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 struct isl_tab
*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) {
941 /* Update the rows signs after a pivot of "row" and "col", with "row_sgn"
942 * the original sign of the pivot element.
943 * We only keep track of row signs during PILP solving and in this case
944 * we only pivot a row with negative sign (meaning the value is always
945 * non-positive) using a positive pivot element.
947 * For each row j, the new value of the parametric constant is equal to
949 * a_j0 - a_jc a_r0/a_rc
951 * where a_j0 is the original parametric constant, a_rc is the pivot element,
952 * a_r0 is the parametric constant of the pivot row and a_jc is the
953 * pivot column entry of the row j.
954 * Since a_r0 is non-positive and a_rc is positive, the sign of row j
955 * remains the same if a_jc has the same sign as the row j or if
956 * a_jc is zero. In all other cases, we reset the sign to "unknown".
958 static void update_row_sign(struct isl_tab
*tab
, int row
, int col
, int row_sgn
)
961 struct isl_mat
*mat
= tab
->mat
;
962 unsigned off
= 2 + tab
->M
;
967 if (tab
->row_sign
[row
] == 0)
969 isl_assert(mat
->ctx
, row_sgn
> 0, return);
970 isl_assert(mat
->ctx
, tab
->row_sign
[row
] == isl_tab_row_neg
, return);
971 tab
->row_sign
[row
] = isl_tab_row_pos
;
972 for (i
= 0; i
< tab
->n_row
; ++i
) {
976 s
= isl_int_sgn(mat
->row
[i
][off
+ col
]);
979 if (!tab
->row_sign
[i
])
981 if (s
< 0 && tab
->row_sign
[i
] == isl_tab_row_neg
)
983 if (s
> 0 && tab
->row_sign
[i
] == isl_tab_row_pos
)
985 tab
->row_sign
[i
] = isl_tab_row_unknown
;
989 /* Given a row number "row" and a column number "col", pivot the tableau
990 * such that the associated variables are interchanged.
991 * The given row in the tableau expresses
993 * x_r = a_r0 + \sum_i a_ri x_i
997 * x_c = 1/a_rc x_r - a_r0/a_rc + sum_{i \ne r} -a_ri/a_rc
999 * Substituting this equality into the other rows
1001 * x_j = a_j0 + \sum_i a_ji x_i
1003 * with a_jc \ne 0, we obtain
1005 * 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
1012 * where i is any other column and j is any other row,
1013 * is therefore transformed into
1015 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1016 * 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)
1018 * The transformation is performed along the following steps
1020 * d_r/n_rc n_ri/n_rc
1023 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1026 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1027 * n_jc/(|n_rc| d_j) n_ji/(|n_rc| d_j)
1029 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1030 * n_jc/(|n_rc| d_j) (n_ji |n_rc|)/(|n_rc| d_j)
1032 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1033 * n_jc/(|n_rc| d_j) (n_ji |n_rc| - s(n_rc)n_jc n_ri)/(|n_rc| d_j)
1035 * s(n_rc)d_r/|n_rc| -s(n_rc)n_ri/|n_rc|
1036 * 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)
1039 int isl_tab_pivot(struct isl_tab
*tab
, int row
, int col
)
1044 struct isl_mat
*mat
= tab
->mat
;
1045 struct isl_tab_var
*var
;
1046 unsigned off
= 2 + tab
->M
;
1048 isl_int_swap(mat
->row
[row
][0], mat
->row
[row
][off
+ col
]);
1049 sgn
= isl_int_sgn(mat
->row
[row
][0]);
1051 isl_int_neg(mat
->row
[row
][0], mat
->row
[row
][0]);
1052 isl_int_neg(mat
->row
[row
][off
+ col
], mat
->row
[row
][off
+ col
]);
1054 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1055 if (j
== off
- 1 + col
)
1057 isl_int_neg(mat
->row
[row
][1 + j
], mat
->row
[row
][1 + j
]);
1059 if (!isl_int_is_one(mat
->row
[row
][0]))
1060 isl_seq_normalize(mat
->ctx
, mat
->row
[row
], off
+ tab
->n_col
);
1061 for (i
= 0; i
< tab
->n_row
; ++i
) {
1064 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1066 isl_int_mul(mat
->row
[i
][0], mat
->row
[i
][0], mat
->row
[row
][0]);
1067 for (j
= 0; j
< off
- 1 + tab
->n_col
; ++j
) {
1068 if (j
== off
- 1 + col
)
1070 isl_int_mul(mat
->row
[i
][1 + j
],
1071 mat
->row
[i
][1 + j
], mat
->row
[row
][0]);
1072 isl_int_addmul(mat
->row
[i
][1 + j
],
1073 mat
->row
[i
][off
+ col
], mat
->row
[row
][1 + j
]);
1075 isl_int_mul(mat
->row
[i
][off
+ col
],
1076 mat
->row
[i
][off
+ col
], mat
->row
[row
][off
+ col
]);
1077 if (!isl_int_is_one(mat
->row
[i
][0]))
1078 isl_seq_normalize(mat
->ctx
, mat
->row
[i
], off
+ tab
->n_col
);
1080 t
= tab
->row_var
[row
];
1081 tab
->row_var
[row
] = tab
->col_var
[col
];
1082 tab
->col_var
[col
] = t
;
1083 var
= isl_tab_var_from_row(tab
, row
);
1086 var
= var_from_col(tab
, col
);
1089 update_row_sign(tab
, row
, col
, sgn
);
1092 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
1093 if (isl_int_is_zero(mat
->row
[i
][off
+ col
]))
1095 if (!isl_tab_var_from_row(tab
, i
)->frozen
&&
1096 isl_tab_row_is_redundant(tab
, i
)) {
1097 int redo
= isl_tab_mark_redundant(tab
, i
);
1107 /* If "var" represents a column variable, then pivot is up (sgn > 0)
1108 * or down (sgn < 0) to a row. The variable is assumed not to be
1109 * unbounded in the specified direction.
1110 * If sgn = 0, then the variable is unbounded in both directions,
1111 * and we pivot with any row we can find.
1113 static int to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
) WARN_UNUSED
;
1114 static int to_row(struct isl_tab
*tab
, struct isl_tab_var
*var
, int sign
)
1117 unsigned off
= 2 + tab
->M
;
1123 for (r
= tab
->n_redundant
; r
< tab
->n_row
; ++r
)
1124 if (!isl_int_is_zero(tab
->mat
->row
[r
][off
+var
->index
]))
1126 isl_assert(tab
->mat
->ctx
, r
< tab
->n_row
, return -1);
1128 r
= pivot_row(tab
, NULL
, sign
, var
->index
);
1129 isl_assert(tab
->mat
->ctx
, r
>= 0, return -1);
1132 return isl_tab_pivot(tab
, r
, var
->index
);
1135 static void check_table(struct isl_tab
*tab
)
1141 for (i
= 0; i
< tab
->n_row
; ++i
) {
1142 if (!isl_tab_var_from_row(tab
, i
)->is_nonneg
)
1144 assert(!isl_int_is_neg(tab
->mat
->row
[i
][1]));
1148 /* Return the sign of the maximal value of "var".
1149 * If the sign is not negative, then on return from this function,
1150 * the sample value will also be non-negative.
1152 * If "var" is manifestly unbounded wrt positive values, we are done.
1153 * Otherwise, we pivot the variable up to a row if needed
1154 * Then we continue pivoting down until either
1155 * - no more down pivots can be performed
1156 * - the sample value is positive
1157 * - the variable is pivoted into a manifestly unbounded column
1159 static int sign_of_max(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1163 if (max_is_manifestly_unbounded(tab
, var
))
1165 if (to_row(tab
, var
, 1) < 0)
1167 while (!isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1168 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1170 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1171 if (isl_tab_pivot(tab
, row
, col
) < 0)
1173 if (!var
->is_row
) /* manifestly unbounded */
1179 static int row_is_neg(struct isl_tab
*tab
, int row
)
1182 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1183 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1185 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1187 return isl_int_is_neg(tab
->mat
->row
[row
][1]);
1190 static int row_sgn(struct isl_tab
*tab
, int row
)
1193 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1194 if (!isl_int_is_zero(tab
->mat
->row
[row
][2]))
1195 return isl_int_sgn(tab
->mat
->row
[row
][2]);
1197 return isl_int_sgn(tab
->mat
->row
[row
][1]);
1200 /* Perform pivots until the row variable "var" has a non-negative
1201 * sample value or until no more upward pivots can be performed.
1202 * Return the sign of the sample value after the pivots have been
1205 static int restore_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1209 while (row_is_neg(tab
, var
->index
)) {
1210 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1213 if (isl_tab_pivot(tab
, row
, col
) < 0)
1215 if (!var
->is_row
) /* manifestly unbounded */
1218 return row_sgn(tab
, var
->index
);
1221 /* Perform pivots until we are sure that the row variable "var"
1222 * can attain non-negative values. After return from this
1223 * function, "var" is still a row variable, but its sample
1224 * value may not be non-negative, even if the function returns 1.
1226 static int at_least_zero(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1230 while (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1231 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1234 if (row
== var
->index
) /* manifestly unbounded */
1236 if (isl_tab_pivot(tab
, row
, col
) < 0)
1239 return !isl_int_is_neg(tab
->mat
->row
[var
->index
][1]);
1242 /* Return a negative value if "var" can attain negative values.
1243 * Return a non-negative value otherwise.
1245 * If "var" is manifestly unbounded wrt negative values, we are done.
1246 * Otherwise, if var is in a column, we can pivot it down to a row.
1247 * Then we continue pivoting down until either
1248 * - the pivot would result in a manifestly unbounded column
1249 * => we don't perform the pivot, but simply return -1
1250 * - no more down pivots can be performed
1251 * - the sample value is negative
1252 * If the sample value becomes negative and the variable is supposed
1253 * to be nonnegative, then we undo the last pivot.
1254 * However, if the last pivot has made the pivoting variable
1255 * obviously redundant, then it may have moved to another row.
1256 * In that case we look for upward pivots until we reach a non-negative
1259 static int sign_of_min(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1262 struct isl_tab_var
*pivot_var
= NULL
;
1264 if (min_is_manifestly_unbounded(tab
, var
))
1268 row
= pivot_row(tab
, NULL
, -1, col
);
1269 pivot_var
= var_from_col(tab
, col
);
1270 if (isl_tab_pivot(tab
, row
, col
) < 0)
1272 if (var
->is_redundant
)
1274 if (isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1275 if (var
->is_nonneg
) {
1276 if (!pivot_var
->is_redundant
&&
1277 pivot_var
->index
== row
) {
1278 if (isl_tab_pivot(tab
, row
, col
) < 0)
1281 if (restore_row(tab
, var
) < -1)
1287 if (var
->is_redundant
)
1289 while (!isl_int_is_neg(tab
->mat
->row
[var
->index
][1])) {
1290 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1291 if (row
== var
->index
)
1294 return isl_int_sgn(tab
->mat
->row
[var
->index
][1]);
1295 pivot_var
= var_from_col(tab
, col
);
1296 if (isl_tab_pivot(tab
, row
, col
) < 0)
1298 if (var
->is_redundant
)
1301 if (pivot_var
&& var
->is_nonneg
) {
1302 /* pivot back to non-negative value */
1303 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
) {
1304 if (isl_tab_pivot(tab
, row
, col
) < 0)
1307 if (restore_row(tab
, var
) < -1)
1313 static int row_at_most_neg_one(struct isl_tab
*tab
, int row
)
1316 if (isl_int_is_pos(tab
->mat
->row
[row
][2]))
1318 if (isl_int_is_neg(tab
->mat
->row
[row
][2]))
1321 return isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
1322 isl_int_abs_ge(tab
->mat
->row
[row
][1],
1323 tab
->mat
->row
[row
][0]);
1326 /* Return 1 if "var" can attain values <= -1.
1327 * Return 0 otherwise.
1329 * The sample value of "var" is assumed to be non-negative when the
1330 * the function is called and will be made non-negative again before
1331 * the function returns.
1333 int isl_tab_min_at_most_neg_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1336 struct isl_tab_var
*pivot_var
;
1338 if (min_is_manifestly_unbounded(tab
, var
))
1342 row
= pivot_row(tab
, NULL
, -1, col
);
1343 pivot_var
= var_from_col(tab
, col
);
1344 if (isl_tab_pivot(tab
, row
, col
) < 0)
1346 if (var
->is_redundant
)
1348 if (row_at_most_neg_one(tab
, var
->index
)) {
1349 if (var
->is_nonneg
) {
1350 if (!pivot_var
->is_redundant
&&
1351 pivot_var
->index
== row
) {
1352 if (isl_tab_pivot(tab
, row
, col
) < 0)
1355 if (restore_row(tab
, var
) < -1)
1361 if (var
->is_redundant
)
1364 find_pivot(tab
, var
, var
, -1, &row
, &col
);
1365 if (row
== var
->index
)
1369 pivot_var
= var_from_col(tab
, col
);
1370 if (isl_tab_pivot(tab
, row
, col
) < 0)
1372 if (var
->is_redundant
)
1374 } while (!row_at_most_neg_one(tab
, var
->index
));
1375 if (var
->is_nonneg
) {
1376 /* pivot back to non-negative value */
1377 if (!pivot_var
->is_redundant
&& pivot_var
->index
== row
)
1378 if (isl_tab_pivot(tab
, row
, col
) < 0)
1380 if (restore_row(tab
, var
) < -1)
1386 /* Return 1 if "var" can attain values >= 1.
1387 * Return 0 otherwise.
1389 static int at_least_one(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1394 if (max_is_manifestly_unbounded(tab
, var
))
1396 if (to_row(tab
, var
, 1) < 0)
1398 r
= tab
->mat
->row
[var
->index
];
1399 while (isl_int_lt(r
[1], r
[0])) {
1400 find_pivot(tab
, var
, var
, 1, &row
, &col
);
1402 return isl_int_ge(r
[1], r
[0]);
1403 if (row
== var
->index
) /* manifestly unbounded */
1405 if (isl_tab_pivot(tab
, row
, col
) < 0)
1411 static void swap_cols(struct isl_tab
*tab
, int col1
, int col2
)
1414 unsigned off
= 2 + tab
->M
;
1415 t
= tab
->col_var
[col1
];
1416 tab
->col_var
[col1
] = tab
->col_var
[col2
];
1417 tab
->col_var
[col2
] = t
;
1418 var_from_col(tab
, col1
)->index
= col1
;
1419 var_from_col(tab
, col2
)->index
= col2
;
1420 tab
->mat
= isl_mat_swap_cols(tab
->mat
, off
+ col1
, off
+ col2
);
1423 /* Mark column with index "col" as representing a zero variable.
1424 * If we may need to undo the operation the column is kept,
1425 * but no longer considered.
1426 * Otherwise, the column is simply removed.
1428 * The column may be interchanged with some other column. If it
1429 * is interchanged with a later column, return 1. Otherwise return 0.
1430 * If the columns are checked in order in the calling function,
1431 * then a return value of 1 means that the column with the given
1432 * column number may now contain a different column that
1433 * hasn't been checked yet.
1435 int isl_tab_kill_col(struct isl_tab
*tab
, int col
)
1437 var_from_col(tab
, col
)->is_zero
= 1;
1438 if (tab
->need_undo
) {
1439 if (isl_tab_push_var(tab
, isl_tab_undo_zero
,
1440 var_from_col(tab
, col
)) < 0)
1442 if (col
!= tab
->n_dead
)
1443 swap_cols(tab
, col
, tab
->n_dead
);
1447 if (col
!= tab
->n_col
- 1)
1448 swap_cols(tab
, col
, tab
->n_col
- 1);
1449 var_from_col(tab
, tab
->n_col
- 1)->index
= -1;
1455 /* Row variable "var" is non-negative and cannot attain any values
1456 * larger than zero. This means that the coefficients of the unrestricted
1457 * column variables are zero and that the coefficients of the non-negative
1458 * column variables are zero or negative.
1459 * Each of the non-negative variables with a negative coefficient can
1460 * then also be written as the negative sum of non-negative variables
1461 * and must therefore also be zero.
1463 static int close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
1464 static int close_row(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1467 struct isl_mat
*mat
= tab
->mat
;
1468 unsigned off
= 2 + tab
->M
;
1470 isl_assert(tab
->mat
->ctx
, var
->is_nonneg
, return -1);
1473 if (isl_tab_push_var(tab
, isl_tab_undo_zero
, var
) < 0)
1475 for (j
= tab
->n_dead
; j
< tab
->n_col
; ++j
) {
1476 if (isl_int_is_zero(mat
->row
[var
->index
][off
+ j
]))
1478 isl_assert(tab
->mat
->ctx
,
1479 isl_int_is_neg(mat
->row
[var
->index
][off
+ j
]), return -1);
1480 if (isl_tab_kill_col(tab
, j
))
1483 if (isl_tab_mark_redundant(tab
, var
->index
) < 0)
1488 /* Add a constraint to the tableau and allocate a row for it.
1489 * Return the index into the constraint array "con".
1491 int isl_tab_allocate_con(struct isl_tab
*tab
)
1495 isl_assert(tab
->mat
->ctx
, tab
->n_row
< tab
->mat
->n_row
, return -1);
1496 isl_assert(tab
->mat
->ctx
, tab
->n_con
< tab
->max_con
, return -1);
1499 tab
->con
[r
].index
= tab
->n_row
;
1500 tab
->con
[r
].is_row
= 1;
1501 tab
->con
[r
].is_nonneg
= 0;
1502 tab
->con
[r
].is_zero
= 0;
1503 tab
->con
[r
].is_redundant
= 0;
1504 tab
->con
[r
].frozen
= 0;
1505 tab
->con
[r
].negated
= 0;
1506 tab
->row_var
[tab
->n_row
] = ~r
;
1510 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]) < 0)
1516 /* Add a variable to the tableau and allocate a column for it.
1517 * Return the index into the variable array "var".
1519 int isl_tab_allocate_var(struct isl_tab
*tab
)
1523 unsigned off
= 2 + tab
->M
;
1525 isl_assert(tab
->mat
->ctx
, tab
->n_col
< tab
->mat
->n_col
, return -1);
1526 isl_assert(tab
->mat
->ctx
, tab
->n_var
< tab
->max_var
, return -1);
1529 tab
->var
[r
].index
= tab
->n_col
;
1530 tab
->var
[r
].is_row
= 0;
1531 tab
->var
[r
].is_nonneg
= 0;
1532 tab
->var
[r
].is_zero
= 0;
1533 tab
->var
[r
].is_redundant
= 0;
1534 tab
->var
[r
].frozen
= 0;
1535 tab
->var
[r
].negated
= 0;
1536 tab
->col_var
[tab
->n_col
] = r
;
1538 for (i
= 0; i
< tab
->n_row
; ++i
)
1539 isl_int_set_si(tab
->mat
->row
[i
][off
+ tab
->n_col
], 0);
1543 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->var
[r
]) < 0)
1549 /* Add a row to the tableau. The row is given as an affine combination
1550 * of the original variables and needs to be expressed in terms of the
1553 * We add each term in turn.
1554 * If r = n/d_r is the current sum and we need to add k x, then
1555 * if x is a column variable, we increase the numerator of
1556 * this column by k d_r
1557 * if x = f/d_x is a row variable, then the new representation of r is
1559 * n k f d_x/g n + d_r/g k f m/d_r n + m/d_g k f
1560 * --- + --- = ------------------- = -------------------
1561 * d_r d_r d_r d_x/g m
1563 * with g the gcd of d_r and d_x and m the lcm of d_r and d_x.
1565 int isl_tab_add_row(struct isl_tab
*tab
, isl_int
*line
)
1571 unsigned off
= 2 + tab
->M
;
1573 r
= isl_tab_allocate_con(tab
);
1579 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1580 isl_int_set_si(row
[0], 1);
1581 isl_int_set(row
[1], line
[0]);
1582 isl_seq_clr(row
+ 2, tab
->M
+ tab
->n_col
);
1583 for (i
= 0; i
< tab
->n_var
; ++i
) {
1584 if (tab
->var
[i
].is_zero
)
1586 if (tab
->var
[i
].is_row
) {
1588 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1589 isl_int_swap(a
, row
[0]);
1590 isl_int_divexact(a
, row
[0], a
);
1592 row
[0], tab
->mat
->row
[tab
->var
[i
].index
][0]);
1593 isl_int_mul(b
, b
, line
[1 + i
]);
1594 isl_seq_combine(row
+ 1, a
, row
+ 1,
1595 b
, tab
->mat
->row
[tab
->var
[i
].index
] + 1,
1596 1 + tab
->M
+ tab
->n_col
);
1598 isl_int_addmul(row
[off
+ tab
->var
[i
].index
],
1599 line
[1 + i
], row
[0]);
1600 if (tab
->M
&& i
>= tab
->n_param
&& i
< tab
->n_var
- tab
->n_div
)
1601 isl_int_submul(row
[2], line
[1 + i
], row
[0]);
1603 isl_seq_normalize(tab
->mat
->ctx
, row
, off
+ tab
->n_col
);
1608 tab
->row_sign
[tab
->con
[r
].index
] = 0;
1613 static int drop_row(struct isl_tab
*tab
, int row
)
1615 isl_assert(tab
->mat
->ctx
, ~tab
->row_var
[row
] == tab
->n_con
- 1, return -1);
1616 if (row
!= tab
->n_row
- 1)
1617 swap_rows(tab
, row
, tab
->n_row
- 1);
1623 static int drop_col(struct isl_tab
*tab
, int col
)
1625 isl_assert(tab
->mat
->ctx
, tab
->col_var
[col
] == tab
->n_var
- 1, return -1);
1626 if (col
!= tab
->n_col
- 1)
1627 swap_cols(tab
, col
, tab
->n_col
- 1);
1633 /* Add inequality "ineq" and check if it conflicts with the
1634 * previously added constraints or if it is obviously redundant.
1636 struct isl_tab
*isl_tab_add_ineq(struct isl_tab
*tab
, isl_int
*ineq
)
1645 struct isl_basic_set
*bset
= tab
->bset
;
1647 isl_assert(tab
->mat
->ctx
, tab
->n_eq
== bset
->n_eq
, goto error
);
1648 isl_assert(tab
->mat
->ctx
,
1649 tab
->n_con
== bset
->n_eq
+ bset
->n_ineq
, goto error
);
1650 tab
->bset
= isl_basic_set_add_ineq(tab
->bset
, ineq
);
1651 if (isl_tab_push(tab
, isl_tab_undo_bset_ineq
) < 0)
1658 isl_int_swap(ineq
[0], cst
);
1660 r
= isl_tab_add_row(tab
, ineq
);
1662 isl_int_swap(ineq
[0], cst
);
1667 tab
->con
[r
].is_nonneg
= 1;
1668 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1670 if (isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
)) {
1671 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1676 sgn
= restore_row(tab
, &tab
->con
[r
]);
1680 return isl_tab_mark_empty(tab
);
1681 if (tab
->con
[r
].is_row
&& isl_tab_row_is_redundant(tab
, tab
->con
[r
].index
))
1682 if (isl_tab_mark_redundant(tab
, tab
->con
[r
].index
) < 0)
1690 /* Pivot a non-negative variable down until it reaches the value zero
1691 * and then pivot the variable into a column position.
1693 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
1694 static int to_col(struct isl_tab
*tab
, struct isl_tab_var
*var
)
1698 unsigned off
= 2 + tab
->M
;
1703 while (isl_int_is_pos(tab
->mat
->row
[var
->index
][1])) {
1704 find_pivot(tab
, var
, NULL
, -1, &row
, &col
);
1705 isl_assert(tab
->mat
->ctx
, row
!= -1, return -1);
1706 if (isl_tab_pivot(tab
, row
, col
) < 0)
1712 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
)
1713 if (!isl_int_is_zero(tab
->mat
->row
[var
->index
][off
+ i
]))
1716 isl_assert(tab
->mat
->ctx
, i
< tab
->n_col
, return -1);
1717 if (isl_tab_pivot(tab
, var
->index
, i
) < 0)
1723 /* We assume Gaussian elimination has been performed on the equalities.
1724 * The equalities can therefore never conflict.
1725 * Adding the equalities is currently only really useful for a later call
1726 * to isl_tab_ineq_type.
1728 static struct isl_tab
*add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1735 r
= isl_tab_add_row(tab
, eq
);
1739 r
= tab
->con
[r
].index
;
1740 i
= isl_seq_first_non_zero(tab
->mat
->row
[r
] + 2 + tab
->M
+ tab
->n_dead
,
1741 tab
->n_col
- tab
->n_dead
);
1742 isl_assert(tab
->mat
->ctx
, i
>= 0, goto error
);
1744 if (isl_tab_pivot(tab
, r
, i
) < 0)
1746 if (isl_tab_kill_col(tab
, i
) < 0)
1756 static int row_is_manifestly_zero(struct isl_tab
*tab
, int row
)
1758 unsigned off
= 2 + tab
->M
;
1760 if (!isl_int_is_zero(tab
->mat
->row
[row
][1]))
1762 if (tab
->M
&& !isl_int_is_zero(tab
->mat
->row
[row
][2]))
1764 return isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
1765 tab
->n_col
- tab
->n_dead
) == -1;
1768 /* Add an equality that is known to be valid for the given tableau.
1770 struct isl_tab
*isl_tab_add_valid_eq(struct isl_tab
*tab
, isl_int
*eq
)
1772 struct isl_tab_var
*var
;
1777 r
= isl_tab_add_row(tab
, eq
);
1783 if (row_is_manifestly_zero(tab
, r
)) {
1785 if (isl_tab_mark_redundant(tab
, r
) < 0)
1790 if (isl_int_is_neg(tab
->mat
->row
[r
][1])) {
1791 isl_seq_neg(tab
->mat
->row
[r
] + 1, tab
->mat
->row
[r
] + 1,
1796 if (to_col(tab
, var
) < 0)
1799 if (isl_tab_kill_col(tab
, var
->index
) < 0)
1808 static int add_zero_row(struct isl_tab
*tab
)
1813 r
= isl_tab_allocate_con(tab
);
1817 row
= tab
->mat
->row
[tab
->con
[r
].index
];
1818 isl_seq_clr(row
+ 1, 1 + tab
->M
+ tab
->n_col
);
1819 isl_int_set_si(row
[0], 1);
1824 /* Add equality "eq" and check if it conflicts with the
1825 * previously added constraints or if it is obviously redundant.
1827 struct isl_tab
*isl_tab_add_eq(struct isl_tab
*tab
, isl_int
*eq
)
1829 struct isl_tab_undo
*snap
= NULL
;
1830 struct isl_tab_var
*var
;
1838 isl_assert(tab
->mat
->ctx
, !tab
->M
, goto error
);
1841 snap
= isl_tab_snap(tab
);
1845 isl_int_swap(eq
[0], cst
);
1847 r
= isl_tab_add_row(tab
, eq
);
1849 isl_int_swap(eq
[0], cst
);
1857 if (row_is_manifestly_zero(tab
, row
)) {
1859 if (isl_tab_rollback(tab
, snap
) < 0)
1867 tab
->bset
= isl_basic_set_add_ineq(tab
->bset
, eq
);
1868 if (isl_tab_push(tab
, isl_tab_undo_bset_ineq
) < 0)
1870 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1871 tab
->bset
= isl_basic_set_add_ineq(tab
->bset
, eq
);
1872 isl_seq_neg(eq
, eq
, 1 + tab
->n_var
);
1873 if (isl_tab_push(tab
, isl_tab_undo_bset_ineq
) < 0)
1877 if (add_zero_row(tab
) < 0)
1881 sgn
= isl_int_sgn(tab
->mat
->row
[row
][1]);
1884 isl_seq_neg(tab
->mat
->row
[row
] + 1, tab
->mat
->row
[row
] + 1,
1891 sgn
= sign_of_max(tab
, var
);
1895 return isl_tab_mark_empty(tab
);
1899 if (to_col(tab
, var
) < 0)
1902 if (isl_tab_kill_col(tab
, var
->index
) < 0)
1911 struct isl_tab
*isl_tab_from_basic_map(struct isl_basic_map
*bmap
)
1914 struct isl_tab
*tab
;
1918 tab
= isl_tab_alloc(bmap
->ctx
,
1919 isl_basic_map_total_dim(bmap
) + bmap
->n_ineq
+ 1,
1920 isl_basic_map_total_dim(bmap
), 0);
1923 tab
->rational
= ISL_F_ISSET(bmap
, ISL_BASIC_MAP_RATIONAL
);
1924 if (ISL_F_ISSET(bmap
, ISL_BASIC_MAP_EMPTY
))
1925 return isl_tab_mark_empty(tab
);
1926 for (i
= 0; i
< bmap
->n_eq
; ++i
) {
1927 tab
= add_eq(tab
, bmap
->eq
[i
]);
1931 for (i
= 0; i
< bmap
->n_ineq
; ++i
) {
1932 tab
= isl_tab_add_ineq(tab
, bmap
->ineq
[i
]);
1933 if (!tab
|| tab
->empty
)
1939 struct isl_tab
*isl_tab_from_basic_set(struct isl_basic_set
*bset
)
1941 return isl_tab_from_basic_map((struct isl_basic_map
*)bset
);
1944 /* Construct a tableau corresponding to the recession cone of "bset".
1946 struct isl_tab
*isl_tab_from_recession_cone(struct isl_basic_set
*bset
)
1950 struct isl_tab
*tab
;
1954 tab
= isl_tab_alloc(bset
->ctx
, bset
->n_eq
+ bset
->n_ineq
,
1955 isl_basic_set_total_dim(bset
), 0);
1958 tab
->rational
= ISL_F_ISSET(bset
, ISL_BASIC_SET_RATIONAL
);
1962 for (i
= 0; i
< bset
->n_eq
; ++i
) {
1963 isl_int_swap(bset
->eq
[i
][0], cst
);
1964 tab
= add_eq(tab
, bset
->eq
[i
]);
1965 isl_int_swap(bset
->eq
[i
][0], cst
);
1969 for (i
= 0; i
< bset
->n_ineq
; ++i
) {
1971 isl_int_swap(bset
->ineq
[i
][0], cst
);
1972 r
= isl_tab_add_row(tab
, bset
->ineq
[i
]);
1973 isl_int_swap(bset
->ineq
[i
][0], cst
);
1976 tab
->con
[r
].is_nonneg
= 1;
1977 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
1989 /* Assuming "tab" is the tableau of a cone, check if the cone is
1990 * bounded, i.e., if it is empty or only contains the origin.
1992 int isl_tab_cone_is_bounded(struct isl_tab
*tab
)
2000 if (tab
->n_dead
== tab
->n_col
)
2004 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2005 struct isl_tab_var
*var
;
2007 var
= isl_tab_var_from_row(tab
, i
);
2008 if (!var
->is_nonneg
)
2010 sgn
= sign_of_max(tab
, var
);
2015 if (close_row(tab
, var
) < 0)
2019 if (tab
->n_dead
== tab
->n_col
)
2021 if (i
== tab
->n_row
)
2026 int isl_tab_sample_is_integer(struct isl_tab
*tab
)
2033 for (i
= 0; i
< tab
->n_var
; ++i
) {
2035 if (!tab
->var
[i
].is_row
)
2037 row
= tab
->var
[i
].index
;
2038 if (!isl_int_is_divisible_by(tab
->mat
->row
[row
][1],
2039 tab
->mat
->row
[row
][0]))
2045 static struct isl_vec
*extract_integer_sample(struct isl_tab
*tab
)
2048 struct isl_vec
*vec
;
2050 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2054 isl_int_set_si(vec
->block
.data
[0], 1);
2055 for (i
= 0; i
< tab
->n_var
; ++i
) {
2056 if (!tab
->var
[i
].is_row
)
2057 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
2059 int row
= tab
->var
[i
].index
;
2060 isl_int_divexact(vec
->block
.data
[1 + i
],
2061 tab
->mat
->row
[row
][1], tab
->mat
->row
[row
][0]);
2068 struct isl_vec
*isl_tab_get_sample_value(struct isl_tab
*tab
)
2071 struct isl_vec
*vec
;
2077 vec
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_var
);
2083 isl_int_set_si(vec
->block
.data
[0], 1);
2084 for (i
= 0; i
< tab
->n_var
; ++i
) {
2086 if (!tab
->var
[i
].is_row
) {
2087 isl_int_set_si(vec
->block
.data
[1 + i
], 0);
2090 row
= tab
->var
[i
].index
;
2091 isl_int_gcd(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
2092 isl_int_divexact(m
, tab
->mat
->row
[row
][0], m
);
2093 isl_seq_scale(vec
->block
.data
, vec
->block
.data
, m
, 1 + i
);
2094 isl_int_divexact(m
, vec
->block
.data
[0], tab
->mat
->row
[row
][0]);
2095 isl_int_mul(vec
->block
.data
[1 + i
], m
, tab
->mat
->row
[row
][1]);
2097 vec
= isl_vec_normalize(vec
);
2103 /* Update "bmap" based on the results of the tableau "tab".
2104 * In particular, implicit equalities are made explicit, redundant constraints
2105 * are removed and if the sample value happens to be integer, it is stored
2106 * in "bmap" (unless "bmap" already had an integer sample).
2108 * The tableau is assumed to have been created from "bmap" using
2109 * isl_tab_from_basic_map.
2111 struct isl_basic_map
*isl_basic_map_update_from_tab(struct isl_basic_map
*bmap
,
2112 struct isl_tab
*tab
)
2124 bmap
= isl_basic_map_set_to_empty(bmap
);
2126 for (i
= bmap
->n_ineq
- 1; i
>= 0; --i
) {
2127 if (isl_tab_is_equality(tab
, n_eq
+ i
))
2128 isl_basic_map_inequality_to_equality(bmap
, i
);
2129 else if (isl_tab_is_redundant(tab
, n_eq
+ i
))
2130 isl_basic_map_drop_inequality(bmap
, i
);
2132 if (!tab
->rational
&&
2133 !bmap
->sample
&& isl_tab_sample_is_integer(tab
))
2134 bmap
->sample
= extract_integer_sample(tab
);
2138 struct isl_basic_set
*isl_basic_set_update_from_tab(struct isl_basic_set
*bset
,
2139 struct isl_tab
*tab
)
2141 return (struct isl_basic_set
*)isl_basic_map_update_from_tab(
2142 (struct isl_basic_map
*)bset
, tab
);
2145 /* Given a non-negative variable "var", add a new non-negative variable
2146 * that is the opposite of "var", ensuring that var can only attain the
2148 * If var = n/d is a row variable, then the new variable = -n/d.
2149 * If var is a column variables, then the new variable = -var.
2150 * If the new variable cannot attain non-negative values, then
2151 * the resulting tableau is empty.
2152 * Otherwise, we know the value will be zero and we close the row.
2154 static struct isl_tab
*cut_to_hyperplane(struct isl_tab
*tab
,
2155 struct isl_tab_var
*var
)
2160 unsigned off
= 2 + tab
->M
;
2164 isl_assert(tab
->mat
->ctx
, !var
->is_redundant
, goto error
);
2166 if (isl_tab_extend_cons(tab
, 1) < 0)
2170 tab
->con
[r
].index
= tab
->n_row
;
2171 tab
->con
[r
].is_row
= 1;
2172 tab
->con
[r
].is_nonneg
= 0;
2173 tab
->con
[r
].is_zero
= 0;
2174 tab
->con
[r
].is_redundant
= 0;
2175 tab
->con
[r
].frozen
= 0;
2176 tab
->con
[r
].negated
= 0;
2177 tab
->row_var
[tab
->n_row
] = ~r
;
2178 row
= tab
->mat
->row
[tab
->n_row
];
2181 isl_int_set(row
[0], tab
->mat
->row
[var
->index
][0]);
2182 isl_seq_neg(row
+ 1,
2183 tab
->mat
->row
[var
->index
] + 1, 1 + tab
->n_col
);
2185 isl_int_set_si(row
[0], 1);
2186 isl_seq_clr(row
+ 1, 1 + tab
->n_col
);
2187 isl_int_set_si(row
[off
+ var
->index
], -1);
2192 if (isl_tab_push_var(tab
, isl_tab_undo_allocate
, &tab
->con
[r
]) < 0)
2195 sgn
= sign_of_max(tab
, &tab
->con
[r
]);
2199 return isl_tab_mark_empty(tab
);
2200 tab
->con
[r
].is_nonneg
= 1;
2201 if (isl_tab_push_var(tab
, isl_tab_undo_nonneg
, &tab
->con
[r
]) < 0)
2204 if (close_row(tab
, &tab
->con
[r
]) < 0)
2213 /* Given a tableau "tab" and an inequality constraint "con" of the tableau,
2214 * relax the inequality by one. That is, the inequality r >= 0 is replaced
2215 * by r' = r + 1 >= 0.
2216 * If r is a row variable, we simply increase the constant term by one
2217 * (taking into account the denominator).
2218 * If r is a column variable, then we need to modify each row that
2219 * refers to r = r' - 1 by substituting this equality, effectively
2220 * subtracting the coefficient of the column from the constant.
2222 struct isl_tab
*isl_tab_relax(struct isl_tab
*tab
, int con
)
2224 struct isl_tab_var
*var
;
2225 unsigned off
= 2 + tab
->M
;
2230 var
= &tab
->con
[con
];
2232 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
2233 if (to_row(tab
, var
, 1) < 0)
2237 isl_int_add(tab
->mat
->row
[var
->index
][1],
2238 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
2242 for (i
= 0; i
< tab
->n_row
; ++i
) {
2243 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2245 isl_int_sub(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
2246 tab
->mat
->row
[i
][off
+ var
->index
]);
2251 if (isl_tab_push_var(tab
, isl_tab_undo_relax
, var
) < 0)
2260 struct isl_tab
*isl_tab_select_facet(struct isl_tab
*tab
, int con
)
2265 return cut_to_hyperplane(tab
, &tab
->con
[con
]);
2268 static int may_be_equality(struct isl_tab
*tab
, int row
)
2270 unsigned off
= 2 + tab
->M
;
2271 return (tab
->rational
? isl_int_is_zero(tab
->mat
->row
[row
][1])
2272 : isl_int_lt(tab
->mat
->row
[row
][1],
2273 tab
->mat
->row
[row
][0])) &&
2274 isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
2275 tab
->n_col
- tab
->n_dead
) != -1;
2278 /* Check for (near) equalities among the constraints.
2279 * A constraint is an equality if it is non-negative and if
2280 * its maximal value is either
2281 * - zero (in case of rational tableaus), or
2282 * - strictly less than 1 (in case of integer tableaus)
2284 * We first mark all non-redundant and non-dead variables that
2285 * are not frozen and not obviously not an equality.
2286 * Then we iterate over all marked variables if they can attain
2287 * any values larger than zero or at least one.
2288 * If the maximal value is zero, we mark any column variables
2289 * that appear in the row as being zero and mark the row as being redundant.
2290 * Otherwise, if the maximal value is strictly less than one (and the
2291 * tableau is integer), then we restrict the value to being zero
2292 * by adding an opposite non-negative variable.
2294 struct isl_tab
*isl_tab_detect_implicit_equalities(struct isl_tab
*tab
)
2303 if (tab
->n_dead
== tab
->n_col
)
2307 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2308 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2309 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2310 may_be_equality(tab
, i
);
2314 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2315 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2316 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2321 struct isl_tab_var
*var
;
2323 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2324 var
= isl_tab_var_from_row(tab
, i
);
2328 if (i
== tab
->n_row
) {
2329 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2330 var
= var_from_col(tab
, i
);
2334 if (i
== tab
->n_col
)
2339 sgn
= sign_of_max(tab
, var
);
2343 if (close_row(tab
, var
) < 0)
2345 } else if (!tab
->rational
&& !at_least_one(tab
, var
)) {
2346 tab
= cut_to_hyperplane(tab
, var
);
2347 return isl_tab_detect_implicit_equalities(tab
);
2349 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2350 var
= isl_tab_var_from_row(tab
, i
);
2353 if (may_be_equality(tab
, i
))
2366 static int con_is_redundant(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2370 if (tab
->rational
) {
2371 int sgn
= sign_of_min(tab
, var
);
2376 int irred
= isl_tab_min_at_most_neg_one(tab
, var
);
2383 /* Check for (near) redundant constraints.
2384 * A constraint is redundant if it is non-negative and if
2385 * its minimal value (temporarily ignoring the non-negativity) is either
2386 * - zero (in case of rational tableaus), or
2387 * - strictly larger than -1 (in case of integer tableaus)
2389 * We first mark all non-redundant and non-dead variables that
2390 * are not frozen and not obviously negatively unbounded.
2391 * Then we iterate over all marked variables if they can attain
2392 * any values smaller than zero or at most negative one.
2393 * If not, we mark the row as being redundant (assuming it hasn't
2394 * been detected as being obviously redundant in the mean time).
2396 struct isl_tab
*isl_tab_detect_redundant(struct isl_tab
*tab
)
2405 if (tab
->n_redundant
== tab
->n_row
)
2409 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2410 struct isl_tab_var
*var
= isl_tab_var_from_row(tab
, i
);
2411 var
->marked
= !var
->frozen
&& var
->is_nonneg
;
2415 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2416 struct isl_tab_var
*var
= var_from_col(tab
, i
);
2417 var
->marked
= !var
->frozen
&& var
->is_nonneg
&&
2418 !min_is_manifestly_unbounded(tab
, var
);
2423 struct isl_tab_var
*var
;
2425 for (i
= tab
->n_redundant
; i
< tab
->n_row
; ++i
) {
2426 var
= isl_tab_var_from_row(tab
, i
);
2430 if (i
== tab
->n_row
) {
2431 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2432 var
= var_from_col(tab
, i
);
2436 if (i
== tab
->n_col
)
2441 red
= con_is_redundant(tab
, var
);
2444 if (red
&& !var
->is_redundant
)
2445 if (isl_tab_mark_redundant(tab
, var
->index
) < 0)
2447 for (i
= tab
->n_dead
; i
< tab
->n_col
; ++i
) {
2448 var
= var_from_col(tab
, i
);
2451 if (!min_is_manifestly_unbounded(tab
, var
))
2464 int isl_tab_is_equality(struct isl_tab
*tab
, int con
)
2471 if (tab
->con
[con
].is_zero
)
2473 if (tab
->con
[con
].is_redundant
)
2475 if (!tab
->con
[con
].is_row
)
2476 return tab
->con
[con
].index
< tab
->n_dead
;
2478 row
= tab
->con
[con
].index
;
2481 return isl_int_is_zero(tab
->mat
->row
[row
][1]) &&
2482 isl_seq_first_non_zero(tab
->mat
->row
[row
] + 2 + tab
->n_dead
,
2483 tab
->n_col
- tab
->n_dead
) == -1;
2486 /* Return the minimial value of the affine expression "f" with denominator
2487 * "denom" in *opt, *opt_denom, assuming the tableau is not empty and
2488 * the expression cannot attain arbitrarily small values.
2489 * If opt_denom is NULL, then *opt is rounded up to the nearest integer.
2490 * The return value reflects the nature of the result (empty, unbounded,
2491 * minmimal value returned in *opt).
2493 enum isl_lp_result
isl_tab_min(struct isl_tab
*tab
,
2494 isl_int
*f
, isl_int denom
, isl_int
*opt
, isl_int
*opt_denom
,
2498 enum isl_lp_result res
= isl_lp_ok
;
2499 struct isl_tab_var
*var
;
2500 struct isl_tab_undo
*snap
;
2503 return isl_lp_empty
;
2505 snap
= isl_tab_snap(tab
);
2506 r
= isl_tab_add_row(tab
, f
);
2508 return isl_lp_error
;
2510 isl_int_mul(tab
->mat
->row
[var
->index
][0],
2511 tab
->mat
->row
[var
->index
][0], denom
);
2514 find_pivot(tab
, var
, var
, -1, &row
, &col
);
2515 if (row
== var
->index
) {
2516 res
= isl_lp_unbounded
;
2521 if (isl_tab_pivot(tab
, row
, col
) < 0)
2522 return isl_lp_error
;
2524 if (ISL_FL_ISSET(flags
, ISL_TAB_SAVE_DUAL
)) {
2527 isl_vec_free(tab
->dual
);
2528 tab
->dual
= isl_vec_alloc(tab
->mat
->ctx
, 1 + tab
->n_con
);
2530 return isl_lp_error
;
2531 isl_int_set(tab
->dual
->el
[0], tab
->mat
->row
[var
->index
][0]);
2532 for (i
= 0; i
< tab
->n_con
; ++i
) {
2534 if (tab
->con
[i
].is_row
) {
2535 isl_int_set_si(tab
->dual
->el
[1 + i
], 0);
2538 pos
= 2 + tab
->M
+ tab
->con
[i
].index
;
2539 if (tab
->con
[i
].negated
)
2540 isl_int_neg(tab
->dual
->el
[1 + i
],
2541 tab
->mat
->row
[var
->index
][pos
]);
2543 isl_int_set(tab
->dual
->el
[1 + i
],
2544 tab
->mat
->row
[var
->index
][pos
]);
2547 if (opt
&& res
== isl_lp_ok
) {
2549 isl_int_set(*opt
, tab
->mat
->row
[var
->index
][1]);
2550 isl_int_set(*opt_denom
, tab
->mat
->row
[var
->index
][0]);
2552 isl_int_cdiv_q(*opt
, tab
->mat
->row
[var
->index
][1],
2553 tab
->mat
->row
[var
->index
][0]);
2555 if (isl_tab_rollback(tab
, snap
) < 0)
2556 return isl_lp_error
;
2560 int isl_tab_is_redundant(struct isl_tab
*tab
, int con
)
2564 if (tab
->con
[con
].is_zero
)
2566 if (tab
->con
[con
].is_redundant
)
2568 return tab
->con
[con
].is_row
&& tab
->con
[con
].index
< tab
->n_redundant
;
2571 /* Take a snapshot of the tableau that can be restored by s call to
2574 struct isl_tab_undo
*isl_tab_snap(struct isl_tab
*tab
)
2582 /* Undo the operation performed by isl_tab_relax.
2584 static int unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
) WARN_UNUSED
;
2585 static int unrelax(struct isl_tab
*tab
, struct isl_tab_var
*var
)
2587 unsigned off
= 2 + tab
->M
;
2589 if (!var
->is_row
&& !max_is_manifestly_unbounded(tab
, var
))
2590 if (to_row(tab
, var
, 1) < 0)
2594 isl_int_sub(tab
->mat
->row
[var
->index
][1],
2595 tab
->mat
->row
[var
->index
][1], tab
->mat
->row
[var
->index
][0]);
2599 for (i
= 0; i
< tab
->n_row
; ++i
) {
2600 if (isl_int_is_zero(tab
->mat
->row
[i
][off
+ var
->index
]))
2602 isl_int_add(tab
->mat
->row
[i
][1], tab
->mat
->row
[i
][1],
2603 tab
->mat
->row
[i
][off
+ var
->index
]);
2611 static int perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
) WARN_UNUSED
;
2612 static int perform_undo_var(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2614 struct isl_tab_var
*var
= var_from_index(tab
, undo
->u
.var_index
);
2615 switch(undo
->type
) {
2616 case isl_tab_undo_nonneg
:
2619 case isl_tab_undo_redundant
:
2620 var
->is_redundant
= 0;
2623 case isl_tab_undo_zero
:
2628 case isl_tab_undo_allocate
:
2629 if (undo
->u
.var_index
>= 0) {
2630 isl_assert(tab
->mat
->ctx
, !var
->is_row
, return -1);
2631 drop_col(tab
, var
->index
);
2635 if (!max_is_manifestly_unbounded(tab
, var
)) {
2636 if (to_row(tab
, var
, 1) < 0)
2638 } else if (!min_is_manifestly_unbounded(tab
, var
)) {
2639 if (to_row(tab
, var
, -1) < 0)
2642 if (to_row(tab
, var
, 0) < 0)
2645 drop_row(tab
, var
->index
);
2647 case isl_tab_undo_relax
:
2648 return unrelax(tab
, var
);
2654 /* Restore the tableau to the state where the basic variables
2655 * are those in "col_var".
2656 * We first construct a list of variables that are currently in
2657 * the basis, but shouldn't. Then we iterate over all variables
2658 * that should be in the basis and for each one that is currently
2659 * not in the basis, we exchange it with one of the elements of the
2660 * list constructed before.
2661 * We can always find an appropriate variable to pivot with because
2662 * the current basis is mapped to the old basis by a non-singular
2663 * matrix and so we can never end up with a zero row.
2665 static int restore_basis(struct isl_tab
*tab
, int *col_var
)
2669 int *extra
= NULL
; /* current columns that contain bad stuff */
2670 unsigned off
= 2 + tab
->M
;
2672 extra
= isl_alloc_array(tab
->mat
->ctx
, int, tab
->n_col
);
2675 for (i
= 0; i
< tab
->n_col
; ++i
) {
2676 for (j
= 0; j
< tab
->n_col
; ++j
)
2677 if (tab
->col_var
[i
] == col_var
[j
])
2681 extra
[n_extra
++] = i
;
2683 for (i
= 0; i
< tab
->n_col
&& n_extra
> 0; ++i
) {
2684 struct isl_tab_var
*var
;
2687 for (j
= 0; j
< tab
->n_col
; ++j
)
2688 if (col_var
[i
] == tab
->col_var
[j
])
2692 var
= var_from_index(tab
, col_var
[i
]);
2694 for (j
= 0; j
< n_extra
; ++j
)
2695 if (!isl_int_is_zero(tab
->mat
->row
[row
][off
+extra
[j
]]))
2697 isl_assert(tab
->mat
->ctx
, j
< n_extra
, goto error
);
2698 if (isl_tab_pivot(tab
, row
, extra
[j
]) < 0)
2700 extra
[j
] = extra
[--n_extra
];
2712 /* Remove all samples with index n or greater, i.e., those samples
2713 * that were added since we saved this number of samples in
2714 * isl_tab_save_samples.
2716 static void drop_samples_since(struct isl_tab
*tab
, int n
)
2720 for (i
= tab
->n_sample
- 1; i
>= 0 && tab
->n_sample
> n
; --i
) {
2721 if (tab
->sample_index
[i
] < n
)
2724 if (i
!= tab
->n_sample
- 1) {
2725 int t
= tab
->sample_index
[tab
->n_sample
-1];
2726 tab
->sample_index
[tab
->n_sample
-1] = tab
->sample_index
[i
];
2727 tab
->sample_index
[i
] = t
;
2728 isl_mat_swap_rows(tab
->samples
, tab
->n_sample
-1, i
);
2734 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
) WARN_UNUSED
;
2735 static int perform_undo(struct isl_tab
*tab
, struct isl_tab_undo
*undo
)
2737 switch (undo
->type
) {
2738 case isl_tab_undo_empty
:
2741 case isl_tab_undo_nonneg
:
2742 case isl_tab_undo_redundant
:
2743 case isl_tab_undo_zero
:
2744 case isl_tab_undo_allocate
:
2745 case isl_tab_undo_relax
:
2746 return perform_undo_var(tab
, undo
);
2747 case isl_tab_undo_bset_eq
:
2748 return isl_basic_set_free_equality(tab
->bset
, 1);
2749 case isl_tab_undo_bset_ineq
:
2750 return isl_basic_set_free_inequality(tab
->bset
, 1);
2751 case isl_tab_undo_bset_div
:
2752 if (isl_basic_set_free_div(tab
->bset
, 1) < 0)
2755 tab
->samples
->n_col
--;
2757 case isl_tab_undo_saved_basis
:
2758 if (restore_basis(tab
, undo
->u
.col_var
) < 0)
2761 case isl_tab_undo_drop_sample
:
2764 case isl_tab_undo_saved_samples
:
2765 drop_samples_since(tab
, undo
->u
.n
);
2767 case isl_tab_undo_callback
:
2768 return undo
->u
.callback
->run(undo
->u
.callback
);
2770 isl_assert(tab
->mat
->ctx
, 0, return -1);
2775 /* Return the tableau to the state it was in when the snapshot "snap"
2778 int isl_tab_rollback(struct isl_tab
*tab
, struct isl_tab_undo
*snap
)
2780 struct isl_tab_undo
*undo
, *next
;
2786 for (undo
= tab
->top
; undo
&& undo
!= &tab
->bottom
; undo
= next
) {
2790 if (perform_undo(tab
, undo
) < 0) {
2804 /* The given row "row" represents an inequality violated by all
2805 * points in the tableau. Check for some special cases of such
2806 * separating constraints.
2807 * In particular, if the row has been reduced to the constant -1,
2808 * then we know the inequality is adjacent (but opposite) to
2809 * an equality in the tableau.
2810 * If the row has been reduced to r = -1 -r', with r' an inequality
2811 * of the tableau, then the inequality is adjacent (but opposite)
2812 * to the inequality r'.
2814 static enum isl_ineq_type
separation_type(struct isl_tab
*tab
, unsigned row
)
2817 unsigned off
= 2 + tab
->M
;
2820 return isl_ineq_separate
;
2822 if (!isl_int_is_one(tab
->mat
->row
[row
][0]))
2823 return isl_ineq_separate
;
2824 if (!isl_int_is_negone(tab
->mat
->row
[row
][1]))
2825 return isl_ineq_separate
;
2827 pos
= isl_seq_first_non_zero(tab
->mat
->row
[row
] + off
+ tab
->n_dead
,
2828 tab
->n_col
- tab
->n_dead
);
2830 return isl_ineq_adj_eq
;
2832 if (!isl_int_is_negone(tab
->mat
->row
[row
][off
+ tab
->n_dead
+ pos
]))
2833 return isl_ineq_separate
;
2835 pos
= isl_seq_first_non_zero(
2836 tab
->mat
->row
[row
] + off
+ tab
->n_dead
+ pos
+ 1,
2837 tab
->n_col
- tab
->n_dead
- pos
- 1);
2839 return pos
== -1 ? isl_ineq_adj_ineq
: isl_ineq_separate
;
2842 /* Check the effect of inequality "ineq" on the tableau "tab".
2844 * isl_ineq_redundant: satisfied by all points in the tableau
2845 * isl_ineq_separate: satisfied by no point in the tableau
2846 * isl_ineq_cut: satisfied by some by not all points
2847 * isl_ineq_adj_eq: adjacent to an equality
2848 * isl_ineq_adj_ineq: adjacent to an inequality.
2850 enum isl_ineq_type
isl_tab_ineq_type(struct isl_tab
*tab
, isl_int
*ineq
)
2852 enum isl_ineq_type type
= isl_ineq_error
;
2853 struct isl_tab_undo
*snap
= NULL
;
2858 return isl_ineq_error
;
2860 if (isl_tab_extend_cons(tab
, 1) < 0)
2861 return isl_ineq_error
;
2863 snap
= isl_tab_snap(tab
);
2865 con
= isl_tab_add_row(tab
, ineq
);
2869 row
= tab
->con
[con
].index
;
2870 if (isl_tab_row_is_redundant(tab
, row
))
2871 type
= isl_ineq_redundant
;
2872 else if (isl_int_is_neg(tab
->mat
->row
[row
][1]) &&
2874 isl_int_abs_ge(tab
->mat
->row
[row
][1],
2875 tab
->mat
->row
[row
][0]))) {
2876 int nonneg
= at_least_zero(tab
, &tab
->con
[con
]);
2880 type
= isl_ineq_cut
;
2882 type
= separation_type(tab
, row
);
2884 int red
= con_is_redundant(tab
, &tab
->con
[con
]);
2888 type
= isl_ineq_cut
;
2890 type
= isl_ineq_redundant
;
2893 if (isl_tab_rollback(tab
, snap
))
2894 return isl_ineq_error
;
2897 return isl_ineq_error
;
2900 void isl_tab_dump(struct isl_tab
*tab
, FILE *out
, int indent
)
2906 fprintf(out
, "%*snull tab\n", indent
, "");
2909 fprintf(out
, "%*sn_redundant: %d, n_dead: %d", indent
, "",
2910 tab
->n_redundant
, tab
->n_dead
);
2912 fprintf(out
, ", rational");
2914 fprintf(out
, ", empty");
2916 fprintf(out
, "%*s[", indent
, "");
2917 for (i
= 0; i
< tab
->n_var
; ++i
) {
2919 fprintf(out
, (i
== tab
->n_param
||
2920 i
== tab
->n_var
- tab
->n_div
) ? "; "
2922 fprintf(out
, "%c%d%s", tab
->var
[i
].is_row
? 'r' : 'c',
2924 tab
->var
[i
].is_zero
? " [=0]" :
2925 tab
->var
[i
].is_redundant
? " [R]" : "");
2927 fprintf(out
, "]\n");
2928 fprintf(out
, "%*s[", indent
, "");
2929 for (i
= 0; i
< tab
->n_con
; ++i
) {
2932 fprintf(out
, "%c%d%s", tab
->con
[i
].is_row
? 'r' : 'c',
2934 tab
->con
[i
].is_zero
? " [=0]" :
2935 tab
->con
[i
].is_redundant
? " [R]" : "");
2937 fprintf(out
, "]\n");
2938 fprintf(out
, "%*s[", indent
, "");
2939 for (i
= 0; i
< tab
->n_row
; ++i
) {
2940 const char *sign
= "";
2943 if (tab
->row_sign
) {
2944 if (tab
->row_sign
[i
] == isl_tab_row_unknown
)
2946 else if (tab
->row_sign
[i
] == isl_tab_row_neg
)
2948 else if (tab
->row_sign
[i
] == isl_tab_row_pos
)
2953 fprintf(out
, "r%d: %d%s%s", i
, tab
->row_var
[i
],
2954 isl_tab_var_from_row(tab
, i
)->is_nonneg
? " [>=0]" : "", sign
);
2956 fprintf(out
, "]\n");
2957 fprintf(out
, "%*s[", indent
, "");
2958 for (i
= 0; i
< tab
->n_col
; ++i
) {
2961 fprintf(out
, "c%d: %d%s", i
, tab
->col_var
[i
],
2962 var_from_col(tab
, i
)->is_nonneg
? " [>=0]" : "");
2964 fprintf(out
, "]\n");
2965 r
= tab
->mat
->n_row
;
2966 tab
->mat
->n_row
= tab
->n_row
;
2967 c
= tab
->mat
->n_col
;
2968 tab
->mat
->n_col
= 2 + tab
->M
+ tab
->n_col
;
2969 isl_mat_dump(tab
->mat
, out
, indent
);
2970 tab
->mat
->n_row
= r
;
2971 tab
->mat
->n_col
= c
;
2973 isl_basic_set_dump(tab
->bset
, out
, indent
);