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->ctx, struct isl_tab);
215 dup->mat = isl_mat_dup(tab->mat);
218 dup->var = isl_alloc_array(tab->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->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->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->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->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 assert(!isl_int_is_neg(tab->mat->row[i][2]));
1182 if (isl_int_is_pos(tab->mat->row[i][2]))
1185 assert(!isl_int_is_neg(tab->mat->row[i][1]));
1189 /* Return the sign of the maximal value of "var".
1190 * If the sign is not negative, then on return from this function,
1191 * the sample value will also be non-negative.
1193 * If "var" is manifestly unbounded wrt positive values, we are done.
1194 * Otherwise, we pivot the variable up to a row if needed
1195 * Then we continue pivoting down until either
1196 * - no more down pivots can be performed
1197 * - the sample value is positive
1198 * - the variable is pivoted into a manifestly unbounded column
1200 static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
1204 if (max_is_manifestly_unbounded(tab, var))
1206 if (to_row(tab, var, 1) < 0)
1208 while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
1209 find_pivot(tab, var, var, 1, &row, &col);
1211 return isl_int_sgn(tab->mat->row[var->index][1]);
1212 if (isl_tab_pivot(tab, row, col) < 0)
1214 if (!var->is_row) /* manifestly unbounded */
1220 int isl_tab_sign_of_max(struct isl_tab *tab, int con)
1222 struct isl_tab_var *var;
1227 var = &tab->con[con];
1228 isl_assert(tab->mat->ctx, !var->is_redundant, return -2);
1229 isl_assert(tab->mat->ctx, !var->is_zero, return -2);
1231 return sign_of_max(tab, var);
1234 static int row_is_neg(struct isl_tab *tab, int row)
1237 return isl_int_is_neg(tab->mat->row[row][1]);
1238 if (isl_int_is_pos(tab->mat->row[row][2]))
1240 if (isl_int_is_neg(tab->mat->row[row][2]))
1242 return isl_int_is_neg(tab->mat->row[row][1]);
1245 static int row_sgn(struct isl_tab *tab, int row)
1248 return isl_int_sgn(tab->mat->row[row][1]);
1249 if (!isl_int_is_zero(tab->mat->row[row][2]))
1250 return isl_int_sgn(tab->mat->row[row][2]);
1252 return isl_int_sgn(tab->mat->row[row][1]);
1255 /* Perform pivots until the row variable "var" has a non-negative
1256 * sample value or until no more upward pivots can be performed.
1257 * Return the sign of the sample value after the pivots have been
1260 static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
1264 while (row_is_neg(tab, var->index)) {
1265 find_pivot(tab, var, var, 1, &row, &col);
1268 if (isl_tab_pivot(tab, row, col) < 0)
1270 if (!var->is_row) /* manifestly unbounded */
1273 return row_sgn(tab, var->index);
1276 /* Perform pivots until we are sure that the row variable "var"
1277 * can attain non-negative values. After return from this
1278 * function, "var" is still a row variable, but its sample
1279 * value may not be non-negative, even if the function returns 1.
1281 static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
1285 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
1286 find_pivot(tab, var, var, 1, &row, &col);
1289 if (row == var->index) /* manifestly unbounded */
1291 if (isl_tab_pivot(tab, row, col) < 0)
1294 return !isl_int_is_neg(tab->mat->row[var->index][1]);
1297 /* Return a negative value if "var" can attain negative values.
1298 * Return a non-negative value otherwise.
1300 * If "var" is manifestly unbounded wrt negative values, we are done.
1301 * Otherwise, if var is in a column, we can pivot it down to a row.
1302 * Then we continue pivoting down until either
1303 * - the pivot would result in a manifestly unbounded column
1304 * => we don't perform the pivot, but simply return -1
1305 * - no more down pivots can be performed
1306 * - the sample value is negative
1307 * If the sample value becomes negative and the variable is supposed
1308 * to be nonnegative, then we undo the last pivot.
1309 * However, if the last pivot has made the pivoting variable
1310 * obviously redundant, then it may have moved to another row.
1311 * In that case we look for upward pivots until we reach a non-negative
1314 static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
1317 struct isl_tab_var *pivot_var = NULL;
1319 if (min_is_manifestly_unbounded(tab, var))
1323 row = pivot_row(tab, NULL, -1, col);
1324 pivot_var = var_from_col(tab, col);
1325 if (isl_tab_pivot(tab, row, col) < 0)
1327 if (var->is_redundant)
1329 if (isl_int_is_neg(tab->mat->row[var->index][1])) {
1330 if (var->is_nonneg) {
1331 if (!pivot_var->is_redundant &&
1332 pivot_var->index == row) {
1333 if (isl_tab_pivot(tab, row, col) < 0)
1336 if (restore_row(tab, var) < -1)
1342 if (var->is_redundant)
1344 while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
1345 find_pivot(tab, var, var, -1, &row, &col);
1346 if (row == var->index)
1349 return isl_int_sgn(tab->mat->row[var->index][1]);
1350 pivot_var = var_from_col(tab, col);
1351 if (isl_tab_pivot(tab, row, col) < 0)
1353 if (var->is_redundant)
1356 if (pivot_var && var->is_nonneg) {
1357 /* pivot back to non-negative value */
1358 if (!pivot_var->is_redundant && pivot_var->index == row) {
1359 if (isl_tab_pivot(tab, row, col) < 0)
1362 if (restore_row(tab, var) < -1)
1368 static int row_at_most_neg_one(struct isl_tab *tab, int row)
1371 if (isl_int_is_pos(tab->mat->row[row][2]))
1373 if (isl_int_is_neg(tab->mat->row[row][2]))
1376 return isl_int_is_neg(tab->mat->row[row][1]) &&
1377 isl_int_abs_ge(tab->mat->row[row][1],
1378 tab->mat->row[row][0]);
1381 /* Return 1 if "var" can attain values <= -1.
1382 * Return 0 otherwise.
1384 * The sample value of "var" is assumed to be non-negative when the
1385 * the function is called. If 1 is returned then the constraint
1386 * is not redundant and the sample value is made non-negative again before
1387 * the function returns.
1389 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
1392 struct isl_tab_var *pivot_var;
1394 if (min_is_manifestly_unbounded(tab, var))
1398 row = pivot_row(tab, NULL, -1, col);
1399 pivot_var = var_from_col(tab, col);
1400 if (isl_tab_pivot(tab, row, col) < 0)
1402 if (var->is_redundant)
1404 if (row_at_most_neg_one(tab, var->index)) {
1405 if (var->is_nonneg) {
1406 if (!pivot_var->is_redundant &&
1407 pivot_var->index == row) {
1408 if (isl_tab_pivot(tab, row, col) < 0)
1411 if (restore_row(tab, var) < -1)
1417 if (var->is_redundant)
1420 find_pivot(tab, var, var, -1, &row, &col);
1421 if (row == var->index) {
1422 if (restore_row(tab, var) < -1)
1428 pivot_var = var_from_col(tab, col);
1429 if (isl_tab_pivot(tab, row, col) < 0)
1431 if (var->is_redundant)
1433 } while (!row_at_most_neg_one(tab, var->index));
1434 if (var->is_nonneg) {
1435 /* pivot back to non-negative value */
1436 if (!pivot_var->is_redundant && pivot_var->index == row)
1437 if (isl_tab_pivot(tab, row, col) < 0)
1439 if (restore_row(tab, var) < -1)
1445 /* Return 1 if "var" can attain values >= 1.
1446 * Return 0 otherwise.
1448 static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
1453 if (max_is_manifestly_unbounded(tab, var))
1455 if (to_row(tab, var, 1) < 0)
1457 r = tab->mat->row[var->index];
1458 while (isl_int_lt(r[1], r[0])) {
1459 find_pivot(tab, var, var, 1, &row, &col);
1461 return isl_int_ge(r[1], r[0]);
1462 if (row == var->index) /* manifestly unbounded */
1464 if (isl_tab_pivot(tab, row, col) < 0)
1470 static void swap_cols(struct isl_tab *tab, int col1, int col2)
1473 unsigned off = 2 + tab->M;
1474 t = tab->col_var[col1];
1475 tab->col_var[col1] = tab->col_var[col2];
1476 tab->col_var[col2] = t;
1477 var_from_col(tab, col1)->index = col1;
1478 var_from_col(tab, col2)->index = col2;
1479 tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2);
1482 /* Mark column with index "col" as representing a zero variable.
1483 * If we may need to undo the operation the column is kept,
1484 * but no longer considered.
1485 * Otherwise, the column is simply removed.
1487 * The column may be interchanged with some other column. If it
1488 * is interchanged with a later column, return 1. Otherwise return 0.
1489 * If the columns are checked in order in the calling function,
1490 * then a return value of 1 means that the column with the given
1491 * column number may now contain a different column that
1492 * hasn't been checked yet.
1494 int isl_tab_kill_col(struct isl_tab *tab, int col)
1496 var_from_col(tab, col)->is_zero = 1;
1497 if (tab->need_undo) {
1498 if (isl_tab_push_var(tab, isl_tab_undo_zero,
1499 var_from_col(tab, col)) < 0)
1501 if (col != tab->n_dead)
1502 swap_cols(tab, col, tab->n_dead);
1506 if (col != tab->n_col - 1)
1507 swap_cols(tab, col, tab->n_col - 1);
1508 var_from_col(tab, tab->n_col - 1)->index = -1;
1514 /* Row variable "var" is non-negative and cannot attain any values
1515 * larger than zero. This means that the coefficients of the unrestricted
1516 * column variables are zero and that the coefficients of the non-negative
1517 * column variables are zero or negative.
1518 * Each of the non-negative variables with a negative coefficient can
1519 * then also be written as the negative sum of non-negative variables
1520 * and must therefore also be zero.
1522 static int close_row(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
1523 static int close_row(struct isl_tab *tab, struct isl_tab_var *var)
1526 struct isl_mat *mat = tab->mat;
1527 unsigned off = 2 + tab->M;
1529 isl_assert(tab->mat->ctx, var->is_nonneg, return -1);
1532 if (isl_tab_push_var(tab, isl_tab_undo_zero, var) < 0)
1534 for (j = tab->n_dead; j < tab->n_col; ++j) {
1535 if (isl_int_is_zero(mat->row[var->index][off + j]))
1537 isl_assert(tab->mat->ctx,
1538 isl_int_is_neg(mat->row[var->index][off + j]), return -1);
1539 if (isl_tab_kill_col(tab, j))
1542 if (isl_tab_mark_redundant(tab, var->index) < 0)
1547 /* Add a constraint to the tableau and allocate a row for it.
1548 * Return the index into the constraint array "con".
1550 int isl_tab_allocate_con(struct isl_tab *tab)
1554 isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
1555 isl_assert(tab->mat->ctx, tab->n_con < tab->max_con, return -1);
1558 tab->con[r].index = tab->n_row;
1559 tab->con[r].is_row = 1;
1560 tab->con[r].is_nonneg = 0;
1561 tab->con[r].is_zero = 0;
1562 tab->con[r].is_redundant = 0;
1563 tab->con[r].frozen = 0;
1564 tab->con[r].negated = 0;
1565 tab->row_var[tab->n_row] = ~r;
1569 if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
1575 /* Add a variable to the tableau and allocate a column for it.
1576 * Return the index into the variable array "var".
1578 int isl_tab_allocate_var(struct isl_tab *tab)
1582 unsigned off = 2 + tab->M;
1584 isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
1585 isl_assert(tab->mat->ctx, tab->n_var < tab->max_var, return -1);
1588 tab->var[r].index = tab->n_col;
1589 tab->var[r].is_row = 0;
1590 tab->var[r].is_nonneg = 0;
1591 tab->var[r].is_zero = 0;
1592 tab->var[r].is_redundant = 0;
1593 tab->var[r].frozen = 0;
1594 tab->var[r].negated = 0;
1595 tab->col_var[tab->n_col] = r;
1597 for (i = 0; i < tab->n_row; ++i)
1598 isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
1602 if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]) < 0)
1608 /* Add a row to the tableau. The row is given as an affine combination
1609 * of the original variables and needs to be expressed in terms of the
1612 * We add each term in turn.
1613 * If r = n/d_r is the current sum and we need to add k x, then
1614 * if x is a column variable, we increase the numerator of
1615 * this column by k d_r
1616 * if x = f/d_x is a row variable, then the new representation of r is
1618 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1619 * --- + --- = ------------------- = -------------------
1620 * d_r d_r d_r d_x/g m
1622 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1624 int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
1630 unsigned off = 2 + tab->M;
1632 r = isl_tab_allocate_con(tab);
1638 row = tab->mat->row[tab->con[r].index];
1639 isl_int_set_si(row[0], 1);
1640 isl_int_set(row[1], line[0]);
1641 isl_seq_clr(row + 2, tab->M + tab->n_col);
1642 for (i = 0; i < tab->n_var; ++i) {
1643 if (tab->var[i].is_zero)
1645 if (tab->var[i].is_row) {
1647 row[0], tab->mat->row[tab->var[i].index][0]);
1648 isl_int_swap(a, row[0]);
1649 isl_int_divexact(a, row[0], a);
1651 row[0], tab->mat->row[tab->var[i].index][0]);
1652 isl_int_mul(b, b, line[1 + i]);
1653 isl_seq_combine(row + 1, a, row + 1,
1654 b, tab->mat->row[tab->var[i].index] + 1,
1655 1 + tab->M + tab->n_col);
1657 isl_int_addmul(row[off + tab->var[i].index],
1658 line[1 + i], row[0]);
1659 if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
1660 isl_int_submul(row[2], line[1 + i], row[0]);
1662 isl_seq_normalize(tab->mat->ctx, row, off + tab->n_col);
1667 tab->row_sign[tab->con[r].index] = isl_tab_row_unknown;
1672 static int drop_row(struct isl_tab *tab, int row)
1674 isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
1675 if (row != tab->n_row - 1)
1676 swap_rows(tab, row, tab->n_row - 1);
1682 static int drop_col(struct isl_tab *tab, int col)
1684 isl_assert(tab->mat->ctx, tab->col_var[col] == tab->n_var - 1, return -1);
1685 if (col != tab->n_col - 1)
1686 swap_cols(tab, col, tab->n_col - 1);
1692 /* Add inequality "ineq" and check if it conflicts with the
1693 * previously added constraints or if it is obviously redundant.
1695 int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
1704 struct isl_basic_map *bmap = tab->bmap;
1706 isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, return -1);
1707 isl_assert(tab->mat->ctx,
1708 tab->n_con == bmap->n_eq + bmap->n_ineq, return -1);
1709 tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
1710 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1717 isl_int_swap(ineq[0], cst);
1719 r = isl_tab_add_row(tab, ineq);
1721 isl_int_swap(ineq[0], cst);
1726 tab->con[r].is_nonneg = 1;
1727 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1729 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1730 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1735 sgn = restore_row(tab, &tab->con[r]);
1739 return isl_tab_mark_empty(tab);
1740 if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
1741 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1746 /* Pivot a non-negative variable down until it reaches the value zero
1747 * and then pivot the variable into a column position.
1749 static int to_col(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
1750 static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
1754 unsigned off = 2 + tab->M;
1759 while (isl_int_is_pos(tab->mat->row[var->index][1])) {
1760 find_pivot(tab, var, NULL, -1, &row, &col);
1761 isl_assert(tab->mat->ctx, row != -1, return -1);
1762 if (isl_tab_pivot(tab, row, col) < 0)
1768 for (i = tab->n_dead; i < tab->n_col; ++i)
1769 if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
1772 isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
1773 if (isl_tab_pivot(tab, var->index, i) < 0)
1779 /* We assume Gaussian elimination has been performed on the equalities.
1780 * The equalities can therefore never conflict.
1781 * Adding the equalities is currently only really useful for a later call
1782 * to isl_tab_ineq_type.
1784 static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
1791 r = isl_tab_add_row(tab, eq);
1795 r = tab->con[r].index;
1796 i = isl_seq_first_non_zero(tab->mat->row[r] + 2 + tab->M + tab->n_dead,
1797 tab->n_col - tab->n_dead);
1798 isl_assert(tab->mat->ctx, i >= 0, goto error);
1800 if (isl_tab_pivot(tab, r, i) < 0)
1802 if (isl_tab_kill_col(tab, i) < 0)
1812 static int row_is_manifestly_zero(struct isl_tab *tab, int row)
1814 unsigned off = 2 + tab->M;
1816 if (!isl_int_is_zero(tab->mat->row[row][1]))
1818 if (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))
1820 return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1821 tab->n_col - tab->n_dead) == -1;
1824 /* Add an equality that is known to be valid for the given tableau.
1826 struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
1828 struct isl_tab_var *var;
1833 r = isl_tab_add_row(tab, eq);
1839 if (row_is_manifestly_zero(tab, r)) {
1841 if (isl_tab_mark_redundant(tab, r) < 0)
1846 if (isl_int_is_neg(tab->mat->row[r][1])) {
1847 isl_seq_neg(tab->mat->row[r] + 1, tab->mat->row[r] + 1,
1852 if (to_col(tab, var) < 0)
1855 if (isl_tab_kill_col(tab, var->index) < 0)
1864 static int add_zero_row(struct isl_tab *tab)
1869 r = isl_tab_allocate_con(tab);
1873 row = tab->mat->row[tab->con[r].index];
1874 isl_seq_clr(row + 1, 1 + tab->M + tab->n_col);
1875 isl_int_set_si(row[0], 1);
1880 /* Add equality "eq" and check if it conflicts with the
1881 * previously added constraints or if it is obviously redundant.
1883 struct isl_tab *isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
1885 struct isl_tab_undo *snap = NULL;
1886 struct isl_tab_var *var;
1894 isl_assert(tab->mat->ctx, !tab->M, goto error);
1897 snap = isl_tab_snap(tab);
1901 isl_int_swap(eq[0], cst);
1903 r = isl_tab_add_row(tab, eq);
1905 isl_int_swap(eq[0], cst);
1913 if (row_is_manifestly_zero(tab, row)) {
1915 if (isl_tab_rollback(tab, snap) < 0)
1923 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
1924 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1926 isl_seq_neg(eq, eq, 1 + tab->n_var);
1927 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
1928 isl_seq_neg(eq, eq, 1 + tab->n_var);
1929 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1933 if (add_zero_row(tab) < 0)
1937 sgn = isl_int_sgn(tab->mat->row[row][1]);
1940 isl_seq_neg(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
1947 sgn = sign_of_max(tab, var);
1951 if (isl_tab_mark_empty(tab) < 0)
1958 if (to_col(tab, var) < 0)
1961 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 tab = isl_tab_add_eq(tab, bset->eq[i] + offset);
2181 tab = add_eq(tab, bset->eq[i]);
2182 isl_int_swap(bset->eq[i][offset], cst);
2186 for (i = 0; i < bset->n_ineq; ++i) {
2188 isl_int_swap(bset->ineq[i][offset], cst);
2189 r = isl_tab_add_row(tab, bset->ineq[i] + offset);
2190 isl_int_swap(bset->ineq[i][offset], cst);
2193 tab->con[r].is_nonneg = 1;
2194 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
2206 /* Assuming "tab" is the tableau of a cone, check if the cone is
2207 * bounded, i.e., if it is empty or only contains the origin.
2209 int isl_tab_cone_is_bounded(struct isl_tab *tab)
2217 if (tab->n_dead == tab->n_col)
2221 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2222 struct isl_tab_var *var;
2224 var = isl_tab_var_from_row(tab, i);
2225 if (!var->is_nonneg)
2227 sgn = sign_of_max(tab, var);
2232 if (close_row(tab, var) < 0)
2236 if (tab->n_dead == tab->n_col)
2238 if (i == tab->n_row)
2243 int isl_tab_sample_is_integer(struct isl_tab *tab)
2250 for (i = 0; i < tab->n_var; ++i) {
2252 if (!tab->var[i].is_row)
2254 row = tab->var[i].index;
2255 if (!isl_int_is_divisible_by(tab->mat->row[row][1],
2256 tab->mat->row[row][0]))
2262 static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
2265 struct isl_vec *vec;
2267 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
2271 isl_int_set_si(vec->block.data[0], 1);
2272 for (i = 0; i < tab->n_var; ++i) {
2273 if (!tab->var[i].is_row)
2274 isl_int_set_si(vec->block.data[1 + i], 0);
2276 int row = tab->var[i].index;
2277 isl_int_divexact(vec->block.data[1 + i],
2278 tab->mat->row[row][1], tab->mat->row[row][0]);
2285 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
2288 struct isl_vec *vec;
2294 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
2300 isl_int_set_si(vec->block.data[0], 1);
2301 for (i = 0; i < tab->n_var; ++i) {
2303 if (!tab->var[i].is_row) {
2304 isl_int_set_si(vec->block.data[1 + i], 0);
2307 row = tab->var[i].index;
2308 isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
2309 isl_int_divexact(m, tab->mat->row[row][0], m);
2310 isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
2311 isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
2312 isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
2314 vec = isl_vec_normalize(vec);
2320 /* Update "bmap" based on the results of the tableau "tab".
2321 * In particular, implicit equalities are made explicit, redundant constraints
2322 * are removed and if the sample value happens to be integer, it is stored
2323 * in "bmap" (unless "bmap" already had an integer sample).
2325 * The tableau is assumed to have been created from "bmap" using
2326 * isl_tab_from_basic_map.
2328 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
2329 struct isl_tab *tab)
2341 bmap = isl_basic_map_set_to_empty(bmap);
2343 for (i = bmap->n_ineq - 1; i >= 0; --i) {
2344 if (isl_tab_is_equality(tab, n_eq + i))
2345 isl_basic_map_inequality_to_equality(bmap, i);
2346 else if (isl_tab_is_redundant(tab, n_eq + i))
2347 isl_basic_map_drop_inequality(bmap, i);
2349 if (bmap->n_eq != n_eq)
2350 isl_basic_map_gauss(bmap, NULL);
2351 if (!tab->rational &&
2352 !bmap->sample && isl_tab_sample_is_integer(tab))
2353 bmap->sample = extract_integer_sample(tab);
2357 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
2358 struct isl_tab *tab)
2360 return (struct isl_basic_set *)isl_basic_map_update_from_tab(
2361 (struct isl_basic_map *)bset, tab);
2364 /* Given a non-negative variable "var", add a new non-negative variable
2365 * that is the opposite of "var", ensuring that var can only attain the
2367 * If var = n/d is a row variable, then the new variable = -n/d.
2368 * If var is a column variables, then the new variable = -var.
2369 * If the new variable cannot attain non-negative values, then
2370 * the resulting tableau is empty.
2371 * Otherwise, we know the value will be zero and we close the row.
2373 static int cut_to_hyperplane(struct isl_tab *tab, struct isl_tab_var *var)
2378 unsigned off = 2 + tab->M;
2382 isl_assert(tab->mat->ctx, !var->is_redundant, return -1);
2383 isl_assert(tab->mat->ctx, var->is_nonneg, return -1);
2385 if (isl_tab_extend_cons(tab, 1) < 0)
2389 tab->con[r].index = tab->n_row;
2390 tab->con[r].is_row = 1;
2391 tab->con[r].is_nonneg = 0;
2392 tab->con[r].is_zero = 0;
2393 tab->con[r].is_redundant = 0;
2394 tab->con[r].frozen = 0;
2395 tab->con[r].negated = 0;
2396 tab->row_var[tab->n_row] = ~r;
2397 row = tab->mat->row[tab->n_row];
2400 isl_int_set(row[0], tab->mat->row[var->index][0]);
2401 isl_seq_neg(row + 1,
2402 tab->mat->row[var->index] + 1, 1 + tab->n_col);
2404 isl_int_set_si(row[0], 1);
2405 isl_seq_clr(row + 1, 1 + tab->n_col);
2406 isl_int_set_si(row[off + var->index], -1);
2411 if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
2414 sgn = sign_of_max(tab, &tab->con[r]);
2418 if (isl_tab_mark_empty(tab) < 0)
2422 tab->con[r].is_nonneg = 1;
2423 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
2426 if (close_row(tab, &tab->con[r]) < 0)
2432 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2433 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2434 * by r' = r + 1 >= 0.
2435 * If r is a row variable, we simply increase the constant term by one
2436 * (taking into account the denominator).
2437 * If r is a column variable, then we need to modify each row that
2438 * refers to r = r' - 1 by substituting this equality, effectively
2439 * subtracting the coefficient of the column from the constant.
2440 * We should only do this if the minimum is manifestly unbounded,
2441 * however. Otherwise, we may end up with negative sample values
2442 * for non-negative variables.
2443 * So, if r is a column variable with a minimum that is not
2444 * manifestly unbounded, then we need to move it to a row.
2445 * However, the sample value of this row may be negative,
2446 * even after the relaxation, so we need to restore it.
2447 * We therefore prefer to pivot a column up to a row, if possible.
2449 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
2451 struct isl_tab_var *var;
2452 unsigned off = 2 + tab->M;
2457 var = &tab->con[con];
2459 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
2460 if (to_row(tab, var, 1) < 0)
2462 if (!var->is_row && !min_is_manifestly_unbounded(tab, var))
2463 if (to_row(tab, var, -1) < 0)
2467 isl_int_add(tab->mat->row[var->index][1],
2468 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
2469 if (restore_row(tab, var) < 0)
2474 for (i = 0; i < tab->n_row; ++i) {
2475 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2477 isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
2478 tab->mat->row[i][off + var->index]);
2483 if (isl_tab_push_var(tab, isl_tab_undo_relax, var) < 0)
2492 int isl_tab_select_facet(struct isl_tab *tab, int con)
2497 return cut_to_hyperplane(tab, &tab->con[con]);
2500 static int may_be_equality(struct isl_tab *tab, int row)
2502 unsigned off = 2 + tab->M;
2503 return tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
2504 : isl_int_lt(tab->mat->row[row][1],
2505 tab->mat->row[row][0]);
2508 /* Check for (near) equalities among the constraints.
2509 * A constraint is an equality if it is non-negative and if
2510 * its maximal value is either
2511 * - zero (in case of rational tableaus), or
2512 * - strictly less than 1 (in case of integer tableaus)
2514 * We first mark all non-redundant and non-dead variables that
2515 * are not frozen and not obviously not an equality.
2516 * Then we iterate over all marked variables if they can attain
2517 * any values larger than zero or at least one.
2518 * If the maximal value is zero, we mark any column variables
2519 * that appear in the row as being zero and mark the row as being redundant.
2520 * Otherwise, if the maximal value is strictly less than one (and the
2521 * tableau is integer), then we restrict the value to being zero
2522 * by adding an opposite non-negative variable.
2524 int isl_tab_detect_implicit_equalities(struct isl_tab *tab)
2533 if (tab->n_dead == tab->n_col)
2537 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2538 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
2539 var->marked = !var->frozen && var->is_nonneg &&
2540 may_be_equality(tab, i);
2544 for (i = tab->n_dead; i < tab->n_col; ++i) {
2545 struct isl_tab_var *var = var_from_col(tab, i);
2546 var->marked = !var->frozen && var->is_nonneg;
2551 struct isl_tab_var *var;
2553 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2554 var = isl_tab_var_from_row(tab, i);
2558 if (i == tab->n_row) {
2559 for (i = tab->n_dead; i < tab->n_col; ++i) {
2560 var = var_from_col(tab, i);
2564 if (i == tab->n_col)
2569 sgn = sign_of_max(tab, var);
2573 if (close_row(tab, var) < 0)
2575 } else if (!tab->rational && !at_least_one(tab, var)) {
2576 if (cut_to_hyperplane(tab, var) < 0)
2578 return isl_tab_detect_implicit_equalities(tab);
2580 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2581 var = isl_tab_var_from_row(tab, i);
2584 if (may_be_equality(tab, i))
2594 static int con_is_redundant(struct isl_tab *tab, struct isl_tab_var *var)
2598 if (tab->rational) {
2599 int sgn = sign_of_min(tab, var);
2604 int irred = isl_tab_min_at_most_neg_one(tab, var);
2611 /* Check for (near) redundant constraints.
2612 * A constraint is redundant if it is non-negative and if
2613 * its minimal value (temporarily ignoring the non-negativity) is either
2614 * - zero (in case of rational tableaus), or
2615 * - strictly larger than -1 (in case of integer tableaus)
2617 * We first mark all non-redundant and non-dead variables that
2618 * are not frozen and not obviously negatively unbounded.
2619 * Then we iterate over all marked variables if they can attain
2620 * any values smaller than zero or at most negative one.
2621 * If not, we mark the row as being redundant (assuming it hasn't
2622 * been detected as being obviously redundant in the mean time).
2624 int isl_tab_detect_redundant(struct isl_tab *tab)
2633 if (tab->n_redundant == tab->n_row)
2637 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2638 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
2639 var->marked = !var->frozen && var->is_nonneg;
2643 for (i = tab->n_dead; i < tab->n_col; ++i) {
2644 struct isl_tab_var *var = var_from_col(tab, i);
2645 var->marked = !var->frozen && var->is_nonneg &&
2646 !min_is_manifestly_unbounded(tab, var);
2651 struct isl_tab_var *var;
2653 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2654 var = isl_tab_var_from_row(tab, i);
2658 if (i == tab->n_row) {
2659 for (i = tab->n_dead; i < tab->n_col; ++i) {
2660 var = var_from_col(tab, i);
2664 if (i == tab->n_col)
2669 red = con_is_redundant(tab, var);
2672 if (red && !var->is_redundant)
2673 if (isl_tab_mark_redundant(tab, var->index) < 0)
2675 for (i = tab->n_dead; i < tab->n_col; ++i) {
2676 var = var_from_col(tab, i);
2679 if (!min_is_manifestly_unbounded(tab, var))
2689 int isl_tab_is_equality(struct isl_tab *tab, int con)
2696 if (tab->con[con].is_zero)
2698 if (tab->con[con].is_redundant)
2700 if (!tab->con[con].is_row)
2701 return tab->con[con].index < tab->n_dead;
2703 row = tab->con[con].index;
2706 return isl_int_is_zero(tab->mat->row[row][1]) &&
2707 isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
2708 tab->n_col - tab->n_dead) == -1;
2711 /* Return the minimial value of the affine expression "f" with denominator
2712 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
2713 * the expression cannot attain arbitrarily small values.
2714 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
2715 * The return value reflects the nature of the result (empty, unbounded,
2716 * minmimal value returned in *opt).
2718 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
2719 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
2723 enum isl_lp_result res = isl_lp_ok;
2724 struct isl_tab_var *var;
2725 struct isl_tab_undo *snap;
2728 return isl_lp_empty;
2730 snap = isl_tab_snap(tab);
2731 r = isl_tab_add_row(tab, f);
2733 return isl_lp_error;
2735 isl_int_mul(tab->mat->row[var->index][0],
2736 tab->mat->row[var->index][0], denom);
2739 find_pivot(tab, var, var, -1, &row, &col);
2740 if (row == var->index) {
2741 res = isl_lp_unbounded;
2746 if (isl_tab_pivot(tab, row, col) < 0)
2747 return isl_lp_error;
2749 if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
2752 isl_vec_free(tab->dual);
2753 tab->dual = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_con);
2755 return isl_lp_error;
2756 isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
2757 for (i = 0; i < tab->n_con; ++i) {
2759 if (tab->con[i].is_row) {
2760 isl_int_set_si(tab->dual->el[1 + i], 0);
2763 pos = 2 + tab->M + tab->con[i].index;
2764 if (tab->con[i].negated)
2765 isl_int_neg(tab->dual->el[1 + i],
2766 tab->mat->row[var->index][pos]);
2768 isl_int_set(tab->dual->el[1 + i],
2769 tab->mat->row[var->index][pos]);
2772 if (opt && res == isl_lp_ok) {
2774 isl_int_set(*opt, tab->mat->row[var->index][1]);
2775 isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
2777 isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
2778 tab->mat->row[var->index][0]);
2780 if (isl_tab_rollback(tab, snap) < 0)
2781 return isl_lp_error;
2785 int isl_tab_is_redundant(struct isl_tab *tab, int con)
2789 if (tab->con[con].is_zero)
2791 if (tab->con[con].is_redundant)
2793 return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
2796 /* Take a snapshot of the tableau that can be restored by s call to
2799 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
2807 /* Undo the operation performed by isl_tab_relax.
2809 static int unrelax(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
2810 static int unrelax(struct isl_tab *tab, struct isl_tab_var *var)
2812 unsigned off = 2 + tab->M;
2814 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
2815 if (to_row(tab, var, 1) < 0)
2819 isl_int_sub(tab->mat->row[var->index][1],
2820 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
2821 if (var->is_nonneg) {
2822 int sgn = restore_row(tab, var);
2823 isl_assert(tab->mat->ctx, sgn >= 0, return -1);
2828 for (i = 0; i < tab->n_row; ++i) {
2829 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2831 isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
2832 tab->mat->row[i][off + var->index]);
2840 static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
2841 static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
2843 struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
2844 switch(undo->type) {
2845 case isl_tab_undo_nonneg:
2848 case isl_tab_undo_redundant:
2849 var->is_redundant = 0;
2851 restore_row(tab, isl_tab_var_from_row(tab, tab->n_redundant));
2853 case isl_tab_undo_freeze:
2856 case isl_tab_undo_zero:
2861 case isl_tab_undo_allocate:
2862 if (undo->u.var_index >= 0) {
2863 isl_assert(tab->mat->ctx, !var->is_row, return -1);
2864 drop_col(tab, var->index);
2868 if (!max_is_manifestly_unbounded(tab, var)) {
2869 if (to_row(tab, var, 1) < 0)
2871 } else if (!min_is_manifestly_unbounded(tab, var)) {
2872 if (to_row(tab, var, -1) < 0)
2875 if (to_row(tab, var, 0) < 0)
2878 drop_row(tab, var->index);
2880 case isl_tab_undo_relax:
2881 return unrelax(tab, var);
2887 /* Restore the tableau to the state where the basic variables
2888 * are those in "col_var".
2889 * We first construct a list of variables that are currently in
2890 * the basis, but shouldn't. Then we iterate over all variables
2891 * that should be in the basis and for each one that is currently
2892 * not in the basis, we exchange it with one of the elements of the
2893 * list constructed before.
2894 * We can always find an appropriate variable to pivot with because
2895 * the current basis is mapped to the old basis by a non-singular
2896 * matrix and so we can never end up with a zero row.
2898 static int restore_basis(struct isl_tab *tab, int *col_var)
2902 int *extra = NULL; /* current columns that contain bad stuff */
2903 unsigned off = 2 + tab->M;
2905 extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
2908 for (i = 0; i < tab->n_col; ++i) {
2909 for (j = 0; j < tab->n_col; ++j)
2910 if (tab->col_var[i] == col_var[j])
2914 extra[n_extra++] = i;
2916 for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
2917 struct isl_tab_var *var;
2920 for (j = 0; j < tab->n_col; ++j)
2921 if (col_var[i] == tab->col_var[j])
2925 var = var_from_index(tab, col_var[i]);
2927 for (j = 0; j < n_extra; ++j)
2928 if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
2930 isl_assert(tab->mat->ctx, j < n_extra, goto error);
2931 if (isl_tab_pivot(tab, row, extra[j]) < 0)
2933 extra[j] = extra[--n_extra];
2945 /* Remove all samples with index n or greater, i.e., those samples
2946 * that were added since we saved this number of samples in
2947 * isl_tab_save_samples.
2949 static void drop_samples_since(struct isl_tab *tab, int n)
2953 for (i = tab->n_sample - 1; i >= 0 && tab->n_sample > n; --i) {
2954 if (tab->sample_index[i] < n)
2957 if (i != tab->n_sample - 1) {
2958 int t = tab->sample_index[tab->n_sample-1];
2959 tab->sample_index[tab->n_sample-1] = tab->sample_index[i];
2960 tab->sample_index[i] = t;
2961 isl_mat_swap_rows(tab->samples, tab->n_sample-1, i);
2967 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
2968 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
2970 switch (undo->type) {
2971 case isl_tab_undo_empty:
2974 case isl_tab_undo_nonneg:
2975 case isl_tab_undo_redundant:
2976 case isl_tab_undo_freeze:
2977 case isl_tab_undo_zero:
2978 case isl_tab_undo_allocate:
2979 case isl_tab_undo_relax:
2980 return perform_undo_var(tab, undo);
2981 case isl_tab_undo_bmap_eq:
2982 return isl_basic_map_free_equality(tab->bmap, 1);
2983 case isl_tab_undo_bmap_ineq:
2984 return isl_basic_map_free_inequality(tab->bmap, 1);
2985 case isl_tab_undo_bmap_div:
2986 if (isl_basic_map_free_div(tab->bmap, 1) < 0)
2989 tab->samples->n_col--;
2991 case isl_tab_undo_saved_basis:
2992 if (restore_basis(tab, undo->u.col_var) < 0)
2995 case isl_tab_undo_drop_sample:
2998 case isl_tab_undo_saved_samples:
2999 drop_samples_since(tab, undo->u.n);
3001 case isl_tab_undo_callback:
3002 return undo->u.callback->run(undo->u.callback);
3004 isl_assert(tab->mat->ctx, 0, return -1);
3009 /* Return the tableau to the state it was in when the snapshot "snap"
3012 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
3014 struct isl_tab_undo *undo, *next;
3020 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
3024 if (perform_undo(tab, undo) < 0) {
3038 /* The given row "row" represents an inequality violated by all
3039 * points in the tableau. Check for some special cases of such
3040 * separating constraints.
3041 * In particular, if the row has been reduced to the constant -1,
3042 * then we know the inequality is adjacent (but opposite) to
3043 * an equality in the tableau.
3044 * If the row has been reduced to r = -1 -r', with r' an inequality
3045 * of the tableau, then the inequality is adjacent (but opposite)
3046 * to the inequality r'.
3048 static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
3051 unsigned off = 2 + tab->M;
3054 return isl_ineq_separate;
3056 if (!isl_int_is_one(tab->mat->row[row][0]))
3057 return isl_ineq_separate;
3058 if (!isl_int_is_negone(tab->mat->row[row][1]))
3059 return isl_ineq_separate;
3061 pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
3062 tab->n_col - tab->n_dead);
3064 return isl_ineq_adj_eq;
3066 if (!isl_int_is_negone(tab->mat->row[row][off + tab->n_dead + pos]))
3067 return isl_ineq_separate;
3069 pos = isl_seq_first_non_zero(
3070 tab->mat->row[row] + off + tab->n_dead + pos + 1,
3071 tab->n_col - tab->n_dead - pos - 1);
3073 return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
3076 /* Check the effect of inequality "ineq" on the tableau "tab".
3078 * isl_ineq_redundant: satisfied by all points in the tableau
3079 * isl_ineq_separate: satisfied by no point in the tableau
3080 * isl_ineq_cut: satisfied by some by not all points
3081 * isl_ineq_adj_eq: adjacent to an equality
3082 * isl_ineq_adj_ineq: adjacent to an inequality.
3084 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
3086 enum isl_ineq_type type = isl_ineq_error;
3087 struct isl_tab_undo *snap = NULL;
3092 return isl_ineq_error;
3094 if (isl_tab_extend_cons(tab, 1) < 0)
3095 return isl_ineq_error;
3097 snap = isl_tab_snap(tab);
3099 con = isl_tab_add_row(tab, ineq);
3103 row = tab->con[con].index;
3104 if (isl_tab_row_is_redundant(tab, row))
3105 type = isl_ineq_redundant;
3106 else if (isl_int_is_neg(tab->mat->row[row][1]) &&
3108 isl_int_abs_ge(tab->mat->row[row][1],
3109 tab->mat->row[row][0]))) {
3110 int nonneg = at_least_zero(tab, &tab->con[con]);
3114 type = isl_ineq_cut;
3116 type = separation_type(tab, row);
3118 int red = con_is_redundant(tab, &tab->con[con]);
3122 type = isl_ineq_cut;
3124 type = isl_ineq_redundant;
3127 if (isl_tab_rollback(tab, snap))
3128 return isl_ineq_error;
3131 return isl_ineq_error;
3134 int isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap)
3139 isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, return -1);
3140 isl_assert(tab->mat->ctx,
3141 tab->n_con == bmap->n_eq + bmap->n_ineq, return -1);
3147 isl_basic_map_free(bmap);
3151 int isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset)
3153 return isl_tab_track_bmap(tab, (isl_basic_map *)bset);
3156 __isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab)
3161 return (isl_basic_set *)tab->bmap;
3164 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent)
3170 fprintf(out, "%*snull tab\n", indent, "");
3173 fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
3174 tab->n_redundant, tab->n_dead);
3176 fprintf(out, ", rational");
3178 fprintf(out, ", empty");
3180 fprintf(out, "%*s[", indent, "");
3181 for (i = 0; i < tab->n_var; ++i) {
3183 fprintf(out, (i == tab->n_param ||
3184 i == tab->n_var - tab->n_div) ? "; "
3186 fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
3188 tab->var[i].is_zero ? " [=0]" :
3189 tab->var[i].is_redundant ? " [R]" : "");
3191 fprintf(out, "]\n");
3192 fprintf(out, "%*s[", indent, "");
3193 for (i = 0; i < tab->n_con; ++i) {
3196 fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
3198 tab->con[i].is_zero ? " [=0]" :
3199 tab->con[i].is_redundant ? " [R]" : "");
3201 fprintf(out, "]\n");
3202 fprintf(out, "%*s[", indent, "");
3203 for (i = 0; i < tab->n_row; ++i) {
3204 const char *sign = "";
3207 if (tab->row_sign) {
3208 if (tab->row_sign[i] == isl_tab_row_unknown)
3210 else if (tab->row_sign[i] == isl_tab_row_neg)
3212 else if (tab->row_sign[i] == isl_tab_row_pos)
3217 fprintf(out, "r%d: %d%s%s", i, tab->row_var[i],
3218 isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
3220 fprintf(out, "]\n");
3221 fprintf(out, "%*s[", indent, "");
3222 for (i = 0; i < tab->n_col; ++i) {
3225 fprintf(out, "c%d: %d%s", i, tab->col_var[i],
3226 var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
3228 fprintf(out, "]\n");
3229 r = tab->mat->n_row;
3230 tab->mat->n_row = tab->n_row;
3231 c = tab->mat->n_col;
3232 tab->mat->n_col = 2 + tab->M + tab->n_col;
3233 isl_mat_dump(tab->mat, out, indent);
3234 tab->mat->n_row = r;
3235 tab->mat->n_col = c;
3237 isl_basic_map_dump(tab->bmap, out, indent);