isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
2422 isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
2424 vec = isl_vec_normalize(vec);
2426 isl_int_clear(m);
2427 return vec;
2430 /* Update "bmap" based on the results of the tableau "tab".
2431 * In particular, implicit equalities are made explicit, redundant constraints
2432 * are removed and if the sample value happens to be integer, it is stored
2433 * in "bmap" (unless "bmap" already had an integer sample).
2435 * The tableau is assumed to have been created from "bmap" using
2436 * isl_tab_from_basic_map.
2438 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
2439 struct isl_tab *tab)
2441 int i;
2442 unsigned n_eq;
2444 if (!bmap)
2445 return NULL;
2446 if (!tab)
2447 return bmap;
2449 n_eq = tab->n_eq;
2450 if (tab->empty)
2451 bmap = isl_basic_map_set_to_empty(bmap);
2452 else
2453 for (i = bmap->n_ineq - 1; i >= 0; --i) {
2454 if (isl_tab_is_equality(tab, n_eq + i))
2455 isl_basic_map_inequality_to_equality(bmap, i);
2456 else if (isl_tab_is_redundant(tab, n_eq + i))
2457 isl_basic_map_drop_inequality(bmap, i);
2459 if (bmap->n_eq != n_eq)
2460 isl_basic_map_gauss(bmap, NULL);
2461 if (!tab->rational &&
2462 !bmap->sample && isl_tab_sample_is_integer(tab))
2463 bmap->sample = extract_integer_sample(tab);
2464 return bmap;
2467 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
2468 struct isl_tab *tab)
2470 return (struct isl_basic_set *)isl_basic_map_update_from_tab(
2471 (struct isl_basic_map *)bset, tab);
2474 /* Given a non-negative variable "var", add a new non-negative variable
2475 * that is the opposite of "var", ensuring that var can only attain the
2476 * value zero.
2477 * If var = n/d is a row variable, then the new variable = -n/d.
2478 * If var is a column variables, then the new variable = -var.
2479 * If the new variable cannot attain non-negative values, then
2480 * the resulting tableau is empty.
2481 * Otherwise, we know the value will be zero and we close the row.
2483 static int cut_to_hyperplane(struct isl_tab *tab, struct isl_tab_var *var)
2485 unsigned r;
2486 isl_int *row;
2487 int sgn;
2488 unsigned off = 2 + tab->M;
2490 if (var->is_zero)
2491 return 0;
2492 isl_assert(tab->mat->ctx, !var->is_redundant, return -1);
2493 isl_assert(tab->mat->ctx, var->is_nonneg, return -1);
2495 if (isl_tab_extend_cons(tab, 1) < 0)
2496 return -1;
2498 r = tab->n_con;
2499 tab->con[r].index = tab->n_row;
2500 tab->con[r].is_row = 1;
2501 tab->con[r].is_nonneg = 0;
2502 tab->con[r].is_zero = 0;
2503 tab->con[r].is_redundant = 0;
2504 tab->con[r].frozen = 0;
2505 tab->con[r].negated = 0;
2506 tab->row_var[tab->n_row] = ~r;
2507 row = tab->mat->row[tab->n_row];
2509 if (var->is_row) {
2510 isl_int_set(row[0], tab->mat->row[var->index][0]);
2511 isl_seq_neg(row + 1,
2512 tab->mat->row[var->index] + 1, 1 + tab->n_col);
2513 } else {
2514 isl_int_set_si(row[0], 1);
2515 isl_seq_clr(row + 1, 1 + tab->n_col);
2516 isl_int_set_si(row[off + var->index], -1);
2519 tab->n_row++;
2520 tab->n_con++;
2521 if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
2522 return -1;
2524 sgn = sign_of_max(tab, &tab->con[r]);
2525 if (sgn < -1)
2526 return -1;
2527 if (sgn < 0) {
2528 if (isl_tab_mark_empty(tab) < 0)
2529 return -1;
2530 return 0;
2532 tab->con[r].is_nonneg = 1;
2533 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
2534 return -1;
2535 /* sgn == 0 */
2536 if (close_row(tab, &tab->con[r]) < 0)
2537 return -1;
2539 return 0;
2542 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2543 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2544 * by r' = r + 1 >= 0.
2545 * If r is a row variable, we simply increase the constant term by one
2546 * (taking into account the denominator).
2547 * If r is a column variable, then we need to modify each row that
2548 * refers to r = r' - 1 by substituting this equality, effectively
2549 * subtracting the coefficient of the column from the constant.
2550 * We should only do this if the minimum is manifestly unbounded,
2551 * however. Otherwise, we may end up with negative sample values
2552 * for non-negative variables.
2553 * So, if r is a column variable with a minimum that is not
2554 * manifestly unbounded, then we need to move it to a row.
2555 * However, the sample value of this row may be negative,
2556 * even after the relaxation, so we need to restore it.
2557 * We therefore prefer to pivot a column up to a row, if possible.
2559 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
2561 struct isl_tab_var *var;
2562 unsigned off = 2 + tab->M;
2564 if (!tab)
2565 return NULL;
2567 var = &tab->con[con];
2569 if (var->is_row && (var->index < 0 || var->index < tab->n_redundant))
2570 isl_die(tab->mat->ctx, isl_error_invalid,
2571 "cannot relax redundant constraint", goto error);
2572 if (!var->is_row && (var->index < 0 || var->index < tab->n_dead))
2573 isl_die(tab->mat->ctx, isl_error_invalid,
2574 "cannot relax dead constraint", goto error);
2576 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
2577 if (to_row(tab, var, 1) < 0)
2578 goto error;
2579 if (!var->is_row && !min_is_manifestly_unbounded(tab, var))
2580 if (to_row(tab, var, -1) < 0)
2581 goto error;
2583 if (var->is_row) {
2584 isl_int_add(tab->mat->row[var->index][1],
2585 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
2586 if (restore_row(tab, var) < 0)
2587 goto error;
2588 } else {
2589 int i;
2591 for (i = 0; i < tab->n_row; ++i) {
2592 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2593 continue;
2594 isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
2595 tab->mat->row[i][off + var->index]);
2600 if (isl_tab_push_var(tab, isl_tab_undo_relax, var) < 0)
2601 goto error;
2603 return tab;
2604 error:
2605 isl_tab_free(tab);
2606 return NULL;
2609 /* Remove the sign constraint from constraint "con".
2611 * If the constraint variable was originally marked non-negative,
2612 * then we make sure we mark it non-negative again during rollback.
2614 int isl_tab_unrestrict(struct isl_tab *tab, int con)
2616 struct isl_tab_var *var;
2618 if (!tab)
2619 return -1;
2621 var = &tab->con[con];
2622 if (!var->is_nonneg)
2623 return 0;
2625 var->is_nonneg = 0;
2626 if (isl_tab_push_var(tab, isl_tab_undo_unrestrict, var) < 0)
2627 return -1;
2629 return 0;
2632 int isl_tab_select_facet(struct isl_tab *tab, int con)
2634 if (!tab)
2635 return -1;
2637 return cut_to_hyperplane(tab, &tab->con[con]);
2640 static int may_be_equality(struct isl_tab *tab, int row)
2642 return tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
2643 : isl_int_lt(tab->mat->row[row][1],
2644 tab->mat->row[row][0]);
2647 /* Check for (near) equalities among the constraints.
2648 * A constraint is an equality if it is non-negative and if
2649 * its maximal value is either
2650 * - zero (in case of rational tableaus), or
2651 * - strictly less than 1 (in case of integer tableaus)
2653 * We first mark all non-redundant and non-dead variables that
2654 * are not frozen and not obviously not an equality.
2655 * Then we iterate over all marked variables if they can attain
2656 * any values larger than zero or at least one.
2657 * If the maximal value is zero, we mark any column variables
2658 * that appear in the row as being zero and mark the row as being redundant.
2659 * Otherwise, if the maximal value is strictly less than one (and the
2660 * tableau is integer), then we restrict the value to being zero
2661 * by adding an opposite non-negative variable.
2663 int isl_tab_detect_implicit_equalities(struct isl_tab *tab)
2665 int i;
2666 unsigned n_marked;
2668 if (!tab)
2669 return -1;
2670 if (tab->empty)
2671 return 0;
2672 if (tab->n_dead == tab->n_col)
2673 return 0;
2675 n_marked = 0;
2676 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2677 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
2678 var->marked = !var->frozen && var->is_nonneg &&
2679 may_be_equality(tab, i);
2680 if (var->marked)
2681 n_marked++;
2683 for (i = tab->n_dead; i < tab->n_col; ++i) {
2684 struct isl_tab_var *var = var_from_col(tab, i);
2685 var->marked = !var->frozen && var->is_nonneg;
2686 if (var->marked)
2687 n_marked++;
2689 while (n_marked) {
2690 struct isl_tab_var *var;
2691 int sgn;
2692 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2693 var = isl_tab_var_from_row(tab, i);
2694 if (var->marked)
2695 break;
2697 if (i == tab->n_row) {
2698 for (i = tab->n_dead; i < tab->n_col; ++i) {
2699 var = var_from_col(tab, i);
2700 if (var->marked)
2701 break;
2703 if (i == tab->n_col)
2704 break;
2706 var->marked = 0;
2707 n_marked--;
2708 sgn = sign_of_max(tab, var);
2709 if (sgn < 0)
2710 return -1;
2711 if (sgn == 0) {
2712 if (close_row(tab, var) < 0)
2713 return -1;
2714 } else if (!tab->rational && !at_least_one(tab, var)) {
2715 if (cut_to_hyperplane(tab, var) < 0)
2716 return -1;
2717 return isl_tab_detect_implicit_equalities(tab);
2719 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2720 var = isl_tab_var_from_row(tab, i);
2721 if (!var->marked)
2722 continue;
2723 if (may_be_equality(tab, i))
2724 continue;
2725 var->marked = 0;
2726 n_marked--;
2730 return 0;
2733 /* Update the element of row_var or col_var that corresponds to
2734 * constraint tab->con[i] to a move from position "old" to position "i".
2736 static int update_con_after_move(struct isl_tab *tab, int i, int old)
2738 int *p;
2739 int index;
2741 index = tab->con[i].index;
2742 if (index == -1)
2743 return 0;
2744 p = tab->con[i].is_row ? tab->row_var : tab->col_var;
2745 if (p[index] != ~old)
2746 isl_die(tab->mat->ctx, isl_error_internal,
2747 "broken internal state", return -1);
2748 p[index] = ~i;
2750 return 0;
2753 /* Rotate the "n" constraints starting at "first" to the right,
2754 * putting the last constraint in the position of the first constraint.
2756 static int rotate_constraints(struct isl_tab *tab, int first, int n)
2758 int i, last;
2759 struct isl_tab_var var;
2761 if (n <= 1)
2762 return 0;
2764 last = first + n - 1;
2765 var = tab->con[last];
2766 for (i = last; i > first; --i) {
2767 tab->con[i] = tab->con[i - 1];
2768 if (update_con_after_move(tab, i, i - 1) < 0)
2769 return -1;
2771 tab->con[first] = var;
2772 if (update_con_after_move(tab, first, last) < 0)
2773 return -1;
2775 return 0;
2778 /* Make the equalities that are implicit in "bmap" but that have been
2779 * detected in the corresponding "tab" explicit in "bmap" and update
2780 * "tab" to reflect the new order of the constraints.
2782 * In particular, if inequality i is an implicit equality then
2783 * isl_basic_map_inequality_to_equality will move the inequality
2784 * in front of the other equality and it will move the last inequality
2785 * in the position of inequality i.
2786 * In the tableau, the inequalities of "bmap" are stored after the equalities
2787 * and so the original order
2789 * E E E E E A A A I B B B B L
2791 * is changed into
2793 * I E E E E E A A A L B B B B
2795 * where I is the implicit equality, the E are equalities,
2796 * the A inequalities before I, the B inequalities after I and
2797 * L the last inequality.
2798 * We therefore need to rotate to the right two sets of constraints,
2799 * those up to and including I and those after I.
2801 * If "tab" contains any constraints that are not in "bmap" then they
2802 * appear after those in "bmap" and they should be left untouched.
2804 * Note that this function leaves "bmap" in a temporary state
2805 * as it does not call isl_basic_map_gauss. Calling this function
2806 * is the responsibility of the caller.
2808 __isl_give isl_basic_map *isl_tab_make_equalities_explicit(struct isl_tab *tab,
2809 __isl_take isl_basic_map *bmap)
2811 int i;
2813 if (!tab || !bmap)
2814 return isl_basic_map_free(bmap);
2815 if (tab->empty)
2816 return bmap;
2818 for (i = bmap->n_ineq - 1; i >= 0; --i) {
2819 if (!isl_tab_is_equality(tab, bmap->n_eq + i))
2820 continue;
2821 isl_basic_map_inequality_to_equality(bmap, i);
2822 if (rotate_constraints(tab, 0, tab->n_eq + i + 1) < 0)
2823 return isl_basic_map_free(bmap);
2824 if (rotate_constraints(tab, tab->n_eq + i + 1,
2825 bmap->n_ineq - i) < 0)
2826 return isl_basic_map_free(bmap);
2827 tab->n_eq++;
2830 return bmap;
2833 static int con_is_redundant(struct isl_tab *tab, struct isl_tab_var *var)
2835 if (!tab)
2836 return -1;
2837 if (tab->rational) {
2838 int sgn = sign_of_min(tab, var);
2839 if (sgn < -1)
2840 return -1;
2841 return sgn >= 0;
2842 } else {
2843 int irred = isl_tab_min_at_most_neg_one(tab, var);
2844 if (irred < 0)
2845 return -1;
2846 return !irred;
2850 /* Check for (near) redundant constraints.
2851 * A constraint is redundant if it is non-negative and if
2852 * its minimal value (temporarily ignoring the non-negativity) is either
2853 * - zero (in case of rational tableaus), or
2854 * - strictly larger than -1 (in case of integer tableaus)
2856 * We first mark all non-redundant and non-dead variables that
2857 * are not frozen and not obviously negatively unbounded.
2858 * Then we iterate over all marked variables if they can attain
2859 * any values smaller than zero or at most negative one.
2860 * If not, we mark the row as being redundant (assuming it hasn't
2861 * been detected as being obviously redundant in the mean time).
2863 int isl_tab_detect_redundant(struct isl_tab *tab)
2865 int i;
2866 unsigned n_marked;
2868 if (!tab)
2869 return -1;
2870 if (tab->empty)
2871 return 0;
2872 if (tab->n_redundant == tab->n_row)
2873 return 0;
2875 n_marked = 0;
2876 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2877 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
2878 var->marked = !var->frozen && var->is_nonneg;
2879 if (var->marked)
2880 n_marked++;
2882 for (i = tab->n_dead; i < tab->n_col; ++i) {
2883 struct isl_tab_var *var = var_from_col(tab, i);
2884 var->marked = !var->frozen && var->is_nonneg &&
2885 !min_is_manifestly_unbounded(tab, var);
2886 if (var->marked)
2887 n_marked++;
2889 while (n_marked) {
2890 struct isl_tab_var *var;
2891 int red;
2892 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2893 var = isl_tab_var_from_row(tab, i);
2894 if (var->marked)
2895 break;
2897 if (i == tab->n_row) {
2898 for (i = tab->n_dead; i < tab->n_col; ++i) {
2899 var = var_from_col(tab, i);
2900 if (var->marked)
2901 break;
2903 if (i == tab->n_col)
2904 break;
2906 var->marked = 0;
2907 n_marked--;
2908 red = con_is_redundant(tab, var);
2909 if (red < 0)
2910 return -1;
2911 if (red && !var->is_redundant)
2912 if (isl_tab_mark_redundant(tab, var->index) < 0)
2913 return -1;
2914 for (i = tab->n_dead; i < tab->n_col; ++i) {
2915 var = var_from_col(tab, i);
2916 if (!var->marked)
2917 continue;
2918 if (!min_is_manifestly_unbounded(tab, var))
2919 continue;
2920 var->marked = 0;
2921 n_marked--;
2925 return 0;
2928 int isl_tab_is_equality(struct isl_tab *tab, int con)
2930 int row;
2931 unsigned off;
2933 if (!tab)
2934 return -1;
2935 if (tab->con[con].is_zero)
2936 return 1;
2937 if (tab->con[con].is_redundant)
2938 return 0;
2939 if (!tab->con[con].is_row)
2940 return tab->con[con].index < tab->n_dead;
2942 row = tab->con[con].index;
2944 off = 2 + tab->M;
2945 return isl_int_is_zero(tab->mat->row[row][1]) &&
2946 (!tab->M || isl_int_is_zero(tab->mat->row[row][2])) &&
2947 isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
2948 tab->n_col - tab->n_dead) == -1;
2951 /* Return the minimal value of the affine expression "f" with denominator
2952 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
2953 * the expression cannot attain arbitrarily small values.
2954 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
2955 * The return value reflects the nature of the result (empty, unbounded,
2956 * minimal value returned in *opt).
2958 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
2959 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
2960 unsigned flags)
2962 int r;
2963 enum isl_lp_result res = isl_lp_ok;
2964 struct isl_tab_var *var;
2965 struct isl_tab_undo *snap;
2967 if (!tab)
2968 return isl_lp_error;
2970 if (tab->empty)
2971 return isl_lp_empty;
2973 snap = isl_tab_snap(tab);
2974 r = isl_tab_add_row(tab, f);
2975 if (r < 0)
2976 return isl_lp_error;
2977 var = &tab->con[r];
2978 for (;;) {
2979 int row, col;
2980 find_pivot(tab, var, var, -1, &row, &col);
2981 if (row == var->index) {
2982 res = isl_lp_unbounded;
2983 break;
2985 if (row == -1)
2986 break;
2987 if (isl_tab_pivot(tab, row, col) < 0)
2988 return isl_lp_error;
2990 isl_int_mul(tab->mat->row[var->index][0],
2991 tab->mat->row[var->index][0], denom);
2992 if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
2993 int i;
2995 isl_vec_free(tab->dual);
2996 tab->dual = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_con);
2997 if (!tab->dual)
2998 return isl_lp_error;
2999 isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
3000 for (i = 0; i < tab->n_con; ++i) {
3001 int pos;
3002 if (tab->con[i].is_row) {
3003 isl_int_set_si(tab->dual->el[1 + i], 0);
3004 continue;
3006 pos = 2 + tab->M + tab->con[i].index;
3007 if (tab->con[i].negated)
3008 isl_int_neg(tab->dual->el[1 + i],
3009 tab->mat->row[var->index][pos]);
3010 else
3011 isl_int_set(tab->dual->el[1 + i],
3012 tab->mat->row[var->index][pos]);
3015 if (opt && res == isl_lp_ok) {
3016 if (opt_denom) {
3017 isl_int_set(*opt, tab->mat->row[var->index][1]);
3018 isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
3019 } else
3020 isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
3021 tab->mat->row[var->index][0]);
3023 if (isl_tab_rollback(tab, snap) < 0)
3024 return isl_lp_error;
3025 return res;
3028 int isl_tab_is_redundant(struct isl_tab *tab, int con)
3030 if (!tab)
3031 return -1;
3032 if (tab->con[con].is_zero)
3033 return 0;
3034 if (tab->con[con].is_redundant)
3035 return 1;
3036 return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
3039 /* Take a snapshot of the tableau that can be restored by s call to
3040 * isl_tab_rollback.
3042 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
3044 if (!tab)
3045 return NULL;
3046 tab->need_undo = 1;
3047 return tab->top;
3050 /* Undo the operation performed by isl_tab_relax.
3052 static int unrelax(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
3053 static int unrelax(struct isl_tab *tab, struct isl_tab_var *var)
3055 unsigned off = 2 + tab->M;
3057 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
3058 if (to_row(tab, var, 1) < 0)
3059 return -1;
3061 if (var->is_row) {
3062 isl_int_sub(tab->mat->row[var->index][1],
3063 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
3064 if (var->is_nonneg) {
3065 int sgn = restore_row(tab, var);
3066 isl_assert(tab->mat->ctx, sgn >= 0, return -1);
3068 } else {
3069 int i;
3071 for (i = 0; i < tab->n_row; ++i) {
3072 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
3073 continue;
3074 isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
3075 tab->mat->row[i][off + var->index]);
3080 return 0;
3083 /* Undo the operation performed by isl_tab_unrestrict.
3085 * In particular, mark the variable as being non-negative and make
3086 * sure the sample value respects this constraint.
3088 static int ununrestrict(struct isl_tab *tab, struct isl_tab_var *var)
3090 var->is_nonneg = 1;
3092 if (var->is_row && restore_row(tab, var) < -1)
3093 return -1;
3095 return 0;
3098 static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
3099 static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
3101 struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
3102 switch (undo->type) {
3103 case isl_tab_undo_nonneg:
3104 var->is_nonneg = 0;
3105 break;
3106 case isl_tab_undo_redundant:
3107 var->is_redundant = 0;
3108 tab->n_redundant--;
3109 restore_row(tab, isl_tab_var_from_row(tab, tab->n_redundant));
3110 break;
3111 case isl_tab_undo_freeze:
3112 var->frozen = 0;
3113 break;
3114 case isl_tab_undo_zero:
3115 var->is_zero = 0;
3116 if (!var->is_row)
3117 tab->n_dead--;
3118 break;
3119 case isl_tab_undo_allocate:
3120 if (undo->u.var_index >= 0) {
3121 isl_assert(tab->mat->ctx, !var->is_row, return -1);
3122 drop_col(tab, var->index);
3123 break;
3125 if (!var->is_row) {
3126 if (!max_is_manifestly_unbounded(tab, var)) {
3127 if (to_row(tab, var, 1) < 0)
3128 return -1;
3129 } else if (!min_is_manifestly_unbounded(tab, var)) {
3130 if (to_row(tab, var, -1) < 0)
3131 return -1;
3132 } else
3133 if (to_row(tab, var, 0) < 0)
3134 return -1;
3136 drop_row(tab, var->index);
3137 break;
3138 case isl_tab_undo_relax:
3139 return unrelax(tab, var);
3140 case isl_tab_undo_unrestrict:
3141 return ununrestrict(tab, var);
3142 default:
3143 isl_die(tab->mat->ctx, isl_error_internal,
3144 "perform_undo_var called on invalid undo record",
3145 return -1);
3148 return 0;
3151 /* Restore the tableau to the state where the basic variables
3152 * are those in "col_var".
3153 * We first construct a list of variables that are currently in
3154 * the basis, but shouldn't. Then we iterate over all variables
3155 * that should be in the basis and for each one that is currently
3156 * not in the basis, we exchange it with one of the elements of the
3157 * list constructed before.
3158 * We can always find an appropriate variable to pivot with because
3159 * the current basis is mapped to the old basis by a non-singular
3160 * matrix and so we can never end up with a zero row.
3162 static int restore_basis(struct isl_tab *tab, int *col_var)
3164 int i, j;
3165 int n_extra = 0;
3166 int *extra = NULL; /* current columns that contain bad stuff */
3167 unsigned off = 2 + tab->M;
3169 extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
3170 if (!extra)
3171 goto error;
3172 for (i = 0; i < tab->n_col; ++i) {
3173 for (j = 0; j < tab->n_col; ++j)
3174 if (tab->col_var[i] == col_var[j])
3175 break;
3176 if (j < tab->n_col)
3177 continue;
3178 extra[n_extra++] = i;
3180 for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
3181 struct isl_tab_var *var;
3182 int row;
3184 for (j = 0; j < tab->n_col; ++j)
3185 if (col_var[i] == tab->col_var[j])
3186 break;
3187 if (j < tab->n_col)
3188 continue;
3189 var = var_from_index(tab, col_var[i]);
3190 row = var->index;
3191 for (j = 0; j < n_extra; ++j)
3192 if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
3193 break;
3194 isl_assert(tab->mat->ctx, j < n_extra, goto error);
3195 if (isl_tab_pivot(tab, row, extra[j]) < 0)
3196 goto error;
3197 extra[j] = extra[--n_extra];
3200 free(extra);
3201 return 0;
3202 error:
3203 free(extra);
3204 return -1;
3207 /* Remove all samples with index n or greater, i.e., those samples
3208 * that were added since we saved this number of samples in
3209 * isl_tab_save_samples.
3211 static void drop_samples_since(struct isl_tab *tab, int n)
3213 int i;
3215 for (i = tab->n_sample - 1; i >= 0 && tab->n_sample > n; --i) {
3216 if (tab->sample_index[i] < n)
3217 continue;
3219 if (i != tab->n_sample - 1) {
3220 int t = tab->sample_index[tab->n_sample-1];
3221 tab->sample_index[tab->n_sample-1] = tab->sample_index[i];
3222 tab->sample_index[i] = t;
3223 isl_mat_swap_rows(tab->samples, tab->n_sample-1, i);
3225 tab->n_sample--;
3229 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
3230 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
3232 switch (undo->type) {
3233 case isl_tab_undo_empty:
3234 tab->empty = 0;
3235 break;
3236 case isl_tab_undo_nonneg:
3237 case isl_tab_undo_redundant:
3238 case isl_tab_undo_freeze:
3239 case isl_tab_undo_zero:
3240 case isl_tab_undo_allocate:
3241 case isl_tab_undo_relax:
3242 case isl_tab_undo_unrestrict:
3243 return perform_undo_var(tab, undo);
3244 case isl_tab_undo_bmap_eq:
3245 return isl_basic_map_free_equality(tab->bmap, 1);
3246 case isl_tab_undo_bmap_ineq:
3247 return isl_basic_map_free_inequality(tab->bmap, 1);
3248 case isl_tab_undo_bmap_div:
3249 if (isl_basic_map_free_div(tab->bmap, 1) < 0)
3250 return -1;
3251 if (tab->samples)
3252 tab->samples->n_col--;
3253 break;
3254 case isl_tab_undo_saved_basis:
3255 if (restore_basis(tab, undo->u.col_var) < 0)
3256 return -1;
3257 break;
3258 case isl_tab_undo_drop_sample:
3259 tab->n_outside--;
3260 break;
3261 case isl_tab_undo_saved_samples:
3262 drop_samples_since(tab, undo->u.n);
3263 break;
3264 case isl_tab_undo_callback:
3265 return undo->u.callback->run(undo->u.callback);
3266 default:
3267 isl_assert(tab->mat->ctx, 0, return -1);
3269 return 0;
3272 /* Return the tableau to the state it was in when the snapshot "snap"
3273 * was taken.
3275 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
3277 struct isl_tab_undo *undo, *next;
3279 if (!tab)
3280 return -1;
3282 tab->in_undo = 1;
3283 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
3284 next = undo->next;
3285 if (undo == snap)
3286 break;
3287 if (perform_undo(tab, undo) < 0) {
3288 tab->top = undo;
3289 free_undo(tab);
3290 tab->in_undo = 0;
3291 return -1;
3293 free_undo_record(undo);
3295 tab->in_undo = 0;
3296 tab->top = undo;
3297 if (!undo)
3298 return -1;
3299 return 0;
3302 /* The given row "row" represents an inequality violated by all
3303 * points in the tableau. Check for some special cases of such
3304 * separating constraints.
3305 * In particular, if the row has been reduced to the constant -1,
3306 * then we know the inequality is adjacent (but opposite) to
3307 * an equality in the tableau.
3308 * If the row has been reduced to r = c*(-1 -r'), with r' an inequality
3309 * of the tableau and c a positive constant, then the inequality
3310 * is adjacent (but opposite) to the inequality r'.
3312 static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
3314 int pos;
3315 unsigned off = 2 + tab->M;
3317 if (tab->rational)
3318 return isl_ineq_separate;
3320 if (!isl_int_is_one(tab->mat->row[row][0]))
3321 return isl_ineq_separate;
3323 pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
3324 tab->n_col - tab->n_dead);
3325 if (pos == -1) {
3326 if (isl_int_is_negone(tab->mat->row[row][1]))
3327 return isl_ineq_adj_eq;
3328 else
3329 return isl_ineq_separate;
3332 if (!isl_int_eq(tab->mat->row[row][1],
3333 tab->mat->row[row][off + tab->n_dead + pos]))
3334 return isl_ineq_separate;
3336 pos = isl_seq_first_non_zero(
3337 tab->mat->row[row] + off + tab->n_dead + pos + 1,
3338 tab->n_col - tab->n_dead - pos - 1);
3340 return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
3343 /* Check the effect of inequality "ineq" on the tableau "tab".
3344 * The result may be
3345 * isl_ineq_redundant: satisfied by all points in the tableau
3346 * isl_ineq_separate: satisfied by no point in the tableau
3347 * isl_ineq_cut: satisfied by some by not all points
3348 * isl_ineq_adj_eq: adjacent to an equality
3349 * isl_ineq_adj_ineq: adjacent to an inequality.
3351 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
3353 enum isl_ineq_type type = isl_ineq_error;
3354 struct isl_tab_undo *snap = NULL;
3355 int con;
3356 int row;
3358 if (!tab)
3359 return isl_ineq_error;
3361 if (isl_tab_extend_cons(tab, 1) < 0)
3362 return isl_ineq_error;
3364 snap = isl_tab_snap(tab);
3366 con = isl_tab_add_row(tab, ineq);
3367 if (con < 0)
3368 goto error;
3370 row = tab->con[con].index;
3371 if (isl_tab_row_is_redundant(tab, row))
3372 type = isl_ineq_redundant;
3373 else if (isl_int_is_neg(tab->mat->row[row][1]) &&
3374 (tab->rational ||
3375 isl_int_abs_ge(tab->mat->row[row][1],
3376 tab->mat->row[row][0]))) {
3377 int nonneg = at_least_zero(tab, &tab->con[con]);
3378 if (nonneg < 0)
3379 goto error;
3380 if (nonneg)
3381 type = isl_ineq_cut;
3382 else
3383 type = separation_type(tab, row);
3384 } else {
3385 int red = con_is_redundant(tab, &tab->con[con]);
3386 if (red < 0)
3387 goto error;
3388 if (!red)
3389 type = isl_ineq_cut;
3390 else
3391 type = isl_ineq_redundant;
3394 if (isl_tab_rollback(tab, snap))
3395 return isl_ineq_error;
3396 return type;
3397 error:
3398 return isl_ineq_error;
3401 int isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap)
3403 bmap = isl_basic_map_cow(bmap);
3404 if (!tab || !bmap)
3405 goto error;
3407 if (tab->empty) {
3408 bmap = isl_basic_map_set_to_empty(bmap);
3409 if (!bmap)
3410 goto error;
3411 tab->bmap = bmap;
3412 return 0;
3415 isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, goto error);
3416 isl_assert(tab->mat->ctx,
3417 tab->n_con == bmap->n_eq + bmap->n_ineq, goto error);
3419 tab->bmap = bmap;
3421 return 0;
3422 error:
3423 isl_basic_map_free(bmap);
3424 return -1;
3427 int isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset)
3429 return isl_tab_track_bmap(tab, (isl_basic_map *)bset);
3432 __isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab)
3434 if (!tab)
3435 return NULL;
3437 return (isl_basic_set *)tab->bmap;
3440 static void isl_tab_print_internal(__isl_keep struct isl_tab *tab,
3441 FILE *out, int indent)
3443 unsigned r, c;
3444 int i;
3446 if (!tab) {
3447 fprintf(out, "%*snull tab\n", indent, "");
3448 return;
3450 fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
3451 tab->n_redundant, tab->n_dead);
3452 if (tab->rational)
3453 fprintf(out, ", rational");
3454 if (tab->empty)
3455 fprintf(out, ", empty");
3456 fprintf(out, "\n");
3457 fprintf(out, "%*s[", indent, "");
3458 for (i = 0; i < tab->n_var; ++i) {
3459 if (i)
3460 fprintf(out, (i == tab->n_param ||
3461 i == tab->n_var - tab->n_div) ? "; "
3462 : ", ");
3463 fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
3464 tab->var[i].index,
3465 tab->var[i].is_zero ? " [=0]" :
3466 tab->var[i].is_redundant ? " [R]" : "");
3468 fprintf(out, "]\n");
3469 fprintf(out, "%*s[", indent, "");
3470 for (i = 0; i < tab->n_con; ++i) {
3471 if (i)
3472 fprintf(out, ", ");
3473 fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
3474 tab->con[i].index,
3475 tab->con[i].is_zero ? " [=0]" :
3476 tab->con[i].is_redundant ? " [R]" : "");
3478 fprintf(out, "]\n");
3479 fprintf(out, "%*s[", indent, "");
3480 for (i = 0; i < tab->n_row; ++i) {
3481 const char *sign = "";
3482 if (i)
3483 fprintf(out, ", ");
3484 if (tab->row_sign) {
3485 if (tab->row_sign[i] == isl_tab_row_unknown)
3486 sign = "?";
3487 else if (tab->row_sign[i] == isl_tab_row_neg)
3488 sign = "-";
3489 else if (tab->row_sign[i] == isl_tab_row_pos)
3490 sign = "+";
3491 else
3492 sign = "+-";
3494 fprintf(out, "r%d: %d%s%s", i, tab->row_var[i],
3495 isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
3497 fprintf(out, "]\n");
3498 fprintf(out, "%*s[", indent, "");
3499 for (i = 0; i < tab->n_col; ++i) {
3500 if (i)
3501 fprintf(out, ", ");
3502 fprintf(out, "c%d: %d%s", i, tab->col_var[i],
3503 var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
3505 fprintf(out, "]\n");
3506 r = tab->mat->n_row;
3507 tab->mat->n_row = tab->n_row;
3508 c = tab->mat->n_col;
3509 tab->mat->n_col = 2 + tab->M + tab->n_col;
3510 isl_mat_print_internal(tab->mat, out, indent);
3511 tab->mat->n_row = r;
3512 tab->mat->n_col = c;
3513 if (tab->bmap)
3514 isl_basic_map_print_internal(tab->bmap, out, indent);
3517 void isl_tab_dump(__isl_keep struct isl_tab *tab)
3519 isl_tab_print_internal(tab, stderr, 0);