1 #include "isl_map_private.h"
5 * The implementation of tableaus in this file was inspired by Section 8
6 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
7 * prover for program checking".
10 struct isl_tab
*isl_tab_alloc(struct isl_ctx
*ctx
,
11 unsigned n_row
, unsigned n_var
)
16 tab
= isl_calloc_type(ctx
, struct isl_tab
);
19 tab
->mat
= isl_mat_alloc(ctx
, n_row
, 2 + n_var
);
22 tab
->var
= isl_alloc_array(ctx
, struct isl_tab_var
, n_var
);
25 tab
->con
= isl_alloc_array(ctx
, struct isl_tab_var
, n_row
);
28 tab
->col_var
= isl_alloc_array(ctx
, int, n_var
);
31 tab
->row_var
= isl_alloc_array(ctx
, int, n_row
);
34 for (i
= 0; i
< n_var
; ++i
) {
35 tab
->var
[i
].index
= i
;
36 tab
->var
[i
].is_row
= 0;
37 tab
->var
[i
].is_nonneg
= 0;
38 tab
->var
[i
].is_zero
= 0;
39 tab
->var
[i
].is_redundant
= 0;
40 tab
->var
[i
].frozen
= 0;
53 tab
->bottom
.type
= isl_tab_undo_bottom
;
54 tab
->bottom
.next
= NULL
;
55 tab
->top
= &tab
->bottom
;
58 isl_tab_free(ctx
, tab
);
62 static int extend_cons(struct isl_ctx
*ctx
, struct isl_tab
*tab
, unsigned n_new
)
64 if (tab
->max_con
< tab
->n_con
+ n_new
) {
65 struct isl_tab_var
*con
;
67 con
= isl_realloc_array(ctx
, tab
->con
,
68 struct isl_tab_var
, tab
->max_con
+ n_new
);
72 tab
->max_con
+= n_new
;
74 if (tab
->mat
->n_row
< tab
->n_row
+ n_new
) {
77 tab
->mat
= isl_mat_extend(ctx
, tab
->mat
,
78 tab
->n_row
+ n_new
, tab
->n_col
);
81 row_var
= isl_realloc_array(ctx
, tab
->row_var
,
82 int, tab
->mat
->n_row
);
85 tab
->row_var
= row_var
;
90 struct isl_tab
*isl_tab_extend(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
93 if (extend_cons(ctx
, tab
, n_new
) >= 0)
96 isl_tab_free(ctx
, tab
);
100 static void free_undo(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
102 struct isl_tab_undo
*undo
, *next
;
104 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
111 void isl_tab_free(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
116 isl_mat_free(ctx
, tab
->mat
);
124 static struct isl_tab_var
*var_from_index(struct isl_ctx
*ctx
,
125 struct isl_tab
*tab
, int i
)
130 return &tab
->con
[~i
];
133 static struct isl_tab_var
*var_from_row(struct isl_ctx
*ctx
,
134 struct isl_tab
*tab
, int i
)
136 return var_from_index(ctx
, tab
, tab
->row_var
[i
]);
139 static struct isl_tab_var
*var_from_col(struct isl_ctx
*ctx
,
140 struct isl_tab
*tab
, int i
)
142 return var_from_index(ctx
, tab
, tab
->col_var
[i
]);
145 /* Check if there are any upper bounds on column variable "var",
146 * i.e., non-negative rows where var appears with a negative coefficient.
147 * Return 1 if there are no such bounds.
149 static int max_is_manifestly_unbounded(struct isl_ctx
*ctx
,
150 struct isl_tab
*tab
, struct isl_tab_var
*var
)
156 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
157 if (!isl_int_is_neg(tab
->mat
->row
[i
][2 + var
->index
]))
159 if (var_from_row(ctx
, tab
, i
)->is_nonneg
)
165 /* Check if there are any lower bounds on column variable "var",
166 * i.e., non-negative rows where var appears with a positive coefficient.
167 * Return 1 if there are no such bounds.
169 static int min_is_manifestly_unbounded(struct isl_ctx
*ctx
,
170 struct isl_tab
*tab
, struct isl_tab_var
*var
)
176 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
177 if (!isl_int_is_pos(tab
->mat
->row
[i
][2 + var
->index
]))
179 if (var_from_row(ctx
, tab
, i
)->is_nonneg
)
185 /* Given the index of a column "c", return the index of a row
186 * that can be used to pivot the column in, with either an increase
187 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
188 * If "var" is not NULL, then the row returned will be different from
189 * the one associated with "var".
191 * Each row in the tableau is of the form
193 * x_r = a_r0 + \sum_i a_ri x_i
195 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
196 * impose any limit on the increase or decrease in the value of x_c
197 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
198 * for the row with the smallest (most stringent) such bound.
199 * Note that the common denominator of each row drops out of the fraction.
200 * To check if row j has a smaller bound than row r, i.e.,
201 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
202 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
203 * where -sign(a_jc) is equal to "sgn".
205 static int pivot_row(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
206 struct isl_tab_var
*var
, int sgn
, int c
)
213 for (j
= tab
->n_redundant
; j
< tab
->n_row
; ++j
) {
214 if (var
&& j
== var
->index
)
216 if (!var_from_row(ctx
, tab
, j
)->is_nonneg
)
218 if (sgn
* isl_int_sgn(tab
->mat
->row
[j
][2 + c
]) >= 0)
224 isl_int_mul(t
, tab
->mat
->row
[r
][1], tab
->mat
->row
[j
][2 + c
]);
225 isl_int_submul(t
, tab
->mat
->row
[j
][1], tab
->mat
->row
[r
][2 + c
]);
226 tsgn
= sgn
* isl_int_sgn(t
);
227 if (tsgn
< 0 || (tsgn
== 0 &&
228 tab
->row_var
[j
] < tab
->row_var
[r
]))
235 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
236 * (sgn < 0) the value of row variable var.
237 * As the given row in the tableau is of the form
239 * x_r = a_r0 + \sum_i a_ri x_i
241 * we need to find a column such that the sign of a_ri is equal to "sgn"
242 * (such that an increase in x_i will have the desired effect) or a
243 * column with a variable that may attain negative values.
244 * If a_ri is positive, then we need to move x_i in the same direction
245 * to obtain the desired effect. Otherwise, x_i has to move in the
246 * opposite direction.
248 static void find_pivot(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
249 struct isl_tab_var
*var
, int sgn
, int *row
, int *col
)
256 isl_assert(ctx
, var
->is_row
, return);
257 tr
= tab
->mat
->row
[var
->index
];
260 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
261 if (isl_int_is_zero(tr
[2 + j
]))
263 if (isl_int_sgn(tr
[2 + j
]) != sgn
&&
264 var_from_col(ctx
, tab
, j
)->is_nonneg
)
266 if (c
< 0 || tab
->col_var
[j
] < tab
->col_var
[c
])
272 sgn
*= isl_int_sgn(tr
[2 + c
]);
273 r
= pivot_row(ctx
, tab
, var
, sgn
, c
);
274 *row
= r
< 0 ? var
->index
: r
;
278 /* Return 1 if row "row" represents an obviously redundant inequality.
280 * - it represents an inequality or a variable
281 * - that is the sum of a non-negative sample value and a positive
282 * combination of zero or more non-negative variables.
284 static int is_redundant(struct isl_ctx
*ctx
, struct isl_tab
*tab
, int row
)
288 if (tab
->row_var
[row
] < 0 && !var_from_row(ctx
, tab
, row
)->is_nonneg
)
291 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
294 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
295 if (isl_int_is_zero(tab
->mat
->row
[row
][2 + i
]))
297 if (isl_int_is_neg(tab
->mat
->row
[row
][2 + i
]))
299 if (!var_from_col(ctx
, tab
, i
)->is_nonneg
)
305 static void swap_rows(struct isl_ctx
*ctx
,
306 struct isl_tab
*tab
, int row1
, int row2
)
309 t
= tab
->row_var
[row1
];
310 tab
->row_var
[row1
] = tab
->row_var
[row2
];
311 tab
->row_var
[row2
] = t
;
312 var_from_row(ctx
, tab
, row1
)->index
= row1
;
313 var_from_row(ctx
, tab
, row2
)->index
= row2
;
314 tab
->mat
= isl_mat_swap_rows(ctx
, tab
->mat
, row1
, row2
);
317 static void push(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
318 enum isl_tab_undo_type type
, struct isl_tab_var
*var
)
320 struct isl_tab_undo
*undo
;
325 undo
= isl_alloc_type(ctx
, struct isl_tab_undo
);
333 undo
->next
= tab
->top
;
337 /* Mark row with index "row" as being redundant.
338 * If we may need to undo the operation or if the row represents
339 * a variable of the original problem, the row is kept,
340 * but no longer considered when looking for a pivot row.
341 * Otherwise, the row is simply removed.
343 * The row may be interchanged with some other row. If it
344 * is interchanged with a later row, return 1. Otherwise return 0.
345 * If the rows are checked in order in the calling function,
346 * then a return value of 1 means that the row with the given
347 * row number may now contain a different row that hasn't been checked yet.
349 static int mark_redundant(struct isl_ctx
*ctx
,
350 struct isl_tab
*tab
, int row
)
352 struct isl_tab_var
*var
= var_from_row(ctx
, tab
, row
);
353 var
->is_redundant
= 1;
354 isl_assert(ctx
, row
>= tab
->n_redundant
, return);
355 if (tab
->need_undo
|| tab
->row_var
[row
] >= 0) {
356 if (tab
->row_var
[row
] >= 0) {
358 push(ctx
, tab
, isl_tab_undo_nonneg
, var
);
360 if (row
!= tab
->n_redundant
)
361 swap_rows(ctx
, tab
, row
, tab
->n_redundant
);
362 push(ctx
, tab
, isl_tab_undo_redundant
, var
);
366 if (row
!= tab
->n_row
- 1)
367 swap_rows(ctx
, tab
, row
, tab
->n_row
- 1);
368 var_from_row(ctx
, tab
, tab
->n_row
- 1)->index
= -1;
374 static void mark_empty(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
376 if (!tab
->empty
&& tab
->need_undo
)
377 push(ctx
, tab
, isl_tab_undo_empty
, NULL
);
381 /* Given a row number "row" and a column number "col", pivot the tableau
382 * such that the associated variable are interchanged.
383 * The given row in the tableau expresses
385 * x_r = a_r0 + \sum_i a_ri x_i
389 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
391 * Substituting this equality into the other rows
393 * x_j = a_j0 + \sum_i a_ji x_i
395 * with a_jc \ne 0, we obtain
397 * 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
404 * where i is any other column and j is any other row,
405 * is therefore transformed into
407 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
408 * 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)
410 * The transformation is performed along the following steps
415 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
418 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
419 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
421 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
422 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
424 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
425 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
427 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
428 * 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)
431 static void pivot(struct isl_ctx
*ctx
,
432 struct isl_tab
*tab
, int row
, int col
)
437 struct isl_mat
*mat
= tab
->mat
;
438 struct isl_tab_var
*var
;
440 isl_int_swap(mat
->row
[row
][0], mat
->row
[row
][2 + col
]);
441 sgn
= isl_int_sgn(mat
->row
[row
][0]);
443 isl_int_neg(mat
->row
[row
][0], mat
->row
[row
][0]);
444 isl_int_neg(mat
->row
[row
][2 + col
], mat
->row
[row
][2 + col
]);
446 for (j
= 0; j
< 1 + tab
->n_col
; ++j
) {
449 isl_int_neg(mat
->row
[row
][1 + j
], mat
->row
[row
][1 + j
]);
451 if (!isl_int_is_one(mat
->row
[row
][0]))
452 isl_seq_normalize(mat
->row
[row
], 2 + tab
->n_col
);
453 for (i
= 0; i
< tab
->n_row
; ++i
) {
456 if (isl_int_is_zero(mat
->row
[i
][2 + col
]))
458 isl_int_mul(mat
->row
[i
][0], mat
->row
[i
][0], mat
->row
[row
][0]);
459 for (j
= 0; j
< 1 + tab
->n_col
; ++j
) {
462 isl_int_mul(mat
->row
[i
][1 + j
],
463 mat
->row
[i
][1 + j
], mat
->row
[row
][0]);
464 isl_int_addmul(mat
->row
[i
][1 + j
],
465 mat
->row
[i
][2 + col
], mat
->row
[row
][1 + j
]);
467 isl_int_mul(mat
->row
[i
][2 + col
],
468 mat
->row
[i
][2 + col
], mat
->row
[row
][2 + col
]);
469 if (!isl_int_is_one(mat
->row
[row
][0]))
470 isl_seq_normalize(mat
->row
[i
], 2 + tab
->n_col
);
472 t
= tab
->row_var
[row
];
473 tab
->row_var
[row
] = tab
->col_var
[col
];
474 tab
->col_var
[col
] = t
;
475 var
= var_from_row(ctx
, tab
, row
);
478 var
= var_from_col(ctx
, tab
, col
);
481 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
482 if (isl_int_is_zero(mat
->row
[i
][2 + col
]))
484 if (!var_from_row(ctx
, tab
, i
)->frozen
&&
485 is_redundant(ctx
, tab
, i
))
486 if (mark_redundant(ctx
, tab
, i
))
491 /* If "var" represents a column variable, then pivot is up (sgn > 0)
492 * or down (sgn < 0) to a row. The variable is assumed not to be
493 * unbounded in the specified direction.
495 static void to_row(struct isl_ctx
*ctx
,
496 struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
)
503 r
= pivot_row(ctx
, tab
, NULL
, sign
, var
->index
);
504 isl_assert(ctx
, r
>= 0, return);
505 pivot(ctx
, tab
, r
, var
->index
);
508 static void check_table(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
514 for (i
= 0; i
< tab
->n_row
; ++i
) {
515 if (!var_from_row(ctx
, tab
, i
)->is_nonneg
)
517 assert(!isl_int_is_neg(tab
->mat
->row
[i
][1]));
521 /* Return the sign of the maximal value of "var".
522 * If the sign is not negative, then on return from this function,
523 * the sample value will also be non-negative.
525 * If "var" is manifestly unbounded wrt positive values, we are done.
526 * Otherwise, we pivot the variable up to a row if needed
527 * Then we continue pivoting down until either
528 * - no more down pivots can be performed
529 * - the sample value is positive
530 * - the variable is pivoted into a manifestly unbounded column
532 static int sign_of_max(struct isl_ctx
*ctx
,
533 struct isl_tab
*tab
, struct isl_tab_var
*var
)
537 if (max_is_manifestly_unbounded(ctx
, tab
, var
))
539 to_row(ctx
, tab
, var
, 1);
540 while (!isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
541 find_pivot(ctx
, tab
, var
, 1, &row
, &col
);
543 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
544 pivot(ctx
, tab
, row
, col
);
545 if (!var
->is_row
) /* manifestly unbounded */
551 /* Perform pivots until the row variable "var" has a non-negative
552 * sample value or until no more upward pivots can be performed.
553 * Return the sign of the sample value after the pivots have been
556 static int restore_row(struct isl_ctx
*ctx
,
557 struct isl_tab
*tab
, struct isl_tab_var
*var
)
561 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
562 find_pivot(ctx
, tab
, var
, 1, &row
, &col
);
565 pivot(ctx
, tab
, row
, col
);
566 if (!var
->is_row
) /* manifestly unbounded */
569 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
572 /* Perform pivots until we are sure that the row variable "var"
573 * can attain non-negative values. After return from this
574 * function, "var" is still a row variable, but its sample
575 * value may not be non-negative, even if the function returns 1.
577 static int at_least_zero(struct isl_ctx
*ctx
,
578 struct isl_tab
*tab
, struct isl_tab_var
*var
)
582 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
583 find_pivot(ctx
, tab
, var
, 1, &row
, &col
);
586 if (row
== var
->index
) /* manifestly unbounded */
588 pivot(ctx
, tab
, row
, col
);
590 return !isl_int_is_neg(tab
->mat
->row
[var
->index
][1]);
593 /* Return a negative value if "var" can attain negative values.
594 * Return a non-negative value otherwise.
596 * If "var" is manifestly unbounded wrt negative values, we are done.
597 * Otherwise, if var is in a column, we can pivot it down to a row.
598 * Then we continue pivoting down until either
599 * - the pivot would result in a manifestly unbounded column
600 * => we don't perform the pivot, but simply return -1
601 * - no more down pivots can be performed
602 * - the sample value is negative
603 * If the sample value becomes negative and the variable is supposed
604 * to be nonnegative, then we undo the last pivot.
605 * However, if the last pivot has made the pivoting variable
606 * obviously redundant, then it may have moved to another row.
607 * In that case we look for upward pivots until we reach a non-negative
610 static int sign_of_min(struct isl_ctx
*ctx
,
611 struct isl_tab
*tab
, struct isl_tab_var
*var
)
614 struct isl_tab_var
*pivot_var
;
616 if (min_is_manifestly_unbounded(ctx
, tab
, var
))
620 row
= pivot_row(ctx
, tab
, NULL
, -1, col
);
621 pivot_var
= var_from_col(ctx
, tab
, col
);
622 pivot(ctx
, tab
, row
, col
);
623 if (var
->is_redundant
)
625 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
626 if (var
->is_nonneg
) {
627 if (!pivot_var
->is_redundant
&&
628 pivot_var
->index
== row
)
629 pivot(ctx
, tab
, row
, col
);
631 restore_row(ctx
, tab
, var
);
636 if (var
->is_redundant
)
638 while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
639 find_pivot(ctx
, tab
, var
, -1, &row
, &col
);
640 if (row
== var
->index
)
643 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
644 pivot_var
= var_from_col(ctx
, tab
, col
);
645 pivot(ctx
, tab
, row
, col
);
646 if (var
->is_redundant
)
649 if (var
->is_nonneg
) {
650 /* pivot back to non-negative value */
651 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
652 pivot(ctx
, tab
, row
, col
);
654 restore_row(ctx
, tab
, var
);
659 /* Return 1 if "var" can attain values <= -1.
660 * Return 0 otherwise.
662 * The sample value of "var" is assumed to be non-negative when the
663 * the function is called and will be made non-negative again before
664 * the function returns.
666 static int min_at_most_neg_one(struct isl_ctx
*ctx
,
667 struct isl_tab
*tab
, struct isl_tab_var
*var
)
670 struct isl_tab_var
*pivot_var
;
672 if (min_is_manifestly_unbounded(ctx
, tab
, var
))
676 row
= pivot_row(ctx
, tab
, NULL
, -1, col
);
677 pivot_var
= var_from_col(ctx
, tab
, col
);
678 pivot(ctx
, tab
, row
, col
);
679 if (var
->is_redundant
)
681 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1]) &&
682 isl_int_abs_ge(tab
->mat
->row
[var
->index
][1],
683 tab
->mat
->row
[var
->index
][0])) {
684 if (var
->is_nonneg
) {
685 if (!pivot_var
->is_redundant
&&
686 pivot_var
->index
== row
)
687 pivot(ctx
, tab
, row
, col
);
689 restore_row(ctx
, tab
, var
);
694 if (var
->is_redundant
)
697 find_pivot(ctx
, tab
, var
, -1, &row
, &col
);
698 if (row
== var
->index
)
702 pivot_var
= var_from_col(ctx
, tab
, col
);
703 pivot(ctx
, tab
, row
, col
);
704 if (var
->is_redundant
)
706 } while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1]) ||
707 isl_int_abs_lt(tab
->mat
->row
[var
->index
][1],
708 tab
->mat
->row
[var
->index
][0]));
709 if (var
->is_nonneg
) {
710 /* pivot back to non-negative value */
711 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
712 pivot(ctx
, tab
, row
, col
);
713 restore_row(ctx
, tab
, var
);
718 /* Return 1 if "var" can attain values >= 1.
719 * Return 0 otherwise.
721 static int at_least_one(struct isl_ctx
*ctx
,
722 struct isl_tab
*tab
, struct isl_tab_var
*var
)
727 if (max_is_manifestly_unbounded(ctx
, tab
, var
))
729 to_row(ctx
, tab
, var
, 1);
730 r
= tab
->mat
->row
[var
->index
];
731 while (isl_int_lt(r
[1], r
[0])) {
732 find_pivot(ctx
, tab
, var
, 1, &row
, &col
);
734 return isl_int_ge(r
[1], r
[0]);
735 if (row
== var
->index
) /* manifestly unbounded */
737 pivot(ctx
, tab
, row
, col
);
742 static void swap_cols(struct isl_ctx
*ctx
,
743 struct isl_tab
*tab
, int col1
, int col2
)
746 t
= tab
->col_var
[col1
];
747 tab
->col_var
[col1
] = tab
->col_var
[col2
];
748 tab
->col_var
[col2
] = t
;
749 var_from_col(ctx
, tab
, col1
)->index
= col1
;
750 var_from_col(ctx
, tab
, col2
)->index
= col2
;
751 tab
->mat
= isl_mat_swap_cols(ctx
, tab
->mat
, 2 + col1
, 2 + col2
);
754 /* Mark column with index "col" as representing a zero variable.
755 * If we may need to undo the operation the column is kept,
756 * but no longer considered.
757 * Otherwise, the column is simply removed.
759 * The column may be interchanged with some other column. If it
760 * is interchanged with a later column, return 1. Otherwise return 0.
761 * If the columns are checked in order in the calling function,
762 * then a return value of 1 means that the column with the given
763 * column number may now contain a different column that
764 * hasn't been checked yet.
766 static int kill_col(struct isl_ctx
*ctx
,
767 struct isl_tab
*tab
, int col
)
769 var_from_col(ctx
, tab
, col
)->is_zero
= 1;
770 if (tab
->need_undo
) {
771 push(ctx
, tab
, isl_tab_undo_zero
, var_from_col(ctx
, tab
, col
));
772 if (col
!= tab
->n_dead
)
773 swap_cols(ctx
, tab
, col
, tab
->n_dead
);
777 if (col
!= tab
->n_col
- 1)
778 swap_cols(ctx
, tab
, col
, tab
->n_col
- 1);
779 var_from_col(ctx
, tab
, tab
->n_col
- 1)->index
= -1;
785 /* Row variable "var" is non-negative and cannot attain any values
786 * larger than zero. This means that the coefficients of the unrestricted
787 * column variables are zero and that the coefficients of the non-negative
788 * column variables are zero or negative.
789 * Each of the non-negative variables with a negative coefficient can
790 * then also be written as the negative sum of non-negative variables
791 * and must therefore also be zero.
793 static void close_row(struct isl_ctx
*ctx
,
794 struct isl_tab
*tab
, struct isl_tab_var
*var
)
797 struct isl_mat
*mat
= tab
->mat
;
799 isl_assert(ctx
, var
->is_nonneg
, return);
801 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
802 if (isl_int_is_zero(mat
->row
[var
->index
][2 + j
]))
804 isl_assert(ctx
, isl_int_is_neg(mat
->row
[var
->index
][2 + j
]),
806 if (kill_col(ctx
, tab
, j
))
809 mark_redundant(ctx
, tab
, var
->index
);
812 /* Add a row to the tableau. The row is given as an affine combination
813 * of the original variables and needs to be expressed in terms of the
816 * We add each term in turn.
817 * If r = n/d_r is the current sum and we need to add k x, then
818 * if x is a column variable, we increase the numerator of
819 * this column by k d_r
820 * if x = f/d_x is a row variable, then the new representation of r is
822 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
823 * --- + --- = ------------------- = -------------------
824 * d_r d_r d_r d_x/g m
826 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
828 static int add_row(struct isl_ctx
*ctx
, struct isl_tab
*tab
, isl_int
*line
)
835 isl_assert(ctx
, tab
->n_row
< tab
->mat
->n_row
, return -1);
840 tab
->con
[r
].index
= tab
->n_row
;
841 tab
->con
[r
].is_row
= 1;
842 tab
->con
[r
].is_nonneg
= 0;
843 tab
->con
[r
].is_zero
= 0;
844 tab
->con
[r
].is_redundant
= 0;
845 tab
->con
[r
].frozen
= 0;
846 tab
->row_var
[tab
->n_row
] = ~r
;
847 row
= tab
->mat
->row
[tab
->n_row
];
848 isl_int_set_si(row
[0], 1);
849 isl_int_set(row
[1], line
[0]);
850 isl_seq_clr(row
+ 2, tab
->n_col
);
851 for (i
= 0; i
< tab
->n_var
; ++i
) {
852 if (tab
->var
[i
].is_zero
)
854 if (tab
->var
[i
].is_row
) {
856 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
857 isl_int_swap(a
, row
[0]);
858 isl_int_divexact(a
, row
[0], a
);
860 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
861 isl_int_mul(b
, b
, line
[1 + i
]);
862 isl_seq_combine(row
+ 1, a
, row
+ 1,
863 b
, tab
->mat
->row
[tab
->var
[i
].index
] + 1,
866 isl_int_addmul(row
[2 + tab
->var
[i
].index
],
867 line
[1 + i
], row
[0]);
869 isl_seq_normalize(row
, 2 + tab
->n_col
);
872 push(ctx
, tab
, isl_tab_undo_allocate
, &tab
->con
[r
]);
879 static int drop_row(struct isl_ctx
*ctx
, struct isl_tab
*tab
, int row
)
881 isl_assert(ctx
, ~tab
->row_var
[row
] == tab
->n_con
- 1, return -1);
882 if (row
!= tab
->n_row
- 1)
883 swap_rows(ctx
, tab
, row
, tab
->n_row
- 1);
889 /* Add inequality "ineq" and check if it conflicts with the
890 * previously added constraints or if it is obviously redundant.
892 struct isl_tab
*isl_tab_add_ineq(struct isl_ctx
*ctx
,
893 struct isl_tab
*tab
, isl_int
*ineq
)
900 r
= add_row(ctx
, tab
, ineq
);
903 tab
->con
[r
].is_nonneg
= 1;
904 push(ctx
, tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
905 if (is_redundant(ctx
, tab
, tab
->con
[r
].index
)) {
906 mark_redundant(ctx
, tab
, tab
->con
[r
].index
);
910 sgn
= restore_row(ctx
, tab
, &tab
->con
[r
]);
912 mark_empty(ctx
, tab
);
913 else if (tab
->con
[r
].is_row
&&
914 is_redundant(ctx
, tab
, tab
->con
[r
].index
))
915 mark_redundant(ctx
, tab
, tab
->con
[r
].index
);
918 isl_tab_free(ctx
, tab
);
922 /* We assume Gaussian elimination has been performed on the equalities.
923 * The equalities can therefore never conflict.
924 * Adding the equalities is currently only really useful for a later call
925 * to isl_tab_ineq_type.
927 static struct isl_tab
*add_eq(struct isl_ctx
*ctx
,
928 struct isl_tab
*tab
, isl_int
*eq
)
935 r
= add_row(ctx
, tab
, eq
);
939 r
= tab
->con
[r
].index
;
940 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
941 if (isl_int_is_zero(tab
->mat
->row
[r
][2 + i
]))
943 pivot(ctx
, tab
, r
, i
);
944 kill_col(ctx
, tab
, i
);
950 isl_tab_free(ctx
, tab
);
954 struct isl_tab
*isl_tab_from_basic_map(struct isl_basic_map
*bmap
)
961 tab
= isl_tab_alloc(bmap
->ctx
,
962 isl_basic_map_total_dim(bmap
) + bmap
->n_ineq
+ 1,
963 isl_basic_map_total_dim(bmap
));
966 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
967 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
968 mark_empty(bmap
->ctx
, tab
);
971 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
972 tab
= add_eq(bmap
->ctx
, tab
, bmap
->eq
[i
]);
976 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
977 tab
= isl_tab_add_ineq(bmap
->ctx
, tab
, bmap
->ineq
[i
]);
978 if (!tab
|| tab
->empty
)
984 struct isl_tab
*isl_tab_from_basic_set(struct isl_basic_set
*bset
)
986 return isl_tab_from_basic_map((struct isl_basic_map
*)bset
);
989 /* Construct a tableau corresponding to the recession cone of "bmap".
991 struct isl_tab
*isl_tab_from_recession_cone(struct isl_basic_map
*bmap
)
999 tab
= isl_tab_alloc(bmap
->ctx
, bmap
->n_eq
+ bmap
->n_ineq
,
1000 isl_basic_map_total_dim(bmap
));
1003 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
1006 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1007 isl_int_swap(bmap
->eq
[i
][0], cst
);
1008 tab
= add_eq(bmap
->ctx
, tab
, bmap
->eq
[i
]);
1009 isl_int_swap(bmap
->eq
[i
][0], cst
);
1013 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1015 isl_int_swap(bmap
->ineq
[i
][0], cst
);
1016 r
= add_row(bmap
->ctx
, tab
, bmap
->ineq
[i
]);
1017 isl_int_swap(bmap
->ineq
[i
][0], cst
);
1020 tab
->con
[r
].is_nonneg
= 1;
1021 push(bmap
->ctx
, tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1028 isl_tab_free(bmap
->ctx
, tab
);
1032 /* Assuming "tab" is the tableau of a cone, check if the cone is
1033 * bounded, i.e., if it is empty or only contains the origin.
1035 int isl_tab_cone_is_bounded(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
1043 if (tab
->n_dead
== tab
->n_col
)
1046 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1047 struct isl_tab_var
*var
;
1048 var
= var_from_row(ctx
, tab
, i
);
1049 if (!var
->is_nonneg
)
1051 if (sign_of_max(ctx
, tab
, var
) == 0)
1052 close_row(ctx
, tab
, var
);
1055 if (tab
->n_dead
== tab
->n_col
)
1061 static int sample_is_integer(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
1065 for (i
= 0; i
< tab
->n_var
; ++i
) {
1067 if (!tab
->var
[i
].is_row
)
1069 row
= tab
->var
[i
].index
;
1070 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1071 tab
->mat
->row
[row
][0]))
1077 static struct isl_vec
*extract_integer_sample(struct isl_ctx
*ctx
,
1078 struct isl_tab
*tab
)
1081 struct isl_vec
*vec
;
1083 vec
= isl_vec_alloc(ctx
, 1 + tab
->n_var
);
1087 isl_int_set_si(vec
->block
.data
[0], 1);
1088 for (i
= 0; i
< tab
->n_var
; ++i
) {
1089 if (!tab
->var
[i
].is_row
)
1090 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
1092 int row
= tab
->var
[i
].index
;
1093 isl_int_divexact(vec
->block
.data
[1 + i
],
1094 tab
->mat
->row
[row
][1], tab
->mat
->row
[row
][0]);
1101 /* Update "bmap" based on the results of the tableau "tab".
1102 * In particular, implicit equalities are made explicit, redundant constraints
1103 * are removed and if the sample value happens to be integer, it is stored
1104 * in "bmap" (unless "bmap" already had an integer sample).
1106 * The tableau is assumed to have been created from "bmap" using
1107 * isl_tab_from_basic_map.
1109 struct isl_basic_map
*isl_basic_map_update_from_tab(struct isl_basic_map
*bmap
,
1110 struct isl_tab
*tab
)
1122 bmap
= isl_basic_map_set_to_empty(bmap
);
1124 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1125 if (isl_tab_is_equality(bmap
->ctx
, tab
, n_eq
+ i
))
1126 isl_basic_map_inequality_to_equality(bmap
, i
);
1127 else if (isl_tab_is_redundant(bmap
->ctx
, tab
, n_eq
+ i
))
1128 isl_basic_map_drop_inequality(bmap
, i
);
1130 if (!tab
->rational
&&
1131 !bmap
->sample
&& sample_is_integer(bmap
->ctx
, tab
))
1132 bmap
->sample
= extract_integer_sample(bmap
->ctx
, tab
);
1136 struct isl_basic_set
*isl_basic_set_update_from_tab(struct isl_basic_set
*bset
,
1137 struct isl_tab
*tab
)
1139 return (struct isl_basic_set
*)isl_basic_map_update_from_tab(
1140 (struct isl_basic_map
*)bset
, tab
);
1143 /* Given a non-negative variable "var", add a new non-negative variable
1144 * that is the opposite of "var", ensuring that var can only attain the
1146 * If var = n/d is a row variable, then the new variable = -n/d.
1147 * If var is a column variables, then the new variable = -var.
1148 * If the new variable cannot attain non-negative values, then
1149 * the resulting tableau is empty.
1150 * Otherwise, we know the value will be zero and we close the row.
1152 static struct isl_tab
*cut_to_hyperplane(struct isl_ctx
*ctx
,
1153 struct isl_tab
*tab
, struct isl_tab_var
*var
)
1159 if (extend_cons(ctx
, tab
, 1) < 0)
1163 tab
->con
[r
].index
= tab
->n_row
;
1164 tab
->con
[r
].is_row
= 1;
1165 tab
->con
[r
].is_nonneg
= 0;
1166 tab
->con
[r
].is_zero
= 0;
1167 tab
->con
[r
].is_redundant
= 0;
1168 tab
->con
[r
].frozen
= 0;
1169 tab
->row_var
[tab
->n_row
] = ~r
;
1170 row
= tab
->mat
->row
[tab
->n_row
];
1173 isl_int_set(row
[0], tab
->mat
->row
[var
->index
][0]);
1174 isl_seq_neg(row
+ 1,
1175 tab
->mat
->row
[var
->index
] + 1, 1 + tab
->n_col
);
1177 isl_int_set_si(row
[0], 1);
1178 isl_seq_clr(row
+ 1, 1 + tab
->n_col
);
1179 isl_int_set_si(row
[2 + var
->index
], -1);
1184 push(ctx
, tab
, isl_tab_undo_allocate
, &tab
->con
[r
]);
1186 sgn
= sign_of_max(ctx
, tab
, &tab
->con
[r
]);
1188 mark_empty(ctx
, tab
);
1190 tab
->con
[r
].is_nonneg
= 1;
1191 push(ctx
, tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1193 close_row(ctx
, tab
, &tab
->con
[r
]);
1198 isl_tab_free(ctx
, tab
);
1202 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
1203 * relax the inequality by one. That is, the inequality r >= 0 is replaced
1204 * by r' = r + 1 >= 0.
1205 * If r is a row variable, we simply increase the constant term by one
1206 * (taking into account the denominator).
1207 * If r is a column variable, then we need to modify each row that
1208 * refers to r = r' - 1 by substituting this equality, effectively
1209 * subtracting the coefficient of the column from the constant.
1211 struct isl_tab
*isl_tab_relax(struct isl_ctx
*ctx
,
1212 struct isl_tab
*tab
, int con
)
1214 struct isl_tab_var
*var
;
1218 var
= &tab
->con
[con
];
1220 if (!var
->is_row
&& !max_is_manifestly_unbounded(ctx
, tab
, var
))
1221 to_row(ctx
, tab
, var
, 1);
1224 isl_int_add(tab
->mat
->row
[var
->index
][1],
1225 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
1229 for (i
= 0; i
< tab
->n_row
; ++i
) {
1230 if (isl_int_is_zero(tab
->mat
->row
[i
][2 + var
->index
]))
1232 isl_int_sub(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
1233 tab
->mat
->row
[i
][2 + var
->index
]);
1238 push(ctx
, tab
, isl_tab_undo_relax
, var
);
1243 struct isl_tab
*isl_tab_select_facet(struct isl_ctx
*ctx
,
1244 struct isl_tab
*tab
, int con
)
1249 return cut_to_hyperplane(ctx
, tab
, &tab
->con
[con
]);
1252 static int may_be_equality(struct isl_tab
*tab
, int row
)
1254 return (tab
->rational
? isl_int_is_zero(tab
->mat
->row
[row
][1])
1255 : isl_int_lt(tab
->mat
->row
[row
][1],
1256 tab
->mat
->row
[row
][0])) &&
1257 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1258 tab
->n_col
- tab
->n_dead
) != -1;
1261 /* Check for (near) equalities among the constraints.
1262 * A constraint is an equality if it is non-negative and if
1263 * its maximal value is either
1264 * - zero (in case of rational tableaus), or
1265 * - strictly less than 1 (in case of integer tableaus)
1267 * We first mark all non-redundant and non-dead variables that
1268 * are not frozen and not obviously not an equality.
1269 * Then we iterate over all marked variables if they can attain
1270 * any values larger than zero or at least one.
1271 * If the maximal value is zero, we mark any column variables
1272 * that appear in the row as being zero and mark the row as being redundant.
1273 * Otherwise, if the maximal value is strictly less than one (and the
1274 * tableau is integer), then we restrict the value to being zero
1275 * by adding an opposite non-negative variable.
1277 struct isl_tab
*isl_tab_detect_equalities(struct isl_ctx
*ctx
,
1278 struct isl_tab
*tab
)
1287 if (tab
->n_dead
== tab
->n_col
)
1291 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1292 struct isl_tab_var
*var
= var_from_row(ctx
, tab
, i
);
1293 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
1294 may_be_equality(tab
, i
);
1298 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1299 struct isl_tab_var
*var
= var_from_col(ctx
, tab
, i
);
1300 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
1305 struct isl_tab_var
*var
;
1306 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1307 var
= var_from_row(ctx
, tab
, i
);
1311 if (i
== tab
->n_row
) {
1312 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1313 var
= var_from_col(ctx
, tab
, i
);
1317 if (i
== tab
->n_col
)
1322 if (sign_of_max(ctx
, tab
, var
) == 0)
1323 close_row(ctx
, tab
, var
);
1324 else if (!tab
->rational
&& !at_least_one(ctx
, tab
, var
)) {
1325 tab
= cut_to_hyperplane(ctx
, tab
, var
);
1326 return isl_tab_detect_equalities(ctx
, tab
);
1328 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1329 var
= var_from_row(ctx
, tab
, i
);
1332 if (may_be_equality(tab
, i
))
1342 /* Check for (near) redundant constraints.
1343 * A constraint is redundant if it is non-negative and if
1344 * its minimal value (temporarily ignoring the non-negativity) is either
1345 * - zero (in case of rational tableaus), or
1346 * - strictly larger than -1 (in case of integer tableaus)
1348 * We first mark all non-redundant and non-dead variables that
1349 * are not frozen and not obviously negatively unbounded.
1350 * Then we iterate over all marked variables if they can attain
1351 * any values smaller than zero or at most negative one.
1352 * If not, we mark the row as being redundant (assuming it hasn't
1353 * been detected as being obviously redundant in the mean time).
1355 struct isl_tab
*isl_tab_detect_redundant(struct isl_ctx
*ctx
,
1356 struct isl_tab
*tab
)
1365 if (tab
->n_redundant
== tab
->n_row
)
1369 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1370 struct isl_tab_var
*var
= var_from_row(ctx
, tab
, i
);
1371 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
1375 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1376 struct isl_tab_var
*var
= var_from_col(ctx
, tab
, i
);
1377 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
1378 !min_is_manifestly_unbounded(ctx
, tab
, var
);
1383 struct isl_tab_var
*var
;
1384 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1385 var
= var_from_row(ctx
, tab
, i
);
1389 if (i
== tab
->n_row
) {
1390 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1391 var
= var_from_col(ctx
, tab
, i
);
1395 if (i
== tab
->n_col
)
1400 if ((tab
->rational
? (sign_of_min(ctx
, tab
, var
) >= 0)
1401 : !min_at_most_neg_one(ctx
, tab
, var
)) &&
1403 mark_redundant(ctx
, tab
, var
->index
);
1404 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1405 var
= var_from_col(ctx
, tab
, i
);
1408 if (!min_is_manifestly_unbounded(ctx
, tab
, var
))
1418 int isl_tab_is_equality(struct isl_ctx
*ctx
, struct isl_tab
*tab
, int con
)
1424 if (tab
->con
[con
].is_zero
)
1426 if (tab
->con
[con
].is_redundant
)
1428 if (!tab
->con
[con
].is_row
)
1429 return tab
->con
[con
].index
< tab
->n_dead
;
1431 row
= tab
->con
[con
].index
;
1433 return isl_int_is_zero(tab
->mat
->row
[row
][1]) &&
1434 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1435 tab
->n_col
- tab
->n_dead
) == -1;
1438 /* Return the minimial value of the affine expression "f" with denominator
1439 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
1440 * the expression cannot attain arbitrarily small values.
1441 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
1442 * The return value reflects the nature of the result (empty, unbounded,
1443 * minmimal value returned in *opt).
1445 enum isl_lp_result
isl_tab_min(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1446 isl_int
*f
, isl_int denom
, isl_int
*opt
, isl_int
*opt_denom
)
1449 enum isl_lp_result res
= isl_lp_ok
;
1450 struct isl_tab_var
*var
;
1453 return isl_lp_empty
;
1455 r
= add_row(ctx
, tab
, f
);
1457 return isl_lp_error
;
1459 isl_int_mul(tab
->mat
->row
[var
->index
][0],
1460 tab
->mat
->row
[var
->index
][0], denom
);
1463 find_pivot(ctx
, tab
, var
, -1, &row
, &col
);
1464 if (row
== var
->index
) {
1465 res
= isl_lp_unbounded
;
1470 pivot(ctx
, tab
, row
, col
);
1472 if (drop_row(ctx
, tab
, var
->index
) < 0)
1473 return isl_lp_error
;
1474 if (res
== isl_lp_ok
) {
1476 isl_int_set(*opt
, tab
->mat
->row
[var
->index
][1]);
1477 isl_int_set(*opt_denom
, tab
->mat
->row
[var
->index
][0]);
1479 isl_int_cdiv_q(*opt
, tab
->mat
->row
[var
->index
][1],
1480 tab
->mat
->row
[var
->index
][0]);
1485 int isl_tab_is_redundant(struct isl_ctx
*ctx
, struct isl_tab
*tab
, int con
)
1492 if (tab
->con
[con
].is_zero
)
1494 if (tab
->con
[con
].is_redundant
)
1496 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
1499 /* Take a snapshot of the tableau that can be restored by s call to
1502 struct isl_tab_undo
*isl_tab_snap(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
1510 /* Undo the operation performed by isl_tab_relax.
1512 static void unrelax(struct isl_ctx
*ctx
,
1513 struct isl_tab
*tab
, struct isl_tab_var
*var
)
1515 if (!var
->is_row
&& !max_is_manifestly_unbounded(ctx
, tab
, var
))
1516 to_row(ctx
, tab
, var
, 1);
1519 isl_int_sub(tab
->mat
->row
[var
->index
][1],
1520 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
1524 for (i
= 0; i
< tab
->n_row
; ++i
) {
1525 if (isl_int_is_zero(tab
->mat
->row
[i
][2 + var
->index
]))
1527 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
1528 tab
->mat
->row
[i
][2 + var
->index
]);
1534 static void perform_undo(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1535 struct isl_tab_undo
*undo
)
1537 switch(undo
->type
) {
1538 case isl_tab_undo_empty
:
1541 case isl_tab_undo_nonneg
:
1542 undo
->var
->is_nonneg
= 0;
1544 case isl_tab_undo_redundant
:
1545 undo
->var
->is_redundant
= 0;
1548 case isl_tab_undo_zero
:
1549 undo
->var
->is_zero
= 0;
1552 case isl_tab_undo_allocate
:
1553 if (!undo
->var
->is_row
) {
1554 if (max_is_manifestly_unbounded(ctx
, tab
, undo
->var
))
1555 to_row(ctx
, tab
, undo
->var
, -1);
1557 to_row(ctx
, tab
, undo
->var
, 1);
1559 drop_row(ctx
, tab
, undo
->var
->index
);
1561 case isl_tab_undo_relax
:
1562 unrelax(ctx
, tab
, undo
->var
);
1567 /* Return the tableau to the state it was in when the snapshot "snap"
1570 int isl_tab_rollback(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1571 struct isl_tab_undo
*snap
)
1573 struct isl_tab_undo
*undo
, *next
;
1578 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
1582 perform_undo(ctx
, tab
, undo
);
1591 /* The given row "row" represents an inequality violated by all
1592 * points in the tableau. Check for some special cases of such
1593 * separating constraints.
1594 * In particular, if the row has been reduced to the constant -1,
1595 * then we know the inequality is adjacent (but opposite) to
1596 * an equality in the tableau.
1597 * If the row has been reduced to r = -1 -r', with r' an inequality
1598 * of the tableau, then the inequality is adjacent (but opposite)
1599 * to the inequality r'.
1601 static enum isl_ineq_type
separation_type(struct isl_ctx
*ctx
,
1602 struct isl_tab
*tab
, unsigned row
)
1607 return isl_ineq_separate
;
1609 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
1610 return isl_ineq_separate
;
1611 if (!isl_int_is_negone(tab
->mat
->row
[row
][1]))
1612 return isl_ineq_separate
;
1614 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1615 tab
->n_col
- tab
->n_dead
);
1617 return isl_ineq_adj_eq
;
1619 if (!isl_int_is_negone(tab
->mat
->row
[row
][2 + tab
->n_dead
+ pos
]))
1620 return isl_ineq_separate
;
1622 pos
= isl_seq_first_non_zero(
1623 tab
->mat
->row
[row
] + 2 + tab
->n_dead
+ pos
+ 1,
1624 tab
->n_col
- tab
->n_dead
- pos
- 1);
1626 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
1629 /* Check the effect of inequality "ineq" on the tableau "tab".
1631 * isl_ineq_redundant: satisfied by all points in the tableau
1632 * isl_ineq_separate: satisfied by no point in tha tableau
1633 * isl_ineq_cut: satisfied by some by not all points
1634 * isl_ineq_adj_eq: adjacent to an equality
1635 * isl_ineq_adj_ineq: adjacent to an inequality.
1637 enum isl_ineq_type
isl_tab_ineq_type(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1640 enum isl_ineq_type type
= isl_ineq_error
;
1641 struct isl_tab_undo
*snap
= NULL
;
1646 return isl_ineq_error
;
1648 if (extend_cons(ctx
, tab
, 1) < 0)
1649 return isl_ineq_error
;
1651 snap
= isl_tab_snap(ctx
, tab
);
1653 con
= add_row(ctx
, tab
, ineq
);
1657 row
= tab
->con
[con
].index
;
1658 if (is_redundant(ctx
, tab
, row
))
1659 type
= isl_ineq_redundant
;
1660 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
1662 isl_int_abs_ge(tab
->mat
->row
[row
][1],
1663 tab
->mat
->row
[row
][0]))) {
1664 if (at_least_zero(ctx
, tab
, &tab
->con
[con
]))
1665 type
= isl_ineq_cut
;
1667 type
= separation_type(ctx
, tab
, row
);
1668 } else if (tab
->rational
? (sign_of_min(ctx
, tab
, &tab
->con
[con
]) < 0)
1669 : min_at_most_neg_one(ctx
, tab
, &tab
->con
[con
]))
1670 type
= isl_ineq_cut
;
1672 type
= isl_ineq_redundant
;
1674 if (isl_tab_rollback(ctx
, tab
, snap
))
1675 return isl_ineq_error
;
1678 isl_tab_rollback(ctx
, tab
, snap
);
1679 return isl_ineq_error
;
1682 void isl_tab_dump(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1683 FILE *out
, int indent
)
1689 fprintf(out
, "%*snull tab\n", indent
, "");
1692 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
1693 tab
->n_redundant
, tab
->n_dead
);
1695 fprintf(out
, ", rational");
1697 fprintf(out
, ", empty");
1699 fprintf(out
, "%*s[", indent
, "");
1700 for (i
= 0; i
< tab
->n_var
; ++i
) {
1703 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
1705 tab
->var
[i
].is_zero
? " [=0]" :
1706 tab
->var
[i
].is_redundant
? " [R]" : "");
1708 fprintf(out
, "]\n");
1709 fprintf(out
, "%*s[", indent
, "");
1710 for (i
= 0; i
< tab
->n_con
; ++i
) {
1713 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
1715 tab
->con
[i
].is_zero
? " [=0]" :
1716 tab
->con
[i
].is_redundant
? " [R]" : "");
1718 fprintf(out
, "]\n");
1719 fprintf(out
, "%*s[", indent
, "");
1720 for (i
= 0; i
< tab
->n_row
; ++i
) {
1723 fprintf(out
, "r%d: %d%s", i
, tab
->row_var
[i
],
1724 var_from_row(ctx
, tab
, i
)->is_nonneg
? " [>=0]" : "");
1726 fprintf(out
, "]\n");
1727 fprintf(out
, "%*s[", indent
, "");
1728 for (i
= 0; i
< tab
->n_col
; ++i
) {
1731 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
1732 var_from_col(ctx
, tab
, i
)->is_nonneg
? " [>=0]" : "");
1734 fprintf(out
, "]\n");
1735 r
= tab
->mat
->n_row
;
1736 tab
->mat
->n_row
= tab
->n_row
;
1737 c
= tab
->mat
->n_col
;
1738 tab
->mat
->n_col
= 2 + tab
->n_col
;
1739 isl_mat_dump(ctx
, tab
->mat
, out
, indent
);
1740 tab
->mat
->n_row
= r
;
1741 tab
->mat
->n_col
= c
;