2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 #include "isl_map_private.h"
16 * The implementation of tableaus in this file was inspired by Section 8
17 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
18 * prover for program checking".
21 struct isl_tab
*isl_tab_alloc(struct isl_ctx
*ctx
,
22 unsigned n_row
, unsigned n_var
, unsigned M
)
28 tab
= isl_calloc_type(ctx
, struct isl_tab
);
31 tab
->mat
= isl_mat_alloc(ctx
, n_row
, off
+ n_var
);
34 tab
->var
= isl_alloc_array(ctx
, struct isl_tab_var
, n_var
);
37 tab
->con
= isl_alloc_array(ctx
, struct isl_tab_var
, n_row
);
40 tab
->col_var
= isl_alloc_array(ctx
, int, n_var
);
43 tab
->row_var
= isl_alloc_array(ctx
, int, n_row
);
46 for (i
= 0; i
< n_var
; ++i
) {
47 tab
->var
[i
].index
= i
;
48 tab
->var
[i
].is_row
= 0;
49 tab
->var
[i
].is_nonneg
= 0;
50 tab
->var
[i
].is_zero
= 0;
51 tab
->var
[i
].is_redundant
= 0;
52 tab
->var
[i
].frozen
= 0;
53 tab
->var
[i
].negated
= 0;
67 tab
->strict_redundant
= 0;
74 tab
->bottom
.type
= isl_tab_undo_bottom
;
75 tab
->bottom
.next
= NULL
;
76 tab
->top
= &tab
->bottom
;
88 int isl_tab_extend_cons(struct isl_tab
*tab
, unsigned n_new
)
97 if (tab
->max_con
< tab
->n_con
+ n_new
) {
98 struct isl_tab_var
*con
;
100 con
= isl_realloc_array(tab
->mat
->ctx
, tab
->con
,
101 struct isl_tab_var
, tab
->max_con
+ n_new
);
105 tab
->max_con
+= n_new
;
107 if (tab
->mat
->n_row
< tab
->n_row
+ n_new
) {
110 tab
->mat
= isl_mat_extend(tab
->mat
,
111 tab
->n_row
+ n_new
, off
+ tab
->n_col
);
114 row_var
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_var
,
115 int, tab
->mat
->n_row
);
118 tab
->row_var
= row_var
;
120 enum isl_tab_row_sign
*s
;
121 s
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_sign
,
122 enum isl_tab_row_sign
, tab
->mat
->n_row
);
131 /* Make room for at least n_new extra variables.
132 * Return -1 if anything went wrong.
134 int isl_tab_extend_vars(struct isl_tab
*tab
, unsigned n_new
)
136 struct isl_tab_var
*var
;
137 unsigned off
= 2 + tab
->M
;
139 if (tab
->max_var
< tab
->n_var
+ n_new
) {
140 var
= isl_realloc_array(tab
->mat
->ctx
, tab
->var
,
141 struct isl_tab_var
, tab
->n_var
+ n_new
);
145 tab
->max_var
+= n_new
;
148 if (tab
->mat
->n_col
< off
+ tab
->n_col
+ n_new
) {
151 tab
->mat
= isl_mat_extend(tab
->mat
,
152 tab
->mat
->n_row
, off
+ tab
->n_col
+ n_new
);
155 p
= isl_realloc_array(tab
->mat
->ctx
, tab
->col_var
,
156 int, tab
->n_col
+ n_new
);
165 struct isl_tab
*isl_tab_extend(struct isl_tab
*tab
, unsigned n_new
)
167 if (isl_tab_extend_cons(tab
, n_new
) >= 0)
174 static void free_undo(struct isl_tab
*tab
)
176 struct isl_tab_undo
*undo
, *next
;
178 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
185 void isl_tab_free(struct isl_tab
*tab
)
190 isl_mat_free(tab
->mat
);
191 isl_vec_free(tab
->dual
);
192 isl_basic_map_free(tab
->bmap
);
198 isl_mat_free(tab
->samples
);
199 free(tab
->sample_index
);
200 isl_mat_free(tab
->basis
);
204 struct isl_tab
*isl_tab_dup(struct isl_tab
*tab
)
214 dup
= isl_calloc_type(tab
->mat
->ctx
, struct isl_tab
);
217 dup
->mat
= isl_mat_dup(tab
->mat
);
220 dup
->var
= isl_alloc_array(tab
->mat
->ctx
, struct isl_tab_var
, tab
->max_var
);
223 for (i
= 0; i
< tab
->n_var
; ++i
)
224 dup
->var
[i
] = tab
->var
[i
];
225 dup
->con
= isl_alloc_array(tab
->mat
->ctx
, struct isl_tab_var
, tab
->max_con
);
228 for (i
= 0; i
< tab
->n_con
; ++i
)
229 dup
->con
[i
] = tab
->con
[i
];
230 dup
->col_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->mat
->n_col
- off
);
233 for (i
= 0; i
< tab
->n_col
; ++i
)
234 dup
->col_var
[i
] = tab
->col_var
[i
];
235 dup
->row_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->mat
->n_row
);
238 for (i
= 0; i
< tab
->n_row
; ++i
)
239 dup
->row_var
[i
] = tab
->row_var
[i
];
241 dup
->row_sign
= isl_alloc_array(tab
->mat
->ctx
, enum isl_tab_row_sign
,
245 for (i
= 0; i
< tab
->n_row
; ++i
)
246 dup
->row_sign
[i
] = tab
->row_sign
[i
];
249 dup
->samples
= isl_mat_dup(tab
->samples
);
252 dup
->sample_index
= isl_alloc_array(tab
->mat
->ctx
, int,
253 tab
->samples
->n_row
);
254 if (!dup
->sample_index
)
256 dup
->n_sample
= tab
->n_sample
;
257 dup
->n_outside
= tab
->n_outside
;
259 dup
->n_row
= tab
->n_row
;
260 dup
->n_con
= tab
->n_con
;
261 dup
->n_eq
= tab
->n_eq
;
262 dup
->max_con
= tab
->max_con
;
263 dup
->n_col
= tab
->n_col
;
264 dup
->n_var
= tab
->n_var
;
265 dup
->max_var
= tab
->max_var
;
266 dup
->n_param
= tab
->n_param
;
267 dup
->n_div
= tab
->n_div
;
268 dup
->n_dead
= tab
->n_dead
;
269 dup
->n_redundant
= tab
->n_redundant
;
270 dup
->rational
= tab
->rational
;
271 dup
->empty
= tab
->empty
;
272 dup
->strict_redundant
= 0;
276 tab
->cone
= tab
->cone
;
277 dup
->bottom
.type
= isl_tab_undo_bottom
;
278 dup
->bottom
.next
= NULL
;
279 dup
->top
= &dup
->bottom
;
281 dup
->n_zero
= tab
->n_zero
;
282 dup
->n_unbounded
= tab
->n_unbounded
;
283 dup
->basis
= isl_mat_dup(tab
->basis
);
291 /* Construct the coefficient matrix of the product tableau
293 * mat{1,2} is the coefficient matrix of tableau {1,2}
294 * row{1,2} is the number of rows in tableau {1,2}
295 * col{1,2} is the number of columns in tableau {1,2}
296 * off is the offset to the coefficient column (skipping the
297 * denominator, the constant term and the big parameter if any)
298 * r{1,2} is the number of redundant rows in tableau {1,2}
299 * d{1,2} is the number of dead columns in tableau {1,2}
301 * The order of the rows and columns in the result is as explained
302 * in isl_tab_product.
304 static struct isl_mat
*tab_mat_product(struct isl_mat
*mat1
,
305 struct isl_mat
*mat2
, unsigned row1
, unsigned row2
,
306 unsigned col1
, unsigned col2
,
307 unsigned off
, unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
310 struct isl_mat
*prod
;
313 prod
= isl_mat_alloc(mat1
->ctx
, mat1
->n_row
+ mat2
->n_row
,
317 for (i
= 0; i
< r1
; ++i
) {
318 isl_seq_cpy(prod
->row
[n
+ i
], mat1
->row
[i
], off
+ d1
);
319 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
, d2
);
320 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
+ d2
,
321 mat1
->row
[i
] + off
+ d1
, col1
- d1
);
322 isl_seq_clr(prod
->row
[n
+ i
] + off
+ col1
+ d1
, col2
- d2
);
326 for (i
= 0; i
< r2
; ++i
) {
327 isl_seq_cpy(prod
->row
[n
+ i
], mat2
->row
[i
], off
);
328 isl_seq_clr(prod
->row
[n
+ i
] + off
, d1
);
329 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
,
330 mat2
->row
[i
] + off
, d2
);
331 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
+ d2
, col1
- d1
);
332 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ col1
+ d1
,
333 mat2
->row
[i
] + off
+ d2
, col2
- d2
);
337 for (i
= 0; i
< row1
- r1
; ++i
) {
338 isl_seq_cpy(prod
->row
[n
+ i
], mat1
->row
[r1
+ i
], off
+ d1
);
339 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
, d2
);
340 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
+ d2
,
341 mat1
->row
[r1
+ i
] + off
+ d1
, col1
- d1
);
342 isl_seq_clr(prod
->row
[n
+ i
] + off
+ col1
+ d1
, col2
- d2
);
346 for (i
= 0; i
< row2
- r2
; ++i
) {
347 isl_seq_cpy(prod
->row
[n
+ i
], mat2
->row
[r2
+ i
], off
);
348 isl_seq_clr(prod
->row
[n
+ i
] + off
, d1
);
349 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
,
350 mat2
->row
[r2
+ i
] + off
, d2
);
351 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
+ d2
, col1
- d1
);
352 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ col1
+ d1
,
353 mat2
->row
[r2
+ i
] + off
+ d2
, col2
- d2
);
359 /* Update the row or column index of a variable that corresponds
360 * to a variable in the first input tableau.
362 static void update_index1(struct isl_tab_var
*var
,
363 unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
365 if (var
->index
== -1)
367 if (var
->is_row
&& var
->index
>= r1
)
369 if (!var
->is_row
&& var
->index
>= d1
)
373 /* Update the row or column index of a variable that corresponds
374 * to a variable in the second input tableau.
376 static void update_index2(struct isl_tab_var
*var
,
377 unsigned row1
, unsigned col1
,
378 unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
380 if (var
->index
== -1)
395 /* Create a tableau that represents the Cartesian product of the sets
396 * represented by tableaus tab1 and tab2.
397 * The order of the rows in the product is
398 * - redundant rows of tab1
399 * - redundant rows of tab2
400 * - non-redundant rows of tab1
401 * - non-redundant rows of tab2
402 * The order of the columns is
405 * - coefficient of big parameter, if any
406 * - dead columns of tab1
407 * - dead columns of tab2
408 * - live columns of tab1
409 * - live columns of tab2
410 * The order of the variables and the constraints is a concatenation
411 * of order in the two input tableaus.
413 struct isl_tab
*isl_tab_product(struct isl_tab
*tab1
, struct isl_tab
*tab2
)
416 struct isl_tab
*prod
;
418 unsigned r1
, r2
, d1
, d2
;
423 isl_assert(tab1
->mat
->ctx
, tab1
->M
== tab2
->M
, return NULL
);
424 isl_assert(tab1
->mat
->ctx
, tab1
->rational
== tab2
->rational
, return NULL
);
425 isl_assert(tab1
->mat
->ctx
, tab1
->cone
== tab2
->cone
, return NULL
);
426 isl_assert(tab1
->mat
->ctx
, !tab1
->row_sign
, return NULL
);
427 isl_assert(tab1
->mat
->ctx
, !tab2
->row_sign
, return NULL
);
428 isl_assert(tab1
->mat
->ctx
, tab1
->n_param
== 0, return NULL
);
429 isl_assert(tab1
->mat
->ctx
, tab2
->n_param
== 0, return NULL
);
430 isl_assert(tab1
->mat
->ctx
, tab1
->n_div
== 0, return NULL
);
431 isl_assert(tab1
->mat
->ctx
, tab2
->n_div
== 0, return NULL
);
434 r1
= tab1
->n_redundant
;
435 r2
= tab2
->n_redundant
;
438 prod
= isl_calloc_type(tab1
->mat
->ctx
, struct isl_tab
);
441 prod
->mat
= tab_mat_product(tab1
->mat
, tab2
->mat
,
442 tab1
->n_row
, tab2
->n_row
,
443 tab1
->n_col
, tab2
->n_col
, off
, r1
, r2
, d1
, d2
);
446 prod
->var
= isl_alloc_array(tab1
->mat
->ctx
, struct isl_tab_var
,
447 tab1
->max_var
+ tab2
->max_var
);
450 for (i
= 0; i
< tab1
->n_var
; ++i
) {
451 prod
->var
[i
] = tab1
->var
[i
];
452 update_index1(&prod
->var
[i
], r1
, r2
, d1
, d2
);
454 for (i
= 0; i
< tab2
->n_var
; ++i
) {
455 prod
->var
[tab1
->n_var
+ i
] = tab2
->var
[i
];
456 update_index2(&prod
->var
[tab1
->n_var
+ i
],
457 tab1
->n_row
, tab1
->n_col
,
460 prod
->con
= isl_alloc_array(tab1
->mat
->ctx
, struct isl_tab_var
,
461 tab1
->max_con
+ tab2
->max_con
);
464 for (i
= 0; i
< tab1
->n_con
; ++i
) {
465 prod
->con
[i
] = tab1
->con
[i
];
466 update_index1(&prod
->con
[i
], r1
, r2
, d1
, d2
);
468 for (i
= 0; i
< tab2
->n_con
; ++i
) {
469 prod
->con
[tab1
->n_con
+ i
] = tab2
->con
[i
];
470 update_index2(&prod
->con
[tab1
->n_con
+ i
],
471 tab1
->n_row
, tab1
->n_col
,
474 prod
->col_var
= isl_alloc_array(tab1
->mat
->ctx
, int,
475 tab1
->n_col
+ tab2
->n_col
);
478 for (i
= 0; i
< tab1
->n_col
; ++i
) {
479 int pos
= i
< d1
? i
: i
+ d2
;
480 prod
->col_var
[pos
] = tab1
->col_var
[i
];
482 for (i
= 0; i
< tab2
->n_col
; ++i
) {
483 int pos
= i
< d2
? d1
+ i
: tab1
->n_col
+ i
;
484 int t
= tab2
->col_var
[i
];
489 prod
->col_var
[pos
] = t
;
491 prod
->row_var
= isl_alloc_array(tab1
->mat
->ctx
, int,
492 tab1
->mat
->n_row
+ tab2
->mat
->n_row
);
495 for (i
= 0; i
< tab1
->n_row
; ++i
) {
496 int pos
= i
< r1
? i
: i
+ r2
;
497 prod
->row_var
[pos
] = tab1
->row_var
[i
];
499 for (i
= 0; i
< tab2
->n_row
; ++i
) {
500 int pos
= i
< r2
? r1
+ i
: tab1
->n_row
+ i
;
501 int t
= tab2
->row_var
[i
];
506 prod
->row_var
[pos
] = t
;
508 prod
->samples
= NULL
;
509 prod
->sample_index
= NULL
;
510 prod
->n_row
= tab1
->n_row
+ tab2
->n_row
;
511 prod
->n_con
= tab1
->n_con
+ tab2
->n_con
;
513 prod
->max_con
= tab1
->max_con
+ tab2
->max_con
;
514 prod
->n_col
= tab1
->n_col
+ tab2
->n_col
;
515 prod
->n_var
= tab1
->n_var
+ tab2
->n_var
;
516 prod
->max_var
= tab1
->max_var
+ tab2
->max_var
;
519 prod
->n_dead
= tab1
->n_dead
+ tab2
->n_dead
;
520 prod
->n_redundant
= tab1
->n_redundant
+ tab2
->n_redundant
;
521 prod
->rational
= tab1
->rational
;
522 prod
->empty
= tab1
->empty
|| tab2
->empty
;
523 prod
->strict_redundant
= tab1
->strict_redundant
|| tab2
->strict_redundant
;
527 prod
->cone
= tab1
->cone
;
528 prod
->bottom
.type
= isl_tab_undo_bottom
;
529 prod
->bottom
.next
= NULL
;
530 prod
->top
= &prod
->bottom
;
533 prod
->n_unbounded
= 0;
542 static struct isl_tab_var
*var_from_index(struct isl_tab
*tab
, int i
)
547 return &tab
->con
[~i
];
550 struct isl_tab_var
*isl_tab_var_from_row(struct isl_tab
*tab
, int i
)
552 return var_from_index(tab
, tab
->row_var
[i
]);
555 static struct isl_tab_var
*var_from_col(struct isl_tab
*tab
, int i
)
557 return var_from_index(tab
, tab
->col_var
[i
]);
560 /* Check if there are any upper bounds on column variable "var",
561 * i.e., non-negative rows where var appears with a negative coefficient.
562 * Return 1 if there are no such bounds.
564 static int max_is_manifestly_unbounded(struct isl_tab
*tab
,
565 struct isl_tab_var
*var
)
568 unsigned off
= 2 + tab
->M
;
572 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
573 if (!isl_int_is_neg(tab
->mat
->row
[i
][off
+ var
->index
]))
575 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
581 /* Check if there are any lower bounds on column variable "var",
582 * i.e., non-negative rows where var appears with a positive coefficient.
583 * Return 1 if there are no such bounds.
585 static int min_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_pos(tab
->mat
->row
[i
][off
+ var
->index
]))
596 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
602 static int row_cmp(struct isl_tab
*tab
, int r1
, int r2
, int c
, isl_int t
)
604 unsigned off
= 2 + tab
->M
;
608 isl_int_mul(t
, tab
->mat
->row
[r1
][2], tab
->mat
->row
[r2
][off
+c
]);
609 isl_int_submul(t
, tab
->mat
->row
[r2
][2], tab
->mat
->row
[r1
][off
+c
]);
614 isl_int_mul(t
, tab
->mat
->row
[r1
][1], tab
->mat
->row
[r2
][off
+ c
]);
615 isl_int_submul(t
, tab
->mat
->row
[r2
][1], tab
->mat
->row
[r1
][off
+ c
]);
616 return isl_int_sgn(t
);
619 /* Given the index of a column "c", return the index of a row
620 * that can be used to pivot the column in, with either an increase
621 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
622 * If "var" is not NULL, then the row returned will be different from
623 * the one associated with "var".
625 * Each row in the tableau is of the form
627 * x_r = a_r0 + \sum_i a_ri x_i
629 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
630 * impose any limit on the increase or decrease in the value of x_c
631 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
632 * for the row with the smallest (most stringent) such bound.
633 * Note that the common denominator of each row drops out of the fraction.
634 * To check if row j has a smaller bound than row r, i.e.,
635 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
636 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
637 * where -sign(a_jc) is equal to "sgn".
639 static int pivot_row(struct isl_tab
*tab
,
640 struct isl_tab_var
*var
, int sgn
, int c
)
644 unsigned off
= 2 + tab
->M
;
648 for (j
= tab
->n_redundant
; j
< tab
->n_row
; ++j
) {
649 if (var
&& j
== var
->index
)
651 if (!isl_tab_var_from_row(tab
, j
)->is_nonneg
)
653 if (sgn
* isl_int_sgn(tab
->mat
->row
[j
][off
+ c
]) >= 0)
659 tsgn
= sgn
* row_cmp(tab
, r
, j
, c
, t
);
660 if (tsgn
< 0 || (tsgn
== 0 &&
661 tab
->row_var
[j
] < tab
->row_var
[r
]))
668 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
669 * (sgn < 0) the value of row variable var.
670 * If not NULL, then skip_var is a row variable that should be ignored
671 * while looking for a pivot row. It is usually equal to var.
673 * As the given row in the tableau is of the form
675 * x_r = a_r0 + \sum_i a_ri x_i
677 * we need to find a column such that the sign of a_ri is equal to "sgn"
678 * (such that an increase in x_i will have the desired effect) or a
679 * column with a variable that may attain negative values.
680 * If a_ri is positive, then we need to move x_i in the same direction
681 * to obtain the desired effect. Otherwise, x_i has to move in the
682 * opposite direction.
684 static void find_pivot(struct isl_tab
*tab
,
685 struct isl_tab_var
*var
, struct isl_tab_var
*skip_var
,
686 int sgn
, int *row
, int *col
)
693 isl_assert(tab
->mat
->ctx
, var
->is_row
, return);
694 tr
= tab
->mat
->row
[var
->index
] + 2 + tab
->M
;
697 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
698 if (isl_int_is_zero(tr
[j
]))
700 if (isl_int_sgn(tr
[j
]) != sgn
&&
701 var_from_col(tab
, j
)->is_nonneg
)
703 if (c
< 0 || tab
->col_var
[j
] < tab
->col_var
[c
])
709 sgn
*= isl_int_sgn(tr
[c
]);
710 r
= pivot_row(tab
, skip_var
, sgn
, c
);
711 *row
= r
< 0 ? var
->index
: r
;
715 /* Return 1 if row "row" represents an obviously redundant inequality.
717 * - it represents an inequality or a variable
718 * - that is the sum of a non-negative sample value and a positive
719 * combination of zero or more non-negative constraints.
721 int isl_tab_row_is_redundant(struct isl_tab
*tab
, int row
)
724 unsigned off
= 2 + tab
->M
;
726 if (tab
->row_var
[row
] < 0 && !isl_tab_var_from_row(tab
, row
)->is_nonneg
)
729 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
731 if (tab
->strict_redundant
&& isl_int_is_zero(tab
->mat
->row
[row
][1]))
733 if (tab
->M
&& isl_int_is_neg(tab
->mat
->row
[row
][2]))
736 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
737 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ i
]))
739 if (tab
->col_var
[i
] >= 0)
741 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ i
]))
743 if (!var_from_col(tab
, i
)->is_nonneg
)
749 static void swap_rows(struct isl_tab
*tab
, int row1
, int row2
)
752 enum isl_tab_row_sign s
;
754 t
= tab
->row_var
[row1
];
755 tab
->row_var
[row1
] = tab
->row_var
[row2
];
756 tab
->row_var
[row2
] = t
;
757 isl_tab_var_from_row(tab
, row1
)->index
= row1
;
758 isl_tab_var_from_row(tab
, row2
)->index
= row2
;
759 tab
->mat
= isl_mat_swap_rows(tab
->mat
, row1
, row2
);
763 s
= tab
->row_sign
[row1
];
764 tab
->row_sign
[row1
] = tab
->row_sign
[row2
];
765 tab
->row_sign
[row2
] = s
;
768 static int push_union(struct isl_tab
*tab
,
769 enum isl_tab_undo_type type
, union isl_tab_undo_val u
) WARN_UNUSED
;
770 static int push_union(struct isl_tab
*tab
,
771 enum isl_tab_undo_type type
, union isl_tab_undo_val u
)
773 struct isl_tab_undo
*undo
;
778 undo
= isl_alloc_type(tab
->mat
->ctx
, struct isl_tab_undo
);
783 undo
->next
= tab
->top
;
789 int isl_tab_push_var(struct isl_tab
*tab
,
790 enum isl_tab_undo_type type
, struct isl_tab_var
*var
)
792 union isl_tab_undo_val u
;
794 u
.var_index
= tab
->row_var
[var
->index
];
796 u
.var_index
= tab
->col_var
[var
->index
];
797 return push_union(tab
, type
, u
);
800 int isl_tab_push(struct isl_tab
*tab
, enum isl_tab_undo_type type
)
802 union isl_tab_undo_val u
= { 0 };
803 return push_union(tab
, type
, u
);
806 /* Push a record on the undo stack describing the current basic
807 * variables, so that the this state can be restored during rollback.
809 int isl_tab_push_basis(struct isl_tab
*tab
)
812 union isl_tab_undo_val u
;
814 u
.col_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
817 for (i
= 0; i
< tab
->n_col
; ++i
)
818 u
.col_var
[i
] = tab
->col_var
[i
];
819 return push_union(tab
, isl_tab_undo_saved_basis
, u
);
822 int isl_tab_push_callback(struct isl_tab
*tab
, struct isl_tab_callback
*callback
)
824 union isl_tab_undo_val u
;
825 u
.callback
= callback
;
826 return push_union(tab
, isl_tab_undo_callback
, u
);
829 struct isl_tab
*isl_tab_init_samples(struct isl_tab
*tab
)
836 tab
->samples
= isl_mat_alloc(tab
->mat
->ctx
, 1, 1 + tab
->n_var
);
839 tab
->sample_index
= isl_alloc_array(tab
->mat
->ctx
, int, 1);
840 if (!tab
->sample_index
)
848 struct isl_tab
*isl_tab_add_sample(struct isl_tab
*tab
,
849 __isl_take isl_vec
*sample
)
854 if (tab
->n_sample
+ 1 > tab
->samples
->n_row
) {
855 int *t
= isl_realloc_array(tab
->mat
->ctx
,
856 tab
->sample_index
, int, tab
->n_sample
+ 1);
859 tab
->sample_index
= t
;
862 tab
->samples
= isl_mat_extend(tab
->samples
,
863 tab
->n_sample
+ 1, tab
->samples
->n_col
);
867 isl_seq_cpy(tab
->samples
->row
[tab
->n_sample
], sample
->el
, sample
->size
);
868 isl_vec_free(sample
);
869 tab
->sample_index
[tab
->n_sample
] = tab
->n_sample
;
874 isl_vec_free(sample
);
879 struct isl_tab
*isl_tab_drop_sample(struct isl_tab
*tab
, int s
)
881 if (s
!= tab
->n_outside
) {
882 int t
= tab
->sample_index
[tab
->n_outside
];
883 tab
->sample_index
[tab
->n_outside
] = tab
->sample_index
[s
];
884 tab
->sample_index
[s
] = t
;
885 isl_mat_swap_rows(tab
->samples
, tab
->n_outside
, s
);
888 if (isl_tab_push(tab
, isl_tab_undo_drop_sample
) < 0) {
896 /* Record the current number of samples so that we can remove newer
897 * samples during a rollback.
899 int isl_tab_save_samples(struct isl_tab
*tab
)
901 union isl_tab_undo_val u
;
907 return push_union(tab
, isl_tab_undo_saved_samples
, u
);
910 /* Mark row with index "row" as being redundant.
911 * If we may need to undo the operation or if the row represents
912 * a variable of the original problem, the row is kept,
913 * but no longer considered when looking for a pivot row.
914 * Otherwise, the row is simply removed.
916 * The row may be interchanged with some other row. If it
917 * is interchanged with a later row, return 1. Otherwise return 0.
918 * If the rows are checked in order in the calling function,
919 * then a return value of 1 means that the row with the given
920 * row number may now contain a different row that hasn't been checked yet.
922 int isl_tab_mark_redundant(struct isl_tab
*tab
, int row
)
924 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, row
);
925 var
->is_redundant
= 1;
926 isl_assert(tab
->mat
->ctx
, row
>= tab
->n_redundant
, return -1);
927 if (tab
->need_undo
|| tab
->row_var
[row
] >= 0) {
928 if (tab
->row_var
[row
] >= 0 && !var
->is_nonneg
) {
930 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, var
) < 0)
933 if (row
!= tab
->n_redundant
)
934 swap_rows(tab
, row
, tab
->n_redundant
);
936 return isl_tab_push_var(tab
, isl_tab_undo_redundant
, var
);
938 if (row
!= tab
->n_row
- 1)
939 swap_rows(tab
, row
, tab
->n_row
- 1);
940 isl_tab_var_from_row(tab
, tab
->n_row
- 1)->index
= -1;
946 int isl_tab_mark_empty(struct isl_tab
*tab
)
950 if (!tab
->empty
&& tab
->need_undo
)
951 if (isl_tab_push(tab
, isl_tab_undo_empty
) < 0)
957 int isl_tab_freeze_constraint(struct isl_tab
*tab
, int con
)
959 struct isl_tab_var
*var
;
964 var
= &tab
->con
[con
];
972 return isl_tab_push_var(tab
, isl_tab_undo_freeze
, var
);
977 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
978 * the original sign of the pivot element.
979 * We only keep track of row signs during PILP solving and in this case
980 * we only pivot a row with negative sign (meaning the value is always
981 * non-positive) using a positive pivot element.
983 * For each row j, the new value of the parametric constant is equal to
985 * a_j0 - a_jc a_r0/a_rc
987 * where a_j0 is the original parametric constant, a_rc is the pivot element,
988 * a_r0 is the parametric constant of the pivot row and a_jc is the
989 * pivot column entry of the row j.
990 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
991 * remains the same if a_jc has the same sign as the row j or if
992 * a_jc is zero. In all other cases, we reset the sign to "unknown".
994 static void update_row_sign(struct isl_tab
*tab
, int row
, int col
, int row_sgn
)
997 struct isl_mat
*mat
= tab
->mat
;
998 unsigned off
= 2 + tab
->M
;
1003 if (tab
->row_sign
[row
] == 0)
1005 isl_assert(mat
->ctx
, row_sgn
> 0, return);
1006 isl_assert(mat
->ctx
, tab
->row_sign
[row
] == isl_tab_row_neg
, return);
1007 tab
->row_sign
[row
] = isl_tab_row_pos
;
1008 for (i
= 0; i
< tab
->n_row
; ++i
) {
1012 s
= isl_int_sgn(mat
->row
[i
][off
+ col
]);
1015 if (!tab
->row_sign
[i
])
1017 if (s
< 0 && tab
->row_sign
[i
] == isl_tab_row_neg
)
1019 if (s
> 0 && tab
->row_sign
[i
] == isl_tab_row_pos
)
1021 tab
->row_sign
[i
] = isl_tab_row_unknown
;
1025 /* Given a row number "row" and a column number "col", pivot the tableau
1026 * such that the associated variables are interchanged.
1027 * The given row in the tableau expresses
1029 * x_r = a_r0 + \sum_i a_ri x_i
1033 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
1035 * Substituting this equality into the other rows
1037 * x_j = a_j0 + \sum_i a_ji x_i
1039 * with a_jc \ne 0, we obtain
1041 * 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
1048 * where i is any other column and j is any other row,
1049 * is therefore transformed into
1051 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1052 * 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)
1054 * The transformation is performed along the following steps
1056 * d_r/n_rc n_ri/n_rc
1059 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1062 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1063 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
1065 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1066 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
1068 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1069 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
1071 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1072 * 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)
1075 int isl_tab_pivot(struct isl_tab
*tab
, int row
, int col
)
1080 struct isl_mat
*mat
= tab
->mat
;
1081 struct isl_tab_var
*var
;
1082 unsigned off
= 2 + tab
->M
;
1084 isl_int_swap(mat
->row
[row
][0], mat
->row
[row
][off
+ col
]);
1085 sgn
= isl_int_sgn(mat
->row
[row
][0]);
1087 isl_int_neg(mat
->row
[row
][0], mat
->row
[row
][0]);
1088 isl_int_neg(mat
->row
[row
][off
+ col
], mat
->row
[row
][off
+ col
]);
1090 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1091 if (j
== off
- 1 + col
)
1093 isl_int_neg(mat
->row
[row
][1 + j
], mat
->row
[row
][1 + j
]);
1095 if (!isl_int_is_one(mat
->row
[row
][0]))
1096 isl_seq_normalize(mat
->ctx
, mat
->row
[row
], off
+ tab
->n_col
);
1097 for (i
= 0; i
< tab
->n_row
; ++i
) {
1100 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1102 isl_int_mul(mat
->row
[i
][0], mat
->row
[i
][0], mat
->row
[row
][0]);
1103 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1104 if (j
== off
- 1 + col
)
1106 isl_int_mul(mat
->row
[i
][1 + j
],
1107 mat
->row
[i
][1 + j
], mat
->row
[row
][0]);
1108 isl_int_addmul(mat
->row
[i
][1 + j
],
1109 mat
->row
[i
][off
+ col
], mat
->row
[row
][1 + j
]);
1111 isl_int_mul(mat
->row
[i
][off
+ col
],
1112 mat
->row
[i
][off
+ col
], mat
->row
[row
][off
+ col
]);
1113 if (!isl_int_is_one(mat
->row
[i
][0]))
1114 isl_seq_normalize(mat
->ctx
, mat
->row
[i
], off
+ tab
->n_col
);
1116 t
= tab
->row_var
[row
];
1117 tab
->row_var
[row
] = tab
->col_var
[col
];
1118 tab
->col_var
[col
] = t
;
1119 var
= isl_tab_var_from_row(tab
, row
);
1122 var
= var_from_col(tab
, col
);
1125 update_row_sign(tab
, row
, col
, sgn
);
1128 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1129 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1131 if (!isl_tab_var_from_row(tab
, i
)->frozen
&&
1132 isl_tab_row_is_redundant(tab
, i
)) {
1133 int redo
= isl_tab_mark_redundant(tab
, i
);
1143 /* If "var" represents a column variable, then pivot is up (sgn > 0)
1144 * or down (sgn < 0) to a row. The variable is assumed not to be
1145 * unbounded in the specified direction.
1146 * If sgn = 0, then the variable is unbounded in both directions,
1147 * and we pivot with any row we can find.
1149 static int to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
) WARN_UNUSED
;
1150 static int to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
)
1153 unsigned off
= 2 + tab
->M
;
1159 for (r
= tab
->n_redundant
; r
< tab
->n_row
; ++r
)
1160 if (!isl_int_is_zero(tab
->mat
->row
[r
][off
+var
->index
]))
1162 isl_assert(tab
->mat
->ctx
, r
< tab
->n_row
, return -1);
1164 r
= pivot_row(tab
, NULL
, sign
, var
->index
);
1165 isl_assert(tab
->mat
->ctx
, r
>= 0, return -1);
1168 return isl_tab_pivot(tab
, r
, var
->index
);
1171 static void check_table(struct isl_tab
*tab
)
1177 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1178 struct isl_tab_var
*var
;
1179 var
= isl_tab_var_from_row(tab
, i
);
1180 if (!var
->is_nonneg
)
1183 isl_assert(tab
->mat
->ctx
,
1184 !isl_int_is_neg(tab
->mat
->row
[i
][2]), abort());
1185 if (isl_int_is_pos(tab
->mat
->row
[i
][2]))
1188 isl_assert(tab
->mat
->ctx
, !isl_int_is_neg(tab
->mat
->row
[i
][1]),
1193 /* Return the sign of the maximal value of "var".
1194 * If the sign is not negative, then on return from this function,
1195 * the sample value will also be non-negative.
1197 * If "var" is manifestly unbounded wrt positive values, we are done.
1198 * Otherwise, we pivot the variable up to a row if needed
1199 * Then we continue pivoting down until either
1200 * - no more down pivots can be performed
1201 * - the sample value is positive
1202 * - the variable is pivoted into a manifestly unbounded column
1204 static int sign_of_max(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1208 if (max_is_manifestly_unbounded(tab
, var
))
1210 if (to_row(tab
, var
, 1) < 0)
1212 while (!isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1213 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1215 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1216 if (isl_tab_pivot(tab
, row
, col
) < 0)
1218 if (!var
->is_row
) /* manifestly unbounded */
1224 int isl_tab_sign_of_max(struct isl_tab
*tab
, int con
)
1226 struct isl_tab_var
*var
;
1231 var
= &tab
->con
[con
];
1232 isl_assert(tab
->mat
->ctx
, !var
->is_redundant
, return -2);
1233 isl_assert(tab
->mat
->ctx
, !var
->is_zero
, return -2);
1235 return sign_of_max(tab
, var
);
1238 static int row_is_neg(struct isl_tab
*tab
, int row
)
1241 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1242 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1244 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1246 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1249 static int row_sgn(struct isl_tab
*tab
, int row
)
1252 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1253 if (!isl_int_is_zero(tab
->mat
->row
[row
][2]))
1254 return isl_int_sgn(tab
->mat
->row
[row
][2]);
1256 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1259 /* Perform pivots until the row variable "var" has a non-negative
1260 * sample value or until no more upward pivots can be performed.
1261 * Return the sign of the sample value after the pivots have been
1264 static int restore_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1268 while (row_is_neg(tab
, var
->index
)) {
1269 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1272 if (isl_tab_pivot(tab
, row
, col
) < 0)
1274 if (!var
->is_row
) /* manifestly unbounded */
1277 return row_sgn(tab
, var
->index
);
1280 /* Perform pivots until we are sure that the row variable "var"
1281 * can attain non-negative values. After return from this
1282 * function, "var" is still a row variable, but its sample
1283 * value may not be non-negative, even if the function returns 1.
1285 static int at_least_zero(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1289 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1290 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1293 if (row
== var
->index
) /* manifestly unbounded */
1295 if (isl_tab_pivot(tab
, row
, col
) < 0)
1298 return !isl_int_is_neg(tab
->mat
->row
[var
->index
][1]);
1301 /* Return a negative value if "var" can attain negative values.
1302 * Return a non-negative value otherwise.
1304 * If "var" is manifestly unbounded wrt negative values, we are done.
1305 * Otherwise, if var is in a column, we can pivot it down to a row.
1306 * Then we continue pivoting down until either
1307 * - the pivot would result in a manifestly unbounded column
1308 * => we don't perform the pivot, but simply return -1
1309 * - no more down pivots can be performed
1310 * - the sample value is negative
1311 * If the sample value becomes negative and the variable is supposed
1312 * to be nonnegative, then we undo the last pivot.
1313 * However, if the last pivot has made the pivoting variable
1314 * obviously redundant, then it may have moved to another row.
1315 * In that case we look for upward pivots until we reach a non-negative
1318 static int sign_of_min(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1321 struct isl_tab_var
*pivot_var
= NULL
;
1323 if (min_is_manifestly_unbounded(tab
, var
))
1327 row
= pivot_row(tab
, NULL
, -1, col
);
1328 pivot_var
= var_from_col(tab
, col
);
1329 if (isl_tab_pivot(tab
, row
, col
) < 0)
1331 if (var
->is_redundant
)
1333 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1334 if (var
->is_nonneg
) {
1335 if (!pivot_var
->is_redundant
&&
1336 pivot_var
->index
== row
) {
1337 if (isl_tab_pivot(tab
, row
, col
) < 0)
1340 if (restore_row(tab
, var
) < -1)
1346 if (var
->is_redundant
)
1348 while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1349 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1350 if (row
== var
->index
)
1353 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1354 pivot_var
= var_from_col(tab
, col
);
1355 if (isl_tab_pivot(tab
, row
, col
) < 0)
1357 if (var
->is_redundant
)
1360 if (pivot_var
&& var
->is_nonneg
) {
1361 /* pivot back to non-negative value */
1362 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
) {
1363 if (isl_tab_pivot(tab
, row
, col
) < 0)
1366 if (restore_row(tab
, var
) < -1)
1372 static int row_at_most_neg_one(struct isl_tab
*tab
, int row
)
1375 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1377 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1380 return isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
1381 isl_int_abs_ge(tab
->mat
->row
[row
][1],
1382 tab
->mat
->row
[row
][0]);
1385 /* Return 1 if "var" can attain values <= -1.
1386 * Return 0 otherwise.
1388 * The sample value of "var" is assumed to be non-negative when the
1389 * the function is called. If 1 is returned then the constraint
1390 * is not redundant and the sample value is made non-negative again before
1391 * the function returns.
1393 int isl_tab_min_at_most_neg_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1396 struct isl_tab_var
*pivot_var
;
1398 if (min_is_manifestly_unbounded(tab
, var
))
1402 row
= pivot_row(tab
, NULL
, -1, col
);
1403 pivot_var
= var_from_col(tab
, col
);
1404 if (isl_tab_pivot(tab
, row
, col
) < 0)
1406 if (var
->is_redundant
)
1408 if (row_at_most_neg_one(tab
, var
->index
)) {
1409 if (var
->is_nonneg
) {
1410 if (!pivot_var
->is_redundant
&&
1411 pivot_var
->index
== row
) {
1412 if (isl_tab_pivot(tab
, row
, col
) < 0)
1415 if (restore_row(tab
, var
) < -1)
1421 if (var
->is_redundant
)
1424 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1425 if (row
== var
->index
) {
1426 if (restore_row(tab
, var
) < -1)
1432 pivot_var
= var_from_col(tab
, col
);
1433 if (isl_tab_pivot(tab
, row
, col
) < 0)
1435 if (var
->is_redundant
)
1437 } while (!row_at_most_neg_one(tab
, var
->index
));
1438 if (var
->is_nonneg
) {
1439 /* pivot back to non-negative value */
1440 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
1441 if (isl_tab_pivot(tab
, row
, col
) < 0)
1443 if (restore_row(tab
, var
) < -1)
1449 /* Return 1 if "var" can attain values >= 1.
1450 * Return 0 otherwise.
1452 static int at_least_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1457 if (max_is_manifestly_unbounded(tab
, var
))
1459 if (to_row(tab
, var
, 1) < 0)
1461 r
= tab
->mat
->row
[var
->index
];
1462 while (isl_int_lt(r
[1], r
[0])) {
1463 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1465 return isl_int_ge(r
[1], r
[0]);
1466 if (row
== var
->index
) /* manifestly unbounded */
1468 if (isl_tab_pivot(tab
, row
, col
) < 0)
1474 static void swap_cols(struct isl_tab
*tab
, int col1
, int col2
)
1477 unsigned off
= 2 + tab
->M
;
1478 t
= tab
->col_var
[col1
];
1479 tab
->col_var
[col1
] = tab
->col_var
[col2
];
1480 tab
->col_var
[col2
] = t
;
1481 var_from_col(tab
, col1
)->index
= col1
;
1482 var_from_col(tab
, col2
)->index
= col2
;
1483 tab
->mat
= isl_mat_swap_cols(tab
->mat
, off
+ col1
, off
+ col2
);
1486 /* Mark column with index "col" as representing a zero variable.
1487 * If we may need to undo the operation the column is kept,
1488 * but no longer considered.
1489 * Otherwise, the column is simply removed.
1491 * The column may be interchanged with some other column. If it
1492 * is interchanged with a later column, return 1. Otherwise return 0.
1493 * If the columns are checked in order in the calling function,
1494 * then a return value of 1 means that the column with the given
1495 * column number may now contain a different column that
1496 * hasn't been checked yet.
1498 int isl_tab_kill_col(struct isl_tab
*tab
, int col
)
1500 var_from_col(tab
, col
)->is_zero
= 1;
1501 if (tab
->need_undo
) {
1502 if (isl_tab_push_var(tab
, isl_tab_undo_zero
,
1503 var_from_col(tab
, col
)) < 0)
1505 if (col
!= tab
->n_dead
)
1506 swap_cols(tab
, col
, tab
->n_dead
);
1510 if (col
!= tab
->n_col
- 1)
1511 swap_cols(tab
, col
, tab
->n_col
- 1);
1512 var_from_col(tab
, tab
->n_col
- 1)->index
= -1;
1518 /* Row variable "var" is non-negative and cannot attain any values
1519 * larger than zero. This means that the coefficients of the unrestricted
1520 * column variables are zero and that the coefficients of the non-negative
1521 * column variables are zero or negative.
1522 * Each of the non-negative variables with a negative coefficient can
1523 * then also be written as the negative sum of non-negative variables
1524 * and must therefore also be zero.
1526 static int close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
1527 static int close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1530 struct isl_mat
*mat
= tab
->mat
;
1531 unsigned off
= 2 + tab
->M
;
1533 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return -1);
1536 if (isl_tab_push_var(tab
, isl_tab_undo_zero
, var
) < 0)
1538 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1540 if (isl_int_is_zero(mat
->row
[var
->index
][off
+ j
]))
1542 isl_assert(tab
->mat
->ctx
,
1543 isl_int_is_neg(mat
->row
[var
->index
][off
+ j
]), return -1);
1544 recheck
= isl_tab_kill_col(tab
, j
);
1550 if (isl_tab_mark_redundant(tab
, var
->index
) < 0)
1555 /* Add a constraint to the tableau and allocate a row for it.
1556 * Return the index into the constraint array "con".
1558 int isl_tab_allocate_con(struct isl_tab
*tab
)
1562 isl_assert(tab
->mat
->ctx
, tab
->n_row
< tab
->mat
->n_row
, return -1);
1563 isl_assert(tab
->mat
->ctx
, tab
->n_con
< tab
->max_con
, return -1);
1566 tab
->con
[r
].index
= tab
->n_row
;
1567 tab
->con
[r
].is_row
= 1;
1568 tab
->con
[r
].is_nonneg
= 0;
1569 tab
->con
[r
].is_zero
= 0;
1570 tab
->con
[r
].is_redundant
= 0;
1571 tab
->con
[r
].frozen
= 0;
1572 tab
->con
[r
].negated
= 0;
1573 tab
->row_var
[tab
->n_row
] = ~r
;
1577 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]) < 0)
1583 /* Add a variable to the tableau and allocate a column for it.
1584 * Return the index into the variable array "var".
1586 int isl_tab_allocate_var(struct isl_tab
*tab
)
1590 unsigned off
= 2 + tab
->M
;
1592 isl_assert(tab
->mat
->ctx
, tab
->n_col
< tab
->mat
->n_col
, return -1);
1593 isl_assert(tab
->mat
->ctx
, tab
->n_var
< tab
->max_var
, return -1);
1596 tab
->var
[r
].index
= tab
->n_col
;
1597 tab
->var
[r
].is_row
= 0;
1598 tab
->var
[r
].is_nonneg
= 0;
1599 tab
->var
[r
].is_zero
= 0;
1600 tab
->var
[r
].is_redundant
= 0;
1601 tab
->var
[r
].frozen
= 0;
1602 tab
->var
[r
].negated
= 0;
1603 tab
->col_var
[tab
->n_col
] = r
;
1605 for (i
= 0; i
< tab
->n_row
; ++i
)
1606 isl_int_set_si(tab
->mat
->row
[i
][off
+ tab
->n_col
], 0);
1610 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->var
[r
]) < 0)
1616 /* Add a row to the tableau. The row is given as an affine combination
1617 * of the original variables and needs to be expressed in terms of the
1620 * We add each term in turn.
1621 * If r = n/d_r is the current sum and we need to add k x, then
1622 * if x is a column variable, we increase the numerator of
1623 * this column by k d_r
1624 * if x = f/d_x is a row variable, then the new representation of r is
1626 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1627 * --- + --- = ------------------- = -------------------
1628 * d_r d_r d_r d_x/g m
1630 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1632 int isl_tab_add_row(struct isl_tab
*tab
, isl_int
*line
)
1638 unsigned off
= 2 + tab
->M
;
1640 r
= isl_tab_allocate_con(tab
);
1646 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1647 isl_int_set_si(row
[0], 1);
1648 isl_int_set(row
[1], line
[0]);
1649 isl_seq_clr(row
+ 2, tab
->M
+ tab
->n_col
);
1650 for (i
= 0; i
< tab
->n_var
; ++i
) {
1651 if (tab
->var
[i
].is_zero
)
1653 if (tab
->var
[i
].is_row
) {
1655 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1656 isl_int_swap(a
, row
[0]);
1657 isl_int_divexact(a
, row
[0], a
);
1659 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1660 isl_int_mul(b
, b
, line
[1 + i
]);
1661 isl_seq_combine(row
+ 1, a
, row
+ 1,
1662 b
, tab
->mat
->row
[tab
->var
[i
].index
] + 1,
1663 1 + tab
->M
+ tab
->n_col
);
1665 isl_int_addmul(row
[off
+ tab
->var
[i
].index
],
1666 line
[1 + i
], row
[0]);
1667 if (tab
->M
&& i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
1668 isl_int_submul(row
[2], line
[1 + i
], row
[0]);
1670 isl_seq_normalize(tab
->mat
->ctx
, row
, off
+ tab
->n_col
);
1675 tab
->row_sign
[tab
->con
[r
].index
] = isl_tab_row_unknown
;
1680 static int drop_row(struct isl_tab
*tab
, int row
)
1682 isl_assert(tab
->mat
->ctx
, ~tab
->row_var
[row
] == tab
->n_con
- 1, return -1);
1683 if (row
!= tab
->n_row
- 1)
1684 swap_rows(tab
, row
, tab
->n_row
- 1);
1690 static int drop_col(struct isl_tab
*tab
, int col
)
1692 isl_assert(tab
->mat
->ctx
, tab
->col_var
[col
] == tab
->n_var
- 1, return -1);
1693 if (col
!= tab
->n_col
- 1)
1694 swap_cols(tab
, col
, tab
->n_col
- 1);
1700 /* Add inequality "ineq" and check if it conflicts with the
1701 * previously added constraints or if it is obviously redundant.
1703 int isl_tab_add_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1712 struct isl_basic_map
*bmap
= tab
->bmap
;
1714 isl_assert(tab
->mat
->ctx
, tab
->n_eq
== bmap
->n_eq
, return -1);
1715 isl_assert(tab
->mat
->ctx
,
1716 tab
->n_con
== bmap
->n_eq
+ bmap
->n_ineq
, return -1);
1717 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, ineq
);
1718 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1725 isl_int_swap(ineq
[0], cst
);
1727 r
= isl_tab_add_row(tab
, ineq
);
1729 isl_int_swap(ineq
[0], cst
);
1734 tab
->con
[r
].is_nonneg
= 1;
1735 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1737 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1738 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1743 sgn
= restore_row(tab
, &tab
->con
[r
]);
1747 return isl_tab_mark_empty(tab
);
1748 if (tab
->con
[r
].is_row
&& isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1749 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1754 /* Pivot a non-negative variable down until it reaches the value zero
1755 * and then pivot the variable into a column position.
1757 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
1758 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1762 unsigned off
= 2 + tab
->M
;
1767 while (isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1768 find_pivot(tab
, var
, NULL
, -1, &row
, &col
);
1769 isl_assert(tab
->mat
->ctx
, row
!= -1, return -1);
1770 if (isl_tab_pivot(tab
, row
, col
) < 0)
1776 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
)
1777 if (!isl_int_is_zero(tab
->mat
->row
[var
->index
][off
+ i
]))
1780 isl_assert(tab
->mat
->ctx
, i
< tab
->n_col
, return -1);
1781 if (isl_tab_pivot(tab
, var
->index
, i
) < 0)
1787 /* We assume Gaussian elimination has been performed on the equalities.
1788 * The equalities can therefore never conflict.
1789 * Adding the equalities is currently only really useful for a later call
1790 * to isl_tab_ineq_type.
1792 static struct isl_tab
*add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1799 r
= isl_tab_add_row(tab
, eq
);
1803 r
= tab
->con
[r
].index
;
1804 i
= isl_seq_first_non_zero(tab
->mat
->row
[r
] + 2 + tab
->M
+ tab
->n_dead
,
1805 tab
->n_col
- tab
->n_dead
);
1806 isl_assert(tab
->mat
->ctx
, i
>= 0, goto error
);
1808 if (isl_tab_pivot(tab
, r
, i
) < 0)
1810 if (isl_tab_kill_col(tab
, i
) < 0)
1820 static int row_is_manifestly_zero(struct isl_tab
*tab
, int row
)
1822 unsigned off
= 2 + tab
->M
;
1824 if (!isl_int_is_zero(tab
->mat
->row
[row
][1]))
1826 if (tab
->M
&& !isl_int_is_zero(tab
->mat
->row
[row
][2]))
1828 return isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1829 tab
->n_col
- tab
->n_dead
) == -1;
1832 /* Add an equality that is known to be valid for the given tableau.
1834 int isl_tab_add_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1836 struct isl_tab_var
*var
;
1841 r
= isl_tab_add_row(tab
, eq
);
1847 if (row_is_manifestly_zero(tab
, r
)) {
1849 if (isl_tab_mark_redundant(tab
, r
) < 0)
1854 if (isl_int_is_neg(tab
->mat
->row
[r
][1])) {
1855 isl_seq_neg(tab
->mat
->row
[r
] + 1, tab
->mat
->row
[r
] + 1,
1860 if (to_col(tab
, var
) < 0)
1863 if (isl_tab_kill_col(tab
, var
->index
) < 0)
1869 static int add_zero_row(struct isl_tab
*tab
)
1874 r
= isl_tab_allocate_con(tab
);
1878 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1879 isl_seq_clr(row
+ 1, 1 + tab
->M
+ tab
->n_col
);
1880 isl_int_set_si(row
[0], 1);
1885 /* Add equality "eq" and check if it conflicts with the
1886 * previously added constraints or if it is obviously redundant.
1888 int isl_tab_add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1890 struct isl_tab_undo
*snap
= NULL
;
1891 struct isl_tab_var
*var
;
1899 isl_assert(tab
->mat
->ctx
, !tab
->M
, return -1);
1902 snap
= isl_tab_snap(tab
);
1906 isl_int_swap(eq
[0], cst
);
1908 r
= isl_tab_add_row(tab
, eq
);
1910 isl_int_swap(eq
[0], cst
);
1918 if (row_is_manifestly_zero(tab
, row
)) {
1920 if (isl_tab_rollback(tab
, snap
) < 0)
1928 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1929 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1931 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1932 tab
->bmap
= isl_basic_map_add_ineq(tab
->bmap
, eq
);
1933 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1934 if (isl_tab_push(tab
, isl_tab_undo_bmap_ineq
) < 0)
1938 if (add_zero_row(tab
) < 0)
1942 sgn
= isl_int_sgn(tab
->mat
->row
[row
][1]);
1945 isl_seq_neg(tab
->mat
->row
[row
] + 1, tab
->mat
->row
[row
] + 1,
1952 sgn
= sign_of_max(tab
, var
);
1956 if (isl_tab_mark_empty(tab
) < 0)
1963 if (to_col(tab
, var
) < 0)
1966 if (isl_tab_kill_col(tab
, var
->index
) < 0)
1972 /* Construct and return an inequality that expresses an upper bound
1974 * In particular, if the div is given by
1978 * then the inequality expresses
1982 static struct isl_vec
*ineq_for_div(struct isl_basic_map
*bmap
, unsigned div
)
1986 struct isl_vec
*ineq
;
1991 total
= isl_basic_map_total_dim(bmap
);
1992 div_pos
= 1 + total
- bmap
->n_div
+ div
;
1994 ineq
= isl_vec_alloc(bmap
->ctx
, 1 + total
);
1998 isl_seq_cpy(ineq
->el
, bmap
->div
[div
] + 1, 1 + total
);
1999 isl_int_neg(ineq
->el
[div_pos
], bmap
->div
[div
][0]);
2003 /* For a div d = floor(f/m), add the constraints
2006 * -(f-(m-1)) + m d >= 0
2008 * Note that the second constraint is the negation of
2012 * If add_ineq is not NULL, then this function is used
2013 * instead of isl_tab_add_ineq to effectively add the inequalities.
2015 static int add_div_constraints(struct isl_tab
*tab
, unsigned div
,
2016 int (*add_ineq
)(void *user
, isl_int
*), void *user
)
2020 struct isl_vec
*ineq
;
2022 total
= isl_basic_map_total_dim(tab
->bmap
);
2023 div_pos
= 1 + total
- tab
->bmap
->n_div
+ div
;
2025 ineq
= ineq_for_div(tab
->bmap
, div
);
2030 if (add_ineq(user
, ineq
->el
) < 0)
2033 if (isl_tab_add_ineq(tab
, ineq
->el
) < 0)
2037 isl_seq_neg(ineq
->el
, tab
->bmap
->div
[div
] + 1, 1 + total
);
2038 isl_int_set(ineq
->el
[div_pos
], tab
->bmap
->div
[div
][0]);
2039 isl_int_add(ineq
->el
[0], ineq
->el
[0], ineq
->el
[div_pos
]);
2040 isl_int_sub_ui(ineq
->el
[0], ineq
->el
[0], 1);
2043 if (add_ineq(user
, ineq
->el
) < 0)
2046 if (isl_tab_add_ineq(tab
, ineq
->el
) < 0)
2058 /* Add an extra div, prescrived by "div" to the tableau and
2059 * the associated bmap (which is assumed to be non-NULL).
2061 * If add_ineq is not NULL, then this function is used instead
2062 * of isl_tab_add_ineq to add the div constraints.
2063 * This complication is needed because the code in isl_tab_pip
2064 * wants to perform some extra processing when an inequality
2065 * is added to the tableau.
2067 int isl_tab_add_div(struct isl_tab
*tab
, __isl_keep isl_vec
*div
,
2068 int (*add_ineq
)(void *user
, isl_int
*), void *user
)
2078 isl_assert(tab
->mat
->ctx
, tab
->bmap
, return -1);
2080 for (i
= 0; i
< tab
->n_var
; ++i
) {
2081 if (isl_int_is_neg(div
->el
[2 + i
]))
2083 if (isl_int_is_zero(div
->el
[2 + i
]))
2085 if (!tab
->var
[i
].is_nonneg
)
2088 nonneg
= i
== tab
->n_var
&& !isl_int_is_neg(div
->el
[1]);
2090 if (isl_tab_extend_cons(tab
, 3) < 0)
2092 if (isl_tab_extend_vars(tab
, 1) < 0)
2094 r
= isl_tab_allocate_var(tab
);
2099 tab
->var
[r
].is_nonneg
= 1;
2101 tab
->bmap
= isl_basic_map_extend_dim(tab
->bmap
,
2102 isl_basic_map_get_dim(tab
->bmap
), 1, 0, 2);
2103 k
= isl_basic_map_alloc_div(tab
->bmap
);
2106 isl_seq_cpy(tab
->bmap
->div
[k
], div
->el
, div
->size
);
2107 if (isl_tab_push(tab
, isl_tab_undo_bmap_div
) < 0)
2110 if (add_div_constraints(tab
, k
, add_ineq
, user
) < 0)
2116 struct isl_tab
*isl_tab_from_basic_map(struct isl_basic_map
*bmap
)
2119 struct isl_tab
*tab
;
2123 tab
= isl_tab_alloc(bmap
->ctx
,
2124 isl_basic_map_total_dim(bmap
) + bmap
->n_ineq
+ 1,
2125 isl_basic_map_total_dim(bmap
), 0);
2128 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
2129 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
2130 if (isl_tab_mark_empty(tab
) < 0)
2134 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
2135 tab
= add_eq(tab
, bmap
->eq
[i
]);
2139 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
2140 if (isl_tab_add_ineq(tab
, bmap
->ineq
[i
]) < 0)
2151 struct isl_tab
*isl_tab_from_basic_set(struct isl_basic_set
*bset
)
2153 return isl_tab_from_basic_map((struct isl_basic_map
*)bset
);
2156 /* Construct a tableau corresponding to the recession cone of "bset".
2158 struct isl_tab
*isl_tab_from_recession_cone(__isl_keep isl_basic_set
*bset
,
2163 struct isl_tab
*tab
;
2164 unsigned offset
= 0;
2169 offset
= isl_basic_set_dim(bset
, isl_dim_param
);
2170 tab
= isl_tab_alloc(bset
->ctx
, bset
->n_eq
+ bset
->n_ineq
,
2171 isl_basic_set_total_dim(bset
) - offset
, 0);
2174 tab
->rational
= ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
);
2178 for (i
= 0; i
< bset
->n_eq
; ++i
) {
2179 isl_int_swap(bset
->eq
[i
][offset
], cst
);
2181 if (isl_tab_add_eq(tab
, bset
->eq
[i
] + offset
) < 0)
2184 tab
= add_eq(tab
, bset
->eq
[i
]);
2185 isl_int_swap(bset
->eq
[i
][offset
], cst
);
2189 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
2191 isl_int_swap(bset
->ineq
[i
][offset
], cst
);
2192 r
= isl_tab_add_row(tab
, bset
->ineq
[i
] + offset
);
2193 isl_int_swap(bset
->ineq
[i
][offset
], cst
);
2196 tab
->con
[r
].is_nonneg
= 1;
2197 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2209 /* Assuming "tab" is the tableau of a cone, check if the cone is
2210 * bounded, i.e., if it is empty or only contains the origin.
2212 int isl_tab_cone_is_bounded(struct isl_tab
*tab
)
2220 if (tab
->n_dead
== tab
->n_col
)
2224 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2225 struct isl_tab_var
*var
;
2227 var
= isl_tab_var_from_row(tab
, i
);
2228 if (!var
->is_nonneg
)
2230 sgn
= sign_of_max(tab
, var
);
2235 if (close_row(tab
, var
) < 0)
2239 if (tab
->n_dead
== tab
->n_col
)
2241 if (i
== tab
->n_row
)
2246 int isl_tab_sample_is_integer(struct isl_tab
*tab
)
2253 for (i
= 0; i
< tab
->n_var
; ++i
) {
2255 if (!tab
->var
[i
].is_row
)
2257 row
= tab
->var
[i
].index
;
2258 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
2259 tab
->mat
->row
[row
][0]))
2265 static struct isl_vec
*extract_integer_sample(struct isl_tab
*tab
)
2268 struct isl_vec
*vec
;
2270 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2274 isl_int_set_si(vec
->block
.data
[0], 1);
2275 for (i
= 0; i
< tab
->n_var
; ++i
) {
2276 if (!tab
->var
[i
].is_row
)
2277 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
2279 int row
= tab
->var
[i
].index
;
2280 isl_int_divexact(vec
->block
.data
[1 + i
],
2281 tab
->mat
->row
[row
][1], tab
->mat
->row
[row
][0]);
2288 struct isl_vec
*isl_tab_get_sample_value(struct isl_tab
*tab
)
2291 struct isl_vec
*vec
;
2297 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2303 isl_int_set_si(vec
->block
.data
[0], 1);
2304 for (i
= 0; i
< tab
->n_var
; ++i
) {
2306 if (!tab
->var
[i
].is_row
) {
2307 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
2310 row
= tab
->var
[i
].index
;
2311 isl_int_gcd(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
2312 isl_int_divexact(m
, tab
->mat
->row
[row
][0], m
);
2313 isl_seq_scale(vec
->block
.data
, vec
->block
.data
, m
, 1 + i
);
2314 isl_int_divexact(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
2315 isl_int_mul(vec
->block
.data
[1 + i
], m
, tab
->mat
->row
[row
][1]);
2317 vec
= isl_vec_normalize(vec
);
2323 /* Update "bmap" based on the results of the tableau "tab".
2324 * In particular, implicit equalities are made explicit, redundant constraints
2325 * are removed and if the sample value happens to be integer, it is stored
2326 * in "bmap" (unless "bmap" already had an integer sample).
2328 * The tableau is assumed to have been created from "bmap" using
2329 * isl_tab_from_basic_map.
2331 struct isl_basic_map
*isl_basic_map_update_from_tab(struct isl_basic_map
*bmap
,
2332 struct isl_tab
*tab
)
2344 bmap
= isl_basic_map_set_to_empty(bmap
);
2346 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
2347 if (isl_tab_is_equality(tab
, n_eq
+ i
))
2348 isl_basic_map_inequality_to_equality(bmap
, i
);
2349 else if (isl_tab_is_redundant(tab
, n_eq
+ i
))
2350 isl_basic_map_drop_inequality(bmap
, i
);
2352 if (bmap
->n_eq
!= n_eq
)
2353 isl_basic_map_gauss(bmap
, NULL
);
2354 if (!tab
->rational
&&
2355 !bmap
->sample
&& isl_tab_sample_is_integer(tab
))
2356 bmap
->sample
= extract_integer_sample(tab
);
2360 struct isl_basic_set
*isl_basic_set_update_from_tab(struct isl_basic_set
*bset
,
2361 struct isl_tab
*tab
)
2363 return (struct isl_basic_set
*)isl_basic_map_update_from_tab(
2364 (struct isl_basic_map
*)bset
, tab
);
2367 /* Given a non-negative variable "var", add a new non-negative variable
2368 * that is the opposite of "var", ensuring that var can only attain the
2370 * If var = n/d is a row variable, then the new variable = -n/d.
2371 * If var is a column variables, then the new variable = -var.
2372 * If the new variable cannot attain non-negative values, then
2373 * the resulting tableau is empty.
2374 * Otherwise, we know the value will be zero and we close the row.
2376 static int cut_to_hyperplane(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2381 unsigned off
= 2 + tab
->M
;
2385 isl_assert(tab
->mat
->ctx
, !var
->is_redundant
, return -1);
2386 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return -1);
2388 if (isl_tab_extend_cons(tab
, 1) < 0)
2392 tab
->con
[r
].index
= tab
->n_row
;
2393 tab
->con
[r
].is_row
= 1;
2394 tab
->con
[r
].is_nonneg
= 0;
2395 tab
->con
[r
].is_zero
= 0;
2396 tab
->con
[r
].is_redundant
= 0;
2397 tab
->con
[r
].frozen
= 0;
2398 tab
->con
[r
].negated
= 0;
2399 tab
->row_var
[tab
->n_row
] = ~r
;
2400 row
= tab
->mat
->row
[tab
->n_row
];
2403 isl_int_set(row
[0], tab
->mat
->row
[var
->index
][0]);
2404 isl_seq_neg(row
+ 1,
2405 tab
->mat
->row
[var
->index
] + 1, 1 + tab
->n_col
);
2407 isl_int_set_si(row
[0], 1);
2408 isl_seq_clr(row
+ 1, 1 + tab
->n_col
);
2409 isl_int_set_si(row
[off
+ var
->index
], -1);
2414 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]) < 0)
2417 sgn
= sign_of_max(tab
, &tab
->con
[r
]);
2421 if (isl_tab_mark_empty(tab
) < 0)
2425 tab
->con
[r
].is_nonneg
= 1;
2426 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2429 if (close_row(tab
, &tab
->con
[r
]) < 0)
2435 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2436 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2437 * by r' = r + 1 >= 0.
2438 * If r is a row variable, we simply increase the constant term by one
2439 * (taking into account the denominator).
2440 * If r is a column variable, then we need to modify each row that
2441 * refers to r = r' - 1 by substituting this equality, effectively
2442 * subtracting the coefficient of the column from the constant.
2443 * We should only do this if the minimum is manifestly unbounded,
2444 * however. Otherwise, we may end up with negative sample values
2445 * for non-negative variables.
2446 * So, if r is a column variable with a minimum that is not
2447 * manifestly unbounded, then we need to move it to a row.
2448 * However, the sample value of this row may be negative,
2449 * even after the relaxation, so we need to restore it.
2450 * We therefore prefer to pivot a column up to a row, if possible.
2452 struct isl_tab
*isl_tab_relax(struct isl_tab
*tab
, int con
)
2454 struct isl_tab_var
*var
;
2455 unsigned off
= 2 + tab
->M
;
2460 var
= &tab
->con
[con
];
2462 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
2463 if (to_row(tab
, var
, 1) < 0)
2465 if (!var
->is_row
&& !min_is_manifestly_unbounded(tab
, var
))
2466 if (to_row(tab
, var
, -1) < 0)
2470 isl_int_add(tab
->mat
->row
[var
->index
][1],
2471 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
2472 if (restore_row(tab
, var
) < 0)
2477 for (i
= 0; i
< tab
->n_row
; ++i
) {
2478 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2480 isl_int_sub(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
2481 tab
->mat
->row
[i
][off
+ var
->index
]);
2486 if (isl_tab_push_var(tab
, isl_tab_undo_relax
, var
) < 0)
2495 int isl_tab_select_facet(struct isl_tab
*tab
, int con
)
2500 return cut_to_hyperplane(tab
, &tab
->con
[con
]);
2503 static int may_be_equality(struct isl_tab
*tab
, int row
)
2505 unsigned off
= 2 + tab
->M
;
2506 return tab
->rational
? isl_int_is_zero(tab
->mat
->row
[row
][1])
2507 : isl_int_lt(tab
->mat
->row
[row
][1],
2508 tab
->mat
->row
[row
][0]);
2511 /* Check for (near) equalities among the constraints.
2512 * A constraint is an equality if it is non-negative and if
2513 * its maximal value is either
2514 * - zero (in case of rational tableaus), or
2515 * - strictly less than 1 (in case of integer tableaus)
2517 * We first mark all non-redundant and non-dead variables that
2518 * are not frozen and not obviously not an equality.
2519 * Then we iterate over all marked variables if they can attain
2520 * any values larger than zero or at least one.
2521 * If the maximal value is zero, we mark any column variables
2522 * that appear in the row as being zero and mark the row as being redundant.
2523 * Otherwise, if the maximal value is strictly less than one (and the
2524 * tableau is integer), then we restrict the value to being zero
2525 * by adding an opposite non-negative variable.
2527 int isl_tab_detect_implicit_equalities(struct isl_tab
*tab
)
2536 if (tab
->n_dead
== tab
->n_col
)
2540 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2541 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2542 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2543 may_be_equality(tab
, i
);
2547 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2548 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2549 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2554 struct isl_tab_var
*var
;
2556 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2557 var
= isl_tab_var_from_row(tab
, i
);
2561 if (i
== tab
->n_row
) {
2562 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2563 var
= var_from_col(tab
, i
);
2567 if (i
== tab
->n_col
)
2572 sgn
= sign_of_max(tab
, var
);
2576 if (close_row(tab
, var
) < 0)
2578 } else if (!tab
->rational
&& !at_least_one(tab
, var
)) {
2579 if (cut_to_hyperplane(tab
, var
) < 0)
2581 return isl_tab_detect_implicit_equalities(tab
);
2583 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2584 var
= isl_tab_var_from_row(tab
, i
);
2587 if (may_be_equality(tab
, i
))
2597 static int con_is_redundant(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2601 if (tab
->rational
) {
2602 int sgn
= sign_of_min(tab
, var
);
2607 int irred
= isl_tab_min_at_most_neg_one(tab
, var
);
2614 /* Check for (near) redundant constraints.
2615 * A constraint is redundant if it is non-negative and if
2616 * its minimal value (temporarily ignoring the non-negativity) is either
2617 * - zero (in case of rational tableaus), or
2618 * - strictly larger than -1 (in case of integer tableaus)
2620 * We first mark all non-redundant and non-dead variables that
2621 * are not frozen and not obviously negatively unbounded.
2622 * Then we iterate over all marked variables if they can attain
2623 * any values smaller than zero or at most negative one.
2624 * If not, we mark the row as being redundant (assuming it hasn't
2625 * been detected as being obviously redundant in the mean time).
2627 int isl_tab_detect_redundant(struct isl_tab
*tab
)
2636 if (tab
->n_redundant
== tab
->n_row
)
2640 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2641 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2642 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2646 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2647 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2648 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2649 !min_is_manifestly_unbounded(tab
, var
);
2654 struct isl_tab_var
*var
;
2656 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2657 var
= isl_tab_var_from_row(tab
, i
);
2661 if (i
== tab
->n_row
) {
2662 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2663 var
= var_from_col(tab
, i
);
2667 if (i
== tab
->n_col
)
2672 red
= con_is_redundant(tab
, var
);
2675 if (red
&& !var
->is_redundant
)
2676 if (isl_tab_mark_redundant(tab
, var
->index
) < 0)
2678 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2679 var
= var_from_col(tab
, i
);
2682 if (!min_is_manifestly_unbounded(tab
, var
))
2692 int isl_tab_is_equality(struct isl_tab
*tab
, int con
)
2699 if (tab
->con
[con
].is_zero
)
2701 if (tab
->con
[con
].is_redundant
)
2703 if (!tab
->con
[con
].is_row
)
2704 return tab
->con
[con
].index
< tab
->n_dead
;
2706 row
= tab
->con
[con
].index
;
2709 return isl_int_is_zero(tab
->mat
->row
[row
][1]) &&
2710 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
2711 tab
->n_col
- tab
->n_dead
) == -1;
2714 /* Return the minimial value of the affine expression "f" with denominator
2715 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
2716 * the expression cannot attain arbitrarily small values.
2717 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
2718 * The return value reflects the nature of the result (empty, unbounded,
2719 * minmimal value returned in *opt).
2721 enum isl_lp_result
isl_tab_min(struct isl_tab
*tab
,
2722 isl_int
*f
, isl_int denom
, isl_int
*opt
, isl_int
*opt_denom
,
2726 enum isl_lp_result res
= isl_lp_ok
;
2727 struct isl_tab_var
*var
;
2728 struct isl_tab_undo
*snap
;
2731 return isl_lp_error
;
2734 return isl_lp_empty
;
2736 snap
= isl_tab_snap(tab
);
2737 r
= isl_tab_add_row(tab
, f
);
2739 return isl_lp_error
;
2741 isl_int_mul(tab
->mat
->row
[var
->index
][0],
2742 tab
->mat
->row
[var
->index
][0], denom
);
2745 find_pivot(tab
, var
, var
, -1, &row
, &col
);
2746 if (row
== var
->index
) {
2747 res
= isl_lp_unbounded
;
2752 if (isl_tab_pivot(tab
, row
, col
) < 0)
2753 return isl_lp_error
;
2755 if (ISL_FL_ISSET(flags
, ISL_TAB_SAVE_DUAL
)) {
2758 isl_vec_free(tab
->dual
);
2759 tab
->dual
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_con
);
2761 return isl_lp_error
;
2762 isl_int_set(tab
->dual
->el
[0], tab
->mat
->row
[var
->index
][0]);
2763 for (i
= 0; i
< tab
->n_con
; ++i
) {
2765 if (tab
->con
[i
].is_row
) {
2766 isl_int_set_si(tab
->dual
->el
[1 + i
], 0);
2769 pos
= 2 + tab
->M
+ tab
->con
[i
].index
;
2770 if (tab
->con
[i
].negated
)
2771 isl_int_neg(tab
->dual
->el
[1 + i
],
2772 tab
->mat
->row
[var
->index
][pos
]);
2774 isl_int_set(tab
->dual
->el
[1 + i
],
2775 tab
->mat
->row
[var
->index
][pos
]);
2778 if (opt
&& res
== isl_lp_ok
) {
2780 isl_int_set(*opt
, tab
->mat
->row
[var
->index
][1]);
2781 isl_int_set(*opt_denom
, tab
->mat
->row
[var
->index
][0]);
2783 isl_int_cdiv_q(*opt
, tab
->mat
->row
[var
->index
][1],
2784 tab
->mat
->row
[var
->index
][0]);
2786 if (isl_tab_rollback(tab
, snap
) < 0)
2787 return isl_lp_error
;
2791 int isl_tab_is_redundant(struct isl_tab
*tab
, int con
)
2795 if (tab
->con
[con
].is_zero
)
2797 if (tab
->con
[con
].is_redundant
)
2799 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
2802 /* Take a snapshot of the tableau that can be restored by s call to
2805 struct isl_tab_undo
*isl_tab_snap(struct isl_tab
*tab
)
2813 /* Undo the operation performed by isl_tab_relax.
2815 static int unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
2816 static int unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2818 unsigned off
= 2 + tab
->M
;
2820 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
2821 if (to_row(tab
, var
, 1) < 0)
2825 isl_int_sub(tab
->mat
->row
[var
->index
][1],
2826 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
2827 if (var
->is_nonneg
) {
2828 int sgn
= restore_row(tab
, var
);
2829 isl_assert(tab
->mat
->ctx
, sgn
>= 0, return -1);
2834 for (i
= 0; i
< tab
->n_row
; ++i
) {
2835 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2837 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
2838 tab
->mat
->row
[i
][off
+ var
->index
]);
2846 static int perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
) WARN_UNUSED
;
2847 static int perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2849 struct isl_tab_var
*var
= var_from_index(tab
, undo
->u
.var_index
);
2850 switch(undo
->type
) {
2851 case isl_tab_undo_nonneg
:
2854 case isl_tab_undo_redundant
:
2855 var
->is_redundant
= 0;
2857 restore_row(tab
, isl_tab_var_from_row(tab
, tab
->n_redundant
));
2859 case isl_tab_undo_freeze
:
2862 case isl_tab_undo_zero
:
2867 case isl_tab_undo_allocate
:
2868 if (undo
->u
.var_index
>= 0) {
2869 isl_assert(tab
->mat
->ctx
, !var
->is_row
, return -1);
2870 drop_col(tab
, var
->index
);
2874 if (!max_is_manifestly_unbounded(tab
, var
)) {
2875 if (to_row(tab
, var
, 1) < 0)
2877 } else if (!min_is_manifestly_unbounded(tab
, var
)) {
2878 if (to_row(tab
, var
, -1) < 0)
2881 if (to_row(tab
, var
, 0) < 0)
2884 drop_row(tab
, var
->index
);
2886 case isl_tab_undo_relax
:
2887 return unrelax(tab
, var
);
2893 /* Restore the tableau to the state where the basic variables
2894 * are those in "col_var".
2895 * We first construct a list of variables that are currently in
2896 * the basis, but shouldn't. Then we iterate over all variables
2897 * that should be in the basis and for each one that is currently
2898 * not in the basis, we exchange it with one of the elements of the
2899 * list constructed before.
2900 * We can always find an appropriate variable to pivot with because
2901 * the current basis is mapped to the old basis by a non-singular
2902 * matrix and so we can never end up with a zero row.
2904 static int restore_basis(struct isl_tab
*tab
, int *col_var
)
2908 int *extra
= NULL
; /* current columns that contain bad stuff */
2909 unsigned off
= 2 + tab
->M
;
2911 extra
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
2914 for (i
= 0; i
< tab
->n_col
; ++i
) {
2915 for (j
= 0; j
< tab
->n_col
; ++j
)
2916 if (tab
->col_var
[i
] == col_var
[j
])
2920 extra
[n_extra
++] = i
;
2922 for (i
= 0; i
< tab
->n_col
&& n_extra
> 0; ++i
) {
2923 struct isl_tab_var
*var
;
2926 for (j
= 0; j
< tab
->n_col
; ++j
)
2927 if (col_var
[i
] == tab
->col_var
[j
])
2931 var
= var_from_index(tab
, col_var
[i
]);
2933 for (j
= 0; j
< n_extra
; ++j
)
2934 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+extra
[j
]]))
2936 isl_assert(tab
->mat
->ctx
, j
< n_extra
, goto error
);
2937 if (isl_tab_pivot(tab
, row
, extra
[j
]) < 0)
2939 extra
[j
] = extra
[--n_extra
];
2951 /* Remove all samples with index n or greater, i.e., those samples
2952 * that were added since we saved this number of samples in
2953 * isl_tab_save_samples.
2955 static void drop_samples_since(struct isl_tab
*tab
, int n
)
2959 for (i
= tab
->n_sample
- 1; i
>= 0 && tab
->n_sample
> n
; --i
) {
2960 if (tab
->sample_index
[i
] < n
)
2963 if (i
!= tab
->n_sample
- 1) {
2964 int t
= tab
->sample_index
[tab
->n_sample
-1];
2965 tab
->sample_index
[tab
->n_sample
-1] = tab
->sample_index
[i
];
2966 tab
->sample_index
[i
] = t
;
2967 isl_mat_swap_rows(tab
->samples
, tab
->n_sample
-1, i
);
2973 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
) WARN_UNUSED
;
2974 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2976 switch (undo
->type
) {
2977 case isl_tab_undo_empty
:
2980 case isl_tab_undo_nonneg
:
2981 case isl_tab_undo_redundant
:
2982 case isl_tab_undo_freeze
:
2983 case isl_tab_undo_zero
:
2984 case isl_tab_undo_allocate
:
2985 case isl_tab_undo_relax
:
2986 return perform_undo_var(tab
, undo
);
2987 case isl_tab_undo_bmap_eq
:
2988 return isl_basic_map_free_equality(tab
->bmap
, 1);
2989 case isl_tab_undo_bmap_ineq
:
2990 return isl_basic_map_free_inequality(tab
->bmap
, 1);
2991 case isl_tab_undo_bmap_div
:
2992 if (isl_basic_map_free_div(tab
->bmap
, 1) < 0)
2995 tab
->samples
->n_col
--;
2997 case isl_tab_undo_saved_basis
:
2998 if (restore_basis(tab
, undo
->u
.col_var
) < 0)
3001 case isl_tab_undo_drop_sample
:
3004 case isl_tab_undo_saved_samples
:
3005 drop_samples_since(tab
, undo
->u
.n
);
3007 case isl_tab_undo_callback
:
3008 return undo
->u
.callback
->run(undo
->u
.callback
);
3010 isl_assert(tab
->mat
->ctx
, 0, return -1);
3015 /* Return the tableau to the state it was in when the snapshot "snap"
3018 int isl_tab_rollback(struct isl_tab
*tab
, struct isl_tab_undo
*snap
)
3020 struct isl_tab_undo
*undo
, *next
;
3026 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
3030 if (perform_undo(tab
, undo
) < 0) {
3044 /* The given row "row" represents an inequality violated by all
3045 * points in the tableau. Check for some special cases of such
3046 * separating constraints.
3047 * In particular, if the row has been reduced to the constant -1,
3048 * then we know the inequality is adjacent (but opposite) to
3049 * an equality in the tableau.
3050 * If the row has been reduced to r = -1 -r', with r' an inequality
3051 * of the tableau, then the inequality is adjacent (but opposite)
3052 * to the inequality r'.
3054 static enum isl_ineq_type
separation_type(struct isl_tab
*tab
, unsigned row
)
3057 unsigned off
= 2 + tab
->M
;
3060 return isl_ineq_separate
;
3062 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
3063 return isl_ineq_separate
;
3064 if (!isl_int_is_negone(tab
->mat
->row
[row
][1]))
3065 return isl_ineq_separate
;
3067 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
3068 tab
->n_col
- tab
->n_dead
);
3070 return isl_ineq_adj_eq
;
3072 if (!isl_int_is_negone(tab
->mat
->row
[row
][off
+ tab
->n_dead
+ pos
]))
3073 return isl_ineq_separate
;
3075 pos
= isl_seq_first_non_zero(
3076 tab
->mat
->row
[row
] + off
+ tab
->n_dead
+ pos
+ 1,
3077 tab
->n_col
- tab
->n_dead
- pos
- 1);
3079 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
3082 /* Check the effect of inequality "ineq" on the tableau "tab".
3084 * isl_ineq_redundant: satisfied by all points in the tableau
3085 * isl_ineq_separate: satisfied by no point in the tableau
3086 * isl_ineq_cut: satisfied by some by not all points
3087 * isl_ineq_adj_eq: adjacent to an equality
3088 * isl_ineq_adj_ineq: adjacent to an inequality.
3090 enum isl_ineq_type
isl_tab_ineq_type(struct isl_tab
*tab
, isl_int
*ineq
)
3092 enum isl_ineq_type type
= isl_ineq_error
;
3093 struct isl_tab_undo
*snap
= NULL
;
3098 return isl_ineq_error
;
3100 if (isl_tab_extend_cons(tab
, 1) < 0)
3101 return isl_ineq_error
;
3103 snap
= isl_tab_snap(tab
);
3105 con
= isl_tab_add_row(tab
, ineq
);
3109 row
= tab
->con
[con
].index
;
3110 if (isl_tab_row_is_redundant(tab
, row
))
3111 type
= isl_ineq_redundant
;
3112 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
3114 isl_int_abs_ge(tab
->mat
->row
[row
][1],
3115 tab
->mat
->row
[row
][0]))) {
3116 int nonneg
= at_least_zero(tab
, &tab
->con
[con
]);
3120 type
= isl_ineq_cut
;
3122 type
= separation_type(tab
, row
);
3124 int red
= con_is_redundant(tab
, &tab
->con
[con
]);
3128 type
= isl_ineq_cut
;
3130 type
= isl_ineq_redundant
;
3133 if (isl_tab_rollback(tab
, snap
))
3134 return isl_ineq_error
;
3137 return isl_ineq_error
;
3140 int isl_tab_track_bmap(struct isl_tab
*tab
, __isl_take isl_basic_map
*bmap
)
3145 isl_assert(tab
->mat
->ctx
, tab
->n_eq
== bmap
->n_eq
, return -1);
3146 isl_assert(tab
->mat
->ctx
,
3147 tab
->n_con
== bmap
->n_eq
+ bmap
->n_ineq
, return -1);
3153 isl_basic_map_free(bmap
);
3157 int isl_tab_track_bset(struct isl_tab
*tab
, __isl_take isl_basic_set
*bset
)
3159 return isl_tab_track_bmap(tab
, (isl_basic_map
*)bset
);
3162 __isl_keep isl_basic_set
*isl_tab_peek_bset(struct isl_tab
*tab
)
3167 return (isl_basic_set
*)tab
->bmap
;
3170 void isl_tab_dump(struct isl_tab
*tab
, FILE *out
, int indent
)
3176 fprintf(out
, "%*snull tab\n", indent
, "");
3179 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
3180 tab
->n_redundant
, tab
->n_dead
);
3182 fprintf(out
, ", rational");
3184 fprintf(out
, ", empty");
3186 fprintf(out
, "%*s[", indent
, "");
3187 for (i
= 0; i
< tab
->n_var
; ++i
) {
3189 fprintf(out
, (i
== tab
->n_param
||
3190 i
== tab
->n_var
- tab
->n_div
) ? "; "
3192 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
3194 tab
->var
[i
].is_zero
? " [=0]" :
3195 tab
->var
[i
].is_redundant
? " [R]" : "");
3197 fprintf(out
, "]\n");
3198 fprintf(out
, "%*s[", indent
, "");
3199 for (i
= 0; i
< tab
->n_con
; ++i
) {
3202 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
3204 tab
->con
[i
].is_zero
? " [=0]" :
3205 tab
->con
[i
].is_redundant
? " [R]" : "");
3207 fprintf(out
, "]\n");
3208 fprintf(out
, "%*s[", indent
, "");
3209 for (i
= 0; i
< tab
->n_row
; ++i
) {
3210 const char *sign
= "";
3213 if (tab
->row_sign
) {
3214 if (tab
->row_sign
[i
] == isl_tab_row_unknown
)
3216 else if (tab
->row_sign
[i
] == isl_tab_row_neg
)
3218 else if (tab
->row_sign
[i
] == isl_tab_row_pos
)
3223 fprintf(out
, "r%d: %d%s%s", i
, tab
->row_var
[i
],
3224 isl_tab_var_from_row(tab
, i
)->is_nonneg
? " [>=0]" : "", sign
);
3226 fprintf(out
, "]\n");
3227 fprintf(out
, "%*s[", indent
, "");
3228 for (i
= 0; i
< tab
->n_col
; ++i
) {
3231 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
3232 var_from_col(tab
, i
)->is_nonneg
? " [>=0]" : "");
3234 fprintf(out
, "]\n");
3235 r
= tab
->mat
->n_row
;
3236 tab
->mat
->n_row
= tab
->n_row
;
3237 c
= tab
->mat
->n_col
;
3238 tab
->mat
->n_col
= 2 + tab
->M
+ tab
->n_col
;
3239 isl_mat_dump(tab
->mat
, out
, indent
);
3240 tab
->mat
->n_row
= r
;
3241 tab
->mat
->n_col
= c
;
3243 isl_basic_map_dump(tab
->bmap
, out
, indent
);