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 */
570 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
573 /* Perform pivots until we are sure that the row variable "var"
574 * can attain non-negative values. After return from this
575 * function, "var" is still a row variable, but its sample
576 * value may not be non-negative, even if the function returns 1.
578 static int at_least_zero(struct isl_ctx
*ctx
,
579 struct isl_tab
*tab
, struct isl_tab_var
*var
)
583 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
584 find_pivot(ctx
, tab
, var
, 1, &row
, &col
);
587 if (row
== var
->index
) /* manifestly unbounded */
589 pivot(ctx
, tab
, row
, col
);
591 return !isl_int_is_neg(tab
->mat
->row
[var
->index
][1]);
594 /* Return a negative value if "var" can attain negative values.
595 * Return a non-negative value otherwise.
597 * If "var" is manifestly unbounded wrt negative values, we are done.
598 * Otherwise, if var is in a column, we can pivot it down to a row.
599 * Then we continue pivoting down until either
600 * - the pivot would result in a manifestly unbounded column
601 * => we don't perform the pivot, but simply return -1
602 * - no more down pivots can be performed
603 * - the sample value is negative
604 * If the sample value becomes negative and the variable is supposed
605 * to be nonnegative, then we undo the last pivot.
606 * However, if the last pivot has made the pivoting variable
607 * obviously redundant, then it may have moved to another row.
608 * In that case we look for upward pivots until we reach a non-negative
611 static int sign_of_min(struct isl_ctx
*ctx
,
612 struct isl_tab
*tab
, struct isl_tab_var
*var
)
615 struct isl_tab_var
*pivot_var
;
617 if (min_is_manifestly_unbounded(ctx
, tab
, var
))
621 row
= pivot_row(ctx
, tab
, NULL
, -1, col
);
622 pivot_var
= var_from_col(ctx
, tab
, col
);
623 pivot(ctx
, tab
, row
, col
);
624 if (var
->is_redundant
)
626 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
627 if (var
->is_nonneg
) {
628 if (!pivot_var
->is_redundant
&&
629 pivot_var
->index
== row
)
630 pivot(ctx
, tab
, row
, col
);
632 restore_row(ctx
, tab
, var
);
637 if (var
->is_redundant
)
639 while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
640 find_pivot(ctx
, tab
, var
, -1, &row
, &col
);
641 if (row
== var
->index
)
644 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
645 pivot_var
= var_from_col(ctx
, tab
, col
);
646 pivot(ctx
, tab
, row
, col
);
647 if (var
->is_redundant
)
650 if (var
->is_nonneg
) {
651 /* pivot back to non-negative value */
652 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
653 pivot(ctx
, tab
, row
, col
);
655 restore_row(ctx
, tab
, var
);
660 /* Return 1 if "var" can attain values <= -1.
661 * Return 0 otherwise.
663 * The sample value of "var" is assumed to be non-negative when the
664 * the function is called and will be made non-negative again before
665 * the function returns.
667 static int min_at_most_neg_one(struct isl_ctx
*ctx
,
668 struct isl_tab
*tab
, struct isl_tab_var
*var
)
671 struct isl_tab_var
*pivot_var
;
673 if (min_is_manifestly_unbounded(ctx
, tab
, var
))
677 row
= pivot_row(ctx
, tab
, NULL
, -1, col
);
678 pivot_var
= var_from_col(ctx
, tab
, col
);
679 pivot(ctx
, tab
, row
, col
);
680 if (var
->is_redundant
)
682 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1]) &&
683 isl_int_abs_ge(tab
->mat
->row
[var
->index
][1],
684 tab
->mat
->row
[var
->index
][0])) {
685 if (var
->is_nonneg
) {
686 if (!pivot_var
->is_redundant
&&
687 pivot_var
->index
== row
)
688 pivot(ctx
, tab
, row
, col
);
690 restore_row(ctx
, tab
, var
);
695 if (var
->is_redundant
)
698 find_pivot(ctx
, tab
, var
, -1, &row
, &col
);
699 if (row
== var
->index
)
703 pivot_var
= var_from_col(ctx
, tab
, col
);
704 pivot(ctx
, tab
, row
, col
);
705 if (var
->is_redundant
)
707 } while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1]) ||
708 isl_int_abs_lt(tab
->mat
->row
[var
->index
][1],
709 tab
->mat
->row
[var
->index
][0]));
710 if (var
->is_nonneg
) {
711 /* pivot back to non-negative value */
712 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
713 pivot(ctx
, tab
, row
, col
);
714 restore_row(ctx
, tab
, var
);
719 /* Return 1 if "var" can attain values >= 1.
720 * Return 0 otherwise.
722 static int at_least_one(struct isl_ctx
*ctx
,
723 struct isl_tab
*tab
, struct isl_tab_var
*var
)
728 if (max_is_manifestly_unbounded(ctx
, tab
, var
))
730 to_row(ctx
, tab
, var
, 1);
731 r
= tab
->mat
->row
[var
->index
];
732 while (isl_int_lt(r
[1], r
[0])) {
733 find_pivot(ctx
, tab
, var
, 1, &row
, &col
);
735 return isl_int_ge(r
[1], r
[0]);
736 if (row
== var
->index
) /* manifestly unbounded */
738 pivot(ctx
, tab
, row
, col
);
743 static void swap_cols(struct isl_ctx
*ctx
,
744 struct isl_tab
*tab
, int col1
, int col2
)
747 t
= tab
->col_var
[col1
];
748 tab
->col_var
[col1
] = tab
->col_var
[col2
];
749 tab
->col_var
[col2
] = t
;
750 var_from_col(ctx
, tab
, col1
)->index
= col1
;
751 var_from_col(ctx
, tab
, col2
)->index
= col2
;
752 tab
->mat
= isl_mat_swap_cols(ctx
, tab
->mat
, 2 + col1
, 2 + col2
);
755 /* Mark column with index "col" as representing a zero variable.
756 * If we may need to undo the operation the column is kept,
757 * but no longer considered.
758 * Otherwise, the column is simply removed.
760 * The column may be interchanged with some other column. If it
761 * is interchanged with a later column, return 1. Otherwise return 0.
762 * If the columns are checked in order in the calling function,
763 * then a return value of 1 means that the column with the given
764 * column number may now contain a different column that
765 * hasn't been checked yet.
767 static int kill_col(struct isl_ctx
*ctx
,
768 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
= restore_row(ctx
, tab
, &tab
->con
[r
]);
913 mark_empty(ctx
, tab
);
914 else if (tab
->con
[r
].is_row
&&
915 is_redundant(ctx
, tab
, tab
->con
[r
].index
))
916 mark_redundant(ctx
, tab
, tab
->con
[r
].index
);
919 isl_tab_free(ctx
, tab
);
923 /* We assume Gaussian elimination has been performed on the equalities.
924 * The equalities can therefore never conflict.
925 * Adding the equalities is currently only really useful for a later call
926 * to isl_tab_ineq_type.
928 static struct isl_tab
*add_eq(struct isl_ctx
*ctx
,
929 struct isl_tab
*tab
, isl_int
*eq
)
936 r
= add_row(ctx
, tab
, eq
);
940 r
= tab
->con
[r
].index
;
941 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
942 if (isl_int_is_zero(tab
->mat
->row
[r
][2 + i
]))
944 pivot(ctx
, tab
, r
, i
);
945 kill_col(ctx
, tab
, i
);
952 isl_tab_free(ctx
, tab
);
956 struct isl_tab
*isl_tab_from_basic_map(struct isl_basic_map
*bmap
)
963 tab
= isl_tab_alloc(bmap
->ctx
,
964 isl_basic_map_total_dim(bmap
) + bmap
->n_ineq
+ 1,
965 isl_basic_map_total_dim(bmap
));
968 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
969 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
970 mark_empty(bmap
->ctx
, tab
);
973 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
974 tab
= add_eq(bmap
->ctx
, tab
, bmap
->eq
[i
]);
978 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
979 tab
= isl_tab_add_ineq(bmap
->ctx
, tab
, bmap
->ineq
[i
]);
980 if (!tab
|| tab
->empty
)
986 struct isl_tab
*isl_tab_from_basic_set(struct isl_basic_set
*bset
)
988 return isl_tab_from_basic_map((struct isl_basic_map
*)bset
);
991 /* Construct a tableau corresponding to the recession cone of "bmap".
993 struct isl_tab
*isl_tab_from_recession_cone(struct isl_basic_map
*bmap
)
1001 tab
= isl_tab_alloc(bmap
->ctx
, bmap
->n_eq
+ bmap
->n_ineq
,
1002 isl_basic_map_total_dim(bmap
));
1005 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
1008 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1009 isl_int_swap(bmap
->eq
[i
][0], cst
);
1010 tab
= add_eq(bmap
->ctx
, tab
, bmap
->eq
[i
]);
1011 isl_int_swap(bmap
->eq
[i
][0], cst
);
1015 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1017 isl_int_swap(bmap
->ineq
[i
][0], cst
);
1018 r
= add_row(bmap
->ctx
, tab
, bmap
->ineq
[i
]);
1019 isl_int_swap(bmap
->ineq
[i
][0], cst
);
1022 tab
->con
[r
].is_nonneg
= 1;
1023 push(bmap
->ctx
, tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1030 isl_tab_free(bmap
->ctx
, tab
);
1034 /* Assuming "tab" is the tableau of a cone, check if the cone is
1035 * bounded, i.e., if it is empty or only contains the origin.
1037 int isl_tab_cone_is_bounded(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
1045 if (tab
->n_dead
== tab
->n_col
)
1048 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1049 struct isl_tab_var
*var
;
1050 var
= var_from_row(ctx
, tab
, i
);
1051 if (!var
->is_nonneg
)
1053 if (sign_of_max(ctx
, tab
, var
) == 0)
1054 close_row(ctx
, tab
, var
);
1057 if (tab
->n_dead
== tab
->n_col
)
1063 static int sample_is_integer(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
1067 for (i
= 0; i
< tab
->n_var
; ++i
) {
1069 if (!tab
->var
[i
].is_row
)
1071 row
= tab
->var
[i
].index
;
1072 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1073 tab
->mat
->row
[row
][0]))
1079 static struct isl_vec
*extract_integer_sample(struct isl_ctx
*ctx
,
1080 struct isl_tab
*tab
)
1083 struct isl_vec
*vec
;
1085 vec
= isl_vec_alloc(ctx
, 1 + tab
->n_var
);
1089 isl_int_set_si(vec
->block
.data
[0], 1);
1090 for (i
= 0; i
< tab
->n_var
; ++i
) {
1091 if (!tab
->var
[i
].is_row
)
1092 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
1094 int row
= tab
->var
[i
].index
;
1095 isl_int_divexact(vec
->block
.data
[1 + i
],
1096 tab
->mat
->row
[row
][1], tab
->mat
->row
[row
][0]);
1103 struct isl_vec
*isl_tab_get_sample_value(struct isl_ctx
*ctx
,
1104 struct isl_tab
*tab
)
1107 struct isl_vec
*vec
;
1113 vec
= isl_vec_alloc(ctx
, 1 + tab
->n_var
);
1119 isl_int_set_si(vec
->block
.data
[0], 1);
1120 for (i
= 0; i
< tab
->n_var
; ++i
) {
1122 if (!tab
->var
[i
].is_row
) {
1123 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
1126 row
= tab
->var
[i
].index
;
1127 isl_int_gcd(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
1128 isl_int_divexact(m
, tab
->mat
->row
[row
][0], m
);
1129 isl_seq_scale(vec
->block
.data
, vec
->block
.data
, m
, 1 + i
);
1130 isl_int_divexact(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
1131 isl_int_mul(vec
->block
.data
[1 + i
], m
, tab
->mat
->row
[row
][1]);
1133 isl_seq_normalize(vec
->block
.data
, vec
->size
);
1139 /* Update "bmap" based on the results of the tableau "tab".
1140 * In particular, implicit equalities are made explicit, redundant constraints
1141 * are removed and if the sample value happens to be integer, it is stored
1142 * in "bmap" (unless "bmap" already had an integer sample).
1144 * The tableau is assumed to have been created from "bmap" using
1145 * isl_tab_from_basic_map.
1147 struct isl_basic_map
*isl_basic_map_update_from_tab(struct isl_basic_map
*bmap
,
1148 struct isl_tab
*tab
)
1160 bmap
= isl_basic_map_set_to_empty(bmap
);
1162 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
1163 if (isl_tab_is_equality(bmap
->ctx
, tab
, n_eq
+ i
))
1164 isl_basic_map_inequality_to_equality(bmap
, i
);
1165 else if (isl_tab_is_redundant(bmap
->ctx
, tab
, n_eq
+ i
))
1166 isl_basic_map_drop_inequality(bmap
, i
);
1168 if (!tab
->rational
&&
1169 !bmap
->sample
&& sample_is_integer(bmap
->ctx
, tab
))
1170 bmap
->sample
= extract_integer_sample(bmap
->ctx
, tab
);
1174 struct isl_basic_set
*isl_basic_set_update_from_tab(struct isl_basic_set
*bset
,
1175 struct isl_tab
*tab
)
1177 return (struct isl_basic_set
*)isl_basic_map_update_from_tab(
1178 (struct isl_basic_map
*)bset
, tab
);
1181 /* Given a non-negative variable "var", add a new non-negative variable
1182 * that is the opposite of "var", ensuring that var can only attain the
1184 * If var = n/d is a row variable, then the new variable = -n/d.
1185 * If var is a column variables, then the new variable = -var.
1186 * If the new variable cannot attain non-negative values, then
1187 * the resulting tableau is empty.
1188 * Otherwise, we know the value will be zero and we close the row.
1190 static struct isl_tab
*cut_to_hyperplane(struct isl_ctx
*ctx
,
1191 struct isl_tab
*tab
, struct isl_tab_var
*var
)
1197 if (extend_cons(ctx
, tab
, 1) < 0)
1201 tab
->con
[r
].index
= tab
->n_row
;
1202 tab
->con
[r
].is_row
= 1;
1203 tab
->con
[r
].is_nonneg
= 0;
1204 tab
->con
[r
].is_zero
= 0;
1205 tab
->con
[r
].is_redundant
= 0;
1206 tab
->con
[r
].frozen
= 0;
1207 tab
->row_var
[tab
->n_row
] = ~r
;
1208 row
= tab
->mat
->row
[tab
->n_row
];
1211 isl_int_set(row
[0], tab
->mat
->row
[var
->index
][0]);
1212 isl_seq_neg(row
+ 1,
1213 tab
->mat
->row
[var
->index
] + 1, 1 + tab
->n_col
);
1215 isl_int_set_si(row
[0], 1);
1216 isl_seq_clr(row
+ 1, 1 + tab
->n_col
);
1217 isl_int_set_si(row
[2 + var
->index
], -1);
1222 push(ctx
, tab
, isl_tab_undo_allocate
, &tab
->con
[r
]);
1224 sgn
= sign_of_max(ctx
, tab
, &tab
->con
[r
]);
1226 mark_empty(ctx
, tab
);
1228 tab
->con
[r
].is_nonneg
= 1;
1229 push(ctx
, tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]);
1231 close_row(ctx
, tab
, &tab
->con
[r
]);
1236 isl_tab_free(ctx
, tab
);
1240 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
1241 * relax the inequality by one. That is, the inequality r >= 0 is replaced
1242 * by r' = r + 1 >= 0.
1243 * If r is a row variable, we simply increase the constant term by one
1244 * (taking into account the denominator).
1245 * If r is a column variable, then we need to modify each row that
1246 * refers to r = r' - 1 by substituting this equality, effectively
1247 * subtracting the coefficient of the column from the constant.
1249 struct isl_tab
*isl_tab_relax(struct isl_ctx
*ctx
,
1250 struct isl_tab
*tab
, int con
)
1252 struct isl_tab_var
*var
;
1256 var
= &tab
->con
[con
];
1258 if (!var
->is_row
&& !max_is_manifestly_unbounded(ctx
, tab
, var
))
1259 to_row(ctx
, tab
, var
, 1);
1262 isl_int_add(tab
->mat
->row
[var
->index
][1],
1263 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
1267 for (i
= 0; i
< tab
->n_row
; ++i
) {
1268 if (isl_int_is_zero(tab
->mat
->row
[i
][2 + var
->index
]))
1270 isl_int_sub(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
1271 tab
->mat
->row
[i
][2 + var
->index
]);
1276 push(ctx
, tab
, isl_tab_undo_relax
, var
);
1281 struct isl_tab
*isl_tab_select_facet(struct isl_ctx
*ctx
,
1282 struct isl_tab
*tab
, int con
)
1287 return cut_to_hyperplane(ctx
, tab
, &tab
->con
[con
]);
1290 static int may_be_equality(struct isl_tab
*tab
, int row
)
1292 return (tab
->rational
? isl_int_is_zero(tab
->mat
->row
[row
][1])
1293 : isl_int_lt(tab
->mat
->row
[row
][1],
1294 tab
->mat
->row
[row
][0])) &&
1295 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1296 tab
->n_col
- tab
->n_dead
) != -1;
1299 /* Check for (near) equalities among the constraints.
1300 * A constraint is an equality if it is non-negative and if
1301 * its maximal value is either
1302 * - zero (in case of rational tableaus), or
1303 * - strictly less than 1 (in case of integer tableaus)
1305 * We first mark all non-redundant and non-dead variables that
1306 * are not frozen and not obviously not an equality.
1307 * Then we iterate over all marked variables if they can attain
1308 * any values larger than zero or at least one.
1309 * If the maximal value is zero, we mark any column variables
1310 * that appear in the row as being zero and mark the row as being redundant.
1311 * Otherwise, if the maximal value is strictly less than one (and the
1312 * tableau is integer), then we restrict the value to being zero
1313 * by adding an opposite non-negative variable.
1315 struct isl_tab
*isl_tab_detect_equalities(struct isl_ctx
*ctx
,
1316 struct isl_tab
*tab
)
1325 if (tab
->n_dead
== tab
->n_col
)
1329 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1330 struct isl_tab_var
*var
= var_from_row(ctx
, tab
, i
);
1331 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
1332 may_be_equality(tab
, i
);
1336 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1337 struct isl_tab_var
*var
= var_from_col(ctx
, tab
, i
);
1338 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
1343 struct isl_tab_var
*var
;
1344 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1345 var
= var_from_row(ctx
, tab
, i
);
1349 if (i
== tab
->n_row
) {
1350 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1351 var
= var_from_col(ctx
, tab
, i
);
1355 if (i
== tab
->n_col
)
1360 if (sign_of_max(ctx
, tab
, var
) == 0)
1361 close_row(ctx
, tab
, var
);
1362 else if (!tab
->rational
&& !at_least_one(ctx
, tab
, var
)) {
1363 tab
= cut_to_hyperplane(ctx
, tab
, var
);
1364 return isl_tab_detect_equalities(ctx
, tab
);
1366 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1367 var
= var_from_row(ctx
, tab
, i
);
1370 if (may_be_equality(tab
, i
))
1380 /* Check for (near) redundant constraints.
1381 * A constraint is redundant if it is non-negative and if
1382 * its minimal value (temporarily ignoring the non-negativity) is either
1383 * - zero (in case of rational tableaus), or
1384 * - strictly larger than -1 (in case of integer tableaus)
1386 * We first mark all non-redundant and non-dead variables that
1387 * are not frozen and not obviously negatively unbounded.
1388 * Then we iterate over all marked variables if they can attain
1389 * any values smaller than zero or at most negative one.
1390 * If not, we mark the row as being redundant (assuming it hasn't
1391 * been detected as being obviously redundant in the mean time).
1393 struct isl_tab
*isl_tab_detect_redundant(struct isl_ctx
*ctx
,
1394 struct isl_tab
*tab
)
1403 if (tab
->n_redundant
== tab
->n_row
)
1407 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1408 struct isl_tab_var
*var
= var_from_row(ctx
, tab
, i
);
1409 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
1413 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1414 struct isl_tab_var
*var
= var_from_col(ctx
, tab
, i
);
1415 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
1416 !min_is_manifestly_unbounded(ctx
, tab
, var
);
1421 struct isl_tab_var
*var
;
1422 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1423 var
= var_from_row(ctx
, tab
, i
);
1427 if (i
== tab
->n_row
) {
1428 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1429 var
= var_from_col(ctx
, tab
, i
);
1433 if (i
== tab
->n_col
)
1438 if ((tab
->rational
? (sign_of_min(ctx
, tab
, var
) >= 0)
1439 : !min_at_most_neg_one(ctx
, tab
, var
)) &&
1441 mark_redundant(ctx
, tab
, var
->index
);
1442 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
1443 var
= var_from_col(ctx
, tab
, i
);
1446 if (!min_is_manifestly_unbounded(ctx
, tab
, var
))
1456 int isl_tab_is_equality(struct isl_ctx
*ctx
, struct isl_tab
*tab
, int con
)
1462 if (tab
->con
[con
].is_zero
)
1464 if (tab
->con
[con
].is_redundant
)
1466 if (!tab
->con
[con
].is_row
)
1467 return tab
->con
[con
].index
< tab
->n_dead
;
1469 row
= tab
->con
[con
].index
;
1471 return isl_int_is_zero(tab
->mat
->row
[row
][1]) &&
1472 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1473 tab
->n_col
- tab
->n_dead
) == -1;
1476 /* Return the minimial value of the affine expression "f" with denominator
1477 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
1478 * the expression cannot attain arbitrarily small values.
1479 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
1480 * The return value reflects the nature of the result (empty, unbounded,
1481 * minmimal value returned in *opt).
1483 enum isl_lp_result
isl_tab_min(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1484 isl_int
*f
, isl_int denom
, isl_int
*opt
, isl_int
*opt_denom
)
1487 enum isl_lp_result res
= isl_lp_ok
;
1488 struct isl_tab_var
*var
;
1491 return isl_lp_empty
;
1493 r
= add_row(ctx
, tab
, f
);
1495 return isl_lp_error
;
1497 isl_int_mul(tab
->mat
->row
[var
->index
][0],
1498 tab
->mat
->row
[var
->index
][0], denom
);
1501 find_pivot(ctx
, tab
, var
, -1, &row
, &col
);
1502 if (row
== var
->index
) {
1503 res
= isl_lp_unbounded
;
1508 pivot(ctx
, tab
, row
, col
);
1510 if (drop_row(ctx
, tab
, var
->index
) < 0)
1511 return isl_lp_error
;
1512 if (res
== isl_lp_ok
) {
1514 isl_int_set(*opt
, tab
->mat
->row
[var
->index
][1]);
1515 isl_int_set(*opt_denom
, tab
->mat
->row
[var
->index
][0]);
1517 isl_int_cdiv_q(*opt
, tab
->mat
->row
[var
->index
][1],
1518 tab
->mat
->row
[var
->index
][0]);
1523 int isl_tab_is_redundant(struct isl_ctx
*ctx
, struct isl_tab
*tab
, int con
)
1530 if (tab
->con
[con
].is_zero
)
1532 if (tab
->con
[con
].is_redundant
)
1534 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
1537 /* Take a snapshot of the tableau that can be restored by s call to
1540 struct isl_tab_undo
*isl_tab_snap(struct isl_ctx
*ctx
, struct isl_tab
*tab
)
1548 /* Undo the operation performed by isl_tab_relax.
1550 static void unrelax(struct isl_ctx
*ctx
,
1551 struct isl_tab
*tab
, struct isl_tab_var
*var
)
1553 if (!var
->is_row
&& !max_is_manifestly_unbounded(ctx
, tab
, var
))
1554 to_row(ctx
, tab
, var
, 1);
1557 isl_int_sub(tab
->mat
->row
[var
->index
][1],
1558 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
1562 for (i
= 0; i
< tab
->n_row
; ++i
) {
1563 if (isl_int_is_zero(tab
->mat
->row
[i
][2 + var
->index
]))
1565 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
1566 tab
->mat
->row
[i
][2 + var
->index
]);
1572 static void perform_undo(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1573 struct isl_tab_undo
*undo
)
1575 switch(undo
->type
) {
1576 case isl_tab_undo_empty
:
1579 case isl_tab_undo_nonneg
:
1580 undo
->var
->is_nonneg
= 0;
1582 case isl_tab_undo_redundant
:
1583 undo
->var
->is_redundant
= 0;
1586 case isl_tab_undo_zero
:
1587 undo
->var
->is_zero
= 0;
1590 case isl_tab_undo_allocate
:
1591 if (!undo
->var
->is_row
) {
1592 if (max_is_manifestly_unbounded(ctx
, tab
, undo
->var
))
1593 to_row(ctx
, tab
, undo
->var
, -1);
1595 to_row(ctx
, tab
, undo
->var
, 1);
1597 drop_row(ctx
, tab
, undo
->var
->index
);
1599 case isl_tab_undo_relax
:
1600 unrelax(ctx
, tab
, undo
->var
);
1605 /* Return the tableau to the state it was in when the snapshot "snap"
1608 int isl_tab_rollback(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1609 struct isl_tab_undo
*snap
)
1611 struct isl_tab_undo
*undo
, *next
;
1616 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
1620 perform_undo(ctx
, tab
, undo
);
1629 /* The given row "row" represents an inequality violated by all
1630 * points in the tableau. Check for some special cases of such
1631 * separating constraints.
1632 * In particular, if the row has been reduced to the constant -1,
1633 * then we know the inequality is adjacent (but opposite) to
1634 * an equality in the tableau.
1635 * If the row has been reduced to r = -1 -r', with r' an inequality
1636 * of the tableau, then the inequality is adjacent (but opposite)
1637 * to the inequality r'.
1639 static enum isl_ineq_type
separation_type(struct isl_ctx
*ctx
,
1640 struct isl_tab
*tab
, unsigned row
)
1645 return isl_ineq_separate
;
1647 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
1648 return isl_ineq_separate
;
1649 if (!isl_int_is_negone(tab
->mat
->row
[row
][1]))
1650 return isl_ineq_separate
;
1652 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
1653 tab
->n_col
- tab
->n_dead
);
1655 return isl_ineq_adj_eq
;
1657 if (!isl_int_is_negone(tab
->mat
->row
[row
][2 + tab
->n_dead
+ pos
]))
1658 return isl_ineq_separate
;
1660 pos
= isl_seq_first_non_zero(
1661 tab
->mat
->row
[row
] + 2 + tab
->n_dead
+ pos
+ 1,
1662 tab
->n_col
- tab
->n_dead
- pos
- 1);
1664 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
1667 /* Check the effect of inequality "ineq" on the tableau "tab".
1669 * isl_ineq_redundant: satisfied by all points in the tableau
1670 * isl_ineq_separate: satisfied by no point in the tableau
1671 * isl_ineq_cut: satisfied by some by not all points
1672 * isl_ineq_adj_eq: adjacent to an equality
1673 * isl_ineq_adj_ineq: adjacent to an inequality.
1675 enum isl_ineq_type
isl_tab_ineq_type(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1678 enum isl_ineq_type type
= isl_ineq_error
;
1679 struct isl_tab_undo
*snap
= NULL
;
1684 return isl_ineq_error
;
1686 if (extend_cons(ctx
, tab
, 1) < 0)
1687 return isl_ineq_error
;
1689 snap
= isl_tab_snap(ctx
, tab
);
1691 con
= add_row(ctx
, tab
, ineq
);
1695 row
= tab
->con
[con
].index
;
1696 if (is_redundant(ctx
, tab
, row
))
1697 type
= isl_ineq_redundant
;
1698 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
1700 isl_int_abs_ge(tab
->mat
->row
[row
][1],
1701 tab
->mat
->row
[row
][0]))) {
1702 if (at_least_zero(ctx
, tab
, &tab
->con
[con
]))
1703 type
= isl_ineq_cut
;
1705 type
= separation_type(ctx
, tab
, row
);
1706 } else if (tab
->rational
? (sign_of_min(ctx
, tab
, &tab
->con
[con
]) < 0)
1707 : min_at_most_neg_one(ctx
, tab
, &tab
->con
[con
]))
1708 type
= isl_ineq_cut
;
1710 type
= isl_ineq_redundant
;
1712 if (isl_tab_rollback(ctx
, tab
, snap
))
1713 return isl_ineq_error
;
1716 isl_tab_rollback(ctx
, tab
, snap
);
1717 return isl_ineq_error
;
1720 void isl_tab_dump(struct isl_ctx
*ctx
, struct isl_tab
*tab
,
1721 FILE *out
, int indent
)
1727 fprintf(out
, "%*snull tab\n", indent
, "");
1730 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
1731 tab
->n_redundant
, tab
->n_dead
);
1733 fprintf(out
, ", rational");
1735 fprintf(out
, ", empty");
1737 fprintf(out
, "%*s[", indent
, "");
1738 for (i
= 0; i
< tab
->n_var
; ++i
) {
1741 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
1743 tab
->var
[i
].is_zero
? " [=0]" :
1744 tab
->var
[i
].is_redundant
? " [R]" : "");
1746 fprintf(out
, "]\n");
1747 fprintf(out
, "%*s[", indent
, "");
1748 for (i
= 0; i
< tab
->n_con
; ++i
) {
1751 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
1753 tab
->con
[i
].is_zero
? " [=0]" :
1754 tab
->con
[i
].is_redundant
? " [R]" : "");
1756 fprintf(out
, "]\n");
1757 fprintf(out
, "%*s[", indent
, "");
1758 for (i
= 0; i
< tab
->n_row
; ++i
) {
1761 fprintf(out
, "r%d: %d%s", i
, tab
->row_var
[i
],
1762 var_from_row(ctx
, tab
, i
)->is_nonneg
? " [>=0]" : "");
1764 fprintf(out
, "]\n");
1765 fprintf(out
, "%*s[", indent
, "");
1766 for (i
= 0; i
< tab
->n_col
; ++i
) {
1769 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
1770 var_from_col(ctx
, tab
, i
)->is_nonneg
? " [>=0]" : "");
1772 fprintf(out
, "]\n");
1773 r
= tab
->mat
->n_row
;
1774 tab
->mat
->n_row
= tab
->n_row
;
1775 c
= tab
->mat
->n_col
;
1776 tab
->mat
->n_col
= 2 + tab
->n_col
;
1777 isl_mat_dump(ctx
, tab
->mat
, out
, indent
);
1778 tab
->mat
->n_row
= r
;
1779 tab
->mat
->n_col
= c
;