1 #include "isl_map_private.h"
5 * The implementation of tableaus in this file was inspired by Section 8
6 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
7 * prover for program checking".
10 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
11 unsigned n_row, unsigned n_var)
16 tab = isl_calloc_type(ctx, struct isl_tab);
19 tab->mat = isl_mat_alloc(ctx, n_row, 2 + n_var);
22 tab->var = isl_alloc_array(ctx, struct isl_tab_var, n_var);
25 tab->con = isl_alloc_array(ctx, struct isl_tab_var, n_row);
28 tab->col_var = isl_alloc_array(ctx, int, n_var);
31 tab->row_var = isl_alloc_array(ctx, int, n_row);
34 for (i = 0; i < n_var; ++i) {
35 tab->var[i].index = i;
36 tab->var[i].is_row = 0;
37 tab->var[i].is_nonneg = 0;
38 tab->var[i].is_zero = 0;
39 tab->var[i].is_redundant = 0;
40 tab->var[i].frozen = 0;
54 tab->bottom.type = isl_tab_undo_bottom;
55 tab->bottom.next = NULL;
56 tab->top = &tab->bottom;
59 isl_tab_free(ctx, tab);
63 static int extend_cons(struct isl_ctx *ctx, struct isl_tab *tab, unsigned n_new)
65 if (tab->max_con < tab->n_con + n_new) {
66 struct isl_tab_var *con;
68 con = isl_realloc_array(ctx, tab->con,
69 struct isl_tab_var, tab->max_con + n_new);
73 tab->max_con += n_new;
75 if (tab->mat->n_row < tab->n_row + n_new) {
78 tab->mat = isl_mat_extend(ctx, tab->mat,
79 tab->n_row + n_new, tab->n_col);
82 row_var = isl_realloc_array(ctx, tab->row_var,
83 int, tab->mat->n_row);
86 tab->row_var = row_var;
91 struct isl_tab *isl_tab_extend(struct isl_ctx *ctx, struct isl_tab *tab,
94 if (extend_cons(ctx, tab, n_new) >= 0)
97 isl_tab_free(ctx, tab);
101 static void free_undo(struct isl_ctx *ctx, struct isl_tab *tab)
103 struct isl_tab_undo *undo, *next;
105 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
112 void isl_tab_free(struct isl_ctx *ctx, struct isl_tab *tab)
117 isl_mat_free(ctx, tab->mat);
125 static struct isl_tab_var *var_from_index(struct isl_ctx *ctx,
126 struct isl_tab *tab, int i)
131 return &tab->con[~i];
134 static struct isl_tab_var *var_from_row(struct isl_ctx *ctx,
135 struct isl_tab *tab, int i)
137 return var_from_index(ctx, tab, tab->row_var[i]);
140 static struct isl_tab_var *var_from_col(struct isl_ctx *ctx,
141 struct isl_tab *tab, int i)
143 return var_from_index(ctx, tab, tab->col_var[i]);
146 /* Check if there are any upper bounds on column variable "var",
147 * i.e., non-negative rows where var appears with a negative coefficient.
148 * Return 1 if there are no such bounds.
150 static int max_is_manifestly_unbounded(struct isl_ctx *ctx,
151 struct isl_tab *tab, struct isl_tab_var *var)
157 for (i = tab->n_redundant; i < tab->n_row; ++i) {
158 if (!isl_int_is_neg(tab->mat->row[i][2 + var->index]))
160 if (var_from_row(ctx, tab, i)->is_nonneg)
166 /* Check if there are any lower bounds on column variable "var",
167 * i.e., non-negative rows where var appears with a positive coefficient.
168 * Return 1 if there are no such bounds.
170 static int min_is_manifestly_unbounded(struct isl_ctx *ctx,
171 struct isl_tab *tab, struct isl_tab_var *var)
177 for (i = tab->n_redundant; i < tab->n_row; ++i) {
178 if (!isl_int_is_pos(tab->mat->row[i][2 + var->index]))
180 if (var_from_row(ctx, tab, i)->is_nonneg)
186 /* Given the index of a column "c", return the index of a row
187 * that can be used to pivot the column in, with either an increase
188 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
189 * If "var" is not NULL, then the row returned will be different from
190 * the one associated with "var".
192 * Each row in the tableau is of the form
194 * x_r = a_r0 + \sum_i a_ri x_i
196 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
197 * impose any limit on the increase or decrease in the value of x_c
198 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
199 * for the row with the smallest (most stringent) such bound.
200 * Note that the common denominator of each row drops out of the fraction.
201 * To check if row j has a smaller bound than row r, i.e.,
202 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
203 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
204 * where -sign(a_jc) is equal to "sgn".
206 static int pivot_row(struct isl_ctx *ctx, struct isl_tab *tab,
207 struct isl_tab_var *var, int sgn, int c)
214 for (j = tab->n_redundant; j < tab->n_row; ++j) {
215 if (var && j == var->index)
217 if (!var_from_row(ctx, tab, j)->is_nonneg)
219 if (sgn * isl_int_sgn(tab->mat->row[j][2 + c]) >= 0)
225 isl_int_mul(t, tab->mat->row[r][1], tab->mat->row[j][2 + c]);
226 isl_int_submul(t, tab->mat->row[j][1], tab->mat->row[r][2 + c]);
227 tsgn = sgn * isl_int_sgn(t);
228 if (tsgn < 0 || (tsgn == 0 &&
229 tab->row_var[j] < tab->row_var[r]))
236 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
237 * (sgn < 0) the value of row variable var.
238 * As the given row in the tableau is of the form
240 * x_r = a_r0 + \sum_i a_ri x_i
242 * we need to find a column such that the sign of a_ri is equal to "sgn"
243 * (such that an increase in x_i will have the desired effect) or a
244 * column with a variable that may attain negative values.
245 * If a_ri is positive, then we need to move x_i in the same direction
246 * to obtain the desired effect. Otherwise, x_i has to move in the
247 * opposite direction.
249 static void find_pivot(struct isl_ctx *ctx, struct isl_tab *tab,
250 struct isl_tab_var *var, int sgn, int *row, int *col)
257 isl_assert(ctx, var->is_row, return);
258 tr = tab->mat->row[var->index];
261 for (j = tab->n_dead; j < tab->n_col; ++j) {
262 if (isl_int_is_zero(tr[2 + j]))
264 if (isl_int_sgn(tr[2 + j]) != sgn &&
265 var_from_col(ctx, tab, j)->is_nonneg)
267 if (c < 0 || tab->col_var[j] < tab->col_var[c])
273 sgn *= isl_int_sgn(tr[2 + c]);
274 r = pivot_row(ctx, tab, var, sgn, c);
275 *row = r < 0 ? var->index : r;
279 /* Return 1 if row "row" represents an obviously redundant inequality.
281 * - it represents an inequality or a variable
282 * - that is the sum of a non-negative sample value and a positive
283 * combination of zero or more non-negative variables.
285 static int is_redundant(struct isl_ctx *ctx, struct isl_tab *tab, int row)
289 if (tab->row_var[row] < 0 && !var_from_row(ctx, tab, row)->is_nonneg)
292 if (isl_int_is_neg(tab->mat->row[row][1]))
295 for (i = tab->n_dead; i < tab->n_col; ++i) {
296 if (isl_int_is_zero(tab->mat->row[row][2 + i]))
298 if (isl_int_is_neg(tab->mat->row[row][2 + i]))
300 if (!var_from_col(ctx, tab, i)->is_nonneg)
306 static void swap_rows(struct isl_ctx *ctx,
307 struct isl_tab *tab, int row1, int row2)
310 t = tab->row_var[row1];
311 tab->row_var[row1] = tab->row_var[row2];
312 tab->row_var[row2] = t;
313 var_from_row(ctx, tab, row1)->index = row1;
314 var_from_row(ctx, tab, row2)->index = row2;
315 tab->mat = isl_mat_swap_rows(ctx, tab->mat, row1, row2);
318 static void push(struct isl_ctx *ctx, struct isl_tab *tab,
319 enum isl_tab_undo_type type, struct isl_tab_var *var)
321 struct isl_tab_undo *undo;
326 undo = isl_alloc_type(ctx, struct isl_tab_undo);
334 undo->next = tab->top;
338 /* Mark row with index "row" as being redundant.
339 * If we may need to undo the operation or if the row represents
340 * a variable of the original problem, the row is kept,
341 * but no longer considered when looking for a pivot row.
342 * Otherwise, the row is simply removed.
344 * The row may be interchanged with some other row. If it
345 * is interchanged with a later row, return 1. Otherwise return 0.
346 * If the rows are checked in order in the calling function,
347 * then a return value of 1 means that the row with the given
348 * row number may now contain a different row that hasn't been checked yet.
350 static int mark_redundant(struct isl_ctx *ctx,
351 struct isl_tab *tab, int row)
353 struct isl_tab_var *var = var_from_row(ctx, tab, row);
354 var->is_redundant = 1;
355 isl_assert(ctx, row >= tab->n_redundant, return);
356 if (tab->need_undo || tab->row_var[row] >= 0) {
357 if (tab->row_var[row] >= 0) {
359 push(ctx, tab, isl_tab_undo_nonneg, var);
361 if (row != tab->n_redundant)
362 swap_rows(ctx, tab, row, tab->n_redundant);
363 push(ctx, tab, isl_tab_undo_redundant, var);
367 if (row != tab->n_row - 1)
368 swap_rows(ctx, tab, row, tab->n_row - 1);
369 var_from_row(ctx, tab, tab->n_row - 1)->index = -1;
375 static void mark_empty(struct isl_ctx *ctx, struct isl_tab *tab)
377 if (!tab->empty && tab->need_undo)
378 push(ctx, tab, isl_tab_undo_empty, NULL);
382 /* Given a row number "row" and a column number "col", pivot the tableau
383 * such that the associated variable are interchanged.
384 * The given row in the tableau expresses
386 * x_r = a_r0 + \sum_i a_ri x_i
390 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
392 * Substituting this equality into the other rows
394 * x_j = a_j0 + \sum_i a_ji x_i
396 * with a_jc \ne 0, we obtain
398 * 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
405 * where i is any other column and j is any other row,
406 * is therefore transformed into
408 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
409 * 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)
411 * The transformation is performed along the following steps
416 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
419 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
420 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
422 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
423 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
425 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
426 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
428 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
429 * 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)
432 static void pivot(struct isl_ctx *ctx,
433 struct isl_tab *tab, int row, int col)
438 struct isl_mat *mat = tab->mat;
439 struct isl_tab_var *var;
441 isl_int_swap(mat->row[row][0], mat->row[row][2 + col]);
442 sgn = isl_int_sgn(mat->row[row][0]);
444 isl_int_neg(mat->row[row][0], mat->row[row][0]);
445 isl_int_neg(mat->row[row][2 + col], mat->row[row][2 + col]);
447 for (j = 0; j < 1 + tab->n_col; ++j) {
450 isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
452 if (!isl_int_is_one(mat->row[row][0]))
453 isl_seq_normalize(mat->row[row], 2 + tab->n_col);
454 for (i = 0; i < tab->n_row; ++i) {
457 if (isl_int_is_zero(mat->row[i][2 + col]))
459 isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
460 for (j = 0; j < 1 + tab->n_col; ++j) {
463 isl_int_mul(mat->row[i][1 + j],
464 mat->row[i][1 + j], mat->row[row][0]);
465 isl_int_addmul(mat->row[i][1 + j],
466 mat->row[i][2 + col], mat->row[row][1 + j]);
468 isl_int_mul(mat->row[i][2 + col],
469 mat->row[i][2 + col], mat->row[row][2 + col]);
470 if (!isl_int_is_one(mat->row[row][0]))
471 isl_seq_normalize(mat->row[i], 2 + tab->n_col);
473 t = tab->row_var[row];
474 tab->row_var[row] = tab->col_var[col];
475 tab->col_var[col] = t;
476 var = var_from_row(ctx, tab, row);
479 var = var_from_col(ctx, tab, col);
482 for (i = tab->n_redundant; i < tab->n_row; ++i) {
483 if (isl_int_is_zero(mat->row[i][2 + col]))
485 if (!var_from_row(ctx, tab, i)->frozen &&
486 is_redundant(ctx, tab, i))
487 if (mark_redundant(ctx, tab, i))
492 /* If "var" represents a column variable, then pivot is up (sgn > 0)
493 * or down (sgn < 0) to a row. The variable is assumed not to be
494 * unbounded in the specified direction.
496 static void to_row(struct isl_ctx *ctx,
497 struct isl_tab *tab, struct isl_tab_var *var, int sign)
504 r = pivot_row(ctx, tab, NULL, sign, var->index);
505 isl_assert(ctx, r >= 0, return);
506 pivot(ctx, tab, r, var->index);
509 static void check_table(struct isl_ctx *ctx, struct isl_tab *tab)
515 for (i = 0; i < tab->n_row; ++i) {
516 if (!var_from_row(ctx, tab, i)->is_nonneg)
518 assert(!isl_int_is_neg(tab->mat->row[i][1]));
522 /* Return the sign of the maximal value of "var".
523 * If the sign is not negative, then on return from this function,
524 * the sample value will also be non-negative.
526 * If "var" is manifestly unbounded wrt positive values, we are done.
527 * Otherwise, we pivot the variable up to a row if needed
528 * Then we continue pivoting down until either
529 * - no more down pivots can be performed
530 * - the sample value is positive
531 * - the variable is pivoted into a manifestly unbounded column
533 static int sign_of_max(struct isl_ctx *ctx,
534 struct isl_tab *tab, struct isl_tab_var *var)
538 if (max_is_manifestly_unbounded(ctx, tab, var))
540 to_row(ctx, tab, var, 1);
541 while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
542 find_pivot(ctx, tab, var, 1, &row, &col);
544 return isl_int_sgn(tab->mat->row[var->index][1]);
545 pivot(ctx, tab, row, col);
546 if (!var->is_row) /* manifestly unbounded */
552 /* Perform pivots until the row variable "var" has a non-negative
553 * sample value or until no more upward pivots can be performed.
554 * Return the sign of the sample value after the pivots have been
557 static int restore_row(struct isl_ctx *ctx,
558 struct isl_tab *tab, struct isl_tab_var *var)
562 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
563 find_pivot(ctx, tab, var, 1, &row, &col);
566 pivot(ctx, tab, row, col);
567 if (!var->is_row) /* manifestly unbounded */
570 return isl_int_sgn(tab->mat->row[var->index][1]);
573 /* Perform pivots until we are sure that the row variable "var"
574 * can attain non-negative values. After return from this
575 * function, "var" is still a row variable, but its sample
576 * value may not be non-negative, even if the function returns 1.
578 static int at_least_zero(struct isl_ctx *ctx,
579 struct isl_tab *tab, struct isl_tab_var *var)
583 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
584 find_pivot(ctx, tab, var, 1, &row, &col);
587 if (row == var->index) /* manifestly unbounded */
589 pivot(ctx, tab, row, col);
591 return !isl_int_is_neg(tab->mat->row[var->index][1]);
594 /* Return a negative value if "var" can attain negative values.
595 * Return a non-negative value otherwise.
597 * If "var" is manifestly unbounded wrt negative values, we are done.
598 * Otherwise, if var is in a column, we can pivot it down to a row.
599 * Then we continue pivoting down until either
600 * - the pivot would result in a manifestly unbounded column
601 * => we don't perform the pivot, but simply return -1
602 * - no more down pivots can be performed
603 * - the sample value is negative
604 * If the sample value becomes negative and the variable is supposed
605 * to be nonnegative, then we undo the last pivot.
606 * However, if the last pivot has made the pivoting variable
607 * obviously redundant, then it may have moved to another row.
608 * In that case we look for upward pivots until we reach a non-negative
611 static int sign_of_min(struct isl_ctx *ctx,
612 struct isl_tab *tab, struct isl_tab_var *var)
615 struct isl_tab_var *pivot_var;
617 if (min_is_manifestly_unbounded(ctx, tab, var))
621 row = pivot_row(ctx, tab, NULL, -1, col);
622 pivot_var = var_from_col(ctx, tab, col);
623 pivot(ctx, tab, row, col);
624 if (var->is_redundant)
626 if (isl_int_is_neg(tab->mat->row[var->index][1])) {
627 if (var->is_nonneg) {
628 if (!pivot_var->is_redundant &&
629 pivot_var->index == row)
630 pivot(ctx, tab, row, col);
632 restore_row(ctx, tab, var);
637 if (var->is_redundant)
639 while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
640 find_pivot(ctx, tab, var, -1, &row, &col);
641 if (row == var->index)
644 return isl_int_sgn(tab->mat->row[var->index][1]);
645 pivot_var = var_from_col(ctx, tab, col);
646 pivot(ctx, tab, row, col);
647 if (var->is_redundant)
650 if (var->is_nonneg) {
651 /* pivot back to non-negative value */
652 if (!pivot_var->is_redundant && pivot_var->index == row)
653 pivot(ctx, tab, row, col);
655 restore_row(ctx, tab, var);
660 /* Return 1 if "var" can attain values <= -1.
661 * Return 0 otherwise.
663 * The sample value of "var" is assumed to be non-negative when the
664 * the function is called and will be made non-negative again before
665 * the function returns.
667 static int min_at_most_neg_one(struct isl_ctx *ctx,
668 struct isl_tab *tab, struct isl_tab_var *var)
671 struct isl_tab_var *pivot_var;
673 if (min_is_manifestly_unbounded(ctx, tab, var))
677 row = pivot_row(ctx, tab, NULL, -1, col);
678 pivot_var = var_from_col(ctx, tab, col);
679 pivot(ctx, tab, row, col);
680 if (var->is_redundant)
682 if (isl_int_is_neg(tab->mat->row[var->index][1]) &&
683 isl_int_abs_ge(tab->mat->row[var->index][1],
684 tab->mat->row[var->index][0])) {
685 if (var->is_nonneg) {
686 if (!pivot_var->is_redundant &&
687 pivot_var->index == row)
688 pivot(ctx, tab, row, col);
690 restore_row(ctx, tab, var);
695 if (var->is_redundant)
698 find_pivot(ctx, tab, var, -1, &row, &col);
699 if (row == var->index)
703 pivot_var = var_from_col(ctx, tab, col);
704 pivot(ctx, tab, row, col);
705 if (var->is_redundant)
707 } while (!isl_int_is_neg(tab->mat->row[var->index][1]) ||
708 isl_int_abs_lt(tab->mat->row[var->index][1],
709 tab->mat->row[var->index][0]));
710 if (var->is_nonneg) {
711 /* pivot back to non-negative value */
712 if (!pivot_var->is_redundant && pivot_var->index == row)
713 pivot(ctx, tab, row, col);
714 restore_row(ctx, tab, var);
719 /* Return 1 if "var" can attain values >= 1.
720 * Return 0 otherwise.
722 static int at_least_one(struct isl_ctx *ctx,
723 struct isl_tab *tab, struct isl_tab_var *var)
728 if (max_is_manifestly_unbounded(ctx, tab, var))
730 to_row(ctx, tab, var, 1);
731 r = tab->mat->row[var->index];
732 while (isl_int_lt(r[1], r[0])) {
733 find_pivot(ctx, tab, var, 1, &row, &col);
735 return isl_int_ge(r[1], r[0]);
736 if (row == var->index) /* manifestly unbounded */
738 pivot(ctx, tab, row, col);
743 static void swap_cols(struct isl_ctx *ctx,
744 struct isl_tab *tab, int col1, int col2)
747 t = tab->col_var[col1];
748 tab->col_var[col1] = tab->col_var[col2];
749 tab->col_var[col2] = t;
750 var_from_col(ctx, tab, col1)->index = col1;
751 var_from_col(ctx, tab, col2)->index = col2;
752 tab->mat = isl_mat_swap_cols(ctx, tab->mat, 2 + col1, 2 + col2);
755 /* Mark column with index "col" as representing a zero variable.
756 * If we may need to undo the operation the column is kept,
757 * but no longer considered.
758 * Otherwise, the column is simply removed.
760 * The column may be interchanged with some other column. If it
761 * is interchanged with a later column, return 1. Otherwise return 0.
762 * If the columns are checked in order in the calling function,
763 * then a return value of 1 means that the column with the given
764 * column number may now contain a different column that
765 * hasn't been checked yet.
767 static int kill_col(struct isl_ctx *ctx,
768 struct isl_tab *tab, int col)
770 var_from_col(ctx, tab, col)->is_zero = 1;
771 if (tab->need_undo) {
772 push(ctx, tab, isl_tab_undo_zero, var_from_col(ctx, tab, col));
773 if (col != tab->n_dead)
774 swap_cols(ctx, tab, col, tab->n_dead);
778 if (col != tab->n_col - 1)
779 swap_cols(ctx, tab, col, tab->n_col - 1);
780 var_from_col(ctx, tab, tab->n_col - 1)->index = -1;
786 /* Row variable "var" is non-negative and cannot attain any values
787 * larger than zero. This means that the coefficients of the unrestricted
788 * column variables are zero and that the coefficients of the non-negative
789 * column variables are zero or negative.
790 * Each of the non-negative variables with a negative coefficient can
791 * then also be written as the negative sum of non-negative variables
792 * and must therefore also be zero.
794 static void close_row(struct isl_ctx *ctx,
795 struct isl_tab *tab, struct isl_tab_var *var)
798 struct isl_mat *mat = tab->mat;
800 isl_assert(ctx, var->is_nonneg, return);
802 for (j = tab->n_dead; j < tab->n_col; ++j) {
803 if (isl_int_is_zero(mat->row[var->index][2 + j]))
805 isl_assert(ctx, isl_int_is_neg(mat->row[var->index][2 + j]),
807 if (kill_col(ctx, tab, j))
810 mark_redundant(ctx, tab, var->index);
813 /* Add a row to the tableau. The row is given as an affine combination
814 * of the original variables and needs to be expressed in terms of the
817 * We add each term in turn.
818 * If r = n/d_r is the current sum and we need to add k x, then
819 * if x is a column variable, we increase the numerator of
820 * this column by k d_r
821 * if x = f/d_x is a row variable, then the new representation of r is
823 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
824 * --- + --- = ------------------- = -------------------
825 * d_r d_r d_r d_x/g m
827 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
829 static int add_row(struct isl_ctx *ctx, struct isl_tab *tab, isl_int *line)
836 isl_assert(ctx, tab->n_row < tab->mat->n_row, return -1);
841 tab->con[r].index = tab->n_row;
842 tab->con[r].is_row = 1;
843 tab->con[r].is_nonneg = 0;
844 tab->con[r].is_zero = 0;
845 tab->con[r].is_redundant = 0;
846 tab->con[r].frozen = 0;
847 tab->row_var[tab->n_row] = ~r;
848 row = tab->mat->row[tab->n_row];
849 isl_int_set_si(row[0], 1);
850 isl_int_set(row[1], line[0]);
851 isl_seq_clr(row + 2, tab->n_col);
852 for (i = 0; i < tab->n_var; ++i) {
853 if (tab->var[i].is_zero)
855 if (tab->var[i].is_row) {
857 row[0], tab->mat->row[tab->var[i].index][0]);
858 isl_int_swap(a, row[0]);
859 isl_int_divexact(a, row[0], a);
861 row[0], tab->mat->row[tab->var[i].index][0]);
862 isl_int_mul(b, b, line[1 + i]);
863 isl_seq_combine(row + 1, a, row + 1,
864 b, tab->mat->row[tab->var[i].index] + 1,
867 isl_int_addmul(row[2 + tab->var[i].index],
868 line[1 + i], row[0]);
870 isl_seq_normalize(row, 2 + tab->n_col);
873 push(ctx, tab, isl_tab_undo_allocate, &tab->con[r]);
880 static int drop_row(struct isl_ctx *ctx, struct isl_tab *tab, int row)
882 isl_assert(ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
883 if (row != tab->n_row - 1)
884 swap_rows(ctx, tab, row, tab->n_row - 1);
890 /* Add inequality "ineq" and check if it conflicts with the
891 * previously added constraints or if it is obviously redundant.
893 struct isl_tab *isl_tab_add_ineq(struct isl_ctx *ctx,
894 struct isl_tab *tab, isl_int *ineq)
901 r = add_row(ctx, tab, ineq);
904 tab->con[r].is_nonneg = 1;
905 push(ctx, tab, isl_tab_undo_nonneg, &tab->con[r]);
906 if (is_redundant(ctx, tab, tab->con[r].index)) {
907 mark_redundant(ctx, tab, tab->con[r].index);
911 sgn = restore_row(ctx, tab, &tab->con[r]);
913 mark_empty(ctx, tab);
914 else if (tab->con[r].is_row &&
915 is_redundant(ctx, tab, tab->con[r].index))
916 mark_redundant(ctx, tab, tab->con[r].index);
919 isl_tab_free(ctx, tab);
923 /* We assume Gaussian elimination has been performed on the equalities.
924 * The equalities can therefore never conflict.
925 * Adding the equalities is currently only really useful for a later call
926 * to isl_tab_ineq_type.
928 static struct isl_tab *add_eq(struct isl_ctx *ctx,
929 struct isl_tab *tab, isl_int *eq)
936 r = add_row(ctx, tab, eq);
940 r = tab->con[r].index;
941 for (i = tab->n_dead; i < tab->n_col; ++i) {
942 if (isl_int_is_zero(tab->mat->row[r][2 + i]))
944 pivot(ctx, tab, r, i);
945 kill_col(ctx, tab, i);
952 isl_tab_free(ctx, tab);
956 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap)
963 tab = isl_tab_alloc(bmap->ctx,
964 isl_basic_map_total_dim(bmap) + bmap->n_ineq + 1,
965 isl_basic_map_total_dim(bmap));
968 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
969 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY)) {
970 mark_empty(bmap->ctx, tab);
973 for (i = 0; i < bmap->n_eq; ++i) {
974 tab = add_eq(bmap->ctx, tab, bmap->eq[i]);
978 for (i = 0; i < bmap->n_ineq; ++i) {
979 tab = isl_tab_add_ineq(bmap->ctx, tab, bmap->ineq[i]);
980 if (!tab || tab->empty)
986 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset)
988 return isl_tab_from_basic_map((struct isl_basic_map *)bset);
991 /* Construct a tableau corresponding to the recession cone of "bmap".
993 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_map *bmap)
1001 tab = isl_tab_alloc(bmap->ctx, bmap->n_eq + bmap->n_ineq,
1002 isl_basic_map_total_dim(bmap));
1005 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
1008 for (i = 0; i < bmap->n_eq; ++i) {
1009 isl_int_swap(bmap->eq[i][0], cst);
1010 tab = add_eq(bmap->ctx, tab, bmap->eq[i]);
1011 isl_int_swap(bmap->eq[i][0], cst);
1015 for (i = 0; i < bmap->n_ineq; ++i) {
1017 isl_int_swap(bmap->ineq[i][0], cst);
1018 r = add_row(bmap->ctx, tab, bmap->ineq[i]);
1019 isl_int_swap(bmap->ineq[i][0], cst);
1022 tab->con[r].is_nonneg = 1;
1023 push(bmap->ctx, tab, isl_tab_undo_nonneg, &tab->con[r]);
1030 isl_tab_free(bmap->ctx, tab);
1034 /* Assuming "tab" is the tableau of a cone, check if the cone is
1035 * bounded, i.e., if it is empty or only contains the origin.
1037 int isl_tab_cone_is_bounded(struct isl_ctx *ctx, struct isl_tab *tab)
1045 if (tab->n_dead == tab->n_col)
1048 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1049 struct isl_tab_var *var;
1050 var = var_from_row(ctx, tab, i);
1051 if (!var->is_nonneg)
1053 if (sign_of_max(ctx, tab, var) == 0)
1054 close_row(ctx, tab, var);
1057 if (tab->n_dead == tab->n_col)
1063 static int sample_is_integer(struct isl_ctx *ctx, struct isl_tab *tab)
1067 for (i = 0; i < tab->n_var; ++i) {
1069 if (!tab->var[i].is_row)
1071 row = tab->var[i].index;
1072 if (!isl_int_is_divisible_by(tab->mat->row[row][1],
1073 tab->mat->row[row][0]))
1079 static struct isl_vec *extract_integer_sample(struct isl_ctx *ctx,
1080 struct isl_tab *tab)
1083 struct isl_vec *vec;
1085 vec = isl_vec_alloc(ctx, 1 + tab->n_var);
1089 isl_int_set_si(vec->block.data[0], 1);
1090 for (i = 0; i < tab->n_var; ++i) {
1091 if (!tab->var[i].is_row)
1092 isl_int_set_si(vec->block.data[1 + i], 0);
1094 int row = tab->var[i].index;
1095 isl_int_divexact(vec->block.data[1 + i],
1096 tab->mat->row[row][1], tab->mat->row[row][0]);
1103 struct isl_vec *isl_tab_get_sample_value(struct isl_ctx *ctx,
1104 struct isl_tab *tab)
1107 struct isl_vec *vec;
1113 vec = isl_vec_alloc(ctx, 1 + tab->n_var);
1119 isl_int_set_si(vec->block.data[0], 1);
1120 for (i = 0; i < tab->n_var; ++i) {
1122 if (!tab->var[i].is_row) {
1123 isl_int_set_si(vec->block.data[1 + i], 0);
1126 row = tab->var[i].index;
1127 isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
1128 isl_int_divexact(m, tab->mat->row[row][0], m);
1129 isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
1130 isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
1131 isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
1133 isl_seq_normalize(vec->block.data, vec->size);
1139 /* Update "bmap" based on the results of the tableau "tab".
1140 * In particular, implicit equalities are made explicit, redundant constraints
1141 * are removed and if the sample value happens to be integer, it is stored
1142 * in "bmap" (unless "bmap" already had an integer sample).
1144 * The tableau is assumed to have been created from "bmap" using
1145 * isl_tab_from_basic_map.
1147 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
1148 struct isl_tab *tab)
1160 bmap = isl_basic_map_set_to_empty(bmap);
1162 for (i = bmap->n_ineq - 1; i >= 0; --i) {
1163 if (isl_tab_is_equality(bmap->ctx, tab, n_eq + i))
1164 isl_basic_map_inequality_to_equality(bmap, i);
1165 else if (isl_tab_is_redundant(bmap->ctx, tab, n_eq + i))
1166 isl_basic_map_drop_inequality(bmap, i);
1168 if (!tab->rational &&
1169 !bmap->sample && sample_is_integer(bmap->ctx, tab))
1170 bmap->sample = extract_integer_sample(bmap->ctx, tab);
1174 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
1175 struct isl_tab *tab)
1177 return (struct isl_basic_set *)isl_basic_map_update_from_tab(
1178 (struct isl_basic_map *)bset, tab);
1181 /* Given a non-negative variable "var", add a new non-negative variable
1182 * that is the opposite of "var", ensuring that var can only attain the
1184 * If var = n/d is a row variable, then the new variable = -n/d.
1185 * If var is a column variables, then the new variable = -var.
1186 * If the new variable cannot attain non-negative values, then
1187 * the resulting tableau is empty.
1188 * Otherwise, we know the value will be zero and we close the row.
1190 static struct isl_tab *cut_to_hyperplane(struct isl_ctx *ctx,
1191 struct isl_tab *tab, struct isl_tab_var *var)
1197 if (extend_cons(ctx, tab, 1) < 0)
1201 tab->con[r].index = tab->n_row;
1202 tab->con[r].is_row = 1;
1203 tab->con[r].is_nonneg = 0;
1204 tab->con[r].is_zero = 0;
1205 tab->con[r].is_redundant = 0;
1206 tab->con[r].frozen = 0;
1207 tab->row_var[tab->n_row] = ~r;
1208 row = tab->mat->row[tab->n_row];
1211 isl_int_set(row[0], tab->mat->row[var->index][0]);
1212 isl_seq_neg(row + 1,
1213 tab->mat->row[var->index] + 1, 1 + tab->n_col);
1215 isl_int_set_si(row[0], 1);
1216 isl_seq_clr(row + 1, 1 + tab->n_col);
1217 isl_int_set_si(row[2 + var->index], -1);
1222 push(ctx, tab, isl_tab_undo_allocate, &tab->con[r]);
1224 sgn = sign_of_max(ctx, tab, &tab->con[r]);
1226 mark_empty(ctx, tab);
1228 tab->con[r].is_nonneg = 1;
1229 push(ctx, tab, isl_tab_undo_nonneg, &tab->con[r]);
1231 close_row(ctx, tab, &tab->con[r]);
1236 isl_tab_free(ctx, tab);
1240 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
1241 * relax the inequality by one. That is, the inequality r >= 0 is replaced
1242 * by r' = r + 1 >= 0.
1243 * If r is a row variable, we simply increase the constant term by one
1244 * (taking into account the denominator).
1245 * If r is a column variable, then we need to modify each row that
1246 * refers to r = r' - 1 by substituting this equality, effectively
1247 * subtracting the coefficient of the column from the constant.
1249 struct isl_tab *isl_tab_relax(struct isl_ctx *ctx,
1250 struct isl_tab *tab, int con)
1252 struct isl_tab_var *var;
1256 var = &tab->con[con];
1258 if (!var->is_row && !max_is_manifestly_unbounded(ctx, tab, var))
1259 to_row(ctx, tab, var, 1);
1262 isl_int_add(tab->mat->row[var->index][1],
1263 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
1267 for (i = 0; i < tab->n_row; ++i) {
1268 if (isl_int_is_zero(tab->mat->row[i][2 + var->index]))
1270 isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
1271 tab->mat->row[i][2 + var->index]);
1276 push(ctx, tab, isl_tab_undo_relax, var);
1281 struct isl_tab *isl_tab_select_facet(struct isl_ctx *ctx,
1282 struct isl_tab *tab, int con)
1287 return cut_to_hyperplane(ctx, tab, &tab->con[con]);
1290 static int may_be_equality(struct isl_tab *tab, int row)
1292 return (tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
1293 : isl_int_lt(tab->mat->row[row][1],
1294 tab->mat->row[row][0])) &&
1295 isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
1296 tab->n_col - tab->n_dead) != -1;
1299 /* Check for (near) equalities among the constraints.
1300 * A constraint is an equality if it is non-negative and if
1301 * its maximal value is either
1302 * - zero (in case of rational tableaus), or
1303 * - strictly less than 1 (in case of integer tableaus)
1305 * We first mark all non-redundant and non-dead variables that
1306 * are not frozen and not obviously not an equality.
1307 * Then we iterate over all marked variables if they can attain
1308 * any values larger than zero or at least one.
1309 * If the maximal value is zero, we mark any column variables
1310 * that appear in the row as being zero and mark the row as being redundant.
1311 * Otherwise, if the maximal value is strictly less than one (and the
1312 * tableau is integer), then we restrict the value to being zero
1313 * by adding an opposite non-negative variable.
1315 struct isl_tab *isl_tab_detect_equalities(struct isl_ctx *ctx,
1316 struct isl_tab *tab)
1325 if (tab->n_dead == tab->n_col)
1329 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1330 struct isl_tab_var *var = var_from_row(ctx, tab, i);
1331 var->marked = !var->frozen && var->is_nonneg &&
1332 may_be_equality(tab, i);
1336 for (i = tab->n_dead; i < tab->n_col; ++i) {
1337 struct isl_tab_var *var = var_from_col(ctx, tab, i);
1338 var->marked = !var->frozen && var->is_nonneg;
1343 struct isl_tab_var *var;
1344 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1345 var = var_from_row(ctx, tab, i);
1349 if (i == tab->n_row) {
1350 for (i = tab->n_dead; i < tab->n_col; ++i) {
1351 var = var_from_col(ctx, tab, i);
1355 if (i == tab->n_col)
1360 if (sign_of_max(ctx, tab, var) == 0)
1361 close_row(ctx, tab, var);
1362 else if (!tab->rational && !at_least_one(ctx, tab, var)) {
1363 tab = cut_to_hyperplane(ctx, tab, var);
1364 return isl_tab_detect_equalities(ctx, tab);
1366 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1367 var = var_from_row(ctx, tab, i);
1370 if (may_be_equality(tab, i))
1380 /* Check for (near) redundant constraints.
1381 * A constraint is redundant if it is non-negative and if
1382 * its minimal value (temporarily ignoring the non-negativity) is either
1383 * - zero (in case of rational tableaus), or
1384 * - strictly larger than -1 (in case of integer tableaus)
1386 * We first mark all non-redundant and non-dead variables that
1387 * are not frozen and not obviously negatively unbounded.
1388 * Then we iterate over all marked variables if they can attain
1389 * any values smaller than zero or at most negative one.
1390 * If not, we mark the row as being redundant (assuming it hasn't
1391 * been detected as being obviously redundant in the mean time).
1393 struct isl_tab *isl_tab_detect_redundant(struct isl_ctx *ctx,
1394 struct isl_tab *tab)
1403 if (tab->n_redundant == tab->n_row)
1407 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1408 struct isl_tab_var *var = var_from_row(ctx, tab, i);
1409 var->marked = !var->frozen && var->is_nonneg;
1413 for (i = tab->n_dead; i < tab->n_col; ++i) {
1414 struct isl_tab_var *var = var_from_col(ctx, tab, i);
1415 var->marked = !var->frozen && var->is_nonneg &&
1416 !min_is_manifestly_unbounded(ctx, tab, var);
1421 struct isl_tab_var *var;
1422 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1423 var = var_from_row(ctx, tab, i);
1427 if (i == tab->n_row) {
1428 for (i = tab->n_dead; i < tab->n_col; ++i) {
1429 var = var_from_col(ctx, tab, i);
1433 if (i == tab->n_col)
1438 if ((tab->rational ? (sign_of_min(ctx, tab, var) >= 0)
1439 : !min_at_most_neg_one(ctx, tab, var)) &&
1441 mark_redundant(ctx, tab, var->index);
1442 for (i = tab->n_dead; i < tab->n_col; ++i) {
1443 var = var_from_col(ctx, tab, i);
1446 if (!min_is_manifestly_unbounded(ctx, tab, var))
1456 int isl_tab_is_equality(struct isl_ctx *ctx, struct isl_tab *tab, int con)
1462 if (tab->con[con].is_zero)
1464 if (tab->con[con].is_redundant)
1466 if (!tab->con[con].is_row)
1467 return tab->con[con].index < tab->n_dead;
1469 row = tab->con[con].index;
1471 return isl_int_is_zero(tab->mat->row[row][1]) &&
1472 isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
1473 tab->n_col - tab->n_dead) == -1;
1476 /* Return the minimial value of the affine expression "f" with denominator
1477 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
1478 * the expression cannot attain arbitrarily small values.
1479 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
1480 * The return value reflects the nature of the result (empty, unbounded,
1481 * minmimal value returned in *opt).
1483 enum isl_lp_result isl_tab_min(struct isl_ctx *ctx, struct isl_tab *tab,
1484 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom)
1487 enum isl_lp_result res = isl_lp_ok;
1488 struct isl_tab_var *var;
1491 return isl_lp_empty;
1493 r = add_row(ctx, tab, f);
1495 return isl_lp_error;
1497 isl_int_mul(tab->mat->row[var->index][0],
1498 tab->mat->row[var->index][0], denom);
1501 find_pivot(ctx, tab, var, -1, &row, &col);
1502 if (row == var->index) {
1503 res = isl_lp_unbounded;
1508 pivot(ctx, tab, row, col);
1510 if (drop_row(ctx, tab, var->index) < 0)
1511 return isl_lp_error;
1512 if (res == isl_lp_ok) {
1514 isl_int_set(*opt, tab->mat->row[var->index][1]);
1515 isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
1517 isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
1518 tab->mat->row[var->index][0]);
1523 int isl_tab_is_redundant(struct isl_ctx *ctx, struct isl_tab *tab, int con)
1530 if (tab->con[con].is_zero)
1532 if (tab->con[con].is_redundant)
1534 return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
1537 /* Take a snapshot of the tableau that can be restored by s call to
1540 struct isl_tab_undo *isl_tab_snap(struct isl_ctx *ctx, struct isl_tab *tab)
1548 /* Undo the operation performed by isl_tab_relax.
1550 static void unrelax(struct isl_ctx *ctx,
1551 struct isl_tab *tab, struct isl_tab_var *var)
1553 if (!var->is_row && !max_is_manifestly_unbounded(ctx, tab, var))
1554 to_row(ctx, tab, var, 1);
1557 isl_int_sub(tab->mat->row[var->index][1],
1558 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
1562 for (i = 0; i < tab->n_row; ++i) {
1563 if (isl_int_is_zero(tab->mat->row[i][2 + var->index]))
1565 isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
1566 tab->mat->row[i][2 + var->index]);
1572 static void perform_undo(struct isl_ctx *ctx, struct isl_tab *tab,
1573 struct isl_tab_undo *undo)
1575 switch(undo->type) {
1576 case isl_tab_undo_empty:
1579 case isl_tab_undo_nonneg:
1580 undo->var->is_nonneg = 0;
1582 case isl_tab_undo_redundant:
1583 undo->var->is_redundant = 0;
1586 case isl_tab_undo_zero:
1587 undo->var->is_zero = 0;
1590 case isl_tab_undo_allocate:
1591 if (!undo->var->is_row) {
1592 if (max_is_manifestly_unbounded(ctx, tab, undo->var))
1593 to_row(ctx, tab, undo->var, -1);
1595 to_row(ctx, tab, undo->var, 1);
1597 drop_row(ctx, tab, undo->var->index);
1599 case isl_tab_undo_relax:
1600 unrelax(ctx, tab, undo->var);
1605 /* Return the tableau to the state it was in when the snapshot "snap"
1608 int isl_tab_rollback(struct isl_ctx *ctx, struct isl_tab *tab,
1609 struct isl_tab_undo *snap)
1611 struct isl_tab_undo *undo, *next;
1616 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
1620 perform_undo(ctx, tab, undo);
1629 /* The given row "row" represents an inequality violated by all
1630 * points in the tableau. Check for some special cases of such
1631 * separating constraints.
1632 * In particular, if the row has been reduced to the constant -1,
1633 * then we know the inequality is adjacent (but opposite) to
1634 * an equality in the tableau.
1635 * If the row has been reduced to r = -1 -r', with r' an inequality
1636 * of the tableau, then the inequality is adjacent (but opposite)
1637 * to the inequality r'.
1639 static enum isl_ineq_type separation_type(struct isl_ctx *ctx,
1640 struct isl_tab *tab, unsigned row)
1645 return isl_ineq_separate;
1647 if (!isl_int_is_one(tab->mat->row[row][0]))
1648 return isl_ineq_separate;
1649 if (!isl_int_is_negone(tab->mat->row[row][1]))
1650 return isl_ineq_separate;
1652 pos = isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
1653 tab->n_col - tab->n_dead);
1655 return isl_ineq_adj_eq;
1657 if (!isl_int_is_negone(tab->mat->row[row][2 + tab->n_dead + pos]))
1658 return isl_ineq_separate;
1660 pos = isl_seq_first_non_zero(
1661 tab->mat->row[row] + 2 + tab->n_dead + pos + 1,
1662 tab->n_col - tab->n_dead - pos - 1);
1664 return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
1667 /* Check the effect of inequality "ineq" on the tableau "tab".
1669 * isl_ineq_redundant: satisfied by all points in the tableau
1670 * isl_ineq_separate: satisfied by no point in the tableau
1671 * isl_ineq_cut: satisfied by some by not all points
1672 * isl_ineq_adj_eq: adjacent to an equality
1673 * isl_ineq_adj_ineq: adjacent to an inequality.
1675 enum isl_ineq_type isl_tab_ineq_type(struct isl_ctx *ctx, struct isl_tab *tab,
1678 enum isl_ineq_type type = isl_ineq_error;
1679 struct isl_tab_undo *snap = NULL;
1684 return isl_ineq_error;
1686 if (extend_cons(ctx, tab, 1) < 0)
1687 return isl_ineq_error;
1689 snap = isl_tab_snap(ctx, tab);
1691 con = add_row(ctx, tab, ineq);
1695 row = tab->con[con].index;
1696 if (is_redundant(ctx, tab, row))
1697 type = isl_ineq_redundant;
1698 else if (isl_int_is_neg(tab->mat->row[row][1]) &&
1700 isl_int_abs_ge(tab->mat->row[row][1],
1701 tab->mat->row[row][0]))) {
1702 if (at_least_zero(ctx, tab, &tab->con[con]))
1703 type = isl_ineq_cut;
1705 type = separation_type(ctx, tab, row);
1706 } else if (tab->rational ? (sign_of_min(ctx, tab, &tab->con[con]) < 0)
1707 : min_at_most_neg_one(ctx, tab, &tab->con[con]))
1708 type = isl_ineq_cut;
1710 type = isl_ineq_redundant;
1712 if (isl_tab_rollback(ctx, tab, snap))
1713 return isl_ineq_error;
1716 isl_tab_rollback(ctx, tab, snap);
1717 return isl_ineq_error;
1720 void isl_tab_dump(struct isl_ctx *ctx, struct isl_tab *tab,
1721 FILE *out, int indent)
1727 fprintf(out, "%*snull tab\n", indent, "");
1730 fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
1731 tab->n_redundant, tab->n_dead);
1733 fprintf(out, ", rational");
1735 fprintf(out, ", empty");
1737 fprintf(out, "%*s[", indent, "");
1738 for (i = 0; i < tab->n_var; ++i) {
1741 fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
1743 tab->var[i].is_zero ? " [=0]" :
1744 tab->var[i].is_redundant ? " [R]" : "");
1746 fprintf(out, "]\n");
1747 fprintf(out, "%*s[", indent, "");
1748 for (i = 0; i < tab->n_con; ++i) {
1751 fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
1753 tab->con[i].is_zero ? " [=0]" :
1754 tab->con[i].is_redundant ? " [R]" : "");
1756 fprintf(out, "]\n");
1757 fprintf(out, "%*s[", indent, "");
1758 for (i = 0; i < tab->n_row; ++i) {
1761 fprintf(out, "r%d: %d%s", i, tab->row_var[i],
1762 var_from_row(ctx, tab, i)->is_nonneg ? " [>=0]" : "");
1764 fprintf(out, "]\n");
1765 fprintf(out, "%*s[", indent, "");
1766 for (i = 0; i < tab->n_col; ++i) {
1769 fprintf(out, "c%d: %d%s", i, tab->col_var[i],
1770 var_from_col(ctx, tab, i)->is_nonneg ? " [>=0]" : "");
1772 fprintf(out, "]\n");
1773 r = tab->mat->n_row;
1774 tab->mat->n_row = tab->n_row;
1775 c = tab->mat->n_col;
1776 tab->mat->n_col = 2 + tab->n_col;
1777 isl_mat_dump(ctx, tab->mat, out, indent);
1778 tab->mat->n_row = r;
1779 tab->mat->n_col = c;