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;
55 tab
->bottom
.type
= isl_tab_undo_bottom
;
56 tab
->bottom
.next
= NULL
;
57 tab
->top
= &tab
->bottom
;
64 static int extend_cons(struct isl_tab
*tab
, unsigned n_new
)
66 if (tab
->max_con
< tab
->n_con
+ n_new
) {
67 struct isl_tab_var
*con
;
69 con
= isl_realloc_array(tab
->mat
->ctx
, tab
->con
,
70 struct isl_tab_var
, tab
->max_con
+ n_new
);
74 tab
->max_con
+= n_new
;
76 if (tab
->mat
->n_row
< tab
->n_row
+ n_new
) {
79 tab
->mat
= isl_mat_extend(tab
->mat
,
80 tab
->n_row
+ n_new
, tab
->n_col
);
83 row_var
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_var
,
84 int, tab
->mat
->n_row
);
87 tab
->row_var
= row_var
;
92 struct isl_tab
*isl_tab_extend(struct isl_tab
*tab
, unsigned n_new
)
94 if (extend_cons(tab
, n_new
) >= 0)
101 static void free_undo(struct isl_tab
*tab
)
103 struct isl_tab_undo
*undo
, *next
;
105 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
112 void isl_tab_free(struct isl_tab
*tab
)
117 isl_mat_free(tab
->mat
);
118 isl_vec_free(tab
->dual
);
126 static struct isl_tab_var
*var_from_index(struct isl_tab
*tab
, int i
)
131 return &tab
->con
[~i
];
134 static struct isl_tab_var
*var_from_row(struct isl_tab
*tab
, int i
)
136 return var_from_index(tab
, tab
->row_var
[i
]);
139 static struct isl_tab_var
*var_from_col(struct isl_tab
*tab
, int i
)
141 return var_from_index(tab
, tab
->col_var
[i
]);
144 /* Check if there are any upper bounds on column variable "var",
145 * i.e., non-negative rows where var appears with a negative coefficient.
146 * Return 1 if there are no such bounds.
148 static int max_is_manifestly_unbounded(struct isl_tab
*tab
,
149 struct isl_tab_var
*var
)
155 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
156 if (!isl_int_is_neg(tab
->mat
->row
[i
][2 + var
->index
]))
158 if (var_from_row(tab
, i
)->is_nonneg
)
164 /* Check if there are any lower bounds on column variable "var",
165 * i.e., non-negative rows where var appears with a positive coefficient.
166 * Return 1 if there are no such bounds.
168 static int min_is_manifestly_unbounded(struct isl_tab
*tab
,
169 struct isl_tab_var
*var
)
175 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
176 if (!isl_int_is_pos(tab
->mat
->row
[i
][2 + var
->index
]))
178 if (var_from_row(tab
, i
)->is_nonneg
)
184 /* Given the index of a column "c", return the index of a row
185 * that can be used to pivot the column in, with either an increase
186 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
187 * If "var" is not NULL, then the row returned will be different from
188 * the one associated with "var".
190 * Each row in the tableau is of the form
192 * x_r = a_r0 + \sum_i a_ri x_i
194 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
195 * impose any limit on the increase or decrease in the value of x_c
196 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
197 * for the row with the smallest (most stringent) such bound.
198 * Note that the common denominator of each row drops out of the fraction.
199 * To check if row j has a smaller bound than row r, i.e.,
200 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
201 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
202 * where -sign(a_jc) is equal to "sgn".
204 static int pivot_row(struct isl_tab
*tab
,
205 struct isl_tab_var
*var
, int sgn
, int c
)
212 for (j
= tab
->n_redundant
; j
< tab
->n_row
; ++j
) {
213 if (var
&& j
== var
->index
)
215 if (!var_from_row(tab
, j
)->is_nonneg
)
217 if (sgn
* isl_int_sgn(tab
->mat
->row
[j
][2 + c
]) >= 0)
223 isl_int_mul(t
, tab
->mat
->row
[r
][1], tab
->mat
->row
[j
][2 + c
]);
224 isl_int_submul(t
, tab
->mat
->row
[j
][1], tab
->mat
->row
[r
][2 + c
]);
225 tsgn
= sgn
* isl_int_sgn(t
);
226 if (tsgn
< 0 || (tsgn
== 0 &&
227 tab
->row_var
[j
] < tab
->row_var
[r
]))
234 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
235 * (sgn < 0) the value of row variable var.
236 * If not NULL, then skip_var is a row variable that should be ignored
237 * while looking for a pivot row. It is usually equal to var.
239 * As the given row in the tableau is of the form
241 * x_r = a_r0 + \sum_i a_ri x_i
243 * we need to find a column such that the sign of a_ri is equal to "sgn"
244 * (such that an increase in x_i will have the desired effect) or a
245 * column with a variable that may attain negative values.
246 * If a_ri is positive, then we need to move x_i in the same direction
247 * to obtain the desired effect. Otherwise, x_i has to move in the
248 * opposite direction.
250 static void find_pivot(struct isl_tab
*tab
,
251 struct isl_tab_var
*var
, struct isl_tab_var
*skip_var
,
252 int sgn
, int *row
, int *col
)
259 isl_assert(tab
->mat
->ctx
, var
->is_row
, return);
260 tr
= tab
->mat
->row
[var
->index
];
263 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
264 if (isl_int_is_zero(tr
[2 + j
]))
266 if (isl_int_sgn(tr
[2 + j
]) != sgn
&&
267 var_from_col(tab
, j
)->is_nonneg
)
269 if (c
< 0 || tab
->col_var
[j
] < tab
->col_var
[c
])
275 sgn
*= isl_int_sgn(tr
[2 + c
]);
276 r
= pivot_row(tab
, skip_var
, sgn
, c
);
277 *row
= r
< 0 ? var
->index
: r
;
281 /* Return 1 if row "row" represents an obviously redundant inequality.
283 * - it represents an inequality or a variable
284 * - that is the sum of a non-negative sample value and a positive
285 * combination of zero or more non-negative variables.
287 static int is_redundant(struct isl_tab
*tab
, int row
)
291 if (tab
->row_var
[row
] < 0 && !var_from_row(tab
, row
)->is_nonneg
)
294 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
297 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
298 if (isl_int_is_zero(tab
->mat
->row
[row
][2 + i
]))
300 if (isl_int_is_neg(tab
->mat
->row
[row
][2 + i
]))
302 if (!var_from_col(tab
, i
)->is_nonneg
)
308 static void swap_rows(struct isl_tab
*tab
, int row1
, int row2
)
311 t
= tab
->row_var
[row1
];
312 tab
->row_var
[row1
] = tab
->row_var
[row2
];
313 tab
->row_var
[row2
] = t
;
314 var_from_row(tab
, row1
)->index
= row1
;
315 var_from_row(tab
, row2
)->index
= row2
;
316 tab
->mat
= isl_mat_swap_rows(tab
->mat
, row1
, row2
);
319 static void push(struct isl_tab
*tab
,
320 enum isl_tab_undo_type type
, struct isl_tab_var
*var
)
322 struct isl_tab_undo
*undo
;
327 undo
= isl_alloc_type(tab
->mat
->ctx
, struct isl_tab_undo
);
335 undo
->next
= tab
->top
;
339 /* Mark row with index "row" as being redundant.
340 * If we may need to undo the operation or if the row represents
341 * a variable of the original problem, the row is kept,
342 * but no longer considered when looking for a pivot row.
343 * Otherwise, the row is simply removed.
345 * The row may be interchanged with some other row. If it
346 * is interchanged with a later row, return 1. Otherwise return 0.
347 * If the rows are checked in order in the calling function,
348 * then a return value of 1 means that the row with the given
349 * row number may now contain a different row that hasn't been checked yet.
351 static int mark_redundant(struct isl_tab
*tab
, int row
)
353 struct isl_tab_var
*var
= var_from_row(tab
, row
);
354 var
->is_redundant
= 1;
355 isl_assert(tab
->mat
->ctx
, row
>= tab
->n_redundant
, return);
356 if (tab
->need_undo
|| tab
->row_var
[row
] >= 0) {
357 if (tab
->row_var
[row
] >= 0 && !var
->is_nonneg
) {
359 push(tab
, isl_tab_undo_nonneg
, var
);
361 if (row
!= tab
->n_redundant
)
362 swap_rows(tab
, row
, tab
->n_redundant
);
363 push(tab
, isl_tab_undo_redundant
, var
);
367 if (row
!= tab
->n_row
- 1)
368 swap_rows(tab
, row
, tab
->n_row
- 1);
369 var_from_row(tab
, tab
->n_row
- 1)->index
= -1;
375 static struct isl_tab
*mark_empty(struct isl_tab
*tab
)
377 if (!tab
->empty
&& tab
->need_undo
)
378 push(tab
, isl_tab_undo_empty
, NULL
);
383 /* Given a row number "row" and a column number "col", pivot the tableau
384 * such that the associated variables are interchanged.
385 * The given row in the tableau expresses
387 * x_r = a_r0 + \sum_i a_ri x_i
391 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
393 * Substituting this equality into the other rows
395 * x_j = a_j0 + \sum_i a_ji x_i
397 * with a_jc \ne 0, we obtain
399 * 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
406 * where i is any other column and j is any other row,
407 * is therefore transformed into
409 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
410 * 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)
412 * The transformation is performed along the following steps
417 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
420 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
421 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
423 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
424 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
426 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
427 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
429 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
430 * 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)
433 static void pivot(struct isl_tab
*tab
, int row
, int col
)
438 struct isl_mat
*mat
= tab
->mat
;
439 struct isl_tab_var
*var
;
441 isl_int_swap(mat
->row
[row
][0], mat
->row
[row
][2 + col
]);
442 sgn
= isl_int_sgn(mat
->row
[row
][0]);
444 isl_int_neg(mat
->row
[row
][0], mat
->row
[row
][0]);
445 isl_int_neg(mat
->row
[row
][2 + col
], mat
->row
[row
][2 + col
]);
447 for (j
= 0; j
< 1 + tab
->n_col
; ++j
) {
450 isl_int_neg(mat
->row
[row
][1 + j
], mat
->row
[row
][1 + j
]);
452 if (!isl_int_is_one(mat
->row
[row
][0]))
453 isl_seq_normalize(mat
->row
[row
], 2 + tab
->n_col
);
454 for (i
= 0; i
< tab
->n_row
; ++i
) {
457 if (isl_int_is_zero(mat
->row
[i
][2 + col
]))
459 isl_int_mul(mat
->row
[i
][0], mat
->row
[i
][0], mat
->row
[row
][0]);
460 for (j
= 0; j
< 1 + tab
->n_col
; ++j
) {
463 isl_int_mul(mat
->row
[i
][1 + j
],
464 mat
->row
[i
][1 + j
], mat
->row
[row
][0]);
465 isl_int_addmul(mat
->row
[i
][1 + j
],
466 mat
->row
[i
][2 + col
], mat
->row
[row
][1 + j
]);
468 isl_int_mul(mat
->row
[i
][2 + col
],
469 mat
->row
[i
][2 + col
], mat
->row
[row
][2 + col
]);
470 if (!isl_int_is_one(mat
->row
[row
][0]))
471 isl_seq_normalize(mat
->row
[i
], 2 + tab
->n_col
);
473 t
= tab
->row_var
[row
];
474 tab
->row_var
[row
] = tab
->col_var
[col
];
475 tab
->col_var
[col
] = t
;
476 var
= var_from_row(tab
, row
);
479 var
= var_from_col(tab
, col
);
484 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
485 if (isl_int_is_zero(mat
->row
[i
][2 + col
]))
487 if (!var_from_row(tab
, i
)->frozen
&&
488 is_redundant(tab
, i
))
489 if (mark_redundant(tab
, i
))
494 /* If "var" represents a column variable, then pivot is up (sgn > 0)
495 * or down (sgn < 0) to a row. The variable is assumed not to be
496 * unbounded in the specified direction.
497 * If sgn = 0, then the variable is unbounded in both directions,
498 * and we pivot with any row we can find.
500 static void to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
)
508 for (r
= tab
->n_redundant
; r
< tab
->n_row
; ++r
)
509 if (!isl_int_is_zero(tab
->mat
->row
[r
][2 + var
->index
]))
511 isl_assert(tab
->mat
->ctx
, r
< tab
->n_row
, return);
513 r
= pivot_row(tab
, NULL
, sign
, var
->index
);
514 isl_assert(tab
->mat
->ctx
, r
>= 0, return);
517 pivot(tab
, r
, var
->index
);
520 static void check_table(struct isl_tab
*tab
)
526 for (i
= 0; i
< tab
->n_row
; ++i
) {
527 if (!var_from_row(tab
, i
)->is_nonneg
)
529 assert(!isl_int_is_neg(tab
->mat
->row
[i
][1]));
533 /* Return the sign of the maximal value of "var".
534 * If the sign is not negative, then on return from this function,
535 * the sample value will also be non-negative.
537 * If "var" is manifestly unbounded wrt positive values, we are done.
538 * Otherwise, we pivot the variable up to a row if needed
539 * Then we continue pivoting down until either
540 * - no more down pivots can be performed
541 * - the sample value is positive
542 * - the variable is pivoted into a manifestly unbounded column
544 static int sign_of_max(struct isl_tab
*tab
, struct isl_tab_var
*var
)
548 if (max_is_manifestly_unbounded(tab
, var
))
551 while (!isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
552 find_pivot(tab
, var
, var
, 1, &row
, &col
);
554 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
555 pivot(tab
, row
, col
);
556 if (!var
->is_row
) /* manifestly unbounded */
562 /* Perform pivots until the row variable "var" has a non-negative
563 * sample value or until no more upward pivots can be performed.
564 * Return the sign of the sample value after the pivots have been
567 static int restore_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
571 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
572 find_pivot(tab
, var
, var
, 1, &row
, &col
);
575 pivot(tab
, row
, col
);
576 if (!var
->is_row
) /* manifestly unbounded */
579 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
582 /* Perform pivots until we are sure that the row variable "var"
583 * can attain non-negative values. After return from this
584 * function, "var" is still a row variable, but its sample
585 * value may not be non-negative, even if the function returns 1.
587 static int at_least_zero(struct isl_tab
*tab
, struct isl_tab_var
*var
)
591 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
592 find_pivot(tab
, var
, var
, 1, &row
, &col
);
595 if (row
== var
->index
) /* manifestly unbounded */
597 pivot(tab
, row
, col
);
599 return !isl_int_is_neg(tab
->mat
->row
[var
->index
][1]);
602 /* Return a negative value if "var" can attain negative values.
603 * Return a non-negative value otherwise.
605 * If "var" is manifestly unbounded wrt negative values, we are done.
606 * Otherwise, if var is in a column, we can pivot it down to a row.
607 * Then we continue pivoting down until either
608 * - the pivot would result in a manifestly unbounded column
609 * => we don't perform the pivot, but simply return -1
610 * - no more down pivots can be performed
611 * - the sample value is negative
612 * If the sample value becomes negative and the variable is supposed
613 * to be nonnegative, then we undo the last pivot.
614 * However, if the last pivot has made the pivoting variable
615 * obviously redundant, then it may have moved to another row.
616 * In that case we look for upward pivots until we reach a non-negative
619 static int sign_of_min(struct isl_tab
*tab
, struct isl_tab_var
*var
)
622 struct isl_tab_var
*pivot_var
;
624 if (min_is_manifestly_unbounded(tab
, var
))
628 row
= pivot_row(tab
, NULL
, -1, col
);
629 pivot_var
= var_from_col(tab
, col
);
630 pivot(tab
, row
, col
);
631 if (var
->is_redundant
)
633 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
634 if (var
->is_nonneg
) {
635 if (!pivot_var
->is_redundant
&&
636 pivot_var
->index
== row
)
637 pivot(tab
, row
, col
);
639 restore_row(tab
, var
);
644 if (var
->is_redundant
)
646 while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
647 find_pivot(tab
, var
, var
, -1, &row
, &col
);
648 if (row
== var
->index
)
651 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
652 pivot_var
= var_from_col(tab
, col
);
653 pivot(tab
, row
, col
);
654 if (var
->is_redundant
)
657 if (var
->is_nonneg
) {
658 /* pivot back to non-negative value */
659 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
660 pivot(tab
, row
, col
);
662 restore_row(tab
, var
);
667 /* Return 1 if "var" can attain values <= -1.
668 * Return 0 otherwise.
670 * The sample value of "var" is assumed to be non-negative when the
671 * the function is called and will be made non-negative again before
672 * the function returns.
674 static int min_at_most_neg_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
677 struct isl_tab_var
*pivot_var
;
679 if (min_is_manifestly_unbounded(tab
, var
))
683 row
= pivot_row(tab
, NULL
, -1, col
);
684 pivot_var
= var_from_col(tab
, col
);
685 pivot(tab
, row
, col
);
686 if (var
->is_redundant
)
688 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1]) &&
689 isl_int_abs_ge(tab
->mat
->row
[var
->index
][1],
690 tab
->mat
->row
[var
->index
][0])) {
691 if (var
->is_nonneg
) {
692 if (!pivot_var
->is_redundant
&&
693 pivot_var
->index
== row
)
694 pivot(tab
, row
, col
);
696 restore_row(tab
, var
);
701 if (var
->is_redundant
)
704 find_pivot(tab
, var
, var
, -1, &row
, &col
);
705 if (row
== var
->index
)
709 pivot_var
= var_from_col(tab
, col
);
710 pivot(tab
, row
, col
);
711 if (var
->is_redundant
)
713 } while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1]) ||
714 isl_int_abs_lt(tab
->mat
->row
[var
->index
][1],
715 tab
->mat
->row
[var
->index
][0]));
716 if (var
->is_nonneg
) {
717 /* pivot back to non-negative value */
718 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
719 pivot(tab
, row
, col
);
720 restore_row(tab
, var
);
725 /* Return 1 if "var" can attain values >= 1.
726 * Return 0 otherwise.
728 static int at_least_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
733 if (max_is_manifestly_unbounded(tab
, var
))
736 r
= tab
->mat
->row
[var
->index
];
737 while (isl_int_lt(r
[1], r
[0])) {
738 find_pivot(tab
, var
, var
, 1, &row
, &col
);
740 return isl_int_ge(r
[1], r
[0]);
741 if (row
== var
->index
) /* manifestly unbounded */
743 pivot(tab
, row
, col
);
748 static void swap_cols(struct isl_tab
*tab
, int col1
, int col2
)
751 t
= tab
->col_var
[col1
];
752 tab
->col_var
[col1
] = tab
->col_var
[col2
];
753 tab
->col_var
[col2
] = t
;
754 var_from_col(tab
, col1
)->index
= col1
;
755 var_from_col(tab
, col2
)->index
= col2
;
756 tab
->mat
= isl_mat_swap_cols(tab
->mat
, 2 + col1
, 2 + col2
);
759 /* Mark column with index "col" as representing a zero variable.
760 * If we may need to undo the operation the column is kept,
761 * but no longer considered.
762 * Otherwise, the column is simply removed.
764 * The column may be interchanged with some other column. If it
765 * is interchanged with a later column, return 1. Otherwise return 0.
766 * If the columns are checked in order in the calling function,
767 * then a return value of 1 means that the column with the given
768 * column number may now contain a different column that
769 * hasn't been checked yet.
771 static int kill_col(struct isl_tab
*tab
, int col
)
773 var_from_col(tab
, col
)->is_zero
= 1;
774 if (tab
->need_undo
) {
775 push(tab
, isl_tab_undo_zero
, var_from_col(tab
, col
));
776 if (col
!= tab
->n_dead
)
777 swap_cols(tab
, col
, tab
->n_dead
);
781 if (col
!= tab
->n_col
- 1)
782 swap_cols(tab
, col
, tab
->n_col
- 1);
783 var_from_col(tab
, tab
->n_col
- 1)->index
= -1;
789 /* Row variable "var" is non-negative and cannot attain any values
790 * larger than zero. This means that the coefficients of the unrestricted
791 * column variables are zero and that the coefficients of the non-negative
792 * column variables are zero or negative.
793 * Each of the non-negative variables with a negative coefficient can
794 * then also be written as the negative sum of non-negative variables
795 * and must therefore also be zero.
797 static void close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
800 struct isl_mat
*mat
= tab
->mat
;
802 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return);
804 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
805 if (isl_int_is_zero(mat
->row
[var
->index
][2 + j
]))
807 isl_assert(tab
->mat
->ctx
,
808 isl_int_is_neg(mat
->row
[var
->index
][2 + j
]), return);
809 if (kill_col(tab
, j
))
812 mark_redundant(tab
, var
->index
);
815 /* Add a constraint to the tableau and allocate a row for it.
816 * Return the index into the constraint array "con".
818 static int allocate_con(struct isl_tab
*tab
)
822 isl_assert(tab
->mat
->ctx
, tab
->n_row
< tab
->mat
->n_row
, return -1);
825 tab
->con
[r
].index
= tab
->n_row
;
826 tab
->con
[r
].is_row
= 1;
827 tab
->con
[r
].is_nonneg
= 0;
828 tab
->con
[r
].is_zero
= 0;
829 tab
->con
[r
].is_redundant
= 0;
830 tab
->con
[r
].frozen
= 0;
831 tab
->row_var
[tab
->n_row
] = ~r
;
835 push(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]);
840 /* Add a row to the tableau. The row is given as an affine combination
841 * of the original variables and needs to be expressed in terms of the
844 * We add each term in turn.
845 * If r = n/d_r is the current sum and we need to add k x, then
846 * if x is a column variable, we increase the numerator of
847 * this column by k d_r
848 * if x = f/d_x is a row variable, then the new representation of r is
850 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
851 * --- + --- = ------------------- = -------------------
852 * d_r d_r d_r d_x/g m
854 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
856 static int add_row(struct isl_tab
*tab
, isl_int
*line
)
863 r
= allocate_con(tab
);
869 row
= tab
->mat
->row
[tab
->con
[r
].index
];
870 isl_int_set_si(row
[0], 1);
871 isl_int_set(row
[1], line
[0]);
872 isl_seq_clr(row
+ 2, tab
->n_col
);
873 for (i
= 0; i
< tab
->n_var
; ++i
) {
874 if (tab
->var
[i
].is_zero
)
876 if (tab
->var
[i
].is_row
) {
878 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
879 isl_int_swap(a
, row
[0]);
880 isl_int_divexact(a
, row
[0], a
);
882 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
883 isl_int_mul(b
, b
, line
[1 + i
]);
884 isl_seq_combine(row
+ 1, a
, row
+ 1,
885 b
, tab
->mat
->row
[tab
->var
[i
].index
] + 1,
888 isl_int_addmul(row
[2 + tab
->var
[i
].index
],
889 line
[1 + i
], row
[0]);
891 isl_seq_normalize(row
, 2 + tab
->n_col
);
898 static int drop_row(struct isl_tab
*tab
, int row
)
900 isl_assert(tab
->mat
->ctx
, ~tab
->row_var
[row
] == tab
->n_con
- 1, return -1);
901 if (row
!= tab
->n_row
- 1)
902 swap_rows(tab
, row
, tab
->n_row
- 1);
908 /* Add inequality "ineq" and check if it conflicts with the
909 * previously added constraints or if it is obviously redundant.
911 struct isl_tab
*isl_tab_add_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
918 r
= add_row(tab
, ineq
);
921 tab
->con
[r
].is_nonneg
= 1;
922 push(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
923 if (is_redundant(tab
, tab
->con
[r
].index
)) {
924 mark_redundant(tab
, tab
->con
[r
].index
);
928 sgn
= restore_row(tab
, &tab
->con
[r
]);
930 return mark_empty(tab
);
931 if (tab
->con
[r
].is_row
&& is_redundant(tab
, tab
->con
[r
].index
))
932 mark_redundant(tab
, tab
->con
[r
].index
);
939 /* Pivot a non-negative variable down until it reaches the value zero
940 * and then pivot the variable into a column position.
942 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
)
950 while (isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
951 find_pivot(tab
, var
, NULL
, -1, &row
, &col
);
952 isl_assert(tab
->mat
->ctx
, row
!= -1, return -1);
953 pivot(tab
, row
, col
);
958 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
)
959 if (!isl_int_is_zero(tab
->mat
->row
[var
->index
][2 + i
]))
962 isl_assert(tab
->mat
->ctx
, i
< tab
->n_col
, return -1);
963 pivot(tab
, var
->index
, i
);
968 /* We assume Gaussian elimination has been performed on the equalities.
969 * The equalities can therefore never conflict.
970 * Adding the equalities is currently only really useful for a later call
971 * to isl_tab_ineq_type.
973 static struct isl_tab
*add_eq(struct isl_tab
*tab
, isl_int
*eq
)
980 r
= add_row(tab
, eq
);
984 r
= tab
->con
[r
].index
;
985 i
= isl_seq_first_non_zero(tab
->mat
->row
[r
] + 2 + tab
->n_dead
,
986 tab
->n_col
- tab
->n_dead
);
987 isl_assert(tab
->mat
->ctx
, i
>= 0, goto error
);
999 /* Add an equality that is known to be valid for the given tableau.
1001 struct isl_tab
*isl_tab_add_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1003 struct isl_tab_var
*var
;
1009 r
= add_row(tab
, eq
);
1015 if (isl_int_is_neg(tab
->mat
->row
[r
][1]))
1016 isl_seq_neg(tab
->mat
->row
[r
] + 1, tab
->mat
->row
[r
] + 1,
1019 if (to_col(tab
, var
) < 0)
1022 kill_col(tab
, var
->index
);
1030 struct isl_tab
*isl_tab_from_basic_map(struct isl_basic_map
*bmap
)
1033 struct isl_tab
*tab
;
1037 tab
= isl_tab_alloc(bmap
->ctx
,
1038 isl_basic_map_total_dim(bmap
) + bmap
->n_ineq
+ 1,
1039 isl_basic_map_total_dim(bmap
));
1042 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
1043 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1044 return mark_empty(tab
);
1045 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1046 tab
= add_eq(tab
, bmap
->eq
[i
]);
1050 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1051 tab
= isl_tab_add_ineq(tab
, bmap
->ineq
[i
]);
1052 if (!tab
|| tab
->empty
)
1058 struct isl_tab
*isl_tab_from_basic_set(struct isl_basic_set
*bset
)
1060 return isl_tab_from_basic_map((struct isl_basic_map
*)bset
);
1063 /* Construct a tableau corresponding to the recession cone of "bmap".
1065 struct isl_tab
*isl_tab_from_recession_cone(struct isl_basic_map
*bmap
)
1069 struct isl_tab
*tab
;
1073 tab
= isl_tab_alloc(bmap
->ctx
, bmap
->n_eq
+ bmap
->n_ineq
,
1074 isl_basic_map_total_dim(bmap
));
1077 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
1080 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1081 isl_int_swap(bmap
->eq
[i
][0], cst
);
1082 tab
= add_eq(tab
, bmap
->eq
[i
]);
1083 isl_int_swap(bmap
->eq
[i
][0], cst
);
1087 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1089 isl_int_swap(bmap
->ineq
[i
][0], cst
);
1090 r
= add_row(tab
, bmap
->ineq
[i
]);
1091 isl_int_swap(bmap
->ineq
[i
][0], cst
);
1094 tab
->con
[r
].is_nonneg
= 1;
1095 push(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1106 /* Assuming "tab" is the tableau of a cone, check if the cone is
1107 * bounded, i.e., if it is empty or only contains the origin.
1109 int isl_tab_cone_is_bounded(struct isl_tab
*tab
)
1117 if (tab
->n_dead
== tab
->n_col
)
1121 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1122 struct isl_tab_var
*var
;
1123 var
= var_from_row(tab
, i
);
1124 if (!var
->is_nonneg
)
1126 if (sign_of_max(tab
, var
) != 0)
1128 close_row(tab
, var
);
1131 if (tab
->n_dead
== tab
->n_col
)
1133 if (i
== tab
->n_row
)
1138 int isl_tab_sample_is_integer(struct isl_tab
*tab
)
1145 for (i
= 0; i
< tab
->n_var
; ++i
) {
1147 if (!tab
->var
[i
].is_row
)
1149 row
= tab
->var
[i
].index
;
1150 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1151 tab
->mat
->row
[row
][0]))
1157 static struct isl_vec
*extract_integer_sample(struct isl_tab
*tab
)
1160 struct isl_vec
*vec
;
1162 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
1166 isl_int_set_si(vec
->block
.data
[0], 1);
1167 for (i
= 0; i
< tab
->n_var
; ++i
) {
1168 if (!tab
->var
[i
].is_row
)
1169 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
1171 int row
= tab
->var
[i
].index
;
1172 isl_int_divexact(vec
->block
.data
[1 + i
],
1173 tab
->mat
->row
[row
][1], tab
->mat
->row
[row
][0]);
1180 struct isl_vec
*isl_tab_get_sample_value(struct isl_tab
*tab
)
1183 struct isl_vec
*vec
;
1189 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
1195 isl_int_set_si(vec
->block
.data
[0], 1);
1196 for (i
= 0; i
< tab
->n_var
; ++i
) {
1198 if (!tab
->var
[i
].is_row
) {
1199 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
1202 row
= tab
->var
[i
].index
;
1203 isl_int_gcd(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
1204 isl_int_divexact(m
, tab
->mat
->row
[row
][0], m
);
1205 isl_seq_scale(vec
->block
.data
, vec
->block
.data
, m
, 1 + i
);
1206 isl_int_divexact(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
1207 isl_int_mul(vec
->block
.data
[1 + i
], m
, tab
->mat
->row
[row
][1]);
1209 isl_seq_normalize(vec
->block
.data
, vec
->size
);
1215 /* Update "bmap" based on the results of the tableau "tab".
1216 * In particular, implicit equalities are made explicit, redundant constraints
1217 * are removed and if the sample value happens to be integer, it is stored
1218 * in "bmap" (unless "bmap" already had an integer sample).
1220 * The tableau is assumed to have been created from "bmap" using
1221 * isl_tab_from_basic_map.
1223 struct isl_basic_map
*isl_basic_map_update_from_tab(struct isl_basic_map
*bmap
,
1224 struct isl_tab
*tab
)
1236 bmap
= isl_basic_map_set_to_empty(bmap
);
1238 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1239 if (isl_tab_is_equality(tab
, n_eq
+ i
))
1240 isl_basic_map_inequality_to_equality(bmap
, i
);
1241 else if (isl_tab_is_redundant(tab
, n_eq
+ i
))
1242 isl_basic_map_drop_inequality(bmap
, i
);
1244 if (!tab
->rational
&&
1245 !bmap
->sample
&& isl_tab_sample_is_integer(tab
))
1246 bmap
->sample
= extract_integer_sample(tab
);
1250 struct isl_basic_set
*isl_basic_set_update_from_tab(struct isl_basic_set
*bset
,
1251 struct isl_tab
*tab
)
1253 return (struct isl_basic_set
*)isl_basic_map_update_from_tab(
1254 (struct isl_basic_map
*)bset
, tab
);
1257 /* Given a non-negative variable "var", add a new non-negative variable
1258 * that is the opposite of "var", ensuring that var can only attain the
1260 * If var = n/d is a row variable, then the new variable = -n/d.
1261 * If var is a column variables, then the new variable = -var.
1262 * If the new variable cannot attain non-negative values, then
1263 * the resulting tableau is empty.
1264 * Otherwise, we know the value will be zero and we close the row.
1266 static struct isl_tab
*cut_to_hyperplane(struct isl_tab
*tab
,
1267 struct isl_tab_var
*var
)
1273 if (extend_cons(tab
, 1) < 0)
1277 tab
->con
[r
].index
= tab
->n_row
;
1278 tab
->con
[r
].is_row
= 1;
1279 tab
->con
[r
].is_nonneg
= 0;
1280 tab
->con
[r
].is_zero
= 0;
1281 tab
->con
[r
].is_redundant
= 0;
1282 tab
->con
[r
].frozen
= 0;
1283 tab
->row_var
[tab
->n_row
] = ~r
;
1284 row
= tab
->mat
->row
[tab
->n_row
];
1287 isl_int_set(row
[0], tab
->mat
->row
[var
->index
][0]);
1288 isl_seq_neg(row
+ 1,
1289 tab
->mat
->row
[var
->index
] + 1, 1 + tab
->n_col
);
1291 isl_int_set_si(row
[0], 1);
1292 isl_seq_clr(row
+ 1, 1 + tab
->n_col
);
1293 isl_int_set_si(row
[2 + var
->index
], -1);
1298 push(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]);
1300 sgn
= sign_of_max(tab
, &tab
->con
[r
]);
1302 return mark_empty(tab
);
1303 tab
->con
[r
].is_nonneg
= 1;
1304 push(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1306 close_row(tab
, &tab
->con
[r
]);
1314 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
1315 * relax the inequality by one. That is, the inequality r >= 0 is replaced
1316 * by r' = r + 1 >= 0.
1317 * If r is a row variable, we simply increase the constant term by one
1318 * (taking into account the denominator).
1319 * If r is a column variable, then we need to modify each row that
1320 * refers to r = r' - 1 by substituting this equality, effectively
1321 * subtracting the coefficient of the column from the constant.
1323 struct isl_tab
*isl_tab_relax(struct isl_tab
*tab
, int con
)
1325 struct isl_tab_var
*var
;
1329 var
= &tab
->con
[con
];
1331 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
1332 to_row(tab
, var
, 1);
1335 isl_int_add(tab
->mat
->row
[var
->index
][1],
1336 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
1340 for (i
= 0; i
< tab
->n_row
; ++i
) {
1341 if (isl_int_is_zero(tab
->mat
->row
[i
][2 + var
->index
]))
1343 isl_int_sub(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
1344 tab
->mat
->row
[i
][2 + var
->index
]);
1349 push(tab
, isl_tab_undo_relax
, var
);
1354 struct isl_tab
*isl_tab_select_facet(struct isl_tab
*tab
, int con
)
1359 return cut_to_hyperplane(tab
, &tab
->con
[con
]);
1362 static int may_be_equality(struct isl_tab
*tab
, int row
)
1364 return (tab
->rational
? isl_int_is_zero(tab
->mat
->row
[row
][1])
1365 : isl_int_lt(tab
->mat
->row
[row
][1],
1366 tab
->mat
->row
[row
][0])) &&
1367 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1368 tab
->n_col
- tab
->n_dead
) != -1;
1371 /* Check for (near) equalities among the constraints.
1372 * A constraint is an equality if it is non-negative and if
1373 * its maximal value is either
1374 * - zero (in case of rational tableaus), or
1375 * - strictly less than 1 (in case of integer tableaus)
1377 * We first mark all non-redundant and non-dead variables that
1378 * are not frozen and not obviously not an equality.
1379 * Then we iterate over all marked variables if they can attain
1380 * any values larger than zero or at least one.
1381 * If the maximal value is zero, we mark any column variables
1382 * that appear in the row as being zero and mark the row as being redundant.
1383 * Otherwise, if the maximal value is strictly less than one (and the
1384 * tableau is integer), then we restrict the value to being zero
1385 * by adding an opposite non-negative variable.
1387 struct isl_tab
*isl_tab_detect_equalities(struct isl_tab
*tab
)
1396 if (tab
->n_dead
== tab
->n_col
)
1400 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1401 struct isl_tab_var
*var
= var_from_row(tab
, i
);
1402 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
1403 may_be_equality(tab
, i
);
1407 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1408 struct isl_tab_var
*var
= var_from_col(tab
, i
);
1409 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
1414 struct isl_tab_var
*var
;
1415 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1416 var
= var_from_row(tab
, i
);
1420 if (i
== tab
->n_row
) {
1421 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1422 var
= var_from_col(tab
, i
);
1426 if (i
== tab
->n_col
)
1431 if (sign_of_max(tab
, var
) == 0)
1432 close_row(tab
, var
);
1433 else if (!tab
->rational
&& !at_least_one(tab
, var
)) {
1434 tab
= cut_to_hyperplane(tab
, var
);
1435 return isl_tab_detect_equalities(tab
);
1437 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1438 var
= var_from_row(tab
, i
);
1441 if (may_be_equality(tab
, i
))
1451 /* Check for (near) redundant constraints.
1452 * A constraint is redundant if it is non-negative and if
1453 * its minimal value (temporarily ignoring the non-negativity) is either
1454 * - zero (in case of rational tableaus), or
1455 * - strictly larger than -1 (in case of integer tableaus)
1457 * We first mark all non-redundant and non-dead variables that
1458 * are not frozen and not obviously negatively unbounded.
1459 * Then we iterate over all marked variables if they can attain
1460 * any values smaller than zero or at most negative one.
1461 * If not, we mark the row as being redundant (assuming it hasn't
1462 * been detected as being obviously redundant in the mean time).
1464 struct isl_tab
*isl_tab_detect_redundant(struct isl_tab
*tab
)
1473 if (tab
->n_redundant
== tab
->n_row
)
1477 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1478 struct isl_tab_var
*var
= var_from_row(tab
, i
);
1479 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
1483 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1484 struct isl_tab_var
*var
= var_from_col(tab
, i
);
1485 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
1486 !min_is_manifestly_unbounded(tab
, var
);
1491 struct isl_tab_var
*var
;
1492 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1493 var
= var_from_row(tab
, i
);
1497 if (i
== tab
->n_row
) {
1498 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1499 var
= var_from_col(tab
, i
);
1503 if (i
== tab
->n_col
)
1508 if ((tab
->rational
? (sign_of_min(tab
, var
) >= 0)
1509 : !min_at_most_neg_one(tab
, var
)) &&
1511 mark_redundant(tab
, var
->index
);
1512 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1513 var
= var_from_col(tab
, i
);
1516 if (!min_is_manifestly_unbounded(tab
, var
))
1526 int isl_tab_is_equality(struct isl_tab
*tab
, int con
)
1532 if (tab
->con
[con
].is_zero
)
1534 if (tab
->con
[con
].is_redundant
)
1536 if (!tab
->con
[con
].is_row
)
1537 return tab
->con
[con
].index
< tab
->n_dead
;
1539 row
= tab
->con
[con
].index
;
1541 return isl_int_is_zero(tab
->mat
->row
[row
][1]) &&
1542 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1543 tab
->n_col
- tab
->n_dead
) == -1;
1546 /* Return the minimial value of the affine expression "f" with denominator
1547 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
1548 * the expression cannot attain arbitrarily small values.
1549 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
1550 * The return value reflects the nature of the result (empty, unbounded,
1551 * minmimal value returned in *opt).
1553 enum isl_lp_result
isl_tab_min(struct isl_tab
*tab
,
1554 isl_int
*f
, isl_int denom
, isl_int
*opt
, isl_int
*opt_denom
,
1558 enum isl_lp_result res
= isl_lp_ok
;
1559 struct isl_tab_var
*var
;
1560 struct isl_tab_undo
*snap
;
1563 return isl_lp_empty
;
1565 snap
= isl_tab_snap(tab
);
1566 r
= add_row(tab
, f
);
1568 return isl_lp_error
;
1570 isl_int_mul(tab
->mat
->row
[var
->index
][0],
1571 tab
->mat
->row
[var
->index
][0], denom
);
1574 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1575 if (row
== var
->index
) {
1576 res
= isl_lp_unbounded
;
1581 pivot(tab
, row
, col
);
1583 if (isl_tab_rollback(tab
, snap
) < 0)
1584 return isl_lp_error
;
1585 if (ISL_FL_ISSET(flags
, ISL_TAB_SAVE_DUAL
)) {
1588 isl_vec_free(tab
->dual
);
1589 tab
->dual
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_con
);
1591 return isl_lp_error
;
1592 isl_int_set(tab
->dual
->el
[0], tab
->mat
->row
[var
->index
][0]);
1593 for (i
= 0; i
< tab
->n_con
; ++i
) {
1594 if (tab
->con
[i
].is_row
)
1595 isl_int_set_si(tab
->dual
->el
[1 + i
], 0);
1597 int pos
= 2 + tab
->con
[i
].index
;
1598 isl_int_set(tab
->dual
->el
[1 + i
],
1599 tab
->mat
->row
[var
->index
][pos
]);
1603 if (res
== isl_lp_ok
) {
1605 isl_int_set(*opt
, tab
->mat
->row
[var
->index
][1]);
1606 isl_int_set(*opt_denom
, tab
->mat
->row
[var
->index
][0]);
1608 isl_int_cdiv_q(*opt
, tab
->mat
->row
[var
->index
][1],
1609 tab
->mat
->row
[var
->index
][0]);
1614 int isl_tab_is_redundant(struct isl_tab
*tab
, int con
)
1621 if (tab
->con
[con
].is_zero
)
1623 if (tab
->con
[con
].is_redundant
)
1625 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
1628 /* Take a snapshot of the tableau that can be restored by s call to
1631 struct isl_tab_undo
*isl_tab_snap(struct isl_tab
*tab
)
1639 /* Undo the operation performed by isl_tab_relax.
1641 static void unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1643 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
1644 to_row(tab
, var
, 1);
1647 isl_int_sub(tab
->mat
->row
[var
->index
][1],
1648 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
1652 for (i
= 0; i
< tab
->n_row
; ++i
) {
1653 if (isl_int_is_zero(tab
->mat
->row
[i
][2 + var
->index
]))
1655 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
1656 tab
->mat
->row
[i
][2 + var
->index
]);
1662 static void perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
1664 switch(undo
->type
) {
1665 case isl_tab_undo_empty
:
1668 case isl_tab_undo_nonneg
:
1669 undo
->var
->is_nonneg
= 0;
1671 case isl_tab_undo_redundant
:
1672 undo
->var
->is_redundant
= 0;
1675 case isl_tab_undo_zero
:
1676 undo
->var
->is_zero
= 0;
1679 case isl_tab_undo_allocate
:
1680 if (!undo
->var
->is_row
) {
1681 if (!max_is_manifestly_unbounded(tab
, undo
->var
))
1682 to_row(tab
, undo
->var
, 1);
1683 else if (!min_is_manifestly_unbounded(tab
, undo
->var
))
1684 to_row(tab
, undo
->var
, -1);
1686 to_row(tab
, undo
->var
, 0);
1688 drop_row(tab
, undo
->var
->index
);
1690 case isl_tab_undo_relax
:
1691 unrelax(tab
, undo
->var
);
1696 /* Return the tableau to the state it was in when the snapshot "snap"
1699 int isl_tab_rollback(struct isl_tab
*tab
, struct isl_tab_undo
*snap
)
1701 struct isl_tab_undo
*undo
, *next
;
1707 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
1711 perform_undo(tab
, undo
);
1721 /* The given row "row" represents an inequality violated by all
1722 * points in the tableau. Check for some special cases of such
1723 * separating constraints.
1724 * In particular, if the row has been reduced to the constant -1,
1725 * then we know the inequality is adjacent (but opposite) to
1726 * an equality in the tableau.
1727 * If the row has been reduced to r = -1 -r', with r' an inequality
1728 * of the tableau, then the inequality is adjacent (but opposite)
1729 * to the inequality r'.
1731 static enum isl_ineq_type
separation_type(struct isl_tab
*tab
, unsigned row
)
1736 return isl_ineq_separate
;
1738 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
1739 return isl_ineq_separate
;
1740 if (!isl_int_is_negone(tab
->mat
->row
[row
][1]))
1741 return isl_ineq_separate
;
1743 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1744 tab
->n_col
- tab
->n_dead
);
1746 return isl_ineq_adj_eq
;
1748 if (!isl_int_is_negone(tab
->mat
->row
[row
][2 + tab
->n_dead
+ pos
]))
1749 return isl_ineq_separate
;
1751 pos
= isl_seq_first_non_zero(
1752 tab
->mat
->row
[row
] + 2 + tab
->n_dead
+ pos
+ 1,
1753 tab
->n_col
- tab
->n_dead
- pos
- 1);
1755 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
1758 /* Check the effect of inequality "ineq" on the tableau "tab".
1760 * isl_ineq_redundant: satisfied by all points in the tableau
1761 * isl_ineq_separate: satisfied by no point in the tableau
1762 * isl_ineq_cut: satisfied by some by not all points
1763 * isl_ineq_adj_eq: adjacent to an equality
1764 * isl_ineq_adj_ineq: adjacent to an inequality.
1766 enum isl_ineq_type
isl_tab_ineq_type(struct isl_tab
*tab
, isl_int
*ineq
)
1768 enum isl_ineq_type type
= isl_ineq_error
;
1769 struct isl_tab_undo
*snap
= NULL
;
1774 return isl_ineq_error
;
1776 if (extend_cons(tab
, 1) < 0)
1777 return isl_ineq_error
;
1779 snap
= isl_tab_snap(tab
);
1781 con
= add_row(tab
, ineq
);
1785 row
= tab
->con
[con
].index
;
1786 if (is_redundant(tab
, row
))
1787 type
= isl_ineq_redundant
;
1788 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
1790 isl_int_abs_ge(tab
->mat
->row
[row
][1],
1791 tab
->mat
->row
[row
][0]))) {
1792 if (at_least_zero(tab
, &tab
->con
[con
]))
1793 type
= isl_ineq_cut
;
1795 type
= separation_type(tab
, row
);
1796 } else if (tab
->rational
? (sign_of_min(tab
, &tab
->con
[con
]) < 0)
1797 : min_at_most_neg_one(tab
, &tab
->con
[con
]))
1798 type
= isl_ineq_cut
;
1800 type
= isl_ineq_redundant
;
1802 if (isl_tab_rollback(tab
, snap
))
1803 return isl_ineq_error
;
1806 isl_tab_rollback(tab
, snap
);
1807 return isl_ineq_error
;
1810 void isl_tab_dump(struct isl_tab
*tab
, FILE *out
, int indent
)
1816 fprintf(out
, "%*snull tab\n", indent
, "");
1819 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
1820 tab
->n_redundant
, tab
->n_dead
);
1822 fprintf(out
, ", rational");
1824 fprintf(out
, ", empty");
1826 fprintf(out
, "%*s[", indent
, "");
1827 for (i
= 0; i
< tab
->n_var
; ++i
) {
1830 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
1832 tab
->var
[i
].is_zero
? " [=0]" :
1833 tab
->var
[i
].is_redundant
? " [R]" : "");
1835 fprintf(out
, "]\n");
1836 fprintf(out
, "%*s[", indent
, "");
1837 for (i
= 0; i
< tab
->n_con
; ++i
) {
1840 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
1842 tab
->con
[i
].is_zero
? " [=0]" :
1843 tab
->con
[i
].is_redundant
? " [R]" : "");
1845 fprintf(out
, "]\n");
1846 fprintf(out
, "%*s[", indent
, "");
1847 for (i
= 0; i
< tab
->n_row
; ++i
) {
1850 fprintf(out
, "r%d: %d%s", i
, tab
->row_var
[i
],
1851 var_from_row(tab
, i
)->is_nonneg
? " [>=0]" : "");
1853 fprintf(out
, "]\n");
1854 fprintf(out
, "%*s[", indent
, "");
1855 for (i
= 0; i
< tab
->n_col
; ++i
) {
1858 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
1859 var_from_col(tab
, i
)->is_nonneg
? " [>=0]" : "");
1861 fprintf(out
, "]\n");
1862 r
= tab
->mat
->n_row
;
1863 tab
->mat
->n_row
= tab
->n_row
;
1864 c
= tab
->mat
->n_col
;
1865 tab
->mat
->n_col
= 2 + tab
->n_col
;
1866 isl_mat_dump(tab
->mat
, out
, indent
);
1867 tab
->mat
->n_row
= r
;
1868 tab
->mat
->n_col
= c
;