2 #include "isl_map_private.h"
7 * The implementation of tableaus in this file was inspired by Section 8
8 * of David Detlefs, Greg Nelson and James B. Saxe, "Simplify: a theorem
9 * prover for program checking".
12 struct isl_tab
*isl_tab_alloc(struct isl_ctx
*ctx
,
13 unsigned n_row
, unsigned n_var
, unsigned M
)
19 tab
= isl_calloc_type(ctx
, struct isl_tab
);
22 tab
->mat
= isl_mat_alloc(ctx
, n_row
, off
+ n_var
);
25 tab
->var
= isl_alloc_array(ctx
, struct isl_tab_var
, n_var
);
28 tab
->con
= isl_alloc_array(ctx
, struct isl_tab_var
, n_row
);
31 tab
->col_var
= isl_alloc_array(ctx
, int, n_var
);
34 tab
->row_var
= isl_alloc_array(ctx
, int, n_row
);
37 for (i
= 0; i
< n_var
; ++i
) {
38 tab
->var
[i
].index
= i
;
39 tab
->var
[i
].is_row
= 0;
40 tab
->var
[i
].is_nonneg
= 0;
41 tab
->var
[i
].is_zero
= 0;
42 tab
->var
[i
].is_redundant
= 0;
43 tab
->var
[i
].frozen
= 0;
44 tab
->var
[i
].negated
= 0;
64 tab
->bottom
.type
= isl_tab_undo_bottom
;
65 tab
->bottom
.next
= NULL
;
66 tab
->top
= &tab
->bottom
;
78 int isl_tab_extend_cons(struct isl_tab
*tab
, unsigned n_new
)
80 unsigned off
= 2 + tab
->M
;
85 if (tab
->max_con
< tab
->n_con
+ n_new
) {
86 struct isl_tab_var
*con
;
88 con
= isl_realloc_array(tab
->mat
->ctx
, tab
->con
,
89 struct isl_tab_var
, tab
->max_con
+ n_new
);
93 tab
->max_con
+= n_new
;
95 if (tab
->mat
->n_row
< tab
->n_row
+ n_new
) {
98 tab
->mat
= isl_mat_extend(tab
->mat
,
99 tab
->n_row
+ n_new
, off
+ tab
->n_col
);
102 row_var
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_var
,
103 int, tab
->mat
->n_row
);
106 tab
->row_var
= row_var
;
108 enum isl_tab_row_sign
*s
;
109 s
= isl_realloc_array(tab
->mat
->ctx
, tab
->row_sign
,
110 enum isl_tab_row_sign
, tab
->mat
->n_row
);
119 /* Make room for at least n_new extra variables.
120 * Return -1 if anything went wrong.
122 int isl_tab_extend_vars(struct isl_tab
*tab
, unsigned n_new
)
124 struct isl_tab_var
*var
;
125 unsigned off
= 2 + tab
->M
;
127 if (tab
->max_var
< tab
->n_var
+ n_new
) {
128 var
= isl_realloc_array(tab
->mat
->ctx
, tab
->var
,
129 struct isl_tab_var
, tab
->n_var
+ n_new
);
133 tab
->max_var
+= n_new
;
136 if (tab
->mat
->n_col
< off
+ tab
->n_col
+ n_new
) {
139 tab
->mat
= isl_mat_extend(tab
->mat
,
140 tab
->mat
->n_row
, off
+ tab
->n_col
+ n_new
);
143 p
= isl_realloc_array(tab
->mat
->ctx
, tab
->col_var
,
144 int, tab
->n_col
+ n_new
);
153 struct isl_tab
*isl_tab_extend(struct isl_tab
*tab
, unsigned n_new
)
155 if (isl_tab_extend_cons(tab
, n_new
) >= 0)
162 static void free_undo(struct isl_tab
*tab
)
164 struct isl_tab_undo
*undo
, *next
;
166 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
173 void isl_tab_free(struct isl_tab
*tab
)
178 isl_mat_free(tab
->mat
);
179 isl_vec_free(tab
->dual
);
180 isl_basic_set_free(tab
->bset
);
186 isl_mat_free(tab
->samples
);
187 free(tab
->sample_index
);
188 isl_mat_free(tab
->basis
);
192 struct isl_tab
*isl_tab_dup(struct isl_tab
*tab
)
202 dup
= isl_calloc_type(tab
->ctx
, struct isl_tab
);
205 dup
->mat
= isl_mat_dup(tab
->mat
);
208 dup
->var
= isl_alloc_array(tab
->ctx
, struct isl_tab_var
, tab
->max_var
);
211 for (i
= 0; i
< tab
->n_var
; ++i
)
212 dup
->var
[i
] = tab
->var
[i
];
213 dup
->con
= isl_alloc_array(tab
->ctx
, struct isl_tab_var
, tab
->max_con
);
216 for (i
= 0; i
< tab
->n_con
; ++i
)
217 dup
->con
[i
] = tab
->con
[i
];
218 dup
->col_var
= isl_alloc_array(tab
->ctx
, int, tab
->mat
->n_col
- off
);
221 for (i
= 0; i
< tab
->n_col
; ++i
)
222 dup
->col_var
[i
] = tab
->col_var
[i
];
223 dup
->row_var
= isl_alloc_array(tab
->ctx
, int, tab
->mat
->n_row
);
226 for (i
= 0; i
< tab
->n_row
; ++i
)
227 dup
->row_var
[i
] = tab
->row_var
[i
];
229 dup
->row_sign
= isl_alloc_array(tab
->ctx
, enum isl_tab_row_sign
,
233 for (i
= 0; i
< tab
->n_row
; ++i
)
234 dup
->row_sign
[i
] = tab
->row_sign
[i
];
237 dup
->samples
= isl_mat_dup(tab
->samples
);
240 dup
->sample_index
= isl_alloc_array(tab
->mat
->ctx
, int,
241 tab
->samples
->n_row
);
242 if (!dup
->sample_index
)
244 dup
->n_sample
= tab
->n_sample
;
245 dup
->n_outside
= tab
->n_outside
;
247 dup
->n_row
= tab
->n_row
;
248 dup
->n_con
= tab
->n_con
;
249 dup
->n_eq
= tab
->n_eq
;
250 dup
->max_con
= tab
->max_con
;
251 dup
->n_col
= tab
->n_col
;
252 dup
->n_var
= tab
->n_var
;
253 dup
->max_var
= tab
->max_var
;
254 dup
->n_param
= tab
->n_param
;
255 dup
->n_div
= tab
->n_div
;
256 dup
->n_dead
= tab
->n_dead
;
257 dup
->n_redundant
= tab
->n_redundant
;
258 dup
->rational
= tab
->rational
;
259 dup
->empty
= tab
->empty
;
263 tab
->cone
= tab
->cone
;
264 dup
->bottom
.type
= isl_tab_undo_bottom
;
265 dup
->bottom
.next
= NULL
;
266 dup
->top
= &dup
->bottom
;
268 dup
->n_zero
= tab
->n_zero
;
269 dup
->n_unbounded
= tab
->n_unbounded
;
270 dup
->basis
= isl_mat_dup(tab
->basis
);
278 /* Construct the coefficient matrix of the product tableau
280 * mat{1,2} is the coefficient matrix of tableau {1,2}
281 * row{1,2} is the number of rows in tableau {1,2}
282 * col{1,2} is the number of columns in tableau {1,2}
283 * off is the offset to the coefficient column (skipping the
284 * denominator, the constant term and the big parameter if any)
285 * r{1,2} is the number of redundant rows in tableau {1,2}
286 * d{1,2} is the number of dead columns in tableau {1,2}
288 * The order of the rows and columns in the result is as explained
289 * in isl_tab_product.
291 static struct isl_mat
*tab_mat_product(struct isl_mat
*mat1
,
292 struct isl_mat
*mat2
, unsigned row1
, unsigned row2
,
293 unsigned col1
, unsigned col2
,
294 unsigned off
, unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
297 struct isl_mat
*prod
;
300 prod
= isl_mat_alloc(mat1
->ctx
, mat1
->n_row
+ mat2
->n_row
,
304 for (i
= 0; i
< r1
; ++i
) {
305 isl_seq_cpy(prod
->row
[n
+ i
], mat1
->row
[i
], off
+ d1
);
306 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
, d2
);
307 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
+ d2
,
308 mat1
->row
[i
] + off
+ d1
, col1
- d1
);
309 isl_seq_clr(prod
->row
[n
+ i
] + off
+ col1
+ d1
, col2
- d2
);
313 for (i
= 0; i
< r2
; ++i
) {
314 isl_seq_cpy(prod
->row
[n
+ i
], mat2
->row
[i
], off
);
315 isl_seq_clr(prod
->row
[n
+ i
] + off
, d1
);
316 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
,
317 mat2
->row
[i
] + off
, d2
);
318 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
+ d2
, col1
- d1
);
319 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ col1
+ d1
,
320 mat2
->row
[i
] + off
+ d2
, col2
- d2
);
324 for (i
= 0; i
< row1
- r1
; ++i
) {
325 isl_seq_cpy(prod
->row
[n
+ i
], mat1
->row
[r1
+ i
], off
+ d1
);
326 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
, d2
);
327 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
+ d2
,
328 mat1
->row
[r1
+ i
] + off
+ d1
, col1
- d1
);
329 isl_seq_clr(prod
->row
[n
+ i
] + off
+ col1
+ d1
, col2
- d2
);
333 for (i
= 0; i
< row2
- r2
; ++i
) {
334 isl_seq_cpy(prod
->row
[n
+ i
], mat2
->row
[r2
+ i
], off
);
335 isl_seq_clr(prod
->row
[n
+ i
] + off
, d1
);
336 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ d1
,
337 mat2
->row
[r2
+ i
] + off
, d2
);
338 isl_seq_clr(prod
->row
[n
+ i
] + off
+ d1
+ d2
, col1
- d1
);
339 isl_seq_cpy(prod
->row
[n
+ i
] + off
+ col1
+ d1
,
340 mat2
->row
[r2
+ i
] + off
+ d2
, col2
- d2
);
346 /* Update the row or column index of a variable that corresponds
347 * to a variable in the first input tableau.
349 static void update_index1(struct isl_tab_var
*var
,
350 unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
352 if (var
->index
== -1)
354 if (var
->is_row
&& var
->index
>= r1
)
356 if (!var
->is_row
&& var
->index
>= d1
)
360 /* Update the row or column index of a variable that corresponds
361 * to a variable in the second input tableau.
363 static void update_index2(struct isl_tab_var
*var
,
364 unsigned row1
, unsigned col1
,
365 unsigned r1
, unsigned r2
, unsigned d1
, unsigned d2
)
367 if (var
->index
== -1)
382 /* Create a tableau that represents the Cartesian product of the sets
383 * represented by tableaus tab1 and tab2.
384 * The order of the rows in the product is
385 * - redundant rows of tab1
386 * - redundant rows of tab2
387 * - non-redundant rows of tab1
388 * - non-redundant rows of tab2
389 * The order of the columns is
392 * - coefficient of big parameter, if any
393 * - dead columns of tab1
394 * - dead columns of tab2
395 * - live columns of tab1
396 * - live columns of tab2
397 * The order of the variables and the constraints is a concatenation
398 * of order in the two input tableaus.
400 struct isl_tab
*isl_tab_product(struct isl_tab
*tab1
, struct isl_tab
*tab2
)
403 struct isl_tab
*prod
;
405 unsigned r1
, r2
, d1
, d2
;
410 isl_assert(tab1
->mat
->ctx
, tab1
->M
== tab2
->M
, return NULL
);
411 isl_assert(tab1
->mat
->ctx
, tab1
->rational
== tab2
->rational
, return NULL
);
412 isl_assert(tab1
->mat
->ctx
, tab1
->cone
== tab2
->cone
, return NULL
);
413 isl_assert(tab1
->mat
->ctx
, !tab1
->row_sign
, return NULL
);
414 isl_assert(tab1
->mat
->ctx
, !tab2
->row_sign
, return NULL
);
415 isl_assert(tab1
->mat
->ctx
, tab1
->n_param
== 0, return NULL
);
416 isl_assert(tab1
->mat
->ctx
, tab2
->n_param
== 0, return NULL
);
417 isl_assert(tab1
->mat
->ctx
, tab1
->n_div
== 0, return NULL
);
418 isl_assert(tab1
->mat
->ctx
, tab2
->n_div
== 0, return NULL
);
421 r1
= tab1
->n_redundant
;
422 r2
= tab2
->n_redundant
;
425 prod
= isl_calloc_type(tab1
->mat
->ctx
, struct isl_tab
);
428 prod
->mat
= tab_mat_product(tab1
->mat
, tab2
->mat
,
429 tab1
->n_row
, tab2
->n_row
,
430 tab1
->n_col
, tab2
->n_col
, off
, r1
, r2
, d1
, d2
);
433 prod
->var
= isl_alloc_array(tab1
->mat
->ctx
, struct isl_tab_var
,
434 tab1
->max_var
+ tab2
->max_var
);
437 for (i
= 0; i
< tab1
->n_var
; ++i
) {
438 prod
->var
[i
] = tab1
->var
[i
];
439 update_index1(&prod
->var
[i
], r1
, r2
, d1
, d2
);
441 for (i
= 0; i
< tab2
->n_var
; ++i
) {
442 prod
->var
[tab1
->n_var
+ i
] = tab2
->var
[i
];
443 update_index2(&prod
->var
[tab1
->n_var
+ i
],
444 tab1
->n_row
, tab1
->n_col
,
447 prod
->con
= isl_alloc_array(tab1
->mat
->ctx
, struct isl_tab_var
,
448 tab1
->max_con
+ tab2
->max_con
);
451 for (i
= 0; i
< tab1
->n_con
; ++i
) {
452 prod
->con
[i
] = tab1
->con
[i
];
453 update_index1(&prod
->con
[i
], r1
, r2
, d1
, d2
);
455 for (i
= 0; i
< tab2
->n_con
; ++i
) {
456 prod
->con
[tab1
->n_con
+ i
] = tab2
->con
[i
];
457 update_index2(&prod
->con
[tab1
->n_con
+ i
],
458 tab1
->n_row
, tab1
->n_col
,
461 prod
->col_var
= isl_alloc_array(tab1
->mat
->ctx
, int,
462 tab1
->n_col
+ tab2
->n_col
);
465 for (i
= 0; i
< tab1
->n_col
; ++i
) {
466 int pos
= i
< d1
? i
: i
+ d2
;
467 prod
->col_var
[pos
] = tab1
->col_var
[i
];
469 for (i
= 0; i
< tab2
->n_col
; ++i
) {
470 int pos
= i
< d2
? d1
+ i
: tab1
->n_col
+ i
;
471 int t
= tab2
->col_var
[i
];
476 prod
->col_var
[pos
] = t
;
478 prod
->row_var
= isl_alloc_array(tab1
->mat
->ctx
, int,
479 tab1
->mat
->n_row
+ tab2
->mat
->n_row
);
482 for (i
= 0; i
< tab1
->n_row
; ++i
) {
483 int pos
= i
< r1
? i
: i
+ r2
;
484 prod
->row_var
[pos
] = tab1
->row_var
[i
];
486 for (i
= 0; i
< tab2
->n_row
; ++i
) {
487 int pos
= i
< r2
? r1
+ i
: tab1
->n_row
+ i
;
488 int t
= tab2
->row_var
[i
];
493 prod
->row_var
[pos
] = t
;
495 prod
->samples
= NULL
;
496 prod
->sample_index
= NULL
;
497 prod
->n_row
= tab1
->n_row
+ tab2
->n_row
;
498 prod
->n_con
= tab1
->n_con
+ tab2
->n_con
;
500 prod
->max_con
= tab1
->max_con
+ tab2
->max_con
;
501 prod
->n_col
= tab1
->n_col
+ tab2
->n_col
;
502 prod
->n_var
= tab1
->n_var
+ tab2
->n_var
;
503 prod
->max_var
= tab1
->max_var
+ tab2
->max_var
;
506 prod
->n_dead
= tab1
->n_dead
+ tab2
->n_dead
;
507 prod
->n_redundant
= tab1
->n_redundant
+ tab2
->n_redundant
;
508 prod
->rational
= tab1
->rational
;
509 prod
->empty
= tab1
->empty
|| tab2
->empty
;
513 prod
->cone
= tab1
->cone
;
514 prod
->bottom
.type
= isl_tab_undo_bottom
;
515 prod
->bottom
.next
= NULL
;
516 prod
->top
= &prod
->bottom
;
519 prod
->n_unbounded
= 0;
528 static struct isl_tab_var
*var_from_index(struct isl_tab
*tab
, int i
)
533 return &tab
->con
[~i
];
536 struct isl_tab_var
*isl_tab_var_from_row(struct isl_tab
*tab
, int i
)
538 return var_from_index(tab
, tab
->row_var
[i
]);
541 static struct isl_tab_var
*var_from_col(struct isl_tab
*tab
, int i
)
543 return var_from_index(tab
, tab
->col_var
[i
]);
546 /* Check if there are any upper bounds on column variable "var",
547 * i.e., non-negative rows where var appears with a negative coefficient.
548 * Return 1 if there are no such bounds.
550 static int max_is_manifestly_unbounded(struct isl_tab
*tab
,
551 struct isl_tab_var
*var
)
554 unsigned off
= 2 + tab
->M
;
558 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
559 if (!isl_int_is_neg(tab
->mat
->row
[i
][off
+ var
->index
]))
561 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
567 /* Check if there are any lower bounds on column variable "var",
568 * i.e., non-negative rows where var appears with a positive coefficient.
569 * Return 1 if there are no such bounds.
571 static int min_is_manifestly_unbounded(struct isl_tab
*tab
,
572 struct isl_tab_var
*var
)
575 unsigned off
= 2 + tab
->M
;
579 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
580 if (!isl_int_is_pos(tab
->mat
->row
[i
][off
+ var
->index
]))
582 if (isl_tab_var_from_row(tab
, i
)->is_nonneg
)
588 static int row_cmp(struct isl_tab
*tab
, int r1
, int r2
, int c
, isl_int t
)
590 unsigned off
= 2 + tab
->M
;
594 isl_int_mul(t
, tab
->mat
->row
[r1
][2], tab
->mat
->row
[r2
][off
+c
]);
595 isl_int_submul(t
, tab
->mat
->row
[r2
][2], tab
->mat
->row
[r1
][off
+c
]);
600 isl_int_mul(t
, tab
->mat
->row
[r1
][1], tab
->mat
->row
[r2
][off
+ c
]);
601 isl_int_submul(t
, tab
->mat
->row
[r2
][1], tab
->mat
->row
[r1
][off
+ c
]);
602 return isl_int_sgn(t
);
605 /* Given the index of a column "c", return the index of a row
606 * that can be used to pivot the column in, with either an increase
607 * (sgn > 0) or a decrease (sgn < 0) of the corresponding variable.
608 * If "var" is not NULL, then the row returned will be different from
609 * the one associated with "var".
611 * Each row in the tableau is of the form
613 * x_r = a_r0 + \sum_i a_ri x_i
615 * Only rows with x_r >= 0 and with the sign of a_ri opposite to "sgn"
616 * impose any limit on the increase or decrease in the value of x_c
617 * and this bound is equal to a_r0 / |a_rc|. We are therefore looking
618 * for the row with the smallest (most stringent) such bound.
619 * Note that the common denominator of each row drops out of the fraction.
620 * To check if row j has a smaller bound than row r, i.e.,
621 * a_j0 / |a_jc| < a_r0 / |a_rc| or a_j0 |a_rc| < a_r0 |a_jc|,
622 * we check if -sign(a_jc) (a_j0 a_rc - a_r0 a_jc) < 0,
623 * where -sign(a_jc) is equal to "sgn".
625 static int pivot_row(struct isl_tab
*tab
,
626 struct isl_tab_var
*var
, int sgn
, int c
)
630 unsigned off
= 2 + tab
->M
;
634 for (j
= tab
->n_redundant
; j
< tab
->n_row
; ++j
) {
635 if (var
&& j
== var
->index
)
637 if (!isl_tab_var_from_row(tab
, j
)->is_nonneg
)
639 if (sgn
* isl_int_sgn(tab
->mat
->row
[j
][off
+ c
]) >= 0)
645 tsgn
= sgn
* row_cmp(tab
, r
, j
, c
, t
);
646 if (tsgn
< 0 || (tsgn
== 0 &&
647 tab
->row_var
[j
] < tab
->row_var
[r
]))
654 /* Find a pivot (row and col) that will increase (sgn > 0) or decrease
655 * (sgn < 0) the value of row variable var.
656 * If not NULL, then skip_var is a row variable that should be ignored
657 * while looking for a pivot row. It is usually equal to var.
659 * As the given row in the tableau is of the form
661 * x_r = a_r0 + \sum_i a_ri x_i
663 * we need to find a column such that the sign of a_ri is equal to "sgn"
664 * (such that an increase in x_i will have the desired effect) or a
665 * column with a variable that may attain negative values.
666 * If a_ri is positive, then we need to move x_i in the same direction
667 * to obtain the desired effect. Otherwise, x_i has to move in the
668 * opposite direction.
670 static void find_pivot(struct isl_tab
*tab
,
671 struct isl_tab_var
*var
, struct isl_tab_var
*skip_var
,
672 int sgn
, int *row
, int *col
)
679 isl_assert(tab
->mat
->ctx
, var
->is_row
, return);
680 tr
= tab
->mat
->row
[var
->index
] + 2 + tab
->M
;
683 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
684 if (isl_int_is_zero(tr
[j
]))
686 if (isl_int_sgn(tr
[j
]) != sgn
&&
687 var_from_col(tab
, j
)->is_nonneg
)
689 if (c
< 0 || tab
->col_var
[j
] < tab
->col_var
[c
])
695 sgn
*= isl_int_sgn(tr
[c
]);
696 r
= pivot_row(tab
, skip_var
, sgn
, c
);
697 *row
= r
< 0 ? var
->index
: r
;
701 /* Return 1 if row "row" represents an obviously redundant inequality.
703 * - it represents an inequality or a variable
704 * - that is the sum of a non-negative sample value and a positive
705 * combination of zero or more non-negative constraints.
707 int isl_tab_row_is_redundant(struct isl_tab
*tab
, int row
)
710 unsigned off
= 2 + tab
->M
;
712 if (tab
->row_var
[row
] < 0 && !isl_tab_var_from_row(tab
, row
)->is_nonneg
)
715 if (isl_int_is_neg(tab
->mat
->row
[row
][1]))
717 if (tab
->M
&& isl_int_is_neg(tab
->mat
->row
[row
][2]))
720 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
721 if (isl_int_is_zero(tab
->mat
->row
[row
][off
+ i
]))
723 if (tab
->col_var
[i
] >= 0)
725 if (isl_int_is_neg(tab
->mat
->row
[row
][off
+ i
]))
727 if (!var_from_col(tab
, i
)->is_nonneg
)
733 static void swap_rows(struct isl_tab
*tab
, int row1
, int row2
)
736 t
= tab
->row_var
[row1
];
737 tab
->row_var
[row1
] = tab
->row_var
[row2
];
738 tab
->row_var
[row2
] = t
;
739 isl_tab_var_from_row(tab
, row1
)->index
= row1
;
740 isl_tab_var_from_row(tab
, row2
)->index
= row2
;
741 tab
->mat
= isl_mat_swap_rows(tab
->mat
, row1
, row2
);
745 t
= tab
->row_sign
[row1
];
746 tab
->row_sign
[row1
] = tab
->row_sign
[row2
];
747 tab
->row_sign
[row2
] = t
;
750 static int push_union(struct isl_tab
*tab
,
751 enum isl_tab_undo_type type
, union isl_tab_undo_val u
) WARN_UNUSED
;
752 static int push_union(struct isl_tab
*tab
,
753 enum isl_tab_undo_type type
, union isl_tab_undo_val u
)
755 struct isl_tab_undo
*undo
;
760 undo
= isl_alloc_type(tab
->mat
->ctx
, struct isl_tab_undo
);
765 undo
->next
= tab
->top
;
771 int isl_tab_push_var(struct isl_tab
*tab
,
772 enum isl_tab_undo_type type
, struct isl_tab_var
*var
)
774 union isl_tab_undo_val u
;
776 u
.var_index
= tab
->row_var
[var
->index
];
778 u
.var_index
= tab
->col_var
[var
->index
];
779 return push_union(tab
, type
, u
);
782 int isl_tab_push(struct isl_tab
*tab
, enum isl_tab_undo_type type
)
784 union isl_tab_undo_val u
= { 0 };
785 return push_union(tab
, type
, u
);
788 /* Push a record on the undo stack describing the current basic
789 * variables, so that the this state can be restored during rollback.
791 int isl_tab_push_basis(struct isl_tab
*tab
)
794 union isl_tab_undo_val u
;
796 u
.col_var
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
799 for (i
= 0; i
< tab
->n_col
; ++i
)
800 u
.col_var
[i
] = tab
->col_var
[i
];
801 return push_union(tab
, isl_tab_undo_saved_basis
, u
);
804 int isl_tab_push_callback(struct isl_tab
*tab
, struct isl_tab_callback
*callback
)
806 union isl_tab_undo_val u
;
807 u
.callback
= callback
;
808 return push_union(tab
, isl_tab_undo_callback
, u
);
811 struct isl_tab
*isl_tab_init_samples(struct isl_tab
*tab
)
818 tab
->samples
= isl_mat_alloc(tab
->mat
->ctx
, 1, 1 + tab
->n_var
);
821 tab
->sample_index
= isl_alloc_array(tab
->mat
->ctx
, int, 1);
822 if (!tab
->sample_index
)
830 struct isl_tab
*isl_tab_add_sample(struct isl_tab
*tab
,
831 __isl_take isl_vec
*sample
)
836 if (tab
->n_sample
+ 1 > tab
->samples
->n_row
) {
837 int *t
= isl_realloc_array(tab
->mat
->ctx
,
838 tab
->sample_index
, int, tab
->n_sample
+ 1);
841 tab
->sample_index
= t
;
844 tab
->samples
= isl_mat_extend(tab
->samples
,
845 tab
->n_sample
+ 1, tab
->samples
->n_col
);
849 isl_seq_cpy(tab
->samples
->row
[tab
->n_sample
], sample
->el
, sample
->size
);
850 isl_vec_free(sample
);
851 tab
->sample_index
[tab
->n_sample
] = tab
->n_sample
;
856 isl_vec_free(sample
);
861 struct isl_tab
*isl_tab_drop_sample(struct isl_tab
*tab
, int s
)
863 if (s
!= tab
->n_outside
) {
864 int t
= tab
->sample_index
[tab
->n_outside
];
865 tab
->sample_index
[tab
->n_outside
] = tab
->sample_index
[s
];
866 tab
->sample_index
[s
] = t
;
867 isl_mat_swap_rows(tab
->samples
, tab
->n_outside
, s
);
870 if (isl_tab_push(tab
, isl_tab_undo_drop_sample
) < 0) {
878 /* Record the current number of samples so that we can remove newer
879 * samples during a rollback.
881 int isl_tab_save_samples(struct isl_tab
*tab
)
883 union isl_tab_undo_val u
;
889 return push_union(tab
, isl_tab_undo_saved_samples
, u
);
892 /* Mark row with index "row" as being redundant.
893 * If we may need to undo the operation or if the row represents
894 * a variable of the original problem, the row is kept,
895 * but no longer considered when looking for a pivot row.
896 * Otherwise, the row is simply removed.
898 * The row may be interchanged with some other row. If it
899 * is interchanged with a later row, return 1. Otherwise return 0.
900 * If the rows are checked in order in the calling function,
901 * then a return value of 1 means that the row with the given
902 * row number may now contain a different row that hasn't been checked yet.
904 int isl_tab_mark_redundant(struct isl_tab
*tab
, int row
)
906 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, row
);
907 var
->is_redundant
= 1;
908 isl_assert(tab
->mat
->ctx
, row
>= tab
->n_redundant
, return -1);
909 if (tab
->need_undo
|| tab
->row_var
[row
] >= 0) {
910 if (tab
->row_var
[row
] >= 0 && !var
->is_nonneg
) {
912 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, var
) < 0)
915 if (row
!= tab
->n_redundant
)
916 swap_rows(tab
, row
, tab
->n_redundant
);
918 return isl_tab_push_var(tab
, isl_tab_undo_redundant
, var
);
920 if (row
!= tab
->n_row
- 1)
921 swap_rows(tab
, row
, tab
->n_row
- 1);
922 isl_tab_var_from_row(tab
, tab
->n_row
- 1)->index
= -1;
928 int isl_tab_mark_empty(struct isl_tab
*tab
)
932 if (!tab
->empty
&& tab
->need_undo
)
933 if (isl_tab_push(tab
, isl_tab_undo_empty
) < 0)
939 int isl_tab_freeze_constraint(struct isl_tab
*tab
, int con
)
941 struct isl_tab_var
*var
;
946 var
= &tab
->con
[con
];
954 return isl_tab_push_var(tab
, isl_tab_undo_freeze
, var
);
959 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
960 * the original sign of the pivot element.
961 * We only keep track of row signs during PILP solving and in this case
962 * we only pivot a row with negative sign (meaning the value is always
963 * non-positive) using a positive pivot element.
965 * For each row j, the new value of the parametric constant is equal to
967 * a_j0 - a_jc a_r0/a_rc
969 * where a_j0 is the original parametric constant, a_rc is the pivot element,
970 * a_r0 is the parametric constant of the pivot row and a_jc is the
971 * pivot column entry of the row j.
972 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
973 * remains the same if a_jc has the same sign as the row j or if
974 * a_jc is zero. In all other cases, we reset the sign to "unknown".
976 static void update_row_sign(struct isl_tab
*tab
, int row
, int col
, int row_sgn
)
979 struct isl_mat
*mat
= tab
->mat
;
980 unsigned off
= 2 + tab
->M
;
985 if (tab
->row_sign
[row
] == 0)
987 isl_assert(mat
->ctx
, row_sgn
> 0, return);
988 isl_assert(mat
->ctx
, tab
->row_sign
[row
] == isl_tab_row_neg
, return);
989 tab
->row_sign
[row
] = isl_tab_row_pos
;
990 for (i
= 0; i
< tab
->n_row
; ++i
) {
994 s
= isl_int_sgn(mat
->row
[i
][off
+ col
]);
997 if (!tab
->row_sign
[i
])
999 if (s
< 0 && tab
->row_sign
[i
] == isl_tab_row_neg
)
1001 if (s
> 0 && tab
->row_sign
[i
] == isl_tab_row_pos
)
1003 tab
->row_sign
[i
] = isl_tab_row_unknown
;
1007 /* Given a row number "row" and a column number "col", pivot the tableau
1008 * such that the associated variables are interchanged.
1009 * The given row in the tableau expresses
1011 * x_r = a_r0 + \sum_i a_ri x_i
1015 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
1017 * Substituting this equality into the other rows
1019 * x_j = a_j0 + \sum_i a_ji x_i
1021 * with a_jc \ne 0, we obtain
1023 * 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
1030 * where i is any other column and j is any other row,
1031 * is therefore transformed into
1033 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1034 * 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)
1036 * The transformation is performed along the following steps
1038 * d_r/n_rc n_ri/n_rc
1041 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1044 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1045 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
1047 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1048 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
1050 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1051 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
1053 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1054 * 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)
1057 int isl_tab_pivot(struct isl_tab
*tab
, int row
, int col
)
1062 struct isl_mat
*mat
= tab
->mat
;
1063 struct isl_tab_var
*var
;
1064 unsigned off
= 2 + tab
->M
;
1066 isl_int_swap(mat
->row
[row
][0], mat
->row
[row
][off
+ col
]);
1067 sgn
= isl_int_sgn(mat
->row
[row
][0]);
1069 isl_int_neg(mat
->row
[row
][0], mat
->row
[row
][0]);
1070 isl_int_neg(mat
->row
[row
][off
+ col
], mat
->row
[row
][off
+ col
]);
1072 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1073 if (j
== off
- 1 + col
)
1075 isl_int_neg(mat
->row
[row
][1 + j
], mat
->row
[row
][1 + j
]);
1077 if (!isl_int_is_one(mat
->row
[row
][0]))
1078 isl_seq_normalize(mat
->ctx
, mat
->row
[row
], off
+ tab
->n_col
);
1079 for (i
= 0; i
< tab
->n_row
; ++i
) {
1082 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1084 isl_int_mul(mat
->row
[i
][0], mat
->row
[i
][0], mat
->row
[row
][0]);
1085 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1086 if (j
== off
- 1 + col
)
1088 isl_int_mul(mat
->row
[i
][1 + j
],
1089 mat
->row
[i
][1 + j
], mat
->row
[row
][0]);
1090 isl_int_addmul(mat
->row
[i
][1 + j
],
1091 mat
->row
[i
][off
+ col
], mat
->row
[row
][1 + j
]);
1093 isl_int_mul(mat
->row
[i
][off
+ col
],
1094 mat
->row
[i
][off
+ col
], mat
->row
[row
][off
+ col
]);
1095 if (!isl_int_is_one(mat
->row
[i
][0]))
1096 isl_seq_normalize(mat
->ctx
, mat
->row
[i
], off
+ tab
->n_col
);
1098 t
= tab
->row_var
[row
];
1099 tab
->row_var
[row
] = tab
->col_var
[col
];
1100 tab
->col_var
[col
] = t
;
1101 var
= isl_tab_var_from_row(tab
, row
);
1104 var
= var_from_col(tab
, col
);
1107 update_row_sign(tab
, row
, col
, sgn
);
1110 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1111 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1113 if (!isl_tab_var_from_row(tab
, i
)->frozen
&&
1114 isl_tab_row_is_redundant(tab
, i
)) {
1115 int redo
= isl_tab_mark_redundant(tab
, i
);
1125 /* If "var" represents a column variable, then pivot is up (sgn > 0)
1126 * or down (sgn < 0) to a row. The variable is assumed not to be
1127 * unbounded in the specified direction.
1128 * If sgn = 0, then the variable is unbounded in both directions,
1129 * and we pivot with any row we can find.
1131 static int to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
) WARN_UNUSED
;
1132 static int to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
)
1135 unsigned off
= 2 + tab
->M
;
1141 for (r
= tab
->n_redundant
; r
< tab
->n_row
; ++r
)
1142 if (!isl_int_is_zero(tab
->mat
->row
[r
][off
+var
->index
]))
1144 isl_assert(tab
->mat
->ctx
, r
< tab
->n_row
, return -1);
1146 r
= pivot_row(tab
, NULL
, sign
, var
->index
);
1147 isl_assert(tab
->mat
->ctx
, r
>= 0, return -1);
1150 return isl_tab_pivot(tab
, r
, var
->index
);
1153 static void check_table(struct isl_tab
*tab
)
1159 for (i
= 0; i
< tab
->n_row
; ++i
) {
1160 if (!isl_tab_var_from_row(tab
, i
)->is_nonneg
)
1162 assert(!isl_int_is_neg(tab
->mat
->row
[i
][1]));
1166 /* Return the sign of the maximal value of "var".
1167 * If the sign is not negative, then on return from this function,
1168 * the sample value will also be non-negative.
1170 * If "var" is manifestly unbounded wrt positive values, we are done.
1171 * Otherwise, we pivot the variable up to a row if needed
1172 * Then we continue pivoting down until either
1173 * - no more down pivots can be performed
1174 * - the sample value is positive
1175 * - the variable is pivoted into a manifestly unbounded column
1177 static int sign_of_max(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1181 if (max_is_manifestly_unbounded(tab
, var
))
1183 if (to_row(tab
, var
, 1) < 0)
1185 while (!isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1186 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1188 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1189 if (isl_tab_pivot(tab
, row
, col
) < 0)
1191 if (!var
->is_row
) /* manifestly unbounded */
1197 static int row_is_neg(struct isl_tab
*tab
, int row
)
1200 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1201 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1203 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1205 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1208 static int row_sgn(struct isl_tab
*tab
, int row
)
1211 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1212 if (!isl_int_is_zero(tab
->mat
->row
[row
][2]))
1213 return isl_int_sgn(tab
->mat
->row
[row
][2]);
1215 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1218 /* Perform pivots until the row variable "var" has a non-negative
1219 * sample value or until no more upward pivots can be performed.
1220 * Return the sign of the sample value after the pivots have been
1223 static int restore_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1227 while (row_is_neg(tab
, var
->index
)) {
1228 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1231 if (isl_tab_pivot(tab
, row
, col
) < 0)
1233 if (!var
->is_row
) /* manifestly unbounded */
1236 return row_sgn(tab
, var
->index
);
1239 /* Perform pivots until we are sure that the row variable "var"
1240 * can attain non-negative values. After return from this
1241 * function, "var" is still a row variable, but its sample
1242 * value may not be non-negative, even if the function returns 1.
1244 static int at_least_zero(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1248 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1249 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1252 if (row
== var
->index
) /* manifestly unbounded */
1254 if (isl_tab_pivot(tab
, row
, col
) < 0)
1257 return !isl_int_is_neg(tab
->mat
->row
[var
->index
][1]);
1260 /* Return a negative value if "var" can attain negative values.
1261 * Return a non-negative value otherwise.
1263 * If "var" is manifestly unbounded wrt negative values, we are done.
1264 * Otherwise, if var is in a column, we can pivot it down to a row.
1265 * Then we continue pivoting down until either
1266 * - the pivot would result in a manifestly unbounded column
1267 * => we don't perform the pivot, but simply return -1
1268 * - no more down pivots can be performed
1269 * - the sample value is negative
1270 * If the sample value becomes negative and the variable is supposed
1271 * to be nonnegative, then we undo the last pivot.
1272 * However, if the last pivot has made the pivoting variable
1273 * obviously redundant, then it may have moved to another row.
1274 * In that case we look for upward pivots until we reach a non-negative
1277 static int sign_of_min(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1280 struct isl_tab_var
*pivot_var
= NULL
;
1282 if (min_is_manifestly_unbounded(tab
, var
))
1286 row
= pivot_row(tab
, NULL
, -1, col
);
1287 pivot_var
= var_from_col(tab
, col
);
1288 if (isl_tab_pivot(tab
, row
, col
) < 0)
1290 if (var
->is_redundant
)
1292 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1293 if (var
->is_nonneg
) {
1294 if (!pivot_var
->is_redundant
&&
1295 pivot_var
->index
== row
) {
1296 if (isl_tab_pivot(tab
, row
, col
) < 0)
1299 if (restore_row(tab
, var
) < -1)
1305 if (var
->is_redundant
)
1307 while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1308 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1309 if (row
== var
->index
)
1312 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1313 pivot_var
= var_from_col(tab
, col
);
1314 if (isl_tab_pivot(tab
, row
, col
) < 0)
1316 if (var
->is_redundant
)
1319 if (pivot_var
&& var
->is_nonneg
) {
1320 /* pivot back to non-negative value */
1321 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
) {
1322 if (isl_tab_pivot(tab
, row
, col
) < 0)
1325 if (restore_row(tab
, var
) < -1)
1331 static int row_at_most_neg_one(struct isl_tab
*tab
, int row
)
1334 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1336 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1339 return isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
1340 isl_int_abs_ge(tab
->mat
->row
[row
][1],
1341 tab
->mat
->row
[row
][0]);
1344 /* Return 1 if "var" can attain values <= -1.
1345 * Return 0 otherwise.
1347 * The sample value of "var" is assumed to be non-negative when the
1348 * the function is called and will be made non-negative again before
1349 * the function returns.
1351 int isl_tab_min_at_most_neg_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1354 struct isl_tab_var
*pivot_var
;
1356 if (min_is_manifestly_unbounded(tab
, var
))
1360 row
= pivot_row(tab
, NULL
, -1, col
);
1361 pivot_var
= var_from_col(tab
, col
);
1362 if (isl_tab_pivot(tab
, row
, col
) < 0)
1364 if (var
->is_redundant
)
1366 if (row_at_most_neg_one(tab
, var
->index
)) {
1367 if (var
->is_nonneg
) {
1368 if (!pivot_var
->is_redundant
&&
1369 pivot_var
->index
== row
) {
1370 if (isl_tab_pivot(tab
, row
, col
) < 0)
1373 if (restore_row(tab
, var
) < -1)
1379 if (var
->is_redundant
)
1382 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1383 if (row
== var
->index
)
1387 pivot_var
= var_from_col(tab
, col
);
1388 if (isl_tab_pivot(tab
, row
, col
) < 0)
1390 if (var
->is_redundant
)
1392 } while (!row_at_most_neg_one(tab
, var
->index
));
1393 if (var
->is_nonneg
) {
1394 /* pivot back to non-negative value */
1395 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
1396 if (isl_tab_pivot(tab
, row
, col
) < 0)
1398 if (restore_row(tab
, var
) < -1)
1404 /* Return 1 if "var" can attain values >= 1.
1405 * Return 0 otherwise.
1407 static int at_least_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1412 if (max_is_manifestly_unbounded(tab
, var
))
1414 if (to_row(tab
, var
, 1) < 0)
1416 r
= tab
->mat
->row
[var
->index
];
1417 while (isl_int_lt(r
[1], r
[0])) {
1418 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1420 return isl_int_ge(r
[1], r
[0]);
1421 if (row
== var
->index
) /* manifestly unbounded */
1423 if (isl_tab_pivot(tab
, row
, col
) < 0)
1429 static void swap_cols(struct isl_tab
*tab
, int col1
, int col2
)
1432 unsigned off
= 2 + tab
->M
;
1433 t
= tab
->col_var
[col1
];
1434 tab
->col_var
[col1
] = tab
->col_var
[col2
];
1435 tab
->col_var
[col2
] = t
;
1436 var_from_col(tab
, col1
)->index
= col1
;
1437 var_from_col(tab
, col2
)->index
= col2
;
1438 tab
->mat
= isl_mat_swap_cols(tab
->mat
, off
+ col1
, off
+ col2
);
1441 /* Mark column with index "col" as representing a zero variable.
1442 * If we may need to undo the operation the column is kept,
1443 * but no longer considered.
1444 * Otherwise, the column is simply removed.
1446 * The column may be interchanged with some other column. If it
1447 * is interchanged with a later column, return 1. Otherwise return 0.
1448 * If the columns are checked in order in the calling function,
1449 * then a return value of 1 means that the column with the given
1450 * column number may now contain a different column that
1451 * hasn't been checked yet.
1453 int isl_tab_kill_col(struct isl_tab
*tab
, int col
)
1455 var_from_col(tab
, col
)->is_zero
= 1;
1456 if (tab
->need_undo
) {
1457 if (isl_tab_push_var(tab
, isl_tab_undo_zero
,
1458 var_from_col(tab
, col
)) < 0)
1460 if (col
!= tab
->n_dead
)
1461 swap_cols(tab
, col
, tab
->n_dead
);
1465 if (col
!= tab
->n_col
- 1)
1466 swap_cols(tab
, col
, tab
->n_col
- 1);
1467 var_from_col(tab
, tab
->n_col
- 1)->index
= -1;
1473 /* Row variable "var" is non-negative and cannot attain any values
1474 * larger than zero. This means that the coefficients of the unrestricted
1475 * column variables are zero and that the coefficients of the non-negative
1476 * column variables are zero or negative.
1477 * Each of the non-negative variables with a negative coefficient can
1478 * then also be written as the negative sum of non-negative variables
1479 * and must therefore also be zero.
1481 static int close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
1482 static int close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1485 struct isl_mat
*mat
= tab
->mat
;
1486 unsigned off
= 2 + tab
->M
;
1488 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return -1);
1491 if (isl_tab_push_var(tab
, isl_tab_undo_zero
, var
) < 0)
1493 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1494 if (isl_int_is_zero(mat
->row
[var
->index
][off
+ j
]))
1496 isl_assert(tab
->mat
->ctx
,
1497 isl_int_is_neg(mat
->row
[var
->index
][off
+ j
]), return -1);
1498 if (isl_tab_kill_col(tab
, j
))
1501 if (isl_tab_mark_redundant(tab
, var
->index
) < 0)
1506 /* Add a constraint to the tableau and allocate a row for it.
1507 * Return the index into the constraint array "con".
1509 int isl_tab_allocate_con(struct isl_tab
*tab
)
1513 isl_assert(tab
->mat
->ctx
, tab
->n_row
< tab
->mat
->n_row
, return -1);
1514 isl_assert(tab
->mat
->ctx
, tab
->n_con
< tab
->max_con
, return -1);
1517 tab
->con
[r
].index
= tab
->n_row
;
1518 tab
->con
[r
].is_row
= 1;
1519 tab
->con
[r
].is_nonneg
= 0;
1520 tab
->con
[r
].is_zero
= 0;
1521 tab
->con
[r
].is_redundant
= 0;
1522 tab
->con
[r
].frozen
= 0;
1523 tab
->con
[r
].negated
= 0;
1524 tab
->row_var
[tab
->n_row
] = ~r
;
1528 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]) < 0)
1534 /* Add a variable to the tableau and allocate a column for it.
1535 * Return the index into the variable array "var".
1537 int isl_tab_allocate_var(struct isl_tab
*tab
)
1541 unsigned off
= 2 + tab
->M
;
1543 isl_assert(tab
->mat
->ctx
, tab
->n_col
< tab
->mat
->n_col
, return -1);
1544 isl_assert(tab
->mat
->ctx
, tab
->n_var
< tab
->max_var
, return -1);
1547 tab
->var
[r
].index
= tab
->n_col
;
1548 tab
->var
[r
].is_row
= 0;
1549 tab
->var
[r
].is_nonneg
= 0;
1550 tab
->var
[r
].is_zero
= 0;
1551 tab
->var
[r
].is_redundant
= 0;
1552 tab
->var
[r
].frozen
= 0;
1553 tab
->var
[r
].negated
= 0;
1554 tab
->col_var
[tab
->n_col
] = r
;
1556 for (i
= 0; i
< tab
->n_row
; ++i
)
1557 isl_int_set_si(tab
->mat
->row
[i
][off
+ tab
->n_col
], 0);
1561 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->var
[r
]) < 0)
1567 /* Add a row to the tableau. The row is given as an affine combination
1568 * of the original variables and needs to be expressed in terms of the
1571 * We add each term in turn.
1572 * If r = n/d_r is the current sum and we need to add k x, then
1573 * if x is a column variable, we increase the numerator of
1574 * this column by k d_r
1575 * if x = f/d_x is a row variable, then the new representation of r is
1577 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1578 * --- + --- = ------------------- = -------------------
1579 * d_r d_r d_r d_x/g m
1581 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1583 int isl_tab_add_row(struct isl_tab
*tab
, isl_int
*line
)
1589 unsigned off
= 2 + tab
->M
;
1591 r
= isl_tab_allocate_con(tab
);
1597 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1598 isl_int_set_si(row
[0], 1);
1599 isl_int_set(row
[1], line
[0]);
1600 isl_seq_clr(row
+ 2, tab
->M
+ tab
->n_col
);
1601 for (i
= 0; i
< tab
->n_var
; ++i
) {
1602 if (tab
->var
[i
].is_zero
)
1604 if (tab
->var
[i
].is_row
) {
1606 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1607 isl_int_swap(a
, row
[0]);
1608 isl_int_divexact(a
, row
[0], a
);
1610 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1611 isl_int_mul(b
, b
, line
[1 + i
]);
1612 isl_seq_combine(row
+ 1, a
, row
+ 1,
1613 b
, tab
->mat
->row
[tab
->var
[i
].index
] + 1,
1614 1 + tab
->M
+ tab
->n_col
);
1616 isl_int_addmul(row
[off
+ tab
->var
[i
].index
],
1617 line
[1 + i
], row
[0]);
1618 if (tab
->M
&& i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
1619 isl_int_submul(row
[2], line
[1 + i
], row
[0]);
1621 isl_seq_normalize(tab
->mat
->ctx
, row
, off
+ tab
->n_col
);
1626 tab
->row_sign
[tab
->con
[r
].index
] = 0;
1631 static int drop_row(struct isl_tab
*tab
, int row
)
1633 isl_assert(tab
->mat
->ctx
, ~tab
->row_var
[row
] == tab
->n_con
- 1, return -1);
1634 if (row
!= tab
->n_row
- 1)
1635 swap_rows(tab
, row
, tab
->n_row
- 1);
1641 static int drop_col(struct isl_tab
*tab
, int col
)
1643 isl_assert(tab
->mat
->ctx
, tab
->col_var
[col
] == tab
->n_var
- 1, return -1);
1644 if (col
!= tab
->n_col
- 1)
1645 swap_cols(tab
, col
, tab
->n_col
- 1);
1651 /* Add inequality "ineq" and check if it conflicts with the
1652 * previously added constraints or if it is obviously redundant.
1654 int isl_tab_add_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1663 struct isl_basic_set
*bset
= tab
->bset
;
1665 isl_assert(tab
->mat
->ctx
, tab
->n_eq
== bset
->n_eq
, return -1);
1666 isl_assert(tab
->mat
->ctx
,
1667 tab
->n_con
== bset
->n_eq
+ bset
->n_ineq
, return -1);
1668 tab
->bset
= isl_basic_set_add_ineq(tab
->bset
, ineq
);
1669 if (isl_tab_push(tab
, isl_tab_undo_bset_ineq
) < 0)
1676 isl_int_swap(ineq
[0], cst
);
1678 r
= isl_tab_add_row(tab
, ineq
);
1680 isl_int_swap(ineq
[0], cst
);
1685 tab
->con
[r
].is_nonneg
= 1;
1686 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1688 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1689 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1694 sgn
= restore_row(tab
, &tab
->con
[r
]);
1698 return isl_tab_mark_empty(tab
);
1699 if (tab
->con
[r
].is_row
&& isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1700 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1705 /* Pivot a non-negative variable down until it reaches the value zero
1706 * and then pivot the variable into a column position.
1708 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
1709 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1713 unsigned off
= 2 + tab
->M
;
1718 while (isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1719 find_pivot(tab
, var
, NULL
, -1, &row
, &col
);
1720 isl_assert(tab
->mat
->ctx
, row
!= -1, return -1);
1721 if (isl_tab_pivot(tab
, row
, col
) < 0)
1727 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
)
1728 if (!isl_int_is_zero(tab
->mat
->row
[var
->index
][off
+ i
]))
1731 isl_assert(tab
->mat
->ctx
, i
< tab
->n_col
, return -1);
1732 if (isl_tab_pivot(tab
, var
->index
, i
) < 0)
1738 /* We assume Gaussian elimination has been performed on the equalities.
1739 * The equalities can therefore never conflict.
1740 * Adding the equalities is currently only really useful for a later call
1741 * to isl_tab_ineq_type.
1743 static struct isl_tab
*add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1750 r
= isl_tab_add_row(tab
, eq
);
1754 r
= tab
->con
[r
].index
;
1755 i
= isl_seq_first_non_zero(tab
->mat
->row
[r
] + 2 + tab
->M
+ tab
->n_dead
,
1756 tab
->n_col
- tab
->n_dead
);
1757 isl_assert(tab
->mat
->ctx
, i
>= 0, goto error
);
1759 if (isl_tab_pivot(tab
, r
, i
) < 0)
1761 if (isl_tab_kill_col(tab
, i
) < 0)
1771 static int row_is_manifestly_zero(struct isl_tab
*tab
, int row
)
1773 unsigned off
= 2 + tab
->M
;
1775 if (!isl_int_is_zero(tab
->mat
->row
[row
][1]))
1777 if (tab
->M
&& !isl_int_is_zero(tab
->mat
->row
[row
][2]))
1779 return isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1780 tab
->n_col
- tab
->n_dead
) == -1;
1783 /* Add an equality that is known to be valid for the given tableau.
1785 struct isl_tab
*isl_tab_add_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1787 struct isl_tab_var
*var
;
1792 r
= isl_tab_add_row(tab
, eq
);
1798 if (row_is_manifestly_zero(tab
, r
)) {
1800 if (isl_tab_mark_redundant(tab
, r
) < 0)
1805 if (isl_int_is_neg(tab
->mat
->row
[r
][1])) {
1806 isl_seq_neg(tab
->mat
->row
[r
] + 1, tab
->mat
->row
[r
] + 1,
1811 if (to_col(tab
, var
) < 0)
1814 if (isl_tab_kill_col(tab
, var
->index
) < 0)
1823 static int add_zero_row(struct isl_tab
*tab
)
1828 r
= isl_tab_allocate_con(tab
);
1832 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1833 isl_seq_clr(row
+ 1, 1 + tab
->M
+ tab
->n_col
);
1834 isl_int_set_si(row
[0], 1);
1839 /* Add equality "eq" and check if it conflicts with the
1840 * previously added constraints or if it is obviously redundant.
1842 struct isl_tab
*isl_tab_add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1844 struct isl_tab_undo
*snap
= NULL
;
1845 struct isl_tab_var
*var
;
1853 isl_assert(tab
->mat
->ctx
, !tab
->M
, goto error
);
1856 snap
= isl_tab_snap(tab
);
1860 isl_int_swap(eq
[0], cst
);
1862 r
= isl_tab_add_row(tab
, eq
);
1864 isl_int_swap(eq
[0], cst
);
1872 if (row_is_manifestly_zero(tab
, row
)) {
1874 if (isl_tab_rollback(tab
, snap
) < 0)
1882 tab
->bset
= isl_basic_set_add_ineq(tab
->bset
, eq
);
1883 if (isl_tab_push(tab
, isl_tab_undo_bset_ineq
) < 0)
1885 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1886 tab
->bset
= isl_basic_set_add_ineq(tab
->bset
, eq
);
1887 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1888 if (isl_tab_push(tab
, isl_tab_undo_bset_ineq
) < 0)
1892 if (add_zero_row(tab
) < 0)
1896 sgn
= isl_int_sgn(tab
->mat
->row
[row
][1]);
1899 isl_seq_neg(tab
->mat
->row
[row
] + 1, tab
->mat
->row
[row
] + 1,
1906 sgn
= sign_of_max(tab
, var
);
1910 if (isl_tab_mark_empty(tab
) < 0)
1917 if (to_col(tab
, var
) < 0)
1920 if (isl_tab_kill_col(tab
, var
->index
) < 0)
1929 struct isl_tab
*isl_tab_from_basic_map(struct isl_basic_map
*bmap
)
1932 struct isl_tab
*tab
;
1936 tab
= isl_tab_alloc(bmap
->ctx
,
1937 isl_basic_map_total_dim(bmap
) + bmap
->n_ineq
+ 1,
1938 isl_basic_map_total_dim(bmap
), 0);
1941 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
1942 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
)) {
1943 if (isl_tab_mark_empty(tab
) < 0)
1947 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1948 tab
= add_eq(tab
, bmap
->eq
[i
]);
1952 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1953 if (isl_tab_add_ineq(tab
, bmap
->ineq
[i
]) < 0)
1964 struct isl_tab
*isl_tab_from_basic_set(struct isl_basic_set
*bset
)
1966 return isl_tab_from_basic_map((struct isl_basic_map
*)bset
);
1969 /* Construct a tableau corresponding to the recession cone of "bset".
1971 struct isl_tab
*isl_tab_from_recession_cone(struct isl_basic_set
*bset
)
1975 struct isl_tab
*tab
;
1979 tab
= isl_tab_alloc(bset
->ctx
, bset
->n_eq
+ bset
->n_ineq
,
1980 isl_basic_set_total_dim(bset
), 0);
1983 tab
->rational
= ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
);
1987 for (i
= 0; i
< bset
->n_eq
; ++i
) {
1988 isl_int_swap(bset
->eq
[i
][0], cst
);
1989 tab
= add_eq(tab
, bset
->eq
[i
]);
1990 isl_int_swap(bset
->eq
[i
][0], cst
);
1994 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
1996 isl_int_swap(bset
->ineq
[i
][0], cst
);
1997 r
= isl_tab_add_row(tab
, bset
->ineq
[i
]);
1998 isl_int_swap(bset
->ineq
[i
][0], cst
);
2001 tab
->con
[r
].is_nonneg
= 1;
2002 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2014 /* Assuming "tab" is the tableau of a cone, check if the cone is
2015 * bounded, i.e., if it is empty or only contains the origin.
2017 int isl_tab_cone_is_bounded(struct isl_tab
*tab
)
2025 if (tab
->n_dead
== tab
->n_col
)
2029 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2030 struct isl_tab_var
*var
;
2032 var
= isl_tab_var_from_row(tab
, i
);
2033 if (!var
->is_nonneg
)
2035 sgn
= sign_of_max(tab
, var
);
2040 if (close_row(tab
, var
) < 0)
2044 if (tab
->n_dead
== tab
->n_col
)
2046 if (i
== tab
->n_row
)
2051 int isl_tab_sample_is_integer(struct isl_tab
*tab
)
2058 for (i
= 0; i
< tab
->n_var
; ++i
) {
2060 if (!tab
->var
[i
].is_row
)
2062 row
= tab
->var
[i
].index
;
2063 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
2064 tab
->mat
->row
[row
][0]))
2070 static struct isl_vec
*extract_integer_sample(struct isl_tab
*tab
)
2073 struct isl_vec
*vec
;
2075 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2079 isl_int_set_si(vec
->block
.data
[0], 1);
2080 for (i
= 0; i
< tab
->n_var
; ++i
) {
2081 if (!tab
->var
[i
].is_row
)
2082 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
2084 int row
= tab
->var
[i
].index
;
2085 isl_int_divexact(vec
->block
.data
[1 + i
],
2086 tab
->mat
->row
[row
][1], tab
->mat
->row
[row
][0]);
2093 struct isl_vec
*isl_tab_get_sample_value(struct isl_tab
*tab
)
2096 struct isl_vec
*vec
;
2102 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2108 isl_int_set_si(vec
->block
.data
[0], 1);
2109 for (i
= 0; i
< tab
->n_var
; ++i
) {
2111 if (!tab
->var
[i
].is_row
) {
2112 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
2115 row
= tab
->var
[i
].index
;
2116 isl_int_gcd(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
2117 isl_int_divexact(m
, tab
->mat
->row
[row
][0], m
);
2118 isl_seq_scale(vec
->block
.data
, vec
->block
.data
, m
, 1 + i
);
2119 isl_int_divexact(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
2120 isl_int_mul(vec
->block
.data
[1 + i
], m
, tab
->mat
->row
[row
][1]);
2122 vec
= isl_vec_normalize(vec
);
2128 /* Update "bmap" based on the results of the tableau "tab".
2129 * In particular, implicit equalities are made explicit, redundant constraints
2130 * are removed and if the sample value happens to be integer, it is stored
2131 * in "bmap" (unless "bmap" already had an integer sample).
2133 * The tableau is assumed to have been created from "bmap" using
2134 * isl_tab_from_basic_map.
2136 struct isl_basic_map
*isl_basic_map_update_from_tab(struct isl_basic_map
*bmap
,
2137 struct isl_tab
*tab
)
2149 bmap
= isl_basic_map_set_to_empty(bmap
);
2151 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
2152 if (isl_tab_is_equality(tab
, n_eq
+ i
))
2153 isl_basic_map_inequality_to_equality(bmap
, i
);
2154 else if (isl_tab_is_redundant(tab
, n_eq
+ i
))
2155 isl_basic_map_drop_inequality(bmap
, i
);
2157 if (!tab
->rational
&&
2158 !bmap
->sample
&& isl_tab_sample_is_integer(tab
))
2159 bmap
->sample
= extract_integer_sample(tab
);
2163 struct isl_basic_set
*isl_basic_set_update_from_tab(struct isl_basic_set
*bset
,
2164 struct isl_tab
*tab
)
2166 return (struct isl_basic_set
*)isl_basic_map_update_from_tab(
2167 (struct isl_basic_map
*)bset
, tab
);
2170 /* Given a non-negative variable "var", add a new non-negative variable
2171 * that is the opposite of "var", ensuring that var can only attain the
2173 * If var = n/d is a row variable, then the new variable = -n/d.
2174 * If var is a column variables, then the new variable = -var.
2175 * If the new variable cannot attain non-negative values, then
2176 * the resulting tableau is empty.
2177 * Otherwise, we know the value will be zero and we close the row.
2179 static struct isl_tab
*cut_to_hyperplane(struct isl_tab
*tab
,
2180 struct isl_tab_var
*var
)
2185 unsigned off
= 2 + tab
->M
;
2189 isl_assert(tab
->mat
->ctx
, !var
->is_redundant
, goto error
);
2191 if (isl_tab_extend_cons(tab
, 1) < 0)
2195 tab
->con
[r
].index
= tab
->n_row
;
2196 tab
->con
[r
].is_row
= 1;
2197 tab
->con
[r
].is_nonneg
= 0;
2198 tab
->con
[r
].is_zero
= 0;
2199 tab
->con
[r
].is_redundant
= 0;
2200 tab
->con
[r
].frozen
= 0;
2201 tab
->con
[r
].negated
= 0;
2202 tab
->row_var
[tab
->n_row
] = ~r
;
2203 row
= tab
->mat
->row
[tab
->n_row
];
2206 isl_int_set(row
[0], tab
->mat
->row
[var
->index
][0]);
2207 isl_seq_neg(row
+ 1,
2208 tab
->mat
->row
[var
->index
] + 1, 1 + tab
->n_col
);
2210 isl_int_set_si(row
[0], 1);
2211 isl_seq_clr(row
+ 1, 1 + tab
->n_col
);
2212 isl_int_set_si(row
[off
+ var
->index
], -1);
2217 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]) < 0)
2220 sgn
= sign_of_max(tab
, &tab
->con
[r
]);
2224 if (isl_tab_mark_empty(tab
) < 0)
2228 tab
->con
[r
].is_nonneg
= 1;
2229 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2232 if (close_row(tab
, &tab
->con
[r
]) < 0)
2241 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2242 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2243 * by r' = r + 1 >= 0.
2244 * If r is a row variable, we simply increase the constant term by one
2245 * (taking into account the denominator).
2246 * If r is a column variable, then we need to modify each row that
2247 * refers to r = r' - 1 by substituting this equality, effectively
2248 * subtracting the coefficient of the column from the constant.
2250 struct isl_tab
*isl_tab_relax(struct isl_tab
*tab
, int con
)
2252 struct isl_tab_var
*var
;
2253 unsigned off
= 2 + tab
->M
;
2258 var
= &tab
->con
[con
];
2260 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
2261 if (to_row(tab
, var
, 1) < 0)
2265 isl_int_add(tab
->mat
->row
[var
->index
][1],
2266 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
2270 for (i
= 0; i
< tab
->n_row
; ++i
) {
2271 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2273 isl_int_sub(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
2274 tab
->mat
->row
[i
][off
+ var
->index
]);
2279 if (isl_tab_push_var(tab
, isl_tab_undo_relax
, var
) < 0)
2288 struct isl_tab
*isl_tab_select_facet(struct isl_tab
*tab
, int con
)
2293 return cut_to_hyperplane(tab
, &tab
->con
[con
]);
2296 static int may_be_equality(struct isl_tab
*tab
, int row
)
2298 unsigned off
= 2 + tab
->M
;
2299 return (tab
->rational
? isl_int_is_zero(tab
->mat
->row
[row
][1])
2300 : isl_int_lt(tab
->mat
->row
[row
][1],
2301 tab
->mat
->row
[row
][0])) &&
2302 isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
2303 tab
->n_col
- tab
->n_dead
) != -1;
2306 /* Check for (near) equalities among the constraints.
2307 * A constraint is an equality if it is non-negative and if
2308 * its maximal value is either
2309 * - zero (in case of rational tableaus), or
2310 * - strictly less than 1 (in case of integer tableaus)
2312 * We first mark all non-redundant and non-dead variables that
2313 * are not frozen and not obviously not an equality.
2314 * Then we iterate over all marked variables if they can attain
2315 * any values larger than zero or at least one.
2316 * If the maximal value is zero, we mark any column variables
2317 * that appear in the row as being zero and mark the row as being redundant.
2318 * Otherwise, if the maximal value is strictly less than one (and the
2319 * tableau is integer), then we restrict the value to being zero
2320 * by adding an opposite non-negative variable.
2322 struct isl_tab
*isl_tab_detect_implicit_equalities(struct isl_tab
*tab
)
2331 if (tab
->n_dead
== tab
->n_col
)
2335 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2336 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2337 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2338 may_be_equality(tab
, i
);
2342 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2343 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2344 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2349 struct isl_tab_var
*var
;
2351 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2352 var
= isl_tab_var_from_row(tab
, i
);
2356 if (i
== tab
->n_row
) {
2357 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2358 var
= var_from_col(tab
, i
);
2362 if (i
== tab
->n_col
)
2367 sgn
= sign_of_max(tab
, var
);
2371 if (close_row(tab
, var
) < 0)
2373 } else if (!tab
->rational
&& !at_least_one(tab
, var
)) {
2374 tab
= cut_to_hyperplane(tab
, var
);
2375 return isl_tab_detect_implicit_equalities(tab
);
2377 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2378 var
= isl_tab_var_from_row(tab
, i
);
2381 if (may_be_equality(tab
, i
))
2394 static int con_is_redundant(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2398 if (tab
->rational
) {
2399 int sgn
= sign_of_min(tab
, var
);
2404 int irred
= isl_tab_min_at_most_neg_one(tab
, var
);
2411 /* Check for (near) redundant constraints.
2412 * A constraint is redundant if it is non-negative and if
2413 * its minimal value (temporarily ignoring the non-negativity) is either
2414 * - zero (in case of rational tableaus), or
2415 * - strictly larger than -1 (in case of integer tableaus)
2417 * We first mark all non-redundant and non-dead variables that
2418 * are not frozen and not obviously negatively unbounded.
2419 * Then we iterate over all marked variables if they can attain
2420 * any values smaller than zero or at most negative one.
2421 * If not, we mark the row as being redundant (assuming it hasn't
2422 * been detected as being obviously redundant in the mean time).
2424 int isl_tab_detect_redundant(struct isl_tab
*tab
)
2433 if (tab
->n_redundant
== tab
->n_row
)
2437 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2438 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2439 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2443 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2444 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2445 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2446 !min_is_manifestly_unbounded(tab
, var
);
2451 struct isl_tab_var
*var
;
2453 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2454 var
= isl_tab_var_from_row(tab
, i
);
2458 if (i
== tab
->n_row
) {
2459 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2460 var
= var_from_col(tab
, i
);
2464 if (i
== tab
->n_col
)
2469 red
= con_is_redundant(tab
, var
);
2472 if (red
&& !var
->is_redundant
)
2473 if (isl_tab_mark_redundant(tab
, var
->index
) < 0)
2475 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2476 var
= var_from_col(tab
, i
);
2479 if (!min_is_manifestly_unbounded(tab
, var
))
2489 int isl_tab_is_equality(struct isl_tab
*tab
, int con
)
2496 if (tab
->con
[con
].is_zero
)
2498 if (tab
->con
[con
].is_redundant
)
2500 if (!tab
->con
[con
].is_row
)
2501 return tab
->con
[con
].index
< tab
->n_dead
;
2503 row
= tab
->con
[con
].index
;
2506 return isl_int_is_zero(tab
->mat
->row
[row
][1]) &&
2507 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
2508 tab
->n_col
- tab
->n_dead
) == -1;
2511 /* Return the minimial value of the affine expression "f" with denominator
2512 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
2513 * the expression cannot attain arbitrarily small values.
2514 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
2515 * The return value reflects the nature of the result (empty, unbounded,
2516 * minmimal value returned in *opt).
2518 enum isl_lp_result
isl_tab_min(struct isl_tab
*tab
,
2519 isl_int
*f
, isl_int denom
, isl_int
*opt
, isl_int
*opt_denom
,
2523 enum isl_lp_result res
= isl_lp_ok
;
2524 struct isl_tab_var
*var
;
2525 struct isl_tab_undo
*snap
;
2528 return isl_lp_empty
;
2530 snap
= isl_tab_snap(tab
);
2531 r
= isl_tab_add_row(tab
, f
);
2533 return isl_lp_error
;
2535 isl_int_mul(tab
->mat
->row
[var
->index
][0],
2536 tab
->mat
->row
[var
->index
][0], denom
);
2539 find_pivot(tab
, var
, var
, -1, &row
, &col
);
2540 if (row
== var
->index
) {
2541 res
= isl_lp_unbounded
;
2546 if (isl_tab_pivot(tab
, row
, col
) < 0)
2547 return isl_lp_error
;
2549 if (ISL_FL_ISSET(flags
, ISL_TAB_SAVE_DUAL
)) {
2552 isl_vec_free(tab
->dual
);
2553 tab
->dual
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_con
);
2555 return isl_lp_error
;
2556 isl_int_set(tab
->dual
->el
[0], tab
->mat
->row
[var
->index
][0]);
2557 for (i
= 0; i
< tab
->n_con
; ++i
) {
2559 if (tab
->con
[i
].is_row
) {
2560 isl_int_set_si(tab
->dual
->el
[1 + i
], 0);
2563 pos
= 2 + tab
->M
+ tab
->con
[i
].index
;
2564 if (tab
->con
[i
].negated
)
2565 isl_int_neg(tab
->dual
->el
[1 + i
],
2566 tab
->mat
->row
[var
->index
][pos
]);
2568 isl_int_set(tab
->dual
->el
[1 + i
],
2569 tab
->mat
->row
[var
->index
][pos
]);
2572 if (opt
&& res
== isl_lp_ok
) {
2574 isl_int_set(*opt
, tab
->mat
->row
[var
->index
][1]);
2575 isl_int_set(*opt_denom
, tab
->mat
->row
[var
->index
][0]);
2577 isl_int_cdiv_q(*opt
, tab
->mat
->row
[var
->index
][1],
2578 tab
->mat
->row
[var
->index
][0]);
2580 if (isl_tab_rollback(tab
, snap
) < 0)
2581 return isl_lp_error
;
2585 int isl_tab_is_redundant(struct isl_tab
*tab
, int con
)
2589 if (tab
->con
[con
].is_zero
)
2591 if (tab
->con
[con
].is_redundant
)
2593 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
2596 /* Take a snapshot of the tableau that can be restored by s call to
2599 struct isl_tab_undo
*isl_tab_snap(struct isl_tab
*tab
)
2607 /* Undo the operation performed by isl_tab_relax.
2609 static int unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
2610 static int unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2612 unsigned off
= 2 + tab
->M
;
2614 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
2615 if (to_row(tab
, var
, 1) < 0)
2619 isl_int_sub(tab
->mat
->row
[var
->index
][1],
2620 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
2624 for (i
= 0; i
< tab
->n_row
; ++i
) {
2625 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2627 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
2628 tab
->mat
->row
[i
][off
+ var
->index
]);
2636 static int perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
) WARN_UNUSED
;
2637 static int perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2639 struct isl_tab_var
*var
= var_from_index(tab
, undo
->u
.var_index
);
2640 switch(undo
->type
) {
2641 case isl_tab_undo_nonneg
:
2644 case isl_tab_undo_redundant
:
2645 var
->is_redundant
= 0;
2648 case isl_tab_undo_freeze
:
2651 case isl_tab_undo_zero
:
2656 case isl_tab_undo_allocate
:
2657 if (undo
->u
.var_index
>= 0) {
2658 isl_assert(tab
->mat
->ctx
, !var
->is_row
, return -1);
2659 drop_col(tab
, var
->index
);
2663 if (!max_is_manifestly_unbounded(tab
, var
)) {
2664 if (to_row(tab
, var
, 1) < 0)
2666 } else if (!min_is_manifestly_unbounded(tab
, var
)) {
2667 if (to_row(tab
, var
, -1) < 0)
2670 if (to_row(tab
, var
, 0) < 0)
2673 drop_row(tab
, var
->index
);
2675 case isl_tab_undo_relax
:
2676 return unrelax(tab
, var
);
2682 /* Restore the tableau to the state where the basic variables
2683 * are those in "col_var".
2684 * We first construct a list of variables that are currently in
2685 * the basis, but shouldn't. Then we iterate over all variables
2686 * that should be in the basis and for each one that is currently
2687 * not in the basis, we exchange it with one of the elements of the
2688 * list constructed before.
2689 * We can always find an appropriate variable to pivot with because
2690 * the current basis is mapped to the old basis by a non-singular
2691 * matrix and so we can never end up with a zero row.
2693 static int restore_basis(struct isl_tab
*tab
, int *col_var
)
2697 int *extra
= NULL
; /* current columns that contain bad stuff */
2698 unsigned off
= 2 + tab
->M
;
2700 extra
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
2703 for (i
= 0; i
< tab
->n_col
; ++i
) {
2704 for (j
= 0; j
< tab
->n_col
; ++j
)
2705 if (tab
->col_var
[i
] == col_var
[j
])
2709 extra
[n_extra
++] = i
;
2711 for (i
= 0; i
< tab
->n_col
&& n_extra
> 0; ++i
) {
2712 struct isl_tab_var
*var
;
2715 for (j
= 0; j
< tab
->n_col
; ++j
)
2716 if (col_var
[i
] == tab
->col_var
[j
])
2720 var
= var_from_index(tab
, col_var
[i
]);
2722 for (j
= 0; j
< n_extra
; ++j
)
2723 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+extra
[j
]]))
2725 isl_assert(tab
->mat
->ctx
, j
< n_extra
, goto error
);
2726 if (isl_tab_pivot(tab
, row
, extra
[j
]) < 0)
2728 extra
[j
] = extra
[--n_extra
];
2740 /* Remove all samples with index n or greater, i.e., those samples
2741 * that were added since we saved this number of samples in
2742 * isl_tab_save_samples.
2744 static void drop_samples_since(struct isl_tab
*tab
, int n
)
2748 for (i
= tab
->n_sample
- 1; i
>= 0 && tab
->n_sample
> n
; --i
) {
2749 if (tab
->sample_index
[i
] < n
)
2752 if (i
!= tab
->n_sample
- 1) {
2753 int t
= tab
->sample_index
[tab
->n_sample
-1];
2754 tab
->sample_index
[tab
->n_sample
-1] = tab
->sample_index
[i
];
2755 tab
->sample_index
[i
] = t
;
2756 isl_mat_swap_rows(tab
->samples
, tab
->n_sample
-1, i
);
2762 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
) WARN_UNUSED
;
2763 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2765 switch (undo
->type
) {
2766 case isl_tab_undo_empty
:
2769 case isl_tab_undo_nonneg
:
2770 case isl_tab_undo_redundant
:
2771 case isl_tab_undo_freeze
:
2772 case isl_tab_undo_zero
:
2773 case isl_tab_undo_allocate
:
2774 case isl_tab_undo_relax
:
2775 return perform_undo_var(tab
, undo
);
2776 case isl_tab_undo_bset_eq
:
2777 return isl_basic_set_free_equality(tab
->bset
, 1);
2778 case isl_tab_undo_bset_ineq
:
2779 return isl_basic_set_free_inequality(tab
->bset
, 1);
2780 case isl_tab_undo_bset_div
:
2781 if (isl_basic_set_free_div(tab
->bset
, 1) < 0)
2784 tab
->samples
->n_col
--;
2786 case isl_tab_undo_saved_basis
:
2787 if (restore_basis(tab
, undo
->u
.col_var
) < 0)
2790 case isl_tab_undo_drop_sample
:
2793 case isl_tab_undo_saved_samples
:
2794 drop_samples_since(tab
, undo
->u
.n
);
2796 case isl_tab_undo_callback
:
2797 return undo
->u
.callback
->run(undo
->u
.callback
);
2799 isl_assert(tab
->mat
->ctx
, 0, return -1);
2804 /* Return the tableau to the state it was in when the snapshot "snap"
2807 int isl_tab_rollback(struct isl_tab
*tab
, struct isl_tab_undo
*snap
)
2809 struct isl_tab_undo
*undo
, *next
;
2815 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
2819 if (perform_undo(tab
, undo
) < 0) {
2833 /* The given row "row" represents an inequality violated by all
2834 * points in the tableau. Check for some special cases of such
2835 * separating constraints.
2836 * In particular, if the row has been reduced to the constant -1,
2837 * then we know the inequality is adjacent (but opposite) to
2838 * an equality in the tableau.
2839 * If the row has been reduced to r = -1 -r', with r' an inequality
2840 * of the tableau, then the inequality is adjacent (but opposite)
2841 * to the inequality r'.
2843 static enum isl_ineq_type
separation_type(struct isl_tab
*tab
, unsigned row
)
2846 unsigned off
= 2 + tab
->M
;
2849 return isl_ineq_separate
;
2851 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
2852 return isl_ineq_separate
;
2853 if (!isl_int_is_negone(tab
->mat
->row
[row
][1]))
2854 return isl_ineq_separate
;
2856 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
2857 tab
->n_col
- tab
->n_dead
);
2859 return isl_ineq_adj_eq
;
2861 if (!isl_int_is_negone(tab
->mat
->row
[row
][off
+ tab
->n_dead
+ pos
]))
2862 return isl_ineq_separate
;
2864 pos
= isl_seq_first_non_zero(
2865 tab
->mat
->row
[row
] + off
+ tab
->n_dead
+ pos
+ 1,
2866 tab
->n_col
- tab
->n_dead
- pos
- 1);
2868 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
2871 /* Check the effect of inequality "ineq" on the tableau "tab".
2873 * isl_ineq_redundant: satisfied by all points in the tableau
2874 * isl_ineq_separate: satisfied by no point in the tableau
2875 * isl_ineq_cut: satisfied by some by not all points
2876 * isl_ineq_adj_eq: adjacent to an equality
2877 * isl_ineq_adj_ineq: adjacent to an inequality.
2879 enum isl_ineq_type
isl_tab_ineq_type(struct isl_tab
*tab
, isl_int
*ineq
)
2881 enum isl_ineq_type type
= isl_ineq_error
;
2882 struct isl_tab_undo
*snap
= NULL
;
2887 return isl_ineq_error
;
2889 if (isl_tab_extend_cons(tab
, 1) < 0)
2890 return isl_ineq_error
;
2892 snap
= isl_tab_snap(tab
);
2894 con
= isl_tab_add_row(tab
, ineq
);
2898 row
= tab
->con
[con
].index
;
2899 if (isl_tab_row_is_redundant(tab
, row
))
2900 type
= isl_ineq_redundant
;
2901 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
2903 isl_int_abs_ge(tab
->mat
->row
[row
][1],
2904 tab
->mat
->row
[row
][0]))) {
2905 int nonneg
= at_least_zero(tab
, &tab
->con
[con
]);
2909 type
= isl_ineq_cut
;
2911 type
= separation_type(tab
, row
);
2913 int red
= con_is_redundant(tab
, &tab
->con
[con
]);
2917 type
= isl_ineq_cut
;
2919 type
= isl_ineq_redundant
;
2922 if (isl_tab_rollback(tab
, snap
))
2923 return isl_ineq_error
;
2926 return isl_ineq_error
;
2929 void isl_tab_dump(struct isl_tab
*tab
, FILE *out
, int indent
)
2935 fprintf(out
, "%*snull tab\n", indent
, "");
2938 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
2939 tab
->n_redundant
, tab
->n_dead
);
2941 fprintf(out
, ", rational");
2943 fprintf(out
, ", empty");
2945 fprintf(out
, "%*s[", indent
, "");
2946 for (i
= 0; i
< tab
->n_var
; ++i
) {
2948 fprintf(out
, (i
== tab
->n_param
||
2949 i
== tab
->n_var
- tab
->n_div
) ? "; "
2951 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
2953 tab
->var
[i
].is_zero
? " [=0]" :
2954 tab
->var
[i
].is_redundant
? " [R]" : "");
2956 fprintf(out
, "]\n");
2957 fprintf(out
, "%*s[", indent
, "");
2958 for (i
= 0; i
< tab
->n_con
; ++i
) {
2961 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
2963 tab
->con
[i
].is_zero
? " [=0]" :
2964 tab
->con
[i
].is_redundant
? " [R]" : "");
2966 fprintf(out
, "]\n");
2967 fprintf(out
, "%*s[", indent
, "");
2968 for (i
= 0; i
< tab
->n_row
; ++i
) {
2969 const char *sign
= "";
2972 if (tab
->row_sign
) {
2973 if (tab
->row_sign
[i
] == isl_tab_row_unknown
)
2975 else if (tab
->row_sign
[i
] == isl_tab_row_neg
)
2977 else if (tab
->row_sign
[i
] == isl_tab_row_pos
)
2982 fprintf(out
, "r%d: %d%s%s", i
, tab
->row_var
[i
],
2983 isl_tab_var_from_row(tab
, i
)->is_nonneg
? " [>=0]" : "", sign
);
2985 fprintf(out
, "]\n");
2986 fprintf(out
, "%*s[", indent
, "");
2987 for (i
= 0; i
< tab
->n_col
; ++i
) {
2990 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
2991 var_from_col(tab
, i
)->is_nonneg
? " [>=0]" : "");
2993 fprintf(out
, "]\n");
2994 r
= tab
->mat
->n_row
;
2995 tab
->mat
->n_row
= tab
->n_row
;
2996 c
= tab
->mat
->n_col
;
2997 tab
->mat
->n_col
= 2 + tab
->M
+ tab
->n_col
;
2998 isl_mat_dump(tab
->mat
, out
, indent
);
2999 tab
->mat
->n_row
= r
;
3000 tab
->mat
->n_col
= c
;
3002 isl_basic_set_dump(tab
->bset
, out
, indent
);