2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the MIT license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 #include <isl_ctx_private.h>
11 #include <isl_mat_private.h>
12 #include "isl_map_private.h"
15 #include <isl_config.h>
18 * The implementation of tableaus in this file was inspired by Section 8
19 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
20 * prover for program checking".
23 struct isl_tab
*isl_tab_alloc(struct isl_ctx
*ctx
,
24 unsigned n_row
, unsigned n_var
, unsigned M
)
30 tab
= isl_calloc_type(ctx
, struct isl_tab
);
33 tab
->mat
= isl_mat_alloc(ctx
, n_row
, off
+ n_var
);
36 tab
->var
= isl_alloc_array(ctx
, struct isl_tab_var
, n_var
);
39 tab
->con
= isl_alloc_array(ctx
, struct isl_tab_var
, n_row
);
42 tab
->col_var
= isl_alloc_array(ctx
, int, n_var
);
45 tab
->row_var
= isl_alloc_array(ctx
, int, n_row
);
48 for (i
= 0; i
< n_var
; ++i
) {
49 tab
->var
[i
].index
= i
;
50 tab
->var
[i
].is_row
= 0;
51 tab
->var
[i
].is_nonneg
= 0;
52 tab
->var
[i
].is_zero
= 0;
53 tab
->var
[i
].is_redundant
= 0;
54 tab
->var
[i
].frozen
= 0;
55 tab
->var
[i
].negated
= 0;
69 tab
->strict_redundant
= 0;
76 tab
->bottom
.type
= isl_tab_undo_bottom
;
77 tab
->bottom
.next
= NULL
;
78 tab
->top
= &tab
->bottom
;
90 int isl_tab_extend_cons(struct isl_tab
*tab
, unsigned n_new
)
99 if (tab
->max_con
< tab
->n_con
+ n_new
) {
100 struct isl_tab_var
*con
;
102 con
= isl_realloc_array(tab
->mat
->ctx
, tab
->con
,
103 struct isl_tab_var
, tab
->max_con
+ n_new
);
107 tab
->max_con
+= n_new
;
109 if (tab
->mat
->n_row
< tab
->n_row
+ n_new
) {
112 tab
->mat
= isl_mat_extend(tab
->mat
,
113 tab
->n_row
+ n_new
, off
+ tab
->n_col
);
116 row_var
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_var
,
117 int, tab
->mat
->n_row
);
120 tab
->row_var
= row_var
;
122 enum isl_tab_row_sign
*s
;
123 s
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_sign
,
124 enum isl_tab_row_sign
, tab
->mat
->n_row
);
133 /* Make room for at least n_new extra variables.
134 * Return -1 if anything went wrong.
136 int isl_tab_extend_vars(struct isl_tab
*tab
, unsigned n_new
)
138 struct isl_tab_var
*var
;
139 unsigned off
= 2 + tab
->M
;
141 if (tab
->max_var
< tab
->n_var
+ n_new
) {
142 var
= isl_realloc_array(tab
->mat
->ctx
, tab
->var
,
143 struct isl_tab_var
, tab
->n_var
+ n_new
);
147 tab
->max_var
+= n_new
;
150 if (tab
->mat
->n_col
< off
+ tab
->n_col
+ n_new
) {
153 tab
->mat
= isl_mat_extend(tab
->mat
,
154 tab
->mat
->n_row
, off
+ tab
->n_col
+ n_new
);
157 p
= isl_realloc_array(tab
->mat
->ctx
, tab
->col_var
,
158 int, tab
->n_col
+ n_new
);
167 struct isl_tab
*isl_tab_extend(struct isl_tab
*tab
, unsigned n_new
)
169 if (isl_tab_extend_cons(tab
, n_new
) >= 0)
176 static void free_undo_record(struct isl_tab_undo
*undo
)
178 switch (undo
->type
) {
179 case isl_tab_undo_saved_basis
:
180 free(undo
->u
.col_var
);
187 static void free_undo(struct isl_tab
*tab
)
189 struct isl_tab_undo
*undo
, *next
;
191 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
193 free_undo_record(undo
);
198 void isl_tab_free(struct isl_tab
*tab
)
203 isl_mat_free(tab
->mat
);
204 isl_vec_free(tab
->dual
);
205 isl_basic_map_free(tab
->bmap
);
211 isl_mat_free(tab
->samples
);
212 free(tab
->sample_index
);
213 isl_mat_free(tab
->basis
);
217 struct isl_tab
*isl_tab_dup(struct isl_tab
*tab
)
227 dup
= isl_calloc_type(tab
->mat
->ctx
, struct isl_tab
);
230 dup
->mat
= isl_mat_dup(tab
->mat
);
233 dup
->var
= isl_alloc_array(tab
->mat
->ctx
, struct isl_tab_var
, tab
->max_var
);
236 for (i
= 0; i
< tab
->n_var
; ++i
)
237 dup
->var
[i
] = tab
->var
[i
];
238 dup
->con
= isl_alloc_array(tab
->mat
->ctx
, struct isl_tab_var
, tab
->max_con
);
241 for (i
= 0; i
< tab
->n_con
; ++i
)
242 dup
->con
[i
] = tab
->con
[i
];
243 dup
->col_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->mat
->n_col
- off
);
246 for (i
= 0; i
< tab
->n_col
; ++i
)
247 dup
->col_var
[i
] = tab
->col_var
[i
];
248 dup
->row_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->mat
->n_row
);
251 for (i
= 0; i
< tab
->n_row
; ++i
)
252 dup
->row_var
[i
] = tab
->row_var
[i
];
254 dup
->row_sign
= isl_alloc_array(tab
->mat
->ctx
, enum isl_tab_row_sign
,
258 for (i
= 0; i
< tab
->n_row
; ++i
)
259 dup
->row_sign
[i
] = tab
->row_sign
[i
];
262 dup
->samples
= isl_mat_dup(tab
->samples
);
265 dup
->sample_index
= isl_alloc_array(tab
->mat
->ctx
, int,
266 tab
->samples
->n_row
);
267 if (!dup
->sample_index
)
269 dup
->n_sample
= tab
->n_sample
;
270 dup
->n_outside
= tab
->n_outside
;
272 dup
->n_row
= tab
->n_row
;
273 dup
->n_con
= tab
->n_con
;
274 dup
->n_eq
= tab
->n_eq
;
275 dup
->max_con
= tab
->max_con
;
276 dup
->n_col
= tab
->n_col
;
277 dup
->n_var
= tab
->n_var
;
278 dup
->max_var
= tab
->max_var
;
279 dup
->n_param
= tab
->n_param
;
280 dup
->n_div
= tab
->n_div
;
281 dup
->n_dead
= tab
->n_dead
;
282 dup
->n_redundant
= tab
->n_redundant
;
283 dup
->rational
= tab
->rational
;
284 dup
->empty
= tab
->empty
;
285 dup
->strict_redundant
= 0;
289 tab
->cone
= tab
->cone
;
290 dup
->bottom
.type
= isl_tab_undo_bottom
;
291 dup
->bottom
.next
= NULL
;
292 dup
->top
= &dup
->bottom
;
294 dup
->n_zero
= tab
->n_zero
;
295 dup
->n_unbounded
= tab
->n_unbounded
;
296 dup
->basis
= isl_mat_dup(tab
->basis
);
304 /* Construct the coefficient matrix of the product tableau
306 * mat{1,2} is the coefficient matrix of tableau {1,2}
307 * row{1,2} is the number of rows in tableau {1,2}
308 * col{1,2} is the number of columns in tableau {1,2}
309 * off is the offset to the coefficient column (skipping the
310 * denominator, the constant term and the big parameter if any)
311 * r{1,2} is the number of redundant rows in tableau {1,2}
312 * d{1,2} is the number of dead columns in tableau {1,2}
314 * The order of the rows and columns in the result is as explained
315 * in isl_tab_product.
317 static struct isl_mat
*tab_mat_product(struct isl_mat
*mat1
,
318 struct isl_mat
*mat2
, unsigned row1
, unsigned row2
,
319 unsigned col1
, unsigned col2
,
320 unsigned off
, unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
323 struct isl_mat
*prod
;
326 prod
= isl_mat_alloc(mat1
->ctx
, mat1
->n_row
+ mat2
->n_row
,
332 for (i
= 0; i
< r1
; ++i
) {
333 isl_seq_cpy(prod
->row
[n
+ i
], mat1
->row
[i
], off
+ d1
);
334 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
, d2
);
335 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
+ d2
,
336 mat1
->row
[i
] + off
+ d1
, col1
- d1
);
337 isl_seq_clr(prod
->row
[n
+ i
] + off
+ col1
+ d1
, col2
- d2
);
341 for (i
= 0; i
< r2
; ++i
) {
342 isl_seq_cpy(prod
->row
[n
+ i
], mat2
->row
[i
], off
);
343 isl_seq_clr(prod
->row
[n
+ i
] + off
, d1
);
344 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
,
345 mat2
->row
[i
] + off
, d2
);
346 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
+ d2
, col1
- d1
);
347 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ col1
+ d1
,
348 mat2
->row
[i
] + off
+ d2
, col2
- d2
);
352 for (i
= 0; i
< row1
- r1
; ++i
) {
353 isl_seq_cpy(prod
->row
[n
+ i
], mat1
->row
[r1
+ i
], off
+ d1
);
354 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
, d2
);
355 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
+ d2
,
356 mat1
->row
[r1
+ i
] + off
+ d1
, col1
- d1
);
357 isl_seq_clr(prod
->row
[n
+ i
] + off
+ col1
+ d1
, col2
- d2
);
361 for (i
= 0; i
< row2
- r2
; ++i
) {
362 isl_seq_cpy(prod
->row
[n
+ i
], mat2
->row
[r2
+ i
], off
);
363 isl_seq_clr(prod
->row
[n
+ i
] + off
, d1
);
364 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
,
365 mat2
->row
[r2
+ i
] + off
, d2
);
366 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
+ d2
, col1
- d1
);
367 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ col1
+ d1
,
368 mat2
->row
[r2
+ i
] + off
+ d2
, col2
- d2
);
374 /* Update the row or column index of a variable that corresponds
375 * to a variable in the first input tableau.
377 static void update_index1(struct isl_tab_var
*var
,
378 unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
380 if (var
->index
== -1)
382 if (var
->is_row
&& var
->index
>= r1
)
384 if (!var
->is_row
&& var
->index
>= d1
)
388 /* Update the row or column index of a variable that corresponds
389 * to a variable in the second input tableau.
391 static void update_index2(struct isl_tab_var
*var
,
392 unsigned row1
, unsigned col1
,
393 unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
395 if (var
->index
== -1)
410 /* Create a tableau that represents the Cartesian product of the sets
411 * represented by tableaus tab1 and tab2.
412 * The order of the rows in the product is
413 * - redundant rows of tab1
414 * - redundant rows of tab2
415 * - non-redundant rows of tab1
416 * - non-redundant rows of tab2
417 * The order of the columns is
420 * - coefficient of big parameter, if any
421 * - dead columns of tab1
422 * - dead columns of tab2
423 * - live columns of tab1
424 * - live columns of tab2
425 * The order of the variables and the constraints is a concatenation
426 * of order in the two input tableaus.
428 struct isl_tab
*isl_tab_product(struct isl_tab
*tab1
, struct isl_tab
*tab2
)
431 struct isl_tab
*prod
;
433 unsigned r1
, r2
, d1
, d2
;
438 isl_assert(tab1
->mat
->ctx
, tab1
->M
== tab2
->M
, return NULL
);
439 isl_assert(tab1
->mat
->ctx
, tab1
->rational
== tab2
->rational
, return NULL
);
440 isl_assert(tab1
->mat
->ctx
, tab1
->cone
== tab2
->cone
, return NULL
);
441 isl_assert(tab1
->mat
->ctx
, !tab1
->row_sign
, return NULL
);
442 isl_assert(tab1
->mat
->ctx
, !tab2
->row_sign
, return NULL
);
443 isl_assert(tab1
->mat
->ctx
, tab1
->n_param
== 0, return NULL
);
444 isl_assert(tab1
->mat
->ctx
, tab2
->n_param
== 0, return NULL
);
445 isl_assert(tab1
->mat
->ctx
, tab1
->n_div
== 0, return NULL
);
446 isl_assert(tab1
->mat
->ctx
, tab2
->n_div
== 0, return NULL
);
449 r1
= tab1
->n_redundant
;
450 r2
= tab2
->n_redundant
;
453 prod
= isl_calloc_type(tab1
->mat
->ctx
, struct isl_tab
);
456 prod
->mat
= tab_mat_product(tab1
->mat
, tab2
->mat
,
457 tab1
->n_row
, tab2
->n_row
,
458 tab1
->n_col
, tab2
->n_col
, off
, r1
, r2
, d1
, d2
);
461 prod
->var
= isl_alloc_array(tab1
->mat
->ctx
, struct isl_tab_var
,
462 tab1
->max_var
+ tab2
->max_var
);
465 for (i
= 0; i
< tab1
->n_var
; ++i
) {
466 prod
->var
[i
] = tab1
->var
[i
];
467 update_index1(&prod
->var
[i
], r1
, r2
, d1
, d2
);
469 for (i
= 0; i
< tab2
->n_var
; ++i
) {
470 prod
->var
[tab1
->n_var
+ i
] = tab2
->var
[i
];
471 update_index2(&prod
->var
[tab1
->n_var
+ i
],
472 tab1
->n_row
, tab1
->n_col
,
475 prod
->con
= isl_alloc_array(tab1
->mat
->ctx
, struct isl_tab_var
,
476 tab1
->max_con
+ tab2
->max_con
);
479 for (i
= 0; i
< tab1
->n_con
; ++i
) {
480 prod
->con
[i
] = tab1
->con
[i
];
481 update_index1(&prod
->con
[i
], r1
, r2
, d1
, d2
);
483 for (i
= 0; i
< tab2
->n_con
; ++i
) {
484 prod
->con
[tab1
->n_con
+ i
] = tab2
->con
[i
];
485 update_index2(&prod
->con
[tab1
->n_con
+ i
],
486 tab1
->n_row
, tab1
->n_col
,
489 prod
->col_var
= isl_alloc_array(tab1
->mat
->ctx
, int,
490 tab1
->n_col
+ tab2
->n_col
);
493 for (i
= 0; i
< tab1
->n_col
; ++i
) {
494 int pos
= i
< d1
? i
: i
+ d2
;
495 prod
->col_var
[pos
] = tab1
->col_var
[i
];
497 for (i
= 0; i
< tab2
->n_col
; ++i
) {
498 int pos
= i
< d2
? d1
+ i
: tab1
->n_col
+ i
;
499 int t
= tab2
->col_var
[i
];
504 prod
->col_var
[pos
] = t
;
506 prod
->row_var
= isl_alloc_array(tab1
->mat
->ctx
, int,
507 tab1
->mat
->n_row
+ tab2
->mat
->n_row
);
510 for (i
= 0; i
< tab1
->n_row
; ++i
) {
511 int pos
= i
< r1
? i
: i
+ r2
;
512 prod
->row_var
[pos
] = tab1
->row_var
[i
];
514 for (i
= 0; i
< tab2
->n_row
; ++i
) {
515 int pos
= i
< r2
? r1
+ i
: tab1
->n_row
+ i
;
516 int t
= tab2
->row_var
[i
];
521 prod
->row_var
[pos
] = t
;
523 prod
->samples
= NULL
;
524 prod
->sample_index
= NULL
;
525 prod
->n_row
= tab1
->n_row
+ tab2
->n_row
;
526 prod
->n_con
= tab1
->n_con
+ tab2
->n_con
;
528 prod
->max_con
= tab1
->max_con
+ tab2
->max_con
;
529 prod
->n_col
= tab1
->n_col
+ tab2
->n_col
;
530 prod
->n_var
= tab1
->n_var
+ tab2
->n_var
;
531 prod
->max_var
= tab1
->max_var
+ tab2
->max_var
;
534 prod
->n_dead
= tab1
->n_dead
+ tab2
->n_dead
;
535 prod
->n_redundant
= tab1
->n_redundant
+ tab2
->n_redundant
;
536 prod
->rational
= tab1
->rational
;
537 prod
->empty
= tab1
->empty
|| tab2
->empty
;
538 prod
->strict_redundant
= tab1
->strict_redundant
|| tab2
->strict_redundant
;
542 prod
->cone
= tab1
->cone
;
543 prod
->bottom
.type
= isl_tab_undo_bottom
;
544 prod
->bottom
.next
= NULL
;
545 prod
->top
= &prod
->bottom
;
548 prod
->n_unbounded
= 0;
557 static struct isl_tab_var
*var_from_index(struct isl_tab
*tab
, int i
)
562 return &tab
->con
[~i
];
565 struct isl_tab_var
*isl_tab_var_from_row(struct isl_tab
*tab
, int i
)
567 return var_from_index(tab
, tab
->row_var
[i
]);
570 static struct isl_tab_var
*var_from_col(struct isl_tab
*tab
, int i
)
572 return var_from_index(tab
, tab
->col_var
[i
]);
575 /* Check if there are any upper bounds on column variable "var",
576 * i.e., non-negative rows where var appears with a negative coefficient.
577 * Return 1 if there are no such bounds.
579 static int max_is_manifestly_unbounded(struct isl_tab
*tab
,
580 struct isl_tab_var
*var
)
583 unsigned off
= 2 + tab
->M
;
587 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
588 if (!isl_int_is_neg(tab
->mat
->row
[i
][off
+ var
->index
]))
590 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
596 /* Check if there are any lower bounds on column variable "var",
597 * i.e., non-negative rows where var appears with a positive coefficient.
598 * Return 1 if there are no such bounds.
600 static int min_is_manifestly_unbounded(struct isl_tab
*tab
,
601 struct isl_tab_var
*var
)
604 unsigned off
= 2 + tab
->M
;
608 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
609 if (!isl_int_is_pos(tab
->mat
->row
[i
][off
+ var
->index
]))
611 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
617 static int row_cmp(struct isl_tab
*tab
, int r1
, int r2
, int c
, isl_int t
)
619 unsigned off
= 2 + tab
->M
;
623 isl_int_mul(t
, tab
->mat
->row
[r1
][2], tab
->mat
->row
[r2
][off
+c
]);
624 isl_int_submul(t
, tab
->mat
->row
[r2
][2], tab
->mat
->row
[r1
][off
+c
]);
629 isl_int_mul(t
, tab
->mat
->row
[r1
][1], tab
->mat
->row
[r2
][off
+ c
]);
630 isl_int_submul(t
, tab
->mat
->row
[r2
][1], tab
->mat
->row
[r1
][off
+ c
]);
631 return isl_int_sgn(t
);
634 /* Given the index of a column "c", return the index of a row
635 * that can be used to pivot the column in, with either an increase
636 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
637 * If "var" is not NULL, then the row returned will be different from
638 * the one associated with "var".
640 * Each row in the tableau is of the form
642 * x_r = a_r0 + \sum_i a_ri x_i
644 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
645 * impose any limit on the increase or decrease in the value of x_c
646 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
647 * for the row with the smallest (most stringent) such bound.
648 * Note that the common denominator of each row drops out of the fraction.
649 * To check if row j has a smaller bound than row r, i.e.,
650 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
651 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
652 * where -sign(a_jc) is equal to "sgn".
654 static int pivot_row(struct isl_tab
*tab
,
655 struct isl_tab_var
*var
, int sgn
, int c
)
659 unsigned off
= 2 + tab
->M
;
663 for (j
= tab
->n_redundant
; j
< tab
->n_row
; ++j
) {
664 if (var
&& j
== var
->index
)
666 if (!isl_tab_var_from_row(tab
, j
)->is_nonneg
)
668 if (sgn
* isl_int_sgn(tab
->mat
->row
[j
][off
+ c
]) >= 0)
674 tsgn
= sgn
* row_cmp(tab
, r
, j
, c
, t
);
675 if (tsgn
< 0 || (tsgn
== 0 &&
676 tab
->row_var
[j
] < tab
->row_var
[r
]))
683 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
684 * (sgn < 0) the value of row variable var.
685 * If not NULL, then skip_var is a row variable that should be ignored
686 * while looking for a pivot row. It is usually equal to var.
688 * As the given row in the tableau is of the form
690 * x_r = a_r0 + \sum_i a_ri x_i
692 * we need to find a column such that the sign of a_ri is equal to "sgn"
693 * (such that an increase in x_i will have the desired effect) or a
694 * column with a variable that may attain negative values.
695 * If a_ri is positive, then we need to move x_i in the same direction
696 * to obtain the desired effect. Otherwise, x_i has to move in the
697 * opposite direction.
699 static void find_pivot(struct isl_tab
*tab
,
700 struct isl_tab_var
*var
, struct isl_tab_var
*skip_var
,
701 int sgn
, int *row
, int *col
)
708 isl_assert(tab
->mat
->ctx
, var
->is_row
, return);
709 tr
= tab
->mat
->row
[var
->index
] + 2 + tab
->M
;
712 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
713 if (isl_int_is_zero(tr
[j
]))
715 if (isl_int_sgn(tr
[j
]) != sgn
&&
716 var_from_col(tab
, j
)->is_nonneg
)
718 if (c
< 0 || tab
->col_var
[j
] < tab
->col_var
[c
])
724 sgn
*= isl_int_sgn(tr
[c
]);
725 r
= pivot_row(tab
, skip_var
, sgn
, c
);
726 *row
= r
< 0 ? var
->index
: r
;
730 /* Return 1 if row "row" represents an obviously redundant inequality.
732 * - it represents an inequality or a variable
733 * - that is the sum of a non-negative sample value and a positive
734 * combination of zero or more non-negative constraints.
736 int isl_tab_row_is_redundant(struct isl_tab
*tab
, int row
)
739 unsigned off
= 2 + tab
->M
;
741 if (tab
->row_var
[row
] < 0 && !isl_tab_var_from_row(tab
, row
)->is_nonneg
)
744 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
746 if (tab
->strict_redundant
&& isl_int_is_zero(tab
->mat
->row
[row
][1]))
748 if (tab
->M
&& isl_int_is_neg(tab
->mat
->row
[row
][2]))
751 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
752 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ i
]))
754 if (tab
->col_var
[i
] >= 0)
756 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ i
]))
758 if (!var_from_col(tab
, i
)->is_nonneg
)
764 static void swap_rows(struct isl_tab
*tab
, int row1
, int row2
)
767 enum isl_tab_row_sign s
;
769 t
= tab
->row_var
[row1
];
770 tab
->row_var
[row1
] = tab
->row_var
[row2
];
771 tab
->row_var
[row2
] = t
;
772 isl_tab_var_from_row(tab
, row1
)->index
= row1
;
773 isl_tab_var_from_row(tab
, row2
)->index
= row2
;
774 tab
->mat
= isl_mat_swap_rows(tab
->mat
, row1
, row2
);
778 s
= tab
->row_sign
[row1
];
779 tab
->row_sign
[row1
] = tab
->row_sign
[row2
];
780 tab
->row_sign
[row2
] = s
;
783 static int push_union(struct isl_tab
*tab
,
784 enum isl_tab_undo_type type
, union isl_tab_undo_val u
) WARN_UNUSED
;
785 static int push_union(struct isl_tab
*tab
,
786 enum isl_tab_undo_type type
, union isl_tab_undo_val u
)
788 struct isl_tab_undo
*undo
;
795 undo
= isl_alloc_type(tab
->mat
->ctx
, struct isl_tab_undo
);
800 undo
->next
= tab
->top
;
806 int isl_tab_push_var(struct isl_tab
*tab
,
807 enum isl_tab_undo_type type
, struct isl_tab_var
*var
)
809 union isl_tab_undo_val u
;
811 u
.var_index
= tab
->row_var
[var
->index
];
813 u
.var_index
= tab
->col_var
[var
->index
];
814 return push_union(tab
, type
, u
);
817 int isl_tab_push(struct isl_tab
*tab
, enum isl_tab_undo_type type
)
819 union isl_tab_undo_val u
= { 0 };
820 return push_union(tab
, type
, u
);
823 /* Push a record on the undo stack describing the current basic
824 * variables, so that the this state can be restored during rollback.
826 int isl_tab_push_basis(struct isl_tab
*tab
)
829 union isl_tab_undo_val u
;
831 u
.col_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
834 for (i
= 0; i
< tab
->n_col
; ++i
)
835 u
.col_var
[i
] = tab
->col_var
[i
];
836 return push_union(tab
, isl_tab_undo_saved_basis
, u
);
839 int isl_tab_push_callback(struct isl_tab
*tab
, struct isl_tab_callback
*callback
)
841 union isl_tab_undo_val u
;
842 u
.callback
= callback
;
843 return push_union(tab
, isl_tab_undo_callback
, u
);
846 struct isl_tab
*isl_tab_init_samples(struct isl_tab
*tab
)
853 tab
->samples
= isl_mat_alloc(tab
->mat
->ctx
, 1, 1 + tab
->n_var
);
856 tab
->sample_index
= isl_alloc_array(tab
->mat
->ctx
, int, 1);
857 if (!tab
->sample_index
)
865 struct isl_tab
*isl_tab_add_sample(struct isl_tab
*tab
,
866 __isl_take isl_vec
*sample
)
871 if (tab
->n_sample
+ 1 > tab
->samples
->n_row
) {
872 int *t
= isl_realloc_array(tab
->mat
->ctx
,
873 tab
->sample_index
, int, tab
->n_sample
+ 1);
876 tab
->sample_index
= t
;
879 tab
->samples
= isl_mat_extend(tab
->samples
,
880 tab
->n_sample
+ 1, tab
->samples
->n_col
);
884 isl_seq_cpy(tab
->samples
->row
[tab
->n_sample
], sample
->el
, sample
->size
);
885 isl_vec_free(sample
);
886 tab
->sample_index
[tab
->n_sample
] = tab
->n_sample
;
891 isl_vec_free(sample
);
896 struct isl_tab
*isl_tab_drop_sample(struct isl_tab
*tab
, int s
)
898 if (s
!= tab
->n_outside
) {
899 int t
= tab
->sample_index
[tab
->n_outside
];
900 tab
->sample_index
[tab
->n_outside
] = tab
->sample_index
[s
];
901 tab
->sample_index
[s
] = t
;
902 isl_mat_swap_rows(tab
->samples
, tab
->n_outside
, s
);
905 if (isl_tab_push(tab
, isl_tab_undo_drop_sample
) < 0) {
913 /* Record the current number of samples so that we can remove newer
914 * samples during a rollback.
916 int isl_tab_save_samples(struct isl_tab
*tab
)
918 union isl_tab_undo_val u
;
924 return push_union(tab
, isl_tab_undo_saved_samples
, u
);
927 /* Mark row with index "row" as being redundant.
928 * If we may need to undo the operation or if the row represents
929 * a variable of the original problem, the row is kept,
930 * but no longer considered when looking for a pivot row.
931 * Otherwise, the row is simply removed.
933 * The row may be interchanged with some other row. If it
934 * is interchanged with a later row, return 1. Otherwise return 0.
935 * If the rows are checked in order in the calling function,
936 * then a return value of 1 means that the row with the given
937 * row number may now contain a different row that hasn't been checked yet.
939 int isl_tab_mark_redundant(struct isl_tab
*tab
, int row
)
941 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, row
);
942 var
->is_redundant
= 1;
943 isl_assert(tab
->mat
->ctx
, row
>= tab
->n_redundant
, return -1);
944 if (tab
->preserve
|| tab
->need_undo
|| tab
->row_var
[row
] >= 0) {
945 if (tab
->row_var
[row
] >= 0 && !var
->is_nonneg
) {
947 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, var
) < 0)
950 if (row
!= tab
->n_redundant
)
951 swap_rows(tab
, row
, tab
->n_redundant
);
953 return isl_tab_push_var(tab
, isl_tab_undo_redundant
, var
);
955 if (row
!= tab
->n_row
- 1)
956 swap_rows(tab
, row
, tab
->n_row
- 1);
957 isl_tab_var_from_row(tab
, tab
->n_row
- 1)->index
= -1;
963 int isl_tab_mark_empty(struct isl_tab
*tab
)
967 if (!tab
->empty
&& tab
->need_undo
)
968 if (isl_tab_push(tab
, isl_tab_undo_empty
) < 0)
974 int isl_tab_freeze_constraint(struct isl_tab
*tab
, int con
)
976 struct isl_tab_var
*var
;
981 var
= &tab
->con
[con
];
989 return isl_tab_push_var(tab
, isl_tab_undo_freeze
, var
);
994 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
995 * the original sign of the pivot element.
996 * We only keep track of row signs during PILP solving and in this case
997 * we only pivot a row with negative sign (meaning the value is always
998 * non-positive) using a positive pivot element.
1000 * For each row j, the new value of the parametric constant is equal to
1002 * a_j0 - a_jc a_r0/a_rc
1004 * where a_j0 is the original parametric constant, a_rc is the pivot element,
1005 * a_r0 is the parametric constant of the pivot row and a_jc is the
1006 * pivot column entry of the row j.
1007 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
1008 * remains the same if a_jc has the same sign as the row j or if
1009 * a_jc is zero. In all other cases, we reset the sign to "unknown".
1011 static void update_row_sign(struct isl_tab
*tab
, int row
, int col
, int row_sgn
)
1014 struct isl_mat
*mat
= tab
->mat
;
1015 unsigned off
= 2 + tab
->M
;
1020 if (tab
->row_sign
[row
] == 0)
1022 isl_assert(mat
->ctx
, row_sgn
> 0, return);
1023 isl_assert(mat
->ctx
, tab
->row_sign
[row
] == isl_tab_row_neg
, return);
1024 tab
->row_sign
[row
] = isl_tab_row_pos
;
1025 for (i
= 0; i
< tab
->n_row
; ++i
) {
1029 s
= isl_int_sgn(mat
->row
[i
][off
+ col
]);
1032 if (!tab
->row_sign
[i
])
1034 if (s
< 0 && tab
->row_sign
[i
] == isl_tab_row_neg
)
1036 if (s
> 0 && tab
->row_sign
[i
] == isl_tab_row_pos
)
1038 tab
->row_sign
[i
] = isl_tab_row_unknown
;
1042 /* Given a row number "row" and a column number "col", pivot the tableau
1043 * such that the associated variables are interchanged.
1044 * The given row in the tableau expresses
1046 * x_r = a_r0 + \sum_i a_ri x_i
1050 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
1052 * Substituting this equality into the other rows
1054 * x_j = a_j0 + \sum_i a_ji x_i
1056 * with a_jc \ne 0, we obtain
1058 * 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
1065 * where i is any other column and j is any other row,
1066 * is therefore transformed into
1068 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1069 * 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)
1071 * The transformation is performed along the following steps
1073 * d_r/n_rc n_ri/n_rc
1076 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1079 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1080 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
1082 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1083 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
1085 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1086 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
1088 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1089 * 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)
1092 int isl_tab_pivot(struct isl_tab
*tab
, int row
, int col
)
1097 struct isl_mat
*mat
= tab
->mat
;
1098 struct isl_tab_var
*var
;
1099 unsigned off
= 2 + tab
->M
;
1101 if (tab
->mat
->ctx
->abort
) {
1102 isl_ctx_set_error(tab
->mat
->ctx
, isl_error_abort
);
1106 isl_int_swap(mat
->row
[row
][0], mat
->row
[row
][off
+ col
]);
1107 sgn
= isl_int_sgn(mat
->row
[row
][0]);
1109 isl_int_neg(mat
->row
[row
][0], mat
->row
[row
][0]);
1110 isl_int_neg(mat
->row
[row
][off
+ col
], mat
->row
[row
][off
+ col
]);
1112 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1113 if (j
== off
- 1 + col
)
1115 isl_int_neg(mat
->row
[row
][1 + j
], mat
->row
[row
][1 + j
]);
1117 if (!isl_int_is_one(mat
->row
[row
][0]))
1118 isl_seq_normalize(mat
->ctx
, mat
->row
[row
], off
+ tab
->n_col
);
1119 for (i
= 0; i
< tab
->n_row
; ++i
) {
1122 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1124 isl_int_mul(mat
->row
[i
][0], mat
->row
[i
][0], mat
->row
[row
][0]);
1125 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1126 if (j
== off
- 1 + col
)
1128 isl_int_mul(mat
->row
[i
][1 + j
],
1129 mat
->row
[i
][1 + j
], mat
->row
[row
][0]);
1130 isl_int_addmul(mat
->row
[i
][1 + j
],
1131 mat
->row
[i
][off
+ col
], mat
->row
[row
][1 + j
]);
1133 isl_int_mul(mat
->row
[i
][off
+ col
],
1134 mat
->row
[i
][off
+ col
], mat
->row
[row
][off
+ col
]);
1135 if (!isl_int_is_one(mat
->row
[i
][0]))
1136 isl_seq_normalize(mat
->ctx
, mat
->row
[i
], off
+ tab
->n_col
);
1138 t
= tab
->row_var
[row
];
1139 tab
->row_var
[row
] = tab
->col_var
[col
];
1140 tab
->col_var
[col
] = t
;
1141 var
= isl_tab_var_from_row(tab
, row
);
1144 var
= var_from_col(tab
, col
);
1147 update_row_sign(tab
, row
, col
, sgn
);
1150 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1151 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1153 if (!isl_tab_var_from_row(tab
, i
)->frozen
&&
1154 isl_tab_row_is_redundant(tab
, i
)) {
1155 int redo
= isl_tab_mark_redundant(tab
, i
);
1165 /* If "var" represents a column variable, then pivot is up (sgn > 0)
1166 * or down (sgn < 0) to a row. The variable is assumed not to be
1167 * unbounded in the specified direction.
1168 * If sgn = 0, then the variable is unbounded in both directions,
1169 * and we pivot with any row we can find.
1171 static int to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
) WARN_UNUSED
;
1172 static int to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
)
1175 unsigned off
= 2 + tab
->M
;
1181 for (r
= tab
->n_redundant
; r
< tab
->n_row
; ++r
)
1182 if (!isl_int_is_zero(tab
->mat
->row
[r
][off
+var
->index
]))
1184 isl_assert(tab
->mat
->ctx
, r
< tab
->n_row
, return -1);
1186 r
= pivot_row(tab
, NULL
, sign
, var
->index
);
1187 isl_assert(tab
->mat
->ctx
, r
>= 0, return -1);
1190 return isl_tab_pivot(tab
, r
, var
->index
);
1193 /* Check whether all variables that are marked as non-negative
1194 * also have a non-negative sample value. This function is not
1195 * called from the current code but is useful during debugging.
1197 static void check_table(struct isl_tab
*tab
) __attribute__ ((unused
));
1198 static void check_table(struct isl_tab
*tab
)
1204 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1205 struct isl_tab_var
*var
;
1206 var
= isl_tab_var_from_row(tab
, i
);
1207 if (!var
->is_nonneg
)
1210 isl_assert(tab
->mat
->ctx
,
1211 !isl_int_is_neg(tab
->mat
->row
[i
][2]), abort());
1212 if (isl_int_is_pos(tab
->mat
->row
[i
][2]))
1215 isl_assert(tab
->mat
->ctx
, !isl_int_is_neg(tab
->mat
->row
[i
][1]),
1220 /* Return the sign of the maximal value of "var".
1221 * If the sign is not negative, then on return from this function,
1222 * the sample value will also be non-negative.
1224 * If "var" is manifestly unbounded wrt positive values, we are done.
1225 * Otherwise, we pivot the variable up to a row if needed
1226 * Then we continue pivoting down until either
1227 * - no more down pivots can be performed
1228 * - the sample value is positive
1229 * - the variable is pivoted into a manifestly unbounded column
1231 static int sign_of_max(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1235 if (max_is_manifestly_unbounded(tab
, var
))
1237 if (to_row(tab
, var
, 1) < 0)
1239 while (!isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1240 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1242 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1243 if (isl_tab_pivot(tab
, row
, col
) < 0)
1245 if (!var
->is_row
) /* manifestly unbounded */
1251 int isl_tab_sign_of_max(struct isl_tab
*tab
, int con
)
1253 struct isl_tab_var
*var
;
1258 var
= &tab
->con
[con
];
1259 isl_assert(tab
->mat
->ctx
, !var
->is_redundant
, return -2);
1260 isl_assert(tab
->mat
->ctx
, !var
->is_zero
, return -2);
1262 return sign_of_max(tab
, var
);
1265 static int row_is_neg(struct isl_tab
*tab
, int row
)
1268 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1269 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1271 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1273 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1276 static int row_sgn(struct isl_tab
*tab
, int row
)
1279 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1280 if (!isl_int_is_zero(tab
->mat
->row
[row
][2]))
1281 return isl_int_sgn(tab
->mat
->row
[row
][2]);
1283 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1286 /* Perform pivots until the row variable "var" has a non-negative
1287 * sample value or until no more upward pivots can be performed.
1288 * Return the sign of the sample value after the pivots have been
1291 static int restore_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1295 while (row_is_neg(tab
, var
->index
)) {
1296 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1299 if (isl_tab_pivot(tab
, row
, col
) < 0)
1301 if (!var
->is_row
) /* manifestly unbounded */
1304 return row_sgn(tab
, var
->index
);
1307 /* Perform pivots until we are sure that the row variable "var"
1308 * can attain non-negative values. After return from this
1309 * function, "var" is still a row variable, but its sample
1310 * value may not be non-negative, even if the function returns 1.
1312 static int at_least_zero(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1316 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1317 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1320 if (row
== var
->index
) /* manifestly unbounded */
1322 if (isl_tab_pivot(tab
, row
, col
) < 0)
1325 return !isl_int_is_neg(tab
->mat
->row
[var
->index
][1]);
1328 /* Return a negative value if "var" can attain negative values.
1329 * Return a non-negative value otherwise.
1331 * If "var" is manifestly unbounded wrt negative values, we are done.
1332 * Otherwise, if var is in a column, we can pivot it down to a row.
1333 * Then we continue pivoting down until either
1334 * - the pivot would result in a manifestly unbounded column
1335 * => we don't perform the pivot, but simply return -1
1336 * - no more down pivots can be performed
1337 * - the sample value is negative
1338 * If the sample value becomes negative and the variable is supposed
1339 * to be nonnegative, then we undo the last pivot.
1340 * However, if the last pivot has made the pivoting variable
1341 * obviously redundant, then it may have moved to another row.
1342 * In that case we look for upward pivots until we reach a non-negative
1345 static int sign_of_min(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1348 struct isl_tab_var
*pivot_var
= NULL
;
1350 if (min_is_manifestly_unbounded(tab
, var
))
1354 row
= pivot_row(tab
, NULL
, -1, col
);
1355 pivot_var
= var_from_col(tab
, col
);
1356 if (isl_tab_pivot(tab
, row
, col
) < 0)
1358 if (var
->is_redundant
)
1360 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1361 if (var
->is_nonneg
) {
1362 if (!pivot_var
->is_redundant
&&
1363 pivot_var
->index
== row
) {
1364 if (isl_tab_pivot(tab
, row
, col
) < 0)
1367 if (restore_row(tab
, var
) < -1)
1373 if (var
->is_redundant
)
1375 while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1376 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1377 if (row
== var
->index
)
1380 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1381 pivot_var
= var_from_col(tab
, col
);
1382 if (isl_tab_pivot(tab
, row
, col
) < 0)
1384 if (var
->is_redundant
)
1387 if (pivot_var
&& var
->is_nonneg
) {
1388 /* pivot back to non-negative value */
1389 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
) {
1390 if (isl_tab_pivot(tab
, row
, col
) < 0)
1393 if (restore_row(tab
, var
) < -1)
1399 static int row_at_most_neg_one(struct isl_tab
*tab
, int row
)
1402 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1404 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1407 return isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
1408 isl_int_abs_ge(tab
->mat
->row
[row
][1],
1409 tab
->mat
->row
[row
][0]);
1412 /* Return 1 if "var" can attain values <= -1.
1413 * Return 0 otherwise.
1415 * The sample value of "var" is assumed to be non-negative when the
1416 * the function is called. If 1 is returned then the constraint
1417 * is not redundant and the sample value is made non-negative again before
1418 * the function returns.
1420 int isl_tab_min_at_most_neg_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1423 struct isl_tab_var
*pivot_var
;
1425 if (min_is_manifestly_unbounded(tab
, var
))
1429 row
= pivot_row(tab
, NULL
, -1, col
);
1430 pivot_var
= var_from_col(tab
, col
);
1431 if (isl_tab_pivot(tab
, row
, col
) < 0)
1433 if (var
->is_redundant
)
1435 if (row_at_most_neg_one(tab
, var
->index
)) {
1436 if (var
->is_nonneg
) {
1437 if (!pivot_var
->is_redundant
&&
1438 pivot_var
->index
== row
) {
1439 if (isl_tab_pivot(tab
, row
, col
) < 0)
1442 if (restore_row(tab
, var
) < -1)
1448 if (var
->is_redundant
)
1451 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1452 if (row
== var
->index
) {
1453 if (restore_row(tab
, var
) < -1)
1459 pivot_var
= var_from_col(tab
, col
);
1460 if (isl_tab_pivot(tab
, row
, col
) < 0)
1462 if (var
->is_redundant
)
1464 } while (!row_at_most_neg_one(tab
, var
->index
));
1465 if (var
->is_nonneg
) {
1466 /* pivot back to non-negative value */
1467 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
1468 if (isl_tab_pivot(tab
, row
, col
) < 0)
1470 if (restore_row(tab
, var
) < -1)
1476 /* Return 1 if "var" can attain values >= 1.
1477 * Return 0 otherwise.
1479 static int at_least_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1484 if (max_is_manifestly_unbounded(tab
, var
))
1486 if (to_row(tab
, var
, 1) < 0)
1488 r
= tab
->mat
->row
[var
->index
];
1489 while (isl_int_lt(r
[1], r
[0])) {
1490 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1492 return isl_int_ge(r
[1], r
[0]);
1493 if (row
== var
->index
) /* manifestly unbounded */
1495 if (isl_tab_pivot(tab
, row
, col
) < 0)
1501 static void swap_cols(struct isl_tab
*tab
, int col1
, int col2
)
1504 unsigned off
= 2 + tab
->M
;
1505 t
= tab
->col_var
[col1
];
1506 tab
->col_var
[col1
] = tab
->col_var
[col2
];
1507 tab
->col_var
[col2
] = t
;
1508 var_from_col(tab
, col1
)->index
= col1
;
1509 var_from_col(tab
, col2
)->index
= col2
;
1510 tab
->mat
= isl_mat_swap_cols(tab
->mat
, off
+ col1
, off
+ col2
);
1513 /* Mark column with index "col" as representing a zero variable.
1514 * If we may need to undo the operation the column is kept,
1515 * but no longer considered.
1516 * Otherwise, the column is simply removed.
1518 * The column may be interchanged with some other column. If it
1519 * is interchanged with a later column, return 1. Otherwise return 0.
1520 * If the columns are checked in order in the calling function,
1521 * then a return value of 1 means that the column with the given
1522 * column number may now contain a different column that
1523 * hasn't been checked yet.
1525 int isl_tab_kill_col(struct isl_tab
*tab
, int col
)
1527 var_from_col(tab
, col
)->is_zero
= 1;
1528 if (tab
->need_undo
) {
1529 if (isl_tab_push_var(tab
, isl_tab_undo_zero
,
1530 var_from_col(tab
, col
)) < 0)
1532 if (col
!= tab
->n_dead
)
1533 swap_cols(tab
, col
, tab
->n_dead
);
1537 if (col
!= tab
->n_col
- 1)
1538 swap_cols(tab
, col
, tab
->n_col
- 1);
1539 var_from_col(tab
, tab
->n_col
- 1)->index
= -1;
1545 static int row_is_manifestly_non_integral(struct isl_tab
*tab
, int row
)
1547 unsigned off
= 2 + tab
->M
;
1549 if (tab
->M
&& !isl_int_eq(tab
->mat
->row
[row
][2],
1550 tab
->mat
->row
[row
][0]))
1552 if (isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1553 tab
->n_col
- tab
->n_dead
) != -1)
1556 return !isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1557 tab
->mat
->row
[row
][0]);
1560 /* For integer tableaus, check if any of the coordinates are stuck
1561 * at a non-integral value.
1563 static int tab_is_manifestly_empty(struct isl_tab
*tab
)
1572 for (i
= 0; i
< tab
->n_var
; ++i
) {
1573 if (!tab
->var
[i
].is_row
)
1575 if (row_is_manifestly_non_integral(tab
, tab
->var
[i
].index
))
1582 /* Row variable "var" is non-negative and cannot attain any values
1583 * larger than zero. This means that the coefficients of the unrestricted
1584 * column variables are zero and that the coefficients of the non-negative
1585 * column variables are zero or negative.
1586 * Each of the non-negative variables with a negative coefficient can
1587 * then also be written as the negative sum of non-negative variables
1588 * and must therefore also be zero.
1590 static int close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
1591 static int close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1594 struct isl_mat
*mat
= tab
->mat
;
1595 unsigned off
= 2 + tab
->M
;
1597 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return -1);
1600 if (isl_tab_push_var(tab
, isl_tab_undo_zero
, var
) < 0)
1602 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1604 if (isl_int_is_zero(mat
->row
[var
->index
][off
+ j
]))
1606 isl_assert(tab
->mat
->ctx
,
1607 isl_int_is_neg(mat
->row
[var
->index
][off
+ j
]), return -1);
1608 recheck
= isl_tab_kill_col(tab
, j
);
1614 if (isl_tab_mark_redundant(tab
, var
->index
) < 0)
1616 if (tab_is_manifestly_empty(tab
) && isl_tab_mark_empty(tab
) < 0)
1621 /* Add a constraint to the tableau and allocate a row for it.
1622 * Return the index into the constraint array "con".
1624 int isl_tab_allocate_con(struct isl_tab
*tab
)
1628 isl_assert(tab
->mat
->ctx
, tab
->n_row
< tab
->mat
->n_row
, return -1);
1629 isl_assert(tab
->mat
->ctx
, tab
->n_con
< tab
->max_con
, return -1);
1632 tab
->con
[r
].index
= tab
->n_row
;
1633 tab
->con
[r
].is_row
= 1;
1634 tab
->con
[r
].is_nonneg
= 0;
1635 tab
->con
[r
].is_zero
= 0;
1636 tab
->con
[r
].is_redundant
= 0;
1637 tab
->con
[r
].frozen
= 0;
1638 tab
->con
[r
].negated
= 0;
1639 tab
->row_var
[tab
->n_row
] = ~r
;
1643 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]) < 0)
1649 /* Add a variable to the tableau and allocate a column for it.
1650 * Return the index into the variable array "var".
1652 int isl_tab_allocate_var(struct isl_tab
*tab
)
1656 unsigned off
= 2 + tab
->M
;
1658 isl_assert(tab
->mat
->ctx
, tab
->n_col
< tab
->mat
->n_col
, return -1);
1659 isl_assert(tab
->mat
->ctx
, tab
->n_var
< tab
->max_var
, return -1);
1662 tab
->var
[r
].index
= tab
->n_col
;
1663 tab
->var
[r
].is_row
= 0;
1664 tab
->var
[r
].is_nonneg
= 0;
1665 tab
->var
[r
].is_zero
= 0;
1666 tab
->var
[r
].is_redundant
= 0;
1667 tab
->var
[r
].frozen
= 0;
1668 tab
->var
[r
].negated
= 0;
1669 tab
->col_var
[tab
->n_col
] = r
;
1671 for (i
= 0; i
< tab
->n_row
; ++i
)
1672 isl_int_set_si(tab
->mat
->row
[i
][off
+ tab
->n_col
], 0);
1676 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->var
[r
]) < 0)
1682 /* Add a row to the tableau. The row is given as an affine combination
1683 * of the original variables and needs to be expressed in terms of the
1686 * We add each term in turn.
1687 * If r = n/d_r is the current sum and we need to add k x, then
1688 * if x is a column variable, we increase the numerator of
1689 * this column by k d_r
1690 * if x = f/d_x is a row variable, then the new representation of r is
1692 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1693 * --- + --- = ------------------- = -------------------
1694 * d_r d_r d_r d_x/g m
1696 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1698 * If tab->M is set, then, internally, each variable x is represented
1699 * as x' - M. We then also need no subtract k d_r from the coefficient of M.
1701 int isl_tab_add_row(struct isl_tab
*tab
, isl_int
*line
)
1707 unsigned off
= 2 + tab
->M
;
1709 r
= isl_tab_allocate_con(tab
);
1715 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1716 isl_int_set_si(row
[0], 1);
1717 isl_int_set(row
[1], line
[0]);
1718 isl_seq_clr(row
+ 2, tab
->M
+ tab
->n_col
);
1719 for (i
= 0; i
< tab
->n_var
; ++i
) {
1720 if (tab
->var
[i
].is_zero
)
1722 if (tab
->var
[i
].is_row
) {
1724 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1725 isl_int_swap(a
, row
[0]);
1726 isl_int_divexact(a
, row
[0], a
);
1728 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1729 isl_int_mul(b
, b
, line
[1 + i
]);
1730 isl_seq_combine(row
+ 1, a
, row
+ 1,
1731 b
, tab
->mat
->row
[tab
->var
[i
].index
] + 1,
1732 1 + tab
->M
+ tab
->n_col
);
1734 isl_int_addmul(row
[off
+ tab
->var
[i
].index
],
1735 line
[1 + i
], row
[0]);
1736 if (tab
->M
&& i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
1737 isl_int_submul(row
[2], line
[1 + i
], row
[0]);
1739 isl_seq_normalize(tab
->mat
->ctx
, row
, off
+ tab
->n_col
);
1744 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_unknown
;
1749 static int drop_row(struct isl_tab
*tab
, int row
)
1751 isl_assert(tab
->mat
->ctx
, ~tab
->row_var
[row
] == tab
->n_con
- 1, return -1);
1752 if (row
!= tab
->n_row
- 1)
1753 swap_rows(tab
, row
, tab
->n_row
- 1);
1759 static int drop_col(struct isl_tab
*tab
, int col
)
1761 isl_assert(tab
->mat
->ctx
, tab
->col_var
[col
] == tab
->n_var
- 1, return -1);
1762 if (col
!= tab
->n_col
- 1)
1763 swap_cols(tab
, col
, tab
->n_col
- 1);
1769 /* Add inequality "ineq" and check if it conflicts with the
1770 * previously added constraints or if it is obviously redundant.
1772 int isl_tab_add_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1781 struct isl_basic_map
*bmap
= tab
->bmap
;
1783 isl_assert(tab
->mat
->ctx
, tab
->n_eq
== bmap
->n_eq
, return -1);
1784 isl_assert(tab
->mat
->ctx
,
1785 tab
->n_con
== bmap
->n_eq
+ bmap
->n_ineq
, return -1);
1786 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, ineq
);
1787 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1794 isl_int_swap(ineq
[0], cst
);
1796 r
= isl_tab_add_row(tab
, ineq
);
1798 isl_int_swap(ineq
[0], cst
);
1803 tab
->con
[r
].is_nonneg
= 1;
1804 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1806 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1807 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1812 sgn
= restore_row(tab
, &tab
->con
[r
]);
1816 return isl_tab_mark_empty(tab
);
1817 if (tab
->con
[r
].is_row
&& isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1818 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1823 /* Pivot a non-negative variable down until it reaches the value zero
1824 * and then pivot the variable into a column position.
1826 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
1827 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1831 unsigned off
= 2 + tab
->M
;
1836 while (isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1837 find_pivot(tab
, var
, NULL
, -1, &row
, &col
);
1838 isl_assert(tab
->mat
->ctx
, row
!= -1, return -1);
1839 if (isl_tab_pivot(tab
, row
, col
) < 0)
1845 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
)
1846 if (!isl_int_is_zero(tab
->mat
->row
[var
->index
][off
+ i
]))
1849 isl_assert(tab
->mat
->ctx
, i
< tab
->n_col
, return -1);
1850 if (isl_tab_pivot(tab
, var
->index
, i
) < 0)
1856 /* We assume Gaussian elimination has been performed on the equalities.
1857 * The equalities can therefore never conflict.
1858 * Adding the equalities is currently only really useful for a later call
1859 * to isl_tab_ineq_type.
1861 static struct isl_tab
*add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1868 r
= isl_tab_add_row(tab
, eq
);
1872 r
= tab
->con
[r
].index
;
1873 i
= isl_seq_first_non_zero(tab
->mat
->row
[r
] + 2 + tab
->M
+ tab
->n_dead
,
1874 tab
->n_col
- tab
->n_dead
);
1875 isl_assert(tab
->mat
->ctx
, i
>= 0, goto error
);
1877 if (isl_tab_pivot(tab
, r
, i
) < 0)
1879 if (isl_tab_kill_col(tab
, i
) < 0)
1889 static int row_is_manifestly_zero(struct isl_tab
*tab
, int row
)
1891 unsigned off
= 2 + tab
->M
;
1893 if (!isl_int_is_zero(tab
->mat
->row
[row
][1]))
1895 if (tab
->M
&& !isl_int_is_zero(tab
->mat
->row
[row
][2]))
1897 return isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1898 tab
->n_col
- tab
->n_dead
) == -1;
1901 /* Add an equality that is known to be valid for the given tableau.
1903 int isl_tab_add_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1905 struct isl_tab_var
*var
;
1910 r
= isl_tab_add_row(tab
, eq
);
1916 if (row_is_manifestly_zero(tab
, r
)) {
1918 if (isl_tab_mark_redundant(tab
, r
) < 0)
1923 if (isl_int_is_neg(tab
->mat
->row
[r
][1])) {
1924 isl_seq_neg(tab
->mat
->row
[r
] + 1, tab
->mat
->row
[r
] + 1,
1929 if (to_col(tab
, var
) < 0)
1932 if (isl_tab_kill_col(tab
, var
->index
) < 0)
1938 static int add_zero_row(struct isl_tab
*tab
)
1943 r
= isl_tab_allocate_con(tab
);
1947 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1948 isl_seq_clr(row
+ 1, 1 + tab
->M
+ tab
->n_col
);
1949 isl_int_set_si(row
[0], 1);
1954 /* Add equality "eq" and check if it conflicts with the
1955 * previously added constraints or if it is obviously redundant.
1957 int isl_tab_add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1959 struct isl_tab_undo
*snap
= NULL
;
1960 struct isl_tab_var
*var
;
1968 isl_assert(tab
->mat
->ctx
, !tab
->M
, return -1);
1971 snap
= isl_tab_snap(tab
);
1975 isl_int_swap(eq
[0], cst
);
1977 r
= isl_tab_add_row(tab
, eq
);
1979 isl_int_swap(eq
[0], cst
);
1987 if (row_is_manifestly_zero(tab
, row
)) {
1989 if (isl_tab_rollback(tab
, snap
) < 0)
1997 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1998 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
2000 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
2001 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
2002 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
2003 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
2007 if (add_zero_row(tab
) < 0)
2011 sgn
= isl_int_sgn(tab
->mat
->row
[row
][1]);
2014 isl_seq_neg(tab
->mat
->row
[row
] + 1, tab
->mat
->row
[row
] + 1,
2021 sgn
= sign_of_max(tab
, var
);
2025 if (isl_tab_mark_empty(tab
) < 0)
2032 if (to_col(tab
, var
) < 0)
2035 if (isl_tab_kill_col(tab
, var
->index
) < 0)
2041 /* Construct and return an inequality that expresses an upper bound
2043 * In particular, if the div is given by
2047 * then the inequality expresses
2051 static struct isl_vec
*ineq_for_div(struct isl_basic_map
*bmap
, unsigned div
)
2055 struct isl_vec
*ineq
;
2060 total
= isl_basic_map_total_dim(bmap
);
2061 div_pos
= 1 + total
- bmap
->n_div
+ div
;
2063 ineq
= isl_vec_alloc(bmap
->ctx
, 1 + total
);
2067 isl_seq_cpy(ineq
->el
, bmap
->div
[div
] + 1, 1 + total
);
2068 isl_int_neg(ineq
->el
[div_pos
], bmap
->div
[div
][0]);
2072 /* For a div d = floor(f/m), add the constraints
2075 * -(f-(m-1)) + m d >= 0
2077 * Note that the second constraint is the negation of
2081 * If add_ineq is not NULL, then this function is used
2082 * instead of isl_tab_add_ineq to effectively add the inequalities.
2084 static int add_div_constraints(struct isl_tab
*tab
, unsigned div
,
2085 int (*add_ineq
)(void *user
, isl_int
*), void *user
)
2089 struct isl_vec
*ineq
;
2091 total
= isl_basic_map_total_dim(tab
->bmap
);
2092 div_pos
= 1 + total
- tab
->bmap
->n_div
+ div
;
2094 ineq
= ineq_for_div(tab
->bmap
, div
);
2099 if (add_ineq(user
, ineq
->el
) < 0)
2102 if (isl_tab_add_ineq(tab
, ineq
->el
) < 0)
2106 isl_seq_neg(ineq
->el
, tab
->bmap
->div
[div
] + 1, 1 + total
);
2107 isl_int_set(ineq
->el
[div_pos
], tab
->bmap
->div
[div
][0]);
2108 isl_int_add(ineq
->el
[0], ineq
->el
[0], ineq
->el
[div_pos
]);
2109 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
2112 if (add_ineq(user
, ineq
->el
) < 0)
2115 if (isl_tab_add_ineq(tab
, ineq
->el
) < 0)
2127 /* Check whether the div described by "div" is obviously non-negative.
2128 * If we are using a big parameter, then we will encode the div
2129 * as div' = M + div, which is always non-negative.
2130 * Otherwise, we check whether div is a non-negative affine combination
2131 * of non-negative variables.
2133 static int div_is_nonneg(struct isl_tab
*tab
, __isl_keep isl_vec
*div
)
2140 if (isl_int_is_neg(div
->el
[1]))
2143 for (i
= 0; i
< tab
->n_var
; ++i
) {
2144 if (isl_int_is_neg(div
->el
[2 + i
]))
2146 if (isl_int_is_zero(div
->el
[2 + i
]))
2148 if (!tab
->var
[i
].is_nonneg
)
2155 /* Add an extra div, prescribed by "div" to the tableau and
2156 * the associated bmap (which is assumed to be non-NULL).
2158 * If add_ineq is not NULL, then this function is used instead
2159 * of isl_tab_add_ineq to add the div constraints.
2160 * This complication is needed because the code in isl_tab_pip
2161 * wants to perform some extra processing when an inequality
2162 * is added to the tableau.
2164 int isl_tab_add_div(struct isl_tab
*tab
, __isl_keep isl_vec
*div
,
2165 int (*add_ineq
)(void *user
, isl_int
*), void *user
)
2174 isl_assert(tab
->mat
->ctx
, tab
->bmap
, return -1);
2176 nonneg
= div_is_nonneg(tab
, div
);
2178 if (isl_tab_extend_cons(tab
, 3) < 0)
2180 if (isl_tab_extend_vars(tab
, 1) < 0)
2182 r
= isl_tab_allocate_var(tab
);
2187 tab
->var
[r
].is_nonneg
= 1;
2189 tab
->bmap
= isl_basic_map_extend_space(tab
->bmap
,
2190 isl_basic_map_get_space(tab
->bmap
), 1, 0, 2);
2191 k
= isl_basic_map_alloc_div(tab
->bmap
);
2194 isl_seq_cpy(tab
->bmap
->div
[k
], div
->el
, div
->size
);
2195 if (isl_tab_push(tab
, isl_tab_undo_bmap_div
) < 0)
2198 if (add_div_constraints(tab
, k
, add_ineq
, user
) < 0)
2204 /* If "track" is set, then we want to keep track of all constraints in tab
2205 * in its bmap field. This field is initialized from a copy of "bmap",
2206 * so we need to make sure that all constraints in "bmap" also appear
2207 * in the constructed tab.
2209 __isl_give
struct isl_tab
*isl_tab_from_basic_map(
2210 __isl_keep isl_basic_map
*bmap
, int track
)
2213 struct isl_tab
*tab
;
2217 tab
= isl_tab_alloc(bmap
->ctx
,
2218 isl_basic_map_total_dim(bmap
) + bmap
->n_ineq
+ 1,
2219 isl_basic_map_total_dim(bmap
), 0);
2222 tab
->preserve
= track
;
2223 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
2224 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
2225 if (isl_tab_mark_empty(tab
) < 0)
2229 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2230 tab
= add_eq(tab
, bmap
->eq
[i
]);
2234 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2235 if (isl_tab_add_ineq(tab
, bmap
->ineq
[i
]) < 0)
2241 if (track
&& isl_tab_track_bmap(tab
, isl_basic_map_copy(bmap
)) < 0)
2249 __isl_give
struct isl_tab
*isl_tab_from_basic_set(
2250 __isl_keep isl_basic_set
*bset
, int track
)
2252 return isl_tab_from_basic_map(bset
, track
);
2255 /* Construct a tableau corresponding to the recession cone of "bset".
2257 struct isl_tab
*isl_tab_from_recession_cone(__isl_keep isl_basic_set
*bset
,
2262 struct isl_tab
*tab
;
2263 unsigned offset
= 0;
2268 offset
= isl_basic_set_dim(bset
, isl_dim_param
);
2269 tab
= isl_tab_alloc(bset
->ctx
, bset
->n_eq
+ bset
->n_ineq
,
2270 isl_basic_set_total_dim(bset
) - offset
, 0);
2273 tab
->rational
= ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
);
2277 for (i
= 0; i
< bset
->n_eq
; ++i
) {
2278 isl_int_swap(bset
->eq
[i
][offset
], cst
);
2280 if (isl_tab_add_eq(tab
, bset
->eq
[i
] + offset
) < 0)
2283 tab
= add_eq(tab
, bset
->eq
[i
]);
2284 isl_int_swap(bset
->eq
[i
][offset
], cst
);
2288 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2290 isl_int_swap(bset
->ineq
[i
][offset
], cst
);
2291 r
= isl_tab_add_row(tab
, bset
->ineq
[i
] + offset
);
2292 isl_int_swap(bset
->ineq
[i
][offset
], cst
);
2295 tab
->con
[r
].is_nonneg
= 1;
2296 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2308 /* Assuming "tab" is the tableau of a cone, check if the cone is
2309 * bounded, i.e., if it is empty or only contains the origin.
2311 int isl_tab_cone_is_bounded(struct isl_tab
*tab
)
2319 if (tab
->n_dead
== tab
->n_col
)
2323 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2324 struct isl_tab_var
*var
;
2326 var
= isl_tab_var_from_row(tab
, i
);
2327 if (!var
->is_nonneg
)
2329 sgn
= sign_of_max(tab
, var
);
2334 if (close_row(tab
, var
) < 0)
2338 if (tab
->n_dead
== tab
->n_col
)
2340 if (i
== tab
->n_row
)
2345 int isl_tab_sample_is_integer(struct isl_tab
*tab
)
2352 for (i
= 0; i
< tab
->n_var
; ++i
) {
2354 if (!tab
->var
[i
].is_row
)
2356 row
= tab
->var
[i
].index
;
2357 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
2358 tab
->mat
->row
[row
][0]))
2364 static struct isl_vec
*extract_integer_sample(struct isl_tab
*tab
)
2367 struct isl_vec
*vec
;
2369 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2373 isl_int_set_si(vec
->block
.data
[0], 1);
2374 for (i
= 0; i
< tab
->n_var
; ++i
) {
2375 if (!tab
->var
[i
].is_row
)
2376 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
2378 int row
= tab
->var
[i
].index
;
2379 isl_int_divexact(vec
->block
.data
[1 + i
],
2380 tab
->mat
->row
[row
][1], tab
->mat
->row
[row
][0]);
2387 struct isl_vec
*isl_tab_get_sample_value(struct isl_tab
*tab
)
2390 struct isl_vec
*vec
;
2396 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2402 isl_int_set_si(vec
->block
.data
[0], 1);
2403 for (i
= 0; i
< tab
->n_var
; ++i
) {
2405 if (!tab
->var
[i
].is_row
) {
2406 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
2409 row
= tab
->var
[i
].index
;
2410 isl_int_gcd(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
2411 isl_int_divexact(m
, tab
->mat
->row
[row
][0], m
);
2412 isl_seq_scale(vec
->block
.data
, vec
->block
.data
, m
, 1 + i
);
2413 isl_int_divexact(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
2414 isl_int_mul(vec
->block
.data
[1 + i
], m
, tab
->mat
->row
[row
][1]);
2416 vec
= isl_vec_normalize(vec
);
2422 /* Update "bmap" based on the results of the tableau "tab".
2423 * In particular, implicit equalities are made explicit, redundant constraints
2424 * are removed and if the sample value happens to be integer, it is stored
2425 * in "bmap" (unless "bmap" already had an integer sample).
2427 * The tableau is assumed to have been created from "bmap" using
2428 * isl_tab_from_basic_map.
2430 struct isl_basic_map
*isl_basic_map_update_from_tab(struct isl_basic_map
*bmap
,
2431 struct isl_tab
*tab
)
2443 bmap
= isl_basic_map_set_to_empty(bmap
);
2445 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
2446 if (isl_tab_is_equality(tab
, n_eq
+ i
))
2447 isl_basic_map_inequality_to_equality(bmap
, i
);
2448 else if (isl_tab_is_redundant(tab
, n_eq
+ i
))
2449 isl_basic_map_drop_inequality(bmap
, i
);
2451 if (bmap
->n_eq
!= n_eq
)
2452 isl_basic_map_gauss(bmap
, NULL
);
2453 if (!tab
->rational
&&
2454 !bmap
->sample
&& isl_tab_sample_is_integer(tab
))
2455 bmap
->sample
= extract_integer_sample(tab
);
2459 struct isl_basic_set
*isl_basic_set_update_from_tab(struct isl_basic_set
*bset
,
2460 struct isl_tab
*tab
)
2462 return (struct isl_basic_set
*)isl_basic_map_update_from_tab(
2463 (struct isl_basic_map
*)bset
, tab
);
2466 /* Given a non-negative variable "var", add a new non-negative variable
2467 * that is the opposite of "var", ensuring that var can only attain the
2469 * If var = n/d is a row variable, then the new variable = -n/d.
2470 * If var is a column variables, then the new variable = -var.
2471 * If the new variable cannot attain non-negative values, then
2472 * the resulting tableau is empty.
2473 * Otherwise, we know the value will be zero and we close the row.
2475 static int cut_to_hyperplane(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2480 unsigned off
= 2 + tab
->M
;
2484 isl_assert(tab
->mat
->ctx
, !var
->is_redundant
, return -1);
2485 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return -1);
2487 if (isl_tab_extend_cons(tab
, 1) < 0)
2491 tab
->con
[r
].index
= tab
->n_row
;
2492 tab
->con
[r
].is_row
= 1;
2493 tab
->con
[r
].is_nonneg
= 0;
2494 tab
->con
[r
].is_zero
= 0;
2495 tab
->con
[r
].is_redundant
= 0;
2496 tab
->con
[r
].frozen
= 0;
2497 tab
->con
[r
].negated
= 0;
2498 tab
->row_var
[tab
->n_row
] = ~r
;
2499 row
= tab
->mat
->row
[tab
->n_row
];
2502 isl_int_set(row
[0], tab
->mat
->row
[var
->index
][0]);
2503 isl_seq_neg(row
+ 1,
2504 tab
->mat
->row
[var
->index
] + 1, 1 + tab
->n_col
);
2506 isl_int_set_si(row
[0], 1);
2507 isl_seq_clr(row
+ 1, 1 + tab
->n_col
);
2508 isl_int_set_si(row
[off
+ var
->index
], -1);
2513 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]) < 0)
2516 sgn
= sign_of_max(tab
, &tab
->con
[r
]);
2520 if (isl_tab_mark_empty(tab
) < 0)
2524 tab
->con
[r
].is_nonneg
= 1;
2525 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2528 if (close_row(tab
, &tab
->con
[r
]) < 0)
2534 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2535 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2536 * by r' = r + 1 >= 0.
2537 * If r is a row variable, we simply increase the constant term by one
2538 * (taking into account the denominator).
2539 * If r is a column variable, then we need to modify each row that
2540 * refers to r = r' - 1 by substituting this equality, effectively
2541 * subtracting the coefficient of the column from the constant.
2542 * We should only do this if the minimum is manifestly unbounded,
2543 * however. Otherwise, we may end up with negative sample values
2544 * for non-negative variables.
2545 * So, if r is a column variable with a minimum that is not
2546 * manifestly unbounded, then we need to move it to a row.
2547 * However, the sample value of this row may be negative,
2548 * even after the relaxation, so we need to restore it.
2549 * We therefore prefer to pivot a column up to a row, if possible.
2551 struct isl_tab
*isl_tab_relax(struct isl_tab
*tab
, int con
)
2553 struct isl_tab_var
*var
;
2554 unsigned off
= 2 + tab
->M
;
2559 var
= &tab
->con
[con
];
2561 if (var
->is_row
&& (var
->index
< 0 || var
->index
< tab
->n_redundant
))
2562 isl_die(tab
->mat
->ctx
, isl_error_invalid
,
2563 "cannot relax redundant constraint", goto error
);
2564 if (!var
->is_row
&& (var
->index
< 0 || var
->index
< tab
->n_dead
))
2565 isl_die(tab
->mat
->ctx
, isl_error_invalid
,
2566 "cannot relax dead constraint", goto error
);
2568 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
2569 if (to_row(tab
, var
, 1) < 0)
2571 if (!var
->is_row
&& !min_is_manifestly_unbounded(tab
, var
))
2572 if (to_row(tab
, var
, -1) < 0)
2576 isl_int_add(tab
->mat
->row
[var
->index
][1],
2577 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
2578 if (restore_row(tab
, var
) < 0)
2583 for (i
= 0; i
< tab
->n_row
; ++i
) {
2584 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2586 isl_int_sub(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
2587 tab
->mat
->row
[i
][off
+ var
->index
]);
2592 if (isl_tab_push_var(tab
, isl_tab_undo_relax
, var
) < 0)
2601 int isl_tab_select_facet(struct isl_tab
*tab
, int con
)
2606 return cut_to_hyperplane(tab
, &tab
->con
[con
]);
2609 static int may_be_equality(struct isl_tab
*tab
, int row
)
2611 return tab
->rational
? isl_int_is_zero(tab
->mat
->row
[row
][1])
2612 : isl_int_lt(tab
->mat
->row
[row
][1],
2613 tab
->mat
->row
[row
][0]);
2616 /* Check for (near) equalities among the constraints.
2617 * A constraint is an equality if it is non-negative and if
2618 * its maximal value is either
2619 * - zero (in case of rational tableaus), or
2620 * - strictly less than 1 (in case of integer tableaus)
2622 * We first mark all non-redundant and non-dead variables that
2623 * are not frozen and not obviously not an equality.
2624 * Then we iterate over all marked variables if they can attain
2625 * any values larger than zero or at least one.
2626 * If the maximal value is zero, we mark any column variables
2627 * that appear in the row as being zero and mark the row as being redundant.
2628 * Otherwise, if the maximal value is strictly less than one (and the
2629 * tableau is integer), then we restrict the value to being zero
2630 * by adding an opposite non-negative variable.
2632 int isl_tab_detect_implicit_equalities(struct isl_tab
*tab
)
2641 if (tab
->n_dead
== tab
->n_col
)
2645 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2646 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2647 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2648 may_be_equality(tab
, i
);
2652 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2653 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2654 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2659 struct isl_tab_var
*var
;
2661 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2662 var
= isl_tab_var_from_row(tab
, i
);
2666 if (i
== tab
->n_row
) {
2667 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2668 var
= var_from_col(tab
, i
);
2672 if (i
== tab
->n_col
)
2677 sgn
= sign_of_max(tab
, var
);
2681 if (close_row(tab
, var
) < 0)
2683 } else if (!tab
->rational
&& !at_least_one(tab
, var
)) {
2684 if (cut_to_hyperplane(tab
, var
) < 0)
2686 return isl_tab_detect_implicit_equalities(tab
);
2688 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2689 var
= isl_tab_var_from_row(tab
, i
);
2692 if (may_be_equality(tab
, i
))
2702 static int con_is_redundant(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2706 if (tab
->rational
) {
2707 int sgn
= sign_of_min(tab
, var
);
2712 int irred
= isl_tab_min_at_most_neg_one(tab
, var
);
2719 /* Check for (near) redundant constraints.
2720 * A constraint is redundant if it is non-negative and if
2721 * its minimal value (temporarily ignoring the non-negativity) is either
2722 * - zero (in case of rational tableaus), or
2723 * - strictly larger than -1 (in case of integer tableaus)
2725 * We first mark all non-redundant and non-dead variables that
2726 * are not frozen and not obviously negatively unbounded.
2727 * Then we iterate over all marked variables if they can attain
2728 * any values smaller than zero or at most negative one.
2729 * If not, we mark the row as being redundant (assuming it hasn't
2730 * been detected as being obviously redundant in the mean time).
2732 int isl_tab_detect_redundant(struct isl_tab
*tab
)
2741 if (tab
->n_redundant
== tab
->n_row
)
2745 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2746 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2747 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2751 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2752 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2753 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2754 !min_is_manifestly_unbounded(tab
, var
);
2759 struct isl_tab_var
*var
;
2761 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2762 var
= isl_tab_var_from_row(tab
, i
);
2766 if (i
== tab
->n_row
) {
2767 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2768 var
= var_from_col(tab
, i
);
2772 if (i
== tab
->n_col
)
2777 red
= con_is_redundant(tab
, var
);
2780 if (red
&& !var
->is_redundant
)
2781 if (isl_tab_mark_redundant(tab
, var
->index
) < 0)
2783 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2784 var
= var_from_col(tab
, i
);
2787 if (!min_is_manifestly_unbounded(tab
, var
))
2797 int isl_tab_is_equality(struct isl_tab
*tab
, int con
)
2804 if (tab
->con
[con
].is_zero
)
2806 if (tab
->con
[con
].is_redundant
)
2808 if (!tab
->con
[con
].is_row
)
2809 return tab
->con
[con
].index
< tab
->n_dead
;
2811 row
= tab
->con
[con
].index
;
2814 return isl_int_is_zero(tab
->mat
->row
[row
][1]) &&
2815 (!tab
->M
|| isl_int_is_zero(tab
->mat
->row
[row
][2])) &&
2816 isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
2817 tab
->n_col
- tab
->n_dead
) == -1;
2820 /* Return the minimal value of the affine expression "f" with denominator
2821 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
2822 * the expression cannot attain arbitrarily small values.
2823 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
2824 * The return value reflects the nature of the result (empty, unbounded,
2825 * minimal value returned in *opt).
2827 enum isl_lp_result
isl_tab_min(struct isl_tab
*tab
,
2828 isl_int
*f
, isl_int denom
, isl_int
*opt
, isl_int
*opt_denom
,
2832 enum isl_lp_result res
= isl_lp_ok
;
2833 struct isl_tab_var
*var
;
2834 struct isl_tab_undo
*snap
;
2837 return isl_lp_error
;
2840 return isl_lp_empty
;
2842 snap
= isl_tab_snap(tab
);
2843 r
= isl_tab_add_row(tab
, f
);
2845 return isl_lp_error
;
2849 find_pivot(tab
, var
, var
, -1, &row
, &col
);
2850 if (row
== var
->index
) {
2851 res
= isl_lp_unbounded
;
2856 if (isl_tab_pivot(tab
, row
, col
) < 0)
2857 return isl_lp_error
;
2859 isl_int_mul(tab
->mat
->row
[var
->index
][0],
2860 tab
->mat
->row
[var
->index
][0], denom
);
2861 if (ISL_FL_ISSET(flags
, ISL_TAB_SAVE_DUAL
)) {
2864 isl_vec_free(tab
->dual
);
2865 tab
->dual
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_con
);
2867 return isl_lp_error
;
2868 isl_int_set(tab
->dual
->el
[0], tab
->mat
->row
[var
->index
][0]);
2869 for (i
= 0; i
< tab
->n_con
; ++i
) {
2871 if (tab
->con
[i
].is_row
) {
2872 isl_int_set_si(tab
->dual
->el
[1 + i
], 0);
2875 pos
= 2 + tab
->M
+ tab
->con
[i
].index
;
2876 if (tab
->con
[i
].negated
)
2877 isl_int_neg(tab
->dual
->el
[1 + i
],
2878 tab
->mat
->row
[var
->index
][pos
]);
2880 isl_int_set(tab
->dual
->el
[1 + i
],
2881 tab
->mat
->row
[var
->index
][pos
]);
2884 if (opt
&& res
== isl_lp_ok
) {
2886 isl_int_set(*opt
, tab
->mat
->row
[var
->index
][1]);
2887 isl_int_set(*opt_denom
, tab
->mat
->row
[var
->index
][0]);
2889 isl_int_cdiv_q(*opt
, tab
->mat
->row
[var
->index
][1],
2890 tab
->mat
->row
[var
->index
][0]);
2892 if (isl_tab_rollback(tab
, snap
) < 0)
2893 return isl_lp_error
;
2897 int isl_tab_is_redundant(struct isl_tab
*tab
, int con
)
2901 if (tab
->con
[con
].is_zero
)
2903 if (tab
->con
[con
].is_redundant
)
2905 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
2908 /* Take a snapshot of the tableau that can be restored by s call to
2911 struct isl_tab_undo
*isl_tab_snap(struct isl_tab
*tab
)
2919 /* Undo the operation performed by isl_tab_relax.
2921 static int unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
2922 static int unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2924 unsigned off
= 2 + tab
->M
;
2926 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
2927 if (to_row(tab
, var
, 1) < 0)
2931 isl_int_sub(tab
->mat
->row
[var
->index
][1],
2932 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
2933 if (var
->is_nonneg
) {
2934 int sgn
= restore_row(tab
, var
);
2935 isl_assert(tab
->mat
->ctx
, sgn
>= 0, return -1);
2940 for (i
= 0; i
< tab
->n_row
; ++i
) {
2941 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2943 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
2944 tab
->mat
->row
[i
][off
+ var
->index
]);
2952 static int perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
) WARN_UNUSED
;
2953 static int perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2955 struct isl_tab_var
*var
= var_from_index(tab
, undo
->u
.var_index
);
2956 switch (undo
->type
) {
2957 case isl_tab_undo_nonneg
:
2960 case isl_tab_undo_redundant
:
2961 var
->is_redundant
= 0;
2963 restore_row(tab
, isl_tab_var_from_row(tab
, tab
->n_redundant
));
2965 case isl_tab_undo_freeze
:
2968 case isl_tab_undo_zero
:
2973 case isl_tab_undo_allocate
:
2974 if (undo
->u
.var_index
>= 0) {
2975 isl_assert(tab
->mat
->ctx
, !var
->is_row
, return -1);
2976 drop_col(tab
, var
->index
);
2980 if (!max_is_manifestly_unbounded(tab
, var
)) {
2981 if (to_row(tab
, var
, 1) < 0)
2983 } else if (!min_is_manifestly_unbounded(tab
, var
)) {
2984 if (to_row(tab
, var
, -1) < 0)
2987 if (to_row(tab
, var
, 0) < 0)
2990 drop_row(tab
, var
->index
);
2992 case isl_tab_undo_relax
:
2993 return unrelax(tab
, var
);
2995 isl_die(tab
->mat
->ctx
, isl_error_internal
,
2996 "perform_undo_var called on invalid undo record",
3003 /* Restore the tableau to the state where the basic variables
3004 * are those in "col_var".
3005 * We first construct a list of variables that are currently in
3006 * the basis, but shouldn't. Then we iterate over all variables
3007 * that should be in the basis and for each one that is currently
3008 * not in the basis, we exchange it with one of the elements of the
3009 * list constructed before.
3010 * We can always find an appropriate variable to pivot with because
3011 * the current basis is mapped to the old basis by a non-singular
3012 * matrix and so we can never end up with a zero row.
3014 static int restore_basis(struct isl_tab
*tab
, int *col_var
)
3018 int *extra
= NULL
; /* current columns that contain bad stuff */
3019 unsigned off
= 2 + tab
->M
;
3021 extra
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
3024 for (i
= 0; i
< tab
->n_col
; ++i
) {
3025 for (j
= 0; j
< tab
->n_col
; ++j
)
3026 if (tab
->col_var
[i
] == col_var
[j
])
3030 extra
[n_extra
++] = i
;
3032 for (i
= 0; i
< tab
->n_col
&& n_extra
> 0; ++i
) {
3033 struct isl_tab_var
*var
;
3036 for (j
= 0; j
< tab
->n_col
; ++j
)
3037 if (col_var
[i
] == tab
->col_var
[j
])
3041 var
= var_from_index(tab
, col_var
[i
]);
3043 for (j
= 0; j
< n_extra
; ++j
)
3044 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+extra
[j
]]))
3046 isl_assert(tab
->mat
->ctx
, j
< n_extra
, goto error
);
3047 if (isl_tab_pivot(tab
, row
, extra
[j
]) < 0)
3049 extra
[j
] = extra
[--n_extra
];
3059 /* Remove all samples with index n or greater, i.e., those samples
3060 * that were added since we saved this number of samples in
3061 * isl_tab_save_samples.
3063 static void drop_samples_since(struct isl_tab
*tab
, int n
)
3067 for (i
= tab
->n_sample
- 1; i
>= 0 && tab
->n_sample
> n
; --i
) {
3068 if (tab
->sample_index
[i
] < n
)
3071 if (i
!= tab
->n_sample
- 1) {
3072 int t
= tab
->sample_index
[tab
->n_sample
-1];
3073 tab
->sample_index
[tab
->n_sample
-1] = tab
->sample_index
[i
];
3074 tab
->sample_index
[i
] = t
;
3075 isl_mat_swap_rows(tab
->samples
, tab
->n_sample
-1, i
);
3081 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
) WARN_UNUSED
;
3082 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
3084 switch (undo
->type
) {
3085 case isl_tab_undo_empty
:
3088 case isl_tab_undo_nonneg
:
3089 case isl_tab_undo_redundant
:
3090 case isl_tab_undo_freeze
:
3091 case isl_tab_undo_zero
:
3092 case isl_tab_undo_allocate
:
3093 case isl_tab_undo_relax
:
3094 return perform_undo_var(tab
, undo
);
3095 case isl_tab_undo_bmap_eq
:
3096 return isl_basic_map_free_equality(tab
->bmap
, 1);
3097 case isl_tab_undo_bmap_ineq
:
3098 return isl_basic_map_free_inequality(tab
->bmap
, 1);
3099 case isl_tab_undo_bmap_div
:
3100 if (isl_basic_map_free_div(tab
->bmap
, 1) < 0)
3103 tab
->samples
->n_col
--;
3105 case isl_tab_undo_saved_basis
:
3106 if (restore_basis(tab
, undo
->u
.col_var
) < 0)
3109 case isl_tab_undo_drop_sample
:
3112 case isl_tab_undo_saved_samples
:
3113 drop_samples_since(tab
, undo
->u
.n
);
3115 case isl_tab_undo_callback
:
3116 return undo
->u
.callback
->run(undo
->u
.callback
);
3118 isl_assert(tab
->mat
->ctx
, 0, return -1);
3123 /* Return the tableau to the state it was in when the snapshot "snap"
3126 int isl_tab_rollback(struct isl_tab
*tab
, struct isl_tab_undo
*snap
)
3128 struct isl_tab_undo
*undo
, *next
;
3134 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
3138 if (perform_undo(tab
, undo
) < 0) {
3144 free_undo_record(undo
);
3153 /* The given row "row" represents an inequality violated by all
3154 * points in the tableau. Check for some special cases of such
3155 * separating constraints.
3156 * In particular, if the row has been reduced to the constant -1,
3157 * then we know the inequality is adjacent (but opposite) to
3158 * an equality in the tableau.
3159 * If the row has been reduced to r = c*(-1 -r'), with r' an inequality
3160 * of the tableau and c a positive constant, then the inequality
3161 * is adjacent (but opposite) to the inequality r'.
3163 static enum isl_ineq_type
separation_type(struct isl_tab
*tab
, unsigned row
)
3166 unsigned off
= 2 + tab
->M
;
3169 return isl_ineq_separate
;
3171 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
3172 return isl_ineq_separate
;
3174 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
3175 tab
->n_col
- tab
->n_dead
);
3177 if (isl_int_is_negone(tab
->mat
->row
[row
][1]))
3178 return isl_ineq_adj_eq
;
3180 return isl_ineq_separate
;
3183 if (!isl_int_eq(tab
->mat
->row
[row
][1],
3184 tab
->mat
->row
[row
][off
+ tab
->n_dead
+ pos
]))
3185 return isl_ineq_separate
;
3187 pos
= isl_seq_first_non_zero(
3188 tab
->mat
->row
[row
] + off
+ tab
->n_dead
+ pos
+ 1,
3189 tab
->n_col
- tab
->n_dead
- pos
- 1);
3191 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
3194 /* Check the effect of inequality "ineq" on the tableau "tab".
3196 * isl_ineq_redundant: satisfied by all points in the tableau
3197 * isl_ineq_separate: satisfied by no point in the tableau
3198 * isl_ineq_cut: satisfied by some by not all points
3199 * isl_ineq_adj_eq: adjacent to an equality
3200 * isl_ineq_adj_ineq: adjacent to an inequality.
3202 enum isl_ineq_type
isl_tab_ineq_type(struct isl_tab
*tab
, isl_int
*ineq
)
3204 enum isl_ineq_type type
= isl_ineq_error
;
3205 struct isl_tab_undo
*snap
= NULL
;
3210 return isl_ineq_error
;
3212 if (isl_tab_extend_cons(tab
, 1) < 0)
3213 return isl_ineq_error
;
3215 snap
= isl_tab_snap(tab
);
3217 con
= isl_tab_add_row(tab
, ineq
);
3221 row
= tab
->con
[con
].index
;
3222 if (isl_tab_row_is_redundant(tab
, row
))
3223 type
= isl_ineq_redundant
;
3224 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
3226 isl_int_abs_ge(tab
->mat
->row
[row
][1],
3227 tab
->mat
->row
[row
][0]))) {
3228 int nonneg
= at_least_zero(tab
, &tab
->con
[con
]);
3232 type
= isl_ineq_cut
;
3234 type
= separation_type(tab
, row
);
3236 int red
= con_is_redundant(tab
, &tab
->con
[con
]);
3240 type
= isl_ineq_cut
;
3242 type
= isl_ineq_redundant
;
3245 if (isl_tab_rollback(tab
, snap
))
3246 return isl_ineq_error
;
3249 return isl_ineq_error
;
3252 int isl_tab_track_bmap(struct isl_tab
*tab
, __isl_take isl_basic_map
*bmap
)
3254 bmap
= isl_basic_map_cow(bmap
);
3259 bmap
= isl_basic_map_set_to_empty(bmap
);
3266 isl_assert(tab
->mat
->ctx
, tab
->n_eq
== bmap
->n_eq
, goto error
);
3267 isl_assert(tab
->mat
->ctx
,
3268 tab
->n_con
== bmap
->n_eq
+ bmap
->n_ineq
, goto error
);
3274 isl_basic_map_free(bmap
);
3278 int isl_tab_track_bset(struct isl_tab
*tab
, __isl_take isl_basic_set
*bset
)
3280 return isl_tab_track_bmap(tab
, (isl_basic_map
*)bset
);
3283 __isl_keep isl_basic_set
*isl_tab_peek_bset(struct isl_tab
*tab
)
3288 return (isl_basic_set
*)tab
->bmap
;
3291 static void isl_tab_print_internal(__isl_keep
struct isl_tab
*tab
,
3292 FILE *out
, int indent
)
3298 fprintf(out
, "%*snull tab\n", indent
, "");
3301 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
3302 tab
->n_redundant
, tab
->n_dead
);
3304 fprintf(out
, ", rational");
3306 fprintf(out
, ", empty");
3308 fprintf(out
, "%*s[", indent
, "");
3309 for (i
= 0; i
< tab
->n_var
; ++i
) {
3311 fprintf(out
, (i
== tab
->n_param
||
3312 i
== tab
->n_var
- tab
->n_div
) ? "; "
3314 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
3316 tab
->var
[i
].is_zero
? " [=0]" :
3317 tab
->var
[i
].is_redundant
? " [R]" : "");
3319 fprintf(out
, "]\n");
3320 fprintf(out
, "%*s[", indent
, "");
3321 for (i
= 0; i
< tab
->n_con
; ++i
) {
3324 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
3326 tab
->con
[i
].is_zero
? " [=0]" :
3327 tab
->con
[i
].is_redundant
? " [R]" : "");
3329 fprintf(out
, "]\n");
3330 fprintf(out
, "%*s[", indent
, "");
3331 for (i
= 0; i
< tab
->n_row
; ++i
) {
3332 const char *sign
= "";
3335 if (tab
->row_sign
) {
3336 if (tab
->row_sign
[i
] == isl_tab_row_unknown
)
3338 else if (tab
->row_sign
[i
] == isl_tab_row_neg
)
3340 else if (tab
->row_sign
[i
] == isl_tab_row_pos
)
3345 fprintf(out
, "r%d: %d%s%s", i
, tab
->row_var
[i
],
3346 isl_tab_var_from_row(tab
, i
)->is_nonneg
? " [>=0]" : "", sign
);
3348 fprintf(out
, "]\n");
3349 fprintf(out
, "%*s[", indent
, "");
3350 for (i
= 0; i
< tab
->n_col
; ++i
) {
3353 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
3354 var_from_col(tab
, i
)->is_nonneg
? " [>=0]" : "");
3356 fprintf(out
, "]\n");
3357 r
= tab
->mat
->n_row
;
3358 tab
->mat
->n_row
= tab
->n_row
;
3359 c
= tab
->mat
->n_col
;
3360 tab
->mat
->n_col
= 2 + tab
->M
+ tab
->n_col
;
3361 isl_mat_print_internal(tab
->mat
, out
, indent
);
3362 tab
->mat
->n_row
= r
;
3363 tab
->mat
->n_col
= c
;
3365 isl_basic_map_print_internal(tab
->bmap
, out
, indent
);
3368 void isl_tab_dump(__isl_keep
struct isl_tab
*tab
)
3370 isl_tab_print_internal(tab
, stderr
, 0);