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) {
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 void mark_empty(struct isl_tab
*tab
)
377 if (!tab
->empty
&& tab
->need_undo
)
378 push(tab
, isl_tab_undo_empty
, NULL
);
382 /* Given a row number "row" and a column number "col", pivot the tableau
383 * such that the associated variables are interchanged.
384 * The given row in the tableau expresses
386 * x_r = a_r0 + \sum_i a_ri x_i
390 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
392 * Substituting this equality into the other rows
394 * x_j = a_j0 + \sum_i a_ji x_i
396 * with a_jc \ne 0, we obtain
398 * 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
405 * where i is any other column and j is any other row,
406 * is therefore transformed into
408 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
409 * 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)
411 * The transformation is performed along the following steps
416 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
419 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
420 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
422 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
423 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
425 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
426 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
428 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
429 * 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)
432 static void pivot(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(tab
, row
);
478 var
= var_from_col(tab
, col
);
483 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
484 if (isl_int_is_zero(mat
->row
[i
][2 + col
]))
486 if (!var_from_row(tab
, i
)->frozen
&&
487 is_redundant(tab
, i
))
488 if (mark_redundant(tab
, i
))
493 /* If "var" represents a column variable, then pivot is up (sgn > 0)
494 * or down (sgn < 0) to a row. The variable is assumed not to be
495 * unbounded in the specified direction.
497 static void to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
)
504 r
= pivot_row(tab
, NULL
, sign
, var
->index
);
505 isl_assert(tab
->mat
->ctx
, r
>= 0, return);
506 pivot(tab
, r
, var
->index
);
509 static void check_table(struct isl_tab
*tab
)
515 for (i
= 0; i
< tab
->n_row
; ++i
) {
516 if (!var_from_row(tab
, i
)->is_nonneg
)
518 assert(!isl_int_is_neg(tab
->mat
->row
[i
][1]));
522 /* Return the sign of the maximal value of "var".
523 * If the sign is not negative, then on return from this function,
524 * the sample value will also be non-negative.
526 * If "var" is manifestly unbounded wrt positive values, we are done.
527 * Otherwise, we pivot the variable up to a row if needed
528 * Then we continue pivoting down until either
529 * - no more down pivots can be performed
530 * - the sample value is positive
531 * - the variable is pivoted into a manifestly unbounded column
533 static int sign_of_max(struct isl_tab
*tab
, struct isl_tab_var
*var
)
537 if (max_is_manifestly_unbounded(tab
, var
))
540 while (!isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
541 find_pivot(tab
, var
, var
, 1, &row
, &col
);
543 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
544 pivot(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_tab
*tab
, struct isl_tab_var
*var
)
560 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
561 find_pivot(tab
, var
, var
, 1, &row
, &col
);
564 pivot(tab
, row
, col
);
565 if (!var
->is_row
) /* manifestly unbounded */
568 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
571 /* Perform pivots until we are sure that the row variable "var"
572 * can attain non-negative values. After return from this
573 * function, "var" is still a row variable, but its sample
574 * value may not be non-negative, even if the function returns 1.
576 static int at_least_zero(struct isl_tab
*tab
, struct isl_tab_var
*var
)
580 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
581 find_pivot(tab
, var
, var
, 1, &row
, &col
);
584 if (row
== var
->index
) /* manifestly unbounded */
586 pivot(tab
, row
, col
);
588 return !isl_int_is_neg(tab
->mat
->row
[var
->index
][1]);
591 /* Return a negative value if "var" can attain negative values.
592 * Return a non-negative value otherwise.
594 * If "var" is manifestly unbounded wrt negative values, we are done.
595 * Otherwise, if var is in a column, we can pivot it down to a row.
596 * Then we continue pivoting down until either
597 * - the pivot would result in a manifestly unbounded column
598 * => we don't perform the pivot, but simply return -1
599 * - no more down pivots can be performed
600 * - the sample value is negative
601 * If the sample value becomes negative and the variable is supposed
602 * to be nonnegative, then we undo the last pivot.
603 * However, if the last pivot has made the pivoting variable
604 * obviously redundant, then it may have moved to another row.
605 * In that case we look for upward pivots until we reach a non-negative
608 static int sign_of_min(struct isl_tab
*tab
, struct isl_tab_var
*var
)
611 struct isl_tab_var
*pivot_var
;
613 if (min_is_manifestly_unbounded(tab
, var
))
617 row
= pivot_row(tab
, NULL
, -1, col
);
618 pivot_var
= var_from_col(tab
, col
);
619 pivot(tab
, row
, col
);
620 if (var
->is_redundant
)
622 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
623 if (var
->is_nonneg
) {
624 if (!pivot_var
->is_redundant
&&
625 pivot_var
->index
== row
)
626 pivot(tab
, row
, col
);
628 restore_row(tab
, var
);
633 if (var
->is_redundant
)
635 while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
636 find_pivot(tab
, var
, var
, -1, &row
, &col
);
637 if (row
== var
->index
)
640 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
641 pivot_var
= var_from_col(tab
, col
);
642 pivot(tab
, row
, col
);
643 if (var
->is_redundant
)
646 if (var
->is_nonneg
) {
647 /* pivot back to non-negative value */
648 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
649 pivot(tab
, row
, col
);
651 restore_row(tab
, var
);
656 /* Return 1 if "var" can attain values <= -1.
657 * Return 0 otherwise.
659 * The sample value of "var" is assumed to be non-negative when the
660 * the function is called and will be made non-negative again before
661 * the function returns.
663 static int min_at_most_neg_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
666 struct isl_tab_var
*pivot_var
;
668 if (min_is_manifestly_unbounded(tab
, var
))
672 row
= pivot_row(tab
, NULL
, -1, col
);
673 pivot_var
= var_from_col(tab
, col
);
674 pivot(tab
, row
, col
);
675 if (var
->is_redundant
)
677 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1]) &&
678 isl_int_abs_ge(tab
->mat
->row
[var
->index
][1],
679 tab
->mat
->row
[var
->index
][0])) {
680 if (var
->is_nonneg
) {
681 if (!pivot_var
->is_redundant
&&
682 pivot_var
->index
== row
)
683 pivot(tab
, row
, col
);
685 restore_row(tab
, var
);
690 if (var
->is_redundant
)
693 find_pivot(tab
, var
, var
, -1, &row
, &col
);
694 if (row
== var
->index
)
698 pivot_var
= var_from_col(tab
, col
);
699 pivot(tab
, row
, col
);
700 if (var
->is_redundant
)
702 } while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1]) ||
703 isl_int_abs_lt(tab
->mat
->row
[var
->index
][1],
704 tab
->mat
->row
[var
->index
][0]));
705 if (var
->is_nonneg
) {
706 /* pivot back to non-negative value */
707 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
708 pivot(tab
, row
, col
);
709 restore_row(tab
, var
);
714 /* Return 1 if "var" can attain values >= 1.
715 * Return 0 otherwise.
717 static int at_least_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
722 if (max_is_manifestly_unbounded(tab
, var
))
725 r
= tab
->mat
->row
[var
->index
];
726 while (isl_int_lt(r
[1], r
[0])) {
727 find_pivot(tab
, var
, var
, 1, &row
, &col
);
729 return isl_int_ge(r
[1], r
[0]);
730 if (row
== var
->index
) /* manifestly unbounded */
732 pivot(tab
, row
, col
);
737 static void swap_cols(struct isl_tab
*tab
, int col1
, int col2
)
740 t
= tab
->col_var
[col1
];
741 tab
->col_var
[col1
] = tab
->col_var
[col2
];
742 tab
->col_var
[col2
] = t
;
743 var_from_col(tab
, col1
)->index
= col1
;
744 var_from_col(tab
, col2
)->index
= col2
;
745 tab
->mat
= isl_mat_swap_cols(tab
->mat
, 2 + col1
, 2 + col2
);
748 /* Mark column with index "col" as representing a zero variable.
749 * If we may need to undo the operation the column is kept,
750 * but no longer considered.
751 * Otherwise, the column is simply removed.
753 * The column may be interchanged with some other column. If it
754 * is interchanged with a later column, return 1. Otherwise return 0.
755 * If the columns are checked in order in the calling function,
756 * then a return value of 1 means that the column with the given
757 * column number may now contain a different column that
758 * hasn't been checked yet.
760 static int kill_col(struct isl_tab
*tab
, int col
)
762 var_from_col(tab
, col
)->is_zero
= 1;
763 if (tab
->need_undo
) {
764 push(tab
, isl_tab_undo_zero
, var_from_col(tab
, col
));
765 if (col
!= tab
->n_dead
)
766 swap_cols(tab
, col
, tab
->n_dead
);
770 if (col
!= tab
->n_col
- 1)
771 swap_cols(tab
, col
, tab
->n_col
- 1);
772 var_from_col(tab
, tab
->n_col
- 1)->index
= -1;
778 /* Row variable "var" is non-negative and cannot attain any values
779 * larger than zero. This means that the coefficients of the unrestricted
780 * column variables are zero and that the coefficients of the non-negative
781 * column variables are zero or negative.
782 * Each of the non-negative variables with a negative coefficient can
783 * then also be written as the negative sum of non-negative variables
784 * and must therefore also be zero.
786 static void close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
789 struct isl_mat
*mat
= tab
->mat
;
791 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return);
793 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
794 if (isl_int_is_zero(mat
->row
[var
->index
][2 + j
]))
796 isl_assert(tab
->mat
->ctx
,
797 isl_int_is_neg(mat
->row
[var
->index
][2 + j
]), return);
798 if (kill_col(tab
, j
))
801 mark_redundant(tab
, var
->index
);
804 /* Add a row to the tableau. The row is given as an affine combination
805 * of the original variables and needs to be expressed in terms of the
808 * We add each term in turn.
809 * If r = n/d_r is the current sum and we need to add k x, then
810 * if x is a column variable, we increase the numerator of
811 * this column by k d_r
812 * if x = f/d_x is a row variable, then the new representation of r is
814 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
815 * --- + --- = ------------------- = -------------------
816 * d_r d_r d_r d_x/g m
818 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
820 static int add_row(struct isl_tab
*tab
, isl_int
*line
)
827 isl_assert(tab
->mat
->ctx
, tab
->n_row
< tab
->mat
->n_row
, return -1);
832 tab
->con
[r
].index
= tab
->n_row
;
833 tab
->con
[r
].is_row
= 1;
834 tab
->con
[r
].is_nonneg
= 0;
835 tab
->con
[r
].is_zero
= 0;
836 tab
->con
[r
].is_redundant
= 0;
837 tab
->con
[r
].frozen
= 0;
838 tab
->row_var
[tab
->n_row
] = ~r
;
839 row
= tab
->mat
->row
[tab
->n_row
];
840 isl_int_set_si(row
[0], 1);
841 isl_int_set(row
[1], line
[0]);
842 isl_seq_clr(row
+ 2, tab
->n_col
);
843 for (i
= 0; i
< tab
->n_var
; ++i
) {
844 if (tab
->var
[i
].is_zero
)
846 if (tab
->var
[i
].is_row
) {
848 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
849 isl_int_swap(a
, row
[0]);
850 isl_int_divexact(a
, row
[0], a
);
852 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
853 isl_int_mul(b
, b
, line
[1 + i
]);
854 isl_seq_combine(row
+ 1, a
, row
+ 1,
855 b
, tab
->mat
->row
[tab
->var
[i
].index
] + 1,
858 isl_int_addmul(row
[2 + tab
->var
[i
].index
],
859 line
[1 + i
], row
[0]);
861 isl_seq_normalize(row
, 2 + tab
->n_col
);
864 push(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]);
871 static int drop_row(struct isl_tab
*tab
, int row
)
873 isl_assert(tab
->mat
->ctx
, ~tab
->row_var
[row
] == tab
->n_con
- 1, return -1);
874 if (row
!= tab
->n_row
- 1)
875 swap_rows(tab
, row
, tab
->n_row
- 1);
881 /* Add inequality "ineq" and check if it conflicts with the
882 * previously added constraints or if it is obviously redundant.
884 struct isl_tab
*isl_tab_add_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
891 r
= add_row(tab
, ineq
);
894 tab
->con
[r
].is_nonneg
= 1;
895 push(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
896 if (is_redundant(tab
, tab
->con
[r
].index
)) {
897 mark_redundant(tab
, tab
->con
[r
].index
);
901 sgn
= restore_row(tab
, &tab
->con
[r
]);
904 else if (tab
->con
[r
].is_row
&&
905 is_redundant(tab
, tab
->con
[r
].index
))
906 mark_redundant(tab
, tab
->con
[r
].index
);
913 /* Pivot a non-negative variable down until it reaches the value zero
914 * and then pivot the variable into a column position.
916 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
)
924 while (isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
925 find_pivot(tab
, var
, NULL
, -1, &row
, &col
);
926 isl_assert(tab
->mat
->ctx
, row
!= -1, return -1);
927 pivot(tab
, row
, col
);
932 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
)
933 if (!isl_int_is_zero(tab
->mat
->row
[var
->index
][2 + i
]))
936 isl_assert(tab
->mat
->ctx
, i
< tab
->n_col
, return -1);
937 pivot(tab
, var
->index
, i
);
942 /* We assume Gaussian elimination has been performed on the equalities.
943 * The equalities can therefore never conflict.
944 * Adding the equalities is currently only really useful for a later call
945 * to isl_tab_ineq_type.
947 static struct isl_tab
*add_eq(struct isl_tab
*tab
, isl_int
*eq
)
954 r
= add_row(tab
, eq
);
958 r
= tab
->con
[r
].index
;
959 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
960 if (isl_int_is_zero(tab
->mat
->row
[r
][2 + i
]))
974 /* Add an equality that is known to be valid for the given tableau.
976 struct isl_tab
*isl_tab_add_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
978 struct isl_tab_var
*var
;
984 r
= add_row(tab
, eq
);
990 if (isl_int_is_neg(tab
->mat
->row
[r
][1]))
991 isl_seq_neg(tab
->mat
->row
[r
] + 1, tab
->mat
->row
[r
] + 1,
994 if (to_col(tab
, var
) < 0)
997 kill_col(tab
, var
->index
);
1005 struct isl_tab
*isl_tab_from_basic_map(struct isl_basic_map
*bmap
)
1008 struct isl_tab
*tab
;
1012 tab
= isl_tab_alloc(bmap
->ctx
,
1013 isl_basic_map_total_dim(bmap
) + bmap
->n_ineq
+ 1,
1014 isl_basic_map_total_dim(bmap
));
1017 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
1018 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
1022 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1023 tab
= add_eq(tab
, bmap
->eq
[i
]);
1027 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1028 tab
= isl_tab_add_ineq(tab
, bmap
->ineq
[i
]);
1029 if (!tab
|| tab
->empty
)
1035 struct isl_tab
*isl_tab_from_basic_set(struct isl_basic_set
*bset
)
1037 return isl_tab_from_basic_map((struct isl_basic_map
*)bset
);
1040 /* Construct a tableau corresponding to the recession cone of "bmap".
1042 struct isl_tab
*isl_tab_from_recession_cone(struct isl_basic_map
*bmap
)
1046 struct isl_tab
*tab
;
1050 tab
= isl_tab_alloc(bmap
->ctx
, bmap
->n_eq
+ bmap
->n_ineq
,
1051 isl_basic_map_total_dim(bmap
));
1054 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
1057 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1058 isl_int_swap(bmap
->eq
[i
][0], cst
);
1059 tab
= add_eq(tab
, bmap
->eq
[i
]);
1060 isl_int_swap(bmap
->eq
[i
][0], cst
);
1064 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1066 isl_int_swap(bmap
->ineq
[i
][0], cst
);
1067 r
= add_row(tab
, bmap
->ineq
[i
]);
1068 isl_int_swap(bmap
->ineq
[i
][0], cst
);
1071 tab
->con
[r
].is_nonneg
= 1;
1072 push(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1083 /* Assuming "tab" is the tableau of a cone, check if the cone is
1084 * bounded, i.e., if it is empty or only contains the origin.
1086 int isl_tab_cone_is_bounded(struct isl_tab
*tab
)
1094 if (tab
->n_dead
== tab
->n_col
)
1098 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1099 struct isl_tab_var
*var
;
1100 var
= var_from_row(tab
, i
);
1101 if (!var
->is_nonneg
)
1103 if (sign_of_max(tab
, var
) != 0)
1105 close_row(tab
, var
);
1108 if (tab
->n_dead
== tab
->n_col
)
1110 if (i
== tab
->n_row
)
1115 int isl_tab_sample_is_integer(struct isl_tab
*tab
)
1122 for (i
= 0; i
< tab
->n_var
; ++i
) {
1124 if (!tab
->var
[i
].is_row
)
1126 row
= tab
->var
[i
].index
;
1127 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1128 tab
->mat
->row
[row
][0]))
1134 static struct isl_vec
*extract_integer_sample(struct isl_tab
*tab
)
1137 struct isl_vec
*vec
;
1139 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
1143 isl_int_set_si(vec
->block
.data
[0], 1);
1144 for (i
= 0; i
< tab
->n_var
; ++i
) {
1145 if (!tab
->var
[i
].is_row
)
1146 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
1148 int row
= tab
->var
[i
].index
;
1149 isl_int_divexact(vec
->block
.data
[1 + i
],
1150 tab
->mat
->row
[row
][1], tab
->mat
->row
[row
][0]);
1157 struct isl_vec
*isl_tab_get_sample_value(struct isl_tab
*tab
)
1160 struct isl_vec
*vec
;
1166 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
1172 isl_int_set_si(vec
->block
.data
[0], 1);
1173 for (i
= 0; i
< tab
->n_var
; ++i
) {
1175 if (!tab
->var
[i
].is_row
) {
1176 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
1179 row
= tab
->var
[i
].index
;
1180 isl_int_gcd(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
1181 isl_int_divexact(m
, tab
->mat
->row
[row
][0], m
);
1182 isl_seq_scale(vec
->block
.data
, vec
->block
.data
, m
, 1 + i
);
1183 isl_int_divexact(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
1184 isl_int_mul(vec
->block
.data
[1 + i
], m
, tab
->mat
->row
[row
][1]);
1186 isl_seq_normalize(vec
->block
.data
, vec
->size
);
1192 /* Update "bmap" based on the results of the tableau "tab".
1193 * In particular, implicit equalities are made explicit, redundant constraints
1194 * are removed and if the sample value happens to be integer, it is stored
1195 * in "bmap" (unless "bmap" already had an integer sample).
1197 * The tableau is assumed to have been created from "bmap" using
1198 * isl_tab_from_basic_map.
1200 struct isl_basic_map
*isl_basic_map_update_from_tab(struct isl_basic_map
*bmap
,
1201 struct isl_tab
*tab
)
1213 bmap
= isl_basic_map_set_to_empty(bmap
);
1215 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1216 if (isl_tab_is_equality(tab
, n_eq
+ i
))
1217 isl_basic_map_inequality_to_equality(bmap
, i
);
1218 else if (isl_tab_is_redundant(tab
, n_eq
+ i
))
1219 isl_basic_map_drop_inequality(bmap
, i
);
1221 if (!tab
->rational
&&
1222 !bmap
->sample
&& isl_tab_sample_is_integer(tab
))
1223 bmap
->sample
= extract_integer_sample(tab
);
1227 struct isl_basic_set
*isl_basic_set_update_from_tab(struct isl_basic_set
*bset
,
1228 struct isl_tab
*tab
)
1230 return (struct isl_basic_set
*)isl_basic_map_update_from_tab(
1231 (struct isl_basic_map
*)bset
, tab
);
1234 /* Given a non-negative variable "var", add a new non-negative variable
1235 * that is the opposite of "var", ensuring that var can only attain the
1237 * If var = n/d is a row variable, then the new variable = -n/d.
1238 * If var is a column variables, then the new variable = -var.
1239 * If the new variable cannot attain non-negative values, then
1240 * the resulting tableau is empty.
1241 * Otherwise, we know the value will be zero and we close the row.
1243 static struct isl_tab
*cut_to_hyperplane(struct isl_tab
*tab
,
1244 struct isl_tab_var
*var
)
1250 if (extend_cons(tab
, 1) < 0)
1254 tab
->con
[r
].index
= tab
->n_row
;
1255 tab
->con
[r
].is_row
= 1;
1256 tab
->con
[r
].is_nonneg
= 0;
1257 tab
->con
[r
].is_zero
= 0;
1258 tab
->con
[r
].is_redundant
= 0;
1259 tab
->con
[r
].frozen
= 0;
1260 tab
->row_var
[tab
->n_row
] = ~r
;
1261 row
= tab
->mat
->row
[tab
->n_row
];
1264 isl_int_set(row
[0], tab
->mat
->row
[var
->index
][0]);
1265 isl_seq_neg(row
+ 1,
1266 tab
->mat
->row
[var
->index
] + 1, 1 + tab
->n_col
);
1268 isl_int_set_si(row
[0], 1);
1269 isl_seq_clr(row
+ 1, 1 + tab
->n_col
);
1270 isl_int_set_si(row
[2 + var
->index
], -1);
1275 push(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]);
1277 sgn
= sign_of_max(tab
, &tab
->con
[r
]);
1281 tab
->con
[r
].is_nonneg
= 1;
1282 push(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1284 close_row(tab
, &tab
->con
[r
]);
1293 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
1294 * relax the inequality by one. That is, the inequality r >= 0 is replaced
1295 * by r' = r + 1 >= 0.
1296 * If r is a row variable, we simply increase the constant term by one
1297 * (taking into account the denominator).
1298 * If r is a column variable, then we need to modify each row that
1299 * refers to r = r' - 1 by substituting this equality, effectively
1300 * subtracting the coefficient of the column from the constant.
1302 struct isl_tab
*isl_tab_relax(struct isl_tab
*tab
, int con
)
1304 struct isl_tab_var
*var
;
1308 var
= &tab
->con
[con
];
1310 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
1311 to_row(tab
, var
, 1);
1314 isl_int_add(tab
->mat
->row
[var
->index
][1],
1315 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
1319 for (i
= 0; i
< tab
->n_row
; ++i
) {
1320 if (isl_int_is_zero(tab
->mat
->row
[i
][2 + var
->index
]))
1322 isl_int_sub(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
1323 tab
->mat
->row
[i
][2 + var
->index
]);
1328 push(tab
, isl_tab_undo_relax
, var
);
1333 struct isl_tab
*isl_tab_select_facet(struct isl_tab
*tab
, int con
)
1338 return cut_to_hyperplane(tab
, &tab
->con
[con
]);
1341 static int may_be_equality(struct isl_tab
*tab
, int row
)
1343 return (tab
->rational
? isl_int_is_zero(tab
->mat
->row
[row
][1])
1344 : isl_int_lt(tab
->mat
->row
[row
][1],
1345 tab
->mat
->row
[row
][0])) &&
1346 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1347 tab
->n_col
- tab
->n_dead
) != -1;
1350 /* Check for (near) equalities among the constraints.
1351 * A constraint is an equality if it is non-negative and if
1352 * its maximal value is either
1353 * - zero (in case of rational tableaus), or
1354 * - strictly less than 1 (in case of integer tableaus)
1356 * We first mark all non-redundant and non-dead variables that
1357 * are not frozen and not obviously not an equality.
1358 * Then we iterate over all marked variables if they can attain
1359 * any values larger than zero or at least one.
1360 * If the maximal value is zero, we mark any column variables
1361 * that appear in the row as being zero and mark the row as being redundant.
1362 * Otherwise, if the maximal value is strictly less than one (and the
1363 * tableau is integer), then we restrict the value to being zero
1364 * by adding an opposite non-negative variable.
1366 struct isl_tab
*isl_tab_detect_equalities(struct isl_tab
*tab
)
1375 if (tab
->n_dead
== tab
->n_col
)
1379 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1380 struct isl_tab_var
*var
= var_from_row(tab
, i
);
1381 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
1382 may_be_equality(tab
, i
);
1386 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1387 struct isl_tab_var
*var
= var_from_col(tab
, i
);
1388 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
1393 struct isl_tab_var
*var
;
1394 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1395 var
= var_from_row(tab
, i
);
1399 if (i
== tab
->n_row
) {
1400 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1401 var
= var_from_col(tab
, i
);
1405 if (i
== tab
->n_col
)
1410 if (sign_of_max(tab
, var
) == 0)
1411 close_row(tab
, var
);
1412 else if (!tab
->rational
&& !at_least_one(tab
, var
)) {
1413 tab
= cut_to_hyperplane(tab
, var
);
1414 return isl_tab_detect_equalities(tab
);
1416 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1417 var
= var_from_row(tab
, i
);
1420 if (may_be_equality(tab
, i
))
1430 /* Check for (near) redundant constraints.
1431 * A constraint is redundant if it is non-negative and if
1432 * its minimal value (temporarily ignoring the non-negativity) is either
1433 * - zero (in case of rational tableaus), or
1434 * - strictly larger than -1 (in case of integer tableaus)
1436 * We first mark all non-redundant and non-dead variables that
1437 * are not frozen and not obviously negatively unbounded.
1438 * Then we iterate over all marked variables if they can attain
1439 * any values smaller than zero or at most negative one.
1440 * If not, we mark the row as being redundant (assuming it hasn't
1441 * been detected as being obviously redundant in the mean time).
1443 struct isl_tab
*isl_tab_detect_redundant(struct isl_tab
*tab
)
1452 if (tab
->n_redundant
== tab
->n_row
)
1456 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1457 struct isl_tab_var
*var
= var_from_row(tab
, i
);
1458 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
1462 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1463 struct isl_tab_var
*var
= var_from_col(tab
, i
);
1464 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
1465 !min_is_manifestly_unbounded(tab
, var
);
1470 struct isl_tab_var
*var
;
1471 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1472 var
= var_from_row(tab
, i
);
1476 if (i
== tab
->n_row
) {
1477 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1478 var
= var_from_col(tab
, i
);
1482 if (i
== tab
->n_col
)
1487 if ((tab
->rational
? (sign_of_min(tab
, var
) >= 0)
1488 : !min_at_most_neg_one(tab
, var
)) &&
1490 mark_redundant(tab
, var
->index
);
1491 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1492 var
= var_from_col(tab
, i
);
1495 if (!min_is_manifestly_unbounded(tab
, var
))
1505 int isl_tab_is_equality(struct isl_tab
*tab
, int con
)
1511 if (tab
->con
[con
].is_zero
)
1513 if (tab
->con
[con
].is_redundant
)
1515 if (!tab
->con
[con
].is_row
)
1516 return tab
->con
[con
].index
< tab
->n_dead
;
1518 row
= tab
->con
[con
].index
;
1520 return isl_int_is_zero(tab
->mat
->row
[row
][1]) &&
1521 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1522 tab
->n_col
- tab
->n_dead
) == -1;
1525 /* Return the minimial value of the affine expression "f" with denominator
1526 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
1527 * the expression cannot attain arbitrarily small values.
1528 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
1529 * The return value reflects the nature of the result (empty, unbounded,
1530 * minmimal value returned in *opt).
1532 enum isl_lp_result
isl_tab_min(struct isl_tab
*tab
,
1533 isl_int
*f
, isl_int denom
, isl_int
*opt
, isl_int
*opt_denom
,
1537 enum isl_lp_result res
= isl_lp_ok
;
1538 struct isl_tab_var
*var
;
1539 struct isl_tab_undo
*snap
;
1542 return isl_lp_empty
;
1544 snap
= isl_tab_snap(tab
);
1545 r
= add_row(tab
, f
);
1547 return isl_lp_error
;
1549 isl_int_mul(tab
->mat
->row
[var
->index
][0],
1550 tab
->mat
->row
[var
->index
][0], denom
);
1553 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1554 if (row
== var
->index
) {
1555 res
= isl_lp_unbounded
;
1560 pivot(tab
, row
, col
);
1562 if (isl_tab_rollback(tab
, snap
) < 0)
1563 return isl_lp_error
;
1564 if (ISL_FL_ISSET(flags
, ISL_TAB_SAVE_DUAL
)) {
1567 isl_vec_free(tab
->dual
);
1568 tab
->dual
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_con
);
1570 return isl_lp_error
;
1571 isl_int_set(tab
->dual
->el
[0], tab
->mat
->row
[var
->index
][0]);
1572 for (i
= 0; i
< tab
->n_con
; ++i
) {
1573 if (tab
->con
[i
].is_row
)
1574 isl_int_set_si(tab
->dual
->el
[1 + i
], 0);
1576 int pos
= 2 + tab
->con
[i
].index
;
1577 isl_int_set(tab
->dual
->el
[1 + i
],
1578 tab
->mat
->row
[var
->index
][pos
]);
1582 if (res
== isl_lp_ok
) {
1584 isl_int_set(*opt
, tab
->mat
->row
[var
->index
][1]);
1585 isl_int_set(*opt_denom
, tab
->mat
->row
[var
->index
][0]);
1587 isl_int_cdiv_q(*opt
, tab
->mat
->row
[var
->index
][1],
1588 tab
->mat
->row
[var
->index
][0]);
1593 int isl_tab_is_redundant(struct isl_tab
*tab
, int con
)
1600 if (tab
->con
[con
].is_zero
)
1602 if (tab
->con
[con
].is_redundant
)
1604 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
1607 /* Take a snapshot of the tableau that can be restored by s call to
1610 struct isl_tab_undo
*isl_tab_snap(struct isl_tab
*tab
)
1618 /* Undo the operation performed by isl_tab_relax.
1620 static void unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1622 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
1623 to_row(tab
, var
, 1);
1626 isl_int_sub(tab
->mat
->row
[var
->index
][1],
1627 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
1631 for (i
= 0; i
< tab
->n_row
; ++i
) {
1632 if (isl_int_is_zero(tab
->mat
->row
[i
][2 + var
->index
]))
1634 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
1635 tab
->mat
->row
[i
][2 + var
->index
]);
1641 static void perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
1643 switch(undo
->type
) {
1644 case isl_tab_undo_empty
:
1647 case isl_tab_undo_nonneg
:
1648 undo
->var
->is_nonneg
= 0;
1650 case isl_tab_undo_redundant
:
1651 undo
->var
->is_redundant
= 0;
1654 case isl_tab_undo_zero
:
1655 undo
->var
->is_zero
= 0;
1658 case isl_tab_undo_allocate
:
1659 if (!undo
->var
->is_row
) {
1660 if (max_is_manifestly_unbounded(tab
, undo
->var
))
1661 to_row(tab
, undo
->var
, -1);
1663 to_row(tab
, undo
->var
, 1);
1665 drop_row(tab
, undo
->var
->index
);
1667 case isl_tab_undo_relax
:
1668 unrelax(tab
, undo
->var
);
1673 /* Return the tableau to the state it was in when the snapshot "snap"
1676 int isl_tab_rollback(struct isl_tab
*tab
, struct isl_tab_undo
*snap
)
1678 struct isl_tab_undo
*undo
, *next
;
1684 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
1688 perform_undo(tab
, undo
);
1698 /* The given row "row" represents an inequality violated by all
1699 * points in the tableau. Check for some special cases of such
1700 * separating constraints.
1701 * In particular, if the row has been reduced to the constant -1,
1702 * then we know the inequality is adjacent (but opposite) to
1703 * an equality in the tableau.
1704 * If the row has been reduced to r = -1 -r', with r' an inequality
1705 * of the tableau, then the inequality is adjacent (but opposite)
1706 * to the inequality r'.
1708 static enum isl_ineq_type
separation_type(struct isl_tab
*tab
, unsigned row
)
1713 return isl_ineq_separate
;
1715 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
1716 return isl_ineq_separate
;
1717 if (!isl_int_is_negone(tab
->mat
->row
[row
][1]))
1718 return isl_ineq_separate
;
1720 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1721 tab
->n_col
- tab
->n_dead
);
1723 return isl_ineq_adj_eq
;
1725 if (!isl_int_is_negone(tab
->mat
->row
[row
][2 + tab
->n_dead
+ pos
]))
1726 return isl_ineq_separate
;
1728 pos
= isl_seq_first_non_zero(
1729 tab
->mat
->row
[row
] + 2 + tab
->n_dead
+ pos
+ 1,
1730 tab
->n_col
- tab
->n_dead
- pos
- 1);
1732 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
1735 /* Check the effect of inequality "ineq" on the tableau "tab".
1737 * isl_ineq_redundant: satisfied by all points in the tableau
1738 * isl_ineq_separate: satisfied by no point in the tableau
1739 * isl_ineq_cut: satisfied by some by not all points
1740 * isl_ineq_adj_eq: adjacent to an equality
1741 * isl_ineq_adj_ineq: adjacent to an inequality.
1743 enum isl_ineq_type
isl_tab_ineq_type(struct isl_tab
*tab
, isl_int
*ineq
)
1745 enum isl_ineq_type type
= isl_ineq_error
;
1746 struct isl_tab_undo
*snap
= NULL
;
1751 return isl_ineq_error
;
1753 if (extend_cons(tab
, 1) < 0)
1754 return isl_ineq_error
;
1756 snap
= isl_tab_snap(tab
);
1758 con
= add_row(tab
, ineq
);
1762 row
= tab
->con
[con
].index
;
1763 if (is_redundant(tab
, row
))
1764 type
= isl_ineq_redundant
;
1765 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
1767 isl_int_abs_ge(tab
->mat
->row
[row
][1],
1768 tab
->mat
->row
[row
][0]))) {
1769 if (at_least_zero(tab
, &tab
->con
[con
]))
1770 type
= isl_ineq_cut
;
1772 type
= separation_type(tab
, row
);
1773 } else if (tab
->rational
? (sign_of_min(tab
, &tab
->con
[con
]) < 0)
1774 : min_at_most_neg_one(tab
, &tab
->con
[con
]))
1775 type
= isl_ineq_cut
;
1777 type
= isl_ineq_redundant
;
1779 if (isl_tab_rollback(tab
, snap
))
1780 return isl_ineq_error
;
1783 isl_tab_rollback(tab
, snap
);
1784 return isl_ineq_error
;
1787 void isl_tab_dump(struct isl_tab
*tab
, FILE *out
, int indent
)
1793 fprintf(out
, "%*snull tab\n", indent
, "");
1796 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
1797 tab
->n_redundant
, tab
->n_dead
);
1799 fprintf(out
, ", rational");
1801 fprintf(out
, ", empty");
1803 fprintf(out
, "%*s[", indent
, "");
1804 for (i
= 0; i
< tab
->n_var
; ++i
) {
1807 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
1809 tab
->var
[i
].is_zero
? " [=0]" :
1810 tab
->var
[i
].is_redundant
? " [R]" : "");
1812 fprintf(out
, "]\n");
1813 fprintf(out
, "%*s[", indent
, "");
1814 for (i
= 0; i
< tab
->n_con
; ++i
) {
1817 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
1819 tab
->con
[i
].is_zero
? " [=0]" :
1820 tab
->con
[i
].is_redundant
? " [R]" : "");
1822 fprintf(out
, "]\n");
1823 fprintf(out
, "%*s[", indent
, "");
1824 for (i
= 0; i
< tab
->n_row
; ++i
) {
1827 fprintf(out
, "r%d: %d%s", i
, tab
->row_var
[i
],
1828 var_from_row(tab
, i
)->is_nonneg
? " [>=0]" : "");
1830 fprintf(out
, "]\n");
1831 fprintf(out
, "%*s[", indent
, "");
1832 for (i
= 0; i
< tab
->n_col
; ++i
) {
1835 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
1836 var_from_col(tab
, i
)->is_nonneg
? " [>=0]" : "");
1838 fprintf(out
, "]\n");
1839 r
= tab
->mat
->n_row
;
1840 tab
->mat
->n_row
= tab
->n_row
;
1841 c
= tab
->mat
->n_col
;
1842 tab
->mat
->n_col
= 2 + tab
->n_col
;
1843 isl_mat_dump(tab
->mat
, out
, indent
);
1844 tab
->mat
->n_row
= r
;
1845 tab
->mat
->n_col
= c
;