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
10 #include <isl_mat_private.h>
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)
97 if (tab->max_con < tab->n_con + n_new) {
98 struct isl_tab_var *con;
100 con = isl_realloc_array(tab->mat->ctx, tab->con,
101 struct isl_tab_var, tab->max_con + n_new);
105 tab->max_con += n_new;
107 if (tab->mat->n_row < tab->n_row + n_new) {
110 tab->mat = isl_mat_extend(tab->mat,
111 tab->n_row + n_new, off + tab->n_col);
114 row_var = isl_realloc_array(tab->mat->ctx, tab->row_var,
115 int, tab->mat->n_row);
118 tab->row_var = row_var;
120 enum isl_tab_row_sign *s;
121 s = isl_realloc_array(tab->mat->ctx, tab->row_sign,
122 enum isl_tab_row_sign, tab->mat->n_row);
131 /* Make room for at least n_new extra variables.
132 * Return -1 if anything went wrong.
134 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new)
136 struct isl_tab_var *var;
137 unsigned off = 2 + tab->M;
139 if (tab->max_var < tab->n_var + n_new) {
140 var = isl_realloc_array(tab->mat->ctx, tab->var,
141 struct isl_tab_var, tab->n_var + n_new);
145 tab->max_var += n_new;
148 if (tab->mat->n_col < off + tab->n_col + n_new) {
151 tab->mat = isl_mat_extend(tab->mat,
152 tab->mat->n_row, off + tab->n_col + n_new);
155 p = isl_realloc_array(tab->mat->ctx, tab->col_var,
156 int, tab->n_col + n_new);
165 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new)
167 if (isl_tab_extend_cons(tab, n_new) >= 0)
174 static void free_undo(struct isl_tab *tab)
176 struct isl_tab_undo *undo, *next;
178 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
185 void isl_tab_free(struct isl_tab *tab)
190 isl_mat_free(tab->mat);
191 isl_vec_free(tab->dual);
192 isl_basic_map_free(tab->bmap);
198 isl_mat_free(tab->samples);
199 free(tab->sample_index);
200 isl_mat_free(tab->basis);
204 struct isl_tab *isl_tab_dup(struct isl_tab *tab)
214 dup = isl_calloc_type(tab->mat->ctx, struct isl_tab);
217 dup->mat = isl_mat_dup(tab->mat);
220 dup->var = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_var);
223 for (i = 0; i < tab->n_var; ++i)
224 dup->var[i] = tab->var[i];
225 dup->con = isl_alloc_array(tab->mat->ctx, struct isl_tab_var, tab->max_con);
228 for (i = 0; i < tab->n_con; ++i)
229 dup->con[i] = tab->con[i];
230 dup->col_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_col - off);
233 for (i = 0; i < tab->n_col; ++i)
234 dup->col_var[i] = tab->col_var[i];
235 dup->row_var = isl_alloc_array(tab->mat->ctx, int, tab->mat->n_row);
238 for (i = 0; i < tab->n_row; ++i)
239 dup->row_var[i] = tab->row_var[i];
241 dup->row_sign = isl_alloc_array(tab->mat->ctx, enum isl_tab_row_sign,
245 for (i = 0; i < tab->n_row; ++i)
246 dup->row_sign[i] = tab->row_sign[i];
249 dup->samples = isl_mat_dup(tab->samples);
252 dup->sample_index = isl_alloc_array(tab->mat->ctx, int,
253 tab->samples->n_row);
254 if (!dup->sample_index)
256 dup->n_sample = tab->n_sample;
257 dup->n_outside = tab->n_outside;
259 dup->n_row = tab->n_row;
260 dup->n_con = tab->n_con;
261 dup->n_eq = tab->n_eq;
262 dup->max_con = tab->max_con;
263 dup->n_col = tab->n_col;
264 dup->n_var = tab->n_var;
265 dup->max_var = tab->max_var;
266 dup->n_param = tab->n_param;
267 dup->n_div = tab->n_div;
268 dup->n_dead = tab->n_dead;
269 dup->n_redundant = tab->n_redundant;
270 dup->rational = tab->rational;
271 dup->empty = tab->empty;
272 dup->strict_redundant = 0;
276 tab->cone = tab->cone;
277 dup->bottom.type = isl_tab_undo_bottom;
278 dup->bottom.next = NULL;
279 dup->top = &dup->bottom;
281 dup->n_zero = tab->n_zero;
282 dup->n_unbounded = tab->n_unbounded;
283 dup->basis = isl_mat_dup(tab->basis);
291 /* Construct the coefficient matrix of the product tableau
293 * mat{1,2} is the coefficient matrix of tableau {1,2}
294 * row{1,2} is the number of rows in tableau {1,2}
295 * col{1,2} is the number of columns in tableau {1,2}
296 * off is the offset to the coefficient column (skipping the
297 * denominator, the constant term and the big parameter if any)
298 * r{1,2} is the number of redundant rows in tableau {1,2}
299 * d{1,2} is the number of dead columns in tableau {1,2}
301 * The order of the rows and columns in the result is as explained
302 * in isl_tab_product.
304 static struct isl_mat *tab_mat_product(struct isl_mat *mat1,
305 struct isl_mat *mat2, unsigned row1, unsigned row2,
306 unsigned col1, unsigned col2,
307 unsigned off, unsigned r1, unsigned r2, unsigned d1, unsigned d2)
310 struct isl_mat *prod;
313 prod = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
319 for (i = 0; i < r1; ++i) {
320 isl_seq_cpy(prod->row[n + i], mat1->row[i], off + d1);
321 isl_seq_clr(prod->row[n + i] + off + d1, d2);
322 isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
323 mat1->row[i] + off + d1, col1 - d1);
324 isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
328 for (i = 0; i < r2; ++i) {
329 isl_seq_cpy(prod->row[n + i], mat2->row[i], off);
330 isl_seq_clr(prod->row[n + i] + off, d1);
331 isl_seq_cpy(prod->row[n + i] + off + d1,
332 mat2->row[i] + off, d2);
333 isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
334 isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
335 mat2->row[i] + off + d2, col2 - d2);
339 for (i = 0; i < row1 - r1; ++i) {
340 isl_seq_cpy(prod->row[n + i], mat1->row[r1 + i], off + d1);
341 isl_seq_clr(prod->row[n + i] + off + d1, d2);
342 isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
343 mat1->row[r1 + i] + off + d1, col1 - d1);
344 isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
348 for (i = 0; i < row2 - r2; ++i) {
349 isl_seq_cpy(prod->row[n + i], mat2->row[r2 + i], off);
350 isl_seq_clr(prod->row[n + i] + off, d1);
351 isl_seq_cpy(prod->row[n + i] + off + d1,
352 mat2->row[r2 + i] + off, d2);
353 isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
354 isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
355 mat2->row[r2 + i] + off + d2, col2 - d2);
361 /* Update the row or column index of a variable that corresponds
362 * to a variable in the first input tableau.
364 static void update_index1(struct isl_tab_var *var,
365 unsigned r1, unsigned r2, unsigned d1, unsigned d2)
367 if (var->index == -1)
369 if (var->is_row && var->index >= r1)
371 if (!var->is_row && var->index >= d1)
375 /* Update the row or column index of a variable that corresponds
376 * to a variable in the second input tableau.
378 static void update_index2(struct isl_tab_var *var,
379 unsigned row1, unsigned col1,
380 unsigned r1, unsigned r2, unsigned d1, unsigned d2)
382 if (var->index == -1)
397 /* Create a tableau that represents the Cartesian product of the sets
398 * represented by tableaus tab1 and tab2.
399 * The order of the rows in the product is
400 * - redundant rows of tab1
401 * - redundant rows of tab2
402 * - non-redundant rows of tab1
403 * - non-redundant rows of tab2
404 * The order of the columns is
407 * - coefficient of big parameter, if any
408 * - dead columns of tab1
409 * - dead columns of tab2
410 * - live columns of tab1
411 * - live columns of tab2
412 * The order of the variables and the constraints is a concatenation
413 * of order in the two input tableaus.
415 struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2)
418 struct isl_tab *prod;
420 unsigned r1, r2, d1, d2;
425 isl_assert(tab1->mat->ctx, tab1->M == tab2->M, return NULL);
426 isl_assert(tab1->mat->ctx, tab1->rational == tab2->rational, return NULL);
427 isl_assert(tab1->mat->ctx, tab1->cone == tab2->cone, return NULL);
428 isl_assert(tab1->mat->ctx, !tab1->row_sign, return NULL);
429 isl_assert(tab1->mat->ctx, !tab2->row_sign, return NULL);
430 isl_assert(tab1->mat->ctx, tab1->n_param == 0, return NULL);
431 isl_assert(tab1->mat->ctx, tab2->n_param == 0, return NULL);
432 isl_assert(tab1->mat->ctx, tab1->n_div == 0, return NULL);
433 isl_assert(tab1->mat->ctx, tab2->n_div == 0, return NULL);
436 r1 = tab1->n_redundant;
437 r2 = tab2->n_redundant;
440 prod = isl_calloc_type(tab1->mat->ctx, struct isl_tab);
443 prod->mat = tab_mat_product(tab1->mat, tab2->mat,
444 tab1->n_row, tab2->n_row,
445 tab1->n_col, tab2->n_col, off, r1, r2, d1, d2);
448 prod->var = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
449 tab1->max_var + tab2->max_var);
452 for (i = 0; i < tab1->n_var; ++i) {
453 prod->var[i] = tab1->var[i];
454 update_index1(&prod->var[i], r1, r2, d1, d2);
456 for (i = 0; i < tab2->n_var; ++i) {
457 prod->var[tab1->n_var + i] = tab2->var[i];
458 update_index2(&prod->var[tab1->n_var + i],
459 tab1->n_row, tab1->n_col,
462 prod->con = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
463 tab1->max_con + tab2->max_con);
466 for (i = 0; i < tab1->n_con; ++i) {
467 prod->con[i] = tab1->con[i];
468 update_index1(&prod->con[i], r1, r2, d1, d2);
470 for (i = 0; i < tab2->n_con; ++i) {
471 prod->con[tab1->n_con + i] = tab2->con[i];
472 update_index2(&prod->con[tab1->n_con + i],
473 tab1->n_row, tab1->n_col,
476 prod->col_var = isl_alloc_array(tab1->mat->ctx, int,
477 tab1->n_col + tab2->n_col);
480 for (i = 0; i < tab1->n_col; ++i) {
481 int pos = i < d1 ? i : i + d2;
482 prod->col_var[pos] = tab1->col_var[i];
484 for (i = 0; i < tab2->n_col; ++i) {
485 int pos = i < d2 ? d1 + i : tab1->n_col + i;
486 int t = tab2->col_var[i];
491 prod->col_var[pos] = t;
493 prod->row_var = isl_alloc_array(tab1->mat->ctx, int,
494 tab1->mat->n_row + tab2->mat->n_row);
497 for (i = 0; i < tab1->n_row; ++i) {
498 int pos = i < r1 ? i : i + r2;
499 prod->row_var[pos] = tab1->row_var[i];
501 for (i = 0; i < tab2->n_row; ++i) {
502 int pos = i < r2 ? r1 + i : tab1->n_row + i;
503 int t = tab2->row_var[i];
508 prod->row_var[pos] = t;
510 prod->samples = NULL;
511 prod->sample_index = NULL;
512 prod->n_row = tab1->n_row + tab2->n_row;
513 prod->n_con = tab1->n_con + tab2->n_con;
515 prod->max_con = tab1->max_con + tab2->max_con;
516 prod->n_col = tab1->n_col + tab2->n_col;
517 prod->n_var = tab1->n_var + tab2->n_var;
518 prod->max_var = tab1->max_var + tab2->max_var;
521 prod->n_dead = tab1->n_dead + tab2->n_dead;
522 prod->n_redundant = tab1->n_redundant + tab2->n_redundant;
523 prod->rational = tab1->rational;
524 prod->empty = tab1->empty || tab2->empty;
525 prod->strict_redundant = tab1->strict_redundant || tab2->strict_redundant;
529 prod->cone = tab1->cone;
530 prod->bottom.type = isl_tab_undo_bottom;
531 prod->bottom.next = NULL;
532 prod->top = &prod->bottom;
535 prod->n_unbounded = 0;
544 static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i)
549 return &tab->con[~i];
552 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
554 return var_from_index(tab, tab->row_var[i]);
557 static struct isl_tab_var *var_from_col(struct isl_tab *tab, int i)
559 return var_from_index(tab, tab->col_var[i]);
562 /* Check if there are any upper bounds on column variable "var",
563 * i.e., non-negative rows where var appears with a negative coefficient.
564 * Return 1 if there are no such bounds.
566 static int max_is_manifestly_unbounded(struct isl_tab *tab,
567 struct isl_tab_var *var)
570 unsigned off = 2 + tab->M;
574 for (i = tab->n_redundant; i < tab->n_row; ++i) {
575 if (!isl_int_is_neg(tab->mat->row[i][off + var->index]))
577 if (isl_tab_var_from_row(tab, i)->is_nonneg)
583 /* Check if there are any lower bounds on column variable "var",
584 * i.e., non-negative rows where var appears with a positive coefficient.
585 * Return 1 if there are no such bounds.
587 static int min_is_manifestly_unbounded(struct isl_tab *tab,
588 struct isl_tab_var *var)
591 unsigned off = 2 + tab->M;
595 for (i = tab->n_redundant; i < tab->n_row; ++i) {
596 if (!isl_int_is_pos(tab->mat->row[i][off + var->index]))
598 if (isl_tab_var_from_row(tab, i)->is_nonneg)
604 static int row_cmp(struct isl_tab *tab, int r1, int r2, int c, isl_int t)
606 unsigned off = 2 + tab->M;
610 isl_int_mul(t, tab->mat->row[r1][2], tab->mat->row[r2][off+c]);
611 isl_int_submul(t, tab->mat->row[r2][2], tab->mat->row[r1][off+c]);
616 isl_int_mul(t, tab->mat->row[r1][1], tab->mat->row[r2][off + c]);
617 isl_int_submul(t, tab->mat->row[r2][1], tab->mat->row[r1][off + c]);
618 return isl_int_sgn(t);
621 /* Given the index of a column "c", return the index of a row
622 * that can be used to pivot the column in, with either an increase
623 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
624 * If "var" is not NULL, then the row returned will be different from
625 * the one associated with "var".
627 * Each row in the tableau is of the form
629 * x_r = a_r0 + \sum_i a_ri x_i
631 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
632 * impose any limit on the increase or decrease in the value of x_c
633 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
634 * for the row with the smallest (most stringent) such bound.
635 * Note that the common denominator of each row drops out of the fraction.
636 * To check if row j has a smaller bound than row r, i.e.,
637 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
638 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
639 * where -sign(a_jc) is equal to "sgn".
641 static int pivot_row(struct isl_tab *tab,
642 struct isl_tab_var *var, int sgn, int c)
646 unsigned off = 2 + tab->M;
650 for (j = tab->n_redundant; j < tab->n_row; ++j) {
651 if (var && j == var->index)
653 if (!isl_tab_var_from_row(tab, j)->is_nonneg)
655 if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
661 tsgn = sgn * row_cmp(tab, r, j, c, t);
662 if (tsgn < 0 || (tsgn == 0 &&
663 tab->row_var[j] < tab->row_var[r]))
670 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
671 * (sgn < 0) the value of row variable var.
672 * If not NULL, then skip_var is a row variable that should be ignored
673 * while looking for a pivot row. It is usually equal to var.
675 * As the given row in the tableau is of the form
677 * x_r = a_r0 + \sum_i a_ri x_i
679 * we need to find a column such that the sign of a_ri is equal to "sgn"
680 * (such that an increase in x_i will have the desired effect) or a
681 * column with a variable that may attain negative values.
682 * If a_ri is positive, then we need to move x_i in the same direction
683 * to obtain the desired effect. Otherwise, x_i has to move in the
684 * opposite direction.
686 static void find_pivot(struct isl_tab *tab,
687 struct isl_tab_var *var, struct isl_tab_var *skip_var,
688 int sgn, int *row, int *col)
695 isl_assert(tab->mat->ctx, var->is_row, return);
696 tr = tab->mat->row[var->index] + 2 + tab->M;
699 for (j = tab->n_dead; j < tab->n_col; ++j) {
700 if (isl_int_is_zero(tr[j]))
702 if (isl_int_sgn(tr[j]) != sgn &&
703 var_from_col(tab, j)->is_nonneg)
705 if (c < 0 || tab->col_var[j] < tab->col_var[c])
711 sgn *= isl_int_sgn(tr[c]);
712 r = pivot_row(tab, skip_var, sgn, c);
713 *row = r < 0 ? var->index : r;
717 /* Return 1 if row "row" represents an obviously redundant inequality.
719 * - it represents an inequality or a variable
720 * - that is the sum of a non-negative sample value and a positive
721 * combination of zero or more non-negative constraints.
723 int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
726 unsigned off = 2 + tab->M;
728 if (tab->row_var[row] < 0 && !isl_tab_var_from_row(tab, row)->is_nonneg)
731 if (isl_int_is_neg(tab->mat->row[row][1]))
733 if (tab->strict_redundant && isl_int_is_zero(tab->mat->row[row][1]))
735 if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
738 for (i = tab->n_dead; i < tab->n_col; ++i) {
739 if (isl_int_is_zero(tab->mat->row[row][off + i]))
741 if (tab->col_var[i] >= 0)
743 if (isl_int_is_neg(tab->mat->row[row][off + i]))
745 if (!var_from_col(tab, i)->is_nonneg)
751 static void swap_rows(struct isl_tab *tab, int row1, int row2)
754 enum isl_tab_row_sign s;
756 t = tab->row_var[row1];
757 tab->row_var[row1] = tab->row_var[row2];
758 tab->row_var[row2] = t;
759 isl_tab_var_from_row(tab, row1)->index = row1;
760 isl_tab_var_from_row(tab, row2)->index = row2;
761 tab->mat = isl_mat_swap_rows(tab->mat, row1, row2);
765 s = tab->row_sign[row1];
766 tab->row_sign[row1] = tab->row_sign[row2];
767 tab->row_sign[row2] = s;
770 static int push_union(struct isl_tab *tab,
771 enum isl_tab_undo_type type, union isl_tab_undo_val u) WARN_UNUSED;
772 static int push_union(struct isl_tab *tab,
773 enum isl_tab_undo_type type, union isl_tab_undo_val u)
775 struct isl_tab_undo *undo;
780 undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
785 undo->next = tab->top;
791 int isl_tab_push_var(struct isl_tab *tab,
792 enum isl_tab_undo_type type, struct isl_tab_var *var)
794 union isl_tab_undo_val u;
796 u.var_index = tab->row_var[var->index];
798 u.var_index = tab->col_var[var->index];
799 return push_union(tab, type, u);
802 int isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
804 union isl_tab_undo_val u = { 0 };
805 return push_union(tab, type, u);
808 /* Push a record on the undo stack describing the current basic
809 * variables, so that the this state can be restored during rollback.
811 int isl_tab_push_basis(struct isl_tab *tab)
814 union isl_tab_undo_val u;
816 u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
819 for (i = 0; i < tab->n_col; ++i)
820 u.col_var[i] = tab->col_var[i];
821 return push_union(tab, isl_tab_undo_saved_basis, u);
824 int isl_tab_push_callback(struct isl_tab *tab, struct isl_tab_callback *callback)
826 union isl_tab_undo_val u;
827 u.callback = callback;
828 return push_union(tab, isl_tab_undo_callback, u);
831 struct isl_tab *isl_tab_init_samples(struct isl_tab *tab)
838 tab->samples = isl_mat_alloc(tab->mat->ctx, 1, 1 + tab->n_var);
841 tab->sample_index = isl_alloc_array(tab->mat->ctx, int, 1);
842 if (!tab->sample_index)
850 struct isl_tab *isl_tab_add_sample(struct isl_tab *tab,
851 __isl_take isl_vec *sample)
856 if (tab->n_sample + 1 > tab->samples->n_row) {
857 int *t = isl_realloc_array(tab->mat->ctx,
858 tab->sample_index, int, tab->n_sample + 1);
861 tab->sample_index = t;
864 tab->samples = isl_mat_extend(tab->samples,
865 tab->n_sample + 1, tab->samples->n_col);
869 isl_seq_cpy(tab->samples->row[tab->n_sample], sample->el, sample->size);
870 isl_vec_free(sample);
871 tab->sample_index[tab->n_sample] = tab->n_sample;
876 isl_vec_free(sample);
881 struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s)
883 if (s != tab->n_outside) {
884 int t = tab->sample_index[tab->n_outside];
885 tab->sample_index[tab->n_outside] = tab->sample_index[s];
886 tab->sample_index[s] = t;
887 isl_mat_swap_rows(tab->samples, tab->n_outside, s);
890 if (isl_tab_push(tab, isl_tab_undo_drop_sample) < 0) {
898 /* Record the current number of samples so that we can remove newer
899 * samples during a rollback.
901 int isl_tab_save_samples(struct isl_tab *tab)
903 union isl_tab_undo_val u;
909 return push_union(tab, isl_tab_undo_saved_samples, u);
912 /* Mark row with index "row" as being redundant.
913 * If we may need to undo the operation or if the row represents
914 * a variable of the original problem, the row is kept,
915 * but no longer considered when looking for a pivot row.
916 * Otherwise, the row is simply removed.
918 * The row may be interchanged with some other row. If it
919 * is interchanged with a later row, return 1. Otherwise return 0.
920 * If the rows are checked in order in the calling function,
921 * then a return value of 1 means that the row with the given
922 * row number may now contain a different row that hasn't been checked yet.
924 int isl_tab_mark_redundant(struct isl_tab *tab, int row)
926 struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
927 var->is_redundant = 1;
928 isl_assert(tab->mat->ctx, row >= tab->n_redundant, return -1);
929 if (tab->need_undo || tab->row_var[row] >= 0) {
930 if (tab->row_var[row] >= 0 && !var->is_nonneg) {
932 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, var) < 0)
935 if (row != tab->n_redundant)
936 swap_rows(tab, row, tab->n_redundant);
938 return isl_tab_push_var(tab, isl_tab_undo_redundant, var);
940 if (row != tab->n_row - 1)
941 swap_rows(tab, row, tab->n_row - 1);
942 isl_tab_var_from_row(tab, tab->n_row - 1)->index = -1;
948 int isl_tab_mark_empty(struct isl_tab *tab)
952 if (!tab->empty && tab->need_undo)
953 if (isl_tab_push(tab, isl_tab_undo_empty) < 0)
959 int isl_tab_freeze_constraint(struct isl_tab *tab, int con)
961 struct isl_tab_var *var;
966 var = &tab->con[con];
974 return isl_tab_push_var(tab, isl_tab_undo_freeze, var);
979 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
980 * the original sign of the pivot element.
981 * We only keep track of row signs during PILP solving and in this case
982 * we only pivot a row with negative sign (meaning the value is always
983 * non-positive) using a positive pivot element.
985 * For each row j, the new value of the parametric constant is equal to
987 * a_j0 - a_jc a_r0/a_rc
989 * where a_j0 is the original parametric constant, a_rc is the pivot element,
990 * a_r0 is the parametric constant of the pivot row and a_jc is the
991 * pivot column entry of the row j.
992 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
993 * remains the same if a_jc has the same sign as the row j or if
994 * a_jc is zero. In all other cases, we reset the sign to "unknown".
996 static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
999 struct isl_mat *mat = tab->mat;
1000 unsigned off = 2 + tab->M;
1005 if (tab->row_sign[row] == 0)
1007 isl_assert(mat->ctx, row_sgn > 0, return);
1008 isl_assert(mat->ctx, tab->row_sign[row] == isl_tab_row_neg, return);
1009 tab->row_sign[row] = isl_tab_row_pos;
1010 for (i = 0; i < tab->n_row; ++i) {
1014 s = isl_int_sgn(mat->row[i][off + col]);
1017 if (!tab->row_sign[i])
1019 if (s < 0 && tab->row_sign[i] == isl_tab_row_neg)
1021 if (s > 0 && tab->row_sign[i] == isl_tab_row_pos)
1023 tab->row_sign[i] = isl_tab_row_unknown;
1027 /* Given a row number "row" and a column number "col", pivot the tableau
1028 * such that the associated variables are interchanged.
1029 * The given row in the tableau expresses
1031 * x_r = a_r0 + \sum_i a_ri x_i
1035 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
1037 * Substituting this equality into the other rows
1039 * x_j = a_j0 + \sum_i a_ji x_i
1041 * with a_jc \ne 0, we obtain
1043 * 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
1050 * where i is any other column and j is any other row,
1051 * is therefore transformed into
1053 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1054 * 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)
1056 * The transformation is performed along the following steps
1058 * d_r/n_rc n_ri/n_rc
1061 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1064 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1065 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
1067 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1068 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
1070 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1071 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
1073 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1074 * 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)
1077 int isl_tab_pivot(struct isl_tab *tab, int row, int col)
1082 struct isl_mat *mat = tab->mat;
1083 struct isl_tab_var *var;
1084 unsigned off = 2 + tab->M;
1086 isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
1087 sgn = isl_int_sgn(mat->row[row][0]);
1089 isl_int_neg(mat->row[row][0], mat->row[row][0]);
1090 isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]);
1092 for (j = 0; j < off - 1 + tab->n_col; ++j) {
1093 if (j == off - 1 + col)
1095 isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
1097 if (!isl_int_is_one(mat->row[row][0]))
1098 isl_seq_normalize(mat->ctx, mat->row[row], off + tab->n_col);
1099 for (i = 0; i < tab->n_row; ++i) {
1102 if (isl_int_is_zero(mat->row[i][off + col]))
1104 isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
1105 for (j = 0; j < off - 1 + tab->n_col; ++j) {
1106 if (j == off - 1 + col)
1108 isl_int_mul(mat->row[i][1 + j],
1109 mat->row[i][1 + j], mat->row[row][0]);
1110 isl_int_addmul(mat->row[i][1 + j],
1111 mat->row[i][off + col], mat->row[row][1 + j]);
1113 isl_int_mul(mat->row[i][off + col],
1114 mat->row[i][off + col], mat->row[row][off + col]);
1115 if (!isl_int_is_one(mat->row[i][0]))
1116 isl_seq_normalize(mat->ctx, mat->row[i], off + tab->n_col);
1118 t = tab->row_var[row];
1119 tab->row_var[row] = tab->col_var[col];
1120 tab->col_var[col] = t;
1121 var = isl_tab_var_from_row(tab, row);
1124 var = var_from_col(tab, col);
1127 update_row_sign(tab, row, col, sgn);
1130 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1131 if (isl_int_is_zero(mat->row[i][off + col]))
1133 if (!isl_tab_var_from_row(tab, i)->frozen &&
1134 isl_tab_row_is_redundant(tab, i)) {
1135 int redo = isl_tab_mark_redundant(tab, i);
1145 /* If "var" represents a column variable, then pivot is up (sgn > 0)
1146 * or down (sgn < 0) to a row. The variable is assumed not to be
1147 * unbounded in the specified direction.
1148 * If sgn = 0, then the variable is unbounded in both directions,
1149 * and we pivot with any row we can find.
1151 static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign) WARN_UNUSED;
1152 static int to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
1155 unsigned off = 2 + tab->M;
1161 for (r = tab->n_redundant; r < tab->n_row; ++r)
1162 if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
1164 isl_assert(tab->mat->ctx, r < tab->n_row, return -1);
1166 r = pivot_row(tab, NULL, sign, var->index);
1167 isl_assert(tab->mat->ctx, r >= 0, return -1);
1170 return isl_tab_pivot(tab, r, var->index);
1173 static void check_table(struct isl_tab *tab)
1179 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1180 struct isl_tab_var *var;
1181 var = isl_tab_var_from_row(tab, i);
1182 if (!var->is_nonneg)
1185 isl_assert(tab->mat->ctx,
1186 !isl_int_is_neg(tab->mat->row[i][2]), abort());
1187 if (isl_int_is_pos(tab->mat->row[i][2]))
1190 isl_assert(tab->mat->ctx, !isl_int_is_neg(tab->mat->row[i][1]),
1195 /* Return the sign of the maximal value of "var".
1196 * If the sign is not negative, then on return from this function,
1197 * the sample value will also be non-negative.
1199 * If "var" is manifestly unbounded wrt positive values, we are done.
1200 * Otherwise, we pivot the variable up to a row if needed
1201 * Then we continue pivoting down until either
1202 * - no more down pivots can be performed
1203 * - the sample value is positive
1204 * - the variable is pivoted into a manifestly unbounded column
1206 static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
1210 if (max_is_manifestly_unbounded(tab, var))
1212 if (to_row(tab, var, 1) < 0)
1214 while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
1215 find_pivot(tab, var, var, 1, &row, &col);
1217 return isl_int_sgn(tab->mat->row[var->index][1]);
1218 if (isl_tab_pivot(tab, row, col) < 0)
1220 if (!var->is_row) /* manifestly unbounded */
1226 int isl_tab_sign_of_max(struct isl_tab *tab, int con)
1228 struct isl_tab_var *var;
1233 var = &tab->con[con];
1234 isl_assert(tab->mat->ctx, !var->is_redundant, return -2);
1235 isl_assert(tab->mat->ctx, !var->is_zero, return -2);
1237 return sign_of_max(tab, var);
1240 static int row_is_neg(struct isl_tab *tab, int row)
1243 return isl_int_is_neg(tab->mat->row[row][1]);
1244 if (isl_int_is_pos(tab->mat->row[row][2]))
1246 if (isl_int_is_neg(tab->mat->row[row][2]))
1248 return isl_int_is_neg(tab->mat->row[row][1]);
1251 static int row_sgn(struct isl_tab *tab, int row)
1254 return isl_int_sgn(tab->mat->row[row][1]);
1255 if (!isl_int_is_zero(tab->mat->row[row][2]))
1256 return isl_int_sgn(tab->mat->row[row][2]);
1258 return isl_int_sgn(tab->mat->row[row][1]);
1261 /* Perform pivots until the row variable "var" has a non-negative
1262 * sample value or until no more upward pivots can be performed.
1263 * Return the sign of the sample value after the pivots have been
1266 static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
1270 while (row_is_neg(tab, var->index)) {
1271 find_pivot(tab, var, var, 1, &row, &col);
1274 if (isl_tab_pivot(tab, row, col) < 0)
1276 if (!var->is_row) /* manifestly unbounded */
1279 return row_sgn(tab, var->index);
1282 /* Perform pivots until we are sure that the row variable "var"
1283 * can attain non-negative values. After return from this
1284 * function, "var" is still a row variable, but its sample
1285 * value may not be non-negative, even if the function returns 1.
1287 static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
1291 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
1292 find_pivot(tab, var, var, 1, &row, &col);
1295 if (row == var->index) /* manifestly unbounded */
1297 if (isl_tab_pivot(tab, row, col) < 0)
1300 return !isl_int_is_neg(tab->mat->row[var->index][1]);
1303 /* Return a negative value if "var" can attain negative values.
1304 * Return a non-negative value otherwise.
1306 * If "var" is manifestly unbounded wrt negative values, we are done.
1307 * Otherwise, if var is in a column, we can pivot it down to a row.
1308 * Then we continue pivoting down until either
1309 * - the pivot would result in a manifestly unbounded column
1310 * => we don't perform the pivot, but simply return -1
1311 * - no more down pivots can be performed
1312 * - the sample value is negative
1313 * If the sample value becomes negative and the variable is supposed
1314 * to be nonnegative, then we undo the last pivot.
1315 * However, if the last pivot has made the pivoting variable
1316 * obviously redundant, then it may have moved to another row.
1317 * In that case we look for upward pivots until we reach a non-negative
1320 static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
1323 struct isl_tab_var *pivot_var = NULL;
1325 if (min_is_manifestly_unbounded(tab, var))
1329 row = pivot_row(tab, NULL, -1, col);
1330 pivot_var = var_from_col(tab, col);
1331 if (isl_tab_pivot(tab, row, col) < 0)
1333 if (var->is_redundant)
1335 if (isl_int_is_neg(tab->mat->row[var->index][1])) {
1336 if (var->is_nonneg) {
1337 if (!pivot_var->is_redundant &&
1338 pivot_var->index == row) {
1339 if (isl_tab_pivot(tab, row, col) < 0)
1342 if (restore_row(tab, var) < -1)
1348 if (var->is_redundant)
1350 while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
1351 find_pivot(tab, var, var, -1, &row, &col);
1352 if (row == var->index)
1355 return isl_int_sgn(tab->mat->row[var->index][1]);
1356 pivot_var = var_from_col(tab, col);
1357 if (isl_tab_pivot(tab, row, col) < 0)
1359 if (var->is_redundant)
1362 if (pivot_var && var->is_nonneg) {
1363 /* pivot back to non-negative value */
1364 if (!pivot_var->is_redundant && pivot_var->index == row) {
1365 if (isl_tab_pivot(tab, row, col) < 0)
1368 if (restore_row(tab, var) < -1)
1374 static int row_at_most_neg_one(struct isl_tab *tab, int row)
1377 if (isl_int_is_pos(tab->mat->row[row][2]))
1379 if (isl_int_is_neg(tab->mat->row[row][2]))
1382 return isl_int_is_neg(tab->mat->row[row][1]) &&
1383 isl_int_abs_ge(tab->mat->row[row][1],
1384 tab->mat->row[row][0]);
1387 /* Return 1 if "var" can attain values <= -1.
1388 * Return 0 otherwise.
1390 * The sample value of "var" is assumed to be non-negative when the
1391 * the function is called. If 1 is returned then the constraint
1392 * is not redundant and the sample value is made non-negative again before
1393 * the function returns.
1395 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
1398 struct isl_tab_var *pivot_var;
1400 if (min_is_manifestly_unbounded(tab, var))
1404 row = pivot_row(tab, NULL, -1, col);
1405 pivot_var = var_from_col(tab, col);
1406 if (isl_tab_pivot(tab, row, col) < 0)
1408 if (var->is_redundant)
1410 if (row_at_most_neg_one(tab, var->index)) {
1411 if (var->is_nonneg) {
1412 if (!pivot_var->is_redundant &&
1413 pivot_var->index == row) {
1414 if (isl_tab_pivot(tab, row, col) < 0)
1417 if (restore_row(tab, var) < -1)
1423 if (var->is_redundant)
1426 find_pivot(tab, var, var, -1, &row, &col);
1427 if (row == var->index) {
1428 if (restore_row(tab, var) < -1)
1434 pivot_var = var_from_col(tab, col);
1435 if (isl_tab_pivot(tab, row, col) < 0)
1437 if (var->is_redundant)
1439 } while (!row_at_most_neg_one(tab, var->index));
1440 if (var->is_nonneg) {
1441 /* pivot back to non-negative value */
1442 if (!pivot_var->is_redundant && pivot_var->index == row)
1443 if (isl_tab_pivot(tab, row, col) < 0)
1445 if (restore_row(tab, var) < -1)
1451 /* Return 1 if "var" can attain values >= 1.
1452 * Return 0 otherwise.
1454 static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
1459 if (max_is_manifestly_unbounded(tab, var))
1461 if (to_row(tab, var, 1) < 0)
1463 r = tab->mat->row[var->index];
1464 while (isl_int_lt(r[1], r[0])) {
1465 find_pivot(tab, var, var, 1, &row, &col);
1467 return isl_int_ge(r[1], r[0]);
1468 if (row == var->index) /* manifestly unbounded */
1470 if (isl_tab_pivot(tab, row, col) < 0)
1476 static void swap_cols(struct isl_tab *tab, int col1, int col2)
1479 unsigned off = 2 + tab->M;
1480 t = tab->col_var[col1];
1481 tab->col_var[col1] = tab->col_var[col2];
1482 tab->col_var[col2] = t;
1483 var_from_col(tab, col1)->index = col1;
1484 var_from_col(tab, col2)->index = col2;
1485 tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2);
1488 /* Mark column with index "col" as representing a zero variable.
1489 * If we may need to undo the operation the column is kept,
1490 * but no longer considered.
1491 * Otherwise, the column is simply removed.
1493 * The column may be interchanged with some other column. If it
1494 * is interchanged with a later column, return 1. Otherwise return 0.
1495 * If the columns are checked in order in the calling function,
1496 * then a return value of 1 means that the column with the given
1497 * column number may now contain a different column that
1498 * hasn't been checked yet.
1500 int isl_tab_kill_col(struct isl_tab *tab, int col)
1502 var_from_col(tab, col)->is_zero = 1;
1503 if (tab->need_undo) {
1504 if (isl_tab_push_var(tab, isl_tab_undo_zero,
1505 var_from_col(tab, col)) < 0)
1507 if (col != tab->n_dead)
1508 swap_cols(tab, col, tab->n_dead);
1512 if (col != tab->n_col - 1)
1513 swap_cols(tab, col, tab->n_col - 1);
1514 var_from_col(tab, tab->n_col - 1)->index = -1;
1520 /* Row variable "var" is non-negative and cannot attain any values
1521 * larger than zero. This means that the coefficients of the unrestricted
1522 * column variables are zero and that the coefficients of the non-negative
1523 * column variables are zero or negative.
1524 * Each of the non-negative variables with a negative coefficient can
1525 * then also be written as the negative sum of non-negative variables
1526 * and must therefore also be zero.
1528 static int close_row(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
1529 static int close_row(struct isl_tab *tab, struct isl_tab_var *var)
1532 struct isl_mat *mat = tab->mat;
1533 unsigned off = 2 + tab->M;
1535 isl_assert(tab->mat->ctx, var->is_nonneg, return -1);
1538 if (isl_tab_push_var(tab, isl_tab_undo_zero, var) < 0)
1540 for (j = tab->n_dead; j < tab->n_col; ++j) {
1542 if (isl_int_is_zero(mat->row[var->index][off + j]))
1544 isl_assert(tab->mat->ctx,
1545 isl_int_is_neg(mat->row[var->index][off + j]), return -1);
1546 recheck = isl_tab_kill_col(tab, j);
1552 if (isl_tab_mark_redundant(tab, var->index) < 0)
1557 /* Add a constraint to the tableau and allocate a row for it.
1558 * Return the index into the constraint array "con".
1560 int isl_tab_allocate_con(struct isl_tab *tab)
1564 isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
1565 isl_assert(tab->mat->ctx, tab->n_con < tab->max_con, return -1);
1568 tab->con[r].index = tab->n_row;
1569 tab->con[r].is_row = 1;
1570 tab->con[r].is_nonneg = 0;
1571 tab->con[r].is_zero = 0;
1572 tab->con[r].is_redundant = 0;
1573 tab->con[r].frozen = 0;
1574 tab->con[r].negated = 0;
1575 tab->row_var[tab->n_row] = ~r;
1579 if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
1585 /* Add a variable to the tableau and allocate a column for it.
1586 * Return the index into the variable array "var".
1588 int isl_tab_allocate_var(struct isl_tab *tab)
1592 unsigned off = 2 + tab->M;
1594 isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
1595 isl_assert(tab->mat->ctx, tab->n_var < tab->max_var, return -1);
1598 tab->var[r].index = tab->n_col;
1599 tab->var[r].is_row = 0;
1600 tab->var[r].is_nonneg = 0;
1601 tab->var[r].is_zero = 0;
1602 tab->var[r].is_redundant = 0;
1603 tab->var[r].frozen = 0;
1604 tab->var[r].negated = 0;
1605 tab->col_var[tab->n_col] = r;
1607 for (i = 0; i < tab->n_row; ++i)
1608 isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
1612 if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]) < 0)
1618 /* Add a row to the tableau. The row is given as an affine combination
1619 * of the original variables and needs to be expressed in terms of the
1622 * We add each term in turn.
1623 * If r = n/d_r is the current sum and we need to add k x, then
1624 * if x is a column variable, we increase the numerator of
1625 * this column by k d_r
1626 * if x = f/d_x is a row variable, then the new representation of r is
1628 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1629 * --- + --- = ------------------- = -------------------
1630 * d_r d_r d_r d_x/g m
1632 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1634 * If tab->M is set, then, internally, each variable x is represented
1635 * as x' - M. We then also need no subtract k d_r from the coefficient of M.
1637 int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
1643 unsigned off = 2 + tab->M;
1645 r = isl_tab_allocate_con(tab);
1651 row = tab->mat->row[tab->con[r].index];
1652 isl_int_set_si(row[0], 1);
1653 isl_int_set(row[1], line[0]);
1654 isl_seq_clr(row + 2, tab->M + tab->n_col);
1655 for (i = 0; i < tab->n_var; ++i) {
1656 if (tab->var[i].is_zero)
1658 if (tab->var[i].is_row) {
1660 row[0], tab->mat->row[tab->var[i].index][0]);
1661 isl_int_swap(a, row[0]);
1662 isl_int_divexact(a, row[0], a);
1664 row[0], tab->mat->row[tab->var[i].index][0]);
1665 isl_int_mul(b, b, line[1 + i]);
1666 isl_seq_combine(row + 1, a, row + 1,
1667 b, tab->mat->row[tab->var[i].index] + 1,
1668 1 + tab->M + tab->n_col);
1670 isl_int_addmul(row[off + tab->var[i].index],
1671 line[1 + i], row[0]);
1672 if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
1673 isl_int_submul(row[2], line[1 + i], row[0]);
1675 isl_seq_normalize(tab->mat->ctx, row, off + tab->n_col);
1680 tab->row_sign[tab->con[r].index] = isl_tab_row_unknown;
1685 static int drop_row(struct isl_tab *tab, int row)
1687 isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
1688 if (row != tab->n_row - 1)
1689 swap_rows(tab, row, tab->n_row - 1);
1695 static int drop_col(struct isl_tab *tab, int col)
1697 isl_assert(tab->mat->ctx, tab->col_var[col] == tab->n_var - 1, return -1);
1698 if (col != tab->n_col - 1)
1699 swap_cols(tab, col, tab->n_col - 1);
1705 /* Add inequality "ineq" and check if it conflicts with the
1706 * previously added constraints or if it is obviously redundant.
1708 int isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
1717 struct isl_basic_map *bmap = tab->bmap;
1719 isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, return -1);
1720 isl_assert(tab->mat->ctx,
1721 tab->n_con == bmap->n_eq + bmap->n_ineq, return -1);
1722 tab->bmap = isl_basic_map_add_ineq(tab->bmap, ineq);
1723 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1730 isl_int_swap(ineq[0], cst);
1732 r = isl_tab_add_row(tab, ineq);
1734 isl_int_swap(ineq[0], cst);
1739 tab->con[r].is_nonneg = 1;
1740 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
1742 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1743 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1748 sgn = restore_row(tab, &tab->con[r]);
1752 return isl_tab_mark_empty(tab);
1753 if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
1754 if (isl_tab_mark_redundant(tab, tab->con[r].index) < 0)
1759 /* Pivot a non-negative variable down until it reaches the value zero
1760 * and then pivot the variable into a column position.
1762 static int to_col(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
1763 static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
1767 unsigned off = 2 + tab->M;
1772 while (isl_int_is_pos(tab->mat->row[var->index][1])) {
1773 find_pivot(tab, var, NULL, -1, &row, &col);
1774 isl_assert(tab->mat->ctx, row != -1, return -1);
1775 if (isl_tab_pivot(tab, row, col) < 0)
1781 for (i = tab->n_dead; i < tab->n_col; ++i)
1782 if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
1785 isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
1786 if (isl_tab_pivot(tab, var->index, i) < 0)
1792 /* We assume Gaussian elimination has been performed on the equalities.
1793 * The equalities can therefore never conflict.
1794 * Adding the equalities is currently only really useful for a later call
1795 * to isl_tab_ineq_type.
1797 static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
1804 r = isl_tab_add_row(tab, eq);
1808 r = tab->con[r].index;
1809 i = isl_seq_first_non_zero(tab->mat->row[r] + 2 + tab->M + tab->n_dead,
1810 tab->n_col - tab->n_dead);
1811 isl_assert(tab->mat->ctx, i >= 0, goto error);
1813 if (isl_tab_pivot(tab, r, i) < 0)
1815 if (isl_tab_kill_col(tab, i) < 0)
1825 static int row_is_manifestly_zero(struct isl_tab *tab, int row)
1827 unsigned off = 2 + tab->M;
1829 if (!isl_int_is_zero(tab->mat->row[row][1]))
1831 if (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))
1833 return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1834 tab->n_col - tab->n_dead) == -1;
1837 /* Add an equality that is known to be valid for the given tableau.
1839 int isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
1841 struct isl_tab_var *var;
1846 r = isl_tab_add_row(tab, eq);
1852 if (row_is_manifestly_zero(tab, r)) {
1854 if (isl_tab_mark_redundant(tab, r) < 0)
1859 if (isl_int_is_neg(tab->mat->row[r][1])) {
1860 isl_seq_neg(tab->mat->row[r] + 1, tab->mat->row[r] + 1,
1865 if (to_col(tab, var) < 0)
1868 if (isl_tab_kill_col(tab, var->index) < 0)
1874 static int add_zero_row(struct isl_tab *tab)
1879 r = isl_tab_allocate_con(tab);
1883 row = tab->mat->row[tab->con[r].index];
1884 isl_seq_clr(row + 1, 1 + tab->M + tab->n_col);
1885 isl_int_set_si(row[0], 1);
1890 /* Add equality "eq" and check if it conflicts with the
1891 * previously added constraints or if it is obviously redundant.
1893 int isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
1895 struct isl_tab_undo *snap = NULL;
1896 struct isl_tab_var *var;
1904 isl_assert(tab->mat->ctx, !tab->M, return -1);
1907 snap = isl_tab_snap(tab);
1911 isl_int_swap(eq[0], cst);
1913 r = isl_tab_add_row(tab, eq);
1915 isl_int_swap(eq[0], cst);
1923 if (row_is_manifestly_zero(tab, row)) {
1925 if (isl_tab_rollback(tab, snap) < 0)
1933 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
1934 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1936 isl_seq_neg(eq, eq, 1 + tab->n_var);
1937 tab->bmap = isl_basic_map_add_ineq(tab->bmap, eq);
1938 isl_seq_neg(eq, eq, 1 + tab->n_var);
1939 if (isl_tab_push(tab, isl_tab_undo_bmap_ineq) < 0)
1943 if (add_zero_row(tab) < 0)
1947 sgn = isl_int_sgn(tab->mat->row[row][1]);
1950 isl_seq_neg(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
1957 sgn = sign_of_max(tab, var);
1961 if (isl_tab_mark_empty(tab) < 0)
1968 if (to_col(tab, var) < 0)
1971 if (isl_tab_kill_col(tab, var->index) < 0)
1977 /* Construct and return an inequality that expresses an upper bound
1979 * In particular, if the div is given by
1983 * then the inequality expresses
1987 static struct isl_vec *ineq_for_div(struct isl_basic_map *bmap, unsigned div)
1991 struct isl_vec *ineq;
1996 total = isl_basic_map_total_dim(bmap);
1997 div_pos = 1 + total - bmap->n_div + div;
1999 ineq = isl_vec_alloc(bmap->ctx, 1 + total);
2003 isl_seq_cpy(ineq->el, bmap->div[div] + 1, 1 + total);
2004 isl_int_neg(ineq->el[div_pos], bmap->div[div][0]);
2008 /* For a div d = floor(f/m), add the constraints
2011 * -(f-(m-1)) + m d >= 0
2013 * Note that the second constraint is the negation of
2017 * If add_ineq is not NULL, then this function is used
2018 * instead of isl_tab_add_ineq to effectively add the inequalities.
2020 static int add_div_constraints(struct isl_tab *tab, unsigned div,
2021 int (*add_ineq)(void *user, isl_int *), void *user)
2025 struct isl_vec *ineq;
2027 total = isl_basic_map_total_dim(tab->bmap);
2028 div_pos = 1 + total - tab->bmap->n_div + div;
2030 ineq = ineq_for_div(tab->bmap, div);
2035 if (add_ineq(user, ineq->el) < 0)
2038 if (isl_tab_add_ineq(tab, ineq->el) < 0)
2042 isl_seq_neg(ineq->el, tab->bmap->div[div] + 1, 1 + total);
2043 isl_int_set(ineq->el[div_pos], tab->bmap->div[div][0]);
2044 isl_int_add(ineq->el[0], ineq->el[0], ineq->el[div_pos]);
2045 isl_int_sub_ui(ineq->el[0], ineq->el[0], 1);
2048 if (add_ineq(user, ineq->el) < 0)
2051 if (isl_tab_add_ineq(tab, ineq->el) < 0)
2063 /* Check whether the div described by "div" is obviously non-negative.
2064 * If we are using a big parameter, then we will encode the div
2065 * as div' = M + div, which is always non-negative.
2066 * Otherwise, we check whether div is a non-negative affine combination
2067 * of non-negative variables.
2069 static int div_is_nonneg(struct isl_tab *tab, __isl_keep isl_vec *div)
2076 if (isl_int_is_neg(div->el[1]))
2079 for (i = 0; i < tab->n_var; ++i) {
2080 if (isl_int_is_neg(div->el[2 + i]))
2082 if (isl_int_is_zero(div->el[2 + i]))
2084 if (!tab->var[i].is_nonneg)
2091 /* Add an extra div, prescribed by "div" to the tableau and
2092 * the associated bmap (which is assumed to be non-NULL).
2094 * If add_ineq is not NULL, then this function is used instead
2095 * of isl_tab_add_ineq to add the div constraints.
2096 * This complication is needed because the code in isl_tab_pip
2097 * wants to perform some extra processing when an inequality
2098 * is added to the tableau.
2100 int isl_tab_add_div(struct isl_tab *tab, __isl_keep isl_vec *div,
2101 int (*add_ineq)(void *user, isl_int *), void *user)
2110 isl_assert(tab->mat->ctx, tab->bmap, return -1);
2112 nonneg = div_is_nonneg(tab, div);
2114 if (isl_tab_extend_cons(tab, 3) < 0)
2116 if (isl_tab_extend_vars(tab, 1) < 0)
2118 r = isl_tab_allocate_var(tab);
2123 tab->var[r].is_nonneg = 1;
2125 tab->bmap = isl_basic_map_extend_dim(tab->bmap,
2126 isl_basic_map_get_dim(tab->bmap), 1, 0, 2);
2127 k = isl_basic_map_alloc_div(tab->bmap);
2130 isl_seq_cpy(tab->bmap->div[k], div->el, div->size);
2131 if (isl_tab_push(tab, isl_tab_undo_bmap_div) < 0)
2134 if (add_div_constraints(tab, k, add_ineq, user) < 0)
2140 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap)
2143 struct isl_tab *tab;
2147 tab = isl_tab_alloc(bmap->ctx,
2148 isl_basic_map_total_dim(bmap) + bmap->n_ineq + 1,
2149 isl_basic_map_total_dim(bmap), 0);
2152 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
2153 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
2154 if (isl_tab_mark_empty(tab) < 0)
2158 for (i = 0; i < bmap->n_eq; ++i) {
2159 tab = add_eq(tab, bmap->eq[i]);
2163 for (i = 0; i < bmap->n_ineq; ++i) {
2164 if (isl_tab_add_ineq(tab, bmap->ineq[i]) < 0)
2175 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset)
2177 return isl_tab_from_basic_map((struct isl_basic_map *)bset);
2180 /* Construct a tableau corresponding to the recession cone of "bset".
2182 struct isl_tab *isl_tab_from_recession_cone(__isl_keep isl_basic_set *bset,
2187 struct isl_tab *tab;
2188 unsigned offset = 0;
2193 offset = isl_basic_set_dim(bset, isl_dim_param);
2194 tab = isl_tab_alloc(bset->ctx, bset->n_eq + bset->n_ineq,
2195 isl_basic_set_total_dim(bset) - offset, 0);
2198 tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
2202 for (i = 0; i < bset->n_eq; ++i) {
2203 isl_int_swap(bset->eq[i][offset], cst);
2205 if (isl_tab_add_eq(tab, bset->eq[i] + offset) < 0)
2208 tab = add_eq(tab, bset->eq[i]);
2209 isl_int_swap(bset->eq[i][offset], cst);
2213 for (i = 0; i < bset->n_ineq; ++i) {
2215 isl_int_swap(bset->ineq[i][offset], cst);
2216 r = isl_tab_add_row(tab, bset->ineq[i] + offset);
2217 isl_int_swap(bset->ineq[i][offset], cst);
2220 tab->con[r].is_nonneg = 1;
2221 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
2233 /* Assuming "tab" is the tableau of a cone, check if the cone is
2234 * bounded, i.e., if it is empty or only contains the origin.
2236 int isl_tab_cone_is_bounded(struct isl_tab *tab)
2244 if (tab->n_dead == tab->n_col)
2248 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2249 struct isl_tab_var *var;
2251 var = isl_tab_var_from_row(tab, i);
2252 if (!var->is_nonneg)
2254 sgn = sign_of_max(tab, var);
2259 if (close_row(tab, var) < 0)
2263 if (tab->n_dead == tab->n_col)
2265 if (i == tab->n_row)
2270 int isl_tab_sample_is_integer(struct isl_tab *tab)
2277 for (i = 0; i < tab->n_var; ++i) {
2279 if (!tab->var[i].is_row)
2281 row = tab->var[i].index;
2282 if (!isl_int_is_divisible_by(tab->mat->row[row][1],
2283 tab->mat->row[row][0]))
2289 static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
2292 struct isl_vec *vec;
2294 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
2298 isl_int_set_si(vec->block.data[0], 1);
2299 for (i = 0; i < tab->n_var; ++i) {
2300 if (!tab->var[i].is_row)
2301 isl_int_set_si(vec->block.data[1 + i], 0);
2303 int row = tab->var[i].index;
2304 isl_int_divexact(vec->block.data[1 + i],
2305 tab->mat->row[row][1], tab->mat->row[row][0]);
2312 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
2315 struct isl_vec *vec;
2321 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
2327 isl_int_set_si(vec->block.data[0], 1);
2328 for (i = 0; i < tab->n_var; ++i) {
2330 if (!tab->var[i].is_row) {
2331 isl_int_set_si(vec->block.data[1 + i], 0);
2334 row = tab->var[i].index;
2335 isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
2336 isl_int_divexact(m, tab->mat->row[row][0], m);
2337 isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
2338 isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
2339 isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
2341 vec = isl_vec_normalize(vec);
2347 /* Update "bmap" based on the results of the tableau "tab".
2348 * In particular, implicit equalities are made explicit, redundant constraints
2349 * are removed and if the sample value happens to be integer, it is stored
2350 * in "bmap" (unless "bmap" already had an integer sample).
2352 * The tableau is assumed to have been created from "bmap" using
2353 * isl_tab_from_basic_map.
2355 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
2356 struct isl_tab *tab)
2368 bmap = isl_basic_map_set_to_empty(bmap);
2370 for (i = bmap->n_ineq - 1; i >= 0; --i) {
2371 if (isl_tab_is_equality(tab, n_eq + i))
2372 isl_basic_map_inequality_to_equality(bmap, i);
2373 else if (isl_tab_is_redundant(tab, n_eq + i))
2374 isl_basic_map_drop_inequality(bmap, i);
2376 if (bmap->n_eq != n_eq)
2377 isl_basic_map_gauss(bmap, NULL);
2378 if (!tab->rational &&
2379 !bmap->sample && isl_tab_sample_is_integer(tab))
2380 bmap->sample = extract_integer_sample(tab);
2384 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
2385 struct isl_tab *tab)
2387 return (struct isl_basic_set *)isl_basic_map_update_from_tab(
2388 (struct isl_basic_map *)bset, tab);
2391 /* Given a non-negative variable "var", add a new non-negative variable
2392 * that is the opposite of "var", ensuring that var can only attain the
2394 * If var = n/d is a row variable, then the new variable = -n/d.
2395 * If var is a column variables, then the new variable = -var.
2396 * If the new variable cannot attain non-negative values, then
2397 * the resulting tableau is empty.
2398 * Otherwise, we know the value will be zero and we close the row.
2400 static int cut_to_hyperplane(struct isl_tab *tab, struct isl_tab_var *var)
2405 unsigned off = 2 + tab->M;
2409 isl_assert(tab->mat->ctx, !var->is_redundant, return -1);
2410 isl_assert(tab->mat->ctx, var->is_nonneg, return -1);
2412 if (isl_tab_extend_cons(tab, 1) < 0)
2416 tab->con[r].index = tab->n_row;
2417 tab->con[r].is_row = 1;
2418 tab->con[r].is_nonneg = 0;
2419 tab->con[r].is_zero = 0;
2420 tab->con[r].is_redundant = 0;
2421 tab->con[r].frozen = 0;
2422 tab->con[r].negated = 0;
2423 tab->row_var[tab->n_row] = ~r;
2424 row = tab->mat->row[tab->n_row];
2427 isl_int_set(row[0], tab->mat->row[var->index][0]);
2428 isl_seq_neg(row + 1,
2429 tab->mat->row[var->index] + 1, 1 + tab->n_col);
2431 isl_int_set_si(row[0], 1);
2432 isl_seq_clr(row + 1, 1 + tab->n_col);
2433 isl_int_set_si(row[off + var->index], -1);
2438 if (isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]) < 0)
2441 sgn = sign_of_max(tab, &tab->con[r]);
2445 if (isl_tab_mark_empty(tab) < 0)
2449 tab->con[r].is_nonneg = 1;
2450 if (isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]) < 0)
2453 if (close_row(tab, &tab->con[r]) < 0)
2459 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2460 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2461 * by r' = r + 1 >= 0.
2462 * If r is a row variable, we simply increase the constant term by one
2463 * (taking into account the denominator).
2464 * If r is a column variable, then we need to modify each row that
2465 * refers to r = r' - 1 by substituting this equality, effectively
2466 * subtracting the coefficient of the column from the constant.
2467 * We should only do this if the minimum is manifestly unbounded,
2468 * however. Otherwise, we may end up with negative sample values
2469 * for non-negative variables.
2470 * So, if r is a column variable with a minimum that is not
2471 * manifestly unbounded, then we need to move it to a row.
2472 * However, the sample value of this row may be negative,
2473 * even after the relaxation, so we need to restore it.
2474 * We therefore prefer to pivot a column up to a row, if possible.
2476 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
2478 struct isl_tab_var *var;
2479 unsigned off = 2 + tab->M;
2484 var = &tab->con[con];
2486 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
2487 if (to_row(tab, var, 1) < 0)
2489 if (!var->is_row && !min_is_manifestly_unbounded(tab, var))
2490 if (to_row(tab, var, -1) < 0)
2494 isl_int_add(tab->mat->row[var->index][1],
2495 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
2496 if (restore_row(tab, var) < 0)
2501 for (i = 0; i < tab->n_row; ++i) {
2502 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2504 isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
2505 tab->mat->row[i][off + var->index]);
2510 if (isl_tab_push_var(tab, isl_tab_undo_relax, var) < 0)
2519 int isl_tab_select_facet(struct isl_tab *tab, int con)
2524 return cut_to_hyperplane(tab, &tab->con[con]);
2527 static int may_be_equality(struct isl_tab *tab, int row)
2529 unsigned off = 2 + tab->M;
2530 return tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
2531 : isl_int_lt(tab->mat->row[row][1],
2532 tab->mat->row[row][0]);
2535 /* Check for (near) equalities among the constraints.
2536 * A constraint is an equality if it is non-negative and if
2537 * its maximal value is either
2538 * - zero (in case of rational tableaus), or
2539 * - strictly less than 1 (in case of integer tableaus)
2541 * We first mark all non-redundant and non-dead variables that
2542 * are not frozen and not obviously not an equality.
2543 * Then we iterate over all marked variables if they can attain
2544 * any values larger than zero or at least one.
2545 * If the maximal value is zero, we mark any column variables
2546 * that appear in the row as being zero and mark the row as being redundant.
2547 * Otherwise, if the maximal value is strictly less than one (and the
2548 * tableau is integer), then we restrict the value to being zero
2549 * by adding an opposite non-negative variable.
2551 int isl_tab_detect_implicit_equalities(struct isl_tab *tab)
2560 if (tab->n_dead == tab->n_col)
2564 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2565 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
2566 var->marked = !var->frozen && var->is_nonneg &&
2567 may_be_equality(tab, i);
2571 for (i = tab->n_dead; i < tab->n_col; ++i) {
2572 struct isl_tab_var *var = var_from_col(tab, i);
2573 var->marked = !var->frozen && var->is_nonneg;
2578 struct isl_tab_var *var;
2580 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2581 var = isl_tab_var_from_row(tab, i);
2585 if (i == tab->n_row) {
2586 for (i = tab->n_dead; i < tab->n_col; ++i) {
2587 var = var_from_col(tab, i);
2591 if (i == tab->n_col)
2596 sgn = sign_of_max(tab, var);
2600 if (close_row(tab, var) < 0)
2602 } else if (!tab->rational && !at_least_one(tab, var)) {
2603 if (cut_to_hyperplane(tab, var) < 0)
2605 return isl_tab_detect_implicit_equalities(tab);
2607 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2608 var = isl_tab_var_from_row(tab, i);
2611 if (may_be_equality(tab, i))
2621 static int con_is_redundant(struct isl_tab *tab, struct isl_tab_var *var)
2625 if (tab->rational) {
2626 int sgn = sign_of_min(tab, var);
2631 int irred = isl_tab_min_at_most_neg_one(tab, var);
2638 /* Check for (near) redundant constraints.
2639 * A constraint is redundant if it is non-negative and if
2640 * its minimal value (temporarily ignoring the non-negativity) is either
2641 * - zero (in case of rational tableaus), or
2642 * - strictly larger than -1 (in case of integer tableaus)
2644 * We first mark all non-redundant and non-dead variables that
2645 * are not frozen and not obviously negatively unbounded.
2646 * Then we iterate over all marked variables if they can attain
2647 * any values smaller than zero or at most negative one.
2648 * If not, we mark the row as being redundant (assuming it hasn't
2649 * been detected as being obviously redundant in the mean time).
2651 int isl_tab_detect_redundant(struct isl_tab *tab)
2660 if (tab->n_redundant == tab->n_row)
2664 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2665 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
2666 var->marked = !var->frozen && var->is_nonneg;
2670 for (i = tab->n_dead; i < tab->n_col; ++i) {
2671 struct isl_tab_var *var = var_from_col(tab, i);
2672 var->marked = !var->frozen && var->is_nonneg &&
2673 !min_is_manifestly_unbounded(tab, var);
2678 struct isl_tab_var *var;
2680 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2681 var = isl_tab_var_from_row(tab, i);
2685 if (i == tab->n_row) {
2686 for (i = tab->n_dead; i < tab->n_col; ++i) {
2687 var = var_from_col(tab, i);
2691 if (i == tab->n_col)
2696 red = con_is_redundant(tab, var);
2699 if (red && !var->is_redundant)
2700 if (isl_tab_mark_redundant(tab, var->index) < 0)
2702 for (i = tab->n_dead; i < tab->n_col; ++i) {
2703 var = var_from_col(tab, i);
2706 if (!min_is_manifestly_unbounded(tab, var))
2716 int isl_tab_is_equality(struct isl_tab *tab, int con)
2723 if (tab->con[con].is_zero)
2725 if (tab->con[con].is_redundant)
2727 if (!tab->con[con].is_row)
2728 return tab->con[con].index < tab->n_dead;
2730 row = tab->con[con].index;
2733 return isl_int_is_zero(tab->mat->row[row][1]) &&
2734 (!tab->M || isl_int_is_zero(tab->mat->row[row][2])) &&
2735 isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
2736 tab->n_col - tab->n_dead) == -1;
2739 /* Return the minimal value of the affine expression "f" with denominator
2740 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
2741 * the expression cannot attain arbitrarily small values.
2742 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
2743 * The return value reflects the nature of the result (empty, unbounded,
2744 * minimal value returned in *opt).
2746 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
2747 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
2751 enum isl_lp_result res = isl_lp_ok;
2752 struct isl_tab_var *var;
2753 struct isl_tab_undo *snap;
2756 return isl_lp_error;
2759 return isl_lp_empty;
2761 snap = isl_tab_snap(tab);
2762 r = isl_tab_add_row(tab, f);
2764 return isl_lp_error;
2768 find_pivot(tab, var, var, -1, &row, &col);
2769 if (row == var->index) {
2770 res = isl_lp_unbounded;
2775 if (isl_tab_pivot(tab, row, col) < 0)
2776 return isl_lp_error;
2778 isl_int_mul(tab->mat->row[var->index][0],
2779 tab->mat->row[var->index][0], denom);
2780 if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
2783 isl_vec_free(tab->dual);
2784 tab->dual = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_con);
2786 return isl_lp_error;
2787 isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
2788 for (i = 0; i < tab->n_con; ++i) {
2790 if (tab->con[i].is_row) {
2791 isl_int_set_si(tab->dual->el[1 + i], 0);
2794 pos = 2 + tab->M + tab->con[i].index;
2795 if (tab->con[i].negated)
2796 isl_int_neg(tab->dual->el[1 + i],
2797 tab->mat->row[var->index][pos]);
2799 isl_int_set(tab->dual->el[1 + i],
2800 tab->mat->row[var->index][pos]);
2803 if (opt && res == isl_lp_ok) {
2805 isl_int_set(*opt, tab->mat->row[var->index][1]);
2806 isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
2808 isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
2809 tab->mat->row[var->index][0]);
2811 if (isl_tab_rollback(tab, snap) < 0)
2812 return isl_lp_error;
2816 int isl_tab_is_redundant(struct isl_tab *tab, int con)
2820 if (tab->con[con].is_zero)
2822 if (tab->con[con].is_redundant)
2824 return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
2827 /* Take a snapshot of the tableau that can be restored by s call to
2830 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
2838 /* Undo the operation performed by isl_tab_relax.
2840 static int unrelax(struct isl_tab *tab, struct isl_tab_var *var) WARN_UNUSED;
2841 static int unrelax(struct isl_tab *tab, struct isl_tab_var *var)
2843 unsigned off = 2 + tab->M;
2845 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
2846 if (to_row(tab, var, 1) < 0)
2850 isl_int_sub(tab->mat->row[var->index][1],
2851 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
2852 if (var->is_nonneg) {
2853 int sgn = restore_row(tab, var);
2854 isl_assert(tab->mat->ctx, sgn >= 0, return -1);
2859 for (i = 0; i < tab->n_row; ++i) {
2860 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2862 isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
2863 tab->mat->row[i][off + var->index]);
2871 static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
2872 static int perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
2874 struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
2875 switch(undo->type) {
2876 case isl_tab_undo_nonneg:
2879 case isl_tab_undo_redundant:
2880 var->is_redundant = 0;
2882 restore_row(tab, isl_tab_var_from_row(tab, tab->n_redundant));
2884 case isl_tab_undo_freeze:
2887 case isl_tab_undo_zero:
2892 case isl_tab_undo_allocate:
2893 if (undo->u.var_index >= 0) {
2894 isl_assert(tab->mat->ctx, !var->is_row, return -1);
2895 drop_col(tab, var->index);
2899 if (!max_is_manifestly_unbounded(tab, var)) {
2900 if (to_row(tab, var, 1) < 0)
2902 } else if (!min_is_manifestly_unbounded(tab, var)) {
2903 if (to_row(tab, var, -1) < 0)
2906 if (to_row(tab, var, 0) < 0)
2909 drop_row(tab, var->index);
2911 case isl_tab_undo_relax:
2912 return unrelax(tab, var);
2918 /* Restore the tableau to the state where the basic variables
2919 * are those in "col_var".
2920 * We first construct a list of variables that are currently in
2921 * the basis, but shouldn't. Then we iterate over all variables
2922 * that should be in the basis and for each one that is currently
2923 * not in the basis, we exchange it with one of the elements of the
2924 * list constructed before.
2925 * We can always find an appropriate variable to pivot with because
2926 * the current basis is mapped to the old basis by a non-singular
2927 * matrix and so we can never end up with a zero row.
2929 static int restore_basis(struct isl_tab *tab, int *col_var)
2933 int *extra = NULL; /* current columns that contain bad stuff */
2934 unsigned off = 2 + tab->M;
2936 extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
2939 for (i = 0; i < tab->n_col; ++i) {
2940 for (j = 0; j < tab->n_col; ++j)
2941 if (tab->col_var[i] == col_var[j])
2945 extra[n_extra++] = i;
2947 for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
2948 struct isl_tab_var *var;
2951 for (j = 0; j < tab->n_col; ++j)
2952 if (col_var[i] == tab->col_var[j])
2956 var = var_from_index(tab, col_var[i]);
2958 for (j = 0; j < n_extra; ++j)
2959 if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
2961 isl_assert(tab->mat->ctx, j < n_extra, goto error);
2962 if (isl_tab_pivot(tab, row, extra[j]) < 0)
2964 extra[j] = extra[--n_extra];
2976 /* Remove all samples with index n or greater, i.e., those samples
2977 * that were added since we saved this number of samples in
2978 * isl_tab_save_samples.
2980 static void drop_samples_since(struct isl_tab *tab, int n)
2984 for (i = tab->n_sample - 1; i >= 0 && tab->n_sample > n; --i) {
2985 if (tab->sample_index[i] < n)
2988 if (i != tab->n_sample - 1) {
2989 int t = tab->sample_index[tab->n_sample-1];
2990 tab->sample_index[tab->n_sample-1] = tab->sample_index[i];
2991 tab->sample_index[i] = t;
2992 isl_mat_swap_rows(tab->samples, tab->n_sample-1, i);
2998 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo) WARN_UNUSED;
2999 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
3001 switch (undo->type) {
3002 case isl_tab_undo_empty:
3005 case isl_tab_undo_nonneg:
3006 case isl_tab_undo_redundant:
3007 case isl_tab_undo_freeze:
3008 case isl_tab_undo_zero:
3009 case isl_tab_undo_allocate:
3010 case isl_tab_undo_relax:
3011 return perform_undo_var(tab, undo);
3012 case isl_tab_undo_bmap_eq:
3013 return isl_basic_map_free_equality(tab->bmap, 1);
3014 case isl_tab_undo_bmap_ineq:
3015 return isl_basic_map_free_inequality(tab->bmap, 1);
3016 case isl_tab_undo_bmap_div:
3017 if (isl_basic_map_free_div(tab->bmap, 1) < 0)
3020 tab->samples->n_col--;
3022 case isl_tab_undo_saved_basis:
3023 if (restore_basis(tab, undo->u.col_var) < 0)
3026 case isl_tab_undo_drop_sample:
3029 case isl_tab_undo_saved_samples:
3030 drop_samples_since(tab, undo->u.n);
3032 case isl_tab_undo_callback:
3033 return undo->u.callback->run(undo->u.callback);
3035 isl_assert(tab->mat->ctx, 0, return -1);
3040 /* Return the tableau to the state it was in when the snapshot "snap"
3043 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
3045 struct isl_tab_undo *undo, *next;
3051 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
3055 if (perform_undo(tab, undo) < 0) {
3070 /* The given row "row" represents an inequality violated by all
3071 * points in the tableau. Check for some special cases of such
3072 * separating constraints.
3073 * In particular, if the row has been reduced to the constant -1,
3074 * then we know the inequality is adjacent (but opposite) to
3075 * an equality in the tableau.
3076 * If the row has been reduced to r = -1 -r', with r' an inequality
3077 * of the tableau, then the inequality is adjacent (but opposite)
3078 * to the inequality r'.
3080 static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
3083 unsigned off = 2 + tab->M;
3086 return isl_ineq_separate;
3088 if (!isl_int_is_one(tab->mat->row[row][0]))
3089 return isl_ineq_separate;
3090 if (!isl_int_is_negone(tab->mat->row[row][1]))
3091 return isl_ineq_separate;
3093 pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
3094 tab->n_col - tab->n_dead);
3096 return isl_ineq_adj_eq;
3098 if (!isl_int_is_negone(tab->mat->row[row][off + tab->n_dead + pos]))
3099 return isl_ineq_separate;
3101 pos = isl_seq_first_non_zero(
3102 tab->mat->row[row] + off + tab->n_dead + pos + 1,
3103 tab->n_col - tab->n_dead - pos - 1);
3105 return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
3108 /* Check the effect of inequality "ineq" on the tableau "tab".
3110 * isl_ineq_redundant: satisfied by all points in the tableau
3111 * isl_ineq_separate: satisfied by no point in the tableau
3112 * isl_ineq_cut: satisfied by some by not all points
3113 * isl_ineq_adj_eq: adjacent to an equality
3114 * isl_ineq_adj_ineq: adjacent to an inequality.
3116 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
3118 enum isl_ineq_type type = isl_ineq_error;
3119 struct isl_tab_undo *snap = NULL;
3124 return isl_ineq_error;
3126 if (isl_tab_extend_cons(tab, 1) < 0)
3127 return isl_ineq_error;
3129 snap = isl_tab_snap(tab);
3131 con = isl_tab_add_row(tab, ineq);
3135 row = tab->con[con].index;
3136 if (isl_tab_row_is_redundant(tab, row))
3137 type = isl_ineq_redundant;
3138 else if (isl_int_is_neg(tab->mat->row[row][1]) &&
3140 isl_int_abs_ge(tab->mat->row[row][1],
3141 tab->mat->row[row][0]))) {
3142 int nonneg = at_least_zero(tab, &tab->con[con]);
3146 type = isl_ineq_cut;
3148 type = separation_type(tab, row);
3150 int red = con_is_redundant(tab, &tab->con[con]);
3154 type = isl_ineq_cut;
3156 type = isl_ineq_redundant;
3159 if (isl_tab_rollback(tab, snap))
3160 return isl_ineq_error;
3163 return isl_ineq_error;
3166 int isl_tab_track_bmap(struct isl_tab *tab, __isl_take isl_basic_map *bmap)
3171 isl_assert(tab->mat->ctx, tab->n_eq == bmap->n_eq, return -1);
3172 isl_assert(tab->mat->ctx,
3173 tab->n_con == bmap->n_eq + bmap->n_ineq, return -1);
3179 isl_basic_map_free(bmap);
3183 int isl_tab_track_bset(struct isl_tab *tab, __isl_take isl_basic_set *bset)
3185 return isl_tab_track_bmap(tab, (isl_basic_map *)bset);
3188 __isl_keep isl_basic_set *isl_tab_peek_bset(struct isl_tab *tab)
3193 return (isl_basic_set *)tab->bmap;
3196 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent)
3202 fprintf(out, "%*snull tab\n", indent, "");
3205 fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
3206 tab->n_redundant, tab->n_dead);
3208 fprintf(out, ", rational");
3210 fprintf(out, ", empty");
3212 fprintf(out, "%*s[", indent, "");
3213 for (i = 0; i < tab->n_var; ++i) {
3215 fprintf(out, (i == tab->n_param ||
3216 i == tab->n_var - tab->n_div) ? "; "
3218 fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
3220 tab->var[i].is_zero ? " [=0]" :
3221 tab->var[i].is_redundant ? " [R]" : "");
3223 fprintf(out, "]\n");
3224 fprintf(out, "%*s[", indent, "");
3225 for (i = 0; i < tab->n_con; ++i) {
3228 fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
3230 tab->con[i].is_zero ? " [=0]" :
3231 tab->con[i].is_redundant ? " [R]" : "");
3233 fprintf(out, "]\n");
3234 fprintf(out, "%*s[", indent, "");
3235 for (i = 0; i < tab->n_row; ++i) {
3236 const char *sign = "";
3239 if (tab->row_sign) {
3240 if (tab->row_sign[i] == isl_tab_row_unknown)
3242 else if (tab->row_sign[i] == isl_tab_row_neg)
3244 else if (tab->row_sign[i] == isl_tab_row_pos)
3249 fprintf(out, "r%d: %d%s%s", i, tab->row_var[i],
3250 isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
3252 fprintf(out, "]\n");
3253 fprintf(out, "%*s[", indent, "");
3254 for (i = 0; i < tab->n_col; ++i) {
3257 fprintf(out, "c%d: %d%s", i, tab->col_var[i],
3258 var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
3260 fprintf(out, "]\n");
3261 r = tab->mat->n_row;
3262 tab->mat->n_row = tab->n_row;
3263 c = tab->mat->n_col;
3264 tab->mat->n_col = 2 + tab->M + tab->n_col;
3265 isl_mat_dump(tab->mat, out, indent);
3266 tab->mat->n_row = r;
3267 tab->mat->n_col = c;
3269 isl_basic_map_print_internal(tab->bmap, out, indent);