2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 #include "isl_map_private.h"
16 * The implementation of tableaus in this file was inspired by Section 8
17 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
18 * prover for program checking".
21 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
22 unsigned n_row, unsigned n_var, unsigned M)
28 tab = isl_calloc_type(ctx, struct isl_tab);
31 tab->mat = isl_mat_alloc(ctx, n_row, off + n_var);
34 tab->var = isl_alloc_array(ctx, struct isl_tab_var, n_var);
37 tab->con = isl_alloc_array(ctx, struct isl_tab_var, n_row);
40 tab->col_var = isl_alloc_array(ctx, int, n_var);
43 tab->row_var = isl_alloc_array(ctx, int, n_row);
46 for (i = 0; i < n_var; ++i) {
47 tab->var[i].index = i;
48 tab->var[i].is_row = 0;
49 tab->var[i].is_nonneg = 0;
50 tab->var[i].is_zero = 0;
51 tab->var[i].is_redundant = 0;
52 tab->var[i].frozen = 0;
53 tab->var[i].negated = 0;
67 tab->strict_redundant = 0;
74 tab->bottom.type = isl_tab_undo_bottom;
75 tab->bottom.next = NULL;
76 tab->top = &tab->bottom;
88 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new)
90 unsigned off = 2 + tab->M;
95 if (tab->max_con < tab->n_con + n_new) {
96 struct isl_tab_var *con;
98 con = isl_realloc_array(tab->mat->ctx, tab->con,
99 struct isl_tab_var, tab->max_con + n_new);
103 tab->max_con += n_new;
105 if (tab->mat->n_row < tab->n_row + n_new) {
108 tab->mat = isl_mat_extend(tab->mat,
109 tab->n_row + n_new, off + tab->n_col);
112 row_var = isl_realloc_array(tab->mat->ctx, tab->row_var,
113 int, tab->mat->n_row);
116 tab->row_var = row_var;
118 enum isl_tab_row_sign *s;
119 s = isl_realloc_array(tab->mat->ctx, tab->row_sign,
120 enum isl_tab_row_sign, tab->mat->n_row);
129 /* Make room for at least n_new extra variables.
130 * Return -1 if anything went wrong.
132 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new)
134 struct isl_tab_var *var;
135 unsigned off = 2 + tab->M;
137 if (tab->max_var < tab->n_var + n_new) {
138 var = isl_realloc_array(tab->mat->ctx, tab->var,
139 struct isl_tab_var, tab->n_var + n_new);
143 tab->max_var += n_new;
146 if (tab->mat->n_col < off + tab->n_col + n_new) {
149 tab->mat = isl_mat_extend(tab->mat,
150 tab->mat->n_row, off + tab->n_col + n_new);
153 p = isl_realloc_array(tab->mat->ctx, tab->col_var,
154 int, tab->n_col + n_new);
163 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new)
165 if (isl_tab_extend_cons(tab, n_new) >= 0)
172 static void free_undo(struct isl_tab *tab)
174 struct isl_tab_undo *undo, *next;
176 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
183 void isl_tab_free(struct isl_tab *tab)
188 isl_mat_free(tab->mat);
189 isl_vec_free(tab->dual);
190 isl_basic_map_free(tab->bmap);
196 isl_mat_free(tab->samples);
197 free(tab->sample_index);
198 isl_mat_free(tab->basis);
202 struct isl_tab *isl_tab_dup(struct isl_tab *tab)
212 dup = isl_calloc_type(tab->mat->ctx, struct isl_tab);
215 dup->mat = isl_mat_dup(tab->mat);
218 dup->var = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_var);
221 for (i = 0; i < tab->n_var; ++i)
222 dup->var[i] = tab->var[i];
223 dup->con = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_con);
226 for (i = 0; i < tab->n_con; ++i)
227 dup->con[i] = tab->con[i];
228 dup->col_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_col - off);
231 for (i = 0; i < tab->n_col; ++i)
232 dup->col_var[i] = tab->col_var[i];
233 dup->row_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_row);
236 for (i = 0; i < tab->n_row; ++i)
237 dup->row_var[i] = tab->row_var[i];
239 dup->row_sign = isl_alloc_array(tab->mat->ctx, enum isl_tab_row_sign,
243 for (i = 0; i < tab->n_row; ++i)
244 dup->row_sign[i] = tab->row_sign[i];
247 dup->samples = isl_mat_dup(tab->samples);
250 dup->sample_index = isl_alloc_array(tab->mat->ctx, int,
251 tab->samples->n_row);
252 if (!dup->sample_index)
254 dup->n_sample = tab->n_sample;
255 dup->n_outside = tab->n_outside;
257 dup->n_row = tab->n_row;
258 dup->n_con = tab->n_con;
259 dup->n_eq = tab->n_eq;
260 dup->max_con = tab->max_con;
261 dup->n_col = tab->n_col;
262 dup->n_var = tab->n_var;
263 dup->max_var = tab->max_var;
264 dup->n_param = tab->n_param;
265 dup->n_div = tab->n_div;
266 dup->n_dead = tab->n_dead;
267 dup->n_redundant = tab->n_redundant;
268 dup->rational = tab->rational;
269 dup->empty = tab->empty;
270 dup->strict_redundant = 0;
274 tab->cone = tab->cone;
275 dup->bottom.type = isl_tab_undo_bottom;
276 dup->bottom.next = NULL;
277 dup->top = &dup->bottom;
279 dup->n_zero = tab->n_zero;
280 dup->n_unbounded = tab->n_unbounded;
281 dup->basis = isl_mat_dup(tab->basis);
289 /* Construct the coefficient matrix of the product tableau
291 * mat{1,2} is the coefficient matrix of tableau {1,2}
292 * row{1,2} is the number of rows in tableau {1,2}
293 * col{1,2} is the number of columns in tableau {1,2}
294 * off is the offset to the coefficient column (skipping the
295 * denominator, the constant term and the big parameter if any)
296 * r{1,2} is the number of redundant rows in tableau {1,2}
297 * d{1,2} is the number of dead columns in tableau {1,2}
299 * The order of the rows and columns in the result is as explained
300 * in isl_tab_product.
302 static struct isl_mat *tab_mat_product(struct isl_mat *mat1,
303 struct isl_mat *mat2, unsigned row1, unsigned row2,
304 unsigned col1, unsigned col2,
305 unsigned off, unsigned r1, unsigned r2, unsigned d1, unsigned d2)
308 struct isl_mat *prod;
311 prod = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
315 for (i = 0; i < r1; ++i) {
316 isl_seq_cpy(prod->row[n + i], mat1->row[i], off + d1);
317 isl_seq_clr(prod->row[n + i] + off + d1, d2);
318 isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
319 mat1->row[i] + off + d1, col1 - d1);
320 isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
324 for (i = 0; i < r2; ++i) {
325 isl_seq_cpy(prod->row[n + i], mat2->row[i], off);
326 isl_seq_clr(prod->row[n + i] + off, d1);
327 isl_seq_cpy(prod->row[n + i] + off + d1,
328 mat2->row[i] + off, d2);
329 isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
330 isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
331 mat2->row[i] + off + d2, col2 - d2);
335 for (i = 0; i < row1 - r1; ++i) {
336 isl_seq_cpy(prod->row[n + i], mat1->row[r1 + i], off + d1);
337 isl_seq_clr(prod->row[n + i] + off + d1, d2);
338 isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
339 mat1->row[r1 + i] + off + d1, col1 - d1);
340 isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
344 for (i = 0; i < row2 - r2; ++i) {
345 isl_seq_cpy(prod->row[n + i], mat2->row[r2 + i], off);
346 isl_seq_clr(prod->row[n + i] + off, d1);
347 isl_seq_cpy(prod->row[n + i] + off + d1,
348 mat2->row[r2 + i] + off, d2);
349 isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
350 isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
351 mat2->row[r2 + i] + off + d2, col2 - d2);
357 /* Update the row or column index of a variable that corresponds
358 * to a variable in the first input tableau.
360 static void update_index1(struct isl_tab_var *var,
361 unsigned r1, unsigned r2, unsigned d1, unsigned d2)
363 if (var->index == -1)
365 if (var->is_row && var->index >= r1)
367 if (!var->is_row && var->index >= d1)
371 /* Update the row or column index of a variable that corresponds
372 * to a variable in the second input tableau.
374 static void update_index2(struct isl_tab_var *var,
375 unsigned row1, unsigned col1,
376 unsigned r1, unsigned r2, unsigned d1, unsigned d2)
378 if (var->index == -1)
393 /* Create a tableau that represents the Cartesian product of the sets
394 * represented by tableaus tab1 and tab2.
395 * The order of the rows in the product is
396 * - redundant rows of tab1
397 * - redundant rows of tab2
398 * - non-redundant rows of tab1
399 * - non-redundant rows of tab2
400 * The order of the columns is
403 * - coefficient of big parameter, if any
404 * - dead columns of tab1
405 * - dead columns of tab2
406 * - live columns of tab1
407 * - live columns of tab2
408 * The order of the variables and the constraints is a concatenation
409 * of order in the two input tableaus.
411 struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2)
414 struct isl_tab *prod;
416 unsigned r1, r2, d1, d2;
421 isl_assert(tab1->mat->ctx, tab1->M == tab2->M, return NULL);
422 isl_assert(tab1->mat->ctx, tab1->rational == tab2->rational, return NULL);
423 isl_assert(tab1->mat->ctx, tab1->cone == tab2->cone, return NULL);
424 isl_assert(tab1->mat->ctx, !tab1->row_sign, return NULL);
425 isl_assert(tab1->mat->ctx, !tab2->row_sign, return NULL);
426 isl_assert(tab1->mat->ctx, tab1->n_param == 0, return NULL);
427 isl_assert(tab1->mat->ctx, tab2->n_param == 0, return NULL);
428 isl_assert(tab1->mat->ctx, tab1->n_div == 0, return NULL);
429 isl_assert(tab1->mat->ctx, tab2->n_div == 0, return NULL);
432 r1 = tab1->n_redundant;
433 r2 = tab2->n_redundant;
436 prod = isl_calloc_type(tab1->mat->ctx, struct isl_tab);
439 prod->mat = tab_mat_product(tab1->mat, tab2->mat,
440 tab1->n_row, tab2->n_row,
441 tab1->n_col, tab2->n_col, off, r1, r2, d1, d2);
444 prod->var = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
445 tab1->max_var + tab2->max_var);
448 for (i = 0; i < tab1->n_var; ++i) {
449 prod->var[i] = tab1->var[i];
450 update_index1(&prod->var[i], r1, r2, d1, d2);
452 for (i = 0; i < tab2->n_var; ++i) {
453 prod->var[tab1->n_var + i] = tab2->var[i];
454 update_index2(&prod->var[tab1->n_var + i],
455 tab1->n_row, tab1->n_col,
458 prod->con = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
459 tab1->max_con + tab2->max_con);
462 for (i = 0; i < tab1->n_con; ++i) {
463 prod->con[i] = tab1->con[i];
464 update_index1(&prod->con[i], r1, r2, d1, d2);
466 for (i = 0; i < tab2->n_con; ++i) {
467 prod->con[tab1->n_con + i] = tab2->con[i];
468 update_index2(&prod->con[tab1->n_con + i],
469 tab1->n_row, tab1->n_col,
472 prod->col_var = isl_alloc_array(tab1->mat->ctx, int,
473 tab1->n_col + tab2->n_col);
476 for (i = 0; i < tab1->n_col; ++i) {
477 int pos = i < d1 ? i : i + d2;
478 prod->col_var[pos] = tab1->col_var[i];
480 for (i = 0; i < tab2->n_col; ++i) {
481 int pos = i < d2 ? d1 + i : tab1->n_col + i;
482 int t = tab2->col_var[i];
487 prod->col_var[pos] = t;
489 prod->row_var = isl_alloc_array(tab1->mat->ctx, int,
490 tab1->mat->n_row + tab2->mat->n_row);
493 for (i = 0; i < tab1->n_row; ++i) {
494 int pos = i < r1 ? i : i + r2;
495 prod->row_var[pos] = tab1->row_var[i];
497 for (i = 0; i < tab2->n_row; ++i) {
498 int pos = i < r2 ? r1 + i : tab1->n_row + i;
499 int t = tab2->row_var[i];
504 prod->row_var[pos] = t;
506 prod->samples = NULL;
507 prod->sample_index = NULL;
508 prod->n_row = tab1->n_row + tab2->n_row;
509 prod->n_con = tab1->n_con + tab2->n_con;
511 prod->max_con = tab1->max_con + tab2->max_con;
512 prod->n_col = tab1->n_col + tab2->n_col;
513 prod->n_var = tab1->n_var + tab2->n_var;
514 prod->max_var = tab1->max_var + tab2->max_var;
517 prod->n_dead = tab1->n_dead + tab2->n_dead;
518 prod->n_redundant = tab1->n_redundant + tab2->n_redundant;
519 prod->rational = tab1->rational;
520 prod->empty = tab1->empty || tab2->empty;
521 prod->strict_redundant = tab1->strict_redundant || tab2->strict_redundant;
525 prod->cone = tab1->cone;
526 prod->bottom.type = isl_tab_undo_bottom;
527 prod->bottom.next = NULL;
528 prod->top = &prod->bottom;
531 prod->n_unbounded = 0;
540 static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i)
545 return &tab->con[~i];
548 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
550 return var_from_index(tab, tab->row_var[i]);
553 static struct isl_tab_var *var_from_col(struct isl_tab *tab, int i)
555 return var_from_index(tab, tab->col_var[i]);
558 /* Check if there are any upper bounds on column variable "var",
559 * i.e., non-negative rows where var appears with a negative coefficient.
560 * Return 1 if there are no such bounds.
562 static int max_is_manifestly_unbounded(struct isl_tab *tab,
563 struct isl_tab_var *var)
566 unsigned off = 2 + tab->M;
570 for (i = tab->n_redundant; i < tab->n_row; ++i) {
571 if (!isl_int_is_neg(tab->mat->row[i][off + var->index]))
573 if (isl_tab_var_from_row(tab, i)->is_nonneg)
579 /* Check if there are any lower bounds on column variable "var",
580 * i.e., non-negative rows where var appears with a positive coefficient.
581 * Return 1 if there are no such bounds.
583 static int min_is_manifestly_unbounded(struct isl_tab *tab,
584 struct isl_tab_var *var)
587 unsigned off = 2 + tab->M;
591 for (i = tab->n_redundant; i < tab->n_row; ++i) {
592 if (!isl_int_is_pos(tab->mat->row[i][off + var->index]))
594 if (isl_tab_var_from_row(tab, i)->is_nonneg)
600 static int row_cmp(struct isl_tab *tab, int r1, int r2, int c, isl_int t)
602 unsigned off = 2 + tab->M;
606 isl_int_mul(t, tab->mat->row[r1][2], tab->mat->row[r2][off+c]);
607 isl_int_submul(t, tab->mat->row[r2][2], tab->mat->row[r1][off+c]);
612 isl_int_mul(t, tab->mat->row[r1][1], tab->mat->row[r2][off + c]);
613 isl_int_submul(t, tab->mat->row[r2][1], tab->mat->row[r1][off + c]);
614 return isl_int_sgn(t);
617 /* Given the index of a column "c", return the index of a row
618 * that can be used to pivot the column in, with either an increase
619 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
620 * If "var" is not NULL, then the row returned will be different from
621 * the one associated with "var".
623 * Each row in the tableau is of the form
625 * x_r = a_r0 + \sum_i a_ri x_i
627 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
628 * impose any limit on the increase or decrease in the value of x_c
629 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
630 * for the row with the smallest (most stringent) such bound.
631 * Note that the common denominator of each row drops out of the fraction.
632 * To check if row j has a smaller bound than row r, i.e.,
633 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
634 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
635 * where -sign(a_jc) is equal to "sgn".
637 static int pivot_row(struct isl_tab *tab,
638 struct isl_tab_var *var, int sgn, int c)
642 unsigned off = 2 + tab->M;
646 for (j = tab->n_redundant; j < tab->n_row; ++j) {
647 if (var && j == var->index)
649 if (!isl_tab_var_from_row(tab, j)->is_nonneg)
651 if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
657 tsgn = sgn * row_cmp(tab, r, j, c, t);
658 if (tsgn < 0 || (tsgn == 0 &&
659 tab->row_var[j] < tab->row_var[r]))
666 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
667 * (sgn < 0) the value of row variable var.
668 * If not NULL, then skip_var is a row variable that should be ignored
669 * while looking for a pivot row. It is usually equal to var.
671 * As the given row in the tableau is of the form
673 * x_r = a_r0 + \sum_i a_ri x_i
675 * we need to find a column such that the sign of a_ri is equal to "sgn"
676 * (such that an increase in x_i will have the desired effect) or a
677 * column with a variable that may attain negative values.
678 * If a_ri is positive, then we need to move x_i in the same direction
679 * to obtain the desired effect. Otherwise, x_i has to move in the
680 * opposite direction.
682 static void find_pivot(struct isl_tab *tab,
683 struct isl_tab_var *var, struct isl_tab_var *skip_var,
684 int sgn, int *row, int *col)
691 isl_assert(tab->mat->ctx, var->is_row, return);
692 tr = tab->mat->row[var->index] + 2 + tab->M;
695 for (j = tab->n_dead; j < tab->n_col; ++j) {
696 if (isl_int_is_zero(tr[j]))
698 if (isl_int_sgn(tr[j]) != sgn &&
699 var_from_col(tab, j)->is_nonneg)
701 if (c < 0 || tab->col_var[j] < tab->col_var[c])
707 sgn *= isl_int_sgn(tr[c]);
708 r = pivot_row(tab, skip_var, sgn, c);
709 *row = r < 0 ? var->index : r;
713 /* Return 1 if row "row" represents an obviously redundant inequality.
715 * - it represents an inequality or a variable
716 * - that is the sum of a non-negative sample value and a positive
717 * combination of zero or more non-negative constraints.
719 int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
722 unsigned off = 2 + tab->M;
724 if (tab->row_var[row] < 0 && !isl_tab_var_from_row(tab, row)->is_nonneg)
727 if (isl_int_is_neg(tab->mat->row[row][1]))
729 if (tab->strict_redundant && isl_int_is_zero(tab->mat->row[row][1]))
731 if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
734 for (i = tab->n_dead; i < tab->n_col; ++i) {
735 if (isl_int_is_zero(tab->mat->row[row][off + i]))
737 if (tab->col_var[i] >= 0)
739 if (isl_int_is_neg(tab->mat->row[row][off + i]))
741 if (!var_from_col(tab, i)->is_nonneg)
747 static void swap_rows(struct isl_tab *tab, int row1, int row2)
750 enum isl_tab_row_sign s;
752 t = tab->row_var[row1];
753 tab->row_var[row1] = tab->row_var[row2];
754 tab->row_var[row2] = t;
755 isl_tab_var_from_row(tab, row1)->index = row1;
756 isl_tab_var_from_row(tab, row2)->index = row2;
757 tab->mat = isl_mat_swap_rows(tab->mat, row1, row2);
761 s = tab->row_sign[row1];
762 tab->row_sign[row1] = tab->row_sign[row2];
763 tab->row_sign[row2] = s;
766 static int push_union(struct isl_tab *tab,
767 enum isl_tab_undo_type type, union isl_tab_undo_val u) WARN_UNUSED;
768 static int push_union(struct isl_tab *tab,
769 enum isl_tab_undo_type type, union isl_tab_undo_val u)
771 struct isl_tab_undo *undo;
776 undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
781 undo->next = tab->top;
787 int isl_tab_push_var(struct isl_tab *tab,
788 enum isl_tab_undo_type type, struct isl_tab_var *var)
790 union isl_tab_undo_val u;
792 u.var_index = tab->row_var[var->index];
794 u.var_index = tab->col_var[var->index];
795 return push_union(tab, type, u);
798 int isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
800 union isl_tab_undo_val u = { 0 };
801 return push_union(tab, type, u);
804 /* Push a record on the undo stack describing the current basic
805 * variables, so that the this state can be restored during rollback.
807 int isl_tab_push_basis(struct isl_tab *tab)
810 union isl_tab_undo_val u;
812 u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
815 for (i = 0; i < tab->n_col; ++i)
816 u.col_var[i] = tab->col_var[i];
817 return push_union(tab, isl_tab_undo_saved_basis, u);
820 int isl_tab_push_callback(struct isl_tab *tab, struct isl_tab_callback *callback)
822 union isl_tab_undo_val u;
823 u.callback = callback;
824 return push_union(tab, isl_tab_undo_callback, u);
827 struct isl_tab *isl_tab_init_samples(struct isl_tab *tab)
834 tab->samples = isl_mat_alloc(tab->mat->ctx, 1, 1 + tab->n_var);
837 tab->sample_index = isl_alloc_array(tab->mat->ctx, int, 1);
838 if (!tab->sample_index)
846 struct isl_tab *isl_tab_add_sample(struct isl_tab *tab,
847 __isl_take isl_vec *sample)
852 if (tab->n_sample + 1 > tab->samples->n_row) {
853 int *t = isl_realloc_array(tab->mat->ctx,
854 tab->sample_index, int, tab->n_sample + 1);
857 tab->sample_index = t;
860 tab->samples = isl_mat_extend(tab->samples,
861 tab->n_sample + 1, tab->samples->n_col);
865 isl_seq_cpy(tab->samples->row[tab->n_sample], sample->el, sample->size);
866 isl_vec_free(sample);
867 tab->sample_index[tab->n_sample] = tab->n_sample;
872 isl_vec_free(sample);
877 struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s)
879 if (s != tab->n_outside) {
880 int t = tab->sample_index[tab->n_outside];
881 tab->sample_index[tab->n_outside] = tab->sample_index[s];
882 tab->sample_index[s] = t;
883 isl_mat_swap_rows(tab->samples, tab->n_outside, s);
886 if (isl_tab_push(tab, isl_tab_undo_drop_sample) < 0) {
894 /* Record the current number of samples so that we can remove newer
895 * samples during a rollback.
897 int isl_tab_save_samples(struct isl_tab *tab)
899 union isl_tab_undo_val u;
905 return push_union(tab, isl_tab_undo_saved_samples, u);
908 /* Mark row with index "row" as being redundant.
909 * If we may need to undo the operation or if the row represents
910 * a variable of the original problem, the row is kept,
911 * but no longer considered when looking for a pivot row.
912 * Otherwise, the row is simply removed.
914 * The row may be interchanged with some other row. If it
915 * is interchanged with a later row, return 1. Otherwise return 0.
916 * If the rows are checked in order in the calling function,
917 * then a return value of 1 means that the row with the given
918 * row number may now contain a different row that hasn't been checked yet.
920 int isl_tab_mark_redundant(struct isl_tab *tab, int row)
922 struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
923 var->is_redundant = 1;
924 isl_assert(tab->mat->ctx, row >= tab->n_redundant, return -1);
925 if (tab->need_undo || tab->row_var[row] >= 0) {
926 if (tab->row_var[row] >= 0 && !var->is_nonneg) {
928 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, var) < 0)
931 if (row != tab->n_redundant)
932 swap_rows(tab, row, tab->n_redundant);
934 return isl_tab_push_var(tab, isl_tab_undo_redundant, var);
936 if (row != tab->n_row - 1)
937 swap_rows(tab, row, tab->n_row - 1);
938 isl_tab_var_from_row(tab, tab->n_row - 1)->index = -1;
944 int isl_tab_mark_empty(struct isl_tab *tab)
948 if (!tab->empty && tab->need_undo)
949 if (isl_tab_push(tab, isl_tab_undo_empty) < 0)
955 int isl_tab_freeze_constraint(struct isl_tab *tab, int con)
957 struct isl_tab_var *var;
962 var = &tab->con[con];
970 return isl_tab_push_var(tab, isl_tab_undo_freeze, var);
975 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
976 * the original sign of the pivot element.
977 * We only keep track of row signs during PILP solving and in this case
978 * we only pivot a row with negative sign (meaning the value is always
979 * non-positive) using a positive pivot element.
981 * For each row j, the new value of the parametric constant is equal to
983 * a_j0 - a_jc a_r0/a_rc
985 * where a_j0 is the original parametric constant, a_rc is the pivot element,
986 * a_r0 is the parametric constant of the pivot row and a_jc is the
987 * pivot column entry of the row j.
988 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
989 * remains the same if a_jc has the same sign as the row j or if
990 * a_jc is zero. In all other cases, we reset the sign to "unknown".
992 static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
995 struct isl_mat *mat = tab->mat;
996 unsigned off = 2 + tab->M;
1001 if (tab->row_sign[row] == 0)
1003 isl_assert(mat->ctx, row_sgn > 0, return);
1004 isl_assert(mat->ctx, tab->row_sign[row] == isl_tab_row_neg, return);
1005 tab->row_sign[row] = isl_tab_row_pos;
1006 for (i = 0; i < tab->n_row; ++i) {
1010 s = isl_int_sgn(mat->row[i][off + col]);
1013 if (!tab->row_sign[i])
1015 if (s < 0 && tab->row_sign[i] == isl_tab_row_neg)
1017 if (s > 0 && tab->row_sign[i] == isl_tab_row_pos)
1019 tab->row_sign[i] = isl_tab_row_unknown;
1023 /* Given a row number "row" and a column number "col", pivot the tableau
1024 * such that the associated variables are interchanged.
1025 * The given row in the tableau expresses
1027 * x_r = a_r0 + \sum_i a_ri x_i
1031 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
1033 * Substituting this equality into the other rows
1035 * x_j = a_j0 + \sum_i a_ji x_i
1037 * with a_jc \ne 0, we obtain
1039 * 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
1046 * where i is any other column and j is any other row,
1047 * is therefore transformed into
1049 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1050 * 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)
1052 * The transformation is performed along the following steps
1054 * d_r/n_rc n_ri/n_rc
1057 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1060 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1061 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
1063 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1064 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
1066 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1067 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
1069 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1070 * 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)
1073 int isl_tab_pivot(struct isl_tab *tab, int row, int col)
1078 struct isl_mat *mat = tab->mat;
1079 struct isl_tab_var *var;
1080 unsigned off = 2 + tab->M;
1082 isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
1083 sgn = isl_int_sgn(mat->row[row][0]);
1085 isl_int_neg(mat->row[row][0], mat->row[row][0]);
1086 isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]);
1088 for (j = 0; j < off - 1 + tab->n_col; ++j) {
1089 if (j == off - 1 + col)
1091 isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
1093 if (!isl_int_is_one(mat->row[row][0]))
1094 isl_seq_normalize(mat->ctx, mat->row[row], off + tab->n_col);
1095 for (i = 0; i < tab->n_row; ++i) {
1098 if (isl_int_is_zero(mat->row[i][off + col]))
1100 isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
1101 for (j = 0; j < off - 1 + tab->n_col; ++j) {
1102 if (j == off - 1 + col)
1104 isl_int_mul(mat->row[i][1 + j],
1105 mat->row[i][1 + j], mat->row[row][0]);
1106 isl_int_addmul(mat->row[i][1 + j],
1107 mat->row[i][off + col], mat->row[row][1 + j]);
1109 isl_int_mul(mat->row[i][off + col],
1110 mat->row[i][off + col], mat->row[row][off + col]);
1111 if (!isl_int_is_one(mat->row[i][0]))
1112 isl_seq_normalize(mat->ctx, mat->row[i], off + tab->n_col);
1114 t = tab->row_var[row];
1115 tab->row_var[row] = tab->col_var[col];
1116 tab->col_var[col] = t;
1117 var = isl_tab_var_from_row(tab, row);
1120 var = var_from_col(tab, col);
1123 update_row_sign(tab, row, col, sgn);
1126 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1127 if (isl_int_is_zero(mat->row[i][off + col]))
1129 if (!isl_tab_var_from_row(tab, i)->frozen &&
1130 isl_tab_row_is_redundant(tab, i)) {
1131 int redo = isl_tab_mark_redundant(tab, i);
1141 /* If "var" represents a column variable, then pivot is up (sgn > 0)
1142 * or down (sgn < 0) to a row. The variable is assumed not to be
1143 * unbounded in the specified direction.
1144 * If sgn = 0, then the variable is unbounded in both directions,
1145 * and we pivot with any row we can find.
1147 static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign) WARN_UNUSED;
1148 static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
1151 unsigned off = 2 + tab->M;
1157 for (r = tab->n_redundant; r < tab->n_row; ++r)
1158 if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
1160 isl_assert(tab->mat->ctx, r < tab->n_row, return -1);
1162 r = pivot_row(tab, NULL, sign, var->index);
1163 isl_assert(tab->mat->ctx, r >= 0, return -1);
1166 return isl_tab_pivot(tab, r, var->index);
1169 static void check_table(struct isl_tab *tab)
1175 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1176 struct isl_tab_var *var;
1177 var = isl_tab_var_from_row(tab, i);
1178 if (!var->is_nonneg)
1181 isl_assert(tab->mat->ctx,
1182 !isl_int_is_neg(tab->mat->row[i][2]), abort());
1183 if (isl_int_is_pos(tab->mat->row[i][2]))
1186 isl_assert(tab->mat->ctx, !isl_int_is_neg(tab->mat->row[i][1]),
1191 /* Return the sign of the maximal value of "var".
1192 * If the sign is not negative, then on return from this function,
1193 * the sample value will also be non-negative.
1195 * If "var" is manifestly unbounded wrt positive values, we are done.
1196 * Otherwise, we pivot the variable up to a row if needed
1197 * Then we continue pivoting down until either
1198 * - no more down pivots can be performed
1199 * - the sample value is positive
1200 * - the variable is pivoted into a manifestly unbounded column
1202 static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
1206 if (max_is_manifestly_unbounded(tab, var))
1208 if (to_row(tab, var, 1) < 0)
1210 while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
1211 find_pivot(tab, var, var, 1, &row, &col);
1213 return isl_int_sgn(tab->mat->row[var->index][1]);
1214 if (isl_tab_pivot(tab, row, col) < 0)
1216 if (!var->is_row) /* manifestly unbounded */
1222 int isl_tab_sign_of_max(struct isl_tab *tab, int con)
1224 struct isl_tab_var *var;
1229 var = &tab->con[con];
1230 isl_assert(tab->mat->ctx, !var->is_redundant, return -2);
1231 isl_assert(tab->mat->ctx, !var->is_zero, return -2);
1233 return sign_of_max(tab, var);
1236 static int row_is_neg(struct isl_tab *tab, int row)
1239 return isl_int_is_neg(tab->mat->row[row][1]);
1240 if (isl_int_is_pos(tab->mat->row[row][2]))
1242 if (isl_int_is_neg(tab->mat->row[row][2]))
1244 return isl_int_is_neg(tab->mat->row[row][1]);
1247 static int row_sgn(struct isl_tab *tab, int row)
1250 return isl_int_sgn(tab->mat->row[row][1]);
1251 if (!isl_int_is_zero(tab->mat->row[row][2]))
1252 return isl_int_sgn(tab->mat->row[row][2]);
1254 return isl_int_sgn(tab->mat->row[row][1]);
1257 /* Perform pivots until the row variable "var" has a non-negative
1258 * sample value or until no more upward pivots can be performed.
1259 * Return the sign of the sample value after the pivots have been
1262 static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
1266 while (row_is_neg(tab, var->index)) {
1267 find_pivot(tab, var, var, 1, &row, &col);
1270 if (isl_tab_pivot(tab, row, col) < 0)
1272 if (!var->is_row) /* manifestly unbounded */
1275 return row_sgn(tab, var->index);
1278 /* Perform pivots until we are sure that the row variable "var"
1279 * can attain non-negative values. After return from this
1280 * function, "var" is still a row variable, but its sample
1281 * value may not be non-negative, even if the function returns 1.
1283 static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
1287 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
1288 find_pivot(tab, var, var, 1, &row, &col);
1291 if (row == var->index) /* manifestly unbounded */
1293 if (isl_tab_pivot(tab, row, col) < 0)
1296 return !isl_int_is_neg(tab->mat->row[var->index][1]);
1299 /* Return a negative value if "var" can attain negative values.
1300 * Return a non-negative value otherwise.
1302 * If "var" is manifestly unbounded wrt negative values, we are done.
1303 * Otherwise, if var is in a column, we can pivot it down to a row.
1304 * Then we continue pivoting down until either
1305 * - the pivot would result in a manifestly unbounded column
1306 * => we don't perform the pivot, but simply return -1
1307 * - no more down pivots can be performed
1308 * - the sample value is negative
1309 * If the sample value becomes negative and the variable is supposed
1310 * to be nonnegative, then we undo the last pivot.
1311 * However, if the last pivot has made the pivoting variable
1312 * obviously redundant, then it may have moved to another row.
1313 * In that case we look for upward pivots until we reach a non-negative
1316 static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
1319 struct isl_tab_var *pivot_var = NULL;
1321 if (min_is_manifestly_unbounded(tab, var))
1325 row = pivot_row(tab, NULL, -1, col);
1326 pivot_var = var_from_col(tab, col);
1327 if (isl_tab_pivot(tab, row, col) < 0)
1329 if (var->is_redundant)
1331 if (isl_int_is_neg(tab->mat->row[var->index][1])) {
1332 if (var->is_nonneg) {
1333 if (!pivot_var->is_redundant &&
1334 pivot_var->index == row) {
1335 if (isl_tab_pivot(tab, row, col) < 0)
1338 if (restore_row(tab, var) < -1)
1344 if (var->is_redundant)
1346 while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
1347 find_pivot(tab, var, var, -1, &row, &col);
1348 if (row == var->index)
1351 return isl_int_sgn(tab->mat->row[var->index][1]);
1352 pivot_var = var_from_col(tab, col);
1353 if (isl_tab_pivot(tab, row, col) < 0)
1355 if (var->is_redundant)
1358 if (pivot_var && var->is_nonneg) {
1359 /* pivot back to non-negative value */
1360 if (!pivot_var->is_redundant && pivot_var->index == row) {
1361 if (isl_tab_pivot(tab, row, col) < 0)
1364 if (restore_row(tab, var) < -1)
1370 static int row_at_most_neg_one(struct isl_tab *tab, int row)
1373 if (isl_int_is_pos(tab->mat->row[row][2]))
1375 if (isl_int_is_neg(tab->mat->row[row][2]))
1378 return isl_int_is_neg(tab->mat->row[row][1]) &&
1379 isl_int_abs_ge(tab->mat->row[row][1],
1380 tab->mat->row[row][0]);
1383 /* Return 1 if "var" can attain values <= -1.
1384 * Return 0 otherwise.
1386 * The sample value of "var" is assumed to be non-negative when the
1387 * the function is called. If 1 is returned then the constraint
1388 * is not redundant and the sample value is made non-negative again before
1389 * the function returns.
1391 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
1394 struct isl_tab_var *pivot_var;
1396 if (min_is_manifestly_unbounded(tab, var))
1400 row = pivot_row(tab, NULL, -1, col);
1401 pivot_var = var_from_col(tab, col);
1402 if (isl_tab_pivot(tab, row, col) < 0)
1404 if (var->is_redundant)
1406 if (row_at_most_neg_one(tab, var->index)) {
1407 if (var->is_nonneg) {
1408 if (!pivot_var->is_redundant &&
1409 pivot_var->index == row) {
1410 if (isl_tab_pivot(tab, row, col) < 0)
1413 if (restore_row(tab, var) < -1)
1419 if (var->is_redundant)
1422 find_pivot(tab, var, var, -1, &row, &col);
1423 if (row == var->index) {
1424 if (restore_row(tab, var) < -1)
1430 pivot_var = var_from_col(tab, col);
1431 if (isl_tab_pivot(tab, row, col) < 0)
1433 if (var->is_redundant)
1435 } while (!row_at_most_neg_one(tab, var->index));
1436 if (var->is_nonneg) {
1437 /* pivot back to non-negative value */
1438 if (!pivot_var->is_redundant && pivot_var->index == row)
1439 if (isl_tab_pivot(tab, row, col) < 0)
1441 if (restore_row(tab, var) < -1)
1447 /* Return 1 if "var" can attain values >= 1.
1448 * Return 0 otherwise.
1450 static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
1455 if (max_is_manifestly_unbounded(tab, var))
1457 if (to_row(tab, var, 1) < 0)
1459 r = tab->mat->row[var->index];
1460 while (isl_int_lt(r[1], r[0])) {
1461 find_pivot(tab, var, var, 1, &row, &col);
1463 return isl_int_ge(r[1], r[0]);
1464 if (row == var->index) /* manifestly unbounded */
1466 if (isl_tab_pivot(tab, row, col) < 0)
1472 static void swap_cols(struct isl_tab *tab, int col1, int col2)
1475 unsigned off = 2 + tab->M;
1476 t = tab->col_var[col1];
1477 tab->col_var[col1] = tab->col_var[col2];
1478 tab->col_var[col2] = t;
1479 var_from_col(tab, col1)->index = col1;
1480 var_from_col(tab, col2)->index = col2;
1481 tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2);
1484 /* Mark column with index "col" as representing a zero variable.
1485 * If we may need to undo the operation the column is kept,
1486 * but no longer considered.
1487 * Otherwise, the column is simply removed.
1489 * The column may be interchanged with some other column. If it
1490 * is interchanged with a later column, return 1. Otherwise return 0.
1491 * If the columns are checked in order in the calling function,
1492 * then a return value of 1 means that the column with the given
1493 * column number may now contain a different column that
1494 * hasn't been checked yet.
1496 int isl_tab_kill_col(struct isl_tab *tab, int col)
1498 var_from_col(tab, col)->is_zero = 1;
1499 if (tab->need_undo) {
1500 if (isl_tab_push_var(tab, isl_tab_undo_zero,
1501 var_from_col(tab, col)) < 0)
1503 if (col != tab->n_dead)
1504 swap_cols(tab, col, tab->n_dead);
1508 if (col != tab->n_col - 1)
1509 swap_cols(tab, col, tab->n_col - 1);
1510 var_from_col(tab, tab->n_col - 1)->index = -1;
1516 /* Row variable "var" is non-negative and cannot attain any values
1517 * larger than zero. This means that the coefficients of the unrestricted
1518 * column variables are zero and that the coefficients of the non-negative
1519 * column variables are zero or negative.
1520 * Each of the non-negative variables with a negative coefficient can
1521 * then also be written as the negative sum of non-negative variables
1522 * and must therefore also be zero.
1524 static int close_row(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
1525 static int close_row(struct isl_tab *tab, struct isl_tab_var *var)
1528 struct isl_mat *mat = tab->mat;
1529 unsigned off = 2 + tab->M;
1531 isl_assert(tab->mat->ctx, var->is_nonneg, return -1);
1534 if (isl_tab_push_var(tab, isl_tab_undo_zero, var) < 0)
1536 for (j = tab->n_dead; j < tab->n_col; ++j) {
1538 if (isl_int_is_zero(mat->row[var->index][off + j]))
1540 isl_assert(tab->mat->ctx,
1541 isl_int_is_neg(mat->row[var->index][off + j]), return -1);
1542 recheck = isl_tab_kill_col(tab, j);
1548 if (isl_tab_mark_redundant(tab, var->index) < 0)
1553 /* Add a constraint to the tableau and allocate a row for it.
1554 * Return the index into the constraint array "con".
1556 int isl_tab_allocate_con(struct isl_tab *tab)
1560 isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
1561 isl_assert(tab->mat->ctx, tab->n_con < tab->max_con, return -1);
1564 tab->con[r].index = tab->n_row;
1565 tab->con[r].is_row = 1;
1566 tab->con[r].is_nonneg = 0;
1567 tab->con[r].is_zero = 0;
1568 tab->con[r].is_redundant = 0;
1569 tab->con[r].frozen = 0;
1570 tab->con[r].negated = 0;
1571 tab->row_var[tab->n_row] = ~r;
1575 if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
1581 /* Add a variable to the tableau and allocate a column for it.
1582 * Return the index into the variable array "var".
1584 int isl_tab_allocate_var(struct isl_tab *tab)
1588 unsigned off = 2 + tab->M;
1590 isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
1591 isl_assert(tab->mat->ctx, tab->n_var < tab->max_var, return -1);
1594 tab->var[r].index = tab->n_col;
1595 tab->var[r].is_row = 0;
1596 tab->var[r].is_nonneg = 0;
1597 tab->var[r].is_zero = 0;
1598 tab->var[r].is_redundant = 0;
1599 tab->var[r].frozen = 0;
1600 tab->var[r].negated = 0;
1601 tab->col_var[tab->n_col] = r;
1603 for (i = 0; i < tab->n_row; ++i)
1604 isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
1608 if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]) < 0)
1614 /* Add a row to the tableau. The row is given as an affine combination
1615 * of the original variables and needs to be expressed in terms of the
1618 * We add each term in turn.
1619 * If r = n/d_r is the current sum and we need to add k x, then
1620 * if x is a column variable, we increase the numerator of
1621 * this column by k d_r
1622 * if x = f/d_x is a row variable, then the new representation of r is
1624 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1625 * --- + --- = ------------------- = -------------------
1626 * d_r d_r d_r d_x/g m
1628 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1630 int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
1636 unsigned off = 2 + tab->M;
1638 r = isl_tab_allocate_con(tab);
1644 row = tab->mat->row[tab->con[r].index];
1645 isl_int_set_si(row[0], 1);
1646 isl_int_set(row[1], line[0]);
1647 isl_seq_clr(row + 2, tab->M + tab->n_col);
1648 for (i = 0; i < tab->n_var; ++i) {
1649 if (tab->var[i].is_zero)
1651 if (tab->var[i].is_row) {
1653 row[0], tab->mat->row[tab->var[i].index][0]);
1654 isl_int_swap(a, row[0]);
1655 isl_int_divexact(a, row[0], a);
1657 row[0], tab->mat->row[tab->var[i].index][0]);
1658 isl_int_mul(b, b, line[1 + i]);
1659 isl_seq_combine(row + 1, a, row + 1,
1660 b, tab->mat->row[tab->var[i].index] + 1,
1661 1 + tab->M + tab->n_col);
1663 isl_int_addmul(row[off + tab->var[i].index],
1664 line[1 + i], row[0]);
1665 if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
1666 isl_int_submul(row[2], line[1 + i], row[0]);
1668 isl_seq_normalize(tab->mat->ctx, row, off + tab->n_col);
1673 tab->row_sign[tab->con[r].index] = isl_tab_row_unknown;
1678 static int drop_row(struct isl_tab *tab, int row)
1680 isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
1681 if (row != tab->n_row - 1)
1682 swap_rows(tab, row, tab->n_row - 1);
1688 static int drop_col(struct isl_tab *tab, int col)
1690 isl_assert(tab->mat->ctx, tab->col_var[col] == tab->n_var - 1, return -1);
1691 if (col != tab->n_col - 1)
1692 swap_cols(tab, col, tab->n_col - 1);
1698 /* Add inequality "ineq" and check if it conflicts with the
1699 * previously added constraints or if it is obviously redundant.
1701 int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
1710 struct isl_basic_map *bmap = tab->bmap;
1712 isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, return -1);
1713 isl_assert(tab->mat->ctx,
1714 tab->n_con == bmap->n_eq + bmap->n_ineq, return -1);
1715 tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
1716 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1723 isl_int_swap(ineq[0], cst);
1725 r = isl_tab_add_row(tab, ineq);
1727 isl_int_swap(ineq[0], cst);
1732 tab->con[r].is_nonneg = 1;
1733 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1735 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1736 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1741 sgn = restore_row(tab, &tab->con[r]);
1745 return isl_tab_mark_empty(tab);
1746 if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
1747 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1752 /* Pivot a non-negative variable down until it reaches the value zero
1753 * and then pivot the variable into a column position.
1755 static int to_col(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
1756 static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
1760 unsigned off = 2 + tab->M;
1765 while (isl_int_is_pos(tab->mat->row[var->index][1])) {
1766 find_pivot(tab, var, NULL, -1, &row, &col);
1767 isl_assert(tab->mat->ctx, row != -1, return -1);
1768 if (isl_tab_pivot(tab, row, col) < 0)
1774 for (i = tab->n_dead; i < tab->n_col; ++i)
1775 if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
1778 isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
1779 if (isl_tab_pivot(tab, var->index, i) < 0)
1785 /* We assume Gaussian elimination has been performed on the equalities.
1786 * The equalities can therefore never conflict.
1787 * Adding the equalities is currently only really useful for a later call
1788 * to isl_tab_ineq_type.
1790 static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
1797 r = isl_tab_add_row(tab, eq);
1801 r = tab->con[r].index;
1802 i = isl_seq_first_non_zero(tab->mat->row[r] + 2 + tab->M + tab->n_dead,
1803 tab->n_col - tab->n_dead);
1804 isl_assert(tab->mat->ctx, i >= 0, goto error);
1806 if (isl_tab_pivot(tab, r, i) < 0)
1808 if (isl_tab_kill_col(tab, i) < 0)
1818 static int row_is_manifestly_zero(struct isl_tab *tab, int row)
1820 unsigned off = 2 + tab->M;
1822 if (!isl_int_is_zero(tab->mat->row[row][1]))
1824 if (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))
1826 return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1827 tab->n_col - tab->n_dead) == -1;
1830 /* Add an equality that is known to be valid for the given tableau.
1832 int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
1834 struct isl_tab_var *var;
1839 r = isl_tab_add_row(tab, eq);
1845 if (row_is_manifestly_zero(tab, r)) {
1847 if (isl_tab_mark_redundant(tab, r) < 0)
1852 if (isl_int_is_neg(tab->mat->row[r][1])) {
1853 isl_seq_neg(tab->mat->row[r] + 1, tab->mat->row[r] + 1,
1858 if (to_col(tab, var) < 0)
1861 if (isl_tab_kill_col(tab, var->index) < 0)
1867 static int add_zero_row(struct isl_tab *tab)
1872 r = isl_tab_allocate_con(tab);
1876 row = tab->mat->row[tab->con[r].index];
1877 isl_seq_clr(row + 1, 1 + tab->M + tab->n_col);
1878 isl_int_set_si(row[0], 1);
1883 /* Add equality "eq" and check if it conflicts with the
1884 * previously added constraints or if it is obviously redundant.
1886 int isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
1888 struct isl_tab_undo *snap = NULL;
1889 struct isl_tab_var *var;
1897 isl_assert(tab->mat->ctx, !tab->M, return -1);
1900 snap = isl_tab_snap(tab);
1904 isl_int_swap(eq[0], cst);
1906 r = isl_tab_add_row(tab, eq);
1908 isl_int_swap(eq[0], cst);
1916 if (row_is_manifestly_zero(tab, row)) {
1918 if (isl_tab_rollback(tab, snap) < 0)
1926 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
1927 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1929 isl_seq_neg(eq, eq, 1 + tab->n_var);
1930 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
1931 isl_seq_neg(eq, eq, 1 + tab->n_var);
1932 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1936 if (add_zero_row(tab) < 0)
1940 sgn = isl_int_sgn(tab->mat->row[row][1]);
1943 isl_seq_neg(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
1950 sgn = sign_of_max(tab, var);
1954 if (isl_tab_mark_empty(tab) < 0)
1961 if (to_col(tab, var) < 0)
1964 if (isl_tab_kill_col(tab, var->index) < 0)
1970 /* Construct and return an inequality that expresses an upper bound
1972 * In particular, if the div is given by
1976 * then the inequality expresses
1980 static struct isl_vec *ineq_for_div(struct isl_basic_map *bmap, unsigned div)
1984 struct isl_vec *ineq;
1989 total = isl_basic_map_total_dim(bmap);
1990 div_pos = 1 + total - bmap->n_div + div;
1992 ineq = isl_vec_alloc(bmap->ctx, 1 + total);
1996 isl_seq_cpy(ineq->el, bmap->div[div] + 1, 1 + total);
1997 isl_int_neg(ineq->el[div_pos], bmap->div[div][0]);
2001 /* For a div d = floor(f/m), add the constraints
2004 * -(f-(m-1)) + m d >= 0
2006 * Note that the second constraint is the negation of
2010 * If add_ineq is not NULL, then this function is used
2011 * instead of isl_tab_add_ineq to effectively add the inequalities.
2013 static int add_div_constraints(struct isl_tab *tab, unsigned div,
2014 int (*add_ineq)(void *user, isl_int *), void *user)
2018 struct isl_vec *ineq;
2020 total = isl_basic_map_total_dim(tab->bmap);
2021 div_pos = 1 + total - tab->bmap->n_div + div;
2023 ineq = ineq_for_div(tab->bmap, div);
2028 if (add_ineq(user, ineq->el) < 0)
2031 if (isl_tab_add_ineq(tab, ineq->el) < 0)
2035 isl_seq_neg(ineq->el, tab->bmap->div[div] + 1, 1 + total);
2036 isl_int_set(ineq->el[div_pos], tab->bmap->div[div][0]);
2037 isl_int_add(ineq->el[0], ineq->el[0], ineq->el[div_pos]);
2038 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
2041 if (add_ineq(user, ineq->el) < 0)
2044 if (isl_tab_add_ineq(tab, ineq->el) < 0)
2056 /* Add an extra div, prescrived by "div" to the tableau and
2057 * the associated bmap (which is assumed to be non-NULL).
2059 * If add_ineq is not NULL, then this function is used instead
2060 * of isl_tab_add_ineq to add the div constraints.
2061 * This complication is needed because the code in isl_tab_pip
2062 * wants to perform some extra processing when an inequality
2063 * is added to the tableau.
2065 int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
2066 int (*add_ineq)(void *user, isl_int *), void *user)
2076 isl_assert(tab->mat->ctx, tab->bmap, return -1);
2078 for (i = 0; i < tab->n_var; ++i) {
2079 if (isl_int_is_neg(div->el[2 + i]))
2081 if (isl_int_is_zero(div->el[2 + i]))
2083 if (!tab->var[i].is_nonneg)
2086 nonneg = i == tab->n_var && !isl_int_is_neg(div->el[1]);
2088 if (isl_tab_extend_cons(tab, 3) < 0)
2090 if (isl_tab_extend_vars(tab, 1) < 0)
2092 r = isl_tab_allocate_var(tab);
2097 tab->var[r].is_nonneg = 1;
2099 tab->bmap = isl_basic_map_extend_dim(tab->bmap,
2100 isl_basic_map_get_dim(tab->bmap), 1, 0, 2);
2101 k = isl_basic_map_alloc_div(tab->bmap);
2104 isl_seq_cpy(tab->bmap->div[k], div->el, div->size);
2105 if (isl_tab_push(tab, isl_tab_undo_bmap_div) < 0)
2108 if (add_div_constraints(tab, k, add_ineq, user) < 0)
2114 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap)
2117 struct isl_tab *tab;
2121 tab = isl_tab_alloc(bmap->ctx,
2122 isl_basic_map_total_dim(bmap) + bmap->n_ineq + 1,
2123 isl_basic_map_total_dim(bmap), 0);
2126 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
2127 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
2128 if (isl_tab_mark_empty(tab) < 0)
2132 for (i = 0; i < bmap->n_eq; ++i) {
2133 tab = add_eq(tab, bmap->eq[i]);
2137 for (i = 0; i < bmap->n_ineq; ++i) {
2138 if (isl_tab_add_ineq(tab, bmap->ineq[i]) < 0)
2149 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset)
2151 return isl_tab_from_basic_map((struct isl_basic_map *)bset);
2154 /* Construct a tableau corresponding to the recession cone of "bset".
2156 struct isl_tab *isl_tab_from_recession_cone(__isl_keep isl_basic_set *bset,
2161 struct isl_tab *tab;
2162 unsigned offset = 0;
2167 offset = isl_basic_set_dim(bset, isl_dim_param);
2168 tab = isl_tab_alloc(bset->ctx, bset->n_eq + bset->n_ineq,
2169 isl_basic_set_total_dim(bset) - offset, 0);
2172 tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
2176 for (i = 0; i < bset->n_eq; ++i) {
2177 isl_int_swap(bset->eq[i][offset], cst);
2179 if (isl_tab_add_eq(tab, bset->eq[i] + offset) < 0)
2182 tab = add_eq(tab, bset->eq[i]);
2183 isl_int_swap(bset->eq[i][offset], cst);
2187 for (i = 0; i < bset->n_ineq; ++i) {
2189 isl_int_swap(bset->ineq[i][offset], cst);
2190 r = isl_tab_add_row(tab, bset->ineq[i] + offset);
2191 isl_int_swap(bset->ineq[i][offset], cst);
2194 tab->con[r].is_nonneg = 1;
2195 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
2207 /* Assuming "tab" is the tableau of a cone, check if the cone is
2208 * bounded, i.e., if it is empty or only contains the origin.
2210 int isl_tab_cone_is_bounded(struct isl_tab *tab)
2218 if (tab->n_dead == tab->n_col)
2222 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2223 struct isl_tab_var *var;
2225 var = isl_tab_var_from_row(tab, i);
2226 if (!var->is_nonneg)
2228 sgn = sign_of_max(tab, var);
2233 if (close_row(tab, var) < 0)
2237 if (tab->n_dead == tab->n_col)
2239 if (i == tab->n_row)
2244 int isl_tab_sample_is_integer(struct isl_tab *tab)
2251 for (i = 0; i < tab->n_var; ++i) {
2253 if (!tab->var[i].is_row)
2255 row = tab->var[i].index;
2256 if (!isl_int_is_divisible_by(tab->mat->row[row][1],
2257 tab->mat->row[row][0]))
2263 static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
2266 struct isl_vec *vec;
2268 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
2272 isl_int_set_si(vec->block.data[0], 1);
2273 for (i = 0; i < tab->n_var; ++i) {
2274 if (!tab->var[i].is_row)
2275 isl_int_set_si(vec->block.data[1 + i], 0);
2277 int row = tab->var[i].index;
2278 isl_int_divexact(vec->block.data[1 + i],
2279 tab->mat->row[row][1], tab->mat->row[row][0]);
2286 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
2289 struct isl_vec *vec;
2295 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
2301 isl_int_set_si(vec->block.data[0], 1);
2302 for (i = 0; i < tab->n_var; ++i) {
2304 if (!tab->var[i].is_row) {
2305 isl_int_set_si(vec->block.data[1 + i], 0);
2308 row = tab->var[i].index;
2309 isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
2310 isl_int_divexact(m, tab->mat->row[row][0], m);
2311 isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
2312 isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
2313 isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
2315 vec = isl_vec_normalize(vec);
2321 /* Update "bmap" based on the results of the tableau "tab".
2322 * In particular, implicit equalities are made explicit, redundant constraints
2323 * are removed and if the sample value happens to be integer, it is stored
2324 * in "bmap" (unless "bmap" already had an integer sample).
2326 * The tableau is assumed to have been created from "bmap" using
2327 * isl_tab_from_basic_map.
2329 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
2330 struct isl_tab *tab)
2342 bmap = isl_basic_map_set_to_empty(bmap);
2344 for (i = bmap->n_ineq - 1; i >= 0; --i) {
2345 if (isl_tab_is_equality(tab, n_eq + i))
2346 isl_basic_map_inequality_to_equality(bmap, i);
2347 else if (isl_tab_is_redundant(tab, n_eq + i))
2348 isl_basic_map_drop_inequality(bmap, i);
2350 if (bmap->n_eq != n_eq)
2351 isl_basic_map_gauss(bmap, NULL);
2352 if (!tab->rational &&
2353 !bmap->sample && isl_tab_sample_is_integer(tab))
2354 bmap->sample = extract_integer_sample(tab);
2358 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
2359 struct isl_tab *tab)
2361 return (struct isl_basic_set *)isl_basic_map_update_from_tab(
2362 (struct isl_basic_map *)bset, tab);
2365 /* Given a non-negative variable "var", add a new non-negative variable
2366 * that is the opposite of "var", ensuring that var can only attain the
2368 * If var = n/d is a row variable, then the new variable = -n/d.
2369 * If var is a column variables, then the new variable = -var.
2370 * If the new variable cannot attain non-negative values, then
2371 * the resulting tableau is empty.
2372 * Otherwise, we know the value will be zero and we close the row.
2374 static int cut_to_hyperplane(struct isl_tab *tab, struct isl_tab_var *var)
2379 unsigned off = 2 + tab->M;
2383 isl_assert(tab->mat->ctx, !var->is_redundant, return -1);
2384 isl_assert(tab->mat->ctx, var->is_nonneg, return -1);
2386 if (isl_tab_extend_cons(tab, 1) < 0)
2390 tab->con[r].index = tab->n_row;
2391 tab->con[r].is_row = 1;
2392 tab->con[r].is_nonneg = 0;
2393 tab->con[r].is_zero = 0;
2394 tab->con[r].is_redundant = 0;
2395 tab->con[r].frozen = 0;
2396 tab->con[r].negated = 0;
2397 tab->row_var[tab->n_row] = ~r;
2398 row = tab->mat->row[tab->n_row];
2401 isl_int_set(row[0], tab->mat->row[var->index][0]);
2402 isl_seq_neg(row + 1,
2403 tab->mat->row[var->index] + 1, 1 + tab->n_col);
2405 isl_int_set_si(row[0], 1);
2406 isl_seq_clr(row + 1, 1 + tab->n_col);
2407 isl_int_set_si(row[off + var->index], -1);
2412 if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
2415 sgn = sign_of_max(tab, &tab->con[r]);
2419 if (isl_tab_mark_empty(tab) < 0)
2423 tab->con[r].is_nonneg = 1;
2424 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
2427 if (close_row(tab, &tab->con[r]) < 0)
2433 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2434 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2435 * by r' = r + 1 >= 0.
2436 * If r is a row variable, we simply increase the constant term by one
2437 * (taking into account the denominator).
2438 * If r is a column variable, then we need to modify each row that
2439 * refers to r = r' - 1 by substituting this equality, effectively
2440 * subtracting the coefficient of the column from the constant.
2441 * We should only do this if the minimum is manifestly unbounded,
2442 * however. Otherwise, we may end up with negative sample values
2443 * for non-negative variables.
2444 * So, if r is a column variable with a minimum that is not
2445 * manifestly unbounded, then we need to move it to a row.
2446 * However, the sample value of this row may be negative,
2447 * even after the relaxation, so we need to restore it.
2448 * We therefore prefer to pivot a column up to a row, if possible.
2450 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
2452 struct isl_tab_var *var;
2453 unsigned off = 2 + tab->M;
2458 var = &tab->con[con];
2460 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
2461 if (to_row(tab, var, 1) < 0)
2463 if (!var->is_row && !min_is_manifestly_unbounded(tab, var))
2464 if (to_row(tab, var, -1) < 0)
2468 isl_int_add(tab->mat->row[var->index][1],
2469 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
2470 if (restore_row(tab, var) < 0)
2475 for (i = 0; i < tab->n_row; ++i) {
2476 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2478 isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
2479 tab->mat->row[i][off + var->index]);
2484 if (isl_tab_push_var(tab, isl_tab_undo_relax, var) < 0)
2493 int isl_tab_select_facet(struct isl_tab *tab, int con)
2498 return cut_to_hyperplane(tab, &tab->con[con]);
2501 static int may_be_equality(struct isl_tab *tab, int row)
2503 unsigned off = 2 + tab->M;
2504 return tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
2505 : isl_int_lt(tab->mat->row[row][1],
2506 tab->mat->row[row][0]);
2509 /* Check for (near) equalities among the constraints.
2510 * A constraint is an equality if it is non-negative and if
2511 * its maximal value is either
2512 * - zero (in case of rational tableaus), or
2513 * - strictly less than 1 (in case of integer tableaus)
2515 * We first mark all non-redundant and non-dead variables that
2516 * are not frozen and not obviously not an equality.
2517 * Then we iterate over all marked variables if they can attain
2518 * any values larger than zero or at least one.
2519 * If the maximal value is zero, we mark any column variables
2520 * that appear in the row as being zero and mark the row as being redundant.
2521 * Otherwise, if the maximal value is strictly less than one (and the
2522 * tableau is integer), then we restrict the value to being zero
2523 * by adding an opposite non-negative variable.
2525 int isl_tab_detect_implicit_equalities(struct isl_tab *tab)
2534 if (tab->n_dead == tab->n_col)
2538 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2539 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
2540 var->marked = !var->frozen && var->is_nonneg &&
2541 may_be_equality(tab, i);
2545 for (i = tab->n_dead; i < tab->n_col; ++i) {
2546 struct isl_tab_var *var = var_from_col(tab, i);
2547 var->marked = !var->frozen && var->is_nonneg;
2552 struct isl_tab_var *var;
2554 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2555 var = isl_tab_var_from_row(tab, i);
2559 if (i == tab->n_row) {
2560 for (i = tab->n_dead; i < tab->n_col; ++i) {
2561 var = var_from_col(tab, i);
2565 if (i == tab->n_col)
2570 sgn = sign_of_max(tab, var);
2574 if (close_row(tab, var) < 0)
2576 } else if (!tab->rational && !at_least_one(tab, var)) {
2577 if (cut_to_hyperplane(tab, var) < 0)
2579 return isl_tab_detect_implicit_equalities(tab);
2581 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2582 var = isl_tab_var_from_row(tab, i);
2585 if (may_be_equality(tab, i))
2595 static int con_is_redundant(struct isl_tab *tab, struct isl_tab_var *var)
2599 if (tab->rational) {
2600 int sgn = sign_of_min(tab, var);
2605 int irred = isl_tab_min_at_most_neg_one(tab, var);
2612 /* Check for (near) redundant constraints.
2613 * A constraint is redundant if it is non-negative and if
2614 * its minimal value (temporarily ignoring the non-negativity) is either
2615 * - zero (in case of rational tableaus), or
2616 * - strictly larger than -1 (in case of integer tableaus)
2618 * We first mark all non-redundant and non-dead variables that
2619 * are not frozen and not obviously negatively unbounded.
2620 * Then we iterate over all marked variables if they can attain
2621 * any values smaller than zero or at most negative one.
2622 * If not, we mark the row as being redundant (assuming it hasn't
2623 * been detected as being obviously redundant in the mean time).
2625 int isl_tab_detect_redundant(struct isl_tab *tab)
2634 if (tab->n_redundant == tab->n_row)
2638 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2639 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
2640 var->marked = !var->frozen && var->is_nonneg;
2644 for (i = tab->n_dead; i < tab->n_col; ++i) {
2645 struct isl_tab_var *var = var_from_col(tab, i);
2646 var->marked = !var->frozen && var->is_nonneg &&
2647 !min_is_manifestly_unbounded(tab, var);
2652 struct isl_tab_var *var;
2654 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2655 var = isl_tab_var_from_row(tab, i);
2659 if (i == tab->n_row) {
2660 for (i = tab->n_dead; i < tab->n_col; ++i) {
2661 var = var_from_col(tab, i);
2665 if (i == tab->n_col)
2670 red = con_is_redundant(tab, var);
2673 if (red && !var->is_redundant)
2674 if (isl_tab_mark_redundant(tab, var->index) < 0)
2676 for (i = tab->n_dead; i < tab->n_col; ++i) {
2677 var = var_from_col(tab, i);
2680 if (!min_is_manifestly_unbounded(tab, var))
2690 int isl_tab_is_equality(struct isl_tab *tab, int con)
2697 if (tab->con[con].is_zero)
2699 if (tab->con[con].is_redundant)
2701 if (!tab->con[con].is_row)
2702 return tab->con[con].index < tab->n_dead;
2704 row = tab->con[con].index;
2707 return isl_int_is_zero(tab->mat->row[row][1]) &&
2708 isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
2709 tab->n_col - tab->n_dead) == -1;
2712 /* Return the minimial value of the affine expression "f" with denominator
2713 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
2714 * the expression cannot attain arbitrarily small values.
2715 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
2716 * The return value reflects the nature of the result (empty, unbounded,
2717 * minmimal value returned in *opt).
2719 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
2720 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
2724 enum isl_lp_result res = isl_lp_ok;
2725 struct isl_tab_var *var;
2726 struct isl_tab_undo *snap;
2729 return isl_lp_error;
2732 return isl_lp_empty;
2734 snap = isl_tab_snap(tab);
2735 r = isl_tab_add_row(tab, f);
2737 return isl_lp_error;
2739 isl_int_mul(tab->mat->row[var->index][0],
2740 tab->mat->row[var->index][0], denom);
2743 find_pivot(tab, var, var, -1, &row, &col);
2744 if (row == var->index) {
2745 res = isl_lp_unbounded;
2750 if (isl_tab_pivot(tab, row, col) < 0)
2751 return isl_lp_error;
2753 if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
2756 isl_vec_free(tab->dual);
2757 tab->dual = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_con);
2759 return isl_lp_error;
2760 isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
2761 for (i = 0; i < tab->n_con; ++i) {
2763 if (tab->con[i].is_row) {
2764 isl_int_set_si(tab->dual->el[1 + i], 0);
2767 pos = 2 + tab->M + tab->con[i].index;
2768 if (tab->con[i].negated)
2769 isl_int_neg(tab->dual->el[1 + i],
2770 tab->mat->row[var->index][pos]);
2772 isl_int_set(tab->dual->el[1 + i],
2773 tab->mat->row[var->index][pos]);
2776 if (opt && res == isl_lp_ok) {
2778 isl_int_set(*opt, tab->mat->row[var->index][1]);
2779 isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
2781 isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
2782 tab->mat->row[var->index][0]);
2784 if (isl_tab_rollback(tab, snap) < 0)
2785 return isl_lp_error;
2789 int isl_tab_is_redundant(struct isl_tab *tab, int con)
2793 if (tab->con[con].is_zero)
2795 if (tab->con[con].is_redundant)
2797 return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
2800 /* Take a snapshot of the tableau that can be restored by s call to
2803 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
2811 /* Undo the operation performed by isl_tab_relax.
2813 static int unrelax(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
2814 static int unrelax(struct isl_tab *tab, struct isl_tab_var *var)
2816 unsigned off = 2 + tab->M;
2818 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
2819 if (to_row(tab, var, 1) < 0)
2823 isl_int_sub(tab->mat->row[var->index][1],
2824 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
2825 if (var->is_nonneg) {
2826 int sgn = restore_row(tab, var);
2827 isl_assert(tab->mat->ctx, sgn >= 0, return -1);
2832 for (i = 0; i < tab->n_row; ++i) {
2833 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2835 isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
2836 tab->mat->row[i][off + var->index]);
2844 static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
2845 static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
2847 struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
2848 switch(undo->type) {
2849 case isl_tab_undo_nonneg:
2852 case isl_tab_undo_redundant:
2853 var->is_redundant = 0;
2855 restore_row(tab, isl_tab_var_from_row(tab, tab->n_redundant));
2857 case isl_tab_undo_freeze:
2860 case isl_tab_undo_zero:
2865 case isl_tab_undo_allocate:
2866 if (undo->u.var_index >= 0) {
2867 isl_assert(tab->mat->ctx, !var->is_row, return -1);
2868 drop_col(tab, var->index);
2872 if (!max_is_manifestly_unbounded(tab, var)) {
2873 if (to_row(tab, var, 1) < 0)
2875 } else if (!min_is_manifestly_unbounded(tab, var)) {
2876 if (to_row(tab, var, -1) < 0)
2879 if (to_row(tab, var, 0) < 0)
2882 drop_row(tab, var->index);
2884 case isl_tab_undo_relax:
2885 return unrelax(tab, var);
2891 /* Restore the tableau to the state where the basic variables
2892 * are those in "col_var".
2893 * We first construct a list of variables that are currently in
2894 * the basis, but shouldn't. Then we iterate over all variables
2895 * that should be in the basis and for each one that is currently
2896 * not in the basis, we exchange it with one of the elements of the
2897 * list constructed before.
2898 * We can always find an appropriate variable to pivot with because
2899 * the current basis is mapped to the old basis by a non-singular
2900 * matrix and so we can never end up with a zero row.
2902 static int restore_basis(struct isl_tab *tab, int *col_var)
2906 int *extra = NULL; /* current columns that contain bad stuff */
2907 unsigned off = 2 + tab->M;
2909 extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
2912 for (i = 0; i < tab->n_col; ++i) {
2913 for (j = 0; j < tab->n_col; ++j)
2914 if (tab->col_var[i] == col_var[j])
2918 extra[n_extra++] = i;
2920 for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
2921 struct isl_tab_var *var;
2924 for (j = 0; j < tab->n_col; ++j)
2925 if (col_var[i] == tab->col_var[j])
2929 var = var_from_index(tab, col_var[i]);
2931 for (j = 0; j < n_extra; ++j)
2932 if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
2934 isl_assert(tab->mat->ctx, j < n_extra, goto error);
2935 if (isl_tab_pivot(tab, row, extra[j]) < 0)
2937 extra[j] = extra[--n_extra];
2949 /* Remove all samples with index n or greater, i.e., those samples
2950 * that were added since we saved this number of samples in
2951 * isl_tab_save_samples.
2953 static void drop_samples_since(struct isl_tab *tab, int n)
2957 for (i = tab->n_sample - 1; i >= 0 && tab->n_sample > n; --i) {
2958 if (tab->sample_index[i] < n)
2961 if (i != tab->n_sample - 1) {
2962 int t = tab->sample_index[tab->n_sample-1];
2963 tab->sample_index[tab->n_sample-1] = tab->sample_index[i];
2964 tab->sample_index[i] = t;
2965 isl_mat_swap_rows(tab->samples, tab->n_sample-1, i);
2971 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
2972 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
2974 switch (undo->type) {
2975 case isl_tab_undo_empty:
2978 case isl_tab_undo_nonneg:
2979 case isl_tab_undo_redundant:
2980 case isl_tab_undo_freeze:
2981 case isl_tab_undo_zero:
2982 case isl_tab_undo_allocate:
2983 case isl_tab_undo_relax:
2984 return perform_undo_var(tab, undo);
2985 case isl_tab_undo_bmap_eq:
2986 return isl_basic_map_free_equality(tab->bmap, 1);
2987 case isl_tab_undo_bmap_ineq:
2988 return isl_basic_map_free_inequality(tab->bmap, 1);
2989 case isl_tab_undo_bmap_div:
2990 if (isl_basic_map_free_div(tab->bmap, 1) < 0)
2993 tab->samples->n_col--;
2995 case isl_tab_undo_saved_basis:
2996 if (restore_basis(tab, undo->u.col_var) < 0)
2999 case isl_tab_undo_drop_sample:
3002 case isl_tab_undo_saved_samples:
3003 drop_samples_since(tab, undo->u.n);
3005 case isl_tab_undo_callback:
3006 return undo->u.callback->run(undo->u.callback);
3008 isl_assert(tab->mat->ctx, 0, return -1);
3013 /* Return the tableau to the state it was in when the snapshot "snap"
3016 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
3018 struct isl_tab_undo *undo, *next;
3024 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
3028 if (perform_undo(tab, undo) < 0) {
3042 /* The given row "row" represents an inequality violated by all
3043 * points in the tableau. Check for some special cases of such
3044 * separating constraints.
3045 * In particular, if the row has been reduced to the constant -1,
3046 * then we know the inequality is adjacent (but opposite) to
3047 * an equality in the tableau.
3048 * If the row has been reduced to r = -1 -r', with r' an inequality
3049 * of the tableau, then the inequality is adjacent (but opposite)
3050 * to the inequality r'.
3052 static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
3055 unsigned off = 2 + tab->M;
3058 return isl_ineq_separate;
3060 if (!isl_int_is_one(tab->mat->row[row][0]))
3061 return isl_ineq_separate;
3062 if (!isl_int_is_negone(tab->mat->row[row][1]))
3063 return isl_ineq_separate;
3065 pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
3066 tab->n_col - tab->n_dead);
3068 return isl_ineq_adj_eq;
3070 if (!isl_int_is_negone(tab->mat->row[row][off + tab->n_dead + pos]))
3071 return isl_ineq_separate;
3073 pos = isl_seq_first_non_zero(
3074 tab->mat->row[row] + off + tab->n_dead + pos + 1,
3075 tab->n_col - tab->n_dead - pos - 1);
3077 return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
3080 /* Check the effect of inequality "ineq" on the tableau "tab".
3082 * isl_ineq_redundant: satisfied by all points in the tableau
3083 * isl_ineq_separate: satisfied by no point in the tableau
3084 * isl_ineq_cut: satisfied by some by not all points
3085 * isl_ineq_adj_eq: adjacent to an equality
3086 * isl_ineq_adj_ineq: adjacent to an inequality.
3088 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
3090 enum isl_ineq_type type = isl_ineq_error;
3091 struct isl_tab_undo *snap = NULL;
3096 return isl_ineq_error;
3098 if (isl_tab_extend_cons(tab, 1) < 0)
3099 return isl_ineq_error;
3101 snap = isl_tab_snap(tab);
3103 con = isl_tab_add_row(tab, ineq);
3107 row = tab->con[con].index;
3108 if (isl_tab_row_is_redundant(tab, row))
3109 type = isl_ineq_redundant;
3110 else if (isl_int_is_neg(tab->mat->row[row][1]) &&
3112 isl_int_abs_ge(tab->mat->row[row][1],
3113 tab->mat->row[row][0]))) {
3114 int nonneg = at_least_zero(tab, &tab->con[con]);
3118 type = isl_ineq_cut;
3120 type = separation_type(tab, row);
3122 int red = con_is_redundant(tab, &tab->con[con]);
3126 type = isl_ineq_cut;
3128 type = isl_ineq_redundant;
3131 if (isl_tab_rollback(tab, snap))
3132 return isl_ineq_error;
3135 return isl_ineq_error;
3138 int isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap)
3143 isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, return -1);
3144 isl_assert(tab->mat->ctx,
3145 tab->n_con == bmap->n_eq + bmap->n_ineq, return -1);
3151 isl_basic_map_free(bmap);
3155 int isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset)
3157 return isl_tab_track_bmap(tab, (isl_basic_map *)bset);
3160 __isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab)
3165 return (isl_basic_set *)tab->bmap;
3168 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent)
3174 fprintf(out, "%*snull tab\n", indent, "");
3177 fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
3178 tab->n_redundant, tab->n_dead);
3180 fprintf(out, ", rational");
3182 fprintf(out, ", empty");
3184 fprintf(out, "%*s[", indent, "");
3185 for (i = 0; i < tab->n_var; ++i) {
3187 fprintf(out, (i == tab->n_param ||
3188 i == tab->n_var - tab->n_div) ? "; "
3190 fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
3192 tab->var[i].is_zero ? " [=0]" :
3193 tab->var[i].is_redundant ? " [R]" : "");
3195 fprintf(out, "]\n");
3196 fprintf(out, "%*s[", indent, "");
3197 for (i = 0; i < tab->n_con; ++i) {
3200 fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
3202 tab->con[i].is_zero ? " [=0]" :
3203 tab->con[i].is_redundant ? " [R]" : "");
3205 fprintf(out, "]\n");
3206 fprintf(out, "%*s[", indent, "");
3207 for (i = 0; i < tab->n_row; ++i) {
3208 const char *sign = "";
3211 if (tab->row_sign) {
3212 if (tab->row_sign[i] == isl_tab_row_unknown)
3214 else if (tab->row_sign[i] == isl_tab_row_neg)
3216 else if (tab->row_sign[i] == isl_tab_row_pos)
3221 fprintf(out, "r%d: %d%s%s", i, tab->row_var[i],
3222 isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
3224 fprintf(out, "]\n");
3225 fprintf(out, "%*s[", indent, "");
3226 for (i = 0; i < tab->n_col; ++i) {
3229 fprintf(out, "c%d: %d%s", i, tab->col_var[i],
3230 var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
3232 fprintf(out, "]\n");
3233 r = tab->mat->n_row;
3234 tab->mat->n_row = tab->n_row;
3235 c = tab->mat->n_col;
3236 tab->mat->n_col = 2 + tab->M + tab->n_col;
3237 isl_mat_dump(tab->mat, out, indent);
3238 tab->mat->n_row = r;
3239 tab->mat->n_col = c;
3241 isl_basic_map_dump(tab->bmap, out, indent);