2 #include "isl_map_private.h"
7 * The implementation of tableaus in this file was inspired by Section 8
8 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
9 * prover for program checking".
12 struct isl_tab *isl_tab_alloc(struct isl_ctx *ctx,
13 unsigned n_row, unsigned n_var, unsigned M)
19 tab = isl_calloc_type(ctx, struct isl_tab);
22 tab->mat = isl_mat_alloc(ctx, n_row, off + n_var);
25 tab->var = isl_alloc_array(ctx, struct isl_tab_var, n_var);
28 tab->con = isl_alloc_array(ctx, struct isl_tab_var, n_row);
31 tab->col_var = isl_alloc_array(ctx, int, n_var);
34 tab->row_var = isl_alloc_array(ctx, int, n_row);
37 for (i = 0; i < n_var; ++i) {
38 tab->var[i].index = i;
39 tab->var[i].is_row = 0;
40 tab->var[i].is_nonneg = 0;
41 tab->var[i].is_zero = 0;
42 tab->var[i].is_redundant = 0;
43 tab->var[i].frozen = 0;
44 tab->var[i].negated = 0;
63 tab->bottom.type = isl_tab_undo_bottom;
64 tab->bottom.next = NULL;
65 tab->top = &tab->bottom;
77 int isl_tab_extend_cons(struct isl_tab *tab, unsigned n_new)
79 unsigned off = 2 + tab->M;
84 if (tab->max_con < tab->n_con + n_new) {
85 struct isl_tab_var *con;
87 con = isl_realloc_array(tab->mat->ctx, tab->con,
88 struct isl_tab_var, tab->max_con + n_new);
92 tab->max_con += n_new;
94 if (tab->mat->n_row < tab->n_row + n_new) {
97 tab->mat = isl_mat_extend(tab->mat,
98 tab->n_row + n_new, off + tab->n_col);
101 row_var = isl_realloc_array(tab->mat->ctx, tab->row_var,
102 int, tab->mat->n_row);
105 tab->row_var = row_var;
107 enum isl_tab_row_sign *s;
108 s = isl_realloc_array(tab->mat->ctx, tab->row_sign,
109 enum isl_tab_row_sign, tab->mat->n_row);
118 /* Make room for at least n_new extra variables.
119 * Return -1 if anything went wrong.
121 int isl_tab_extend_vars(struct isl_tab *tab, unsigned n_new)
123 struct isl_tab_var *var;
124 unsigned off = 2 + tab->M;
126 if (tab->max_var < tab->n_var + n_new) {
127 var = isl_realloc_array(tab->mat->ctx, tab->var,
128 struct isl_tab_var, tab->n_var + n_new);
132 tab->max_var += n_new;
135 if (tab->mat->n_col < off + tab->n_col + n_new) {
138 tab->mat = isl_mat_extend(tab->mat,
139 tab->mat->n_row, off + tab->n_col + n_new);
142 p = isl_realloc_array(tab->mat->ctx, tab->col_var,
143 int, tab->n_col + n_new);
152 struct isl_tab *isl_tab_extend(struct isl_tab *tab, unsigned n_new)
154 if (isl_tab_extend_cons(tab, n_new) >= 0)
161 static void free_undo(struct isl_tab *tab)
163 struct isl_tab_undo *undo, *next;
165 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
172 void isl_tab_free(struct isl_tab *tab)
177 isl_mat_free(tab->mat);
178 isl_vec_free(tab->dual);
179 isl_basic_set_free(tab->bset);
185 isl_mat_free(tab->samples);
186 free(tab->sample_index);
187 isl_mat_free(tab->basis);
191 struct isl_tab *isl_tab_dup(struct isl_tab *tab)
201 dup = isl_calloc_type(tab->ctx, struct isl_tab);
204 dup->mat = isl_mat_dup(tab->mat);
207 dup->var = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_var);
210 for (i = 0; i < tab->n_var; ++i)
211 dup->var[i] = tab->var[i];
212 dup->con = isl_alloc_array(tab->ctx, struct isl_tab_var, tab->max_con);
215 for (i = 0; i < tab->n_con; ++i)
216 dup->con[i] = tab->con[i];
217 dup->col_var = isl_alloc_array(tab->ctx, int, tab->mat->n_col - off);
220 for (i = 0; i < tab->n_col; ++i)
221 dup->col_var[i] = tab->col_var[i];
222 dup->row_var = isl_alloc_array(tab->ctx, int, tab->mat->n_row);
225 for (i = 0; i < tab->n_row; ++i)
226 dup->row_var[i] = tab->row_var[i];
228 dup->row_sign = isl_alloc_array(tab->ctx, enum isl_tab_row_sign,
232 for (i = 0; i < tab->n_row; ++i)
233 dup->row_sign[i] = tab->row_sign[i];
236 dup->samples = isl_mat_dup(tab->samples);
239 dup->sample_index = isl_alloc_array(tab->mat->ctx, int,
240 tab->samples->n_row);
241 if (!dup->sample_index)
243 dup->n_sample = tab->n_sample;
244 dup->n_outside = tab->n_outside;
246 dup->n_row = tab->n_row;
247 dup->n_con = tab->n_con;
248 dup->n_eq = tab->n_eq;
249 dup->max_con = tab->max_con;
250 dup->n_col = tab->n_col;
251 dup->n_var = tab->n_var;
252 dup->max_var = tab->max_var;
253 dup->n_param = tab->n_param;
254 dup->n_div = tab->n_div;
255 dup->n_dead = tab->n_dead;
256 dup->n_redundant = tab->n_redundant;
257 dup->rational = tab->rational;
258 dup->empty = tab->empty;
262 dup->bottom.type = isl_tab_undo_bottom;
263 dup->bottom.next = NULL;
264 dup->top = &dup->bottom;
266 dup->n_zero = tab->n_zero;
267 dup->n_unbounded = tab->n_unbounded;
268 dup->basis = isl_mat_dup(tab->basis);
276 /* Construct the coefficient matrix of the product tableau
278 * mat{1,2} is the coefficient matrix of tableau {1,2}
279 * row{1,2} is the number of rows in tableau {1,2}
280 * col{1,2} is the number of columns in tableau {1,2}
281 * off is the offset to the coefficient column (skipping the
282 * denominator, the constant term and the big parameter if any)
283 * r{1,2} is the number of redundant rows in tableau {1,2}
284 * d{1,2} is the number of dead columns in tableau {1,2}
286 * The order of the rows and columns in the result is as explained
287 * in isl_tab_product.
289 static struct isl_mat *tab_mat_product(struct isl_mat *mat1,
290 struct isl_mat *mat2, unsigned row1, unsigned row2,
291 unsigned col1, unsigned col2,
292 unsigned off, unsigned r1, unsigned r2, unsigned d1, unsigned d2)
295 struct isl_mat *prod;
298 prod = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
302 for (i = 0; i < r1; ++i) {
303 isl_seq_cpy(prod->row[n + i], mat1->row[i], off + d1);
304 isl_seq_clr(prod->row[n + i] + off + d1, d2);
305 isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
306 mat1->row[i] + off + d1, col1 - d1);
307 isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
311 for (i = 0; i < r2; ++i) {
312 isl_seq_cpy(prod->row[n + i], mat2->row[i], off);
313 isl_seq_clr(prod->row[n + i] + off, d1);
314 isl_seq_cpy(prod->row[n + i] + off + d1,
315 mat2->row[i] + off, d2);
316 isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
317 isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
318 mat2->row[i] + off + d2, col2 - d2);
322 for (i = 0; i < row1 - r1; ++i) {
323 isl_seq_cpy(prod->row[n + i], mat1->row[r1 + i], off + d1);
324 isl_seq_clr(prod->row[n + i] + off + d1, d2);
325 isl_seq_cpy(prod->row[n + i] + off + d1 + d2,
326 mat1->row[r1 + i] + off + d1, col1 - d1);
327 isl_seq_clr(prod->row[n + i] + off + col1 + d1, col2 - d2);
331 for (i = 0; i < row2 - r2; ++i) {
332 isl_seq_cpy(prod->row[n + i], mat2->row[r2 + i], off);
333 isl_seq_clr(prod->row[n + i] + off, d1);
334 isl_seq_cpy(prod->row[n + i] + off + d1,
335 mat2->row[r2 + i] + off, d2);
336 isl_seq_clr(prod->row[n + i] + off + d1 + d2, col1 - d1);
337 isl_seq_cpy(prod->row[n + i] + off + col1 + d1,
338 mat2->row[r2 + i] + off + d2, col2 - d2);
344 /* Update the row or column index of a variable that corresponds
345 * to a variable in the first input tableau.
347 static void update_index1(struct isl_tab_var *var,
348 unsigned r1, unsigned r2, unsigned d1, unsigned d2)
350 if (var->index == -1)
352 if (var->is_row && var->index >= r1)
354 if (!var->is_row && var->index >= d1)
358 /* Update the row or column index of a variable that corresponds
359 * to a variable in the second input tableau.
361 static void update_index2(struct isl_tab_var *var,
362 unsigned row1, unsigned col1,
363 unsigned r1, unsigned r2, unsigned d1, unsigned d2)
365 if (var->index == -1)
380 /* Create a tableau that represents the Cartesian product of the sets
381 * represented by tableaus tab1 and tab2.
382 * The order of the rows in the product is
383 * - redundant rows of tab1
384 * - redundant rows of tab2
385 * - non-redundant rows of tab1
386 * - non-redundant rows of tab2
387 * The order of the columns is
390 * - coefficient of big parameter, if any
391 * - dead columns of tab1
392 * - dead columns of tab2
393 * - live columns of tab1
394 * - live columns of tab2
395 * The order of the variables and the constraints is a concatenation
396 * of order in the two input tableaus.
398 struct isl_tab *isl_tab_product(struct isl_tab *tab1, struct isl_tab *tab2)
401 struct isl_tab *prod;
403 unsigned r1, r2, d1, d2;
408 isl_assert(tab1->mat->ctx, tab1->M == tab2->M, return NULL);
409 isl_assert(tab1->mat->ctx, tab1->rational == tab2->rational, return NULL);
410 isl_assert(tab1->mat->ctx, !tab1->row_sign, return NULL);
411 isl_assert(tab1->mat->ctx, !tab2->row_sign, return NULL);
412 isl_assert(tab1->mat->ctx, tab1->n_param == 0, return NULL);
413 isl_assert(tab1->mat->ctx, tab2->n_param == 0, return NULL);
414 isl_assert(tab1->mat->ctx, tab1->n_div == 0, return NULL);
415 isl_assert(tab1->mat->ctx, tab2->n_div == 0, return NULL);
418 r1 = tab1->n_redundant;
419 r2 = tab2->n_redundant;
422 prod = isl_calloc_type(tab1->mat->ctx, struct isl_tab);
425 prod->mat = tab_mat_product(tab1->mat, tab2->mat,
426 tab1->n_row, tab2->n_row,
427 tab1->n_col, tab2->n_col, off, r1, r2, d1, d2);
430 prod->var = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
431 tab1->max_var + tab2->max_var);
434 for (i = 0; i < tab1->n_var; ++i) {
435 prod->var[i] = tab1->var[i];
436 update_index1(&prod->var[i], r1, r2, d1, d2);
438 for (i = 0; i < tab2->n_var; ++i) {
439 prod->var[tab1->n_var + i] = tab2->var[i];
440 update_index2(&prod->var[tab1->n_var + i],
441 tab1->n_row, tab1->n_col,
444 prod->con = isl_alloc_array(tab1->mat->ctx, struct isl_tab_var,
445 tab1->max_con + tab2->max_con);
448 for (i = 0; i < tab1->n_con; ++i) {
449 prod->con[i] = tab1->con[i];
450 update_index1(&prod->con[i], r1, r2, d1, d2);
452 for (i = 0; i < tab2->n_con; ++i) {
453 prod->con[tab1->n_con + i] = tab2->con[i];
454 update_index2(&prod->con[tab1->n_con + i],
455 tab1->n_row, tab1->n_col,
458 prod->col_var = isl_alloc_array(tab1->mat->ctx, int,
459 tab1->n_col + tab2->n_col);
462 for (i = 0; i < tab1->n_col; ++i) {
463 int pos = i < d1 ? i : i + d2;
464 prod->col_var[pos] = tab1->col_var[i];
466 for (i = 0; i < tab2->n_col; ++i) {
467 int pos = i < d2 ? d1 + i : tab1->n_col + i;
468 int t = tab2->col_var[i];
473 prod->col_var[pos] = t;
475 prod->row_var = isl_alloc_array(tab1->mat->ctx, int,
476 tab1->mat->n_row + tab2->mat->n_row);
479 for (i = 0; i < tab1->n_row; ++i) {
480 int pos = i < r1 ? i : i + r2;
481 prod->row_var[pos] = tab1->row_var[i];
483 for (i = 0; i < tab2->n_row; ++i) {
484 int pos = i < r2 ? r1 + i : tab1->n_row + i;
485 int t = tab2->row_var[i];
490 prod->row_var[pos] = t;
492 prod->samples = NULL;
493 prod->sample_index = NULL;
494 prod->n_row = tab1->n_row + tab2->n_row;
495 prod->n_con = tab1->n_con + tab2->n_con;
497 prod->max_con = tab1->max_con + tab2->max_con;
498 prod->n_col = tab1->n_col + tab2->n_col;
499 prod->n_var = tab1->n_var + tab2->n_var;
500 prod->max_var = tab1->max_var + tab2->max_var;
503 prod->n_dead = tab1->n_dead + tab2->n_dead;
504 prod->n_redundant = tab1->n_redundant + tab2->n_redundant;
505 prod->rational = tab1->rational;
506 prod->empty = tab1->empty || tab2->empty;
510 prod->bottom.type = isl_tab_undo_bottom;
511 prod->bottom.next = NULL;
512 prod->top = &prod->bottom;
515 prod->n_unbounded = 0;
524 static struct isl_tab_var *var_from_index(struct isl_tab *tab, int i)
529 return &tab->con[~i];
532 struct isl_tab_var *isl_tab_var_from_row(struct isl_tab *tab, int i)
534 return var_from_index(tab, tab->row_var[i]);
537 static struct isl_tab_var *var_from_col(struct isl_tab *tab, int i)
539 return var_from_index(tab, tab->col_var[i]);
542 /* Check if there are any upper bounds on column variable "var",
543 * i.e., non-negative rows where var appears with a negative coefficient.
544 * Return 1 if there are no such bounds.
546 static int max_is_manifestly_unbounded(struct isl_tab *tab,
547 struct isl_tab_var *var)
550 unsigned off = 2 + tab->M;
554 for (i = tab->n_redundant; i < tab->n_row; ++i) {
555 if (!isl_int_is_neg(tab->mat->row[i][off + var->index]))
557 if (isl_tab_var_from_row(tab, i)->is_nonneg)
563 /* Check if there are any lower bounds on column variable "var",
564 * i.e., non-negative rows where var appears with a positive coefficient.
565 * Return 1 if there are no such bounds.
567 static int min_is_manifestly_unbounded(struct isl_tab *tab,
568 struct isl_tab_var *var)
571 unsigned off = 2 + tab->M;
575 for (i = tab->n_redundant; i < tab->n_row; ++i) {
576 if (!isl_int_is_pos(tab->mat->row[i][off + var->index]))
578 if (isl_tab_var_from_row(tab, i)->is_nonneg)
584 static int row_cmp(struct isl_tab *tab, int r1, int r2, int c, isl_int t)
586 unsigned off = 2 + tab->M;
590 isl_int_mul(t, tab->mat->row[r1][2], tab->mat->row[r2][off+c]);
591 isl_int_submul(t, tab->mat->row[r2][2], tab->mat->row[r1][off+c]);
596 isl_int_mul(t, tab->mat->row[r1][1], tab->mat->row[r2][off + c]);
597 isl_int_submul(t, tab->mat->row[r2][1], tab->mat->row[r1][off + c]);
598 return isl_int_sgn(t);
601 /* Given the index of a column "c", return the index of a row
602 * that can be used to pivot the column in, with either an increase
603 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
604 * If "var" is not NULL, then the row returned will be different from
605 * the one associated with "var".
607 * Each row in the tableau is of the form
609 * x_r = a_r0 + \sum_i a_ri x_i
611 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
612 * impose any limit on the increase or decrease in the value of x_c
613 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
614 * for the row with the smallest (most stringent) such bound.
615 * Note that the common denominator of each row drops out of the fraction.
616 * To check if row j has a smaller bound than row r, i.e.,
617 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
618 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
619 * where -sign(a_jc) is equal to "sgn".
621 static int pivot_row(struct isl_tab *tab,
622 struct isl_tab_var *var, int sgn, int c)
626 unsigned off = 2 + tab->M;
630 for (j = tab->n_redundant; j < tab->n_row; ++j) {
631 if (var && j == var->index)
633 if (!isl_tab_var_from_row(tab, j)->is_nonneg)
635 if (sgn * isl_int_sgn(tab->mat->row[j][off + c]) >= 0)
641 tsgn = sgn * row_cmp(tab, r, j, c, t);
642 if (tsgn < 0 || (tsgn == 0 &&
643 tab->row_var[j] < tab->row_var[r]))
650 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
651 * (sgn < 0) the value of row variable var.
652 * If not NULL, then skip_var is a row variable that should be ignored
653 * while looking for a pivot row. It is usually equal to var.
655 * As the given row in the tableau is of the form
657 * x_r = a_r0 + \sum_i a_ri x_i
659 * we need to find a column such that the sign of a_ri is equal to "sgn"
660 * (such that an increase in x_i will have the desired effect) or a
661 * column with a variable that may attain negative values.
662 * If a_ri is positive, then we need to move x_i in the same direction
663 * to obtain the desired effect. Otherwise, x_i has to move in the
664 * opposite direction.
666 static void find_pivot(struct isl_tab *tab,
667 struct isl_tab_var *var, struct isl_tab_var *skip_var,
668 int sgn, int *row, int *col)
675 isl_assert(tab->mat->ctx, var->is_row, return);
676 tr = tab->mat->row[var->index] + 2 + tab->M;
679 for (j = tab->n_dead; j < tab->n_col; ++j) {
680 if (isl_int_is_zero(tr[j]))
682 if (isl_int_sgn(tr[j]) != sgn &&
683 var_from_col(tab, j)->is_nonneg)
685 if (c < 0 || tab->col_var[j] < tab->col_var[c])
691 sgn *= isl_int_sgn(tr[c]);
692 r = pivot_row(tab, skip_var, sgn, c);
693 *row = r < 0 ? var->index : r;
697 /* Return 1 if row "row" represents an obviously redundant inequality.
699 * - it represents an inequality or a variable
700 * - that is the sum of a non-negative sample value and a positive
701 * combination of zero or more non-negative variables.
703 int isl_tab_row_is_redundant(struct isl_tab *tab, int row)
706 unsigned off = 2 + tab->M;
708 if (tab->row_var[row] < 0 && !isl_tab_var_from_row(tab, row)->is_nonneg)
711 if (isl_int_is_neg(tab->mat->row[row][1]))
713 if (tab->M && isl_int_is_neg(tab->mat->row[row][2]))
716 for (i = tab->n_dead; i < tab->n_col; ++i) {
717 if (isl_int_is_zero(tab->mat->row[row][off + i]))
719 if (isl_int_is_neg(tab->mat->row[row][off + i]))
721 if (!var_from_col(tab, i)->is_nonneg)
727 static void swap_rows(struct isl_tab *tab, int row1, int row2)
730 t = tab->row_var[row1];
731 tab->row_var[row1] = tab->row_var[row2];
732 tab->row_var[row2] = t;
733 isl_tab_var_from_row(tab, row1)->index = row1;
734 isl_tab_var_from_row(tab, row2)->index = row2;
735 tab->mat = isl_mat_swap_rows(tab->mat, row1, row2);
739 t = tab->row_sign[row1];
740 tab->row_sign[row1] = tab->row_sign[row2];
741 tab->row_sign[row2] = t;
744 static void push_union(struct isl_tab *tab,
745 enum isl_tab_undo_type type, union isl_tab_undo_val u)
747 struct isl_tab_undo *undo;
752 undo = isl_alloc_type(tab->mat->ctx, struct isl_tab_undo);
760 undo->next = tab->top;
764 void isl_tab_push_var(struct isl_tab *tab,
765 enum isl_tab_undo_type type, struct isl_tab_var *var)
767 union isl_tab_undo_val u;
769 u.var_index = tab->row_var[var->index];
771 u.var_index = tab->col_var[var->index];
772 push_union(tab, type, u);
775 void isl_tab_push(struct isl_tab *tab, enum isl_tab_undo_type type)
777 union isl_tab_undo_val u = { 0 };
778 push_union(tab, type, u);
781 /* Push a record on the undo stack describing the current basic
782 * variables, so that the this state can be restored during rollback.
784 void isl_tab_push_basis(struct isl_tab *tab)
787 union isl_tab_undo_val u;
789 u.col_var = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
795 for (i = 0; i < tab->n_col; ++i)
796 u.col_var[i] = tab->col_var[i];
797 push_union(tab, isl_tab_undo_saved_basis, u);
800 struct isl_tab *isl_tab_init_samples(struct isl_tab *tab)
807 tab->samples = isl_mat_alloc(tab->mat->ctx, 1, 1 + tab->n_var);
810 tab->sample_index = isl_alloc_array(tab->mat->ctx, int, 1);
811 if (!tab->sample_index)
819 struct isl_tab *isl_tab_add_sample(struct isl_tab *tab,
820 __isl_take isl_vec *sample)
825 if (tab->n_sample + 1 > tab->samples->n_row) {
826 int *t = isl_realloc_array(tab->mat->ctx,
827 tab->sample_index, int, tab->n_sample + 1);
830 tab->sample_index = t;
833 tab->samples = isl_mat_extend(tab->samples,
834 tab->n_sample + 1, tab->samples->n_col);
838 isl_seq_cpy(tab->samples->row[tab->n_sample], sample->el, sample->size);
839 isl_vec_free(sample);
840 tab->sample_index[tab->n_sample] = tab->n_sample;
845 isl_vec_free(sample);
850 struct isl_tab *isl_tab_drop_sample(struct isl_tab *tab, int s)
852 if (s != tab->n_outside) {
853 int t = tab->sample_index[tab->n_outside];
854 tab->sample_index[tab->n_outside] = tab->sample_index[s];
855 tab->sample_index[s] = t;
856 isl_mat_swap_rows(tab->samples, tab->n_outside, s);
859 isl_tab_push(tab, isl_tab_undo_drop_sample);
864 /* Record the current number of samples so that we can remove newer
865 * samples during a rollback.
867 void isl_tab_save_samples(struct isl_tab *tab)
869 union isl_tab_undo_val u;
875 push_union(tab, isl_tab_undo_saved_samples, u);
878 /* Mark row with index "row" as being redundant.
879 * If we may need to undo the operation or if the row represents
880 * a variable of the original problem, the row is kept,
881 * but no longer considered when looking for a pivot row.
882 * Otherwise, the row is simply removed.
884 * The row may be interchanged with some other row. If it
885 * is interchanged with a later row, return 1. Otherwise return 0.
886 * If the rows are checked in order in the calling function,
887 * then a return value of 1 means that the row with the given
888 * row number may now contain a different row that hasn't been checked yet.
890 int isl_tab_mark_redundant(struct isl_tab *tab, int row)
892 struct isl_tab_var *var = isl_tab_var_from_row(tab, row);
893 var->is_redundant = 1;
894 isl_assert(tab->mat->ctx, row >= tab->n_redundant, return -1);
895 if (tab->need_undo || tab->row_var[row] >= 0) {
896 if (tab->row_var[row] >= 0 && !var->is_nonneg) {
898 isl_tab_push_var(tab, isl_tab_undo_nonneg, var);
900 if (row != tab->n_redundant)
901 swap_rows(tab, row, tab->n_redundant);
902 isl_tab_push_var(tab, isl_tab_undo_redundant, var);
906 if (row != tab->n_row - 1)
907 swap_rows(tab, row, tab->n_row - 1);
908 isl_tab_var_from_row(tab, tab->n_row - 1)->index = -1;
914 struct isl_tab *isl_tab_mark_empty(struct isl_tab *tab)
916 if (!tab->empty && tab->need_undo)
917 isl_tab_push(tab, isl_tab_undo_empty);
922 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
923 * the original sign of the pivot element.
924 * We only keep track of row signs during PILP solving and in this case
925 * we only pivot a row with negative sign (meaning the value is always
926 * non-positive) using a positive pivot element.
928 * For each row j, the new value of the parametric constant is equal to
930 * a_j0 - a_jc a_r0/a_rc
932 * where a_j0 is the original parametric constant, a_rc is the pivot element,
933 * a_r0 is the parametric constant of the pivot row and a_jc is the
934 * pivot column entry of the row j.
935 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
936 * remains the same if a_jc has the same sign as the row j or if
937 * a_jc is zero. In all other cases, we reset the sign to "unknown".
939 static void update_row_sign(struct isl_tab *tab, int row, int col, int row_sgn)
942 struct isl_mat *mat = tab->mat;
943 unsigned off = 2 + tab->M;
948 if (tab->row_sign[row] == 0)
950 isl_assert(mat->ctx, row_sgn > 0, return);
951 isl_assert(mat->ctx, tab->row_sign[row] == isl_tab_row_neg, return);
952 tab->row_sign[row] = isl_tab_row_pos;
953 for (i = 0; i < tab->n_row; ++i) {
957 s = isl_int_sgn(mat->row[i][off + col]);
960 if (!tab->row_sign[i])
962 if (s < 0 && tab->row_sign[i] == isl_tab_row_neg)
964 if (s > 0 && tab->row_sign[i] == isl_tab_row_pos)
966 tab->row_sign[i] = isl_tab_row_unknown;
970 /* Given a row number "row" and a column number "col", pivot the tableau
971 * such that the associated variables are interchanged.
972 * The given row in the tableau expresses
974 * x_r = a_r0 + \sum_i a_ri x_i
978 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
980 * Substituting this equality into the other rows
982 * x_j = a_j0 + \sum_i a_ji x_i
984 * with a_jc \ne 0, we obtain
986 * 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
993 * where i is any other column and j is any other row,
994 * is therefore transformed into
996 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
997 * 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)
999 * The transformation is performed along the following steps
1001 * d_r/n_rc n_ri/n_rc
1004 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1007 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1008 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
1010 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1011 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
1013 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1014 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
1016 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1017 * 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)
1020 void isl_tab_pivot(struct isl_tab *tab, int row, int col)
1025 struct isl_mat *mat = tab->mat;
1026 struct isl_tab_var *var;
1027 unsigned off = 2 + tab->M;
1029 isl_int_swap(mat->row[row][0], mat->row[row][off + col]);
1030 sgn = isl_int_sgn(mat->row[row][0]);
1032 isl_int_neg(mat->row[row][0], mat->row[row][0]);
1033 isl_int_neg(mat->row[row][off + col], mat->row[row][off + col]);
1035 for (j = 0; j < off - 1 + tab->n_col; ++j) {
1036 if (j == off - 1 + col)
1038 isl_int_neg(mat->row[row][1 + j], mat->row[row][1 + j]);
1040 if (!isl_int_is_one(mat->row[row][0]))
1041 isl_seq_normalize(mat->ctx, mat->row[row], off + tab->n_col);
1042 for (i = 0; i < tab->n_row; ++i) {
1045 if (isl_int_is_zero(mat->row[i][off + col]))
1047 isl_int_mul(mat->row[i][0], mat->row[i][0], mat->row[row][0]);
1048 for (j = 0; j < off - 1 + tab->n_col; ++j) {
1049 if (j == off - 1 + col)
1051 isl_int_mul(mat->row[i][1 + j],
1052 mat->row[i][1 + j], mat->row[row][0]);
1053 isl_int_addmul(mat->row[i][1 + j],
1054 mat->row[i][off + col], mat->row[row][1 + j]);
1056 isl_int_mul(mat->row[i][off + col],
1057 mat->row[i][off + col], mat->row[row][off + col]);
1058 if (!isl_int_is_one(mat->row[i][0]))
1059 isl_seq_normalize(mat->ctx, mat->row[i], off + tab->n_col);
1061 t = tab->row_var[row];
1062 tab->row_var[row] = tab->col_var[col];
1063 tab->col_var[col] = t;
1064 var = isl_tab_var_from_row(tab, row);
1067 var = var_from_col(tab, col);
1070 update_row_sign(tab, row, col, sgn);
1073 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1074 if (isl_int_is_zero(mat->row[i][off + col]))
1076 if (!isl_tab_var_from_row(tab, i)->frozen &&
1077 isl_tab_row_is_redundant(tab, i))
1078 if (isl_tab_mark_redundant(tab, i))
1083 /* If "var" represents a column variable, then pivot is up (sgn > 0)
1084 * or down (sgn < 0) to a row. The variable is assumed not to be
1085 * unbounded in the specified direction.
1086 * If sgn = 0, then the variable is unbounded in both directions,
1087 * and we pivot with any row we can find.
1089 static void to_row(struct isl_tab *tab, struct isl_tab_var *var, int sign)
1092 unsigned off = 2 + tab->M;
1098 for (r = tab->n_redundant; r < tab->n_row; ++r)
1099 if (!isl_int_is_zero(tab->mat->row[r][off+var->index]))
1101 isl_assert(tab->mat->ctx, r < tab->n_row, return);
1103 r = pivot_row(tab, NULL, sign, var->index);
1104 isl_assert(tab->mat->ctx, r >= 0, return);
1107 isl_tab_pivot(tab, r, var->index);
1110 static void check_table(struct isl_tab *tab)
1116 for (i = 0; i < tab->n_row; ++i) {
1117 if (!isl_tab_var_from_row(tab, i)->is_nonneg)
1119 assert(!isl_int_is_neg(tab->mat->row[i][1]));
1123 /* Return the sign of the maximal value of "var".
1124 * If the sign is not negative, then on return from this function,
1125 * the sample value will also be non-negative.
1127 * If "var" is manifestly unbounded wrt positive values, we are done.
1128 * Otherwise, we pivot the variable up to a row if needed
1129 * Then we continue pivoting down until either
1130 * - no more down pivots can be performed
1131 * - the sample value is positive
1132 * - the variable is pivoted into a manifestly unbounded column
1134 static int sign_of_max(struct isl_tab *tab, struct isl_tab_var *var)
1138 if (max_is_manifestly_unbounded(tab, var))
1140 to_row(tab, var, 1);
1141 while (!isl_int_is_pos(tab->mat->row[var->index][1])) {
1142 find_pivot(tab, var, var, 1, &row, &col);
1144 return isl_int_sgn(tab->mat->row[var->index][1]);
1145 isl_tab_pivot(tab, row, col);
1146 if (!var->is_row) /* manifestly unbounded */
1152 static int row_is_neg(struct isl_tab *tab, int row)
1155 return isl_int_is_neg(tab->mat->row[row][1]);
1156 if (isl_int_is_pos(tab->mat->row[row][2]))
1158 if (isl_int_is_neg(tab->mat->row[row][2]))
1160 return isl_int_is_neg(tab->mat->row[row][1]);
1163 static int row_sgn(struct isl_tab *tab, int row)
1166 return isl_int_sgn(tab->mat->row[row][1]);
1167 if (!isl_int_is_zero(tab->mat->row[row][2]))
1168 return isl_int_sgn(tab->mat->row[row][2]);
1170 return isl_int_sgn(tab->mat->row[row][1]);
1173 /* Perform pivots until the row variable "var" has a non-negative
1174 * sample value or until no more upward pivots can be performed.
1175 * Return the sign of the sample value after the pivots have been
1178 static int restore_row(struct isl_tab *tab, struct isl_tab_var *var)
1182 while (row_is_neg(tab, var->index)) {
1183 find_pivot(tab, var, var, 1, &row, &col);
1186 isl_tab_pivot(tab, row, col);
1187 if (!var->is_row) /* manifestly unbounded */
1190 return row_sgn(tab, var->index);
1193 /* Perform pivots until we are sure that the row variable "var"
1194 * can attain non-negative values. After return from this
1195 * function, "var" is still a row variable, but its sample
1196 * value may not be non-negative, even if the function returns 1.
1198 static int at_least_zero(struct isl_tab *tab, struct isl_tab_var *var)
1202 while (isl_int_is_neg(tab->mat->row[var->index][1])) {
1203 find_pivot(tab, var, var, 1, &row, &col);
1206 if (row == var->index) /* manifestly unbounded */
1208 isl_tab_pivot(tab, row, col);
1210 return !isl_int_is_neg(tab->mat->row[var->index][1]);
1213 /* Return a negative value if "var" can attain negative values.
1214 * Return a non-negative value otherwise.
1216 * If "var" is manifestly unbounded wrt negative values, we are done.
1217 * Otherwise, if var is in a column, we can pivot it down to a row.
1218 * Then we continue pivoting down until either
1219 * - the pivot would result in a manifestly unbounded column
1220 * => we don't perform the pivot, but simply return -1
1221 * - no more down pivots can be performed
1222 * - the sample value is negative
1223 * If the sample value becomes negative and the variable is supposed
1224 * to be nonnegative, then we undo the last pivot.
1225 * However, if the last pivot has made the pivoting variable
1226 * obviously redundant, then it may have moved to another row.
1227 * In that case we look for upward pivots until we reach a non-negative
1230 static int sign_of_min(struct isl_tab *tab, struct isl_tab_var *var)
1233 struct isl_tab_var *pivot_var = NULL;
1235 if (min_is_manifestly_unbounded(tab, var))
1239 row = pivot_row(tab, NULL, -1, col);
1240 pivot_var = var_from_col(tab, col);
1241 isl_tab_pivot(tab, row, col);
1242 if (var->is_redundant)
1244 if (isl_int_is_neg(tab->mat->row[var->index][1])) {
1245 if (var->is_nonneg) {
1246 if (!pivot_var->is_redundant &&
1247 pivot_var->index == row)
1248 isl_tab_pivot(tab, row, col);
1250 restore_row(tab, var);
1255 if (var->is_redundant)
1257 while (!isl_int_is_neg(tab->mat->row[var->index][1])) {
1258 find_pivot(tab, var, var, -1, &row, &col);
1259 if (row == var->index)
1262 return isl_int_sgn(tab->mat->row[var->index][1]);
1263 pivot_var = var_from_col(tab, col);
1264 isl_tab_pivot(tab, row, col);
1265 if (var->is_redundant)
1268 if (pivot_var && var->is_nonneg) {
1269 /* pivot back to non-negative value */
1270 if (!pivot_var->is_redundant && pivot_var->index == row)
1271 isl_tab_pivot(tab, row, col);
1273 restore_row(tab, var);
1278 static int row_at_most_neg_one(struct isl_tab *tab, int row)
1281 if (isl_int_is_pos(tab->mat->row[row][2]))
1283 if (isl_int_is_neg(tab->mat->row[row][2]))
1286 return isl_int_is_neg(tab->mat->row[row][1]) &&
1287 isl_int_abs_ge(tab->mat->row[row][1],
1288 tab->mat->row[row][0]);
1291 /* Return 1 if "var" can attain values <= -1.
1292 * Return 0 otherwise.
1294 * The sample value of "var" is assumed to be non-negative when the
1295 * the function is called and will be made non-negative again before
1296 * the function returns.
1298 int isl_tab_min_at_most_neg_one(struct isl_tab *tab, struct isl_tab_var *var)
1301 struct isl_tab_var *pivot_var;
1303 if (min_is_manifestly_unbounded(tab, var))
1307 row = pivot_row(tab, NULL, -1, col);
1308 pivot_var = var_from_col(tab, col);
1309 isl_tab_pivot(tab, row, col);
1310 if (var->is_redundant)
1312 if (row_at_most_neg_one(tab, var->index)) {
1313 if (var->is_nonneg) {
1314 if (!pivot_var->is_redundant &&
1315 pivot_var->index == row)
1316 isl_tab_pivot(tab, row, col);
1318 restore_row(tab, var);
1323 if (var->is_redundant)
1326 find_pivot(tab, var, var, -1, &row, &col);
1327 if (row == var->index)
1331 pivot_var = var_from_col(tab, col);
1332 isl_tab_pivot(tab, row, col);
1333 if (var->is_redundant)
1335 } while (!row_at_most_neg_one(tab, var->index));
1336 if (var->is_nonneg) {
1337 /* pivot back to non-negative value */
1338 if (!pivot_var->is_redundant && pivot_var->index == row)
1339 isl_tab_pivot(tab, row, col);
1340 restore_row(tab, var);
1345 /* Return 1 if "var" can attain values >= 1.
1346 * Return 0 otherwise.
1348 static int at_least_one(struct isl_tab *tab, struct isl_tab_var *var)
1353 if (max_is_manifestly_unbounded(tab, var))
1355 to_row(tab, var, 1);
1356 r = tab->mat->row[var->index];
1357 while (isl_int_lt(r[1], r[0])) {
1358 find_pivot(tab, var, var, 1, &row, &col);
1360 return isl_int_ge(r[1], r[0]);
1361 if (row == var->index) /* manifestly unbounded */
1363 isl_tab_pivot(tab, row, col);
1368 static void swap_cols(struct isl_tab *tab, int col1, int col2)
1371 unsigned off = 2 + tab->M;
1372 t = tab->col_var[col1];
1373 tab->col_var[col1] = tab->col_var[col2];
1374 tab->col_var[col2] = t;
1375 var_from_col(tab, col1)->index = col1;
1376 var_from_col(tab, col2)->index = col2;
1377 tab->mat = isl_mat_swap_cols(tab->mat, off + col1, off + col2);
1380 /* Mark column with index "col" as representing a zero variable.
1381 * If we may need to undo the operation the column is kept,
1382 * but no longer considered.
1383 * Otherwise, the column is simply removed.
1385 * The column may be interchanged with some other column. If it
1386 * is interchanged with a later column, return 1. Otherwise return 0.
1387 * If the columns are checked in order in the calling function,
1388 * then a return value of 1 means that the column with the given
1389 * column number may now contain a different column that
1390 * hasn't been checked yet.
1392 int isl_tab_kill_col(struct isl_tab *tab, int col)
1394 var_from_col(tab, col)->is_zero = 1;
1395 if (tab->need_undo) {
1396 isl_tab_push_var(tab, isl_tab_undo_zero, var_from_col(tab, col));
1397 if (col != tab->n_dead)
1398 swap_cols(tab, col, tab->n_dead);
1402 if (col != tab->n_col - 1)
1403 swap_cols(tab, col, tab->n_col - 1);
1404 var_from_col(tab, tab->n_col - 1)->index = -1;
1410 /* Row variable "var" is non-negative and cannot attain any values
1411 * larger than zero. This means that the coefficients of the unrestricted
1412 * column variables are zero and that the coefficients of the non-negative
1413 * column variables are zero or negative.
1414 * Each of the non-negative variables with a negative coefficient can
1415 * then also be written as the negative sum of non-negative variables
1416 * and must therefore also be zero.
1418 static void close_row(struct isl_tab *tab, struct isl_tab_var *var)
1421 struct isl_mat *mat = tab->mat;
1422 unsigned off = 2 + tab->M;
1424 isl_assert(tab->mat->ctx, var->is_nonneg, return);
1427 isl_tab_push_var(tab, isl_tab_undo_zero, var);
1428 for (j = tab->n_dead; j < tab->n_col; ++j) {
1429 if (isl_int_is_zero(mat->row[var->index][off + j]))
1431 isl_assert(tab->mat->ctx,
1432 isl_int_is_neg(mat->row[var->index][off + j]), return);
1433 if (isl_tab_kill_col(tab, j))
1436 isl_tab_mark_redundant(tab, var->index);
1439 /* Add a constraint to the tableau and allocate a row for it.
1440 * Return the index into the constraint array "con".
1442 int isl_tab_allocate_con(struct isl_tab *tab)
1446 isl_assert(tab->mat->ctx, tab->n_row < tab->mat->n_row, return -1);
1447 isl_assert(tab->mat->ctx, tab->n_con < tab->max_con, return -1);
1450 tab->con[r].index = tab->n_row;
1451 tab->con[r].is_row = 1;
1452 tab->con[r].is_nonneg = 0;
1453 tab->con[r].is_zero = 0;
1454 tab->con[r].is_redundant = 0;
1455 tab->con[r].frozen = 0;
1456 tab->con[r].negated = 0;
1457 tab->row_var[tab->n_row] = ~r;
1461 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
1466 /* Add a variable to the tableau and allocate a column for it.
1467 * Return the index into the variable array "var".
1469 int isl_tab_allocate_var(struct isl_tab *tab)
1473 unsigned off = 2 + tab->M;
1475 isl_assert(tab->mat->ctx, tab->n_col < tab->mat->n_col, return -1);
1476 isl_assert(tab->mat->ctx, tab->n_var < tab->max_var, return -1);
1479 tab->var[r].index = tab->n_col;
1480 tab->var[r].is_row = 0;
1481 tab->var[r].is_nonneg = 0;
1482 tab->var[r].is_zero = 0;
1483 tab->var[r].is_redundant = 0;
1484 tab->var[r].frozen = 0;
1485 tab->var[r].negated = 0;
1486 tab->col_var[tab->n_col] = r;
1488 for (i = 0; i < tab->n_row; ++i)
1489 isl_int_set_si(tab->mat->row[i][off + tab->n_col], 0);
1493 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->var[r]);
1498 /* Add a row to the tableau. The row is given as an affine combination
1499 * of the original variables and needs to be expressed in terms of the
1502 * We add each term in turn.
1503 * If r = n/d_r is the current sum and we need to add k x, then
1504 * if x is a column variable, we increase the numerator of
1505 * this column by k d_r
1506 * if x = f/d_x is a row variable, then the new representation of r is
1508 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1509 * --- + --- = ------------------- = -------------------
1510 * d_r d_r d_r d_x/g m
1512 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1514 int isl_tab_add_row(struct isl_tab *tab, isl_int *line)
1520 unsigned off = 2 + tab->M;
1522 r = isl_tab_allocate_con(tab);
1528 row = tab->mat->row[tab->con[r].index];
1529 isl_int_set_si(row[0], 1);
1530 isl_int_set(row[1], line[0]);
1531 isl_seq_clr(row + 2, tab->M + tab->n_col);
1532 for (i = 0; i < tab->n_var; ++i) {
1533 if (tab->var[i].is_zero)
1535 if (tab->var[i].is_row) {
1537 row[0], tab->mat->row[tab->var[i].index][0]);
1538 isl_int_swap(a, row[0]);
1539 isl_int_divexact(a, row[0], a);
1541 row[0], tab->mat->row[tab->var[i].index][0]);
1542 isl_int_mul(b, b, line[1 + i]);
1543 isl_seq_combine(row + 1, a, row + 1,
1544 b, tab->mat->row[tab->var[i].index] + 1,
1545 1 + tab->M + tab->n_col);
1547 isl_int_addmul(row[off + tab->var[i].index],
1548 line[1 + i], row[0]);
1549 if (tab->M && i >= tab->n_param && i < tab->n_var - tab->n_div)
1550 isl_int_submul(row[2], line[1 + i], row[0]);
1552 isl_seq_normalize(tab->mat->ctx, row, off + tab->n_col);
1557 tab->row_sign[tab->con[r].index] = 0;
1562 static int drop_row(struct isl_tab *tab, int row)
1564 isl_assert(tab->mat->ctx, ~tab->row_var[row] == tab->n_con - 1, return -1);
1565 if (row != tab->n_row - 1)
1566 swap_rows(tab, row, tab->n_row - 1);
1572 static int drop_col(struct isl_tab *tab, int col)
1574 isl_assert(tab->mat->ctx, tab->col_var[col] == tab->n_var - 1, return -1);
1575 if (col != tab->n_col - 1)
1576 swap_cols(tab, col, tab->n_col - 1);
1582 /* Add inequality "ineq" and check if it conflicts with the
1583 * previously added constraints or if it is obviously redundant.
1585 struct isl_tab *isl_tab_add_ineq(struct isl_tab *tab, isl_int *ineq)
1593 struct isl_basic_set *bset = tab->bset;
1595 isl_assert(tab->mat->ctx, tab->n_eq == bset->n_eq, goto error);
1596 isl_assert(tab->mat->ctx,
1597 tab->n_con == bset->n_eq + bset->n_ineq, goto error);
1598 tab->bset = isl_basic_set_add_ineq(tab->bset, ineq);
1599 isl_tab_push(tab, isl_tab_undo_bset_ineq);
1603 r = isl_tab_add_row(tab, ineq);
1606 tab->con[r].is_nonneg = 1;
1607 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1608 if (isl_tab_row_is_redundant(tab, tab->con[r].index)) {
1609 isl_tab_mark_redundant(tab, tab->con[r].index);
1613 sgn = restore_row(tab, &tab->con[r]);
1615 return isl_tab_mark_empty(tab);
1616 if (tab->con[r].is_row && isl_tab_row_is_redundant(tab, tab->con[r].index))
1617 isl_tab_mark_redundant(tab, tab->con[r].index);
1624 /* Pivot a non-negative variable down until it reaches the value zero
1625 * and then pivot the variable into a column position.
1627 static int to_col(struct isl_tab *tab, struct isl_tab_var *var)
1631 unsigned off = 2 + tab->M;
1636 while (isl_int_is_pos(tab->mat->row[var->index][1])) {
1637 find_pivot(tab, var, NULL, -1, &row, &col);
1638 isl_assert(tab->mat->ctx, row != -1, return -1);
1639 isl_tab_pivot(tab, row, col);
1644 for (i = tab->n_dead; i < tab->n_col; ++i)
1645 if (!isl_int_is_zero(tab->mat->row[var->index][off + i]))
1648 isl_assert(tab->mat->ctx, i < tab->n_col, return -1);
1649 isl_tab_pivot(tab, var->index, i);
1654 /* We assume Gaussian elimination has been performed on the equalities.
1655 * The equalities can therefore never conflict.
1656 * Adding the equalities is currently only really useful for a later call
1657 * to isl_tab_ineq_type.
1659 static struct isl_tab *add_eq(struct isl_tab *tab, isl_int *eq)
1666 r = isl_tab_add_row(tab, eq);
1670 r = tab->con[r].index;
1671 i = isl_seq_first_non_zero(tab->mat->row[r] + 2 + tab->M + tab->n_dead,
1672 tab->n_col - tab->n_dead);
1673 isl_assert(tab->mat->ctx, i >= 0, goto error);
1675 isl_tab_pivot(tab, r, i);
1676 isl_tab_kill_col(tab, i);
1685 static int row_is_manifestly_zero(struct isl_tab *tab, int row)
1687 unsigned off = 2 + tab->M;
1689 if (!isl_int_is_zero(tab->mat->row[row][1]))
1691 if (tab->M && !isl_int_is_zero(tab->mat->row[row][2]))
1693 return isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
1694 tab->n_col - tab->n_dead) == -1;
1697 /* Add an equality that is known to be valid for the given tableau.
1699 struct isl_tab *isl_tab_add_valid_eq(struct isl_tab *tab, isl_int *eq)
1701 struct isl_tab_var *var;
1706 r = isl_tab_add_row(tab, eq);
1712 if (row_is_manifestly_zero(tab, r)) {
1714 isl_tab_mark_redundant(tab, r);
1718 if (isl_int_is_neg(tab->mat->row[r][1])) {
1719 isl_seq_neg(tab->mat->row[r] + 1, tab->mat->row[r] + 1,
1724 if (to_col(tab, var) < 0)
1727 isl_tab_kill_col(tab, var->index);
1735 static int add_zero_row(struct isl_tab *tab)
1740 r = isl_tab_allocate_con(tab);
1744 row = tab->mat->row[tab->con[r].index];
1745 isl_seq_clr(row + 1, 1 + tab->M + tab->n_col);
1746 isl_int_set_si(row[0], 1);
1751 /* Add equality "eq" and check if it conflicts with the
1752 * previously added constraints or if it is obviously redundant.
1754 struct isl_tab *isl_tab_add_eq(struct isl_tab *tab, isl_int *eq)
1756 struct isl_tab_undo *snap = NULL;
1757 struct isl_tab_var *var;
1764 isl_assert(tab->mat->ctx, !tab->M, goto error);
1767 snap = isl_tab_snap(tab);
1769 r = isl_tab_add_row(tab, eq);
1775 if (row_is_manifestly_zero(tab, row)) {
1777 if (isl_tab_rollback(tab, snap) < 0)
1785 tab->bset = isl_basic_set_add_ineq(tab->bset, eq);
1786 isl_tab_push(tab, isl_tab_undo_bset_ineq);
1787 isl_seq_neg(eq, eq, 1 + tab->n_var);
1788 tab->bset = isl_basic_set_add_ineq(tab->bset, eq);
1789 isl_seq_neg(eq, eq, 1 + tab->n_var);
1790 isl_tab_push(tab, isl_tab_undo_bset_ineq);
1793 if (add_zero_row(tab) < 0)
1797 sgn = isl_int_sgn(tab->mat->row[row][1]);
1800 isl_seq_neg(tab->mat->row[row] + 1, tab->mat->row[row] + 1,
1806 if (sgn < 0 && sign_of_max(tab, var) < 0)
1807 return isl_tab_mark_empty(tab);
1810 if (to_col(tab, var) < 0)
1813 isl_tab_kill_col(tab, var->index);
1821 struct isl_tab *isl_tab_from_basic_map(struct isl_basic_map *bmap)
1824 struct isl_tab *tab;
1828 tab = isl_tab_alloc(bmap->ctx,
1829 isl_basic_map_total_dim(bmap) + bmap->n_ineq + 1,
1830 isl_basic_map_total_dim(bmap), 0);
1833 tab->rational = ISL_F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
1834 if (ISL_F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
1835 return isl_tab_mark_empty(tab);
1836 for (i = 0; i < bmap->n_eq; ++i) {
1837 tab = add_eq(tab, bmap->eq[i]);
1841 for (i = 0; i < bmap->n_ineq; ++i) {
1842 tab = isl_tab_add_ineq(tab, bmap->ineq[i]);
1843 if (!tab || tab->empty)
1849 struct isl_tab *isl_tab_from_basic_set(struct isl_basic_set *bset)
1851 return isl_tab_from_basic_map((struct isl_basic_map *)bset);
1854 /* Construct a tableau corresponding to the recession cone of "bset".
1856 struct isl_tab *isl_tab_from_recession_cone(struct isl_basic_set *bset)
1860 struct isl_tab *tab;
1864 tab = isl_tab_alloc(bset->ctx, bset->n_eq + bset->n_ineq,
1865 isl_basic_set_total_dim(bset), 0);
1868 tab->rational = ISL_F_ISSET(bset, ISL_BASIC_SET_RATIONAL);
1871 for (i = 0; i < bset->n_eq; ++i) {
1872 isl_int_swap(bset->eq[i][0], cst);
1873 tab = add_eq(tab, bset->eq[i]);
1874 isl_int_swap(bset->eq[i][0], cst);
1878 for (i = 0; i < bset->n_ineq; ++i) {
1880 isl_int_swap(bset->ineq[i][0], cst);
1881 r = isl_tab_add_row(tab, bset->ineq[i]);
1882 isl_int_swap(bset->ineq[i][0], cst);
1885 tab->con[r].is_nonneg = 1;
1886 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
1897 /* Assuming "tab" is the tableau of a cone, check if the cone is
1898 * bounded, i.e., if it is empty or only contains the origin.
1900 int isl_tab_cone_is_bounded(struct isl_tab *tab)
1908 if (tab->n_dead == tab->n_col)
1912 for (i = tab->n_redundant; i < tab->n_row; ++i) {
1913 struct isl_tab_var *var;
1914 var = isl_tab_var_from_row(tab, i);
1915 if (!var->is_nonneg)
1917 if (sign_of_max(tab, var) != 0)
1919 close_row(tab, var);
1922 if (tab->n_dead == tab->n_col)
1924 if (i == tab->n_row)
1929 int isl_tab_sample_is_integer(struct isl_tab *tab)
1936 for (i = 0; i < tab->n_var; ++i) {
1938 if (!tab->var[i].is_row)
1940 row = tab->var[i].index;
1941 if (!isl_int_is_divisible_by(tab->mat->row[row][1],
1942 tab->mat->row[row][0]))
1948 static struct isl_vec *extract_integer_sample(struct isl_tab *tab)
1951 struct isl_vec *vec;
1953 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
1957 isl_int_set_si(vec->block.data[0], 1);
1958 for (i = 0; i < tab->n_var; ++i) {
1959 if (!tab->var[i].is_row)
1960 isl_int_set_si(vec->block.data[1 + i], 0);
1962 int row = tab->var[i].index;
1963 isl_int_divexact(vec->block.data[1 + i],
1964 tab->mat->row[row][1], tab->mat->row[row][0]);
1971 struct isl_vec *isl_tab_get_sample_value(struct isl_tab *tab)
1974 struct isl_vec *vec;
1980 vec = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_var);
1986 isl_int_set_si(vec->block.data[0], 1);
1987 for (i = 0; i < tab->n_var; ++i) {
1989 if (!tab->var[i].is_row) {
1990 isl_int_set_si(vec->block.data[1 + i], 0);
1993 row = tab->var[i].index;
1994 isl_int_gcd(m, vec->block.data[0], tab->mat->row[row][0]);
1995 isl_int_divexact(m, tab->mat->row[row][0], m);
1996 isl_seq_scale(vec->block.data, vec->block.data, m, 1 + i);
1997 isl_int_divexact(m, vec->block.data[0], tab->mat->row[row][0]);
1998 isl_int_mul(vec->block.data[1 + i], m, tab->mat->row[row][1]);
2000 vec = isl_vec_normalize(vec);
2006 /* Update "bmap" based on the results of the tableau "tab".
2007 * In particular, implicit equalities are made explicit, redundant constraints
2008 * are removed and if the sample value happens to be integer, it is stored
2009 * in "bmap" (unless "bmap" already had an integer sample).
2011 * The tableau is assumed to have been created from "bmap" using
2012 * isl_tab_from_basic_map.
2014 struct isl_basic_map *isl_basic_map_update_from_tab(struct isl_basic_map *bmap,
2015 struct isl_tab *tab)
2027 bmap = isl_basic_map_set_to_empty(bmap);
2029 for (i = bmap->n_ineq - 1; i >= 0; --i) {
2030 if (isl_tab_is_equality(tab, n_eq + i))
2031 isl_basic_map_inequality_to_equality(bmap, i);
2032 else if (isl_tab_is_redundant(tab, n_eq + i))
2033 isl_basic_map_drop_inequality(bmap, i);
2035 if (!tab->rational &&
2036 !bmap->sample && isl_tab_sample_is_integer(tab))
2037 bmap->sample = extract_integer_sample(tab);
2041 struct isl_basic_set *isl_basic_set_update_from_tab(struct isl_basic_set *bset,
2042 struct isl_tab *tab)
2044 return (struct isl_basic_set *)isl_basic_map_update_from_tab(
2045 (struct isl_basic_map *)bset, tab);
2048 /* Given a non-negative variable "var", add a new non-negative variable
2049 * that is the opposite of "var", ensuring that var can only attain the
2051 * If var = n/d is a row variable, then the new variable = -n/d.
2052 * If var is a column variables, then the new variable = -var.
2053 * If the new variable cannot attain non-negative values, then
2054 * the resulting tableau is empty.
2055 * Otherwise, we know the value will be zero and we close the row.
2057 static struct isl_tab *cut_to_hyperplane(struct isl_tab *tab,
2058 struct isl_tab_var *var)
2063 unsigned off = 2 + tab->M;
2067 isl_assert(tab->mat->ctx, !var->is_redundant, goto error);
2069 if (isl_tab_extend_cons(tab, 1) < 0)
2073 tab->con[r].index = tab->n_row;
2074 tab->con[r].is_row = 1;
2075 tab->con[r].is_nonneg = 0;
2076 tab->con[r].is_zero = 0;
2077 tab->con[r].is_redundant = 0;
2078 tab->con[r].frozen = 0;
2079 tab->con[r].negated = 0;
2080 tab->row_var[tab->n_row] = ~r;
2081 row = tab->mat->row[tab->n_row];
2084 isl_int_set(row[0], tab->mat->row[var->index][0]);
2085 isl_seq_neg(row + 1,
2086 tab->mat->row[var->index] + 1, 1 + tab->n_col);
2088 isl_int_set_si(row[0], 1);
2089 isl_seq_clr(row + 1, 1 + tab->n_col);
2090 isl_int_set_si(row[off + var->index], -1);
2095 isl_tab_push_var(tab, isl_tab_undo_allocate, &tab->con[r]);
2097 sgn = sign_of_max(tab, &tab->con[r]);
2099 return isl_tab_mark_empty(tab);
2100 tab->con[r].is_nonneg = 1;
2101 isl_tab_push_var(tab, isl_tab_undo_nonneg, &tab->con[r]);
2103 close_row(tab, &tab->con[r]);
2111 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2112 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2113 * by r' = r + 1 >= 0.
2114 * If r is a row variable, we simply increase the constant term by one
2115 * (taking into account the denominator).
2116 * If r is a column variable, then we need to modify each row that
2117 * refers to r = r' - 1 by substituting this equality, effectively
2118 * subtracting the coefficient of the column from the constant.
2120 struct isl_tab *isl_tab_relax(struct isl_tab *tab, int con)
2122 struct isl_tab_var *var;
2123 unsigned off = 2 + tab->M;
2128 var = &tab->con[con];
2130 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
2131 to_row(tab, var, 1);
2134 isl_int_add(tab->mat->row[var->index][1],
2135 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
2139 for (i = 0; i < tab->n_row; ++i) {
2140 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2142 isl_int_sub(tab->mat->row[i][1], tab->mat->row[i][1],
2143 tab->mat->row[i][off + var->index]);
2148 isl_tab_push_var(tab, isl_tab_undo_relax, var);
2153 struct isl_tab *isl_tab_select_facet(struct isl_tab *tab, int con)
2158 return cut_to_hyperplane(tab, &tab->con[con]);
2161 static int may_be_equality(struct isl_tab *tab, int row)
2163 unsigned off = 2 + tab->M;
2164 return (tab->rational ? isl_int_is_zero(tab->mat->row[row][1])
2165 : isl_int_lt(tab->mat->row[row][1],
2166 tab->mat->row[row][0])) &&
2167 isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
2168 tab->n_col - tab->n_dead) != -1;
2171 /* Check for (near) equalities among the constraints.
2172 * A constraint is an equality if it is non-negative and if
2173 * its maximal value is either
2174 * - zero (in case of rational tableaus), or
2175 * - strictly less than 1 (in case of integer tableaus)
2177 * We first mark all non-redundant and non-dead variables that
2178 * are not frozen and not obviously not an equality.
2179 * Then we iterate over all marked variables if they can attain
2180 * any values larger than zero or at least one.
2181 * If the maximal value is zero, we mark any column variables
2182 * that appear in the row as being zero and mark the row as being redundant.
2183 * Otherwise, if the maximal value is strictly less than one (and the
2184 * tableau is integer), then we restrict the value to being zero
2185 * by adding an opposite non-negative variable.
2187 struct isl_tab *isl_tab_detect_implicit_equalities(struct isl_tab *tab)
2196 if (tab->n_dead == tab->n_col)
2200 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2201 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
2202 var->marked = !var->frozen && var->is_nonneg &&
2203 may_be_equality(tab, i);
2207 for (i = tab->n_dead; i < tab->n_col; ++i) {
2208 struct isl_tab_var *var = var_from_col(tab, i);
2209 var->marked = !var->frozen && var->is_nonneg;
2214 struct isl_tab_var *var;
2215 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2216 var = isl_tab_var_from_row(tab, i);
2220 if (i == tab->n_row) {
2221 for (i = tab->n_dead; i < tab->n_col; ++i) {
2222 var = var_from_col(tab, i);
2226 if (i == tab->n_col)
2231 if (sign_of_max(tab, var) == 0)
2232 close_row(tab, var);
2233 else if (!tab->rational && !at_least_one(tab, var)) {
2234 tab = cut_to_hyperplane(tab, var);
2235 return isl_tab_detect_implicit_equalities(tab);
2237 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2238 var = isl_tab_var_from_row(tab, i);
2241 if (may_be_equality(tab, i))
2251 /* Check for (near) redundant constraints.
2252 * A constraint is redundant if it is non-negative and if
2253 * its minimal value (temporarily ignoring the non-negativity) is either
2254 * - zero (in case of rational tableaus), or
2255 * - strictly larger than -1 (in case of integer tableaus)
2257 * We first mark all non-redundant and non-dead variables that
2258 * are not frozen and not obviously negatively unbounded.
2259 * Then we iterate over all marked variables if they can attain
2260 * any values smaller than zero or at most negative one.
2261 * If not, we mark the row as being redundant (assuming it hasn't
2262 * been detected as being obviously redundant in the mean time).
2264 struct isl_tab *isl_tab_detect_redundant(struct isl_tab *tab)
2273 if (tab->n_redundant == tab->n_row)
2277 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2278 struct isl_tab_var *var = isl_tab_var_from_row(tab, i);
2279 var->marked = !var->frozen && var->is_nonneg;
2283 for (i = tab->n_dead; i < tab->n_col; ++i) {
2284 struct isl_tab_var *var = var_from_col(tab, i);
2285 var->marked = !var->frozen && var->is_nonneg &&
2286 !min_is_manifestly_unbounded(tab, var);
2291 struct isl_tab_var *var;
2292 for (i = tab->n_redundant; i < tab->n_row; ++i) {
2293 var = isl_tab_var_from_row(tab, i);
2297 if (i == tab->n_row) {
2298 for (i = tab->n_dead; i < tab->n_col; ++i) {
2299 var = var_from_col(tab, i);
2303 if (i == tab->n_col)
2308 if ((tab->rational ? (sign_of_min(tab, var) >= 0)
2309 : !isl_tab_min_at_most_neg_one(tab, var)) &&
2311 isl_tab_mark_redundant(tab, var->index);
2312 for (i = tab->n_dead; i < tab->n_col; ++i) {
2313 var = var_from_col(tab, i);
2316 if (!min_is_manifestly_unbounded(tab, var))
2326 int isl_tab_is_equality(struct isl_tab *tab, int con)
2333 if (tab->con[con].is_zero)
2335 if (tab->con[con].is_redundant)
2337 if (!tab->con[con].is_row)
2338 return tab->con[con].index < tab->n_dead;
2340 row = tab->con[con].index;
2343 return isl_int_is_zero(tab->mat->row[row][1]) &&
2344 isl_seq_first_non_zero(tab->mat->row[row] + 2 + tab->n_dead,
2345 tab->n_col - tab->n_dead) == -1;
2348 /* Return the minimial value of the affine expression "f" with denominator
2349 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
2350 * the expression cannot attain arbitrarily small values.
2351 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
2352 * The return value reflects the nature of the result (empty, unbounded,
2353 * minmimal value returned in *opt).
2355 enum isl_lp_result isl_tab_min(struct isl_tab *tab,
2356 isl_int *f, isl_int denom, isl_int *opt, isl_int *opt_denom,
2360 enum isl_lp_result res = isl_lp_ok;
2361 struct isl_tab_var *var;
2362 struct isl_tab_undo *snap;
2365 return isl_lp_empty;
2367 snap = isl_tab_snap(tab);
2368 r = isl_tab_add_row(tab, f);
2370 return isl_lp_error;
2372 isl_int_mul(tab->mat->row[var->index][0],
2373 tab->mat->row[var->index][0], denom);
2376 find_pivot(tab, var, var, -1, &row, &col);
2377 if (row == var->index) {
2378 res = isl_lp_unbounded;
2383 isl_tab_pivot(tab, row, col);
2385 if (ISL_FL_ISSET(flags, ISL_TAB_SAVE_DUAL)) {
2388 isl_vec_free(tab->dual);
2389 tab->dual = isl_vec_alloc(tab->mat->ctx, 1 + tab->n_con);
2391 return isl_lp_error;
2392 isl_int_set(tab->dual->el[0], tab->mat->row[var->index][0]);
2393 for (i = 0; i < tab->n_con; ++i) {
2395 if (tab->con[i].is_row) {
2396 isl_int_set_si(tab->dual->el[1 + i], 0);
2399 pos = 2 + tab->M + tab->con[i].index;
2400 if (tab->con[i].negated)
2401 isl_int_neg(tab->dual->el[1 + i],
2402 tab->mat->row[var->index][pos]);
2404 isl_int_set(tab->dual->el[1 + i],
2405 tab->mat->row[var->index][pos]);
2408 if (opt && res == isl_lp_ok) {
2410 isl_int_set(*opt, tab->mat->row[var->index][1]);
2411 isl_int_set(*opt_denom, tab->mat->row[var->index][0]);
2413 isl_int_cdiv_q(*opt, tab->mat->row[var->index][1],
2414 tab->mat->row[var->index][0]);
2416 if (isl_tab_rollback(tab, snap) < 0)
2417 return isl_lp_error;
2421 int isl_tab_is_redundant(struct isl_tab *tab, int con)
2425 if (tab->con[con].is_zero)
2427 if (tab->con[con].is_redundant)
2429 return tab->con[con].is_row && tab->con[con].index < tab->n_redundant;
2432 /* Take a snapshot of the tableau that can be restored by s call to
2435 struct isl_tab_undo *isl_tab_snap(struct isl_tab *tab)
2443 /* Undo the operation performed by isl_tab_relax.
2445 static void unrelax(struct isl_tab *tab, struct isl_tab_var *var)
2447 unsigned off = 2 + tab->M;
2449 if (!var->is_row && !max_is_manifestly_unbounded(tab, var))
2450 to_row(tab, var, 1);
2453 isl_int_sub(tab->mat->row[var->index][1],
2454 tab->mat->row[var->index][1], tab->mat->row[var->index][0]);
2458 for (i = 0; i < tab->n_row; ++i) {
2459 if (isl_int_is_zero(tab->mat->row[i][off + var->index]))
2461 isl_int_add(tab->mat->row[i][1], tab->mat->row[i][1],
2462 tab->mat->row[i][off + var->index]);
2468 static void perform_undo_var(struct isl_tab *tab, struct isl_tab_undo *undo)
2470 struct isl_tab_var *var = var_from_index(tab, undo->u.var_index);
2471 switch(undo->type) {
2472 case isl_tab_undo_nonneg:
2475 case isl_tab_undo_redundant:
2476 var->is_redundant = 0;
2479 case isl_tab_undo_zero:
2484 case isl_tab_undo_allocate:
2485 if (undo->u.var_index >= 0) {
2486 isl_assert(tab->mat->ctx, !var->is_row, return);
2487 drop_col(tab, var->index);
2491 if (!max_is_manifestly_unbounded(tab, var))
2492 to_row(tab, var, 1);
2493 else if (!min_is_manifestly_unbounded(tab, var))
2494 to_row(tab, var, -1);
2496 to_row(tab, var, 0);
2498 drop_row(tab, var->index);
2500 case isl_tab_undo_relax:
2506 /* Restore the tableau to the state where the basic variables
2507 * are those in "col_var".
2508 * We first construct a list of variables that are currently in
2509 * the basis, but shouldn't. Then we iterate over all variables
2510 * that should be in the basis and for each one that is currently
2511 * not in the basis, we exchange it with one of the elements of the
2512 * list constructed before.
2513 * We can always find an appropriate variable to pivot with because
2514 * the current basis is mapped to the old basis by a non-singular
2515 * matrix and so we can never end up with a zero row.
2517 static int restore_basis(struct isl_tab *tab, int *col_var)
2521 int *extra = NULL; /* current columns that contain bad stuff */
2522 unsigned off = 2 + tab->M;
2524 extra = isl_alloc_array(tab->mat->ctx, int, tab->n_col);
2527 for (i = 0; i < tab->n_col; ++i) {
2528 for (j = 0; j < tab->n_col; ++j)
2529 if (tab->col_var[i] == col_var[j])
2533 extra[n_extra++] = i;
2535 for (i = 0; i < tab->n_col && n_extra > 0; ++i) {
2536 struct isl_tab_var *var;
2539 for (j = 0; j < tab->n_col; ++j)
2540 if (col_var[i] == tab->col_var[j])
2544 var = var_from_index(tab, col_var[i]);
2546 for (j = 0; j < n_extra; ++j)
2547 if (!isl_int_is_zero(tab->mat->row[row][off+extra[j]]))
2549 isl_assert(tab->mat->ctx, j < n_extra, goto error);
2550 isl_tab_pivot(tab, row, extra[j]);
2551 extra[j] = extra[--n_extra];
2563 /* Remove all samples with index n or greater, i.e., those samples
2564 * that were added since we saved this number of samples in
2565 * isl_tab_save_samples.
2567 static int drop_samples_since(struct isl_tab *tab, int n)
2571 for (i = tab->n_sample - 1; i >= 0 && tab->n_sample > n; --i) {
2572 if (tab->sample_index[i] < n)
2575 if (i != tab->n_sample - 1) {
2576 int t = tab->sample_index[tab->n_sample-1];
2577 tab->sample_index[tab->n_sample-1] = tab->sample_index[i];
2578 tab->sample_index[i] = t;
2579 isl_mat_swap_rows(tab->samples, tab->n_sample-1, i);
2585 static int perform_undo(struct isl_tab *tab, struct isl_tab_undo *undo)
2587 switch (undo->type) {
2588 case isl_tab_undo_empty:
2591 case isl_tab_undo_nonneg:
2592 case isl_tab_undo_redundant:
2593 case isl_tab_undo_zero:
2594 case isl_tab_undo_allocate:
2595 case isl_tab_undo_relax:
2596 perform_undo_var(tab, undo);
2598 case isl_tab_undo_bset_eq:
2599 isl_basic_set_free_equality(tab->bset, 1);
2601 case isl_tab_undo_bset_ineq:
2602 isl_basic_set_free_inequality(tab->bset, 1);
2604 case isl_tab_undo_bset_div:
2605 isl_basic_set_free_div(tab->bset, 1);
2607 tab->samples->n_col--;
2609 case isl_tab_undo_saved_basis:
2610 if (restore_basis(tab, undo->u.col_var) < 0)
2613 case isl_tab_undo_drop_sample:
2616 case isl_tab_undo_saved_samples:
2617 drop_samples_since(tab, undo->u.n);
2620 isl_assert(tab->mat->ctx, 0, return -1);
2625 /* Return the tableau to the state it was in when the snapshot "snap"
2628 int isl_tab_rollback(struct isl_tab *tab, struct isl_tab_undo *snap)
2630 struct isl_tab_undo *undo, *next;
2636 for (undo = tab->top; undo && undo != &tab->bottom; undo = next) {
2640 if (perform_undo(tab, undo) < 0) {
2654 /* The given row "row" represents an inequality violated by all
2655 * points in the tableau. Check for some special cases of such
2656 * separating constraints.
2657 * In particular, if the row has been reduced to the constant -1,
2658 * then we know the inequality is adjacent (but opposite) to
2659 * an equality in the tableau.
2660 * If the row has been reduced to r = -1 -r', with r' an inequality
2661 * of the tableau, then the inequality is adjacent (but opposite)
2662 * to the inequality r'.
2664 static enum isl_ineq_type separation_type(struct isl_tab *tab, unsigned row)
2667 unsigned off = 2 + tab->M;
2670 return isl_ineq_separate;
2672 if (!isl_int_is_one(tab->mat->row[row][0]))
2673 return isl_ineq_separate;
2674 if (!isl_int_is_negone(tab->mat->row[row][1]))
2675 return isl_ineq_separate;
2677 pos = isl_seq_first_non_zero(tab->mat->row[row] + off + tab->n_dead,
2678 tab->n_col - tab->n_dead);
2680 return isl_ineq_adj_eq;
2682 if (!isl_int_is_negone(tab->mat->row[row][off + tab->n_dead + pos]))
2683 return isl_ineq_separate;
2685 pos = isl_seq_first_non_zero(
2686 tab->mat->row[row] + off + tab->n_dead + pos + 1,
2687 tab->n_col - tab->n_dead - pos - 1);
2689 return pos == -1 ? isl_ineq_adj_ineq : isl_ineq_separate;
2692 /* Check the effect of inequality "ineq" on the tableau "tab".
2694 * isl_ineq_redundant: satisfied by all points in the tableau
2695 * isl_ineq_separate: satisfied by no point in the tableau
2696 * isl_ineq_cut: satisfied by some by not all points
2697 * isl_ineq_adj_eq: adjacent to an equality
2698 * isl_ineq_adj_ineq: adjacent to an inequality.
2700 enum isl_ineq_type isl_tab_ineq_type(struct isl_tab *tab, isl_int *ineq)
2702 enum isl_ineq_type type = isl_ineq_error;
2703 struct isl_tab_undo *snap = NULL;
2708 return isl_ineq_error;
2710 if (isl_tab_extend_cons(tab, 1) < 0)
2711 return isl_ineq_error;
2713 snap = isl_tab_snap(tab);
2715 con = isl_tab_add_row(tab, ineq);
2719 row = tab->con[con].index;
2720 if (isl_tab_row_is_redundant(tab, row))
2721 type = isl_ineq_redundant;
2722 else if (isl_int_is_neg(tab->mat->row[row][1]) &&
2724 isl_int_abs_ge(tab->mat->row[row][1],
2725 tab->mat->row[row][0]))) {
2726 if (at_least_zero(tab, &tab->con[con]))
2727 type = isl_ineq_cut;
2729 type = separation_type(tab, row);
2730 } else if (tab->rational ? (sign_of_min(tab, &tab->con[con]) < 0)
2731 : isl_tab_min_at_most_neg_one(tab, &tab->con[con]))
2732 type = isl_ineq_cut;
2734 type = isl_ineq_redundant;
2736 if (isl_tab_rollback(tab, snap))
2737 return isl_ineq_error;
2740 isl_tab_rollback(tab, snap);
2741 return isl_ineq_error;
2744 void isl_tab_dump(struct isl_tab *tab, FILE *out, int indent)
2750 fprintf(out, "%*snull tab\n", indent, "");
2753 fprintf(out, "%*sn_redundant: %d, n_dead: %d", indent, "",
2754 tab->n_redundant, tab->n_dead);
2756 fprintf(out, ", rational");
2758 fprintf(out, ", empty");
2760 fprintf(out, "%*s[", indent, "");
2761 for (i = 0; i < tab->n_var; ++i) {
2763 fprintf(out, (i == tab->n_param ||
2764 i == tab->n_var - tab->n_div) ? "; "
2766 fprintf(out, "%c%d%s", tab->var[i].is_row ? 'r' : 'c',
2768 tab->var[i].is_zero ? " [=0]" :
2769 tab->var[i].is_redundant ? " [R]" : "");
2771 fprintf(out, "]\n");
2772 fprintf(out, "%*s[", indent, "");
2773 for (i = 0; i < tab->n_con; ++i) {
2776 fprintf(out, "%c%d%s", tab->con[i].is_row ? 'r' : 'c',
2778 tab->con[i].is_zero ? " [=0]" :
2779 tab->con[i].is_redundant ? " [R]" : "");
2781 fprintf(out, "]\n");
2782 fprintf(out, "%*s[", indent, "");
2783 for (i = 0; i < tab->n_row; ++i) {
2784 const char *sign = "";
2787 if (tab->row_sign) {
2788 if (tab->row_sign[i] == isl_tab_row_unknown)
2790 else if (tab->row_sign[i] == isl_tab_row_neg)
2792 else if (tab->row_sign[i] == isl_tab_row_pos)
2797 fprintf(out, "r%d: %d%s%s", i, tab->row_var[i],
2798 isl_tab_var_from_row(tab, i)->is_nonneg ? " [>=0]" : "", sign);
2800 fprintf(out, "]\n");
2801 fprintf(out, "%*s[", indent, "");
2802 for (i = 0; i < tab->n_col; ++i) {
2805 fprintf(out, "c%d: %d%s", i, tab->col_var[i],
2806 var_from_col(tab, i)->is_nonneg ? " [>=0]" : "");
2808 fprintf(out, "]\n");
2809 r = tab->mat->n_row;
2810 tab->mat->n_row = tab->n_row;
2811 c = tab->mat->n_col;
2812 tab->mat->n_col = 2 + tab->M + tab->n_col;
2813 isl_mat_dump(tab->mat, out, indent);
2814 tab->mat->n_row = r;
2815 tab->mat->n_col = c;
2817 isl_basic_set_dump(tab->bset, out, indent);