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
;
72 int isl_tab_extend_cons(struct isl_tab
*tab
, unsigned n_new
)
74 unsigned off
= 2 + tab
->M
;
75 if (tab
->max_con
< tab
->n_con
+ n_new
) {
76 struct isl_tab_var
*con
;
78 con
= isl_realloc_array(tab
->mat
->ctx
, tab
->con
,
79 struct isl_tab_var
, tab
->max_con
+ n_new
);
83 tab
->max_con
+= n_new
;
85 if (tab
->mat
->n_row
< tab
->n_row
+ n_new
) {
88 tab
->mat
= isl_mat_extend(tab
->mat
,
89 tab
->n_row
+ n_new
, off
+ tab
->n_col
);
92 row_var
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_var
,
93 int, tab
->mat
->n_row
);
96 tab
->row_var
= row_var
;
98 enum isl_tab_row_sign
*s
;
99 s
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_sign
,
100 enum isl_tab_row_sign
, tab
->mat
->n_row
);
109 /* Make room for at least n_new extra variables.
110 * Return -1 if anything went wrong.
112 int isl_tab_extend_vars(struct isl_tab
*tab
, unsigned n_new
)
114 struct isl_tab_var
*var
;
115 unsigned off
= 2 + tab
->M
;
117 if (tab
->max_var
< tab
->n_var
+ n_new
) {
118 var
= isl_realloc_array(tab
->mat
->ctx
, tab
->var
,
119 struct isl_tab_var
, tab
->n_var
+ n_new
);
123 tab
->max_var
+= n_new
;
126 if (tab
->mat
->n_col
< off
+ tab
->n_col
+ n_new
) {
129 tab
->mat
= isl_mat_extend(tab
->mat
,
130 tab
->mat
->n_row
, off
+ tab
->n_col
+ n_new
);
133 p
= isl_realloc_array(tab
->mat
->ctx
, tab
->col_var
,
134 int, tab
->mat
->n_col
);
143 struct isl_tab
*isl_tab_extend(struct isl_tab
*tab
, unsigned n_new
)
145 if (isl_tab_extend_cons(tab
, n_new
) >= 0)
152 static void free_undo(struct isl_tab
*tab
)
154 struct isl_tab_undo
*undo
, *next
;
156 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
163 void isl_tab_free(struct isl_tab
*tab
)
168 isl_mat_free(tab
->mat
);
169 isl_vec_free(tab
->dual
);
170 isl_basic_set_free(tab
->bset
);
176 isl_mat_free(tab
->samples
);
180 struct isl_tab
*isl_tab_dup(struct isl_tab
*tab
)
188 dup
= isl_calloc_type(tab
->ctx
, struct isl_tab
);
191 dup
->mat
= isl_mat_dup(tab
->mat
);
194 dup
->var
= isl_alloc_array(tab
->ctx
, struct isl_tab_var
, tab
->max_var
);
197 for (i
= 0; i
< tab
->n_var
; ++i
)
198 dup
->var
[i
] = tab
->var
[i
];
199 dup
->con
= isl_alloc_array(tab
->ctx
, struct isl_tab_var
, tab
->max_con
);
202 for (i
= 0; i
< tab
->n_con
; ++i
)
203 dup
->con
[i
] = tab
->con
[i
];
204 dup
->col_var
= isl_alloc_array(tab
->ctx
, int, tab
->mat
->n_col
);
207 for (i
= 0; i
< tab
->n_var
; ++i
)
208 dup
->col_var
[i
] = tab
->col_var
[i
];
209 dup
->row_var
= isl_alloc_array(tab
->ctx
, int, tab
->mat
->n_row
);
212 for (i
= 0; i
< tab
->n_row
; ++i
)
213 dup
->row_var
[i
] = tab
->row_var
[i
];
215 dup
->row_sign
= isl_alloc_array(tab
->ctx
, enum isl_tab_row_sign
,
219 for (i
= 0; i
< tab
->n_row
; ++i
)
220 dup
->row_sign
[i
] = tab
->row_sign
[i
];
223 dup
->samples
= isl_mat_dup(tab
->samples
);
226 dup
->n_sample
= tab
->n_sample
;
227 dup
->n_outside
= tab
->n_outside
;
229 dup
->n_row
= tab
->n_row
;
230 dup
->n_con
= tab
->n_con
;
231 dup
->n_eq
= tab
->n_eq
;
232 dup
->max_con
= tab
->max_con
;
233 dup
->n_col
= tab
->n_col
;
234 dup
->n_var
= tab
->n_var
;
235 dup
->max_var
= tab
->max_var
;
236 dup
->n_param
= tab
->n_param
;
237 dup
->n_div
= tab
->n_div
;
238 dup
->n_dead
= tab
->n_dead
;
239 dup
->n_redundant
= tab
->n_redundant
;
240 dup
->rational
= tab
->rational
;
241 dup
->empty
= tab
->empty
;
245 dup
->bottom
.type
= isl_tab_undo_bottom
;
246 dup
->bottom
.next
= NULL
;
247 dup
->top
= &dup
->bottom
;
254 static struct isl_tab_var
*var_from_index(struct isl_tab
*tab
, int i
)
259 return &tab
->con
[~i
];
262 struct isl_tab_var
*isl_tab_var_from_row(struct isl_tab
*tab
, int i
)
264 return var_from_index(tab
, tab
->row_var
[i
]);
267 static struct isl_tab_var
*var_from_col(struct isl_tab
*tab
, int i
)
269 return var_from_index(tab
, tab
->col_var
[i
]);
272 /* Check if there are any upper bounds on column variable "var",
273 * i.e., non-negative rows where var appears with a negative coefficient.
274 * Return 1 if there are no such bounds.
276 static int max_is_manifestly_unbounded(struct isl_tab
*tab
,
277 struct isl_tab_var
*var
)
280 unsigned off
= 2 + tab
->M
;
284 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
285 if (!isl_int_is_neg(tab
->mat
->row
[i
][off
+ var
->index
]))
287 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
293 /* Check if there are any lower bounds on column variable "var",
294 * i.e., non-negative rows where var appears with a positive coefficient.
295 * Return 1 if there are no such bounds.
297 static int min_is_manifestly_unbounded(struct isl_tab
*tab
,
298 struct isl_tab_var
*var
)
301 unsigned off
= 2 + tab
->M
;
305 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
306 if (!isl_int_is_pos(tab
->mat
->row
[i
][off
+ var
->index
]))
308 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
314 static int row_cmp(struct isl_tab
*tab
, int r1
, int r2
, int c
, isl_int t
)
316 unsigned off
= 2 + tab
->M
;
320 isl_int_mul(t
, tab
->mat
->row
[r1
][2], tab
->mat
->row
[r2
][off
+c
]);
321 isl_int_submul(t
, tab
->mat
->row
[r2
][2], tab
->mat
->row
[r1
][off
+c
]);
326 isl_int_mul(t
, tab
->mat
->row
[r1
][1], tab
->mat
->row
[r2
][off
+ c
]);
327 isl_int_submul(t
, tab
->mat
->row
[r2
][1], tab
->mat
->row
[r1
][off
+ c
]);
328 return isl_int_sgn(t
);
331 /* Given the index of a column "c", return the index of a row
332 * that can be used to pivot the column in, with either an increase
333 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
334 * If "var" is not NULL, then the row returned will be different from
335 * the one associated with "var".
337 * Each row in the tableau is of the form
339 * x_r = a_r0 + \sum_i a_ri x_i
341 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
342 * impose any limit on the increase or decrease in the value of x_c
343 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
344 * for the row with the smallest (most stringent) such bound.
345 * Note that the common denominator of each row drops out of the fraction.
346 * To check if row j has a smaller bound than row r, i.e.,
347 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
348 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
349 * where -sign(a_jc) is equal to "sgn".
351 static int pivot_row(struct isl_tab
*tab
,
352 struct isl_tab_var
*var
, int sgn
, int c
)
356 unsigned off
= 2 + tab
->M
;
360 for (j
= tab
->n_redundant
; j
< tab
->n_row
; ++j
) {
361 if (var
&& j
== var
->index
)
363 if (!isl_tab_var_from_row(tab
, j
)->is_nonneg
)
365 if (sgn
* isl_int_sgn(tab
->mat
->row
[j
][off
+ c
]) >= 0)
371 tsgn
= sgn
* row_cmp(tab
, r
, j
, c
, t
);
372 if (tsgn
< 0 || (tsgn
== 0 &&
373 tab
->row_var
[j
] < tab
->row_var
[r
]))
380 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
381 * (sgn < 0) the value of row variable var.
382 * If not NULL, then skip_var is a row variable that should be ignored
383 * while looking for a pivot row. It is usually equal to var.
385 * As the given row in the tableau is of the form
387 * x_r = a_r0 + \sum_i a_ri x_i
389 * we need to find a column such that the sign of a_ri is equal to "sgn"
390 * (such that an increase in x_i will have the desired effect) or a
391 * column with a variable that may attain negative values.
392 * If a_ri is positive, then we need to move x_i in the same direction
393 * to obtain the desired effect. Otherwise, x_i has to move in the
394 * opposite direction.
396 static void find_pivot(struct isl_tab
*tab
,
397 struct isl_tab_var
*var
, struct isl_tab_var
*skip_var
,
398 int sgn
, int *row
, int *col
)
405 isl_assert(tab
->mat
->ctx
, var
->is_row
, return);
406 tr
= tab
->mat
->row
[var
->index
] + 2 + tab
->M
;
409 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
410 if (isl_int_is_zero(tr
[j
]))
412 if (isl_int_sgn(tr
[j
]) != sgn
&&
413 var_from_col(tab
, j
)->is_nonneg
)
415 if (c
< 0 || tab
->col_var
[j
] < tab
->col_var
[c
])
421 sgn
*= isl_int_sgn(tr
[c
]);
422 r
= pivot_row(tab
, skip_var
, sgn
, c
);
423 *row
= r
< 0 ? var
->index
: r
;
427 /* Return 1 if row "row" represents an obviously redundant inequality.
429 * - it represents an inequality or a variable
430 * - that is the sum of a non-negative sample value and a positive
431 * combination of zero or more non-negative variables.
433 int isl_tab_row_is_redundant(struct isl_tab
*tab
, int row
)
436 unsigned off
= 2 + tab
->M
;
438 if (tab
->row_var
[row
] < 0 && !isl_tab_var_from_row(tab
, row
)->is_nonneg
)
441 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
443 if (tab
->M
&& isl_int_is_neg(tab
->mat
->row
[row
][2]))
446 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
447 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ i
]))
449 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ i
]))
451 if (!var_from_col(tab
, i
)->is_nonneg
)
457 static void swap_rows(struct isl_tab
*tab
, int row1
, int row2
)
460 t
= tab
->row_var
[row1
];
461 tab
->row_var
[row1
] = tab
->row_var
[row2
];
462 tab
->row_var
[row2
] = t
;
463 isl_tab_var_from_row(tab
, row1
)->index
= row1
;
464 isl_tab_var_from_row(tab
, row2
)->index
= row2
;
465 tab
->mat
= isl_mat_swap_rows(tab
->mat
, row1
, row2
);
469 t
= tab
->row_sign
[row1
];
470 tab
->row_sign
[row1
] = tab
->row_sign
[row2
];
471 tab
->row_sign
[row2
] = t
;
474 static void push_union(struct isl_tab
*tab
,
475 enum isl_tab_undo_type type
, union isl_tab_undo_val u
)
477 struct isl_tab_undo
*undo
;
482 undo
= isl_alloc_type(tab
->mat
->ctx
, struct isl_tab_undo
);
490 undo
->next
= tab
->top
;
494 void isl_tab_push_var(struct isl_tab
*tab
,
495 enum isl_tab_undo_type type
, struct isl_tab_var
*var
)
497 union isl_tab_undo_val u
;
499 u
.var_index
= tab
->row_var
[var
->index
];
501 u
.var_index
= tab
->col_var
[var
->index
];
502 push_union(tab
, type
, u
);
505 void isl_tab_push(struct isl_tab
*tab
, enum isl_tab_undo_type type
)
507 union isl_tab_undo_val u
= { 0 };
508 push_union(tab
, type
, u
);
511 /* Push a record on the undo stack describing the current basic
512 * variables, so that the this state can be restored during rollback.
514 void isl_tab_push_basis(struct isl_tab
*tab
)
517 union isl_tab_undo_val u
;
519 u
.col_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
525 for (i
= 0; i
< tab
->n_col
; ++i
)
526 u
.col_var
[i
] = tab
->col_var
[i
];
527 push_union(tab
, isl_tab_undo_saved_basis
, u
);
530 /* Mark row with index "row" as being redundant.
531 * If we may need to undo the operation or if the row represents
532 * a variable of the original problem, the row is kept,
533 * but no longer considered when looking for a pivot row.
534 * Otherwise, the row is simply removed.
536 * The row may be interchanged with some other row. If it
537 * is interchanged with a later row, return 1. Otherwise return 0.
538 * If the rows are checked in order in the calling function,
539 * then a return value of 1 means that the row with the given
540 * row number may now contain a different row that hasn't been checked yet.
542 int isl_tab_mark_redundant(struct isl_tab
*tab
, int row
)
544 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, row
);
545 var
->is_redundant
= 1;
546 isl_assert(tab
->mat
->ctx
, row
>= tab
->n_redundant
, return -1);
547 if (tab
->need_undo
|| tab
->row_var
[row
] >= 0) {
548 if (tab
->row_var
[row
] >= 0 && !var
->is_nonneg
) {
550 isl_tab_push_var(tab
, isl_tab_undo_nonneg
, var
);
552 if (row
!= tab
->n_redundant
)
553 swap_rows(tab
, row
, tab
->n_redundant
);
554 isl_tab_push_var(tab
, isl_tab_undo_redundant
, var
);
558 if (row
!= tab
->n_row
- 1)
559 swap_rows(tab
, row
, tab
->n_row
- 1);
560 isl_tab_var_from_row(tab
, tab
->n_row
- 1)->index
= -1;
566 struct isl_tab
*isl_tab_mark_empty(struct isl_tab
*tab
)
568 if (!tab
->empty
&& tab
->need_undo
)
569 isl_tab_push(tab
, isl_tab_undo_empty
);
574 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
575 * the original sign of the pivot element.
576 * We only keep track of row signs during PILP solving and in this case
577 * we only pivot a row with negative sign (meaning the value is always
578 * non-positive) using a positive pivot element.
580 * For each row j, the new value of the parametric constant is equal to
582 * a_j0 - a_jc a_r0/a_rc
584 * where a_j0 is the original parametric constant, a_rc is the pivot element,
585 * a_r0 is the parametric constant of the pivot row and a_jc is the
586 * pivot column entry of the row j.
587 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
588 * remains the same if a_jc has the same sign as the row j or if
589 * a_jc is zero. In all other cases, we reset the sign to "unknown".
591 static void update_row_sign(struct isl_tab
*tab
, int row
, int col
, int row_sgn
)
594 struct isl_mat
*mat
= tab
->mat
;
595 unsigned off
= 2 + tab
->M
;
600 if (tab
->row_sign
[row
] == 0)
602 isl_assert(mat
->ctx
, row_sgn
> 0, return);
603 isl_assert(mat
->ctx
, tab
->row_sign
[row
] == isl_tab_row_neg
, return);
604 tab
->row_sign
[row
] = isl_tab_row_pos
;
605 for (i
= 0; i
< tab
->n_row
; ++i
) {
609 s
= isl_int_sgn(mat
->row
[i
][off
+ col
]);
612 if (!tab
->row_sign
[i
])
614 if (s
< 0 && tab
->row_sign
[i
] == isl_tab_row_neg
)
616 if (s
> 0 && tab
->row_sign
[i
] == isl_tab_row_pos
)
618 tab
->row_sign
[i
] = isl_tab_row_unknown
;
622 /* Given a row number "row" and a column number "col", pivot the tableau
623 * such that the associated variables are interchanged.
624 * The given row in the tableau expresses
626 * x_r = a_r0 + \sum_i a_ri x_i
630 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
632 * Substituting this equality into the other rows
634 * x_j = a_j0 + \sum_i a_ji x_i
636 * with a_jc \ne 0, we obtain
638 * 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
645 * where i is any other column and j is any other row,
646 * is therefore transformed into
648 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
649 * 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)
651 * The transformation is performed along the following steps
656 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
659 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
660 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
662 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
663 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
665 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
666 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
668 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
669 * 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)
672 void isl_tab_pivot(struct isl_tab
*tab
, int row
, int col
)
677 struct isl_mat
*mat
= tab
->mat
;
678 struct isl_tab_var
*var
;
679 unsigned off
= 2 + tab
->M
;
681 isl_int_swap(mat
->row
[row
][0], mat
->row
[row
][off
+ col
]);
682 sgn
= isl_int_sgn(mat
->row
[row
][0]);
684 isl_int_neg(mat
->row
[row
][0], mat
->row
[row
][0]);
685 isl_int_neg(mat
->row
[row
][off
+ col
], mat
->row
[row
][off
+ col
]);
687 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
688 if (j
== off
- 1 + col
)
690 isl_int_neg(mat
->row
[row
][1 + j
], mat
->row
[row
][1 + j
]);
692 if (!isl_int_is_one(mat
->row
[row
][0]))
693 isl_seq_normalize(mat
->ctx
, mat
->row
[row
], off
+ tab
->n_col
);
694 for (i
= 0; i
< tab
->n_row
; ++i
) {
697 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
699 isl_int_mul(mat
->row
[i
][0], mat
->row
[i
][0], mat
->row
[row
][0]);
700 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
701 if (j
== off
- 1 + col
)
703 isl_int_mul(mat
->row
[i
][1 + j
],
704 mat
->row
[i
][1 + j
], mat
->row
[row
][0]);
705 isl_int_addmul(mat
->row
[i
][1 + j
],
706 mat
->row
[i
][off
+ col
], mat
->row
[row
][1 + j
]);
708 isl_int_mul(mat
->row
[i
][off
+ col
],
709 mat
->row
[i
][off
+ col
], mat
->row
[row
][off
+ col
]);
710 if (!isl_int_is_one(mat
->row
[i
][0]))
711 isl_seq_normalize(mat
->ctx
, mat
->row
[i
], off
+ tab
->n_col
);
713 t
= tab
->row_var
[row
];
714 tab
->row_var
[row
] = tab
->col_var
[col
];
715 tab
->col_var
[col
] = t
;
716 var
= isl_tab_var_from_row(tab
, row
);
719 var
= var_from_col(tab
, col
);
722 update_row_sign(tab
, row
, col
, sgn
);
725 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
726 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
728 if (!isl_tab_var_from_row(tab
, i
)->frozen
&&
729 isl_tab_row_is_redundant(tab
, i
))
730 if (isl_tab_mark_redundant(tab
, i
))
735 /* If "var" represents a column variable, then pivot is up (sgn > 0)
736 * or down (sgn < 0) to a row. The variable is assumed not to be
737 * unbounded in the specified direction.
738 * If sgn = 0, then the variable is unbounded in both directions,
739 * and we pivot with any row we can find.
741 static void to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
)
744 unsigned off
= 2 + tab
->M
;
750 for (r
= tab
->n_redundant
; r
< tab
->n_row
; ++r
)
751 if (!isl_int_is_zero(tab
->mat
->row
[r
][off
+var
->index
]))
753 isl_assert(tab
->mat
->ctx
, r
< tab
->n_row
, return);
755 r
= pivot_row(tab
, NULL
, sign
, var
->index
);
756 isl_assert(tab
->mat
->ctx
, r
>= 0, return);
759 isl_tab_pivot(tab
, r
, var
->index
);
762 static void check_table(struct isl_tab
*tab
)
768 for (i
= 0; i
< tab
->n_row
; ++i
) {
769 if (!isl_tab_var_from_row(tab
, i
)->is_nonneg
)
771 assert(!isl_int_is_neg(tab
->mat
->row
[i
][1]));
775 /* Return the sign of the maximal value of "var".
776 * If the sign is not negative, then on return from this function,
777 * the sample value will also be non-negative.
779 * If "var" is manifestly unbounded wrt positive values, we are done.
780 * Otherwise, we pivot the variable up to a row if needed
781 * Then we continue pivoting down until either
782 * - no more down pivots can be performed
783 * - the sample value is positive
784 * - the variable is pivoted into a manifestly unbounded column
786 static int sign_of_max(struct isl_tab
*tab
, struct isl_tab_var
*var
)
790 if (max_is_manifestly_unbounded(tab
, var
))
793 while (!isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
794 find_pivot(tab
, var
, var
, 1, &row
, &col
);
796 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
797 isl_tab_pivot(tab
, row
, col
);
798 if (!var
->is_row
) /* manifestly unbounded */
804 static int row_is_neg(struct isl_tab
*tab
, int row
)
807 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
808 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
810 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
812 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
815 static int row_sgn(struct isl_tab
*tab
, int row
)
818 return isl_int_sgn(tab
->mat
->row
[row
][1]);
819 if (!isl_int_is_zero(tab
->mat
->row
[row
][2]))
820 return isl_int_sgn(tab
->mat
->row
[row
][2]);
822 return isl_int_sgn(tab
->mat
->row
[row
][1]);
825 /* Perform pivots until the row variable "var" has a non-negative
826 * sample value or until no more upward pivots can be performed.
827 * Return the sign of the sample value after the pivots have been
830 static int restore_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
834 while (row_is_neg(tab
, var
->index
)) {
835 find_pivot(tab
, var
, var
, 1, &row
, &col
);
838 isl_tab_pivot(tab
, row
, col
);
839 if (!var
->is_row
) /* manifestly unbounded */
842 return row_sgn(tab
, var
->index
);
845 /* Perform pivots until we are sure that the row variable "var"
846 * can attain non-negative values. After return from this
847 * function, "var" is still a row variable, but its sample
848 * value may not be non-negative, even if the function returns 1.
850 static int at_least_zero(struct isl_tab
*tab
, struct isl_tab_var
*var
)
854 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
855 find_pivot(tab
, var
, var
, 1, &row
, &col
);
858 if (row
== var
->index
) /* manifestly unbounded */
860 isl_tab_pivot(tab
, row
, col
);
862 return !isl_int_is_neg(tab
->mat
->row
[var
->index
][1]);
865 /* Return a negative value if "var" can attain negative values.
866 * Return a non-negative value otherwise.
868 * If "var" is manifestly unbounded wrt negative values, we are done.
869 * Otherwise, if var is in a column, we can pivot it down to a row.
870 * Then we continue pivoting down until either
871 * - the pivot would result in a manifestly unbounded column
872 * => we don't perform the pivot, but simply return -1
873 * - no more down pivots can be performed
874 * - the sample value is negative
875 * If the sample value becomes negative and the variable is supposed
876 * to be nonnegative, then we undo the last pivot.
877 * However, if the last pivot has made the pivoting variable
878 * obviously redundant, then it may have moved to another row.
879 * In that case we look for upward pivots until we reach a non-negative
882 static int sign_of_min(struct isl_tab
*tab
, struct isl_tab_var
*var
)
885 struct isl_tab_var
*pivot_var
= NULL
;
887 if (min_is_manifestly_unbounded(tab
, var
))
891 row
= pivot_row(tab
, NULL
, -1, col
);
892 pivot_var
= var_from_col(tab
, col
);
893 isl_tab_pivot(tab
, row
, col
);
894 if (var
->is_redundant
)
896 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
897 if (var
->is_nonneg
) {
898 if (!pivot_var
->is_redundant
&&
899 pivot_var
->index
== row
)
900 isl_tab_pivot(tab
, row
, col
);
902 restore_row(tab
, var
);
907 if (var
->is_redundant
)
909 while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
910 find_pivot(tab
, var
, var
, -1, &row
, &col
);
911 if (row
== var
->index
)
914 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
915 pivot_var
= var_from_col(tab
, col
);
916 isl_tab_pivot(tab
, row
, col
);
917 if (var
->is_redundant
)
920 if (pivot_var
&& var
->is_nonneg
) {
921 /* pivot back to non-negative value */
922 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
923 isl_tab_pivot(tab
, row
, col
);
925 restore_row(tab
, var
);
930 static int row_at_most_neg_one(struct isl_tab
*tab
, int row
)
933 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
935 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
938 return isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
939 isl_int_abs_ge(tab
->mat
->row
[row
][1],
940 tab
->mat
->row
[row
][0]);
943 /* Return 1 if "var" can attain values <= -1.
944 * Return 0 otherwise.
946 * The sample value of "var" is assumed to be non-negative when the
947 * the function is called and will be made non-negative again before
948 * the function returns.
950 int isl_tab_min_at_most_neg_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
953 struct isl_tab_var
*pivot_var
;
955 if (min_is_manifestly_unbounded(tab
, var
))
959 row
= pivot_row(tab
, NULL
, -1, col
);
960 pivot_var
= var_from_col(tab
, col
);
961 isl_tab_pivot(tab
, row
, col
);
962 if (var
->is_redundant
)
964 if (row_at_most_neg_one(tab
, var
->index
)) {
965 if (var
->is_nonneg
) {
966 if (!pivot_var
->is_redundant
&&
967 pivot_var
->index
== row
)
968 isl_tab_pivot(tab
, row
, col
);
970 restore_row(tab
, var
);
975 if (var
->is_redundant
)
978 find_pivot(tab
, var
, var
, -1, &row
, &col
);
979 if (row
== var
->index
)
983 pivot_var
= var_from_col(tab
, col
);
984 isl_tab_pivot(tab
, row
, col
);
985 if (var
->is_redundant
)
987 } while (!row_at_most_neg_one(tab
, var
->index
));
988 if (var
->is_nonneg
) {
989 /* pivot back to non-negative value */
990 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
991 isl_tab_pivot(tab
, row
, col
);
992 restore_row(tab
, var
);
997 /* Return 1 if "var" can attain values >= 1.
998 * Return 0 otherwise.
1000 static int at_least_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1005 if (max_is_manifestly_unbounded(tab
, var
))
1007 to_row(tab
, var
, 1);
1008 r
= tab
->mat
->row
[var
->index
];
1009 while (isl_int_lt(r
[1], r
[0])) {
1010 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1012 return isl_int_ge(r
[1], r
[0]);
1013 if (row
== var
->index
) /* manifestly unbounded */
1015 isl_tab_pivot(tab
, row
, col
);
1020 static void swap_cols(struct isl_tab
*tab
, int col1
, int col2
)
1023 unsigned off
= 2 + tab
->M
;
1024 t
= tab
->col_var
[col1
];
1025 tab
->col_var
[col1
] = tab
->col_var
[col2
];
1026 tab
->col_var
[col2
] = t
;
1027 var_from_col(tab
, col1
)->index
= col1
;
1028 var_from_col(tab
, col2
)->index
= col2
;
1029 tab
->mat
= isl_mat_swap_cols(tab
->mat
, off
+ col1
, off
+ col2
);
1032 /* Mark column with index "col" as representing a zero variable.
1033 * If we may need to undo the operation the column is kept,
1034 * but no longer considered.
1035 * Otherwise, the column is simply removed.
1037 * The column may be interchanged with some other column. If it
1038 * is interchanged with a later column, return 1. Otherwise return 0.
1039 * If the columns are checked in order in the calling function,
1040 * then a return value of 1 means that the column with the given
1041 * column number may now contain a different column that
1042 * hasn't been checked yet.
1044 int isl_tab_kill_col(struct isl_tab
*tab
, int col
)
1046 var_from_col(tab
, col
)->is_zero
= 1;
1047 if (tab
->need_undo
) {
1048 isl_tab_push_var(tab
, isl_tab_undo_zero
, var_from_col(tab
, col
));
1049 if (col
!= tab
->n_dead
)
1050 swap_cols(tab
, col
, tab
->n_dead
);
1054 if (col
!= tab
->n_col
- 1)
1055 swap_cols(tab
, col
, tab
->n_col
- 1);
1056 var_from_col(tab
, tab
->n_col
- 1)->index
= -1;
1062 /* Row variable "var" is non-negative and cannot attain any values
1063 * larger than zero. This means that the coefficients of the unrestricted
1064 * column variables are zero and that the coefficients of the non-negative
1065 * column variables are zero or negative.
1066 * Each of the non-negative variables with a negative coefficient can
1067 * then also be written as the negative sum of non-negative variables
1068 * and must therefore also be zero.
1070 static void close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1073 struct isl_mat
*mat
= tab
->mat
;
1074 unsigned off
= 2 + tab
->M
;
1076 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return);
1078 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1079 if (isl_int_is_zero(mat
->row
[var
->index
][off
+ j
]))
1081 isl_assert(tab
->mat
->ctx
,
1082 isl_int_is_neg(mat
->row
[var
->index
][off
+ j
]), return);
1083 if (isl_tab_kill_col(tab
, j
))
1086 isl_tab_mark_redundant(tab
, var
->index
);
1089 /* Add a constraint to the tableau and allocate a row for it.
1090 * Return the index into the constraint array "con".
1092 int isl_tab_allocate_con(struct isl_tab
*tab
)
1096 isl_assert(tab
->mat
->ctx
, tab
->n_row
< tab
->mat
->n_row
, return -1);
1099 tab
->con
[r
].index
= tab
->n_row
;
1100 tab
->con
[r
].is_row
= 1;
1101 tab
->con
[r
].is_nonneg
= 0;
1102 tab
->con
[r
].is_zero
= 0;
1103 tab
->con
[r
].is_redundant
= 0;
1104 tab
->con
[r
].frozen
= 0;
1105 tab
->con
[r
].negated
= 0;
1106 tab
->row_var
[tab
->n_row
] = ~r
;
1110 isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]);
1115 /* Add a variable to the tableau and allocate a column for it.
1116 * Return the index into the variable array "var".
1118 int isl_tab_allocate_var(struct isl_tab
*tab
)
1122 unsigned off
= 2 + tab
->M
;
1124 isl_assert(tab
->mat
->ctx
, tab
->n_col
< tab
->mat
->n_col
, return -1);
1125 isl_assert(tab
->mat
->ctx
, tab
->n_var
< tab
->max_var
, return -1);
1128 tab
->var
[r
].index
= tab
->n_col
;
1129 tab
->var
[r
].is_row
= 0;
1130 tab
->var
[r
].is_nonneg
= 0;
1131 tab
->var
[r
].is_zero
= 0;
1132 tab
->var
[r
].is_redundant
= 0;
1133 tab
->var
[r
].frozen
= 0;
1134 tab
->var
[r
].negated
= 0;
1135 tab
->col_var
[tab
->n_col
] = r
;
1137 for (i
= 0; i
< tab
->n_row
; ++i
)
1138 isl_int_set_si(tab
->mat
->row
[i
][off
+ tab
->n_col
], 0);
1142 isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->var
[r
]);
1147 /* Add a row to the tableau. The row is given as an affine combination
1148 * of the original variables and needs to be expressed in terms of the
1151 * We add each term in turn.
1152 * If r = n/d_r is the current sum and we need to add k x, then
1153 * if x is a column variable, we increase the numerator of
1154 * this column by k d_r
1155 * if x = f/d_x is a row variable, then the new representation of r is
1157 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1158 * --- + --- = ------------------- = -------------------
1159 * d_r d_r d_r d_x/g m
1161 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1163 int isl_tab_add_row(struct isl_tab
*tab
, isl_int
*line
)
1169 unsigned off
= 2 + tab
->M
;
1171 r
= isl_tab_allocate_con(tab
);
1177 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1178 isl_int_set_si(row
[0], 1);
1179 isl_int_set(row
[1], line
[0]);
1180 isl_seq_clr(row
+ 2, tab
->M
+ tab
->n_col
);
1181 for (i
= 0; i
< tab
->n_var
; ++i
) {
1182 if (tab
->var
[i
].is_zero
)
1184 if (tab
->var
[i
].is_row
) {
1186 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1187 isl_int_swap(a
, row
[0]);
1188 isl_int_divexact(a
, row
[0], a
);
1190 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1191 isl_int_mul(b
, b
, line
[1 + i
]);
1192 isl_seq_combine(row
+ 1, a
, row
+ 1,
1193 b
, tab
->mat
->row
[tab
->var
[i
].index
] + 1,
1194 1 + tab
->M
+ tab
->n_col
);
1196 isl_int_addmul(row
[off
+ tab
->var
[i
].index
],
1197 line
[1 + i
], row
[0]);
1198 if (tab
->M
&& i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
1199 isl_int_submul(row
[2], line
[1 + i
], row
[0]);
1201 isl_seq_normalize(tab
->mat
->ctx
, row
, off
+ tab
->n_col
);
1206 tab
->row_sign
[tab
->con
[r
].index
] = 0;
1211 static int drop_row(struct isl_tab
*tab
, int row
)
1213 isl_assert(tab
->mat
->ctx
, ~tab
->row_var
[row
] == tab
->n_con
- 1, return -1);
1214 if (row
!= tab
->n_row
- 1)
1215 swap_rows(tab
, row
, tab
->n_row
- 1);
1221 static int drop_col(struct isl_tab
*tab
, int col
)
1223 isl_assert(tab
->mat
->ctx
, tab
->col_var
[col
] == tab
->n_var
- 1, return -1);
1224 if (col
!= tab
->n_col
- 1)
1225 swap_cols(tab
, col
, tab
->n_col
- 1);
1231 /* Add inequality "ineq" and check if it conflicts with the
1232 * previously added constraints or if it is obviously redundant.
1234 struct isl_tab
*isl_tab_add_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1241 r
= isl_tab_add_row(tab
, ineq
);
1244 tab
->con
[r
].is_nonneg
= 1;
1245 isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1246 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1247 isl_tab_mark_redundant(tab
, tab
->con
[r
].index
);
1251 sgn
= restore_row(tab
, &tab
->con
[r
]);
1253 return isl_tab_mark_empty(tab
);
1254 if (tab
->con
[r
].is_row
&& isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1255 isl_tab_mark_redundant(tab
, tab
->con
[r
].index
);
1262 /* Pivot a non-negative variable down until it reaches the value zero
1263 * and then pivot the variable into a column position.
1265 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1269 unsigned off
= 2 + tab
->M
;
1274 while (isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1275 find_pivot(tab
, var
, NULL
, -1, &row
, &col
);
1276 isl_assert(tab
->mat
->ctx
, row
!= -1, return -1);
1277 isl_tab_pivot(tab
, row
, col
);
1282 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
)
1283 if (!isl_int_is_zero(tab
->mat
->row
[var
->index
][off
+ i
]))
1286 isl_assert(tab
->mat
->ctx
, i
< tab
->n_col
, return -1);
1287 isl_tab_pivot(tab
, var
->index
, i
);
1292 /* We assume Gaussian elimination has been performed on the equalities.
1293 * The equalities can therefore never conflict.
1294 * Adding the equalities is currently only really useful for a later call
1295 * to isl_tab_ineq_type.
1297 static struct isl_tab
*add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1304 r
= isl_tab_add_row(tab
, eq
);
1308 r
= tab
->con
[r
].index
;
1309 i
= isl_seq_first_non_zero(tab
->mat
->row
[r
] + 2 + tab
->M
+ tab
->n_dead
,
1310 tab
->n_col
- tab
->n_dead
);
1311 isl_assert(tab
->mat
->ctx
, i
>= 0, goto error
);
1313 isl_tab_pivot(tab
, r
, i
);
1314 isl_tab_kill_col(tab
, i
);
1323 /* Add an equality that is known to be valid for the given tableau.
1325 struct isl_tab
*isl_tab_add_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1327 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
)
1955 if (tab
->con
[con
].is_zero
)
1957 if (tab
->con
[con
].is_redundant
)
1959 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
1962 /* Take a snapshot of the tableau that can be restored by s call to
1965 struct isl_tab_undo
*isl_tab_snap(struct isl_tab
*tab
)
1973 /* Undo the operation performed by isl_tab_relax.
1975 static void unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1977 unsigned off
= 2 + tab
->M
;
1979 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
1980 to_row(tab
, var
, 1);
1983 isl_int_sub(tab
->mat
->row
[var
->index
][1],
1984 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
1988 for (i
= 0; i
< tab
->n_row
; ++i
) {
1989 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
1991 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
1992 tab
->mat
->row
[i
][off
+ var
->index
]);
1998 static void perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2000 struct isl_tab_var
*var
= var_from_index(tab
, undo
->u
.var_index
);
2001 switch(undo
->type
) {
2002 case isl_tab_undo_nonneg
:
2005 case isl_tab_undo_redundant
:
2006 var
->is_redundant
= 0;
2009 case isl_tab_undo_zero
:
2013 case isl_tab_undo_allocate
:
2014 if (undo
->u
.var_index
>= 0) {
2015 isl_assert(tab
->mat
->ctx
, !var
->is_row
, return);
2016 drop_col(tab
, var
->index
);
2020 if (!max_is_manifestly_unbounded(tab
, var
))
2021 to_row(tab
, var
, 1);
2022 else if (!min_is_manifestly_unbounded(tab
, var
))
2023 to_row(tab
, var
, -1);
2025 to_row(tab
, var
, 0);
2027 drop_row(tab
, var
->index
);
2029 case isl_tab_undo_relax
:
2035 /* Restore the tableau to the state where the basic variables
2036 * are those in "col_var".
2037 * We first construct a list of variables that are currently in
2038 * the basis, but shouldn't. Then we iterate over all variables
2039 * that should be in the basis and for each one that is currently
2040 * not in the basis, we exchange it with one of the elements of the
2041 * list constructed before.
2042 * We can always find an appropriate variable to pivot with because
2043 * the current basis is mapped to the old basis by a non-singular
2044 * matrix and so we can never end up with a zero row.
2046 static int restore_basis(struct isl_tab
*tab
, int *col_var
)
2050 int *extra
= NULL
; /* current columns that contain bad stuff */
2051 unsigned off
= 2 + tab
->M
;
2053 extra
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
2056 for (i
= 0; i
< tab
->n_col
; ++i
) {
2057 for (j
= 0; j
< tab
->n_col
; ++j
)
2058 if (tab
->col_var
[i
] == col_var
[j
])
2062 extra
[n_extra
++] = i
;
2064 for (i
= 0; i
< tab
->n_col
&& n_extra
> 0; ++i
) {
2065 struct isl_tab_var
*var
;
2068 for (j
= 0; j
< tab
->n_col
; ++j
)
2069 if (col_var
[i
] == tab
->col_var
[j
])
2073 var
= var_from_index(tab
, col_var
[i
]);
2075 for (j
= 0; j
< n_extra
; ++j
)
2076 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+extra
[j
]]))
2078 isl_assert(tab
->mat
->ctx
, j
< n_extra
, goto error
);
2079 isl_tab_pivot(tab
, row
, extra
[j
]);
2080 extra
[j
] = extra
[--n_extra
];
2092 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2094 switch (undo
->type
) {
2095 case isl_tab_undo_empty
:
2098 case isl_tab_undo_nonneg
:
2099 case isl_tab_undo_redundant
:
2100 case isl_tab_undo_zero
:
2101 case isl_tab_undo_allocate
:
2102 case isl_tab_undo_relax
:
2103 perform_undo_var(tab
, undo
);
2105 case isl_tab_undo_bset_eq
:
2106 isl_basic_set_free_equality(tab
->bset
, 1);
2108 case isl_tab_undo_bset_ineq
:
2109 isl_basic_set_free_inequality(tab
->bset
, 1);
2111 case isl_tab_undo_bset_div
:
2112 isl_basic_set_free_div(tab
->bset
, 1);
2114 tab
->samples
->n_col
--;
2116 case isl_tab_undo_saved_basis
:
2117 if (restore_basis(tab
, undo
->u
.col_var
) < 0)
2120 case isl_tab_undo_drop_sample
:
2124 isl_assert(tab
->mat
->ctx
, 0, return -1);
2129 /* Return the tableau to the state it was in when the snapshot "snap"
2132 int isl_tab_rollback(struct isl_tab
*tab
, struct isl_tab_undo
*snap
)
2134 struct isl_tab_undo
*undo
, *next
;
2140 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
2144 if (perform_undo(tab
, undo
) < 0) {
2158 /* The given row "row" represents an inequality violated by all
2159 * points in the tableau. Check for some special cases of such
2160 * separating constraints.
2161 * In particular, if the row has been reduced to the constant -1,
2162 * then we know the inequality is adjacent (but opposite) to
2163 * an equality in the tableau.
2164 * If the row has been reduced to r = -1 -r', with r' an inequality
2165 * of the tableau, then the inequality is adjacent (but opposite)
2166 * to the inequality r'.
2168 static enum isl_ineq_type
separation_type(struct isl_tab
*tab
, unsigned row
)
2171 unsigned off
= 2 + tab
->M
;
2174 return isl_ineq_separate
;
2176 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
2177 return isl_ineq_separate
;
2178 if (!isl_int_is_negone(tab
->mat
->row
[row
][1]))
2179 return isl_ineq_separate
;
2181 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
2182 tab
->n_col
- tab
->n_dead
);
2184 return isl_ineq_adj_eq
;
2186 if (!isl_int_is_negone(tab
->mat
->row
[row
][off
+ tab
->n_dead
+ pos
]))
2187 return isl_ineq_separate
;
2189 pos
= isl_seq_first_non_zero(
2190 tab
->mat
->row
[row
] + off
+ tab
->n_dead
+ pos
+ 1,
2191 tab
->n_col
- tab
->n_dead
- pos
- 1);
2193 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
2196 /* Check the effect of inequality "ineq" on the tableau "tab".
2198 * isl_ineq_redundant: satisfied by all points in the tableau
2199 * isl_ineq_separate: satisfied by no point in the tableau
2200 * isl_ineq_cut: satisfied by some by not all points
2201 * isl_ineq_adj_eq: adjacent to an equality
2202 * isl_ineq_adj_ineq: adjacent to an inequality.
2204 enum isl_ineq_type
isl_tab_ineq_type(struct isl_tab
*tab
, isl_int
*ineq
)
2206 enum isl_ineq_type type
= isl_ineq_error
;
2207 struct isl_tab_undo
*snap
= NULL
;
2212 return isl_ineq_error
;
2214 if (isl_tab_extend_cons(tab
, 1) < 0)
2215 return isl_ineq_error
;
2217 snap
= isl_tab_snap(tab
);
2219 con
= isl_tab_add_row(tab
, ineq
);
2223 row
= tab
->con
[con
].index
;
2224 if (isl_tab_row_is_redundant(tab
, row
))
2225 type
= isl_ineq_redundant
;
2226 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
2228 isl_int_abs_ge(tab
->mat
->row
[row
][1],
2229 tab
->mat
->row
[row
][0]))) {
2230 if (at_least_zero(tab
, &tab
->con
[con
]))
2231 type
= isl_ineq_cut
;
2233 type
= separation_type(tab
, row
);
2234 } else if (tab
->rational
? (sign_of_min(tab
, &tab
->con
[con
]) < 0)
2235 : isl_tab_min_at_most_neg_one(tab
, &tab
->con
[con
]))
2236 type
= isl_ineq_cut
;
2238 type
= isl_ineq_redundant
;
2240 if (isl_tab_rollback(tab
, snap
))
2241 return isl_ineq_error
;
2244 isl_tab_rollback(tab
, snap
);
2245 return isl_ineq_error
;
2248 void isl_tab_dump(struct isl_tab
*tab
, FILE *out
, int indent
)
2254 fprintf(out
, "%*snull tab\n", indent
, "");
2257 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
2258 tab
->n_redundant
, tab
->n_dead
);
2260 fprintf(out
, ", rational");
2262 fprintf(out
, ", empty");
2264 fprintf(out
, "%*s[", indent
, "");
2265 for (i
= 0; i
< tab
->n_var
; ++i
) {
2267 fprintf(out
, (i
== tab
->n_param
||
2268 i
== tab
->n_var
- tab
->n_div
) ? "; "
2270 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
2272 tab
->var
[i
].is_zero
? " [=0]" :
2273 tab
->var
[i
].is_redundant
? " [R]" : "");
2275 fprintf(out
, "]\n");
2276 fprintf(out
, "%*s[", indent
, "");
2277 for (i
= 0; i
< tab
->n_con
; ++i
) {
2280 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
2282 tab
->con
[i
].is_zero
? " [=0]" :
2283 tab
->con
[i
].is_redundant
? " [R]" : "");
2285 fprintf(out
, "]\n");
2286 fprintf(out
, "%*s[", indent
, "");
2287 for (i
= 0; i
< tab
->n_row
; ++i
) {
2288 const char *sign
= "";
2291 if (tab
->row_sign
) {
2292 if (tab
->row_sign
[i
] == isl_tab_row_unknown
)
2294 else if (tab
->row_sign
[i
] == isl_tab_row_neg
)
2296 else if (tab
->row_sign
[i
] == isl_tab_row_pos
)
2301 fprintf(out
, "r%d: %d%s%s", i
, tab
->row_var
[i
],
2302 isl_tab_var_from_row(tab
, i
)->is_nonneg
? " [>=0]" : "", sign
);
2304 fprintf(out
, "]\n");
2305 fprintf(out
, "%*s[", indent
, "");
2306 for (i
= 0; i
< tab
->n_col
; ++i
) {
2309 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
2310 var_from_col(tab
, i
)->is_nonneg
? " [>=0]" : "");
2312 fprintf(out
, "]\n");
2313 r
= tab
->mat
->n_row
;
2314 tab
->mat
->n_row
= tab
->n_row
;
2315 c
= tab
->mat
->n_col
;
2316 tab
->mat
->n_col
= 2 + tab
->M
+ tab
->n_col
;
2317 isl_mat_dump(tab
->mat
, out
, indent
);
2318 tab
->mat
->n_row
= r
;
2319 tab
->mat
->n_col
= c
;
2321 isl_basic_set_dump(tab
->bset
, out
, indent
);