2 #include "isl_map_private.h"
6 * The implementation of tableaus in this file was inspired by Section 8
7 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
8 * prover for program checking".
11 struct isl_tab
*isl_tab_alloc(struct isl_ctx
*ctx
,
12 unsigned n_row
, unsigned n_var
, unsigned M
)
18 tab
= isl_calloc_type(ctx
, struct isl_tab
);
21 tab
->mat
= isl_mat_alloc(ctx
, n_row
, off
+ n_var
);
24 tab
->var
= isl_alloc_array(ctx
, struct isl_tab_var
, n_var
);
27 tab
->con
= isl_alloc_array(ctx
, struct isl_tab_var
, n_row
);
30 tab
->col_var
= isl_alloc_array(ctx
, int, n_var
);
33 tab
->row_var
= isl_alloc_array(ctx
, int, n_row
);
36 for (i
= 0; i
< n_var
; ++i
) {
37 tab
->var
[i
].index
= i
;
38 tab
->var
[i
].is_row
= 0;
39 tab
->var
[i
].is_nonneg
= 0;
40 tab
->var
[i
].is_zero
= 0;
41 tab
->var
[i
].is_redundant
= 0;
42 tab
->var
[i
].frozen
= 0;
43 tab
->var
[i
].negated
= 0;
62 tab
->bottom
.type
= isl_tab_undo_bottom
;
63 tab
->bottom
.next
= NULL
;
64 tab
->top
= &tab
->bottom
;
71 int isl_tab_extend_cons(struct isl_tab
*tab
, unsigned n_new
)
73 unsigned off
= 2 + tab
->M
;
74 if (tab
->max_con
< tab
->n_con
+ n_new
) {
75 struct isl_tab_var
*con
;
77 con
= isl_realloc_array(tab
->mat
->ctx
, tab
->con
,
78 struct isl_tab_var
, tab
->max_con
+ n_new
);
82 tab
->max_con
+= n_new
;
84 if (tab
->mat
->n_row
< tab
->n_row
+ n_new
) {
87 tab
->mat
= isl_mat_extend(tab
->mat
,
88 tab
->n_row
+ n_new
, off
+ tab
->n_col
);
91 row_var
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_var
,
92 int, tab
->mat
->n_row
);
95 tab
->row_var
= row_var
;
97 enum isl_tab_row_sign
*s
;
98 s
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_sign
,
99 enum isl_tab_row_sign
, tab
->mat
->n_row
);
108 /* Make room for at least n_new extra variables.
109 * Return -1 if anything went wrong.
111 int isl_tab_extend_vars(struct isl_tab
*tab
, unsigned n_new
)
113 struct isl_tab_var
*var
;
114 unsigned off
= 2 + tab
->M
;
116 if (tab
->max_var
< tab
->n_var
+ n_new
) {
117 var
= isl_realloc_array(tab
->mat
->ctx
, tab
->var
,
118 struct isl_tab_var
, tab
->n_var
+ n_new
);
122 tab
->max_var
+= n_new
;
125 if (tab
->mat
->n_col
< off
+ tab
->n_col
+ n_new
) {
128 tab
->mat
= isl_mat_extend(tab
->mat
,
129 tab
->mat
->n_row
, off
+ tab
->n_col
+ n_new
);
132 p
= isl_realloc_array(tab
->mat
->ctx
, tab
->col_var
,
133 int, tab
->mat
->n_col
);
142 struct isl_tab
*isl_tab_extend(struct isl_tab
*tab
, unsigned n_new
)
144 if (isl_tab_extend_cons(tab
, n_new
) >= 0)
151 static void free_undo(struct isl_tab
*tab
)
153 struct isl_tab_undo
*undo
, *next
;
155 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
162 void isl_tab_free(struct isl_tab
*tab
)
167 isl_mat_free(tab
->mat
);
168 isl_vec_free(tab
->dual
);
169 isl_basic_set_free(tab
->bset
);
175 isl_mat_free(tab
->samples
);
179 struct isl_tab
*isl_tab_dup(struct isl_tab
*tab
)
187 dup
= isl_calloc_type(tab
->ctx
, struct isl_tab
);
190 dup
->mat
= isl_mat_dup(tab
->mat
);
193 dup
->var
= isl_alloc_array(tab
->ctx
, struct isl_tab_var
, tab
->max_var
);
196 for (i
= 0; i
< tab
->n_var
; ++i
)
197 dup
->var
[i
] = tab
->var
[i
];
198 dup
->con
= isl_alloc_array(tab
->ctx
, struct isl_tab_var
, tab
->max_con
);
201 for (i
= 0; i
< tab
->n_con
; ++i
)
202 dup
->con
[i
] = tab
->con
[i
];
203 dup
->col_var
= isl_alloc_array(tab
->ctx
, int, tab
->mat
->n_col
);
206 for (i
= 0; i
< tab
->n_var
; ++i
)
207 dup
->col_var
[i
] = tab
->col_var
[i
];
208 dup
->row_var
= isl_alloc_array(tab
->ctx
, int, tab
->mat
->n_row
);
211 for (i
= 0; i
< tab
->n_row
; ++i
)
212 dup
->row_var
[i
] = tab
->row_var
[i
];
214 dup
->row_sign
= isl_alloc_array(tab
->ctx
, enum isl_tab_row_sign
,
218 for (i
= 0; i
< tab
->n_row
; ++i
)
219 dup
->row_sign
[i
] = tab
->row_sign
[i
];
222 dup
->samples
= isl_mat_dup(tab
->samples
);
225 dup
->n_sample
= tab
->n_sample
;
226 dup
->n_outside
= tab
->n_outside
;
228 dup
->n_row
= tab
->n_row
;
229 dup
->n_con
= tab
->n_con
;
230 dup
->n_eq
= tab
->n_eq
;
231 dup
->max_con
= tab
->max_con
;
232 dup
->n_col
= tab
->n_col
;
233 dup
->n_var
= tab
->n_var
;
234 dup
->max_var
= tab
->max_var
;
235 dup
->n_param
= tab
->n_param
;
236 dup
->n_div
= tab
->n_div
;
237 dup
->n_dead
= tab
->n_dead
;
238 dup
->n_redundant
= tab
->n_redundant
;
239 dup
->rational
= tab
->rational
;
240 dup
->empty
= tab
->empty
;
244 dup
->bottom
.type
= isl_tab_undo_bottom
;
245 dup
->bottom
.next
= NULL
;
246 dup
->top
= &dup
->bottom
;
253 static struct isl_tab_var
*var_from_index(struct isl_tab
*tab
, int i
)
258 return &tab
->con
[~i
];
261 struct isl_tab_var
*isl_tab_var_from_row(struct isl_tab
*tab
, int i
)
263 return var_from_index(tab
, tab
->row_var
[i
]);
266 static struct isl_tab_var
*var_from_col(struct isl_tab
*tab
, int i
)
268 return var_from_index(tab
, tab
->col_var
[i
]);
271 /* Check if there are any upper bounds on column variable "var",
272 * i.e., non-negative rows where var appears with a negative coefficient.
273 * Return 1 if there are no such bounds.
275 static int max_is_manifestly_unbounded(struct isl_tab
*tab
,
276 struct isl_tab_var
*var
)
279 unsigned off
= 2 + tab
->M
;
283 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
284 if (!isl_int_is_neg(tab
->mat
->row
[i
][off
+ var
->index
]))
286 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
292 /* Check if there are any lower bounds on column variable "var",
293 * i.e., non-negative rows where var appears with a positive coefficient.
294 * Return 1 if there are no such bounds.
296 static int min_is_manifestly_unbounded(struct isl_tab
*tab
,
297 struct isl_tab_var
*var
)
300 unsigned off
= 2 + tab
->M
;
304 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
305 if (!isl_int_is_pos(tab
->mat
->row
[i
][off
+ var
->index
]))
307 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
313 static int row_cmp(struct isl_tab
*tab
, int r1
, int r2
, int c
, isl_int t
)
315 unsigned off
= 2 + tab
->M
;
319 isl_int_mul(t
, tab
->mat
->row
[r1
][2], tab
->mat
->row
[r2
][off
+c
]);
320 isl_int_submul(t
, tab
->mat
->row
[r2
][2], tab
->mat
->row
[r1
][off
+c
]);
325 isl_int_mul(t
, tab
->mat
->row
[r1
][1], tab
->mat
->row
[r2
][off
+ c
]);
326 isl_int_submul(t
, tab
->mat
->row
[r2
][1], tab
->mat
->row
[r1
][off
+ c
]);
327 return isl_int_sgn(t
);
330 /* Given the index of a column "c", return the index of a row
331 * that can be used to pivot the column in, with either an increase
332 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
333 * If "var" is not NULL, then the row returned will be different from
334 * the one associated with "var".
336 * Each row in the tableau is of the form
338 * x_r = a_r0 + \sum_i a_ri x_i
340 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
341 * impose any limit on the increase or decrease in the value of x_c
342 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
343 * for the row with the smallest (most stringent) such bound.
344 * Note that the common denominator of each row drops out of the fraction.
345 * To check if row j has a smaller bound than row r, i.e.,
346 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
347 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
348 * where -sign(a_jc) is equal to "sgn".
350 static int pivot_row(struct isl_tab
*tab
,
351 struct isl_tab_var
*var
, int sgn
, int c
)
355 unsigned off
= 2 + tab
->M
;
359 for (j
= tab
->n_redundant
; j
< tab
->n_row
; ++j
) {
360 if (var
&& j
== var
->index
)
362 if (!isl_tab_var_from_row(tab
, j
)->is_nonneg
)
364 if (sgn
* isl_int_sgn(tab
->mat
->row
[j
][off
+ c
]) >= 0)
370 tsgn
= sgn
* row_cmp(tab
, r
, j
, c
, t
);
371 if (tsgn
< 0 || (tsgn
== 0 &&
372 tab
->row_var
[j
] < tab
->row_var
[r
]))
379 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
380 * (sgn < 0) the value of row variable var.
381 * If not NULL, then skip_var is a row variable that should be ignored
382 * while looking for a pivot row. It is usually equal to var.
384 * As the given row in the tableau is of the form
386 * x_r = a_r0 + \sum_i a_ri x_i
388 * we need to find a column such that the sign of a_ri is equal to "sgn"
389 * (such that an increase in x_i will have the desired effect) or a
390 * column with a variable that may attain negative values.
391 * If a_ri is positive, then we need to move x_i in the same direction
392 * to obtain the desired effect. Otherwise, x_i has to move in the
393 * opposite direction.
395 static void find_pivot(struct isl_tab
*tab
,
396 struct isl_tab_var
*var
, struct isl_tab_var
*skip_var
,
397 int sgn
, int *row
, int *col
)
404 isl_assert(tab
->mat
->ctx
, var
->is_row
, return);
405 tr
= tab
->mat
->row
[var
->index
] + 2 + tab
->M
;
408 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
409 if (isl_int_is_zero(tr
[j
]))
411 if (isl_int_sgn(tr
[j
]) != sgn
&&
412 var_from_col(tab
, j
)->is_nonneg
)
414 if (c
< 0 || tab
->col_var
[j
] < tab
->col_var
[c
])
420 sgn
*= isl_int_sgn(tr
[c
]);
421 r
= pivot_row(tab
, skip_var
, sgn
, c
);
422 *row
= r
< 0 ? var
->index
: r
;
426 /* Return 1 if row "row" represents an obviously redundant inequality.
428 * - it represents an inequality or a variable
429 * - that is the sum of a non-negative sample value and a positive
430 * combination of zero or more non-negative variables.
432 int isl_tab_row_is_redundant(struct isl_tab
*tab
, int row
)
435 unsigned off
= 2 + tab
->M
;
437 if (tab
->row_var
[row
] < 0 && !isl_tab_var_from_row(tab
, row
)->is_nonneg
)
440 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
442 if (tab
->M
&& isl_int_is_neg(tab
->mat
->row
[row
][2]))
445 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
446 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ i
]))
448 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ i
]))
450 if (!var_from_col(tab
, i
)->is_nonneg
)
456 static void swap_rows(struct isl_tab
*tab
, int row1
, int row2
)
459 t
= tab
->row_var
[row1
];
460 tab
->row_var
[row1
] = tab
->row_var
[row2
];
461 tab
->row_var
[row2
] = t
;
462 isl_tab_var_from_row(tab
, row1
)->index
= row1
;
463 isl_tab_var_from_row(tab
, row2
)->index
= row2
;
464 tab
->mat
= isl_mat_swap_rows(tab
->mat
, row1
, row2
);
468 t
= tab
->row_sign
[row1
];
469 tab
->row_sign
[row1
] = tab
->row_sign
[row2
];
470 tab
->row_sign
[row2
] = t
;
473 static void push_union(struct isl_tab
*tab
,
474 enum isl_tab_undo_type type
, union isl_tab_undo_val u
)
476 struct isl_tab_undo
*undo
;
481 undo
= isl_alloc_type(tab
->mat
->ctx
, struct isl_tab_undo
);
489 undo
->next
= tab
->top
;
493 void isl_tab_push_var(struct isl_tab
*tab
,
494 enum isl_tab_undo_type type
, struct isl_tab_var
*var
)
496 union isl_tab_undo_val u
;
498 u
.var_index
= tab
->row_var
[var
->index
];
500 u
.var_index
= tab
->col_var
[var
->index
];
501 push_union(tab
, type
, u
);
504 void isl_tab_push(struct isl_tab
*tab
, enum isl_tab_undo_type type
)
506 union isl_tab_undo_val u
= { 0 };
507 push_union(tab
, type
, u
);
510 /* Push a record on the undo stack describing the current basic
511 * variables, so that the this state can be restored during rollback.
513 void isl_tab_push_basis(struct isl_tab
*tab
)
516 union isl_tab_undo_val u
;
518 u
.col_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
524 for (i
= 0; i
< tab
->n_col
; ++i
)
525 u
.col_var
[i
] = tab
->col_var
[i
];
526 push_union(tab
, isl_tab_undo_saved_basis
, u
);
529 /* Mark row with index "row" as being redundant.
530 * If we may need to undo the operation or if the row represents
531 * a variable of the original problem, the row is kept,
532 * but no longer considered when looking for a pivot row.
533 * Otherwise, the row is simply removed.
535 * The row may be interchanged with some other row. If it
536 * is interchanged with a later row, return 1. Otherwise return 0.
537 * If the rows are checked in order in the calling function,
538 * then a return value of 1 means that the row with the given
539 * row number may now contain a different row that hasn't been checked yet.
541 int isl_tab_mark_redundant(struct isl_tab
*tab
, int row
)
543 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, row
);
544 var
->is_redundant
= 1;
545 isl_assert(tab
->mat
->ctx
, row
>= tab
->n_redundant
, return);
546 if (tab
->need_undo
|| tab
->row_var
[row
] >= 0) {
547 if (tab
->row_var
[row
] >= 0 && !var
->is_nonneg
) {
549 isl_tab_push_var(tab
, isl_tab_undo_nonneg
, var
);
551 if (row
!= tab
->n_redundant
)
552 swap_rows(tab
, row
, tab
->n_redundant
);
553 isl_tab_push_var(tab
, isl_tab_undo_redundant
, var
);
557 if (row
!= tab
->n_row
- 1)
558 swap_rows(tab
, row
, tab
->n_row
- 1);
559 isl_tab_var_from_row(tab
, tab
->n_row
- 1)->index
= -1;
565 struct isl_tab
*isl_tab_mark_empty(struct isl_tab
*tab
)
567 if (!tab
->empty
&& tab
->need_undo
)
568 isl_tab_push(tab
, isl_tab_undo_empty
);
573 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
574 * the original sign of the pivot element.
575 * We only keep track of row signs during PILP solving and in this case
576 * we only pivot a row with negative sign (meaning the value is always
577 * non-positive) using a positive pivot element.
579 * For each row j, the new value of the parametric constant is equal to
581 * a_j0 - a_jc a_r0/a_rc
583 * where a_j0 is the original parametric constant, a_rc is the pivot element,
584 * a_r0 is the parametric constant of the pivot row and a_jc is the
585 * pivot column entry of the row j.
586 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
587 * remains the same if a_jc has the same sign as the row j or if
588 * a_jc is zero. In all other cases, we reset the sign to "unknown".
590 static void update_row_sign(struct isl_tab
*tab
, int row
, int col
, int row_sgn
)
593 struct isl_mat
*mat
= tab
->mat
;
594 unsigned off
= 2 + tab
->M
;
599 if (tab
->row_sign
[row
] == 0)
601 isl_assert(mat
->ctx
, row_sgn
> 0, return);
602 isl_assert(mat
->ctx
, tab
->row_sign
[row
] == isl_tab_row_neg
, return);
603 tab
->row_sign
[row
] = isl_tab_row_pos
;
604 for (i
= 0; i
< tab
->n_row
; ++i
) {
608 s
= isl_int_sgn(mat
->row
[i
][off
+ col
]);
611 if (!tab
->row_sign
[i
])
613 if (s
< 0 && tab
->row_sign
[i
] == isl_tab_row_neg
)
615 if (s
> 0 && tab
->row_sign
[i
] == isl_tab_row_pos
)
617 tab
->row_sign
[i
] = isl_tab_row_unknown
;
621 /* Given a row number "row" and a column number "col", pivot the tableau
622 * such that the associated variables are interchanged.
623 * The given row in the tableau expresses
625 * x_r = a_r0 + \sum_i a_ri x_i
629 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
631 * Substituting this equality into the other rows
633 * x_j = a_j0 + \sum_i a_ji x_i
635 * with a_jc \ne 0, we obtain
637 * 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
644 * where i is any other column and j is any other row,
645 * is therefore transformed into
647 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
648 * 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)
650 * The transformation is performed along the following steps
655 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
658 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
659 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
661 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
662 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
664 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
665 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
667 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
668 * 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)
671 void isl_tab_pivot(struct isl_tab
*tab
, int row
, int col
)
676 struct isl_mat
*mat
= tab
->mat
;
677 struct isl_tab_var
*var
;
678 unsigned off
= 2 + tab
->M
;
680 isl_int_swap(mat
->row
[row
][0], mat
->row
[row
][off
+ col
]);
681 sgn
= isl_int_sgn(mat
->row
[row
][0]);
683 isl_int_neg(mat
->row
[row
][0], mat
->row
[row
][0]);
684 isl_int_neg(mat
->row
[row
][off
+ col
], mat
->row
[row
][off
+ col
]);
686 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
687 if (j
== off
- 1 + col
)
689 isl_int_neg(mat
->row
[row
][1 + j
], mat
->row
[row
][1 + j
]);
691 if (!isl_int_is_one(mat
->row
[row
][0]))
692 isl_seq_normalize(mat
->row
[row
], off
+ tab
->n_col
);
693 for (i
= 0; i
< tab
->n_row
; ++i
) {
696 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
698 isl_int_mul(mat
->row
[i
][0], mat
->row
[i
][0], mat
->row
[row
][0]);
699 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
700 if (j
== off
- 1 + col
)
702 isl_int_mul(mat
->row
[i
][1 + j
],
703 mat
->row
[i
][1 + j
], mat
->row
[row
][0]);
704 isl_int_addmul(mat
->row
[i
][1 + j
],
705 mat
->row
[i
][off
+ col
], mat
->row
[row
][1 + j
]);
707 isl_int_mul(mat
->row
[i
][off
+ col
],
708 mat
->row
[i
][off
+ col
], mat
->row
[row
][off
+ col
]);
709 if (!isl_int_is_one(mat
->row
[i
][0]))
710 isl_seq_normalize(mat
->row
[i
], off
+ tab
->n_col
);
712 t
= tab
->row_var
[row
];
713 tab
->row_var
[row
] = tab
->col_var
[col
];
714 tab
->col_var
[col
] = t
;
715 var
= isl_tab_var_from_row(tab
, row
);
718 var
= var_from_col(tab
, col
);
721 update_row_sign(tab
, row
, col
, sgn
);
724 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
725 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
727 if (!isl_tab_var_from_row(tab
, i
)->frozen
&&
728 isl_tab_row_is_redundant(tab
, i
))
729 if (isl_tab_mark_redundant(tab
, i
))
734 /* If "var" represents a column variable, then pivot is up (sgn > 0)
735 * or down (sgn < 0) to a row. The variable is assumed not to be
736 * unbounded in the specified direction.
737 * If sgn = 0, then the variable is unbounded in both directions,
738 * and we pivot with any row we can find.
740 static void to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
)
743 unsigned off
= 2 + tab
->M
;
749 for (r
= tab
->n_redundant
; r
< tab
->n_row
; ++r
)
750 if (!isl_int_is_zero(tab
->mat
->row
[r
][off
+var
->index
]))
752 isl_assert(tab
->mat
->ctx
, r
< tab
->n_row
, return);
754 r
= pivot_row(tab
, NULL
, sign
, var
->index
);
755 isl_assert(tab
->mat
->ctx
, r
>= 0, return);
758 isl_tab_pivot(tab
, r
, var
->index
);
761 static void check_table(struct isl_tab
*tab
)
767 for (i
= 0; i
< tab
->n_row
; ++i
) {
768 if (!isl_tab_var_from_row(tab
, i
)->is_nonneg
)
770 assert(!isl_int_is_neg(tab
->mat
->row
[i
][1]));
774 /* Return the sign of the maximal value of "var".
775 * If the sign is not negative, then on return from this function,
776 * the sample value will also be non-negative.
778 * If "var" is manifestly unbounded wrt positive values, we are done.
779 * Otherwise, we pivot the variable up to a row if needed
780 * Then we continue pivoting down until either
781 * - no more down pivots can be performed
782 * - the sample value is positive
783 * - the variable is pivoted into a manifestly unbounded column
785 static int sign_of_max(struct isl_tab
*tab
, struct isl_tab_var
*var
)
789 if (max_is_manifestly_unbounded(tab
, var
))
792 while (!isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
793 find_pivot(tab
, var
, var
, 1, &row
, &col
);
795 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
796 isl_tab_pivot(tab
, row
, col
);
797 if (!var
->is_row
) /* manifestly unbounded */
803 static int row_is_neg(struct isl_tab
*tab
, int row
)
806 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
807 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
809 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
811 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
814 static int row_sgn(struct isl_tab
*tab
, int row
)
817 return isl_int_sgn(tab
->mat
->row
[row
][1]);
818 if (!isl_int_is_zero(tab
->mat
->row
[row
][2]))
819 return isl_int_sgn(tab
->mat
->row
[row
][2]);
821 return isl_int_sgn(tab
->mat
->row
[row
][1]);
824 /* Perform pivots until the row variable "var" has a non-negative
825 * sample value or until no more upward pivots can be performed.
826 * Return the sign of the sample value after the pivots have been
829 static int restore_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
833 while (row_is_neg(tab
, var
->index
)) {
834 find_pivot(tab
, var
, var
, 1, &row
, &col
);
837 isl_tab_pivot(tab
, row
, col
);
838 if (!var
->is_row
) /* manifestly unbounded */
841 return row_sgn(tab
, var
->index
);
844 /* Perform pivots until we are sure that the row variable "var"
845 * can attain non-negative values. After return from this
846 * function, "var" is still a row variable, but its sample
847 * value may not be non-negative, even if the function returns 1.
849 static int at_least_zero(struct isl_tab
*tab
, struct isl_tab_var
*var
)
853 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
854 find_pivot(tab
, var
, var
, 1, &row
, &col
);
857 if (row
== var
->index
) /* manifestly unbounded */
859 isl_tab_pivot(tab
, row
, col
);
861 return !isl_int_is_neg(tab
->mat
->row
[var
->index
][1]);
864 /* Return a negative value if "var" can attain negative values.
865 * Return a non-negative value otherwise.
867 * If "var" is manifestly unbounded wrt negative values, we are done.
868 * Otherwise, if var is in a column, we can pivot it down to a row.
869 * Then we continue pivoting down until either
870 * - the pivot would result in a manifestly unbounded column
871 * => we don't perform the pivot, but simply return -1
872 * - no more down pivots can be performed
873 * - the sample value is negative
874 * If the sample value becomes negative and the variable is supposed
875 * to be nonnegative, then we undo the last pivot.
876 * However, if the last pivot has made the pivoting variable
877 * obviously redundant, then it may have moved to another row.
878 * In that case we look for upward pivots until we reach a non-negative
881 static int sign_of_min(struct isl_tab
*tab
, struct isl_tab_var
*var
)
884 struct isl_tab_var
*pivot_var
;
886 if (min_is_manifestly_unbounded(tab
, var
))
890 row
= pivot_row(tab
, NULL
, -1, col
);
891 pivot_var
= var_from_col(tab
, col
);
892 isl_tab_pivot(tab
, row
, col
);
893 if (var
->is_redundant
)
895 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
896 if (var
->is_nonneg
) {
897 if (!pivot_var
->is_redundant
&&
898 pivot_var
->index
== row
)
899 isl_tab_pivot(tab
, row
, col
);
901 restore_row(tab
, var
);
906 if (var
->is_redundant
)
908 while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
909 find_pivot(tab
, var
, var
, -1, &row
, &col
);
910 if (row
== var
->index
)
913 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
914 pivot_var
= var_from_col(tab
, col
);
915 isl_tab_pivot(tab
, row
, col
);
916 if (var
->is_redundant
)
919 if (var
->is_nonneg
) {
920 /* pivot back to non-negative value */
921 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
922 isl_tab_pivot(tab
, row
, col
);
924 restore_row(tab
, var
);
929 static int row_at_most_neg_one(struct isl_tab
*tab
, int row
)
932 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
934 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
937 return isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
938 isl_int_abs_ge(tab
->mat
->row
[row
][1],
939 tab
->mat
->row
[row
][0]);
942 /* Return 1 if "var" can attain values <= -1.
943 * Return 0 otherwise.
945 * The sample value of "var" is assumed to be non-negative when the
946 * the function is called and will be made non-negative again before
947 * the function returns.
949 int isl_tab_min_at_most_neg_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
952 struct isl_tab_var
*pivot_var
;
954 if (min_is_manifestly_unbounded(tab
, var
))
958 row
= pivot_row(tab
, NULL
, -1, col
);
959 pivot_var
= var_from_col(tab
, col
);
960 isl_tab_pivot(tab
, row
, col
);
961 if (var
->is_redundant
)
963 if (row_at_most_neg_one(tab
, var
->index
)) {
964 if (var
->is_nonneg
) {
965 if (!pivot_var
->is_redundant
&&
966 pivot_var
->index
== row
)
967 isl_tab_pivot(tab
, row
, col
);
969 restore_row(tab
, var
);
974 if (var
->is_redundant
)
977 find_pivot(tab
, var
, var
, -1, &row
, &col
);
978 if (row
== var
->index
)
982 pivot_var
= var_from_col(tab
, col
);
983 isl_tab_pivot(tab
, row
, col
);
984 if (var
->is_redundant
)
986 } while (!row_at_most_neg_one(tab
, var
->index
));
987 if (var
->is_nonneg
) {
988 /* pivot back to non-negative value */
989 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
990 isl_tab_pivot(tab
, row
, col
);
991 restore_row(tab
, var
);
996 /* Return 1 if "var" can attain values >= 1.
997 * Return 0 otherwise.
999 static int at_least_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1004 if (max_is_manifestly_unbounded(tab
, var
))
1006 to_row(tab
, var
, 1);
1007 r
= tab
->mat
->row
[var
->index
];
1008 while (isl_int_lt(r
[1], r
[0])) {
1009 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1011 return isl_int_ge(r
[1], r
[0]);
1012 if (row
== var
->index
) /* manifestly unbounded */
1014 isl_tab_pivot(tab
, row
, col
);
1019 static void swap_cols(struct isl_tab
*tab
, int col1
, int col2
)
1022 unsigned off
= 2 + tab
->M
;
1023 t
= tab
->col_var
[col1
];
1024 tab
->col_var
[col1
] = tab
->col_var
[col2
];
1025 tab
->col_var
[col2
] = t
;
1026 var_from_col(tab
, col1
)->index
= col1
;
1027 var_from_col(tab
, col2
)->index
= col2
;
1028 tab
->mat
= isl_mat_swap_cols(tab
->mat
, off
+ col1
, off
+ col2
);
1031 /* Mark column with index "col" as representing a zero variable.
1032 * If we may need to undo the operation the column is kept,
1033 * but no longer considered.
1034 * Otherwise, the column is simply removed.
1036 * The column may be interchanged with some other column. If it
1037 * is interchanged with a later column, return 1. Otherwise return 0.
1038 * If the columns are checked in order in the calling function,
1039 * then a return value of 1 means that the column with the given
1040 * column number may now contain a different column that
1041 * hasn't been checked yet.
1043 int isl_tab_kill_col(struct isl_tab
*tab
, int col
)
1045 var_from_col(tab
, col
)->is_zero
= 1;
1046 if (tab
->need_undo
) {
1047 isl_tab_push_var(tab
, isl_tab_undo_zero
, var_from_col(tab
, col
));
1048 if (col
!= tab
->n_dead
)
1049 swap_cols(tab
, col
, tab
->n_dead
);
1053 if (col
!= tab
->n_col
- 1)
1054 swap_cols(tab
, col
, tab
->n_col
- 1);
1055 var_from_col(tab
, tab
->n_col
- 1)->index
= -1;
1061 /* Row variable "var" is non-negative and cannot attain any values
1062 * larger than zero. This means that the coefficients of the unrestricted
1063 * column variables are zero and that the coefficients of the non-negative
1064 * column variables are zero or negative.
1065 * Each of the non-negative variables with a negative coefficient can
1066 * then also be written as the negative sum of non-negative variables
1067 * and must therefore also be zero.
1069 static void close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1072 struct isl_mat
*mat
= tab
->mat
;
1073 unsigned off
= 2 + tab
->M
;
1075 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return);
1077 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1078 if (isl_int_is_zero(mat
->row
[var
->index
][off
+ j
]))
1080 isl_assert(tab
->mat
->ctx
,
1081 isl_int_is_neg(mat
->row
[var
->index
][off
+ j
]), return);
1082 if (isl_tab_kill_col(tab
, j
))
1085 isl_tab_mark_redundant(tab
, var
->index
);
1088 /* Add a constraint to the tableau and allocate a row for it.
1089 * Return the index into the constraint array "con".
1091 int isl_tab_allocate_con(struct isl_tab
*tab
)
1095 isl_assert(tab
->mat
->ctx
, tab
->n_row
< tab
->mat
->n_row
, return -1);
1098 tab
->con
[r
].index
= tab
->n_row
;
1099 tab
->con
[r
].is_row
= 1;
1100 tab
->con
[r
].is_nonneg
= 0;
1101 tab
->con
[r
].is_zero
= 0;
1102 tab
->con
[r
].is_redundant
= 0;
1103 tab
->con
[r
].frozen
= 0;
1104 tab
->con
[r
].negated
= 0;
1105 tab
->row_var
[tab
->n_row
] = ~r
;
1109 isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]);
1114 /* Add a variable to the tableau and allocate a column for it.
1115 * Return the index into the variable array "var".
1117 int isl_tab_allocate_var(struct isl_tab
*tab
)
1121 unsigned off
= 2 + tab
->M
;
1123 isl_assert(tab
->mat
->ctx
, tab
->n_col
< tab
->mat
->n_col
, return -1);
1124 isl_assert(tab
->mat
->ctx
, tab
->n_var
< tab
->max_var
, return -1);
1127 tab
->var
[r
].index
= tab
->n_col
;
1128 tab
->var
[r
].is_row
= 0;
1129 tab
->var
[r
].is_nonneg
= 0;
1130 tab
->var
[r
].is_zero
= 0;
1131 tab
->var
[r
].is_redundant
= 0;
1132 tab
->var
[r
].frozen
= 0;
1133 tab
->var
[r
].negated
= 0;
1134 tab
->col_var
[tab
->n_col
] = r
;
1136 for (i
= 0; i
< tab
->n_row
; ++i
)
1137 isl_int_set_si(tab
->mat
->row
[i
][off
+ tab
->n_col
], 0);
1141 isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->var
[r
]);
1146 /* Add a row to the tableau. The row is given as an affine combination
1147 * of the original variables and needs to be expressed in terms of the
1150 * We add each term in turn.
1151 * If r = n/d_r is the current sum and we need to add k x, then
1152 * if x is a column variable, we increase the numerator of
1153 * this column by k d_r
1154 * if x = f/d_x is a row variable, then the new representation of r is
1156 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1157 * --- + --- = ------------------- = -------------------
1158 * d_r d_r d_r d_x/g m
1160 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1162 int isl_tab_add_row(struct isl_tab
*tab
, isl_int
*line
)
1168 unsigned off
= 2 + tab
->M
;
1170 r
= isl_tab_allocate_con(tab
);
1176 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1177 isl_int_set_si(row
[0], 1);
1178 isl_int_set(row
[1], line
[0]);
1179 isl_seq_clr(row
+ 2, tab
->M
+ tab
->n_col
);
1180 for (i
= 0; i
< tab
->n_var
; ++i
) {
1181 if (tab
->var
[i
].is_zero
)
1183 if (tab
->var
[i
].is_row
) {
1185 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1186 isl_int_swap(a
, row
[0]);
1187 isl_int_divexact(a
, row
[0], a
);
1189 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1190 isl_int_mul(b
, b
, line
[1 + i
]);
1191 isl_seq_combine(row
+ 1, a
, row
+ 1,
1192 b
, tab
->mat
->row
[tab
->var
[i
].index
] + 1,
1193 1 + tab
->M
+ tab
->n_col
);
1195 isl_int_addmul(row
[off
+ tab
->var
[i
].index
],
1196 line
[1 + i
], row
[0]);
1197 if (tab
->M
&& i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
1198 isl_int_submul(row
[2], line
[1 + i
], row
[0]);
1200 isl_seq_normalize(row
, off
+ tab
->n_col
);
1205 tab
->row_sign
[tab
->con
[r
].index
] = 0;
1210 static int drop_row(struct isl_tab
*tab
, int row
)
1212 isl_assert(tab
->mat
->ctx
, ~tab
->row_var
[row
] == tab
->n_con
- 1, return -1);
1213 if (row
!= tab
->n_row
- 1)
1214 swap_rows(tab
, row
, tab
->n_row
- 1);
1220 static int drop_col(struct isl_tab
*tab
, int col
)
1222 isl_assert(tab
->mat
->ctx
, tab
->col_var
[col
] == tab
->n_var
- 1, return -1);
1223 if (col
!= tab
->n_col
- 1)
1224 swap_cols(tab
, col
, tab
->n_col
- 1);
1230 /* Add inequality "ineq" and check if it conflicts with the
1231 * previously added constraints or if it is obviously redundant.
1233 struct isl_tab
*isl_tab_add_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1240 r
= isl_tab_add_row(tab
, ineq
);
1243 tab
->con
[r
].is_nonneg
= 1;
1244 isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1245 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1246 isl_tab_mark_redundant(tab
, tab
->con
[r
].index
);
1250 sgn
= restore_row(tab
, &tab
->con
[r
]);
1252 return isl_tab_mark_empty(tab
);
1253 if (tab
->con
[r
].is_row
&& isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1254 isl_tab_mark_redundant(tab
, tab
->con
[r
].index
);
1261 /* Pivot a non-negative variable down until it reaches the value zero
1262 * and then pivot the variable into a column position.
1264 int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1268 unsigned off
= 2 + tab
->M
;
1273 while (isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1274 find_pivot(tab
, var
, NULL
, -1, &row
, &col
);
1275 isl_assert(tab
->mat
->ctx
, row
!= -1, return -1);
1276 isl_tab_pivot(tab
, row
, col
);
1281 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
)
1282 if (!isl_int_is_zero(tab
->mat
->row
[var
->index
][off
+ i
]))
1285 isl_assert(tab
->mat
->ctx
, i
< tab
->n_col
, return -1);
1286 isl_tab_pivot(tab
, var
->index
, i
);
1291 /* We assume Gaussian elimination has been performed on the equalities.
1292 * The equalities can therefore never conflict.
1293 * Adding the equalities is currently only really useful for a later call
1294 * to isl_tab_ineq_type.
1296 static struct isl_tab
*add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1303 r
= isl_tab_add_row(tab
, eq
);
1307 r
= tab
->con
[r
].index
;
1308 i
= isl_seq_first_non_zero(tab
->mat
->row
[r
] + 2 + tab
->M
+ tab
->n_dead
,
1309 tab
->n_col
- tab
->n_dead
);
1310 isl_assert(tab
->mat
->ctx
, i
>= 0, goto error
);
1312 isl_tab_pivot(tab
, r
, i
);
1313 isl_tab_kill_col(tab
, i
);
1322 /* Add an equality that is known to be valid for the given tableau.
1324 struct isl_tab
*isl_tab_add_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1326 struct isl_tab_var
*var
;
1332 r
= isl_tab_add_row(tab
, eq
);
1338 if (isl_int_is_neg(tab
->mat
->row
[r
][1])) {
1339 isl_seq_neg(tab
->mat
->row
[r
] + 1, tab
->mat
->row
[r
] + 1,
1344 if (to_col(tab
, var
) < 0)
1347 isl_tab_kill_col(tab
, var
->index
);
1355 struct isl_tab
*isl_tab_from_basic_map(struct isl_basic_map
*bmap
)
1358 struct isl_tab
*tab
;
1362 tab
= isl_tab_alloc(bmap
->ctx
,
1363 isl_basic_map_total_dim(bmap
) + bmap
->n_ineq
+ 1,
1364 isl_basic_map_total_dim(bmap
), 0);
1367 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
1368 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1369 return isl_tab_mark_empty(tab
);
1370 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1371 tab
= add_eq(tab
, bmap
->eq
[i
]);
1375 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1376 tab
= isl_tab_add_ineq(tab
, bmap
->ineq
[i
]);
1377 if (!tab
|| tab
->empty
)
1383 struct isl_tab
*isl_tab_from_basic_set(struct isl_basic_set
*bset
)
1385 return isl_tab_from_basic_map((struct isl_basic_map
*)bset
);
1388 /* Construct a tableau corresponding to the recession cone of "bmap".
1390 struct isl_tab
*isl_tab_from_recession_cone(struct isl_basic_map
*bmap
)
1394 struct isl_tab
*tab
;
1398 tab
= isl_tab_alloc(bmap
->ctx
, bmap
->n_eq
+ bmap
->n_ineq
,
1399 isl_basic_map_total_dim(bmap
), 0);
1402 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
1405 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1406 isl_int_swap(bmap
->eq
[i
][0], cst
);
1407 tab
= add_eq(tab
, bmap
->eq
[i
]);
1408 isl_int_swap(bmap
->eq
[i
][0], cst
);
1412 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1414 isl_int_swap(bmap
->ineq
[i
][0], cst
);
1415 r
= isl_tab_add_row(tab
, bmap
->ineq
[i
]);
1416 isl_int_swap(bmap
->ineq
[i
][0], cst
);
1419 tab
->con
[r
].is_nonneg
= 1;
1420 isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1431 /* Assuming "tab" is the tableau of a cone, check if the cone is
1432 * bounded, i.e., if it is empty or only contains the origin.
1434 int isl_tab_cone_is_bounded(struct isl_tab
*tab
)
1442 if (tab
->n_dead
== tab
->n_col
)
1446 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1447 struct isl_tab_var
*var
;
1448 var
= isl_tab_var_from_row(tab
, i
);
1449 if (!var
->is_nonneg
)
1451 if (sign_of_max(tab
, var
) != 0)
1453 close_row(tab
, var
);
1456 if (tab
->n_dead
== tab
->n_col
)
1458 if (i
== tab
->n_row
)
1463 int isl_tab_sample_is_integer(struct isl_tab
*tab
)
1470 for (i
= 0; i
< tab
->n_var
; ++i
) {
1472 if (!tab
->var
[i
].is_row
)
1474 row
= tab
->var
[i
].index
;
1475 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1476 tab
->mat
->row
[row
][0]))
1482 static struct isl_vec
*extract_integer_sample(struct isl_tab
*tab
)
1485 struct isl_vec
*vec
;
1487 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
1491 isl_int_set_si(vec
->block
.data
[0], 1);
1492 for (i
= 0; i
< tab
->n_var
; ++i
) {
1493 if (!tab
->var
[i
].is_row
)
1494 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
1496 int row
= tab
->var
[i
].index
;
1497 isl_int_divexact(vec
->block
.data
[1 + i
],
1498 tab
->mat
->row
[row
][1], tab
->mat
->row
[row
][0]);
1505 struct isl_vec
*isl_tab_get_sample_value(struct isl_tab
*tab
)
1508 struct isl_vec
*vec
;
1514 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
1520 isl_int_set_si(vec
->block
.data
[0], 1);
1521 for (i
= 0; i
< tab
->n_var
; ++i
) {
1523 if (!tab
->var
[i
].is_row
) {
1524 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
1527 row
= tab
->var
[i
].index
;
1528 isl_int_gcd(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
1529 isl_int_divexact(m
, tab
->mat
->row
[row
][0], m
);
1530 isl_seq_scale(vec
->block
.data
, vec
->block
.data
, m
, 1 + i
);
1531 isl_int_divexact(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
1532 isl_int_mul(vec
->block
.data
[1 + i
], m
, tab
->mat
->row
[row
][1]);
1534 vec
= isl_vec_normalize(vec
);
1540 /* Update "bmap" based on the results of the tableau "tab".
1541 * In particular, implicit equalities are made explicit, redundant constraints
1542 * are removed and if the sample value happens to be integer, it is stored
1543 * in "bmap" (unless "bmap" already had an integer sample).
1545 * The tableau is assumed to have been created from "bmap" using
1546 * isl_tab_from_basic_map.
1548 struct isl_basic_map
*isl_basic_map_update_from_tab(struct isl_basic_map
*bmap
,
1549 struct isl_tab
*tab
)
1561 bmap
= isl_basic_map_set_to_empty(bmap
);
1563 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1564 if (isl_tab_is_equality(tab
, n_eq
+ i
))
1565 isl_basic_map_inequality_to_equality(bmap
, i
);
1566 else if (isl_tab_is_redundant(tab
, n_eq
+ i
))
1567 isl_basic_map_drop_inequality(bmap
, i
);
1569 if (!tab
->rational
&&
1570 !bmap
->sample
&& isl_tab_sample_is_integer(tab
))
1571 bmap
->sample
= extract_integer_sample(tab
);
1575 struct isl_basic_set
*isl_basic_set_update_from_tab(struct isl_basic_set
*bset
,
1576 struct isl_tab
*tab
)
1578 return (struct isl_basic_set
*)isl_basic_map_update_from_tab(
1579 (struct isl_basic_map
*)bset
, tab
);
1582 /* Given a non-negative variable "var", add a new non-negative variable
1583 * that is the opposite of "var", ensuring that var can only attain the
1585 * If var = n/d is a row variable, then the new variable = -n/d.
1586 * If var is a column variables, then the new variable = -var.
1587 * If the new variable cannot attain non-negative values, then
1588 * the resulting tableau is empty.
1589 * Otherwise, we know the value will be zero and we close the row.
1591 static struct isl_tab
*cut_to_hyperplane(struct isl_tab
*tab
,
1592 struct isl_tab_var
*var
)
1597 unsigned off
= 2 + tab
->M
;
1599 if (isl_tab_extend_cons(tab
, 1) < 0)
1603 tab
->con
[r
].index
= tab
->n_row
;
1604 tab
->con
[r
].is_row
= 1;
1605 tab
->con
[r
].is_nonneg
= 0;
1606 tab
->con
[r
].is_zero
= 0;
1607 tab
->con
[r
].is_redundant
= 0;
1608 tab
->con
[r
].frozen
= 0;
1609 tab
->con
[r
].negated
= 0;
1610 tab
->row_var
[tab
->n_row
] = ~r
;
1611 row
= tab
->mat
->row
[tab
->n_row
];
1614 isl_int_set(row
[0], tab
->mat
->row
[var
->index
][0]);
1615 isl_seq_neg(row
+ 1,
1616 tab
->mat
->row
[var
->index
] + 1, 1 + tab
->n_col
);
1618 isl_int_set_si(row
[0], 1);
1619 isl_seq_clr(row
+ 1, 1 + tab
->n_col
);
1620 isl_int_set_si(row
[off
+ var
->index
], -1);
1625 isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]);
1627 sgn
= sign_of_max(tab
, &tab
->con
[r
]);
1629 return isl_tab_mark_empty(tab
);
1630 tab
->con
[r
].is_nonneg
= 1;
1631 isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1633 close_row(tab
, &tab
->con
[r
]);
1641 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
1642 * relax the inequality by one. That is, the inequality r >= 0 is replaced
1643 * by r' = r + 1 >= 0.
1644 * If r is a row variable, we simply increase the constant term by one
1645 * (taking into account the denominator).
1646 * If r is a column variable, then we need to modify each row that
1647 * refers to r = r' - 1 by substituting this equality, effectively
1648 * subtracting the coefficient of the column from the constant.
1650 struct isl_tab
*isl_tab_relax(struct isl_tab
*tab
, int con
)
1652 struct isl_tab_var
*var
;
1653 unsigned off
= 2 + tab
->M
;
1658 var
= &tab
->con
[con
];
1660 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
1661 to_row(tab
, var
, 1);
1664 isl_int_add(tab
->mat
->row
[var
->index
][1],
1665 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
1669 for (i
= 0; i
< tab
->n_row
; ++i
) {
1670 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
1672 isl_int_sub(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
1673 tab
->mat
->row
[i
][off
+ var
->index
]);
1678 isl_tab_push_var(tab
, isl_tab_undo_relax
, var
);
1683 struct isl_tab
*isl_tab_select_facet(struct isl_tab
*tab
, int con
)
1688 return cut_to_hyperplane(tab
, &tab
->con
[con
]);
1691 static int may_be_equality(struct isl_tab
*tab
, int row
)
1693 unsigned off
= 2 + tab
->M
;
1694 return (tab
->rational
? isl_int_is_zero(tab
->mat
->row
[row
][1])
1695 : isl_int_lt(tab
->mat
->row
[row
][1],
1696 tab
->mat
->row
[row
][0])) &&
1697 isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1698 tab
->n_col
- tab
->n_dead
) != -1;
1701 /* Check for (near) equalities among the constraints.
1702 * A constraint is an equality if it is non-negative and if
1703 * its maximal value is either
1704 * - zero (in case of rational tableaus), or
1705 * - strictly less than 1 (in case of integer tableaus)
1707 * We first mark all non-redundant and non-dead variables that
1708 * are not frozen and not obviously not an equality.
1709 * Then we iterate over all marked variables if they can attain
1710 * any values larger than zero or at least one.
1711 * If the maximal value is zero, we mark any column variables
1712 * that appear in the row as being zero and mark the row as being redundant.
1713 * Otherwise, if the maximal value is strictly less than one (and the
1714 * tableau is integer), then we restrict the value to being zero
1715 * by adding an opposite non-negative variable.
1717 struct isl_tab
*isl_tab_detect_equalities(struct isl_tab
*tab
)
1726 if (tab
->n_dead
== tab
->n_col
)
1730 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1731 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
1732 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
1733 may_be_equality(tab
, i
);
1737 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1738 struct isl_tab_var
*var
= var_from_col(tab
, i
);
1739 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
1744 struct isl_tab_var
*var
;
1745 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1746 var
= isl_tab_var_from_row(tab
, i
);
1750 if (i
== tab
->n_row
) {
1751 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1752 var
= var_from_col(tab
, i
);
1756 if (i
== tab
->n_col
)
1761 if (sign_of_max(tab
, var
) == 0)
1762 close_row(tab
, var
);
1763 else if (!tab
->rational
&& !at_least_one(tab
, var
)) {
1764 tab
= cut_to_hyperplane(tab
, var
);
1765 return isl_tab_detect_equalities(tab
);
1767 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1768 var
= isl_tab_var_from_row(tab
, i
);
1771 if (may_be_equality(tab
, i
))
1781 /* Check for (near) redundant constraints.
1782 * A constraint is redundant if it is non-negative and if
1783 * its minimal value (temporarily ignoring the non-negativity) is either
1784 * - zero (in case of rational tableaus), or
1785 * - strictly larger than -1 (in case of integer tableaus)
1787 * We first mark all non-redundant and non-dead variables that
1788 * are not frozen and not obviously negatively unbounded.
1789 * Then we iterate over all marked variables if they can attain
1790 * any values smaller than zero or at most negative one.
1791 * If not, we mark the row as being redundant (assuming it hasn't
1792 * been detected as being obviously redundant in the mean time).
1794 struct isl_tab
*isl_tab_detect_redundant(struct isl_tab
*tab
)
1803 if (tab
->n_redundant
== tab
->n_row
)
1807 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1808 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
1809 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
1813 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1814 struct isl_tab_var
*var
= var_from_col(tab
, i
);
1815 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
1816 !min_is_manifestly_unbounded(tab
, var
);
1821 struct isl_tab_var
*var
;
1822 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1823 var
= isl_tab_var_from_row(tab
, i
);
1827 if (i
== tab
->n_row
) {
1828 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1829 var
= var_from_col(tab
, i
);
1833 if (i
== tab
->n_col
)
1838 if ((tab
->rational
? (sign_of_min(tab
, var
) >= 0)
1839 : !isl_tab_min_at_most_neg_one(tab
, var
)) &&
1841 isl_tab_mark_redundant(tab
, var
->index
);
1842 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1843 var
= var_from_col(tab
, i
);
1846 if (!min_is_manifestly_unbounded(tab
, var
))
1856 int isl_tab_is_equality(struct isl_tab
*tab
, int con
)
1863 if (tab
->con
[con
].is_zero
)
1865 if (tab
->con
[con
].is_redundant
)
1867 if (!tab
->con
[con
].is_row
)
1868 return tab
->con
[con
].index
< tab
->n_dead
;
1870 row
= tab
->con
[con
].index
;
1873 return isl_int_is_zero(tab
->mat
->row
[row
][1]) &&
1874 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1875 tab
->n_col
- tab
->n_dead
) == -1;
1878 /* Return the minimial value of the affine expression "f" with denominator
1879 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
1880 * the expression cannot attain arbitrarily small values.
1881 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
1882 * The return value reflects the nature of the result (empty, unbounded,
1883 * minmimal value returned in *opt).
1885 enum isl_lp_result
isl_tab_min(struct isl_tab
*tab
,
1886 isl_int
*f
, isl_int denom
, isl_int
*opt
, isl_int
*opt_denom
,
1890 enum isl_lp_result res
= isl_lp_ok
;
1891 struct isl_tab_var
*var
;
1892 struct isl_tab_undo
*snap
;
1895 return isl_lp_empty
;
1897 snap
= isl_tab_snap(tab
);
1898 r
= isl_tab_add_row(tab
, f
);
1900 return isl_lp_error
;
1902 isl_int_mul(tab
->mat
->row
[var
->index
][0],
1903 tab
->mat
->row
[var
->index
][0], denom
);
1906 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1907 if (row
== var
->index
) {
1908 res
= isl_lp_unbounded
;
1913 isl_tab_pivot(tab
, row
, col
);
1915 if (ISL_FL_ISSET(flags
, ISL_TAB_SAVE_DUAL
)) {
1918 isl_vec_free(tab
->dual
);
1919 tab
->dual
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_con
);
1921 return isl_lp_error
;
1922 isl_int_set(tab
->dual
->el
[0], tab
->mat
->row
[var
->index
][0]);
1923 for (i
= 0; i
< tab
->n_con
; ++i
) {
1925 if (tab
->con
[i
].is_row
) {
1926 isl_int_set_si(tab
->dual
->el
[1 + i
], 0);
1929 pos
= 2 + tab
->M
+ tab
->con
[i
].index
;
1930 if (tab
->con
[i
].negated
)
1931 isl_int_neg(tab
->dual
->el
[1 + i
],
1932 tab
->mat
->row
[var
->index
][pos
]);
1934 isl_int_set(tab
->dual
->el
[1 + i
],
1935 tab
->mat
->row
[var
->index
][pos
]);
1938 if (opt
&& res
== isl_lp_ok
) {
1940 isl_int_set(*opt
, tab
->mat
->row
[var
->index
][1]);
1941 isl_int_set(*opt_denom
, tab
->mat
->row
[var
->index
][0]);
1943 isl_int_cdiv_q(*opt
, tab
->mat
->row
[var
->index
][1],
1944 tab
->mat
->row
[var
->index
][0]);
1946 if (isl_tab_rollback(tab
, snap
) < 0)
1947 return isl_lp_error
;
1951 int isl_tab_is_redundant(struct isl_tab
*tab
, int con
)
1958 if (tab
->con
[con
].is_zero
)
1960 if (tab
->con
[con
].is_redundant
)
1962 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
1965 /* Take a snapshot of the tableau that can be restored by s call to
1968 struct isl_tab_undo
*isl_tab_snap(struct isl_tab
*tab
)
1976 /* Undo the operation performed by isl_tab_relax.
1978 static void unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1980 unsigned off
= 2 + tab
->M
;
1982 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
1983 to_row(tab
, var
, 1);
1986 isl_int_sub(tab
->mat
->row
[var
->index
][1],
1987 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
1991 for (i
= 0; i
< tab
->n_row
; ++i
) {
1992 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
1994 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
1995 tab
->mat
->row
[i
][off
+ var
->index
]);
2001 static void perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2003 struct isl_tab_var
*var
= var_from_index(tab
, undo
->u
.var_index
);
2004 switch(undo
->type
) {
2005 case isl_tab_undo_nonneg
:
2008 case isl_tab_undo_redundant
:
2009 var
->is_redundant
= 0;
2012 case isl_tab_undo_zero
:
2016 case isl_tab_undo_allocate
:
2017 if (undo
->u
.var_index
>= 0) {
2018 isl_assert(tab
->mat
->ctx
, !var
->is_row
, return);
2019 drop_col(tab
, var
->index
);
2023 if (!max_is_manifestly_unbounded(tab
, var
))
2024 to_row(tab
, var
, 1);
2025 else if (!min_is_manifestly_unbounded(tab
, var
))
2026 to_row(tab
, var
, -1);
2028 to_row(tab
, var
, 0);
2030 drop_row(tab
, var
->index
);
2032 case isl_tab_undo_relax
:
2038 /* Restore the tableau to the state where the basic variables
2039 * are those in "col_var".
2040 * We first construct a list of variables that are currently in
2041 * the basis, but shouldn't. Then we iterate over all variables
2042 * that should be in the basis and for each one that is currently
2043 * not in the basis, we exchange it with one of the elements of the
2044 * list constructed before.
2045 * We can always find an appropriate variable to pivot with because
2046 * the current basis is mapped to the old basis by a non-singular
2047 * matrix and so we can never end up with a zero row.
2049 static int restore_basis(struct isl_tab
*tab
, int *col_var
)
2053 int *extra
= NULL
; /* current columns that contain bad stuff */
2054 unsigned off
= 2 + tab
->M
;
2056 extra
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
2059 for (i
= 0; i
< tab
->n_col
; ++i
) {
2060 for (j
= 0; j
< tab
->n_col
; ++j
)
2061 if (tab
->col_var
[i
] == col_var
[j
])
2065 extra
[n_extra
++] = i
;
2067 for (i
= 0; i
< tab
->n_col
&& n_extra
> 0; ++i
) {
2068 struct isl_tab_var
*var
;
2071 for (j
= 0; j
< tab
->n_col
; ++j
)
2072 if (col_var
[i
] == tab
->col_var
[j
])
2076 var
= var_from_index(tab
, col_var
[i
]);
2078 for (j
= 0; j
< n_extra
; ++j
)
2079 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+extra
[j
]]))
2081 isl_assert(tab
->mat
->ctx
, j
< n_extra
, goto error
);
2082 isl_tab_pivot(tab
, row
, extra
[j
]);
2083 extra
[j
] = extra
[--n_extra
];
2095 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2097 switch (undo
->type
) {
2098 case isl_tab_undo_empty
:
2101 case isl_tab_undo_nonneg
:
2102 case isl_tab_undo_redundant
:
2103 case isl_tab_undo_zero
:
2104 case isl_tab_undo_allocate
:
2105 case isl_tab_undo_relax
:
2106 perform_undo_var(tab
, undo
);
2108 case isl_tab_undo_bset_eq
:
2109 isl_basic_set_free_equality(tab
->bset
, 1);
2111 case isl_tab_undo_bset_ineq
:
2112 isl_basic_set_free_inequality(tab
->bset
, 1);
2114 case isl_tab_undo_bset_div
:
2115 isl_basic_set_free_div(tab
->bset
, 1);
2117 tab
->samples
->n_col
--;
2119 case isl_tab_undo_saved_basis
:
2120 if (restore_basis(tab
, undo
->u
.col_var
) < 0)
2123 case isl_tab_undo_drop_sample
:
2127 isl_assert(tab
->mat
->ctx
, 0, return -1);
2132 /* Return the tableau to the state it was in when the snapshot "snap"
2135 int isl_tab_rollback(struct isl_tab
*tab
, struct isl_tab_undo
*snap
)
2137 struct isl_tab_undo
*undo
, *next
;
2143 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
2147 if (perform_undo(tab
, undo
) < 0) {
2161 /* The given row "row" represents an inequality violated by all
2162 * points in the tableau. Check for some special cases of such
2163 * separating constraints.
2164 * In particular, if the row has been reduced to the constant -1,
2165 * then we know the inequality is adjacent (but opposite) to
2166 * an equality in the tableau.
2167 * If the row has been reduced to r = -1 -r', with r' an inequality
2168 * of the tableau, then the inequality is adjacent (but opposite)
2169 * to the inequality r'.
2171 static enum isl_ineq_type
separation_type(struct isl_tab
*tab
, unsigned row
)
2174 unsigned off
= 2 + tab
->M
;
2177 return isl_ineq_separate
;
2179 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
2180 return isl_ineq_separate
;
2181 if (!isl_int_is_negone(tab
->mat
->row
[row
][1]))
2182 return isl_ineq_separate
;
2184 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
2185 tab
->n_col
- tab
->n_dead
);
2187 return isl_ineq_adj_eq
;
2189 if (!isl_int_is_negone(tab
->mat
->row
[row
][off
+ tab
->n_dead
+ pos
]))
2190 return isl_ineq_separate
;
2192 pos
= isl_seq_first_non_zero(
2193 tab
->mat
->row
[row
] + off
+ tab
->n_dead
+ pos
+ 1,
2194 tab
->n_col
- tab
->n_dead
- pos
- 1);
2196 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
2199 /* Check the effect of inequality "ineq" on the tableau "tab".
2201 * isl_ineq_redundant: satisfied by all points in the tableau
2202 * isl_ineq_separate: satisfied by no point in the tableau
2203 * isl_ineq_cut: satisfied by some by not all points
2204 * isl_ineq_adj_eq: adjacent to an equality
2205 * isl_ineq_adj_ineq: adjacent to an inequality.
2207 enum isl_ineq_type
isl_tab_ineq_type(struct isl_tab
*tab
, isl_int
*ineq
)
2209 enum isl_ineq_type type
= isl_ineq_error
;
2210 struct isl_tab_undo
*snap
= NULL
;
2215 return isl_ineq_error
;
2217 if (isl_tab_extend_cons(tab
, 1) < 0)
2218 return isl_ineq_error
;
2220 snap
= isl_tab_snap(tab
);
2222 con
= isl_tab_add_row(tab
, ineq
);
2226 row
= tab
->con
[con
].index
;
2227 if (isl_tab_row_is_redundant(tab
, row
))
2228 type
= isl_ineq_redundant
;
2229 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
2231 isl_int_abs_ge(tab
->mat
->row
[row
][1],
2232 tab
->mat
->row
[row
][0]))) {
2233 if (at_least_zero(tab
, &tab
->con
[con
]))
2234 type
= isl_ineq_cut
;
2236 type
= separation_type(tab
, row
);
2237 } else if (tab
->rational
? (sign_of_min(tab
, &tab
->con
[con
]) < 0)
2238 : isl_tab_min_at_most_neg_one(tab
, &tab
->con
[con
]))
2239 type
= isl_ineq_cut
;
2241 type
= isl_ineq_redundant
;
2243 if (isl_tab_rollback(tab
, snap
))
2244 return isl_ineq_error
;
2247 isl_tab_rollback(tab
, snap
);
2248 return isl_ineq_error
;
2251 void isl_tab_dump(struct isl_tab
*tab
, FILE *out
, int indent
)
2257 fprintf(out
, "%*snull tab\n", indent
, "");
2260 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
2261 tab
->n_redundant
, tab
->n_dead
);
2263 fprintf(out
, ", rational");
2265 fprintf(out
, ", empty");
2267 fprintf(out
, "%*s[", indent
, "");
2268 for (i
= 0; i
< tab
->n_var
; ++i
) {
2270 fprintf(out
, (i
== tab
->n_param
||
2271 i
== tab
->n_var
- tab
->n_div
) ? "; "
2273 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
2275 tab
->var
[i
].is_zero
? " [=0]" :
2276 tab
->var
[i
].is_redundant
? " [R]" : "");
2278 fprintf(out
, "]\n");
2279 fprintf(out
, "%*s[", indent
, "");
2280 for (i
= 0; i
< tab
->n_con
; ++i
) {
2283 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
2285 tab
->con
[i
].is_zero
? " [=0]" :
2286 tab
->con
[i
].is_redundant
? " [R]" : "");
2288 fprintf(out
, "]\n");
2289 fprintf(out
, "%*s[", indent
, "");
2290 for (i
= 0; i
< tab
->n_row
; ++i
) {
2291 const char *sign
= "";
2294 if (tab
->row_sign
) {
2295 if (tab
->row_sign
[i
] == isl_tab_row_unknown
)
2297 else if (tab
->row_sign
[i
] == isl_tab_row_neg
)
2299 else if (tab
->row_sign
[i
] == isl_tab_row_pos
)
2304 fprintf(out
, "r%d: %d%s%s", i
, tab
->row_var
[i
],
2305 isl_tab_var_from_row(tab
, i
)->is_nonneg
? " [>=0]" : "", sign
);
2307 fprintf(out
, "]\n");
2308 fprintf(out
, "%*s[", indent
, "");
2309 for (i
= 0; i
< tab
->n_col
; ++i
) {
2312 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
2313 var_from_col(tab
, i
)->is_nonneg
? " [>=0]" : "");
2315 fprintf(out
, "]\n");
2316 r
= tab
->mat
->n_row
;
2317 tab
->mat
->n_row
= tab
->n_row
;
2318 c
= tab
->mat
->n_col
;
2319 tab
->mat
->n_col
= 2 + tab
->M
+ tab
->n_col
;
2320 isl_mat_dump(tab
->mat
, out
, indent
);
2321 tab
->mat
->n_row
= r
;
2322 tab
->mat
->n_col
= c
;
2324 isl_basic_set_dump(tab
->bset
, out
, indent
);