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;
54 tab
->bottom
.type
= isl_tab_undo_bottom
;
55 tab
->bottom
.next
= NULL
;
56 tab
->top
= &tab
->bottom
;
59 isl_tab_free(ctx
, tab
);
63 static int extend_cons(struct isl_ctx
*ctx
, struct isl_tab
*tab
, unsigned n_new
)
65 if (tab
->max_con
< tab
->n_con
+ n_new
) {
66 struct isl_tab_var
*con
;
68 con
= isl_realloc_array(ctx
, tab
->con
,
69 struct isl_tab_var
, tab
->max_con
+ n_new
);
73 tab
->max_con
+= n_new
;
75 if (tab
->mat
->n_row
< tab
->n_row
+ n_new
) {
78 tab
->mat
= isl_mat_extend(ctx
, tab
->mat
,
79 tab
->n_row
+ n_new
, tab
->n_col
);
82 row_var
= isl_realloc_array(ctx
, tab
->row_var
,
83 int, tab
->mat
->n_row
);
86 tab
->row_var
= row_var
;
91 struct isl_tab
*isl_tab_extend(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
94 if (extend_cons(ctx
, tab
, n_new
) >= 0)
97 isl_tab_free(ctx
, tab
);
101 static void free_undo(struct isl_ctx
*ctx
, 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_ctx
*ctx
, struct isl_tab
*tab
)
117 isl_mat_free(ctx
, tab
->mat
);
125 static struct isl_tab_var
*var_from_index(struct isl_ctx
*ctx
,
126 struct isl_tab
*tab
, int i
)
131 return &tab
->con
[~i
];
134 static struct isl_tab_var
*var_from_row(struct isl_ctx
*ctx
,
135 struct isl_tab
*tab
, int i
)
137 return var_from_index(ctx
, tab
, tab
->row_var
[i
]);
140 static struct isl_tab_var
*var_from_col(struct isl_ctx
*ctx
,
141 struct isl_tab
*tab
, int i
)
143 return var_from_index(ctx
, tab
, tab
->col_var
[i
]);
146 /* Check if there are any upper bounds on column variable "var",
147 * i.e., non-negative rows where var appears with a negative coefficient.
148 * Return 1 if there are no such bounds.
150 static int max_is_manifestly_unbounded(struct isl_ctx
*ctx
,
151 struct isl_tab
*tab
, struct isl_tab_var
*var
)
157 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
158 if (!isl_int_is_neg(tab
->mat
->row
[i
][2 + var
->index
]))
160 if (var_from_row(ctx
, tab
, i
)->is_nonneg
)
166 /* Check if there are any lower bounds on column variable "var",
167 * i.e., non-negative rows where var appears with a positive coefficient.
168 * Return 1 if there are no such bounds.
170 static int min_is_manifestly_unbounded(struct isl_ctx
*ctx
,
171 struct isl_tab
*tab
, struct isl_tab_var
*var
)
177 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
178 if (!isl_int_is_pos(tab
->mat
->row
[i
][2 + var
->index
]))
180 if (var_from_row(ctx
, tab
, i
)->is_nonneg
)
186 /* Given the index of a column "c", return the index of a row
187 * that can be used to pivot the column in, with either an increase
188 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
189 * If "var" is not NULL, then the row returned will be different from
190 * the one associated with "var".
192 * Each row in the tableau is of the form
194 * x_r = a_r0 + \sum_i a_ri x_i
196 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
197 * impose any limit on the increase or decrease in the value of x_c
198 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
199 * for the row with the smallest (most stringent) such bound.
200 * Note that the common denominator of each row drops out of the fraction.
201 * To check if row j has a smaller bound than row r, i.e.,
202 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
203 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
204 * where -sign(a_jc) is equal to "sgn".
206 static int pivot_row(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
207 struct isl_tab_var
*var
, int sgn
, int c
)
214 for (j
= tab
->n_redundant
; j
< tab
->n_row
; ++j
) {
215 if (var
&& j
== var
->index
)
217 if (!var_from_row(ctx
, tab
, j
)->is_nonneg
)
219 if (sgn
* isl_int_sgn(tab
->mat
->row
[j
][2 + c
]) >= 0)
225 isl_int_mul(t
, tab
->mat
->row
[r
][1], tab
->mat
->row
[j
][2 + c
]);
226 isl_int_submul(t
, tab
->mat
->row
[j
][1], tab
->mat
->row
[r
][2 + c
]);
227 tsgn
= sgn
* isl_int_sgn(t
);
228 if (tsgn
< 0 || (tsgn
== 0 &&
229 tab
->row_var
[j
] < tab
->row_var
[r
]))
236 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
237 * (sgn < 0) the value of row variable var.
238 * As the given row in the tableau is of the form
240 * x_r = a_r0 + \sum_i a_ri x_i
242 * we need to find a column such that the sign of a_ri is equal to "sgn"
243 * (such that an increase in x_i will have the desired effect) or a
244 * column with a variable that may attain negative values.
245 * If a_ri is positive, then we need to move x_i in the same direction
246 * to obtain the desired effect. Otherwise, x_i has to move in the
247 * opposite direction.
249 static void find_pivot(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
250 struct isl_tab_var
*var
, int sgn
, int *row
, int *col
)
257 isl_assert(ctx
, var
->is_row
, return);
258 tr
= tab
->mat
->row
[var
->index
];
261 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
262 if (isl_int_is_zero(tr
[2 + j
]))
264 if (isl_int_sgn(tr
[2 + j
]) != sgn
&&
265 var_from_col(ctx
, tab
, j
)->is_nonneg
)
267 if (c
< 0 || tab
->col_var
[j
] < tab
->col_var
[c
])
273 sgn
*= isl_int_sgn(tr
[2 + c
]);
274 r
= pivot_row(ctx
, tab
, var
, sgn
, c
);
275 *row
= r
< 0 ? var
->index
: r
;
279 /* Return 1 if row "row" represents an obviously redundant inequality.
281 * - it represents an inequality or a variable
282 * - that is the sum of a non-negative sample value and a positive
283 * combination of zero or more non-negative variables.
285 static int is_redundant(struct isl_ctx
*ctx
, struct isl_tab
*tab
, int row
)
289 if (tab
->row_var
[row
] < 0 && !var_from_row(ctx
, tab
, row
)->is_nonneg
)
292 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
295 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
296 if (isl_int_is_zero(tab
->mat
->row
[row
][2 + i
]))
298 if (isl_int_is_neg(tab
->mat
->row
[row
][2 + i
]))
300 if (!var_from_col(ctx
, tab
, i
)->is_nonneg
)
306 static void swap_rows(struct isl_ctx
*ctx
,
307 struct isl_tab
*tab
, int row1
, int row2
)
310 t
= tab
->row_var
[row1
];
311 tab
->row_var
[row1
] = tab
->row_var
[row2
];
312 tab
->row_var
[row2
] = t
;
313 var_from_row(ctx
, tab
, row1
)->index
= row1
;
314 var_from_row(ctx
, tab
, row2
)->index
= row2
;
315 tab
->mat
= isl_mat_swap_rows(ctx
, tab
->mat
, row1
, row2
);
318 static void push(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
319 enum isl_tab_undo_type type
, struct isl_tab_var
*var
)
321 struct isl_tab_undo
*undo
;
326 undo
= isl_alloc_type(ctx
, struct isl_tab_undo
);
334 undo
->next
= tab
->top
;
338 /* Mark row with index "row" as being redundant.
339 * If we may need to undo the operation or if the row represents
340 * a variable of the original problem, the row is kept,
341 * but no longer considered when looking for a pivot row.
342 * Otherwise, the row is simply removed.
344 * The row may be interchanged with some other row. If it
345 * is interchanged with a later row, return 1. Otherwise return 0.
346 * If the rows are checked in order in the calling function,
347 * then a return value of 1 means that the row with the given
348 * row number may now contain a different row that hasn't been checked yet.
350 static int mark_redundant(struct isl_ctx
*ctx
,
351 struct isl_tab
*tab
, int row
)
353 struct isl_tab_var
*var
= var_from_row(ctx
, tab
, row
);
354 var
->is_redundant
= 1;
355 isl_assert(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(ctx
, tab
, isl_tab_undo_nonneg
, var
);
361 if (row
!= tab
->n_redundant
)
362 swap_rows(ctx
, tab
, row
, tab
->n_redundant
);
363 push(ctx
, tab
, isl_tab_undo_redundant
, var
);
367 if (row
!= tab
->n_row
- 1)
368 swap_rows(ctx
, tab
, row
, tab
->n_row
- 1);
369 var_from_row(ctx
, tab
, tab
->n_row
- 1)->index
= -1;
375 static void mark_empty(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
377 if (!tab
->empty
&& tab
->need_undo
)
378 push(ctx
, 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 variable 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_ctx
*ctx
,
433 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(ctx
, tab
, row
);
479 var
= var_from_col(ctx
, tab
, col
);
482 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
483 if (isl_int_is_zero(mat
->row
[i
][2 + col
]))
485 if (!var_from_row(ctx
, tab
, i
)->frozen
&&
486 is_redundant(ctx
, tab
, i
))
487 if (mark_redundant(ctx
, tab
, i
))
492 /* If "var" represents a column variable, then pivot is up (sgn > 0)
493 * or down (sgn < 0) to a row. The variable is assumed not to be
494 * unbounded in the specified direction.
496 static void to_row(struct isl_ctx
*ctx
,
497 struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
)
504 r
= pivot_row(ctx
, tab
, NULL
, sign
, var
->index
);
505 isl_assert(ctx
, r
>= 0, return);
506 pivot(ctx
, tab
, r
, var
->index
);
509 static void check_table(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
515 for (i
= 0; i
< tab
->n_row
; ++i
) {
516 if (!var_from_row(ctx
, 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_ctx
*ctx
,
534 struct isl_tab
*tab
, struct isl_tab_var
*var
)
538 if (max_is_manifestly_unbounded(ctx
, tab
, var
))
540 to_row(ctx
, tab
, var
, 1);
541 while (!isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
542 find_pivot(ctx
, tab
, var
, 1, &row
, &col
);
544 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
545 pivot(ctx
, tab
, row
, col
);
546 if (!var
->is_row
) /* manifestly unbounded */
552 /* Perform pivots until the row variable "var" has a non-negative
553 * sample value or until no more upward pivots can be performed.
554 * Return the sign of the sample value after the pivots have been
557 static int restore_row(struct isl_ctx
*ctx
,
558 struct isl_tab
*tab
, struct isl_tab_var
*var
)
562 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
563 find_pivot(ctx
, tab
, var
, 1, &row
, &col
);
566 pivot(ctx
, tab
, row
, col
);
567 if (!var
->is_row
) /* manifestly unbounded */
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
)
770 var_from_col(ctx
, tab
, col
)->is_zero
= 1;
771 if (tab
->need_undo
) {
772 push(ctx
, tab
, isl_tab_undo_zero
, var_from_col(ctx
, tab
, col
));
773 if (col
!= tab
->n_dead
)
774 swap_cols(ctx
, tab
, col
, tab
->n_dead
);
778 if (col
!= tab
->n_col
- 1)
779 swap_cols(ctx
, tab
, col
, tab
->n_col
- 1);
780 var_from_col(ctx
, tab
, tab
->n_col
- 1)->index
= -1;
786 /* Row variable "var" is non-negative and cannot attain any values
787 * larger than zero. This means that the coefficients of the unrestricted
788 * column variables are zero and that the coefficients of the non-negative
789 * column variables are zero or negative.
790 * Each of the non-negative variables with a negative coefficient can
791 * then also be written as the negative sum of non-negative variables
792 * and must therefore also be zero.
794 static void close_row(struct isl_ctx
*ctx
,
795 struct isl_tab
*tab
, struct isl_tab_var
*var
)
798 struct isl_mat
*mat
= tab
->mat
;
800 isl_assert(ctx
, var
->is_nonneg
, return);
802 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
803 if (isl_int_is_zero(mat
->row
[var
->index
][2 + j
]))
805 isl_assert(ctx
, isl_int_is_neg(mat
->row
[var
->index
][2 + j
]),
807 if (kill_col(ctx
, tab
, j
))
810 mark_redundant(ctx
, tab
, var
->index
);
813 /* Add a row to the tableau. The row is given as an affine combination
814 * of the original variables and needs to be expressed in terms of the
817 * We add each term in turn.
818 * If r = n/d_r is the current sum and we need to add k x, then
819 * if x is a column variable, we increase the numerator of
820 * this column by k d_r
821 * if x = f/d_x is a row variable, then the new representation of r is
823 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
824 * --- + --- = ------------------- = -------------------
825 * d_r d_r d_r d_x/g m
827 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
829 static int add_row(struct isl_ctx
*ctx
, struct isl_tab
*tab
, isl_int
*line
)
836 isl_assert(ctx
, tab
->n_row
< tab
->mat
->n_row
, return -1);
841 tab
->con
[r
].index
= tab
->n_row
;
842 tab
->con
[r
].is_row
= 1;
843 tab
->con
[r
].is_nonneg
= 0;
844 tab
->con
[r
].is_zero
= 0;
845 tab
->con
[r
].is_redundant
= 0;
846 tab
->con
[r
].frozen
= 0;
847 tab
->row_var
[tab
->n_row
] = ~r
;
848 row
= tab
->mat
->row
[tab
->n_row
];
849 isl_int_set_si(row
[0], 1);
850 isl_int_set(row
[1], line
[0]);
851 isl_seq_clr(row
+ 2, tab
->n_col
);
852 for (i
= 0; i
< tab
->n_var
; ++i
) {
853 if (tab
->var
[i
].is_zero
)
855 if (tab
->var
[i
].is_row
) {
857 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
858 isl_int_swap(a
, row
[0]);
859 isl_int_divexact(a
, row
[0], a
);
861 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
862 isl_int_mul(b
, b
, line
[1 + i
]);
863 isl_seq_combine(row
+ 1, a
, row
+ 1,
864 b
, tab
->mat
->row
[tab
->var
[i
].index
] + 1,
867 isl_int_addmul(row
[2 + tab
->var
[i
].index
],
868 line
[1 + i
], row
[0]);
870 isl_seq_normalize(row
, 2 + tab
->n_col
);
873 push(ctx
, tab
, isl_tab_undo_allocate
, &tab
->con
[r
]);
880 static int drop_row(struct isl_ctx
*ctx
, struct isl_tab
*tab
, int row
)
882 isl_assert(ctx
, ~tab
->row_var
[row
] == tab
->n_con
- 1, return -1);
883 if (row
!= tab
->n_row
- 1)
884 swap_rows(ctx
, tab
, row
, tab
->n_row
- 1);
890 /* Add inequality "ineq" and check if it conflicts with the
891 * previously added constraints or if it is obviously redundant.
893 struct isl_tab
*isl_tab_add_ineq(struct isl_ctx
*ctx
,
894 struct isl_tab
*tab
, isl_int
*ineq
)
901 r
= add_row(ctx
, tab
, ineq
);
904 tab
->con
[r
].is_nonneg
= 1;
905 push(ctx
, tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
906 if (is_redundant(ctx
, tab
, tab
->con
[r
].index
)) {
907 mark_redundant(ctx
, tab
, tab
->con
[r
].index
);
911 sgn
= sign_of_max(ctx
, tab
, &tab
->con
[r
]);
913 mark_empty(ctx
, tab
);
916 close_row(ctx
, tab
, &tab
->con
[r
]);
917 else if (tab
->con
[r
].is_row
&&
918 is_redundant(ctx
, tab
, tab
->con
[r
].index
))
919 mark_redundant(ctx
, tab
, tab
->con
[r
].index
);
923 isl_tab_free(ctx
, tab
);
927 /* We assume Gaussian elimination has been performed on the equalities.
928 * The equalities can therefore never conflict.
929 * Adding the equalities is currently only really useful for a later call
930 * to isl_tab_ineq_type.
932 static struct isl_tab
*add_eq(struct isl_ctx
*ctx
,
933 struct isl_tab
*tab
, isl_int
*eq
)
940 r
= add_row(ctx
, tab
, eq
);
944 r
= tab
->con
[r
].index
;
945 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
946 if (isl_int_is_zero(tab
->mat
->row
[r
][2 + i
]))
948 pivot(ctx
, tab
, r
, i
);
949 kill_col(ctx
, tab
, i
);
955 isl_tab_free(ctx
, tab
);
959 struct isl_tab
*isl_tab_from_basic_map(struct isl_basic_map
*bmap
)
966 tab
= isl_tab_alloc(bmap
->ctx
,
967 isl_basic_map_total_dim(bmap
) + bmap
->n_ineq
+ 1,
968 isl_basic_map_total_dim(bmap
));
971 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
972 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
973 mark_empty(bmap
->ctx
, tab
);
976 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
977 tab
= add_eq(bmap
->ctx
, tab
, bmap
->eq
[i
]);
982 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
983 tab
= isl_tab_add_ineq(bmap
->ctx
, tab
, bmap
->ineq
[i
]);
984 if (!tab
|| tab
->empty
)
990 struct isl_tab
*isl_tab_from_basic_set(struct isl_basic_set
*bset
)
992 return isl_tab_from_basic_map((struct isl_basic_map
*)bset
);
995 /* Construct a tableau corresponding to the recession cone of "bmap".
997 struct isl_tab
*isl_tab_from_recession_cone(struct isl_basic_map
*bmap
)
1001 struct isl_tab
*tab
;
1005 tab
= isl_tab_alloc(bmap
->ctx
, bmap
->n_eq
+ bmap
->n_ineq
,
1006 isl_basic_map_total_dim(bmap
));
1009 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
1012 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1013 isl_int_swap(bmap
->eq
[i
][0], cst
);
1014 tab
= add_eq(bmap
->ctx
, tab
, bmap
->eq
[i
]);
1015 isl_int_swap(bmap
->eq
[i
][0], cst
);
1019 tab
->killed_col
= 0;
1020 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1022 isl_int_swap(bmap
->ineq
[i
][0], cst
);
1023 r
= add_row(bmap
->ctx
, tab
, bmap
->ineq
[i
]);
1024 isl_int_swap(bmap
->ineq
[i
][0], cst
);
1027 tab
->con
[r
].is_nonneg
= 1;
1028 push(bmap
->ctx
, tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1035 isl_tab_free(bmap
->ctx
, tab
);
1039 /* Assuming "tab" is the tableau of a cone, check if the cone is
1040 * bounded, i.e., if it is empty or only contains the origin.
1042 int isl_tab_cone_is_bounded(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
1050 if (tab
->n_dead
== tab
->n_col
)
1053 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1054 struct isl_tab_var
*var
;
1055 var
= var_from_row(ctx
, tab
, i
);
1056 if (!var
->is_nonneg
)
1058 if (sign_of_max(ctx
, tab
, var
) == 0)
1059 close_row(ctx
, tab
, var
);
1062 if (tab
->n_dead
== tab
->n_col
)
1068 static int sample_is_integer(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
1072 for (i
= 0; i
< tab
->n_var
; ++i
) {
1074 if (!tab
->var
[i
].is_row
)
1076 row
= tab
->var
[i
].index
;
1077 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1078 tab
->mat
->row
[row
][0]))
1084 static struct isl_vec
*extract_integer_sample(struct isl_ctx
*ctx
,
1085 struct isl_tab
*tab
)
1088 struct isl_vec
*vec
;
1090 vec
= isl_vec_alloc(ctx
, 1 + tab
->n_var
);
1094 isl_int_set_si(vec
->block
.data
[0], 1);
1095 for (i
= 0; i
< tab
->n_var
; ++i
) {
1096 if (!tab
->var
[i
].is_row
)
1097 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
1099 int row
= tab
->var
[i
].index
;
1100 isl_int_divexact(vec
->block
.data
[1 + i
],
1101 tab
->mat
->row
[row
][1], tab
->mat
->row
[row
][0]);
1108 /* Update "bmap" based on the results of the tableau "tab".
1109 * In particular, implicit equalities are made explicit, redundant constraints
1110 * are removed and if the sample value happens to be integer, it is stored
1111 * in "bmap" (unless "bmap" already had an integer sample).
1113 * The tableau is assumed to have been created from "bmap" using
1114 * isl_tab_from_basic_map.
1116 struct isl_basic_map
*isl_basic_map_update_from_tab(struct isl_basic_map
*bmap
,
1117 struct isl_tab
*tab
)
1129 bmap
= isl_basic_map_set_to_empty(bmap
);
1131 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1132 if (isl_tab_is_equality(bmap
->ctx
, tab
, n_eq
+ i
))
1133 isl_basic_map_inequality_to_equality(bmap
, i
);
1134 else if (isl_tab_is_redundant(bmap
->ctx
, tab
, n_eq
+ i
))
1135 isl_basic_map_drop_inequality(bmap
, i
);
1137 if (!tab
->rational
&&
1138 !bmap
->sample
&& sample_is_integer(bmap
->ctx
, tab
))
1139 bmap
->sample
= extract_integer_sample(bmap
->ctx
, tab
);
1143 struct isl_basic_set
*isl_basic_set_update_from_tab(struct isl_basic_set
*bset
,
1144 struct isl_tab
*tab
)
1146 return (struct isl_basic_set
*)isl_basic_map_update_from_tab(
1147 (struct isl_basic_map
*)bset
, tab
);
1150 /* Given a non-negative variable "var", add a new non-negative variable
1151 * that is the opposite of "var", ensuring that var can only attain the
1153 * If var = n/d is a row variable, then the new variable = -n/d.
1154 * If var is a column variables, then the new variable = -var.
1155 * If the new variable cannot attain non-negative values, then
1156 * the resulting tableau is empty.
1157 * Otherwise, we know the value will be zero and we close the row.
1159 static struct isl_tab
*cut_to_hyperplane(struct isl_ctx
*ctx
,
1160 struct isl_tab
*tab
, struct isl_tab_var
*var
)
1166 if (extend_cons(ctx
, tab
, 1) < 0)
1170 tab
->con
[r
].index
= tab
->n_row
;
1171 tab
->con
[r
].is_row
= 1;
1172 tab
->con
[r
].is_nonneg
= 0;
1173 tab
->con
[r
].is_zero
= 0;
1174 tab
->con
[r
].is_redundant
= 0;
1175 tab
->con
[r
].frozen
= 0;
1176 tab
->row_var
[tab
->n_row
] = ~r
;
1177 row
= tab
->mat
->row
[tab
->n_row
];
1180 isl_int_set(row
[0], tab
->mat
->row
[var
->index
][0]);
1181 isl_seq_neg(row
+ 1,
1182 tab
->mat
->row
[var
->index
] + 1, 1 + tab
->n_col
);
1184 isl_int_set_si(row
[0], 1);
1185 isl_seq_clr(row
+ 1, 1 + tab
->n_col
);
1186 isl_int_set_si(row
[2 + var
->index
], -1);
1191 push(ctx
, tab
, isl_tab_undo_allocate
, &tab
->con
[r
]);
1193 sgn
= sign_of_max(ctx
, tab
, &tab
->con
[r
]);
1195 mark_empty(ctx
, tab
);
1197 tab
->con
[r
].is_nonneg
= 1;
1198 push(ctx
, tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1200 close_row(ctx
, tab
, &tab
->con
[r
]);
1205 isl_tab_free(ctx
, tab
);
1209 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
1210 * relax the inequality by one. That is, the inequality r >= 0 is replaced
1211 * by r' = r + 1 >= 0.
1212 * If r is a row variable, we simply increase the constant term by one
1213 * (taking into account the denominator).
1214 * If r is a column variable, then we need to modify each row that
1215 * refers to r = r' - 1 by substituting this equality, effectively
1216 * subtracting the coefficient of the column from the constant.
1218 struct isl_tab
*isl_tab_relax(struct isl_ctx
*ctx
,
1219 struct isl_tab
*tab
, int con
)
1221 struct isl_tab_var
*var
;
1225 var
= &tab
->con
[con
];
1227 if (!var
->is_row
&& !max_is_manifestly_unbounded(ctx
, tab
, var
))
1228 to_row(ctx
, tab
, var
, 1);
1231 isl_int_add(tab
->mat
->row
[var
->index
][1],
1232 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
1236 for (i
= 0; i
< tab
->n_row
; ++i
) {
1237 if (isl_int_is_zero(tab
->mat
->row
[i
][2 + var
->index
]))
1239 isl_int_sub(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
1240 tab
->mat
->row
[i
][2 + var
->index
]);
1245 push(ctx
, tab
, isl_tab_undo_relax
, var
);
1250 struct isl_tab
*isl_tab_select_facet(struct isl_ctx
*ctx
,
1251 struct isl_tab
*tab
, int con
)
1256 return cut_to_hyperplane(ctx
, tab
, &tab
->con
[con
]);
1259 static int may_be_equality(struct isl_tab
*tab
, int row
)
1261 return (tab
->rational
? isl_int_is_zero(tab
->mat
->row
[row
][1])
1262 : isl_int_lt(tab
->mat
->row
[row
][1],
1263 tab
->mat
->row
[row
][0])) &&
1264 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1265 tab
->n_col
- tab
->n_dead
) != -1;
1268 /* Check for (near) equalities among the constraints.
1269 * A constraint is an equality if it is non-negative and if
1270 * its maximal value is either
1271 * - zero (in case of rational tableaus), or
1272 * - strictly less than 1 (in case of integer tableaus)
1274 * When the rows are added to the tableau, they are already
1275 * checked for being equal to zero. If none of the rows
1276 * have been determined to be zero (killed_col is not set)
1277 * and we are dealing with a rational tableau, then we wouldn't
1278 * be able to find any zero row, so we can return immediately.
1280 * We first mark all non-redundant and non-dead variables that
1281 * are not frozen and not obviously not an equality.
1282 * Then we iterate over all marked variables if they can attain
1283 * any values larger than zero or at least one.
1284 * If the maximal value is zero, we mark any column variables
1285 * that appear in the row as being zero and mark the row as being redundant.
1286 * Otherwise, if the maximal value is strictly less than one (and the
1287 * tableau is integer), then we restrict the value to being zero
1288 * by adding an opposite non-negative variable.
1290 struct isl_tab
*isl_tab_detect_equalities(struct isl_ctx
*ctx
,
1291 struct isl_tab
*tab
)
1300 if (tab
->rational
&& !tab
->killed_col
)
1302 if (tab
->n_dead
== tab
->n_col
)
1306 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1307 struct isl_tab_var
*var
= var_from_row(ctx
, tab
, i
);
1308 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
1309 may_be_equality(tab
, i
);
1313 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1314 struct isl_tab_var
*var
= var_from_col(ctx
, tab
, i
);
1315 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
1320 struct isl_tab_var
*var
;
1321 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1322 var
= var_from_row(ctx
, tab
, i
);
1326 if (i
== tab
->n_row
) {
1327 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1328 var
= var_from_col(ctx
, tab
, i
);
1332 if (i
== tab
->n_col
)
1337 if (sign_of_max(ctx
, tab
, var
) == 0)
1338 close_row(ctx
, tab
, var
);
1339 else if (!tab
->rational
&& !at_least_one(ctx
, tab
, var
)) {
1340 tab
= cut_to_hyperplane(ctx
, tab
, var
);
1341 return isl_tab_detect_equalities(ctx
, tab
);
1343 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1344 var
= var_from_row(ctx
, tab
, i
);
1347 if (may_be_equality(tab
, i
))
1354 tab
->killed_col
= 0;
1358 /* Check for (near) redundant constraints.
1359 * A constraint is redundant if it is non-negative and if
1360 * its minimal value (temporarily ignoring the non-negativity) is either
1361 * - zero (in case of rational tableaus), or
1362 * - strictly larger than -1 (in case of integer tableaus)
1364 * We first mark all non-redundant and non-dead variables that
1365 * are not frozen and not obviously negatively unbounded.
1366 * Then we iterate over all marked variables if they can attain
1367 * any values smaller than zero or at most negative one.
1368 * If not, we mark the row as being redundant (assuming it hasn't
1369 * been detected as being obviously redundant in the mean time).
1371 struct isl_tab
*isl_tab_detect_redundant(struct isl_ctx
*ctx
,
1372 struct isl_tab
*tab
)
1381 if (tab
->n_redundant
== tab
->n_row
)
1385 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1386 struct isl_tab_var
*var
= var_from_row(ctx
, tab
, i
);
1387 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
1391 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1392 struct isl_tab_var
*var
= var_from_col(ctx
, tab
, i
);
1393 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
1394 !min_is_manifestly_unbounded(ctx
, tab
, var
);
1399 struct isl_tab_var
*var
;
1400 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1401 var
= var_from_row(ctx
, tab
, i
);
1405 if (i
== tab
->n_row
) {
1406 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1407 var
= var_from_col(ctx
, tab
, i
);
1411 if (i
== tab
->n_col
)
1416 if ((tab
->rational
? (sign_of_min(ctx
, tab
, var
) >= 0)
1417 : !min_at_most_neg_one(ctx
, tab
, var
)) &&
1419 mark_redundant(ctx
, tab
, var
->index
);
1420 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1421 var
= var_from_col(ctx
, tab
, i
);
1424 if (!min_is_manifestly_unbounded(ctx
, tab
, var
))
1434 int isl_tab_is_equality(struct isl_ctx
*ctx
, struct isl_tab
*tab
, int con
)
1440 if (tab
->con
[con
].is_zero
)
1442 if (tab
->con
[con
].is_redundant
)
1444 if (!tab
->con
[con
].is_row
)
1445 return tab
->con
[con
].index
< tab
->n_dead
;
1447 row
= tab
->con
[con
].index
;
1449 return isl_int_is_zero(tab
->mat
->row
[row
][1]) &&
1450 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1451 tab
->n_col
- tab
->n_dead
) == -1;
1454 /* Return the minimial value of the affine expression "f" with denominator
1455 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
1456 * the expression cannot attain arbitrarily small values.
1457 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
1458 * The return value reflects the nature of the result (empty, unbounded,
1459 * minmimal value returned in *opt).
1461 enum isl_lp_result
isl_tab_min(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1462 isl_int
*f
, isl_int denom
, isl_int
*opt
, isl_int
*opt_denom
)
1465 enum isl_lp_result res
= isl_lp_ok
;
1466 struct isl_tab_var
*var
;
1469 return isl_lp_empty
;
1471 r
= add_row(ctx
, tab
, f
);
1473 return isl_lp_error
;
1475 isl_int_mul(tab
->mat
->row
[var
->index
][0],
1476 tab
->mat
->row
[var
->index
][0], denom
);
1479 find_pivot(ctx
, tab
, var
, -1, &row
, &col
);
1480 if (row
== var
->index
) {
1481 res
= isl_lp_unbounded
;
1486 pivot(ctx
, tab
, row
, col
);
1488 if (drop_row(ctx
, tab
, var
->index
) < 0)
1489 return isl_lp_error
;
1490 if (res
== isl_lp_ok
) {
1492 isl_int_set(*opt
, tab
->mat
->row
[var
->index
][1]);
1493 isl_int_set(*opt_denom
, tab
->mat
->row
[var
->index
][0]);
1495 isl_int_cdiv_q(*opt
, tab
->mat
->row
[var
->index
][1],
1496 tab
->mat
->row
[var
->index
][0]);
1501 int isl_tab_is_redundant(struct isl_ctx
*ctx
, struct isl_tab
*tab
, int con
)
1508 if (tab
->con
[con
].is_zero
)
1510 if (tab
->con
[con
].is_redundant
)
1512 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
1515 /* Take a snapshot of the tableau that can be restored by s call to
1518 struct isl_tab_undo
*isl_tab_snap(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
1526 /* Undo the operation performed by isl_tab_relax.
1528 static void unrelax(struct isl_ctx
*ctx
,
1529 struct isl_tab
*tab
, struct isl_tab_var
*var
)
1531 if (!var
->is_row
&& !max_is_manifestly_unbounded(ctx
, tab
, var
))
1532 to_row(ctx
, tab
, var
, 1);
1535 isl_int_sub(tab
->mat
->row
[var
->index
][1],
1536 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
1540 for (i
= 0; i
< tab
->n_row
; ++i
) {
1541 if (isl_int_is_zero(tab
->mat
->row
[i
][2 + var
->index
]))
1543 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
1544 tab
->mat
->row
[i
][2 + var
->index
]);
1550 static void perform_undo(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1551 struct isl_tab_undo
*undo
)
1553 switch(undo
->type
) {
1554 case isl_tab_undo_empty
:
1557 case isl_tab_undo_nonneg
:
1558 undo
->var
->is_nonneg
= 0;
1560 case isl_tab_undo_redundant
:
1561 undo
->var
->is_redundant
= 0;
1564 case isl_tab_undo_zero
:
1565 undo
->var
->is_zero
= 0;
1568 case isl_tab_undo_allocate
:
1569 if (!undo
->var
->is_row
) {
1570 if (max_is_manifestly_unbounded(ctx
, tab
, undo
->var
))
1571 to_row(ctx
, tab
, undo
->var
, -1);
1573 to_row(ctx
, tab
, undo
->var
, 1);
1575 drop_row(ctx
, tab
, undo
->var
->index
);
1577 case isl_tab_undo_relax
:
1578 unrelax(ctx
, tab
, undo
->var
);
1583 /* Return the tableau to the state it was in when the snapshot "snap"
1586 int isl_tab_rollback(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1587 struct isl_tab_undo
*snap
)
1589 struct isl_tab_undo
*undo
, *next
;
1594 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
1598 perform_undo(ctx
, tab
, undo
);
1607 /* The given row "row" represents an inequality violated by all
1608 * points in the tableau. Check for some special cases of such
1609 * separating constraints.
1610 * In particular, if the row has been reduced to the constant -1,
1611 * then we know the inequality is adjacent (but opposite) to
1612 * an equality in the tableau.
1613 * If the row has been reduced to r = -1 -r', with r' an inequality
1614 * of the tableau, then the inequality is adjacent (but opposite)
1615 * to the inequality r'.
1617 static enum isl_ineq_type
separation_type(struct isl_ctx
*ctx
,
1618 struct isl_tab
*tab
, unsigned row
)
1623 return isl_ineq_separate
;
1625 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
1626 return isl_ineq_separate
;
1627 if (!isl_int_is_negone(tab
->mat
->row
[row
][1]))
1628 return isl_ineq_separate
;
1630 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1631 tab
->n_col
- tab
->n_dead
);
1633 return isl_ineq_adj_eq
;
1635 if (!isl_int_is_negone(tab
->mat
->row
[row
][2 + tab
->n_dead
+ pos
]))
1636 return isl_ineq_separate
;
1638 pos
= isl_seq_first_non_zero(
1639 tab
->mat
->row
[row
] + 2 + tab
->n_dead
+ pos
+ 1,
1640 tab
->n_col
- tab
->n_dead
- pos
- 1);
1642 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
1645 /* Check the effect of inequality "ineq" on the tableau "tab".
1647 * isl_ineq_redundant: satisfied by all points in the tableau
1648 * isl_ineq_separate: satisfied by no point in tha tableau
1649 * isl_ineq_cut: satisfied by some by not all points
1650 * isl_ineq_adj_eq: adjacent to an equality
1651 * isl_ineq_adj_ineq: adjacent to an inequality.
1653 enum isl_ineq_type
isl_tab_ineq_type(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1656 enum isl_ineq_type type
= isl_ineq_error
;
1657 struct isl_tab_undo
*snap
= NULL
;
1662 return isl_ineq_error
;
1664 if (extend_cons(ctx
, tab
, 1) < 0)
1665 return isl_ineq_error
;
1667 snap
= isl_tab_snap(ctx
, tab
);
1669 con
= add_row(ctx
, tab
, ineq
);
1673 row
= tab
->con
[con
].index
;
1674 if (is_redundant(ctx
, tab
, row
))
1675 type
= isl_ineq_redundant
;
1676 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
1678 isl_int_abs_ge(tab
->mat
->row
[row
][1],
1679 tab
->mat
->row
[row
][0]))) {
1680 if (at_least_zero(ctx
, tab
, &tab
->con
[con
]))
1681 type
= isl_ineq_cut
;
1683 type
= separation_type(ctx
, tab
, row
);
1684 } else if (tab
->rational
? (sign_of_min(ctx
, tab
, &tab
->con
[con
]) < 0)
1685 : min_at_most_neg_one(ctx
, tab
, &tab
->con
[con
]))
1686 type
= isl_ineq_cut
;
1688 type
= isl_ineq_redundant
;
1690 if (isl_tab_rollback(ctx
, tab
, snap
))
1691 return isl_ineq_error
;
1694 isl_tab_rollback(ctx
, tab
, snap
);
1695 return isl_ineq_error
;
1698 void isl_tab_dump(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1699 FILE *out
, int indent
)
1705 fprintf(out
, "%*snull tab\n", indent
, "");
1708 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
1709 tab
->n_redundant
, tab
->n_dead
);
1711 fprintf(out
, ", rational");
1713 fprintf(out
, ", empty");
1714 if (tab
->killed_col
)
1715 fprintf(out
, ", killed_col");
1717 fprintf(out
, "%*s[", indent
, "");
1718 for (i
= 0; i
< tab
->n_var
; ++i
) {
1721 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
1723 tab
->var
[i
].is_zero
? " [=0]" :
1724 tab
->var
[i
].is_redundant
? " [R]" : "");
1726 fprintf(out
, "]\n");
1727 fprintf(out
, "%*s[", indent
, "");
1728 for (i
= 0; i
< tab
->n_con
; ++i
) {
1731 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
1733 tab
->con
[i
].is_zero
? " [=0]" :
1734 tab
->con
[i
].is_redundant
? " [R]" : "");
1736 fprintf(out
, "]\n");
1737 fprintf(out
, "%*s[", indent
, "");
1738 for (i
= 0; i
< tab
->n_row
; ++i
) {
1741 fprintf(out
, "r%d: %d%s", i
, tab
->row_var
[i
],
1742 var_from_row(ctx
, tab
, i
)->is_nonneg
? " [>=0]" : "");
1744 fprintf(out
, "]\n");
1745 fprintf(out
, "%*s[", indent
, "");
1746 for (i
= 0; i
< tab
->n_col
; ++i
) {
1749 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
1750 var_from_col(ctx
, tab
, i
)->is_nonneg
? " [>=0]" : "");
1752 fprintf(out
, "]\n");
1753 r
= tab
->mat
->n_row
;
1754 tab
->mat
->n_row
= tab
->n_row
;
1755 c
= tab
->mat
->n_col
;
1756 tab
->mat
->n_col
= 2 + tab
->n_col
;
1757 isl_mat_dump(ctx
, tab
->mat
, out
, indent
);
1758 tab
->mat
->n_row
= r
;
1759 tab
->mat
->n_col
= c
;