2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2013 Ecole Normale Superieure
4 * Copyright 2014 INRIA Rocquencourt
5 * Copyright 2016 Sven Verdoolaege
7 * Use of this software is governed by the MIT license
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
12 * and Inria Paris - Rocquencourt, Domaine de Voluceau - Rocquencourt,
13 * B.P. 105 - 78153 Le Chesnay, France
16 #include <isl_ctx_private.h>
17 #include <isl_mat_private.h>
18 #include <isl_vec_private.h>
19 #include "isl_map_private.h"
22 #include <isl_config.h>
24 #include <bset_to_bmap.c>
25 #include <bset_from_bmap.c>
28 * The implementation of tableaus in this file was inspired by Section 8
29 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
30 * prover for program checking".
33 struct isl_tab
*isl_tab_alloc(struct isl_ctx
*ctx
,
34 unsigned n_row
, unsigned n_var
, unsigned M
)
40 tab
= isl_calloc_type(ctx
, struct isl_tab
);
43 tab
->mat
= isl_mat_alloc(ctx
, n_row
, off
+ n_var
);
46 tab
->var
= isl_alloc_array(ctx
, struct isl_tab_var
, n_var
);
47 if (n_var
&& !tab
->var
)
49 tab
->con
= isl_alloc_array(ctx
, struct isl_tab_var
, n_row
);
50 if (n_row
&& !tab
->con
)
52 tab
->col_var
= isl_alloc_array(ctx
, int, n_var
);
53 if (n_var
&& !tab
->col_var
)
55 tab
->row_var
= isl_alloc_array(ctx
, int, n_row
);
56 if (n_row
&& !tab
->row_var
)
58 for (i
= 0; i
< n_var
; ++i
) {
59 tab
->var
[i
].index
= i
;
60 tab
->var
[i
].is_row
= 0;
61 tab
->var
[i
].is_nonneg
= 0;
62 tab
->var
[i
].is_zero
= 0;
63 tab
->var
[i
].is_redundant
= 0;
64 tab
->var
[i
].frozen
= 0;
65 tab
->var
[i
].negated
= 0;
79 tab
->strict_redundant
= 0;
86 tab
->bottom
.type
= isl_tab_undo_bottom
;
87 tab
->bottom
.next
= NULL
;
88 tab
->top
= &tab
->bottom
;
100 isl_ctx
*isl_tab_get_ctx(struct isl_tab
*tab
)
102 return tab
? isl_mat_get_ctx(tab
->mat
) : NULL
;
105 int isl_tab_extend_cons(struct isl_tab
*tab
, unsigned n_new
)
114 if (tab
->max_con
< tab
->n_con
+ n_new
) {
115 struct isl_tab_var
*con
;
117 con
= isl_realloc_array(tab
->mat
->ctx
, tab
->con
,
118 struct isl_tab_var
, tab
->max_con
+ n_new
);
122 tab
->max_con
+= n_new
;
124 if (tab
->mat
->n_row
< tab
->n_row
+ n_new
) {
127 tab
->mat
= isl_mat_extend(tab
->mat
,
128 tab
->n_row
+ n_new
, off
+ tab
->n_col
);
131 row_var
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_var
,
132 int, tab
->mat
->n_row
);
135 tab
->row_var
= row_var
;
137 enum isl_tab_row_sign
*s
;
138 s
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_sign
,
139 enum isl_tab_row_sign
, tab
->mat
->n_row
);
148 /* Make room for at least n_new extra variables.
149 * Return -1 if anything went wrong.
151 int isl_tab_extend_vars(struct isl_tab
*tab
, unsigned n_new
)
153 struct isl_tab_var
*var
;
154 unsigned off
= 2 + tab
->M
;
156 if (tab
->max_var
< tab
->n_var
+ n_new
) {
157 var
= isl_realloc_array(tab
->mat
->ctx
, tab
->var
,
158 struct isl_tab_var
, tab
->n_var
+ n_new
);
162 tab
->max_var
= tab
->n_var
+ n_new
;
165 if (tab
->mat
->n_col
< off
+ tab
->n_col
+ n_new
) {
168 tab
->mat
= isl_mat_extend(tab
->mat
,
169 tab
->mat
->n_row
, off
+ tab
->n_col
+ n_new
);
172 p
= isl_realloc_array(tab
->mat
->ctx
, tab
->col_var
,
173 int, tab
->n_col
+ n_new
);
182 static void free_undo_record(struct isl_tab_undo
*undo
)
184 switch (undo
->type
) {
185 case isl_tab_undo_saved_basis
:
186 free(undo
->u
.col_var
);
193 static void free_undo(struct isl_tab
*tab
)
195 struct isl_tab_undo
*undo
, *next
;
197 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
199 free_undo_record(undo
);
204 void isl_tab_free(struct isl_tab
*tab
)
209 isl_mat_free(tab
->mat
);
210 isl_vec_free(tab
->dual
);
211 isl_basic_map_free(tab
->bmap
);
217 isl_mat_free(tab
->samples
);
218 free(tab
->sample_index
);
219 isl_mat_free(tab
->basis
);
223 struct isl_tab
*isl_tab_dup(struct isl_tab
*tab
)
233 dup
= isl_calloc_type(tab
->mat
->ctx
, struct isl_tab
);
236 dup
->mat
= isl_mat_dup(tab
->mat
);
239 dup
->var
= isl_alloc_array(tab
->mat
->ctx
, struct isl_tab_var
, tab
->max_var
);
240 if (tab
->max_var
&& !dup
->var
)
242 for (i
= 0; i
< tab
->n_var
; ++i
)
243 dup
->var
[i
] = tab
->var
[i
];
244 dup
->con
= isl_alloc_array(tab
->mat
->ctx
, struct isl_tab_var
, tab
->max_con
);
245 if (tab
->max_con
&& !dup
->con
)
247 for (i
= 0; i
< tab
->n_con
; ++i
)
248 dup
->con
[i
] = tab
->con
[i
];
249 dup
->col_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->mat
->n_col
- off
);
250 if ((tab
->mat
->n_col
- off
) && !dup
->col_var
)
252 for (i
= 0; i
< tab
->n_col
; ++i
)
253 dup
->col_var
[i
] = tab
->col_var
[i
];
254 dup
->row_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->mat
->n_row
);
255 if (tab
->mat
->n_row
&& !dup
->row_var
)
257 for (i
= 0; i
< tab
->n_row
; ++i
)
258 dup
->row_var
[i
] = tab
->row_var
[i
];
260 dup
->row_sign
= isl_alloc_array(tab
->mat
->ctx
, enum isl_tab_row_sign
,
262 if (tab
->mat
->n_row
&& !dup
->row_sign
)
264 for (i
= 0; i
< tab
->n_row
; ++i
)
265 dup
->row_sign
[i
] = tab
->row_sign
[i
];
268 dup
->samples
= isl_mat_dup(tab
->samples
);
271 dup
->sample_index
= isl_alloc_array(tab
->mat
->ctx
, int,
272 tab
->samples
->n_row
);
273 if (tab
->samples
->n_row
&& !dup
->sample_index
)
275 dup
->n_sample
= tab
->n_sample
;
276 dup
->n_outside
= tab
->n_outside
;
278 dup
->n_row
= tab
->n_row
;
279 dup
->n_con
= tab
->n_con
;
280 dup
->n_eq
= tab
->n_eq
;
281 dup
->max_con
= tab
->max_con
;
282 dup
->n_col
= tab
->n_col
;
283 dup
->n_var
= tab
->n_var
;
284 dup
->max_var
= tab
->max_var
;
285 dup
->n_param
= tab
->n_param
;
286 dup
->n_div
= tab
->n_div
;
287 dup
->n_dead
= tab
->n_dead
;
288 dup
->n_redundant
= tab
->n_redundant
;
289 dup
->rational
= tab
->rational
;
290 dup
->empty
= tab
->empty
;
291 dup
->strict_redundant
= 0;
295 tab
->cone
= tab
->cone
;
296 dup
->bottom
.type
= isl_tab_undo_bottom
;
297 dup
->bottom
.next
= NULL
;
298 dup
->top
= &dup
->bottom
;
300 dup
->n_zero
= tab
->n_zero
;
301 dup
->n_unbounded
= tab
->n_unbounded
;
302 dup
->basis
= isl_mat_dup(tab
->basis
);
310 /* Construct the coefficient matrix of the product tableau
312 * mat{1,2} is the coefficient matrix of tableau {1,2}
313 * row{1,2} is the number of rows in tableau {1,2}
314 * col{1,2} is the number of columns in tableau {1,2}
315 * off is the offset to the coefficient column (skipping the
316 * denominator, the constant term and the big parameter if any)
317 * r{1,2} is the number of redundant rows in tableau {1,2}
318 * d{1,2} is the number of dead columns in tableau {1,2}
320 * The order of the rows and columns in the result is as explained
321 * in isl_tab_product.
323 static struct isl_mat
*tab_mat_product(struct isl_mat
*mat1
,
324 struct isl_mat
*mat2
, unsigned row1
, unsigned row2
,
325 unsigned col1
, unsigned col2
,
326 unsigned off
, unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
329 struct isl_mat
*prod
;
332 prod
= isl_mat_alloc(mat1
->ctx
, mat1
->n_row
+ mat2
->n_row
,
338 for (i
= 0; i
< r1
; ++i
) {
339 isl_seq_cpy(prod
->row
[n
+ i
], mat1
->row
[i
], off
+ d1
);
340 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
, d2
);
341 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
+ d2
,
342 mat1
->row
[i
] + off
+ d1
, col1
- d1
);
343 isl_seq_clr(prod
->row
[n
+ i
] + off
+ col1
+ d1
, col2
- d2
);
347 for (i
= 0; i
< r2
; ++i
) {
348 isl_seq_cpy(prod
->row
[n
+ i
], mat2
->row
[i
], off
);
349 isl_seq_clr(prod
->row
[n
+ i
] + off
, d1
);
350 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
,
351 mat2
->row
[i
] + off
, d2
);
352 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
+ d2
, col1
- d1
);
353 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ col1
+ d1
,
354 mat2
->row
[i
] + off
+ d2
, col2
- d2
);
358 for (i
= 0; i
< row1
- r1
; ++i
) {
359 isl_seq_cpy(prod
->row
[n
+ i
], mat1
->row
[r1
+ i
], off
+ d1
);
360 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
, d2
);
361 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
+ d2
,
362 mat1
->row
[r1
+ i
] + off
+ d1
, col1
- d1
);
363 isl_seq_clr(prod
->row
[n
+ i
] + off
+ col1
+ d1
, col2
- d2
);
367 for (i
= 0; i
< row2
- r2
; ++i
) {
368 isl_seq_cpy(prod
->row
[n
+ i
], mat2
->row
[r2
+ i
], off
);
369 isl_seq_clr(prod
->row
[n
+ i
] + off
, d1
);
370 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
,
371 mat2
->row
[r2
+ i
] + off
, d2
);
372 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
+ d2
, col1
- d1
);
373 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ col1
+ d1
,
374 mat2
->row
[r2
+ i
] + off
+ d2
, col2
- d2
);
380 /* Update the row or column index of a variable that corresponds
381 * to a variable in the first input tableau.
383 static void update_index1(struct isl_tab_var
*var
,
384 unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
386 if (var
->index
== -1)
388 if (var
->is_row
&& var
->index
>= r1
)
390 if (!var
->is_row
&& var
->index
>= d1
)
394 /* Update the row or column index of a variable that corresponds
395 * to a variable in the second input tableau.
397 static void update_index2(struct isl_tab_var
*var
,
398 unsigned row1
, unsigned col1
,
399 unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
401 if (var
->index
== -1)
416 /* Create a tableau that represents the Cartesian product of the sets
417 * represented by tableaus tab1 and tab2.
418 * The order of the rows in the product is
419 * - redundant rows of tab1
420 * - redundant rows of tab2
421 * - non-redundant rows of tab1
422 * - non-redundant rows of tab2
423 * The order of the columns is
426 * - coefficient of big parameter, if any
427 * - dead columns of tab1
428 * - dead columns of tab2
429 * - live columns of tab1
430 * - live columns of tab2
431 * The order of the variables and the constraints is a concatenation
432 * of order in the two input tableaus.
434 struct isl_tab
*isl_tab_product(struct isl_tab
*tab1
, struct isl_tab
*tab2
)
437 struct isl_tab
*prod
;
439 unsigned r1
, r2
, d1
, d2
;
444 isl_assert(tab1
->mat
->ctx
, tab1
->M
== tab2
->M
, return NULL
);
445 isl_assert(tab1
->mat
->ctx
, tab1
->rational
== tab2
->rational
, return NULL
);
446 isl_assert(tab1
->mat
->ctx
, tab1
->cone
== tab2
->cone
, return NULL
);
447 isl_assert(tab1
->mat
->ctx
, !tab1
->row_sign
, return NULL
);
448 isl_assert(tab1
->mat
->ctx
, !tab2
->row_sign
, return NULL
);
449 isl_assert(tab1
->mat
->ctx
, tab1
->n_param
== 0, return NULL
);
450 isl_assert(tab1
->mat
->ctx
, tab2
->n_param
== 0, return NULL
);
451 isl_assert(tab1
->mat
->ctx
, tab1
->n_div
== 0, return NULL
);
452 isl_assert(tab1
->mat
->ctx
, tab2
->n_div
== 0, return NULL
);
455 r1
= tab1
->n_redundant
;
456 r2
= tab2
->n_redundant
;
459 prod
= isl_calloc_type(tab1
->mat
->ctx
, struct isl_tab
);
462 prod
->mat
= tab_mat_product(tab1
->mat
, tab2
->mat
,
463 tab1
->n_row
, tab2
->n_row
,
464 tab1
->n_col
, tab2
->n_col
, off
, r1
, r2
, d1
, d2
);
467 prod
->var
= isl_alloc_array(tab1
->mat
->ctx
, struct isl_tab_var
,
468 tab1
->max_var
+ tab2
->max_var
);
469 if ((tab1
->max_var
+ tab2
->max_var
) && !prod
->var
)
471 for (i
= 0; i
< tab1
->n_var
; ++i
) {
472 prod
->var
[i
] = tab1
->var
[i
];
473 update_index1(&prod
->var
[i
], r1
, r2
, d1
, d2
);
475 for (i
= 0; i
< tab2
->n_var
; ++i
) {
476 prod
->var
[tab1
->n_var
+ i
] = tab2
->var
[i
];
477 update_index2(&prod
->var
[tab1
->n_var
+ i
],
478 tab1
->n_row
, tab1
->n_col
,
481 prod
->con
= isl_alloc_array(tab1
->mat
->ctx
, struct isl_tab_var
,
482 tab1
->max_con
+ tab2
->max_con
);
483 if ((tab1
->max_con
+ tab2
->max_con
) && !prod
->con
)
485 for (i
= 0; i
< tab1
->n_con
; ++i
) {
486 prod
->con
[i
] = tab1
->con
[i
];
487 update_index1(&prod
->con
[i
], r1
, r2
, d1
, d2
);
489 for (i
= 0; i
< tab2
->n_con
; ++i
) {
490 prod
->con
[tab1
->n_con
+ i
] = tab2
->con
[i
];
491 update_index2(&prod
->con
[tab1
->n_con
+ i
],
492 tab1
->n_row
, tab1
->n_col
,
495 prod
->col_var
= isl_alloc_array(tab1
->mat
->ctx
, int,
496 tab1
->n_col
+ tab2
->n_col
);
497 if ((tab1
->n_col
+ tab2
->n_col
) && !prod
->col_var
)
499 for (i
= 0; i
< tab1
->n_col
; ++i
) {
500 int pos
= i
< d1
? i
: i
+ d2
;
501 prod
->col_var
[pos
] = tab1
->col_var
[i
];
503 for (i
= 0; i
< tab2
->n_col
; ++i
) {
504 int pos
= i
< d2
? d1
+ i
: tab1
->n_col
+ i
;
505 int t
= tab2
->col_var
[i
];
510 prod
->col_var
[pos
] = t
;
512 prod
->row_var
= isl_alloc_array(tab1
->mat
->ctx
, int,
513 tab1
->mat
->n_row
+ tab2
->mat
->n_row
);
514 if ((tab1
->mat
->n_row
+ tab2
->mat
->n_row
) && !prod
->row_var
)
516 for (i
= 0; i
< tab1
->n_row
; ++i
) {
517 int pos
= i
< r1
? i
: i
+ r2
;
518 prod
->row_var
[pos
] = tab1
->row_var
[i
];
520 for (i
= 0; i
< tab2
->n_row
; ++i
) {
521 int pos
= i
< r2
? r1
+ i
: tab1
->n_row
+ i
;
522 int t
= tab2
->row_var
[i
];
527 prod
->row_var
[pos
] = t
;
529 prod
->samples
= NULL
;
530 prod
->sample_index
= NULL
;
531 prod
->n_row
= tab1
->n_row
+ tab2
->n_row
;
532 prod
->n_con
= tab1
->n_con
+ tab2
->n_con
;
534 prod
->max_con
= tab1
->max_con
+ tab2
->max_con
;
535 prod
->n_col
= tab1
->n_col
+ tab2
->n_col
;
536 prod
->n_var
= tab1
->n_var
+ tab2
->n_var
;
537 prod
->max_var
= tab1
->max_var
+ tab2
->max_var
;
540 prod
->n_dead
= tab1
->n_dead
+ tab2
->n_dead
;
541 prod
->n_redundant
= tab1
->n_redundant
+ tab2
->n_redundant
;
542 prod
->rational
= tab1
->rational
;
543 prod
->empty
= tab1
->empty
|| tab2
->empty
;
544 prod
->strict_redundant
= tab1
->strict_redundant
|| tab2
->strict_redundant
;
548 prod
->cone
= tab1
->cone
;
549 prod
->bottom
.type
= isl_tab_undo_bottom
;
550 prod
->bottom
.next
= NULL
;
551 prod
->top
= &prod
->bottom
;
554 prod
->n_unbounded
= 0;
563 static struct isl_tab_var
*var_from_index(struct isl_tab
*tab
, int i
)
568 return &tab
->con
[~i
];
571 struct isl_tab_var
*isl_tab_var_from_row(struct isl_tab
*tab
, int i
)
573 return var_from_index(tab
, tab
->row_var
[i
]);
576 static struct isl_tab_var
*var_from_col(struct isl_tab
*tab
, int i
)
578 return var_from_index(tab
, tab
->col_var
[i
]);
581 /* Check if there are any upper bounds on column variable "var",
582 * i.e., non-negative rows where var appears with a negative coefficient.
583 * Return 1 if there are no such bounds.
585 static int max_is_manifestly_unbounded(struct isl_tab
*tab
,
586 struct isl_tab_var
*var
)
589 unsigned off
= 2 + tab
->M
;
593 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
594 if (!isl_int_is_neg(tab
->mat
->row
[i
][off
+ var
->index
]))
596 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
602 /* Check if there are any lower bounds on column variable "var",
603 * i.e., non-negative rows where var appears with a positive coefficient.
604 * Return 1 if there are no such bounds.
606 static int min_is_manifestly_unbounded(struct isl_tab
*tab
,
607 struct isl_tab_var
*var
)
610 unsigned off
= 2 + tab
->M
;
614 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
615 if (!isl_int_is_pos(tab
->mat
->row
[i
][off
+ var
->index
]))
617 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
623 static int row_cmp(struct isl_tab
*tab
, int r1
, int r2
, int c
, isl_int
*t
)
625 unsigned off
= 2 + tab
->M
;
629 isl_int_mul(*t
, tab
->mat
->row
[r1
][2], tab
->mat
->row
[r2
][off
+c
]);
630 isl_int_submul(*t
, tab
->mat
->row
[r2
][2], tab
->mat
->row
[r1
][off
+c
]);
635 isl_int_mul(*t
, tab
->mat
->row
[r1
][1], tab
->mat
->row
[r2
][off
+ c
]);
636 isl_int_submul(*t
, tab
->mat
->row
[r2
][1], tab
->mat
->row
[r1
][off
+ c
]);
637 return isl_int_sgn(*t
);
640 /* Given the index of a column "c", return the index of a row
641 * that can be used to pivot the column in, with either an increase
642 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
643 * If "var" is not NULL, then the row returned will be different from
644 * the one associated with "var".
646 * Each row in the tableau is of the form
648 * x_r = a_r0 + \sum_i a_ri x_i
650 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
651 * impose any limit on the increase or decrease in the value of x_c
652 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
653 * for the row with the smallest (most stringent) such bound.
654 * Note that the common denominator of each row drops out of the fraction.
655 * To check if row j has a smaller bound than row r, i.e.,
656 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
657 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
658 * where -sign(a_jc) is equal to "sgn".
660 static int pivot_row(struct isl_tab
*tab
,
661 struct isl_tab_var
*var
, int sgn
, int c
)
665 unsigned off
= 2 + tab
->M
;
669 for (j
= tab
->n_redundant
; j
< tab
->n_row
; ++j
) {
670 if (var
&& j
== var
->index
)
672 if (!isl_tab_var_from_row(tab
, j
)->is_nonneg
)
674 if (sgn
* isl_int_sgn(tab
->mat
->row
[j
][off
+ c
]) >= 0)
680 tsgn
= sgn
* row_cmp(tab
, r
, j
, c
, &t
);
681 if (tsgn
< 0 || (tsgn
== 0 &&
682 tab
->row_var
[j
] < tab
->row_var
[r
]))
689 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
690 * (sgn < 0) the value of row variable var.
691 * If not NULL, then skip_var is a row variable that should be ignored
692 * while looking for a pivot row. It is usually equal to var.
694 * As the given row in the tableau is of the form
696 * x_r = a_r0 + \sum_i a_ri x_i
698 * we need to find a column such that the sign of a_ri is equal to "sgn"
699 * (such that an increase in x_i will have the desired effect) or a
700 * column with a variable that may attain negative values.
701 * If a_ri is positive, then we need to move x_i in the same direction
702 * to obtain the desired effect. Otherwise, x_i has to move in the
703 * opposite direction.
705 static void find_pivot(struct isl_tab
*tab
,
706 struct isl_tab_var
*var
, struct isl_tab_var
*skip_var
,
707 int sgn
, int *row
, int *col
)
714 isl_assert(tab
->mat
->ctx
, var
->is_row
, return);
715 tr
= tab
->mat
->row
[var
->index
] + 2 + tab
->M
;
718 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
719 if (isl_int_is_zero(tr
[j
]))
721 if (isl_int_sgn(tr
[j
]) != sgn
&&
722 var_from_col(tab
, j
)->is_nonneg
)
724 if (c
< 0 || tab
->col_var
[j
] < tab
->col_var
[c
])
730 sgn
*= isl_int_sgn(tr
[c
]);
731 r
= pivot_row(tab
, skip_var
, sgn
, c
);
732 *row
= r
< 0 ? var
->index
: r
;
736 /* Return 1 if row "row" represents an obviously redundant inequality.
738 * - it represents an inequality or a variable
739 * - that is the sum of a non-negative sample value and a positive
740 * combination of zero or more non-negative constraints.
742 int isl_tab_row_is_redundant(struct isl_tab
*tab
, int row
)
745 unsigned off
= 2 + tab
->M
;
747 if (tab
->row_var
[row
] < 0 && !isl_tab_var_from_row(tab
, row
)->is_nonneg
)
750 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
752 if (tab
->strict_redundant
&& isl_int_is_zero(tab
->mat
->row
[row
][1]))
754 if (tab
->M
&& isl_int_is_neg(tab
->mat
->row
[row
][2]))
757 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
758 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ i
]))
760 if (tab
->col_var
[i
] >= 0)
762 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ i
]))
764 if (!var_from_col(tab
, i
)->is_nonneg
)
770 static void swap_rows(struct isl_tab
*tab
, int row1
, int row2
)
773 enum isl_tab_row_sign s
;
775 t
= tab
->row_var
[row1
];
776 tab
->row_var
[row1
] = tab
->row_var
[row2
];
777 tab
->row_var
[row2
] = t
;
778 isl_tab_var_from_row(tab
, row1
)->index
= row1
;
779 isl_tab_var_from_row(tab
, row2
)->index
= row2
;
780 tab
->mat
= isl_mat_swap_rows(tab
->mat
, row1
, row2
);
784 s
= tab
->row_sign
[row1
];
785 tab
->row_sign
[row1
] = tab
->row_sign
[row2
];
786 tab
->row_sign
[row2
] = s
;
789 static isl_stat
push_union(struct isl_tab
*tab
,
790 enum isl_tab_undo_type type
, union isl_tab_undo_val u
) WARN_UNUSED
;
792 /* Push record "u" onto the undo stack of "tab", provided "tab"
793 * keeps track of undo information.
795 * If the record cannot be pushed, then mark the undo stack as invalid
796 * such that a later rollback attempt will not try to undo earlier
797 * records without having been able to undo the current record.
799 static isl_stat
push_union(struct isl_tab
*tab
,
800 enum isl_tab_undo_type type
, union isl_tab_undo_val u
)
802 struct isl_tab_undo
*undo
;
805 return isl_stat_error
;
809 undo
= isl_alloc_type(tab
->mat
->ctx
, struct isl_tab_undo
);
814 undo
->next
= tab
->top
;
821 return isl_stat_error
;
824 isl_stat
isl_tab_push_var(struct isl_tab
*tab
,
825 enum isl_tab_undo_type type
, struct isl_tab_var
*var
)
827 union isl_tab_undo_val u
;
829 u
.var_index
= tab
->row_var
[var
->index
];
831 u
.var_index
= tab
->col_var
[var
->index
];
832 return push_union(tab
, type
, u
);
835 isl_stat
isl_tab_push(struct isl_tab
*tab
, enum isl_tab_undo_type type
)
837 union isl_tab_undo_val u
= { 0 };
838 return push_union(tab
, type
, u
);
841 /* Push a record on the undo stack describing the current basic
842 * variables, so that the this state can be restored during rollback.
844 isl_stat
isl_tab_push_basis(struct isl_tab
*tab
)
847 union isl_tab_undo_val u
;
849 u
.col_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
850 if (tab
->n_col
&& !u
.col_var
)
851 return isl_stat_error
;
852 for (i
= 0; i
< tab
->n_col
; ++i
)
853 u
.col_var
[i
] = tab
->col_var
[i
];
854 return push_union(tab
, isl_tab_undo_saved_basis
, u
);
857 isl_stat
isl_tab_push_callback(struct isl_tab
*tab
,
858 struct isl_tab_callback
*callback
)
860 union isl_tab_undo_val u
;
861 u
.callback
= callback
;
862 return push_union(tab
, isl_tab_undo_callback
, u
);
865 struct isl_tab
*isl_tab_init_samples(struct isl_tab
*tab
)
872 tab
->samples
= isl_mat_alloc(tab
->mat
->ctx
, 1, 1 + tab
->n_var
);
875 tab
->sample_index
= isl_alloc_array(tab
->mat
->ctx
, int, 1);
876 if (!tab
->sample_index
)
884 int isl_tab_add_sample(struct isl_tab
*tab
, __isl_take isl_vec
*sample
)
889 if (tab
->n_sample
+ 1 > tab
->samples
->n_row
) {
890 int *t
= isl_realloc_array(tab
->mat
->ctx
,
891 tab
->sample_index
, int, tab
->n_sample
+ 1);
894 tab
->sample_index
= t
;
897 tab
->samples
= isl_mat_extend(tab
->samples
,
898 tab
->n_sample
+ 1, tab
->samples
->n_col
);
902 isl_seq_cpy(tab
->samples
->row
[tab
->n_sample
], sample
->el
, sample
->size
);
903 isl_vec_free(sample
);
904 tab
->sample_index
[tab
->n_sample
] = tab
->n_sample
;
909 isl_vec_free(sample
);
913 struct isl_tab
*isl_tab_drop_sample(struct isl_tab
*tab
, int s
)
915 if (s
!= tab
->n_outside
) {
916 int t
= tab
->sample_index
[tab
->n_outside
];
917 tab
->sample_index
[tab
->n_outside
] = tab
->sample_index
[s
];
918 tab
->sample_index
[s
] = t
;
919 isl_mat_swap_rows(tab
->samples
, tab
->n_outside
, s
);
922 if (isl_tab_push(tab
, isl_tab_undo_drop_sample
) < 0) {
930 /* Record the current number of samples so that we can remove newer
931 * samples during a rollback.
933 isl_stat
isl_tab_save_samples(struct isl_tab
*tab
)
935 union isl_tab_undo_val u
;
938 return isl_stat_error
;
941 return push_union(tab
, isl_tab_undo_saved_samples
, u
);
944 /* Mark row with index "row" as being redundant.
945 * If we may need to undo the operation or if the row represents
946 * a variable of the original problem, the row is kept,
947 * but no longer considered when looking for a pivot row.
948 * Otherwise, the row is simply removed.
950 * The row may be interchanged with some other row. If it
951 * is interchanged with a later row, return 1. Otherwise return 0.
952 * If the rows are checked in order in the calling function,
953 * then a return value of 1 means that the row with the given
954 * row number may now contain a different row that hasn't been checked yet.
956 int isl_tab_mark_redundant(struct isl_tab
*tab
, int row
)
958 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, row
);
959 var
->is_redundant
= 1;
960 isl_assert(tab
->mat
->ctx
, row
>= tab
->n_redundant
, return -1);
961 if (tab
->preserve
|| tab
->need_undo
|| tab
->row_var
[row
] >= 0) {
962 if (tab
->row_var
[row
] >= 0 && !var
->is_nonneg
) {
964 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, var
) < 0)
967 if (row
!= tab
->n_redundant
)
968 swap_rows(tab
, row
, tab
->n_redundant
);
970 return isl_tab_push_var(tab
, isl_tab_undo_redundant
, var
);
972 if (row
!= tab
->n_row
- 1)
973 swap_rows(tab
, row
, tab
->n_row
- 1);
974 isl_tab_var_from_row(tab
, tab
->n_row
- 1)->index
= -1;
980 /* Mark "tab" as a rational tableau.
981 * If it wasn't marked as a rational tableau already and if we may
982 * need to undo changes, then arrange for the marking to be undone
985 int isl_tab_mark_rational(struct isl_tab
*tab
)
989 if (!tab
->rational
&& tab
->need_undo
)
990 if (isl_tab_push(tab
, isl_tab_undo_rational
) < 0)
996 isl_stat
isl_tab_mark_empty(struct isl_tab
*tab
)
999 return isl_stat_error
;
1000 if (!tab
->empty
&& tab
->need_undo
)
1001 if (isl_tab_push(tab
, isl_tab_undo_empty
) < 0)
1002 return isl_stat_error
;
1007 int isl_tab_freeze_constraint(struct isl_tab
*tab
, int con
)
1009 struct isl_tab_var
*var
;
1014 var
= &tab
->con
[con
];
1022 return isl_tab_push_var(tab
, isl_tab_undo_freeze
, var
);
1027 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
1028 * the original sign of the pivot element.
1029 * We only keep track of row signs during PILP solving and in this case
1030 * we only pivot a row with negative sign (meaning the value is always
1031 * non-positive) using a positive pivot element.
1033 * For each row j, the new value of the parametric constant is equal to
1035 * a_j0 - a_jc a_r0/a_rc
1037 * where a_j0 is the original parametric constant, a_rc is the pivot element,
1038 * a_r0 is the parametric constant of the pivot row and a_jc is the
1039 * pivot column entry of the row j.
1040 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
1041 * remains the same if a_jc has the same sign as the row j or if
1042 * a_jc is zero. In all other cases, we reset the sign to "unknown".
1044 static void update_row_sign(struct isl_tab
*tab
, int row
, int col
, int row_sgn
)
1047 struct isl_mat
*mat
= tab
->mat
;
1048 unsigned off
= 2 + tab
->M
;
1053 if (tab
->row_sign
[row
] == 0)
1055 isl_assert(mat
->ctx
, row_sgn
> 0, return);
1056 isl_assert(mat
->ctx
, tab
->row_sign
[row
] == isl_tab_row_neg
, return);
1057 tab
->row_sign
[row
] = isl_tab_row_pos
;
1058 for (i
= 0; i
< tab
->n_row
; ++i
) {
1062 s
= isl_int_sgn(mat
->row
[i
][off
+ col
]);
1065 if (!tab
->row_sign
[i
])
1067 if (s
< 0 && tab
->row_sign
[i
] == isl_tab_row_neg
)
1069 if (s
> 0 && tab
->row_sign
[i
] == isl_tab_row_pos
)
1071 tab
->row_sign
[i
] = isl_tab_row_unknown
;
1075 /* Given a row number "row" and a column number "col", pivot the tableau
1076 * such that the associated variables are interchanged.
1077 * The given row in the tableau expresses
1079 * x_r = a_r0 + \sum_i a_ri x_i
1083 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
1085 * Substituting this equality into the other rows
1087 * x_j = a_j0 + \sum_i a_ji x_i
1089 * with a_jc \ne 0, we obtain
1091 * 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
1098 * where i is any other column and j is any other row,
1099 * is therefore transformed into
1101 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1102 * 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)
1104 * The transformation is performed along the following steps
1106 * d_r/n_rc n_ri/n_rc
1109 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1112 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1113 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
1115 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1116 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
1118 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1119 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
1121 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1122 * 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)
1125 int isl_tab_pivot(struct isl_tab
*tab
, int row
, int col
)
1131 struct isl_mat
*mat
= tab
->mat
;
1132 struct isl_tab_var
*var
;
1133 unsigned off
= 2 + tab
->M
;
1135 ctx
= isl_tab_get_ctx(tab
);
1136 if (isl_ctx_next_operation(ctx
) < 0)
1139 isl_int_swap(mat
->row
[row
][0], mat
->row
[row
][off
+ col
]);
1140 sgn
= isl_int_sgn(mat
->row
[row
][0]);
1142 isl_int_neg(mat
->row
[row
][0], mat
->row
[row
][0]);
1143 isl_int_neg(mat
->row
[row
][off
+ col
], mat
->row
[row
][off
+ col
]);
1145 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1146 if (j
== off
- 1 + col
)
1148 isl_int_neg(mat
->row
[row
][1 + j
], mat
->row
[row
][1 + j
]);
1150 if (!isl_int_is_one(mat
->row
[row
][0]))
1151 isl_seq_normalize(mat
->ctx
, mat
->row
[row
], off
+ tab
->n_col
);
1152 for (i
= 0; i
< tab
->n_row
; ++i
) {
1155 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1157 isl_int_mul(mat
->row
[i
][0], mat
->row
[i
][0], mat
->row
[row
][0]);
1158 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1159 if (j
== off
- 1 + col
)
1161 isl_int_mul(mat
->row
[i
][1 + j
],
1162 mat
->row
[i
][1 + j
], mat
->row
[row
][0]);
1163 isl_int_addmul(mat
->row
[i
][1 + j
],
1164 mat
->row
[i
][off
+ col
], mat
->row
[row
][1 + j
]);
1166 isl_int_mul(mat
->row
[i
][off
+ col
],
1167 mat
->row
[i
][off
+ col
], mat
->row
[row
][off
+ col
]);
1168 if (!isl_int_is_one(mat
->row
[i
][0]))
1169 isl_seq_normalize(mat
->ctx
, mat
->row
[i
], off
+ tab
->n_col
);
1171 t
= tab
->row_var
[row
];
1172 tab
->row_var
[row
] = tab
->col_var
[col
];
1173 tab
->col_var
[col
] = t
;
1174 var
= isl_tab_var_from_row(tab
, row
);
1177 var
= var_from_col(tab
, col
);
1180 update_row_sign(tab
, row
, col
, sgn
);
1183 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1184 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1186 if (!isl_tab_var_from_row(tab
, i
)->frozen
&&
1187 isl_tab_row_is_redundant(tab
, i
)) {
1188 int redo
= isl_tab_mark_redundant(tab
, i
);
1198 /* If "var" represents a column variable, then pivot is up (sgn > 0)
1199 * or down (sgn < 0) to a row. The variable is assumed not to be
1200 * unbounded in the specified direction.
1201 * If sgn = 0, then the variable is unbounded in both directions,
1202 * and we pivot with any row we can find.
1204 static int to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
) WARN_UNUSED
;
1205 static int to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
)
1208 unsigned off
= 2 + tab
->M
;
1214 for (r
= tab
->n_redundant
; r
< tab
->n_row
; ++r
)
1215 if (!isl_int_is_zero(tab
->mat
->row
[r
][off
+var
->index
]))
1217 isl_assert(tab
->mat
->ctx
, r
< tab
->n_row
, return -1);
1219 r
= pivot_row(tab
, NULL
, sign
, var
->index
);
1220 isl_assert(tab
->mat
->ctx
, r
>= 0, return -1);
1223 return isl_tab_pivot(tab
, r
, var
->index
);
1226 /* Check whether all variables that are marked as non-negative
1227 * also have a non-negative sample value. This function is not
1228 * called from the current code but is useful during debugging.
1230 static void check_table(struct isl_tab
*tab
) __attribute__ ((unused
));
1231 static void check_table(struct isl_tab
*tab
)
1237 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1238 struct isl_tab_var
*var
;
1239 var
= isl_tab_var_from_row(tab
, i
);
1240 if (!var
->is_nonneg
)
1243 isl_assert(tab
->mat
->ctx
,
1244 !isl_int_is_neg(tab
->mat
->row
[i
][2]), abort());
1245 if (isl_int_is_pos(tab
->mat
->row
[i
][2]))
1248 isl_assert(tab
->mat
->ctx
, !isl_int_is_neg(tab
->mat
->row
[i
][1]),
1253 /* Return the sign of the maximal value of "var".
1254 * If the sign is not negative, then on return from this function,
1255 * the sample value will also be non-negative.
1257 * If "var" is manifestly unbounded wrt positive values, we are done.
1258 * Otherwise, we pivot the variable up to a row if needed
1259 * Then we continue pivoting down until either
1260 * - no more down pivots can be performed
1261 * - the sample value is positive
1262 * - the variable is pivoted into a manifestly unbounded column
1264 static int sign_of_max(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1268 if (max_is_manifestly_unbounded(tab
, var
))
1270 if (to_row(tab
, var
, 1) < 0)
1272 while (!isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1273 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1275 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1276 if (isl_tab_pivot(tab
, row
, col
) < 0)
1278 if (!var
->is_row
) /* manifestly unbounded */
1284 int isl_tab_sign_of_max(struct isl_tab
*tab
, int con
)
1286 struct isl_tab_var
*var
;
1291 var
= &tab
->con
[con
];
1292 isl_assert(tab
->mat
->ctx
, !var
->is_redundant
, return -2);
1293 isl_assert(tab
->mat
->ctx
, !var
->is_zero
, return -2);
1295 return sign_of_max(tab
, var
);
1298 static int row_is_neg(struct isl_tab
*tab
, int row
)
1301 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1302 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1304 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1306 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1309 static int row_sgn(struct isl_tab
*tab
, int row
)
1312 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1313 if (!isl_int_is_zero(tab
->mat
->row
[row
][2]))
1314 return isl_int_sgn(tab
->mat
->row
[row
][2]);
1316 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1319 /* Perform pivots until the row variable "var" has a non-negative
1320 * sample value or until no more upward pivots can be performed.
1321 * Return the sign of the sample value after the pivots have been
1324 static int restore_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1328 while (row_is_neg(tab
, var
->index
)) {
1329 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1332 if (isl_tab_pivot(tab
, row
, col
) < 0)
1334 if (!var
->is_row
) /* manifestly unbounded */
1337 return row_sgn(tab
, var
->index
);
1340 /* Perform pivots until we are sure that the row variable "var"
1341 * can attain non-negative values. After return from this
1342 * function, "var" is still a row variable, but its sample
1343 * value may not be non-negative, even if the function returns 1.
1345 static int at_least_zero(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1349 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1350 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1353 if (row
== var
->index
) /* manifestly unbounded */
1355 if (isl_tab_pivot(tab
, row
, col
) < 0)
1358 return !isl_int_is_neg(tab
->mat
->row
[var
->index
][1]);
1361 /* Return a negative value if "var" can attain negative values.
1362 * Return a non-negative value otherwise.
1364 * If "var" is manifestly unbounded wrt negative values, we are done.
1365 * Otherwise, if var is in a column, we can pivot it down to a row.
1366 * Then we continue pivoting down until either
1367 * - the pivot would result in a manifestly unbounded column
1368 * => we don't perform the pivot, but simply return -1
1369 * - no more down pivots can be performed
1370 * - the sample value is negative
1371 * If the sample value becomes negative and the variable is supposed
1372 * to be nonnegative, then we undo the last pivot.
1373 * However, if the last pivot has made the pivoting variable
1374 * obviously redundant, then it may have moved to another row.
1375 * In that case we look for upward pivots until we reach a non-negative
1378 static int sign_of_min(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1381 struct isl_tab_var
*pivot_var
= NULL
;
1383 if (min_is_manifestly_unbounded(tab
, var
))
1387 row
= pivot_row(tab
, NULL
, -1, col
);
1388 pivot_var
= var_from_col(tab
, col
);
1389 if (isl_tab_pivot(tab
, row
, col
) < 0)
1391 if (var
->is_redundant
)
1393 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1394 if (var
->is_nonneg
) {
1395 if (!pivot_var
->is_redundant
&&
1396 pivot_var
->index
== row
) {
1397 if (isl_tab_pivot(tab
, row
, col
) < 0)
1400 if (restore_row(tab
, var
) < -1)
1406 if (var
->is_redundant
)
1408 while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1409 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1410 if (row
== var
->index
)
1413 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1414 pivot_var
= var_from_col(tab
, col
);
1415 if (isl_tab_pivot(tab
, row
, col
) < 0)
1417 if (var
->is_redundant
)
1420 if (pivot_var
&& var
->is_nonneg
) {
1421 /* pivot back to non-negative value */
1422 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
) {
1423 if (isl_tab_pivot(tab
, row
, col
) < 0)
1426 if (restore_row(tab
, var
) < -1)
1432 static int row_at_most_neg_one(struct isl_tab
*tab
, int row
)
1435 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1437 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1440 return isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
1441 isl_int_abs_ge(tab
->mat
->row
[row
][1],
1442 tab
->mat
->row
[row
][0]);
1445 /* Return 1 if "var" can attain values <= -1.
1446 * Return 0 otherwise.
1448 * If the variable "var" is supposed to be non-negative (is_nonneg is set),
1449 * then the sample value of "var" is assumed to be non-negative when the
1450 * the function is called. If 1 is returned then the constraint
1451 * is not redundant and the sample value is made non-negative again before
1452 * the function returns.
1454 int isl_tab_min_at_most_neg_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1457 struct isl_tab_var
*pivot_var
;
1459 if (min_is_manifestly_unbounded(tab
, var
))
1463 row
= pivot_row(tab
, NULL
, -1, col
);
1464 pivot_var
= var_from_col(tab
, col
);
1465 if (isl_tab_pivot(tab
, row
, col
) < 0)
1467 if (var
->is_redundant
)
1469 if (row_at_most_neg_one(tab
, var
->index
)) {
1470 if (var
->is_nonneg
) {
1471 if (!pivot_var
->is_redundant
&&
1472 pivot_var
->index
== row
) {
1473 if (isl_tab_pivot(tab
, row
, col
) < 0)
1476 if (restore_row(tab
, var
) < -1)
1482 if (var
->is_redundant
)
1485 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1486 if (row
== var
->index
) {
1487 if (var
->is_nonneg
&& restore_row(tab
, var
) < -1)
1493 pivot_var
= var_from_col(tab
, col
);
1494 if (isl_tab_pivot(tab
, row
, col
) < 0)
1496 if (var
->is_redundant
)
1498 } while (!row_at_most_neg_one(tab
, var
->index
));
1499 if (var
->is_nonneg
) {
1500 /* pivot back to non-negative value */
1501 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
1502 if (isl_tab_pivot(tab
, row
, col
) < 0)
1504 if (restore_row(tab
, var
) < -1)
1510 /* Return 1 if "var" can attain values >= 1.
1511 * Return 0 otherwise.
1513 static int at_least_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1518 if (max_is_manifestly_unbounded(tab
, var
))
1520 if (to_row(tab
, var
, 1) < 0)
1522 r
= tab
->mat
->row
[var
->index
];
1523 while (isl_int_lt(r
[1], r
[0])) {
1524 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1526 return isl_int_ge(r
[1], r
[0]);
1527 if (row
== var
->index
) /* manifestly unbounded */
1529 if (isl_tab_pivot(tab
, row
, col
) < 0)
1535 static void swap_cols(struct isl_tab
*tab
, int col1
, int col2
)
1538 unsigned off
= 2 + tab
->M
;
1539 t
= tab
->col_var
[col1
];
1540 tab
->col_var
[col1
] = tab
->col_var
[col2
];
1541 tab
->col_var
[col2
] = t
;
1542 var_from_col(tab
, col1
)->index
= col1
;
1543 var_from_col(tab
, col2
)->index
= col2
;
1544 tab
->mat
= isl_mat_swap_cols(tab
->mat
, off
+ col1
, off
+ col2
);
1547 /* Mark column with index "col" as representing a zero variable.
1548 * If we may need to undo the operation the column is kept,
1549 * but no longer considered.
1550 * Otherwise, the column is simply removed.
1552 * The column may be interchanged with some other column. If it
1553 * is interchanged with a later column, return 1. Otherwise return 0.
1554 * If the columns are checked in order in the calling function,
1555 * then a return value of 1 means that the column with the given
1556 * column number may now contain a different column that
1557 * hasn't been checked yet.
1559 int isl_tab_kill_col(struct isl_tab
*tab
, int col
)
1561 var_from_col(tab
, col
)->is_zero
= 1;
1562 if (tab
->need_undo
) {
1563 if (isl_tab_push_var(tab
, isl_tab_undo_zero
,
1564 var_from_col(tab
, col
)) < 0)
1566 if (col
!= tab
->n_dead
)
1567 swap_cols(tab
, col
, tab
->n_dead
);
1571 if (col
!= tab
->n_col
- 1)
1572 swap_cols(tab
, col
, tab
->n_col
- 1);
1573 var_from_col(tab
, tab
->n_col
- 1)->index
= -1;
1579 static int row_is_manifestly_non_integral(struct isl_tab
*tab
, int row
)
1581 unsigned off
= 2 + tab
->M
;
1583 if (tab
->M
&& !isl_int_eq(tab
->mat
->row
[row
][2],
1584 tab
->mat
->row
[row
][0]))
1586 if (isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1587 tab
->n_col
- tab
->n_dead
) != -1)
1590 return !isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
1591 tab
->mat
->row
[row
][0]);
1594 /* For integer tableaus, check if any of the coordinates are stuck
1595 * at a non-integral value.
1597 static int tab_is_manifestly_empty(struct isl_tab
*tab
)
1606 for (i
= 0; i
< tab
->n_var
; ++i
) {
1607 if (!tab
->var
[i
].is_row
)
1609 if (row_is_manifestly_non_integral(tab
, tab
->var
[i
].index
))
1616 /* Row variable "var" is non-negative and cannot attain any values
1617 * larger than zero. This means that the coefficients of the unrestricted
1618 * column variables are zero and that the coefficients of the non-negative
1619 * column variables are zero or negative.
1620 * Each of the non-negative variables with a negative coefficient can
1621 * then also be written as the negative sum of non-negative variables
1622 * and must therefore also be zero.
1624 * If "temp_var" is set, then "var" is a temporary variable that
1625 * will be removed after this function returns and for which
1626 * no information is recorded on the undo stack.
1627 * Do not add any undo records involving this variable in this case
1628 * since the variable will have been removed before any future undo
1629 * operations. Also avoid marking the variable as redundant,
1630 * since that either adds an undo record or needlessly removes the row
1631 * (the caller will take care of removing the row).
1633 static isl_stat
close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
,
1634 int temp_var
) WARN_UNUSED
;
1635 static isl_stat
close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
,
1639 struct isl_mat
*mat
= tab
->mat
;
1640 unsigned off
= 2 + tab
->M
;
1642 if (!var
->is_nonneg
)
1643 isl_die(isl_tab_get_ctx(tab
), isl_error_internal
,
1644 "expecting non-negative variable",
1645 return isl_stat_error
);
1647 if (!temp_var
&& tab
->need_undo
)
1648 if (isl_tab_push_var(tab
, isl_tab_undo_zero
, var
) < 0)
1649 return isl_stat_error
;
1650 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1652 if (isl_int_is_zero(mat
->row
[var
->index
][off
+ j
]))
1654 if (isl_int_is_pos(mat
->row
[var
->index
][off
+ j
]))
1655 isl_die(isl_tab_get_ctx(tab
), isl_error_internal
,
1656 "row cannot have positive coefficients",
1657 return isl_stat_error
);
1658 recheck
= isl_tab_kill_col(tab
, j
);
1660 return isl_stat_error
;
1664 if (!temp_var
&& isl_tab_mark_redundant(tab
, var
->index
) < 0)
1665 return isl_stat_error
;
1666 if (tab_is_manifestly_empty(tab
) && isl_tab_mark_empty(tab
) < 0)
1667 return isl_stat_error
;
1671 /* Add a constraint to the tableau and allocate a row for it.
1672 * Return the index into the constraint array "con".
1674 * This function assumes that at least one more row and at least
1675 * one more element in the constraint array are available in the tableau.
1677 int isl_tab_allocate_con(struct isl_tab
*tab
)
1681 isl_assert(tab
->mat
->ctx
, tab
->n_row
< tab
->mat
->n_row
, return -1);
1682 isl_assert(tab
->mat
->ctx
, tab
->n_con
< tab
->max_con
, return -1);
1685 tab
->con
[r
].index
= tab
->n_row
;
1686 tab
->con
[r
].is_row
= 1;
1687 tab
->con
[r
].is_nonneg
= 0;
1688 tab
->con
[r
].is_zero
= 0;
1689 tab
->con
[r
].is_redundant
= 0;
1690 tab
->con
[r
].frozen
= 0;
1691 tab
->con
[r
].negated
= 0;
1692 tab
->row_var
[tab
->n_row
] = ~r
;
1696 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]) < 0)
1702 /* Move the entries in tab->var up one position, starting at "first",
1703 * creating room for an extra entry at position "first".
1704 * Since some of the entries of tab->row_var and tab->col_var contain
1705 * indices into this array, they have to be updated accordingly.
1707 static int var_insert_entry(struct isl_tab
*tab
, int first
)
1711 if (tab
->n_var
>= tab
->max_var
)
1712 isl_die(isl_tab_get_ctx(tab
), isl_error_internal
,
1713 "not enough room for new variable", return -1);
1714 if (first
> tab
->n_var
)
1715 isl_die(isl_tab_get_ctx(tab
), isl_error_internal
,
1716 "invalid initial position", return -1);
1718 for (i
= tab
->n_var
- 1; i
>= first
; --i
) {
1719 tab
->var
[i
+ 1] = tab
->var
[i
];
1720 if (tab
->var
[i
+ 1].is_row
)
1721 tab
->row_var
[tab
->var
[i
+ 1].index
]++;
1723 tab
->col_var
[tab
->var
[i
+ 1].index
]++;
1731 /* Drop the entry at position "first" in tab->var, moving all
1732 * subsequent entries down.
1733 * Since some of the entries of tab->row_var and tab->col_var contain
1734 * indices into this array, they have to be updated accordingly.
1736 static int var_drop_entry(struct isl_tab
*tab
, int first
)
1740 if (first
>= tab
->n_var
)
1741 isl_die(isl_tab_get_ctx(tab
), isl_error_internal
,
1742 "invalid initial position", return -1);
1746 for (i
= first
; i
< tab
->n_var
; ++i
) {
1747 tab
->var
[i
] = tab
->var
[i
+ 1];
1748 if (tab
->var
[i
+ 1].is_row
)
1749 tab
->row_var
[tab
->var
[i
].index
]--;
1751 tab
->col_var
[tab
->var
[i
].index
]--;
1757 /* Add a variable to the tableau at position "r" and allocate a column for it.
1758 * Return the index into the variable array "var", i.e., "r",
1761 int isl_tab_insert_var(struct isl_tab
*tab
, int r
)
1764 unsigned off
= 2 + tab
->M
;
1766 isl_assert(tab
->mat
->ctx
, tab
->n_col
< tab
->mat
->n_col
, return -1);
1768 if (var_insert_entry(tab
, r
) < 0)
1771 tab
->var
[r
].index
= tab
->n_col
;
1772 tab
->var
[r
].is_row
= 0;
1773 tab
->var
[r
].is_nonneg
= 0;
1774 tab
->var
[r
].is_zero
= 0;
1775 tab
->var
[r
].is_redundant
= 0;
1776 tab
->var
[r
].frozen
= 0;
1777 tab
->var
[r
].negated
= 0;
1778 tab
->col_var
[tab
->n_col
] = r
;
1780 for (i
= 0; i
< tab
->n_row
; ++i
)
1781 isl_int_set_si(tab
->mat
->row
[i
][off
+ tab
->n_col
], 0);
1784 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->var
[r
]) < 0)
1790 /* Add a variable to the tableau and allocate a column for it.
1791 * Return the index into the variable array "var".
1793 int isl_tab_allocate_var(struct isl_tab
*tab
)
1798 return isl_tab_insert_var(tab
, tab
->n_var
);
1801 /* Add a row to the tableau. The row is given as an affine combination
1802 * of the original variables and needs to be expressed in terms of the
1805 * This function assumes that at least one more row and at least
1806 * one more element in the constraint array are available in the tableau.
1808 * We add each term in turn.
1809 * If r = n/d_r is the current sum and we need to add k x, then
1810 * if x is a column variable, we increase the numerator of
1811 * this column by k d_r
1812 * if x = f/d_x is a row variable, then the new representation of r is
1814 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1815 * --- + --- = ------------------- = -------------------
1816 * d_r d_r d_r d_x/g m
1818 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1820 * If tab->M is set, then, internally, each variable x is represented
1821 * as x' - M. We then also need no subtract k d_r from the coefficient of M.
1823 int isl_tab_add_row(struct isl_tab
*tab
, isl_int
*line
)
1829 unsigned off
= 2 + tab
->M
;
1831 r
= isl_tab_allocate_con(tab
);
1837 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1838 isl_int_set_si(row
[0], 1);
1839 isl_int_set(row
[1], line
[0]);
1840 isl_seq_clr(row
+ 2, tab
->M
+ tab
->n_col
);
1841 for (i
= 0; i
< tab
->n_var
; ++i
) {
1842 if (tab
->var
[i
].is_zero
)
1844 if (tab
->var
[i
].is_row
) {
1846 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1847 isl_int_swap(a
, row
[0]);
1848 isl_int_divexact(a
, row
[0], a
);
1850 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1851 isl_int_mul(b
, b
, line
[1 + i
]);
1852 isl_seq_combine(row
+ 1, a
, row
+ 1,
1853 b
, tab
->mat
->row
[tab
->var
[i
].index
] + 1,
1854 1 + tab
->M
+ tab
->n_col
);
1856 isl_int_addmul(row
[off
+ tab
->var
[i
].index
],
1857 line
[1 + i
], row
[0]);
1858 if (tab
->M
&& i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
1859 isl_int_submul(row
[2], line
[1 + i
], row
[0]);
1861 isl_seq_normalize(tab
->mat
->ctx
, row
, off
+ tab
->n_col
);
1866 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_unknown
;
1871 static isl_stat
drop_row(struct isl_tab
*tab
, int row
)
1873 isl_assert(tab
->mat
->ctx
, ~tab
->row_var
[row
] == tab
->n_con
- 1,
1874 return isl_stat_error
);
1875 if (row
!= tab
->n_row
- 1)
1876 swap_rows(tab
, row
, tab
->n_row
- 1);
1882 /* Drop the variable in column "col" along with the column.
1883 * The column is removed first because it may need to be moved
1884 * into the last position and this process requires
1885 * the contents of the col_var array in a state
1886 * before the removal of the variable.
1888 static isl_stat
drop_col(struct isl_tab
*tab
, int col
)
1892 var
= tab
->col_var
[col
];
1893 if (col
!= tab
->n_col
- 1)
1894 swap_cols(tab
, col
, tab
->n_col
- 1);
1896 if (var_drop_entry(tab
, var
) < 0)
1897 return isl_stat_error
;
1901 /* Add inequality "ineq" and check if it conflicts with the
1902 * previously added constraints or if it is obviously redundant.
1904 * This function assumes that at least one more row and at least
1905 * one more element in the constraint array are available in the tableau.
1907 isl_stat
isl_tab_add_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1914 return isl_stat_error
;
1916 struct isl_basic_map
*bmap
= tab
->bmap
;
1918 isl_assert(tab
->mat
->ctx
, tab
->n_eq
== bmap
->n_eq
,
1919 return isl_stat_error
);
1920 isl_assert(tab
->mat
->ctx
,
1921 tab
->n_con
== bmap
->n_eq
+ bmap
->n_ineq
,
1922 return isl_stat_error
);
1923 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, ineq
);
1924 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1925 return isl_stat_error
;
1927 return isl_stat_error
;
1931 isl_int_set_si(cst
, 0);
1932 isl_int_swap(ineq
[0], cst
);
1934 r
= isl_tab_add_row(tab
, ineq
);
1936 isl_int_swap(ineq
[0], cst
);
1940 return isl_stat_error
;
1941 tab
->con
[r
].is_nonneg
= 1;
1942 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1943 return isl_stat_error
;
1944 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1945 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1946 return isl_stat_error
;
1950 sgn
= restore_row(tab
, &tab
->con
[r
]);
1952 return isl_stat_error
;
1954 return isl_tab_mark_empty(tab
);
1955 if (tab
->con
[r
].is_row
&& isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1956 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1957 return isl_stat_error
;
1961 /* Pivot a non-negative variable down until it reaches the value zero
1962 * and then pivot the variable into a column position.
1964 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
1965 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1969 unsigned off
= 2 + tab
->M
;
1974 while (isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1975 find_pivot(tab
, var
, NULL
, -1, &row
, &col
);
1976 isl_assert(tab
->mat
->ctx
, row
!= -1, return -1);
1977 if (isl_tab_pivot(tab
, row
, col
) < 0)
1983 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
)
1984 if (!isl_int_is_zero(tab
->mat
->row
[var
->index
][off
+ i
]))
1987 isl_assert(tab
->mat
->ctx
, i
< tab
->n_col
, return -1);
1988 if (isl_tab_pivot(tab
, var
->index
, i
) < 0)
1994 /* We assume Gaussian elimination has been performed on the equalities.
1995 * The equalities can therefore never conflict.
1996 * Adding the equalities is currently only really useful for a later call
1997 * to isl_tab_ineq_type.
1999 * This function assumes that at least one more row and at least
2000 * one more element in the constraint array are available in the tableau.
2002 static struct isl_tab
*add_eq(struct isl_tab
*tab
, isl_int
*eq
)
2009 r
= isl_tab_add_row(tab
, eq
);
2013 r
= tab
->con
[r
].index
;
2014 i
= isl_seq_first_non_zero(tab
->mat
->row
[r
] + 2 + tab
->M
+ tab
->n_dead
,
2015 tab
->n_col
- tab
->n_dead
);
2016 isl_assert(tab
->mat
->ctx
, i
>= 0, goto error
);
2018 if (isl_tab_pivot(tab
, r
, i
) < 0)
2020 if (isl_tab_kill_col(tab
, i
) < 0)
2030 /* Does the sample value of row "row" of "tab" involve the big parameter,
2033 static int row_is_big(struct isl_tab
*tab
, int row
)
2035 return tab
->M
&& !isl_int_is_zero(tab
->mat
->row
[row
][2]);
2038 static int row_is_manifestly_zero(struct isl_tab
*tab
, int row
)
2040 unsigned off
= 2 + tab
->M
;
2042 if (!isl_int_is_zero(tab
->mat
->row
[row
][1]))
2044 if (row_is_big(tab
, row
))
2046 return isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
2047 tab
->n_col
- tab
->n_dead
) == -1;
2050 /* Add an equality that is known to be valid for the given tableau.
2052 * This function assumes that at least one more row and at least
2053 * one more element in the constraint array are available in the tableau.
2055 int isl_tab_add_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
2057 struct isl_tab_var
*var
;
2062 r
= isl_tab_add_row(tab
, eq
);
2068 if (row_is_manifestly_zero(tab
, r
)) {
2070 if (isl_tab_mark_redundant(tab
, r
) < 0)
2075 if (isl_int_is_neg(tab
->mat
->row
[r
][1])) {
2076 isl_seq_neg(tab
->mat
->row
[r
] + 1, tab
->mat
->row
[r
] + 1,
2081 if (to_col(tab
, var
) < 0)
2084 if (isl_tab_kill_col(tab
, var
->index
) < 0)
2090 /* Add a zero row to "tab" and return the corresponding index
2091 * in the constraint array.
2093 * This function assumes that at least one more row and at least
2094 * one more element in the constraint array are available in the tableau.
2096 static int add_zero_row(struct isl_tab
*tab
)
2101 r
= isl_tab_allocate_con(tab
);
2105 row
= tab
->mat
->row
[tab
->con
[r
].index
];
2106 isl_seq_clr(row
+ 1, 1 + tab
->M
+ tab
->n_col
);
2107 isl_int_set_si(row
[0], 1);
2112 /* Add equality "eq" and check if it conflicts with the
2113 * previously added constraints or if it is obviously redundant.
2115 * This function assumes that at least one more row and at least
2116 * one more element in the constraint array are available in the tableau.
2117 * If tab->bmap is set, then two rows are needed instead of one.
2119 int isl_tab_add_eq(struct isl_tab
*tab
, isl_int
*eq
)
2121 struct isl_tab_undo
*snap
= NULL
;
2122 struct isl_tab_var
*var
;
2130 isl_assert(tab
->mat
->ctx
, !tab
->M
, return -1);
2133 snap
= isl_tab_snap(tab
);
2137 isl_int_set_si(cst
, 0);
2138 isl_int_swap(eq
[0], cst
);
2140 r
= isl_tab_add_row(tab
, eq
);
2142 isl_int_swap(eq
[0], cst
);
2150 if (row_is_manifestly_zero(tab
, row
)) {
2152 return isl_tab_rollback(tab
, snap
);
2153 return drop_row(tab
, row
);
2157 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
2158 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
2160 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
2161 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
2162 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
2163 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
2167 if (add_zero_row(tab
) < 0)
2171 sgn
= isl_int_sgn(tab
->mat
->row
[row
][1]);
2174 isl_seq_neg(tab
->mat
->row
[row
] + 1, tab
->mat
->row
[row
] + 1,
2181 sgn
= sign_of_max(tab
, var
);
2185 if (isl_tab_mark_empty(tab
) < 0)
2192 if (to_col(tab
, var
) < 0)
2195 if (isl_tab_kill_col(tab
, var
->index
) < 0)
2201 /* Construct and return an inequality that expresses an upper bound
2203 * In particular, if the div is given by
2207 * then the inequality expresses
2211 static __isl_give isl_vec
*ineq_for_div(__isl_keep isl_basic_map
*bmap
,
2216 struct isl_vec
*ineq
;
2218 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2222 div_pos
= 1 + total
- bmap
->n_div
+ div
;
2224 ineq
= isl_vec_alloc(bmap
->ctx
, 1 + total
);
2228 isl_seq_cpy(ineq
->el
, bmap
->div
[div
] + 1, 1 + total
);
2229 isl_int_neg(ineq
->el
[div_pos
], bmap
->div
[div
][0]);
2233 /* For a div d = floor(f/m), add the constraints
2236 * -(f-(m-1)) + m d >= 0
2238 * Note that the second constraint is the negation of
2242 * If add_ineq is not NULL, then this function is used
2243 * instead of isl_tab_add_ineq to effectively add the inequalities.
2245 * This function assumes that at least two more rows and at least
2246 * two more elements in the constraint array are available in the tableau.
2248 static isl_stat
add_div_constraints(struct isl_tab
*tab
, unsigned div
,
2249 isl_stat (*add_ineq
)(void *user
, isl_int
*), void *user
)
2253 struct isl_vec
*ineq
;
2255 total
= isl_basic_map_dim(tab
->bmap
, isl_dim_all
);
2257 return isl_stat_error
;
2258 div_pos
= 1 + total
- tab
->bmap
->n_div
+ div
;
2260 ineq
= ineq_for_div(tab
->bmap
, div
);
2265 if (add_ineq(user
, ineq
->el
) < 0)
2268 if (isl_tab_add_ineq(tab
, ineq
->el
) < 0)
2272 isl_seq_neg(ineq
->el
, tab
->bmap
->div
[div
] + 1, 1 + total
);
2273 isl_int_set(ineq
->el
[div_pos
], tab
->bmap
->div
[div
][0]);
2274 isl_int_add(ineq
->el
[0], ineq
->el
[0], ineq
->el
[div_pos
]);
2275 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
2278 if (add_ineq(user
, ineq
->el
) < 0)
2281 if (isl_tab_add_ineq(tab
, ineq
->el
) < 0)
2290 return isl_stat_error
;
2293 /* Check whether the div described by "div" is obviously non-negative.
2294 * If we are using a big parameter, then we will encode the div
2295 * as div' = M + div, which is always non-negative.
2296 * Otherwise, we check whether div is a non-negative affine combination
2297 * of non-negative variables.
2299 static int div_is_nonneg(struct isl_tab
*tab
, __isl_keep isl_vec
*div
)
2306 if (isl_int_is_neg(div
->el
[1]))
2309 for (i
= 0; i
< tab
->n_var
; ++i
) {
2310 if (isl_int_is_neg(div
->el
[2 + i
]))
2312 if (isl_int_is_zero(div
->el
[2 + i
]))
2314 if (!tab
->var
[i
].is_nonneg
)
2321 /* Insert an extra div, prescribed by "div", to the tableau and
2322 * the associated bmap (which is assumed to be non-NULL).
2323 * The extra integer division is inserted at (tableau) position "pos".
2324 * Return "pos" or -1 if an error occurred.
2326 * If add_ineq is not NULL, then this function is used instead
2327 * of isl_tab_add_ineq to add the div constraints.
2328 * This complication is needed because the code in isl_tab_pip
2329 * wants to perform some extra processing when an inequality
2330 * is added to the tableau.
2332 int isl_tab_insert_div(struct isl_tab
*tab
, int pos
, __isl_keep isl_vec
*div
,
2333 isl_stat (*add_ineq
)(void *user
, isl_int
*), void *user
)
2343 if (div
->size
!= 1 + 1 + tab
->n_var
)
2344 isl_die(isl_tab_get_ctx(tab
), isl_error_invalid
,
2345 "unexpected size", return -1);
2347 n_div
= isl_basic_map_dim(tab
->bmap
, isl_dim_div
);
2350 o_div
= tab
->n_var
- n_div
;
2351 if (pos
< o_div
|| pos
> tab
->n_var
)
2352 isl_die(isl_tab_get_ctx(tab
), isl_error_invalid
,
2353 "invalid position", return -1);
2355 nonneg
= div_is_nonneg(tab
, div
);
2357 if (isl_tab_extend_cons(tab
, 3) < 0)
2359 if (isl_tab_extend_vars(tab
, 1) < 0)
2361 r
= isl_tab_insert_var(tab
, pos
);
2366 tab
->var
[r
].is_nonneg
= 1;
2368 tab
->bmap
= isl_basic_map_insert_div(tab
->bmap
, pos
- o_div
, div
);
2371 if (isl_tab_push_var(tab
, isl_tab_undo_bmap_div
, &tab
->var
[r
]) < 0)
2374 if (add_div_constraints(tab
, pos
- o_div
, add_ineq
, user
) < 0)
2380 /* Add an extra div, prescribed by "div", to the tableau and
2381 * the associated bmap (which is assumed to be non-NULL).
2383 int isl_tab_add_div(struct isl_tab
*tab
, __isl_keep isl_vec
*div
)
2387 return isl_tab_insert_div(tab
, tab
->n_var
, div
, NULL
, NULL
);
2390 /* If "track" is set, then we want to keep track of all constraints in tab
2391 * in its bmap field. This field is initialized from a copy of "bmap",
2392 * so we need to make sure that all constraints in "bmap" also appear
2393 * in the constructed tab.
2395 __isl_give
struct isl_tab
*isl_tab_from_basic_map(
2396 __isl_keep isl_basic_map
*bmap
, int track
)
2399 struct isl_tab
*tab
;
2402 total
= isl_basic_map_dim(bmap
, isl_dim_all
);
2405 tab
= isl_tab_alloc(bmap
->ctx
, total
+ bmap
->n_ineq
+ 1, total
, 0);
2408 tab
->preserve
= track
;
2409 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
2410 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
2411 if (isl_tab_mark_empty(tab
) < 0)
2415 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2416 tab
= add_eq(tab
, bmap
->eq
[i
]);
2420 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2421 if (isl_tab_add_ineq(tab
, bmap
->ineq
[i
]) < 0)
2427 if (track
&& isl_tab_track_bmap(tab
, isl_basic_map_copy(bmap
)) < 0)
2435 __isl_give
struct isl_tab
*isl_tab_from_basic_set(
2436 __isl_keep isl_basic_set
*bset
, int track
)
2438 return isl_tab_from_basic_map(bset
, track
);
2441 /* Construct a tableau corresponding to the recession cone of "bset".
2443 struct isl_tab
*isl_tab_from_recession_cone(__isl_keep isl_basic_set
*bset
,
2448 struct isl_tab
*tab
;
2449 isl_size offset
= 0;
2452 total
= isl_basic_set_dim(bset
, isl_dim_all
);
2454 offset
= isl_basic_set_dim(bset
, isl_dim_param
);
2455 if (total
< 0 || offset
< 0)
2457 tab
= isl_tab_alloc(bset
->ctx
, bset
->n_eq
+ bset
->n_ineq
,
2461 tab
->rational
= ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
);
2465 isl_int_set_si(cst
, 0);
2466 for (i
= 0; i
< bset
->n_eq
; ++i
) {
2467 isl_int_swap(bset
->eq
[i
][offset
], cst
);
2469 if (isl_tab_add_eq(tab
, bset
->eq
[i
] + offset
) < 0)
2472 tab
= add_eq(tab
, bset
->eq
[i
]);
2473 isl_int_swap(bset
->eq
[i
][offset
], cst
);
2477 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2479 isl_int_swap(bset
->ineq
[i
][offset
], cst
);
2480 r
= isl_tab_add_row(tab
, bset
->ineq
[i
] + offset
);
2481 isl_int_swap(bset
->ineq
[i
][offset
], cst
);
2484 tab
->con
[r
].is_nonneg
= 1;
2485 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2497 /* Assuming "tab" is the tableau of a cone, check if the cone is
2498 * bounded, i.e., if it is empty or only contains the origin.
2500 isl_bool
isl_tab_cone_is_bounded(struct isl_tab
*tab
)
2505 return isl_bool_error
;
2507 return isl_bool_true
;
2508 if (tab
->n_dead
== tab
->n_col
)
2509 return isl_bool_true
;
2512 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2513 struct isl_tab_var
*var
;
2515 var
= isl_tab_var_from_row(tab
, i
);
2516 if (!var
->is_nonneg
)
2518 sgn
= sign_of_max(tab
, var
);
2520 return isl_bool_error
;
2522 return isl_bool_false
;
2523 if (close_row(tab
, var
, 0) < 0)
2524 return isl_bool_error
;
2527 if (tab
->n_dead
== tab
->n_col
)
2528 return isl_bool_true
;
2529 if (i
== tab
->n_row
)
2530 return isl_bool_false
;
2534 int isl_tab_sample_is_integer(struct isl_tab
*tab
)
2541 for (i
= 0; i
< tab
->n_var
; ++i
) {
2543 if (!tab
->var
[i
].is_row
)
2545 row
= tab
->var
[i
].index
;
2546 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
2547 tab
->mat
->row
[row
][0]))
2553 static struct isl_vec
*extract_integer_sample(struct isl_tab
*tab
)
2556 struct isl_vec
*vec
;
2558 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2562 isl_int_set_si(vec
->block
.data
[0], 1);
2563 for (i
= 0; i
< tab
->n_var
; ++i
) {
2564 if (!tab
->var
[i
].is_row
)
2565 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
2567 int row
= tab
->var
[i
].index
;
2568 isl_int_divexact(vec
->block
.data
[1 + i
],
2569 tab
->mat
->row
[row
][1], tab
->mat
->row
[row
][0]);
2576 struct isl_vec
*isl_tab_get_sample_value(struct isl_tab
*tab
)
2579 struct isl_vec
*vec
;
2585 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2591 isl_int_set_si(vec
->block
.data
[0], 1);
2592 for (i
= 0; i
< tab
->n_var
; ++i
) {
2594 if (!tab
->var
[i
].is_row
) {
2595 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
2598 row
= tab
->var
[i
].index
;
2599 isl_int_gcd(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
2600 isl_int_divexact(m
, tab
->mat
->row
[row
][0], m
);
2601 isl_seq_scale(vec
->block
.data
, vec
->block
.data
, m
, 1 + i
);
2602 isl_int_divexact(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
2603 isl_int_mul(vec
->block
.data
[1 + i
], m
, tab
->mat
->row
[row
][1]);
2605 vec
= isl_vec_normalize(vec
);
2611 /* Store the sample value of "var" of "tab" rounded up (if sgn > 0)
2612 * or down (if sgn < 0) to the nearest integer in *v.
2614 static void get_rounded_sample_value(struct isl_tab
*tab
,
2615 struct isl_tab_var
*var
, int sgn
, isl_int
*v
)
2618 isl_int_set_si(*v
, 0);
2620 isl_int_cdiv_q(*v
, tab
->mat
->row
[var
->index
][1],
2621 tab
->mat
->row
[var
->index
][0]);
2623 isl_int_fdiv_q(*v
, tab
->mat
->row
[var
->index
][1],
2624 tab
->mat
->row
[var
->index
][0]);
2627 /* Update "bmap" based on the results of the tableau "tab".
2628 * In particular, implicit equalities are made explicit, redundant constraints
2629 * are removed and if the sample value happens to be integer, it is stored
2630 * in "bmap" (unless "bmap" already had an integer sample).
2632 * The tableau is assumed to have been created from "bmap" using
2633 * isl_tab_from_basic_map.
2635 struct isl_basic_map
*isl_basic_map_update_from_tab(struct isl_basic_map
*bmap
,
2636 struct isl_tab
*tab
)
2648 bmap
= isl_basic_map_set_to_empty(bmap
);
2650 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
2651 if (isl_tab_is_equality(tab
, n_eq
+ i
))
2652 isl_basic_map_inequality_to_equality(bmap
, i
);
2653 else if (isl_tab_is_redundant(tab
, n_eq
+ i
))
2654 isl_basic_map_drop_inequality(bmap
, i
);
2656 if (bmap
->n_eq
!= n_eq
)
2657 bmap
= isl_basic_map_gauss(bmap
, NULL
);
2658 if (!tab
->rational
&&
2659 bmap
&& !bmap
->sample
&& isl_tab_sample_is_integer(tab
))
2660 bmap
->sample
= extract_integer_sample(tab
);
2664 struct isl_basic_set
*isl_basic_set_update_from_tab(struct isl_basic_set
*bset
,
2665 struct isl_tab
*tab
)
2667 return bset_from_bmap(isl_basic_map_update_from_tab(bset_to_bmap(bset
),
2671 /* Drop the last constraint added to "tab" in position "r".
2672 * The constraint is expected to have remained in a row.
2674 static isl_stat
drop_last_con_in_row(struct isl_tab
*tab
, int r
)
2676 if (!tab
->con
[r
].is_row
)
2677 isl_die(isl_tab_get_ctx(tab
), isl_error_internal
,
2678 "row unexpectedly moved to column",
2679 return isl_stat_error
);
2680 if (r
+ 1 != tab
->n_con
)
2681 isl_die(isl_tab_get_ctx(tab
), isl_error_internal
,
2682 "additional constraints added", return isl_stat_error
);
2683 if (drop_row(tab
, tab
->con
[r
].index
) < 0)
2684 return isl_stat_error
;
2689 /* Given a non-negative variable "var", temporarily add a new non-negative
2690 * variable that is the opposite of "var", ensuring that "var" can only attain
2691 * the value zero. The new variable is removed again before this function
2692 * returns. However, the effect of forcing "var" to be zero remains.
2693 * If var = n/d is a row variable, then the new variable = -n/d.
2694 * If var is a column variables, then the new variable = -var.
2695 * If the new variable cannot attain non-negative values, then
2696 * the resulting tableau is empty.
2697 * Otherwise, we know the value will be zero and we close the row.
2699 static isl_stat
cut_to_hyperplane(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2704 unsigned off
= 2 + tab
->M
;
2708 if (var
->is_redundant
|| !var
->is_nonneg
)
2709 isl_die(isl_tab_get_ctx(tab
), isl_error_invalid
,
2710 "expecting non-redundant non-negative variable",
2711 return isl_stat_error
);
2713 if (isl_tab_extend_cons(tab
, 1) < 0)
2714 return isl_stat_error
;
2717 tab
->con
[r
].index
= tab
->n_row
;
2718 tab
->con
[r
].is_row
= 1;
2719 tab
->con
[r
].is_nonneg
= 0;
2720 tab
->con
[r
].is_zero
= 0;
2721 tab
->con
[r
].is_redundant
= 0;
2722 tab
->con
[r
].frozen
= 0;
2723 tab
->con
[r
].negated
= 0;
2724 tab
->row_var
[tab
->n_row
] = ~r
;
2725 row
= tab
->mat
->row
[tab
->n_row
];
2728 isl_int_set(row
[0], tab
->mat
->row
[var
->index
][0]);
2729 isl_seq_neg(row
+ 1,
2730 tab
->mat
->row
[var
->index
] + 1, 1 + tab
->n_col
);
2732 isl_int_set_si(row
[0], 1);
2733 isl_seq_clr(row
+ 1, 1 + tab
->n_col
);
2734 isl_int_set_si(row
[off
+ var
->index
], -1);
2740 sgn
= sign_of_max(tab
, &tab
->con
[r
]);
2742 return isl_stat_error
;
2744 if (drop_last_con_in_row(tab
, r
) < 0)
2745 return isl_stat_error
;
2746 if (isl_tab_mark_empty(tab
) < 0)
2747 return isl_stat_error
;
2750 tab
->con
[r
].is_nonneg
= 1;
2752 if (close_row(tab
, &tab
->con
[r
], 1) < 0)
2753 return isl_stat_error
;
2754 if (drop_last_con_in_row(tab
, r
) < 0)
2755 return isl_stat_error
;
2760 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2761 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2762 * by r' = r + 1 >= 0.
2763 * If r is a row variable, we simply increase the constant term by one
2764 * (taking into account the denominator).
2765 * If r is a column variable, then we need to modify each row that
2766 * refers to r = r' - 1 by substituting this equality, effectively
2767 * subtracting the coefficient of the column from the constant.
2768 * We should only do this if the minimum is manifestly unbounded,
2769 * however. Otherwise, we may end up with negative sample values
2770 * for non-negative variables.
2771 * So, if r is a column variable with a minimum that is not
2772 * manifestly unbounded, then we need to move it to a row.
2773 * However, the sample value of this row may be negative,
2774 * even after the relaxation, so we need to restore it.
2775 * We therefore prefer to pivot a column up to a row, if possible.
2777 int isl_tab_relax(struct isl_tab
*tab
, int con
)
2779 struct isl_tab_var
*var
;
2784 var
= &tab
->con
[con
];
2786 if (var
->is_row
&& (var
->index
< 0 || var
->index
< tab
->n_redundant
))
2787 isl_die(tab
->mat
->ctx
, isl_error_invalid
,
2788 "cannot relax redundant constraint", return -1);
2789 if (!var
->is_row
&& (var
->index
< 0 || var
->index
< tab
->n_dead
))
2790 isl_die(tab
->mat
->ctx
, isl_error_invalid
,
2791 "cannot relax dead constraint", return -1);
2793 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
2794 if (to_row(tab
, var
, 1) < 0)
2796 if (!var
->is_row
&& !min_is_manifestly_unbounded(tab
, var
))
2797 if (to_row(tab
, var
, -1) < 0)
2801 isl_int_add(tab
->mat
->row
[var
->index
][1],
2802 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
2803 if (restore_row(tab
, var
) < 0)
2807 unsigned off
= 2 + tab
->M
;
2809 for (i
= 0; i
< tab
->n_row
; ++i
) {
2810 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2812 isl_int_sub(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
2813 tab
->mat
->row
[i
][off
+ var
->index
]);
2818 if (isl_tab_push_var(tab
, isl_tab_undo_relax
, var
) < 0)
2824 /* Replace the variable v at position "pos" in the tableau "tab"
2825 * by v' = v + shift.
2827 * If the variable is in a column, then we first check if we can
2828 * simply plug in v = v' - shift. The effect on a row with
2829 * coefficient f/d for variable v is that the constant term c/d
2830 * is replaced by (c - f * shift)/d. If shift is positive and
2831 * f is negative for each row that needs to remain non-negative,
2832 * then this is clearly safe. In other words, if the minimum of v
2833 * is manifestly unbounded, then we can keep v in a column position.
2834 * Otherwise, we can pivot it down to a row.
2835 * Similarly, if shift is negative, we need to check if the maximum
2836 * of is manifestly unbounded.
2838 * If the variable is in a row (from the start or after pivoting),
2839 * then the constant term c/d is replaced by (c + d * shift)/d.
2841 int isl_tab_shift_var(struct isl_tab
*tab
, int pos
, isl_int shift
)
2843 struct isl_tab_var
*var
;
2847 if (isl_int_is_zero(shift
))
2850 var
= &tab
->var
[pos
];
2852 if (isl_int_is_neg(shift
)) {
2853 if (!max_is_manifestly_unbounded(tab
, var
))
2854 if (to_row(tab
, var
, 1) < 0)
2857 if (!min_is_manifestly_unbounded(tab
, var
))
2858 if (to_row(tab
, var
, -1) < 0)
2864 isl_int_addmul(tab
->mat
->row
[var
->index
][1],
2865 shift
, tab
->mat
->row
[var
->index
][0]);
2868 unsigned off
= 2 + tab
->M
;
2870 for (i
= 0; i
< tab
->n_row
; ++i
) {
2871 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2873 isl_int_submul(tab
->mat
->row
[i
][1],
2874 shift
, tab
->mat
->row
[i
][off
+ var
->index
]);
2882 /* Remove the sign constraint from constraint "con".
2884 * If the constraint variable was originally marked non-negative,
2885 * then we make sure we mark it non-negative again during rollback.
2887 int isl_tab_unrestrict(struct isl_tab
*tab
, int con
)
2889 struct isl_tab_var
*var
;
2894 var
= &tab
->con
[con
];
2895 if (!var
->is_nonneg
)
2899 if (isl_tab_push_var(tab
, isl_tab_undo_unrestrict
, var
) < 0)
2905 int isl_tab_select_facet(struct isl_tab
*tab
, int con
)
2910 return cut_to_hyperplane(tab
, &tab
->con
[con
]);
2913 static int may_be_equality(struct isl_tab
*tab
, int row
)
2915 return tab
->rational
? isl_int_is_zero(tab
->mat
->row
[row
][1])
2916 : isl_int_lt(tab
->mat
->row
[row
][1],
2917 tab
->mat
->row
[row
][0]);
2920 /* Return an isl_tab_var that has been marked or NULL if no such
2921 * variable can be found.
2922 * The marked field has only been set for variables that
2923 * appear in non-redundant rows or non-dead columns.
2925 * Pick the last constraint variable that is marked and
2926 * that appears in either a non-redundant row or a non-dead columns.
2927 * Since the returned variable is tested for being a redundant constraint or
2928 * an implicit equality, there is no need to return any tab variable that
2929 * corresponds to a variable.
2931 static struct isl_tab_var
*select_marked(struct isl_tab
*tab
)
2934 struct isl_tab_var
*var
;
2936 for (i
= tab
->n_con
- 1; i
>= 0; --i
) {
2940 if (var
->is_row
&& var
->index
< tab
->n_redundant
)
2942 if (!var
->is_row
&& var
->index
< tab
->n_dead
)
2951 /* Check for (near) equalities among the constraints.
2952 * A constraint is an equality if it is non-negative and if
2953 * its maximal value is either
2954 * - zero (in case of rational tableaus), or
2955 * - strictly less than 1 (in case of integer tableaus)
2957 * We first mark all non-redundant and non-dead variables that
2958 * are not frozen and not obviously not an equality.
2959 * Then we iterate over all marked variables if they can attain
2960 * any values larger than zero or at least one.
2961 * If the maximal value is zero, we mark any column variables
2962 * that appear in the row as being zero and mark the row as being redundant.
2963 * Otherwise, if the maximal value is strictly less than one (and the
2964 * tableau is integer), then we restrict the value to being zero
2965 * by adding an opposite non-negative variable.
2966 * The order in which the variables are considered is not important.
2968 int isl_tab_detect_implicit_equalities(struct isl_tab
*tab
)
2977 if (tab
->n_dead
== tab
->n_col
)
2981 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2982 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2983 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2984 may_be_equality(tab
, i
);
2988 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2989 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2990 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2995 struct isl_tab_var
*var
;
2997 var
= select_marked(tab
);
3002 sgn
= sign_of_max(tab
, var
);
3006 if (close_row(tab
, var
, 0) < 0)
3008 } else if (!tab
->rational
&& !at_least_one(tab
, var
)) {
3009 if (cut_to_hyperplane(tab
, var
) < 0)
3011 return isl_tab_detect_implicit_equalities(tab
);
3013 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
3014 var
= isl_tab_var_from_row(tab
, i
);
3017 if (may_be_equality(tab
, i
))
3027 /* Update the element of row_var or col_var that corresponds to
3028 * constraint tab->con[i] to a move from position "old" to position "i".
3030 static int update_con_after_move(struct isl_tab
*tab
, int i
, int old
)
3035 index
= tab
->con
[i
].index
;
3038 p
= tab
->con
[i
].is_row
? tab
->row_var
: tab
->col_var
;
3039 if (p
[index
] != ~old
)
3040 isl_die(tab
->mat
->ctx
, isl_error_internal
,
3041 "broken internal state", return -1);
3047 /* Rotate the "n" constraints starting at "first" to the right,
3048 * putting the last constraint in the position of the first constraint.
3050 static int rotate_constraints(struct isl_tab
*tab
, int first
, int n
)
3053 struct isl_tab_var var
;
3058 last
= first
+ n
- 1;
3059 var
= tab
->con
[last
];
3060 for (i
= last
; i
> first
; --i
) {
3061 tab
->con
[i
] = tab
->con
[i
- 1];
3062 if (update_con_after_move(tab
, i
, i
- 1) < 0)
3065 tab
->con
[first
] = var
;
3066 if (update_con_after_move(tab
, first
, last
) < 0)
3072 /* Make the equalities that are implicit in "bmap" but that have been
3073 * detected in the corresponding "tab" explicit in "bmap" and update
3074 * "tab" to reflect the new order of the constraints.
3076 * In particular, if inequality i is an implicit equality then
3077 * isl_basic_map_inequality_to_equality will move the inequality
3078 * in front of the other equality and it will move the last inequality
3079 * in the position of inequality i.
3080 * In the tableau, the inequalities of "bmap" are stored after the equalities
3081 * and so the original order
3083 * E E E E E A A A I B B B B L
3087 * I E E E E E A A A L B B B B
3089 * where I is the implicit equality, the E are equalities,
3090 * the A inequalities before I, the B inequalities after I and
3091 * L the last inequality.
3092 * We therefore need to rotate to the right two sets of constraints,
3093 * those up to and including I and those after I.
3095 * If "tab" contains any constraints that are not in "bmap" then they
3096 * appear after those in "bmap" and they should be left untouched.
3098 * Note that this function leaves "bmap" in a temporary state
3099 * as it does not call isl_basic_map_gauss. Calling this function
3100 * is the responsibility of the caller.
3102 __isl_give isl_basic_map
*isl_tab_make_equalities_explicit(struct isl_tab
*tab
,
3103 __isl_take isl_basic_map
*bmap
)
3108 return isl_basic_map_free(bmap
);
3112 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
3113 if (!isl_tab_is_equality(tab
, bmap
->n_eq
+ i
))
3115 isl_basic_map_inequality_to_equality(bmap
, i
);
3116 if (rotate_constraints(tab
, 0, tab
->n_eq
+ i
+ 1) < 0)
3117 return isl_basic_map_free(bmap
);
3118 if (rotate_constraints(tab
, tab
->n_eq
+ i
+ 1,
3119 bmap
->n_ineq
- i
) < 0)
3120 return isl_basic_map_free(bmap
);
3127 static int con_is_redundant(struct isl_tab
*tab
, struct isl_tab_var
*var
)
3131 if (tab
->rational
) {
3132 int sgn
= sign_of_min(tab
, var
);
3137 int irred
= isl_tab_min_at_most_neg_one(tab
, var
);
3144 /* Check for (near) redundant constraints.
3145 * A constraint is redundant if it is non-negative and if
3146 * its minimal value (temporarily ignoring the non-negativity) is either
3147 * - zero (in case of rational tableaus), or
3148 * - strictly larger than -1 (in case of integer tableaus)
3150 * We first mark all non-redundant and non-dead variables that
3151 * are not frozen and not obviously negatively unbounded.
3152 * Then we iterate over all marked variables if they can attain
3153 * any values smaller than zero or at most negative one.
3154 * If not, we mark the row as being redundant (assuming it hasn't
3155 * been detected as being obviously redundant in the mean time).
3157 int isl_tab_detect_redundant(struct isl_tab
*tab
)
3166 if (tab
->n_redundant
== tab
->n_row
)
3170 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
3171 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
3172 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
3176 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
3177 struct isl_tab_var
*var
= var_from_col(tab
, i
);
3178 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
3179 !min_is_manifestly_unbounded(tab
, var
);
3184 struct isl_tab_var
*var
;
3186 var
= select_marked(tab
);
3191 red
= con_is_redundant(tab
, var
);
3194 if (red
&& !var
->is_redundant
)
3195 if (isl_tab_mark_redundant(tab
, var
->index
) < 0)
3197 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
3198 var
= var_from_col(tab
, i
);
3201 if (!min_is_manifestly_unbounded(tab
, var
))
3211 int isl_tab_is_equality(struct isl_tab
*tab
, int con
)
3218 if (tab
->con
[con
].is_zero
)
3220 if (tab
->con
[con
].is_redundant
)
3222 if (!tab
->con
[con
].is_row
)
3223 return tab
->con
[con
].index
< tab
->n_dead
;
3225 row
= tab
->con
[con
].index
;
3228 return isl_int_is_zero(tab
->mat
->row
[row
][1]) &&
3229 !row_is_big(tab
, row
) &&
3230 isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
3231 tab
->n_col
- tab
->n_dead
) == -1;
3234 /* Return the minimal value of the affine expression "f" with denominator
3235 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
3236 * the expression cannot attain arbitrarily small values.
3237 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
3238 * The return value reflects the nature of the result (empty, unbounded,
3239 * minimal value returned in *opt).
3241 * This function assumes that at least one more row and at least
3242 * one more element in the constraint array are available in the tableau.
3244 enum isl_lp_result
isl_tab_min(struct isl_tab
*tab
,
3245 isl_int
*f
, isl_int denom
, isl_int
*opt
, isl_int
*opt_denom
,
3249 enum isl_lp_result res
= isl_lp_ok
;
3250 struct isl_tab_var
*var
;
3251 struct isl_tab_undo
*snap
;
3254 return isl_lp_error
;
3257 return isl_lp_empty
;
3259 snap
= isl_tab_snap(tab
);
3260 r
= isl_tab_add_row(tab
, f
);
3262 return isl_lp_error
;
3266 find_pivot(tab
, var
, var
, -1, &row
, &col
);
3267 if (row
== var
->index
) {
3268 res
= isl_lp_unbounded
;
3273 if (isl_tab_pivot(tab
, row
, col
) < 0)
3274 return isl_lp_error
;
3276 isl_int_mul(tab
->mat
->row
[var
->index
][0],
3277 tab
->mat
->row
[var
->index
][0], denom
);
3278 if (ISL_FL_ISSET(flags
, ISL_TAB_SAVE_DUAL
)) {
3281 isl_vec_free(tab
->dual
);
3282 tab
->dual
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_con
);
3284 return isl_lp_error
;
3285 isl_int_set(tab
->dual
->el
[0], tab
->mat
->row
[var
->index
][0]);
3286 for (i
= 0; i
< tab
->n_con
; ++i
) {
3288 if (tab
->con
[i
].is_row
) {
3289 isl_int_set_si(tab
->dual
->el
[1 + i
], 0);
3292 pos
= 2 + tab
->M
+ tab
->con
[i
].index
;
3293 if (tab
->con
[i
].negated
)
3294 isl_int_neg(tab
->dual
->el
[1 + i
],
3295 tab
->mat
->row
[var
->index
][pos
]);
3297 isl_int_set(tab
->dual
->el
[1 + i
],
3298 tab
->mat
->row
[var
->index
][pos
]);
3301 if (opt
&& res
== isl_lp_ok
) {
3303 isl_int_set(*opt
, tab
->mat
->row
[var
->index
][1]);
3304 isl_int_set(*opt_denom
, tab
->mat
->row
[var
->index
][0]);
3306 get_rounded_sample_value(tab
, var
, 1, opt
);
3308 if (isl_tab_rollback(tab
, snap
) < 0)
3309 return isl_lp_error
;
3313 /* Is the constraint at position "con" marked as being redundant?
3314 * If it is marked as representing an equality, then it is not
3315 * considered to be redundant.
3316 * Note that isl_tab_mark_redundant marks both the isl_tab_var as
3317 * redundant and moves the corresponding row into the first
3318 * tab->n_redundant positions (or removes the row, assigning it index -1),
3319 * so the final test is actually redundant itself.
3321 int isl_tab_is_redundant(struct isl_tab
*tab
, int con
)
3325 if (con
< 0 || con
>= tab
->n_con
)
3326 isl_die(isl_tab_get_ctx(tab
), isl_error_invalid
,
3327 "position out of bounds", return -1);
3328 if (tab
->con
[con
].is_zero
)
3330 if (tab
->con
[con
].is_redundant
)
3332 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
3335 /* Is variable "var" of "tab" fixed to a constant value by its row
3337 * If so and if "value" is not NULL, then store this constant value
3340 * That is, is it a row variable that only has non-zero coefficients
3343 static isl_bool
is_constant(struct isl_tab
*tab
, struct isl_tab_var
*var
,
3346 unsigned off
= 2 + tab
->M
;
3347 isl_mat
*mat
= tab
->mat
;
3353 return isl_bool_false
;
3355 if (row_is_big(tab
, row
))
3356 return isl_bool_false
;
3357 n
= tab
->n_col
- tab
->n_dead
;
3358 pos
= isl_seq_first_non_zero(mat
->row
[row
] + off
+ tab
->n_dead
, n
);
3360 return isl_bool_false
;
3362 isl_int_divexact(*value
, mat
->row
[row
][1], mat
->row
[row
][0]);
3363 return isl_bool_true
;
3366 /* Has the variable "var' of "tab" reached a value that is greater than
3367 * or equal (if sgn > 0) or smaller than or equal (if sgn < 0) to "target"?
3368 * "tmp" has been initialized by the caller and can be used
3369 * to perform local computations.
3371 * If the sample value involves the big parameter, then any value
3373 * Otherwise check if n/d >= t, i.e., n >= d * t (if sgn > 0)
3374 * or n/d <= t, i.e., n <= d * t (if sgn < 0).
3376 static int reached(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sgn
,
3377 isl_int target
, isl_int
*tmp
)
3379 if (row_is_big(tab
, var
->index
))
3381 isl_int_mul(*tmp
, tab
->mat
->row
[var
->index
][0], target
);
3383 return isl_int_ge(tab
->mat
->row
[var
->index
][1], *tmp
);
3385 return isl_int_le(tab
->mat
->row
[var
->index
][1], *tmp
);
3388 /* Can variable "var" of "tab" attain the value "target" by
3389 * pivoting up (if sgn > 0) or down (if sgn < 0)?
3390 * If not, then pivot up [down] to the greatest [smallest]
3392 * "tmp" has been initialized by the caller and can be used
3393 * to perform local computations.
3395 * If the variable is manifestly unbounded in the desired direction,
3396 * then it can attain any value.
3397 * Otherwise, it can be moved to a row.
3398 * Continue pivoting until the target is reached.
3399 * If no more pivoting can be performed, the maximal [minimal]
3400 * rational value has been reached and the target cannot be reached.
3401 * If the variable would be pivoted into a manifestly unbounded column,
3402 * then the target can be reached.
3404 static isl_bool
var_reaches(struct isl_tab
*tab
, struct isl_tab_var
*var
,
3405 int sgn
, isl_int target
, isl_int
*tmp
)
3409 if (sgn
< 0 && min_is_manifestly_unbounded(tab
, var
))
3410 return isl_bool_true
;
3411 if (sgn
> 0 && max_is_manifestly_unbounded(tab
, var
))
3412 return isl_bool_true
;
3413 if (to_row(tab
, var
, sgn
) < 0)
3414 return isl_bool_error
;
3415 while (!reached(tab
, var
, sgn
, target
, tmp
)) {
3416 find_pivot(tab
, var
, var
, sgn
, &row
, &col
);
3418 return isl_bool_false
;
3419 if (row
== var
->index
)
3420 return isl_bool_true
;
3421 if (isl_tab_pivot(tab
, row
, col
) < 0)
3422 return isl_bool_error
;
3425 return isl_bool_true
;
3428 /* Check if variable "var" of "tab" can only attain a single (integer)
3429 * value, and, if so, add an equality constraint to fix the variable
3430 * to this single value and store the result in "target".
3431 * "target" and "tmp" have been initialized by the caller.
3433 * Given the current sample value, round it down and check
3434 * whether it is possible to attain a strictly smaller integer value.
3435 * If so, the variable is not restricted to a single integer value.
3436 * Otherwise, the search stops at the smallest rational value.
3437 * Round up this value and check whether it is possible to attain
3438 * a strictly greater integer value.
3439 * If so, the variable is not restricted to a single integer value.
3440 * Otherwise, the search stops at the greatest rational value.
3441 * If rounding down this value yields a value that is different
3442 * from rounding up the smallest rational value, then the variable
3443 * cannot attain any integer value. Mark the tableau empty.
3444 * Otherwise, add an equality constraint that fixes the variable
3445 * to the single integer value found.
3447 static isl_bool
detect_constant_with_tmp(struct isl_tab
*tab
,
3448 struct isl_tab_var
*var
, isl_int
*target
, isl_int
*tmp
)
3455 get_rounded_sample_value(tab
, var
, -1, target
);
3456 isl_int_sub_ui(*target
, *target
, 1);
3457 reached
= var_reaches(tab
, var
, -1, *target
, tmp
);
3458 if (reached
< 0 || reached
)
3459 return isl_bool_not(reached
);
3460 get_rounded_sample_value(tab
, var
, 1, target
);
3461 isl_int_add_ui(*target
, *target
, 1);
3462 reached
= var_reaches(tab
, var
, 1, *target
, tmp
);
3463 if (reached
< 0 || reached
)
3464 return isl_bool_not(reached
);
3465 get_rounded_sample_value(tab
, var
, -1, tmp
);
3466 isl_int_sub_ui(*target
, *target
, 1);
3467 if (isl_int_ne(*target
, *tmp
)) {
3468 if (isl_tab_mark_empty(tab
) < 0)
3469 return isl_bool_error
;
3470 return isl_bool_false
;
3473 if (isl_tab_extend_cons(tab
, 1) < 0)
3474 return isl_bool_error
;
3475 eq
= isl_vec_alloc(isl_tab_get_ctx(tab
), 1 + tab
->n_var
);
3477 return isl_bool_error
;
3478 pos
= var
- tab
->var
;
3479 isl_seq_clr(eq
->el
+ 1, tab
->n_var
);
3480 isl_int_set_si(eq
->el
[1 + pos
], -1);
3481 isl_int_set(eq
->el
[0], *target
);
3482 r
= isl_tab_add_eq(tab
, eq
->el
);
3485 return r
< 0 ? isl_bool_error
: isl_bool_true
;
3488 /* Check if variable "var" of "tab" can only attain a single (integer)
3489 * value, and, if so, add an equality constraint to fix the variable
3490 * to this single value and store the result in "value" (if "value"
3493 * If the current sample value involves the big parameter,
3494 * then the variable cannot have a fixed integer value.
3495 * If the variable is already fixed to a single value by its row, then
3496 * there is no need to add another equality constraint.
3498 * Otherwise, allocate some temporary variables and continue
3499 * with detect_constant_with_tmp.
3501 static isl_bool
get_constant(struct isl_tab
*tab
, struct isl_tab_var
*var
,
3504 isl_int target
, tmp
;
3507 if (var
->is_row
&& row_is_big(tab
, var
->index
))
3508 return isl_bool_false
;
3509 is_cst
= is_constant(tab
, var
, value
);
3510 if (is_cst
< 0 || is_cst
)
3514 isl_int_init(target
);
3517 is_cst
= detect_constant_with_tmp(tab
, var
,
3518 value
? value
: &target
, &tmp
);
3522 isl_int_clear(target
);
3527 /* Check if variable "var" of "tab" can only attain a single (integer)
3528 * value, and, if so, add an equality constraint to fix the variable
3529 * to this single value and store the result in "value" (if "value"
3532 * For rational tableaus, nothing needs to be done.
3534 isl_bool
isl_tab_is_constant(struct isl_tab
*tab
, int var
, isl_int
*value
)
3537 return isl_bool_error
;
3538 if (var
< 0 || var
>= tab
->n_var
)
3539 isl_die(isl_tab_get_ctx(tab
), isl_error_invalid
,
3540 "position out of bounds", return isl_bool_error
);
3542 return isl_bool_false
;
3544 return get_constant(tab
, &tab
->var
[var
], value
);
3547 /* Check if any of the variables of "tab" can only attain a single (integer)
3548 * value, and, if so, add equality constraints to fix those variables
3549 * to these single values.
3551 * For rational tableaus, nothing needs to be done.
3553 isl_stat
isl_tab_detect_constants(struct isl_tab
*tab
)
3558 return isl_stat_error
;
3562 for (i
= 0; i
< tab
->n_var
; ++i
) {
3563 if (get_constant(tab
, &tab
->var
[i
], NULL
) < 0)
3564 return isl_stat_error
;
3570 /* Take a snapshot of the tableau that can be restored by a call to
3573 struct isl_tab_undo
*isl_tab_snap(struct isl_tab
*tab
)
3581 /* Does "tab" need to keep track of undo information?
3582 * That is, was a snapshot taken that may need to be restored?
3584 isl_bool
isl_tab_need_undo(struct isl_tab
*tab
)
3587 return isl_bool_error
;
3589 return isl_bool_ok(tab
->need_undo
);
3592 /* Remove all tracking of undo information from "tab", invalidating
3593 * any snapshots that may have been taken of the tableau.
3594 * Since all snapshots have been invalidated, there is also
3595 * no need to start keeping track of undo information again.
3597 void isl_tab_clear_undo(struct isl_tab
*tab
)
3606 /* Undo the operation performed by isl_tab_relax.
3608 static isl_stat
unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
)
3610 static isl_stat
unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
)
3612 unsigned off
= 2 + tab
->M
;
3614 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
3615 if (to_row(tab
, var
, 1) < 0)
3616 return isl_stat_error
;
3619 isl_int_sub(tab
->mat
->row
[var
->index
][1],
3620 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
3621 if (var
->is_nonneg
) {
3622 int sgn
= restore_row(tab
, var
);
3623 isl_assert(tab
->mat
->ctx
, sgn
>= 0,
3624 return isl_stat_error
);
3629 for (i
= 0; i
< tab
->n_row
; ++i
) {
3630 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
3632 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
3633 tab
->mat
->row
[i
][off
+ var
->index
]);
3641 /* Undo the operation performed by isl_tab_unrestrict.
3643 * In particular, mark the variable as being non-negative and make
3644 * sure the sample value respects this constraint.
3646 static isl_stat
ununrestrict(struct isl_tab
*tab
, struct isl_tab_var
*var
)
3650 if (var
->is_row
&& restore_row(tab
, var
) < -1)
3651 return isl_stat_error
;
3656 /* Unmark the last redundant row in "tab" as being redundant.
3657 * This undoes part of the modifications performed by isl_tab_mark_redundant.
3658 * In particular, remove the redundant mark and make
3659 * sure the sample value respects the constraint again.
3660 * A variable that is marked non-negative by isl_tab_mark_redundant
3661 * is covered by a separate undo record.
3663 static isl_stat
restore_last_redundant(struct isl_tab
*tab
)
3665 struct isl_tab_var
*var
;
3667 if (tab
->n_redundant
< 1)
3668 isl_die(isl_tab_get_ctx(tab
), isl_error_internal
,
3669 "no redundant rows", return isl_stat_error
);
3671 var
= isl_tab_var_from_row(tab
, tab
->n_redundant
- 1);
3672 var
->is_redundant
= 0;
3674 restore_row(tab
, var
);
3679 static isl_stat
perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
3681 static isl_stat
perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
3683 struct isl_tab_var
*var
= var_from_index(tab
, undo
->u
.var_index
);
3684 switch (undo
->type
) {
3685 case isl_tab_undo_nonneg
:
3688 case isl_tab_undo_redundant
:
3689 if (!var
->is_row
|| var
->index
!= tab
->n_redundant
- 1)
3690 isl_die(isl_tab_get_ctx(tab
), isl_error_internal
,
3691 "not undoing last redundant row",
3692 return isl_stat_error
);
3693 return restore_last_redundant(tab
);
3694 case isl_tab_undo_freeze
:
3697 case isl_tab_undo_zero
:
3702 case isl_tab_undo_allocate
:
3703 if (undo
->u
.var_index
>= 0) {
3704 isl_assert(tab
->mat
->ctx
, !var
->is_row
,
3705 return isl_stat_error
);
3706 return drop_col(tab
, var
->index
);
3709 if (!max_is_manifestly_unbounded(tab
, var
)) {
3710 if (to_row(tab
, var
, 1) < 0)
3711 return isl_stat_error
;
3712 } else if (!min_is_manifestly_unbounded(tab
, var
)) {
3713 if (to_row(tab
, var
, -1) < 0)
3714 return isl_stat_error
;
3716 if (to_row(tab
, var
, 0) < 0)
3717 return isl_stat_error
;
3719 return drop_row(tab
, var
->index
);
3720 case isl_tab_undo_relax
:
3721 return unrelax(tab
, var
);
3722 case isl_tab_undo_unrestrict
:
3723 return ununrestrict(tab
, var
);
3725 isl_die(tab
->mat
->ctx
, isl_error_internal
,
3726 "perform_undo_var called on invalid undo record",
3727 return isl_stat_error
);
3733 /* Restore all rows that have been marked redundant by isl_tab_mark_redundant
3734 * and that have been preserved in the tableau.
3735 * Note that isl_tab_mark_redundant may also have marked some variables
3736 * as being non-negative before marking them redundant. These need
3737 * to be removed as well as otherwise some constraints could end up
3738 * getting marked redundant with respect to the variable.
3740 isl_stat
isl_tab_restore_redundant(struct isl_tab
*tab
)
3743 return isl_stat_error
;
3746 isl_die(isl_tab_get_ctx(tab
), isl_error_invalid
,
3747 "manually restoring redundant constraints "
3748 "interferes with undo history",
3749 return isl_stat_error
);
3751 while (tab
->n_redundant
> 0) {
3752 if (tab
->row_var
[tab
->n_redundant
- 1] >= 0) {
3753 struct isl_tab_var
*var
;
3755 var
= isl_tab_var_from_row(tab
, tab
->n_redundant
- 1);
3758 restore_last_redundant(tab
);
3763 /* Undo the addition of an integer division to the basic map representation
3764 * of "tab" in position "pos".
3766 static isl_stat
drop_bmap_div(struct isl_tab
*tab
, int pos
)
3771 n_div
= isl_basic_map_dim(tab
->bmap
, isl_dim_div
);
3773 return isl_stat_error
;
3774 off
= tab
->n_var
- n_div
;
3775 if (isl_basic_map_drop_div(tab
->bmap
, pos
- off
) < 0)
3776 return isl_stat_error
;
3778 tab
->samples
= isl_mat_drop_cols(tab
->samples
, 1 + pos
, 1);
3780 return isl_stat_error
;
3786 /* Restore the tableau to the state where the basic variables
3787 * are those in "col_var".
3788 * We first construct a list of variables that are currently in
3789 * the basis, but shouldn't. Then we iterate over all variables
3790 * that should be in the basis and for each one that is currently
3791 * not in the basis, we exchange it with one of the elements of the
3792 * list constructed before.
3793 * We can always find an appropriate variable to pivot with because
3794 * the current basis is mapped to the old basis by a non-singular
3795 * matrix and so we can never end up with a zero row.
3797 static int restore_basis(struct isl_tab
*tab
, int *col_var
)
3801 int *extra
= NULL
; /* current columns that contain bad stuff */
3802 unsigned off
= 2 + tab
->M
;
3804 extra
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
3805 if (tab
->n_col
&& !extra
)
3807 for (i
= 0; i
< tab
->n_col
; ++i
) {
3808 for (j
= 0; j
< tab
->n_col
; ++j
)
3809 if (tab
->col_var
[i
] == col_var
[j
])
3813 extra
[n_extra
++] = i
;
3815 for (i
= 0; i
< tab
->n_col
&& n_extra
> 0; ++i
) {
3816 struct isl_tab_var
*var
;
3819 for (j
= 0; j
< tab
->n_col
; ++j
)
3820 if (col_var
[i
] == tab
->col_var
[j
])
3824 var
= var_from_index(tab
, col_var
[i
]);
3826 for (j
= 0; j
< n_extra
; ++j
)
3827 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+extra
[j
]]))
3829 isl_assert(tab
->mat
->ctx
, j
< n_extra
, goto error
);
3830 if (isl_tab_pivot(tab
, row
, extra
[j
]) < 0)
3832 extra
[j
] = extra
[--n_extra
];
3842 /* Remove all samples with index n or greater, i.e., those samples
3843 * that were added since we saved this number of samples in
3844 * isl_tab_save_samples.
3846 static void drop_samples_since(struct isl_tab
*tab
, int n
)
3850 for (i
= tab
->n_sample
- 1; i
>= 0 && tab
->n_sample
> n
; --i
) {
3851 if (tab
->sample_index
[i
] < n
)
3854 if (i
!= tab
->n_sample
- 1) {
3855 int t
= tab
->sample_index
[tab
->n_sample
-1];
3856 tab
->sample_index
[tab
->n_sample
-1] = tab
->sample_index
[i
];
3857 tab
->sample_index
[i
] = t
;
3858 isl_mat_swap_rows(tab
->samples
, tab
->n_sample
-1, i
);
3864 static isl_stat
perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
3866 static isl_stat
perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
3868 switch (undo
->type
) {
3869 case isl_tab_undo_rational
:
3872 case isl_tab_undo_empty
:
3875 case isl_tab_undo_nonneg
:
3876 case isl_tab_undo_redundant
:
3877 case isl_tab_undo_freeze
:
3878 case isl_tab_undo_zero
:
3879 case isl_tab_undo_allocate
:
3880 case isl_tab_undo_relax
:
3881 case isl_tab_undo_unrestrict
:
3882 return perform_undo_var(tab
, undo
);
3883 case isl_tab_undo_bmap_eq
:
3884 return isl_basic_map_free_equality(tab
->bmap
, 1);
3885 case isl_tab_undo_bmap_ineq
:
3886 return isl_basic_map_free_inequality(tab
->bmap
, 1);
3887 case isl_tab_undo_bmap_div
:
3888 return drop_bmap_div(tab
, undo
->u
.var_index
);
3889 case isl_tab_undo_saved_basis
:
3890 if (restore_basis(tab
, undo
->u
.col_var
) < 0)
3891 return isl_stat_error
;
3893 case isl_tab_undo_drop_sample
:
3896 case isl_tab_undo_saved_samples
:
3897 drop_samples_since(tab
, undo
->u
.n
);
3899 case isl_tab_undo_callback
:
3900 return undo
->u
.callback
->run(undo
->u
.callback
);
3902 isl_assert(tab
->mat
->ctx
, 0, return isl_stat_error
);
3907 /* Return the tableau to the state it was in when the snapshot "snap"
3910 isl_stat
isl_tab_rollback(struct isl_tab
*tab
, struct isl_tab_undo
*snap
)
3912 struct isl_tab_undo
*undo
, *next
;
3915 return isl_stat_error
;
3918 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
3922 if (perform_undo(tab
, undo
) < 0) {
3926 return isl_stat_error
;
3928 free_undo_record(undo
);
3933 return isl_stat_error
;
3937 /* The given row "row" represents an inequality violated by all
3938 * points in the tableau. Check for some special cases of such
3939 * separating constraints.
3940 * In particular, if the row has been reduced to the constant -1,
3941 * then we know the inequality is adjacent (but opposite) to
3942 * an equality in the tableau.
3943 * If the row has been reduced to r = c*(-1 -r'), with r' an inequality
3944 * of the tableau and c a positive constant, then the inequality
3945 * is adjacent (but opposite) to the inequality r'.
3947 static enum isl_ineq_type
separation_type(struct isl_tab
*tab
, unsigned row
)
3950 unsigned off
= 2 + tab
->M
;
3953 return isl_ineq_separate
;
3955 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
3956 return isl_ineq_separate
;
3958 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
3959 tab
->n_col
- tab
->n_dead
);
3961 if (isl_int_is_negone(tab
->mat
->row
[row
][1]))
3962 return isl_ineq_adj_eq
;
3964 return isl_ineq_separate
;
3967 if (!isl_int_eq(tab
->mat
->row
[row
][1],
3968 tab
->mat
->row
[row
][off
+ tab
->n_dead
+ pos
]))
3969 return isl_ineq_separate
;
3971 pos
= isl_seq_first_non_zero(
3972 tab
->mat
->row
[row
] + off
+ tab
->n_dead
+ pos
+ 1,
3973 tab
->n_col
- tab
->n_dead
- pos
- 1);
3975 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
3978 /* Check the effect of inequality "ineq" on the tableau "tab".
3980 * isl_ineq_redundant: satisfied by all points in the tableau
3981 * isl_ineq_separate: satisfied by no point in the tableau
3982 * isl_ineq_cut: satisfied by some by not all points
3983 * isl_ineq_adj_eq: adjacent to an equality
3984 * isl_ineq_adj_ineq: adjacent to an inequality.
3986 enum isl_ineq_type
isl_tab_ineq_type(struct isl_tab
*tab
, isl_int
*ineq
)
3988 enum isl_ineq_type type
= isl_ineq_error
;
3989 struct isl_tab_undo
*snap
= NULL
;
3994 return isl_ineq_error
;
3996 if (isl_tab_extend_cons(tab
, 1) < 0)
3997 return isl_ineq_error
;
3999 snap
= isl_tab_snap(tab
);
4001 con
= isl_tab_add_row(tab
, ineq
);
4005 row
= tab
->con
[con
].index
;
4006 if (isl_tab_row_is_redundant(tab
, row
))
4007 type
= isl_ineq_redundant
;
4008 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
4010 isl_int_abs_ge(tab
->mat
->row
[row
][1],
4011 tab
->mat
->row
[row
][0]))) {
4012 int nonneg
= at_least_zero(tab
, &tab
->con
[con
]);
4016 type
= isl_ineq_cut
;
4018 type
= separation_type(tab
, row
);
4020 int red
= con_is_redundant(tab
, &tab
->con
[con
]);
4024 type
= isl_ineq_cut
;
4026 type
= isl_ineq_redundant
;
4029 if (isl_tab_rollback(tab
, snap
))
4030 return isl_ineq_error
;
4033 return isl_ineq_error
;
4036 isl_stat
isl_tab_track_bmap(struct isl_tab
*tab
, __isl_take isl_basic_map
*bmap
)
4038 bmap
= isl_basic_map_cow(bmap
);
4043 bmap
= isl_basic_map_set_to_empty(bmap
);
4050 isl_assert(tab
->mat
->ctx
, tab
->n_eq
== bmap
->n_eq
, goto error
);
4051 isl_assert(tab
->mat
->ctx
,
4052 tab
->n_con
== bmap
->n_eq
+ bmap
->n_ineq
, goto error
);
4058 isl_basic_map_free(bmap
);
4059 return isl_stat_error
;
4062 isl_stat
isl_tab_track_bset(struct isl_tab
*tab
, __isl_take isl_basic_set
*bset
)
4064 return isl_tab_track_bmap(tab
, bset_to_bmap(bset
));
4067 __isl_keep isl_basic_set
*isl_tab_peek_bset(struct isl_tab
*tab
)
4072 return bset_from_bmap(tab
->bmap
);
4075 static void isl_tab_print_internal(__isl_keep
struct isl_tab
*tab
,
4076 FILE *out
, int indent
)
4082 fprintf(out
, "%*snull tab\n", indent
, "");
4085 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
4086 tab
->n_redundant
, tab
->n_dead
);
4088 fprintf(out
, ", rational");
4090 fprintf(out
, ", empty");
4092 fprintf(out
, "%*s[", indent
, "");
4093 for (i
= 0; i
< tab
->n_var
; ++i
) {
4095 fprintf(out
, (i
== tab
->n_param
||
4096 i
== tab
->n_var
- tab
->n_div
) ? "; "
4098 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
4100 tab
->var
[i
].is_zero
? " [=0]" :
4101 tab
->var
[i
].is_redundant
? " [R]" : "");
4103 fprintf(out
, "]\n");
4104 fprintf(out
, "%*s[", indent
, "");
4105 for (i
= 0; i
< tab
->n_con
; ++i
) {
4108 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
4110 tab
->con
[i
].is_zero
? " [=0]" :
4111 tab
->con
[i
].is_redundant
? " [R]" : "");
4113 fprintf(out
, "]\n");
4114 fprintf(out
, "%*s[", indent
, "");
4115 for (i
= 0; i
< tab
->n_row
; ++i
) {
4116 const char *sign
= "";
4119 if (tab
->row_sign
) {
4120 if (tab
->row_sign
[i
] == isl_tab_row_unknown
)
4122 else if (tab
->row_sign
[i
] == isl_tab_row_neg
)
4124 else if (tab
->row_sign
[i
] == isl_tab_row_pos
)
4129 fprintf(out
, "r%d: %d%s%s", i
, tab
->row_var
[i
],
4130 isl_tab_var_from_row(tab
, i
)->is_nonneg
? " [>=0]" : "", sign
);
4132 fprintf(out
, "]\n");
4133 fprintf(out
, "%*s[", indent
, "");
4134 for (i
= 0; i
< tab
->n_col
; ++i
) {
4137 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
4138 var_from_col(tab
, i
)->is_nonneg
? " [>=0]" : "");
4140 fprintf(out
, "]\n");
4141 r
= tab
->mat
->n_row
;
4142 tab
->mat
->n_row
= tab
->n_row
;
4143 c
= tab
->mat
->n_col
;
4144 tab
->mat
->n_col
= 2 + tab
->M
+ tab
->n_col
;
4145 isl_mat_print_internal(tab
->mat
, out
, indent
);
4146 tab
->mat
->n_row
= r
;
4147 tab
->mat
->n_col
= c
;
4149 isl_basic_map_print_internal(tab
->bmap
, out
, indent
);
4152 void isl_tab_dump(__isl_keep
struct isl_tab
*tab
)
4154 isl_tab_print_internal(tab
, stderr
, 0);