2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2013 Ecole Normale Superieure
5 * Use of this software is governed by the MIT license
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
12 #include <isl_ctx_private.h>
13 #include <isl_mat_private.h>
14 #include "isl_map_private.h"
17 #include <isl_config.h>
20 * The implementation of tableaus in this file was inspired by Section 8
21 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
22 * prover for program checking".
25 struct isl_tab
*isl_tab_alloc(struct isl_ctx
*ctx
,
26 unsigned n_row
, unsigned n_var
, unsigned M
)
32 tab
= isl_calloc_type(ctx
, struct isl_tab
);
35 tab
->mat
= isl_mat_alloc(ctx
, n_row
, off
+ n_var
);
38 tab
->var
= isl_alloc_array(ctx
, struct isl_tab_var
, n_var
);
41 tab
->con
= isl_alloc_array(ctx
, struct isl_tab_var
, n_row
);
44 tab
->col_var
= isl_alloc_array(ctx
, int, n_var
);
47 tab
->row_var
= isl_alloc_array(ctx
, int, n_row
);
50 for (i
= 0; i
< n_var
; ++i
) {
51 tab
->var
[i
].index
= i
;
52 tab
->var
[i
].is_row
= 0;
53 tab
->var
[i
].is_nonneg
= 0;
54 tab
->var
[i
].is_zero
= 0;
55 tab
->var
[i
].is_redundant
= 0;
56 tab
->var
[i
].frozen
= 0;
57 tab
->var
[i
].negated
= 0;
71 tab
->strict_redundant
= 0;
78 tab
->bottom
.type
= isl_tab_undo_bottom
;
79 tab
->bottom
.next
= NULL
;
80 tab
->top
= &tab
->bottom
;
92 int isl_tab_extend_cons(struct isl_tab
*tab
, unsigned n_new
)
101 if (tab
->max_con
< tab
->n_con
+ n_new
) {
102 struct isl_tab_var
*con
;
104 con
= isl_realloc_array(tab
->mat
->ctx
, tab
->con
,
105 struct isl_tab_var
, tab
->max_con
+ n_new
);
109 tab
->max_con
+= n_new
;
111 if (tab
->mat
->n_row
< tab
->n_row
+ n_new
) {
114 tab
->mat
= isl_mat_extend(tab
->mat
,
115 tab
->n_row
+ n_new
, off
+ tab
->n_col
);
118 row_var
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_var
,
119 int, tab
->mat
->n_row
);
122 tab
->row_var
= row_var
;
124 enum isl_tab_row_sign
*s
;
125 s
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_sign
,
126 enum isl_tab_row_sign
, tab
->mat
->n_row
);
135 /* Make room for at least n_new extra variables.
136 * Return -1 if anything went wrong.
138 int isl_tab_extend_vars(struct isl_tab
*tab
, unsigned n_new
)
140 struct isl_tab_var
*var
;
141 unsigned off
= 2 + tab
->M
;
143 if (tab
->max_var
< tab
->n_var
+ n_new
) {
144 var
= isl_realloc_array(tab
->mat
->ctx
, tab
->var
,
145 struct isl_tab_var
, tab
->n_var
+ n_new
);
149 tab
->max_var
+= n_new
;
152 if (tab
->mat
->n_col
< off
+ tab
->n_col
+ n_new
) {
155 tab
->mat
= isl_mat_extend(tab
->mat
,
156 tab
->mat
->n_row
, off
+ tab
->n_col
+ n_new
);
159 p
= isl_realloc_array(tab
->mat
->ctx
, tab
->col_var
,
160 int, tab
->n_col
+ n_new
);
169 struct isl_tab
*isl_tab_extend(struct isl_tab
*tab
, unsigned n_new
)
171 if (isl_tab_extend_cons(tab
, n_new
) >= 0)
178 static void free_undo_record(struct isl_tab_undo
*undo
)
180 switch (undo
->type
) {
181 case isl_tab_undo_saved_basis
:
182 free(undo
->u
.col_var
);
189 static void free_undo(struct isl_tab
*tab
)
191 struct isl_tab_undo
*undo
, *next
;
193 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
195 free_undo_record(undo
);
200 void isl_tab_free(struct isl_tab
*tab
)
205 isl_mat_free(tab
->mat
);
206 isl_vec_free(tab
->dual
);
207 isl_basic_map_free(tab
->bmap
);
213 isl_mat_free(tab
->samples
);
214 free(tab
->sample_index
);
215 isl_mat_free(tab
->basis
);
219 struct isl_tab
*isl_tab_dup(struct isl_tab
*tab
)
229 dup
= isl_calloc_type(tab
->mat
->ctx
, struct isl_tab
);
232 dup
->mat
= isl_mat_dup(tab
->mat
);
235 dup
->var
= isl_alloc_array(tab
->mat
->ctx
, struct isl_tab_var
, tab
->max_var
);
238 for (i
= 0; i
< tab
->n_var
; ++i
)
239 dup
->var
[i
] = tab
->var
[i
];
240 dup
->con
= isl_alloc_array(tab
->mat
->ctx
, struct isl_tab_var
, tab
->max_con
);
243 for (i
= 0; i
< tab
->n_con
; ++i
)
244 dup
->con
[i
] = tab
->con
[i
];
245 dup
->col_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->mat
->n_col
- off
);
248 for (i
= 0; i
< tab
->n_col
; ++i
)
249 dup
->col_var
[i
] = tab
->col_var
[i
];
250 dup
->row_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->mat
->n_row
);
253 for (i
= 0; i
< tab
->n_row
; ++i
)
254 dup
->row_var
[i
] = tab
->row_var
[i
];
256 dup
->row_sign
= isl_alloc_array(tab
->mat
->ctx
, enum isl_tab_row_sign
,
260 for (i
= 0; i
< tab
->n_row
; ++i
)
261 dup
->row_sign
[i
] = tab
->row_sign
[i
];
264 dup
->samples
= isl_mat_dup(tab
->samples
);
267 dup
->sample_index
= isl_alloc_array(tab
->mat
->ctx
, int,
268 tab
->samples
->n_row
);
269 if (!dup
->sample_index
)
271 dup
->n_sample
= tab
->n_sample
;
272 dup
->n_outside
= tab
->n_outside
;
274 dup
->n_row
= tab
->n_row
;
275 dup
->n_con
= tab
->n_con
;
276 dup
->n_eq
= tab
->n_eq
;
277 dup
->max_con
= tab
->max_con
;
278 dup
->n_col
= tab
->n_col
;
279 dup
->n_var
= tab
->n_var
;
280 dup
->max_var
= tab
->max_var
;
281 dup
->n_param
= tab
->n_param
;
282 dup
->n_div
= tab
->n_div
;
283 dup
->n_dead
= tab
->n_dead
;
284 dup
->n_redundant
= tab
->n_redundant
;
285 dup
->rational
= tab
->rational
;
286 dup
->empty
= tab
->empty
;
287 dup
->strict_redundant
= 0;
291 tab
->cone
= tab
->cone
;
292 dup
->bottom
.type
= isl_tab_undo_bottom
;
293 dup
->bottom
.next
= NULL
;
294 dup
->top
= &dup
->bottom
;
296 dup
->n_zero
= tab
->n_zero
;
297 dup
->n_unbounded
= tab
->n_unbounded
;
298 dup
->basis
= isl_mat_dup(tab
->basis
);
306 /* Construct the coefficient matrix of the product tableau
308 * mat{1,2} is the coefficient matrix of tableau {1,2}
309 * row{1,2} is the number of rows in tableau {1,2}
310 * col{1,2} is the number of columns in tableau {1,2}
311 * off is the offset to the coefficient column (skipping the
312 * denominator, the constant term and the big parameter if any)
313 * r{1,2} is the number of redundant rows in tableau {1,2}
314 * d{1,2} is the number of dead columns in tableau {1,2}
316 * The order of the rows and columns in the result is as explained
317 * in isl_tab_product.
319 static struct isl_mat
*tab_mat_product(struct isl_mat
*mat1
,
320 struct isl_mat
*mat2
, unsigned row1
, unsigned row2
,
321 unsigned col1
, unsigned col2
,
322 unsigned off
, unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
325 struct isl_mat
*prod
;
328 prod
= isl_mat_alloc(mat1
->ctx
, mat1
->n_row
+ mat2
->n_row
,
334 for (i
= 0; i
< r1
; ++i
) {
335 isl_seq_cpy(prod
->row
[n
+ i
], mat1
->row
[i
], off
+ d1
);
336 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
, d2
);
337 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
+ d2
,
338 mat1
->row
[i
] + off
+ d1
, col1
- d1
);
339 isl_seq_clr(prod
->row
[n
+ i
] + off
+ col1
+ d1
, col2
- d2
);
343 for (i
= 0; i
< r2
; ++i
) {
344 isl_seq_cpy(prod
->row
[n
+ i
], mat2
->row
[i
], off
);
345 isl_seq_clr(prod
->row
[n
+ i
] + off
, d1
);
346 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
,
347 mat2
->row
[i
] + off
, d2
);
348 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
+ d2
, col1
- d1
);
349 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ col1
+ d1
,
350 mat2
->row
[i
] + off
+ d2
, col2
- d2
);
354 for (i
= 0; i
< row1
- r1
; ++i
) {
355 isl_seq_cpy(prod
->row
[n
+ i
], mat1
->row
[r1
+ i
], off
+ d1
);
356 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
, d2
);
357 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
+ d2
,
358 mat1
->row
[r1
+ i
] + off
+ d1
, col1
- d1
);
359 isl_seq_clr(prod
->row
[n
+ i
] + off
+ col1
+ d1
, col2
- d2
);
363 for (i
= 0; i
< row2
- r2
; ++i
) {
364 isl_seq_cpy(prod
->row
[n
+ i
], mat2
->row
[r2
+ i
], off
);
365 isl_seq_clr(prod
->row
[n
+ i
] + off
, d1
);
366 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
,
367 mat2
->row
[r2
+ i
] + off
, d2
);
368 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
+ d2
, col1
- d1
);
369 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ col1
+ d1
,
370 mat2
->row
[r2
+ i
] + off
+ d2
, col2
- d2
);
376 /* Update the row or column index of a variable that corresponds
377 * to a variable in the first input tableau.
379 static void update_index1(struct isl_tab_var
*var
,
380 unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
382 if (var
->index
== -1)
384 if (var
->is_row
&& var
->index
>= r1
)
386 if (!var
->is_row
&& var
->index
>= d1
)
390 /* Update the row or column index of a variable that corresponds
391 * to a variable in the second input tableau.
393 static void update_index2(struct isl_tab_var
*var
,
394 unsigned row1
, unsigned col1
,
395 unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
397 if (var
->index
== -1)
412 /* Create a tableau that represents the Cartesian product of the sets
413 * represented by tableaus tab1 and tab2.
414 * The order of the rows in the product is
415 * - redundant rows of tab1
416 * - redundant rows of tab2
417 * - non-redundant rows of tab1
418 * - non-redundant rows of tab2
419 * The order of the columns is
422 * - coefficient of big parameter, if any
423 * - dead columns of tab1
424 * - dead columns of tab2
425 * - live columns of tab1
426 * - live columns of tab2
427 * The order of the variables and the constraints is a concatenation
428 * of order in the two input tableaus.
430 struct isl_tab
*isl_tab_product(struct isl_tab
*tab1
, struct isl_tab
*tab2
)
433 struct isl_tab
*prod
;
435 unsigned r1
, r2
, d1
, d2
;
440 isl_assert(tab1
->mat
->ctx
, tab1
->M
== tab2
->M
, return NULL
);
441 isl_assert(tab1
->mat
->ctx
, tab1
->rational
== tab2
->rational
, return NULL
);
442 isl_assert(tab1
->mat
->ctx
, tab1
->cone
== tab2
->cone
, return NULL
);
443 isl_assert(tab1
->mat
->ctx
, !tab1
->row_sign
, return NULL
);
444 isl_assert(tab1
->mat
->ctx
, !tab2
->row_sign
, return NULL
);
445 isl_assert(tab1
->mat
->ctx
, tab1
->n_param
== 0, return NULL
);
446 isl_assert(tab1
->mat
->ctx
, tab2
->n_param
== 0, return NULL
);
447 isl_assert(tab1
->mat
->ctx
, tab1
->n_div
== 0, return NULL
);
448 isl_assert(tab1
->mat
->ctx
, tab2
->n_div
== 0, return NULL
);
451 r1
= tab1
->n_redundant
;
452 r2
= tab2
->n_redundant
;
455 prod
= isl_calloc_type(tab1
->mat
->ctx
, struct isl_tab
);
458 prod
->mat
= tab_mat_product(tab1
->mat
, tab2
->mat
,
459 tab1
->n_row
, tab2
->n_row
,
460 tab1
->n_col
, tab2
->n_col
, off
, r1
, r2
, d1
, d2
);
463 prod
->var
= isl_alloc_array(tab1
->mat
->ctx
, struct isl_tab_var
,
464 tab1
->max_var
+ tab2
->max_var
);
467 for (i
= 0; i
< tab1
->n_var
; ++i
) {
468 prod
->var
[i
] = tab1
->var
[i
];
469 update_index1(&prod
->var
[i
], r1
, r2
, d1
, d2
);
471 for (i
= 0; i
< tab2
->n_var
; ++i
) {
472 prod
->var
[tab1
->n_var
+ i
] = tab2
->var
[i
];
473 update_index2(&prod
->var
[tab1
->n_var
+ i
],
474 tab1
->n_row
, tab1
->n_col
,
477 prod
->con
= isl_alloc_array(tab1
->mat
->ctx
, struct isl_tab_var
,
478 tab1
->max_con
+ tab2
->max_con
);
481 for (i
= 0; i
< tab1
->n_con
; ++i
) {
482 prod
->con
[i
] = tab1
->con
[i
];
483 update_index1(&prod
->con
[i
], r1
, r2
, d1
, d2
);
485 for (i
= 0; i
< tab2
->n_con
; ++i
) {
486 prod
->con
[tab1
->n_con
+ i
] = tab2
->con
[i
];
487 update_index2(&prod
->con
[tab1
->n_con
+ i
],
488 tab1
->n_row
, tab1
->n_col
,
491 prod
->col_var
= isl_alloc_array(tab1
->mat
->ctx
, int,
492 tab1
->n_col
+ tab2
->n_col
);
495 for (i
= 0; i
< tab1
->n_col
; ++i
) {
496 int pos
= i
< d1
? i
: i
+ d2
;
497 prod
->col_var
[pos
] = tab1
->col_var
[i
];
499 for (i
= 0; i
< tab2
->n_col
; ++i
) {
500 int pos
= i
< d2
? d1
+ i
: tab1
->n_col
+ i
;
501 int t
= tab2
->col_var
[i
];
506 prod
->col_var
[pos
] = t
;
508 prod
->row_var
= isl_alloc_array(tab1
->mat
->ctx
, int,
509 tab1
->mat
->n_row
+ tab2
->mat
->n_row
);
512 for (i
= 0; i
< tab1
->n_row
; ++i
) {
513 int pos
= i
< r1
? i
: i
+ r2
;
514 prod
->row_var
[pos
] = tab1
->row_var
[i
];
516 for (i
= 0; i
< tab2
->n_row
; ++i
) {
517 int pos
= i
< r2
? r1
+ i
: tab1
->n_row
+ i
;
518 int t
= tab2
->row_var
[i
];
523 prod
->row_var
[pos
] = t
;
525 prod
->samples
= NULL
;
526 prod
->sample_index
= NULL
;
527 prod
->n_row
= tab1
->n_row
+ tab2
->n_row
;
528 prod
->n_con
= tab1
->n_con
+ tab2
->n_con
;
530 prod
->max_con
= tab1
->max_con
+ tab2
->max_con
;
531 prod
->n_col
= tab1
->n_col
+ tab2
->n_col
;
532 prod
->n_var
= tab1
->n_var
+ tab2
->n_var
;
533 prod
->max_var
= tab1
->max_var
+ tab2
->max_var
;
536 prod
->n_dead
= tab1
->n_dead
+ tab2
->n_dead
;
537 prod
->n_redundant
= tab1
->n_redundant
+ tab2
->n_redundant
;
538 prod
->rational
= tab1
->rational
;
539 prod
->empty
= tab1
->empty
|| tab2
->empty
;
540 prod
->strict_redundant
= tab1
->strict_redundant
|| tab2
->strict_redundant
;
544 prod
->cone
= tab1
->cone
;
545 prod
->bottom
.type
= isl_tab_undo_bottom
;
546 prod
->bottom
.next
= NULL
;
547 prod
->top
= &prod
->bottom
;
550 prod
->n_unbounded
= 0;
559 static struct isl_tab_var
*var_from_index(struct isl_tab
*tab
, int i
)
564 return &tab
->con
[~i
];
567 struct isl_tab_var
*isl_tab_var_from_row(struct isl_tab
*tab
, int i
)
569 return var_from_index(tab
, tab
->row_var
[i
]);
572 static struct isl_tab_var
*var_from_col(struct isl_tab
*tab
, int i
)
574 return var_from_index(tab
, tab
->col_var
[i
]);
577 /* Check if there are any upper bounds on column variable "var",
578 * i.e., non-negative rows where var appears with a negative coefficient.
579 * Return 1 if there are no such bounds.
581 static int max_is_manifestly_unbounded(struct isl_tab
*tab
,
582 struct isl_tab_var
*var
)
585 unsigned off
= 2 + tab
->M
;
589 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
590 if (!isl_int_is_neg(tab
->mat
->row
[i
][off
+ var
->index
]))
592 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
598 /* Check if there are any lower bounds on column variable "var",
599 * i.e., non-negative rows where var appears with a positive coefficient.
600 * Return 1 if there are no such bounds.
602 static int min_is_manifestly_unbounded(struct isl_tab
*tab
,
603 struct isl_tab_var
*var
)
606 unsigned off
= 2 + tab
->M
;
610 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
611 if (!isl_int_is_pos(tab
->mat
->row
[i
][off
+ var
->index
]))
613 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
619 static int row_cmp(struct isl_tab
*tab
, int r1
, int r2
, int c
, isl_int t
)
621 unsigned off
= 2 + tab
->M
;
625 isl_int_mul(t
, tab
->mat
->row
[r1
][2], tab
->mat
->row
[r2
][off
+c
]);
626 isl_int_submul(t
, tab
->mat
->row
[r2
][2], tab
->mat
->row
[r1
][off
+c
]);
631 isl_int_mul(t
, tab
->mat
->row
[r1
][1], tab
->mat
->row
[r2
][off
+ c
]);
632 isl_int_submul(t
, tab
->mat
->row
[r2
][1], tab
->mat
->row
[r1
][off
+ c
]);
633 return isl_int_sgn(t
);
636 /* Given the index of a column "c", return the index of a row
637 * that can be used to pivot the column in, with either an increase
638 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
639 * If "var" is not NULL, then the row returned will be different from
640 * the one associated with "var".
642 * Each row in the tableau is of the form
644 * x_r = a_r0 + \sum_i a_ri x_i
646 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
647 * impose any limit on the increase or decrease in the value of x_c
648 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
649 * for the row with the smallest (most stringent) such bound.
650 * Note that the common denominator of each row drops out of the fraction.
651 * To check if row j has a smaller bound than row r, i.e.,
652 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
653 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
654 * where -sign(a_jc) is equal to "sgn".
656 static int pivot_row(struct isl_tab
*tab
,
657 struct isl_tab_var
*var
, int sgn
, int c
)
661 unsigned off
= 2 + tab
->M
;
665 for (j
= tab
->n_redundant
; j
< tab
->n_row
; ++j
) {
666 if (var
&& j
== var
->index
)
668 if (!isl_tab_var_from_row(tab
, j
)->is_nonneg
)
670 if (sgn
* isl_int_sgn(tab
->mat
->row
[j
][off
+ c
]) >= 0)
676 tsgn
= sgn
* row_cmp(tab
, r
, j
, c
, t
);
677 if (tsgn
< 0 || (tsgn
== 0 &&
678 tab
->row_var
[j
] < tab
->row_var
[r
]))
685 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
686 * (sgn < 0) the value of row variable var.
687 * If not NULL, then skip_var is a row variable that should be ignored
688 * while looking for a pivot row. It is usually equal to var.
690 * As the given row in the tableau is of the form
692 * x_r = a_r0 + \sum_i a_ri x_i
694 * we need to find a column such that the sign of a_ri is equal to "sgn"
695 * (such that an increase in x_i will have the desired effect) or a
696 * column with a variable that may attain negative values.
697 * If a_ri is positive, then we need to move x_i in the same direction
698 * to obtain the desired effect. Otherwise, x_i has to move in the
699 * opposite direction.
701 static void find_pivot(struct isl_tab
*tab
,
702 struct isl_tab_var
*var
, struct isl_tab_var
*skip_var
,
703 int sgn
, int *row
, int *col
)
710 isl_assert(tab
->mat
->ctx
, var
->is_row
, return);
711 tr
= tab
->mat
->row
[var
->index
] + 2 + tab
->M
;
714 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
715 if (isl_int_is_zero(tr
[j
]))
717 if (isl_int_sgn(tr
[j
]) != sgn
&&
718 var_from_col(tab
, j
)->is_nonneg
)
720 if (c
< 0 || tab
->col_var
[j
] < tab
->col_var
[c
])
726 sgn
*= isl_int_sgn(tr
[c
]);
727 r
= pivot_row(tab
, skip_var
, sgn
, c
);
728 *row
= r
< 0 ? var
->index
: r
;
732 /* Return 1 if row "row" represents an obviously redundant inequality.
734 * - it represents an inequality or a variable
735 * - that is the sum of a non-negative sample value and a positive
736 * combination of zero or more non-negative constraints.
738 int isl_tab_row_is_redundant(struct isl_tab
*tab
, int row
)
741 unsigned off
= 2 + tab
->M
;
743 if (tab
->row_var
[row
] < 0 && !isl_tab_var_from_row(tab
, row
)->is_nonneg
)
746 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
748 if (tab
->strict_redundant
&& isl_int_is_zero(tab
->mat
->row
[row
][1]))
750 if (tab
->M
&& isl_int_is_neg(tab
->mat
->row
[row
][2]))
753 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
754 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ i
]))
756 if (tab
->col_var
[i
] >= 0)
758 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ i
]))
760 if (!var_from_col(tab
, i
)->is_nonneg
)
766 static void swap_rows(struct isl_tab
*tab
, int row1
, int row2
)
769 enum isl_tab_row_sign s
;
771 t
= tab
->row_var
[row1
];
772 tab
->row_var
[row1
] = tab
->row_var
[row2
];
773 tab
->row_var
[row2
] = t
;
774 isl_tab_var_from_row(tab
, row1
)->index
= row1
;
775 isl_tab_var_from_row(tab
, row2
)->index
= row2
;
776 tab
->mat
= isl_mat_swap_rows(tab
->mat
, row1
, row2
);
780 s
= tab
->row_sign
[row1
];
781 tab
->row_sign
[row1
] = tab
->row_sign
[row2
];
782 tab
->row_sign
[row2
] = s
;
785 static int push_union(struct isl_tab
*tab
,
786 enum isl_tab_undo_type type
, union isl_tab_undo_val u
) WARN_UNUSED
;
787 static int push_union(struct isl_tab
*tab
,
788 enum isl_tab_undo_type type
, union isl_tab_undo_val u
)
790 struct isl_tab_undo
*undo
;
797 undo
= isl_alloc_type(tab
->mat
->ctx
, struct isl_tab_undo
);
802 undo
->next
= tab
->top
;
808 int isl_tab_push_var(struct isl_tab
*tab
,
809 enum isl_tab_undo_type type
, struct isl_tab_var
*var
)
811 union isl_tab_undo_val u
;
813 u
.var_index
= tab
->row_var
[var
->index
];
815 u
.var_index
= tab
->col_var
[var
->index
];
816 return push_union(tab
, type
, u
);
819 int isl_tab_push(struct isl_tab
*tab
, enum isl_tab_undo_type type
)
821 union isl_tab_undo_val u
= { 0 };
822 return push_union(tab
, type
, u
);
825 /* Push a record on the undo stack describing the current basic
826 * variables, so that the this state can be restored during rollback.
828 int isl_tab_push_basis(struct isl_tab
*tab
)
831 union isl_tab_undo_val u
;
833 u
.col_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
836 for (i
= 0; i
< tab
->n_col
; ++i
)
837 u
.col_var
[i
] = tab
->col_var
[i
];
838 return push_union(tab
, isl_tab_undo_saved_basis
, u
);
841 int isl_tab_push_callback(struct isl_tab
*tab
, struct isl_tab_callback
*callback
)
843 union isl_tab_undo_val u
;
844 u
.callback
= callback
;
845 return push_union(tab
, isl_tab_undo_callback
, u
);
848 struct isl_tab
*isl_tab_init_samples(struct isl_tab
*tab
)
855 tab
->samples
= isl_mat_alloc(tab
->mat
->ctx
, 1, 1 + tab
->n_var
);
858 tab
->sample_index
= isl_alloc_array(tab
->mat
->ctx
, int, 1);
859 if (!tab
->sample_index
)
867 struct isl_tab
*isl_tab_add_sample(struct isl_tab
*tab
,
868 __isl_take isl_vec
*sample
)
873 if (tab
->n_sample
+ 1 > tab
->samples
->n_row
) {
874 int *t
= isl_realloc_array(tab
->mat
->ctx
,
875 tab
->sample_index
, int, tab
->n_sample
+ 1);
878 tab
->sample_index
= t
;
881 tab
->samples
= isl_mat_extend(tab
->samples
,
882 tab
->n_sample
+ 1, tab
->samples
->n_col
);
886 isl_seq_cpy(tab
->samples
->row
[tab
->n_sample
], sample
->el
, sample
->size
);
887 isl_vec_free(sample
);
888 tab
->sample_index
[tab
->n_sample
] = tab
->n_sample
;
893 isl_vec_free(sample
);
898 struct isl_tab
*isl_tab_drop_sample(struct isl_tab
*tab
, int s
)
900 if (s
!= tab
->n_outside
) {
901 int t
= tab
->sample_index
[tab
->n_outside
];
902 tab
->sample_index
[tab
->n_outside
] = tab
->sample_index
[s
];
903 tab
->sample_index
[s
] = t
;
904 isl_mat_swap_rows(tab
->samples
, tab
->n_outside
, s
);
907 if (isl_tab_push(tab
, isl_tab_undo_drop_sample
) < 0) {
915 /* Record the current number of samples so that we can remove newer
916 * samples during a rollback.
918 int isl_tab_save_samples(struct isl_tab
*tab
)
920 union isl_tab_undo_val u
;
926 return push_union(tab
, isl_tab_undo_saved_samples
, u
);
929 /* Mark row with index "row" as being redundant.
930 * If we may need to undo the operation or if the row represents
931 * a variable of the original problem, the row is kept,
932 * but no longer considered when looking for a pivot row.
933 * Otherwise, the row is simply removed.
935 * The row may be interchanged with some other row. If it
936 * is interchanged with a later row, return 1. Otherwise return 0.
937 * If the rows are checked in order in the calling function,
938 * then a return value of 1 means that the row with the given
939 * row number may now contain a different row that hasn't been checked yet.
941 int isl_tab_mark_redundant(struct isl_tab
*tab
, int row
)
943 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, row
);
944 var
->is_redundant
= 1;
945 isl_assert(tab
->mat
->ctx
, row
>= tab
->n_redundant
, return -1);
946 if (tab
->preserve
|| tab
->need_undo
|| tab
->row_var
[row
] >= 0) {
947 if (tab
->row_var
[row
] >= 0 && !var
->is_nonneg
) {
949 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, var
) < 0)
952 if (row
!= tab
->n_redundant
)
953 swap_rows(tab
, row
, tab
->n_redundant
);
955 return isl_tab_push_var(tab
, isl_tab_undo_redundant
, var
);
957 if (row
!= tab
->n_row
- 1)
958 swap_rows(tab
, row
, tab
->n_row
- 1);
959 isl_tab_var_from_row(tab
, tab
->n_row
- 1)->index
= -1;
965 int isl_tab_mark_empty(struct isl_tab
*tab
)
969 if (!tab
->empty
&& tab
->need_undo
)
970 if (isl_tab_push(tab
, isl_tab_undo_empty
) < 0)
976 int isl_tab_freeze_constraint(struct isl_tab
*tab
, int con
)
978 struct isl_tab_var
*var
;
983 var
= &tab
->con
[con
];
991 return isl_tab_push_var(tab
, isl_tab_undo_freeze
, var
);
996 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
997 * the original sign of the pivot element.
998 * We only keep track of row signs during PILP solving and in this case
999 * we only pivot a row with negative sign (meaning the value is always
1000 * non-positive) using a positive pivot element.
1002 * For each row j, the new value of the parametric constant is equal to
1004 * a_j0 - a_jc a_r0/a_rc
1006 * where a_j0 is the original parametric constant, a_rc is the pivot element,
1007 * a_r0 is the parametric constant of the pivot row and a_jc is the
1008 * pivot column entry of the row j.
1009 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
1010 * remains the same if a_jc has the same sign as the row j or if
1011 * a_jc is zero. In all other cases, we reset the sign to "unknown".
1013 static void update_row_sign(struct isl_tab
*tab
, int row
, int col
, int row_sgn
)
1016 struct isl_mat
*mat
= tab
->mat
;
1017 unsigned off
= 2 + tab
->M
;
1022 if (tab
->row_sign
[row
] == 0)
1024 isl_assert(mat
->ctx
, row_sgn
> 0, return);
1025 isl_assert(mat
->ctx
, tab
->row_sign
[row
] == isl_tab_row_neg
, return);
1026 tab
->row_sign
[row
] = isl_tab_row_pos
;
1027 for (i
= 0; i
< tab
->n_row
; ++i
) {
1031 s
= isl_int_sgn(mat
->row
[i
][off
+ col
]);
1034 if (!tab
->row_sign
[i
])
1036 if (s
< 0 && tab
->row_sign
[i
] == isl_tab_row_neg
)
1038 if (s
> 0 && tab
->row_sign
[i
] == isl_tab_row_pos
)
1040 tab
->row_sign
[i
] = isl_tab_row_unknown
;
1044 /* Given a row number "row" and a column number "col", pivot the tableau
1045 * such that the associated variables are interchanged.
1046 * The given row in the tableau expresses
1048 * x_r = a_r0 + \sum_i a_ri x_i
1052 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
1054 * Substituting this equality into the other rows
1056 * x_j = a_j0 + \sum_i a_ji x_i
1058 * with a_jc \ne 0, we obtain
1060 * 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
1067 * where i is any other column and j is any other row,
1068 * is therefore transformed into
1070 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1071 * 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)
1073 * The transformation is performed along the following steps
1075 * d_r/n_rc n_ri/n_rc
1078 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1081 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1082 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
1084 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1085 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
1087 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1088 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
1090 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1091 * 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)
1094 int isl_tab_pivot(struct isl_tab
*tab
, int row
, int col
)
1099 struct isl_mat
*mat
= tab
->mat
;
1100 struct isl_tab_var
*var
;
1101 unsigned off
= 2 + tab
->M
;
1103 if (tab
->mat
->ctx
->abort
) {
1104 isl_ctx_set_error(tab
->mat
->ctx
, isl_error_abort
);
1108 isl_int_swap(mat
->row
[row
][0], mat
->row
[row
][off
+ col
]);
1109 sgn
= isl_int_sgn(mat
->row
[row
][0]);
1111 isl_int_neg(mat
->row
[row
][0], mat
->row
[row
][0]);
1112 isl_int_neg(mat
->row
[row
][off
+ col
], mat
->row
[row
][off
+ col
]);
1114 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1115 if (j
== off
- 1 + col
)
1117 isl_int_neg(mat
->row
[row
][1 + j
], mat
->row
[row
][1 + j
]);
1119 if (!isl_int_is_one(mat
->row
[row
][0]))
1120 isl_seq_normalize(mat
->ctx
, mat
->row
[row
], off
+ tab
->n_col
);
1121 for (i
= 0; i
< tab
->n_row
; ++i
) {
1124 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1126 isl_int_mul(mat
->row
[i
][0], mat
->row
[i
][0], mat
->row
[row
][0]);
1127 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1128 if (j
== off
- 1 + col
)
1130 isl_int_mul(mat
->row
[i
][1 + j
],
1131 mat
->row
[i
][1 + j
], mat
->row
[row
][0]);
1132 isl_int_addmul(mat
->row
[i
][1 + j
],
1133 mat
->row
[i
][off
+ col
], mat
->row
[row
][1 + j
]);
1135 isl_int_mul(mat
->row
[i
][off
+ col
],
1136 mat
->row
[i
][off
+ col
], mat
->row
[row
][off
+ col
]);
1137 if (!isl_int_is_one(mat
->row
[i
][0]))
1138 isl_seq_normalize(mat
->ctx
, mat
->row
[i
], off
+ tab
->n_col
);
1140 t
= tab
->row_var
[row
];
1141 tab
->row_var
[row
] = tab
->col_var
[col
];
1142 tab
->col_var
[col
] = t
;
1143 var
= isl_tab_var_from_row(tab
, row
);
1146 var
= var_from_col(tab
, col
);
1149 update_row_sign(tab
, row
, col
, sgn
);
1152 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1153 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1155 if (!isl_tab_var_from_row(tab
, i
)->frozen
&&
1156 isl_tab_row_is_redundant(tab
, i
)) {
1157 int redo
= isl_tab_mark_redundant(tab
, i
);
1167 /* If "var" represents a column variable, then pivot is up (sgn > 0)
1168 * or down (sgn < 0) to a row. The variable is assumed not to be
1169 * unbounded in the specified direction.
1170 * If sgn = 0, then the variable is unbounded in both directions,
1171 * and we pivot with any row we can find.
1173 static int to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
) WARN_UNUSED
;
1174 static int to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
)
1177 unsigned off
= 2 + tab
->M
;
1183 for (r
= tab
->n_redundant
; r
< tab
->n_row
; ++r
)
1184 if (!isl_int_is_zero(tab
->mat
->row
[r
][off
+var
->index
]))
1186 isl_assert(tab
->mat
->ctx
, r
< tab
->n_row
, return -1);
1188 r
= pivot_row(tab
, NULL
, sign
, var
->index
);
1189 isl_assert(tab
->mat
->ctx
, r
>= 0, return -1);
1192 return isl_tab_pivot(tab
, r
, var
->index
);
1195 /* Check whether all variables that are marked as non-negative
1196 * also have a non-negative sample value. This function is not
1197 * called from the current code but is useful during debugging.
1199 static void check_table(struct isl_tab
*tab
) __attribute__ ((unused
));
1200 static void check_table(struct isl_tab
*tab
)
1206 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1207 struct isl_tab_var
*var
;
1208 var
= isl_tab_var_from_row(tab
, i
);
1209 if (!var
->is_nonneg
)
1212 isl_assert(tab
->mat
->ctx
,
1213 !isl_int_is_neg(tab
->mat
->row
[i
][2]), abort());
1214 if (isl_int_is_pos(tab
->mat
->row
[i
][2]))
1217 isl_assert(tab
->mat
->ctx
, !isl_int_is_neg(tab
->mat
->row
[i
][1]),
1222 /* Return the sign of the maximal value of "var".
1223 * If the sign is not negative, then on return from this function,
1224 * the sample value will also be non-negative.
1226 * If "var" is manifestly unbounded wrt positive values, we are done.
1227 * Otherwise, we pivot the variable up to a row if needed
1228 * Then we continue pivoting down until either
1229 * - no more down pivots can be performed
1230 * - the sample value is positive
1231 * - the variable is pivoted into a manifestly unbounded column
1233 static int sign_of_max(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1237 if (max_is_manifestly_unbounded(tab
, var
))
1239 if (to_row(tab
, var
, 1) < 0)
1241 while (!isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1242 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1244 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1245 if (isl_tab_pivot(tab
, row
, col
) < 0)
1247 if (!var
->is_row
) /* manifestly unbounded */
1253 int isl_tab_sign_of_max(struct isl_tab
*tab
, int con
)
1255 struct isl_tab_var
*var
;
1260 var
= &tab
->con
[con
];
1261 isl_assert(tab
->mat
->ctx
, !var
->is_redundant
, return -2);
1262 isl_assert(tab
->mat
->ctx
, !var
->is_zero
, return -2);
1264 return sign_of_max(tab
, var
);
1267 static int row_is_neg(struct isl_tab
*tab
, int row
)
1270 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1271 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1273 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1275 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1278 static int row_sgn(struct isl_tab
*tab
, int row
)
1281 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1282 if (!isl_int_is_zero(tab
->mat
->row
[row
][2]))
1283 return isl_int_sgn(tab
->mat
->row
[row
][2]);
1285 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1288 /* Perform pivots until the row variable "var" has a non-negative
1289 * sample value or until no more upward pivots can be performed.
1290 * Return the sign of the sample value after the pivots have been
1293 static int restore_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1297 while (row_is_neg(tab
, var
->index
)) {
1298 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1301 if (isl_tab_pivot(tab
, row
, col
) < 0)
1303 if (!var
->is_row
) /* manifestly unbounded */
1306 return row_sgn(tab
, var
->index
);
1309 /* Perform pivots until we are sure that the row variable "var"
1310 * can attain non-negative values. After return from this
1311 * function, "var" is still a row variable, but its sample
1312 * value may not be non-negative, even if the function returns 1.
1314 static int at_least_zero(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1318 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1319 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1322 if (row
== var
->index
) /* manifestly unbounded */
1324 if (isl_tab_pivot(tab
, row
, col
) < 0)
1327 return !isl_int_is_neg(tab
->mat
->row
[var
->index
][1]);
1330 /* Return a negative value if "var" can attain negative values.
1331 * Return a non-negative value otherwise.
1333 * If "var" is manifestly unbounded wrt negative values, we are done.
1334 * Otherwise, if var is in a column, we can pivot it down to a row.
1335 * Then we continue pivoting down until either
1336 * - the pivot would result in a manifestly unbounded column
1337 * => we don't perform the pivot, but simply return -1
1338 * - no more down pivots can be performed
1339 * - the sample value is negative
1340 * If the sample value becomes negative and the variable is supposed
1341 * to be nonnegative, then we undo the last pivot.
1342 * However, if the last pivot has made the pivoting variable
1343 * obviously redundant, then it may have moved to another row.
1344 * In that case we look for upward pivots until we reach a non-negative
1347 static int sign_of_min(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1350 struct isl_tab_var
*pivot_var
= NULL
;
1352 if (min_is_manifestly_unbounded(tab
, var
))
1356 row
= pivot_row(tab
, NULL
, -1, col
);
1357 pivot_var
= var_from_col(tab
, col
);
1358 if (isl_tab_pivot(tab
, row
, col
) < 0)
1360 if (var
->is_redundant
)
1362 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1363 if (var
->is_nonneg
) {
1364 if (!pivot_var
->is_redundant
&&
1365 pivot_var
->index
== row
) {
1366 if (isl_tab_pivot(tab
, row
, col
) < 0)
1369 if (restore_row(tab
, var
) < -1)
1375 if (var
->is_redundant
)
1377 while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1378 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1379 if (row
== var
->index
)
1382 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1383 pivot_var
= var_from_col(tab
, col
);
1384 if (isl_tab_pivot(tab
, row
, col
) < 0)
1386 if (var
->is_redundant
)
1389 if (pivot_var
&& var
->is_nonneg
) {
1390 /* pivot back to non-negative value */
1391 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
) {
1392 if (isl_tab_pivot(tab
, row
, col
) < 0)
1395 if (restore_row(tab
, var
) < -1)
1401 static int row_at_most_neg_one(struct isl_tab
*tab
, int row
)
1404 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1406 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1409 return isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
1410 isl_int_abs_ge(tab
->mat
->row
[row
][1],
1411 tab
->mat
->row
[row
][0]);
1414 /* Return 1 if "var" can attain values <= -1.
1415 * Return 0 otherwise.
1417 * The sample value of "var" is assumed to be non-negative when the
1418 * the function is called. If 1 is returned then the constraint
1419 * is not redundant and the sample value is made non-negative again before
1420 * the function returns.
1422 int isl_tab_min_at_most_neg_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1425 struct isl_tab_var
*pivot_var
;
1427 if (min_is_manifestly_unbounded(tab
, var
))
1431 row
= pivot_row(tab
, NULL
, -1, col
);
1432 pivot_var
= var_from_col(tab
, col
);
1433 if (isl_tab_pivot(tab
, row
, col
) < 0)
1435 if (var
->is_redundant
)
1437 if (row_at_most_neg_one(tab
, var
->index
)) {
1438 if (var
->is_nonneg
) {
1439 if (!pivot_var
->is_redundant
&&
1440 pivot_var
->index
== row
) {
1441 if (isl_tab_pivot(tab
, row
, col
) < 0)
1444 if (restore_row(tab
, var
) < -1)
1450 if (var
->is_redundant
)
1453 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1454 if (row
== var
->index
) {
1455 if (restore_row(tab
, var
) < -1)
1461 pivot_var
= var_from_col(tab
, col
);
1462 if (isl_tab_pivot(tab
, row
, col
) < 0)
1464 if (var
->is_redundant
)
1466 } while (!row_at_most_neg_one(tab
, var
->index
));
1467 if (var
->is_nonneg
) {
1468 /* pivot back to non-negative value */
1469 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
1470 if (isl_tab_pivot(tab
, row
, col
) < 0)
1472 if (restore_row(tab
, var
) < -1)
1478 /* Return 1 if "var" can attain values >= 1.
1479 * Return 0 otherwise.
1481 static int at_least_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1486 if (max_is_manifestly_unbounded(tab
, var
))
1488 if (to_row(tab
, var
, 1) < 0)
1490 r
= tab
->mat
->row
[var
->index
];
1491 while (isl_int_lt(r
[1], r
[0])) {
1492 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1494 return isl_int_ge(r
[1], r
[0]);
1495 if (row
== var
->index
) /* manifestly unbounded */
1497 if (isl_tab_pivot(tab
, row
, col
) < 0)
1503 static void swap_cols(struct isl_tab
*tab
, int col1
, int col2
)
1506 unsigned off
= 2 + tab
->M
;
1507 t
= tab
->col_var
[col1
];
1508 tab
->col_var
[col1
] = tab
->col_var
[col2
];
1509 tab
->col_var
[col2
] = t
;
1510 var_from_col(tab
, col1
)->index
= col1
;
1511 var_from_col(tab
, col2
)->index
= col2
;
1512 tab
->mat
= isl_mat_swap_cols(tab
->mat
, off
+ col1
, off
+ col2
);
1515 /* Mark column with index "col" as representing a zero variable.
1516 * If we may need to undo the operation the column is kept,
1517 * but no longer considered.
1518 * Otherwise, the column is simply removed.
1520 * The column may be interchanged with some other column. If it
1521 * is interchanged with a later column, return 1. Otherwise return 0.
1522 * If the columns are checked in order in the calling function,
1523 * then a return value of 1 means that the column with the given
1524 * column number may now contain a different column that
1525 * hasn't been checked yet.
1527 int isl_tab_kill_col(struct isl_tab
*tab
, int col
)
1529 var_from_col(tab
, col
)->is_zero
= 1;
1530 if (tab
->need_undo
) {
1531 if (isl_tab_push_var(tab
, isl_tab_undo_zero
,
1532 var_from_col(tab
, col
)) < 0)
1534 if (col
!= tab
->n_dead
)
1535 swap_cols(tab
, col
, tab
->n_dead
);
1539 if (col
!= tab
->n_col
- 1)
1540 swap_cols(tab
, col
, tab
->n_col
- 1);
1541 var_from_col(tab
, tab
->n_col
- 1)->index
= -1;
1547 static int row_is_manifestly_non_integral(struct isl_tab
*tab
, int row
)
1549 unsigned off
= 2 + tab
->M
;
1551 if (tab
->M
&& !isl_int_eq(tab
->mat
->row
[row
][2],
1552 tab
->mat
->row
[row
][0]))
1554 if (isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1555 tab
->n_col
- tab
->n_dead
) != -1)
1558 return !isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1559 tab
->mat
->row
[row
][0]);
1562 /* For integer tableaus, check if any of the coordinates are stuck
1563 * at a non-integral value.
1565 static int tab_is_manifestly_empty(struct isl_tab
*tab
)
1574 for (i
= 0; i
< tab
->n_var
; ++i
) {
1575 if (!tab
->var
[i
].is_row
)
1577 if (row_is_manifestly_non_integral(tab
, tab
->var
[i
].index
))
1584 /* Row variable "var" is non-negative and cannot attain any values
1585 * larger than zero. This means that the coefficients of the unrestricted
1586 * column variables are zero and that the coefficients of the non-negative
1587 * column variables are zero or negative.
1588 * Each of the non-negative variables with a negative coefficient can
1589 * then also be written as the negative sum of non-negative variables
1590 * and must therefore also be zero.
1592 static int close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
1593 static int close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1596 struct isl_mat
*mat
= tab
->mat
;
1597 unsigned off
= 2 + tab
->M
;
1599 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return -1);
1602 if (isl_tab_push_var(tab
, isl_tab_undo_zero
, var
) < 0)
1604 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1606 if (isl_int_is_zero(mat
->row
[var
->index
][off
+ j
]))
1608 isl_assert(tab
->mat
->ctx
,
1609 isl_int_is_neg(mat
->row
[var
->index
][off
+ j
]), return -1);
1610 recheck
= isl_tab_kill_col(tab
, j
);
1616 if (isl_tab_mark_redundant(tab
, var
->index
) < 0)
1618 if (tab_is_manifestly_empty(tab
) && isl_tab_mark_empty(tab
) < 0)
1623 /* Add a constraint to the tableau and allocate a row for it.
1624 * Return the index into the constraint array "con".
1626 int isl_tab_allocate_con(struct isl_tab
*tab
)
1630 isl_assert(tab
->mat
->ctx
, tab
->n_row
< tab
->mat
->n_row
, return -1);
1631 isl_assert(tab
->mat
->ctx
, tab
->n_con
< tab
->max_con
, return -1);
1634 tab
->con
[r
].index
= tab
->n_row
;
1635 tab
->con
[r
].is_row
= 1;
1636 tab
->con
[r
].is_nonneg
= 0;
1637 tab
->con
[r
].is_zero
= 0;
1638 tab
->con
[r
].is_redundant
= 0;
1639 tab
->con
[r
].frozen
= 0;
1640 tab
->con
[r
].negated
= 0;
1641 tab
->row_var
[tab
->n_row
] = ~r
;
1645 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]) < 0)
1651 /* Add a variable to the tableau and allocate a column for it.
1652 * Return the index into the variable array "var".
1654 int isl_tab_allocate_var(struct isl_tab
*tab
)
1658 unsigned off
= 2 + tab
->M
;
1660 isl_assert(tab
->mat
->ctx
, tab
->n_col
< tab
->mat
->n_col
, return -1);
1661 isl_assert(tab
->mat
->ctx
, tab
->n_var
< tab
->max_var
, return -1);
1664 tab
->var
[r
].index
= tab
->n_col
;
1665 tab
->var
[r
].is_row
= 0;
1666 tab
->var
[r
].is_nonneg
= 0;
1667 tab
->var
[r
].is_zero
= 0;
1668 tab
->var
[r
].is_redundant
= 0;
1669 tab
->var
[r
].frozen
= 0;
1670 tab
->var
[r
].negated
= 0;
1671 tab
->col_var
[tab
->n_col
] = r
;
1673 for (i
= 0; i
< tab
->n_row
; ++i
)
1674 isl_int_set_si(tab
->mat
->row
[i
][off
+ tab
->n_col
], 0);
1678 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->var
[r
]) < 0)
1684 /* Add a row to the tableau. The row is given as an affine combination
1685 * of the original variables and needs to be expressed in terms of the
1688 * We add each term in turn.
1689 * If r = n/d_r is the current sum and we need to add k x, then
1690 * if x is a column variable, we increase the numerator of
1691 * this column by k d_r
1692 * if x = f/d_x is a row variable, then the new representation of r is
1694 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1695 * --- + --- = ------------------- = -------------------
1696 * d_r d_r d_r d_x/g m
1698 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1700 * If tab->M is set, then, internally, each variable x is represented
1701 * as x' - M. We then also need no subtract k d_r from the coefficient of M.
1703 int isl_tab_add_row(struct isl_tab
*tab
, isl_int
*line
)
1709 unsigned off
= 2 + tab
->M
;
1711 r
= isl_tab_allocate_con(tab
);
1717 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1718 isl_int_set_si(row
[0], 1);
1719 isl_int_set(row
[1], line
[0]);
1720 isl_seq_clr(row
+ 2, tab
->M
+ tab
->n_col
);
1721 for (i
= 0; i
< tab
->n_var
; ++i
) {
1722 if (tab
->var
[i
].is_zero
)
1724 if (tab
->var
[i
].is_row
) {
1726 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1727 isl_int_swap(a
, row
[0]);
1728 isl_int_divexact(a
, row
[0], a
);
1730 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1731 isl_int_mul(b
, b
, line
[1 + i
]);
1732 isl_seq_combine(row
+ 1, a
, row
+ 1,
1733 b
, tab
->mat
->row
[tab
->var
[i
].index
] + 1,
1734 1 + tab
->M
+ tab
->n_col
);
1736 isl_int_addmul(row
[off
+ tab
->var
[i
].index
],
1737 line
[1 + i
], row
[0]);
1738 if (tab
->M
&& i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
1739 isl_int_submul(row
[2], line
[1 + i
], row
[0]);
1741 isl_seq_normalize(tab
->mat
->ctx
, row
, off
+ tab
->n_col
);
1746 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_unknown
;
1751 static int drop_row(struct isl_tab
*tab
, int row
)
1753 isl_assert(tab
->mat
->ctx
, ~tab
->row_var
[row
] == tab
->n_con
- 1, return -1);
1754 if (row
!= tab
->n_row
- 1)
1755 swap_rows(tab
, row
, tab
->n_row
- 1);
1761 static int drop_col(struct isl_tab
*tab
, int col
)
1763 isl_assert(tab
->mat
->ctx
, tab
->col_var
[col
] == tab
->n_var
- 1, return -1);
1764 if (col
!= tab
->n_col
- 1)
1765 swap_cols(tab
, col
, tab
->n_col
- 1);
1771 /* Add inequality "ineq" and check if it conflicts with the
1772 * previously added constraints or if it is obviously redundant.
1774 int isl_tab_add_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1783 struct isl_basic_map
*bmap
= tab
->bmap
;
1785 isl_assert(tab
->mat
->ctx
, tab
->n_eq
== bmap
->n_eq
, return -1);
1786 isl_assert(tab
->mat
->ctx
,
1787 tab
->n_con
== bmap
->n_eq
+ bmap
->n_ineq
, return -1);
1788 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, ineq
);
1789 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1796 isl_int_swap(ineq
[0], cst
);
1798 r
= isl_tab_add_row(tab
, ineq
);
1800 isl_int_swap(ineq
[0], cst
);
1805 tab
->con
[r
].is_nonneg
= 1;
1806 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1808 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1809 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1814 sgn
= restore_row(tab
, &tab
->con
[r
]);
1818 return isl_tab_mark_empty(tab
);
1819 if (tab
->con
[r
].is_row
&& isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1820 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1825 /* Pivot a non-negative variable down until it reaches the value zero
1826 * and then pivot the variable into a column position.
1828 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
1829 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1833 unsigned off
= 2 + tab
->M
;
1838 while (isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1839 find_pivot(tab
, var
, NULL
, -1, &row
, &col
);
1840 isl_assert(tab
->mat
->ctx
, row
!= -1, return -1);
1841 if (isl_tab_pivot(tab
, row
, col
) < 0)
1847 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
)
1848 if (!isl_int_is_zero(tab
->mat
->row
[var
->index
][off
+ i
]))
1851 isl_assert(tab
->mat
->ctx
, i
< tab
->n_col
, return -1);
1852 if (isl_tab_pivot(tab
, var
->index
, i
) < 0)
1858 /* We assume Gaussian elimination has been performed on the equalities.
1859 * The equalities can therefore never conflict.
1860 * Adding the equalities is currently only really useful for a later call
1861 * to isl_tab_ineq_type.
1863 static struct isl_tab
*add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1870 r
= isl_tab_add_row(tab
, eq
);
1874 r
= tab
->con
[r
].index
;
1875 i
= isl_seq_first_non_zero(tab
->mat
->row
[r
] + 2 + tab
->M
+ tab
->n_dead
,
1876 tab
->n_col
- tab
->n_dead
);
1877 isl_assert(tab
->mat
->ctx
, i
>= 0, goto error
);
1879 if (isl_tab_pivot(tab
, r
, i
) < 0)
1881 if (isl_tab_kill_col(tab
, i
) < 0)
1891 static int row_is_manifestly_zero(struct isl_tab
*tab
, int row
)
1893 unsigned off
= 2 + tab
->M
;
1895 if (!isl_int_is_zero(tab
->mat
->row
[row
][1]))
1897 if (tab
->M
&& !isl_int_is_zero(tab
->mat
->row
[row
][2]))
1899 return isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1900 tab
->n_col
- tab
->n_dead
) == -1;
1903 /* Add an equality that is known to be valid for the given tableau.
1905 int isl_tab_add_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1907 struct isl_tab_var
*var
;
1912 r
= isl_tab_add_row(tab
, eq
);
1918 if (row_is_manifestly_zero(tab
, r
)) {
1920 if (isl_tab_mark_redundant(tab
, r
) < 0)
1925 if (isl_int_is_neg(tab
->mat
->row
[r
][1])) {
1926 isl_seq_neg(tab
->mat
->row
[r
] + 1, tab
->mat
->row
[r
] + 1,
1931 if (to_col(tab
, var
) < 0)
1934 if (isl_tab_kill_col(tab
, var
->index
) < 0)
1940 static int add_zero_row(struct isl_tab
*tab
)
1945 r
= isl_tab_allocate_con(tab
);
1949 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1950 isl_seq_clr(row
+ 1, 1 + tab
->M
+ tab
->n_col
);
1951 isl_int_set_si(row
[0], 1);
1956 /* Add equality "eq" and check if it conflicts with the
1957 * previously added constraints or if it is obviously redundant.
1959 int isl_tab_add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1961 struct isl_tab_undo
*snap
= NULL
;
1962 struct isl_tab_var
*var
;
1970 isl_assert(tab
->mat
->ctx
, !tab
->M
, return -1);
1973 snap
= isl_tab_snap(tab
);
1977 isl_int_swap(eq
[0], cst
);
1979 r
= isl_tab_add_row(tab
, eq
);
1981 isl_int_swap(eq
[0], cst
);
1989 if (row_is_manifestly_zero(tab
, row
)) {
1991 if (isl_tab_rollback(tab
, snap
) < 0)
1999 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
2000 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
2002 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
2003 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
2004 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
2005 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
2009 if (add_zero_row(tab
) < 0)
2013 sgn
= isl_int_sgn(tab
->mat
->row
[row
][1]);
2016 isl_seq_neg(tab
->mat
->row
[row
] + 1, tab
->mat
->row
[row
] + 1,
2023 sgn
= sign_of_max(tab
, var
);
2027 if (isl_tab_mark_empty(tab
) < 0)
2034 if (to_col(tab
, var
) < 0)
2037 if (isl_tab_kill_col(tab
, var
->index
) < 0)
2043 /* Construct and return an inequality that expresses an upper bound
2045 * In particular, if the div is given by
2049 * then the inequality expresses
2053 static struct isl_vec
*ineq_for_div(struct isl_basic_map
*bmap
, unsigned div
)
2057 struct isl_vec
*ineq
;
2062 total
= isl_basic_map_total_dim(bmap
);
2063 div_pos
= 1 + total
- bmap
->n_div
+ div
;
2065 ineq
= isl_vec_alloc(bmap
->ctx
, 1 + total
);
2069 isl_seq_cpy(ineq
->el
, bmap
->div
[div
] + 1, 1 + total
);
2070 isl_int_neg(ineq
->el
[div_pos
], bmap
->div
[div
][0]);
2074 /* For a div d = floor(f/m), add the constraints
2077 * -(f-(m-1)) + m d >= 0
2079 * Note that the second constraint is the negation of
2083 * If add_ineq is not NULL, then this function is used
2084 * instead of isl_tab_add_ineq to effectively add the inequalities.
2086 static int add_div_constraints(struct isl_tab
*tab
, unsigned div
,
2087 int (*add_ineq
)(void *user
, isl_int
*), void *user
)
2091 struct isl_vec
*ineq
;
2093 total
= isl_basic_map_total_dim(tab
->bmap
);
2094 div_pos
= 1 + total
- tab
->bmap
->n_div
+ div
;
2096 ineq
= ineq_for_div(tab
->bmap
, div
);
2101 if (add_ineq(user
, ineq
->el
) < 0)
2104 if (isl_tab_add_ineq(tab
, ineq
->el
) < 0)
2108 isl_seq_neg(ineq
->el
, tab
->bmap
->div
[div
] + 1, 1 + total
);
2109 isl_int_set(ineq
->el
[div_pos
], tab
->bmap
->div
[div
][0]);
2110 isl_int_add(ineq
->el
[0], ineq
->el
[0], ineq
->el
[div_pos
]);
2111 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
2114 if (add_ineq(user
, ineq
->el
) < 0)
2117 if (isl_tab_add_ineq(tab
, ineq
->el
) < 0)
2129 /* Check whether the div described by "div" is obviously non-negative.
2130 * If we are using a big parameter, then we will encode the div
2131 * as div' = M + div, which is always non-negative.
2132 * Otherwise, we check whether div is a non-negative affine combination
2133 * of non-negative variables.
2135 static int div_is_nonneg(struct isl_tab
*tab
, __isl_keep isl_vec
*div
)
2142 if (isl_int_is_neg(div
->el
[1]))
2145 for (i
= 0; i
< tab
->n_var
; ++i
) {
2146 if (isl_int_is_neg(div
->el
[2 + i
]))
2148 if (isl_int_is_zero(div
->el
[2 + i
]))
2150 if (!tab
->var
[i
].is_nonneg
)
2157 /* Add an extra div, prescribed by "div" to the tableau and
2158 * the associated bmap (which is assumed to be non-NULL).
2160 * If add_ineq is not NULL, then this function is used instead
2161 * of isl_tab_add_ineq to add the div constraints.
2162 * This complication is needed because the code in isl_tab_pip
2163 * wants to perform some extra processing when an inequality
2164 * is added to the tableau.
2166 int isl_tab_add_div(struct isl_tab
*tab
, __isl_keep isl_vec
*div
,
2167 int (*add_ineq
)(void *user
, isl_int
*), void *user
)
2176 isl_assert(tab
->mat
->ctx
, tab
->bmap
, return -1);
2178 nonneg
= div_is_nonneg(tab
, div
);
2180 if (isl_tab_extend_cons(tab
, 3) < 0)
2182 if (isl_tab_extend_vars(tab
, 1) < 0)
2184 r
= isl_tab_allocate_var(tab
);
2189 tab
->var
[r
].is_nonneg
= 1;
2191 tab
->bmap
= isl_basic_map_extend_space(tab
->bmap
,
2192 isl_basic_map_get_space(tab
->bmap
), 1, 0, 2);
2193 k
= isl_basic_map_alloc_div(tab
->bmap
);
2196 isl_seq_cpy(tab
->bmap
->div
[k
], div
->el
, div
->size
);
2197 if (isl_tab_push(tab
, isl_tab_undo_bmap_div
) < 0)
2200 if (add_div_constraints(tab
, k
, add_ineq
, user
) < 0)
2206 /* If "track" is set, then we want to keep track of all constraints in tab
2207 * in its bmap field. This field is initialized from a copy of "bmap",
2208 * so we need to make sure that all constraints in "bmap" also appear
2209 * in the constructed tab.
2211 __isl_give
struct isl_tab
*isl_tab_from_basic_map(
2212 __isl_keep isl_basic_map
*bmap
, int track
)
2215 struct isl_tab
*tab
;
2219 tab
= isl_tab_alloc(bmap
->ctx
,
2220 isl_basic_map_total_dim(bmap
) + bmap
->n_ineq
+ 1,
2221 isl_basic_map_total_dim(bmap
), 0);
2224 tab
->preserve
= track
;
2225 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
2226 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
2227 if (isl_tab_mark_empty(tab
) < 0)
2231 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2232 tab
= add_eq(tab
, bmap
->eq
[i
]);
2236 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2237 if (isl_tab_add_ineq(tab
, bmap
->ineq
[i
]) < 0)
2243 if (track
&& isl_tab_track_bmap(tab
, isl_basic_map_copy(bmap
)) < 0)
2251 __isl_give
struct isl_tab
*isl_tab_from_basic_set(
2252 __isl_keep isl_basic_set
*bset
, int track
)
2254 return isl_tab_from_basic_map(bset
, track
);
2257 /* Construct a tableau corresponding to the recession cone of "bset".
2259 struct isl_tab
*isl_tab_from_recession_cone(__isl_keep isl_basic_set
*bset
,
2264 struct isl_tab
*tab
;
2265 unsigned offset
= 0;
2270 offset
= isl_basic_set_dim(bset
, isl_dim_param
);
2271 tab
= isl_tab_alloc(bset
->ctx
, bset
->n_eq
+ bset
->n_ineq
,
2272 isl_basic_set_total_dim(bset
) - offset
, 0);
2275 tab
->rational
= ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
);
2279 for (i
= 0; i
< bset
->n_eq
; ++i
) {
2280 isl_int_swap(bset
->eq
[i
][offset
], cst
);
2282 if (isl_tab_add_eq(tab
, bset
->eq
[i
] + offset
) < 0)
2285 tab
= add_eq(tab
, bset
->eq
[i
]);
2286 isl_int_swap(bset
->eq
[i
][offset
], cst
);
2290 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2292 isl_int_swap(bset
->ineq
[i
][offset
], cst
);
2293 r
= isl_tab_add_row(tab
, bset
->ineq
[i
] + offset
);
2294 isl_int_swap(bset
->ineq
[i
][offset
], cst
);
2297 tab
->con
[r
].is_nonneg
= 1;
2298 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2310 /* Assuming "tab" is the tableau of a cone, check if the cone is
2311 * bounded, i.e., if it is empty or only contains the origin.
2313 int isl_tab_cone_is_bounded(struct isl_tab
*tab
)
2321 if (tab
->n_dead
== tab
->n_col
)
2325 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2326 struct isl_tab_var
*var
;
2328 var
= isl_tab_var_from_row(tab
, i
);
2329 if (!var
->is_nonneg
)
2331 sgn
= sign_of_max(tab
, var
);
2336 if (close_row(tab
, var
) < 0)
2340 if (tab
->n_dead
== tab
->n_col
)
2342 if (i
== tab
->n_row
)
2347 int isl_tab_sample_is_integer(struct isl_tab
*tab
)
2354 for (i
= 0; i
< tab
->n_var
; ++i
) {
2356 if (!tab
->var
[i
].is_row
)
2358 row
= tab
->var
[i
].index
;
2359 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
2360 tab
->mat
->row
[row
][0]))
2366 static struct isl_vec
*extract_integer_sample(struct isl_tab
*tab
)
2369 struct isl_vec
*vec
;
2371 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2375 isl_int_set_si(vec
->block
.data
[0], 1);
2376 for (i
= 0; i
< tab
->n_var
; ++i
) {
2377 if (!tab
->var
[i
].is_row
)
2378 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
2380 int row
= tab
->var
[i
].index
;
2381 isl_int_divexact(vec
->block
.data
[1 + i
],
2382 tab
->mat
->row
[row
][1], tab
->mat
->row
[row
][0]);
2389 struct isl_vec
*isl_tab_get_sample_value(struct isl_tab
*tab
)
2392 struct isl_vec
*vec
;
2398 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2404 isl_int_set_si(vec
->block
.data
[0], 1);
2405 for (i
= 0; i
< tab
->n_var
; ++i
) {
2407 if (!tab
->var
[i
].is_row
) {
2408 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
2411 row
= tab
->var
[i
].index
;
2412 isl_int_gcd(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
2413 isl_int_divexact(m
, tab
->mat
->row
[row
][0], m
);
2414 isl_seq_scale(vec
->block
.data
, vec
->block
.data
, m
, 1 + i
);
2415 isl_int_divexact(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
2416 isl_int_mul(vec
->block
.data
[1 + i
], m
, tab
->mat
->row
[row
][1]);
2418 vec
= isl_vec_normalize(vec
);
2424 /* Update "bmap" based on the results of the tableau "tab".
2425 * In particular, implicit equalities are made explicit, redundant constraints
2426 * are removed and if the sample value happens to be integer, it is stored
2427 * in "bmap" (unless "bmap" already had an integer sample).
2429 * The tableau is assumed to have been created from "bmap" using
2430 * isl_tab_from_basic_map.
2432 struct isl_basic_map
*isl_basic_map_update_from_tab(struct isl_basic_map
*bmap
,
2433 struct isl_tab
*tab
)
2445 bmap
= isl_basic_map_set_to_empty(bmap
);
2447 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
2448 if (isl_tab_is_equality(tab
, n_eq
+ i
))
2449 isl_basic_map_inequality_to_equality(bmap
, i
);
2450 else if (isl_tab_is_redundant(tab
, n_eq
+ i
))
2451 isl_basic_map_drop_inequality(bmap
, i
);
2453 if (bmap
->n_eq
!= n_eq
)
2454 isl_basic_map_gauss(bmap
, NULL
);
2455 if (!tab
->rational
&&
2456 !bmap
->sample
&& isl_tab_sample_is_integer(tab
))
2457 bmap
->sample
= extract_integer_sample(tab
);
2461 struct isl_basic_set
*isl_basic_set_update_from_tab(struct isl_basic_set
*bset
,
2462 struct isl_tab
*tab
)
2464 return (struct isl_basic_set
*)isl_basic_map_update_from_tab(
2465 (struct isl_basic_map
*)bset
, tab
);
2468 /* Given a non-negative variable "var", add a new non-negative variable
2469 * that is the opposite of "var", ensuring that var can only attain the
2471 * If var = n/d is a row variable, then the new variable = -n/d.
2472 * If var is a column variables, then the new variable = -var.
2473 * If the new variable cannot attain non-negative values, then
2474 * the resulting tableau is empty.
2475 * Otherwise, we know the value will be zero and we close the row.
2477 static int cut_to_hyperplane(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2482 unsigned off
= 2 + tab
->M
;
2486 isl_assert(tab
->mat
->ctx
, !var
->is_redundant
, return -1);
2487 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return -1);
2489 if (isl_tab_extend_cons(tab
, 1) < 0)
2493 tab
->con
[r
].index
= tab
->n_row
;
2494 tab
->con
[r
].is_row
= 1;
2495 tab
->con
[r
].is_nonneg
= 0;
2496 tab
->con
[r
].is_zero
= 0;
2497 tab
->con
[r
].is_redundant
= 0;
2498 tab
->con
[r
].frozen
= 0;
2499 tab
->con
[r
].negated
= 0;
2500 tab
->row_var
[tab
->n_row
] = ~r
;
2501 row
= tab
->mat
->row
[tab
->n_row
];
2504 isl_int_set(row
[0], tab
->mat
->row
[var
->index
][0]);
2505 isl_seq_neg(row
+ 1,
2506 tab
->mat
->row
[var
->index
] + 1, 1 + tab
->n_col
);
2508 isl_int_set_si(row
[0], 1);
2509 isl_seq_clr(row
+ 1, 1 + tab
->n_col
);
2510 isl_int_set_si(row
[off
+ var
->index
], -1);
2515 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]) < 0)
2518 sgn
= sign_of_max(tab
, &tab
->con
[r
]);
2522 if (isl_tab_mark_empty(tab
) < 0)
2526 tab
->con
[r
].is_nonneg
= 1;
2527 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2530 if (close_row(tab
, &tab
->con
[r
]) < 0)
2536 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2537 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2538 * by r' = r + 1 >= 0.
2539 * If r is a row variable, we simply increase the constant term by one
2540 * (taking into account the denominator).
2541 * If r is a column variable, then we need to modify each row that
2542 * refers to r = r' - 1 by substituting this equality, effectively
2543 * subtracting the coefficient of the column from the constant.
2544 * We should only do this if the minimum is manifestly unbounded,
2545 * however. Otherwise, we may end up with negative sample values
2546 * for non-negative variables.
2547 * So, if r is a column variable with a minimum that is not
2548 * manifestly unbounded, then we need to move it to a row.
2549 * However, the sample value of this row may be negative,
2550 * even after the relaxation, so we need to restore it.
2551 * We therefore prefer to pivot a column up to a row, if possible.
2553 struct isl_tab
*isl_tab_relax(struct isl_tab
*tab
, int con
)
2555 struct isl_tab_var
*var
;
2556 unsigned off
= 2 + tab
->M
;
2561 var
= &tab
->con
[con
];
2563 if (var
->is_row
&& (var
->index
< 0 || var
->index
< tab
->n_redundant
))
2564 isl_die(tab
->mat
->ctx
, isl_error_invalid
,
2565 "cannot relax redundant constraint", goto error
);
2566 if (!var
->is_row
&& (var
->index
< 0 || var
->index
< tab
->n_dead
))
2567 isl_die(tab
->mat
->ctx
, isl_error_invalid
,
2568 "cannot relax dead constraint", goto error
);
2570 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
2571 if (to_row(tab
, var
, 1) < 0)
2573 if (!var
->is_row
&& !min_is_manifestly_unbounded(tab
, var
))
2574 if (to_row(tab
, var
, -1) < 0)
2578 isl_int_add(tab
->mat
->row
[var
->index
][1],
2579 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
2580 if (restore_row(tab
, var
) < 0)
2585 for (i
= 0; i
< tab
->n_row
; ++i
) {
2586 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2588 isl_int_sub(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
2589 tab
->mat
->row
[i
][off
+ var
->index
]);
2594 if (isl_tab_push_var(tab
, isl_tab_undo_relax
, var
) < 0)
2603 int isl_tab_select_facet(struct isl_tab
*tab
, int con
)
2608 return cut_to_hyperplane(tab
, &tab
->con
[con
]);
2611 static int may_be_equality(struct isl_tab
*tab
, int row
)
2613 return tab
->rational
? isl_int_is_zero(tab
->mat
->row
[row
][1])
2614 : isl_int_lt(tab
->mat
->row
[row
][1],
2615 tab
->mat
->row
[row
][0]);
2618 /* Check for (near) equalities among the constraints.
2619 * A constraint is an equality if it is non-negative and if
2620 * its maximal value is either
2621 * - zero (in case of rational tableaus), or
2622 * - strictly less than 1 (in case of integer tableaus)
2624 * We first mark all non-redundant and non-dead variables that
2625 * are not frozen and not obviously not an equality.
2626 * Then we iterate over all marked variables if they can attain
2627 * any values larger than zero or at least one.
2628 * If the maximal value is zero, we mark any column variables
2629 * that appear in the row as being zero and mark the row as being redundant.
2630 * Otherwise, if the maximal value is strictly less than one (and the
2631 * tableau is integer), then we restrict the value to being zero
2632 * by adding an opposite non-negative variable.
2634 int isl_tab_detect_implicit_equalities(struct isl_tab
*tab
)
2643 if (tab
->n_dead
== tab
->n_col
)
2647 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2648 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2649 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2650 may_be_equality(tab
, i
);
2654 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2655 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2656 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2661 struct isl_tab_var
*var
;
2663 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2664 var
= isl_tab_var_from_row(tab
, i
);
2668 if (i
== tab
->n_row
) {
2669 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2670 var
= var_from_col(tab
, i
);
2674 if (i
== tab
->n_col
)
2679 sgn
= sign_of_max(tab
, var
);
2683 if (close_row(tab
, var
) < 0)
2685 } else if (!tab
->rational
&& !at_least_one(tab
, var
)) {
2686 if (cut_to_hyperplane(tab
, var
) < 0)
2688 return isl_tab_detect_implicit_equalities(tab
);
2690 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2691 var
= isl_tab_var_from_row(tab
, i
);
2694 if (may_be_equality(tab
, i
))
2704 /* Update the element of row_var or col_var that corresponds to
2705 * constraint tab->con[i] to a move from position "old" to position "i".
2707 static int update_con_after_move(struct isl_tab
*tab
, int i
, int old
)
2712 index
= tab
->con
[i
].index
;
2715 p
= tab
->con
[i
].is_row
? tab
->row_var
: tab
->col_var
;
2716 if (p
[index
] != ~old
)
2717 isl_die(tab
->mat
->ctx
, isl_error_internal
,
2718 "broken internal state", return -1);
2724 /* Rotate the "n" constraints starting at "first" to the right,
2725 * putting the last constraint in the position of the first constraint.
2727 static int rotate_constraints(struct isl_tab
*tab
, int first
, int n
)
2730 struct isl_tab_var var
;
2735 last
= first
+ n
- 1;
2736 var
= tab
->con
[last
];
2737 for (i
= last
; i
> first
; --i
) {
2738 tab
->con
[i
] = tab
->con
[i
- 1];
2739 if (update_con_after_move(tab
, i
, i
- 1) < 0)
2742 tab
->con
[first
] = var
;
2743 if (update_con_after_move(tab
, first
, last
) < 0)
2749 /* Make the equalities that are implicit in "bmap" but that have been
2750 * detected in the corresponding "tab" explicit in "bmap" and update
2751 * "tab" to reflect the new order of the constraints.
2753 * In particular, if inequality i is an implicit equality then
2754 * isl_basic_map_inequality_to_equality will move the inequality
2755 * in front of the other equality and it will move the last inequality
2756 * in the position of inequality i.
2757 * In the tableau, the inequalities of "bmap" are stored after the equalities
2758 * and so the original order
2760 * E E E E E A A A I B B B B L
2764 * I E E E E E A A A L B B B B
2766 * where I is the implicit equality, the E are equalities,
2767 * the A inequalities before I, the B inequalities after I and
2768 * L the last inequality.
2769 * We therefore need to rotate to the right two sets of constraints,
2770 * those up to and including I and those after I.
2772 * If "tab" contains any constraints that are not in "bmap" then they
2773 * appear after those in "bmap" and they should be left untouched.
2775 * Note that this function leaves "bmap" in a temporary state
2776 * as it does not call isl_basic_map_gauss. Calling this function
2777 * is the responsibility of the caller.
2779 __isl_give isl_basic_map
*isl_tab_make_equalities_explicit(struct isl_tab
*tab
,
2780 __isl_take isl_basic_map
*bmap
)
2785 return isl_basic_map_free(bmap
);
2789 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
2790 if (!isl_tab_is_equality(tab
, bmap
->n_eq
+ i
))
2792 isl_basic_map_inequality_to_equality(bmap
, i
);
2793 if (rotate_constraints(tab
, 0, tab
->n_eq
+ i
+ 1) < 0)
2794 return isl_basic_map_free(bmap
);
2795 if (rotate_constraints(tab
, tab
->n_eq
+ i
+ 1,
2796 bmap
->n_ineq
- i
) < 0)
2797 return isl_basic_map_free(bmap
);
2804 static int con_is_redundant(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2808 if (tab
->rational
) {
2809 int sgn
= sign_of_min(tab
, var
);
2814 int irred
= isl_tab_min_at_most_neg_one(tab
, var
);
2821 /* Check for (near) redundant constraints.
2822 * A constraint is redundant if it is non-negative and if
2823 * its minimal value (temporarily ignoring the non-negativity) is either
2824 * - zero (in case of rational tableaus), or
2825 * - strictly larger than -1 (in case of integer tableaus)
2827 * We first mark all non-redundant and non-dead variables that
2828 * are not frozen and not obviously negatively unbounded.
2829 * Then we iterate over all marked variables if they can attain
2830 * any values smaller than zero or at most negative one.
2831 * If not, we mark the row as being redundant (assuming it hasn't
2832 * been detected as being obviously redundant in the mean time).
2834 int isl_tab_detect_redundant(struct isl_tab
*tab
)
2843 if (tab
->n_redundant
== tab
->n_row
)
2847 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2848 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2849 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2853 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2854 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2855 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2856 !min_is_manifestly_unbounded(tab
, var
);
2861 struct isl_tab_var
*var
;
2863 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2864 var
= isl_tab_var_from_row(tab
, i
);
2868 if (i
== tab
->n_row
) {
2869 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2870 var
= var_from_col(tab
, i
);
2874 if (i
== tab
->n_col
)
2879 red
= con_is_redundant(tab
, var
);
2882 if (red
&& !var
->is_redundant
)
2883 if (isl_tab_mark_redundant(tab
, var
->index
) < 0)
2885 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2886 var
= var_from_col(tab
, i
);
2889 if (!min_is_manifestly_unbounded(tab
, var
))
2899 int isl_tab_is_equality(struct isl_tab
*tab
, int con
)
2906 if (tab
->con
[con
].is_zero
)
2908 if (tab
->con
[con
].is_redundant
)
2910 if (!tab
->con
[con
].is_row
)
2911 return tab
->con
[con
].index
< tab
->n_dead
;
2913 row
= tab
->con
[con
].index
;
2916 return isl_int_is_zero(tab
->mat
->row
[row
][1]) &&
2917 (!tab
->M
|| isl_int_is_zero(tab
->mat
->row
[row
][2])) &&
2918 isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
2919 tab
->n_col
- tab
->n_dead
) == -1;
2922 /* Return the minimal value of the affine expression "f" with denominator
2923 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
2924 * the expression cannot attain arbitrarily small values.
2925 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
2926 * The return value reflects the nature of the result (empty, unbounded,
2927 * minimal value returned in *opt).
2929 enum isl_lp_result
isl_tab_min(struct isl_tab
*tab
,
2930 isl_int
*f
, isl_int denom
, isl_int
*opt
, isl_int
*opt_denom
,
2934 enum isl_lp_result res
= isl_lp_ok
;
2935 struct isl_tab_var
*var
;
2936 struct isl_tab_undo
*snap
;
2939 return isl_lp_error
;
2942 return isl_lp_empty
;
2944 snap
= isl_tab_snap(tab
);
2945 r
= isl_tab_add_row(tab
, f
);
2947 return isl_lp_error
;
2951 find_pivot(tab
, var
, var
, -1, &row
, &col
);
2952 if (row
== var
->index
) {
2953 res
= isl_lp_unbounded
;
2958 if (isl_tab_pivot(tab
, row
, col
) < 0)
2959 return isl_lp_error
;
2961 isl_int_mul(tab
->mat
->row
[var
->index
][0],
2962 tab
->mat
->row
[var
->index
][0], denom
);
2963 if (ISL_FL_ISSET(flags
, ISL_TAB_SAVE_DUAL
)) {
2966 isl_vec_free(tab
->dual
);
2967 tab
->dual
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_con
);
2969 return isl_lp_error
;
2970 isl_int_set(tab
->dual
->el
[0], tab
->mat
->row
[var
->index
][0]);
2971 for (i
= 0; i
< tab
->n_con
; ++i
) {
2973 if (tab
->con
[i
].is_row
) {
2974 isl_int_set_si(tab
->dual
->el
[1 + i
], 0);
2977 pos
= 2 + tab
->M
+ tab
->con
[i
].index
;
2978 if (tab
->con
[i
].negated
)
2979 isl_int_neg(tab
->dual
->el
[1 + i
],
2980 tab
->mat
->row
[var
->index
][pos
]);
2982 isl_int_set(tab
->dual
->el
[1 + i
],
2983 tab
->mat
->row
[var
->index
][pos
]);
2986 if (opt
&& res
== isl_lp_ok
) {
2988 isl_int_set(*opt
, tab
->mat
->row
[var
->index
][1]);
2989 isl_int_set(*opt_denom
, tab
->mat
->row
[var
->index
][0]);
2991 isl_int_cdiv_q(*opt
, tab
->mat
->row
[var
->index
][1],
2992 tab
->mat
->row
[var
->index
][0]);
2994 if (isl_tab_rollback(tab
, snap
) < 0)
2995 return isl_lp_error
;
2999 int isl_tab_is_redundant(struct isl_tab
*tab
, int con
)
3003 if (tab
->con
[con
].is_zero
)
3005 if (tab
->con
[con
].is_redundant
)
3007 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
3010 /* Take a snapshot of the tableau that can be restored by s call to
3013 struct isl_tab_undo
*isl_tab_snap(struct isl_tab
*tab
)
3021 /* Undo the operation performed by isl_tab_relax.
3023 static int unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
3024 static int unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
)
3026 unsigned off
= 2 + tab
->M
;
3028 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
3029 if (to_row(tab
, var
, 1) < 0)
3033 isl_int_sub(tab
->mat
->row
[var
->index
][1],
3034 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
3035 if (var
->is_nonneg
) {
3036 int sgn
= restore_row(tab
, var
);
3037 isl_assert(tab
->mat
->ctx
, sgn
>= 0, return -1);
3042 for (i
= 0; i
< tab
->n_row
; ++i
) {
3043 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
3045 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
3046 tab
->mat
->row
[i
][off
+ var
->index
]);
3054 static int perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
) WARN_UNUSED
;
3055 static int perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
3057 struct isl_tab_var
*var
= var_from_index(tab
, undo
->u
.var_index
);
3058 switch (undo
->type
) {
3059 case isl_tab_undo_nonneg
:
3062 case isl_tab_undo_redundant
:
3063 var
->is_redundant
= 0;
3065 restore_row(tab
, isl_tab_var_from_row(tab
, tab
->n_redundant
));
3067 case isl_tab_undo_freeze
:
3070 case isl_tab_undo_zero
:
3075 case isl_tab_undo_allocate
:
3076 if (undo
->u
.var_index
>= 0) {
3077 isl_assert(tab
->mat
->ctx
, !var
->is_row
, return -1);
3078 drop_col(tab
, var
->index
);
3082 if (!max_is_manifestly_unbounded(tab
, var
)) {
3083 if (to_row(tab
, var
, 1) < 0)
3085 } else if (!min_is_manifestly_unbounded(tab
, var
)) {
3086 if (to_row(tab
, var
, -1) < 0)
3089 if (to_row(tab
, var
, 0) < 0)
3092 drop_row(tab
, var
->index
);
3094 case isl_tab_undo_relax
:
3095 return unrelax(tab
, var
);
3097 isl_die(tab
->mat
->ctx
, isl_error_internal
,
3098 "perform_undo_var called on invalid undo record",
3105 /* Restore the tableau to the state where the basic variables
3106 * are those in "col_var".
3107 * We first construct a list of variables that are currently in
3108 * the basis, but shouldn't. Then we iterate over all variables
3109 * that should be in the basis and for each one that is currently
3110 * not in the basis, we exchange it with one of the elements of the
3111 * list constructed before.
3112 * We can always find an appropriate variable to pivot with because
3113 * the current basis is mapped to the old basis by a non-singular
3114 * matrix and so we can never end up with a zero row.
3116 static int restore_basis(struct isl_tab
*tab
, int *col_var
)
3120 int *extra
= NULL
; /* current columns that contain bad stuff */
3121 unsigned off
= 2 + tab
->M
;
3123 extra
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
3126 for (i
= 0; i
< tab
->n_col
; ++i
) {
3127 for (j
= 0; j
< tab
->n_col
; ++j
)
3128 if (tab
->col_var
[i
] == col_var
[j
])
3132 extra
[n_extra
++] = i
;
3134 for (i
= 0; i
< tab
->n_col
&& n_extra
> 0; ++i
) {
3135 struct isl_tab_var
*var
;
3138 for (j
= 0; j
< tab
->n_col
; ++j
)
3139 if (col_var
[i
] == tab
->col_var
[j
])
3143 var
= var_from_index(tab
, col_var
[i
]);
3145 for (j
= 0; j
< n_extra
; ++j
)
3146 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+extra
[j
]]))
3148 isl_assert(tab
->mat
->ctx
, j
< n_extra
, goto error
);
3149 if (isl_tab_pivot(tab
, row
, extra
[j
]) < 0)
3151 extra
[j
] = extra
[--n_extra
];
3161 /* Remove all samples with index n or greater, i.e., those samples
3162 * that were added since we saved this number of samples in
3163 * isl_tab_save_samples.
3165 static void drop_samples_since(struct isl_tab
*tab
, int n
)
3169 for (i
= tab
->n_sample
- 1; i
>= 0 && tab
->n_sample
> n
; --i
) {
3170 if (tab
->sample_index
[i
] < n
)
3173 if (i
!= tab
->n_sample
- 1) {
3174 int t
= tab
->sample_index
[tab
->n_sample
-1];
3175 tab
->sample_index
[tab
->n_sample
-1] = tab
->sample_index
[i
];
3176 tab
->sample_index
[i
] = t
;
3177 isl_mat_swap_rows(tab
->samples
, tab
->n_sample
-1, i
);
3183 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
) WARN_UNUSED
;
3184 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
3186 switch (undo
->type
) {
3187 case isl_tab_undo_empty
:
3190 case isl_tab_undo_nonneg
:
3191 case isl_tab_undo_redundant
:
3192 case isl_tab_undo_freeze
:
3193 case isl_tab_undo_zero
:
3194 case isl_tab_undo_allocate
:
3195 case isl_tab_undo_relax
:
3196 return perform_undo_var(tab
, undo
);
3197 case isl_tab_undo_bmap_eq
:
3198 return isl_basic_map_free_equality(tab
->bmap
, 1);
3199 case isl_tab_undo_bmap_ineq
:
3200 return isl_basic_map_free_inequality(tab
->bmap
, 1);
3201 case isl_tab_undo_bmap_div
:
3202 if (isl_basic_map_free_div(tab
->bmap
, 1) < 0)
3205 tab
->samples
->n_col
--;
3207 case isl_tab_undo_saved_basis
:
3208 if (restore_basis(tab
, undo
->u
.col_var
) < 0)
3211 case isl_tab_undo_drop_sample
:
3214 case isl_tab_undo_saved_samples
:
3215 drop_samples_since(tab
, undo
->u
.n
);
3217 case isl_tab_undo_callback
:
3218 return undo
->u
.callback
->run(undo
->u
.callback
);
3220 isl_assert(tab
->mat
->ctx
, 0, return -1);
3225 /* Return the tableau to the state it was in when the snapshot "snap"
3228 int isl_tab_rollback(struct isl_tab
*tab
, struct isl_tab_undo
*snap
)
3230 struct isl_tab_undo
*undo
, *next
;
3236 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
3240 if (perform_undo(tab
, undo
) < 0) {
3246 free_undo_record(undo
);
3255 /* The given row "row" represents an inequality violated by all
3256 * points in the tableau. Check for some special cases of such
3257 * separating constraints.
3258 * In particular, if the row has been reduced to the constant -1,
3259 * then we know the inequality is adjacent (but opposite) to
3260 * an equality in the tableau.
3261 * If the row has been reduced to r = c*(-1 -r'), with r' an inequality
3262 * of the tableau and c a positive constant, then the inequality
3263 * is adjacent (but opposite) to the inequality r'.
3265 static enum isl_ineq_type
separation_type(struct isl_tab
*tab
, unsigned row
)
3268 unsigned off
= 2 + tab
->M
;
3271 return isl_ineq_separate
;
3273 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
3274 return isl_ineq_separate
;
3276 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
3277 tab
->n_col
- tab
->n_dead
);
3279 if (isl_int_is_negone(tab
->mat
->row
[row
][1]))
3280 return isl_ineq_adj_eq
;
3282 return isl_ineq_separate
;
3285 if (!isl_int_eq(tab
->mat
->row
[row
][1],
3286 tab
->mat
->row
[row
][off
+ tab
->n_dead
+ pos
]))
3287 return isl_ineq_separate
;
3289 pos
= isl_seq_first_non_zero(
3290 tab
->mat
->row
[row
] + off
+ tab
->n_dead
+ pos
+ 1,
3291 tab
->n_col
- tab
->n_dead
- pos
- 1);
3293 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
3296 /* Check the effect of inequality "ineq" on the tableau "tab".
3298 * isl_ineq_redundant: satisfied by all points in the tableau
3299 * isl_ineq_separate: satisfied by no point in the tableau
3300 * isl_ineq_cut: satisfied by some by not all points
3301 * isl_ineq_adj_eq: adjacent to an equality
3302 * isl_ineq_adj_ineq: adjacent to an inequality.
3304 enum isl_ineq_type
isl_tab_ineq_type(struct isl_tab
*tab
, isl_int
*ineq
)
3306 enum isl_ineq_type type
= isl_ineq_error
;
3307 struct isl_tab_undo
*snap
= NULL
;
3312 return isl_ineq_error
;
3314 if (isl_tab_extend_cons(tab
, 1) < 0)
3315 return isl_ineq_error
;
3317 snap
= isl_tab_snap(tab
);
3319 con
= isl_tab_add_row(tab
, ineq
);
3323 row
= tab
->con
[con
].index
;
3324 if (isl_tab_row_is_redundant(tab
, row
))
3325 type
= isl_ineq_redundant
;
3326 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
3328 isl_int_abs_ge(tab
->mat
->row
[row
][1],
3329 tab
->mat
->row
[row
][0]))) {
3330 int nonneg
= at_least_zero(tab
, &tab
->con
[con
]);
3334 type
= isl_ineq_cut
;
3336 type
= separation_type(tab
, row
);
3338 int red
= con_is_redundant(tab
, &tab
->con
[con
]);
3342 type
= isl_ineq_cut
;
3344 type
= isl_ineq_redundant
;
3347 if (isl_tab_rollback(tab
, snap
))
3348 return isl_ineq_error
;
3351 return isl_ineq_error
;
3354 int isl_tab_track_bmap(struct isl_tab
*tab
, __isl_take isl_basic_map
*bmap
)
3356 bmap
= isl_basic_map_cow(bmap
);
3361 bmap
= isl_basic_map_set_to_empty(bmap
);
3368 isl_assert(tab
->mat
->ctx
, tab
->n_eq
== bmap
->n_eq
, goto error
);
3369 isl_assert(tab
->mat
->ctx
,
3370 tab
->n_con
== bmap
->n_eq
+ bmap
->n_ineq
, goto error
);
3376 isl_basic_map_free(bmap
);
3380 int isl_tab_track_bset(struct isl_tab
*tab
, __isl_take isl_basic_set
*bset
)
3382 return isl_tab_track_bmap(tab
, (isl_basic_map
*)bset
);
3385 __isl_keep isl_basic_set
*isl_tab_peek_bset(struct isl_tab
*tab
)
3390 return (isl_basic_set
*)tab
->bmap
;
3393 static void isl_tab_print_internal(__isl_keep
struct isl_tab
*tab
,
3394 FILE *out
, int indent
)
3400 fprintf(out
, "%*snull tab\n", indent
, "");
3403 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
3404 tab
->n_redundant
, tab
->n_dead
);
3406 fprintf(out
, ", rational");
3408 fprintf(out
, ", empty");
3410 fprintf(out
, "%*s[", indent
, "");
3411 for (i
= 0; i
< tab
->n_var
; ++i
) {
3413 fprintf(out
, (i
== tab
->n_param
||
3414 i
== tab
->n_var
- tab
->n_div
) ? "; "
3416 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
3418 tab
->var
[i
].is_zero
? " [=0]" :
3419 tab
->var
[i
].is_redundant
? " [R]" : "");
3421 fprintf(out
, "]\n");
3422 fprintf(out
, "%*s[", indent
, "");
3423 for (i
= 0; i
< tab
->n_con
; ++i
) {
3426 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
3428 tab
->con
[i
].is_zero
? " [=0]" :
3429 tab
->con
[i
].is_redundant
? " [R]" : "");
3431 fprintf(out
, "]\n");
3432 fprintf(out
, "%*s[", indent
, "");
3433 for (i
= 0; i
< tab
->n_row
; ++i
) {
3434 const char *sign
= "";
3437 if (tab
->row_sign
) {
3438 if (tab
->row_sign
[i
] == isl_tab_row_unknown
)
3440 else if (tab
->row_sign
[i
] == isl_tab_row_neg
)
3442 else if (tab
->row_sign
[i
] == isl_tab_row_pos
)
3447 fprintf(out
, "r%d: %d%s%s", i
, tab
->row_var
[i
],
3448 isl_tab_var_from_row(tab
, i
)->is_nonneg
? " [>=0]" : "", sign
);
3450 fprintf(out
, "]\n");
3451 fprintf(out
, "%*s[", indent
, "");
3452 for (i
= 0; i
< tab
->n_col
; ++i
) {
3455 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
3456 var_from_col(tab
, i
)->is_nonneg
? " [>=0]" : "");
3458 fprintf(out
, "]\n");
3459 r
= tab
->mat
->n_row
;
3460 tab
->mat
->n_row
= tab
->n_row
;
3461 c
= tab
->mat
->n_col
;
3462 tab
->mat
->n_col
= 2 + tab
->M
+ tab
->n_col
;
3463 isl_mat_print_internal(tab
->mat
, out
, indent
);
3464 tab
->mat
->n_row
= r
;
3465 tab
->mat
->n_col
= c
;
3467 isl_basic_map_print_internal(tab
->bmap
, out
, indent
);
3470 void isl_tab_dump(__isl_keep
struct isl_tab
*tab
)
3472 isl_tab_print_internal(tab
, stderr
, 0);