2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 #include "isl_map_private.h"
16 * The implementation of tableaus in this file was inspired by Section 8
17 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
18 * prover for program checking".
21 struct isl_tab
*isl_tab_alloc(struct isl_ctx
*ctx
,
22 unsigned n_row
, unsigned n_var
, unsigned M
)
28 tab
= isl_calloc_type(ctx
, struct isl_tab
);
31 tab
->mat
= isl_mat_alloc(ctx
, n_row
, off
+ n_var
);
34 tab
->var
= isl_alloc_array(ctx
, struct isl_tab_var
, n_var
);
37 tab
->con
= isl_alloc_array(ctx
, struct isl_tab_var
, n_row
);
40 tab
->col_var
= isl_alloc_array(ctx
, int, n_var
);
43 tab
->row_var
= isl_alloc_array(ctx
, int, n_row
);
46 for (i
= 0; i
< n_var
; ++i
) {
47 tab
->var
[i
].index
= i
;
48 tab
->var
[i
].is_row
= 0;
49 tab
->var
[i
].is_nonneg
= 0;
50 tab
->var
[i
].is_zero
= 0;
51 tab
->var
[i
].is_redundant
= 0;
52 tab
->var
[i
].frozen
= 0;
53 tab
->var
[i
].negated
= 0;
67 tab
->strict_redundant
= 0;
74 tab
->bottom
.type
= isl_tab_undo_bottom
;
75 tab
->bottom
.next
= NULL
;
76 tab
->top
= &tab
->bottom
;
88 int isl_tab_extend_cons(struct isl_tab
*tab
, unsigned n_new
)
90 unsigned off
= 2 + tab
->M
;
95 if (tab
->max_con
< tab
->n_con
+ n_new
) {
96 struct isl_tab_var
*con
;
98 con
= isl_realloc_array(tab
->mat
->ctx
, tab
->con
,
99 struct isl_tab_var
, tab
->max_con
+ n_new
);
103 tab
->max_con
+= n_new
;
105 if (tab
->mat
->n_row
< tab
->n_row
+ n_new
) {
108 tab
->mat
= isl_mat_extend(tab
->mat
,
109 tab
->n_row
+ n_new
, off
+ tab
->n_col
);
112 row_var
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_var
,
113 int, tab
->mat
->n_row
);
116 tab
->row_var
= row_var
;
118 enum isl_tab_row_sign
*s
;
119 s
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_sign
,
120 enum isl_tab_row_sign
, tab
->mat
->n_row
);
129 /* Make room for at least n_new extra variables.
130 * Return -1 if anything went wrong.
132 int isl_tab_extend_vars(struct isl_tab
*tab
, unsigned n_new
)
134 struct isl_tab_var
*var
;
135 unsigned off
= 2 + tab
->M
;
137 if (tab
->max_var
< tab
->n_var
+ n_new
) {
138 var
= isl_realloc_array(tab
->mat
->ctx
, tab
->var
,
139 struct isl_tab_var
, tab
->n_var
+ n_new
);
143 tab
->max_var
+= n_new
;
146 if (tab
->mat
->n_col
< off
+ tab
->n_col
+ n_new
) {
149 tab
->mat
= isl_mat_extend(tab
->mat
,
150 tab
->mat
->n_row
, off
+ tab
->n_col
+ n_new
);
153 p
= isl_realloc_array(tab
->mat
->ctx
, tab
->col_var
,
154 int, tab
->n_col
+ n_new
);
163 struct isl_tab
*isl_tab_extend(struct isl_tab
*tab
, unsigned n_new
)
165 if (isl_tab_extend_cons(tab
, n_new
) >= 0)
172 static void free_undo(struct isl_tab
*tab
)
174 struct isl_tab_undo
*undo
, *next
;
176 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
183 void isl_tab_free(struct isl_tab
*tab
)
188 isl_mat_free(tab
->mat
);
189 isl_vec_free(tab
->dual
);
190 isl_basic_map_free(tab
->bmap
);
196 isl_mat_free(tab
->samples
);
197 free(tab
->sample_index
);
198 isl_mat_free(tab
->basis
);
202 struct isl_tab
*isl_tab_dup(struct isl_tab
*tab
)
212 dup
= isl_calloc_type(tab
->ctx
, struct isl_tab
);
215 dup
->mat
= isl_mat_dup(tab
->mat
);
218 dup
->var
= isl_alloc_array(tab
->ctx
, struct isl_tab_var
, tab
->max_var
);
221 for (i
= 0; i
< tab
->n_var
; ++i
)
222 dup
->var
[i
] = tab
->var
[i
];
223 dup
->con
= isl_alloc_array(tab
->ctx
, struct isl_tab_var
, tab
->max_con
);
226 for (i
= 0; i
< tab
->n_con
; ++i
)
227 dup
->con
[i
] = tab
->con
[i
];
228 dup
->col_var
= isl_alloc_array(tab
->ctx
, int, tab
->mat
->n_col
- off
);
231 for (i
= 0; i
< tab
->n_col
; ++i
)
232 dup
->col_var
[i
] = tab
->col_var
[i
];
233 dup
->row_var
= isl_alloc_array(tab
->ctx
, int, tab
->mat
->n_row
);
236 for (i
= 0; i
< tab
->n_row
; ++i
)
237 dup
->row_var
[i
] = tab
->row_var
[i
];
239 dup
->row_sign
= isl_alloc_array(tab
->ctx
, enum isl_tab_row_sign
,
243 for (i
= 0; i
< tab
->n_row
; ++i
)
244 dup
->row_sign
[i
] = tab
->row_sign
[i
];
247 dup
->samples
= isl_mat_dup(tab
->samples
);
250 dup
->sample_index
= isl_alloc_array(tab
->mat
->ctx
, int,
251 tab
->samples
->n_row
);
252 if (!dup
->sample_index
)
254 dup
->n_sample
= tab
->n_sample
;
255 dup
->n_outside
= tab
->n_outside
;
257 dup
->n_row
= tab
->n_row
;
258 dup
->n_con
= tab
->n_con
;
259 dup
->n_eq
= tab
->n_eq
;
260 dup
->max_con
= tab
->max_con
;
261 dup
->n_col
= tab
->n_col
;
262 dup
->n_var
= tab
->n_var
;
263 dup
->max_var
= tab
->max_var
;
264 dup
->n_param
= tab
->n_param
;
265 dup
->n_div
= tab
->n_div
;
266 dup
->n_dead
= tab
->n_dead
;
267 dup
->n_redundant
= tab
->n_redundant
;
268 dup
->rational
= tab
->rational
;
269 dup
->empty
= tab
->empty
;
270 dup
->strict_redundant
= 0;
274 tab
->cone
= tab
->cone
;
275 dup
->bottom
.type
= isl_tab_undo_bottom
;
276 dup
->bottom
.next
= NULL
;
277 dup
->top
= &dup
->bottom
;
279 dup
->n_zero
= tab
->n_zero
;
280 dup
->n_unbounded
= tab
->n_unbounded
;
281 dup
->basis
= isl_mat_dup(tab
->basis
);
289 /* Construct the coefficient matrix of the product tableau
291 * mat{1,2} is the coefficient matrix of tableau {1,2}
292 * row{1,2} is the number of rows in tableau {1,2}
293 * col{1,2} is the number of columns in tableau {1,2}
294 * off is the offset to the coefficient column (skipping the
295 * denominator, the constant term and the big parameter if any)
296 * r{1,2} is the number of redundant rows in tableau {1,2}
297 * d{1,2} is the number of dead columns in tableau {1,2}
299 * The order of the rows and columns in the result is as explained
300 * in isl_tab_product.
302 static struct isl_mat
*tab_mat_product(struct isl_mat
*mat1
,
303 struct isl_mat
*mat2
, unsigned row1
, unsigned row2
,
304 unsigned col1
, unsigned col2
,
305 unsigned off
, unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
308 struct isl_mat
*prod
;
311 prod
= isl_mat_alloc(mat1
->ctx
, mat1
->n_row
+ mat2
->n_row
,
315 for (i
= 0; i
< r1
; ++i
) {
316 isl_seq_cpy(prod
->row
[n
+ i
], mat1
->row
[i
], off
+ d1
);
317 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
, d2
);
318 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
+ d2
,
319 mat1
->row
[i
] + off
+ d1
, col1
- d1
);
320 isl_seq_clr(prod
->row
[n
+ i
] + off
+ col1
+ d1
, col2
- d2
);
324 for (i
= 0; i
< r2
; ++i
) {
325 isl_seq_cpy(prod
->row
[n
+ i
], mat2
->row
[i
], off
);
326 isl_seq_clr(prod
->row
[n
+ i
] + off
, d1
);
327 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
,
328 mat2
->row
[i
] + off
, d2
);
329 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
+ d2
, col1
- d1
);
330 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ col1
+ d1
,
331 mat2
->row
[i
] + off
+ d2
, col2
- d2
);
335 for (i
= 0; i
< row1
- r1
; ++i
) {
336 isl_seq_cpy(prod
->row
[n
+ i
], mat1
->row
[r1
+ i
], off
+ d1
);
337 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
, d2
);
338 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
+ d2
,
339 mat1
->row
[r1
+ i
] + off
+ d1
, col1
- d1
);
340 isl_seq_clr(prod
->row
[n
+ i
] + off
+ col1
+ d1
, col2
- d2
);
344 for (i
= 0; i
< row2
- r2
; ++i
) {
345 isl_seq_cpy(prod
->row
[n
+ i
], mat2
->row
[r2
+ i
], off
);
346 isl_seq_clr(prod
->row
[n
+ i
] + off
, d1
);
347 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
,
348 mat2
->row
[r2
+ i
] + off
, d2
);
349 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
+ d2
, col1
- d1
);
350 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ col1
+ d1
,
351 mat2
->row
[r2
+ i
] + off
+ d2
, col2
- d2
);
357 /* Update the row or column index of a variable that corresponds
358 * to a variable in the first input tableau.
360 static void update_index1(struct isl_tab_var
*var
,
361 unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
363 if (var
->index
== -1)
365 if (var
->is_row
&& var
->index
>= r1
)
367 if (!var
->is_row
&& var
->index
>= d1
)
371 /* Update the row or column index of a variable that corresponds
372 * to a variable in the second input tableau.
374 static void update_index2(struct isl_tab_var
*var
,
375 unsigned row1
, unsigned col1
,
376 unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
378 if (var
->index
== -1)
393 /* Create a tableau that represents the Cartesian product of the sets
394 * represented by tableaus tab1 and tab2.
395 * The order of the rows in the product is
396 * - redundant rows of tab1
397 * - redundant rows of tab2
398 * - non-redundant rows of tab1
399 * - non-redundant rows of tab2
400 * The order of the columns is
403 * - coefficient of big parameter, if any
404 * - dead columns of tab1
405 * - dead columns of tab2
406 * - live columns of tab1
407 * - live columns of tab2
408 * The order of the variables and the constraints is a concatenation
409 * of order in the two input tableaus.
411 struct isl_tab
*isl_tab_product(struct isl_tab
*tab1
, struct isl_tab
*tab2
)
414 struct isl_tab
*prod
;
416 unsigned r1
, r2
, d1
, d2
;
421 isl_assert(tab1
->mat
->ctx
, tab1
->M
== tab2
->M
, return NULL
);
422 isl_assert(tab1
->mat
->ctx
, tab1
->rational
== tab2
->rational
, return NULL
);
423 isl_assert(tab1
->mat
->ctx
, tab1
->cone
== tab2
->cone
, return NULL
);
424 isl_assert(tab1
->mat
->ctx
, !tab1
->row_sign
, return NULL
);
425 isl_assert(tab1
->mat
->ctx
, !tab2
->row_sign
, return NULL
);
426 isl_assert(tab1
->mat
->ctx
, tab1
->n_param
== 0, return NULL
);
427 isl_assert(tab1
->mat
->ctx
, tab2
->n_param
== 0, return NULL
);
428 isl_assert(tab1
->mat
->ctx
, tab1
->n_div
== 0, return NULL
);
429 isl_assert(tab1
->mat
->ctx
, tab2
->n_div
== 0, return NULL
);
432 r1
= tab1
->n_redundant
;
433 r2
= tab2
->n_redundant
;
436 prod
= isl_calloc_type(tab1
->mat
->ctx
, struct isl_tab
);
439 prod
->mat
= tab_mat_product(tab1
->mat
, tab2
->mat
,
440 tab1
->n_row
, tab2
->n_row
,
441 tab1
->n_col
, tab2
->n_col
, off
, r1
, r2
, d1
, d2
);
444 prod
->var
= isl_alloc_array(tab1
->mat
->ctx
, struct isl_tab_var
,
445 tab1
->max_var
+ tab2
->max_var
);
448 for (i
= 0; i
< tab1
->n_var
; ++i
) {
449 prod
->var
[i
] = tab1
->var
[i
];
450 update_index1(&prod
->var
[i
], r1
, r2
, d1
, d2
);
452 for (i
= 0; i
< tab2
->n_var
; ++i
) {
453 prod
->var
[tab1
->n_var
+ i
] = tab2
->var
[i
];
454 update_index2(&prod
->var
[tab1
->n_var
+ i
],
455 tab1
->n_row
, tab1
->n_col
,
458 prod
->con
= isl_alloc_array(tab1
->mat
->ctx
, struct isl_tab_var
,
459 tab1
->max_con
+ tab2
->max_con
);
462 for (i
= 0; i
< tab1
->n_con
; ++i
) {
463 prod
->con
[i
] = tab1
->con
[i
];
464 update_index1(&prod
->con
[i
], r1
, r2
, d1
, d2
);
466 for (i
= 0; i
< tab2
->n_con
; ++i
) {
467 prod
->con
[tab1
->n_con
+ i
] = tab2
->con
[i
];
468 update_index2(&prod
->con
[tab1
->n_con
+ i
],
469 tab1
->n_row
, tab1
->n_col
,
472 prod
->col_var
= isl_alloc_array(tab1
->mat
->ctx
, int,
473 tab1
->n_col
+ tab2
->n_col
);
476 for (i
= 0; i
< tab1
->n_col
; ++i
) {
477 int pos
= i
< d1
? i
: i
+ d2
;
478 prod
->col_var
[pos
] = tab1
->col_var
[i
];
480 for (i
= 0; i
< tab2
->n_col
; ++i
) {
481 int pos
= i
< d2
? d1
+ i
: tab1
->n_col
+ i
;
482 int t
= tab2
->col_var
[i
];
487 prod
->col_var
[pos
] = t
;
489 prod
->row_var
= isl_alloc_array(tab1
->mat
->ctx
, int,
490 tab1
->mat
->n_row
+ tab2
->mat
->n_row
);
493 for (i
= 0; i
< tab1
->n_row
; ++i
) {
494 int pos
= i
< r1
? i
: i
+ r2
;
495 prod
->row_var
[pos
] = tab1
->row_var
[i
];
497 for (i
= 0; i
< tab2
->n_row
; ++i
) {
498 int pos
= i
< r2
? r1
+ i
: tab1
->n_row
+ i
;
499 int t
= tab2
->row_var
[i
];
504 prod
->row_var
[pos
] = t
;
506 prod
->samples
= NULL
;
507 prod
->sample_index
= NULL
;
508 prod
->n_row
= tab1
->n_row
+ tab2
->n_row
;
509 prod
->n_con
= tab1
->n_con
+ tab2
->n_con
;
511 prod
->max_con
= tab1
->max_con
+ tab2
->max_con
;
512 prod
->n_col
= tab1
->n_col
+ tab2
->n_col
;
513 prod
->n_var
= tab1
->n_var
+ tab2
->n_var
;
514 prod
->max_var
= tab1
->max_var
+ tab2
->max_var
;
517 prod
->n_dead
= tab1
->n_dead
+ tab2
->n_dead
;
518 prod
->n_redundant
= tab1
->n_redundant
+ tab2
->n_redundant
;
519 prod
->rational
= tab1
->rational
;
520 prod
->empty
= tab1
->empty
|| tab2
->empty
;
521 prod
->strict_redundant
= tab1
->strict_redundant
|| tab2
->strict_redundant
;
525 prod
->cone
= tab1
->cone
;
526 prod
->bottom
.type
= isl_tab_undo_bottom
;
527 prod
->bottom
.next
= NULL
;
528 prod
->top
= &prod
->bottom
;
531 prod
->n_unbounded
= 0;
540 static struct isl_tab_var
*var_from_index(struct isl_tab
*tab
, int i
)
545 return &tab
->con
[~i
];
548 struct isl_tab_var
*isl_tab_var_from_row(struct isl_tab
*tab
, int i
)
550 return var_from_index(tab
, tab
->row_var
[i
]);
553 static struct isl_tab_var
*var_from_col(struct isl_tab
*tab
, int i
)
555 return var_from_index(tab
, tab
->col_var
[i
]);
558 /* Check if there are any upper bounds on column variable "var",
559 * i.e., non-negative rows where var appears with a negative coefficient.
560 * Return 1 if there are no such bounds.
562 static int max_is_manifestly_unbounded(struct isl_tab
*tab
,
563 struct isl_tab_var
*var
)
566 unsigned off
= 2 + tab
->M
;
570 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
571 if (!isl_int_is_neg(tab
->mat
->row
[i
][off
+ var
->index
]))
573 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
579 /* Check if there are any lower bounds on column variable "var",
580 * i.e., non-negative rows where var appears with a positive coefficient.
581 * Return 1 if there are no such bounds.
583 static int min_is_manifestly_unbounded(struct isl_tab
*tab
,
584 struct isl_tab_var
*var
)
587 unsigned off
= 2 + tab
->M
;
591 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
592 if (!isl_int_is_pos(tab
->mat
->row
[i
][off
+ var
->index
]))
594 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
600 static int row_cmp(struct isl_tab
*tab
, int r1
, int r2
, int c
, isl_int t
)
602 unsigned off
= 2 + tab
->M
;
606 isl_int_mul(t
, tab
->mat
->row
[r1
][2], tab
->mat
->row
[r2
][off
+c
]);
607 isl_int_submul(t
, tab
->mat
->row
[r2
][2], tab
->mat
->row
[r1
][off
+c
]);
612 isl_int_mul(t
, tab
->mat
->row
[r1
][1], tab
->mat
->row
[r2
][off
+ c
]);
613 isl_int_submul(t
, tab
->mat
->row
[r2
][1], tab
->mat
->row
[r1
][off
+ c
]);
614 return isl_int_sgn(t
);
617 /* Given the index of a column "c", return the index of a row
618 * that can be used to pivot the column in, with either an increase
619 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
620 * If "var" is not NULL, then the row returned will be different from
621 * the one associated with "var".
623 * Each row in the tableau is of the form
625 * x_r = a_r0 + \sum_i a_ri x_i
627 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
628 * impose any limit on the increase or decrease in the value of x_c
629 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
630 * for the row with the smallest (most stringent) such bound.
631 * Note that the common denominator of each row drops out of the fraction.
632 * To check if row j has a smaller bound than row r, i.e.,
633 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
634 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
635 * where -sign(a_jc) is equal to "sgn".
637 static int pivot_row(struct isl_tab
*tab
,
638 struct isl_tab_var
*var
, int sgn
, int c
)
642 unsigned off
= 2 + tab
->M
;
646 for (j
= tab
->n_redundant
; j
< tab
->n_row
; ++j
) {
647 if (var
&& j
== var
->index
)
649 if (!isl_tab_var_from_row(tab
, j
)->is_nonneg
)
651 if (sgn
* isl_int_sgn(tab
->mat
->row
[j
][off
+ c
]) >= 0)
657 tsgn
= sgn
* row_cmp(tab
, r
, j
, c
, t
);
658 if (tsgn
< 0 || (tsgn
== 0 &&
659 tab
->row_var
[j
] < tab
->row_var
[r
]))
666 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
667 * (sgn < 0) the value of row variable var.
668 * If not NULL, then skip_var is a row variable that should be ignored
669 * while looking for a pivot row. It is usually equal to var.
671 * As the given row in the tableau is of the form
673 * x_r = a_r0 + \sum_i a_ri x_i
675 * we need to find a column such that the sign of a_ri is equal to "sgn"
676 * (such that an increase in x_i will have the desired effect) or a
677 * column with a variable that may attain negative values.
678 * If a_ri is positive, then we need to move x_i in the same direction
679 * to obtain the desired effect. Otherwise, x_i has to move in the
680 * opposite direction.
682 static void find_pivot(struct isl_tab
*tab
,
683 struct isl_tab_var
*var
, struct isl_tab_var
*skip_var
,
684 int sgn
, int *row
, int *col
)
691 isl_assert(tab
->mat
->ctx
, var
->is_row
, return);
692 tr
= tab
->mat
->row
[var
->index
] + 2 + tab
->M
;
695 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
696 if (isl_int_is_zero(tr
[j
]))
698 if (isl_int_sgn(tr
[j
]) != sgn
&&
699 var_from_col(tab
, j
)->is_nonneg
)
701 if (c
< 0 || tab
->col_var
[j
] < tab
->col_var
[c
])
707 sgn
*= isl_int_sgn(tr
[c
]);
708 r
= pivot_row(tab
, skip_var
, sgn
, c
);
709 *row
= r
< 0 ? var
->index
: r
;
713 /* Return 1 if row "row" represents an obviously redundant inequality.
715 * - it represents an inequality or a variable
716 * - that is the sum of a non-negative sample value and a positive
717 * combination of zero or more non-negative constraints.
719 int isl_tab_row_is_redundant(struct isl_tab
*tab
, int row
)
722 unsigned off
= 2 + tab
->M
;
724 if (tab
->row_var
[row
] < 0 && !isl_tab_var_from_row(tab
, row
)->is_nonneg
)
727 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
729 if (tab
->strict_redundant
&& isl_int_is_zero(tab
->mat
->row
[row
][1]))
731 if (tab
->M
&& isl_int_is_neg(tab
->mat
->row
[row
][2]))
734 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
735 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ i
]))
737 if (tab
->col_var
[i
] >= 0)
739 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ i
]))
741 if (!var_from_col(tab
, i
)->is_nonneg
)
747 static void swap_rows(struct isl_tab
*tab
, int row1
, int row2
)
750 enum isl_tab_row_sign s
;
752 t
= tab
->row_var
[row1
];
753 tab
->row_var
[row1
] = tab
->row_var
[row2
];
754 tab
->row_var
[row2
] = t
;
755 isl_tab_var_from_row(tab
, row1
)->index
= row1
;
756 isl_tab_var_from_row(tab
, row2
)->index
= row2
;
757 tab
->mat
= isl_mat_swap_rows(tab
->mat
, row1
, row2
);
761 s
= tab
->row_sign
[row1
];
762 tab
->row_sign
[row1
] = tab
->row_sign
[row2
];
763 tab
->row_sign
[row2
] = s
;
766 static int push_union(struct isl_tab
*tab
,
767 enum isl_tab_undo_type type
, union isl_tab_undo_val u
) WARN_UNUSED
;
768 static int push_union(struct isl_tab
*tab
,
769 enum isl_tab_undo_type type
, union isl_tab_undo_val u
)
771 struct isl_tab_undo
*undo
;
776 undo
= isl_alloc_type(tab
->mat
->ctx
, struct isl_tab_undo
);
781 undo
->next
= tab
->top
;
787 int isl_tab_push_var(struct isl_tab
*tab
,
788 enum isl_tab_undo_type type
, struct isl_tab_var
*var
)
790 union isl_tab_undo_val u
;
792 u
.var_index
= tab
->row_var
[var
->index
];
794 u
.var_index
= tab
->col_var
[var
->index
];
795 return push_union(tab
, type
, u
);
798 int isl_tab_push(struct isl_tab
*tab
, enum isl_tab_undo_type type
)
800 union isl_tab_undo_val u
= { 0 };
801 return push_union(tab
, type
, u
);
804 /* Push a record on the undo stack describing the current basic
805 * variables, so that the this state can be restored during rollback.
807 int isl_tab_push_basis(struct isl_tab
*tab
)
810 union isl_tab_undo_val u
;
812 u
.col_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
815 for (i
= 0; i
< tab
->n_col
; ++i
)
816 u
.col_var
[i
] = tab
->col_var
[i
];
817 return push_union(tab
, isl_tab_undo_saved_basis
, u
);
820 int isl_tab_push_callback(struct isl_tab
*tab
, struct isl_tab_callback
*callback
)
822 union isl_tab_undo_val u
;
823 u
.callback
= callback
;
824 return push_union(tab
, isl_tab_undo_callback
, u
);
827 struct isl_tab
*isl_tab_init_samples(struct isl_tab
*tab
)
834 tab
->samples
= isl_mat_alloc(tab
->mat
->ctx
, 1, 1 + tab
->n_var
);
837 tab
->sample_index
= isl_alloc_array(tab
->mat
->ctx
, int, 1);
838 if (!tab
->sample_index
)
846 struct isl_tab
*isl_tab_add_sample(struct isl_tab
*tab
,
847 __isl_take isl_vec
*sample
)
852 if (tab
->n_sample
+ 1 > tab
->samples
->n_row
) {
853 int *t
= isl_realloc_array(tab
->mat
->ctx
,
854 tab
->sample_index
, int, tab
->n_sample
+ 1);
857 tab
->sample_index
= t
;
860 tab
->samples
= isl_mat_extend(tab
->samples
,
861 tab
->n_sample
+ 1, tab
->samples
->n_col
);
865 isl_seq_cpy(tab
->samples
->row
[tab
->n_sample
], sample
->el
, sample
->size
);
866 isl_vec_free(sample
);
867 tab
->sample_index
[tab
->n_sample
] = tab
->n_sample
;
872 isl_vec_free(sample
);
877 struct isl_tab
*isl_tab_drop_sample(struct isl_tab
*tab
, int s
)
879 if (s
!= tab
->n_outside
) {
880 int t
= tab
->sample_index
[tab
->n_outside
];
881 tab
->sample_index
[tab
->n_outside
] = tab
->sample_index
[s
];
882 tab
->sample_index
[s
] = t
;
883 isl_mat_swap_rows(tab
->samples
, tab
->n_outside
, s
);
886 if (isl_tab_push(tab
, isl_tab_undo_drop_sample
) < 0) {
894 /* Record the current number of samples so that we can remove newer
895 * samples during a rollback.
897 int isl_tab_save_samples(struct isl_tab
*tab
)
899 union isl_tab_undo_val u
;
905 return push_union(tab
, isl_tab_undo_saved_samples
, u
);
908 /* Mark row with index "row" as being redundant.
909 * If we may need to undo the operation or if the row represents
910 * a variable of the original problem, the row is kept,
911 * but no longer considered when looking for a pivot row.
912 * Otherwise, the row is simply removed.
914 * The row may be interchanged with some other row. If it
915 * is interchanged with a later row, return 1. Otherwise return 0.
916 * If the rows are checked in order in the calling function,
917 * then a return value of 1 means that the row with the given
918 * row number may now contain a different row that hasn't been checked yet.
920 int isl_tab_mark_redundant(struct isl_tab
*tab
, int row
)
922 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, row
);
923 var
->is_redundant
= 1;
924 isl_assert(tab
->mat
->ctx
, row
>= tab
->n_redundant
, return -1);
925 if (tab
->need_undo
|| tab
->row_var
[row
] >= 0) {
926 if (tab
->row_var
[row
] >= 0 && !var
->is_nonneg
) {
928 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, var
) < 0)
931 if (row
!= tab
->n_redundant
)
932 swap_rows(tab
, row
, tab
->n_redundant
);
934 return isl_tab_push_var(tab
, isl_tab_undo_redundant
, var
);
936 if (row
!= tab
->n_row
- 1)
937 swap_rows(tab
, row
, tab
->n_row
- 1);
938 isl_tab_var_from_row(tab
, tab
->n_row
- 1)->index
= -1;
944 int isl_tab_mark_empty(struct isl_tab
*tab
)
948 if (!tab
->empty
&& tab
->need_undo
)
949 if (isl_tab_push(tab
, isl_tab_undo_empty
) < 0)
955 int isl_tab_freeze_constraint(struct isl_tab
*tab
, int con
)
957 struct isl_tab_var
*var
;
962 var
= &tab
->con
[con
];
970 return isl_tab_push_var(tab
, isl_tab_undo_freeze
, var
);
975 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
976 * the original sign of the pivot element.
977 * We only keep track of row signs during PILP solving and in this case
978 * we only pivot a row with negative sign (meaning the value is always
979 * non-positive) using a positive pivot element.
981 * For each row j, the new value of the parametric constant is equal to
983 * a_j0 - a_jc a_r0/a_rc
985 * where a_j0 is the original parametric constant, a_rc is the pivot element,
986 * a_r0 is the parametric constant of the pivot row and a_jc is the
987 * pivot column entry of the row j.
988 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
989 * remains the same if a_jc has the same sign as the row j or if
990 * a_jc is zero. In all other cases, we reset the sign to "unknown".
992 static void update_row_sign(struct isl_tab
*tab
, int row
, int col
, int row_sgn
)
995 struct isl_mat
*mat
= tab
->mat
;
996 unsigned off
= 2 + tab
->M
;
1001 if (tab
->row_sign
[row
] == 0)
1003 isl_assert(mat
->ctx
, row_sgn
> 0, return);
1004 isl_assert(mat
->ctx
, tab
->row_sign
[row
] == isl_tab_row_neg
, return);
1005 tab
->row_sign
[row
] = isl_tab_row_pos
;
1006 for (i
= 0; i
< tab
->n_row
; ++i
) {
1010 s
= isl_int_sgn(mat
->row
[i
][off
+ col
]);
1013 if (!tab
->row_sign
[i
])
1015 if (s
< 0 && tab
->row_sign
[i
] == isl_tab_row_neg
)
1017 if (s
> 0 && tab
->row_sign
[i
] == isl_tab_row_pos
)
1019 tab
->row_sign
[i
] = isl_tab_row_unknown
;
1023 /* Given a row number "row" and a column number "col", pivot the tableau
1024 * such that the associated variables are interchanged.
1025 * The given row in the tableau expresses
1027 * x_r = a_r0 + \sum_i a_ri x_i
1031 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
1033 * Substituting this equality into the other rows
1035 * x_j = a_j0 + \sum_i a_ji x_i
1037 * with a_jc \ne 0, we obtain
1039 * 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
1046 * where i is any other column and j is any other row,
1047 * is therefore transformed into
1049 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1050 * 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)
1052 * The transformation is performed along the following steps
1054 * d_r/n_rc n_ri/n_rc
1057 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1060 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1061 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
1063 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1064 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
1066 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1067 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
1069 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1070 * 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 int isl_tab_pivot(struct isl_tab
*tab
, int row
, int col
)
1078 struct isl_mat
*mat
= tab
->mat
;
1079 struct isl_tab_var
*var
;
1080 unsigned off
= 2 + tab
->M
;
1082 isl_int_swap(mat
->row
[row
][0], mat
->row
[row
][off
+ col
]);
1083 sgn
= isl_int_sgn(mat
->row
[row
][0]);
1085 isl_int_neg(mat
->row
[row
][0], mat
->row
[row
][0]);
1086 isl_int_neg(mat
->row
[row
][off
+ col
], mat
->row
[row
][off
+ col
]);
1088 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1089 if (j
== off
- 1 + col
)
1091 isl_int_neg(mat
->row
[row
][1 + j
], mat
->row
[row
][1 + j
]);
1093 if (!isl_int_is_one(mat
->row
[row
][0]))
1094 isl_seq_normalize(mat
->ctx
, mat
->row
[row
], off
+ tab
->n_col
);
1095 for (i
= 0; i
< tab
->n_row
; ++i
) {
1098 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1100 isl_int_mul(mat
->row
[i
][0], mat
->row
[i
][0], mat
->row
[row
][0]);
1101 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1102 if (j
== off
- 1 + col
)
1104 isl_int_mul(mat
->row
[i
][1 + j
],
1105 mat
->row
[i
][1 + j
], mat
->row
[row
][0]);
1106 isl_int_addmul(mat
->row
[i
][1 + j
],
1107 mat
->row
[i
][off
+ col
], mat
->row
[row
][1 + j
]);
1109 isl_int_mul(mat
->row
[i
][off
+ col
],
1110 mat
->row
[i
][off
+ col
], mat
->row
[row
][off
+ col
]);
1111 if (!isl_int_is_one(mat
->row
[i
][0]))
1112 isl_seq_normalize(mat
->ctx
, mat
->row
[i
], off
+ tab
->n_col
);
1114 t
= tab
->row_var
[row
];
1115 tab
->row_var
[row
] = tab
->col_var
[col
];
1116 tab
->col_var
[col
] = t
;
1117 var
= isl_tab_var_from_row(tab
, row
);
1120 var
= var_from_col(tab
, col
);
1123 update_row_sign(tab
, row
, col
, sgn
);
1126 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1127 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1129 if (!isl_tab_var_from_row(tab
, i
)->frozen
&&
1130 isl_tab_row_is_redundant(tab
, i
)) {
1131 int redo
= isl_tab_mark_redundant(tab
, i
);
1141 /* If "var" represents a column variable, then pivot is up (sgn > 0)
1142 * or down (sgn < 0) to a row. The variable is assumed not to be
1143 * unbounded in the specified direction.
1144 * If sgn = 0, then the variable is unbounded in both directions,
1145 * and we pivot with any row we can find.
1147 static int to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
) WARN_UNUSED
;
1148 static int to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
)
1151 unsigned off
= 2 + tab
->M
;
1157 for (r
= tab
->n_redundant
; r
< tab
->n_row
; ++r
)
1158 if (!isl_int_is_zero(tab
->mat
->row
[r
][off
+var
->index
]))
1160 isl_assert(tab
->mat
->ctx
, r
< tab
->n_row
, return -1);
1162 r
= pivot_row(tab
, NULL
, sign
, var
->index
);
1163 isl_assert(tab
->mat
->ctx
, r
>= 0, return -1);
1166 return isl_tab_pivot(tab
, r
, var
->index
);
1169 static void check_table(struct isl_tab
*tab
)
1175 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1176 struct isl_tab_var
*var
;
1177 var
= isl_tab_var_from_row(tab
, i
);
1178 if (!var
->is_nonneg
)
1181 assert(!isl_int_is_neg(tab
->mat
->row
[i
][2]));
1182 if (isl_int_is_pos(tab
->mat
->row
[i
][2]))
1185 assert(!isl_int_is_neg(tab
->mat
->row
[i
][1]));
1189 /* Return the sign of the maximal value of "var".
1190 * If the sign is not negative, then on return from this function,
1191 * the sample value will also be non-negative.
1193 * If "var" is manifestly unbounded wrt positive values, we are done.
1194 * Otherwise, we pivot the variable up to a row if needed
1195 * Then we continue pivoting down until either
1196 * - no more down pivots can be performed
1197 * - the sample value is positive
1198 * - the variable is pivoted into a manifestly unbounded column
1200 static int sign_of_max(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1204 if (max_is_manifestly_unbounded(tab
, var
))
1206 if (to_row(tab
, var
, 1) < 0)
1208 while (!isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1209 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1211 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1212 if (isl_tab_pivot(tab
, row
, col
) < 0)
1214 if (!var
->is_row
) /* manifestly unbounded */
1220 int isl_tab_sign_of_max(struct isl_tab
*tab
, int con
)
1222 struct isl_tab_var
*var
;
1227 var
= &tab
->con
[con
];
1228 isl_assert(tab
->mat
->ctx
, !var
->is_redundant
, return -2);
1229 isl_assert(tab
->mat
->ctx
, !var
->is_zero
, return -2);
1231 return sign_of_max(tab
, var
);
1234 static int row_is_neg(struct isl_tab
*tab
, int row
)
1237 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1238 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1240 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1242 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1245 static int row_sgn(struct isl_tab
*tab
, int row
)
1248 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1249 if (!isl_int_is_zero(tab
->mat
->row
[row
][2]))
1250 return isl_int_sgn(tab
->mat
->row
[row
][2]);
1252 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1255 /* Perform pivots until the row variable "var" has a non-negative
1256 * sample value or until no more upward pivots can be performed.
1257 * Return the sign of the sample value after the pivots have been
1260 static int restore_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1264 while (row_is_neg(tab
, var
->index
)) {
1265 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1268 if (isl_tab_pivot(tab
, row
, col
) < 0)
1270 if (!var
->is_row
) /* manifestly unbounded */
1273 return row_sgn(tab
, var
->index
);
1276 /* Perform pivots until we are sure that the row variable "var"
1277 * can attain non-negative values. After return from this
1278 * function, "var" is still a row variable, but its sample
1279 * value may not be non-negative, even if the function returns 1.
1281 static int at_least_zero(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1285 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1286 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1289 if (row
== var
->index
) /* manifestly unbounded */
1291 if (isl_tab_pivot(tab
, row
, col
) < 0)
1294 return !isl_int_is_neg(tab
->mat
->row
[var
->index
][1]);
1297 /* Return a negative value if "var" can attain negative values.
1298 * Return a non-negative value otherwise.
1300 * If "var" is manifestly unbounded wrt negative values, we are done.
1301 * Otherwise, if var is in a column, we can pivot it down to a row.
1302 * Then we continue pivoting down until either
1303 * - the pivot would result in a manifestly unbounded column
1304 * => we don't perform the pivot, but simply return -1
1305 * - no more down pivots can be performed
1306 * - the sample value is negative
1307 * If the sample value becomes negative and the variable is supposed
1308 * to be nonnegative, then we undo the last pivot.
1309 * However, if the last pivot has made the pivoting variable
1310 * obviously redundant, then it may have moved to another row.
1311 * In that case we look for upward pivots until we reach a non-negative
1314 static int sign_of_min(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1317 struct isl_tab_var
*pivot_var
= NULL
;
1319 if (min_is_manifestly_unbounded(tab
, var
))
1323 row
= pivot_row(tab
, NULL
, -1, col
);
1324 pivot_var
= var_from_col(tab
, col
);
1325 if (isl_tab_pivot(tab
, row
, col
) < 0)
1327 if (var
->is_redundant
)
1329 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1330 if (var
->is_nonneg
) {
1331 if (!pivot_var
->is_redundant
&&
1332 pivot_var
->index
== row
) {
1333 if (isl_tab_pivot(tab
, row
, col
) < 0)
1336 if (restore_row(tab
, var
) < -1)
1342 if (var
->is_redundant
)
1344 while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1345 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1346 if (row
== var
->index
)
1349 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1350 pivot_var
= var_from_col(tab
, col
);
1351 if (isl_tab_pivot(tab
, row
, col
) < 0)
1353 if (var
->is_redundant
)
1356 if (pivot_var
&& var
->is_nonneg
) {
1357 /* pivot back to non-negative value */
1358 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
) {
1359 if (isl_tab_pivot(tab
, row
, col
) < 0)
1362 if (restore_row(tab
, var
) < -1)
1368 static int row_at_most_neg_one(struct isl_tab
*tab
, int row
)
1371 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1373 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1376 return isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
1377 isl_int_abs_ge(tab
->mat
->row
[row
][1],
1378 tab
->mat
->row
[row
][0]);
1381 /* Return 1 if "var" can attain values <= -1.
1382 * Return 0 otherwise.
1384 * The sample value of "var" is assumed to be non-negative when the
1385 * the function is called. If 1 is returned then the constraint
1386 * is not redundant and the sample value is made non-negative again before
1387 * the function returns.
1389 int isl_tab_min_at_most_neg_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1392 struct isl_tab_var
*pivot_var
;
1394 if (min_is_manifestly_unbounded(tab
, var
))
1398 row
= pivot_row(tab
, NULL
, -1, col
);
1399 pivot_var
= var_from_col(tab
, col
);
1400 if (isl_tab_pivot(tab
, row
, col
) < 0)
1402 if (var
->is_redundant
)
1404 if (row_at_most_neg_one(tab
, var
->index
)) {
1405 if (var
->is_nonneg
) {
1406 if (!pivot_var
->is_redundant
&&
1407 pivot_var
->index
== row
) {
1408 if (isl_tab_pivot(tab
, row
, col
) < 0)
1411 if (restore_row(tab
, var
) < -1)
1417 if (var
->is_redundant
)
1420 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1421 if (row
== var
->index
) {
1422 if (restore_row(tab
, var
) < -1)
1428 pivot_var
= var_from_col(tab
, col
);
1429 if (isl_tab_pivot(tab
, row
, col
) < 0)
1431 if (var
->is_redundant
)
1433 } while (!row_at_most_neg_one(tab
, var
->index
));
1434 if (var
->is_nonneg
) {
1435 /* pivot back to non-negative value */
1436 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
1437 if (isl_tab_pivot(tab
, row
, col
) < 0)
1439 if (restore_row(tab
, var
) < -1)
1445 /* Return 1 if "var" can attain values >= 1.
1446 * Return 0 otherwise.
1448 static int at_least_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1453 if (max_is_manifestly_unbounded(tab
, var
))
1455 if (to_row(tab
, var
, 1) < 0)
1457 r
= tab
->mat
->row
[var
->index
];
1458 while (isl_int_lt(r
[1], r
[0])) {
1459 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1461 return isl_int_ge(r
[1], r
[0]);
1462 if (row
== var
->index
) /* manifestly unbounded */
1464 if (isl_tab_pivot(tab
, row
, col
) < 0)
1470 static void swap_cols(struct isl_tab
*tab
, int col1
, int col2
)
1473 unsigned off
= 2 + tab
->M
;
1474 t
= tab
->col_var
[col1
];
1475 tab
->col_var
[col1
] = tab
->col_var
[col2
];
1476 tab
->col_var
[col2
] = t
;
1477 var_from_col(tab
, col1
)->index
= col1
;
1478 var_from_col(tab
, col2
)->index
= col2
;
1479 tab
->mat
= isl_mat_swap_cols(tab
->mat
, off
+ col1
, off
+ col2
);
1482 /* Mark column with index "col" as representing a zero variable.
1483 * If we may need to undo the operation the column is kept,
1484 * but no longer considered.
1485 * Otherwise, the column is simply removed.
1487 * The column may be interchanged with some other column. If it
1488 * is interchanged with a later column, return 1. Otherwise return 0.
1489 * If the columns are checked in order in the calling function,
1490 * then a return value of 1 means that the column with the given
1491 * column number may now contain a different column that
1492 * hasn't been checked yet.
1494 int isl_tab_kill_col(struct isl_tab
*tab
, int col
)
1496 var_from_col(tab
, col
)->is_zero
= 1;
1497 if (tab
->need_undo
) {
1498 if (isl_tab_push_var(tab
, isl_tab_undo_zero
,
1499 var_from_col(tab
, col
)) < 0)
1501 if (col
!= tab
->n_dead
)
1502 swap_cols(tab
, col
, tab
->n_dead
);
1506 if (col
!= tab
->n_col
- 1)
1507 swap_cols(tab
, col
, tab
->n_col
- 1);
1508 var_from_col(tab
, tab
->n_col
- 1)->index
= -1;
1514 /* Row variable "var" is non-negative and cannot attain any values
1515 * larger than zero. This means that the coefficients of the unrestricted
1516 * column variables are zero and that the coefficients of the non-negative
1517 * column variables are zero or negative.
1518 * Each of the non-negative variables with a negative coefficient can
1519 * then also be written as the negative sum of non-negative variables
1520 * and must therefore also be zero.
1522 static int close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
1523 static int close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1526 struct isl_mat
*mat
= tab
->mat
;
1527 unsigned off
= 2 + tab
->M
;
1529 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return -1);
1532 if (isl_tab_push_var(tab
, isl_tab_undo_zero
, var
) < 0)
1534 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1535 if (isl_int_is_zero(mat
->row
[var
->index
][off
+ j
]))
1537 isl_assert(tab
->mat
->ctx
,
1538 isl_int_is_neg(mat
->row
[var
->index
][off
+ j
]), return -1);
1539 if (isl_tab_kill_col(tab
, j
))
1542 if (isl_tab_mark_redundant(tab
, var
->index
) < 0)
1547 /* Add a constraint to the tableau and allocate a row for it.
1548 * Return the index into the constraint array "con".
1550 int isl_tab_allocate_con(struct isl_tab
*tab
)
1554 isl_assert(tab
->mat
->ctx
, tab
->n_row
< tab
->mat
->n_row
, return -1);
1555 isl_assert(tab
->mat
->ctx
, tab
->n_con
< tab
->max_con
, return -1);
1558 tab
->con
[r
].index
= tab
->n_row
;
1559 tab
->con
[r
].is_row
= 1;
1560 tab
->con
[r
].is_nonneg
= 0;
1561 tab
->con
[r
].is_zero
= 0;
1562 tab
->con
[r
].is_redundant
= 0;
1563 tab
->con
[r
].frozen
= 0;
1564 tab
->con
[r
].negated
= 0;
1565 tab
->row_var
[tab
->n_row
] = ~r
;
1569 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]) < 0)
1575 /* Add a variable to the tableau and allocate a column for it.
1576 * Return the index into the variable array "var".
1578 int isl_tab_allocate_var(struct isl_tab
*tab
)
1582 unsigned off
= 2 + tab
->M
;
1584 isl_assert(tab
->mat
->ctx
, tab
->n_col
< tab
->mat
->n_col
, return -1);
1585 isl_assert(tab
->mat
->ctx
, tab
->n_var
< tab
->max_var
, return -1);
1588 tab
->var
[r
].index
= tab
->n_col
;
1589 tab
->var
[r
].is_row
= 0;
1590 tab
->var
[r
].is_nonneg
= 0;
1591 tab
->var
[r
].is_zero
= 0;
1592 tab
->var
[r
].is_redundant
= 0;
1593 tab
->var
[r
].frozen
= 0;
1594 tab
->var
[r
].negated
= 0;
1595 tab
->col_var
[tab
->n_col
] = r
;
1597 for (i
= 0; i
< tab
->n_row
; ++i
)
1598 isl_int_set_si(tab
->mat
->row
[i
][off
+ tab
->n_col
], 0);
1602 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->var
[r
]) < 0)
1608 /* Add a row to the tableau. The row is given as an affine combination
1609 * of the original variables and needs to be expressed in terms of the
1612 * We add each term in turn.
1613 * If r = n/d_r is the current sum and we need to add k x, then
1614 * if x is a column variable, we increase the numerator of
1615 * this column by k d_r
1616 * if x = f/d_x is a row variable, then the new representation of r is
1618 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1619 * --- + --- = ------------------- = -------------------
1620 * d_r d_r d_r d_x/g m
1622 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1624 int isl_tab_add_row(struct isl_tab
*tab
, isl_int
*line
)
1630 unsigned off
= 2 + tab
->M
;
1632 r
= isl_tab_allocate_con(tab
);
1638 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1639 isl_int_set_si(row
[0], 1);
1640 isl_int_set(row
[1], line
[0]);
1641 isl_seq_clr(row
+ 2, tab
->M
+ tab
->n_col
);
1642 for (i
= 0; i
< tab
->n_var
; ++i
) {
1643 if (tab
->var
[i
].is_zero
)
1645 if (tab
->var
[i
].is_row
) {
1647 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1648 isl_int_swap(a
, row
[0]);
1649 isl_int_divexact(a
, row
[0], a
);
1651 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1652 isl_int_mul(b
, b
, line
[1 + i
]);
1653 isl_seq_combine(row
+ 1, a
, row
+ 1,
1654 b
, tab
->mat
->row
[tab
->var
[i
].index
] + 1,
1655 1 + tab
->M
+ tab
->n_col
);
1657 isl_int_addmul(row
[off
+ tab
->var
[i
].index
],
1658 line
[1 + i
], row
[0]);
1659 if (tab
->M
&& i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
1660 isl_int_submul(row
[2], line
[1 + i
], row
[0]);
1662 isl_seq_normalize(tab
->mat
->ctx
, row
, off
+ tab
->n_col
);
1667 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_unknown
;
1672 static int drop_row(struct isl_tab
*tab
, int row
)
1674 isl_assert(tab
->mat
->ctx
, ~tab
->row_var
[row
] == tab
->n_con
- 1, return -1);
1675 if (row
!= tab
->n_row
- 1)
1676 swap_rows(tab
, row
, tab
->n_row
- 1);
1682 static int drop_col(struct isl_tab
*tab
, int col
)
1684 isl_assert(tab
->mat
->ctx
, tab
->col_var
[col
] == tab
->n_var
- 1, return -1);
1685 if (col
!= tab
->n_col
- 1)
1686 swap_cols(tab
, col
, tab
->n_col
- 1);
1692 /* Add inequality "ineq" and check if it conflicts with the
1693 * previously added constraints or if it is obviously redundant.
1695 int isl_tab_add_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1704 struct isl_basic_map
*bmap
= tab
->bmap
;
1706 isl_assert(tab
->mat
->ctx
, tab
->n_eq
== bmap
->n_eq
, return -1);
1707 isl_assert(tab
->mat
->ctx
,
1708 tab
->n_con
== bmap
->n_eq
+ bmap
->n_ineq
, return -1);
1709 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, ineq
);
1710 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1717 isl_int_swap(ineq
[0], cst
);
1719 r
= isl_tab_add_row(tab
, ineq
);
1721 isl_int_swap(ineq
[0], cst
);
1726 tab
->con
[r
].is_nonneg
= 1;
1727 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1729 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1730 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1735 sgn
= restore_row(tab
, &tab
->con
[r
]);
1739 return isl_tab_mark_empty(tab
);
1740 if (tab
->con
[r
].is_row
&& isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1741 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1746 /* Pivot a non-negative variable down until it reaches the value zero
1747 * and then pivot the variable into a column position.
1749 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
1750 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1754 unsigned off
= 2 + tab
->M
;
1759 while (isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1760 find_pivot(tab
, var
, NULL
, -1, &row
, &col
);
1761 isl_assert(tab
->mat
->ctx
, row
!= -1, return -1);
1762 if (isl_tab_pivot(tab
, row
, col
) < 0)
1768 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
)
1769 if (!isl_int_is_zero(tab
->mat
->row
[var
->index
][off
+ i
]))
1772 isl_assert(tab
->mat
->ctx
, i
< tab
->n_col
, return -1);
1773 if (isl_tab_pivot(tab
, var
->index
, i
) < 0)
1779 /* We assume Gaussian elimination has been performed on the equalities.
1780 * The equalities can therefore never conflict.
1781 * Adding the equalities is currently only really useful for a later call
1782 * to isl_tab_ineq_type.
1784 static struct isl_tab
*add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1791 r
= isl_tab_add_row(tab
, eq
);
1795 r
= tab
->con
[r
].index
;
1796 i
= isl_seq_first_non_zero(tab
->mat
->row
[r
] + 2 + tab
->M
+ tab
->n_dead
,
1797 tab
->n_col
- tab
->n_dead
);
1798 isl_assert(tab
->mat
->ctx
, i
>= 0, goto error
);
1800 if (isl_tab_pivot(tab
, r
, i
) < 0)
1802 if (isl_tab_kill_col(tab
, i
) < 0)
1812 static int row_is_manifestly_zero(struct isl_tab
*tab
, int row
)
1814 unsigned off
= 2 + tab
->M
;
1816 if (!isl_int_is_zero(tab
->mat
->row
[row
][1]))
1818 if (tab
->M
&& !isl_int_is_zero(tab
->mat
->row
[row
][2]))
1820 return isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1821 tab
->n_col
- tab
->n_dead
) == -1;
1824 /* Add an equality that is known to be valid for the given tableau.
1826 struct isl_tab
*isl_tab_add_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1828 struct isl_tab_var
*var
;
1833 r
= isl_tab_add_row(tab
, eq
);
1839 if (row_is_manifestly_zero(tab
, r
)) {
1841 if (isl_tab_mark_redundant(tab
, r
) < 0)
1846 if (isl_int_is_neg(tab
->mat
->row
[r
][1])) {
1847 isl_seq_neg(tab
->mat
->row
[r
] + 1, tab
->mat
->row
[r
] + 1,
1852 if (to_col(tab
, var
) < 0)
1855 if (isl_tab_kill_col(tab
, var
->index
) < 0)
1864 static int add_zero_row(struct isl_tab
*tab
)
1869 r
= isl_tab_allocate_con(tab
);
1873 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1874 isl_seq_clr(row
+ 1, 1 + tab
->M
+ tab
->n_col
);
1875 isl_int_set_si(row
[0], 1);
1880 /* Add equality "eq" and check if it conflicts with the
1881 * previously added constraints or if it is obviously redundant.
1883 struct isl_tab
*isl_tab_add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1885 struct isl_tab_undo
*snap
= NULL
;
1886 struct isl_tab_var
*var
;
1894 isl_assert(tab
->mat
->ctx
, !tab
->M
, goto error
);
1897 snap
= isl_tab_snap(tab
);
1901 isl_int_swap(eq
[0], cst
);
1903 r
= isl_tab_add_row(tab
, eq
);
1905 isl_int_swap(eq
[0], cst
);
1913 if (row_is_manifestly_zero(tab
, row
)) {
1915 if (isl_tab_rollback(tab
, snap
) < 0)
1923 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1924 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1926 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1927 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1928 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1929 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1933 if (add_zero_row(tab
) < 0)
1937 sgn
= isl_int_sgn(tab
->mat
->row
[row
][1]);
1940 isl_seq_neg(tab
->mat
->row
[row
] + 1, tab
->mat
->row
[row
] + 1,
1947 sgn
= sign_of_max(tab
, var
);
1951 if (isl_tab_mark_empty(tab
) < 0)
1958 if (to_col(tab
, var
) < 0)
1961 if (isl_tab_kill_col(tab
, var
->index
) < 0)
1970 /* Construct and return an inequality that expresses an upper bound
1972 * In particular, if the div is given by
1976 * then the inequality expresses
1980 static struct isl_vec
*ineq_for_div(struct isl_basic_map
*bmap
, unsigned div
)
1984 struct isl_vec
*ineq
;
1989 total
= isl_basic_map_total_dim(bmap
);
1990 div_pos
= 1 + total
- bmap
->n_div
+ div
;
1992 ineq
= isl_vec_alloc(bmap
->ctx
, 1 + total
);
1996 isl_seq_cpy(ineq
->el
, bmap
->div
[div
] + 1, 1 + total
);
1997 isl_int_neg(ineq
->el
[div_pos
], bmap
->div
[div
][0]);
2001 /* For a div d = floor(f/m), add the constraints
2004 * -(f-(m-1)) + m d >= 0
2006 * Note that the second constraint is the negation of
2010 * If add_ineq is not NULL, then this function is used
2011 * instead of isl_tab_add_ineq to effectively add the inequalities.
2013 static int add_div_constraints(struct isl_tab
*tab
, unsigned div
,
2014 int (*add_ineq
)(void *user
, isl_int
*), void *user
)
2018 struct isl_vec
*ineq
;
2020 total
= isl_basic_map_total_dim(tab
->bmap
);
2021 div_pos
= 1 + total
- tab
->bmap
->n_div
+ div
;
2023 ineq
= ineq_for_div(tab
->bmap
, div
);
2028 if (add_ineq(user
, ineq
->el
) < 0)
2031 if (isl_tab_add_ineq(tab
, ineq
->el
) < 0)
2035 isl_seq_neg(ineq
->el
, tab
->bmap
->div
[div
] + 1, 1 + total
);
2036 isl_int_set(ineq
->el
[div_pos
], tab
->bmap
->div
[div
][0]);
2037 isl_int_add(ineq
->el
[0], ineq
->el
[0], ineq
->el
[div_pos
]);
2038 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
2041 if (add_ineq(user
, ineq
->el
) < 0)
2044 if (isl_tab_add_ineq(tab
, ineq
->el
) < 0)
2056 /* Add an extra div, prescrived by "div" to the tableau and
2057 * the associated bmap (which is assumed to be non-NULL).
2059 * If add_ineq is not NULL, then this function is used instead
2060 * of isl_tab_add_ineq to add the div constraints.
2061 * This complication is needed because the code in isl_tab_pip
2062 * wants to perform some extra processing when an inequality
2063 * is added to the tableau.
2065 int isl_tab_add_div(struct isl_tab
*tab
, __isl_keep isl_vec
*div
,
2066 int (*add_ineq
)(void *user
, isl_int
*), void *user
)
2076 isl_assert(tab
->mat
->ctx
, tab
->bmap
, return -1);
2078 for (i
= 0; i
< tab
->n_var
; ++i
) {
2079 if (isl_int_is_neg(div
->el
[2 + i
]))
2081 if (isl_int_is_zero(div
->el
[2 + i
]))
2083 if (!tab
->var
[i
].is_nonneg
)
2086 nonneg
= i
== tab
->n_var
&& !isl_int_is_neg(div
->el
[1]);
2088 if (isl_tab_extend_cons(tab
, 3) < 0)
2090 if (isl_tab_extend_vars(tab
, 1) < 0)
2092 r
= isl_tab_allocate_var(tab
);
2097 tab
->var
[r
].is_nonneg
= 1;
2099 tab
->bmap
= isl_basic_map_extend_dim(tab
->bmap
,
2100 isl_basic_map_get_dim(tab
->bmap
), 1, 0, 2);
2101 k
= isl_basic_map_alloc_div(tab
->bmap
);
2104 isl_seq_cpy(tab
->bmap
->div
[k
], div
->el
, div
->size
);
2105 if (isl_tab_push(tab
, isl_tab_undo_bmap_div
) < 0)
2108 if (add_div_constraints(tab
, k
, add_ineq
, user
) < 0)
2114 struct isl_tab
*isl_tab_from_basic_map(struct isl_basic_map
*bmap
)
2117 struct isl_tab
*tab
;
2121 tab
= isl_tab_alloc(bmap
->ctx
,
2122 isl_basic_map_total_dim(bmap
) + bmap
->n_ineq
+ 1,
2123 isl_basic_map_total_dim(bmap
), 0);
2126 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
2127 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
2128 if (isl_tab_mark_empty(tab
) < 0)
2132 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2133 tab
= add_eq(tab
, bmap
->eq
[i
]);
2137 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2138 if (isl_tab_add_ineq(tab
, bmap
->ineq
[i
]) < 0)
2149 struct isl_tab
*isl_tab_from_basic_set(struct isl_basic_set
*bset
)
2151 return isl_tab_from_basic_map((struct isl_basic_map
*)bset
);
2154 /* Construct a tableau corresponding to the recession cone of "bset".
2156 struct isl_tab
*isl_tab_from_recession_cone(__isl_keep isl_basic_set
*bset
,
2161 struct isl_tab
*tab
;
2162 unsigned offset
= 0;
2167 offset
= isl_basic_set_dim(bset
, isl_dim_param
);
2168 tab
= isl_tab_alloc(bset
->ctx
, bset
->n_eq
+ bset
->n_ineq
,
2169 isl_basic_set_total_dim(bset
) - offset
, 0);
2172 tab
->rational
= ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
);
2176 for (i
= 0; i
< bset
->n_eq
; ++i
) {
2177 isl_int_swap(bset
->eq
[i
][offset
], cst
);
2179 tab
= isl_tab_add_eq(tab
, bset
->eq
[i
] + offset
);
2181 tab
= add_eq(tab
, bset
->eq
[i
]);
2182 isl_int_swap(bset
->eq
[i
][offset
], cst
);
2186 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2188 isl_int_swap(bset
->ineq
[i
][offset
], cst
);
2189 r
= isl_tab_add_row(tab
, bset
->ineq
[i
] + offset
);
2190 isl_int_swap(bset
->ineq
[i
][offset
], cst
);
2193 tab
->con
[r
].is_nonneg
= 1;
2194 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2206 /* Assuming "tab" is the tableau of a cone, check if the cone is
2207 * bounded, i.e., if it is empty or only contains the origin.
2209 int isl_tab_cone_is_bounded(struct isl_tab
*tab
)
2217 if (tab
->n_dead
== tab
->n_col
)
2221 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2222 struct isl_tab_var
*var
;
2224 var
= isl_tab_var_from_row(tab
, i
);
2225 if (!var
->is_nonneg
)
2227 sgn
= sign_of_max(tab
, var
);
2232 if (close_row(tab
, var
) < 0)
2236 if (tab
->n_dead
== tab
->n_col
)
2238 if (i
== tab
->n_row
)
2243 int isl_tab_sample_is_integer(struct isl_tab
*tab
)
2250 for (i
= 0; i
< tab
->n_var
; ++i
) {
2252 if (!tab
->var
[i
].is_row
)
2254 row
= tab
->var
[i
].index
;
2255 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
2256 tab
->mat
->row
[row
][0]))
2262 static struct isl_vec
*extract_integer_sample(struct isl_tab
*tab
)
2265 struct isl_vec
*vec
;
2267 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2271 isl_int_set_si(vec
->block
.data
[0], 1);
2272 for (i
= 0; i
< tab
->n_var
; ++i
) {
2273 if (!tab
->var
[i
].is_row
)
2274 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
2276 int row
= tab
->var
[i
].index
;
2277 isl_int_divexact(vec
->block
.data
[1 + i
],
2278 tab
->mat
->row
[row
][1], tab
->mat
->row
[row
][0]);
2285 struct isl_vec
*isl_tab_get_sample_value(struct isl_tab
*tab
)
2288 struct isl_vec
*vec
;
2294 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2300 isl_int_set_si(vec
->block
.data
[0], 1);
2301 for (i
= 0; i
< tab
->n_var
; ++i
) {
2303 if (!tab
->var
[i
].is_row
) {
2304 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
2307 row
= tab
->var
[i
].index
;
2308 isl_int_gcd(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
2309 isl_int_divexact(m
, tab
->mat
->row
[row
][0], m
);
2310 isl_seq_scale(vec
->block
.data
, vec
->block
.data
, m
, 1 + i
);
2311 isl_int_divexact(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
2312 isl_int_mul(vec
->block
.data
[1 + i
], m
, tab
->mat
->row
[row
][1]);
2314 vec
= isl_vec_normalize(vec
);
2320 /* Update "bmap" based on the results of the tableau "tab".
2321 * In particular, implicit equalities are made explicit, redundant constraints
2322 * are removed and if the sample value happens to be integer, it is stored
2323 * in "bmap" (unless "bmap" already had an integer sample).
2325 * The tableau is assumed to have been created from "bmap" using
2326 * isl_tab_from_basic_map.
2328 struct isl_basic_map
*isl_basic_map_update_from_tab(struct isl_basic_map
*bmap
,
2329 struct isl_tab
*tab
)
2341 bmap
= isl_basic_map_set_to_empty(bmap
);
2343 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
2344 if (isl_tab_is_equality(tab
, n_eq
+ i
))
2345 isl_basic_map_inequality_to_equality(bmap
, i
);
2346 else if (isl_tab_is_redundant(tab
, n_eq
+ i
))
2347 isl_basic_map_drop_inequality(bmap
, i
);
2349 if (bmap
->n_eq
!= n_eq
)
2350 isl_basic_map_gauss(bmap
, NULL
);
2351 if (!tab
->rational
&&
2352 !bmap
->sample
&& isl_tab_sample_is_integer(tab
))
2353 bmap
->sample
= extract_integer_sample(tab
);
2357 struct isl_basic_set
*isl_basic_set_update_from_tab(struct isl_basic_set
*bset
,
2358 struct isl_tab
*tab
)
2360 return (struct isl_basic_set
*)isl_basic_map_update_from_tab(
2361 (struct isl_basic_map
*)bset
, tab
);
2364 /* Given a non-negative variable "var", add a new non-negative variable
2365 * that is the opposite of "var", ensuring that var can only attain the
2367 * If var = n/d is a row variable, then the new variable = -n/d.
2368 * If var is a column variables, then the new variable = -var.
2369 * If the new variable cannot attain non-negative values, then
2370 * the resulting tableau is empty.
2371 * Otherwise, we know the value will be zero and we close the row.
2373 static int cut_to_hyperplane(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2378 unsigned off
= 2 + tab
->M
;
2382 isl_assert(tab
->mat
->ctx
, !var
->is_redundant
, return -1);
2383 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return -1);
2385 if (isl_tab_extend_cons(tab
, 1) < 0)
2389 tab
->con
[r
].index
= tab
->n_row
;
2390 tab
->con
[r
].is_row
= 1;
2391 tab
->con
[r
].is_nonneg
= 0;
2392 tab
->con
[r
].is_zero
= 0;
2393 tab
->con
[r
].is_redundant
= 0;
2394 tab
->con
[r
].frozen
= 0;
2395 tab
->con
[r
].negated
= 0;
2396 tab
->row_var
[tab
->n_row
] = ~r
;
2397 row
= tab
->mat
->row
[tab
->n_row
];
2400 isl_int_set(row
[0], tab
->mat
->row
[var
->index
][0]);
2401 isl_seq_neg(row
+ 1,
2402 tab
->mat
->row
[var
->index
] + 1, 1 + tab
->n_col
);
2404 isl_int_set_si(row
[0], 1);
2405 isl_seq_clr(row
+ 1, 1 + tab
->n_col
);
2406 isl_int_set_si(row
[off
+ var
->index
], -1);
2411 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]) < 0)
2414 sgn
= sign_of_max(tab
, &tab
->con
[r
]);
2418 if (isl_tab_mark_empty(tab
) < 0)
2422 tab
->con
[r
].is_nonneg
= 1;
2423 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2426 if (close_row(tab
, &tab
->con
[r
]) < 0)
2432 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2433 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2434 * by r' = r + 1 >= 0.
2435 * If r is a row variable, we simply increase the constant term by one
2436 * (taking into account the denominator).
2437 * If r is a column variable, then we need to modify each row that
2438 * refers to r = r' - 1 by substituting this equality, effectively
2439 * subtracting the coefficient of the column from the constant.
2440 * We should only do this if the minimum is manifestly unbounded,
2441 * however. Otherwise, we may end up with negative sample values
2442 * for non-negative variables.
2443 * So, if r is a column variable with a minimum that is not
2444 * manifestly unbounded, then we need to move it to a row.
2445 * However, the sample value of this row may be negative,
2446 * even after the relaxation, so we need to restore it.
2447 * We therefore prefer to pivot a column up to a row, if possible.
2449 struct isl_tab
*isl_tab_relax(struct isl_tab
*tab
, int con
)
2451 struct isl_tab_var
*var
;
2452 unsigned off
= 2 + tab
->M
;
2457 var
= &tab
->con
[con
];
2459 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
2460 if (to_row(tab
, var
, 1) < 0)
2462 if (!var
->is_row
&& !min_is_manifestly_unbounded(tab
, var
))
2463 if (to_row(tab
, var
, -1) < 0)
2467 isl_int_add(tab
->mat
->row
[var
->index
][1],
2468 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
2469 if (restore_row(tab
, var
) < 0)
2474 for (i
= 0; i
< tab
->n_row
; ++i
) {
2475 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2477 isl_int_sub(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
2478 tab
->mat
->row
[i
][off
+ var
->index
]);
2483 if (isl_tab_push_var(tab
, isl_tab_undo_relax
, var
) < 0)
2492 int isl_tab_select_facet(struct isl_tab
*tab
, int con
)
2497 return cut_to_hyperplane(tab
, &tab
->con
[con
]);
2500 static int may_be_equality(struct isl_tab
*tab
, int row
)
2502 unsigned off
= 2 + tab
->M
;
2503 return tab
->rational
? isl_int_is_zero(tab
->mat
->row
[row
][1])
2504 : isl_int_lt(tab
->mat
->row
[row
][1],
2505 tab
->mat
->row
[row
][0]);
2508 /* Check for (near) equalities among the constraints.
2509 * A constraint is an equality if it is non-negative and if
2510 * its maximal value is either
2511 * - zero (in case of rational tableaus), or
2512 * - strictly less than 1 (in case of integer tableaus)
2514 * We first mark all non-redundant and non-dead variables that
2515 * are not frozen and not obviously not an equality.
2516 * Then we iterate over all marked variables if they can attain
2517 * any values larger than zero or at least one.
2518 * If the maximal value is zero, we mark any column variables
2519 * that appear in the row as being zero and mark the row as being redundant.
2520 * Otherwise, if the maximal value is strictly less than one (and the
2521 * tableau is integer), then we restrict the value to being zero
2522 * by adding an opposite non-negative variable.
2524 int isl_tab_detect_implicit_equalities(struct isl_tab
*tab
)
2533 if (tab
->n_dead
== tab
->n_col
)
2537 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2538 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2539 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2540 may_be_equality(tab
, i
);
2544 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2545 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2546 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2551 struct isl_tab_var
*var
;
2553 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2554 var
= isl_tab_var_from_row(tab
, i
);
2558 if (i
== tab
->n_row
) {
2559 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2560 var
= var_from_col(tab
, i
);
2564 if (i
== tab
->n_col
)
2569 sgn
= sign_of_max(tab
, var
);
2573 if (close_row(tab
, var
) < 0)
2575 } else if (!tab
->rational
&& !at_least_one(tab
, var
)) {
2576 if (cut_to_hyperplane(tab
, var
) < 0)
2578 return isl_tab_detect_implicit_equalities(tab
);
2580 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2581 var
= isl_tab_var_from_row(tab
, i
);
2584 if (may_be_equality(tab
, i
))
2594 static int con_is_redundant(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2598 if (tab
->rational
) {
2599 int sgn
= sign_of_min(tab
, var
);
2604 int irred
= isl_tab_min_at_most_neg_one(tab
, var
);
2611 /* Check for (near) redundant constraints.
2612 * A constraint is redundant if it is non-negative and if
2613 * its minimal value (temporarily ignoring the non-negativity) is either
2614 * - zero (in case of rational tableaus), or
2615 * - strictly larger than -1 (in case of integer tableaus)
2617 * We first mark all non-redundant and non-dead variables that
2618 * are not frozen and not obviously negatively unbounded.
2619 * Then we iterate over all marked variables if they can attain
2620 * any values smaller than zero or at most negative one.
2621 * If not, we mark the row as being redundant (assuming it hasn't
2622 * been detected as being obviously redundant in the mean time).
2624 int isl_tab_detect_redundant(struct isl_tab
*tab
)
2633 if (tab
->n_redundant
== tab
->n_row
)
2637 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2638 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2639 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2643 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2644 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2645 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2646 !min_is_manifestly_unbounded(tab
, var
);
2651 struct isl_tab_var
*var
;
2653 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2654 var
= isl_tab_var_from_row(tab
, i
);
2658 if (i
== tab
->n_row
) {
2659 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2660 var
= var_from_col(tab
, i
);
2664 if (i
== tab
->n_col
)
2669 red
= con_is_redundant(tab
, var
);
2672 if (red
&& !var
->is_redundant
)
2673 if (isl_tab_mark_redundant(tab
, var
->index
) < 0)
2675 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2676 var
= var_from_col(tab
, i
);
2679 if (!min_is_manifestly_unbounded(tab
, var
))
2689 int isl_tab_is_equality(struct isl_tab
*tab
, int con
)
2696 if (tab
->con
[con
].is_zero
)
2698 if (tab
->con
[con
].is_redundant
)
2700 if (!tab
->con
[con
].is_row
)
2701 return tab
->con
[con
].index
< tab
->n_dead
;
2703 row
= tab
->con
[con
].index
;
2706 return isl_int_is_zero(tab
->mat
->row
[row
][1]) &&
2707 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
2708 tab
->n_col
- tab
->n_dead
) == -1;
2711 /* Return the minimial value of the affine expression "f" with denominator
2712 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
2713 * the expression cannot attain arbitrarily small values.
2714 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
2715 * The return value reflects the nature of the result (empty, unbounded,
2716 * minmimal value returned in *opt).
2718 enum isl_lp_result
isl_tab_min(struct isl_tab
*tab
,
2719 isl_int
*f
, isl_int denom
, isl_int
*opt
, isl_int
*opt_denom
,
2723 enum isl_lp_result res
= isl_lp_ok
;
2724 struct isl_tab_var
*var
;
2725 struct isl_tab_undo
*snap
;
2728 return isl_lp_empty
;
2730 snap
= isl_tab_snap(tab
);
2731 r
= isl_tab_add_row(tab
, f
);
2733 return isl_lp_error
;
2735 isl_int_mul(tab
->mat
->row
[var
->index
][0],
2736 tab
->mat
->row
[var
->index
][0], denom
);
2739 find_pivot(tab
, var
, var
, -1, &row
, &col
);
2740 if (row
== var
->index
) {
2741 res
= isl_lp_unbounded
;
2746 if (isl_tab_pivot(tab
, row
, col
) < 0)
2747 return isl_lp_error
;
2749 if (ISL_FL_ISSET(flags
, ISL_TAB_SAVE_DUAL
)) {
2752 isl_vec_free(tab
->dual
);
2753 tab
->dual
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_con
);
2755 return isl_lp_error
;
2756 isl_int_set(tab
->dual
->el
[0], tab
->mat
->row
[var
->index
][0]);
2757 for (i
= 0; i
< tab
->n_con
; ++i
) {
2759 if (tab
->con
[i
].is_row
) {
2760 isl_int_set_si(tab
->dual
->el
[1 + i
], 0);
2763 pos
= 2 + tab
->M
+ tab
->con
[i
].index
;
2764 if (tab
->con
[i
].negated
)
2765 isl_int_neg(tab
->dual
->el
[1 + i
],
2766 tab
->mat
->row
[var
->index
][pos
]);
2768 isl_int_set(tab
->dual
->el
[1 + i
],
2769 tab
->mat
->row
[var
->index
][pos
]);
2772 if (opt
&& res
== isl_lp_ok
) {
2774 isl_int_set(*opt
, tab
->mat
->row
[var
->index
][1]);
2775 isl_int_set(*opt_denom
, tab
->mat
->row
[var
->index
][0]);
2777 isl_int_cdiv_q(*opt
, tab
->mat
->row
[var
->index
][1],
2778 tab
->mat
->row
[var
->index
][0]);
2780 if (isl_tab_rollback(tab
, snap
) < 0)
2781 return isl_lp_error
;
2785 int isl_tab_is_redundant(struct isl_tab
*tab
, int con
)
2789 if (tab
->con
[con
].is_zero
)
2791 if (tab
->con
[con
].is_redundant
)
2793 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
2796 /* Take a snapshot of the tableau that can be restored by s call to
2799 struct isl_tab_undo
*isl_tab_snap(struct isl_tab
*tab
)
2807 /* Undo the operation performed by isl_tab_relax.
2809 static int unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
2810 static int unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2812 unsigned off
= 2 + tab
->M
;
2814 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
2815 if (to_row(tab
, var
, 1) < 0)
2819 isl_int_sub(tab
->mat
->row
[var
->index
][1],
2820 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
2821 if (var
->is_nonneg
) {
2822 int sgn
= restore_row(tab
, var
);
2823 isl_assert(tab
->mat
->ctx
, sgn
>= 0, return -1);
2828 for (i
= 0; i
< tab
->n_row
; ++i
) {
2829 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2831 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
2832 tab
->mat
->row
[i
][off
+ var
->index
]);
2840 static int perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
) WARN_UNUSED
;
2841 static int perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2843 struct isl_tab_var
*var
= var_from_index(tab
, undo
->u
.var_index
);
2844 switch(undo
->type
) {
2845 case isl_tab_undo_nonneg
:
2848 case isl_tab_undo_redundant
:
2849 var
->is_redundant
= 0;
2851 restore_row(tab
, isl_tab_var_from_row(tab
, tab
->n_redundant
));
2853 case isl_tab_undo_freeze
:
2856 case isl_tab_undo_zero
:
2861 case isl_tab_undo_allocate
:
2862 if (undo
->u
.var_index
>= 0) {
2863 isl_assert(tab
->mat
->ctx
, !var
->is_row
, return -1);
2864 drop_col(tab
, var
->index
);
2868 if (!max_is_manifestly_unbounded(tab
, var
)) {
2869 if (to_row(tab
, var
, 1) < 0)
2871 } else if (!min_is_manifestly_unbounded(tab
, var
)) {
2872 if (to_row(tab
, var
, -1) < 0)
2875 if (to_row(tab
, var
, 0) < 0)
2878 drop_row(tab
, var
->index
);
2880 case isl_tab_undo_relax
:
2881 return unrelax(tab
, var
);
2887 /* Restore the tableau to the state where the basic variables
2888 * are those in "col_var".
2889 * We first construct a list of variables that are currently in
2890 * the basis, but shouldn't. Then we iterate over all variables
2891 * that should be in the basis and for each one that is currently
2892 * not in the basis, we exchange it with one of the elements of the
2893 * list constructed before.
2894 * We can always find an appropriate variable to pivot with because
2895 * the current basis is mapped to the old basis by a non-singular
2896 * matrix and so we can never end up with a zero row.
2898 static int restore_basis(struct isl_tab
*tab
, int *col_var
)
2902 int *extra
= NULL
; /* current columns that contain bad stuff */
2903 unsigned off
= 2 + tab
->M
;
2905 extra
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
2908 for (i
= 0; i
< tab
->n_col
; ++i
) {
2909 for (j
= 0; j
< tab
->n_col
; ++j
)
2910 if (tab
->col_var
[i
] == col_var
[j
])
2914 extra
[n_extra
++] = i
;
2916 for (i
= 0; i
< tab
->n_col
&& n_extra
> 0; ++i
) {
2917 struct isl_tab_var
*var
;
2920 for (j
= 0; j
< tab
->n_col
; ++j
)
2921 if (col_var
[i
] == tab
->col_var
[j
])
2925 var
= var_from_index(tab
, col_var
[i
]);
2927 for (j
= 0; j
< n_extra
; ++j
)
2928 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+extra
[j
]]))
2930 isl_assert(tab
->mat
->ctx
, j
< n_extra
, goto error
);
2931 if (isl_tab_pivot(tab
, row
, extra
[j
]) < 0)
2933 extra
[j
] = extra
[--n_extra
];
2945 /* Remove all samples with index n or greater, i.e., those samples
2946 * that were added since we saved this number of samples in
2947 * isl_tab_save_samples.
2949 static void drop_samples_since(struct isl_tab
*tab
, int n
)
2953 for (i
= tab
->n_sample
- 1; i
>= 0 && tab
->n_sample
> n
; --i
) {
2954 if (tab
->sample_index
[i
] < n
)
2957 if (i
!= tab
->n_sample
- 1) {
2958 int t
= tab
->sample_index
[tab
->n_sample
-1];
2959 tab
->sample_index
[tab
->n_sample
-1] = tab
->sample_index
[i
];
2960 tab
->sample_index
[i
] = t
;
2961 isl_mat_swap_rows(tab
->samples
, tab
->n_sample
-1, i
);
2967 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
) WARN_UNUSED
;
2968 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2970 switch (undo
->type
) {
2971 case isl_tab_undo_empty
:
2974 case isl_tab_undo_nonneg
:
2975 case isl_tab_undo_redundant
:
2976 case isl_tab_undo_freeze
:
2977 case isl_tab_undo_zero
:
2978 case isl_tab_undo_allocate
:
2979 case isl_tab_undo_relax
:
2980 return perform_undo_var(tab
, undo
);
2981 case isl_tab_undo_bmap_eq
:
2982 return isl_basic_map_free_equality(tab
->bmap
, 1);
2983 case isl_tab_undo_bmap_ineq
:
2984 return isl_basic_map_free_inequality(tab
->bmap
, 1);
2985 case isl_tab_undo_bmap_div
:
2986 if (isl_basic_map_free_div(tab
->bmap
, 1) < 0)
2989 tab
->samples
->n_col
--;
2991 case isl_tab_undo_saved_basis
:
2992 if (restore_basis(tab
, undo
->u
.col_var
) < 0)
2995 case isl_tab_undo_drop_sample
:
2998 case isl_tab_undo_saved_samples
:
2999 drop_samples_since(tab
, undo
->u
.n
);
3001 case isl_tab_undo_callback
:
3002 return undo
->u
.callback
->run(undo
->u
.callback
);
3004 isl_assert(tab
->mat
->ctx
, 0, return -1);
3009 /* Return the tableau to the state it was in when the snapshot "snap"
3012 int isl_tab_rollback(struct isl_tab
*tab
, struct isl_tab_undo
*snap
)
3014 struct isl_tab_undo
*undo
, *next
;
3020 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
3024 if (perform_undo(tab
, undo
) < 0) {
3038 /* The given row "row" represents an inequality violated by all
3039 * points in the tableau. Check for some special cases of such
3040 * separating constraints.
3041 * In particular, if the row has been reduced to the constant -1,
3042 * then we know the inequality is adjacent (but opposite) to
3043 * an equality in the tableau.
3044 * If the row has been reduced to r = -1 -r', with r' an inequality
3045 * of the tableau, then the inequality is adjacent (but opposite)
3046 * to the inequality r'.
3048 static enum isl_ineq_type
separation_type(struct isl_tab
*tab
, unsigned row
)
3051 unsigned off
= 2 + tab
->M
;
3054 return isl_ineq_separate
;
3056 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
3057 return isl_ineq_separate
;
3058 if (!isl_int_is_negone(tab
->mat
->row
[row
][1]))
3059 return isl_ineq_separate
;
3061 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
3062 tab
->n_col
- tab
->n_dead
);
3064 return isl_ineq_adj_eq
;
3066 if (!isl_int_is_negone(tab
->mat
->row
[row
][off
+ tab
->n_dead
+ pos
]))
3067 return isl_ineq_separate
;
3069 pos
= isl_seq_first_non_zero(
3070 tab
->mat
->row
[row
] + off
+ tab
->n_dead
+ pos
+ 1,
3071 tab
->n_col
- tab
->n_dead
- pos
- 1);
3073 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
3076 /* Check the effect of inequality "ineq" on the tableau "tab".
3078 * isl_ineq_redundant: satisfied by all points in the tableau
3079 * isl_ineq_separate: satisfied by no point in the tableau
3080 * isl_ineq_cut: satisfied by some by not all points
3081 * isl_ineq_adj_eq: adjacent to an equality
3082 * isl_ineq_adj_ineq: adjacent to an inequality.
3084 enum isl_ineq_type
isl_tab_ineq_type(struct isl_tab
*tab
, isl_int
*ineq
)
3086 enum isl_ineq_type type
= isl_ineq_error
;
3087 struct isl_tab_undo
*snap
= NULL
;
3092 return isl_ineq_error
;
3094 if (isl_tab_extend_cons(tab
, 1) < 0)
3095 return isl_ineq_error
;
3097 snap
= isl_tab_snap(tab
);
3099 con
= isl_tab_add_row(tab
, ineq
);
3103 row
= tab
->con
[con
].index
;
3104 if (isl_tab_row_is_redundant(tab
, row
))
3105 type
= isl_ineq_redundant
;
3106 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
3108 isl_int_abs_ge(tab
->mat
->row
[row
][1],
3109 tab
->mat
->row
[row
][0]))) {
3110 int nonneg
= at_least_zero(tab
, &tab
->con
[con
]);
3114 type
= isl_ineq_cut
;
3116 type
= separation_type(tab
, row
);
3118 int red
= con_is_redundant(tab
, &tab
->con
[con
]);
3122 type
= isl_ineq_cut
;
3124 type
= isl_ineq_redundant
;
3127 if (isl_tab_rollback(tab
, snap
))
3128 return isl_ineq_error
;
3131 return isl_ineq_error
;
3134 int isl_tab_track_bmap(struct isl_tab
*tab
, __isl_take isl_basic_map
*bmap
)
3139 isl_assert(tab
->mat
->ctx
, tab
->n_eq
== bmap
->n_eq
, return -1);
3140 isl_assert(tab
->mat
->ctx
,
3141 tab
->n_con
== bmap
->n_eq
+ bmap
->n_ineq
, return -1);
3147 isl_basic_map_free(bmap
);
3151 int isl_tab_track_bset(struct isl_tab
*tab
, __isl_take isl_basic_set
*bset
)
3153 return isl_tab_track_bmap(tab
, (isl_basic_map
*)bset
);
3156 __isl_keep isl_basic_set
*isl_tab_peek_bset(struct isl_tab
*tab
)
3161 return (isl_basic_set
*)tab
->bmap
;
3164 void isl_tab_dump(struct isl_tab
*tab
, FILE *out
, int indent
)
3170 fprintf(out
, "%*snull tab\n", indent
, "");
3173 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
3174 tab
->n_redundant
, tab
->n_dead
);
3176 fprintf(out
, ", rational");
3178 fprintf(out
, ", empty");
3180 fprintf(out
, "%*s[", indent
, "");
3181 for (i
= 0; i
< tab
->n_var
; ++i
) {
3183 fprintf(out
, (i
== tab
->n_param
||
3184 i
== tab
->n_var
- tab
->n_div
) ? "; "
3186 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
3188 tab
->var
[i
].is_zero
? " [=0]" :
3189 tab
->var
[i
].is_redundant
? " [R]" : "");
3191 fprintf(out
, "]\n");
3192 fprintf(out
, "%*s[", indent
, "");
3193 for (i
= 0; i
< tab
->n_con
; ++i
) {
3196 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
3198 tab
->con
[i
].is_zero
? " [=0]" :
3199 tab
->con
[i
].is_redundant
? " [R]" : "");
3201 fprintf(out
, "]\n");
3202 fprintf(out
, "%*s[", indent
, "");
3203 for (i
= 0; i
< tab
->n_row
; ++i
) {
3204 const char *sign
= "";
3207 if (tab
->row_sign
) {
3208 if (tab
->row_sign
[i
] == isl_tab_row_unknown
)
3210 else if (tab
->row_sign
[i
] == isl_tab_row_neg
)
3212 else if (tab
->row_sign
[i
] == isl_tab_row_pos
)
3217 fprintf(out
, "r%d: %d%s%s", i
, tab
->row_var
[i
],
3218 isl_tab_var_from_row(tab
, i
)->is_nonneg
? " [>=0]" : "", sign
);
3220 fprintf(out
, "]\n");
3221 fprintf(out
, "%*s[", indent
, "");
3222 for (i
= 0; i
< tab
->n_col
; ++i
) {
3225 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
3226 var_from_col(tab
, i
)->is_nonneg
? " [>=0]" : "");
3228 fprintf(out
, "]\n");
3229 r
= tab
->mat
->n_row
;
3230 tab
->mat
->n_row
= tab
->n_row
;
3231 c
= tab
->mat
->n_col
;
3232 tab
->mat
->n_col
= 2 + tab
->M
+ tab
->n_col
;
3233 isl_mat_dump(tab
->mat
, out
, indent
);
3234 tab
->mat
->n_row
= r
;
3235 tab
->mat
->n_col
= c
;
3237 isl_basic_map_dump(tab
->bmap
, out
, indent
);